diff --git a/.github/workflows/posix-deps-apt.sh b/.github/workflows/posix-deps-apt.sh index d5538cd9367ec6..ec75be08e16e05 100755 --- a/.github/workflows/posix-deps-apt.sh +++ b/.github/workflows/posix-deps-apt.sh @@ -1,4 +1,8 @@ #!/bin/sh + +# Workaround missing on ubuntu 24.04 libmpdec-dev +sudo add-apt-repository ppa:ondrej/php + apt-get update apt-get -yq install \ @@ -23,4 +27,5 @@ apt-get -yq install \ tk-dev \ uuid-dev \ xvfb \ - zlib1g-dev + zlib1g-dev \ + libmpdec-dev diff --git a/Doc/deprecations/c-api-pending-removal-in-3.15.rst b/Doc/deprecations/c-api-pending-removal-in-3.15.rst index b87f0a5ecde06f..a3e335ecaf4324 100644 --- a/Doc/deprecations/c-api-pending-removal-in-3.15.rst +++ b/Doc/deprecations/c-api-pending-removal-in-3.15.rst @@ -1,7 +1,6 @@ Pending removal in Python 3.15 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -* The bundled copy of ``libmpdecimal``. * The :c:func:`!PyImport_ImportModuleNoBlock`: Use :c:func:`PyImport_ImportModule` instead. * :c:func:`PyWeakref_GetObject` and :c:func:`PyWeakref_GET_OBJECT`: diff --git a/Doc/license.rst b/Doc/license.rst index 480414bb84c4f2..c47dea271a5392 100644 --- a/Doc/license.rst +++ b/Doc/license.rst @@ -975,39 +975,6 @@ on the cfuhash project:: OF THE POSSIBILITY OF SUCH DAMAGE. -libmpdec --------- - -The :mod:`!_decimal` C extension underlying the :mod:`decimal` module -is built using an included copy of the libmpdec -library unless the build is configured ``--with-system-libmpdec``:: - - Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - - Redistribution and use in source and binary forms, with or without - modification, are permitted provided that the following conditions - are met: - - 1. Redistributions of source code must retain the above copyright - notice, this list of conditions and the following disclaimer. - - 2. Redistributions in binary form must reproduce the above copyright - notice, this list of conditions and the following disclaimer in the - documentation and/or other materials provided with the distribution. - - THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - SUCH DAMAGE. - - W3C C14N test suite ------------------- diff --git a/Doc/using/configure.rst b/Doc/using/configure.rst index b914d3397b6dda..7301301182504e 100644 --- a/Doc/using/configure.rst +++ b/Doc/using/configure.rst @@ -416,11 +416,6 @@ Options for third-party dependencies C compiler and linker flags for ``libmpdec``, used by :mod:`decimal` module, overriding ``pkg-config``. - .. note:: - - These environment variables have no effect unless - :option:`--with-system-libmpdec` is specified. - .. option:: LIBLZMA_CFLAGS .. option:: LIBLZMA_LIBS @@ -835,22 +830,6 @@ Libraries options Build the :mod:`!pyexpat` module using an installed ``expat`` library (default is no). -.. option:: --with-system-libmpdec - - Build the ``_decimal`` extension module using an installed ``mpdecimal`` - library, see the :mod:`decimal` module (default is yes). - - .. versionadded:: 3.3 - - .. versionchanged:: 3.13 - Default to using the installed ``mpdecimal`` library. - - .. deprecated-removed:: 3.13 3.15 - A copy of the ``mpdecimal`` library sources will no longer be distributed - with Python 3.15. - - .. seealso:: :option:`LIBMPDEC_CFLAGS` and :option:`LIBMPDEC_LIBS`. - .. option:: --with-readline=readline|editline Designate a backend library for the :mod:`readline` module. diff --git a/Doc/whatsnew/3.13.rst b/Doc/whatsnew/3.13.rst index 580a3d8154dee1..ad2fc8084d4cf3 100644 --- a/Doc/whatsnew/3.13.rst +++ b/Doc/whatsnew/3.13.rst @@ -2590,7 +2590,7 @@ Build Changes .. _mimalloc library: https://github.com/microsoft/mimalloc/ -* The :file:`configure` option :option:`--with-system-libmpdec` +* The :file:`configure` option :option:!--with-system-libmpdec` now defaults to ``yes``. The bundled copy of ``libmpdecimal`` will be removed in Python 3.15. diff --git a/Doc/whatsnew/3.15.rst b/Doc/whatsnew/3.15.rst index 2fe33c4c535919..c62a9fec17f176 100644 --- a/Doc/whatsnew/3.15.rst +++ b/Doc/whatsnew/3.15.rst @@ -254,6 +254,15 @@ that may require changes to your code. Build changes ============= +* Remove the bundled libmpdec_ decimal library from the CPython source tree, + to simplify maintenence and updates. The :mod:`decimal` module will now + unconditionally use the system's libmpdec decimal library. Also remove the + now unused :option:`!--with-system-libmpdec` :program:`configure` flag. + + (Contributed by Sergey B Kirpichev in :gh:`115119`.) + + .. _libmpdec: https://www.bytereef.org/mpdecimal/ + C API changes ============= diff --git a/Mac/BuildScript/build-installer.py b/Mac/BuildScript/build-installer.py index b31cb766a468f4..577dd239b0f72c 100755 --- a/Mac/BuildScript/build-installer.py +++ b/Mac/BuildScript/build-installer.py @@ -1158,7 +1158,6 @@ def buildPython(): print(" NOTE: --with-mimalloc=no pending resolution of weak linking issues") runCommand("%s -C --enable-framework --enable-universalsdk=/ " "--with-mimalloc=no " - "--with-system-libmpdec " "--with-universal-archs=%s " "%s " "%s " diff --git a/Makefile.pre.in b/Makefile.pre.in index b5703fbe6ae974..5568cd3a27b9d8 100644 --- a/Makefile.pre.in +++ b/Makefile.pre.in @@ -225,7 +225,6 @@ RUNSHARED= @RUNSHARED@ ENSUREPIP= @ENSUREPIP@ # Internal static libraries -LIBMPDEC_A= Modules/_decimal/libmpdec/libmpdec.a LIBEXPAT_A= Modules/expat/libexpat.a # HACL* build configuration @@ -589,45 +588,6 @@ LINK_PYTHON_OBJS=@LINK_PYTHON_OBJS@ DTRACE_DEPS = \ Python/ceval.o Python/gc.o Python/import.o Python/sysmodule.o -########################################################################## -# decimal's libmpdec - -LIBMPDEC_OBJS= \ - Modules/_decimal/libmpdec/basearith.o \ - Modules/_decimal/libmpdec/constants.o \ - Modules/_decimal/libmpdec/context.o \ - Modules/_decimal/libmpdec/convolute.o \ - Modules/_decimal/libmpdec/crt.o \ - Modules/_decimal/libmpdec/difradix2.o \ - Modules/_decimal/libmpdec/fnt.o \ - Modules/_decimal/libmpdec/fourstep.o \ - Modules/_decimal/libmpdec/io.o \ - Modules/_decimal/libmpdec/mpalloc.o \ - Modules/_decimal/libmpdec/mpdecimal.o \ - Modules/_decimal/libmpdec/numbertheory.o \ - Modules/_decimal/libmpdec/sixstep.o \ - Modules/_decimal/libmpdec/transpose.o - # _decimal does not use signaling API - # Modules/_decimal/libmpdec/mpsignal.o - -LIBMPDEC_HEADERS= \ - $(srcdir)/Modules/_decimal/libmpdec/basearith.h \ - $(srcdir)/Modules/_decimal/libmpdec/bits.h \ - $(srcdir)/Modules/_decimal/libmpdec/constants.h \ - $(srcdir)/Modules/_decimal/libmpdec/convolute.h \ - $(srcdir)/Modules/_decimal/libmpdec/crt.h \ - $(srcdir)/Modules/_decimal/libmpdec/difradix2.h \ - $(srcdir)/Modules/_decimal/libmpdec/fnt.h \ - $(srcdir)/Modules/_decimal/libmpdec/fourstep.h \ - $(srcdir)/Modules/_decimal/libmpdec/io.h \ - $(srcdir)/Modules/_decimal/libmpdec/mpalloc.h \ - $(srcdir)/Modules/_decimal/libmpdec/mpdecimal.h \ - $(srcdir)/Modules/_decimal/libmpdec/numbertheory.h \ - $(srcdir)/Modules/_decimal/libmpdec/sixstep.h \ - $(srcdir)/Modules/_decimal/libmpdec/transpose.h \ - $(srcdir)/Modules/_decimal/libmpdec/typearith.h \ - $(srcdir)/Modules/_decimal/libmpdec/umodarith.h - ########################################################################## # pyexpat's expat library @@ -945,7 +905,6 @@ coverage-lcov: @lcov $(COVERAGE_LCOV_OPTIONS) --remove $(COVERAGE_INFO) \ '*/Modules/_hacl/*' \ '*/Modules/_ctypes/libffi*/*' \ - '*/Modules/_decimal/libmpdec/*' \ '*/Modules/expat/*' \ '*/Modules/xx*.c' \ '*/Python/pyfpe.c' \ @@ -1410,60 +1369,6 @@ PYTHON_HEADERS= \ \ $(srcdir)/Python/stdlib_module_names.h -########################################################################## -# Build static libmpdec.a -LIBMPDEC_CFLAGS=@LIBMPDEC_CFLAGS@ $(PY_STDMODULE_CFLAGS) $(CCSHARED) - -# "%.o: %c" is not portable -Modules/_decimal/libmpdec/basearith.o: $(srcdir)/Modules/_decimal/libmpdec/basearith.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/basearith.c - -Modules/_decimal/libmpdec/constants.o: $(srcdir)/Modules/_decimal/libmpdec/constants.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/constants.c - -Modules/_decimal/libmpdec/context.o: $(srcdir)/Modules/_decimal/libmpdec/context.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/context.c - -Modules/_decimal/libmpdec/convolute.o: $(srcdir)/Modules/_decimal/libmpdec/convolute.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/convolute.c - -Modules/_decimal/libmpdec/crt.o: $(srcdir)/Modules/_decimal/libmpdec/crt.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/crt.c - -Modules/_decimal/libmpdec/difradix2.o: $(srcdir)/Modules/_decimal/libmpdec/difradix2.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/difradix2.c - -Modules/_decimal/libmpdec/fnt.o: $(srcdir)/Modules/_decimal/libmpdec/fnt.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/fnt.c - -Modules/_decimal/libmpdec/fourstep.o: $(srcdir)/Modules/_decimal/libmpdec/fourstep.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/fourstep.c - -Modules/_decimal/libmpdec/io.o: $(srcdir)/Modules/_decimal/libmpdec/io.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/io.c - -Modules/_decimal/libmpdec/mpalloc.o: $(srcdir)/Modules/_decimal/libmpdec/mpalloc.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/mpalloc.c - -Modules/_decimal/libmpdec/mpdecimal.o: $(srcdir)/Modules/_decimal/libmpdec/mpdecimal.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/mpdecimal.c - -Modules/_decimal/libmpdec/mpsignal.o: $(srcdir)/Modules/_decimal/libmpdec/mpsignal.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/mpsignal.c - -Modules/_decimal/libmpdec/numbertheory.o: $(srcdir)/Modules/_decimal/libmpdec/numbertheory.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/numbertheory.c - -Modules/_decimal/libmpdec/sixstep.o: $(srcdir)/Modules/_decimal/libmpdec/sixstep.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/sixstep.c - -Modules/_decimal/libmpdec/transpose.o: $(srcdir)/Modules/_decimal/libmpdec/transpose.c $(LIBMPDEC_HEADERS) $(PYTHON_HEADERS) - $(CC) -c $(LIBMPDEC_CFLAGS) -o $@ $(srcdir)/Modules/_decimal/libmpdec/transpose.c - -$(LIBMPDEC_A): $(LIBMPDEC_OBJS) - -rm -f $@ - $(AR) $(ARFLAGS) $@ $(LIBMPDEC_OBJS) - ########################################################################## # Build static libexpat.a LIBEXPAT_CFLAGS=@LIBEXPAT_CFLAGS@ $(PY_STDMODULE_CFLAGS) $(CCSHARED) @@ -3321,7 +3226,7 @@ MODULE_UNICODEDATA_DEPS=$(srcdir)/Modules/unicodedata_db.h $(srcdir)/Modules/uni MODULE__CTYPES_DEPS=$(srcdir)/Modules/_ctypes/ctypes.h MODULE__CTYPES_TEST_DEPS=$(srcdir)/Modules/_ctypes/_ctypes_test_generated.c.h MODULE__CTYPES_MALLOC_CLOSURE=@MODULE__CTYPES_MALLOC_CLOSURE@ -MODULE__DECIMAL_DEPS=$(srcdir)/Modules/_decimal/docstrings.h @LIBMPDEC_INTERNAL@ +MODULE__DECIMAL_DEPS=$(srcdir)/Modules/_decimal/docstrings.h MODULE__ELEMENTTREE_DEPS=$(srcdir)/Modules/pyexpat.c @LIBEXPAT_INTERNAL@ MODULE__HASHLIB_DEPS=$(srcdir)/Modules/hashlib.h MODULE__IO_DEPS=$(srcdir)/Modules/_io/_iomodule.h diff --git a/Misc/NEWS.d/3.12.0a2.rst b/Misc/NEWS.d/3.12.0a2.rst index bc028f30636bf7..f09daa97bc156a 100644 --- a/Misc/NEWS.d/3.12.0a2.rst +++ b/Misc/NEWS.d/3.12.0a2.rst @@ -957,7 +957,7 @@ Fix ``make regen-test-levenshtein`` for out-of-tree builds. .. nonce: eVXGEx .. section: Build -Don't use vendored ``libmpdec`` headers if :option:`--with-system-libmpdec` +Don't use vendored ``libmpdec`` headers if :option:`!--with-system-libmpdec` is passed to :program:`configure`. Don't use vendored ``libexpat`` headers if :option:`--with-system-expat` is passed to :program:`configure`. diff --git a/Misc/NEWS.d/3.13.0b1.rst b/Misc/NEWS.d/3.13.0b1.rst index 97731276679ba6..0a75a3908ba669 100644 --- a/Misc/NEWS.d/3.13.0b1.rst +++ b/Misc/NEWS.d/3.13.0b1.rst @@ -1429,7 +1429,7 @@ script) without specifying a value for ``UseTIER2``. .. nonce: LT27pF .. section: Build -The :file:`configure` option :option:`--with-system-libmpdec` now defaults +The :file:`configure` option :option:`!--with-system-libmpdec` now defaults to ``yes``. The bundled copy of ``libmpdecimal`` will be removed in Python 3.15. @@ -1470,7 +1470,7 @@ Increase WASI stack size from 512 KiB to 8 MiB and the initial memory from .. section: Build :program:`configure` now uses :program:`pkg-config` to detect :mod:`decimal` -dependencies if the :option:`--with-system-libmpdec` option is given. +dependencies if the :option:`!--with-system-libmpdec` option is given. .. diff --git a/Misc/NEWS.d/next/Build/2025-05-13-12-38-26.gh-issue-115119.7n0nx3.rst b/Misc/NEWS.d/next/Build/2025-05-13-12-38-26.gh-issue-115119.7n0nx3.rst new file mode 100644 index 00000000000000..0c6804ebf9c890 --- /dev/null +++ b/Misc/NEWS.d/next/Build/2025-05-13-12-38-26.gh-issue-115119.7n0nx3.rst @@ -0,0 +1,2 @@ +Removed bundled copy of the libmpdec, use system library if it's available. +Patch by Sergey B Kirpichev. diff --git a/Misc/sbom.spdx.json b/Misc/sbom.spdx.json index 10a5c646d2a59e..c5762cb84cbf99 100644 --- a/Misc/sbom.spdx.json +++ b/Misc/sbom.spdx.json @@ -994,734 +994,6 @@ } ], "fileName": "Lib/ctypes/macholib/framework.py" - 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"spdxElementId": "SPDXRef-PACKAGE-mpdecimal" } ], "spdxVersion": "SPDX-2.3" diff --git a/Modules/Setup.stdlib.in b/Modules/Setup.stdlib.in index 3a38a60a152e8c..a698a478371a38 100644 --- a/Modules/Setup.stdlib.in +++ b/Modules/Setup.stdlib.in @@ -59,9 +59,7 @@ # needs libm and on some platforms librt @MODULE__DATETIME_TRUE@_datetime _datetimemodule.c -# _decimal uses libmpdec -# either static libmpdec.a from Modules/_decimal/libmpdec or libmpdec.so -# with ./configure --with-system-libmpdec +# _decimal uses the system's libmpdec.so @MODULE__DECIMAL_TRUE@_decimal _decimal/_decimal.c # compression libs and binascii (optional CRC32 from zlib) diff --git a/Modules/_decimal/README.txt b/Modules/_decimal/README.txt index 7eae0f88f28428..e7cdbdfc73100d 100644 --- a/Modules/_decimal/README.txt +++ b/Modules/_decimal/README.txt @@ -41,6 +41,3 @@ NOTE decimal.so is not built from a static libmpdec.a since doing so led to failures on AIX (user report) and Windows (mixing static and dynamic CRTs causes locale problems and more). - - - diff --git a/Modules/_decimal/libmpdec/README.txt b/Modules/_decimal/libmpdec/README.txt deleted file mode 100644 index c1d481dee76452..00000000000000 --- a/Modules/_decimal/libmpdec/README.txt +++ /dev/null @@ -1,88 +0,0 @@ - - -libmpdec -======== - -libmpdec is a fast C/C++ library for correctly-rounded arbitrary precision -decimal floating point arithmetic. It is a complete implementation of -Mike Cowlishaw/IBM's General Decimal Arithmetic Specification. - - -Files required for the Python _decimal module -============================================= - - Core files for small and medium precision arithmetic - ---------------------------------------------------- - - basearith.{c,h} -> Core arithmetic in base 10**9 or 10**19. - bits.h -> Portable detection of least/most significant one-bit. - constants.{c,h} -> Constants that are used in multiple files. - context.c -> Context functions. - io.{c,h} -> Conversions between mpd_t and ASCII strings, - mpd_t formatting (allows UTF-8 fill character). - mpalloc.{c,h} -> Allocation handlers with overflow detection - and functions for switching between static - and dynamic mpd_t. - mpdecimal.{c,h} -> All (quiet) functions of the specification. - typearith.h -> Fast primitives for double word multiplication, - division etc. - - Visual Studio only: - ~~~~~~~~~~~~~~~~~~~ - vcdiv64.asm -> Double word division used in typearith.h. VS 2008 does - not allow inline asm for x64. Also, it does not provide - an intrinsic for double word division. - - Files for bignum arithmetic: - ---------------------------- - - The following files implement the Fast Number Theoretic Transform - used for multiplying coefficients with more than 1024 words (see - mpdecimal.c: _mpd_fntmul()). - - umodarith.h -> Fast low level routines for unsigned modular arithmetic. - numbertheory.{c,h} -> Routines for setting up the Number Theoretic Transform. - difradix2.{c,h} -> Decimation in frequency transform, used as the - "base case" by the following three files: - - fnt.{c,h} -> Transform arrays up to 4096 words. - sixstep.{c,h} -> Transform larger arrays of length 2**n. - fourstep.{c,h} -> Transform larger arrays of length 3 * 2**n. - - convolute.{c,h} -> Fast convolution using one of the three transform - functions. - transpose.{c,h} -> Transpositions needed for the sixstep algorithm. - crt.{c,h} -> Chinese Remainder Theorem: use information from three - transforms modulo three different primes to get the - final result. - - -Pointers to literature, proofs and more -======================================= - - literature/ - ----------- - - REFERENCES.txt -> List of relevant papers. - bignum.txt -> Explanation of the Fast Number Theoretic Transform (FNT). - fnt.py -> Verify constants used in the FNT; Python demo for the - O(N**2) discrete transform. - - matrix-transform.txt -> Proof for the Matrix Fourier Transform used in - fourstep.c. - six-step.txt -> Show that the algorithm used in sixstep.c is - a variant of the Matrix Fourier Transform. - mulmod-64.txt -> Proof for the mulmod64 algorithm from - umodarith.h. - mulmod-ppro.txt -> Proof for the x87 FPU modular multiplication - from umodarith.h. - umodarith.lisp -> ACL2 proofs for many functions from umodarith.h. - - -Library Author -============== - - Stefan Krah - - - diff --git a/Modules/_decimal/libmpdec/basearith.c b/Modules/_decimal/libmpdec/basearith.c deleted file mode 100644 index 85c608fadf5156..00000000000000 --- a/Modules/_decimal/libmpdec/basearith.c +++ /dev/null @@ -1,655 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include - -#include "basearith.h" -#include "constants.h" -#include "typearith.h" - - -/*********************************************************************/ -/* Calculations in base MPD_RADIX */ -/*********************************************************************/ - - -/* - * Knuth, TAOCP, Volume 2, 4.3.1: - * w := sum of u (len m) and v (len n) - * n > 0 and m >= n - * The calling function has to handle a possible final carry. - */ -mpd_uint_t -_mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n) -{ - mpd_uint_t s; - mpd_uint_t carry = 0; - mpd_size_t i; - - assert(n > 0 && m >= n); - - /* add n members of u and v */ - for (i = 0; i < n; i++) { - s = u[i] + (v[i] + carry); - carry = (s < u[i]) | (s >= MPD_RADIX); - w[i] = carry ? s-MPD_RADIX : s; - } - /* if there is a carry, propagate it */ - for (; carry && i < m; i++) { - s = u[i] + carry; - carry = (s == MPD_RADIX); - w[i] = carry ? 0 : s; - } - /* copy the rest of u */ - for (; i < m; i++) { - w[i] = u[i]; - } - - return carry; -} - -/* - * Add the contents of u to w. Carries are propagated further. The caller - * has to make sure that w is big enough. - */ -void -_mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n) -{ - mpd_uint_t s; - mpd_uint_t carry = 0; - mpd_size_t i; - - if (n == 0) return; - - /* add n members of u to w */ - for (i = 0; i < n; i++) { - s = w[i] + (u[i] + carry); - carry = (s < w[i]) | (s >= MPD_RADIX); - w[i] = carry ? s-MPD_RADIX : s; - } - /* if there is a carry, propagate it */ - for (; carry; i++) { - s = w[i] + carry; - carry = (s == MPD_RADIX); - w[i] = carry ? 0 : s; - } -} - -/* - * Add v to w (len m). The calling function has to handle a possible - * final carry. Assumption: m > 0. - */ -mpd_uint_t -_mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v) -{ - mpd_uint_t s; - mpd_uint_t carry; - mpd_size_t i; - - assert(m > 0); - - /* add v to w */ - s = w[0] + v; - carry = (s < v) | (s >= MPD_RADIX); - w[0] = carry ? s-MPD_RADIX : s; - - /* if there is a carry, propagate it */ - for (i = 1; carry && i < m; i++) { - s = w[i] + carry; - carry = (s == MPD_RADIX); - w[i] = carry ? 0 : s; - } - - return carry; -} - -/* Increment u. The calling function has to handle a possible carry. */ -mpd_uint_t -_mpd_baseincr(mpd_uint_t *u, mpd_size_t n) -{ - mpd_uint_t s; - mpd_uint_t carry = 1; - mpd_size_t i; - - assert(n > 0); - - /* if there is a carry, propagate it */ - for (i = 0; carry && i < n; i++) { - s = u[i] + carry; - carry = (s == MPD_RADIX); - u[i] = carry ? 0 : s; - } - - return carry; -} - -/* - * Knuth, TAOCP, Volume 2, 4.3.1: - * w := difference of u (len m) and v (len n). - * number in u >= number in v; - */ -void -_mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n) -{ - mpd_uint_t d; - mpd_uint_t borrow = 0; - mpd_size_t i; - - assert(m > 0 && n > 0); - - /* subtract n members of v from u */ - for (i = 0; i < n; i++) { - d = u[i] - (v[i] + borrow); - borrow = (u[i] < d); - w[i] = borrow ? d + MPD_RADIX : d; - } - /* if there is a borrow, propagate it */ - for (; borrow && i < m; i++) { - d = u[i] - borrow; - borrow = (u[i] == 0); - w[i] = borrow ? MPD_RADIX-1 : d; - } - /* copy the rest of u */ - for (; i < m; i++) { - w[i] = u[i]; - } -} - -/* - * Subtract the contents of u from w. w is larger than u. Borrows are - * propagated further, but eventually w can absorb the final borrow. - */ -void -_mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n) -{ - mpd_uint_t d; - mpd_uint_t borrow = 0; - mpd_size_t i; - - if (n == 0) return; - - /* subtract n members of u from w */ - for (i = 0; i < n; i++) { - d = w[i] - (u[i] + borrow); - borrow = (w[i] < d); - w[i] = borrow ? d + MPD_RADIX : d; - } - /* if there is a borrow, propagate it */ - for (; borrow; i++) { - d = w[i] - borrow; - borrow = (w[i] == 0); - w[i] = borrow ? MPD_RADIX-1 : d; - } -} - -/* w := product of u (len n) and v (single word) */ -void -_mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v) -{ - mpd_uint_t hi, lo; - mpd_uint_t carry = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=0; i < n; i++) { - - _mpd_mul_words(&hi, &lo, u[i], v); - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words_r(&carry, &w[i], hi, lo); - } - w[i] = carry; -} - -/* - * Knuth, TAOCP, Volume 2, 4.3.1: - * w := product of u (len m) and v (len n) - * w must be initialized to zero - */ -void -_mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n) -{ - mpd_uint_t hi, lo; - mpd_uint_t carry; - mpd_size_t i, j; - - assert(m > 0 && n > 0); - - for (j=0; j < n; j++) { - carry = 0; - for (i=0; i < m; i++) { - - _mpd_mul_words(&hi, &lo, u[i], v[j]); - lo = w[i+j] + lo; - if (lo < w[i+j]) hi++; - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words_r(&carry, &w[i+j], hi, lo); - } - w[j+m] = carry; - } -} - -/* - * Knuth, TAOCP Volume 2, 4.3.1, exercise 16: - * w := quotient of u (len n) divided by a single word v - */ -mpd_uint_t -_mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v) -{ - mpd_uint_t hi, lo; - mpd_uint_t rem = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=n-1; i != MPD_SIZE_MAX; i--) { - - _mpd_mul_words(&hi, &lo, rem, MPD_RADIX); - lo = u[i] + lo; - if (lo < u[i]) hi++; - - _mpd_div_words(&w[i], &rem, hi, lo, v); - } - - return rem; -} - -/* - * Knuth, TAOCP Volume 2, 4.3.1: - * q, r := quotient and remainder of uconst (len nplusm) - * divided by vconst (len n) - * nplusm >= n - * - * If r is not NULL, r will contain the remainder. If r is NULL, the - * return value indicates if there is a remainder: 1 for true, 0 for - * false. A return value of -1 indicates an error. - */ -int -_mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, - const mpd_uint_t *uconst, const mpd_uint_t *vconst, - mpd_size_t nplusm, mpd_size_t n) -{ - mpd_uint_t ustatic[MPD_MINALLOC_MAX]; - mpd_uint_t vstatic[MPD_MINALLOC_MAX]; - mpd_uint_t *u = ustatic; - mpd_uint_t *v = vstatic; - mpd_uint_t d, qhat, rhat, w2[2]; - mpd_uint_t hi, lo, x; - mpd_uint_t carry; - mpd_size_t i, j, m; - int retval = 0; - - assert(n > 1 && nplusm >= n); - m = sub_size_t(nplusm, n); - - /* D1: normalize */ - d = MPD_RADIX / (vconst[n-1] + 1); - - if (nplusm >= MPD_MINALLOC_MAX) { - if ((u = mpd_alloc(nplusm+1, sizeof *u)) == NULL) { - return -1; - } - } - if (n >= MPD_MINALLOC_MAX) { - if ((v = mpd_alloc(n+1, sizeof *v)) == NULL) { - mpd_free(u); - return -1; - } - } - - _mpd_shortmul(u, uconst, nplusm, d); - _mpd_shortmul(v, vconst, n, d); - - /* D2: loop */ - for (j=m; j != MPD_SIZE_MAX; j--) { - assert(2 <= j+n && j+n <= nplusm); /* annotation for scan-build */ - - /* D3: calculate qhat and rhat */ - rhat = _mpd_shortdiv(w2, u+j+n-1, 2, v[n-1]); - qhat = w2[1] * MPD_RADIX + w2[0]; - - while (1) { - if (qhat < MPD_RADIX) { - _mpd_singlemul(w2, qhat, v[n-2]); - if (w2[1] <= rhat) { - if (w2[1] != rhat || w2[0] <= u[j+n-2]) { - break; - } - } - } - qhat -= 1; - rhat += v[n-1]; - if (rhat < v[n-1] || rhat >= MPD_RADIX) { - break; - } - } - /* D4: multiply and subtract */ - carry = 0; - for (i=0; i <= n; i++) { - - _mpd_mul_words(&hi, &lo, qhat, v[i]); - - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words_r(&hi, &lo, hi, lo); - - x = u[i+j] - lo; - carry = (u[i+j] < x); - u[i+j] = carry ? x+MPD_RADIX : x; - carry += hi; - } - q[j] = qhat; - /* D5: test remainder */ - if (carry) { - q[j] -= 1; - /* D6: add back */ - (void)_mpd_baseadd(u+j, u+j, v, n+1, n); - } - } - - /* D8: unnormalize */ - if (r != NULL) { - _mpd_shortdiv(r, u, n, d); - /* we are not interested in the return value here */ - retval = 0; - } - else { - retval = !_mpd_isallzero(u, n); - } - - -if (u != ustatic) mpd_free(u); -if (v != vstatic) mpd_free(v); -return retval; -} - -/* - * Left shift of src by 'shift' digits; src may equal dest. - * - * dest := area of n mpd_uint_t with space for srcdigits+shift digits. - * src := coefficient with length m. - * - * The case splits in the function are non-obvious. The following - * equations might help: - * - * Let msdigits denote the number of digits in the most significant - * word of src. Then 1 <= msdigits <= rdigits. - * - * 1) shift = q * rdigits + r - * 2) srcdigits = qsrc * rdigits + msdigits - * 3) destdigits = shift + srcdigits - * = q * rdigits + r + qsrc * rdigits + msdigits - * = q * rdigits + (qsrc * rdigits + (r + msdigits)) - * - * The result has q zero words, followed by the coefficient that - * is left-shifted by r. The case r == 0 is trivial. For r > 0, it - * is important to keep in mind that we always read m source words, - * but write m+1 destination words if r + msdigits > rdigits, m words - * otherwise. - */ -void -_mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n, mpd_size_t m, - mpd_size_t shift) -{ -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__) - /* spurious uninitialized warnings */ - mpd_uint_t l=l, lprev=lprev, h=h; -#else - mpd_uint_t l, lprev, h; -#endif - mpd_uint_t q, r; - mpd_uint_t ph; - - assert(m > 0 && n >= m); - - _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS); - - if (r != 0) { - - ph = mpd_pow10[r]; - - --m; --n; - _mpd_divmod_pow10(&h, &lprev, src[m--], MPD_RDIGITS-r); - if (h != 0) { /* r + msdigits > rdigits <==> h != 0 */ - dest[n--] = h; - } - /* write m-1 shifted words */ - for (; m != MPD_SIZE_MAX; m--,n--) { - _mpd_divmod_pow10(&h, &l, src[m], MPD_RDIGITS-r); - dest[n] = ph * lprev + h; - lprev = l; - } - /* write least significant word */ - dest[q] = ph * lprev; - } - else { - while (--m != MPD_SIZE_MAX) { - dest[m+q] = src[m]; - } - } - - mpd_uint_zero(dest, q); -} - -/* - * Right shift of src by 'shift' digits; src may equal dest. - * Assumption: srcdigits-shift > 0. - * - * dest := area with space for srcdigits-shift digits. - * src := coefficient with length 'slen'. - * - * The case splits in the function rely on the following equations: - * - * Let msdigits denote the number of digits in the most significant - * word of src. Then 1 <= msdigits <= rdigits. - * - * 1) shift = q * rdigits + r - * 2) srcdigits = qsrc * rdigits + msdigits - * 3) destdigits = srcdigits - shift - * = qsrc * rdigits + msdigits - (q * rdigits + r) - * = (qsrc - q) * rdigits + msdigits - r - * - * Since destdigits > 0 and 1 <= msdigits <= rdigits: - * - * 4) qsrc >= q - * 5) qsrc == q ==> msdigits > r - * - * The result has slen-q words if msdigits > r, slen-q-1 words otherwise. - */ -mpd_uint_t -_mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen, - mpd_size_t shift) -{ -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__) - /* spurious uninitialized warnings */ - mpd_uint_t l=l, h=h, hprev=hprev; /* low, high, previous high */ -#else - mpd_uint_t l, h, hprev; /* low, high, previous high */ -#endif - mpd_uint_t rnd, rest; /* rounding digit, rest */ - mpd_uint_t q, r; - mpd_size_t i, j; - mpd_uint_t ph; - - assert(slen > 0); - - _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS); - - rnd = rest = 0; - if (r != 0) { - - ph = mpd_pow10[MPD_RDIGITS-r]; - - _mpd_divmod_pow10(&hprev, &rest, src[q], r); - _mpd_divmod_pow10(&rnd, &rest, rest, r-1); - - if (rest == 0 && q > 0) { - rest = !_mpd_isallzero(src, q); - } - /* write slen-q-1 words */ - for (j=0,i=q+1; i 0) { - _mpd_divmod_pow10(&rnd, &rest, src[q-1], MPD_RDIGITS-1); - /* is there any non-zero digit below rnd? */ - if (rest == 0) rest = !_mpd_isallzero(src, q-1); - } - for (j = 0; j < slen-q; j++) { - dest[j] = src[q+j]; - } - } - - /* 0-4 ==> rnd+rest < 0.5 */ - /* 5 ==> rnd+rest == 0.5 */ - /* 6-9 ==> rnd+rest > 0.5 */ - return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd; -} - - -/*********************************************************************/ -/* Calculations in base b */ -/*********************************************************************/ - -/* - * Add v to w (len m). The calling function has to handle a possible - * final carry. Assumption: m > 0. - */ -mpd_uint_t -_mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v, mpd_uint_t b) -{ - mpd_uint_t s; - mpd_uint_t carry; - mpd_size_t i; - - assert(m > 0); - - /* add v to w */ - s = w[0] + v; - carry = (s < v) | (s >= b); - w[0] = carry ? s-b : s; - - /* if there is a carry, propagate it */ - for (i = 1; carry && i < m; i++) { - s = w[i] + carry; - carry = (s == b); - w[i] = carry ? 0 : s; - } - - return carry; -} - -/* w := product of u (len n) and v (single word). Return carry. */ -mpd_uint_t -_mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v) -{ - mpd_uint_t hi, lo; - mpd_uint_t carry = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=0; i < n; i++) { - - _mpd_mul_words(&hi, &lo, u[i], v); - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words_r(&carry, &w[i], hi, lo); - } - - return carry; -} - -/* w := product of u (len n) and v (single word) */ -mpd_uint_t -_mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v, mpd_uint_t b) -{ - mpd_uint_t hi, lo; - mpd_uint_t carry = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=0; i < n; i++) { - - _mpd_mul_words(&hi, &lo, u[i], v); - lo = carry + lo; - if (lo < carry) hi++; - - _mpd_div_words(&carry, &w[i], hi, lo, b); - } - - return carry; -} - -/* - * Knuth, TAOCP Volume 2, 4.3.1, exercise 16: - * w := quotient of u (len n) divided by a single word v - */ -mpd_uint_t -_mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v, mpd_uint_t b) -{ - mpd_uint_t hi, lo; - mpd_uint_t rem = 0; - mpd_size_t i; - - assert(n > 0); - - for (i=n-1; i != MPD_SIZE_MAX; i--) { - - _mpd_mul_words(&hi, &lo, rem, b); - lo = u[i] + lo; - if (lo < u[i]) hi++; - - _mpd_div_words(&w[i], &rem, hi, lo, v); - } - - return rem; -} diff --git a/Modules/_decimal/libmpdec/basearith.h b/Modules/_decimal/libmpdec/basearith.h deleted file mode 100644 index d35925aaddb48e..00000000000000 --- a/Modules/_decimal/libmpdec/basearith.h +++ /dev/null @@ -1,218 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_BASEARITH_H_ -#define LIBMPDEC_BASEARITH_H_ - - -#include "mpdecimal.h" -#include "typearith.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n); -void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n); -mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v); -mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v, - mpd_uint_t b); -mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n); -void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n); -void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n); -void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t m, mpd_size_t n); -void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v); -mpd_uint_t _mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v); -mpd_uint_t _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v, mpd_uint_t b); -mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v); -mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, - mpd_uint_t v, mpd_uint_t b); -int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst, - const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n); -void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n, - mpd_size_t m, mpd_size_t shift); -mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen, - mpd_size_t shift); - - - -#ifdef CONFIG_64 -extern const mpd_uint_t mprime_rdx; - -/* - * Algorithm from: Division by Invariant Integers using Multiplication, - * T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94 - * Conference on Programming Language Design and Implementation. - * - * http://gmplib.org/~tege/divcnst-pldi94.pdf - * - * Variables from the paper and their translations (See section 8): - * - * N := 64 - * d := MPD_RADIX - * l := 64 - * m' := floor((2**(64+64) - 1)/MPD_RADIX) - 2**64 - * - * Since N-l == 0: - * - * dnorm := d - * n2 := hi - * n10 := lo - * - * ACL2 proof: mpd-div-words-r-correct - */ -static inline void -_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo) -{ - mpd_uint_t n_adj, h, l, t; - mpd_uint_t n1_neg; - - /* n1_neg = if lo >= 2**63 then MPD_UINT_MAX else 0 */ - n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0; - /* n_adj = if lo >= 2**63 then lo+MPD_RADIX else lo */ - n_adj = lo + (n1_neg & MPD_RADIX); - - /* (h, l) = if lo >= 2**63 then m'*(hi+1) else m'*hi */ - _mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg); - l = l + n_adj; - if (l < n_adj) h++; - t = h + hi; - /* At this point t == qest, with q == qest or q == qest+1: - * 1) 0 <= 2**64*hi + lo - qest*MPD_RADIX < 2*MPD_RADIX - */ - - /* t = 2**64-1 - qest = 2**64 - (qest+1) */ - t = MPD_UINT_MAX - t; - - /* (h, l) = 2**64*MPD_RADIX - (qest+1)*MPD_RADIX */ - _mpd_mul_words(&h, &l, t, MPD_RADIX); - l = l + lo; - if (l < lo) h++; - h += hi; - h -= MPD_RADIX; - /* (h, l) = 2**64*hi + lo - (qest+1)*MPD_RADIX (mod 2**128) - * Case q == qest+1: - * a) h == 0, l == r - * b) q := h - t == qest+1 - * c) r := l - * Case q == qest: - * a) h == MPD_UINT_MAX, l == 2**64-(MPD_RADIX-r) - * b) q := h - t == qest - * c) r := l + MPD_RADIX = r - */ - - *q = (h - t); - *r = l + (MPD_RADIX & h); -} -#else -static inline void -_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo) -{ - _mpd_div_words(q, r, hi, lo, MPD_RADIX); -} -#endif - - -/* Multiply two single base MPD_RADIX words, store result in array w[2]. */ -static inline void -_mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v) -{ - mpd_uint_t hi, lo; - - _mpd_mul_words(&hi, &lo, u, v); - _mpd_div_words_r(&w[1], &w[0], hi, lo); -} - -/* Multiply u (len 2) and v (len m, 1 <= m <= 2). */ -static inline void -_mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m) -{ - mpd_uint_t hi, lo; - - _mpd_mul_words(&hi, &lo, u[0], v[0]); - _mpd_div_words_r(&w[1], &w[0], hi, lo); - - _mpd_mul_words(&hi, &lo, u[1], v[0]); - lo = w[1] + lo; - if (lo < w[1]) hi++; - _mpd_div_words_r(&w[2], &w[1], hi, lo); - if (m == 1) return; - - _mpd_mul_words(&hi, &lo, u[0], v[1]); - lo = w[1] + lo; - if (lo < w[1]) hi++; - _mpd_div_words_r(&w[3], &w[1], hi, lo); - - _mpd_mul_words(&hi, &lo, u[1], v[1]); - lo = w[2] + lo; - if (lo < w[2]) hi++; - lo = w[3] + lo; - if (lo < w[3]) hi++; - _mpd_div_words_r(&w[3], &w[2], hi, lo); -} - - -/* - * Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing - * is tested and the coefficient is regarded as "all zero". - */ -static inline int -_mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len) -{ - while (--len >= 0) { - if (data[len] != 0) return 0; - } - return 1; -} - -/* - * Test if all full words from data[len-1] to data[0] are MPD_RADIX-1 - * (all nines). Return true if len == 0. - */ -static inline int -_mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len) -{ - while (--len >= 0) { - if (data[len] != MPD_RADIX-1) return 0; - } - return 1; -} - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_BASEARITH_H_ */ diff --git a/Modules/_decimal/libmpdec/bench.c b/Modules/_decimal/libmpdec/bench.c deleted file mode 100644 index 09138f4ce9c03a..00000000000000 --- a/Modules/_decimal/libmpdec/bench.c +++ /dev/null @@ -1,137 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include -#include -#include - - -static void -err_exit(const char *msg) -{ - fprintf(stderr, "%s\n", msg); - exit(1); -} - -static mpd_t * -new_mpd(void) -{ - mpd_t *x = mpd_qnew(); - if (x == NULL) { - err_exit("out of memory"); - } - - return x; -} - -/* Nonsense version of escape-time algorithm for calculating a mandelbrot - * set. Just for benchmarking. */ -static void -color_point(mpd_t *x0, mpd_t *y0, long maxiter, mpd_context_t *ctx) -{ - mpd_t *x, *y, *sq_x, *sq_y; - mpd_t *two; - - x = new_mpd(); - y = new_mpd(); - mpd_set_u32(x, 0, ctx); - mpd_set_u32(y, 0, ctx); - - sq_x = new_mpd(); - sq_y = new_mpd(); - mpd_set_u32(sq_x, 0, ctx); - mpd_set_u32(sq_y, 0, ctx); - - two = new_mpd(); - mpd_set_u32(two, 2, ctx); - - for (long i = 0; i < maxiter; i++) { - mpd_mul(y, x, y, ctx); - mpd_mul(y, y, two, ctx); - mpd_add(y, y, y0, ctx); - - mpd_sub(x, sq_x, sq_y, ctx); - mpd_add(x, x, x0, ctx); - - mpd_mul(sq_x, x, x, ctx); - mpd_mul(sq_y, y, y, ctx); - } - - mpd_copy(x0, x, ctx); - - mpd_del(two); - mpd_del(sq_y); - mpd_del(sq_x); - mpd_del(y); - mpd_del(x); -} - - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *x0, *y0; - uint32_t prec = 19; - long iter = 10000000; - clock_t start_clock, end_clock; - - if (argc != 3) { - err_exit("usage: bench prec iter\n"); - } - prec = strtoul(argv[1], NULL, 10); - iter = strtol(argv[2], NULL, 10); - - mpd_init(&ctx, prec); - /* no more MPD_MINALLOC changes after here */ - - x0 = new_mpd(); - y0 = new_mpd(); - mpd_set_string(x0, "0.222", &ctx); - mpd_set_string(y0, "0.333", &ctx); - if (ctx.status & MPD_Errors) { - mpd_del(y0); - mpd_del(x0); - err_exit("unexpected error during conversion"); - } - - start_clock = clock(); - color_point(x0, y0, iter, &ctx); - end_clock = clock(); - - mpd_print(x0); - fprintf(stderr, "time: %f\n\n", (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - mpd_del(y0); - mpd_del(x0); - - return 0; -} diff --git a/Modules/_decimal/libmpdec/bench_full.c b/Modules/_decimal/libmpdec/bench_full.c deleted file mode 100644 index 6ab73917e1c32c..00000000000000 --- a/Modules/_decimal/libmpdec/bench_full.c +++ /dev/null @@ -1,193 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include -#include -#include - - -static void -err_exit(const char *msg) -{ - fprintf(stderr, "%s\n", msg); - exit(1); -} - -static mpd_t * -new_mpd(void) -{ - mpd_t *x = mpd_qnew(); - if (x == NULL) { - err_exit("out of memory"); - } - - return x; -} - -/* - * Example from: http://en.wikipedia.org/wiki/Mandelbrot_set - * - * Escape time algorithm for drawing the set: - * - * Point x0, y0 is deemed to be in the Mandelbrot set if the return - * value is maxiter. Lower return values indicate how quickly points - * escaped and can be used for coloring. - */ -static int -color_point(const mpd_t *x0, const mpd_t *y0, const long maxiter, mpd_context_t *ctx) -{ - mpd_t *x, *y, *sq_x, *sq_y; - mpd_t *two, *four, *c; - long i; - - x = new_mpd(); - y = new_mpd(); - mpd_set_u32(x, 0, ctx); - mpd_set_u32(y, 0, ctx); - - sq_x = new_mpd(); - sq_y = new_mpd(); - mpd_set_u32(sq_x, 0, ctx); - mpd_set_u32(sq_y, 0, ctx); - - two = new_mpd(); - four = new_mpd(); - mpd_set_u32(two, 2, ctx); - mpd_set_u32(four, 4, ctx); - - c = new_mpd(); - mpd_set_u32(c, 0, ctx); - - for (i = 0; i < maxiter && mpd_cmp(c, four, ctx) <= 0; i++) { - mpd_mul(y, x, y, ctx); - mpd_mul(y, y, two, ctx); - mpd_add(y, y, y0, ctx); - - mpd_sub(x, sq_x, sq_y, ctx); - mpd_add(x, x, x0, ctx); - - mpd_mul(sq_x, x, x, ctx); - mpd_mul(sq_y, y, y, ctx); - mpd_add(c, sq_x, sq_y, ctx); - } - - mpd_del(c); - mpd_del(four); - mpd_del(two); - mpd_del(sq_y); - mpd_del(sq_x); - mpd_del(y); - mpd_del(x); - - return i; -} - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *x0, *y0; - mpd_t *sqrt_2, *xstep, *ystep; - mpd_ssize_t prec = 19; - - long iter = 1000; - int points[40][80]; - int i, j; - clock_t start_clock, end_clock; - - - if (argc != 3) { - fprintf(stderr, "usage: ./bench prec iter\n"); - exit(1); - } - prec = strtoll(argv[1], NULL, 10); - iter = strtol(argv[2], NULL, 10); - - mpd_init(&ctx, prec); - /* no more MPD_MINALLOC changes after here */ - - sqrt_2 = new_mpd(); - xstep = new_mpd(); - ystep = new_mpd(); - x0 = new_mpd(); - y0 = new_mpd(); - - mpd_set_u32(sqrt_2, 2, &ctx); - mpd_sqrt(sqrt_2, sqrt_2, &ctx); - mpd_div_u32(xstep, sqrt_2, 40, &ctx); - mpd_div_u32(ystep, sqrt_2, 20, &ctx); - - start_clock = clock(); - mpd_copy(y0, sqrt_2, &ctx); - for (i = 0; i < 40; i++) { - mpd_copy(x0, sqrt_2, &ctx); - mpd_set_negative(x0); - for (j = 0; j < 80; j++) { - points[i][j] = color_point(x0, y0, iter, &ctx); - mpd_add(x0, x0, xstep, &ctx); - } - mpd_sub(y0, y0, ystep, &ctx); - } - end_clock = clock(); - -#ifdef BENCH_VERBOSE - for (i = 0; i < 40; i++) { - for (j = 0; j < 80; j++) { - if (points[i][j] == iter) { - putchar('*'); - } - else if (points[i][j] >= 10) { - putchar('+'); - } - else if (points[i][j] >= 5) { - putchar('.'); - } - else { - putchar(' '); - } - } - putchar('\n'); - } - putchar('\n'); -#else - (void)points; /* suppress gcc warning */ -#endif - - printf("time: %f\n\n", (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - mpd_del(y0); - mpd_del(x0); - mpd_del(ystep); - mpd_del(xstep); - mpd_del(sqrt_2); - - return 0; -} diff --git a/Modules/_decimal/libmpdec/bits.h b/Modules/_decimal/libmpdec/bits.h deleted file mode 100644 index aa9c3e77980c03..00000000000000 --- a/Modules/_decimal/libmpdec/bits.h +++ /dev/null @@ -1,188 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_BITS_H_ -#define LIBMPDEC_BITS_H_ - - -#include "mpdecimal.h" - - -/* Check if n is a power of 2. */ -static inline int -ispower2(mpd_size_t n) -{ - return n != 0 && (n & (n-1)) == 0; -} - -#if defined(ANSI) -/* - * Return the most significant bit position of n from 0 to 31 (63). - * Assumptions: n != 0. - */ -static inline int -mpd_bsr(mpd_size_t n) -{ - int pos = 0; - mpd_size_t tmp; - -#ifdef CONFIG_64 - tmp = n >> 32; - if (tmp != 0) { n = tmp; pos += 32; } -#endif - tmp = n >> 16; - if (tmp != 0) { n = tmp; pos += 16; } - tmp = n >> 8; - if (tmp != 0) { n = tmp; pos += 8; } - tmp = n >> 4; - if (tmp != 0) { n = tmp; pos += 4; } - tmp = n >> 2; - if (tmp != 0) { n = tmp; pos += 2; } - tmp = n >> 1; - if (tmp != 0) { n = tmp; pos += 1; } - - return pos + (int)n - 1; -} - -/* - * Return the least significant bit position of n from 0 to 31 (63). - * Assumptions: n != 0. - */ -static inline int -mpd_bsf(mpd_size_t n) -{ - int pos; - -#ifdef CONFIG_64 - pos = 63; - if (n & 0x00000000FFFFFFFFULL) { pos -= 32; } else { n >>= 32; } - if (n & 0x000000000000FFFFULL) { pos -= 16; } else { n >>= 16; } - if (n & 0x00000000000000FFULL) { pos -= 8; } else { n >>= 8; } - if (n & 0x000000000000000FULL) { pos -= 4; } else { n >>= 4; } - if (n & 0x0000000000000003ULL) { pos -= 2; } else { n >>= 2; } - if (n & 0x0000000000000001ULL) { pos -= 1; } -#else - pos = 31; - if (n & 0x000000000000FFFFUL) { pos -= 16; } else { n >>= 16; } - if (n & 0x00000000000000FFUL) { pos -= 8; } else { n >>= 8; } - if (n & 0x000000000000000FUL) { pos -= 4; } else { n >>= 4; } - if (n & 0x0000000000000003UL) { pos -= 2; } else { n >>= 2; } - if (n & 0x0000000000000001UL) { pos -= 1; } -#endif - return pos; -} -/* END ANSI */ - -#elif defined(ASM) -/* - * Bit scan reverse. Assumptions: a != 0. - */ -static inline int -mpd_bsr(mpd_size_t a) -{ - mpd_size_t retval; - - __asm__ ( -#ifdef CONFIG_64 - "bsrq %1, %0\n\t" -#else - "bsr %1, %0\n\t" -#endif - :"=r" (retval) - :"r" (a) - :"cc" - ); - - return (int)retval; -} - -/* - * Bit scan forward. Assumptions: a != 0. - */ -static inline int -mpd_bsf(mpd_size_t a) -{ - mpd_size_t retval; - - __asm__ ( -#ifdef CONFIG_64 - "bsfq %1, %0\n\t" -#else - "bsf %1, %0\n\t" -#endif - :"=r" (retval) - :"r" (a) - :"cc" - ); - - return (int)retval; -} -/* END ASM */ - -#elif defined(MASM) -#include -/* - * Bit scan reverse. Assumptions: a != 0. - */ -static inline int __cdecl -mpd_bsr(mpd_size_t a) -{ - unsigned long retval; - -#ifdef CONFIG_64 - _BitScanReverse64(&retval, a); -#else - _BitScanReverse(&retval, a); -#endif - - return (int)retval; -} - -/* - * Bit scan forward. Assumptions: a != 0. - */ -static inline int __cdecl -mpd_bsf(mpd_size_t a) -{ - unsigned long retval; - -#ifdef CONFIG_64 - _BitScanForward64(&retval, a); -#else - _BitScanForward(&retval, a); -#endif - - return (int)retval; -} -/* END MASM (_MSC_VER) */ -#else - #error "missing preprocessor definitions" -#endif /* BSR/BSF */ - - -#endif /* LIBMPDEC_BITS_H_ */ diff --git a/Modules/_decimal/libmpdec/constants.c b/Modules/_decimal/libmpdec/constants.c deleted file mode 100644 index ed074fa81c6d2e..00000000000000 --- a/Modules/_decimal/libmpdec/constants.c +++ /dev/null @@ -1,130 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include "basearith.h" -#include "constants.h" - - -#if defined(CONFIG_64) - - /* number-theory.c */ - const mpd_uint_t mpd_moduli[3] = { - 18446744069414584321ULL, 18446744056529682433ULL, 18446742974197923841ULL - }; - const mpd_uint_t mpd_roots[3] = {7ULL, 10ULL, 19ULL}; - - /* crt.c */ - const mpd_uint_t INV_P1_MOD_P2 = 18446744055098026669ULL; - const mpd_uint_t INV_P1P2_MOD_P3 = 287064143708160ULL; - const mpd_uint_t LH_P1P2 = 18446744052234715137ULL; /* (P1*P2) % 2^64 */ - const mpd_uint_t UH_P1P2 = 18446744052234715141ULL; /* (P1*P2) / 2^64 */ - - /* transpose.c */ - const mpd_size_t mpd_bits[64] = { - 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, - 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, - 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, - 2147483648ULL, 4294967296ULL, 8589934592ULL, 17179869184ULL, 34359738368ULL, - 68719476736ULL, 137438953472ULL, 274877906944ULL, 549755813888ULL, - 1099511627776ULL, 2199023255552ULL, 4398046511104, 8796093022208ULL, - 17592186044416ULL, 35184372088832ULL, 70368744177664ULL, 140737488355328ULL, - 281474976710656ULL, 562949953421312ULL, 1125899906842624ULL, - 2251799813685248ULL, 4503599627370496ULL, 9007199254740992ULL, - 18014398509481984ULL, 36028797018963968ULL, 72057594037927936ULL, - 144115188075855872ULL, 288230376151711744ULL, 576460752303423488ULL, - 1152921504606846976ULL, 2305843009213693952ULL, 4611686018427387904ULL, - 9223372036854775808ULL - }; - - /* mpdecimal.c */ - const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = { - 1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000, - 10000000000ULL,100000000000ULL,1000000000000ULL,10000000000000ULL, - 100000000000000ULL,1000000000000000ULL,10000000000000000ULL, - 100000000000000000ULL,1000000000000000000ULL,10000000000000000000ULL - }; - - /* magic number for constant division by MPD_RADIX */ - const mpd_uint_t mprime_rdx = 15581492618384294730ULL; - -#elif defined(CONFIG_32) - - /* number-theory.c */ - const mpd_uint_t mpd_moduli[3] = {2113929217UL, 2013265921UL, 1811939329UL}; - const mpd_uint_t mpd_roots[3] = {5UL, 31UL, 13UL}; - - /* PentiumPro modular multiplication: These constants have to be loaded as - * 80 bit long doubles, which are not supported by certain compilers. */ - const uint32_t mpd_invmoduli[3][3] = { - {4293885170U, 2181570688U, 16352U}, /* ((long double) 1 / 2113929217UL) */ - {1698898177U, 2290649223U, 16352U}, /* ((long double) 1 / 2013265921UL) */ - {2716021846U, 2545165803U, 16352U} /* ((long double) 1 / 1811939329UL) */ - }; - - const float MPD_TWO63 = 9223372036854775808.0; /* 2^63 */ - - /* crt.c */ - const mpd_uint_t INV_P1_MOD_P2 = 2013265901UL; - const mpd_uint_t INV_P1P2_MOD_P3 = 54UL; - const mpd_uint_t LH_P1P2 = 4127195137UL; /* (P1*P2) % 2^32 */ - const mpd_uint_t UH_P1P2 = 990904320UL; /* (P1*P2) / 2^32 */ - - /* transpose.c */ - const mpd_size_t mpd_bits[32] = { - 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, - 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, - 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, - 2147483648UL - }; - - /* mpdecimal.c */ - const mpd_uint_t mpd_pow10[MPD_RDIGITS+1] = { - 1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000 - }; - -#else - #error "CONFIG_64 or CONFIG_32 must be defined." -#endif - -const char * const mpd_round_string[MPD_ROUND_GUARD] = { - "ROUND_UP", /* round away from 0 */ - "ROUND_DOWN", /* round toward 0 (truncate) */ - "ROUND_CEILING", /* round toward +infinity */ - "ROUND_FLOOR", /* round toward -infinity */ - "ROUND_HALF_UP", /* 0.5 is rounded up */ - "ROUND_HALF_DOWN", /* 0.5 is rounded down */ - "ROUND_HALF_EVEN", /* 0.5 is rounded to even */ - "ROUND_05UP", /* round zero or five away from 0 */ - "ROUND_TRUNC", /* truncate, but set infinity */ -}; - -const char * const mpd_clamp_string[MPD_CLAMP_GUARD] = { - "CLAMP_DEFAULT", - "CLAMP_IEEE_754" -}; diff --git a/Modules/_decimal/libmpdec/constants.h b/Modules/_decimal/libmpdec/constants.h deleted file mode 100644 index 7c1db839c20ba2..00000000000000 --- a/Modules/_decimal/libmpdec/constants.h +++ /dev/null @@ -1,89 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_CONSTANTS_H_ -#define LIBMPDEC_CONSTANTS_H_ - - -#include "mpdecimal.h" - -#include - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -/* choice of optimized functions */ -#if defined(CONFIG_64) -/* x64 */ - #define MULMOD(a, b) x64_mulmod(a, b, umod) - #define MULMOD2C(a0, a1, w) x64_mulmod2c(a0, a1, w, umod) - #define MULMOD2(a0, b0, a1, b1) x64_mulmod2(a0, b0, a1, b1, umod) - #define POWMOD(base, exp) x64_powmod(base, exp, umod) - #define SETMODULUS(modnum) std_setmodulus(modnum, &umod) - #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod) -#elif defined(PPRO) -/* PentiumPro (or later) gcc inline asm */ - #define MULMOD(a, b) ppro_mulmod(a, b, &dmod, dinvmod) - #define MULMOD2C(a0, a1, w) ppro_mulmod2c(a0, a1, w, &dmod, dinvmod) - #define MULMOD2(a0, b0, a1, b1) ppro_mulmod2(a0, b0, a1, b1, &dmod, dinvmod) - #define POWMOD(base, exp) ppro_powmod(base, exp, &dmod, dinvmod) - #define SETMODULUS(modnum) ppro_setmodulus(modnum, &umod, &dmod, dinvmod) - #define SIZE3_NTT(x0, x1, x2, w3table) ppro_size3_ntt(x0, x1, x2, w3table, umod, &dmod, dinvmod) -#else - /* ANSI C99 */ - #define MULMOD(a, b) std_mulmod(a, b, umod) - #define MULMOD2C(a0, a1, w) std_mulmod2c(a0, a1, w, umod) - #define MULMOD2(a0, b0, a1, b1) std_mulmod2(a0, b0, a1, b1, umod) - #define POWMOD(base, exp) std_powmod(base, exp, umod) - #define SETMODULUS(modnum) std_setmodulus(modnum, &umod) - #define SIZE3_NTT(x0, x1, x2, w3table) std_size3_ntt(x0, x1, x2, w3table, umod) -#endif - -/* PentiumPro (or later) gcc inline asm */ -extern const float MPD_TWO63; -extern const uint32_t mpd_invmoduli[3][3]; - -enum {P1, P2, P3}; - -extern const mpd_uint_t mpd_moduli[]; -extern const mpd_uint_t mpd_roots[]; -extern const mpd_size_t mpd_bits[]; -extern const mpd_uint_t mpd_pow10[]; - -extern const mpd_uint_t INV_P1_MOD_P2; -extern const mpd_uint_t INV_P1P2_MOD_P3; -extern const mpd_uint_t LH_P1P2; -extern const mpd_uint_t UH_P1P2; - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_CONSTANTS_H_ */ diff --git a/Modules/_decimal/libmpdec/context.c b/Modules/_decimal/libmpdec/context.c deleted file mode 100644 index 172794b67d8009..00000000000000 --- a/Modules/_decimal/libmpdec/context.c +++ /dev/null @@ -1,286 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include -#include - - -void -mpd_dflt_traphandler(mpd_context_t *ctx) -{ - (void)ctx; - raise(SIGFPE); -} - -void (* mpd_traphandler)(mpd_context_t *) = mpd_dflt_traphandler; - - -/* Set guaranteed minimum number of coefficient words. The function may - be used once at program start. Setting MPD_MINALLOC to out-of-bounds - values is a catastrophic error, so in that case the function exits rather - than relying on the user to check a return value. */ -void -mpd_setminalloc(mpd_ssize_t n) -{ - static int minalloc_is_set = 0; - - if (minalloc_is_set) { - mpd_err_warn("mpd_setminalloc: ignoring request to set " - "MPD_MINALLOC a second time\n"); - return; - } - if (n < MPD_MINALLOC_MIN || n > MPD_MINALLOC_MAX) { - mpd_err_fatal("illegal value for MPD_MINALLOC"); /* GCOV_NOT_REACHED */ - } - MPD_MINALLOC = n; - minalloc_is_set = 1; -} - -void -mpd_init(mpd_context_t *ctx, mpd_ssize_t prec) -{ - mpd_ssize_t ideal_minalloc; - - mpd_defaultcontext(ctx); - - if (!mpd_qsetprec(ctx, prec)) { - mpd_addstatus_raise(ctx, MPD_Invalid_context); - return; - } - - ideal_minalloc = 2 * ((prec+MPD_RDIGITS-1) / MPD_RDIGITS); - if (ideal_minalloc < MPD_MINALLOC_MIN) ideal_minalloc = MPD_MINALLOC_MIN; - if (ideal_minalloc > MPD_MINALLOC_MAX) ideal_minalloc = MPD_MINALLOC_MAX; - - mpd_setminalloc(ideal_minalloc); -} - -void -mpd_maxcontext(mpd_context_t *ctx) -{ - ctx->prec=MPD_MAX_PREC; - ctx->emax=MPD_MAX_EMAX; - ctx->emin=MPD_MIN_EMIN; - ctx->round=MPD_ROUND_HALF_EVEN; - ctx->traps=MPD_Traps; - ctx->status=0; - ctx->newtrap=0; - ctx->clamp=0; - ctx->allcr=1; -} - -void -mpd_defaultcontext(mpd_context_t *ctx) -{ - ctx->prec=2*MPD_RDIGITS; - ctx->emax=MPD_MAX_EMAX; - ctx->emin=MPD_MIN_EMIN; - ctx->round=MPD_ROUND_HALF_UP; - ctx->traps=MPD_Traps; - ctx->status=0; - ctx->newtrap=0; - ctx->clamp=0; - ctx->allcr=1; -} - -void -mpd_basiccontext(mpd_context_t *ctx) -{ - ctx->prec=9; - ctx->emax=MPD_MAX_EMAX; - ctx->emin=MPD_MIN_EMIN; - ctx->round=MPD_ROUND_HALF_UP; - ctx->traps=MPD_Traps|MPD_Clamped; - ctx->status=0; - ctx->newtrap=0; - ctx->clamp=0; - ctx->allcr=1; -} - -int -mpd_ieee_context(mpd_context_t *ctx, int bits) -{ - if (bits <= 0 || bits > MPD_IEEE_CONTEXT_MAX_BITS || bits % 32) { - return -1; - } - - ctx->prec = 9 * (bits/32) - 2; - ctx->emax = 3 * ((mpd_ssize_t)1<<(bits/16+3)); - ctx->emin = 1 - ctx->emax; - ctx->round=MPD_ROUND_HALF_EVEN; - ctx->traps=0; - ctx->status=0; - ctx->newtrap=0; - ctx->clamp=1; - ctx->allcr=1; - - return 0; -} - -mpd_ssize_t -mpd_getprec(const mpd_context_t *ctx) -{ - return ctx->prec; -} - -mpd_ssize_t -mpd_getemax(const mpd_context_t *ctx) -{ - return ctx->emax; -} - -mpd_ssize_t -mpd_getemin(const mpd_context_t *ctx) -{ - return ctx->emin; -} - -int -mpd_getround(const mpd_context_t *ctx) -{ - return ctx->round; -} - -uint32_t -mpd_gettraps(const mpd_context_t *ctx) -{ - return ctx->traps; -} - -uint32_t -mpd_getstatus(const mpd_context_t *ctx) -{ - return ctx->status; -} - -int -mpd_getclamp(const mpd_context_t *ctx) -{ - return ctx->clamp; -} - -int -mpd_getcr(const mpd_context_t *ctx) -{ - return ctx->allcr; -} - - -int -mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec) -{ - if (prec <= 0 || prec > MPD_MAX_PREC) { - return 0; - } - ctx->prec = prec; - return 1; -} - -int -mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax) -{ - if (emax < 0 || emax > MPD_MAX_EMAX) { - return 0; - } - ctx->emax = emax; - return 1; -} - -int -mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin) -{ - if (emin > 0 || emin < MPD_MIN_EMIN) { - return 0; - } - ctx->emin = emin; - return 1; -} - -int -mpd_qsetround(mpd_context_t *ctx, int round) -{ - if (!(0 <= round && round < MPD_ROUND_GUARD)) { - return 0; - } - ctx->round = round; - return 1; -} - -int -mpd_qsettraps(mpd_context_t *ctx, uint32_t flags) -{ - if (flags > MPD_Max_status) { - return 0; - } - ctx->traps = flags; - return 1; -} - -int -mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags) -{ - if (flags > MPD_Max_status) { - return 0; - } - ctx->status = flags; - return 1; -} - -int -mpd_qsetclamp(mpd_context_t *ctx, int c) -{ - if (c != 0 && c != 1) { - return 0; - } - ctx->clamp = c; - return 1; -} - -int -mpd_qsetcr(mpd_context_t *ctx, int c) -{ - if (c != 0 && c != 1) { - return 0; - } - ctx->allcr = c; - return 1; -} - - -void -mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags) -{ - ctx->status |= flags; - if (flags&ctx->traps) { - ctx->newtrap = (flags&ctx->traps); - mpd_traphandler(ctx); - } -} diff --git a/Modules/_decimal/libmpdec/convolute.c b/Modules/_decimal/libmpdec/convolute.c deleted file mode 100644 index 4bc8e8b5fd32f4..00000000000000 --- a/Modules/_decimal/libmpdec/convolute.c +++ /dev/null @@ -1,171 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" -#include "bits.h" -#include "constants.h" -#include "convolute.h" -#include "fnt.h" -#include "fourstep.h" -#include "numbertheory.h" -#include "sixstep.h" -#include "umodarith.h" - - -/* Bignum: Fast convolution using the Number Theoretic Transform. Used for - the multiplication of very large coefficients. */ - - -/* Convolute the data in c1 and c2. Result is in c1. */ -int -fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum) -{ - int (*fnt)(mpd_uint_t *, mpd_size_t, int); - int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int); -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t n_inv, umod; - mpd_size_t i; - - - SETMODULUS(modnum); - n_inv = POWMOD(n, (umod-2)); - - if (ispower2(n)) { - if (n > SIX_STEP_THRESHOLD) { - fnt = six_step_fnt; - inv_fnt = inv_six_step_fnt; - } - else { - fnt = std_fnt; - inv_fnt = std_inv_fnt; - } - } - else { - fnt = four_step_fnt; - inv_fnt = inv_four_step_fnt; - } - - if (!fnt(c1, n, modnum)) { - return 0; - } - if (!fnt(c2, n, modnum)) { - return 0; - } - for (i = 0; i < n-1; i += 2) { - mpd_uint_t x0 = c1[i]; - mpd_uint_t y0 = c2[i]; - mpd_uint_t x1 = c1[i+1]; - mpd_uint_t y1 = c2[i+1]; - MULMOD2(&x0, y0, &x1, y1); - c1[i] = x0; - c1[i+1] = x1; - } - - if (!inv_fnt(c1, n, modnum)) { - return 0; - } - for (i = 0; i < n-3; i += 4) { - mpd_uint_t x0 = c1[i]; - mpd_uint_t x1 = c1[i+1]; - mpd_uint_t x2 = c1[i+2]; - mpd_uint_t x3 = c1[i+3]; - MULMOD2C(&x0, &x1, n_inv); - MULMOD2C(&x2, &x3, n_inv); - c1[i] = x0; - c1[i+1] = x1; - c1[i+2] = x2; - c1[i+3] = x3; - } - - return 1; -} - -/* Autoconvolute the data in c1. Result is in c1. */ -int -fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum) -{ - int (*fnt)(mpd_uint_t *, mpd_size_t, int); - int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int); -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t n_inv, umod; - mpd_size_t i; - - - SETMODULUS(modnum); - n_inv = POWMOD(n, (umod-2)); - - if (ispower2(n)) { - if (n > SIX_STEP_THRESHOLD) { - fnt = six_step_fnt; - inv_fnt = inv_six_step_fnt; - } - else { - fnt = std_fnt; - inv_fnt = std_inv_fnt; - } - } - else { - fnt = four_step_fnt; - inv_fnt = inv_four_step_fnt; - } - - if (!fnt(c1, n, modnum)) { - return 0; - } - for (i = 0; i < n-1; i += 2) { - mpd_uint_t x0 = c1[i]; - mpd_uint_t x1 = c1[i+1]; - MULMOD2(&x0, x0, &x1, x1); - c1[i] = x0; - c1[i+1] = x1; - } - - if (!inv_fnt(c1, n, modnum)) { - return 0; - } - for (i = 0; i < n-3; i += 4) { - mpd_uint_t x0 = c1[i]; - mpd_uint_t x1 = c1[i+1]; - mpd_uint_t x2 = c1[i+2]; - mpd_uint_t x3 = c1[i+3]; - MULMOD2C(&x0, &x1, n_inv); - MULMOD2C(&x2, &x3, n_inv); - c1[i] = x0; - c1[i+1] = x1; - c1[i+2] = x2; - c1[i+3] = x3; - } - - return 1; -} diff --git a/Modules/_decimal/libmpdec/convolute.h b/Modules/_decimal/libmpdec/convolute.h deleted file mode 100644 index 62edb3e45739cb..00000000000000 --- a/Modules/_decimal/libmpdec/convolute.h +++ /dev/null @@ -1,49 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_CONVOLUTE_H_ -#define LIBMPDEC_CONVOLUTE_H_ - - -#include "mpdecimal.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -#define SIX_STEP_THRESHOLD 4096 - -int fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum); -int fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_CONVOLUTE_H_ */ diff --git a/Modules/_decimal/libmpdec/crt.c b/Modules/_decimal/libmpdec/crt.c deleted file mode 100644 index babcce41bf67cd..00000000000000 --- a/Modules/_decimal/libmpdec/crt.c +++ /dev/null @@ -1,180 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include - -#include "constants.h" -#include "crt.h" -#include "numbertheory.h" -#include "typearith.h" -#include "umodarith.h" - - -/* Bignum: Chinese Remainder Theorem, extends the maximum transform length. */ - - -/* Multiply P1P2 by v, store result in w. */ -static inline void -_crt_mulP1P2_3(mpd_uint_t w[3], mpd_uint_t v) -{ - mpd_uint_t hi1, hi2, lo; - - _mpd_mul_words(&hi1, &lo, LH_P1P2, v); - w[0] = lo; - - _mpd_mul_words(&hi2, &lo, UH_P1P2, v); - lo = hi1 + lo; - if (lo < hi1) hi2++; - - w[1] = lo; - w[2] = hi2; -} - -/* Add 3 words from v to w. The result is known to fit in w. */ -static inline void -_crt_add3(mpd_uint_t w[3], mpd_uint_t v[3]) -{ - mpd_uint_t carry; - - w[0] = w[0] + v[0]; - carry = (w[0] < v[0]); - - w[1] = w[1] + v[1]; - if (w[1] < v[1]) w[2]++; - - w[1] = w[1] + carry; - if (w[1] < carry) w[2]++; - - w[2] += v[2]; -} - -/* Divide 3 words in u by v, store result in w, return remainder. */ -static inline mpd_uint_t -_crt_div3(mpd_uint_t *w, const mpd_uint_t *u, mpd_uint_t v) -{ - mpd_uint_t r1 = u[2]; - mpd_uint_t r2; - - if (r1 < v) { - w[2] = 0; - } - else { - _mpd_div_word(&w[2], &r1, u[2], v); /* GCOV_NOT_REACHED */ - } - - _mpd_div_words(&w[1], &r2, r1, u[1], v); - _mpd_div_words(&w[0], &r1, r2, u[0], v); - - return r1; -} - - -/* - * Chinese Remainder Theorem: - * Algorithm from Joerg Arndt, "Matters Computational", - * Chapter 37.4.1 [http://www.jjj.de/fxt/] - * - * See also Knuth, TAOCP, Volume 2, 4.3.2, exercise 7. - */ - -/* - * CRT with carry: x1, x2, x3 contain numbers modulo p1, p2, p3. For each - * triple of members of the arrays, find the unique z modulo p1*p2*p3, with - * zmax = p1*p2*p3 - 1. - * - * In each iteration of the loop, split z into result[i] = z % MPD_RADIX - * and carry = z / MPD_RADIX. Let N be the size of carry[] and cmax the - * maximum carry. - * - * Limits for the 32-bit build: - * - * N = 2**96 - * cmax = 7711435591312380274 - * - * Limits for the 64 bit build: - * - * N = 2**192 - * cmax = 627710135393475385904124401220046371710 - * - * The following statements hold for both versions: - * - * 1) cmax + zmax < N, so the addition does not overflow. - * - * 2) (cmax + zmax) / MPD_RADIX == cmax. - * - * 3) If c <= cmax, then c_next = (c + zmax) / MPD_RADIX <= cmax. - */ -void -crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize) -{ - mpd_uint_t p1 = mpd_moduli[P1]; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t a1, a2, a3; - mpd_uint_t s; - mpd_uint_t z[3], t[3]; - mpd_uint_t carry[3] = {0,0,0}; - mpd_uint_t hi, lo; - mpd_size_t i; - - for (i = 0; i < rsize; i++) { - - a1 = x1[i]; - a2 = x2[i]; - a3 = x3[i]; - - SETMODULUS(P2); - s = ext_submod(a2, a1, umod); - s = MULMOD(s, INV_P1_MOD_P2); - - _mpd_mul_words(&hi, &lo, s, p1); - lo = lo + a1; - if (lo < a1) hi++; - - SETMODULUS(P3); - s = dw_submod(a3, hi, lo, umod); - s = MULMOD(s, INV_P1P2_MOD_P3); - - z[0] = lo; - z[1] = hi; - z[2] = 0; - - _crt_mulP1P2_3(t, s); - _crt_add3(z, t); - _crt_add3(carry, z); - - x1[i] = _crt_div3(carry, carry, MPD_RADIX); - } - - assert(carry[0] == 0 && carry[1] == 0 && carry[2] == 0); -} diff --git a/Modules/_decimal/libmpdec/crt.h b/Modules/_decimal/libmpdec/crt.h deleted file mode 100644 index ed66753c2510ba..00000000000000 --- a/Modules/_decimal/libmpdec/crt.h +++ /dev/null @@ -1,46 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_CRT_H_ -#define LIBMPDEC_CRT_H_ - - -#include "mpdecimal.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -void crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_CRT_H_ */ diff --git a/Modules/_decimal/libmpdec/difradix2.c b/Modules/_decimal/libmpdec/difradix2.c deleted file mode 100644 index 049ecff65b6eef..00000000000000 --- a/Modules/_decimal/libmpdec/difradix2.c +++ /dev/null @@ -1,173 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include - -#include "bits.h" -#include "constants.h" -#include "difradix2.h" -#include "numbertheory.h" -#include "umodarith.h" - - -/* Bignum: The actual transform routine (decimation in frequency). */ - - -/* - * Generate index pairs (x, bitreverse(x)) and carry out the permutation. - * n must be a power of two. - * Algorithm due to Brent/Lehmann, see Joerg Arndt, "Matters Computational", - * Chapter 1.14.4. [http://www.jjj.de/fxt/] - */ -static inline void -bitreverse_permute(mpd_uint_t a[], mpd_size_t n) -{ - mpd_size_t x = 0; - mpd_size_t r = 0; - mpd_uint_t t; - - do { /* Invariant: r = bitreverse(x) */ - if (r > x) { - t = a[x]; - a[x] = a[r]; - a[r] = t; - } - /* Flip trailing consecutive 1 bits and the first zero bit - * that absorbs a possible carry. */ - x += 1; - /* Mirror the operation on r: Flip n_trailing_zeros(x)+1 - high bits of r. */ - r ^= (n - (n >> (mpd_bsf(x)+1))); - /* The loop invariant is preserved. */ - } while (x < n); -} - - -/* Fast Number Theoretic Transform, decimation in frequency. */ -void -fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams) -{ - mpd_uint_t *wtable = tparams->wtable; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t u0, u1, v0, v1; - mpd_uint_t w, w0, w1, wstep; - mpd_size_t m, mhalf; - mpd_size_t j, r; - - - assert(ispower2(n)); - assert(n >= 4); - - SETMODULUS(tparams->modnum); - - /* m == n */ - mhalf = n / 2; - for (j = 0; j < mhalf; j += 2) { - - w0 = wtable[j]; - w1 = wtable[j+1]; - - u0 = a[j]; - v0 = a[j+mhalf]; - - u1 = a[j+1]; - v1 = a[j+1+mhalf]; - - a[j] = addmod(u0, v0, umod); - v0 = submod(u0, v0, umod); - - a[j+1] = addmod(u1, v1, umod); - v1 = submod(u1, v1, umod); - - MULMOD2(&v0, w0, &v1, w1); - - a[j+mhalf] = v0; - a[j+1+mhalf] = v1; - - } - - wstep = 2; - for (m = n/2; m >= 2; m>>=1, wstep<<=1) { - - mhalf = m / 2; - - /* j == 0 */ - for (r = 0; r < n; r += 2*m) { - - u0 = a[r]; - v0 = a[r+mhalf]; - - u1 = a[m+r]; - v1 = a[m+r+mhalf]; - - a[r] = addmod(u0, v0, umod); - v0 = submod(u0, v0, umod); - - a[m+r] = addmod(u1, v1, umod); - v1 = submod(u1, v1, umod); - - a[r+mhalf] = v0; - a[m+r+mhalf] = v1; - } - - for (j = 1; j < mhalf; j++) { - - w = wtable[j*wstep]; - - for (r = 0; r < n; r += 2*m) { - - u0 = a[r+j]; - v0 = a[r+j+mhalf]; - - u1 = a[m+r+j]; - v1 = a[m+r+j+mhalf]; - - a[r+j] = addmod(u0, v0, umod); - v0 = submod(u0, v0, umod); - - a[m+r+j] = addmod(u1, v1, umod); - v1 = submod(u1, v1, umod); - - MULMOD2C(&v0, &v1, w); - - a[r+j+mhalf] = v0; - a[m+r+j+mhalf] = v1; - } - - } - - } - - bitreverse_permute(a, n); -} diff --git a/Modules/_decimal/libmpdec/difradix2.h b/Modules/_decimal/libmpdec/difradix2.h deleted file mode 100644 index cdcbcf9a71043c..00000000000000 --- a/Modules/_decimal/libmpdec/difradix2.h +++ /dev/null @@ -1,47 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_DIFRADIX2_H_ -#define LIBMPDEC_DIFRADIX2_H_ - - -#include "mpdecimal.h" -#include "numbertheory.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -void fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_DIFRADIX2_H_ */ diff --git a/Modules/_decimal/libmpdec/examples/README.txt b/Modules/_decimal/libmpdec/examples/README.txt deleted file mode 100644 index 69615b45f9821a..00000000000000 --- a/Modules/_decimal/libmpdec/examples/README.txt +++ /dev/null @@ -1,8 +0,0 @@ - - -This directory contains a number of examples. In order to compile, run -(for example): - -gcc -Wall -W -O2 -o powmod powmod.c -lmpdec -lm - - diff --git a/Modules/_decimal/libmpdec/examples/compare.c b/Modules/_decimal/libmpdec/examples/compare.c deleted file mode 100644 index 9051773e116dec..00000000000000 --- a/Modules/_decimal/libmpdec/examples/compare.c +++ /dev/null @@ -1,77 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include -#include -#include -#include - - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *a, *b; - mpd_t *result; - char *rstring; - char status_str[MPD_MAX_FLAG_STRING]; - clock_t start_clock, end_clock; - - if (argc != 3) { - fprintf(stderr, "compare: usage: ./compare x y\n"); - exit(1); - } - - mpd_init(&ctx, 38); - ctx.traps = 0; - - result = mpd_new(&ctx); - a = mpd_new(&ctx); - b = mpd_new(&ctx); - mpd_set_string(a, argv[1], &ctx); - mpd_set_string(b, argv[2], &ctx); - - start_clock = clock(); - mpd_compare(result, a, b, &ctx); - end_clock = clock(); - fprintf(stderr, "time: %f\n\n", - (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - rstring = mpd_to_sci(result, 1); - mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status); - printf("%s %s\n", rstring, status_str); - - mpd_del(a); - mpd_del(b); - mpd_del(result); - mpd_free(rstring); - - return 0; -} - - diff --git a/Modules/_decimal/libmpdec/examples/div.c b/Modules/_decimal/libmpdec/examples/div.c deleted file mode 100644 index b76037d2a64c67..00000000000000 --- a/Modules/_decimal/libmpdec/examples/div.c +++ /dev/null @@ -1,77 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include -#include -#include -#include - - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *a, *b; - mpd_t *result; - char *rstring; - char status_str[MPD_MAX_FLAG_STRING]; - clock_t start_clock, end_clock; - - if (argc != 3) { - fprintf(stderr, "div: usage: ./div x y\n"); - exit(1); - } - - mpd_init(&ctx, 38); - ctx.traps = 0; - - result = mpd_new(&ctx); - a = mpd_new(&ctx); - b = mpd_new(&ctx); - mpd_set_string(a, argv[1], &ctx); - mpd_set_string(b, argv[2], &ctx); - - start_clock = clock(); - mpd_div(result, a, b, &ctx); - end_clock = clock(); - fprintf(stderr, "time: %f\n\n", - (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - rstring = mpd_to_sci(result, 1); - mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status); - printf("%s %s\n", rstring, status_str); - - mpd_del(a); - mpd_del(b); - mpd_del(result); - mpd_free(rstring); - - return 0; -} - - diff --git a/Modules/_decimal/libmpdec/examples/divmod.c b/Modules/_decimal/libmpdec/examples/divmod.c deleted file mode 100644 index 1f2b48306d6d06..00000000000000 --- a/Modules/_decimal/libmpdec/examples/divmod.c +++ /dev/null @@ -1,82 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include -#include -#include -#include - - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *a, *b; - mpd_t *q, *r; - char *qs, *rs; - char status_str[MPD_MAX_FLAG_STRING]; - clock_t start_clock, end_clock; - - if (argc != 3) { - fprintf(stderr, "divmod: usage: ./divmod x y\n"); - exit(1); - } - - mpd_init(&ctx, 38); - ctx.traps = 0; - - q = mpd_new(&ctx); - r = mpd_new(&ctx); - a = mpd_new(&ctx); - b = mpd_new(&ctx); - mpd_set_string(a, argv[1], &ctx); - mpd_set_string(b, argv[2], &ctx); - - start_clock = clock(); - mpd_divmod(q, r, a, b, &ctx); - end_clock = clock(); - fprintf(stderr, "time: %f\n\n", - (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - qs = mpd_to_sci(q, 1); - rs = mpd_to_sci(r, 1); - - mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status); - printf("%s %s %s\n", qs, rs, status_str); - - mpd_del(q); - mpd_del(r); - mpd_del(a); - mpd_del(b); - mpd_free(qs); - mpd_free(rs); - - return 0; -} - - diff --git a/Modules/_decimal/libmpdec/examples/multiply.c b/Modules/_decimal/libmpdec/examples/multiply.c deleted file mode 100644 index 7f2687d15f8273..00000000000000 --- a/Modules/_decimal/libmpdec/examples/multiply.c +++ /dev/null @@ -1,77 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include -#include -#include -#include - - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *a, *b; - mpd_t *result; - char *rstring; - char status_str[MPD_MAX_FLAG_STRING]; - clock_t start_clock, end_clock; - - if (argc != 3) { - fprintf(stderr, "multiply: usage: ./multiply x y\n"); - exit(1); - } - - mpd_init(&ctx, 38); - ctx.traps = 0; - - result = mpd_new(&ctx); - a = mpd_new(&ctx); - b = mpd_new(&ctx); - mpd_set_string(a, argv[1], &ctx); - mpd_set_string(b, argv[2], &ctx); - - start_clock = clock(); - mpd_mul(result, a, b, &ctx); - end_clock = clock(); - fprintf(stderr, "time: %f\n\n", - (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - rstring = mpd_to_sci(result, 1); - mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status); - printf("%s %s\n", rstring, status_str); - - mpd_del(a); - mpd_del(b); - mpd_del(result); - mpd_free(rstring); - - return 0; -} - - diff --git a/Modules/_decimal/libmpdec/examples/pow.c b/Modules/_decimal/libmpdec/examples/pow.c deleted file mode 100644 index 628c1434273573..00000000000000 --- a/Modules/_decimal/libmpdec/examples/pow.c +++ /dev/null @@ -1,77 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include -#include -#include -#include - - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *a, *b; - mpd_t *result; - char *rstring; - char status_str[MPD_MAX_FLAG_STRING]; - clock_t start_clock, end_clock; - - if (argc != 3) { - fprintf(stderr, "pow: usage: ./pow x y\n"); - exit(1); - } - - mpd_init(&ctx, 38); - ctx.traps = 0; - - result = mpd_new(&ctx); - a = mpd_new(&ctx); - b = mpd_new(&ctx); - mpd_set_string(a, argv[1], &ctx); - mpd_set_string(b, argv[2], &ctx); - - start_clock = clock(); - mpd_pow(result, a, b, &ctx); - end_clock = clock(); - fprintf(stderr, "time: %f\n\n", - (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - rstring = mpd_to_sci(result, 1); - mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status); - printf("%s %s\n", rstring, status_str); - - mpd_del(a); - mpd_del(b); - mpd_del(result); - mpd_free(rstring); - - return 0; -} - - diff --git a/Modules/_decimal/libmpdec/examples/powmod.c b/Modules/_decimal/libmpdec/examples/powmod.c deleted file mode 100644 index b422fdbbb955d7..00000000000000 --- a/Modules/_decimal/libmpdec/examples/powmod.c +++ /dev/null @@ -1,80 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include -#include -#include -#include - - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *a, *b, *c; - mpd_t *result; - char *rstring; - char status_str[MPD_MAX_FLAG_STRING]; - clock_t start_clock, end_clock; - - if (argc != 4) { - fprintf(stderr, "powmod: usage: ./powmod x y z\n"); - exit(1); - } - - mpd_init(&ctx, 38); - ctx.traps = 0; - - result = mpd_new(&ctx); - a = mpd_new(&ctx); - b = mpd_new(&ctx); - c = mpd_new(&ctx); - mpd_set_string(a, argv[1], &ctx); - mpd_set_string(b, argv[2], &ctx); - mpd_set_string(c, argv[3], &ctx); - - start_clock = clock(); - mpd_powmod(result, a, b, c, &ctx); - end_clock = clock(); - fprintf(stderr, "time: %f\n\n", - (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - rstring = mpd_to_sci(result, 1); - mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status); - printf("%s %s\n", rstring, status_str); - - mpd_del(a); - mpd_del(b); - mpd_del(c); - mpd_del(result); - mpd_free(rstring); - - return 0; -} - - diff --git a/Modules/_decimal/libmpdec/examples/shift.c b/Modules/_decimal/libmpdec/examples/shift.c deleted file mode 100644 index 6d54e108ca87f0..00000000000000 --- a/Modules/_decimal/libmpdec/examples/shift.c +++ /dev/null @@ -1,77 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include -#include -#include -#include - - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *a, *b; - mpd_t *result; - char *rstring; - char status_str[MPD_MAX_FLAG_STRING]; - clock_t start_clock, end_clock; - - if (argc != 3) { - fprintf(stderr, "shift: usage: ./shift x y\n"); - exit(1); - } - - mpd_init(&ctx, 38); - ctx.traps = 0; - - result = mpd_new(&ctx); - a = mpd_new(&ctx); - b = mpd_new(&ctx); - mpd_set_string(a, argv[1], &ctx); - mpd_set_string(b, argv[2], &ctx); - - start_clock = clock(); - mpd_shift(result, a, b, &ctx); - end_clock = clock(); - fprintf(stderr, "time: %f\n\n", - (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - rstring = mpd_to_sci(result, 1); - mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status); - printf("%s %s\n", rstring, status_str); - - mpd_del(a); - mpd_del(b); - mpd_del(result); - mpd_free(rstring); - - return 0; -} - - diff --git a/Modules/_decimal/libmpdec/examples/sqrt.c b/Modules/_decimal/libmpdec/examples/sqrt.c deleted file mode 100644 index d8272789b18c23..00000000000000 --- a/Modules/_decimal/libmpdec/examples/sqrt.c +++ /dev/null @@ -1,74 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include -#include -#include -#include - - -int -main(int argc, char **argv) -{ - mpd_context_t ctx; - mpd_t *a; - mpd_t *result; - char *rstring; - char status_str[MPD_MAX_FLAG_STRING]; - clock_t start_clock, end_clock; - - if (argc != 2) { - fprintf(stderr, "sqrt: usage: ./sqrt x\n"); - exit(1); - } - - mpd_init(&ctx, 38); - ctx.traps = 0; - - result = mpd_new(&ctx); - a = mpd_new(&ctx); - mpd_set_string(a, argv[1], &ctx); - - start_clock = clock(); - mpd_sqrt(result, a, &ctx); - end_clock = clock(); - fprintf(stderr, "time: %f\n\n", - (double)(end_clock-start_clock)/(double)CLOCKS_PER_SEC); - - rstring = mpd_to_sci(result, 1); - mpd_snprint_flags(status_str, MPD_MAX_FLAG_STRING, ctx.status); - printf("%s %s\n", rstring, status_str); - - mpd_del(a); - mpd_del(result); - mpd_free(rstring); - - return 0; -} - - diff --git a/Modules/_decimal/libmpdec/fnt.c b/Modules/_decimal/libmpdec/fnt.c deleted file mode 100644 index 0dbe98fc71c9ea..00000000000000 --- a/Modules/_decimal/libmpdec/fnt.c +++ /dev/null @@ -1,79 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include - -#include "bits.h" -#include "difradix2.h" -#include "fnt.h" -#include "numbertheory.h" - - -/* Bignum: Fast transform for medium-sized coefficients. */ - - -/* forward transform, sign = -1 */ -int -std_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - struct fnt_params *tparams; - - assert(ispower2(n)); - assert(n >= 4); - assert(n <= 3*MPD_MAXTRANSFORM_2N); - - if ((tparams = _mpd_init_fnt_params(n, -1, modnum)) == NULL) { - return 0; - } - fnt_dif2(a, n, tparams); - - mpd_free(tparams); - return 1; -} - -/* reverse transform, sign = 1 */ -int -std_inv_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - struct fnt_params *tparams; - - assert(ispower2(n)); - assert(n >= 4); - assert(n <= 3*MPD_MAXTRANSFORM_2N); - - if ((tparams = _mpd_init_fnt_params(n, 1, modnum)) == NULL) { - return 0; - } - fnt_dif2(a, n, tparams); - - mpd_free(tparams); - return 1; -} diff --git a/Modules/_decimal/libmpdec/fnt.h b/Modules/_decimal/libmpdec/fnt.h deleted file mode 100644 index 5222c476a3a4f5..00000000000000 --- a/Modules/_decimal/libmpdec/fnt.h +++ /dev/null @@ -1,47 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_FNT_H_ -#define LIBMPDEC_FNT_H_ - - -#include "mpdecimal.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -int std_fnt(mpd_uint_t a[], mpd_size_t n, int modnum); -int std_inv_fnt(mpd_uint_t a[], mpd_size_t n, int modnum); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_FNT_H_ */ diff --git a/Modules/_decimal/libmpdec/fourstep.c b/Modules/_decimal/libmpdec/fourstep.c deleted file mode 100644 index fb173ed5a52e46..00000000000000 --- a/Modules/_decimal/libmpdec/fourstep.c +++ /dev/null @@ -1,259 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include - -#include "constants.h" -#include "fourstep.h" -#include "numbertheory.h" -#include "sixstep.h" -#include "umodarith.h" - - -/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the - form 3 * 2**n (See literature/matrix-transform.txt). */ - - -#ifndef PPRO -static inline void -std_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, - mpd_uint_t w3table[3], mpd_uint_t umod) -{ - mpd_uint_t r1, r2; - mpd_uint_t w; - mpd_uint_t s, tmp; - - - /* k = 0 -> w = 1 */ - s = *x1; - s = addmod(s, *x2, umod); - s = addmod(s, *x3, umod); - - r1 = s; - - /* k = 1 */ - s = *x1; - - w = w3table[1]; - tmp = MULMOD(*x2, w); - s = addmod(s, tmp, umod); - - w = w3table[2]; - tmp = MULMOD(*x3, w); - s = addmod(s, tmp, umod); - - r2 = s; - - /* k = 2 */ - s = *x1; - - w = w3table[2]; - tmp = MULMOD(*x2, w); - s = addmod(s, tmp, umod); - - w = w3table[1]; - tmp = MULMOD(*x3, w); - s = addmod(s, tmp, umod); - - *x3 = s; - *x2 = r2; - *x1 = r1; -} -#else /* PPRO */ -static inline void -ppro_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_uint_t w3table[3], - mpd_uint_t umod, double *dmod, uint32_t dinvmod[3]) -{ - mpd_uint_t r1, r2; - mpd_uint_t w; - mpd_uint_t s, tmp; - - - /* k = 0 -> w = 1 */ - s = *x1; - s = addmod(s, *x2, umod); - s = addmod(s, *x3, umod); - - r1 = s; - - /* k = 1 */ - s = *x1; - - w = w3table[1]; - tmp = ppro_mulmod(*x2, w, dmod, dinvmod); - s = addmod(s, tmp, umod); - - w = w3table[2]; - tmp = ppro_mulmod(*x3, w, dmod, dinvmod); - s = addmod(s, tmp, umod); - - r2 = s; - - /* k = 2 */ - s = *x1; - - w = w3table[2]; - tmp = ppro_mulmod(*x2, w, dmod, dinvmod); - s = addmod(s, tmp, umod); - - w = w3table[1]; - tmp = ppro_mulmod(*x3, w, dmod, dinvmod); - s = addmod(s, tmp, umod); - - *x3 = s; - *x2 = r2; - *x1 = r1; -} -#endif - - -/* forward transform, sign = -1; transform length = 3 * 2**n */ -int -four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - mpd_size_t R = 3; /* number of rows */ - mpd_size_t C = n / 3; /* number of columns */ - mpd_uint_t w3table[3]; - mpd_uint_t kernel, w0, w1, wstep; - mpd_uint_t *s, *p0, *p1, *p2; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_size_t i, k; - - - assert(n >= 48); - assert(n <= 3*MPD_MAXTRANSFORM_2N); - - - /* Length R transform on the columns. */ - SETMODULUS(modnum); - _mpd_init_w3table(w3table, -1, modnum); - for (p0=a, p1=p0+C, p2=p0+2*C; p0= 48); - assert(n <= 3*MPD_MAXTRANSFORM_2N); - - -#if 0 - /* An unordered transform is sufficient for convolution. */ - /* Transpose the matrix, producing an R*C matrix. */ - #include "transpose.h" - transpose_3xpow2(a, C, R); -#endif - - /* Length C transform on the rows. */ - for (s = a; s < a+n; s += C) { - if (!inv_six_step_fnt(s, C, modnum)) { - return 0; - } - } - - /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ - SETMODULUS(modnum); - kernel = _mpd_getkernel(n, 1, modnum); - for (i = 1; i < R; i++) { - w0 = 1; - w1 = POWMOD(kernel, i); - wstep = MULMOD(w1, w1); - for (k = 0; k < C; k += 2) { - mpd_uint_t x0 = a[i*C+k]; - mpd_uint_t x1 = a[i*C+k+1]; - MULMOD2(&x0, w0, &x1, w1); - MULMOD2C(&w0, &w1, wstep); - a[i*C+k] = x0; - a[i*C+k+1] = x1; - } - } - - /* Length R transform on the columns. */ - _mpd_init_w3table(w3table, 1, modnum); - for (p0=a, p1=p0+C, p2=p0+2*C; p0 -#include -#include -#include -#include -#include -#include -#include - -#include "io.h" -#include "typearith.h" - - -/* This file contains functions for decimal <-> string conversions, including - PEP-3101 formatting for numeric types. */ - - -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 7 - #pragma GCC diagnostic ignored "-Wimplicit-fallthrough" - #pragma GCC diagnostic ignored "-Wmisleading-indentation" - #pragma GCC diagnostic ignored "-Warray-bounds" -#endif - - -/* - * Work around the behavior of tolower() and strcasecmp() in certain - * locales. For example, in tr_TR.utf8: - * - * tolower((unsigned char)'I') == 'I' - * - * u is the exact uppercase version of l; n is strlen(l) or strlen(l)+1 - */ -static inline int -_mpd_strneq(const char *s, const char *l, const char *u, size_t n) -{ - while (--n != SIZE_MAX) { - if (*s != *l && *s != *u) { - return 0; - } - s++; u++; l++; - } - - return 1; -} - -static mpd_ssize_t -strtoexp(const char *s) -{ - char *end; - mpd_ssize_t retval; - - errno = 0; - retval = mpd_strtossize(s, &end, 10); - if (errno == 0 && !(*s != '\0' && *end == '\0')) - errno = EINVAL; - - return retval; -} - -/* - * Scan 'len' words. The most significant word contains 'r' digits, - * the remaining words are full words. Skip dpoint. The string 's' must - * consist of digits and an optional single decimal point at 'dpoint'. - */ -static void -string_to_coeff(mpd_uint_t *data, const char *s, const char *dpoint, int r, - size_t len) -{ - int j; - - if (r > 0) { - data[--len] = 0; - for (j = 0; j < r; j++, s++) { - if (s == dpoint) s++; - data[len] = 10 * data[len] + (*s - '0'); - } - } - - while (--len != SIZE_MAX) { - data[len] = 0; - for (j = 0; j < MPD_RDIGITS; j++, s++) { - if (s == dpoint) s++; - data[len] = 10 * data[len] + (*s - '0'); - } - } -} - -/* - * Partially verify a numeric string of the form: - * - * [cdigits][.][cdigits][eE][+-][edigits] - * - * If successful, return a pointer to the location of the first - * relevant coefficient digit. This digit is either non-zero or - * part of one of the following patterns: - * - * ["0\x00", "0.\x00", "0.E", "0.e", "0E", "0e"] - * - * The locations of a single optional dot or indicator are stored - * in 'dpoint' and 'exp'. - * - * The end of the string is stored in 'end'. If an indicator [eE] - * occurs without trailing [edigits], the condition is caught - * later by strtoexp(). - */ -static const char * -scan_dpoint_exp(const char *s, const char **dpoint, const char **exp, - const char **end) -{ - const char *coeff = NULL; - - *dpoint = NULL; - *exp = NULL; - for (; *s != '\0'; s++) { - switch (*s) { - case '.': - if (*dpoint != NULL || *exp != NULL) - return NULL; - *dpoint = s; - break; - case 'E': case 'e': - if (*exp != NULL) - return NULL; - *exp = s; - if (*(s+1) == '+' || *(s+1) == '-') - s++; - break; - default: - if (!isdigit((unsigned char)*s)) - return NULL; - if (coeff == NULL && *exp == NULL) { - if (*s == '0') { - if (!isdigit((unsigned char)*(s+1))) - if (!(*(s+1) == '.' && - isdigit((unsigned char)*(s+2)))) - coeff = s; - } - else { - coeff = s; - } - } - break; - - } - } - - *end = s; - return coeff; -} - -/* scan the payload of a NaN */ -static const char * -scan_payload(const char *s, const char **end) -{ - const char *coeff; - - while (*s == '0') - s++; - coeff = s; - - while (isdigit((unsigned char)*s)) - s++; - *end = s; - - return (*s == '\0') ? coeff : NULL; -} - -/* convert a character string to a decimal */ -void -mpd_qset_string(mpd_t *dec, const char *s, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_ssize_t q, r, len; - const char *coeff, *end; - const char *dpoint = NULL, *exp = NULL; - size_t digits; - uint8_t sign = MPD_POS; - - mpd_set_flags(dec, 0); - dec->len = 0; - dec->exp = 0; - - /* sign */ - if (*s == '+') { - s++; - } - else if (*s == '-') { - mpd_set_negative(dec); - sign = MPD_NEG; - s++; - } - - if (_mpd_strneq(s, "nan", "NAN", 3)) { /* NaN */ - s += 3; - mpd_setspecial(dec, sign, MPD_NAN); - if (*s == '\0') - return; - /* validate payload: digits only */ - if ((coeff = scan_payload(s, &end)) == NULL) - goto conversion_error; - /* payload consists entirely of zeros */ - if (*coeff == '\0') - return; - digits = end - coeff; - /* prec >= 1, clamp is 0 or 1 */ - if (digits > (size_t)(ctx->prec-ctx->clamp)) - goto conversion_error; - } /* sNaN */ - else if (_mpd_strneq(s, "snan", "SNAN", 4)) { - s += 4; - mpd_setspecial(dec, sign, MPD_SNAN); - if (*s == '\0') - return; - /* validate payload: digits only */ - if ((coeff = scan_payload(s, &end)) == NULL) - goto conversion_error; - /* payload consists entirely of zeros */ - if (*coeff == '\0') - return; - digits = end - coeff; - if (digits > (size_t)(ctx->prec-ctx->clamp)) - goto conversion_error; - } - else if (_mpd_strneq(s, "inf", "INF", 3)) { - s += 3; - if (*s == '\0' || _mpd_strneq(s, "inity", "INITY", 6)) { - /* numeric-value: infinity */ - mpd_setspecial(dec, sign, MPD_INF); - return; - } - goto conversion_error; - } - else { - /* scan for start of coefficient, decimal point, indicator, end */ - if ((coeff = scan_dpoint_exp(s, &dpoint, &exp, &end)) == NULL) - goto conversion_error; - - /* numeric-value: [exponent-part] */ - if (exp) { - /* exponent-part */ - end = exp; exp++; - dec->exp = strtoexp(exp); - if (errno) { - if (!(errno == ERANGE && - (dec->exp == MPD_SSIZE_MAX || - dec->exp == MPD_SSIZE_MIN))) - goto conversion_error; - } - } - - digits = end - coeff; - if (dpoint) { - size_t fracdigits = end-dpoint-1; - if (dpoint > coeff) digits--; - - if (fracdigits > MPD_MAX_PREC) { - goto conversion_error; - } - if (dec->exp < MPD_SSIZE_MIN+(mpd_ssize_t)fracdigits) { - dec->exp = MPD_SSIZE_MIN; - } - else { - dec->exp -= (mpd_ssize_t)fracdigits; - } - } - if (digits > MPD_MAX_PREC) { - goto conversion_error; - } - if (dec->exp > MPD_EXP_INF) { - dec->exp = MPD_EXP_INF; - } - if (dec->exp == MPD_SSIZE_MIN) { - dec->exp = MPD_SSIZE_MIN+1; - } - } - - _mpd_idiv_word(&q, &r, (mpd_ssize_t)digits, MPD_RDIGITS); - - len = (r == 0) ? q : q+1; - if (len == 0) { - goto conversion_error; /* GCOV_NOT_REACHED */ - } - if (!mpd_qresize(dec, len, status)) { - mpd_seterror(dec, MPD_Malloc_error, status); - return; - } - dec->len = len; - - string_to_coeff(dec->data, coeff, dpoint, (int)r, len); - - mpd_setdigits(dec); - mpd_qfinalize(dec, ctx, status); - return; - -conversion_error: - /* standard wants a positive NaN */ - mpd_seterror(dec, MPD_Conversion_syntax, status); -} - -/* convert a character string to a decimal, use a maxcontext for conversion */ -void -mpd_qset_string_exact(mpd_t *dec, const char *s, uint32_t *status) -{ - mpd_context_t maxcontext; - - mpd_maxcontext(&maxcontext); - mpd_qset_string(dec, s, &maxcontext, status); - - if (*status & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - /* we want exact results */ - mpd_seterror(dec, MPD_Invalid_operation, status); - } - *status &= MPD_Errors; -} - -/* Print word x with n decimal digits to string s. dot is either NULL - or the location of a decimal point. */ -#define EXTRACT_DIGIT(s, x, d, dot) \ - if (s == dot) *s++ = '.'; *s++ = '0' + (char)(x / d); x %= d -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 12 - #pragma GCC diagnostic push - #pragma GCC diagnostic ignored "-Wstringop-overflow" -#endif -static inline char * -word_to_string(char *s, mpd_uint_t x, int n, char *dot) -{ - switch(n) { -#ifdef CONFIG_64 - case 20: EXTRACT_DIGIT(s, x, 10000000000000000000ULL, dot); /* GCOV_NOT_REACHED */ - case 19: EXTRACT_DIGIT(s, x, 1000000000000000000ULL, dot); - case 18: EXTRACT_DIGIT(s, x, 100000000000000000ULL, dot); - case 17: EXTRACT_DIGIT(s, x, 10000000000000000ULL, dot); - case 16: EXTRACT_DIGIT(s, x, 1000000000000000ULL, dot); - case 15: EXTRACT_DIGIT(s, x, 100000000000000ULL, dot); - case 14: EXTRACT_DIGIT(s, x, 10000000000000ULL, dot); - case 13: EXTRACT_DIGIT(s, x, 1000000000000ULL, dot); - case 12: EXTRACT_DIGIT(s, x, 100000000000ULL, dot); - case 11: EXTRACT_DIGIT(s, x, 10000000000ULL, dot); -#endif - case 10: EXTRACT_DIGIT(s, x, 1000000000UL, dot); - case 9: EXTRACT_DIGIT(s, x, 100000000UL, dot); - case 8: EXTRACT_DIGIT(s, x, 10000000UL, dot); - case 7: EXTRACT_DIGIT(s, x, 1000000UL, dot); - case 6: EXTRACT_DIGIT(s, x, 100000UL, dot); - case 5: EXTRACT_DIGIT(s, x, 10000UL, dot); - case 4: EXTRACT_DIGIT(s, x, 1000UL, dot); - case 3: EXTRACT_DIGIT(s, x, 100UL, dot); - case 2: EXTRACT_DIGIT(s, x, 10UL, dot); - default: if (s == dot) *s++ = '.'; *s++ = '0' + (char)x; - } - - *s = '\0'; - return s; -} -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 12 - #pragma GCC diagnostic pop -#endif - -/* Print exponent x to string s. Undefined for MPD_SSIZE_MIN. */ -static inline char * -exp_to_string(char *s, mpd_ssize_t x) -{ - char sign = '+'; - - if (x < 0) { - sign = '-'; - x = -x; - } - *s++ = sign; - - return word_to_string(s, x, mpd_word_digits(x), NULL); -} - -/* Print the coefficient of dec to string s. len(dec) > 0. */ -static inline char * -coeff_to_string(char *s, const mpd_t *dec) -{ - mpd_uint_t x; - mpd_ssize_t i; - - /* most significant word */ - x = mpd_msword(dec); - s = word_to_string(s, x, mpd_word_digits(x), NULL); - - /* remaining full words */ - for (i=dec->len-2; i >= 0; --i) { - x = dec->data[i]; - s = word_to_string(s, x, MPD_RDIGITS, NULL); - } - - return s; -} - -/* Print the coefficient of dec to string s. len(dec) > 0. dot is either - NULL or a pointer to the location of a decimal point. */ -static inline char * -coeff_to_string_dot(char *s, char *dot, const mpd_t *dec) -{ - mpd_uint_t x; - mpd_ssize_t i; - - /* most significant word */ - x = mpd_msword(dec); - s = word_to_string(s, x, mpd_word_digits(x), dot); - - /* remaining full words */ - for (i=dec->len-2; i >= 0; --i) { - x = dec->data[i]; - s = word_to_string(s, x, MPD_RDIGITS, dot); - } - - return s; -} - -/* Format type */ -#define MPD_FMT_LOWER 0x00000000 -#define MPD_FMT_UPPER 0x00000001 -#define MPD_FMT_TOSCI 0x00000002 -#define MPD_FMT_TOENG 0x00000004 -#define MPD_FMT_EXP 0x00000008 -#define MPD_FMT_FIXED 0x00000010 -#define MPD_FMT_PERCENT 0x00000020 -#define MPD_FMT_SIGN_SPACE 0x00000040 -#define MPD_FMT_SIGN_PLUS 0x00000080 - -/* Default place of the decimal point for MPD_FMT_TOSCI, MPD_FMT_EXP */ -#define MPD_DEFAULT_DOTPLACE 1 - -/* - * Set *result to the string representation of a decimal. Return the length - * of *result, not including the terminating '\0' character. - * - * Formatting is done according to 'flags'. A return value of -1 with *result - * set to NULL indicates MPD_Malloc_error. - * - * 'dplace' is the default place of the decimal point. It is always set to - * MPD_DEFAULT_DOTPLACE except for zeros in combination with MPD_FMT_EXP. - */ -static mpd_ssize_t -_mpd_to_string(char **result, const mpd_t *dec, int flags, mpd_ssize_t dplace) -{ - char *decstring = NULL, *cp = NULL; - mpd_ssize_t ldigits; - mpd_ssize_t mem = 0, k; - - if (mpd_isspecial(dec)) { - - mem = sizeof "-Infinity%"; - if (mpd_isnan(dec) && dec->len > 0) { - /* diagnostic code */ - mem += dec->digits; - } - cp = decstring = mpd_alloc(mem, sizeof *decstring); - if (cp == NULL) { - *result = NULL; - return -1; - } - - if (mpd_isnegative(dec)) { - *cp++ = '-'; - } - else if (flags&MPD_FMT_SIGN_SPACE) { - *cp++ = ' '; - } - else if (flags&MPD_FMT_SIGN_PLUS) { - *cp++ = '+'; - } - - if (mpd_isnan(dec)) { - if (mpd_isqnan(dec)) { - strcpy(cp, "NaN"); - cp += 3; - } - else { - strcpy(cp, "sNaN"); - cp += 4; - } - if (dec->len > 0) { /* diagnostic code */ - cp = coeff_to_string(cp, dec); - } - } - else if (mpd_isinfinite(dec)) { - strcpy(cp, "Infinity"); - cp += 8; - } - else { /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - } - else { - assert(dec->len > 0); - - /* - * For easier manipulation of the decimal point's location - * and the exponent that is finally printed, the number is - * rescaled to a virtual representation with exp = 0. Here - * ldigits denotes the number of decimal digits to the left - * of the decimal point and remains constant once initialized. - * - * dplace is the location of the decimal point relative to - * the start of the coefficient. Note that 3) always holds - * when dplace is shifted. - * - * 1) ldigits := dec->digits - dec->exp - * 2) dplace := ldigits (initially) - * 3) exp := ldigits - dplace (initially exp = 0) - * - * 0.00000_.____._____000000. - * ^ ^ ^ ^ - * | | | | - * | | | `- dplace >= digits - * | | `- dplace in the middle of the coefficient - * | ` dplace = 1 (after the first coefficient digit) - * `- dplace <= 0 - */ - - ldigits = dec->digits + dec->exp; - - if (flags&MPD_FMT_EXP) { - ; - } - else if (flags&MPD_FMT_FIXED || (dec->exp <= 0 && ldigits > -6)) { - /* MPD_FMT_FIXED: always use fixed point notation. - * MPD_FMT_TOSCI, MPD_FMT_TOENG: for a certain range, - * override exponent notation. */ - dplace = ldigits; - } - else if (flags&MPD_FMT_TOENG) { - if (mpd_iszero(dec)) { - /* If the exponent is divisible by three, - * dplace = 1. Otherwise, move dplace one - * or two places to the left. */ - dplace = -1 + mod_mpd_ssize_t(dec->exp+2, 3); - } - else { /* ldigits-1 is the adjusted exponent, which - * should be divisible by three. If not, move - * dplace one or two places to the right. */ - dplace += mod_mpd_ssize_t(ldigits-1, 3); - } - } - - /* - * Basic space requirements: - * - * [-][.][coeffdigits][E][-][expdigits+1][%]['\0'] - * - * If the decimal point lies outside of the coefficient digits, - * space is adjusted accordingly. - */ - if (dplace <= 0) { - mem = -dplace + dec->digits + 2; - } - else if (dplace >= dec->digits) { - mem = dplace; - } - else { - mem = dec->digits; - } - mem += (MPD_EXPDIGITS+1+6); - - cp = decstring = mpd_alloc(mem, sizeof *decstring); - if (cp == NULL) { - *result = NULL; - return -1; - } - - - if (mpd_isnegative(dec)) { - *cp++ = '-'; - } - else if (flags&MPD_FMT_SIGN_SPACE) { - *cp++ = ' '; - } - else if (flags&MPD_FMT_SIGN_PLUS) { - *cp++ = '+'; - } - - if (dplace <= 0) { - /* space: -dplace+dec->digits+2 */ - *cp++ = '0'; - *cp++ = '.'; - for (k = 0; k < -dplace; k++) { - *cp++ = '0'; - } - cp = coeff_to_string(cp, dec); - } - else if (dplace >= dec->digits) { - /* space: dplace */ - cp = coeff_to_string(cp, dec); - for (k = 0; k < dplace-dec->digits; k++) { - *cp++ = '0'; - } - } - else { - /* space: dec->digits+1 */ - cp = coeff_to_string_dot(cp, cp+dplace, dec); - } - - /* - * Conditions for printing an exponent: - * - * MPD_FMT_TOSCI, MPD_FMT_TOENG: only if ldigits != dplace - * MPD_FMT_FIXED: never (ldigits == dplace) - * MPD_FMT_EXP: always - */ - if (ldigits != dplace || flags&MPD_FMT_EXP) { - /* space: expdigits+2 */ - *cp++ = (flags&MPD_FMT_UPPER) ? 'E' : 'e'; - cp = exp_to_string(cp, ldigits-dplace); - } - } - - if (flags&MPD_FMT_PERCENT) { - *cp++ = '%'; - } - - assert(cp < decstring+mem); - assert(cp-decstring < MPD_SSIZE_MAX); - - *cp = '\0'; - *result = decstring; - return (mpd_ssize_t)(cp-decstring); -} - -char * -mpd_to_sci(const mpd_t *dec, int fmt) -{ - char *res; - int flags = MPD_FMT_TOSCI; - - flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER; - (void)_mpd_to_string(&res, dec, flags, MPD_DEFAULT_DOTPLACE); - return res; -} - -char * -mpd_to_eng(const mpd_t *dec, int fmt) -{ - char *res; - int flags = MPD_FMT_TOENG; - - flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER; - (void)_mpd_to_string(&res, dec, flags, MPD_DEFAULT_DOTPLACE); - return res; -} - -mpd_ssize_t -mpd_to_sci_size(char **res, const mpd_t *dec, int fmt) -{ - int flags = MPD_FMT_TOSCI; - - flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER; - return _mpd_to_string(res, dec, flags, MPD_DEFAULT_DOTPLACE); -} - -mpd_ssize_t -mpd_to_eng_size(char **res, const mpd_t *dec, int fmt) -{ - int flags = MPD_FMT_TOENG; - - flags |= fmt ? MPD_FMT_UPPER : MPD_FMT_LOWER; - return _mpd_to_string(res, dec, flags, MPD_DEFAULT_DOTPLACE); -} - -/* Copy a single UTF-8 char to dest. See: The Unicode Standard, version 5.2, - chapter 3.9: Well-formed UTF-8 byte sequences. */ -static int -_mpd_copy_utf8(char dest[5], const char *s) -{ - const unsigned char *cp = (const unsigned char *)s; - unsigned char lb, ub; - int count, i; - - - if (*cp == 0) { - /* empty string */ - dest[0] = '\0'; - return 0; - } - else if (*cp <= 0x7f) { - /* ascii */ - dest[0] = *cp; - dest[1] = '\0'; - return 1; - } - else if (0xc2 <= *cp && *cp <= 0xdf) { - lb = 0x80; ub = 0xbf; - count = 2; - } - else if (*cp == 0xe0) { - lb = 0xa0; ub = 0xbf; - count = 3; - } - else if (*cp <= 0xec) { - lb = 0x80; ub = 0xbf; - count = 3; - } - else if (*cp == 0xed) { - lb = 0x80; ub = 0x9f; - count = 3; - } - else if (*cp <= 0xef) { - lb = 0x80; ub = 0xbf; - count = 3; - } - else if (*cp == 0xf0) { - lb = 0x90; ub = 0xbf; - count = 4; - } - else if (*cp <= 0xf3) { - lb = 0x80; ub = 0xbf; - count = 4; - } - else if (*cp == 0xf4) { - lb = 0x80; ub = 0x8f; - count = 4; - } - else { - /* invalid */ - goto error; - } - - dest[0] = *cp++; - if (*cp < lb || ub < *cp) { - goto error; - } - dest[1] = *cp++; - for (i = 2; i < count; i++) { - if (*cp < 0x80 || 0xbf < *cp) { - goto error; - } - dest[i] = *cp++; - } - dest[i] = '\0'; - - return count; - -error: - dest[0] = '\0'; - return -1; -} - -int -mpd_validate_lconv(mpd_spec_t *spec) -{ - size_t n; -#if CHAR_MAX == SCHAR_MAX - const char *cp = spec->grouping; - while (*cp != '\0') { - if (*cp++ < 0) { - return -1; - } - } -#endif - n = strlen(spec->dot); - if (n == 0 || n > 4) { - return -1; - } - if (strlen(spec->sep) > 4) { - return -1; - } - - return 0; -} - -int -mpd_parse_fmt_str(mpd_spec_t *spec, const char *fmt, int caps) -{ - char *cp = (char *)fmt; - int have_align = 0, n; - - /* defaults */ - spec->min_width = 0; - spec->prec = -1; - spec->type = caps ? 'G' : 'g'; - spec->align = '>'; - spec->sign = '-'; - spec->dot = ""; - spec->sep = ""; - spec->grouping = ""; - - - /* presume that the first character is a UTF-8 fill character */ - if ((n = _mpd_copy_utf8(spec->fill, cp)) < 0) { - return 0; - } - - /* alignment directive, prefixed by a fill character */ - if (*cp && (*(cp+n) == '<' || *(cp+n) == '>' || - *(cp+n) == '=' || *(cp+n) == '^')) { - cp += n; - spec->align = *cp++; - have_align = 1; - } /* alignment directive */ - else { - /* default fill character */ - spec->fill[0] = ' '; - spec->fill[1] = '\0'; - if (*cp == '<' || *cp == '>' || - *cp == '=' || *cp == '^') { - spec->align = *cp++; - have_align = 1; - } - } - - /* sign formatting */ - if (*cp == '+' || *cp == '-' || *cp == ' ') { - spec->sign = *cp++; - } - - /* zero padding */ - if (*cp == '0') { - /* zero padding implies alignment, which should not be - * specified twice. */ - if (have_align) { - return 0; - } - spec->align = 'z'; - spec->fill[0] = *cp++; - spec->fill[1] = '\0'; - } - - /* minimum width */ - if (isdigit((unsigned char)*cp)) { - if (*cp == '0') { - return 0; - } - errno = 0; - spec->min_width = mpd_strtossize(cp, &cp, 10); - if (errno == ERANGE || errno == EINVAL) { - return 0; - } - } - - /* thousands separator */ - if (*cp == ',') { - spec->dot = "."; - spec->sep = ","; - spec->grouping = "\003\003"; - cp++; - } - - /* fraction digits or significant digits */ - if (*cp == '.') { - cp++; - if (!isdigit((unsigned char)*cp)) { - return 0; - } - errno = 0; - spec->prec = mpd_strtossize(cp, &cp, 10); - if (errno == ERANGE || errno == EINVAL) { - return 0; - } - } - - /* type */ - if (*cp == 'E' || *cp == 'e' || *cp == 'F' || *cp == 'f' || - *cp == 'G' || *cp == 'g' || *cp == '%') { - spec->type = *cp++; - } - else if (*cp == 'N' || *cp == 'n') { - /* locale specific conversion */ - struct lconv *lc; - /* separator has already been specified */ - if (*spec->sep) { - return 0; - } - spec->type = *cp++; - spec->type = (spec->type == 'N') ? 'G' : 'g'; - lc = localeconv(); - spec->dot = lc->decimal_point; - spec->sep = lc->thousands_sep; - spec->grouping = lc->grouping; - if (mpd_validate_lconv(spec) < 0) { - return 0; /* GCOV_NOT_REACHED */ - } - } - - /* check correctness */ - if (*cp != '\0') { - return 0; - } - - return 1; -} - -/* - * The following functions assume that spec->min_width <= MPD_MAX_PREC, which - * is made sure in mpd_qformat_spec. Then, even with a spec that inserts a - * four-byte separator after each digit, nbytes in the following struct - * cannot overflow. - */ - -/* Multibyte string */ -typedef struct { - mpd_ssize_t nbytes; /* length in bytes */ - mpd_ssize_t nchars; /* length in chars */ - mpd_ssize_t cur; /* current write index */ - char *data; -} mpd_mbstr_t; - -static inline void -_mpd_bcopy(char *dest, const char *src, mpd_ssize_t n) -{ - while (--n >= 0) { - dest[n] = src[n]; - } -} - -static inline void -_mbstr_copy_char(mpd_mbstr_t *dest, const char *src, mpd_ssize_t n) -{ - dest->nbytes += n; - dest->nchars += (n > 0 ? 1 : 0); - dest->cur -= n; - - if (dest->data != NULL) { - _mpd_bcopy(dest->data+dest->cur, src, n); - } -} - -static inline void -_mbstr_copy_ascii(mpd_mbstr_t *dest, const char *src, mpd_ssize_t n) -{ - dest->nbytes += n; - dest->nchars += n; - dest->cur -= n; - - if (dest->data != NULL) { - _mpd_bcopy(dest->data+dest->cur, src, n); - } -} - -static inline void -_mbstr_copy_pad(mpd_mbstr_t *dest, mpd_ssize_t n) -{ - dest->nbytes += n; - dest->nchars += n; - dest->cur -= n; - - if (dest->data != NULL) { - char *cp = dest->data + dest->cur; - while (--n >= 0) { - cp[n] = '0'; - } - } -} - -/* - * Copy a numeric string to dest->data, adding separators in the integer - * part according to spec->grouping. If leading zero padding is enabled - * and the result is smaller than spec->min_width, continue adding zeros - * and separators until the minimum width is reached. - * - * The final length of dest->data is stored in dest->nbytes. The number - * of UTF-8 characters is stored in dest->nchars. - * - * First run (dest->data == NULL): determine the length of the result - * string and store it in dest->nbytes. - * - * Second run (write to dest->data): data is written in chunks and in - * reverse order, starting with the rest of the numeric string. - */ -static void -_mpd_add_sep_dot(mpd_mbstr_t *dest, - const char *sign, /* location of optional sign */ - const char *src, mpd_ssize_t n_src, /* integer part and length */ - const char *dot, /* location of optional decimal point */ - const char *rest, mpd_ssize_t n_rest, /* remaining part and length */ - const mpd_spec_t *spec) -{ - mpd_ssize_t n_sep, n_sign, consume; - const char *g; - int pad = 0; - - n_sign = sign ? 1 : 0; - n_sep = (mpd_ssize_t)strlen(spec->sep); - /* Initial write index: set to location of '\0' in the output string. - * Irrelevant for the first run. */ - dest->cur = dest->nbytes; - dest->nbytes = dest->nchars = 0; - - _mbstr_copy_ascii(dest, rest, n_rest); - - if (dot) { - _mbstr_copy_char(dest, dot, (mpd_ssize_t)strlen(dot)); - } - - g = spec->grouping; - consume = *g; - while (1) { - /* If the group length is 0 or CHAR_MAX or greater than the - * number of source bytes, consume all remaining bytes. */ - if (*g == 0 || *g == CHAR_MAX || consume > n_src) { - consume = n_src; - } - n_src -= consume; - if (pad) { - _mbstr_copy_pad(dest, consume); - } - else { - _mbstr_copy_ascii(dest, src+n_src, consume); - } - - if (n_src == 0) { - /* Either the real source of intpart digits or the virtual - * source of padding zeros is exhausted. */ - if (spec->align == 'z' && - dest->nchars + n_sign < spec->min_width) { - /* Zero padding is set and length < min_width: - * Generate n_src additional characters. */ - n_src = spec->min_width - (dest->nchars + n_sign); - /* Next iteration: - * case *g == 0 || *g == CHAR_MAX: - * consume all padding characters - * case consume < g*: - * fill remainder of current group - * case consume == g* - * copying is a no-op */ - consume = *g - consume; - /* Switch on virtual source of zeros. */ - pad = 1; - continue; - } - break; - } - - if (n_sep > 0) { - /* If padding is switched on, separators are counted - * as padding characters. This rule does not apply if - * the separator would be the first character of the - * result string. */ - if (pad && n_src > 1) n_src -= 1; - _mbstr_copy_char(dest, spec->sep, n_sep); - } - - /* If non-NUL, use the next value for grouping. */ - if (*g && *(g+1)) g++; - consume = *g; - } - - if (sign) { - _mbstr_copy_ascii(dest, sign, 1); - } - - if (dest->data) { - dest->data[dest->nbytes] = '\0'; - } -} - -/* - * Convert a numeric-string to its locale-specific appearance. - * The string must have one of these forms: - * - * 1) [sign] digits [exponent-part] - * 2) [sign] digits '.' [digits] [exponent-part] - * - * Not allowed, since _mpd_to_string() never returns this form: - * - * 3) [sign] '.' digits [exponent-part] - * - * Input: result->data := original numeric string (ASCII) - * result->bytes := strlen(result->data) - * result->nchars := strlen(result->data) - * - * Output: result->data := modified or original string - * result->bytes := strlen(result->data) - * result->nchars := number of characters (possibly UTF-8) - */ -static int -_mpd_apply_lconv(mpd_mbstr_t *result, const mpd_spec_t *spec, uint32_t *status) -{ - const char *sign = NULL, *intpart = NULL, *dot = NULL; - const char *rest, *dp; - char *decstring; - mpd_ssize_t n_int, n_rest; - - /* original numeric string */ - dp = result->data; - - /* sign */ - if (*dp == '+' || *dp == '-' || *dp == ' ') { - sign = dp++; - } - /* integer part */ - assert(isdigit((unsigned char)*dp)); - intpart = dp++; - while (isdigit((unsigned char)*dp)) { - dp++; - } - n_int = (mpd_ssize_t)(dp-intpart); - /* decimal point */ - if (*dp == '.') { - dp++; dot = spec->dot; - } - /* rest */ - rest = dp; - n_rest = result->nbytes - (mpd_ssize_t)(dp-result->data); - - if (dot == NULL && (*spec->sep == '\0' || *spec->grouping == '\0')) { - /* _mpd_add_sep_dot() would not change anything */ - return 1; - } - - /* Determine the size of the new decimal string after inserting the - * decimal point, optional separators and optional padding. */ - decstring = result->data; - result->data = NULL; - _mpd_add_sep_dot(result, sign, intpart, n_int, dot, - rest, n_rest, spec); - - result->data = mpd_alloc(result->nbytes+1, 1); - if (result->data == NULL) { - *status |= MPD_Malloc_error; - mpd_free(decstring); - return 0; - } - - /* Perform actual writes. */ - _mpd_add_sep_dot(result, sign, intpart, n_int, dot, - rest, n_rest, spec); - - mpd_free(decstring); - return 1; -} - -/* Add padding to the formatted string if necessary. */ -static int -_mpd_add_pad(mpd_mbstr_t *result, const mpd_spec_t *spec, uint32_t *status) -{ - if (result->nchars < spec->min_width) { - mpd_ssize_t add_chars, add_bytes; - size_t lpad = 0, rpad = 0; - size_t n_fill, len, i, j; - char align = spec->align; - uint8_t err = 0; - char *cp; - - n_fill = strlen(spec->fill); - add_chars = (spec->min_width - result->nchars); - /* max value: MPD_MAX_PREC * 4 */ - add_bytes = add_chars * (mpd_ssize_t)n_fill; - - cp = result->data = mpd_realloc(result->data, - result->nbytes+add_bytes+1, - sizeof *result->data, &err); - if (err) { - *status |= MPD_Malloc_error; - mpd_free(result->data); - return 0; - } - - if (align == 'z') { - align = '='; - } - - if (align == '<') { - rpad = add_chars; - } - else if (align == '>' || align == '=') { - lpad = add_chars; - } - else { /* align == '^' */ - lpad = add_chars/2; - rpad = add_chars-lpad; - } - - len = result->nbytes; - if (align == '=' && (*cp == '-' || *cp == '+' || *cp == ' ')) { - /* leave sign in the leading position */ - cp++; len--; - } - - memmove(cp+n_fill*lpad, cp, len); - for (i = 0; i < lpad; i++) { - for (j = 0; j < n_fill; j++) { - cp[i*n_fill+j] = spec->fill[j]; - } - } - cp += (n_fill*lpad + len); - for (i = 0; i < rpad; i++) { - for (j = 0; j < n_fill; j++) { - cp[i*n_fill+j] = spec->fill[j]; - } - } - - result->nbytes += add_bytes; - result->nchars += add_chars; - result->data[result->nbytes] = '\0'; - } - - return 1; -} - -/* Round a number to prec digits. The adjusted exponent stays the same - or increases by one if rounding up crosses a power of ten boundary. - If result->digits would exceed MPD_MAX_PREC+1, MPD_Invalid_operation - is set and the result is NaN. */ -static inline void -_mpd_round(mpd_t *result, const mpd_t *a, mpd_ssize_t prec, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t exp = a->exp + a->digits - prec; - - if (prec <= 0) { - mpd_seterror(result, MPD_Invalid_operation, status); /* GCOV_NOT_REACHED */ - return; /* GCOV_NOT_REACHED */ - } - if (mpd_isspecial(a) || mpd_iszero(a)) { - mpd_qcopy(result, a, status); /* GCOV_NOT_REACHED */ - return; /* GCOV_NOT_REACHED */ - } - - mpd_qrescale_fmt(result, a, exp, ctx, status); - if (result->digits > prec) { - mpd_qrescale_fmt(result, result, exp+1, ctx, status); - } -} - -/* - * Return the string representation of an mpd_t, formatted according to 'spec'. - * The format specification is assumed to be valid. Memory errors are indicated - * as usual. This function is quiet. - */ -char * -mpd_qformat_spec(const mpd_t *dec, const mpd_spec_t *spec, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_uint_t dt[MPD_MINALLOC_MAX]; - mpd_t tmp = {MPD_STATIC|MPD_STATIC_DATA,0,0,0,MPD_MINALLOC_MAX,dt}; - mpd_ssize_t dplace = MPD_DEFAULT_DOTPLACE; - mpd_mbstr_t result; - mpd_spec_t stackspec; - char type = spec->type; - int flags = 0; - - - if (spec->min_width > MPD_MAX_PREC) { - *status |= MPD_Invalid_operation; - return NULL; - } - - if (isupper((unsigned char)type)) { - type = (char)tolower((unsigned char)type); - flags |= MPD_FMT_UPPER; - } - if (spec->sign == ' ') { - flags |= MPD_FMT_SIGN_SPACE; - } - else if (spec->sign == '+') { - flags |= MPD_FMT_SIGN_PLUS; - } - - if (mpd_isspecial(dec)) { - if (spec->align == 'z') { - stackspec = *spec; - stackspec.fill[0] = ' '; - stackspec.fill[1] = '\0'; - stackspec.align = '>'; - spec = &stackspec; - } - assert(strlen(spec->fill) == 1); /* annotation for scan-build */ - if (type == '%') { - flags |= MPD_FMT_PERCENT; - } - } - else { - uint32_t workstatus = 0; - mpd_ssize_t prec; - - switch (type) { - case 'g': flags |= MPD_FMT_TOSCI; break; - case 'e': flags |= MPD_FMT_EXP; break; - case '%': flags |= MPD_FMT_PERCENT; - if (!mpd_qcopy(&tmp, dec, status)) { - return NULL; - } - tmp.exp += 2; - dec = &tmp; - type = 'f'; /* fall through */ - case 'f': flags |= MPD_FMT_FIXED; break; - default: abort(); /* debug: GCOV_NOT_REACHED */ - } - - if (spec->prec >= 0) { - if (spec->prec > MPD_MAX_PREC) { - *status |= MPD_Invalid_operation; - goto error; - } - - switch (type) { - case 'g': - prec = (spec->prec == 0) ? 1 : spec->prec; - if (dec->digits > prec) { - _mpd_round(&tmp, dec, prec, ctx, - &workstatus); - dec = &tmp; - } - break; - case 'e': - if (mpd_iszero(dec)) { - dplace = 1-spec->prec; - } - else { - _mpd_round(&tmp, dec, spec->prec+1, ctx, - &workstatus); - dec = &tmp; - } - break; - case 'f': - mpd_qrescale(&tmp, dec, -spec->prec, ctx, - &workstatus); - dec = &tmp; - break; - } - } - - if (type == 'f') { - if (mpd_iszero(dec) && dec->exp > 0) { - mpd_qrescale(&tmp, dec, 0, ctx, &workstatus); - dec = &tmp; - } - } - - if (workstatus&MPD_Errors) { - *status |= (workstatus&MPD_Errors); - goto error; - } - } - - /* - * At this point, for all scaled or non-scaled decimals: - * 1) 1 <= digits <= MAX_PREC+1 - * 2) adjexp(scaled) = adjexp(orig) [+1] - * 3) case 'g': MIN_ETINY <= exp <= MAX_EMAX+1 - * case 'e': MIN_ETINY-MAX_PREC <= exp <= MAX_EMAX+1 - * case 'f': MIN_ETINY <= exp <= MAX_EMAX+1 - * 4) max memory alloc in _mpd_to_string: - * case 'g': MAX_PREC+36 - * case 'e': MAX_PREC+36 - * case 'f': 2*MPD_MAX_PREC+30 - */ - result.nbytes = _mpd_to_string(&result.data, dec, flags, dplace); - result.nchars = result.nbytes; - if (result.nbytes < 0) { - *status |= MPD_Malloc_error; - goto error; - } - - if (*spec->dot != '\0' && !mpd_isspecial(dec)) { - if (result.nchars > MPD_MAX_PREC+36) { - /* Since a group length of one is not explicitly - * disallowed, ensure that it is always possible to - * insert a four byte separator after each digit. */ - *status |= MPD_Invalid_operation; - mpd_free(result.data); - goto error; - } - if (!_mpd_apply_lconv(&result, spec, status)) { - goto error; - } - } - - if (spec->min_width) { - if (!_mpd_add_pad(&result, spec, status)) { - goto error; - } - } - - mpd_del(&tmp); - return result.data; - -error: - mpd_del(&tmp); - return NULL; -} - -char * -mpd_qformat(const mpd_t *dec, const char *fmt, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_spec_t spec; - - if (!mpd_parse_fmt_str(&spec, fmt, 1)) { - *status |= MPD_Invalid_operation; - return NULL; - } - - return mpd_qformat_spec(dec, &spec, ctx, status); -} - -/* - * The specification has a *condition* called Invalid_operation and an - * IEEE *signal* called Invalid_operation. The former corresponds to - * MPD_Invalid_operation, the latter to MPD_IEEE_Invalid_operation. - * MPD_IEEE_Invalid_operation comprises the following conditions: - * - * [MPD_Conversion_syntax, MPD_Division_impossible, MPD_Division_undefined, - * MPD_Fpu_error, MPD_Invalid_context, MPD_Invalid_operation, - * MPD_Malloc_error] - * - * In the following functions, 'flag' denotes the condition, 'signal' - * denotes the IEEE signal. - */ - -static const char *mpd_flag_string[MPD_NUM_FLAGS] = { - "Clamped", - "Conversion_syntax", - "Division_by_zero", - "Division_impossible", - "Division_undefined", - "Fpu_error", - "Inexact", - "Invalid_context", - "Invalid_operation", - "Malloc_error", - "Not_implemented", - "Overflow", - "Rounded", - "Subnormal", - "Underflow", -}; - -static const char *mpd_signal_string[MPD_NUM_FLAGS] = { - "Clamped", - "IEEE_Invalid_operation", - "Division_by_zero", - "IEEE_Invalid_operation", - "IEEE_Invalid_operation", - "IEEE_Invalid_operation", - "Inexact", - "IEEE_Invalid_operation", - "IEEE_Invalid_operation", - "IEEE_Invalid_operation", - "Not_implemented", - "Overflow", - "Rounded", - "Subnormal", - "Underflow", -}; - -/* print conditions to buffer, separated by spaces */ -int -mpd_snprint_flags(char *dest, int nmemb, uint32_t flags) -{ - char *cp; - int n, j; - - assert(nmemb >= MPD_MAX_FLAG_STRING); - - *dest = '\0'; cp = dest; - for (j = 0; j < MPD_NUM_FLAGS; j++) { - if (flags & (1U<= nmemb) return -1; - cp += n; nmemb -= n; - } - } - - if (cp != dest) { - *(--cp) = '\0'; - } - - return (int)(cp-dest); -} - -/* print conditions to buffer, in list form */ -int -mpd_lsnprint_flags(char *dest, int nmemb, uint32_t flags, const char *flag_string[]) -{ - char *cp; - int n, j; - - assert(nmemb >= MPD_MAX_FLAG_LIST); - if (flag_string == NULL) { - flag_string = mpd_flag_string; - } - - *dest = '['; - *(dest+1) = '\0'; - cp = dest+1; - --nmemb; - - for (j = 0; j < MPD_NUM_FLAGS; j++) { - if (flags & (1U<= nmemb) return -1; - cp += n; nmemb -= n; - } - } - - /* erase the last ", " */ - if (cp != dest+1) { - cp -= 2; - } - - *cp++ = ']'; - *cp = '\0'; - - return (int)(cp-dest); /* strlen, without NUL terminator */ -} - -/* print signals to buffer, in list form */ -int -mpd_lsnprint_signals(char *dest, int nmemb, uint32_t flags, const char *signal_string[]) -{ - char *cp; - int n, j; - int ieee_invalid_done = 0; - - assert(nmemb >= MPD_MAX_SIGNAL_LIST); - if (signal_string == NULL) { - signal_string = mpd_signal_string; - } - - *dest = '['; - *(dest+1) = '\0'; - cp = dest+1; - --nmemb; - - for (j = 0; j < MPD_NUM_FLAGS; j++) { - uint32_t f = flags & (1U<= nmemb) return -1; - cp += n; nmemb -= n; - } - } - - /* erase the last ", " */ - if (cp != dest+1) { - cp -= 2; - } - - *cp++ = ']'; - *cp = '\0'; - - return (int)(cp-dest); /* strlen, without NUL terminator */ -} - -/* The following two functions are mainly intended for debugging. */ -void -mpd_fprint(FILE *file, const mpd_t *dec) -{ - char *decstring; - - decstring = mpd_to_sci(dec, 1); - if (decstring != NULL) { - fprintf(file, "%s\n", decstring); - mpd_free(decstring); - } - else { - fputs("mpd_fprint: output error\n", file); /* GCOV_NOT_REACHED */ - } -} - -void -mpd_print(const mpd_t *dec) -{ - char *decstring; - - decstring = mpd_to_sci(dec, 1); - if (decstring != NULL) { - printf("%s\n", decstring); - mpd_free(decstring); - } - else { - fputs("mpd_fprint: output error\n", stderr); /* GCOV_NOT_REACHED */ - } -} diff --git a/Modules/_decimal/libmpdec/io.h b/Modules/_decimal/libmpdec/io.h deleted file mode 100644 index 79d7c05ce369c6..00000000000000 --- a/Modules/_decimal/libmpdec/io.h +++ /dev/null @@ -1,62 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_IO_H_ -#define LIBMPDEC_IO_H_ - - -#include "mpdecimal.h" - -#include - - -#if SIZE_MAX == MPD_SIZE_MAX - #define mpd_strtossize _mpd_strtossize -#else -#include - -static inline mpd_ssize_t -mpd_strtossize(const char *s, char **end, int base) -{ - int64_t retval; - - errno = 0; - retval = _mpd_strtossize(s, end, base); - if (errno == 0 && (retval > MPD_SSIZE_MAX || retval < MPD_SSIZE_MIN)) { - errno = ERANGE; - } - if (errno == ERANGE) { - return (retval < 0) ? MPD_SSIZE_MIN : MPD_SSIZE_MAX; - } - - return (mpd_ssize_t)retval; -} -#endif - - -#endif /* LIBMPDEC_IO_H_ */ diff --git a/Modules/_decimal/libmpdec/literature/REFERENCES.txt b/Modules/_decimal/libmpdec/literature/REFERENCES.txt deleted file mode 100644 index 9ed5782656a31b..00000000000000 --- a/Modules/_decimal/libmpdec/literature/REFERENCES.txt +++ /dev/null @@ -1,51 +0,0 @@ - - -This document contains links to the literature used in the process of -creating the library. The list is probably not complete. - - -Mike Cowlishaw: General Decimal Arithmetic Specification -http://speleotrove.com/decimal/decarith.html - - -Jean-Michel Muller: On the definition of ulp (x) -lara.inist.fr/bitstream/2332/518/1/LIP-RR2005-09.pdf - - -T. E. Hull, A. Abrham: Properly rounded variable precision square root -http://portal.acm.org/citation.cfm?id=214413 - - -T. E. Hull, A. Abrham: Variable precision exponential function -http://portal.acm.org/citation.cfm?id=6498 - - -Roman E. Maeder: Storage allocation for the Karatsuba integer multiplication -algorithm. http://www.springerlink.com/content/w15058mj6v59t565/ - - -J. M. Pollard: The fast Fourier transform in a finite field -http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0301966-0/home.html - - -David H. Bailey: FFTs in External or Hierarchical Memory -http://crd.lbl.gov/~dhbailey/dhbpapers/ - - -W. Morven Gentleman: Matrix Multiplication and Fast Fourier Transforms -http://www.alcatel-lucent.com/bstj/vol47-1968/articles/bstj47-6-1099.pdf - - -Mikko Tommila: Apfloat documentation -http://www.apfloat.org/apfloat/2.41/apfloat.pdf - - -Joerg Arndt: "Matters Computational" -http://www.jjj.de/fxt/ - - -Karl Hasselstrom: Fast Division of Large Integers -www.treskal.com/kalle/exjobb/original-report.pdf - - - diff --git a/Modules/_decimal/libmpdec/literature/bignum.txt b/Modules/_decimal/libmpdec/literature/bignum.txt deleted file mode 100644 index f34ff67c612ab4..00000000000000 --- a/Modules/_decimal/libmpdec/literature/bignum.txt +++ /dev/null @@ -1,83 +0,0 @@ - - -Bignum support (Fast Number Theoretic Transform or FNT): -======================================================== - -Bignum arithmetic in libmpdec uses the scheme for fast convolution -of integer sequences from: - -J. M. Pollard: The fast Fourier transform in a finite field -http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0301966-0/home.html - - -The transform in a finite field can be used for convolution in the same -way as the Fourier Transform. The main advantages of the Number Theoretic -Transform are that it is both exact and very memory efficient. - - -Convolution in pseudo-code: -~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - fnt_convolute(a, b): - x = fnt(a) # forward transform of a - y = fnt(b) # forward transform of b - z = pairwise multiply x[i] and y[i] - result = inv_fnt(z) # backward transform of z. - - -Extending the maximum transform length (Chinese Remainder Theorem): -------------------------------------------------------------------- - -The maximum transform length is quite limited when using a single -prime field. However, it is possible to use multiple primes and -recover the result using the Chinese Remainder Theorem. - - -Multiplication in pseudo-code: -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - _mpd_fntmul(u, v): - c1 = fnt_convolute(u, v, P1) # convolute modulo prime1 - c2 = fnt_convolute(u, v, P2) # convolute modulo prime2 - c3 = fnt_convolute(u, v, P3) # convolute modulo prime3 - result = crt3(c1, c2, c3) # Chinese Remainder Theorem - - -Optimized transform functions: ------------------------------- - -There are three different fnt() functions: - - std_fnt: "standard" decimation in frequency transform for array lengths - of 2**n. Performs well up to 1024 words. - - sixstep: Cache-friendly algorithm for array lengths of 2**n. Outperforms - std_fnt for large arrays. - - fourstep: Algorithm for array lengths of 3 * 2**n. Also cache friendly - in large parts. - - -List of bignum-only files: --------------------------- - -Functions from these files are only used in _mpd_fntmul(). - - umodarith.h -> fast low level routines for unsigned modular arithmetic - numbertheory.c -> routines for setting up the FNT - difradix2.c -> decimation in frequency transform, used as the - "base case" by the following three files: - - fnt.c -> standard transform for smaller arrays - sixstep.c -> transform large arrays of length 2**n - fourstep.c -> transform arrays of length 3 * 2**n - - convolute.c -> do the actual fast convolution, using one of - the three transform functions. - transpose.c -> transpositions needed for the sixstep algorithm. - crt.c -> Chinese Remainder Theorem: use information from three - transforms modulo three different primes to get the - final result. - - - diff --git a/Modules/_decimal/libmpdec/literature/fnt.py b/Modules/_decimal/libmpdec/literature/fnt.py deleted file mode 100644 index c1285a565db96b..00000000000000 --- a/Modules/_decimal/libmpdec/literature/fnt.py +++ /dev/null @@ -1,208 +0,0 @@ -# -# Copyright (c) 2008-2020 Stefan Krah. All rights reserved. -# -# Redistribution and use in source and binary forms, with or without -# modification, are permitted provided that the following conditions -# are met: -# -# 1. Redistributions of source code must retain the above copyright -# notice, this list of conditions and the following disclaimer. -# -# 2. Redistributions in binary form must reproduce the above copyright -# notice, this list of conditions and the following disclaimer in the -# documentation and/or other materials provided with the distribution. -# -# THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND -# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE -# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS -# OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) -# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY -# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF -# SUCH DAMAGE. -# - - -###################################################################### -# This file lists and checks some of the constants and limits used # -# in libmpdec's Number Theoretic Transform. At the end of the file # -# there is an example function for the plain DFT transform. # -###################################################################### - - -# -# Number theoretic transforms are done in subfields of F(p). P[i] -# are the primes, D[i] = P[i] - 1 are highly composite and w[i] -# are the respective primitive roots of F(p). -# -# The strategy is to convolute two coefficients modulo all three -# primes, then use the Chinese Remainder Theorem on the three -# result arrays to recover the result in the usual base RADIX -# form. -# - -# ====================================================================== -# Primitive roots -# ====================================================================== - -# -# Verify primitive roots: -# -# For a prime field, r is a primitive root if and only if for all prime -# factors f of p-1, r**((p-1)/f) =/= 1 (mod p). -# -def prod(F, E): - """Check that the factorization of P-1 is correct. F is the list of - factors of P-1, E lists the number of occurrences of each factor.""" - x = 1 - for y, z in zip(F, E): - x *= y**z - return x - -def is_primitive_root(r, p, factors, exponents): - """Check if r is a primitive root of F(p).""" - if p != prod(factors, exponents) + 1: - return False - for f in factors: - q, control = divmod(p-1, f) - if control != 0: - return False - if pow(r, q, p) == 1: - return False - return True - - -# ================================================================= -# Constants and limits for the 64-bit version -# ================================================================= - -RADIX = 10**19 - -# Primes P1, P2 and P3: -P = [2**64-2**32+1, 2**64-2**34+1, 2**64-2**40+1] - -# P-1, highly composite. The transform length d is variable and -# must divide D = P-1. Since all D are divisible by 3 * 2**32, -# transform lengths can be 2**n or 3 * 2**n (where n <= 32). -D = [2**32 * 3 * (5 * 17 * 257 * 65537), - 2**34 * 3**2 * (7 * 11 * 31 * 151 * 331), - 2**40 * 3**2 * (5 * 7 * 13 * 17 * 241)] - -# Prime factors of P-1 and their exponents: -F = [(2,3,5,17,257,65537), (2,3,7,11,31,151,331), (2,3,5,7,13,17,241)] -E = [(32,1,1,1,1,1), (34,2,1,1,1,1,1), (40,2,1,1,1,1,1)] - -# Maximum transform length for 2**n. Above that only 3 * 2**31 -# or 3 * 2**32 are possible. -MPD_MAXTRANSFORM_2N = 2**32 - - -# Limits in the terminology of Pollard's paper: -m2 = (MPD_MAXTRANSFORM_2N * 3) // 2 # Maximum length of the smaller array. -M1 = M2 = RADIX-1 # Maximum value per single word. -L = m2 * M1 * M2 -P[0] * P[1] * P[2] > 2 * L - - -# Primitive roots of F(P1), F(P2) and F(P3): -w = [7, 10, 19] - -# The primitive roots are correct: -for i in range(3): - if not is_primitive_root(w[i], P[i], F[i], E[i]): - print("FAIL") - - -# ================================================================= -# Constants and limits for the 32-bit version -# ================================================================= - -RADIX = 10**9 - -# Primes P1, P2 and P3: -P = [2113929217, 2013265921, 1811939329] - -# P-1, highly composite. All D = P-1 are divisible by 3 * 2**25, -# allowing for transform lengths up to 3 * 2**25 words. -D = [2**25 * 3**2 * 7, - 2**27 * 3 * 5, - 2**26 * 3**3] - -# Prime factors of P-1 and their exponents: -F = [(2,3,7), (2,3,5), (2,3)] -E = [(25,2,1), (27,1,1), (26,3)] - -# Maximum transform length for 2**n. Above that only 3 * 2**24 or -# 3 * 2**25 are possible. -MPD_MAXTRANSFORM_2N = 2**25 - - -# Limits in the terminology of Pollard's paper: -m2 = (MPD_MAXTRANSFORM_2N * 3) // 2 # Maximum length of the smaller array. -M1 = M2 = RADIX-1 # Maximum value per single word. -L = m2 * M1 * M2 -P[0] * P[1] * P[2] > 2 * L - - -# Primitive roots of F(P1), F(P2) and F(P3): -w = [5, 31, 13] - -# The primitive roots are correct: -for i in range(3): - if not is_primitive_root(w[i], P[i], F[i], E[i]): - print("FAIL") - - -# ====================================================================== -# Example transform using a single prime -# ====================================================================== - -def ntt(lst, dir): - """Perform a transform on the elements of lst. len(lst) must - be 2**n or 3 * 2**n, where n <= 25. This is the slow DFT.""" - p = 2113929217 # prime - d = len(lst) # transform length - d_prime = pow(d, (p-2), p) # inverse of d - xi = (p-1)//d - w = 5 # primitive root of F(p) - r = pow(w, xi, p) # primitive root of the subfield - r_prime = pow(w, (p-1-xi), p) # inverse of r - if dir == 1: # forward transform - a = lst # input array - A = [0] * d # transformed values - for i in range(d): - s = 0 - for j in range(d): - s += a[j] * pow(r, i*j, p) - A[i] = s % p - return A - elif dir == -1: # backward transform - A = lst # input array - a = [0] * d # transformed values - for j in range(d): - s = 0 - for i in range(d): - s += A[i] * pow(r_prime, i*j, p) - a[j] = (d_prime * s) % p - return a - -def ntt_convolute(a, b): - """convolute arrays a and b.""" - assert(len(a) == len(b)) - x = ntt(a, 1) - y = ntt(b, 1) - for i in range(len(a)): - y[i] = y[i] * x[i] - r = ntt(y, -1) - return r - - -# Example: Two arrays representing 21 and 81 in little-endian: -a = [1, 2, 0, 0] -b = [1, 8, 0, 0] - -assert(ntt_convolute(a, b) == [1, 10, 16, 0]) -assert(21 * 81 == (1*10**0 + 10*10**1 + 16*10**2 + 0*10**3)) diff --git a/Modules/_decimal/libmpdec/literature/matrix-transform.txt b/Modules/_decimal/libmpdec/literature/matrix-transform.txt deleted file mode 100644 index 6e7ad7420909fd..00000000000000 --- a/Modules/_decimal/libmpdec/literature/matrix-transform.txt +++ /dev/null @@ -1,256 +0,0 @@ - - -(* Copyright (c) 2011-2020 Stefan Krah. All rights reserved. *) - - -The Matrix Fourier Transform: -============================= - -In libmpdec, the Matrix Fourier Transform [1] is called four-step transform -after a variant that appears in [2]. The algorithm requires that the input -array can be viewed as an R*C matrix. - -All operations are done modulo p. For readability, the proofs drop all -instances of (mod p). - - -Algorithm four-step (forward transform): ----------------------------------------- - - a := input array - d := len(a) = R * C - p := prime - w := primitive root of unity of the prime field - r := w**((p-1)/d) - A := output array - - 1) Apply a length R FNT to each column. - - 2) Multiply each matrix element (addressed by j*C+m) by r**(j*m). - - 3) Apply a length C FNT to each row. - - 4) Transpose the matrix. - - -Proof (forward transform): --------------------------- - - The algorithm can be derived starting from the regular definition of - the finite-field transform of length d: - - d-1 - ,---- - \ - A[k] = | a[l] * r**(k * l) - / - `---- - l = 0 - - - The sum can be rearranged into the sum of the sums of columns: - - C-1 R-1 - ,---- ,---- - \ \ - = | | a[i * C + j] * r**(k * (i * C + j)) - / / - `---- `---- - j = 0 i = 0 - - - Extracting a constant from the inner sum: - - C-1 R-1 - ,---- ,---- - \ \ - = | r**k*j * | a[i * C + j] * r**(k * i * C) - / / - `---- `---- - j = 0 i = 0 - - - Without any loss of generality, let k = n * R + m, - where n < C and m < R: - - C-1 R-1 - ,---- ,---- - \ \ - A[n*R+m] = | r**(R*n*j) * r**(m*j) * | a[i*C+j] * r**(R*C*n*i) * r**(C*m*i) - / / - `---- `---- - j = 0 i = 0 - - - Since r = w ** ((p-1) / (R*C)): - - a) r**(R*C*n*i) = w**((p-1)*n*i) = 1 - - b) r**(C*m*i) = w**((p-1) / R) ** (m*i) = r_R ** (m*i) - - c) r**(R*n*j) = w**((p-1) / C) ** (n*j) = r_C ** (n*j) - - r_R := root of the subfield of length R. - r_C := root of the subfield of length C. - - - C-1 R-1 - ,---- ,---- - \ \ - A[n*R+m] = | r_C**(n*j) * [ r**(m*j) * | a[i*C+j] * r_R**(m*i) ] - / ^ / - `---- | `---- 1) transform the columns - j = 0 | i = 0 - ^ | - | `-- 2) multiply - | - `-- 3) transform the rows - - - Note that the entire RHS is a function of n and m and that the results - for each pair (n, m) are stored in Fortran order. - - Let the term in square brackets be f(m, j). Step 1) and 2) precalculate - the term for all (m, j). After that, the original matrix is now a lookup - table with the mth element in the jth column at location m * C + j. - - Let the complete RHS be g(m, n). Step 3) does an in-place transform of - length n on all rows. After that, the original matrix is now a lookup - table with the mth element in the nth column at location m * C + n. - - But each (m, n) pair should be written to location n * R + m. Therefore, - step 4) transposes the result of step 3). - - - -Algorithm four-step (inverse transform): ----------------------------------------- - - A := input array - d := len(A) = R * C - p := prime - d' := d**(p-2) # inverse of d - w := primitive root of unity of the prime field - r := w**((p-1)/d) # root of the subfield - r' := w**((p-1) - (p-1)/d) # inverse of r - a := output array - - 0) View the matrix as a C*R matrix. - - 1) Transpose the matrix, producing an R*C matrix. - - 2) Apply a length C FNT to each row. - - 3) Multiply each matrix element (addressed by i*C+n) by r**(i*n). - - 4) Apply a length R FNT to each column. - - -Proof (inverse transform): --------------------------- - - The algorithm can be derived starting from the regular definition of - the finite-field inverse transform of length d: - - d-1 - ,---- - \ - a[k] = d' * | A[l] * r' ** (k * l) - / - `---- - l = 0 - - - The sum can be rearranged into the sum of the sums of columns. Note - that at this stage we still have a C*R matrix, so C denotes the number - of rows: - - R-1 C-1 - ,---- ,---- - \ \ - = d' * | | a[j * R + i] * r' ** (k * (j * R + i)) - / / - `---- `---- - i = 0 j = 0 - - - Extracting a constant from the inner sum: - - R-1 C-1 - ,---- ,---- - \ \ - = d' * | r' ** (k*i) * | a[j * R + i] * r' ** (k * j * R) - / / - `---- `---- - i = 0 j = 0 - - - Without any loss of generality, let k = m * C + n, - where m < R and n < C: - - R-1 C-1 - ,---- ,---- - \ \ - A[m*C+n] = d' * | r' ** (C*m*i) * r' ** (n*i) * | a[j*R+i] * r' ** (R*C*m*j) * r' ** (R*n*j) - / / - `---- `---- - i = 0 j = 0 - - - Since r' = w**((p-1) - (p-1)/d) and d = R*C: - - a) r' ** (R*C*m*j) = w**((p-1)*R*C*m*j - (p-1)*m*j) = 1 - - b) r' ** (C*m*i) = w**((p-1)*C - (p-1)/R) ** (m*i) = r_R' ** (m*i) - - c) r' ** (R*n*j) = r_C' ** (n*j) - - d) d' = d**(p-2) = (R*C) ** (p-2) = R**(p-2) * C**(p-2) = R' * C' - - r_R' := inverse of the root of the subfield of length R. - r_C' := inverse of the root of the subfield of length C. - R' := inverse of R - C' := inverse of C - - - R-1 C-1 - ,---- ,---- 2) transform the rows of a^T - \ \ - A[m*C+n] = R' * | r_R' ** (m*i) * [ r' ** (n*i) * C' * | a[j*R+i] * r_C' ** (n*j) ] - / ^ / ^ - `---- | `---- | - i = 0 | j = 0 | - ^ | `-- 1) Transpose input matrix - | `-- 3) multiply to address elements by - | i * C + j - `-- 3) transform the columns - - - - Note that the entire RHS is a function of m and n and that the results - for each pair (m, n) are stored in C order. - - Let the term in square brackets be f(n, i). Without step 1), the sum - would perform a length C transform on the columns of the input matrix. - This is a) inefficient and b) the results are needed in C order, so - step 1) exchanges rows and columns. - - Step 2) and 3) precalculate f(n, i) for all (n, i). After that, the - original matrix is now a lookup table with the ith element in the nth - column at location i * C + n. - - Let the complete RHS be g(m, n). Step 4) does an in-place transform of - length m on all columns. After that, the original matrix is now a lookup - table with the mth element in the nth column at location m * C + n, - which means that all A[k] = A[m * C + n] are in the correct order. - - --- - - [1] Joerg Arndt: "Matters Computational" - http://www.jjj.de/fxt/ - [2] David H. Bailey: FFTs in External or Hierarchical Memory - http://crd.lbl.gov/~dhbailey/dhbpapers/ - - - diff --git a/Modules/_decimal/libmpdec/literature/mulmod-64.txt b/Modules/_decimal/libmpdec/literature/mulmod-64.txt deleted file mode 100644 index fa967bf95e3030..00000000000000 --- a/Modules/_decimal/libmpdec/literature/mulmod-64.txt +++ /dev/null @@ -1,127 +0,0 @@ - - -(* Copyright (c) 2011-2020 Stefan Krah. All rights reserved. *) - - -========================================================================== - Calculate (a * b) % p using special primes -========================================================================== - -A description of the algorithm can be found in the apfloat manual by -Tommila [1]. - - -Definitions: ------------- - -In the whole document, "==" stands for "is congruent with". - -Result of a * b in terms of high/low words: - - (1) hi * 2**64 + lo = a * b - -Special primes: - - (2) p = 2**64 - z + 1, where z = 2**n - -Single step modular reduction: - - (3) R(hi, lo) = hi * z - hi + lo - - -Strategy: ---------- - - a) Set (hi, lo) to the result of a * b. - - b) Set (hi', lo') to the result of R(hi, lo). - - c) Repeat step b) until 0 <= hi' * 2**64 + lo' < 2*p. - - d) If the result is less than p, return lo'. Otherwise return lo' - p. - - -The reduction step b) preserves congruence: -------------------------------------------- - - hi * 2**64 + lo == hi * z - hi + lo (mod p) - - Proof: - ~~~~~~ - - hi * 2**64 + lo = (2**64 - z + 1) * hi + z * hi - hi + lo - - = p * hi + z * hi - hi + lo - - == z * hi - hi + lo (mod p) - - -Maximum numbers of step b): ---------------------------- - -# To avoid unnecessary formalism, define: - -def R(hi, lo, z): - return divmod(hi * z - hi + lo, 2**64) - -# For simplicity, assume hi=2**64-1, lo=2**64-1 after the -# initial multiplication a * b. This is of course impossible -# but certainly covers all cases. - -# Then, for p1: -hi=2**64-1; lo=2**64-1; z=2**32 -p1 = 2**64 - z + 1 - -hi, lo = R(hi, lo, z) # First reduction -hi, lo = R(hi, lo, z) # Second reduction -hi * 2**64 + lo < 2 * p1 # True - -# For p2: -hi=2**64-1; lo=2**64-1; z=2**34 -p2 = 2**64 - z + 1 - -hi, lo = R(hi, lo, z) # First reduction -hi, lo = R(hi, lo, z) # Second reduction -hi, lo = R(hi, lo, z) # Third reduction -hi * 2**64 + lo < 2 * p2 # True - -# For p3: -hi=2**64-1; lo=2**64-1; z=2**40 -p3 = 2**64 - z + 1 - -hi, lo = R(hi, lo, z) # First reduction -hi, lo = R(hi, lo, z) # Second reduction -hi, lo = R(hi, lo, z) # Third reduction -hi * 2**64 + lo < 2 * p3 # True - - -Step d) preserves congruence and yields a result < p: ------------------------------------------------------ - - Case hi = 0: - - Case lo < p: trivial. - - Case lo >= p: - - lo == lo - p (mod p) # result is congruent - - p <= lo < 2*p -> 0 <= lo - p < p # result is in the correct range - - Case hi = 1: - - p < 2**64 /\ 2**64 + lo < 2*p -> lo < p # lo is always less than p - - 2**64 + lo == 2**64 + (lo - p) (mod p) # result is congruent - - = lo - p # exactly the same value as the previous RHS - # in uint64_t arithmetic. - - p < 2**64 + lo < 2*p -> 0 < 2**64 + (lo - p) < p # correct range - - - -[1] http://www.apfloat.org/apfloat/2.40/apfloat.pdf - - - diff --git a/Modules/_decimal/libmpdec/literature/mulmod-ppro.txt b/Modules/_decimal/libmpdec/literature/mulmod-ppro.txt deleted file mode 100644 index ba804e4b4e7864..00000000000000 --- a/Modules/_decimal/libmpdec/literature/mulmod-ppro.txt +++ /dev/null @@ -1,269 +0,0 @@ - - -(* Copyright (c) 2011-2020 Stefan Krah. All rights reserved. *) - - -======================================================================== - Calculate (a * b) % p using the 80-bit x87 FPU -======================================================================== - -A description of the algorithm can be found in the apfloat manual by -Tommila [1]. - -The proof follows an argument made by Granlund/Montgomery in [2]. - - -Definitions and assumptions: ----------------------------- - -The 80-bit extended precision format uses 64 bits for the significand: - - (1) F = 64 - -The modulus is prime and less than 2**31: - - (2) 2 <= p < 2**31 - -The factors are less than p: - - (3) 0 <= a < p - (4) 0 <= b < p - -The product a * b is less than 2**62 and is thus exact in 64 bits: - - (5) n = a * b - -The product can be represented in terms of quotient and remainder: - - (6) n = q * p + r - -Using (3), (4) and the fact that p is prime, the remainder is always -greater than zero: - - (7) 0 <= q < p /\ 1 <= r < p - - -Strategy: ---------- - -Precalculate the 80-bit long double inverse of p, with a maximum -relative error of 2**(1-F): - - (8) pinv = (long double)1.0 / p - -Calculate an estimate for q = floor(n/p). The multiplication has another -maximum relative error of 2**(1-F): - - (9) qest = n * pinv - -If we can show that q < qest < q+1, then trunc(qest) = q. It is then -easy to recover the remainder r. The complete algorithm is: - - a) Set the control word to 64-bit precision and truncation mode. - - b) n = a * b # Calculate exact product. - - c) qest = n * pinv # Calculate estimate for the quotient. - - d) q = (qest+2**63)-2**63 # Truncate qest to the exact quotient. - - f) r = n - q * p # Calculate remainder. - - -Proof for q < qest < q+1: -------------------------- - -Using the cumulative error, the error bounds for qest are: - - n n * (1 + 2**(1-F))**2 - (9) --------------------- <= qest <= --------------------- - p * (1 + 2**(1-F))**2 p - - - Lemma 1: - -------- - n q * p + r - (10) q < --------------------- = --------------------- - p * (1 + 2**(1-F))**2 p * (1 + 2**(1-F))**2 - - - Proof: - ~~~~~~ - - (I) q * p * (1 + 2**(1-F))**2 < q * p + r - - (II) q * p * 2**(2-F) + q * p * 2**(2-2*F) < r - - Using (1) and (7), it is sufficient to show that: - - (III) q * p * 2**(-62) + q * p * 2**(-126) < 1 <= r - - (III) can easily be verified by substituting the largest possible - values p = 2**31-1 and q = 2**31-2. - - The critical cases occur when r = 1, n = m * p + 1. These cases - can be exhaustively verified with a test program. - - - Lemma 2: - -------- - - n * (1 + 2**(1-F))**2 (q * p + r) * (1 + 2**(1-F))**2 - (11) --------------------- = ------------------------------- < q + 1 - p p - - Proof: - ~~~~~~ - - (I) (q * p + r) + (q * p + r) * 2**(2-F) + (q * p + r) * 2**(2-2*F) < q * p + p - - (II) (q * p + r) * 2**(2-F) + (q * p + r) * 2**(2-2*F) < p - r - - Using (1) and (7), it is sufficient to show that: - - (III) (q * p + r) * 2**(-62) + (q * p + r) * 2**(-126) < 1 <= p - r - - (III) can easily be verified by substituting the largest possible - values p = 2**31-1, q = 2**31-2 and r = 2**31-2. - - The critical cases occur when r = (p - 1), n = m * p - 1. These cases - can be exhaustively verified with a test program. - - -[1] http://www.apfloat.org/apfloat/2.40/apfloat.pdf -[2] http://gmplib.org/~tege/divcnst-pldi94.pdf - [Section 7: "Use of floating point"] - - - -(* Coq proof for (10) and (11) *) - -Require Import ZArith. -Require Import QArith. -Require Import Qpower. -Require Import Qabs. -Require Import Psatz. - -Open Scope Q_scope. - - -Ltac qreduce T := - rewrite <- (Qred_correct (T)); simpl (Qred (T)). - -Theorem Qlt_move_right : - forall x y z:Q, x + z < y <-> x < y - z. -Proof. - intros. - split. - intros. - psatzl Q. - intros. - psatzl Q. -Qed. - -Theorem Qlt_mult_by_z : - forall x y z:Q, 0 < z -> (x < y <-> x * z < y * z). -Proof. - intros. - split. - intros. - apply Qmult_lt_compat_r. trivial. trivial. - intros. - rewrite <- (Qdiv_mult_l x z). rewrite <- (Qdiv_mult_l y z). - apply Qmult_lt_compat_r. - apply Qlt_shift_inv_l. - trivial. psatzl Q. trivial. psatzl Q. psatzl Q. -Qed. - -Theorem Qle_mult_quad : - forall (a b c d:Q), - 0 <= a -> a <= c -> - 0 <= b -> b <= d -> - a * b <= c * d. - intros. - psatz Q. -Qed. - - -Theorem q_lt_qest: - forall (p q r:Q), - (0 < p) -> (p <= (2#1)^31 - 1) -> - (0 <= q) -> (q <= p - 1) -> - (1 <= r) -> (r <= p - 1) -> - q < (q * p + r) / (p * (1 + (2#1)^(-63))^2). -Proof. - intros. - rewrite Qlt_mult_by_z with (z := (p * (1 + (2#1)^(-63))^2)). - - unfold Qdiv. - rewrite <- Qmult_assoc. - rewrite (Qmult_comm (/ (p * (1 + (2 # 1) ^ (-63)) ^ 2)) (p * (1 + (2 # 1) ^ (-63)) ^ 2)). - rewrite Qmult_inv_r. - rewrite Qmult_1_r. - - assert (q * (p * (1 + (2 # 1) ^ (-63)) ^ 2) == q * p + (q * p) * ((2 # 1) ^ (-62) + (2 # 1) ^ (-126))). - qreduce ((1 + (2 # 1) ^ (-63)) ^ 2). - qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)). - ring_simplify. - reflexivity. - rewrite H5. - - rewrite Qplus_comm. - rewrite Qlt_move_right. - ring_simplify (q * p + r - q * p). - qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)). - - apply Qlt_le_trans with (y := 1). - rewrite Qlt_mult_by_z with (z := 85070591730234615865843651857942052864 # 18446744073709551617). - ring_simplify. - - apply Qle_lt_trans with (y := ((2 # 1) ^ 31 - (2#1)) * ((2 # 1) ^ 31 - 1)). - apply Qle_mult_quad. - assumption. psatzl Q. psatzl Q. psatzl Q. psatzl Q. psatzl Q. assumption. psatzl Q. psatzl Q. -Qed. - -Theorem qest_lt_qplus1: - forall (p q r:Q), - (0 < p) -> (p <= (2#1)^31 - 1) -> - (0 <= q) -> (q <= p - 1) -> - (1 <= r) -> (r <= p - 1) -> - ((q * p + r) * (1 + (2#1)^(-63))^2) / p < q + 1. -Proof. - intros. - rewrite Qlt_mult_by_z with (z := p). - - unfold Qdiv. - rewrite <- Qmult_assoc. - rewrite (Qmult_comm (/ p) p). - rewrite Qmult_inv_r. - rewrite Qmult_1_r. - - assert ((q * p + r) * (1 + (2 # 1) ^ (-63)) ^ 2 == q * p + r + (q * p + r) * ((2 # 1) ^ (-62) + (2 # 1) ^ (-126))). - qreduce ((1 + (2 # 1) ^ (-63)) ^ 2). - qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)). - ring_simplify. reflexivity. - rewrite H5. - - rewrite <- Qplus_assoc. rewrite <- Qplus_comm. rewrite Qlt_move_right. - ring_simplify ((q + 1) * p - q * p). - - rewrite <- Qplus_comm. rewrite Qlt_move_right. - - apply Qlt_le_trans with (y := 1). - qreduce ((2 # 1) ^ (-62) + (2 # 1) ^ (-126)). - - rewrite Qlt_mult_by_z with (z := 85070591730234615865843651857942052864 # 18446744073709551617). - ring_simplify. - - ring_simplify in H0. - apply Qle_lt_trans with (y := (2147483646 # 1) * (2147483647 # 1) + (2147483646 # 1)). - - apply Qplus_le_compat. - apply Qle_mult_quad. - assumption. psatzl Q. auto with qarith. assumption. psatzl Q. - auto with qarith. auto with qarith. - psatzl Q. psatzl Q. assumption. -Qed. - - - diff --git a/Modules/_decimal/libmpdec/literature/six-step.txt b/Modules/_decimal/libmpdec/literature/six-step.txt deleted file mode 100644 index 852d5b0df8bf37..00000000000000 --- a/Modules/_decimal/libmpdec/literature/six-step.txt +++ /dev/null @@ -1,63 +0,0 @@ - - -(* Copyright (c) 2011-2020 Stefan Krah. All rights reserved. *) - - -The Six Step Transform: -======================= - -In libmpdec, the six-step transform is the Matrix Fourier Transform (See -matrix-transform.txt) in disguise. It is called six-step transform after -a variant that appears in [1]. The algorithm requires that the input -array can be viewed as an R*C matrix. - - -Algorithm six-step (forward transform): ---------------------------------------- - - 1a) Transpose the matrix. - - 1b) Apply a length R FNT to each row. - - 1c) Transpose the matrix. - - 2) Multiply each matrix element (addressed by j*C+m) by r**(j*m). - - 3) Apply a length C FNT to each row. - - 4) Transpose the matrix. - -Note that steps 1a) - 1c) are exactly equivalent to step 1) of the Matrix -Fourier Transform. For large R, it is faster to transpose twice and do -a transform on the rows than to perform a column transpose directly. - - - -Algorithm six-step (inverse transform): ---------------------------------------- - - 0) View the matrix as a C*R matrix. - - 1) Transpose the matrix, producing an R*C matrix. - - 2) Apply a length C FNT to each row. - - 3) Multiply each matrix element (addressed by i*C+n) by r**(i*n). - - 4a) Transpose the matrix. - - 4b) Apply a length R FNT to each row. - - 4c) Transpose the matrix. - -Again, steps 4a) - 4c) are equivalent to step 4) of the Matrix Fourier -Transform. - - - --- - - [1] David H. Bailey: FFTs in External or Hierarchical Memory - http://crd.lbl.gov/~dhbailey/dhbpapers/ - - diff --git a/Modules/_decimal/libmpdec/literature/umodarith.lisp b/Modules/_decimal/libmpdec/literature/umodarith.lisp deleted file mode 100644 index d71f074a26dcca..00000000000000 --- a/Modules/_decimal/libmpdec/literature/umodarith.lisp +++ /dev/null @@ -1,692 +0,0 @@ -; -; Copyright (c) 2008-2020 Stefan Krah. All rights reserved. -; -; Redistribution and use in source and binary forms, with or without -; modification, are permitted provided that the following conditions -; are met: -; -; 1. Redistributions of source code must retain the above copyright -; notice, this list of conditions and the following disclaimer. -; -; 2. Redistributions in binary form must reproduce the above copyright -; notice, this list of conditions and the following disclaimer in the -; documentation and/or other materials provided with the distribution. -; -; THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND -; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -; ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE -; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS -; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) -; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY -; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF -; SUCH DAMAGE. -; - - -(in-package "ACL2") - -(include-book "arithmetic/top-with-meta" :dir :system) -(include-book "arithmetic-2/floor-mod/floor-mod" :dir :system) - - -;; ===================================================================== -;; Proofs for several functions in umodarith.h -;; ===================================================================== - - - -;; ===================================================================== -;; Helper theorems -;; ===================================================================== - -(defthm elim-mod-m= s m) (mod (- s m) base) s))) - s)) - -(defthmd addmod-correct - (implies (and (< 0 m) (< m base) - (< a m) (<= b m) - (natp m) (natp base) - (natp a) (natp b)) - (equal (addmod a b m base) - (mod (+ a b) m))) - :hints (("Goal" :cases ((<= base (+ a b)))) - ("Subgoal 2.1'" :use ((:instance elim-mod-m= a m) (- a m) a)) - (b (if (>= b m) (- b m) b)) - (d (mod (- a b) base)) - (d (if (< a b) (mod (+ d m) base) d))) - d)) - -; a < 2*m, b < 2*m -(defun ext-submod-2 (a b m base) - (let* ((a (mod a m)) - (b (mod b m)) - (d (mod (- a b) base)) - (d (if (< a b) (mod (+ d m) base) d))) - d)) - -(defthmd ext-submod-ext-submod-2-equal - (implies (and (< 0 m) (< m base) - (< a (* 2 m)) (< b (* 2 m)) - (natp m) (natp base) - (natp a) (natp b)) - (equal (ext-submod a b m base) - (ext-submod-2 a b m base)))) - -(defthmd ext-submod-2-correct - (implies (and (< 0 m) (< m base) - (< a (* 2 m)) (< b (* 2 m)) - (natp m) (natp base) - (natp a) (natp b)) - (equal (ext-submod-2 a b m base) - (mod (- a b) m)))) - - -;; ========================================================================= -;; dw-reduce is correct -;; ========================================================================= - -(defun dw-reduce (hi lo m base) - (let* ((r1 (mod hi m)) - (r2 (mod (+ (* r1 base) lo) m))) - r2)) - -(defthmd dw-reduce-correct - (implies (and (< 0 m) (< m base) - (< hi base) (< lo base) - (natp m) (natp base) - (natp hi) (natp lo)) - (equal (dw-reduce hi lo m base) - (mod (+ (* hi base) lo) m)))) - -(defthmd <=-multiply-both-sides-by-z - (implies (and (rationalp x) (rationalp y) - (< 0 z) (rationalp z)) - (equal (<= x y) - (<= (* z x) (* z y))))) - -(defthmd dw-reduce-aux1 - (implies (and (< 0 m) (< m base) - (natp m) (natp base) - (< lo base) (natp lo) - (< x m) (natp x)) - (< (+ lo (* base x)) (* base m))) - :hints (("Goal" :cases ((<= (+ x 1) m))) - ("Subgoal 1''" :cases ((<= (* base (+ x 1)) (* base m)))) - ("subgoal 1.2" :use ((:instance <=-multiply-both-sides-by-z - (x (+ 1 x)) - (y m) - (z base)))))) - -(defthm dw-reduce-aux2 - (implies (and (< x (* base m)) - (< 0 m) (< m base) - (natp m) (natp base) (natp x)) - (< (floor x m) base))) - -;; This is the necessary condition for using _mpd_div_words(). -(defthmd dw-reduce-second-quotient-fits-in-single-word - (implies (and (< 0 m) (< m base) - (< hi base) (< lo base) - (natp m) (natp base) - (natp hi) (natp lo) - (equal r1 (mod hi m))) - (< (floor (+ (* r1 base) lo) m) - base)) - :hints (("Goal" :cases ((< r1 m))) - ("Subgoal 1''" :cases ((< (+ lo (* base (mod hi m))) (* base m)))) - ("Subgoal 1.2" :use ((:instance dw-reduce-aux1 - (x (mod hi m))))))) - - -;; ========================================================================= -;; dw-submod is correct -;; ========================================================================= - -(defun dw-submod (a hi lo m base) - (let* ((r (dw-reduce hi lo m base)) - (d (mod (- a r) base)) - (d (if (< a r) (mod (+ d m) base) d))) - d)) - -(defthmd dw-submod-aux1 - (implies (and (natp a) (< 0 m) (natp m) - (natp x) (equal r (mod x m))) - (equal (mod (- a x) m) - (mod (- a r) m)))) - -(defthmd dw-submod-correct - (implies (and (< 0 m) (< m base) - (natp a) (< a m) - (< hi base) (< lo base) - (natp m) (natp base) - (natp hi) (natp lo)) - (equal (dw-submod a hi lo m base) - (mod (- a (+ (* base hi) lo)) m))) - :hints (("Goal" :in-theory (disable dw-reduce) - :use ((:instance dw-submod-aux1 - (x (+ lo (* base hi))) - (r (dw-reduce hi lo m base))) - (:instance dw-reduce-correct))))) - - -;; ========================================================================= -;; ANSI C arithmetic for uint64_t -;; ========================================================================= - -(defun add (a b) - (mod (+ a b) - (expt 2 64))) - -(defun sub (a b) - (mod (- a b) - (expt 2 64))) - -(defun << (w n) - (mod (* w (expt 2 n)) - (expt 2 64))) - -(defun >> (w n) - (floor w (expt 2 n))) - -;; join upper and lower half of a double word, yielding a 128 bit number -(defun join (hi lo) - (+ (* (expt 2 64) hi) lo)) - - -;; ============================================================================= -;; Fast modular reduction -;; ============================================================================= - -;; These are the three primes used in the Number Theoretic Transform. -;; A fast modular reduction scheme exists for all of them. -(defmacro p1 () - (+ (expt 2 64) (- (expt 2 32)) 1)) - -(defmacro p2 () - (+ (expt 2 64) (- (expt 2 34)) 1)) - -(defmacro p3 () - (+ (expt 2 64) (- (expt 2 40)) 1)) - - -;; reduce the double word number hi*2**64 + lo (mod p1) -(defun simple-mod-reduce-p1 (hi lo) - (+ (* (expt 2 32) hi) (- hi) lo)) - -;; reduce the double word number hi*2**64 + lo (mod p2) -(defun simple-mod-reduce-p2 (hi lo) - (+ (* (expt 2 34) hi) (- hi) lo)) - -;; reduce the double word number hi*2**64 + lo (mod p3) -(defun simple-mod-reduce-p3 (hi lo) - (+ (* (expt 2 40) hi) (- hi) lo)) - - -; ---------------------------------------------------------- -; The modular reductions given above are correct -; ---------------------------------------------------------- - -(defthmd congruence-p1-aux - (equal (* (expt 2 64) hi) - (+ (* (p1) hi) - (* (expt 2 32) hi) - (- hi)))) - -(defthmd congruence-p2-aux - (equal (* (expt 2 64) hi) - (+ (* (p2) hi) - (* (expt 2 34) hi) - (- hi)))) - -(defthmd congruence-p3-aux - (equal (* (expt 2 64) hi) - (+ (* (p3) hi) - (* (expt 2 40) hi) - (- hi)))) - -(defthmd mod-augment - (implies (and (rationalp x) - (rationalp y) - (rationalp m)) - (equal (mod (+ x y) m) - (mod (+ x (mod y m)) m)))) - -(defthmd simple-mod-reduce-p1-congruent - (implies (and (integerp hi) - (integerp lo)) - (equal (mod (simple-mod-reduce-p1 hi lo) (p1)) - (mod (join hi lo) (p1)))) - :hints (("Goal''" :use ((:instance congruence-p1-aux) - (:instance mod-augment - (m (p1)) - (x (+ (- hi) lo (* (expt 2 32) hi))) - (y (* (p1) hi))))))) - -(defthmd simple-mod-reduce-p2-congruent - (implies (and (integerp hi) - (integerp lo)) - (equal (mod (simple-mod-reduce-p2 hi lo) (p2)) - (mod (join hi lo) (p2)))) - :hints (("Goal''" :use ((:instance congruence-p2-aux) - (:instance mod-augment - (m (p2)) - (x (+ (- hi) lo (* (expt 2 34) hi))) - (y (* (p2) hi))))))) - -(defthmd simple-mod-reduce-p3-congruent - (implies (and (integerp hi) - (integerp lo)) - (equal (mod (simple-mod-reduce-p3 hi lo) (p3)) - (mod (join hi lo) (p3)))) - :hints (("Goal''" :use ((:instance congruence-p3-aux) - (:instance mod-augment - (m (p3)) - (x (+ (- hi) lo (* (expt 2 40) hi))) - (y (* (p3) hi))))))) - - -; --------------------------------------------------------------------- -; We need a number less than 2*p, so that we can use the trick from -; elim-mod-m> hi 32)) - (x (sub lo x)) - (hi (if (> x lo) (+ hi -1) hi)) - (y (<< y 32)) - (lo (add y x)) - (hi (if (< lo y) (+ hi 1) hi))) - (+ (* hi (expt 2 64)) lo))) - -(defun mod-reduce-p2 (hi lo) - (let* ((y hi) - (x y) - (hi (>> hi 30)) - (x (sub lo x)) - (hi (if (> x lo) (+ hi -1) hi)) - (y (<< y 34)) - (lo (add y x)) - (hi (if (< lo y) (+ hi 1) hi))) - (+ (* hi (expt 2 64)) lo))) - -(defun mod-reduce-p3 (hi lo) - (let* ((y hi) - (x y) - (hi (>> hi 24)) - (x (sub lo x)) - (hi (if (> x lo) (+ hi -1) hi)) - (y (<< y 40)) - (lo (add y x)) - (hi (if (< lo y) (+ hi 1) hi))) - (+ (* hi (expt 2 64)) lo))) - - -; ------------------------------------------------------------------------- -; The compiler friendly versions are equal to the simple versions -; ------------------------------------------------------------------------- - -(defthm mod-reduce-aux1 - (implies (and (<= 0 a) (natp a) (natp m) - (< (- m) b) (<= b 0) - (integerp b) - (< (mod (+ b a) m) - (mod a m))) - (equal (mod (+ b a) m) - (+ b (mod a m)))) - :hints (("Subgoal 2" :use ((:instance modaux-1b - (x (+ a b))))))) - -(defthm mod-reduce-aux2 - (implies (and (<= 0 a) (natp a) (natp m) - (< b m) (natp b) - (< (mod (+ b a) m) - (mod a m))) - (equal (+ m (mod (+ b a) m)) - (+ b (mod a m))))) - - -(defthm mod-reduce-aux3 - (implies (and (< 0 a) (natp a) (natp m) - (< (- m) b) (< b 0) - (integerp b) - (<= (mod a m) - (mod (+ b a) m))) - (equal (+ (- m) (mod (+ b a) m)) - (+ b (mod a m)))) - :hints (("Subgoal 1.2'" :use ((:instance modaux-1b - (x b)))) - ("Subgoal 1''" :use ((:instance modaux-2d - (x I)))))) - - -(defthm mod-reduce-aux4 - (implies (and (< 0 a) (natp a) (natp m) - (< b m) (natp b) - (<= (mod a m) - (mod (+ b a) m))) - (equal (mod (+ b a) m) - (+ b (mod a m))))) - - -(defthm mod-reduce-p1==simple-mod-reduce-p1 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (natp hi) (natp lo)) - (equal (mod-reduce-p1 hi lo) - (simple-mod-reduce-p1 hi lo))) - :hints (("Goal" :in-theory (disable expt) - :cases ((< 0 hi))) - ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 32) hi))))) - ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 32) hi))))) - ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 32) hi))))) - ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 32) hi))))))) - - -(defthm mod-reduce-p2==simple-mod-reduce-p2 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (natp hi) (natp lo)) - (equal (mod-reduce-p2 hi lo) - (simple-mod-reduce-p2 hi lo))) - :hints (("Goal" :cases ((< 0 hi))) - ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 34) hi))))) - ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 34) hi))))) - ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 34) hi))))) - ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 34) hi))))))) - - -(defthm mod-reduce-p3==simple-mod-reduce-p3 - (implies (and (< hi (expt 2 64)) - (< lo (expt 2 64)) - (natp hi) (natp lo)) - (equal (mod-reduce-p3 hi lo) - (simple-mod-reduce-p3 hi lo))) - :hints (("Goal" :cases ((< 0 hi))) - ("Subgoal 1.2.2'" :use ((:instance mod-reduce-aux1 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 40) hi))))) - ("Subgoal 1.2.1'" :use ((:instance mod-reduce-aux3 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 40) hi))))) - ("Subgoal 1.1.2'" :use ((:instance mod-reduce-aux2 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 40) hi))))) - ("Subgoal 1.1.1'" :use ((:instance mod-reduce-aux4 - (m (expt 2 64)) - (b (+ (- HI) LO)) - (a (* (expt 2 40) hi))))))) - - - diff --git a/Modules/_decimal/libmpdec/mpalloc.c b/Modules/_decimal/libmpdec/mpalloc.c deleted file mode 100644 index 5871d5c0f53519..00000000000000 --- a/Modules/_decimal/libmpdec/mpalloc.c +++ /dev/null @@ -1,349 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include -#include -#include - -#include "mpalloc.h" -#include "typearith.h" - - -#if defined(_MSC_VER) - #pragma warning(disable : 4232) -#endif - - -/* Guaranteed minimum allocation for a coefficient. May be changed once - at program start using mpd_setminalloc(). */ -mpd_ssize_t MPD_MINALLOC = MPD_MINALLOC_MIN; - -/* Custom allocation and free functions */ -void *(* mpd_mallocfunc)(size_t size) = malloc; -void *(* mpd_reallocfunc)(void *ptr, size_t size) = realloc; -void *(* mpd_callocfunc)(size_t nmemb, size_t size) = calloc; -void (* mpd_free)(void *ptr) = free; - - -/* emulate calloc if it is not available */ -void * -mpd_callocfunc_em(size_t nmemb, size_t size) -{ - void *ptr; - size_t req; - mpd_size_t overflow; - - req = mul_size_t_overflow((mpd_size_t)nmemb, (mpd_size_t)size, - &overflow); - if (overflow) { - return NULL; - } - - ptr = mpd_mallocfunc(req); - if (ptr == NULL) { - return NULL; - } - /* used on uint32_t or uint64_t */ - memset(ptr, 0, req); - - return ptr; -} - - -/* malloc with overflow checking */ -void * -mpd_alloc(mpd_size_t nmemb, mpd_size_t size) -{ - mpd_size_t req, overflow; - - req = mul_size_t_overflow(nmemb, size, &overflow); - if (overflow) { - return NULL; - } - - return mpd_mallocfunc(req); -} - -/* calloc with overflow checking */ -void * -mpd_calloc(mpd_size_t nmemb, mpd_size_t size) -{ - mpd_size_t overflow; - - (void)mul_size_t_overflow(nmemb, size, &overflow); - if (overflow) { - return NULL; - } - - return mpd_callocfunc(nmemb, size); -} - -/* realloc with overflow checking */ -void * -mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err) -{ - void *new; - mpd_size_t req, overflow; - - req = mul_size_t_overflow(nmemb, size, &overflow); - if (overflow) { - *err = 1; - return ptr; - } - - new = mpd_reallocfunc(ptr, req); - if (new == NULL) { - *err = 1; - return ptr; - } - - return new; -} - -/* struct hack malloc with overflow checking */ -void * -mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size) -{ - mpd_size_t req, overflow; - - req = mul_size_t_overflow(nmemb, size, &overflow); - if (overflow) { - return NULL; - } - - req = add_size_t_overflow(req, struct_size, &overflow); - if (overflow) { - return NULL; - } - - return mpd_mallocfunc(req); -} - - -/* Allocate a new decimal with a coefficient of length 'nwords'. In case - of an error the return value is NULL. */ -mpd_t * -mpd_qnew_size(mpd_ssize_t nwords) -{ - mpd_t *result; - - nwords = (nwords < MPD_MINALLOC) ? MPD_MINALLOC : nwords; - - result = mpd_alloc(1, sizeof *result); - if (result == NULL) { - return NULL; - } - - result->data = mpd_alloc(nwords, sizeof *result->data); - if (result->data == NULL) { - mpd_free(result); - return NULL; - } - - result->flags = 0; - result->exp = 0; - result->digits = 0; - result->len = 0; - result->alloc = nwords; - - return result; -} - -/* Allocate a new decimal with a coefficient of length MPD_MINALLOC. - In case of an error the return value is NULL. */ -mpd_t * -mpd_qnew(void) -{ - return mpd_qnew_size(MPD_MINALLOC); -} - -/* Allocate new decimal. Caller can check for NULL or MPD_Malloc_error. - Raises on error. */ -mpd_t * -mpd_new(mpd_context_t *ctx) -{ - mpd_t *result; - - result = mpd_qnew(); - if (result == NULL) { - mpd_addstatus_raise(ctx, MPD_Malloc_error); - } - return result; -} - -/* - * Input: 'result' is a static mpd_t with a static coefficient. - * Assumption: 'nwords' >= result->alloc. - * - * Resize the static coefficient to a larger dynamic one and copy the - * existing data. If successful, the value of 'result' is unchanged. - * Otherwise, set 'result' to NaN and update 'status' with MPD_Malloc_error. - */ -int -mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - mpd_uint_t *p = result->data; - - assert(nwords >= result->alloc); - - result->data = mpd_alloc(nwords, sizeof *result->data); - if (result->data == NULL) { - result->data = p; - mpd_set_qnan(result); - mpd_set_positive(result); - result->exp = result->digits = result->len = 0; - *status |= MPD_Malloc_error; - return 0; - } - - memcpy(result->data, p, result->alloc * (sizeof *result->data)); - result->alloc = nwords; - mpd_set_dynamic_data(result); - return 1; -} - -/* - * Input: 'result' is a static mpd_t with a static coefficient. - * - * Convert the coefficient to a dynamic one that is initialized to zero. If - * malloc fails, set 'result' to NaN and update 'status' with MPD_Malloc_error. - */ -int -mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - mpd_uint_t *p = result->data; - - result->data = mpd_calloc(nwords, sizeof *result->data); - if (result->data == NULL) { - result->data = p; - mpd_set_qnan(result); - mpd_set_positive(result); - result->exp = result->digits = result->len = 0; - *status |= MPD_Malloc_error; - return 0; - } - - result->alloc = nwords; - mpd_set_dynamic_data(result); - - return 1; -} - -/* - * Input: 'result' is a static or a dynamic mpd_t with a dynamic coefficient. - * Resize the coefficient to length 'nwords': - * Case nwords > result->alloc: - * If realloc is successful: - * 'result' has a larger coefficient but the same value. Return 1. - * Otherwise: - * Set 'result' to NaN, update status with MPD_Malloc_error and return 0. - * Case nwords < result->alloc: - * If realloc is successful: - * 'result' has a smaller coefficient. result->len is undefined. Return 1. - * Otherwise (unlikely): - * 'result' is unchanged. Reuse the now oversized coefficient. Return 1. - */ -int -mpd_realloc_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - uint8_t err = 0; - - result->data = mpd_realloc(result->data, nwords, sizeof *result->data, &err); - if (!err) { - result->alloc = nwords; - } - else if (nwords > result->alloc) { - mpd_set_qnan(result); - mpd_set_positive(result); - result->exp = result->digits = result->len = 0; - *status |= MPD_Malloc_error; - return 0; - } - - return 1; -} - -/* - * Input: 'result' is a static mpd_t with a static coefficient. - * Assumption: 'nwords' >= result->alloc. - * - * Resize the static coefficient to a larger dynamic one and copy the - * existing data. - * - * On failure the value of 'result' is unchanged. - */ -int -mpd_switch_to_dyn_cxx(mpd_t *result, mpd_ssize_t nwords) -{ - assert(nwords >= result->alloc); - - mpd_uint_t *data = mpd_alloc(nwords, sizeof *result->data); - if (data == NULL) { - return 0; - } - - memcpy(data, result->data, result->alloc * (sizeof *result->data)); - result->data = data; - result->alloc = nwords; - mpd_set_dynamic_data(result); - return 1; -} - -/* - * Input: 'result' is a static or a dynamic mpd_t with a dynamic coefficient. - * Resize the coefficient to length 'nwords': - * Case nwords > result->alloc: - * If realloc is successful: - * 'result' has a larger coefficient but the same value. Return 1. - * Otherwise: - * 'result' has a the same coefficient. Return 0. - * Case nwords < result->alloc: - * If realloc is successful: - * 'result' has a smaller coefficient. result->len is undefined. Return 1. - * Otherwise (unlikely): - * 'result' is unchanged. Reuse the now oversized coefficient. Return 1. - */ -int -mpd_realloc_dyn_cxx(mpd_t *result, mpd_ssize_t nwords) -{ - uint8_t err = 0; - - mpd_uint_t *p = mpd_realloc(result->data, nwords, sizeof *result->data, &err); - if (!err) { - result->data = p; - result->alloc = nwords; - } - else if (nwords > result->alloc) { - return 0; - } - - return 1; -} diff --git a/Modules/_decimal/libmpdec/mpalloc.h b/Modules/_decimal/libmpdec/mpalloc.h deleted file mode 100644 index 22650044218241..00000000000000 --- a/Modules/_decimal/libmpdec/mpalloc.h +++ /dev/null @@ -1,53 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_MPALLOC_H_ -#define LIBMPDEC_MPALLOC_H_ - - -#include "mpdecimal.h" - -#include - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -int mpd_switch_to_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status); -int mpd_switch_to_dyn_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status); -int mpd_realloc_dyn(mpd_t *result, mpd_ssize_t nwords, uint32_t *status); - -int mpd_switch_to_dyn_cxx(mpd_t *result, mpd_ssize_t nwords); -int mpd_realloc_dyn_cxx(mpd_t *result, mpd_ssize_t nwords); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_MPALLOC_H_ */ diff --git a/Modules/_decimal/libmpdec/mpdecimal.c b/Modules/_decimal/libmpdec/mpdecimal.c deleted file mode 100644 index 959934bda7a449..00000000000000 --- a/Modules/_decimal/libmpdec/mpdecimal.c +++ /dev/null @@ -1,9015 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include -#include -#include -#include -#include - -#include "basearith.h" -#include "bits.h" -#include "constants.h" -#include "convolute.h" -#include "crt.h" -#include "mpalloc.h" -#include "typearith.h" - -#ifdef PPRO - #if defined(_MSC_VER) - #include - #pragma float_control(precise, on) - #pragma fenv_access(on) - #elif !defined(__OpenBSD__) && !defined(__NetBSD__) - /* C99 */ - #include - #pragma STDC FENV_ACCESS ON - #endif -#endif - - -/* Disable warning that is part of -Wextra since gcc 7.0. */ -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 7 - #pragma GCC diagnostic ignored "-Wimplicit-fallthrough" -#endif - - -#if defined(_MSC_VER) - #define ALWAYS_INLINE __forceinline -#elif defined (__IBMC__) || defined(LEGACY_COMPILER) - #define ALWAYS_INLINE - #undef inline - #define inline -#else - #ifdef TEST_COVERAGE - #define ALWAYS_INLINE - #else - #define ALWAYS_INLINE inline __attribute__ ((always_inline)) - #endif -#endif - -/* ClangCL claims to support 128-bit int, but doesn't */ -#if defined(__SIZEOF_INT128__) && defined(__clang__) && defined(_MSC_VER) -#undef __SIZEOF_INT128__ -#endif - - - -#define MPD_NEWTONDIV_CUTOFF 1024L - -#define MPD_NEW_STATIC(name, flags, exp, digits, len) \ - mpd_uint_t name##_data[MPD_MINALLOC_MAX]; \ - mpd_t name = {flags|MPD_STATIC|MPD_STATIC_DATA, exp, digits, \ - len, MPD_MINALLOC_MAX, name##_data} - -#define MPD_NEW_CONST(name, flags, exp, digits, len, alloc, initval) \ - mpd_uint_t name##_data[alloc] = {initval}; \ - mpd_t name = {flags|MPD_STATIC|MPD_CONST_DATA, exp, digits, \ - len, alloc, name##_data} - -#define MPD_NEW_SHARED(name, a) \ - mpd_t name = {(a->flags&~MPD_DATAFLAGS)|MPD_STATIC|MPD_SHARED_DATA, \ - a->exp, a->digits, a->len, a->alloc, a->data} - - -static mpd_uint_t data_one[1] = {1}; -static mpd_uint_t data_zero[1] = {0}; -static const mpd_t one = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_one}; -static const mpd_t minus_one = {MPD_NEG|MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, - data_one}; -static const mpd_t zero = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_zero}; - -static inline void _mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx, - uint32_t *status); -static void _settriple(mpd_t *result, uint8_t sign, mpd_uint_t a, - mpd_ssize_t exp); -static inline mpd_ssize_t _mpd_real_size(mpd_uint_t *data, mpd_ssize_t size); - -static int _mpd_cmp_abs(const mpd_t *a, const mpd_t *b); - -static void _mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status); -static inline void _mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status); -static void _mpd_base_ndivmod(mpd_t *q, mpd_t *r, const mpd_t *a, - const mpd_t *b, uint32_t *status); -static inline void _mpd_qpow_uint(mpd_t *result, const mpd_t *base, - mpd_uint_t exp, uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status); - -static mpd_uint_t mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n); - - -/******************************************************************************/ -/* Version */ -/******************************************************************************/ - -const char * -mpd_version(void) -{ - return MPD_VERSION; -} - - -/******************************************************************************/ -/* Performance critical inline functions */ -/******************************************************************************/ - -#ifdef CONFIG_64 -/* Digits in a word, primarily useful for the most significant word. */ -ALWAYS_INLINE int -mpd_word_digits(mpd_uint_t word) -{ - if (word < mpd_pow10[9]) { - if (word < mpd_pow10[4]) { - if (word < mpd_pow10[2]) { - return (word < mpd_pow10[1]) ? 1 : 2; - } - return (word < mpd_pow10[3]) ? 3 : 4; - } - if (word < mpd_pow10[6]) { - return (word < mpd_pow10[5]) ? 5 : 6; - } - if (word < mpd_pow10[8]) { - return (word < mpd_pow10[7]) ? 7 : 8; - } - return 9; - } - if (word < mpd_pow10[14]) { - if (word < mpd_pow10[11]) { - return (word < mpd_pow10[10]) ? 10 : 11; - } - if (word < mpd_pow10[13]) { - return (word < mpd_pow10[12]) ? 12 : 13; - } - return 14; - } - if (word < mpd_pow10[18]) { - if (word < mpd_pow10[16]) { - return (word < mpd_pow10[15]) ? 15 : 16; - } - return (word < mpd_pow10[17]) ? 17 : 18; - } - - return (word < mpd_pow10[19]) ? 19 : 20; -} -#else -ALWAYS_INLINE int -mpd_word_digits(mpd_uint_t word) -{ - if (word < mpd_pow10[4]) { - if (word < mpd_pow10[2]) { - return (word < mpd_pow10[1]) ? 1 : 2; - } - return (word < mpd_pow10[3]) ? 3 : 4; - } - if (word < mpd_pow10[6]) { - return (word < mpd_pow10[5]) ? 5 : 6; - } - if (word < mpd_pow10[8]) { - return (word < mpd_pow10[7]) ? 7 : 8; - } - - return (word < mpd_pow10[9]) ? 9 : 10; -} -#endif - - -/* Adjusted exponent */ -ALWAYS_INLINE mpd_ssize_t -mpd_adjexp(const mpd_t *dec) -{ - return (dec->exp + dec->digits) - 1; -} - -/* Etiny */ -ALWAYS_INLINE mpd_ssize_t -mpd_etiny(const mpd_context_t *ctx) -{ - return ctx->emin - (ctx->prec - 1); -} - -/* Etop: used for folding down in IEEE clamping */ -ALWAYS_INLINE mpd_ssize_t -mpd_etop(const mpd_context_t *ctx) -{ - return ctx->emax - (ctx->prec - 1); -} - -/* Most significant word */ -ALWAYS_INLINE mpd_uint_t -mpd_msword(const mpd_t *dec) -{ - assert(dec->len > 0); - return dec->data[dec->len-1]; -} - -/* Most significant digit of a word */ -inline mpd_uint_t -mpd_msd(mpd_uint_t word) -{ - int n; - - n = mpd_word_digits(word); - return word / mpd_pow10[n-1]; -} - -/* Least significant digit of a word */ -ALWAYS_INLINE mpd_uint_t -mpd_lsd(mpd_uint_t word) -{ - return word % 10; -} - -/* Coefficient size needed to store 'digits' */ -mpd_ssize_t -mpd_digits_to_size(mpd_ssize_t digits) -{ - mpd_ssize_t q, r; - - _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS); - return (r == 0) ? q : q+1; -} - -/* Number of digits in the exponent. Not defined for MPD_SSIZE_MIN. */ -inline int -mpd_exp_digits(mpd_ssize_t exp) -{ - exp = (exp < 0) ? -exp : exp; - return mpd_word_digits(exp); -} - -/* Canonical */ -ALWAYS_INLINE int -mpd_iscanonical(const mpd_t *dec) -{ - (void)dec; - return 1; -} - -/* Finite */ -ALWAYS_INLINE int -mpd_isfinite(const mpd_t *dec) -{ - return !(dec->flags & MPD_SPECIAL); -} - -/* Infinite */ -ALWAYS_INLINE int -mpd_isinfinite(const mpd_t *dec) -{ - return dec->flags & MPD_INF; -} - -/* NaN */ -ALWAYS_INLINE int -mpd_isnan(const mpd_t *dec) -{ - return dec->flags & (MPD_NAN|MPD_SNAN); -} - -/* Negative */ -ALWAYS_INLINE int -mpd_isnegative(const mpd_t *dec) -{ - return dec->flags & MPD_NEG; -} - -/* Positive */ -ALWAYS_INLINE int -mpd_ispositive(const mpd_t *dec) -{ - return !(dec->flags & MPD_NEG); -} - -/* qNaN */ -ALWAYS_INLINE int -mpd_isqnan(const mpd_t *dec) -{ - return dec->flags & MPD_NAN; -} - -/* Signed */ -ALWAYS_INLINE int -mpd_issigned(const mpd_t *dec) -{ - return dec->flags & MPD_NEG; -} - -/* sNaN */ -ALWAYS_INLINE int -mpd_issnan(const mpd_t *dec) -{ - return dec->flags & MPD_SNAN; -} - -/* Special */ -ALWAYS_INLINE int -mpd_isspecial(const mpd_t *dec) -{ - return dec->flags & MPD_SPECIAL; -} - -/* Zero */ -ALWAYS_INLINE int -mpd_iszero(const mpd_t *dec) -{ - return !mpd_isspecial(dec) && mpd_msword(dec) == 0; -} - -/* Test for zero when specials have been ruled out already */ -ALWAYS_INLINE int -mpd_iszerocoeff(const mpd_t *dec) -{ - return mpd_msword(dec) == 0; -} - -/* Normal */ -inline int -mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx) -{ - if (mpd_isspecial(dec)) return 0; - if (mpd_iszerocoeff(dec)) return 0; - - return mpd_adjexp(dec) >= ctx->emin; -} - -/* Subnormal */ -inline int -mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx) -{ - if (mpd_isspecial(dec)) return 0; - if (mpd_iszerocoeff(dec)) return 0; - - return mpd_adjexp(dec) < ctx->emin; -} - -/* Odd word */ -ALWAYS_INLINE int -mpd_isoddword(mpd_uint_t word) -{ - return word & 1; -} - -/* Odd coefficient */ -ALWAYS_INLINE int -mpd_isoddcoeff(const mpd_t *dec) -{ - return mpd_isoddword(dec->data[0]); -} - -/* 0 if dec is positive, 1 if dec is negative */ -ALWAYS_INLINE uint8_t -mpd_sign(const mpd_t *dec) -{ - return dec->flags & MPD_NEG; -} - -/* 1 if dec is positive, -1 if dec is negative */ -ALWAYS_INLINE int -mpd_arith_sign(const mpd_t *dec) -{ - return 1 - 2 * mpd_isnegative(dec); -} - -/* Radix */ -ALWAYS_INLINE long -mpd_radix(void) -{ - return 10; -} - -/* Dynamic decimal */ -ALWAYS_INLINE int -mpd_isdynamic(const mpd_t *dec) -{ - return !(dec->flags & MPD_STATIC); -} - -/* Static decimal */ -ALWAYS_INLINE int -mpd_isstatic(const mpd_t *dec) -{ - return dec->flags & MPD_STATIC; -} - -/* Data of decimal is dynamic */ -ALWAYS_INLINE int -mpd_isdynamic_data(const mpd_t *dec) -{ - return !(dec->flags & MPD_DATAFLAGS); -} - -/* Data of decimal is static */ -ALWAYS_INLINE int -mpd_isstatic_data(const mpd_t *dec) -{ - return dec->flags & MPD_STATIC_DATA; -} - -/* Data of decimal is shared */ -ALWAYS_INLINE int -mpd_isshared_data(const mpd_t *dec) -{ - return dec->flags & MPD_SHARED_DATA; -} - -/* Data of decimal is const */ -ALWAYS_INLINE int -mpd_isconst_data(const mpd_t *dec) -{ - return dec->flags & MPD_CONST_DATA; -} - - -/******************************************************************************/ -/* Inline memory handling */ -/******************************************************************************/ - -/* Fill destination with zeros */ -ALWAYS_INLINE void -mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len) -{ - mpd_size_t i; - - for (i = 0; i < len; i++) { - dest[i] = 0; - } -} - -/* Free a decimal */ -ALWAYS_INLINE void -mpd_del(mpd_t *dec) -{ - if (mpd_isdynamic_data(dec)) { - mpd_free(dec->data); - } - if (mpd_isdynamic(dec)) { - mpd_free(dec); - } -} - -/* - * Resize the coefficient. Existing data up to 'nwords' is left untouched. - * Return 1 on success, 0 otherwise. - * - * Input invariant: MPD_MINALLOC <= result->alloc. - * - * Case nwords == result->alloc: - * 'result' is unchanged. Return 1. - * - * Case nwords > result->alloc: - * Case realloc success: - * The value of 'result' does not change. Return 1. - * Case realloc failure: - * 'result' is NaN, status is updated with MPD_Malloc_error. Return 0. - * - * Case nwords < result->alloc: - * Case is_static_data or realloc failure [1]: - * 'result' is unchanged. Return 1. - * Case realloc success: - * The value of result is undefined (expected). Return 1. - * - * - * [1] In that case the old (now oversized) area is still valid. - */ -ALWAYS_INLINE int -mpd_qresize(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - assert(!mpd_isconst_data(result)); /* illegal operation for a const */ - assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ - assert(MPD_MINALLOC <= result->alloc); - - nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords; - if (nwords == result->alloc) { - return 1; - } - if (mpd_isstatic_data(result)) { - if (nwords > result->alloc) { - return mpd_switch_to_dyn(result, nwords, status); - } - return 1; - } - - return mpd_realloc_dyn(result, nwords, status); -} - -/* Same as mpd_qresize, but do not set the result no NaN on failure. */ -static ALWAYS_INLINE int -mpd_qresize_cxx(mpd_t *result, mpd_ssize_t nwords) -{ - assert(!mpd_isconst_data(result)); /* illegal operation for a const */ - assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ - assert(MPD_MINALLOC <= result->alloc); - - nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords; - if (nwords == result->alloc) { - return 1; - } - if (mpd_isstatic_data(result)) { - if (nwords > result->alloc) { - return mpd_switch_to_dyn_cxx(result, nwords); - } - return 1; - } - - return mpd_realloc_dyn_cxx(result, nwords); -} - -/* Same as mpd_qresize, but the complete coefficient (including the old - * memory area!) is initialized to zero. */ -ALWAYS_INLINE int -mpd_qresize_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) -{ - assert(!mpd_isconst_data(result)); /* illegal operation for a const */ - assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ - assert(MPD_MINALLOC <= result->alloc); - - nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords; - if (nwords != result->alloc) { - if (mpd_isstatic_data(result)) { - if (nwords > result->alloc) { - return mpd_switch_to_dyn_zero(result, nwords, status); - } - } - else if (!mpd_realloc_dyn(result, nwords, status)) { - return 0; - } - } - - mpd_uint_zero(result->data, nwords); - return 1; -} - -/* - * Reduce memory size for the coefficient to MPD_MINALLOC. In theory, - * realloc may fail even when reducing the memory size. But in that case - * the old memory area is always big enough, so checking for MPD_Malloc_error - * is not imperative. - */ -ALWAYS_INLINE void -mpd_minalloc(mpd_t *result) -{ - assert(!mpd_isconst_data(result)); /* illegal operation for a const */ - assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ - - if (!mpd_isstatic_data(result) && result->alloc > MPD_MINALLOC) { - uint8_t err = 0; - result->data = mpd_realloc(result->data, MPD_MINALLOC, - sizeof *result->data, &err); - if (!err) { - result->alloc = MPD_MINALLOC; - } - } -} - -int -mpd_resize(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (!mpd_qresize(result, nwords, &status)) { - mpd_addstatus_raise(ctx, status); - return 0; - } - return 1; -} - -int -mpd_resize_zero(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (!mpd_qresize_zero(result, nwords, &status)) { - mpd_addstatus_raise(ctx, status); - return 0; - } - return 1; -} - - -/******************************************************************************/ -/* Set attributes of a decimal */ -/******************************************************************************/ - -/* Set digits. Assumption: result->len is initialized and > 0. */ -inline void -mpd_setdigits(mpd_t *result) -{ - mpd_ssize_t wdigits = mpd_word_digits(mpd_msword(result)); - result->digits = wdigits + (result->len-1) * MPD_RDIGITS; -} - -/* Set sign */ -ALWAYS_INLINE void -mpd_set_sign(mpd_t *result, uint8_t sign) -{ - result->flags &= ~MPD_NEG; - result->flags |= sign; -} - -/* Copy sign from another decimal */ -ALWAYS_INLINE void -mpd_signcpy(mpd_t *result, const mpd_t *a) -{ - uint8_t sign = a->flags&MPD_NEG; - - result->flags &= ~MPD_NEG; - result->flags |= sign; -} - -/* Set infinity */ -ALWAYS_INLINE void -mpd_set_infinity(mpd_t *result) -{ - result->flags &= ~MPD_SPECIAL; - result->flags |= MPD_INF; -} - -/* Set qNaN */ -ALWAYS_INLINE void -mpd_set_qnan(mpd_t *result) -{ - result->flags &= ~MPD_SPECIAL; - result->flags |= MPD_NAN; -} - -/* Set sNaN */ -ALWAYS_INLINE void -mpd_set_snan(mpd_t *result) -{ - result->flags &= ~MPD_SPECIAL; - result->flags |= MPD_SNAN; -} - -/* Set to negative */ -ALWAYS_INLINE void -mpd_set_negative(mpd_t *result) -{ - result->flags |= MPD_NEG; -} - -/* Set to positive */ -ALWAYS_INLINE void -mpd_set_positive(mpd_t *result) -{ - result->flags &= ~MPD_NEG; -} - -/* Set to dynamic */ -ALWAYS_INLINE void -mpd_set_dynamic(mpd_t *result) -{ - result->flags &= ~MPD_STATIC; -} - -/* Set to static */ -ALWAYS_INLINE void -mpd_set_static(mpd_t *result) -{ - result->flags |= MPD_STATIC; -} - -/* Set data to dynamic */ -ALWAYS_INLINE void -mpd_set_dynamic_data(mpd_t *result) -{ - result->flags &= ~MPD_DATAFLAGS; -} - -/* Set data to static */ -ALWAYS_INLINE void -mpd_set_static_data(mpd_t *result) -{ - result->flags &= ~MPD_DATAFLAGS; - result->flags |= MPD_STATIC_DATA; -} - -/* Set data to shared */ -ALWAYS_INLINE void -mpd_set_shared_data(mpd_t *result) -{ - result->flags &= ~MPD_DATAFLAGS; - result->flags |= MPD_SHARED_DATA; -} - -/* Set data to const */ -ALWAYS_INLINE void -mpd_set_const_data(mpd_t *result) -{ - result->flags &= ~MPD_DATAFLAGS; - result->flags |= MPD_CONST_DATA; -} - -/* Clear flags, preserving memory attributes. */ -ALWAYS_INLINE void -mpd_clear_flags(mpd_t *result) -{ - result->flags &= (MPD_STATIC|MPD_DATAFLAGS); -} - -/* Set flags, preserving memory attributes. */ -ALWAYS_INLINE void -mpd_set_flags(mpd_t *result, uint8_t flags) -{ - result->flags &= (MPD_STATIC|MPD_DATAFLAGS); - result->flags |= flags; -} - -/* Copy flags, preserving memory attributes of result. */ -ALWAYS_INLINE void -mpd_copy_flags(mpd_t *result, const mpd_t *a) -{ - uint8_t aflags = a->flags; - result->flags &= (MPD_STATIC|MPD_DATAFLAGS); - result->flags |= (aflags & ~(MPD_STATIC|MPD_DATAFLAGS)); -} - -/* Initialize a workcontext from ctx. Set traps, flags and newtrap to 0. */ -static inline void -mpd_workcontext(mpd_context_t *workctx, const mpd_context_t *ctx) -{ - workctx->prec = ctx->prec; - workctx->emax = ctx->emax; - workctx->emin = ctx->emin; - workctx->round = ctx->round; - workctx->traps = 0; - workctx->status = 0; - workctx->newtrap = 0; - workctx->clamp = ctx->clamp; - workctx->allcr = ctx->allcr; -} - - -/******************************************************************************/ -/* Getting and setting parts of decimals */ -/******************************************************************************/ - -/* Flip the sign of a decimal */ -static inline void -_mpd_negate(mpd_t *dec) -{ - dec->flags ^= MPD_NEG; -} - -/* Set coefficient to zero */ -void -mpd_zerocoeff(mpd_t *result) -{ - mpd_minalloc(result); - result->digits = 1; - result->len = 1; - result->data[0] = 0; -} - -/* Set the coefficient to all nines. */ -void -mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t len, r; - - _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS); - len = (r == 0) ? len : len+1; - - if (!mpd_qresize(result, len, status)) { - return; - } - - result->len = len; - result->digits = ctx->prec; - - --len; - if (r > 0) { - result->data[len--] = mpd_pow10[r]-1; - } - for (; len >= 0; --len) { - result->data[len] = MPD_RADIX-1; - } -} - -/* - * Cut off the most significant digits so that the rest fits in ctx->prec. - * Cannot fail. - */ -static void -_mpd_cap(mpd_t *result, const mpd_context_t *ctx) -{ - uint32_t dummy; - mpd_ssize_t len, r; - - if (result->len > 0 && result->digits > ctx->prec) { - _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS); - len = (r == 0) ? len : len+1; - - if (r != 0) { - result->data[len-1] %= mpd_pow10[r]; - } - - len = _mpd_real_size(result->data, len); - /* resize to fewer words cannot fail */ - mpd_qresize(result, len, &dummy); - result->len = len; - mpd_setdigits(result); - } - if (mpd_iszero(result)) { - _settriple(result, mpd_sign(result), 0, result->exp); - } -} - -/* - * Cut off the most significant digits of a NaN payload so that the rest - * fits in ctx->prec - ctx->clamp. Cannot fail. - */ -static void -_mpd_fix_nan(mpd_t *result, const mpd_context_t *ctx) -{ - uint32_t dummy; - mpd_ssize_t prec; - mpd_ssize_t len, r; - - prec = ctx->prec - ctx->clamp; - if (result->len > 0 && result->digits > prec) { - if (prec == 0) { - mpd_minalloc(result); - result->len = result->digits = 0; - } - else { - _mpd_idiv_word(&len, &r, prec, MPD_RDIGITS); - len = (r == 0) ? len : len+1; - - if (r != 0) { - result->data[len-1] %= mpd_pow10[r]; - } - - len = _mpd_real_size(result->data, len); - /* resize to fewer words cannot fail */ - mpd_qresize(result, len, &dummy); - result->len = len; - mpd_setdigits(result); - if (mpd_iszerocoeff(result)) { - /* NaN0 is not a valid representation */ - result->len = result->digits = 0; - } - } - } -} - -/* - * Get n most significant digits from a decimal, where 0 < n <= MPD_UINT_DIGITS. - * Assumes MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for 32 and 64 bit - * machines. - * - * The result of the operation will be in lo. If the operation is impossible, - * hi will be nonzero. This is used to indicate an error. - */ -static inline void -_mpd_get_msdigits(mpd_uint_t *hi, mpd_uint_t *lo, const mpd_t *dec, - unsigned int n) -{ - mpd_uint_t r, tmp; - - assert(0 < n && n <= MPD_RDIGITS+1); - - _mpd_div_word(&tmp, &r, dec->digits, MPD_RDIGITS); - r = (r == 0) ? MPD_RDIGITS : r; /* digits in the most significant word */ - - *hi = 0; - *lo = dec->data[dec->len-1]; - if (n <= r) { - *lo /= mpd_pow10[r-n]; - } - else if (dec->len > 1) { - /* at this point 1 <= r < n <= MPD_RDIGITS+1 */ - _mpd_mul_words(hi, lo, *lo, mpd_pow10[n-r]); - tmp = dec->data[dec->len-2] / mpd_pow10[MPD_RDIGITS-(n-r)]; - *lo = *lo + tmp; - if (*lo < tmp) (*hi)++; - } -} - - -/******************************************************************************/ -/* Gathering information about a decimal */ -/******************************************************************************/ - -/* The real size of the coefficient without leading zero words. */ -static inline mpd_ssize_t -_mpd_real_size(mpd_uint_t *data, mpd_ssize_t size) -{ - while (size > 1 && data[size-1] == 0) { - size--; - } - - return size; -} - -/* Return number of trailing zeros. No errors are possible. */ -mpd_ssize_t -mpd_trail_zeros(const mpd_t *dec) -{ - mpd_uint_t word; - mpd_ssize_t i, tz = 0; - - for (i=0; i < dec->len; ++i) { - if (dec->data[i] != 0) { - word = dec->data[i]; - tz = i * MPD_RDIGITS; - while (word % 10 == 0) { - word /= 10; - tz++; - } - break; - } - } - - return tz; -} - -/* Integer: Undefined for specials */ -static int -_mpd_isint(const mpd_t *dec) -{ - mpd_ssize_t tz; - - if (mpd_iszerocoeff(dec)) { - return 1; - } - - tz = mpd_trail_zeros(dec); - return (dec->exp + tz >= 0); -} - -/* Integer */ -int -mpd_isinteger(const mpd_t *dec) -{ - if (mpd_isspecial(dec)) { - return 0; - } - return _mpd_isint(dec); -} - -/* Word is a power of 10 */ -static int -mpd_word_ispow10(mpd_uint_t word) -{ - int n; - - n = mpd_word_digits(word); - if (word == mpd_pow10[n-1]) { - return 1; - } - - return 0; -} - -/* Coefficient is a power of 10 */ -static int -mpd_coeff_ispow10(const mpd_t *dec) -{ - if (mpd_word_ispow10(mpd_msword(dec))) { - if (_mpd_isallzero(dec->data, dec->len-1)) { - return 1; - } - } - - return 0; -} - -/* All digits of a word are nines */ -static int -mpd_word_isallnine(mpd_uint_t word) -{ - int n; - - n = mpd_word_digits(word); - if (word == mpd_pow10[n]-1) { - return 1; - } - - return 0; -} - -/* All digits of the coefficient are nines */ -static int -mpd_coeff_isallnine(const mpd_t *dec) -{ - if (mpd_word_isallnine(mpd_msword(dec))) { - if (_mpd_isallnine(dec->data, dec->len-1)) { - return 1; - } - } - - return 0; -} - -/* Odd decimal: Undefined for non-integers! */ -int -mpd_isodd(const mpd_t *dec) -{ - mpd_uint_t q, r; - assert(mpd_isinteger(dec)); - if (mpd_iszerocoeff(dec)) return 0; - if (dec->exp < 0) { - _mpd_div_word(&q, &r, -dec->exp, MPD_RDIGITS); - q = dec->data[q] / mpd_pow10[r]; - return mpd_isoddword(q); - } - return dec->exp == 0 && mpd_isoddword(dec->data[0]); -} - -/* Even: Undefined for non-integers! */ -int -mpd_iseven(const mpd_t *dec) -{ - return !mpd_isodd(dec); -} - -/******************************************************************************/ -/* Getting and setting decimals */ -/******************************************************************************/ - -/* Internal function: Set a static decimal from a triple, no error checking. */ -static void -_ssettriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp) -{ - mpd_set_flags(result, sign); - result->exp = exp; - _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX); - result->len = (result->data[1] == 0) ? 1 : 2; - mpd_setdigits(result); -} - -/* Internal function: Set a decimal from a triple, no error checking. */ -static void -_settriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp) -{ - mpd_minalloc(result); - mpd_set_flags(result, sign); - result->exp = exp; - _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX); - result->len = (result->data[1] == 0) ? 1 : 2; - mpd_setdigits(result); -} - -/* Set a special number from a triple */ -void -mpd_setspecial(mpd_t *result, uint8_t sign, uint8_t type) -{ - mpd_minalloc(result); - result->flags &= ~(MPD_NEG|MPD_SPECIAL); - result->flags |= (sign|type); - result->exp = result->digits = result->len = 0; -} - -/* Set result of NaN with an error status */ -void -mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status) -{ - mpd_minalloc(result); - mpd_set_qnan(result); - mpd_set_positive(result); - result->exp = result->digits = result->len = 0; - *status |= flags; -} - -/* quietly set a static decimal from an mpd_ssize_t */ -void -mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_uint_t u; - uint8_t sign = MPD_POS; - - if (a < 0) { - if (a == MPD_SSIZE_MIN) { - u = (mpd_uint_t)MPD_SSIZE_MAX + - (-(MPD_SSIZE_MIN+MPD_SSIZE_MAX)); - } - else { - u = -a; - } - sign = MPD_NEG; - } - else { - u = a; - } - _ssettriple(result, sign, u, 0); - mpd_qfinalize(result, ctx, status); -} - -/* quietly set a static decimal from an mpd_uint_t */ -void -mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - _ssettriple(result, MPD_POS, a, 0); - mpd_qfinalize(result, ctx, status); -} - -/* quietly set a static decimal from an int32_t */ -void -mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qsset_ssize(result, a, ctx, status); -} - -/* quietly set a static decimal from a uint32_t */ -void -mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qsset_uint(result, a, ctx, status); -} - -#ifdef CONFIG_64 -/* quietly set a static decimal from an int64_t */ -void -mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qsset_ssize(result, a, ctx, status); -} - -/* quietly set a static decimal from a uint64_t */ -void -mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qsset_uint(result, a, ctx, status); -} -#endif - -/* quietly set a decimal from an mpd_ssize_t */ -void -mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_minalloc(result); - mpd_qsset_ssize(result, a, ctx, status); -} - -/* quietly set a decimal from an mpd_uint_t */ -void -mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - _settriple(result, MPD_POS, a, 0); - mpd_qfinalize(result, ctx, status); -} - -/* quietly set a decimal from an int32_t */ -void -mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qset_ssize(result, a, ctx, status); -} - -/* quietly set a decimal from a uint32_t */ -void -mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_qset_uint(result, a, ctx, status); -} - -#if defined(CONFIG_32) && !defined(LEGACY_COMPILER) -/* set a decimal from a uint64_t */ -static void -_c32setu64(mpd_t *result, uint64_t u, uint8_t sign, uint32_t *status) -{ - mpd_uint_t w[3]; - uint64_t q; - int i, len; - - len = 0; - do { - q = u / MPD_RADIX; - w[len] = (mpd_uint_t)(u - q * MPD_RADIX); - u = q; len++; - } while (u != 0); - - if (!mpd_qresize(result, len, status)) { - return; - } - for (i = 0; i < len; i++) { - result->data[i] = w[i]; - } - - mpd_set_flags(result, sign); - result->exp = 0; - result->len = len; - mpd_setdigits(result); -} - -static void -_c32_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - _c32setu64(result, a, MPD_POS, status); - mpd_qfinalize(result, ctx, status); -} - -/* set a decimal from an int64_t */ -static void -_c32_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ - uint64_t u; - uint8_t sign = MPD_POS; - - if (a < 0) { - if (a == INT64_MIN) { - u = (uint64_t)INT64_MAX + (-(INT64_MIN+INT64_MAX)); - } - else { - u = -a; - } - sign = MPD_NEG; - } - else { - u = a; - } - _c32setu64(result, u, sign, status); - mpd_qfinalize(result, ctx, status); -} -#endif /* CONFIG_32 && !LEGACY_COMPILER */ - -#ifndef LEGACY_COMPILER -/* quietly set a decimal from an int64_t */ -void -mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ -#ifdef CONFIG_64 - mpd_qset_ssize(result, a, ctx, status); -#else - _c32_qset_i64(result, a, ctx, status); -#endif -} - -/* quietly set a decimal from an int64_t, use a maxcontext for conversion */ -void -mpd_qset_i64_exact(mpd_t *result, int64_t a, uint32_t *status) -{ - mpd_context_t maxcontext; - - mpd_maxcontext(&maxcontext); -#ifdef CONFIG_64 - mpd_qset_ssize(result, a, &maxcontext, status); -#else - _c32_qset_i64(result, a, &maxcontext, status); -#endif - - if (*status & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - /* we want exact results */ - mpd_seterror(result, MPD_Invalid_operation, status); - } - *status &= MPD_Errors; -} - -/* quietly set a decimal from a uint64_t */ -void -mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, - uint32_t *status) -{ -#ifdef CONFIG_64 - mpd_qset_uint(result, a, ctx, status); -#else - _c32_qset_u64(result, a, ctx, status); -#endif -} - -/* quietly set a decimal from a uint64_t, use a maxcontext for conversion */ -void -mpd_qset_u64_exact(mpd_t *result, uint64_t a, uint32_t *status) -{ - mpd_context_t maxcontext; - - mpd_maxcontext(&maxcontext); -#ifdef CONFIG_64 - mpd_qset_uint(result, a, &maxcontext, status); -#else - _c32_qset_u64(result, a, &maxcontext, status); -#endif - - if (*status & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - /* we want exact results */ - mpd_seterror(result, MPD_Invalid_operation, status); - } - *status &= MPD_Errors; -} -#endif /* !LEGACY_COMPILER */ - -/* - * Quietly get an mpd_uint_t from a decimal. Assumes - * MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for - * 32 and 64 bit machines. - * - * If the operation is impossible, MPD_Invalid_operation is set. - */ -static mpd_uint_t -_mpd_qget_uint(int use_sign, const mpd_t *a, uint32_t *status) -{ - mpd_t tmp; - mpd_uint_t tmp_data[2]; - mpd_uint_t lo, hi; - - if (mpd_isspecial(a)) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - if (mpd_iszero(a)) { - return 0; - } - if (use_sign && mpd_isnegative(a)) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - - if (a->digits+a->exp > MPD_RDIGITS+1) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - - if (a->exp < 0) { - if (!_mpd_isint(a)) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - /* At this point a->digits+a->exp <= MPD_RDIGITS+1, - * so the shift fits. */ - tmp.data = tmp_data; - tmp.flags = MPD_STATIC|MPD_STATIC_DATA; - tmp.alloc = 2; - mpd_qsshiftr(&tmp, a, -a->exp); - tmp.exp = 0; - a = &tmp; - } - - _mpd_get_msdigits(&hi, &lo, a, MPD_RDIGITS+1); - if (hi) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - - if (a->exp > 0) { - _mpd_mul_words(&hi, &lo, lo, mpd_pow10[a->exp]); - if (hi) { - *status |= MPD_Invalid_operation; - return MPD_UINT_MAX; - } - } - - return lo; -} - -/* - * Sets Invalid_operation for: - * - specials - * - negative numbers (except negative zero) - * - non-integers - * - overflow - */ -mpd_uint_t -mpd_qget_uint(const mpd_t *a, uint32_t *status) -{ - return _mpd_qget_uint(1, a, status); -} - -/* Same as above, but gets the absolute value, i.e. the sign is ignored. */ -mpd_uint_t -mpd_qabs_uint(const mpd_t *a, uint32_t *status) -{ - return _mpd_qget_uint(0, a, status); -} - -/* quietly get an mpd_ssize_t from a decimal */ -mpd_ssize_t -mpd_qget_ssize(const mpd_t *a, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_uint_t u; - int isneg; - - u = mpd_qabs_uint(a, &workstatus); - if (workstatus&MPD_Invalid_operation) { - *status |= workstatus; - return MPD_SSIZE_MAX; - } - - isneg = mpd_isnegative(a); - if (u <= MPD_SSIZE_MAX) { - return isneg ? -((mpd_ssize_t)u) : (mpd_ssize_t)u; - } - else if (isneg && u+(MPD_SSIZE_MIN+MPD_SSIZE_MAX) == MPD_SSIZE_MAX) { - return MPD_SSIZE_MIN; - } - - *status |= MPD_Invalid_operation; - return MPD_SSIZE_MAX; -} - -#if defined(CONFIG_32) && !defined(LEGACY_COMPILER) -/* - * Quietly get a uint64_t from a decimal. If the operation is impossible, - * MPD_Invalid_operation is set. - */ -static uint64_t -_c32_qget_u64(int use_sign, const mpd_t *a, uint32_t *status) -{ - MPD_NEW_STATIC(tmp,0,0,20,3); - mpd_context_t maxcontext; - uint64_t ret; - - tmp_data[0] = 709551615; - tmp_data[1] = 446744073; - tmp_data[2] = 18; - - if (mpd_isspecial(a)) { - *status |= MPD_Invalid_operation; - return UINT64_MAX; - } - if (mpd_iszero(a)) { - return 0; - } - if (use_sign && mpd_isnegative(a)) { - *status |= MPD_Invalid_operation; - return UINT64_MAX; - } - if (!_mpd_isint(a)) { - *status |= MPD_Invalid_operation; - return UINT64_MAX; - } - - if (_mpd_cmp_abs(a, &tmp) > 0) { - *status |= MPD_Invalid_operation; - return UINT64_MAX; - } - - mpd_maxcontext(&maxcontext); - mpd_qrescale(&tmp, a, 0, &maxcontext, &maxcontext.status); - maxcontext.status &= ~MPD_Rounded; - if (maxcontext.status != 0) { - *status |= (maxcontext.status|MPD_Invalid_operation); /* GCOV_NOT_REACHED */ - return UINT64_MAX; /* GCOV_NOT_REACHED */ - } - - ret = 0; - switch (tmp.len) { - case 3: - ret += (uint64_t)tmp_data[2] * 1000000000000000000ULL; - case 2: - ret += (uint64_t)tmp_data[1] * 1000000000ULL; - case 1: - ret += tmp_data[0]; - break; - default: - abort(); /* GCOV_NOT_REACHED */ - } - - return ret; -} - -static int64_t -_c32_qget_i64(const mpd_t *a, uint32_t *status) -{ - uint64_t u; - int isneg; - - u = _c32_qget_u64(0, a, status); - if (*status&MPD_Invalid_operation) { - return INT64_MAX; - } - - isneg = mpd_isnegative(a); - if (u <= INT64_MAX) { - return isneg ? -((int64_t)u) : (int64_t)u; - } - else if (isneg && u+(INT64_MIN+INT64_MAX) == INT64_MAX) { - return INT64_MIN; - } - - *status |= MPD_Invalid_operation; - return INT64_MAX; -} -#endif /* CONFIG_32 && !LEGACY_COMPILER */ - -#ifdef CONFIG_64 -/* quietly get a uint64_t from a decimal */ -uint64_t -mpd_qget_u64(const mpd_t *a, uint32_t *status) -{ - return mpd_qget_uint(a, status); -} - -/* quietly get an int64_t from a decimal */ -int64_t -mpd_qget_i64(const mpd_t *a, uint32_t *status) -{ - return mpd_qget_ssize(a, status); -} - -/* quietly get a uint32_t from a decimal */ -uint32_t -mpd_qget_u32(const mpd_t *a, uint32_t *status) -{ - uint32_t workstatus = 0; - uint64_t x = mpd_qget_uint(a, &workstatus); - - if (workstatus&MPD_Invalid_operation) { - *status |= workstatus; - return UINT32_MAX; - } - if (x > UINT32_MAX) { - *status |= MPD_Invalid_operation; - return UINT32_MAX; - } - - return (uint32_t)x; -} - -/* quietly get an int32_t from a decimal */ -int32_t -mpd_qget_i32(const mpd_t *a, uint32_t *status) -{ - uint32_t workstatus = 0; - int64_t x = mpd_qget_ssize(a, &workstatus); - - if (workstatus&MPD_Invalid_operation) { - *status |= workstatus; - return INT32_MAX; - } - if (x < INT32_MIN || x > INT32_MAX) { - *status |= MPD_Invalid_operation; - return INT32_MAX; - } - - return (int32_t)x; -} -#else -#ifndef LEGACY_COMPILER -/* quietly get a uint64_t from a decimal */ -uint64_t -mpd_qget_u64(const mpd_t *a, uint32_t *status) -{ - uint32_t workstatus = 0; - uint64_t x = _c32_qget_u64(1, a, &workstatus); - *status |= workstatus; - return x; -} - -/* quietly get an int64_t from a decimal */ -int64_t -mpd_qget_i64(const mpd_t *a, uint32_t *status) -{ - uint32_t workstatus = 0; - int64_t x = _c32_qget_i64(a, &workstatus); - *status |= workstatus; - return x; -} -#endif - -/* quietly get a uint32_t from a decimal */ -uint32_t -mpd_qget_u32(const mpd_t *a, uint32_t *status) -{ - return mpd_qget_uint(a, status); -} - -/* quietly get an int32_t from a decimal */ -int32_t -mpd_qget_i32(const mpd_t *a, uint32_t *status) -{ - return mpd_qget_ssize(a, status); -} -#endif - - -/******************************************************************************/ -/* Filtering input of functions, finalizing output of functions */ -/******************************************************************************/ - -/* - * Check if the operand is NaN, copy to result and return 1 if this is - * the case. Copying can fail since NaNs are allowed to have a payload that - * does not fit in MPD_MINALLOC. - */ -int -mpd_qcheck_nan(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isnan(a)) { - *status |= mpd_issnan(a) ? MPD_Invalid_operation : 0; - mpd_qcopy(result, a, status); - mpd_set_qnan(result); - _mpd_fix_nan(result, ctx); - return 1; - } - return 0; -} - -/* - * Check if either operand is NaN, copy to result and return 1 if this - * is the case. Copying can fail since NaNs are allowed to have a payload - * that does not fit in MPD_MINALLOC. - */ -int -mpd_qcheck_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - if ((a->flags|b->flags)&(MPD_NAN|MPD_SNAN)) { - const mpd_t *choice = b; - if (mpd_issnan(a)) { - choice = a; - *status |= MPD_Invalid_operation; - } - else if (mpd_issnan(b)) { - *status |= MPD_Invalid_operation; - } - else if (mpd_isqnan(a)) { - choice = a; - } - mpd_qcopy(result, choice, status); - mpd_set_qnan(result); - _mpd_fix_nan(result, ctx); - return 1; - } - return 0; -} - -/* - * Check if one of the operands is NaN, copy to result and return 1 if this - * is the case. Copying can fail since NaNs are allowed to have a payload - * that does not fit in MPD_MINALLOC. - */ -static int -mpd_qcheck_3nans(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, - const mpd_context_t *ctx, uint32_t *status) -{ - if ((a->flags|b->flags|c->flags)&(MPD_NAN|MPD_SNAN)) { - const mpd_t *choice = c; - if (mpd_issnan(a)) { - choice = a; - *status |= MPD_Invalid_operation; - } - else if (mpd_issnan(b)) { - choice = b; - *status |= MPD_Invalid_operation; - } - else if (mpd_issnan(c)) { - *status |= MPD_Invalid_operation; - } - else if (mpd_isqnan(a)) { - choice = a; - } - else if (mpd_isqnan(b)) { - choice = b; - } - mpd_qcopy(result, choice, status); - mpd_set_qnan(result); - _mpd_fix_nan(result, ctx); - return 1; - } - return 0; -} - -/* Check if rounding digit 'rnd' leads to an increment. */ -static inline int -_mpd_rnd_incr(const mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx) -{ - int ld; - - switch (ctx->round) { - case MPD_ROUND_DOWN: case MPD_ROUND_TRUNC: - return 0; - case MPD_ROUND_HALF_UP: - return (rnd >= 5); - case MPD_ROUND_HALF_EVEN: - return (rnd > 5) || ((rnd == 5) && mpd_isoddcoeff(dec)); - case MPD_ROUND_CEILING: - return !(rnd == 0 || mpd_isnegative(dec)); - case MPD_ROUND_FLOOR: - return !(rnd == 0 || mpd_ispositive(dec)); - case MPD_ROUND_HALF_DOWN: - return (rnd > 5); - case MPD_ROUND_UP: - return !(rnd == 0); - case MPD_ROUND_05UP: - ld = (int)mpd_lsd(dec->data[0]); - return (!(rnd == 0) && (ld == 0 || ld == 5)); - default: - /* Without a valid context, further results will be undefined. */ - return 0; /* GCOV_NOT_REACHED */ - } -} - -/* - * Apply rounding to a decimal that has been right-shifted into a full - * precision decimal. If an increment leads to an overflow of the precision, - * adjust the coefficient and the exponent and check the new exponent for - * overflow. - */ -static inline void -_mpd_apply_round(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx, - uint32_t *status) -{ - if (_mpd_rnd_incr(dec, rnd, ctx)) { - /* We have a number with exactly ctx->prec digits. The increment - * can only lead to an overflow if the decimal is all nines. In - * that case, the result is a power of ten with prec+1 digits. - * - * If the precision is a multiple of MPD_RDIGITS, this situation is - * detected by _mpd_baseincr returning a carry. - * If the precision is not a multiple of MPD_RDIGITS, we have to - * check if the result has one digit too many. - */ - mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len); - if (carry) { - dec->data[dec->len-1] = mpd_pow10[MPD_RDIGITS-1]; - dec->exp += 1; - _mpd_check_exp(dec, ctx, status); - return; - } - mpd_setdigits(dec); - if (dec->digits > ctx->prec) { - mpd_qshiftr_inplace(dec, 1); - dec->exp += 1; - dec->digits = ctx->prec; - _mpd_check_exp(dec, ctx, status); - } - } -} - -/* - * Apply rounding to a decimal. Allow overflow of the precision. - */ -static inline void -_mpd_apply_round_excess(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx, - uint32_t *status) -{ - if (_mpd_rnd_incr(dec, rnd, ctx)) { - mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len); - if (carry) { - if (!mpd_qresize(dec, dec->len+1, status)) { - return; - } - dec->data[dec->len] = 1; - dec->len += 1; - } - mpd_setdigits(dec); - } -} - -/* - * Apply rounding to a decimal that has been right-shifted into a decimal - * with full precision or less. Return failure if an increment would - * overflow the precision. - */ -static inline int -_mpd_apply_round_fit(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx, - uint32_t *status) -{ - if (_mpd_rnd_incr(dec, rnd, ctx)) { - mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len); - if (carry) { - if (!mpd_qresize(dec, dec->len+1, status)) { - return 0; - } - dec->data[dec->len] = 1; - dec->len += 1; - } - mpd_setdigits(dec); - if (dec->digits > ctx->prec) { - mpd_seterror(dec, MPD_Invalid_operation, status); - return 0; - } - } - return 1; -} - -/* Check a normal number for overflow, underflow, clamping. If the operand - is modified, it will be zero, special or (sub)normal with a coefficient - that fits into the current context precision. */ -static inline void -_mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t adjexp, etiny, shift; - int rnd; - - adjexp = mpd_adjexp(dec); - if (adjexp > ctx->emax) { - - if (mpd_iszerocoeff(dec)) { - dec->exp = ctx->emax; - if (ctx->clamp) { - dec->exp -= (ctx->prec-1); - } - mpd_zerocoeff(dec); - *status |= MPD_Clamped; - return; - } - - switch (ctx->round) { - case MPD_ROUND_HALF_UP: case MPD_ROUND_HALF_EVEN: - case MPD_ROUND_HALF_DOWN: case MPD_ROUND_UP: - case MPD_ROUND_TRUNC: - mpd_setspecial(dec, mpd_sign(dec), MPD_INF); - break; - case MPD_ROUND_DOWN: case MPD_ROUND_05UP: - mpd_qmaxcoeff(dec, ctx, status); - dec->exp = ctx->emax - ctx->prec + 1; - break; - case MPD_ROUND_CEILING: - if (mpd_isnegative(dec)) { - mpd_qmaxcoeff(dec, ctx, status); - dec->exp = ctx->emax - ctx->prec + 1; - } - else { - mpd_setspecial(dec, MPD_POS, MPD_INF); - } - break; - case MPD_ROUND_FLOOR: - if (mpd_ispositive(dec)) { - mpd_qmaxcoeff(dec, ctx, status); - dec->exp = ctx->emax - ctx->prec + 1; - } - else { - mpd_setspecial(dec, MPD_NEG, MPD_INF); - } - break; - default: /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - - *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; - - } /* fold down */ - else if (ctx->clamp && dec->exp > mpd_etop(ctx)) { - /* At this point adjexp=exp+digits-1 <= emax and exp > etop=emax-prec+1: - * (1) shift = exp -emax+prec-1 > 0 - * (2) digits+shift = exp+digits-1 - emax + prec <= prec */ - shift = dec->exp - mpd_etop(ctx); - if (!mpd_qshiftl(dec, dec, shift, status)) { - return; - } - dec->exp -= shift; - *status |= MPD_Clamped; - if (!mpd_iszerocoeff(dec) && adjexp < ctx->emin) { - /* Underflow is impossible, since exp < etiny=emin-prec+1 - * and exp > etop=emax-prec+1 would imply emax < emin. */ - *status |= MPD_Subnormal; - } - } - else if (adjexp < ctx->emin) { - - etiny = mpd_etiny(ctx); - - if (mpd_iszerocoeff(dec)) { - if (dec->exp < etiny) { - dec->exp = etiny; - mpd_zerocoeff(dec); - *status |= MPD_Clamped; - } - return; - } - - *status |= MPD_Subnormal; - if (dec->exp < etiny) { - /* At this point adjexp=exp+digits-1 < emin and exp < etiny=emin-prec+1: - * (1) shift = emin-prec+1 - exp > 0 - * (2) digits-shift = exp+digits-1 - emin + prec < prec */ - shift = etiny - dec->exp; - rnd = (int)mpd_qshiftr_inplace(dec, shift); - dec->exp = etiny; - /* We always have a spare digit in case of an increment. */ - _mpd_apply_round_excess(dec, rnd, ctx, status); - *status |= MPD_Rounded; - if (rnd) { - *status |= (MPD_Inexact|MPD_Underflow); - if (mpd_iszerocoeff(dec)) { - mpd_zerocoeff(dec); - *status |= MPD_Clamped; - } - } - } - /* Case exp >= etiny=emin-prec+1: - * (1) adjexp=exp+digits-1 < emin - * (2) digits < emin-exp+1 <= prec */ - } -} - -/* Transcendental functions do not always set Underflow reliably, - * since they only use as much precision as is necessary for correct - * rounding. If a result like 1.0000000000e-101 is finalized, there - * is no rounding digit that would trigger Underflow. But we can - * assume Inexact, so a short check suffices. */ -static inline void -mpd_check_underflow(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_adjexp(dec) < ctx->emin && !mpd_iszero(dec) && - dec->exp < mpd_etiny(ctx)) { - *status |= MPD_Underflow; - } -} - -/* Check if a normal number must be rounded after the exponent has been checked. */ -static inline void -_mpd_check_round(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status) -{ - mpd_uint_t rnd; - mpd_ssize_t shift; - - /* must handle specials: _mpd_check_exp() can produce infinities or NaNs */ - if (mpd_isspecial(dec)) { - return; - } - - if (dec->digits > ctx->prec) { - shift = dec->digits - ctx->prec; - rnd = mpd_qshiftr_inplace(dec, shift); - dec->exp += shift; - _mpd_apply_round(dec, rnd, ctx, status); - *status |= MPD_Rounded; - if (rnd) { - *status |= MPD_Inexact; - } - } -} - -/* Finalize all operations. */ -void -mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_isspecial(result)) { - if (mpd_isnan(result)) { - _mpd_fix_nan(result, ctx); - } - return; - } - - _mpd_check_exp(result, ctx, status); - _mpd_check_round(result, ctx, status); -} - - -/******************************************************************************/ -/* Copying */ -/******************************************************************************/ - -/* Internal function: Copy a decimal, share data with src: USE WITH CARE! */ -static inline void -_mpd_copy_shared(mpd_t *dest, const mpd_t *src) -{ - dest->flags = src->flags; - dest->exp = src->exp; - dest->digits = src->digits; - dest->len = src->len; - dest->alloc = src->alloc; - dest->data = src->data; - - mpd_set_shared_data(dest); -} - -/* - * Copy a decimal. In case of an error, status is set to MPD_Malloc_error. - */ -int -mpd_qcopy(mpd_t *result, const mpd_t *a, uint32_t *status) -{ - if (result == a) return 1; - - if (!mpd_qresize(result, a->len, status)) { - return 0; - } - - mpd_copy_flags(result, a); - result->exp = a->exp; - result->digits = a->digits; - result->len = a->len; - memcpy(result->data, a->data, a->len * (sizeof *result->data)); - - return 1; -} - -/* Same as mpd_qcopy, but do not set the result to NaN on failure. */ -int -mpd_qcopy_cxx(mpd_t *result, const mpd_t *a) -{ - if (result == a) return 1; - - if (!mpd_qresize_cxx(result, a->len)) { - return 0; - } - - mpd_copy_flags(result, a); - result->exp = a->exp; - result->digits = a->digits; - result->len = a->len; - memcpy(result->data, a->data, a->len * (sizeof *result->data)); - - return 1; -} - -/* - * Copy to a decimal with a static buffer. The caller has to make sure that - * the buffer is big enough. Cannot fail. - */ -static void -mpd_qcopy_static(mpd_t *result, const mpd_t *a) -{ - if (result == a) return; - - memcpy(result->data, a->data, a->len * (sizeof *result->data)); - - mpd_copy_flags(result, a); - result->exp = a->exp; - result->digits = a->digits; - result->len = a->len; -} - -/* - * Return a newly allocated copy of the operand. In case of an error, - * status is set to MPD_Malloc_error and the return value is NULL. - */ -mpd_t * -mpd_qncopy(const mpd_t *a) -{ - mpd_t *result; - - if ((result = mpd_qnew_size(a->len)) == NULL) { - return NULL; - } - memcpy(result->data, a->data, a->len * (sizeof *result->data)); - mpd_copy_flags(result, a); - result->exp = a->exp; - result->digits = a->digits; - result->len = a->len; - - return result; -} - -/* - * Copy a decimal and set the sign to positive. In case of an error, the - * status is set to MPD_Malloc_error. - */ -int -mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status) -{ - if (!mpd_qcopy(result, a, status)) { - return 0; - } - mpd_set_positive(result); - return 1; -} - -/* - * Copy a decimal and negate the sign. In case of an error, the - * status is set to MPD_Malloc_error. - */ -int -mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status) -{ - if (!mpd_qcopy(result, a, status)) { - return 0; - } - _mpd_negate(result); - return 1; -} - -/* - * Copy a decimal, setting the sign of the first operand to the sign of the - * second operand. In case of an error, the status is set to MPD_Malloc_error. - */ -int -mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status) -{ - uint8_t sign_b = mpd_sign(b); /* result may equal b! */ - - if (!mpd_qcopy(result, a, status)) { - return 0; - } - mpd_set_sign(result, sign_b); - return 1; -} - - -/******************************************************************************/ -/* Comparisons */ -/******************************************************************************/ - -/* - * For all functions that compare two operands and return an int the usual - * convention applies to the return value: - * - * -1 if op1 < op2 - * 0 if op1 == op2 - * 1 if op1 > op2 - * - * INT_MAX for error - */ - - -/* Convenience macro. If a and b are not equal, return from the calling - * function with the correct comparison value. */ -#define CMP_EQUAL_OR_RETURN(a, b) \ - if (a != b) { \ - if (a < b) { \ - return -1; \ - } \ - return 1; \ - } - -/* - * Compare the data of big and small. This function does the equivalent - * of first shifting small to the left and then comparing the data of - * big and small, except that no allocation for the left shift is needed. - */ -static int -_mpd_basecmp(mpd_uint_t *big, mpd_uint_t *small, mpd_size_t n, mpd_size_t m, - mpd_size_t shift) -{ -#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__) - /* spurious uninitialized warnings */ - mpd_uint_t l=l, lprev=lprev, h=h; -#else - mpd_uint_t l, lprev, h; -#endif - mpd_uint_t q, r; - mpd_uint_t ph, x; - - assert(m > 0 && n >= m && shift > 0); - - _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS); - - if (r != 0) { - - ph = mpd_pow10[r]; - - --m; --n; - _mpd_divmod_pow10(&h, &lprev, small[m--], MPD_RDIGITS-r); - if (h != 0) { - CMP_EQUAL_OR_RETURN(big[n], h) - --n; - } - for (; m != MPD_SIZE_MAX; m--,n--) { - _mpd_divmod_pow10(&h, &l, small[m], MPD_RDIGITS-r); - x = ph * lprev + h; - CMP_EQUAL_OR_RETURN(big[n], x) - lprev = l; - } - x = ph * lprev; - CMP_EQUAL_OR_RETURN(big[q], x) - } - else { - while (--m != MPD_SIZE_MAX) { - CMP_EQUAL_OR_RETURN(big[m+q], small[m]) - } - } - - return !_mpd_isallzero(big, q); -} - -/* Compare two decimals with the same adjusted exponent. */ -static int -_mpd_cmp_same_adjexp(const mpd_t *a, const mpd_t *b) -{ - mpd_ssize_t shift, i; - - if (a->exp != b->exp) { - /* Cannot wrap: a->exp + a->digits = b->exp + b->digits, so - * a->exp - b->exp = b->digits - a->digits. */ - shift = a->exp - b->exp; - if (shift > 0) { - return -1 * _mpd_basecmp(b->data, a->data, b->len, a->len, shift); - } - else { - return _mpd_basecmp(a->data, b->data, a->len, b->len, -shift); - } - } - - /* - * At this point adjexp(a) == adjexp(b) and a->exp == b->exp, - * so a->digits == b->digits, therefore a->len == b->len. - */ - for (i = a->len-1; i >= 0; --i) { - CMP_EQUAL_OR_RETURN(a->data[i], b->data[i]) - } - - return 0; -} - -/* Compare two numerical values. */ -static int -_mpd_cmp(const mpd_t *a, const mpd_t *b) -{ - mpd_ssize_t adjexp_a, adjexp_b; - - /* equal pointers */ - if (a == b) { - return 0; - } - - /* infinities */ - if (mpd_isinfinite(a)) { - if (mpd_isinfinite(b)) { - return mpd_isnegative(b) - mpd_isnegative(a); - } - return mpd_arith_sign(a); - } - if (mpd_isinfinite(b)) { - return -mpd_arith_sign(b); - } - - /* zeros */ - if (mpd_iszerocoeff(a)) { - if (mpd_iszerocoeff(b)) { - return 0; - } - return -mpd_arith_sign(b); - } - if (mpd_iszerocoeff(b)) { - return mpd_arith_sign(a); - } - - /* different signs */ - if (mpd_sign(a) != mpd_sign(b)) { - return mpd_sign(b) - mpd_sign(a); - } - - /* different adjusted exponents */ - adjexp_a = mpd_adjexp(a); - adjexp_b = mpd_adjexp(b); - if (adjexp_a != adjexp_b) { - if (adjexp_a < adjexp_b) { - return -1 * mpd_arith_sign(a); - } - return mpd_arith_sign(a); - } - - /* same adjusted exponents */ - return _mpd_cmp_same_adjexp(a, b) * mpd_arith_sign(a); -} - -/* Compare the absolutes of two numerical values. */ -static int -_mpd_cmp_abs(const mpd_t *a, const mpd_t *b) -{ - mpd_ssize_t adjexp_a, adjexp_b; - - /* equal pointers */ - if (a == b) { - return 0; - } - - /* infinities */ - if (mpd_isinfinite(a)) { - if (mpd_isinfinite(b)) { - return 0; - } - return 1; - } - if (mpd_isinfinite(b)) { - return -1; - } - - /* zeros */ - if (mpd_iszerocoeff(a)) { - if (mpd_iszerocoeff(b)) { - return 0; - } - return -1; - } - if (mpd_iszerocoeff(b)) { - return 1; - } - - /* different adjusted exponents */ - adjexp_a = mpd_adjexp(a); - adjexp_b = mpd_adjexp(b); - if (adjexp_a != adjexp_b) { - if (adjexp_a < adjexp_b) { - return -1; - } - return 1; - } - - /* same adjusted exponents */ - return _mpd_cmp_same_adjexp(a, b); -} - -/* Compare two values and return an integer result. */ -int -mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status) -{ - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_isnan(a) || mpd_isnan(b)) { - *status |= MPD_Invalid_operation; - return INT_MAX; - } - } - - return _mpd_cmp(a, b); -} - -/* - * Compare a and b, convert the usual integer result to a decimal and - * store it in 'result'. For convenience, the integer result of the comparison - * is returned. Comparisons involving NaNs return NaN/INT_MAX. - */ -int -mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return INT_MAX; - } - } - - c = _mpd_cmp(a, b); - _settriple(result, (c < 0), (c != 0), 0); - return c; -} - -/* Same as mpd_compare(), but signal for all NaNs, i.e. also for quiet NaNs. */ -int -mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - *status |= MPD_Invalid_operation; - return INT_MAX; - } - } - - c = _mpd_cmp(a, b); - _settriple(result, (c < 0), (c != 0), 0); - return c; -} - -/* Compare the operands using a total order. */ -int -mpd_cmp_total(const mpd_t *a, const mpd_t *b) -{ - mpd_t aa, bb; - int nan_a, nan_b; - int c; - - if (mpd_sign(a) != mpd_sign(b)) { - return mpd_sign(b) - mpd_sign(a); - } - - - if (mpd_isnan(a)) { - c = 1; - if (mpd_isnan(b)) { - nan_a = (mpd_isqnan(a)) ? 1 : 0; - nan_b = (mpd_isqnan(b)) ? 1 : 0; - if (nan_b == nan_a) { - if (a->len > 0 && b->len > 0) { - _mpd_copy_shared(&aa, a); - _mpd_copy_shared(&bb, b); - aa.exp = bb.exp = 0; - /* compare payload */ - c = _mpd_cmp_abs(&aa, &bb); - } - else { - c = (a->len > 0) - (b->len > 0); - } - } - else { - c = nan_a - nan_b; - } - } - } - else if (mpd_isnan(b)) { - c = -1; - } - else { - c = _mpd_cmp_abs(a, b); - if (c == 0 && a->exp != b->exp) { - c = (a->exp < b->exp) ? -1 : 1; - } - } - - return c * mpd_arith_sign(a); -} - -/* - * Compare a and b according to a total order, convert the usual integer result - * to a decimal and store it in 'result'. For convenience, the integer result - * of the comparison is returned. - */ -int -mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b) -{ - int c; - - c = mpd_cmp_total(a, b); - _settriple(result, (c < 0), (c != 0), 0); - return c; -} - -/* Compare the magnitude of the operands using a total order. */ -int -mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b) -{ - mpd_t aa, bb; - - _mpd_copy_shared(&aa, a); - _mpd_copy_shared(&bb, b); - - mpd_set_positive(&aa); - mpd_set_positive(&bb); - - return mpd_cmp_total(&aa, &bb); -} - -/* - * Compare the magnitude of a and b according to a total order, convert the - * the usual integer result to a decimal and store it in 'result'. - * For convenience, the integer result of the comparison is returned. - */ -int -mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b) -{ - int c; - - c = mpd_cmp_total_mag(a, b); - _settriple(result, (c < 0), (c != 0), 0); - return c; -} - -/* Determine an ordering for operands that are numerically equal. */ -static inline int -_mpd_cmp_numequal(const mpd_t *a, const mpd_t *b) -{ - int sign_a, sign_b; - int c; - - sign_a = mpd_sign(a); - sign_b = mpd_sign(b); - if (sign_a != sign_b) { - c = sign_b - sign_a; - } - else { - c = (a->exp < b->exp) ? -1 : 1; - c *= mpd_arith_sign(a); - } - - return c; -} - - -/******************************************************************************/ -/* Shifting the coefficient */ -/******************************************************************************/ - -/* - * Shift the coefficient of the operand to the left, no check for specials. - * Both operands may be the same pointer. If the result length has to be - * increased, mpd_qresize() might fail with MPD_Malloc_error. - */ -int -mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status) -{ - mpd_ssize_t size; - - assert(!mpd_isspecial(a)); - assert(n >= 0); - - if (mpd_iszerocoeff(a) || n == 0) { - return mpd_qcopy(result, a, status); - } - - size = mpd_digits_to_size(a->digits+n); - if (!mpd_qresize(result, size, status)) { - return 0; /* result is NaN */ - } - - _mpd_baseshiftl(result->data, a->data, size, a->len, n); - - mpd_copy_flags(result, a); - result->exp = a->exp; - result->digits = a->digits+n; - result->len = size; - - return 1; -} - -/* Determine the rounding indicator if all digits of the coefficient are shifted - * out of the picture. */ -static mpd_uint_t -_mpd_get_rnd(const mpd_uint_t *data, mpd_ssize_t len, int use_msd) -{ - mpd_uint_t rnd = 0, rest = 0, word; - - word = data[len-1]; - /* special treatment for the most significant digit if shift == digits */ - if (use_msd) { - _mpd_divmod_pow10(&rnd, &rest, word, mpd_word_digits(word)-1); - if (len > 1 && rest == 0) { - rest = !_mpd_isallzero(data, len-1); - } - } - else { - rest = !_mpd_isallzero(data, len); - } - - return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd; -} - -/* - * Same as mpd_qshiftr(), but 'result' is an mpd_t with a static coefficient. - * It is the caller's responsibility to ensure that the coefficient is big - * enough. The function cannot fail. - */ -static mpd_uint_t -mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n) -{ - mpd_uint_t rnd; - mpd_ssize_t size; - - assert(!mpd_isspecial(a)); - assert(n >= 0); - - if (mpd_iszerocoeff(a) || n == 0) { - mpd_qcopy_static(result, a); - return 0; - } - - if (n >= a->digits) { - rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits)); - mpd_zerocoeff(result); - } - else { - result->digits = a->digits-n; - size = mpd_digits_to_size(result->digits); - rnd = _mpd_baseshiftr(result->data, a->data, a->len, n); - result->len = size; - } - - mpd_copy_flags(result, a); - result->exp = a->exp; - - return rnd; -} - -/* - * Inplace shift of the coefficient to the right, no check for specials. - * Returns the rounding indicator for mpd_rnd_incr(). - * The function cannot fail. - */ -mpd_uint_t -mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n) -{ - uint32_t dummy; - mpd_uint_t rnd; - mpd_ssize_t size; - - assert(!mpd_isspecial(result)); - assert(n >= 0); - - if (mpd_iszerocoeff(result) || n == 0) { - return 0; - } - - if (n >= result->digits) { - rnd = _mpd_get_rnd(result->data, result->len, (n==result->digits)); - mpd_zerocoeff(result); - } - else { - rnd = _mpd_baseshiftr(result->data, result->data, result->len, n); - result->digits -= n; - size = mpd_digits_to_size(result->digits); - /* reducing the size cannot fail */ - mpd_qresize(result, size, &dummy); - result->len = size; - } - - return rnd; -} - -/* - * Shift the coefficient of the operand to the right, no check for specials. - * Both operands may be the same pointer. Returns the rounding indicator to - * be used by mpd_rnd_incr(). If the result length has to be increased, - * mpd_qcopy() or mpd_qresize() might fail with MPD_Malloc_error. In those - * cases, MPD_UINT_MAX is returned. - */ -mpd_uint_t -mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status) -{ - mpd_uint_t rnd; - mpd_ssize_t size; - - assert(!mpd_isspecial(a)); - assert(n >= 0); - - if (mpd_iszerocoeff(a) || n == 0) { - if (!mpd_qcopy(result, a, status)) { - return MPD_UINT_MAX; - } - return 0; - } - - if (n >= a->digits) { - rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits)); - mpd_zerocoeff(result); - } - else { - result->digits = a->digits-n; - size = mpd_digits_to_size(result->digits); - if (result == a) { - rnd = _mpd_baseshiftr(result->data, a->data, a->len, n); - /* reducing the size cannot fail */ - mpd_qresize(result, size, status); - } - else { - if (!mpd_qresize(result, size, status)) { - return MPD_UINT_MAX; - } - rnd = _mpd_baseshiftr(result->data, a->data, a->len, n); - } - result->len = size; - } - - mpd_copy_flags(result, a); - result->exp = a->exp; - - return rnd; -} - - -/******************************************************************************/ -/* Miscellaneous operations */ -/******************************************************************************/ - -/* Logical And */ -void -mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big = a, *small = b; - mpd_uint_t x, y, z, xbit, ybit; - int k, mswdigits; - mpd_ssize_t i; - - if (mpd_isspecial(a) || mpd_isspecial(b) || - mpd_isnegative(a) || mpd_isnegative(b) || - a->exp != 0 || b->exp != 0) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (b->digits > a->digits) { - big = b; - small = a; - } - if (!mpd_qresize(result, big->len, status)) { - return; - } - - - /* full words */ - for (i = 0; i < small->len-1; i++) { - x = small->data[i]; - y = big->data[i]; - z = 0; - for (k = 0; k < MPD_RDIGITS; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit&ybit) ? mpd_pow10[k] : 0; - } - result->data[i] = z; - } - /* most significant word of small */ - x = small->data[i]; - y = big->data[i]; - z = 0; - mswdigits = mpd_word_digits(x); - for (k = 0; k < mswdigits; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit&ybit) ? mpd_pow10[k] : 0; - } - result->data[i++] = z; - - /* scan the rest of y for digits > 1 */ - for (; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - } - /* scan the rest of big for digits > 1 */ - for (; i < big->len; i++) { - y = big->data[i]; - for (k = 0; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - } - } - - mpd_clear_flags(result); - result->exp = 0; - result->len = _mpd_real_size(result->data, small->len); - mpd_qresize(result, result->len, status); - mpd_setdigits(result); - _mpd_cap(result, ctx); - return; - -invalid_operation: - mpd_seterror(result, MPD_Invalid_operation, status); -} - -/* Class of an operand. Returns a pointer to the constant name. */ -const char * -mpd_class(const mpd_t *a, const mpd_context_t *ctx) -{ - if (mpd_isnan(a)) { - if (mpd_isqnan(a)) - return "NaN"; - else - return "sNaN"; - } - else if (mpd_ispositive(a)) { - if (mpd_isinfinite(a)) - return "+Infinity"; - else if (mpd_iszero(a)) - return "+Zero"; - else if (mpd_isnormal(a, ctx)) - return "+Normal"; - else - return "+Subnormal"; - } - else { - if (mpd_isinfinite(a)) - return "-Infinity"; - else if (mpd_iszero(a)) - return "-Zero"; - else if (mpd_isnormal(a, ctx)) - return "-Normal"; - else - return "-Subnormal"; - } -} - -/* Logical Xor */ -void -mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_uint_t x, z, xbit; - mpd_ssize_t i, digits, len; - mpd_ssize_t q, r; - int k; - - if (mpd_isspecial(a) || mpd_isnegative(a) || a->exp != 0) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - digits = (a->digits < ctx->prec) ? ctx->prec : a->digits; - _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS); - len = (r == 0) ? q : q+1; - if (!mpd_qresize(result, len, status)) { - return; - } - - for (i = 0; i < len; i++) { - x = (i < a->len) ? a->data[i] : 0; - z = 0; - for (k = 0; k < MPD_RDIGITS; k++) { - xbit = x % 10; - x /= 10; - if (xbit > 1) { - goto invalid_operation; - } - z += !xbit ? mpd_pow10[k] : 0; - } - result->data[i] = z; - } - - mpd_clear_flags(result); - result->exp = 0; - result->len = _mpd_real_size(result->data, len); - mpd_qresize(result, result->len, status); - mpd_setdigits(result); - _mpd_cap(result, ctx); - return; - -invalid_operation: - mpd_seterror(result, MPD_Invalid_operation, status); -} - -/* Exponent of the magnitude of the most significant digit of the operand. */ -void -mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - mpd_setspecial(result, MPD_POS, MPD_INF); - } - else if (mpd_iszerocoeff(a)) { - mpd_setspecial(result, MPD_NEG, MPD_INF); - *status |= MPD_Division_by_zero; - } - else { - mpd_qset_ssize(result, mpd_adjexp(a), ctx, status); - } -} - -/* Logical Or */ -void -mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big = a, *small = b; - mpd_uint_t x, y, z, xbit, ybit; - int k, mswdigits; - mpd_ssize_t i; - - if (mpd_isspecial(a) || mpd_isspecial(b) || - mpd_isnegative(a) || mpd_isnegative(b) || - a->exp != 0 || b->exp != 0) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (b->digits > a->digits) { - big = b; - small = a; - } - if (!mpd_qresize(result, big->len, status)) { - return; - } - - - /* full words */ - for (i = 0; i < small->len-1; i++) { - x = small->data[i]; - y = big->data[i]; - z = 0; - for (k = 0; k < MPD_RDIGITS; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit|ybit) ? mpd_pow10[k] : 0; - } - result->data[i] = z; - } - /* most significant word of small */ - x = small->data[i]; - y = big->data[i]; - z = 0; - mswdigits = mpd_word_digits(x); - for (k = 0; k < mswdigits; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit|ybit) ? mpd_pow10[k] : 0; - } - - /* scan for digits > 1 and copy the rest of y */ - for (; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - z += ybit*mpd_pow10[k]; - } - result->data[i++] = z; - /* scan for digits > 1 and copy the rest of big */ - for (; i < big->len; i++) { - y = big->data[i]; - for (k = 0; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - } - result->data[i] = big->data[i]; - } - - mpd_clear_flags(result); - result->exp = 0; - result->len = _mpd_real_size(result->data, big->len); - mpd_qresize(result, result->len, status); - mpd_setdigits(result); - _mpd_cap(result, ctx); - return; - -invalid_operation: - mpd_seterror(result, MPD_Invalid_operation, status); -} - -/* - * Rotate the coefficient of 'a' by 'b' digits. 'b' must be an integer with - * exponent 0. - */ -void -mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - MPD_NEW_STATIC(tmp,0,0,0,0); - MPD_NEW_STATIC(big,0,0,0,0); - MPD_NEW_STATIC(small,0,0,0,0); - mpd_ssize_t n, lshift, rshift; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - } - if (b->exp != 0 || mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - n = mpd_qget_ssize(b, &workstatus); - if (workstatus&MPD_Invalid_operation) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (n > ctx->prec || n < -ctx->prec) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(a)) { - mpd_qcopy(result, a, status); - return; - } - - if (n >= 0) { - lshift = n; - rshift = ctx->prec-n; - } - else { - lshift = ctx->prec+n; - rshift = -n; - } - - if (a->digits > ctx->prec) { - if (!mpd_qcopy(&tmp, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - _mpd_cap(&tmp, ctx); - a = &tmp; - } - - if (!mpd_qshiftl(&big, a, lshift, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - _mpd_cap(&big, ctx); - - if (mpd_qshiftr(&small, a, rshift, status) == MPD_UINT_MAX) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - _mpd_qadd(result, &big, &small, ctx, status); - - -finish: - mpd_del(&tmp); - mpd_del(&big); - mpd_del(&small); -} - -/* - * b must be an integer with exponent 0 and in the range +-2*(emax + prec). - * XXX: In my opinion +-(2*emax + prec) would be more sensible. - * The result is a with the value of b added to its exponent. - */ -void -mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_uint_t n, maxjump; -#ifndef LEGACY_COMPILER - int64_t exp; -#else - mpd_uint_t x; - int x_sign, n_sign; - mpd_ssize_t exp; -#endif - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - } - if (b->exp != 0 || mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - n = mpd_qabs_uint(b, &workstatus); - /* the spec demands this */ - maxjump = 2 * (mpd_uint_t)(ctx->emax + ctx->prec); - - if (n > maxjump || workstatus&MPD_Invalid_operation) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(a)) { - mpd_qcopy(result, a, status); - return; - } - -#ifndef LEGACY_COMPILER - exp = a->exp + (int64_t)n * mpd_arith_sign(b); - exp = (exp > MPD_EXP_INF) ? MPD_EXP_INF : exp; - exp = (exp < MPD_EXP_CLAMP) ? MPD_EXP_CLAMP : exp; -#else - x = (a->exp < 0) ? -a->exp : a->exp; - x_sign = (a->exp < 0) ? 1 : 0; - n_sign = mpd_isnegative(b) ? 1 : 0; - - if (x_sign == n_sign) { - x = x + n; - if (x < n) x = MPD_UINT_MAX; - } - else { - x_sign = (x >= n) ? x_sign : n_sign; - x = (x >= n) ? x - n : n - x; - } - if (!x_sign && x > MPD_EXP_INF) x = MPD_EXP_INF; - if (x_sign && x > -MPD_EXP_CLAMP) x = -MPD_EXP_CLAMP; - exp = x_sign ? -((mpd_ssize_t)x) : (mpd_ssize_t)x; -#endif - - mpd_qcopy(result, a, status); - result->exp = (mpd_ssize_t)exp; - - mpd_qfinalize(result, ctx, status); -} - -/* - * Shift the coefficient by n digits, positive n is a left shift. In the case - * of a left shift, the result is decapitated to fit the context precision. If - * you don't want that, use mpd_shiftl(). - */ -void -mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - mpd_qcopy(result, a, status); - return; - } - - if (n >= 0 && n <= ctx->prec) { - mpd_qshiftl(result, a, n, status); - _mpd_cap(result, ctx); - } - else if (n < 0 && n >= -ctx->prec) { - if (!mpd_qcopy(result, a, status)) { - return; - } - _mpd_cap(result, ctx); - mpd_qshiftr_inplace(result, -n); - } - else { - mpd_seterror(result, MPD_Invalid_operation, status); - } -} - -/* - * Same as mpd_shiftn(), but the shift is specified by the decimal b, which - * must be an integer with a zero exponent. Infinities remain infinities. - */ -void -mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, - uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_ssize_t n; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - } - if (b->exp != 0 || mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - n = mpd_qget_ssize(b, &workstatus); - if (workstatus&MPD_Invalid_operation) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (n > ctx->prec || n < -ctx->prec) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(a)) { - mpd_qcopy(result, a, status); - return; - } - - if (n >= 0) { - mpd_qshiftl(result, a, n, status); - _mpd_cap(result, ctx); - } - else { - if (!mpd_qcopy(result, a, status)) { - return; - } - _mpd_cap(result, ctx); - mpd_qshiftr_inplace(result, -n); - } -} - -/* Logical Xor */ -void -mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big = a, *small = b; - mpd_uint_t x, y, z, xbit, ybit; - int k, mswdigits; - mpd_ssize_t i; - - if (mpd_isspecial(a) || mpd_isspecial(b) || - mpd_isnegative(a) || mpd_isnegative(b) || - a->exp != 0 || b->exp != 0) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (b->digits > a->digits) { - big = b; - small = a; - } - if (!mpd_qresize(result, big->len, status)) { - return; - } - - - /* full words */ - for (i = 0; i < small->len-1; i++) { - x = small->data[i]; - y = big->data[i]; - z = 0; - for (k = 0; k < MPD_RDIGITS; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit^ybit) ? mpd_pow10[k] : 0; - } - result->data[i] = z; - } - /* most significant word of small */ - x = small->data[i]; - y = big->data[i]; - z = 0; - mswdigits = mpd_word_digits(x); - for (k = 0; k < mswdigits; k++) { - xbit = x % 10; - x /= 10; - ybit = y % 10; - y /= 10; - if (xbit > 1 || ybit > 1) { - goto invalid_operation; - } - z += (xbit^ybit) ? mpd_pow10[k] : 0; - } - - /* scan for digits > 1 and copy the rest of y */ - for (; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - z += ybit*mpd_pow10[k]; - } - result->data[i++] = z; - /* scan for digits > 1 and copy the rest of big */ - for (; i < big->len; i++) { - y = big->data[i]; - for (k = 0; k < MPD_RDIGITS; k++) { - ybit = y % 10; - y /= 10; - if (ybit > 1) { - goto invalid_operation; - } - } - result->data[i] = big->data[i]; - } - - mpd_clear_flags(result); - result->exp = 0; - result->len = _mpd_real_size(result->data, big->len); - mpd_qresize(result, result->len, status); - mpd_setdigits(result); - _mpd_cap(result, ctx); - return; - -invalid_operation: - mpd_seterror(result, MPD_Invalid_operation, status); -} - - -/******************************************************************************/ -/* Arithmetic operations */ -/******************************************************************************/ - -/* - * The absolute value of a. If a is negative, the result is the same - * as the result of the minus operation. Otherwise, the result is the - * result of the plus operation. - */ -void -mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - } - - if (mpd_isnegative(a)) { - mpd_qminus(result, a, ctx, status); - } - else { - mpd_qplus(result, a, ctx, status); - } -} - -static inline void -_mpd_ptrswap(const mpd_t **a, const mpd_t **b) -{ - const mpd_t *t = *a; - *a = *b; - *b = t; -} - -/* Add or subtract infinities. */ -static void -_mpd_qaddsub_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b, - uint32_t *status) -{ - if (mpd_isinfinite(a)) { - if (mpd_sign(a) != sign_b && mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } - else { - mpd_setspecial(result, mpd_sign(a), MPD_INF); - } - return; - } - assert(mpd_isinfinite(b)); - mpd_setspecial(result, sign_b, MPD_INF); -} - -/* Add or subtract non-special numbers. */ -static void -_mpd_qaddsub(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big, *small; - MPD_NEW_STATIC(big_aligned,0,0,0,0); - MPD_NEW_CONST(tiny,0,0,1,1,1,1); - mpd_uint_t carry; - mpd_ssize_t newsize, shift; - mpd_ssize_t exp, i; - int swap = 0; - - - /* compare exponents */ - big = a; small = b; - if (big->exp != small->exp) { - if (small->exp > big->exp) { - _mpd_ptrswap(&big, &small); - swap++; - } - /* align the coefficients */ - if (!mpd_iszerocoeff(big)) { - exp = big->exp - 1; - exp += (big->digits > ctx->prec) ? 0 : big->digits-ctx->prec-1; - if (mpd_adjexp(small) < exp) { - /* - * Avoid huge shifts by substituting a value for small that is - * guaranteed to produce the same results. - * - * adjexp(small) < exp if and only if: - * - * bdigits <= prec AND - * bdigits+shift >= prec+2+sdigits AND - * exp = bexp+bdigits-prec-2 - * - * 1234567000000000 -> bdigits + shift - * ----------XX1234 -> sdigits - * ----------X1 -> tiny-digits - * |- prec -| - * - * OR - * - * bdigits > prec AND - * shift > sdigits AND - * exp = bexp-1 - * - * 1234567892100000 -> bdigits + shift - * ----------XX1234 -> sdigits - * ----------X1 -> tiny-digits - * |- prec -| - * - * If tiny is zero, adding or subtracting is a no-op. - * Otherwise, adding tiny generates a non-zero digit either - * below the rounding digit or the least significant digit - * of big. When subtracting, tiny is in the same position as - * the carry that would be generated by subtracting sdigits. - */ - mpd_copy_flags(&tiny, small); - tiny.exp = exp; - tiny.digits = 1; - tiny.len = 1; - tiny.data[0] = mpd_iszerocoeff(small) ? 0 : 1; - small = &tiny; - } - /* This cannot wrap: the difference is positive and <= maxprec */ - shift = big->exp - small->exp; - if (!mpd_qshiftl(&big_aligned, big, shift, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - big = &big_aligned; - } - } - result->exp = small->exp; - - - /* compare length of coefficients */ - if (big->len < small->len) { - _mpd_ptrswap(&big, &small); - swap++; - } - - newsize = big->len; - if (!mpd_qresize(result, newsize, status)) { - goto finish; - } - - if (mpd_sign(a) == sign_b) { - - carry = _mpd_baseadd(result->data, big->data, small->data, - big->len, small->len); - - if (carry) { - newsize = big->len + 1; - if (!mpd_qresize(result, newsize, status)) { - goto finish; - } - result->data[newsize-1] = carry; - } - - result->len = newsize; - mpd_set_flags(result, sign_b); - } - else { - if (big->len == small->len) { - for (i=big->len-1; i >= 0; --i) { - if (big->data[i] != small->data[i]) { - if (big->data[i] < small->data[i]) { - _mpd_ptrswap(&big, &small); - swap++; - } - break; - } - } - } - - _mpd_basesub(result->data, big->data, small->data, - big->len, small->len); - newsize = _mpd_real_size(result->data, big->len); - /* resize to smaller cannot fail */ - (void)mpd_qresize(result, newsize, status); - - result->len = newsize; - sign_b = (swap & 1) ? sign_b : mpd_sign(a); - mpd_set_flags(result, sign_b); - - if (mpd_iszerocoeff(result)) { - mpd_set_positive(result); - if (ctx->round == MPD_ROUND_FLOOR) { - mpd_set_negative(result); - } - } - } - - mpd_setdigits(result); - -finish: - mpd_del(&big_aligned); -} - -/* Add a and b. No specials, no finalizing. */ -static void -_mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status); -} - -/* Subtract b from a. No specials, no finalizing. */ -static void -_mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status); -} - -/* Add a and b. */ -void -mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - _mpd_qaddsub_inf(result, a, b, mpd_sign(b), status); - return; - } - - _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status); - mpd_qfinalize(result, ctx, status); -} - -/* Add a and b. Set NaN/Invalid_operation if the result is inexact. */ -static void -_mpd_qadd_exact(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - - mpd_qadd(result, a, b, ctx, &workstatus); - *status |= workstatus; - if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } -} - -/* Subtract b from a. */ -void -mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - _mpd_qaddsub_inf(result, a, b, !mpd_sign(b), status); - return; - } - - _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status); - mpd_qfinalize(result, ctx, status); -} - -/* Subtract b from a. Set NaN/Invalid_operation if the result is inexact. */ -static void -_mpd_qsub_exact(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - - mpd_qsub(result, a, b, ctx, &workstatus); - *status |= workstatus; - if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } -} - -/* Add decimal and mpd_ssize_t. */ -void -mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_ssize(&bb, b, &maxcontext, status); - mpd_qadd(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Add decimal and mpd_uint_t. */ -void -mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_uint(&bb, b, &maxcontext, status); - mpd_qadd(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Subtract mpd_ssize_t from decimal. */ -void -mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_ssize(&bb, b, &maxcontext, status); - mpd_qsub(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Subtract mpd_uint_t from decimal. */ -void -mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_uint(&bb, b, &maxcontext, status); - mpd_qsub(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Add decimal and int32_t. */ -void -mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qadd_ssize(result, a, b, ctx, status); -} - -/* Add decimal and uint32_t. */ -void -mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qadd_uint(result, a, b, ctx, status); -} - -#ifdef CONFIG_64 -/* Add decimal and int64_t. */ -void -mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qadd_ssize(result, a, b, ctx, status); -} - -/* Add decimal and uint64_t. */ -void -mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qadd_uint(result, a, b, ctx, status); -} -#elif !defined(LEGACY_COMPILER) -/* Add decimal and int64_t. */ -void -mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_i64(&bb, b, &maxcontext, status); - mpd_qadd(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Add decimal and uint64_t. */ -void -mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_u64(&bb, b, &maxcontext, status); - mpd_qadd(result, a, &bb, ctx, status); - mpd_del(&bb); -} -#endif - -/* Subtract int32_t from decimal. */ -void -mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qsub_ssize(result, a, b, ctx, status); -} - -/* Subtract uint32_t from decimal. */ -void -mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qsub_uint(result, a, b, ctx, status); -} - -#ifdef CONFIG_64 -/* Subtract int64_t from decimal. */ -void -mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qsub_ssize(result, a, b, ctx, status); -} - -/* Subtract uint64_t from decimal. */ -void -mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qsub_uint(result, a, b, ctx, status); -} -#elif !defined(LEGACY_COMPILER) -/* Subtract int64_t from decimal. */ -void -mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_i64(&bb, b, &maxcontext, status); - mpd_qsub(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Subtract uint64_t from decimal. */ -void -mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_u64(&bb, b, &maxcontext, status); - mpd_qsub(result, a, &bb, ctx, status); - mpd_del(&bb); -} -#endif - - -/* Divide infinities. */ -static void -_mpd_qdiv_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - if (mpd_isinfinite(a)) { - if (mpd_isinfinite(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF); - return; - } - assert(mpd_isinfinite(b)); - _settriple(result, mpd_sign(a)^mpd_sign(b), 0, mpd_etiny(ctx)); - *status |= MPD_Clamped; -} - -enum {NO_IDEAL_EXP, SET_IDEAL_EXP}; -/* Divide a by b. */ -static void -_mpd_qdiv(int action, mpd_t *q, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - MPD_NEW_STATIC(aligned,0,0,0,0); - mpd_uint_t ld; - mpd_ssize_t shift, exp, tz; - mpd_ssize_t newsize; - mpd_ssize_t ideal_exp; - mpd_uint_t rem; - uint8_t sign_a = mpd_sign(a); - uint8_t sign_b = mpd_sign(b); - - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(q, a, b, ctx, status)) { - return; - } - _mpd_qdiv_inf(q, a, b, ctx, status); - return; - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_seterror(q, MPD_Division_undefined, status); - } - else { - mpd_setspecial(q, sign_a^sign_b, MPD_INF); - *status |= MPD_Division_by_zero; - } - return; - } - if (mpd_iszerocoeff(a)) { - exp = a->exp - b->exp; - _settriple(q, sign_a^sign_b, 0, exp); - mpd_qfinalize(q, ctx, status); - return; - } - - shift = (b->digits - a->digits) + ctx->prec + 1; - ideal_exp = a->exp - b->exp; - exp = ideal_exp - shift; - if (shift > 0) { - if (!mpd_qshiftl(&aligned, a, shift, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - goto finish; - } - a = &aligned; - } - else if (shift < 0) { - shift = -shift; - if (!mpd_qshiftl(&aligned, b, shift, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - goto finish; - } - b = &aligned; - } - - - newsize = a->len - b->len + 1; - if ((q != b && q != a) || (q == b && newsize > b->len)) { - if (!mpd_qresize(q, newsize, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - goto finish; - } - } - - - if (b->len == 1) { - rem = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]); - } - else if (b->len <= MPD_NEWTONDIV_CUTOFF) { - int ret = _mpd_basedivmod(q->data, NULL, a->data, b->data, - a->len, b->len); - if (ret < 0) { - mpd_seterror(q, MPD_Malloc_error, status); - goto finish; - } - rem = ret; - } - else { - MPD_NEW_STATIC(r,0,0,0,0); - _mpd_base_ndivmod(q, &r, a, b, status); - if (mpd_isspecial(q) || mpd_isspecial(&r)) { - mpd_setspecial(q, MPD_POS, MPD_NAN); - mpd_del(&r); - goto finish; - } - rem = !mpd_iszerocoeff(&r); - mpd_del(&r); - newsize = q->len; - } - - newsize = _mpd_real_size(q->data, newsize); - /* resize to smaller cannot fail */ - mpd_qresize(q, newsize, status); - mpd_set_flags(q, sign_a^sign_b); - q->len = newsize; - mpd_setdigits(q); - - shift = ideal_exp - exp; - if (rem) { - ld = mpd_lsd(q->data[0]); - if (ld == 0 || ld == 5) { - q->data[0] += 1; - } - } - else if (action == SET_IDEAL_EXP && shift > 0) { - tz = mpd_trail_zeros(q); - shift = (tz > shift) ? shift : tz; - mpd_qshiftr_inplace(q, shift); - exp += shift; - } - - q->exp = exp; - - -finish: - mpd_del(&aligned); - mpd_qfinalize(q, ctx, status); -} - -/* Divide a by b. */ -void -mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - MPD_NEW_STATIC(aa,0,0,0,0); - MPD_NEW_STATIC(bb,0,0,0,0); - uint32_t xstatus = 0; - - if (q == a) { - if (!mpd_qcopy(&aa, a, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - goto out; - } - a = &aa; - } - - if (q == b) { - if (!mpd_qcopy(&bb, b, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - goto out; - } - b = &bb; - } - - _mpd_qdiv(SET_IDEAL_EXP, q, a, b, ctx, &xstatus); - - if (xstatus & (MPD_Malloc_error|MPD_Division_impossible)) { - /* Inexact quotients (the usual case) fill the entire context precision, - * which can lead to the above errors for very high precisions. Retry - * the operation with a lower precision in case the result is exact. - * - * We need an upper bound for the number of digits of a_coeff / b_coeff - * when the result is exact. If a_coeff' * 1 / b_coeff' is in lowest - * terms, then maxdigits(a_coeff') + maxdigits(1 / b_coeff') is a suitable - * bound. - * - * 1 / b_coeff' is exact iff b_coeff' exclusively has prime factors 2 or 5. - * The largest amount of digits is generated if b_coeff' is a power of 2 or - * a power of 5 and is less than or equal to log5(b_coeff') <= log2(b_coeff'). - * - * We arrive at a total upper bound: - * - * maxdigits(a_coeff') + maxdigits(1 / b_coeff') <= - * log10(a_coeff) + log2(b_coeff) = - * log10(a_coeff) + log10(b_coeff) / log10(2) <= - * a->digits + b->digits * 4; - */ - mpd_context_t workctx = *ctx; - uint32_t ystatus = 0; - - workctx.prec = a->digits + b->digits * 4; - if (workctx.prec >= ctx->prec) { - *status |= (xstatus&MPD_Errors); - goto out; /* No point in retrying, keep the original error. */ - } - - _mpd_qdiv(SET_IDEAL_EXP, q, a, b, &workctx, &ystatus); - if (ystatus != 0) { - ystatus = *status | ((ystatus|xstatus)&MPD_Errors); - mpd_seterror(q, ystatus, status); - } - } - else { - *status |= xstatus; - } - - -out: - mpd_del(&aa); - mpd_del(&bb); -} - -/* Internal function. */ -static void -_mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - MPD_NEW_STATIC(aligned,0,0,0,0); - mpd_ssize_t qsize, rsize; - mpd_ssize_t ideal_exp, expdiff, shift; - uint8_t sign_a = mpd_sign(a); - uint8_t sign_ab = mpd_sign(a)^mpd_sign(b); - - - ideal_exp = (a->exp > b->exp) ? b->exp : a->exp; - if (mpd_iszerocoeff(a)) { - if (!mpd_qcopy(r, a, status)) { - goto nanresult; /* GCOV_NOT_REACHED */ - } - r->exp = ideal_exp; - _settriple(q, sign_ab, 0, 0); - return; - } - - expdiff = mpd_adjexp(a) - mpd_adjexp(b); - if (expdiff < 0) { - if (a->exp > b->exp) { - /* positive and less than b->digits - a->digits */ - shift = a->exp - b->exp; - if (!mpd_qshiftl(r, a, shift, status)) { - goto nanresult; - } - r->exp = ideal_exp; - } - else { - if (!mpd_qcopy(r, a, status)) { - goto nanresult; - } - } - _settriple(q, sign_ab, 0, 0); - return; - } - if (expdiff > ctx->prec) { - *status |= MPD_Division_impossible; - goto nanresult; - } - - - /* - * At this point we have: - * (1) 0 <= a->exp + a->digits - b->exp - b->digits <= prec - * (2) a->exp - b->exp >= b->digits - a->digits - * (3) a->exp - b->exp <= prec + b->digits - a->digits - */ - if (a->exp != b->exp) { - shift = a->exp - b->exp; - if (shift > 0) { - /* by (3), after the shift a->digits <= prec + b->digits */ - if (!mpd_qshiftl(&aligned, a, shift, status)) { - goto nanresult; - } - a = &aligned; - } - else { - shift = -shift; - /* by (2), after the shift b->digits <= a->digits */ - if (!mpd_qshiftl(&aligned, b, shift, status)) { - goto nanresult; - } - b = &aligned; - } - } - - - qsize = a->len - b->len + 1; - if (!(q == a && qsize < a->len) && !(q == b && qsize < b->len)) { - if (!mpd_qresize(q, qsize, status)) { - goto nanresult; - } - } - - rsize = b->len; - if (!(r == a && rsize < a->len)) { - if (!mpd_qresize(r, rsize, status)) { - goto nanresult; - } - } - - if (b->len == 1) { - assert(b->data[0] != 0); /* annotation for scan-build */ - if (a->len == 1) { - _mpd_div_word(&q->data[0], &r->data[0], a->data[0], b->data[0]); - } - else { - r->data[0] = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]); - } - } - else if (b->len <= MPD_NEWTONDIV_CUTOFF) { - int ret; - ret = _mpd_basedivmod(q->data, r->data, a->data, b->data, - a->len, b->len); - if (ret == -1) { - *status |= MPD_Malloc_error; - goto nanresult; - } - } - else { - _mpd_base_ndivmod(q, r, a, b, status); - if (mpd_isspecial(q) || mpd_isspecial(r)) { - goto nanresult; - } - qsize = q->len; - rsize = r->len; - } - - qsize = _mpd_real_size(q->data, qsize); - /* resize to smaller cannot fail */ - mpd_qresize(q, qsize, status); - q->len = qsize; - mpd_setdigits(q); - mpd_set_flags(q, sign_ab); - q->exp = 0; - if (q->digits > ctx->prec) { - *status |= MPD_Division_impossible; - goto nanresult; - } - - rsize = _mpd_real_size(r->data, rsize); - /* resize to smaller cannot fail */ - mpd_qresize(r, rsize, status); - r->len = rsize; - mpd_setdigits(r); - mpd_set_flags(r, sign_a); - r->exp = ideal_exp; - -out: - mpd_del(&aligned); - return; - -nanresult: - mpd_setspecial(q, MPD_POS, MPD_NAN); - mpd_setspecial(r, MPD_POS, MPD_NAN); - goto out; -} - -/* Integer division with remainder. */ -void -mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint8_t sign = mpd_sign(a)^mpd_sign(b); - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(q, a, b, ctx, status)) { - mpd_qcopy(r, q, status); - return; - } - if (mpd_isinfinite(a)) { - if (mpd_isinfinite(b)) { - mpd_setspecial(q, MPD_POS, MPD_NAN); - } - else { - mpd_setspecial(q, sign, MPD_INF); - } - mpd_setspecial(r, MPD_POS, MPD_NAN); - *status |= MPD_Invalid_operation; - return; - } - if (mpd_isinfinite(b)) { - if (!mpd_qcopy(r, a, status)) { - mpd_seterror(q, MPD_Malloc_error, status); - return; - } - mpd_qfinalize(r, ctx, status); - _settriple(q, sign, 0, 0); - return; - } - /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_setspecial(q, MPD_POS, MPD_NAN); - mpd_setspecial(r, MPD_POS, MPD_NAN); - *status |= MPD_Division_undefined; - } - else { - mpd_setspecial(q, sign, MPD_INF); - mpd_setspecial(r, MPD_POS, MPD_NAN); - *status |= (MPD_Division_by_zero|MPD_Invalid_operation); - } - return; - } - - _mpd_qdivmod(q, r, a, b, ctx, status); - mpd_qfinalize(q, ctx, status); - mpd_qfinalize(r, ctx, status); -} - -void -mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - MPD_NEW_STATIC(r,0,0,0,0); - uint8_t sign = mpd_sign(a)^mpd_sign(b); - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(q, a, b, ctx, status)) { - return; - } - if (mpd_isinfinite(a) && mpd_isinfinite(b)) { - mpd_seterror(q, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(a)) { - mpd_setspecial(q, sign, MPD_INF); - return; - } - if (mpd_isinfinite(b)) { - _settriple(q, sign, 0, 0); - return; - } - /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_seterror(q, MPD_Division_undefined, status); - } - else { - mpd_setspecial(q, sign, MPD_INF); - *status |= MPD_Division_by_zero; - } - return; - } - - - _mpd_qdivmod(q, &r, a, b, ctx, status); - mpd_del(&r); - mpd_qfinalize(q, ctx, status); -} - -/* Divide decimal by mpd_ssize_t. */ -void -mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_ssize(&bb, b, &maxcontext, status); - mpd_qdiv(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Divide decimal by mpd_uint_t. */ -void -mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_uint(&bb, b, &maxcontext, status); - mpd_qdiv(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Divide decimal by int32_t. */ -void -mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qdiv_ssize(result, a, b, ctx, status); -} - -/* Divide decimal by uint32_t. */ -void -mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qdiv_uint(result, a, b, ctx, status); -} - -#ifdef CONFIG_64 -/* Divide decimal by int64_t. */ -void -mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qdiv_ssize(result, a, b, ctx, status); -} - -/* Divide decimal by uint64_t. */ -void -mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qdiv_uint(result, a, b, ctx, status); -} -#elif !defined(LEGACY_COMPILER) -/* Divide decimal by int64_t. */ -void -mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_i64(&bb, b, &maxcontext, status); - mpd_qdiv(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Divide decimal by uint64_t. */ -void -mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_u64(&bb, b, &maxcontext, status); - mpd_qdiv(result, a, &bb, ctx, status); - mpd_del(&bb); -} -#endif - -/* Pad the result with trailing zeros if it has fewer digits than prec. */ -static void -_mpd_zeropad(mpd_t *result, const mpd_context_t *ctx, uint32_t *status) -{ - if (!mpd_isspecial(result) && !mpd_iszero(result) && - result->digits < ctx->prec) { - mpd_ssize_t shift = ctx->prec - result->digits; - mpd_qshiftl(result, result, shift, status); - result->exp -= shift; - } -} - -/* Check if the result is guaranteed to be one. */ -static int -_mpd_qexp_check_one(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - MPD_NEW_CONST(lim,0,-(ctx->prec+1),1,1,1,9); - MPD_NEW_SHARED(aa, a); - - mpd_set_positive(&aa); - - /* abs(a) <= 9 * 10**(-prec-1) */ - if (_mpd_cmp(&aa, &lim) <= 0) { - _settriple(result, 0, 1, 0); - *status |= MPD_Rounded|MPD_Inexact; - return 1; - } - - return 0; -} - -/* - * Get the number of iterations for the Horner scheme in _mpd_qexp(). - */ -static inline mpd_ssize_t -_mpd_get_exp_iterations(const mpd_t *r, mpd_ssize_t p) -{ - mpd_ssize_t log10pbyr; /* lower bound for log10(p / abs(r)) */ - mpd_ssize_t n; - - assert(p >= 10); - assert(!mpd_iszero(r)); - assert(-p < mpd_adjexp(r) && mpd_adjexp(r) <= -1); - -#ifdef CONFIG_64 - if (p > (mpd_ssize_t)(1ULL<<52)) { - return MPD_SSIZE_MAX; - } -#endif - - /* - * Lower bound for log10(p / abs(r)): adjexp(p) - (adjexp(r) + 1) - * At this point (for CONFIG_64, CONFIG_32 is not problematic): - * 1) 10 <= p <= 2**52 - * 2) -p < adjexp(r) <= -1 - * 3) 1 <= log10pbyr <= 2**52 + 14 - */ - log10pbyr = (mpd_word_digits(p)-1) - (mpd_adjexp(r)+1); - - /* - * The numerator in the paper is 1.435 * p - 1.182, calculated - * exactly. We compensate for rounding errors by using 1.43503. - * ACL2 proofs: - * 1) exp-iter-approx-lower-bound: The term below evaluated - * in 53-bit floating point arithmetic is greater than or - * equal to the exact term used in the paper. - * 2) exp-iter-approx-upper-bound: The term below is less than - * or equal to 3/2 * p <= 3/2 * 2**52. - */ - n = (mpd_ssize_t)ceil((1.43503*(double)p - 1.182) / (double)log10pbyr); - return n >= 3 ? n : 3; -} - -/* - * Internal function, specials have been dealt with. Apart from Overflow - * and Underflow, two cases must be considered for the error of the result: - * - * 1) abs(a) <= 9 * 10**(-prec-1) ==> result == 1 - * - * Absolute error: abs(1 - e**x) < 10**(-prec) - * ------------------------------------------- - * - * 2) abs(a) > 9 * 10**(-prec-1) - * - * Relative error: abs(result - e**x) < 0.5 * 10**(-prec) * e**x - * ------------------------------------------------------------- - * - * The algorithm is from Hull&Abrham, Variable Precision Exponential Function, - * ACM Transactions on Mathematical Software, Vol. 12, No. 2, June 1986. - * - * Main differences: - * - * - The number of iterations for the Horner scheme is calculated using - * 53-bit floating point arithmetic. - * - * - In the error analysis for ER (relative error accumulated in the - * evaluation of the truncated series) the reduced operand r may - * have any number of digits. - * ACL2 proof: exponent-relative-error - * - * - The analysis for early abortion has been adapted for the mpd_t - * ranges. - */ -static void -_mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(tmp,0,0,0,0); - MPD_NEW_STATIC(sum,0,0,0,0); - MPD_NEW_CONST(word,0,0,1,1,1,1); - mpd_ssize_t j, n, t; - - assert(!mpd_isspecial(a)); - - if (mpd_iszerocoeff(a)) { - _settriple(result, MPD_POS, 1, 0); - return; - } - - /* - * We are calculating e^x = e^(r*10^t) = (e^r)^(10^t), where abs(r) < 1 and t >= 0. - * - * If t > 0, we have: - * - * (1) 0.1 <= r < 1, so e^0.1 <= e^r. If t > MAX_T, overflow occurs: - * - * MAX-EMAX+1 < log10(e^(0.1*10*t)) <= log10(e^(r*10^t)) < adjexp(e^(r*10^t))+1 - * - * (2) -1 < r <= -0.1, so e^r <= e^-0.1. If t > MAX_T, underflow occurs: - * - * adjexp(e^(r*10^t)) <= log10(e^(r*10^t)) <= log10(e^(-0.1*10^t)) < MIN-ETINY - */ -#if defined(CONFIG_64) - #define MPD_EXP_MAX_T 19 -#elif defined(CONFIG_32) - #define MPD_EXP_MAX_T 10 -#endif - t = a->digits + a->exp; - t = (t > 0) ? t : 0; - if (t > MPD_EXP_MAX_T) { - if (mpd_ispositive(a)) { - mpd_setspecial(result, MPD_POS, MPD_INF); - *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; - } - else { - _settriple(result, MPD_POS, 0, mpd_etiny(ctx)); - *status |= (MPD_Inexact|MPD_Rounded|MPD_Subnormal| - MPD_Underflow|MPD_Clamped); - } - return; - } - - /* abs(a) <= 9 * 10**(-prec-1) */ - if (_mpd_qexp_check_one(result, a, ctx, status)) { - return; - } - - mpd_maxcontext(&workctx); - workctx.prec = ctx->prec + t + 2; - workctx.prec = (workctx.prec < 10) ? 10 : workctx.prec; - workctx.round = MPD_ROUND_HALF_EVEN; - - if (!mpd_qcopy(result, a, status)) { - return; - } - result->exp -= t; - - /* - * At this point: - * 1) 9 * 10**(-prec-1) < abs(a) - * 2) 9 * 10**(-prec-t-1) < abs(r) - * 3) log10(9) - prec - t - 1 < log10(abs(r)) < adjexp(abs(r)) + 1 - * 4) - prec - t - 2 < adjexp(abs(r)) <= -1 - */ - n = _mpd_get_exp_iterations(result, workctx.prec); - if (n == MPD_SSIZE_MAX) { - mpd_seterror(result, MPD_Invalid_operation, status); /* GCOV_UNLIKELY */ - return; /* GCOV_UNLIKELY */ - } - - _settriple(&sum, MPD_POS, 1, 0); - - for (j = n-1; j >= 1; j--) { - word.data[0] = j; - mpd_setdigits(&word); - mpd_qdiv(&tmp, result, &word, &workctx, &workctx.status); - mpd_qfma(&sum, &sum, &tmp, &one, &workctx, &workctx.status); - } - -#ifdef CONFIG_64 - _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status); -#else - if (t <= MPD_MAX_POW10) { - _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status); - } - else { - t -= MPD_MAX_POW10; - _mpd_qpow_uint(&tmp, &sum, mpd_pow10[MPD_MAX_POW10], MPD_POS, - &workctx, status); - _mpd_qpow_uint(result, &tmp, mpd_pow10[t], MPD_POS, &workctx, status); - } -#endif - - mpd_del(&tmp); - mpd_del(&sum); - *status |= (workctx.status&MPD_Errors); - *status |= (MPD_Inexact|MPD_Rounded); -} - -/* exp(a) */ -void -mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - _settriple(result, MPD_POS, 0, 0); - } - else { - mpd_setspecial(result, MPD_POS, MPD_INF); - } - return; - } - if (mpd_iszerocoeff(a)) { - _settriple(result, MPD_POS, 1, 0); - return; - } - - workctx = *ctx; - workctx.round = MPD_ROUND_HALF_EVEN; - - if (ctx->allcr) { - MPD_NEW_STATIC(t1, 0,0,0,0); - MPD_NEW_STATIC(t2, 0,0,0,0); - MPD_NEW_STATIC(ulp, 0,0,0,0); - MPD_NEW_STATIC(aa, 0,0,0,0); - mpd_ssize_t prec; - mpd_ssize_t ulpexp; - uint32_t workstatus; - - if (result == a) { - if (!mpd_qcopy(&aa, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - a = &aa; - } - - workctx.clamp = 0; - prec = ctx->prec + 3; - while (1) { - workctx.prec = prec; - workstatus = 0; - - _mpd_qexp(result, a, &workctx, &workstatus); - *status |= workstatus; - - ulpexp = result->exp + result->digits - workctx.prec; - if (workstatus & MPD_Underflow) { - /* The effective work precision is result->digits. */ - ulpexp = result->exp; - } - _ssettriple(&ulp, MPD_POS, 1, ulpexp); - - /* - * At this point [1]: - * 1) abs(result - e**x) < 0.5 * 10**(-prec) * e**x - * 2) result - ulp < e**x < result + ulp - * 3) result - ulp < result < result + ulp - * - * If round(result-ulp)==round(result+ulp), then - * round(result)==round(e**x). Therefore the result - * is correctly rounded. - * - * [1] If abs(a) <= 9 * 10**(-prec-1), use the absolute - * error for a similar argument. - */ - workctx.prec = ctx->prec; - mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status); - mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status); - if (mpd_isspecial(result) || mpd_iszerocoeff(result) || - mpd_qcmp(&t1, &t2, status) == 0) { - workctx.clamp = ctx->clamp; - _mpd_zeropad(result, &workctx, status); - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - break; - } - prec += MPD_RDIGITS; - } - mpd_del(&t1); - mpd_del(&t2); - mpd_del(&ulp); - mpd_del(&aa); - } - else { - _mpd_qexp(result, a, &workctx, status); - _mpd_zeropad(result, &workctx, status); - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - } -} - -/* Fused multiply-add: (a * b) + c, with a single final rounding. */ -void -mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_t *cc = NULL; - - if (result == c) { - if ((cc = mpd_qncopy(c)) == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - c = cc; - } - - _mpd_qmul(result, a, b, ctx, &workstatus); - if (!(workstatus&MPD_Invalid_operation)) { - mpd_qadd(result, result, c, ctx, &workstatus); - } - - if (cc) mpd_del(cc); - *status |= workstatus; -} - -/* - * Schedule the optimal precision increase for the Newton iteration. - * v := input operand - * z_0 := initial approximation - * initprec := natural number such that abs(log(v) - z_0) < 10**-initprec - * maxprec := target precision - * - * For convenience the output klist contains the elements in reverse order: - * klist := [k_n-1, ..., k_0], where - * 1) k_0 <= initprec and - * 2) abs(log(v) - result) < 10**(-2*k_n-1 + 1) <= 10**-maxprec. - */ -static inline int -ln_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], mpd_ssize_t maxprec, - mpd_ssize_t initprec) -{ - mpd_ssize_t k; - int i; - - assert(maxprec >= 2 && initprec >= 2); - if (maxprec <= initprec) return -1; - - i = 0; k = maxprec; - do { - k = (k+2) / 2; - klist[i++] = k; - } while (k > initprec); - - return i-1; -} - -/* The constants have been verified with both decimal.py and mpfr. */ -#ifdef CONFIG_64 -#if MPD_RDIGITS != 19 - #error "mpdecimal.c: MPD_RDIGITS must be 19." -#endif -static const mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = { - 6983716328982174407ULL, 9089704281976336583ULL, 1515961135648465461ULL, - 4416816335727555703ULL, 2900988039194170265ULL, 2307925037472986509ULL, - 107598438319191292ULL, 3466624107184669231ULL, 4450099781311469159ULL, - 9807828059751193854ULL, 7713456862091670584ULL, 1492198849978748873ULL, - 6528728696511086257ULL, 2385392051446341972ULL, 8692180205189339507ULL, - 6518769751037497088ULL, 2375253577097505395ULL, 9095610299291824318ULL, - 982748238504564801ULL, 5438635917781170543ULL, 7547331541421808427ULL, - 752371033310119785ULL, 3171643095059950878ULL, 9785265383207606726ULL, - 2932258279850258550ULL, 5497347726624257094ULL, 2976979522110718264ULL, - 9221477656763693866ULL, 1979650047149510504ULL, 6674183485704422507ULL, - 9702766860595249671ULL, 9278096762712757753ULL, 9314848524948644871ULL, - 6826928280848118428ULL, 754403708474699401ULL, 230105703089634572ULL, - 1929203337658714166ULL, 7589402567763113569ULL, 4208241314695689016ULL, - 2922455440575892572ULL, 9356734206705811364ULL, 2684916746550586856ULL, - 644507064800027750ULL, 9476834636167921018ULL, 5659121373450747856ULL, - 2835522011480466371ULL, 6470806855677432162ULL, 7141748003688084012ULL, - 9619404400222105101ULL, 5504893431493939147ULL, 6674744042432743651ULL, - 2287698219886746543ULL, 7773262884616336622ULL, 1985283935053089653ULL, - 4680843799894826233ULL, 8168948290720832555ULL, 8067566662873690987ULL, - 6248633409525465082ULL, 9829834196778404228ULL, 3524802359972050895ULL, - 3327900967572609677ULL, 110148862877297603ULL, 179914546843642076ULL, - 2302585092994045684ULL -}; -#else -#if MPD_RDIGITS != 9 - #error "mpdecimal.c: MPD_RDIGITS must be 9." -#endif -static const mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = { - 401682692UL, 708474699UL, 720754403UL, 30896345UL, 602301057UL, 765871416UL, - 192920333UL, 763113569UL, 589402567UL, 956890167UL, 82413146UL, 589257242UL, - 245544057UL, 811364292UL, 734206705UL, 868569356UL, 167465505UL, 775026849UL, - 706480002UL, 18064450UL, 636167921UL, 569476834UL, 734507478UL, 156591213UL, - 148046637UL, 283552201UL, 677432162UL, 470806855UL, 880840126UL, 417480036UL, - 210510171UL, 940440022UL, 939147961UL, 893431493UL, 436515504UL, 440424327UL, - 654366747UL, 821988674UL, 622228769UL, 884616336UL, 537773262UL, 350530896UL, - 319852839UL, 989482623UL, 468084379UL, 720832555UL, 168948290UL, 736909878UL, - 675666628UL, 546508280UL, 863340952UL, 404228624UL, 834196778UL, 508959829UL, - 23599720UL, 967735248UL, 96757260UL, 603332790UL, 862877297UL, 760110148UL, - 468436420UL, 401799145UL, 299404568UL, 230258509UL -}; -#endif -/* _mpd_ln10 is used directly for precisions smaller than MINALLOC_MAX*RDIGITS. - Otherwise, it serves as the initial approximation for calculating ln(10). */ -static const mpd_t _mpd_ln10 = { - MPD_STATIC|MPD_CONST_DATA, -(MPD_MINALLOC_MAX*MPD_RDIGITS-1), - MPD_MINALLOC_MAX*MPD_RDIGITS, MPD_MINALLOC_MAX, MPD_MINALLOC_MAX, - (mpd_uint_t *)mpd_ln10_data -}; - -/* - * Set 'result' to log(10). - * Ulp error: abs(result - log(10)) < ulp(log(10)) - * Relative error: abs(result - log(10)) < 5 * 10**-prec * log(10) - * - * NOTE: The relative error is not derived from the ulp error, but - * calculated separately using the fact that 23/10 < log(10) < 24/10. - */ -void -mpd_qln10(mpd_t *result, mpd_ssize_t prec, uint32_t *status) -{ - mpd_context_t varcontext, maxcontext; - MPD_NEW_STATIC(tmp, 0,0,0,0); - MPD_NEW_CONST(static10, 0,0,2,1,1,10); - mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; - mpd_uint_t rnd; - mpd_ssize_t shift; - int i; - - assert(prec >= 1); - - shift = MPD_MINALLOC_MAX*MPD_RDIGITS-prec; - shift = shift < 0 ? 0 : shift; - - rnd = mpd_qshiftr(result, &_mpd_ln10, shift, status); - if (rnd == MPD_UINT_MAX) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - result->exp = -(result->digits-1); - - mpd_maxcontext(&maxcontext); - if (prec < MPD_MINALLOC_MAX*MPD_RDIGITS) { - maxcontext.prec = prec; - _mpd_apply_round_excess(result, rnd, &maxcontext, status); - *status |= (MPD_Inexact|MPD_Rounded); - return; - } - - mpd_maxcontext(&varcontext); - varcontext.round = MPD_ROUND_TRUNC; - - i = ln_schedule_prec(klist, prec+2, -result->exp); - for (; i >= 0; i--) { - varcontext.prec = 2*klist[i]+3; - result->flags ^= MPD_NEG; - _mpd_qexp(&tmp, result, &varcontext, status); - result->flags ^= MPD_NEG; - mpd_qmul(&tmp, &static10, &tmp, &varcontext, status); - mpd_qsub(&tmp, &tmp, &one, &maxcontext, status); - mpd_qadd(result, result, &tmp, &maxcontext, status); - if (mpd_isspecial(result)) { - break; - } - } - - mpd_del(&tmp); - maxcontext.prec = prec; - mpd_qfinalize(result, &maxcontext, status); -} - -/* - * Initial approximations for the ln() iteration. The values have the - * following properties (established with both decimal.py and mpfr): - * - * Index 0 - 400, logarithms of x in [1.00, 5.00]: - * abs(lnapprox[i] * 10**-3 - log((i+100)/100)) < 10**-2 - * abs(lnapprox[i] * 10**-3 - log((i+1+100)/100)) < 10**-2 - * - * Index 401 - 899, logarithms of x in (0.500, 0.999]: - * abs(-lnapprox[i] * 10**-3 - log((i+100)/1000)) < 10**-2 - * abs(-lnapprox[i] * 10**-3 - log((i+1+100)/1000)) < 10**-2 - */ -static const uint16_t lnapprox[900] = { - /* index 0 - 400: log((i+100)/100) * 1000 */ - 0, 10, 20, 30, 39, 49, 58, 68, 77, 86, 95, 104, 113, 122, 131, 140, 148, 157, - 166, 174, 182, 191, 199, 207, 215, 223, 231, 239, 247, 255, 262, 270, 278, - 285, 293, 300, 308, 315, 322, 329, 336, 344, 351, 358, 365, 372, 378, 385, - 392, 399, 406, 412, 419, 425, 432, 438, 445, 451, 457, 464, 470, 476, 482, - 489, 495, 501, 507, 513, 519, 525, 531, 536, 542, 548, 554, 560, 565, 571, - 577, 582, 588, 593, 599, 604, 610, 615, 621, 626, 631, 637, 642, 647, 652, - 658, 663, 668, 673, 678, 683, 688, 693, 698, 703, 708, 713, 718, 723, 728, - 732, 737, 742, 747, 751, 756, 761, 766, 770, 775, 779, 784, 788, 793, 798, - 802, 806, 811, 815, 820, 824, 829, 833, 837, 842, 846, 850, 854, 859, 863, - 867, 871, 876, 880, 884, 888, 892, 896, 900, 904, 908, 912, 916, 920, 924, - 928, 932, 936, 940, 944, 948, 952, 956, 959, 963, 967, 971, 975, 978, 982, - 986, 990, 993, 997, 1001, 1004, 1008, 1012, 1015, 1019, 1022, 1026, 1030, - 1033, 1037, 1040, 1044, 1047, 1051, 1054, 1058, 1061, 1065, 1068, 1072, 1075, - 1078, 1082, 1085, 1089, 1092, 1095, 1099, 1102, 1105, 1109, 1112, 1115, 1118, - 1122, 1125, 1128, 1131, 1135, 1138, 1141, 1144, 1147, 1151, 1154, 1157, 1160, - 1163, 1166, 1169, 1172, 1176, 1179, 1182, 1185, 1188, 1191, 1194, 1197, 1200, - 1203, 1206, 1209, 1212, 1215, 1218, 1221, 1224, 1227, 1230, 1233, 1235, 1238, - 1241, 1244, 1247, 1250, 1253, 1256, 1258, 1261, 1264, 1267, 1270, 1273, 1275, - 1278, 1281, 1284, 1286, 1289, 1292, 1295, 1297, 1300, 1303, 1306, 1308, 1311, - 1314, 1316, 1319, 1322, 1324, 1327, 1330, 1332, 1335, 1338, 1340, 1343, 1345, - 1348, 1351, 1353, 1356, 1358, 1361, 1364, 1366, 1369, 1371, 1374, 1376, 1379, - 1381, 1384, 1386, 1389, 1391, 1394, 1396, 1399, 1401, 1404, 1406, 1409, 1411, - 1413, 1416, 1418, 1421, 1423, 1426, 1428, 1430, 1433, 1435, 1437, 1440, 1442, - 1445, 1447, 1449, 1452, 1454, 1456, 1459, 1461, 1463, 1466, 1468, 1470, 1472, - 1475, 1477, 1479, 1482, 1484, 1486, 1488, 1491, 1493, 1495, 1497, 1500, 1502, - 1504, 1506, 1509, 1511, 1513, 1515, 1517, 1520, 1522, 1524, 1526, 1528, 1530, - 1533, 1535, 1537, 1539, 1541, 1543, 1545, 1548, 1550, 1552, 1554, 1556, 1558, - 1560, 1562, 1564, 1567, 1569, 1571, 1573, 1575, 1577, 1579, 1581, 1583, 1585, - 1587, 1589, 1591, 1593, 1595, 1597, 1599, 1601, 1603, 1605, 1607, 1609, - /* index 401 - 899: -log((i+100)/1000) * 1000 */ - 691, 689, 687, 685, 683, 681, 679, 677, 675, 673, 671, 669, 668, 666, 664, - 662, 660, 658, 656, 654, 652, 650, 648, 646, 644, 642, 641, 639, 637, 635, - 633, 631, 629, 627, 626, 624, 622, 620, 618, 616, 614, 612, 611, 609, 607, - 605, 603, 602, 600, 598, 596, 594, 592, 591, 589, 587, 585, 583, 582, 580, - 578, 576, 574, 573, 571, 569, 567, 566, 564, 562, 560, 559, 557, 555, 553, - 552, 550, 548, 546, 545, 543, 541, 540, 538, 536, 534, 533, 531, 529, 528, - 526, 524, 523, 521, 519, 518, 516, 514, 512, 511, 509, 508, 506, 504, 502, - 501, 499, 498, 496, 494, 493, 491, 489, 488, 486, 484, 483, 481, 480, 478, - 476, 475, 473, 472, 470, 468, 467, 465, 464, 462, 460, 459, 457, 456, 454, - 453, 451, 449, 448, 446, 445, 443, 442, 440, 438, 437, 435, 434, 432, 431, - 429, 428, 426, 425, 423, 422, 420, 419, 417, 416, 414, 412, 411, 410, 408, - 406, 405, 404, 402, 400, 399, 398, 396, 394, 393, 392, 390, 389, 387, 386, - 384, 383, 381, 380, 378, 377, 375, 374, 372, 371, 370, 368, 367, 365, 364, - 362, 361, 360, 358, 357, 355, 354, 352, 351, 350, 348, 347, 345, 344, 342, - 341, 340, 338, 337, 336, 334, 333, 331, 330, 328, 327, 326, 324, 323, 322, - 320, 319, 318, 316, 315, 313, 312, 311, 309, 308, 306, 305, 304, 302, 301, - 300, 298, 297, 296, 294, 293, 292, 290, 289, 288, 286, 285, 284, 282, 281, - 280, 278, 277, 276, 274, 273, 272, 270, 269, 268, 267, 265, 264, 263, 261, - 260, 259, 258, 256, 255, 254, 252, 251, 250, 248, 247, 246, 245, 243, 242, - 241, 240, 238, 237, 236, 234, 233, 232, 231, 229, 228, 227, 226, 224, 223, - 222, 221, 219, 218, 217, 216, 214, 213, 212, 211, 210, 208, 207, 206, 205, - 203, 202, 201, 200, 198, 197, 196, 195, 194, 192, 191, 190, 189, 188, 186, - 185, 184, 183, 182, 180, 179, 178, 177, 176, 174, 173, 172, 171, 170, 168, - 167, 166, 165, 164, 162, 161, 160, 159, 158, 157, 156, 154, 153, 152, 151, - 150, 148, 147, 146, 145, 144, 143, 142, 140, 139, 138, 137, 136, 135, 134, - 132, 131, 130, 129, 128, 127, 126, 124, 123, 122, 121, 120, 119, 118, 116, - 115, 114, 113, 112, 111, 110, 109, 108, 106, 105, 104, 103, 102, 101, 100, - 99, 98, 97, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 84, 83, 82, 81, 80, 79, - 78, 77, 76, 75, 74, 73, 72, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, - 58, 57, 56, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, - 38, 37, 36, 35, 34, 33, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, - 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 -}; - -/* - * Internal ln() function that does not check for specials, zero or one. - * Relative error: abs(result - log(a)) < 0.1 * 10**-prec * abs(log(a)) - */ -static void -_mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t varcontext, maxcontext; - mpd_t *z = result; - MPD_NEW_STATIC(v,0,0,0,0); - MPD_NEW_STATIC(vtmp,0,0,0,0); - MPD_NEW_STATIC(tmp,0,0,0,0); - mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; - mpd_ssize_t maxprec, shift, t; - mpd_ssize_t a_digits, a_exp; - mpd_uint_t dummy, x; - int i; - - assert(!mpd_isspecial(a) && !mpd_iszerocoeff(a)); - - /* - * We are calculating ln(a) = ln(v * 10^t) = ln(v) + t*ln(10), - * where 0.5 < v <= 5. - */ - if (!mpd_qcopy(&v, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - - /* Initial approximation: we have at least one non-zero digit */ - _mpd_get_msdigits(&dummy, &x, &v, 3); - if (x < 10) x *= 10; - if (x < 100) x *= 10; - x -= 100; - - /* a may equal z */ - a_digits = a->digits; - a_exp = a->exp; - - mpd_minalloc(z); - mpd_clear_flags(z); - z->data[0] = lnapprox[x]; - z->len = 1; - z->exp = -3; - mpd_setdigits(z); - - if (x <= 400) { - /* Reduce the input operand to 1.00 <= v <= 5.00. Let y = x + 100, - * so 100 <= y <= 500. Since y contains the most significant digits - * of v, y/100 <= v < (y+1)/100 and abs(z - log(v)) < 10**-2. */ - v.exp = -(a_digits - 1); - t = a_exp + a_digits - 1; - } - else { - /* Reduce the input operand to 0.500 < v <= 0.999. Let y = x + 100, - * so 500 < y <= 999. Since y contains the most significant digits - * of v, y/1000 <= v < (y+1)/1000 and abs(z - log(v)) < 10**-2. */ - v.exp = -a_digits; - t = a_exp + a_digits; - mpd_set_negative(z); - } - - mpd_maxcontext(&maxcontext); - mpd_maxcontext(&varcontext); - varcontext.round = MPD_ROUND_TRUNC; - - maxprec = ctx->prec + 2; - if (t == 0 && (x <= 15 || x >= 800)) { - /* 0.900 <= v <= 1.15: Estimate the magnitude of the logarithm. - * If ln(v) will underflow, skip the loop. Otherwise, adjust the - * precision upwards in order to obtain a sufficient number of - * significant digits. - * - * Case v > 1: - * abs((v-1)/10) < abs((v-1)/v) < abs(ln(v)) < abs(v-1) - * Case v < 1: - * abs(v-1) < abs(ln(v)) < abs((v-1)/v) < abs((v-1)*10) - */ - int cmp = _mpd_cmp(&v, &one); - - /* Upper bound (assume v > 1): abs(v-1), unrounded */ - _mpd_qsub(&tmp, &v, &one, &maxcontext, &maxcontext.status); - if (maxcontext.status & MPD_Errors) { - mpd_seterror(result, MPD_Malloc_error, status); - goto finish; - } - - if (cmp < 0) { - /* v < 1: abs((v-1)*10) */ - tmp.exp += 1; - } - if (mpd_adjexp(&tmp) < mpd_etiny(ctx)) { - /* The upper bound is less than etiny: Underflow to zero */ - _settriple(result, (cmp<0), 1, mpd_etiny(ctx)-1); - goto finish; - } - /* Lower bound: abs((v-1)/10) or abs(v-1) */ - tmp.exp -= 1; - if (mpd_adjexp(&tmp) < 0) { - /* Absolute error of the loop: abs(z - log(v)) < 10**-p. If - * p = ctx->prec+2-adjexp(lower), then the relative error of - * the result is (using 10**adjexp(x) <= abs(x)): - * - * abs(z - log(v)) / abs(log(v)) < 10**-p / abs(log(v)) - * <= 10**(-ctx->prec-2) - */ - maxprec = maxprec - mpd_adjexp(&tmp); - } - } - - i = ln_schedule_prec(klist, maxprec, 2); - for (; i >= 0; i--) { - varcontext.prec = 2*klist[i]+3; - z->flags ^= MPD_NEG; - _mpd_qexp(&tmp, z, &varcontext, status); - z->flags ^= MPD_NEG; - - if (v.digits > varcontext.prec) { - shift = v.digits - varcontext.prec; - mpd_qshiftr(&vtmp, &v, shift, status); - vtmp.exp += shift; - mpd_qmul(&tmp, &vtmp, &tmp, &varcontext, status); - } - else { - mpd_qmul(&tmp, &v, &tmp, &varcontext, status); - } - - mpd_qsub(&tmp, &tmp, &one, &maxcontext, status); - mpd_qadd(z, z, &tmp, &maxcontext, status); - if (mpd_isspecial(z)) { - break; - } - } - - /* - * Case t == 0: - * t * log(10) == 0, the result does not change and the analysis - * above applies. If v < 0.900 or v > 1.15, the relative error is - * less than 10**(-ctx.prec-1). - * Case t != 0: - * z := approx(log(v)) - * y := approx(log(10)) - * p := maxprec = ctx->prec + 2 - * Absolute errors: - * 1) abs(z - log(v)) < 10**-p - * 2) abs(y - log(10)) < 10**-p - * The multiplication is exact, so: - * 3) abs(t*y - t*log(10)) < t*10**-p - * The sum is exact, so: - * 4) abs((z + t*y) - (log(v) + t*log(10))) < (abs(t) + 1) * 10**-p - * Bounds for log(v) and log(10): - * 5) -7/10 < log(v) < 17/10 - * 6) 23/10 < log(10) < 24/10 - * Using 4), 5), 6) and t != 0, the relative error is: - * - * 7) relerr < ((abs(t) + 1)*10**-p) / abs(log(v) + t*log(10)) - * < 0.5 * 10**(-p + 1) = 0.5 * 10**(-ctx->prec-1) - */ - mpd_qln10(&v, maxprec+1, status); - mpd_qmul_ssize(&tmp, &v, t, &maxcontext, status); - mpd_qadd(result, &tmp, z, &maxcontext, status); - - -finish: - *status |= (MPD_Inexact|MPD_Rounded); - mpd_del(&v); - mpd_del(&vtmp); - mpd_del(&tmp); -} - -/* ln(a) */ -void -mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - mpd_ssize_t adjexp, t; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - mpd_setspecial(result, MPD_POS, MPD_INF); - return; - } - if (mpd_iszerocoeff(a)) { - mpd_setspecial(result, MPD_NEG, MPD_INF); - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (_mpd_cmp(a, &one) == 0) { - _settriple(result, MPD_POS, 0, 0); - return; - } - /* - * Check if the result will overflow (0 < x, x != 1): - * 1) log10(x) < 0 iff adjexp(x) < 0 - * 2) 0 < x /\ x <= y ==> adjexp(x) <= adjexp(y) - * 3) 0 < x /\ x != 1 ==> 2 * abs(log10(x)) < abs(log(x)) - * 4) adjexp(x) <= log10(x) < adjexp(x) + 1 - * - * Case adjexp(x) >= 0: - * 5) 2 * adjexp(x) < abs(log(x)) - * Case adjexp(x) > 0: - * 6) adjexp(2 * adjexp(x)) <= adjexp(abs(log(x))) - * Case adjexp(x) == 0: - * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) - * - * Case adjexp(x) < 0: - * 7) 2 * (-adjexp(x) - 1) < abs(log(x)) - * Case adjexp(x) < -1: - * 8) adjexp(2 * (-adjexp(x) - 1)) <= adjexp(abs(log(x))) - * Case adjexp(x) == -1: - * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) - */ - adjexp = mpd_adjexp(a); - t = (adjexp < 0) ? -adjexp-1 : adjexp; - t *= 2; - if (mpd_exp_digits(t)-1 > ctx->emax) { - *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; - mpd_setspecial(result, (adjexp<0), MPD_INF); - return; - } - - workctx = *ctx; - workctx.round = MPD_ROUND_HALF_EVEN; - - if (ctx->allcr) { - MPD_NEW_STATIC(t1, 0,0,0,0); - MPD_NEW_STATIC(t2, 0,0,0,0); - MPD_NEW_STATIC(ulp, 0,0,0,0); - MPD_NEW_STATIC(aa, 0,0,0,0); - mpd_ssize_t prec; - - if (result == a) { - if (!mpd_qcopy(&aa, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - a = &aa; - } - - workctx.clamp = 0; - prec = ctx->prec + 3; - while (1) { - workctx.prec = prec; - _mpd_qln(result, a, &workctx, status); - _ssettriple(&ulp, MPD_POS, 1, - result->exp + result->digits-workctx.prec); - - workctx.prec = ctx->prec; - mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status); - mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status); - if (mpd_isspecial(result) || mpd_iszerocoeff(result) || - mpd_qcmp(&t1, &t2, status) == 0) { - workctx.clamp = ctx->clamp; - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - break; - } - prec += MPD_RDIGITS; - } - mpd_del(&t1); - mpd_del(&t2); - mpd_del(&ulp); - mpd_del(&aa); - } - else { - _mpd_qln(result, a, &workctx, status); - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - } -} - -/* - * Internal log10() function that does not check for specials, zero or one. - * Case SKIP_FINALIZE: - * Relative error: abs(result - log10(a)) < 0.1 * 10**-prec * abs(log10(a)) - * Case DO_FINALIZE: - * Ulp error: abs(result - log10(a)) < ulp(log10(a)) - */ -enum {SKIP_FINALIZE, DO_FINALIZE}; -static void -_mpd_qlog10(int action, mpd_t *result, const mpd_t *a, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(ln10,0,0,0,0); - - mpd_maxcontext(&workctx); - workctx.prec = ctx->prec + 3; - /* relative error: 0.1 * 10**(-p-3). The specific underflow shortcut - * in _mpd_qln() does not change the final result. */ - _mpd_qln(result, a, &workctx, status); - /* relative error: 5 * 10**(-p-3) */ - mpd_qln10(&ln10, workctx.prec, status); - - if (action == DO_FINALIZE) { - workctx = *ctx; - workctx.round = MPD_ROUND_HALF_EVEN; - } - /* SKIP_FINALIZE: relative error: 5 * 10**(-p-3) */ - _mpd_qdiv(NO_IDEAL_EXP, result, result, &ln10, &workctx, status); - - mpd_del(&ln10); -} - -/* log10(a) */ -void -mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - mpd_ssize_t adjexp, t; - - workctx = *ctx; - workctx.round = MPD_ROUND_HALF_EVEN; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - mpd_setspecial(result, MPD_POS, MPD_INF); - return; - } - if (mpd_iszerocoeff(a)) { - mpd_setspecial(result, MPD_NEG, MPD_INF); - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_coeff_ispow10(a)) { - uint8_t sign = 0; - adjexp = mpd_adjexp(a); - if (adjexp < 0) { - sign = 1; - adjexp = -adjexp; - } - _settriple(result, sign, adjexp, 0); - mpd_qfinalize(result, &workctx, status); - return; - } - /* - * Check if the result will overflow (0 < x, x != 1): - * 1) log10(x) < 0 iff adjexp(x) < 0 - * 2) 0 < x /\ x <= y ==> adjexp(x) <= adjexp(y) - * 3) adjexp(x) <= log10(x) < adjexp(x) + 1 - * - * Case adjexp(x) >= 0: - * 4) adjexp(x) <= abs(log10(x)) - * Case adjexp(x) > 0: - * 5) adjexp(adjexp(x)) <= adjexp(abs(log10(x))) - * Case adjexp(x) == 0: - * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) - * - * Case adjexp(x) < 0: - * 6) -adjexp(x) - 1 < abs(log10(x)) - * Case adjexp(x) < -1: - * 7) adjexp(-adjexp(x) - 1) <= adjexp(abs(log(x))) - * Case adjexp(x) == -1: - * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) - */ - adjexp = mpd_adjexp(a); - t = (adjexp < 0) ? -adjexp-1 : adjexp; - if (mpd_exp_digits(t)-1 > ctx->emax) { - *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; - mpd_setspecial(result, (adjexp<0), MPD_INF); - return; - } - - if (ctx->allcr) { - MPD_NEW_STATIC(t1, 0,0,0,0); - MPD_NEW_STATIC(t2, 0,0,0,0); - MPD_NEW_STATIC(ulp, 0,0,0,0); - MPD_NEW_STATIC(aa, 0,0,0,0); - mpd_ssize_t prec; - - if (result == a) { - if (!mpd_qcopy(&aa, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - a = &aa; - } - - workctx.clamp = 0; - prec = ctx->prec + 3; - while (1) { - workctx.prec = prec; - _mpd_qlog10(SKIP_FINALIZE, result, a, &workctx, status); - _ssettriple(&ulp, MPD_POS, 1, - result->exp + result->digits-workctx.prec); - - workctx.prec = ctx->prec; - mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status); - mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status); - if (mpd_isspecial(result) || mpd_iszerocoeff(result) || - mpd_qcmp(&t1, &t2, status) == 0) { - workctx.clamp = ctx->clamp; - mpd_check_underflow(result, &workctx, status); - mpd_qfinalize(result, &workctx, status); - break; - } - prec += MPD_RDIGITS; - } - mpd_del(&t1); - mpd_del(&t2); - mpd_del(&ulp); - mpd_del(&aa); - } - else { - _mpd_qlog10(DO_FINALIZE, result, a, &workctx, status); - mpd_check_underflow(result, &workctx, status); - } -} - -/* - * Maximum of the two operands. Attention: If one operand is a quiet NaN and the - * other is numeric, the numeric operand is returned. This may not be what one - * expects. - */ -void -mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isqnan(a) && !mpd_isnan(b)) { - mpd_qcopy(result, b, status); - } - else if (mpd_isqnan(b) && !mpd_isnan(a)) { - mpd_qcopy(result, a, status); - } - else if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - else { - c = _mpd_cmp(a, b); - if (c == 0) { - c = _mpd_cmp_numequal(a, b); - } - - if (c < 0) { - mpd_qcopy(result, b, status); - } - else { - mpd_qcopy(result, a, status); - } - } - - mpd_qfinalize(result, ctx, status); -} - -/* - * Maximum magnitude: Same as mpd_max(), but compares the operands with their - * sign ignored. - */ -void -mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isqnan(a) && !mpd_isnan(b)) { - mpd_qcopy(result, b, status); - } - else if (mpd_isqnan(b) && !mpd_isnan(a)) { - mpd_qcopy(result, a, status); - } - else if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - else { - c = _mpd_cmp_abs(a, b); - if (c == 0) { - c = _mpd_cmp_numequal(a, b); - } - - if (c < 0) { - mpd_qcopy(result, b, status); - } - else { - mpd_qcopy(result, a, status); - } - } - - mpd_qfinalize(result, ctx, status); -} - -/* - * Minimum of the two operands. Attention: If one operand is a quiet NaN and the - * other is numeric, the numeric operand is returned. This may not be what one - * expects. - */ -void -mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isqnan(a) && !mpd_isnan(b)) { - mpd_qcopy(result, b, status); - } - else if (mpd_isqnan(b) && !mpd_isnan(a)) { - mpd_qcopy(result, a, status); - } - else if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - else { - c = _mpd_cmp(a, b); - if (c == 0) { - c = _mpd_cmp_numequal(a, b); - } - - if (c < 0) { - mpd_qcopy(result, a, status); - } - else { - mpd_qcopy(result, b, status); - } - } - - mpd_qfinalize(result, ctx, status); -} - -/* - * Minimum magnitude: Same as mpd_min(), but compares the operands with their - * sign ignored. - */ -void -mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_isqnan(a) && !mpd_isnan(b)) { - mpd_qcopy(result, b, status); - } - else if (mpd_isqnan(b) && !mpd_isnan(a)) { - mpd_qcopy(result, a, status); - } - else if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - else { - c = _mpd_cmp_abs(a, b); - if (c == 0) { - c = _mpd_cmp_numequal(a, b); - } - - if (c < 0) { - mpd_qcopy(result, a, status); - } - else { - mpd_qcopy(result, b, status); - } - } - - mpd_qfinalize(result, ctx, status); -} - -/* Minimum space needed for the result array in _karatsuba_rec(). */ -static inline mpd_size_t -_kmul_resultsize(mpd_size_t la, mpd_size_t lb) -{ - mpd_size_t n, m; - - n = add_size_t(la, lb); - n = add_size_t(n, 1); - - m = (la+1)/2 + 1; - m = mul_size_t(m, 3); - - return (m > n) ? m : n; -} - -/* Work space needed in _karatsuba_rec(). lim >= 4 */ -static inline mpd_size_t -_kmul_worksize(mpd_size_t n, mpd_size_t lim) -{ - mpd_size_t m; - - if (n <= lim) { - return 0; - } - - m = (n+1)/2 + 1; - - return add_size_t(mul_size_t(m, 2), _kmul_worksize(m, lim)); -} - - -#define MPD_KARATSUBA_BASECASE 16 /* must be >= 4 */ - -/* - * Add the product of a and b to c. - * c must be _kmul_resultsize(la, lb) in size. - * w is used as a work array and must be _kmul_worksize(a, lim) in size. - * Roman E. Maeder, Storage Allocation for the Karatsuba Integer Multiplication - * Algorithm. In "Design and implementation of symbolic computation systems", - * Springer, 1993, ISBN 354057235X, 9783540572350. - */ -static void -_karatsuba_rec(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b, - mpd_uint_t *w, mpd_size_t la, mpd_size_t lb) -{ - mpd_size_t m, lt; - - assert(la >= lb && lb > 0); - assert(la <= MPD_KARATSUBA_BASECASE || w != NULL); - - if (la <= MPD_KARATSUBA_BASECASE) { - _mpd_basemul(c, a, b, la, lb); - return; - } - - m = (la+1)/2; /* ceil(la/2) */ - - /* lb <= m < la */ - if (lb <= m) { - - /* lb can now be larger than la-m */ - if (lb > la-m) { - lt = lb + lb + 1; /* space needed for result array */ - mpd_uint_zero(w, lt); /* clear result array */ - _karatsuba_rec(w, b, a+m, w+lt, lb, la-m); /* b*ah */ - } - else { - lt = (la-m) + (la-m) + 1; /* space needed for result array */ - mpd_uint_zero(w, lt); /* clear result array */ - _karatsuba_rec(w, a+m, b, w+lt, la-m, lb); /* ah*b */ - } - _mpd_baseaddto(c+m, w, (la-m)+lb); /* add ah*b*B**m */ - - lt = m + m + 1; /* space needed for the result array */ - mpd_uint_zero(w, lt); /* clear result array */ - _karatsuba_rec(w, a, b, w+lt, m, lb); /* al*b */ - _mpd_baseaddto(c, w, m+lb); /* add al*b */ - - return; - } - - /* la >= lb > m */ - memcpy(w, a, m * sizeof *w); - w[m] = 0; - _mpd_baseaddto(w, a+m, la-m); - - memcpy(w+(m+1), b, m * sizeof *w); - w[m+1+m] = 0; - _mpd_baseaddto(w+(m+1), b+m, lb-m); - - _karatsuba_rec(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1); - - lt = (la-m) + (la-m) + 1; - mpd_uint_zero(w, lt); - - _karatsuba_rec(w, a+m, b+m, w+lt, la-m, lb-m); - - _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m)); - _mpd_basesubfrom(c+m, w, (la-m) + (lb-m)); - - lt = m + m + 1; - mpd_uint_zero(w, lt); - - _karatsuba_rec(w, a, b, w+lt, m, m); - _mpd_baseaddto(c, w, m+m); - _mpd_basesubfrom(c+m, w, m+m); - - return; -} - -/* - * Multiply u and v, using Karatsuba multiplication. Returns a pointer - * to the result or NULL in case of failure (malloc error). - * Conditions: ulen >= vlen, ulen >= 4 - */ -static mpd_uint_t * -_mpd_kmul(const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t ulen, mpd_size_t vlen, - mpd_size_t *rsize) -{ - mpd_uint_t *result = NULL, *w = NULL; - mpd_size_t m; - - assert(ulen >= 4); - assert(ulen >= vlen); - - *rsize = _kmul_resultsize(ulen, vlen); - if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) { - return NULL; - } - - m = _kmul_worksize(ulen, MPD_KARATSUBA_BASECASE); - if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) { - mpd_free(result); - return NULL; - } - - _karatsuba_rec(result, u, v, w, ulen, vlen); - - - if (w) mpd_free(w); - return result; -} - - -/* - * Determine the minimum length for the number theoretic transform. Valid - * transform lengths are 2**n or 3*2**n, where 2**n <= MPD_MAXTRANSFORM_2N. - * The function finds the shortest length m such that rsize <= m. - */ -static inline mpd_size_t -_mpd_get_transform_len(mpd_size_t rsize) -{ - mpd_size_t log2rsize; - mpd_size_t x, step; - - assert(rsize >= 4); - log2rsize = mpd_bsr(rsize); - - if (rsize <= 1024) { - /* 2**n is faster in this range. */ - x = ((mpd_size_t)1)<>1; - x += step; - return (rsize <= x) ? x : x + step; - } - else if (rsize <= MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2) { - return MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2; - } - else if (rsize <= 3*MPD_MAXTRANSFORM_2N) { - return 3*MPD_MAXTRANSFORM_2N; - } - else { - return MPD_SIZE_MAX; - } -} - -#ifdef PPRO -#ifndef _MSC_VER -static inline unsigned short -_mpd_get_control87(void) -{ - unsigned short cw; - - __asm__ __volatile__ ("fnstcw %0" : "=m" (cw)); - return cw; -} - -static inline void -_mpd_set_control87(unsigned short cw) -{ - __asm__ __volatile__ ("fldcw %0" : : "m" (cw)); -} -#endif - -static unsigned int -mpd_set_fenv(void) -{ - unsigned int cw; -#ifdef _MSC_VER - unsigned int flags = - _EM_INVALID|_EM_DENORMAL|_EM_ZERODIVIDE|_EM_OVERFLOW| - _EM_UNDERFLOW|_EM_INEXACT|_RC_CHOP|_PC_64; - unsigned int mask = _MCW_EM|_MCW_RC|_MCW_PC; - unsigned int dummy; - - __control87_2(0, 0, &cw, NULL); - __control87_2(flags, mask, &dummy, NULL); -#else - cw = _mpd_get_control87(); - _mpd_set_control87(cw|0xF3F); -#endif - return cw; -} - -static void -mpd_restore_fenv(unsigned int cw) -{ -#ifdef _MSC_VER - unsigned int mask = _MCW_EM|_MCW_RC|_MCW_PC; - unsigned int dummy; - - __control87_2(cw, mask, &dummy, NULL); -#else - _mpd_set_control87((unsigned short)cw); -#endif -} -#endif /* PPRO */ - -/* - * Multiply u and v, using the fast number theoretic transform. Returns - * a pointer to the result or NULL in case of failure (malloc error). - */ -static mpd_uint_t * -_mpd_fntmul(const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t ulen, mpd_size_t vlen, - mpd_size_t *rsize) -{ - mpd_uint_t *c1 = NULL, *c2 = NULL, *c3 = NULL, *vtmp = NULL; - mpd_size_t n; - -#ifdef PPRO - unsigned int cw; - cw = mpd_set_fenv(); -#endif - - *rsize = add_size_t(ulen, vlen); - if ((n = _mpd_get_transform_len(*rsize)) == MPD_SIZE_MAX) { - goto malloc_error; - } - - if ((c1 = mpd_calloc(n, sizeof *c1)) == NULL) { - goto malloc_error; - } - if ((c2 = mpd_calloc(n, sizeof *c2)) == NULL) { - goto malloc_error; - } - if ((c3 = mpd_calloc(n, sizeof *c3)) == NULL) { - goto malloc_error; - } - - memcpy(c1, u, ulen * (sizeof *c1)); - memcpy(c2, u, ulen * (sizeof *c2)); - memcpy(c3, u, ulen * (sizeof *c3)); - - if (u == v) { - if (!fnt_autoconvolute(c1, n, P1) || - !fnt_autoconvolute(c2, n, P2) || - !fnt_autoconvolute(c3, n, P3)) { - goto malloc_error; - } - } - else { - if ((vtmp = mpd_calloc(n, sizeof *vtmp)) == NULL) { - goto malloc_error; - } - - memcpy(vtmp, v, vlen * (sizeof *vtmp)); - if (!fnt_convolute(c1, vtmp, n, P1)) { - mpd_free(vtmp); - goto malloc_error; - } - - memcpy(vtmp, v, vlen * (sizeof *vtmp)); - mpd_uint_zero(vtmp+vlen, n-vlen); - if (!fnt_convolute(c2, vtmp, n, P2)) { - mpd_free(vtmp); - goto malloc_error; - } - - memcpy(vtmp, v, vlen * (sizeof *vtmp)); - mpd_uint_zero(vtmp+vlen, n-vlen); - if (!fnt_convolute(c3, vtmp, n, P3)) { - mpd_free(vtmp); - goto malloc_error; - } - - mpd_free(vtmp); - } - - crt3(c1, c2, c3, *rsize); - -out: -#ifdef PPRO - mpd_restore_fenv(cw); -#endif - if (c2) mpd_free(c2); - if (c3) mpd_free(c3); - return c1; - -malloc_error: - if (c1) mpd_free(c1); - c1 = NULL; - goto out; -} - - -/* - * Karatsuba multiplication with FNT/basemul as the base case. - */ -static int -_karatsuba_rec_fnt(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b, - mpd_uint_t *w, mpd_size_t la, mpd_size_t lb) -{ - mpd_size_t m, lt; - - assert(la >= lb && lb > 0); - assert(la <= 3*(MPD_MAXTRANSFORM_2N/2) || w != NULL); - - if (la <= 3*(MPD_MAXTRANSFORM_2N/2)) { - - if (lb <= 192) { - _mpd_basemul(c, b, a, lb, la); - } - else { - mpd_uint_t *result; - mpd_size_t dummy; - - if ((result = _mpd_fntmul(a, b, la, lb, &dummy)) == NULL) { - return 0; - } - memcpy(c, result, (la+lb) * (sizeof *result)); - mpd_free(result); - } - return 1; - } - - m = (la+1)/2; /* ceil(la/2) */ - - /* lb <= m < la */ - if (lb <= m) { - - /* lb can now be larger than la-m */ - if (lb > la-m) { - lt = lb + lb + 1; /* space needed for result array */ - mpd_uint_zero(w, lt); /* clear result array */ - if (!_karatsuba_rec_fnt(w, b, a+m, w+lt, lb, la-m)) { /* b*ah */ - return 0; /* GCOV_UNLIKELY */ - } - } - else { - lt = (la-m) + (la-m) + 1; /* space needed for result array */ - mpd_uint_zero(w, lt); /* clear result array */ - if (!_karatsuba_rec_fnt(w, a+m, b, w+lt, la-m, lb)) { /* ah*b */ - return 0; /* GCOV_UNLIKELY */ - } - } - _mpd_baseaddto(c+m, w, (la-m)+lb); /* add ah*b*B**m */ - - lt = m + m + 1; /* space needed for the result array */ - mpd_uint_zero(w, lt); /* clear result array */ - if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, lb)) { /* al*b */ - return 0; /* GCOV_UNLIKELY */ - } - _mpd_baseaddto(c, w, m+lb); /* add al*b */ - - return 1; - } - - /* la >= lb > m */ - memcpy(w, a, m * sizeof *w); - w[m] = 0; - _mpd_baseaddto(w, a+m, la-m); - - memcpy(w+(m+1), b, m * sizeof *w); - w[m+1+m] = 0; - _mpd_baseaddto(w+(m+1), b+m, lb-m); - - if (!_karatsuba_rec_fnt(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1)) { - return 0; /* GCOV_UNLIKELY */ - } - - lt = (la-m) + (la-m) + 1; - mpd_uint_zero(w, lt); - - if (!_karatsuba_rec_fnt(w, a+m, b+m, w+lt, la-m, lb-m)) { - return 0; /* GCOV_UNLIKELY */ - } - - _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m)); - _mpd_basesubfrom(c+m, w, (la-m) + (lb-m)); - - lt = m + m + 1; - mpd_uint_zero(w, lt); - - if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, m)) { - return 0; /* GCOV_UNLIKELY */ - } - _mpd_baseaddto(c, w, m+m); - _mpd_basesubfrom(c+m, w, m+m); - - return 1; -} - -/* - * Multiply u and v, using Karatsuba multiplication with the FNT as the - * base case. Returns a pointer to the result or NULL in case of failure - * (malloc error). Conditions: ulen >= vlen, ulen >= 4. - */ -static mpd_uint_t * -_mpd_kmul_fnt(const mpd_uint_t *u, const mpd_uint_t *v, - mpd_size_t ulen, mpd_size_t vlen, - mpd_size_t *rsize) -{ - mpd_uint_t *result = NULL, *w = NULL; - mpd_size_t m; - - assert(ulen >= 4); - assert(ulen >= vlen); - - *rsize = _kmul_resultsize(ulen, vlen); - if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) { - return NULL; - } - - m = _kmul_worksize(ulen, 3*(MPD_MAXTRANSFORM_2N/2)); - if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) { - mpd_free(result); /* GCOV_UNLIKELY */ - return NULL; /* GCOV_UNLIKELY */ - } - - if (!_karatsuba_rec_fnt(result, u, v, w, ulen, vlen)) { - mpd_free(result); - result = NULL; - } - - - if (w) mpd_free(w); - return result; -} - - -/* Deal with the special cases of multiplying infinities. */ -static void -_mpd_qmul_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status) -{ - if (mpd_isinfinite(a)) { - if (mpd_iszero(b)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } - else { - mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF); - } - return; - } - assert(mpd_isinfinite(b)); - if (mpd_iszero(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } - else { - mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF); - } -} - -/* - * Internal function: Multiply a and b. _mpd_qmul deals with specials but - * does NOT finalize the result. This is for use in mpd_fma(). - */ -static inline void -_mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - const mpd_t *big = a, *small = b; - mpd_uint_t *rdata = NULL; - mpd_uint_t rbuf[MPD_MINALLOC_MAX]; - mpd_size_t rsize, i; - - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - _mpd_qmul_inf(result, a, b, status); - return; - } - - if (small->len > big->len) { - _mpd_ptrswap(&big, &small); - } - - rsize = big->len + small->len; - - if (big->len == 1) { - _mpd_singlemul(result->data, big->data[0], small->data[0]); - goto finish; - } - if (rsize <= (mpd_size_t)MPD_MINALLOC_MAX) { - if (big->len == 2) { - _mpd_mul_2_le2(rbuf, big->data, small->data, small->len); - } - else { - mpd_uint_zero(rbuf, rsize); - if (small->len == 1) { - _mpd_shortmul(rbuf, big->data, big->len, small->data[0]); - } - else { - _mpd_basemul(rbuf, small->data, big->data, small->len, big->len); - } - } - if (!mpd_qresize(result, rsize, status)) { - return; - } - for(i = 0; i < rsize; i++) { - result->data[i] = rbuf[i]; - } - goto finish; - } - - - if (small->len <= 256) { - rdata = mpd_calloc(rsize, sizeof *rdata); - if (rdata != NULL) { - if (small->len == 1) { - _mpd_shortmul(rdata, big->data, big->len, small->data[0]); - } - else { - _mpd_basemul(rdata, small->data, big->data, small->len, big->len); - } - } - } - else if (rsize <= 1024) { - rdata = _mpd_kmul(big->data, small->data, big->len, small->len, &rsize); - } - else if (rsize <= 3*MPD_MAXTRANSFORM_2N) { - rdata = _mpd_fntmul(big->data, small->data, big->len, small->len, &rsize); - } - else { - rdata = _mpd_kmul_fnt(big->data, small->data, big->len, small->len, &rsize); - } - - if (rdata == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - - if (mpd_isdynamic_data(result)) { - mpd_free(result->data); - } - result->data = rdata; - result->alloc = rsize; - mpd_set_dynamic_data(result); - - -finish: - mpd_set_flags(result, mpd_sign(a)^mpd_sign(b)); - result->exp = big->exp + small->exp; - result->len = _mpd_real_size(result->data, rsize); - /* resize to smaller cannot fail */ - mpd_qresize(result, result->len, status); - mpd_setdigits(result); -} - -/* Multiply a and b. */ -void -mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - _mpd_qmul(result, a, b, ctx, status); - mpd_qfinalize(result, ctx, status); -} - -/* Multiply a and b. Set NaN/Invalid_operation if the result is inexact. */ -static void -_mpd_qmul_exact(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - - mpd_qmul(result, a, b, ctx, &workstatus); - *status |= workstatus; - if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } -} - -/* Multiply decimal and mpd_ssize_t. */ -void -mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_ssize(&bb, b, &maxcontext, status); - mpd_qmul(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Multiply decimal and mpd_uint_t. */ -void -mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qsset_uint(&bb, b, &maxcontext, status); - mpd_qmul(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -void -mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qmul_ssize(result, a, b, ctx, status); -} - -void -mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qmul_uint(result, a, b, ctx, status); -} - -#ifdef CONFIG_64 -void -mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qmul_ssize(result, a, b, ctx, status); -} - -void -mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_qmul_uint(result, a, b, ctx, status); -} -#elif !defined(LEGACY_COMPILER) -/* Multiply decimal and int64_t. */ -void -mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_i64(&bb, b, &maxcontext, status); - mpd_qmul(result, a, &bb, ctx, status); - mpd_del(&bb); -} - -/* Multiply decimal and uint64_t. */ -void -mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(bb,0,0,0,0); - - mpd_maxcontext(&maxcontext); - mpd_qset_u64(&bb, b, &maxcontext, status); - mpd_qmul(result, a, &bb, ctx, status); - mpd_del(&bb); -} -#endif - -/* Like the minus operator. */ -void -mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - } - - if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) { - mpd_qcopy_abs(result, a, status); - } - else { - mpd_qcopy_negate(result, a, status); - } - - mpd_qfinalize(result, ctx, status); -} - -/* Like the plus operator. */ -void -mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - } - - if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) { - mpd_qcopy_abs(result, a, status); - } - else { - mpd_qcopy(result, a, status); - } - - mpd_qfinalize(result, ctx, status); -} - -/* The largest representable number that is smaller than the operand. */ -void -mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1); - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - - assert(mpd_isinfinite(a)); - if (mpd_isnegative(a)) { - mpd_qcopy(result, a, status); - return; - } - else { - mpd_clear_flags(result); - mpd_qmaxcoeff(result, ctx, status); - if (mpd_isnan(result)) { - return; - } - result->exp = mpd_etop(ctx); - return; - } - } - - mpd_workcontext(&workctx, ctx); - workctx.round = MPD_ROUND_FLOOR; - - if (!mpd_qcopy(result, a, status)) { - return; - } - - mpd_qfinalize(result, &workctx, &workctx.status); - if (workctx.status&(MPD_Inexact|MPD_Errors)) { - *status |= (workctx.status&MPD_Errors); - return; - } - - workctx.status = 0; - mpd_qsub(result, a, &tiny, &workctx, &workctx.status); - *status |= (workctx.status&MPD_Errors); -} - -/* The smallest representable number that is larger than the operand. */ -void -mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1); - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - - assert(mpd_isinfinite(a)); - if (mpd_ispositive(a)) { - mpd_qcopy(result, a, status); - } - else { - mpd_clear_flags(result); - mpd_qmaxcoeff(result, ctx, status); - if (mpd_isnan(result)) { - return; - } - mpd_set_flags(result, MPD_NEG); - result->exp = mpd_etop(ctx); - } - return; - } - - mpd_workcontext(&workctx, ctx); - workctx.round = MPD_ROUND_CEILING; - - if (!mpd_qcopy(result, a, status)) { - return; - } - - mpd_qfinalize(result, &workctx, &workctx.status); - if (workctx.status & (MPD_Inexact|MPD_Errors)) { - *status |= (workctx.status&MPD_Errors); - return; - } - - workctx.status = 0; - mpd_qadd(result, a, &tiny, &workctx, &workctx.status); - *status |= (workctx.status&MPD_Errors); -} - -/* - * The number closest to the first operand that is in the direction towards - * the second operand. - */ -void -mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - int c; - - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - - c = _mpd_cmp(a, b); - if (c == 0) { - mpd_qcopy_sign(result, a, b, status); - return; - } - - if (c < 0) { - mpd_qnext_plus(result, a, ctx, status); - } - else { - mpd_qnext_minus(result, a, ctx, status); - } - - if (mpd_isinfinite(result)) { - *status |= (MPD_Overflow|MPD_Rounded|MPD_Inexact); - } - else if (mpd_adjexp(result) < ctx->emin) { - *status |= (MPD_Underflow|MPD_Subnormal|MPD_Rounded|MPD_Inexact); - if (mpd_iszero(result)) { - *status |= MPD_Clamped; - } - } -} - -/* - * Internal function: Integer power with mpd_uint_t exponent. The function - * can fail with MPD_Malloc_error. - * - * The error is equal to the error incurred in k-1 multiplications. Assuming - * the upper bound for the relative error in each operation: - * - * abs(err) = 5 * 10**-prec - * result = x**k * (1 + err)**(k-1) - */ -static inline void -_mpd_qpow_uint(mpd_t *result, const mpd_t *base, mpd_uint_t exp, - uint8_t resultsign, const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_uint_t n; - - if (exp == 0) { - _settriple(result, resultsign, 1, 0); /* GCOV_NOT_REACHED */ - return; /* GCOV_NOT_REACHED */ - } - - if (!mpd_qcopy(result, base, status)) { - return; - } - - n = mpd_bits[mpd_bsr(exp)]; - while (n >>= 1) { - mpd_qmul(result, result, result, ctx, &workstatus); - if (exp & n) { - mpd_qmul(result, result, base, ctx, &workstatus); - } - if (mpd_isspecial(result) || - (mpd_iszerocoeff(result) && (workstatus & MPD_Clamped))) { - break; - } - } - - *status |= workstatus; - mpd_set_sign(result, resultsign); -} - -/* - * Internal function: Integer power with mpd_t exponent, tbase and texp - * are modified!! Function can fail with MPD_Malloc_error. - * - * The error is equal to the error incurred in k multiplications. Assuming - * the upper bound for the relative error in each operation: - * - * abs(err) = 5 * 10**-prec - * result = x**k * (1 + err)**k - */ -static inline void -_mpd_qpow_mpd(mpd_t *result, mpd_t *tbase, mpd_t *texp, uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_context_t maxctx; - MPD_NEW_CONST(two,0,0,1,1,1,2); - - - mpd_maxcontext(&maxctx); - - /* resize to smaller cannot fail */ - mpd_qcopy(result, &one, status); - - while (!mpd_iszero(texp)) { - if (mpd_isodd(texp)) { - mpd_qmul(result, result, tbase, ctx, &workstatus); - *status |= workstatus; - if (mpd_isspecial(result) || - (mpd_iszerocoeff(result) && (workstatus & MPD_Clamped))) { - break; - } - } - mpd_qmul(tbase, tbase, tbase, ctx, &workstatus); - mpd_qdivint(texp, texp, &two, &maxctx, &workstatus); - if (mpd_isnan(tbase) || mpd_isnan(texp)) { - mpd_seterror(result, workstatus&MPD_Errors, status); - return; - } - } - mpd_set_sign(result, resultsign); -} - -/* - * The power function for integer exponents. Relative error _before_ the - * final rounding to prec: - * abs(result - base**exp) < 0.1 * 10**-prec * abs(base**exp) - */ -static void -_mpd_qpow_int(mpd_t *result, const mpd_t *base, const mpd_t *exp, - uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(tbase,0,0,0,0); - MPD_NEW_STATIC(texp,0,0,0,0); - mpd_uint_t n; - - - mpd_workcontext(&workctx, ctx); - workctx.prec += (exp->digits + exp->exp + 2); - workctx.round = MPD_ROUND_HALF_EVEN; - workctx.clamp = 0; - if (mpd_isnegative(exp)) { - uint32_t workstatus = 0; - workctx.prec += 1; - mpd_qdiv(&tbase, &one, base, &workctx, &workstatus); - *status |= workstatus; - if (workstatus&MPD_Errors) { - mpd_setspecial(result, MPD_POS, MPD_NAN); - goto finish; - } - } - else { - if (!mpd_qcopy(&tbase, base, status)) { - mpd_setspecial(result, MPD_POS, MPD_NAN); - goto finish; - } - } - - n = mpd_qabs_uint(exp, &workctx.status); - if (workctx.status&MPD_Invalid_operation) { - if (!mpd_qcopy(&texp, exp, status)) { - mpd_setspecial(result, MPD_POS, MPD_NAN); /* GCOV_UNLIKELY */ - goto finish; /* GCOV_UNLIKELY */ - } - _mpd_qpow_mpd(result, &tbase, &texp, resultsign, &workctx, status); - } - else { - _mpd_qpow_uint(result, &tbase, n, resultsign, &workctx, status); - } - - if (mpd_isinfinite(result)) { - /* for ROUND_DOWN, ROUND_FLOOR, etc. */ - _settriple(result, resultsign, 1, MPD_EXP_INF); - } - -finish: - mpd_del(&tbase); - mpd_del(&texp); - mpd_qfinalize(result, ctx, status); -} - -/* - * If the exponent is infinite and base equals one, the result is one - * with a coefficient of length prec. Otherwise, result is undefined. - * Return the value of the comparison against one. - */ -static int -_qcheck_pow_one_inf(mpd_t *result, const mpd_t *base, uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t shift; - int cmp; - - if ((cmp = _mpd_cmp(base, &one)) == 0) { - shift = ctx->prec-1; - mpd_qshiftl(result, &one, shift, status); - result->exp = -shift; - mpd_set_flags(result, resultsign); - *status |= (MPD_Inexact|MPD_Rounded); - } - - return cmp; -} - -/* - * If abs(base) equals one, calculate the correct power of one result. - * Otherwise, result is undefined. Return the value of the comparison - * against 1. - * - * This is an internal function that does not check for specials. - */ -static int -_qcheck_pow_one(mpd_t *result, const mpd_t *base, const mpd_t *exp, - uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_ssize_t shift; - int cmp; - - if ((cmp = _mpd_cmp_abs(base, &one)) == 0) { - if (_mpd_isint(exp)) { - if (mpd_isnegative(exp)) { - _settriple(result, resultsign, 1, 0); - return 0; - } - /* 1.000**3 = 1.000000000 */ - mpd_qmul_ssize(result, exp, -base->exp, ctx, &workstatus); - if (workstatus&MPD_Errors) { - *status |= (workstatus&MPD_Errors); - return 0; - } - /* digits-1 after exponentiation */ - shift = mpd_qget_ssize(result, &workstatus); - /* shift is MPD_SSIZE_MAX if result is too large */ - if (shift > ctx->prec-1) { - shift = ctx->prec-1; - *status |= MPD_Rounded; - } - } - else if (mpd_ispositive(base)) { - shift = ctx->prec-1; - *status |= (MPD_Inexact|MPD_Rounded); - } - else { - return -2; /* GCOV_NOT_REACHED */ - } - if (!mpd_qshiftl(result, &one, shift, status)) { - return 0; - } - result->exp = -shift; - mpd_set_flags(result, resultsign); - } - - return cmp; -} - -/* - * Detect certain over/underflow of x**y. - * ACL2 proof: pow-bounds.lisp. - * - * Symbols: - * - * e: EXP_INF or EXP_CLAMP - * x: base - * y: exponent - * - * omega(e) = log10(abs(e)) - * zeta(x) = log10(abs(log10(x))) - * theta(y) = log10(abs(y)) - * - * Upper and lower bounds: - * - * ub_omega(e) = ceil(log10(abs(e))) - * lb_theta(y) = floor(log10(abs(y))) - * - * | floor(log10(floor(abs(log10(x))))) if x < 1/10 or x >= 10 - * lb_zeta(x) = | floor(log10(abs(x-1)/10)) if 1/10 <= x < 1 - * | floor(log10(abs((x-1)/100))) if 1 < x < 10 - * - * ub_omega(e) and lb_theta(y) are obviously upper and lower bounds - * for omega(e) and theta(y). - * - * lb_zeta is a lower bound for zeta(x): - * - * x < 1/10 or x >= 10: - * - * abs(log10(x)) >= 1, so the outer log10 is well defined. Since log10 - * is strictly increasing, the end result is a lower bound. - * - * 1/10 <= x < 1: - * - * We use: log10(x) <= (x-1)/log(10) - * abs(log10(x)) >= abs(x-1)/log(10) - * abs(log10(x)) >= abs(x-1)/10 - * - * 1 < x < 10: - * - * We use: (x-1)/(x*log(10)) < log10(x) - * abs((x-1)/100) < abs(log10(x)) - * - * XXX: abs((x-1)/10) would work, need ACL2 proof. - * - * - * Let (0 < x < 1 and y < 0) or (x > 1 and y > 0). (H1) - * Let ub_omega(exp_inf) < lb_zeta(x) + lb_theta(y) (H2) - * - * Then: - * log10(abs(exp_inf)) < log10(abs(log10(x))) + log10(abs(y)). (1) - * exp_inf < log10(x) * y (2) - * 10**exp_inf < x**y (3) - * - * Let (0 < x < 1 and y > 0) or (x > 1 and y < 0). (H3) - * Let ub_omega(exp_clamp) < lb_zeta(x) + lb_theta(y) (H4) - * - * Then: - * log10(abs(exp_clamp)) < log10(abs(log10(x))) + log10(abs(y)). (4) - * log10(x) * y < exp_clamp (5) - * x**y < 10**exp_clamp (6) - * - */ -static mpd_ssize_t -_lower_bound_zeta(const mpd_t *x, uint32_t *status) -{ - mpd_context_t maxctx; - MPD_NEW_STATIC(scratch,0,0,0,0); - mpd_ssize_t t, u; - - t = mpd_adjexp(x); - if (t > 0) { - /* x >= 10 -> floor(log10(floor(abs(log10(x))))) */ - return mpd_exp_digits(t) - 1; - } - else if (t < -1) { - /* x < 1/10 -> floor(log10(floor(abs(log10(x))))) */ - return mpd_exp_digits(t+1) - 1; - } - else { - mpd_maxcontext(&maxctx); - mpd_qsub(&scratch, x, &one, &maxctx, status); - if (mpd_isspecial(&scratch)) { - mpd_del(&scratch); - return MPD_SSIZE_MAX; - } - u = mpd_adjexp(&scratch); - mpd_del(&scratch); - - /* t == -1, 1/10 <= x < 1 -> floor(log10(abs(x-1)/10)) - * t == 0, 1 < x < 10 -> floor(log10(abs(x-1)/100)) */ - return (t == 0) ? u-2 : u-1; - } -} - -/* - * Detect cases of certain overflow/underflow in the power function. - * Assumptions: x != 1, y != 0. The proof above is for positive x. - * If x is negative and y is an odd integer, x**y == -(abs(x)**y), - * so the analysis does not change. - */ -static int -_qcheck_pow_bounds(mpd_t *result, const mpd_t *x, const mpd_t *y, - uint8_t resultsign, - const mpd_context_t *ctx, uint32_t *status) -{ - MPD_NEW_SHARED(abs_x, x); - mpd_ssize_t ub_omega, lb_zeta, lb_theta; - uint8_t sign; - - mpd_set_positive(&abs_x); - - lb_theta = mpd_adjexp(y); - lb_zeta = _lower_bound_zeta(&abs_x, status); - if (lb_zeta == MPD_SSIZE_MAX) { - mpd_seterror(result, MPD_Malloc_error, status); - return 1; - } - - sign = (mpd_adjexp(&abs_x) < 0) ^ mpd_sign(y); - if (sign == 0) { - /* (0 < |x| < 1 and y < 0) or (|x| > 1 and y > 0) */ - ub_omega = mpd_exp_digits(ctx->emax); - if (ub_omega < lb_zeta + lb_theta) { - _settriple(result, resultsign, 1, MPD_EXP_INF); - mpd_qfinalize(result, ctx, status); - return 1; - } - } - else { - /* (0 < |x| < 1 and y > 0) or (|x| > 1 and y < 0). */ - ub_omega = mpd_exp_digits(mpd_etiny(ctx)); - if (ub_omega < lb_zeta + lb_theta) { - _settriple(result, resultsign, 1, mpd_etiny(ctx)-1); - mpd_qfinalize(result, ctx, status); - return 1; - } - } - - return 0; -} - -/* - * TODO: Implement algorithm for computing exact powers from decimal.py. - * In order to prevent infinite loops, this has to be called before - * using Ziv's strategy for correct rounding. - */ -/* -static int -_mpd_qpow_exact(mpd_t *result, const mpd_t *base, const mpd_t *exp, - const mpd_context_t *ctx, uint32_t *status) -{ - return 0; -} -*/ - -/* - * The power function for real exponents. - * Relative error: abs(result - e**y) < e**y * 1/5 * 10**(-prec - 1) - */ -static void -_mpd_qpow_real(mpd_t *result, const mpd_t *base, const mpd_t *exp, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(texp,0,0,0,0); - - if (!mpd_qcopy(&texp, exp, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - - mpd_maxcontext(&workctx); - workctx.prec = (base->digits > ctx->prec) ? base->digits : ctx->prec; - workctx.prec += (4 + MPD_EXPDIGITS); - workctx.round = MPD_ROUND_HALF_EVEN; - workctx.allcr = ctx->allcr; - - /* - * extra := MPD_EXPDIGITS = MPD_EXP_MAX_T - * wp := prec + 4 + extra - * abs(err) < 5 * 10**-wp - * y := log(base) * exp - * Calculate: - * 1) e**(y * (1 + err)**2) * (1 + err) - * = e**y * e**(y * (2*err + err**2)) * (1 + err) - * ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - * Relative error of the underlined term: - * 2) abs(e**(y * (2*err + err**2)) - 1) - * Case abs(y) >= 10**extra: - * 3) adjexp(y)+1 > log10(abs(y)) >= extra - * This triggers the Overflow/Underflow shortcut in _mpd_qexp(), - * so no further analysis is necessary. - * Case abs(y) < 10**extra: - * 4) abs(y * (2*err + err**2)) < 1/5 * 10**(-prec - 2) - * Use (see _mpd_qexp): - * 5) abs(x) <= 9/10 * 10**-p ==> abs(e**x - 1) < 10**-p - * With 2), 4) and 5): - * 6) abs(e**(y * (2*err + err**2)) - 1) < 10**(-prec - 2) - * The complete relative error of 1) is: - * 7) abs(result - e**y) < e**y * 1/5 * 10**(-prec - 1) - */ - mpd_qln(result, base, &workctx, &workctx.status); - mpd_qmul(result, result, &texp, &workctx, &workctx.status); - mpd_qexp(result, result, &workctx, status); - - mpd_del(&texp); - *status |= (workctx.status&MPD_Errors); - *status |= (MPD_Inexact|MPD_Rounded); -} - -/* The power function: base**exp */ -void -mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp, - const mpd_context_t *ctx, uint32_t *status) -{ - uint8_t resultsign = 0; - int intexp = 0; - int cmp; - - if (mpd_isspecial(base) || mpd_isspecial(exp)) { - if (mpd_qcheck_nans(result, base, exp, ctx, status)) { - return; - } - } - if (mpd_isinteger(exp)) { - intexp = 1; - resultsign = mpd_isnegative(base) && mpd_isodd(exp); - } - - if (mpd_iszero(base)) { - if (mpd_iszero(exp)) { - mpd_seterror(result, MPD_Invalid_operation, status); - } - else if (mpd_isnegative(exp)) { - mpd_setspecial(result, resultsign, MPD_INF); - } - else { - _settriple(result, resultsign, 0, 0); - } - return; - } - if (mpd_isnegative(base)) { - if (!intexp || mpd_isinfinite(exp)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - } - if (mpd_isinfinite(exp)) { - /* power of one */ - cmp = _qcheck_pow_one_inf(result, base, resultsign, ctx, status); - if (cmp == 0) { - return; - } - else { - cmp *= mpd_arith_sign(exp); - if (cmp < 0) { - _settriple(result, resultsign, 0, 0); - } - else { - mpd_setspecial(result, resultsign, MPD_INF); - } - } - return; - } - if (mpd_isinfinite(base)) { - if (mpd_iszero(exp)) { - _settriple(result, resultsign, 1, 0); - } - else if (mpd_isnegative(exp)) { - _settriple(result, resultsign, 0, 0); - } - else { - mpd_setspecial(result, resultsign, MPD_INF); - } - return; - } - if (mpd_iszero(exp)) { - _settriple(result, resultsign, 1, 0); - return; - } - if (_qcheck_pow_one(result, base, exp, resultsign, ctx, status) == 0) { - return; - } - if (_qcheck_pow_bounds(result, base, exp, resultsign, ctx, status)) { - return; - } - - if (intexp) { - _mpd_qpow_int(result, base, exp, resultsign, ctx, status); - } - else { - _mpd_qpow_real(result, base, exp, ctx, status); - if (!mpd_isspecial(result) && _mpd_cmp(result, &one) == 0) { - mpd_ssize_t shift = ctx->prec-1; - mpd_qshiftl(result, &one, shift, status); - result->exp = -shift; - } - if (mpd_isinfinite(result)) { - /* for ROUND_DOWN, ROUND_FLOOR, etc. */ - _settriple(result, MPD_POS, 1, MPD_EXP_INF); - } - mpd_qfinalize(result, ctx, status); - } -} - -/* - * Internal function: Integer powmod with mpd_uint_t exponent, base is modified! - * Function can fail with MPD_Malloc_error. - */ -static inline void -_mpd_qpowmod_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp, - const mpd_t *mod, uint32_t *status) -{ - mpd_context_t maxcontext; - - mpd_maxcontext(&maxcontext); - - /* resize to smaller cannot fail */ - mpd_qcopy(result, &one, status); - - while (exp > 0) { - if (exp & 1) { - _mpd_qmul_exact(result, result, base, &maxcontext, status); - mpd_qrem(result, result, mod, &maxcontext, status); - } - _mpd_qmul_exact(base, base, base, &maxcontext, status); - mpd_qrem(base, base, mod, &maxcontext, status); - exp >>= 1; - } -} - -/* The powmod function: (base**exp) % mod */ -void -mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, - const mpd_t *mod, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(tbase,0,0,0,0); - MPD_NEW_STATIC(texp,0,0,0,0); - MPD_NEW_STATIC(tmod,0,0,0,0); - MPD_NEW_STATIC(tmp,0,0,0,0); - MPD_NEW_CONST(two,0,0,1,1,1,2); - mpd_ssize_t tbase_exp, texp_exp; - mpd_ssize_t i; - mpd_t t; - mpd_uint_t r; - uint8_t sign; - - - if (mpd_isspecial(base) || mpd_isspecial(exp) || mpd_isspecial(mod)) { - if (mpd_qcheck_3nans(result, base, exp, mod, ctx, status)) { - return; - } - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - - if (!_mpd_isint(base) || !_mpd_isint(exp) || !_mpd_isint(mod)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_iszerocoeff(mod)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mod->digits+mod->exp > ctx->prec) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - sign = (mpd_isnegative(base)) && (mpd_isodd(exp)); - if (mpd_iszerocoeff(exp)) { - if (mpd_iszerocoeff(base)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - r = (_mpd_cmp_abs(mod, &one)==0) ? 0 : 1; - _settriple(result, sign, r, 0); - return; - } - if (mpd_isnegative(exp)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (mpd_iszerocoeff(base)) { - _settriple(result, sign, 0, 0); - return; - } - - mpd_maxcontext(&maxcontext); - - mpd_qrescale(&tmod, mod, 0, &maxcontext, &maxcontext.status); - if (maxcontext.status&MPD_Errors) { - mpd_seterror(result, maxcontext.status&MPD_Errors, status); - goto out; - } - maxcontext.status = 0; - mpd_set_positive(&tmod); - - mpd_qround_to_int(&tbase, base, &maxcontext, status); - mpd_set_positive(&tbase); - tbase_exp = tbase.exp; - tbase.exp = 0; - - mpd_qround_to_int(&texp, exp, &maxcontext, status); - texp_exp = texp.exp; - texp.exp = 0; - - /* base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo */ - mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status); - mpd_qshiftl(result, &one, tbase_exp, status); - mpd_qrem(result, result, &tmod, &maxcontext, status); - _mpd_qmul_exact(&tbase, &tbase, result, &maxcontext, status); - mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status); - if (mpd_isspecial(&tbase) || - mpd_isspecial(&texp) || - mpd_isspecial(&tmod)) { - goto mpd_errors; - } - - for (i = 0; i < texp_exp; i++) { - _mpd_qpowmod_uint(&tmp, &tbase, 10, &tmod, status); - t = tmp; - tmp = tbase; - tbase = t; - } - if (mpd_isspecial(&tbase)) { - goto mpd_errors; /* GCOV_UNLIKELY */ - } - - /* resize to smaller cannot fail */ - mpd_qcopy(result, &one, status); - while (mpd_isfinite(&texp) && !mpd_iszero(&texp)) { - if (mpd_isodd(&texp)) { - _mpd_qmul_exact(result, result, &tbase, &maxcontext, status); - mpd_qrem(result, result, &tmod, &maxcontext, status); - } - _mpd_qmul_exact(&tbase, &tbase, &tbase, &maxcontext, status); - mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status); - mpd_qdivint(&texp, &texp, &two, &maxcontext, status); - } - if (mpd_isspecial(&texp) || mpd_isspecial(&tbase) || - mpd_isspecial(&tmod) || mpd_isspecial(result)) { - /* MPD_Malloc_error */ - goto mpd_errors; - } - else { - mpd_set_sign(result, sign); - } - -out: - mpd_del(&tbase); - mpd_del(&texp); - mpd_del(&tmod); - mpd_del(&tmp); - return; - -mpd_errors: - mpd_setspecial(result, MPD_POS, MPD_NAN); - goto out; -} - -void -mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_ssize_t b_exp = b->exp; - mpd_ssize_t expdiff, shift; - mpd_uint_t rnd; - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(result, a, b, ctx, status)) { - return; - } - if (mpd_isinfinite(a) && mpd_isinfinite(b)) { - mpd_qcopy(result, a, status); - return; - } - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - if (b->exp > ctx->emax || b->exp < mpd_etiny(ctx)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - if (mpd_iszero(a)) { - _settriple(result, mpd_sign(a), 0, b->exp); - mpd_qfinalize(result, ctx, status); - return; - } - - - expdiff = a->exp - b->exp; - if (a->digits + expdiff > ctx->prec) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - if (expdiff >= 0) { - shift = expdiff; - if (!mpd_qshiftl(result, a, shift, status)) { - return; - } - result->exp = b_exp; - } - else { - /* At this point expdiff < 0 and a->digits+expdiff <= prec, - * so the shift before an increment will fit in prec. */ - shift = -expdiff; - rnd = mpd_qshiftr(result, a, shift, status); - if (rnd == MPD_UINT_MAX) { - return; - } - result->exp = b_exp; - if (!_mpd_apply_round_fit(result, rnd, ctx, status)) { - return; - } - workstatus |= MPD_Rounded; - if (rnd) { - workstatus |= MPD_Inexact; - } - } - - if (mpd_adjexp(result) > ctx->emax || - mpd_adjexp(result) < mpd_etiny(ctx)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - *status |= workstatus; - mpd_qfinalize(result, ctx, status); -} - -void -mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_ssize_t shift, maxexp, maxshift; - uint8_t sign_a = mpd_sign(a); - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - mpd_qcopy(result, a, status); - return; - } - - if (!mpd_qcopy(result, a, status)) { - return; - } - mpd_qfinalize(result, ctx, status); - if (mpd_isspecial(result)) { - return; - } - if (mpd_iszero(result)) { - _settriple(result, sign_a, 0, 0); - return; - } - - shift = mpd_trail_zeros(result); - maxexp = (ctx->clamp) ? mpd_etop(ctx) : ctx->emax; - /* After the finalizing above result->exp <= maxexp. */ - maxshift = maxexp - result->exp; - shift = (shift > maxshift) ? maxshift : shift; - - mpd_qshiftr_inplace(result, shift); - result->exp += shift; -} - -void -mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, - uint32_t *status) -{ - MPD_NEW_STATIC(q,0,0,0,0); - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(r, a, b, ctx, status)) { - return; - } - if (mpd_isinfinite(a)) { - mpd_seterror(r, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(b)) { - mpd_qcopy(r, a, status); - mpd_qfinalize(r, ctx, status); - return; - } - /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_seterror(r, MPD_Division_undefined, status); - } - else { - mpd_seterror(r, MPD_Invalid_operation, status); - } - return; - } - - _mpd_qdivmod(&q, r, a, b, ctx, status); - mpd_del(&q); - mpd_qfinalize(r, ctx, status); -} - -void -mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_context_t workctx; - MPD_NEW_STATIC(btmp,0,0,0,0); - MPD_NEW_STATIC(q,0,0,0,0); - mpd_ssize_t expdiff, qdigits; - int cmp, isodd, allnine; - - assert(r != NULL); /* annotation for scan-build */ - - if (mpd_isspecial(a) || mpd_isspecial(b)) { - if (mpd_qcheck_nans(r, a, b, ctx, status)) { - return; - } - if (mpd_isinfinite(a)) { - mpd_seterror(r, MPD_Invalid_operation, status); - return; - } - if (mpd_isinfinite(b)) { - mpd_qcopy(r, a, status); - mpd_qfinalize(r, ctx, status); - return; - } - /* debug */ - abort(); /* GCOV_NOT_REACHED */ - } - if (mpd_iszerocoeff(b)) { - if (mpd_iszerocoeff(a)) { - mpd_seterror(r, MPD_Division_undefined, status); - } - else { - mpd_seterror(r, MPD_Invalid_operation, status); - } - return; - } - - if (r == b) { - if (!mpd_qcopy(&btmp, b, status)) { - mpd_seterror(r, MPD_Malloc_error, status); - return; - } - b = &btmp; - } - - _mpd_qdivmod(&q, r, a, b, ctx, status); - if (mpd_isnan(&q) || mpd_isnan(r)) { - goto finish; - } - if (mpd_iszerocoeff(r)) { - goto finish; - } - - expdiff = mpd_adjexp(b) - mpd_adjexp(r); - if (-1 <= expdiff && expdiff <= 1) { - - allnine = mpd_coeff_isallnine(&q); - qdigits = q.digits; - isodd = mpd_isodd(&q); - - mpd_maxcontext(&workctx); - if (mpd_sign(a) == mpd_sign(b)) { - /* sign(r) == sign(b) */ - _mpd_qsub(&q, r, b, &workctx, &workctx.status); - } - else { - /* sign(r) != sign(b) */ - _mpd_qadd(&q, r, b, &workctx, &workctx.status); - } - - if (workctx.status&MPD_Errors) { - mpd_seterror(r, workctx.status&MPD_Errors, status); - goto finish; - } - - cmp = _mpd_cmp_abs(&q, r); - if (cmp < 0 || (cmp == 0 && isodd)) { - /* abs(r) > abs(b)/2 or abs(r) == abs(b)/2 and isodd(quotient) */ - if (allnine && qdigits == ctx->prec) { - /* abs(quotient) + 1 == 10**prec */ - mpd_seterror(r, MPD_Division_impossible, status); - goto finish; - } - mpd_qcopy(r, &q, status); - } - } - - -finish: - mpd_del(&btmp); - mpd_del(&q); - mpd_qfinalize(r, ctx, status); -} - -static void -_mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t expdiff, shift; - mpd_uint_t rnd; - - if (mpd_isspecial(a)) { - mpd_qcopy(result, a, status); - return; - } - - if (mpd_iszero(a)) { - _settriple(result, mpd_sign(a), 0, exp); - return; - } - - expdiff = a->exp - exp; - if (expdiff >= 0) { - shift = expdiff; - if (a->digits + shift > MPD_MAX_PREC+1) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - if (!mpd_qshiftl(result, a, shift, status)) { - return; - } - result->exp = exp; - } - else { - shift = -expdiff; - rnd = mpd_qshiftr(result, a, shift, status); - if (rnd == MPD_UINT_MAX) { - return; - } - result->exp = exp; - _mpd_apply_round_excess(result, rnd, ctx, status); - *status |= MPD_Rounded; - if (rnd) { - *status |= MPD_Inexact; - } - } - - if (mpd_issubnormal(result, ctx)) { - *status |= MPD_Subnormal; - } -} - -/* - * Rescale a number so that it has exponent 'exp'. Does not regard context - * precision, emax, emin, but uses the rounding mode. Special numbers are - * quietly copied. Restrictions: - * - * MPD_MIN_ETINY <= exp <= MPD_MAX_EMAX+1 - * result->digits <= MPD_MAX_PREC+1 - */ -void -mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, - const mpd_context_t *ctx, uint32_t *status) -{ - if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - _mpd_qrescale(result, a, exp, ctx, status); -} - -/* - * Same as mpd_qrescale, but with relaxed restrictions. The result of this - * function should only be used for formatting a number and never as input - * for other operations. - * - * MPD_MIN_ETINY-MPD_MAX_PREC <= exp <= MPD_MAX_EMAX+1 - * result->digits <= MPD_MAX_PREC+1 - */ -void -mpd_qrescale_fmt(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, - const mpd_context_t *ctx, uint32_t *status) -{ - if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY-MPD_MAX_PREC) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - _mpd_qrescale(result, a, exp, ctx, status); -} - -/* Round to an integer according to 'action' and ctx->round. */ -enum {TO_INT_EXACT, TO_INT_SILENT, TO_INT_TRUNC}; -static void -_mpd_qround_to_integral(int action, mpd_t *result, const mpd_t *a, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_uint_t rnd; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - mpd_qcopy(result, a, status); - return; - } - if (a->exp >= 0) { - mpd_qcopy(result, a, status); - return; - } - if (mpd_iszerocoeff(a)) { - _settriple(result, mpd_sign(a), 0, 0); - return; - } - - rnd = mpd_qshiftr(result, a, -a->exp, status); - if (rnd == MPD_UINT_MAX) { - return; - } - result->exp = 0; - - if (action == TO_INT_EXACT || action == TO_INT_SILENT) { - _mpd_apply_round_excess(result, rnd, ctx, status); - if (action == TO_INT_EXACT) { - *status |= MPD_Rounded; - if (rnd) { - *status |= MPD_Inexact; - } - } - } -} - -void -mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - (void)_mpd_qround_to_integral(TO_INT_EXACT, result, a, ctx, status); -} - -void -mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, ctx, status); -} - -void -mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - if (mpd_isspecial(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - (void)_mpd_qround_to_integral(TO_INT_TRUNC, result, a, ctx, status); -} - -void -mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx = *ctx; - - if (mpd_isspecial(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - workctx.round = MPD_ROUND_FLOOR; - (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, - &workctx, status); -} - -void -mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx = *ctx; - - if (mpd_isspecial(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - workctx.round = MPD_ROUND_CEILING; - (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, - &workctx, status); -} - -int -mpd_same_quantum(const mpd_t *a, const mpd_t *b) -{ - if (mpd_isspecial(a) || mpd_isspecial(b)) { - return ((mpd_isnan(a) && mpd_isnan(b)) || - (mpd_isinfinite(a) && mpd_isinfinite(b))); - } - - return a->exp == b->exp; -} - -/* Schedule the increase in precision for the Newton iteration. */ -static inline int -recpr_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], - mpd_ssize_t maxprec, mpd_ssize_t initprec) -{ - mpd_ssize_t k; - int i; - - assert(maxprec > 0 && initprec > 0); - if (maxprec <= initprec) return -1; - - i = 0; k = maxprec; - do { - k = (k+1) / 2; - klist[i++] = k; - } while (k > initprec); - - return i-1; -} - -/* - * Initial approximation for the reciprocal: - * k_0 := MPD_RDIGITS-2 - * z_0 := 10**(-k_0) * floor(10**(2*k_0 + 2) / floor(v * 10**(k_0 + 2))) - * Absolute error: - * |1/v - z_0| < 10**(-k_0) - * ACL2 proof: maxerror-inverse-approx - */ -static void -_mpd_qreciprocal_approx(mpd_t *z, const mpd_t *v, uint32_t *status) -{ - mpd_uint_t p10data[2] = {0, mpd_pow10[MPD_RDIGITS-2]}; - mpd_uint_t dummy, word; - int n; - - assert(v->exp == -v->digits); - - _mpd_get_msdigits(&dummy, &word, v, MPD_RDIGITS); - n = mpd_word_digits(word); - word *= mpd_pow10[MPD_RDIGITS-n]; - - mpd_qresize(z, 2, status); - (void)_mpd_shortdiv(z->data, p10data, 2, word); - - mpd_clear_flags(z); - z->exp = -(MPD_RDIGITS-2); - z->len = (z->data[1] == 0) ? 1 : 2; - mpd_setdigits(z); -} - -/* - * Reciprocal, calculated with Newton's Method. Assumption: result != a. - * NOTE: The comments in the function show that certain operations are - * exact. The proof for the maximum error is too long to fit in here. - * ACL2 proof: maxerror-inverse-complete - */ -static void -_mpd_qreciprocal(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t varcontext, maxcontext; - mpd_t *z = result; /* current approximation */ - mpd_t *v; /* a, normalized to a number between 0.1 and 1 */ - MPD_NEW_SHARED(vtmp, a); /* v shares data with a */ - MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */ - MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */ - MPD_NEW_CONST(two,0,0,1,1,1,2); /* const 2 */ - mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; - mpd_ssize_t adj, maxprec, initprec; - uint8_t sign = mpd_sign(a); - int i; - - assert(result != a); - - v = &vtmp; - mpd_clear_flags(v); - adj = v->digits + v->exp; - v->exp = -v->digits; - - /* Initial approximation */ - _mpd_qreciprocal_approx(z, v, status); - - mpd_maxcontext(&varcontext); - mpd_maxcontext(&maxcontext); - varcontext.round = maxcontext.round = MPD_ROUND_TRUNC; - varcontext.emax = maxcontext.emax = MPD_MAX_EMAX + 100; - varcontext.emin = maxcontext.emin = MPD_MIN_EMIN - 100; - maxcontext.prec = MPD_MAX_PREC + 100; - - maxprec = ctx->prec; - maxprec += 2; - initprec = MPD_RDIGITS-3; - - i = recpr_schedule_prec(klist, maxprec, initprec); - for (; i >= 0; i--) { - /* Loop invariant: z->digits <= klist[i]+7 */ - /* Let s := z**2, exact result */ - _mpd_qmul_exact(&s, z, z, &maxcontext, status); - varcontext.prec = 2*klist[i] + 5; - if (v->digits > varcontext.prec) { - /* Let t := v, truncated to n >= 2*k+5 fraction digits */ - mpd_qshiftr(&t, v, v->digits-varcontext.prec, status); - t.exp = -varcontext.prec; - /* Let t := trunc(v)*s, truncated to n >= 2*k+1 fraction digits */ - mpd_qmul(&t, &t, &s, &varcontext, status); - } - else { /* v->digits <= 2*k+5 */ - /* Let t := v*s, truncated to n >= 2*k+1 fraction digits */ - mpd_qmul(&t, v, &s, &varcontext, status); - } - /* Let s := 2*z, exact result */ - _mpd_qmul_exact(&s, z, &two, &maxcontext, status); - /* s.digits < t.digits <= 2*k+5, |adjexp(s)-adjexp(t)| <= 1, - * so the subtraction generates at most 2*k+6 <= klist[i+1]+7 - * digits. The loop invariant is preserved. */ - _mpd_qsub_exact(z, &s, &t, &maxcontext, status); - } - - if (!mpd_isspecial(z)) { - z->exp -= adj; - mpd_set_flags(z, sign); - } - - mpd_del(&s); - mpd_del(&t); - mpd_qfinalize(z, ctx, status); -} - -/* - * Internal function for large numbers: - * - * q, r = divmod(coeff(a), coeff(b)) - * - * Strategy: Multiply the dividend by the reciprocal of the divisor. The - * inexact result is fixed by a small loop, using at most one iteration. - * - * ACL2 proofs: - * ------------ - * 1) q is a natural number. (ndivmod-quotient-natp) - * 2) r is a natural number. (ndivmod-remainder-natp) - * 3) a = q * b + r (ndivmod-q*b+r==a) - * 4) r < b (ndivmod-remainder-<-b) - */ -static void -_mpd_base_ndivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, - uint32_t *status) -{ - mpd_context_t workctx; - mpd_t *qq = q, *rr = r; - mpd_t aa, bb; - int k; - - _mpd_copy_shared(&aa, a); - _mpd_copy_shared(&bb, b); - - mpd_set_positive(&aa); - mpd_set_positive(&bb); - aa.exp = 0; - bb.exp = 0; - - if (q == a || q == b) { - if ((qq = mpd_qnew()) == NULL) { - *status |= MPD_Malloc_error; - goto nanresult; - } - } - if (r == a || r == b) { - if ((rr = mpd_qnew()) == NULL) { - *status |= MPD_Malloc_error; - goto nanresult; - } - } - - mpd_maxcontext(&workctx); - - /* Let prec := adigits - bdigits + 4 */ - workctx.prec = a->digits - b->digits + 1 + 3; - if (a->digits > MPD_MAX_PREC || workctx.prec > MPD_MAX_PREC) { - *status |= MPD_Division_impossible; - goto nanresult; - } - - /* Let x := _mpd_qreciprocal(b, prec) - * Then x is bounded by: - * 1) 1/b - 10**(-prec - bdigits) < x < 1/b + 10**(-prec - bdigits) - * 2) 1/b - 10**(-adigits - 4) < x < 1/b + 10**(-adigits - 4) - */ - _mpd_qreciprocal(rr, &bb, &workctx, &workctx.status); - - /* Get an estimate for the quotient. Let q := a * x - * Then q is bounded by: - * 3) a/b - 10**-4 < q < a/b + 10**-4 - */ - _mpd_qmul(qq, &aa, rr, &workctx, &workctx.status); - /* Truncate q to an integer: - * 4) a/b - 2 < trunc(q) < a/b + 1 - */ - mpd_qtrunc(qq, qq, &workctx, &workctx.status); - - workctx.prec = aa.digits + 3; - workctx.emax = MPD_MAX_EMAX + 3; - workctx.emin = MPD_MIN_EMIN - 3; - /* Multiply the estimate for q by b: - * 5) a - 2 * b < trunc(q) * b < a + b - */ - _mpd_qmul(rr, &bb, qq, &workctx, &workctx.status); - /* Get the estimate for r such that a = q * b + r. */ - _mpd_qsub_exact(rr, &aa, rr, &workctx, &workctx.status); - - /* Fix the result. At this point -b < r < 2*b, so the correction loop - takes at most one iteration. */ - for (k = 0;; k++) { - if (mpd_isspecial(qq) || mpd_isspecial(rr)) { - *status |= (workctx.status&MPD_Errors); - goto nanresult; - } - if (k > 2) { /* Allow two iterations despite the proof. */ - mpd_err_warn("libmpdec: internal error in " /* GCOV_NOT_REACHED */ - "_mpd_base_ndivmod: please report"); /* GCOV_NOT_REACHED */ - *status |= MPD_Invalid_operation; /* GCOV_NOT_REACHED */ - goto nanresult; /* GCOV_NOT_REACHED */ - } - /* r < 0 */ - else if (_mpd_cmp(&zero, rr) == 1) { - _mpd_qadd_exact(rr, rr, &bb, &workctx, &workctx.status); - _mpd_qadd_exact(qq, qq, &minus_one, &workctx, &workctx.status); - } - /* 0 <= r < b */ - else if (_mpd_cmp(rr, &bb) == -1) { - break; - } - /* r >= b */ - else { - _mpd_qsub_exact(rr, rr, &bb, &workctx, &workctx.status); - _mpd_qadd_exact(qq, qq, &one, &workctx, &workctx.status); - } - } - - if (qq != q) { - if (!mpd_qcopy(q, qq, status)) { - goto nanresult; /* GCOV_UNLIKELY */ - } - mpd_del(qq); - } - if (rr != r) { - if (!mpd_qcopy(r, rr, status)) { - goto nanresult; /* GCOV_UNLIKELY */ - } - mpd_del(rr); - } - - *status |= (workctx.status&MPD_Errors); - return; - - -nanresult: - if (qq && qq != q) mpd_del(qq); - if (rr && rr != r) mpd_del(rr); - mpd_setspecial(q, MPD_POS, MPD_NAN); - mpd_setspecial(r, MPD_POS, MPD_NAN); -} - -/* LIBMPDEC_ONLY */ -/* - * Schedule the optimal precision increase for the Newton iteration. - * v := input operand - * z_0 := initial approximation - * initprec := natural number such that abs(sqrt(v) - z_0) < 10**-initprec - * maxprec := target precision - * - * For convenience the output klist contains the elements in reverse order: - * klist := [k_n-1, ..., k_0], where - * 1) k_0 <= initprec and - * 2) abs(sqrt(v) - result) < 10**(-2*k_n-1 + 2) <= 10**-maxprec. - */ -static inline int -invroot_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], - mpd_ssize_t maxprec, mpd_ssize_t initprec) -{ - mpd_ssize_t k; - int i; - - assert(maxprec >= 3 && initprec >= 3); - if (maxprec <= initprec) return -1; - - i = 0; k = maxprec; - do { - k = (k+3) / 2; - klist[i++] = k; - } while (k > initprec); - - return i-1; -} - -/* - * Initial approximation for the inverse square root function. - * Input: - * v := rational number, with 1 <= v < 100 - * vhat := floor(v * 10**6) - * Output: - * z := approximation to 1/sqrt(v), such that abs(z - 1/sqrt(v)) < 10**-3. - */ -static inline void -_invroot_init_approx(mpd_t *z, mpd_uint_t vhat) -{ - mpd_uint_t lo = 1000; - mpd_uint_t hi = 10000; - mpd_uint_t a, sq; - - assert(lo*lo <= vhat && vhat < (hi+1)*(hi+1)); - - for(;;) { - a = (lo + hi) / 2; - sq = a * a; - if (vhat >= sq) { - if (vhat < sq + 2*a + 1) { - break; - } - lo = a + 1; - } - else { - hi = a - 1; - } - } - - /* - * After the binary search we have: - * 1) a**2 <= floor(v * 10**6) < (a + 1)**2 - * This implies: - * 2) a**2 <= v * 10**6 < (a + 1)**2 - * 3) a <= sqrt(v) * 10**3 < a + 1 - * Since 10**3 <= a: - * 4) 0 <= 10**prec/a - 1/sqrt(v) < 10**-prec - * We have: - * 5) 10**3/a - 10**-3 < floor(10**9/a) * 10**-6 <= 10**3/a - * Merging 4) and 5): - * 6) abs(floor(10**9/a) * 10**-6 - 1/sqrt(v)) < 10**-3 - */ - mpd_minalloc(z); - mpd_clear_flags(z); - z->data[0] = 1000000000UL / a; - z->len = 1; - z->exp = -6; - mpd_setdigits(z); -} - -/* - * Set 'result' to 1/sqrt(a). - * Relative error: abs(result - 1/sqrt(a)) < 10**-prec * 1/sqrt(a) - */ -static void -_mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - uint32_t workstatus = 0; - mpd_context_t varcontext, maxcontext; - mpd_t *z = result; /* current approximation */ - mpd_t *v; /* a, normalized to a number between 1 and 100 */ - MPD_NEW_SHARED(vtmp, a); /* by default v will share data with a */ - MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */ - MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */ - MPD_NEW_CONST(one_half,0,-1,1,1,1,5); - MPD_NEW_CONST(three,0,0,1,1,1,3); - mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; - mpd_ssize_t ideal_exp, shift; - mpd_ssize_t adj, tz; - mpd_ssize_t maxprec, fracdigits; - mpd_uint_t vhat, dummy; - int i, n; - - - ideal_exp = -(a->exp - (a->exp & 1)) / 2; - - v = &vtmp; - if (result == a) { - if ((v = mpd_qncopy(a)) == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - } - - /* normalize a to 1 <= v < 100 */ - if ((v->digits+v->exp) & 1) { - fracdigits = v->digits - 1; - v->exp = -fracdigits; - n = (v->digits > 7) ? 7 : (int)v->digits; - /* Let vhat := floor(v * 10**(2*initprec)) */ - _mpd_get_msdigits(&dummy, &vhat, v, n); - if (n < 7) { - vhat *= mpd_pow10[7-n]; - } - } - else { - fracdigits = v->digits - 2; - v->exp = -fracdigits; - n = (v->digits > 8) ? 8 : (int)v->digits; - /* Let vhat := floor(v * 10**(2*initprec)) */ - _mpd_get_msdigits(&dummy, &vhat, v, n); - if (n < 8) { - vhat *= mpd_pow10[8-n]; - } - } - adj = (a->exp-v->exp) / 2; - - /* initial approximation */ - _invroot_init_approx(z, vhat); - - mpd_maxcontext(&maxcontext); - mpd_maxcontext(&varcontext); - varcontext.round = MPD_ROUND_TRUNC; - maxprec = ctx->prec + 1; - - /* initprec == 3 */ - i = invroot_schedule_prec(klist, maxprec, 3); - for (; i >= 0; i--) { - varcontext.prec = 2*klist[i]+2; - mpd_qmul(&s, z, z, &maxcontext, &workstatus); - if (v->digits > varcontext.prec) { - shift = v->digits - varcontext.prec; - mpd_qshiftr(&t, v, shift, &workstatus); - t.exp += shift; - mpd_qmul(&t, &t, &s, &varcontext, &workstatus); - } - else { - mpd_qmul(&t, v, &s, &varcontext, &workstatus); - } - mpd_qsub(&t, &three, &t, &maxcontext, &workstatus); - mpd_qmul(z, z, &t, &varcontext, &workstatus); - mpd_qmul(z, z, &one_half, &maxcontext, &workstatus); - } - - z->exp -= adj; - - tz = mpd_trail_zeros(result); - shift = ideal_exp - result->exp; - shift = (tz > shift) ? shift : tz; - if (shift > 0) { - mpd_qshiftr_inplace(result, shift); - result->exp += shift; - } - - - mpd_del(&s); - mpd_del(&t); - if (v != &vtmp) mpd_del(v); - *status |= (workstatus&MPD_Errors); - *status |= (MPD_Rounded|MPD_Inexact); -} - -void -mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t workctx; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - /* positive infinity */ - _settriple(result, MPD_POS, 0, mpd_etiny(ctx)); - *status |= MPD_Clamped; - return; - } - if (mpd_iszero(a)) { - mpd_setspecial(result, mpd_sign(a), MPD_INF); - *status |= MPD_Division_by_zero; - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - workctx = *ctx; - workctx.prec += 2; - workctx.round = MPD_ROUND_HALF_EVEN; - _mpd_qinvroot(result, a, &workctx, status); - mpd_qfinalize(result, ctx, status); -} -/* END LIBMPDEC_ONLY */ - -/* Algorithm from decimal.py */ -static void -_mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - mpd_context_t maxcontext; - MPD_NEW_STATIC(c,0,0,0,0); - MPD_NEW_STATIC(q,0,0,0,0); - MPD_NEW_STATIC(r,0,0,0,0); - MPD_NEW_CONST(two,0,0,1,1,1,2); - mpd_ssize_t prec, ideal_exp; - mpd_ssize_t l, shift; - int exact = 0; - - - ideal_exp = (a->exp - (a->exp & 1)) / 2; - - if (mpd_isspecial(a)) { - if (mpd_qcheck_nan(result, a, ctx, status)) { - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - mpd_setspecial(result, MPD_POS, MPD_INF); - return; - } - if (mpd_iszero(a)) { - _settriple(result, mpd_sign(a), 0, ideal_exp); - mpd_qfinalize(result, ctx, status); - return; - } - if (mpd_isnegative(a)) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - mpd_maxcontext(&maxcontext); - prec = ctx->prec + 1; - - if (!mpd_qcopy(&c, a, status)) { - goto malloc_error; - } - c.exp = 0; - - if (a->exp & 1) { - if (!mpd_qshiftl(&c, &c, 1, status)) { - goto malloc_error; - } - l = (a->digits >> 1) + 1; - } - else { - l = (a->digits + 1) >> 1; - } - - shift = prec - l; - if (shift >= 0) { - if (!mpd_qshiftl(&c, &c, 2*shift, status)) { - goto malloc_error; - } - exact = 1; - } - else { - exact = !mpd_qshiftr_inplace(&c, -2*shift); - } - - ideal_exp -= shift; - - /* find result = floor(sqrt(c)) using Newton's method */ - if (!mpd_qshiftl(result, &one, prec, status)) { - goto malloc_error; - } - - while (1) { - _mpd_qdivmod(&q, &r, &c, result, &maxcontext, &maxcontext.status); - if (mpd_isspecial(result) || mpd_isspecial(&q)) { - mpd_seterror(result, maxcontext.status&MPD_Errors, status); - goto out; - } - if (_mpd_cmp(result, &q) <= 0) { - break; - } - _mpd_qadd_exact(result, result, &q, &maxcontext, &maxcontext.status); - if (mpd_isspecial(result)) { - mpd_seterror(result, maxcontext.status&MPD_Errors, status); - goto out; - } - _mpd_qdivmod(result, &r, result, &two, &maxcontext, &maxcontext.status); - } - - if (exact) { - _mpd_qmul_exact(&r, result, result, &maxcontext, &maxcontext.status); - if (mpd_isspecial(&r)) { - mpd_seterror(result, maxcontext.status&MPD_Errors, status); - goto out; - } - exact = (_mpd_cmp(&r, &c) == 0); - } - - if (exact) { - if (shift >= 0) { - mpd_qshiftr_inplace(result, shift); - } - else { - if (!mpd_qshiftl(result, result, -shift, status)) { - goto malloc_error; - } - } - ideal_exp += shift; - } - else { - int lsd = (int)mpd_lsd(result->data[0]); - if (lsd == 0 || lsd == 5) { - result->data[0] += 1; - } - } - - result->exp = ideal_exp; - - -out: - mpd_del(&c); - mpd_del(&q); - mpd_del(&r); - maxcontext = *ctx; - maxcontext.round = MPD_ROUND_HALF_EVEN; - mpd_qfinalize(result, &maxcontext, status); - return; - -malloc_error: - mpd_seterror(result, MPD_Malloc_error, status); - goto out; -} - -void -mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, - uint32_t *status) -{ - MPD_NEW_STATIC(aa,0,0,0,0); - uint32_t xstatus = 0; - - if (result == a) { - if (!mpd_qcopy(&aa, a, status)) { - mpd_seterror(result, MPD_Malloc_error, status); - goto out; - } - a = &aa; - } - - _mpd_qsqrt(result, a, ctx, &xstatus); - - if (xstatus & (MPD_Malloc_error|MPD_Division_impossible)) { - /* The above conditions can occur at very high context precisions - * if intermediate values get too large. Retry the operation with - * a lower context precision in case the result is exact. - * - * If the result is exact, an upper bound for the number of digits - * is the number of digits in the input. - * - * NOTE: sqrt(40e9) = 2.0e+5 /\ digits(40e9) = digits(2.0e+5) = 2 - */ - uint32_t ystatus = 0; - mpd_context_t workctx = *ctx; - - workctx.prec = a->digits; - if (workctx.prec >= ctx->prec) { - *status |= (xstatus|MPD_Errors); - goto out; /* No point in repeating this, keep the original error. */ - } - - _mpd_qsqrt(result, a, &workctx, &ystatus); - if (ystatus != 0) { - ystatus = *status | ((xstatus|ystatus)&MPD_Errors); - mpd_seterror(result, ystatus, status); - } - } - else { - *status |= xstatus; - } - -out: - mpd_del(&aa); -} - - -/******************************************************************************/ -/* Base conversions */ -/******************************************************************************/ - -/* Space needed to represent an integer mpd_t in base 'base'. */ -size_t -mpd_sizeinbase(const mpd_t *a, uint32_t base) -{ - double x; - size_t digits; - double upper_bound; - - assert(mpd_isinteger(a)); - assert(base >= 2); - - if (mpd_iszero(a)) { - return 1; - } - - digits = a->digits+a->exp; - -#ifdef CONFIG_64 - /* ceil(2711437152599294 / log10(2)) + 4 == 2**53 */ - if (digits > 2711437152599294ULL) { - return SIZE_MAX; - } - - upper_bound = (double)((1ULL<<53)-1); -#else - upper_bound = (double)(SIZE_MAX-1); -#endif - - x = (double)digits / log10(base); - return (x > upper_bound) ? SIZE_MAX : (size_t)x + 1; -} - -/* Space needed to import a base 'base' integer of length 'srclen'. */ -static mpd_ssize_t -_mpd_importsize(size_t srclen, uint32_t base) -{ - double x; - double upper_bound; - - assert(srclen > 0); - assert(base >= 2); - -#if SIZE_MAX == UINT64_MAX - if (srclen > (1ULL<<53)) { - return MPD_SSIZE_MAX; - } - - assert((1ULL<<53) <= MPD_MAXIMPORT); - upper_bound = (double)((1ULL<<53)-1); -#else - upper_bound = MPD_MAXIMPORT-1; -#endif - - x = (double)srclen * (log10(base)/MPD_RDIGITS); - return (x > upper_bound) ? MPD_SSIZE_MAX : (mpd_ssize_t)x + 1; -} - -static uint8_t -mpd_resize_u16(uint16_t **w, size_t nmemb) -{ - uint8_t err = 0; - *w = mpd_realloc(*w, nmemb, sizeof **w, &err); - return !err; -} - -static uint8_t -mpd_resize_u32(uint32_t **w, size_t nmemb) -{ - uint8_t err = 0; - *w = mpd_realloc(*w, nmemb, sizeof **w, &err); - return !err; -} - -static size_t -_baseconv_to_u16(uint16_t **w, size_t wlen, mpd_uint_t wbase, - mpd_uint_t *u, mpd_ssize_t ulen) -{ - size_t n = 0; - - assert(wlen > 0 && ulen > 0); - assert(wbase <= (1U<<16)); - - do { - if (n >= wlen) { - if (!mpd_resize_u16(w, n+1)) { - return SIZE_MAX; - } - wlen = n+1; - } - (*w)[n++] = (uint16_t)_mpd_shortdiv(u, u, ulen, wbase); - /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */ - ulen = _mpd_real_size(u, ulen); - - } while (u[ulen-1] != 0); - - return n; -} - -static size_t -_coeff_from_u16(mpd_t *w, mpd_ssize_t wlen, - const mpd_uint_t *u, size_t ulen, uint32_t ubase, - uint32_t *status) -{ - mpd_ssize_t n = 0; - mpd_uint_t carry; - - assert(wlen > 0 && ulen > 0); - assert(ubase <= (1U<<16)); - - w->data[n++] = u[--ulen]; - while (--ulen != SIZE_MAX) { - carry = _mpd_shortmul_c(w->data, w->data, n, ubase); - if (carry) { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = carry; - } - carry = _mpd_shortadd(w->data, n, u[ulen]); - if (carry) { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = carry; - } - } - - return n; -} - -/* target base wbase < source base ubase */ -static size_t -_baseconv_to_smaller(uint32_t **w, size_t wlen, uint32_t wbase, - mpd_uint_t *u, mpd_ssize_t ulen, mpd_uint_t ubase) -{ - size_t n = 0; - - assert(wlen > 0 && ulen > 0); - assert(wbase < ubase); - - do { - if (n >= wlen) { - if (!mpd_resize_u32(w, n+1)) { - return SIZE_MAX; - } - wlen = n+1; - } - (*w)[n++] = (uint32_t)_mpd_shortdiv_b(u, u, ulen, wbase, ubase); - /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */ - ulen = _mpd_real_size(u, ulen); - - } while (u[ulen-1] != 0); - - return n; -} - -#ifdef CONFIG_32 -/* target base 'wbase' == source base 'ubase' */ -static size_t -_copy_equal_base(uint32_t **w, size_t wlen, - const uint32_t *u, size_t ulen) -{ - if (wlen < ulen) { - if (!mpd_resize_u32(w, ulen)) { - return SIZE_MAX; - } - } - - memcpy(*w, u, ulen * (sizeof **w)); - return ulen; -} - -/* target base 'wbase' > source base 'ubase' */ -static size_t -_baseconv_to_larger(uint32_t **w, size_t wlen, mpd_uint_t wbase, - const mpd_uint_t *u, size_t ulen, mpd_uint_t ubase) -{ - size_t n = 0; - mpd_uint_t carry; - - assert(wlen > 0 && ulen > 0); - assert(ubase < wbase); - - (*w)[n++] = u[--ulen]; - while (--ulen != SIZE_MAX) { - carry = _mpd_shortmul_b(*w, *w, n, ubase, wbase); - if (carry) { - if (n >= wlen) { - if (!mpd_resize_u32(w, n+1)) { - return SIZE_MAX; - } - wlen = n+1; - } - (*w)[n++] = carry; - } - carry = _mpd_shortadd_b(*w, n, u[ulen], wbase); - if (carry) { - if (n >= wlen) { - if (!mpd_resize_u32(w, n+1)) { - return SIZE_MAX; - } - wlen = n+1; - } - (*w)[n++] = carry; - } - } - - return n; -} - -/* target base wbase < source base ubase */ -static size_t -_coeff_from_larger_base(mpd_t *w, size_t wlen, mpd_uint_t wbase, - mpd_uint_t *u, mpd_ssize_t ulen, mpd_uint_t ubase, - uint32_t *status) -{ - size_t n = 0; - - assert(wlen > 0 && ulen > 0); - assert(wbase < ubase); - - do { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = (uint32_t)_mpd_shortdiv_b(u, u, ulen, wbase, ubase); - /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */ - ulen = _mpd_real_size(u, ulen); - - } while (u[ulen-1] != 0); - - return n; -} -#endif - -/* target base 'wbase' > source base 'ubase' */ -static size_t -_coeff_from_smaller_base(mpd_t *w, mpd_ssize_t wlen, mpd_uint_t wbase, - const uint32_t *u, size_t ulen, mpd_uint_t ubase, - uint32_t *status) -{ - mpd_ssize_t n = 0; - mpd_uint_t carry; - - assert(wlen > 0 && ulen > 0); - assert(wbase > ubase); - - w->data[n++] = u[--ulen]; - while (--ulen != SIZE_MAX) { - carry = _mpd_shortmul_b(w->data, w->data, n, ubase, wbase); - if (carry) { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = carry; - } - carry = _mpd_shortadd_b(w->data, n, u[ulen], wbase); - if (carry) { - if (n >= wlen) { - if (!mpd_qresize(w, n+1, status)) { - return SIZE_MAX; - } - wlen = n+1; - } - w->data[n++] = carry; - } - } - - return n; -} - -/* - * Convert an integer mpd_t to a multiprecision integer with base <= 2**16. - * The least significant word of the result is (*rdata)[0]. - * - * If rdata is NULL, space is allocated by the function and rlen is irrelevant. - * In case of an error any allocated storage is freed and rdata is set back to - * NULL. - * - * If rdata is non-NULL, it MUST be allocated by one of libmpdec's allocation - * functions and rlen MUST be correct. If necessary, the function will resize - * rdata. In case of an error the caller must free rdata. - * - * Return value: In case of success, the exact length of rdata, SIZE_MAX - * otherwise. - */ -size_t -mpd_qexport_u16(uint16_t **rdata, size_t rlen, uint32_t rbase, - const mpd_t *src, uint32_t *status) -{ - MPD_NEW_STATIC(tsrc,0,0,0,0); - int alloc = 0; /* rdata == NULL */ - size_t n; - - assert(rbase <= (1U<<16)); - - if (mpd_isspecial(src) || !_mpd_isint(src)) { - *status |= MPD_Invalid_operation; - return SIZE_MAX; - } - - if (*rdata == NULL) { - rlen = mpd_sizeinbase(src, rbase); - if (rlen == SIZE_MAX) { - *status |= MPD_Invalid_operation; - return SIZE_MAX; - } - *rdata = mpd_alloc(rlen, sizeof **rdata); - if (*rdata == NULL) { - goto malloc_error; - } - alloc = 1; - } - - if (mpd_iszero(src)) { - **rdata = 0; - return 1; - } - - if (src->exp >= 0) { - if (!mpd_qshiftl(&tsrc, src, src->exp, status)) { - goto malloc_error; - } - } - else { - if (mpd_qshiftr(&tsrc, src, -src->exp, status) == MPD_UINT_MAX) { - goto malloc_error; - } - } - - n = _baseconv_to_u16(rdata, rlen, rbase, tsrc.data, tsrc.len); - if (n == SIZE_MAX) { - goto malloc_error; - } - - -out: - mpd_del(&tsrc); - return n; - -malloc_error: - if (alloc) { - mpd_free(*rdata); - *rdata = NULL; - } - n = SIZE_MAX; - *status |= MPD_Malloc_error; - goto out; -} - -/* - * Convert an integer mpd_t to a multiprecision integer with base<=UINT32_MAX. - * The least significant word of the result is (*rdata)[0]. - * - * If rdata is NULL, space is allocated by the function and rlen is irrelevant. - * In case of an error any allocated storage is freed and rdata is set back to - * NULL. - * - * If rdata is non-NULL, it MUST be allocated by one of libmpdec's allocation - * functions and rlen MUST be correct. If necessary, the function will resize - * rdata. In case of an error the caller must free rdata. - * - * Return value: In case of success, the exact length of rdata, SIZE_MAX - * otherwise. - */ -size_t -mpd_qexport_u32(uint32_t **rdata, size_t rlen, uint32_t rbase, - const mpd_t *src, uint32_t *status) -{ - MPD_NEW_STATIC(tsrc,0,0,0,0); - int alloc = 0; /* rdata == NULL */ - size_t n; - - if (mpd_isspecial(src) || !_mpd_isint(src)) { - *status |= MPD_Invalid_operation; - return SIZE_MAX; - } - - if (*rdata == NULL) { - rlen = mpd_sizeinbase(src, rbase); - if (rlen == SIZE_MAX) { - *status |= MPD_Invalid_operation; - return SIZE_MAX; - } - *rdata = mpd_alloc(rlen, sizeof **rdata); - if (*rdata == NULL) { - goto malloc_error; - } - alloc = 1; - } - - if (mpd_iszero(src)) { - **rdata = 0; - return 1; - } - - if (src->exp >= 0) { - if (!mpd_qshiftl(&tsrc, src, src->exp, status)) { - goto malloc_error; - } - } - else { - if (mpd_qshiftr(&tsrc, src, -src->exp, status) == MPD_UINT_MAX) { - goto malloc_error; - } - } - -#ifdef CONFIG_64 - n = _baseconv_to_smaller(rdata, rlen, rbase, - tsrc.data, tsrc.len, MPD_RADIX); -#else - if (rbase == MPD_RADIX) { - n = _copy_equal_base(rdata, rlen, tsrc.data, tsrc.len); - } - else if (rbase < MPD_RADIX) { - n = _baseconv_to_smaller(rdata, rlen, rbase, - tsrc.data, tsrc.len, MPD_RADIX); - } - else { - n = _baseconv_to_larger(rdata, rlen, rbase, - tsrc.data, tsrc.len, MPD_RADIX); - } -#endif - - if (n == SIZE_MAX) { - goto malloc_error; - } - - -out: - mpd_del(&tsrc); - return n; - -malloc_error: - if (alloc) { - mpd_free(*rdata); - *rdata = NULL; - } - n = SIZE_MAX; - *status |= MPD_Malloc_error; - goto out; -} - - -/* - * Converts a multiprecision integer with base <= UINT16_MAX+1 to an mpd_t. - * The least significant word of the source is srcdata[0]. - */ -void -mpd_qimport_u16(mpd_t *result, - const uint16_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t srcbase, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_uint_t *usrc; /* uint16_t src copied to an mpd_uint_t array */ - mpd_ssize_t rlen; /* length of the result */ - size_t n; - - assert(srclen > 0); - assert(srcbase <= (1U<<16)); - - rlen = _mpd_importsize(srclen, srcbase); - if (rlen == MPD_SSIZE_MAX) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc); - if (usrc == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - for (n = 0; n < srclen; n++) { - usrc[n] = srcdata[n]; - } - - if (!mpd_qresize(result, rlen, status)) { - goto finish; - } - - n = _coeff_from_u16(result, rlen, usrc, srclen, srcbase, status); - if (n == SIZE_MAX) { - goto finish; - } - - mpd_set_flags(result, srcsign); - result->exp = 0; - result->len = n; - mpd_setdigits(result); - - mpd_qresize(result, result->len, status); - mpd_qfinalize(result, ctx, status); - - -finish: - mpd_free(usrc); -} - -/* - * Converts a multiprecision integer with base <= UINT32_MAX to an mpd_t. - * The least significant word of the source is srcdata[0]. - */ -void -mpd_qimport_u32(mpd_t *result, - const uint32_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t srcbase, - const mpd_context_t *ctx, uint32_t *status) -{ - mpd_ssize_t rlen; /* length of the result */ - size_t n; - - assert(srclen > 0); - - rlen = _mpd_importsize(srclen, srcbase); - if (rlen == MPD_SSIZE_MAX) { - mpd_seterror(result, MPD_Invalid_operation, status); - return; - } - - if (!mpd_qresize(result, rlen, status)) { - return; - } - -#ifdef CONFIG_64 - n = _coeff_from_smaller_base(result, rlen, MPD_RADIX, - srcdata, srclen, srcbase, - status); -#else - if (srcbase == MPD_RADIX) { - if (!mpd_qresize(result, srclen, status)) { - return; - } - memcpy(result->data, srcdata, srclen * (sizeof *srcdata)); - n = srclen; - } - else if (srcbase < MPD_RADIX) { - n = _coeff_from_smaller_base(result, rlen, MPD_RADIX, - srcdata, srclen, srcbase, - status); - } - else { - mpd_uint_t *usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc); - if (usrc == NULL) { - mpd_seterror(result, MPD_Malloc_error, status); - return; - } - for (n = 0; n < srclen; n++) { - usrc[n] = srcdata[n]; - } - - n = _coeff_from_larger_base(result, rlen, MPD_RADIX, - usrc, (mpd_ssize_t)srclen, srcbase, - status); - mpd_free(usrc); - } -#endif - - if (n == SIZE_MAX) { - return; - } - - mpd_set_flags(result, srcsign); - result->exp = 0; - result->len = n; - mpd_setdigits(result); - - mpd_qresize(result, result->len, status); - mpd_qfinalize(result, ctx, status); -} - - -/******************************************************************************/ -/* From triple */ -/******************************************************************************/ - -#if defined(CONFIG_64) && defined(__SIZEOF_INT128__) -static mpd_ssize_t -_set_coeff(uint64_t data[3], uint64_t hi, uint64_t lo) -{ - __uint128_t d = ((__uint128_t)hi << 64) + lo; - __uint128_t q, r; - - q = d / MPD_RADIX; - r = d % MPD_RADIX; - data[0] = (uint64_t)r; - d = q; - - q = d / MPD_RADIX; - r = d % MPD_RADIX; - data[1] = (uint64_t)r; - d = q; - - q = d / MPD_RADIX; - r = d % MPD_RADIX; - data[2] = (uint64_t)r; - - if (q != 0) { - abort(); /* GCOV_NOT_REACHED */ - } - - return data[2] != 0 ? 3 : (data[1] != 0 ? 2 : 1); -} -#else -static size_t -_uint_from_u16(mpd_uint_t *w, mpd_ssize_t wlen, const uint16_t *u, size_t ulen) -{ - const mpd_uint_t ubase = 1U<<16; - mpd_ssize_t n = 0; - mpd_uint_t carry; - - assert(wlen > 0 && ulen > 0); - - w[n++] = u[--ulen]; - while (--ulen != SIZE_MAX) { - carry = _mpd_shortmul_c(w, w, n, ubase); - if (carry) { - if (n >= wlen) { - abort(); /* GCOV_NOT_REACHED */ - } - w[n++] = carry; - } - carry = _mpd_shortadd(w, n, u[ulen]); - if (carry) { - if (n >= wlen) { - abort(); /* GCOV_NOT_REACHED */ - } - w[n++] = carry; - } - } - - return n; -} - -static mpd_ssize_t -_set_coeff(mpd_uint_t *data, mpd_ssize_t len, uint64_t hi, uint64_t lo) -{ - uint16_t u16[8] = {0}; - - u16[7] = (uint16_t)((hi & 0xFFFF000000000000ULL) >> 48); - u16[6] = (uint16_t)((hi & 0x0000FFFF00000000ULL) >> 32); - u16[5] = (uint16_t)((hi & 0x00000000FFFF0000ULL) >> 16); - u16[4] = (uint16_t) (hi & 0x000000000000FFFFULL); - - u16[3] = (uint16_t)((lo & 0xFFFF000000000000ULL) >> 48); - u16[2] = (uint16_t)((lo & 0x0000FFFF00000000ULL) >> 32); - u16[1] = (uint16_t)((lo & 0x00000000FFFF0000ULL) >> 16); - u16[0] = (uint16_t) (lo & 0x000000000000FFFFULL); - - return (mpd_ssize_t)_uint_from_u16(data, len, u16, 8); -} -#endif - -static int -_set_uint128_coeff_exp(mpd_t *result, uint64_t hi, uint64_t lo, mpd_ssize_t exp) -{ - mpd_uint_t data[5] = {0}; - uint32_t status = 0; - mpd_ssize_t len; - -#if defined(CONFIG_64) && defined(__SIZEOF_INT128__) - len = _set_coeff(data, hi, lo); -#else - len = _set_coeff(data, 5, hi, lo); -#endif - - if (!mpd_qresize(result, len, &status)) { - return -1; - } - - for (mpd_ssize_t i = 0; i < len; i++) { - result->data[i] = data[i]; - } - - result->exp = exp; - result->len = len; - mpd_setdigits(result); - - return 0; -} - -int -mpd_from_uint128_triple(mpd_t *result, const mpd_uint128_triple_t *triple, uint32_t *status) -{ - static const mpd_context_t maxcontext = { - .prec=MPD_MAX_PREC, - .emax=MPD_MAX_EMAX, - .emin=MPD_MIN_EMIN, - .round=MPD_ROUND_HALF_EVEN, - .traps=MPD_Traps, - .status=0, - .newtrap=0, - .clamp=0, - .allcr=1, - }; - const enum mpd_triple_class tag = triple->tag; - const uint8_t sign = triple->sign; - const uint64_t hi = triple->hi; - const uint64_t lo = triple->lo; - mpd_ssize_t exp; - -#ifdef CONFIG_32 - if (triple->exp < MPD_SSIZE_MIN || triple->exp > MPD_SSIZE_MAX) { - goto conversion_error; - } -#endif - exp = (mpd_ssize_t)triple->exp; - - switch (tag) { - case MPD_TRIPLE_QNAN: case MPD_TRIPLE_SNAN: { - if (sign > 1 || exp != 0) { - goto conversion_error; - } - - const uint8_t flags = tag == MPD_TRIPLE_QNAN ? MPD_NAN : MPD_SNAN; - mpd_setspecial(result, sign, flags); - - if (hi == 0 && lo == 0) { /* no payload */ - return 0; - } - - if (_set_uint128_coeff_exp(result, hi, lo, exp) < 0) { - goto malloc_error; - } - - return 0; - } - - case MPD_TRIPLE_INF: { - if (sign > 1 || hi != 0 || lo != 0 || exp != 0) { - goto conversion_error; - } - - mpd_setspecial(result, sign, MPD_INF); - - return 0; - } - - case MPD_TRIPLE_NORMAL: { - if (sign > 1) { - goto conversion_error; - } - - const uint8_t flags = sign ? MPD_NEG : MPD_POS; - mpd_set_flags(result, flags); - - if (exp > MPD_EXP_INF) { - exp = MPD_EXP_INF; - } - if (exp == MPD_SSIZE_MIN) { - exp = MPD_SSIZE_MIN+1; - } - - if (_set_uint128_coeff_exp(result, hi, lo, exp) < 0) { - goto malloc_error; - } - - uint32_t workstatus = 0; - mpd_qfinalize(result, &maxcontext, &workstatus); - if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { - goto conversion_error; - } - - return 0; - } - - default: - goto conversion_error; - } - -conversion_error: - mpd_seterror(result, MPD_Conversion_syntax, status); - return -1; - -malloc_error: - mpd_seterror(result, MPD_Malloc_error, status); - return -1; -} - - -/******************************************************************************/ -/* As triple */ -/******************************************************************************/ - -#if defined(CONFIG_64) && defined(__SIZEOF_INT128__) -static void -_get_coeff(uint64_t *hi, uint64_t *lo, const mpd_t *a) -{ - __uint128_t u128 = 0; - - switch (a->len) { - case 3: - u128 = a->data[2]; /* fall through */ - case 2: - u128 = u128 * MPD_RADIX + a->data[1]; /* fall through */ - case 1: - u128 = u128 * MPD_RADIX + a->data[0]; - break; - default: - abort(); /* GCOV_NOT_REACHED */ - } - - *hi = u128 >> 64; - *lo = (uint64_t)u128; -} -#else -static size_t -_uint_to_u16(uint16_t w[8], mpd_uint_t *u, mpd_ssize_t ulen) -{ - const mpd_uint_t wbase = 1U<<16; - size_t n = 0; - - assert(ulen > 0); - - do { - if (n >= 8) { - abort(); /* GCOV_NOT_REACHED */ - } - w[n++] = (uint16_t)_mpd_shortdiv(u, u, ulen, wbase); - /* ulen is at least 1. u[ulen-1] can only be zero if ulen == 1. */ - ulen = _mpd_real_size(u, ulen); - - } while (u[ulen-1] != 0); - - return n; -} - -static void -_get_coeff(uint64_t *hi, uint64_t *lo, const mpd_t *a) -{ - uint16_t u16[8] = {0}; - mpd_uint_t data[5] = {0}; - - switch (a->len) { - case 5: - data[4] = a->data[4]; /* fall through */ - case 4: - data[3] = a->data[3]; /* fall through */ - case 3: - data[2] = a->data[2]; /* fall through */ - case 2: - data[1] = a->data[1]; /* fall through */ - case 1: - data[0] = a->data[0]; - break; - default: - abort(); /* GCOV_NOT_REACHED */ - } - - _uint_to_u16(u16, data, a->len); - - *hi = (uint64_t)u16[7] << 48; - *hi |= (uint64_t)u16[6] << 32; - *hi |= (uint64_t)u16[5] << 16; - *hi |= (uint64_t)u16[4]; - - *lo = (uint64_t)u16[3] << 48; - *lo |= (uint64_t)u16[2] << 32; - *lo |= (uint64_t)u16[1] << 16; - *lo |= (uint64_t)u16[0]; -} -#endif - -static enum mpd_triple_class -_coeff_as_uint128(uint64_t *hi, uint64_t *lo, const mpd_t *a) -{ -#ifdef CONFIG_64 - static mpd_uint_t uint128_max_data[3] = { 3374607431768211455ULL, 4028236692093846346ULL, 3ULL }; - static const mpd_t uint128_max = { MPD_STATIC|MPD_CONST_DATA, 0, 39, 3, 3, uint128_max_data }; -#else - static mpd_uint_t uint128_max_data[5] = { 768211455U, 374607431U, 938463463U, 282366920U, 340U }; - static const mpd_t uint128_max = { MPD_STATIC|MPD_CONST_DATA, 0, 39, 5, 5, uint128_max_data }; -#endif - enum mpd_triple_class ret = MPD_TRIPLE_NORMAL; - uint32_t status = 0; - mpd_t coeff; - - *hi = *lo = 0ULL; - - if (mpd_isspecial(a)) { - if (mpd_isinfinite(a)) { - return MPD_TRIPLE_INF; - } - - ret = mpd_isqnan(a) ? MPD_TRIPLE_QNAN : MPD_TRIPLE_SNAN; - if (a->len == 0) { /* no payload */ - return ret; - } - } - else if (mpd_iszero(a)) { - return ret; - } - - _mpd_copy_shared(&coeff, a); - mpd_set_flags(&coeff, 0); - coeff.exp = 0; - - if (mpd_qcmp(&coeff, &uint128_max, &status) > 0) { - return MPD_TRIPLE_ERROR; - } - - _get_coeff(hi, lo, &coeff); - return ret; -} - -mpd_uint128_triple_t -mpd_as_uint128_triple(const mpd_t *a) -{ - mpd_uint128_triple_t triple = { MPD_TRIPLE_ERROR, 0, 0, 0, 0 }; - - triple.tag = _coeff_as_uint128(&triple.hi, &triple.lo, a); - if (triple.tag == MPD_TRIPLE_ERROR) { - return triple; - } - - triple.sign = !!mpd_isnegative(a); - if (triple.tag == MPD_TRIPLE_NORMAL) { - triple.exp = a->exp; - } - - return triple; -} diff --git a/Modules/_decimal/libmpdec/mpdecimal.h b/Modules/_decimal/libmpdec/mpdecimal.h deleted file mode 100644 index 24c280b00ebcd0..00000000000000 --- a/Modules/_decimal/libmpdec/mpdecimal.h +++ /dev/null @@ -1,847 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_MPDECIMAL_H_ -#define LIBMPDEC_MPDECIMAL_H_ - - -#ifndef _MSC_VER - #include "pyconfig.h" -#endif - -#ifdef __cplusplus - #include - #include - #include - #include - #include - #define MPD_UINT8_C(x) (static_cast(x)) -extern "C" { -#else - #include - #include - #include - #include - #include - #define MPD_UINT8_C(x) ((uint8_t)x) -#endif - - -#if (defined(__linux__) || defined(__FreeBSD__) || defined(__APPLE__)) && \ - defined(__GNUC__) && __GNUC__ >= 4 && !defined(__INTEL_COMPILER) - #define MPD_PRAGMA(x) _Pragma(x) - #define MPD_HIDE_SYMBOLS_START "GCC visibility push(hidden)" - #define MPD_HIDE_SYMBOLS_END "GCC visibility pop" -#else - #define MPD_PRAGMA(x) - #define MPD_HIDE_SYMBOLS_START - #define MPD_HIDE_SYMBOLS_END -#endif - -#if defined(_MSC_VER) - #define EXTINLINE extern inline -#else - #define EXTINLINE -#endif - - -/* This header file is internal for the purpose of building _decimal.so. - * All symbols should have local scope in the DSO. */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -/******************************************************************************/ -/* Version */ -/******************************************************************************/ - -#define MPD_MAJOR_VERSION 2 -#define MPD_MINOR_VERSION 5 -#define MPD_MICRO_VERSION 1 - -#define MPD_VERSION "2.5.1" - -#define MPD_VERSION_HEX ((MPD_MAJOR_VERSION << 24) | \ - (MPD_MINOR_VERSION << 16) | \ - (MPD_MICRO_VERSION << 8)) - -const char *mpd_version(void); - - -/******************************************************************************/ -/* Configuration */ -/******************************************************************************/ - -#if defined(UNIVERSAL) - #if defined(CONFIG_64) || defined(CONFIG_32) - #error "cannot use CONFIG_64 or CONFIG_32 with UNIVERSAL." - #endif - #if defined(__ppc__) - #define CONFIG_32 - #define ANSI - #elif defined(__ppc64__) - #define CONFIG_64 - #define ANSI - #elif defined(__i386__) - #define CONFIG_32 - #define ANSI - #elif defined(__x86_64__) - #define CONFIG_64 - #define ASM - #elif defined(__arm64__) - #define CONFIG_64 - #define ANSI - #else - #error "unknown architecture for universal build." - #endif -#endif - - -/* BEGIN CONFIG_64 */ -#if defined(CONFIG_64) -/* types for modular and base arithmetic */ -#define MPD_UINT_MAX UINT64_MAX -#define MPD_BITS_PER_UINT 64 -typedef uint64_t mpd_uint_t; /* unsigned mod type */ - -#define MPD_SIZE_MAX SIZE_MAX -typedef size_t mpd_size_t; /* unsigned size type */ - -/* type for exp, digits, len, prec */ -#define MPD_SSIZE_MAX INT64_MAX -#define MPD_SSIZE_MIN INT64_MIN -typedef int64_t mpd_ssize_t; -#define _mpd_strtossize strtoll - -/* decimal arithmetic */ -#define MPD_RADIX 10000000000000000000ULL /* 10**19 */ -#define MPD_RDIGITS 19 -#define MPD_MAX_POW10 19 -#define MPD_EXPDIGITS 19 /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */ - -#define MPD_MAXTRANSFORM_2N 4294967296ULL /* 2**32 */ -#define MPD_MAX_PREC 999999999999999999LL -#define MPD_MAX_PREC_LOG2 64 -#define MPD_ELIMIT 1000000000000000000LL -#define MPD_MAX_EMAX 999999999999999999LL /* ELIMIT-1 */ -#define MPD_MIN_EMIN (-999999999999999999LL) /* -EMAX */ -#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1)) -#define MPD_EXP_INF 2000000000000000001LL -#define MPD_EXP_CLAMP (-4000000000000000001LL) -#define MPD_MAXIMPORT 105263157894736842L /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */ -#define MPD_IEEE_CONTEXT_MAX_BITS 512 /* 16*(log2(MPD_MAX_EMAX / 3)-3) */ - -/* conversion specifiers */ -#define PRI_mpd_uint_t PRIu64 -#define PRI_mpd_ssize_t PRIi64 -/* END CONFIG_64 */ - - -/* BEGIN CONFIG_32 */ -#elif defined(CONFIG_32) -/* types for modular and base arithmetic */ -#define MPD_UINT_MAX UINT32_MAX -#define MPD_BITS_PER_UINT 32 -typedef uint32_t mpd_uint_t; /* unsigned mod type */ - -#ifndef LEGACY_COMPILER -#define MPD_UUINT_MAX UINT64_MAX -typedef uint64_t mpd_uuint_t; /* double width unsigned mod type */ -#endif - -#define MPD_SIZE_MAX SIZE_MAX -typedef size_t mpd_size_t; /* unsigned size type */ - -/* type for dec->len, dec->exp, ctx->prec */ -#define MPD_SSIZE_MAX INT32_MAX -#define MPD_SSIZE_MIN INT32_MIN -typedef int32_t mpd_ssize_t; -#define _mpd_strtossize strtol - -/* decimal arithmetic */ -#define MPD_RADIX 1000000000UL /* 10**9 */ -#define MPD_RDIGITS 9 -#define MPD_MAX_POW10 9 -#define MPD_EXPDIGITS 10 /* MPD_EXPDIGITS <= MPD_RDIGITS+1 */ - -#define MPD_MAXTRANSFORM_2N 33554432UL /* 2**25 */ -#define MPD_MAX_PREC 425000000L -#define MPD_MAX_PREC_LOG2 32 -#define MPD_ELIMIT 425000001L -#define MPD_MAX_EMAX 425000000L /* ELIMIT-1 */ -#define MPD_MIN_EMIN (-425000000L) /* -EMAX */ -#define MPD_MIN_ETINY (MPD_MIN_EMIN-(MPD_MAX_PREC-1)) -#define MPD_EXP_INF 1000000001L /* allows for emax=999999999 in the tests */ -#define MPD_EXP_CLAMP (-2000000001L) /* allows for emin=-999999999 in the tests */ -#define MPD_MAXIMPORT 94444445L /* ceil((2*MPD_MAX_PREC)/MPD_RDIGITS) */ -#define MPD_IEEE_CONTEXT_MAX_BITS 256 /* 16*(log2(MPD_MAX_EMAX / 3)-3) */ - -/* conversion specifiers */ -#define PRI_mpd_uint_t PRIu32 -#define PRI_mpd_ssize_t PRIi32 -/* END CONFIG_32 */ - -#else - #error "define CONFIG_64 or CONFIG_32" -#endif -/* END CONFIG */ - - -#if MPD_SIZE_MAX != MPD_UINT_MAX - #error "unsupported platform: need mpd_size_t == mpd_uint_t" -#endif - - -/******************************************************************************/ -/* Context */ -/******************************************************************************/ - -enum { - MPD_ROUND_UP, /* round away from 0 */ - MPD_ROUND_DOWN, /* round toward 0 (truncate) */ - MPD_ROUND_CEILING, /* round toward +infinity */ - MPD_ROUND_FLOOR, /* round toward -infinity */ - MPD_ROUND_HALF_UP, /* 0.5 is rounded up */ - MPD_ROUND_HALF_DOWN, /* 0.5 is rounded down */ - MPD_ROUND_HALF_EVEN, /* 0.5 is rounded to even */ - MPD_ROUND_05UP, /* round zero or five away from 0 */ - MPD_ROUND_TRUNC, /* truncate, but set infinity */ - MPD_ROUND_GUARD -}; - -enum { MPD_CLAMP_DEFAULT, MPD_CLAMP_IEEE_754, MPD_CLAMP_GUARD }; - -extern const char * const mpd_round_string[MPD_ROUND_GUARD]; -extern const char * const mpd_clamp_string[MPD_CLAMP_GUARD]; - - -typedef struct mpd_context_t { - mpd_ssize_t prec; /* precision */ - mpd_ssize_t emax; /* max positive exp */ - mpd_ssize_t emin; /* min negative exp */ - uint32_t traps; /* status events that should be trapped */ - uint32_t status; /* status flags */ - uint32_t newtrap; /* set by mpd_addstatus_raise() */ - int round; /* rounding mode */ - int clamp; /* clamp mode */ - int allcr; /* all functions correctly rounded */ -} mpd_context_t; - - -/* Status flags */ -#define MPD_Clamped 0x00000001U -#define MPD_Conversion_syntax 0x00000002U -#define MPD_Division_by_zero 0x00000004U -#define MPD_Division_impossible 0x00000008U -#define MPD_Division_undefined 0x00000010U -#define MPD_Fpu_error 0x00000020U -#define MPD_Inexact 0x00000040U -#define MPD_Invalid_context 0x00000080U -#define MPD_Invalid_operation 0x00000100U -#define MPD_Malloc_error 0x00000200U -#define MPD_Not_implemented 0x00000400U -#define MPD_Overflow 0x00000800U -#define MPD_Rounded 0x00001000U -#define MPD_Subnormal 0x00002000U -#define MPD_Underflow 0x00004000U -#define MPD_Max_status (0x00008000U-1U) - -/* Conditions that result in an IEEE 754 exception */ -#define MPD_IEEE_Invalid_operation (MPD_Conversion_syntax | \ - MPD_Division_impossible | \ - MPD_Division_undefined | \ - MPD_Fpu_error | \ - MPD_Invalid_context | \ - MPD_Invalid_operation | \ - MPD_Malloc_error) \ - -/* Errors that require the result of an operation to be set to NaN */ -#define MPD_Errors (MPD_IEEE_Invalid_operation | \ - MPD_Division_by_zero) - -/* Default traps */ -#define MPD_Traps (MPD_IEEE_Invalid_operation | \ - MPD_Division_by_zero | \ - MPD_Overflow | \ - MPD_Underflow) - -/* Official name */ -#define MPD_Insufficient_storage MPD_Malloc_error - -/* IEEE 754 interchange format contexts */ -#define MPD_DECIMAL32 32 -#define MPD_DECIMAL64 64 -#define MPD_DECIMAL128 128 - - -#define MPD_MINALLOC_MIN 2 -#define MPD_MINALLOC_MAX 64 -extern mpd_ssize_t MPD_MINALLOC; -extern void (* mpd_traphandler)(mpd_context_t *); -void mpd_dflt_traphandler(mpd_context_t *); - -void mpd_setminalloc(mpd_ssize_t n); -void mpd_init(mpd_context_t *ctx, mpd_ssize_t prec); - -void mpd_maxcontext(mpd_context_t *ctx); -void mpd_defaultcontext(mpd_context_t *ctx); -void mpd_basiccontext(mpd_context_t *ctx); -int mpd_ieee_context(mpd_context_t *ctx, int bits); - -mpd_ssize_t mpd_getprec(const mpd_context_t *ctx); -mpd_ssize_t mpd_getemax(const mpd_context_t *ctx); -mpd_ssize_t mpd_getemin(const mpd_context_t *ctx); -int mpd_getround(const mpd_context_t *ctx); -uint32_t mpd_gettraps(const mpd_context_t *ctx); -uint32_t mpd_getstatus(const mpd_context_t *ctx); -int mpd_getclamp(const mpd_context_t *ctx); -int mpd_getcr(const mpd_context_t *ctx); - -int mpd_qsetprec(mpd_context_t *ctx, mpd_ssize_t prec); -int mpd_qsetemax(mpd_context_t *ctx, mpd_ssize_t emax); -int mpd_qsetemin(mpd_context_t *ctx, mpd_ssize_t emin); -int mpd_qsetround(mpd_context_t *ctx, int newround); -int mpd_qsettraps(mpd_context_t *ctx, uint32_t flags); -int mpd_qsetstatus(mpd_context_t *ctx, uint32_t flags); -int mpd_qsetclamp(mpd_context_t *ctx, int c); -int mpd_qsetcr(mpd_context_t *ctx, int c); -void mpd_addstatus_raise(mpd_context_t *ctx, uint32_t flags); - - -/******************************************************************************/ -/* Decimal Arithmetic */ -/******************************************************************************/ - -/* mpd_t flags */ -#define MPD_POS MPD_UINT8_C(0) -#define MPD_NEG MPD_UINT8_C(1) -#define MPD_INF MPD_UINT8_C(2) -#define MPD_NAN MPD_UINT8_C(4) -#define MPD_SNAN MPD_UINT8_C(8) -#define MPD_SPECIAL (MPD_INF|MPD_NAN|MPD_SNAN) -#define MPD_STATIC MPD_UINT8_C(16) -#define MPD_STATIC_DATA MPD_UINT8_C(32) -#define MPD_SHARED_DATA MPD_UINT8_C(64) -#define MPD_CONST_DATA MPD_UINT8_C(128) -#define MPD_DATAFLAGS (MPD_STATIC_DATA|MPD_SHARED_DATA|MPD_CONST_DATA) - -/* mpd_t */ -typedef struct mpd_t { - uint8_t flags; - mpd_ssize_t exp; - mpd_ssize_t digits; - mpd_ssize_t len; - mpd_ssize_t alloc; - mpd_uint_t *data; -} mpd_t; - - -/******************************************************************************/ -/* Triple */ -/******************************************************************************/ - -/* status cases for getting a triple */ -enum mpd_triple_class { - MPD_TRIPLE_NORMAL, - MPD_TRIPLE_INF, - MPD_TRIPLE_QNAN, - MPD_TRIPLE_SNAN, - MPD_TRIPLE_ERROR, -}; - -typedef struct { - enum mpd_triple_class tag; - uint8_t sign; - uint64_t hi; - uint64_t lo; - int64_t exp; -} mpd_uint128_triple_t; - -int mpd_from_uint128_triple(mpd_t *result, const mpd_uint128_triple_t *triple, uint32_t *status); -mpd_uint128_triple_t mpd_as_uint128_triple(const mpd_t *a); - - -/******************************************************************************/ -/* Quiet, thread-safe functions */ -/******************************************************************************/ - -/* format specification */ -typedef struct mpd_spec_t { - mpd_ssize_t min_width; /* minimum field width */ - mpd_ssize_t prec; /* fraction digits or significant digits */ - char type; /* conversion specifier */ - char align; /* alignment */ - char sign; /* sign printing/alignment */ - char fill[5]; /* fill character */ - const char *dot; /* decimal point */ - const char *sep; /* thousands separator */ - const char *grouping; /* grouping of digits */ -} mpd_spec_t; - -/* output to a string */ -char *mpd_to_sci(const mpd_t *dec, int fmt); -char *mpd_to_eng(const mpd_t *dec, int fmt); -mpd_ssize_t mpd_to_sci_size(char **res, const mpd_t *dec, int fmt); -mpd_ssize_t mpd_to_eng_size(char **res, const mpd_t *dec, int fmt); -int mpd_validate_lconv(mpd_spec_t *spec); -int mpd_parse_fmt_str(mpd_spec_t *spec, const char *fmt, int caps); -char *mpd_qformat_spec(const mpd_t *dec, const mpd_spec_t *spec, const mpd_context_t *ctx, uint32_t *status); -char *mpd_qformat(const mpd_t *dec, const char *fmt, const mpd_context_t *ctx, uint32_t *status); - -#define MPD_NUM_FLAGS 15 -#define MPD_MAX_FLAG_STRING 208 -#define MPD_MAX_FLAG_LIST (MPD_MAX_FLAG_STRING+18) -#define MPD_MAX_SIGNAL_LIST 121 -int mpd_snprint_flags(char *dest, int nmemb, uint32_t flags); -int mpd_lsnprint_flags(char *dest, int nmemb, uint32_t flags, const char *flag_string[]); -int mpd_lsnprint_signals(char *dest, int nmemb, uint32_t flags, const char *signal_string[]); - -/* output to a file */ -void mpd_fprint(FILE *file, const mpd_t *dec); -void mpd_print(const mpd_t *dec); - -/* assignment from a string */ -void mpd_qset_string(mpd_t *dec, const char *s, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_string_exact(mpd_t *dec, const char *s, uint32_t *status); - -/* set to NaN with error flags */ -void mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status); -/* set a special with sign and type */ -void mpd_setspecial(mpd_t *result, uint8_t sign, uint8_t type); -/* set coefficient to zero or all nines */ -void mpd_zerocoeff(mpd_t *result); -void mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status); - -/* quietly assign a C integer type to an mpd_t */ -void mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status); -#ifndef LEGACY_COMPILER -void mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qset_i64_exact(mpd_t *result, int64_t a, uint32_t *status); -void mpd_qset_u64_exact(mpd_t *result, uint64_t a, uint32_t *status); -#endif - -/* quietly assign a C integer type to an mpd_t with a static coefficient */ -void mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, uint32_t *status); - -/* quietly get a C integer type from an mpd_t */ -mpd_ssize_t mpd_qget_ssize(const mpd_t *dec, uint32_t *status); -mpd_uint_t mpd_qget_uint(const mpd_t *dec, uint32_t *status); -mpd_uint_t mpd_qabs_uint(const mpd_t *dec, uint32_t *status); - -int32_t mpd_qget_i32(const mpd_t *dec, uint32_t *status); -uint32_t mpd_qget_u32(const mpd_t *dec, uint32_t *status); -#ifndef LEGACY_COMPILER -int64_t mpd_qget_i64(const mpd_t *dec, uint32_t *status); -uint64_t mpd_qget_u64(const mpd_t *dec, uint32_t *status); -#endif - -/* quiet functions */ -int mpd_qcheck_nan(mpd_t *nanresult, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -int mpd_qcheck_nans(mpd_t *nanresult, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status); - -const char *mpd_class(const mpd_t *a, const mpd_context_t *ctx); - -int mpd_qcopy(mpd_t *result, const mpd_t *a, uint32_t *status); -int mpd_qcopy_cxx(mpd_t *result, const mpd_t *a); -mpd_t *mpd_qncopy(const mpd_t *a); -int mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status); -int mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status); -int mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status); - -void mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -int mpd_same_quantum(const mpd_t *a, const mpd_t *b); - -void mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -int mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status); -mpd_uint_t mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status); -mpd_uint_t mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n); -void mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx, uint32_t *status); - -int mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status); -int mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -int mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -int mpd_cmp_total(const mpd_t *a, const mpd_t *b); -int mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b); -int mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b); -int mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b); - -void mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); - -void mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, const mpd_context_t *ctx, uint32_t *status); -void mpd_qrescale_fmt(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, const mpd_context_t *ctx, uint32_t *status); -void mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_context_t *ctx, uint32_t *status); -void mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, const mpd_context_t *ctx, uint32_t *status); -void mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qln10(mpd_t *result, mpd_ssize_t prec, uint32_t *status); -void mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, uint32_t *status); - -#ifndef LEGACY_COMPILER -void mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, const mpd_context_t *ctx, uint32_t *status); -void mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, const mpd_context_t *ctx, uint32_t *status); -#endif - - -size_t mpd_sizeinbase(const mpd_t *a, uint32_t base); -void mpd_qimport_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t srcbase, - const mpd_context_t *ctx, uint32_t *status); -void mpd_qimport_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t srcbase, - const mpd_context_t *ctx, uint32_t *status); -size_t mpd_qexport_u16(uint16_t **rdata, size_t rlen, uint32_t base, - const mpd_t *src, uint32_t *status); -size_t mpd_qexport_u32(uint32_t **rdata, size_t rlen, uint32_t base, - const mpd_t *src, uint32_t *status); - - -/******************************************************************************/ -/* Signalling functions */ -/******************************************************************************/ - -char *mpd_format(const mpd_t *dec, const char *fmt, mpd_context_t *ctx); -void mpd_import_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx); -void mpd_import_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen, uint8_t srcsign, uint32_t base, mpd_context_t *ctx); -size_t mpd_export_u16(uint16_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx); -size_t mpd_export_u32(uint32_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, mpd_context_t *ctx); -void mpd_finalize(mpd_t *result, mpd_context_t *ctx); -int mpd_check_nan(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -int mpd_check_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_set_string(mpd_t *result, const char *s, mpd_context_t *ctx); -void mpd_maxcoeff(mpd_t *result, mpd_context_t *ctx); -void mpd_sset_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx); -void mpd_sset_i32(mpd_t *result, int32_t a, mpd_context_t *ctx); -void mpd_sset_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx); -void mpd_sset_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx); -void mpd_set_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx); -void mpd_set_i32(mpd_t *result, int32_t a, mpd_context_t *ctx); -void mpd_set_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx); -void mpd_set_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx); -#ifndef LEGACY_COMPILER -void mpd_set_i64(mpd_t *result, int64_t a, mpd_context_t *ctx); -void mpd_set_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx); -#endif -mpd_ssize_t mpd_get_ssize(const mpd_t *a, mpd_context_t *ctx); -mpd_uint_t mpd_get_uint(const mpd_t *a, mpd_context_t *ctx); -mpd_uint_t mpd_abs_uint(const mpd_t *a, mpd_context_t *ctx); -int32_t mpd_get_i32(const mpd_t *a, mpd_context_t *ctx); -uint32_t mpd_get_u32(const mpd_t *a, mpd_context_t *ctx); -#ifndef LEGACY_COMPILER -int64_t mpd_get_i64(const mpd_t *a, mpd_context_t *ctx); -uint64_t mpd_get_u64(const mpd_t *a, mpd_context_t *ctx); -#endif -void mpd_and(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_copy(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_canonical(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_copy_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_copy_negate(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_copy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_invert(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_logb(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_or(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_rotate(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_scaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_shiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx); -mpd_uint_t mpd_shiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx); -void mpd_shiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx); -void mpd_shift(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_xor(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -int mpd_cmp(const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -int mpd_compare(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -int mpd_compare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_add(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_add_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx); -void mpd_add_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx); -void mpd_add_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx); -void mpd_add_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx); -void mpd_sub(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_sub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx); -void mpd_sub_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx); -void mpd_sub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx); -void mpd_sub_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx); -void mpd_div(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_div_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx); -void mpd_div_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx); -void mpd_div_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx); -void mpd_div_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx); -void mpd_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_divint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_exp(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_fma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, mpd_context_t *ctx); -void mpd_ln(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_log10(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_max(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_max_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_min(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_min_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_mul(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_mul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx); -void mpd_mul_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx); -void mpd_mul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx); -void mpd_mul_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx); -void mpd_next_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_next_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_next_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_pow(mpd_t *result, const mpd_t *base, const mpd_t *exp, mpd_context_t *ctx); -void mpd_powmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, mpd_context_t *ctx); -void mpd_quantize(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_rescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, mpd_context_t *ctx); -void mpd_reduce(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_rem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_rem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx); -void mpd_round_to_intx(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_round_to_int(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_trunc(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_floor(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_ceil(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_sqrt(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); -void mpd_invroot(mpd_t *result, const mpd_t *a, mpd_context_t *ctx); - -#ifndef LEGACY_COMPILER -void mpd_add_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx); -void mpd_add_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx); -void mpd_sub_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx); -void mpd_sub_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx); -void mpd_div_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx); -void mpd_div_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx); -void mpd_mul_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx); -void mpd_mul_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx); -#endif - - -/******************************************************************************/ -/* Configuration specific */ -/******************************************************************************/ - -#ifdef CONFIG_64 -void mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, uint32_t *status); -void mpd_sset_i64(mpd_t *result, int64_t a, mpd_context_t *ctx); -void mpd_sset_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx); -#endif - - -/******************************************************************************/ -/* Get attributes of a decimal */ -/******************************************************************************/ - -EXTINLINE mpd_ssize_t mpd_adjexp(const mpd_t *dec); -EXTINLINE mpd_ssize_t mpd_etiny(const mpd_context_t *ctx); -EXTINLINE mpd_ssize_t mpd_etop(const mpd_context_t *ctx); -EXTINLINE mpd_uint_t mpd_msword(const mpd_t *dec); -EXTINLINE int mpd_word_digits(mpd_uint_t word); -/* most significant digit of a word */ -EXTINLINE mpd_uint_t mpd_msd(mpd_uint_t word); -/* least significant digit of a word */ -EXTINLINE mpd_uint_t mpd_lsd(mpd_uint_t word); -/* coefficient size needed to store 'digits' */ -EXTINLINE mpd_ssize_t mpd_digits_to_size(mpd_ssize_t digits); -/* number of digits in the exponent, undefined for MPD_SSIZE_MIN */ -EXTINLINE int mpd_exp_digits(mpd_ssize_t exp); -EXTINLINE int mpd_iscanonical(const mpd_t *dec); -EXTINLINE int mpd_isfinite(const mpd_t *dec); -EXTINLINE int mpd_isinfinite(const mpd_t *dec); -EXTINLINE int mpd_isinteger(const mpd_t *dec); -EXTINLINE int mpd_isnan(const mpd_t *dec); -EXTINLINE int mpd_isnegative(const mpd_t *dec); -EXTINLINE int mpd_ispositive(const mpd_t *dec); -EXTINLINE int mpd_isqnan(const mpd_t *dec); -EXTINLINE int mpd_issigned(const mpd_t *dec); -EXTINLINE int mpd_issnan(const mpd_t *dec); -EXTINLINE int mpd_isspecial(const mpd_t *dec); -EXTINLINE int mpd_iszero(const mpd_t *dec); -/* undefined for special numbers */ -EXTINLINE int mpd_iszerocoeff(const mpd_t *dec); -EXTINLINE int mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx); -EXTINLINE int mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx); -/* odd word */ -EXTINLINE int mpd_isoddword(mpd_uint_t word); -/* odd coefficient */ -EXTINLINE int mpd_isoddcoeff(const mpd_t *dec); -/* odd decimal, only defined for integers */ -int mpd_isodd(const mpd_t *dec); -/* even decimal, only defined for integers */ -int mpd_iseven(const mpd_t *dec); -/* 0 if dec is positive, 1 if dec is negative */ -EXTINLINE uint8_t mpd_sign(const mpd_t *dec); -/* 1 if dec is positive, -1 if dec is negative */ -EXTINLINE int mpd_arith_sign(const mpd_t *dec); -EXTINLINE long mpd_radix(void); -EXTINLINE int mpd_isdynamic(const mpd_t *dec); -EXTINLINE int mpd_isstatic(const mpd_t *dec); -EXTINLINE int mpd_isdynamic_data(const mpd_t *dec); -EXTINLINE int mpd_isstatic_data(const mpd_t *dec); -EXTINLINE int mpd_isshared_data(const mpd_t *dec); -EXTINLINE int mpd_isconst_data(const mpd_t *dec); -EXTINLINE mpd_ssize_t mpd_trail_zeros(const mpd_t *dec); - - -/******************************************************************************/ -/* Set attributes of a decimal */ -/******************************************************************************/ - -/* set number of decimal digits in the coefficient */ -EXTINLINE void mpd_setdigits(mpd_t *result); -EXTINLINE void mpd_set_sign(mpd_t *result, uint8_t sign); -/* copy sign from another decimal */ -EXTINLINE void mpd_signcpy(mpd_t *result, const mpd_t *a); -EXTINLINE void mpd_set_infinity(mpd_t *result); -EXTINLINE void mpd_set_qnan(mpd_t *result); -EXTINLINE void mpd_set_snan(mpd_t *result); -EXTINLINE void mpd_set_negative(mpd_t *result); -EXTINLINE void mpd_set_positive(mpd_t *result); -EXTINLINE void mpd_set_dynamic(mpd_t *result); -EXTINLINE void mpd_set_static(mpd_t *result); -EXTINLINE void mpd_set_dynamic_data(mpd_t *result); -EXTINLINE void mpd_set_static_data(mpd_t *result); -EXTINLINE void mpd_set_shared_data(mpd_t *result); -EXTINLINE void mpd_set_const_data(mpd_t *result); -EXTINLINE void mpd_clear_flags(mpd_t *result); -EXTINLINE void mpd_set_flags(mpd_t *result, uint8_t flags); -EXTINLINE void mpd_copy_flags(mpd_t *result, const mpd_t *a); - - -/******************************************************************************/ -/* Error Macros */ -/******************************************************************************/ - -#define mpd_err_fatal(...) \ - do {fprintf(stderr, "%s:%d: error: ", __FILE__, __LINE__); \ - fprintf(stderr, __VA_ARGS__); fputc('\n', stderr); \ - abort(); \ - } while (0) -#define mpd_err_warn(...) \ - do {fprintf(stderr, "%s:%d: warning: ", __FILE__, __LINE__); \ - fprintf(stderr, __VA_ARGS__); fputc('\n', stderr); \ - } while (0) - - -/******************************************************************************/ -/* Memory handling */ -/******************************************************************************/ - -extern void *(* mpd_mallocfunc)(size_t size); -extern void *(* mpd_callocfunc)(size_t nmemb, size_t size); -extern void *(* mpd_reallocfunc)(void *ptr, size_t size); -extern void (* mpd_free)(void *ptr); - -void *mpd_callocfunc_em(size_t nmemb, size_t size); - -void *mpd_alloc(mpd_size_t nmemb, mpd_size_t size); -void *mpd_calloc(mpd_size_t nmemb, mpd_size_t size); -void *mpd_realloc(void *ptr, mpd_size_t nmemb, mpd_size_t size, uint8_t *err); -void *mpd_sh_alloc(mpd_size_t struct_size, mpd_size_t nmemb, mpd_size_t size); - -mpd_t *mpd_qnew(void); -mpd_t *mpd_new(mpd_context_t *ctx); -mpd_t *mpd_qnew_size(mpd_ssize_t nwords); -EXTINLINE void mpd_del(mpd_t *dec); - -EXTINLINE void mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len); -EXTINLINE int mpd_qresize(mpd_t *result, mpd_ssize_t nwords, uint32_t *status); -EXTINLINE int mpd_qresize_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status); -EXTINLINE void mpd_minalloc(mpd_t *result); - -int mpd_resize(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx); -int mpd_resize_zero(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#ifdef __cplusplus -} /* END extern "C" */ -#endif - - -#endif /* LIBMPDEC_MPDECIMAL_H_ */ diff --git a/Modules/_decimal/libmpdec/mpsignal.c b/Modules/_decimal/libmpdec/mpsignal.c deleted file mode 100644 index fc2af48f4f3795..00000000000000 --- a/Modules/_decimal/libmpdec/mpsignal.c +++ /dev/null @@ -1,967 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include - - -/* Signaling wrappers for the quiet functions in mpdecimal.c. */ - - -char * -mpd_format(const mpd_t *dec, const char *fmt, mpd_context_t *ctx) -{ - char *ret; - uint32_t status = 0; - ret = mpd_qformat(dec, fmt, ctx, &status); - mpd_addstatus_raise(ctx, status); - return ret; -} - -void -mpd_import_u16(mpd_t *result, const uint16_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t base, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qimport_u16(result, srcdata, srclen, srcsign, base, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_import_u32(mpd_t *result, const uint32_t *srcdata, size_t srclen, - uint8_t srcsign, uint32_t base, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qimport_u32(result, srcdata, srclen, srcsign, base, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -size_t -mpd_export_u16(uint16_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, - mpd_context_t *ctx) -{ - size_t n; - uint32_t status = 0; - n = mpd_qexport_u16(rdata, rlen, base, src, &status); - mpd_addstatus_raise(ctx, status); - return n; -} - -size_t -mpd_export_u32(uint32_t **rdata, size_t rlen, uint32_t base, const mpd_t *src, - mpd_context_t *ctx) -{ - size_t n; - uint32_t status = 0; - n = mpd_qexport_u32(rdata, rlen, base, src, &status); - mpd_addstatus_raise(ctx, status); - return n; -} - -void -mpd_finalize(mpd_t *result, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qfinalize(result, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -int -mpd_check_nan(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (mpd_qcheck_nan(result, a, ctx, &status)) { - mpd_addstatus_raise(ctx, status); - return 1; - } - return 0; -} - -int -mpd_check_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (mpd_qcheck_nans(result, a, b, ctx, &status)) { - mpd_addstatus_raise(ctx, status); - return 1; - } - return 0; -} - -void -mpd_set_string(mpd_t *result, const char *s, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qset_string(result, s, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_maxcoeff(mpd_t *result, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmaxcoeff(result, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -/* set static mpd from signed integer */ -void -mpd_sset_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsset_ssize(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_sset_i32(mpd_t *result, int32_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsset_i32(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifdef CONFIG_64 -void -mpd_sset_i64(mpd_t *result, int64_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsset_i64(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -/* set static mpd from unsigned integer */ -void -mpd_sset_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsset_uint(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_sset_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsset_u32(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifdef CONFIG_64 -void -mpd_sset_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsset_u64(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -/* set mpd from signed integer */ -void -mpd_set_ssize(mpd_t *result, mpd_ssize_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qset_ssize(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_set_i32(mpd_t *result, int32_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qset_i32(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_set_i64(mpd_t *result, int64_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qset_i64(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -/* set mpd from unsigned integer */ -void -mpd_set_uint(mpd_t *result, mpd_uint_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qset_uint(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_set_u32(mpd_t *result, uint32_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qset_u32(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_set_u64(mpd_t *result, uint64_t a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qset_u64(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -/* convert mpd to signed integer */ -mpd_ssize_t -mpd_get_ssize(const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_ssize_t ret; - - ret = mpd_qget_ssize(a, &status); - mpd_addstatus_raise(ctx, status); - return ret; -} - -int32_t -mpd_get_i32(const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - int32_t ret; - - ret = mpd_qget_i32(a, &status); - mpd_addstatus_raise(ctx, status); - return ret; -} - -#ifndef LEGACY_COMPILER -int64_t -mpd_get_i64(const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - int64_t ret; - - ret = mpd_qget_i64(a, &status); - mpd_addstatus_raise(ctx, status); - return ret; -} -#endif - -mpd_uint_t -mpd_get_uint(const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_uint_t ret; - - ret = mpd_qget_uint(a, &status); - mpd_addstatus_raise(ctx, status); - return ret; -} - -mpd_uint_t -mpd_abs_uint(const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_uint_t ret; - - ret = mpd_qabs_uint(a, &status); - mpd_addstatus_raise(ctx, status); - return ret; -} - -uint32_t -mpd_get_u32(const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - uint32_t ret; - - ret = mpd_qget_u32(a, &status); - mpd_addstatus_raise(ctx, status); - return ret; -} - -#ifndef LEGACY_COMPILER -uint64_t -mpd_get_u64(const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - uint64_t ret; - - ret = mpd_qget_u64(a, &status); - mpd_addstatus_raise(ctx, status); - return ret; -} -#endif - -void -mpd_and(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qand(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_copy(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (!mpd_qcopy(result, a, &status)) { - mpd_addstatus_raise(ctx, status); - } -} - -void -mpd_canonical(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - mpd_copy(result, a, ctx); -} - -void -mpd_copy_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (!mpd_qcopy_abs(result, a, &status)) { - mpd_addstatus_raise(ctx, status); - } -} - -void -mpd_copy_negate(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (!mpd_qcopy_negate(result, a, &status)) { - mpd_addstatus_raise(ctx, status); - } -} - -void -mpd_copy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - if (!mpd_qcopy_sign(result, a, b, &status)) { - mpd_addstatus_raise(ctx, status); - } -} - -void -mpd_invert(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qinvert(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_logb(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qlogb(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_or(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qor(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_rotate(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qrotate(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_scaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qscaleb(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_shiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qshiftl(result, a, n, &status); - mpd_addstatus_raise(ctx, status); -} - -mpd_uint_t -mpd_shiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_uint_t rnd; - - rnd = mpd_qshiftr(result, a, n, &status); - mpd_addstatus_raise(ctx, status); - return rnd; -} - -void -mpd_shiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qshiftn(result, a, n, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_shift(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qshift(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_xor(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qxor(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_abs(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qabs(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -int -mpd_cmp(const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - int c; - c = mpd_qcmp(a, b, &status); - mpd_addstatus_raise(ctx, status); - return c; -} - -int -mpd_compare(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - int c; - c = mpd_qcompare(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); - return c; -} - -int -mpd_compare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - int c; - c = mpd_qcompare_signal(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); - return c; -} - -void -mpd_add(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qadd(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_sub(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsub(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_add_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qadd_ssize(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_add_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qadd_i32(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_add_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qadd_i64(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -void -mpd_add_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qadd_uint(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_add_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qadd_u32(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_add_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qadd_u64(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -void -mpd_sub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsub_ssize(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_sub_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsub_i32(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_sub_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsub_i64(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -void -mpd_sub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsub_uint(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_sub_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsub_u32(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_sub_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsub_u64(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -void -mpd_div(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qdiv(q, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_div_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qdiv_ssize(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_div_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qdiv_i32(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_div_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qdiv_i64(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -void -mpd_div_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qdiv_uint(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_div_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qdiv_u32(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_div_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qdiv_u64(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -void -mpd_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qdivmod(q, r, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_divint(mpd_t *q, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qdivint(q, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_exp(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qexp(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_fma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, - mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qfma(result, a, b, c, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_ln(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qln(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_log10(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qlog10(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_max(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmax(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_max_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmax_mag(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_min(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmin(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_min_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmin_mag(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qminus(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_mul(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmul(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_mul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmul_ssize(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_mul_i32(mpd_t *result, const mpd_t *a, int32_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmul_i32(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_mul_i64(mpd_t *result, const mpd_t *a, int64_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmul_i64(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -void -mpd_mul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmul_uint(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_mul_u32(mpd_t *result, const mpd_t *a, uint32_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmul_u32(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -#ifndef LEGACY_COMPILER -void -mpd_mul_u64(mpd_t *result, const mpd_t *a, uint64_t b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qmul_u64(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} -#endif - -void -mpd_next_minus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qnext_minus(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_next_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qnext_plus(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_next_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qnext_toward(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_plus(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qplus(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_pow(mpd_t *result, const mpd_t *base, const mpd_t *exp, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qpow(result, base, exp, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_powmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, const mpd_t *mod, - mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qpowmod(result, base, exp, mod, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_quantize(mpd_t *result, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qquantize(result, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_rescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qrescale(result, a, exp, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_reduce(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qreduce(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_rem(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qrem(r, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_rem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qrem_near(r, a, b, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_round_to_intx(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qround_to_intx(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_round_to_int(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qround_to_int(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_trunc(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qtrunc(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_floor(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qfloor(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_ceil(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qceil(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_sqrt(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qsqrt(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} - -void -mpd_invroot(mpd_t *result, const mpd_t *a, mpd_context_t *ctx) -{ - uint32_t status = 0; - mpd_qinvroot(result, a, ctx, &status); - mpd_addstatus_raise(ctx, status); -} diff --git a/Modules/_decimal/libmpdec/numbertheory.c b/Modules/_decimal/libmpdec/numbertheory.c deleted file mode 100644 index 210e0deb371203..00000000000000 --- a/Modules/_decimal/libmpdec/numbertheory.c +++ /dev/null @@ -1,132 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include - -#include "bits.h" -#include "numbertheory.h" -#include "umodarith.h" - - -/* Bignum: Initialize the Number Theoretic Transform. */ - - -/* - * Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n) - * in the Fourier transform. We have w**n == 1 (mod p). - * n := transform length. - * sign := -1 for forward transform, 1 for backward transform. - * modnum := one of {P1, P2, P3}. - */ -mpd_uint_t -_mpd_getkernel(mpd_uint_t n, int sign, int modnum) -{ - mpd_uint_t umod, p, r, xi; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - - SETMODULUS(modnum); - r = mpd_roots[modnum]; /* primitive root of F(p) */ - p = umod; - xi = (p-1) / n; - - if (sign == -1) - return POWMOD(r, (p-1-xi)); - else - return POWMOD(r, xi); -} - -/* - * Initialize and return transform parameters. - * n := transform length. - * sign := -1 for forward transform, 1 for backward transform. - * modnum := one of {P1, P2, P3}. - */ -struct fnt_params * -_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum) -{ - struct fnt_params *tparams; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t kernel, w; - mpd_uint_t i; - mpd_size_t nhalf; - - assert(ispower2(n)); - assert(sign == -1 || sign == 1); - assert(P1 <= modnum && modnum <= P3); - - nhalf = n/2; - tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t)); - if (tparams == NULL) { - return NULL; - } - - SETMODULUS(modnum); - kernel = _mpd_getkernel(n, sign, modnum); - - tparams->modnum = modnum; - tparams->modulus = umod; - tparams->kernel = kernel; - - /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */ - w = 1; - for (i = 0; i < nhalf; i++) { - tparams->wtable[i] = w; - w = MULMOD(w, kernel); - } - - return tparams; -} - -/* Initialize wtable of size three. */ -void -_mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum) -{ - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t kernel; - - SETMODULUS(modnum); - kernel = _mpd_getkernel(3, sign, modnum); - - w3table[0] = 1; - w3table[1] = kernel; - w3table[2] = POWMOD(kernel, 2); -} diff --git a/Modules/_decimal/libmpdec/numbertheory.h b/Modules/_decimal/libmpdec/numbertheory.h deleted file mode 100644 index 47b7753b831b89..00000000000000 --- a/Modules/_decimal/libmpdec/numbertheory.h +++ /dev/null @@ -1,76 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_NUMBERTHEORY_H_ -#define LIBMPDEC_NUMBERTHEORY_H_ - - -#include "mpdecimal.h" -#include "constants.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -/* transform parameters */ -struct fnt_params { - int modnum; - mpd_uint_t modulus; - mpd_uint_t kernel; - mpd_uint_t wtable[]; -}; - - -mpd_uint_t _mpd_getkernel(mpd_uint_t n, int sign, int modnum); -struct fnt_params *_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum); -void _mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum); - - -#ifdef PPRO -static inline void -ppro_setmodulus(int modnum, mpd_uint_t *umod, double *dmod, uint32_t dinvmod[3]) -{ - *dmod = *umod = mpd_moduli[modnum]; - dinvmod[0] = mpd_invmoduli[modnum][0]; - dinvmod[1] = mpd_invmoduli[modnum][1]; - dinvmod[2] = mpd_invmoduli[modnum][2]; -} -#else -static inline void -std_setmodulus(int modnum, mpd_uint_t *umod) -{ - *umod = mpd_moduli[modnum]; -} -#endif - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_NUMBERTHEORY_H_ */ diff --git a/Modules/_decimal/libmpdec/sixstep.c b/Modules/_decimal/libmpdec/sixstep.c deleted file mode 100644 index a4d1dbed7813c6..00000000000000 --- a/Modules/_decimal/libmpdec/sixstep.c +++ /dev/null @@ -1,214 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include - -#include "bits.h" -#include "constants.h" -#include "difradix2.h" -#include "numbertheory.h" -#include "sixstep.h" -#include "transpose.h" -#include "umodarith.h" - - -/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the - form 2**n (See literature/six-step.txt). */ - - -/* forward transform with sign = -1 */ -int -six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - struct fnt_params *tparams; - mpd_size_t log2n, C, R; - mpd_uint_t kernel; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t *x, w0, w1, wstep; - mpd_size_t i, k; - - - assert(ispower2(n)); - assert(n >= 16); - assert(n <= MPD_MAXTRANSFORM_2N); - - log2n = mpd_bsr(n); - C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */ - R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */ - - - /* Transpose the matrix. */ - if (!transpose_pow2(a, R, C)) { - return 0; - } - - /* Length R transform on the rows. */ - if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) { - return 0; - } - for (x = a; x < a+n; x += R) { - fnt_dif2(x, R, tparams); - } - - /* Transpose the matrix. */ - if (!transpose_pow2(a, C, R)) { - mpd_free(tparams); - return 0; - } - - /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ - SETMODULUS(modnum); - kernel = _mpd_getkernel(n, -1, modnum); - for (i = 1; i < R; i++) { - w0 = 1; /* r**(i*0): initial value for k=0 */ - w1 = POWMOD(kernel, i); /* r**(i*1): initial value for k=1 */ - wstep = MULMOD(w1, w1); /* r**(2*i) */ - for (k = 0; k < C; k += 2) { - mpd_uint_t x0 = a[i*C+k]; - mpd_uint_t x1 = a[i*C+k+1]; - MULMOD2(&x0, w0, &x1, w1); - MULMOD2C(&w0, &w1, wstep); /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */ - a[i*C+k] = x0; - a[i*C+k+1] = x1; - } - } - - /* Length C transform on the rows. */ - if (C != R) { - mpd_free(tparams); - if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) { - return 0; - } - } - for (x = a; x < a+n; x += C) { - fnt_dif2(x, C, tparams); - } - mpd_free(tparams); - -#if 0 - /* An unordered transform is sufficient for convolution. */ - /* Transpose the matrix. */ - if (!transpose_pow2(a, R, C)) { - return 0; - } -#endif - - return 1; -} - - -/* reverse transform, sign = 1 */ -int -inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) -{ - struct fnt_params *tparams; - mpd_size_t log2n, C, R; - mpd_uint_t kernel; - mpd_uint_t umod; -#ifdef PPRO - double dmod; - uint32_t dinvmod[3]; -#endif - mpd_uint_t *x, w0, w1, wstep; - mpd_size_t i, k; - - - assert(ispower2(n)); - assert(n >= 16); - assert(n <= MPD_MAXTRANSFORM_2N); - - log2n = mpd_bsr(n); - C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */ - R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */ - - -#if 0 - /* An unordered transform is sufficient for convolution. */ - /* Transpose the matrix, producing an R*C matrix. */ - if (!transpose_pow2(a, C, R)) { - return 0; - } -#endif - - /* Length C transform on the rows. */ - if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) { - return 0; - } - for (x = a; x < a+n; x += C) { - fnt_dif2(x, C, tparams); - } - - /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ - SETMODULUS(modnum); - kernel = _mpd_getkernel(n, 1, modnum); - for (i = 1; i < R; i++) { - w0 = 1; - w1 = POWMOD(kernel, i); - wstep = MULMOD(w1, w1); - for (k = 0; k < C; k += 2) { - mpd_uint_t x0 = a[i*C+k]; - mpd_uint_t x1 = a[i*C+k+1]; - MULMOD2(&x0, w0, &x1, w1); - MULMOD2C(&w0, &w1, wstep); - a[i*C+k] = x0; - a[i*C+k+1] = x1; - } - } - - /* Transpose the matrix. */ - if (!transpose_pow2(a, R, C)) { - mpd_free(tparams); - return 0; - } - - /* Length R transform on the rows. */ - if (R != C) { - mpd_free(tparams); - if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) { - return 0; - } - } - for (x = a; x < a+n; x += R) { - fnt_dif2(x, R, tparams); - } - mpd_free(tparams); - - /* Transpose the matrix. */ - if (!transpose_pow2(a, C, R)) { - return 0; - } - - return 1; -} diff --git a/Modules/_decimal/libmpdec/sixstep.h b/Modules/_decimal/libmpdec/sixstep.h deleted file mode 100644 index 89b4a33afc7920..00000000000000 --- a/Modules/_decimal/libmpdec/sixstep.h +++ /dev/null @@ -1,47 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_SIXSTEP_H_ -#define LIBMPDEC_SIXSTEP_H_ - - -#include "mpdecimal.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -int six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum); -int inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum); - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_SIXSTEP_H_ */ diff --git a/Modules/_decimal/libmpdec/transpose.c b/Modules/_decimal/libmpdec/transpose.c deleted file mode 100644 index 56321b5f39a733..00000000000000 --- a/Modules/_decimal/libmpdec/transpose.c +++ /dev/null @@ -1,276 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "mpdecimal.h" - -#include -#include -#include -#include -#include - -#include "bits.h" -#include "constants.h" -#include "transpose.h" -#include "typearith.h" - - -#define BUFSIZE 4096 -#define SIDE 128 - - -/* Bignum: The transpose functions are used for very large transforms - in sixstep.c and fourstep.c. */ - - -/* Definition of the matrix transpose */ -void -std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols) -{ - mpd_size_t idest, isrc; - mpd_size_t r, c; - - for (r = 0; r < rows; r++) { - isrc = r * cols; - idest = r; - for (c = 0; c < cols; c++) { - dest[idest] = src[isrc]; - isrc += 1; - idest += rows; - } - } -} - -/* - * Swap half-rows of 2^n * (2*2^n) matrix. - * FORWARD_CYCLE: even/odd permutation of the halfrows. - * BACKWARD_CYCLE: reverse the even/odd permutation. - */ -static int -swap_halfrows_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols, int dir) -{ - mpd_uint_t buf1[BUFSIZE]; - mpd_uint_t buf2[BUFSIZE]; - mpd_uint_t *readbuf, *writebuf, *hp; - mpd_size_t *done, dbits; - mpd_size_t b = BUFSIZE, stride; - mpd_size_t hn, hmax; /* halfrow number */ - mpd_size_t m, r=0; - mpd_size_t offset; - mpd_size_t next; - - - assert(cols == mul_size_t(2, rows)); - - if (dir == FORWARD_CYCLE) { - r = rows; - } - else if (dir == BACKWARD_CYCLE) { - r = 2; - } - else { - abort(); /* GCOV_NOT_REACHED */ - } - - m = cols - 1; - hmax = rows; /* cycles start at odd halfrows */ - dbits = 8 * sizeof *done; - if ((done = mpd_calloc(hmax/(sizeof *done) + 1, sizeof *done)) == NULL) { - return 0; - } - - for (hn = 1; hn <= hmax; hn += 2) { - - if (done[hn/dbits] & mpd_bits[hn%dbits]) { - continue; - } - - readbuf = buf1; writebuf = buf2; - - for (offset = 0; offset < cols/2; offset += b) { - - stride = (offset + b < cols/2) ? b : cols/2-offset; - - hp = matrix + hn*cols/2; - memcpy(readbuf, hp+offset, stride*(sizeof *readbuf)); - pointerswap(&readbuf, &writebuf); - - next = mulmod_size_t(hn, r, m); - hp = matrix + next*cols/2; - - while (next != hn) { - - memcpy(readbuf, hp+offset, stride*(sizeof *readbuf)); - memcpy(hp+offset, writebuf, stride*(sizeof *writebuf)); - pointerswap(&readbuf, &writebuf); - - done[next/dbits] |= mpd_bits[next%dbits]; - - next = mulmod_size_t(next, r, m); - hp = matrix + next*cols/2; - - } - - memcpy(hp+offset, writebuf, stride*(sizeof *writebuf)); - - done[hn/dbits] |= mpd_bits[hn%dbits]; - } - } - - mpd_free(done); - return 1; -} - -/* In-place transpose of a square matrix */ -static inline void -squaretrans(mpd_uint_t *buf, mpd_size_t cols) -{ - mpd_uint_t tmp; - mpd_size_t idest, isrc; - mpd_size_t r, c; - - for (r = 0; r < cols; r++) { - c = r+1; - isrc = r*cols + c; - idest = c*cols + r; - for (c = r+1; c < cols; c++) { - tmp = buf[isrc]; - buf[isrc] = buf[idest]; - buf[idest] = tmp; - isrc += 1; - idest += cols; - } - } -} - -/* - * Transpose 2^n * 2^n matrix. For cache efficiency, the matrix is split into - * square blocks with side length 'SIDE'. First, the blocks are transposed, - * then a square transposition is done on each individual block. - */ -static void -squaretrans_pow2(mpd_uint_t *matrix, mpd_size_t size) -{ - mpd_uint_t buf1[SIDE*SIDE]; - mpd_uint_t buf2[SIDE*SIDE]; - mpd_uint_t *to, *from; - mpd_size_t b = size; - mpd_size_t r, c; - mpd_size_t i; - - while (b > SIDE) b >>= 1; - - for (r = 0; r < size; r += b) { - - for (c = r; c < size; c += b) { - - from = matrix + r*size + c; - to = buf1; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += size; - to += b; - } - squaretrans(buf1, b); - - if (r == c) { - to = matrix + r*size + c; - from = buf1; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += b; - to += size; - } - continue; - } - else { - from = matrix + c*size + r; - to = buf2; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += size; - to += b; - } - squaretrans(buf2, b); - - to = matrix + c*size + r; - from = buf1; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += b; - to += size; - } - - to = matrix + r*size + c; - from = buf2; - for (i = 0; i < b; i++) { - memcpy(to, from, b*(sizeof *to)); - from += b; - to += size; - } - } - } - } - -} - -/* - * In-place transposition of a 2^n x 2^n or a 2^n x (2*2^n) - * or a (2*2^n) x 2^n matrix. - */ -int -transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols) -{ - mpd_size_t size = mul_size_t(rows, cols); - - assert(ispower2(rows)); - assert(ispower2(cols)); - - if (cols == rows) { - squaretrans_pow2(matrix, rows); - } - else if (cols == mul_size_t(2, rows)) { - if (!swap_halfrows_pow2(matrix, rows, cols, FORWARD_CYCLE)) { - return 0; - } - squaretrans_pow2(matrix, rows); - squaretrans_pow2(matrix+(size/2), rows); - } - else if (rows == mul_size_t(2, cols)) { - squaretrans_pow2(matrix, cols); - squaretrans_pow2(matrix+(size/2), cols); - if (!swap_halfrows_pow2(matrix, cols, rows, BACKWARD_CYCLE)) { - return 0; - } - } - else { - abort(); /* GCOV_NOT_REACHED */ - } - - return 1; -} diff --git a/Modules/_decimal/libmpdec/transpose.h b/Modules/_decimal/libmpdec/transpose.h deleted file mode 100644 index e91c18d74356bc..00000000000000 --- a/Modules/_decimal/libmpdec/transpose.h +++ /dev/null @@ -1,61 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_TRANSPOSE_H_ -#define LIBMPDEC_TRANSPOSE_H_ - - -#include "mpdecimal.h" - - -/* Internal header file: all symbols have local scope in the DSO */ -MPD_PRAGMA(MPD_HIDE_SYMBOLS_START) - - -enum {FORWARD_CYCLE, BACKWARD_CYCLE}; - - -void std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols); -int transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols); -void transpose_3xpow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols); - - -static inline void pointerswap(mpd_uint_t **a, mpd_uint_t **b) -{ - mpd_uint_t *tmp; - - tmp = *b; - *b = *a; - *a = tmp; -} - - -MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */ - - -#endif /* LIBMPDEC_TRANSPOSE_H_ */ diff --git a/Modules/_decimal/libmpdec/typearith.h b/Modules/_decimal/libmpdec/typearith.h deleted file mode 100644 index dd3776453d098d..00000000000000 --- a/Modules/_decimal/libmpdec/typearith.h +++ /dev/null @@ -1,668 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_TYPEARITH_H_ -#define LIBMPDEC_TYPEARITH_H_ - - -#include "mpdecimal.h" - -#include - - -/*****************************************************************************/ -/* Low level native arithmetic on basic types */ -/*****************************************************************************/ - - -/** ------------------------------------------------------------ - ** Double width multiplication and division - ** ------------------------------------------------------------ - */ - -#if defined(CONFIG_64) -#if defined(ANSI) -#if defined(HAVE_UINT128_T) -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - __uint128_t hl; - - hl = (__uint128_t)a * b; - - *hi = hl >> 64; - *lo = (mpd_uint_t)hl; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - __uint128_t hl; - - hl = ((__uint128_t)hi<<64) + lo; - *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */ - *r = (mpd_uint_t)(hl - (__uint128_t)(*q) * d); -} -#else -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - uint32_t w[4], carry; - uint32_t ah, al, bh, bl; - uint64_t hl; - - ah = (uint32_t)(a>>32); al = (uint32_t)a; - bh = (uint32_t)(b>>32); bl = (uint32_t)b; - - hl = (uint64_t)al * bl; - w[0] = (uint32_t)hl; - carry = (uint32_t)(hl>>32); - - hl = (uint64_t)ah * bl + carry; - w[1] = (uint32_t)hl; - w[2] = (uint32_t)(hl>>32); - - hl = (uint64_t)al * bh + w[1]; - w[1] = (uint32_t)hl; - carry = (uint32_t)(hl>>32); - - hl = ((uint64_t)ah * bh + w[2]) + carry; - w[2] = (uint32_t)hl; - w[3] = (uint32_t)(hl>>32); - - *hi = ((uint64_t)w[3]<<32) + w[2]; - *lo = ((uint64_t)w[1]<<32) + w[0]; -} - -/* - * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt - * http://www.hackersdelight.org/permissions.htm: - * "You are free to use, copy, and distribute any of the code on this web - * site, whether modified by you or not. You need not give attribution." - * - * Slightly modified, comments are mine. - */ -static inline int -nlz(uint64_t x) -{ - int n; - - if (x == 0) return(64); - - n = 0; - if (x <= 0x00000000FFFFFFFF) {n = n +32; x = x <<32;} - if (x <= 0x0000FFFFFFFFFFFF) {n = n +16; x = x <<16;} - if (x <= 0x00FFFFFFFFFFFFFF) {n = n + 8; x = x << 8;} - if (x <= 0x0FFFFFFFFFFFFFFF) {n = n + 4; x = x << 4;} - if (x <= 0x3FFFFFFFFFFFFFFF) {n = n + 2; x = x << 2;} - if (x <= 0x7FFFFFFFFFFFFFFF) {n = n + 1;} - - return n; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0, - mpd_uint_t v) -{ - const mpd_uint_t b = 4294967296; - mpd_uint_t un1, un0, - vn1, vn0, - q1, q0, - un32, un21, un10, - rhat, t; - int s; - - assert(u1 < v); - - s = nlz(v); - v = v << s; - vn1 = v >> 32; - vn0 = v & 0xFFFFFFFF; - - t = (s == 0) ? 0 : u0 >> (64 - s); - un32 = (u1 << s) | t; - un10 = u0 << s; - - un1 = un10 >> 32; - un0 = un10 & 0xFFFFFFFF; - - q1 = un32 / vn1; - rhat = un32 - q1*vn1; -again1: - if (q1 >= b || q1*vn0 > b*rhat + un1) { - q1 = q1 - 1; - rhat = rhat + vn1; - if (rhat < b) goto again1; - } - - /* - * Before again1 we had: - * (1) q1*vn1 + rhat = un32 - * (2) q1*vn1*b + rhat*b + un1 = un32*b + un1 - * - * The statements inside the if-clause do not change the value - * of the left-hand side of (2), and the loop is only exited - * if q1*vn0 <= rhat*b + un1, so: - * - * (3) q1*vn1*b + q1*vn0 <= un32*b + un1 - * (4) q1*v <= un32*b + un1 - * (5) 0 <= un32*b + un1 - q1*v - * - * By (5) we are certain that the possible add-back step from - * Knuth's algorithm D is never required. - * - * Since the final quotient is less than 2**64, the following - * must be true: - * - * (6) un32*b + un1 - q1*v <= UINT64_MAX - * - * This means that in the following line, the high words - * of un32*b and q1*v can be discarded without any effect - * on the result. - */ - un21 = un32*b + un1 - q1*v; - - q0 = un21 / vn1; - rhat = un21 - q0*vn1; -again2: - if (q0 >= b || q0*vn0 > b*rhat + un0) { - q0 = q0 - 1; - rhat = rhat + vn1; - if (rhat < b) goto again2; - } - - *q = q1*b + q0; - *r = (un21*b + un0 - q0*v) >> s; -} -#endif - -/* END ANSI */ -#elif defined(ASM) -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - mpd_uint_t h, l; - - __asm__ ( "mulq %3\n\t" - : "=d" (h), "=a" (l) - : "%a" (a), "rm" (b) - : "cc" - ); - - *hi = h; - *lo = l; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - mpd_uint_t qq, rr; - - __asm__ ( "divq %4\n\t" - : "=a" (qq), "=d" (rr) - : "a" (lo), "d" (hi), "rm" (d) - : "cc" - ); - - *q = qq; - *r = rr; -} -/* END GCC ASM */ -#elif defined(MASM) -#include -#pragma intrinsic(_umul128) - -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - *lo = _umul128(a, b, hi); -} - -void _mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d); - -/* END MASM (_MSC_VER) */ -#else - #error "need platform specific 128 bit multiplication and division" -#endif - -#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d -static inline void -_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp) -{ - assert(exp <= 19); - - if (exp <= 9) { - if (exp <= 4) { - switch (exp) { - case 0: *q = v; *r = 0; break; - case 1: DIVMOD(q, r, v, 10UL); break; - case 2: DIVMOD(q, r, v, 100UL); break; - case 3: DIVMOD(q, r, v, 1000UL); break; - case 4: DIVMOD(q, r, v, 10000UL); break; - } - } - else { - switch (exp) { - case 5: DIVMOD(q, r, v, 100000UL); break; - case 6: DIVMOD(q, r, v, 1000000UL); break; - case 7: DIVMOD(q, r, v, 10000000UL); break; - case 8: DIVMOD(q, r, v, 100000000UL); break; - case 9: DIVMOD(q, r, v, 1000000000UL); break; - } - } - } - else { - if (exp <= 14) { - switch (exp) { - case 10: DIVMOD(q, r, v, 10000000000ULL); break; - case 11: DIVMOD(q, r, v, 100000000000ULL); break; - case 12: DIVMOD(q, r, v, 1000000000000ULL); break; - case 13: DIVMOD(q, r, v, 10000000000000ULL); break; - case 14: DIVMOD(q, r, v, 100000000000000ULL); break; - } - } - else { - switch (exp) { - case 15: DIVMOD(q, r, v, 1000000000000000ULL); break; - case 16: DIVMOD(q, r, v, 10000000000000000ULL); break; - case 17: DIVMOD(q, r, v, 100000000000000000ULL); break; - case 18: DIVMOD(q, r, v, 1000000000000000000ULL); break; - case 19: DIVMOD(q, r, v, 10000000000000000000ULL); break; /* GCOV_NOT_REACHED */ - } - } - } -} - -/* END CONFIG_64 */ -#elif defined(CONFIG_32) -#if defined(ANSI) -#if !defined(LEGACY_COMPILER) -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - mpd_uuint_t hl; - - hl = (mpd_uuint_t)a * b; - - *hi = hl >> 32; - *lo = (mpd_uint_t)hl; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - mpd_uuint_t hl; - - hl = ((mpd_uuint_t)hi<<32) + lo; - *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */ - *r = (mpd_uint_t)(hl - (mpd_uuint_t)(*q) * d); -} -/* END ANSI + uint64_t */ -#else -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - uint16_t w[4], carry; - uint16_t ah, al, bh, bl; - uint32_t hl; - - ah = (uint16_t)(a>>16); al = (uint16_t)a; - bh = (uint16_t)(b>>16); bl = (uint16_t)b; - - hl = (uint32_t)al * bl; - w[0] = (uint16_t)hl; - carry = (uint16_t)(hl>>16); - - hl = (uint32_t)ah * bl + carry; - w[1] = (uint16_t)hl; - w[2] = (uint16_t)(hl>>16); - - hl = (uint32_t)al * bh + w[1]; - w[1] = (uint16_t)hl; - carry = (uint16_t)(hl>>16); - - hl = ((uint32_t)ah * bh + w[2]) + carry; - w[2] = (uint16_t)hl; - w[3] = (uint16_t)(hl>>16); - - *hi = ((uint32_t)w[3]<<16) + w[2]; - *lo = ((uint32_t)w[1]<<16) + w[0]; -} - -/* - * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt - * http://www.hackersdelight.org/permissions.htm: - * "You are free to use, copy, and distribute any of the code on this web - * site, whether modified by you or not. You need not give attribution." - * - * Slightly modified, comments are mine. - */ -static inline int -nlz(uint32_t x) -{ - int n; - - if (x == 0) return(32); - - n = 0; - if (x <= 0x0000FFFF) {n = n +16; x = x <<16;} - if (x <= 0x00FFFFFF) {n = n + 8; x = x << 8;} - if (x <= 0x0FFFFFFF) {n = n + 4; x = x << 4;} - if (x <= 0x3FFFFFFF) {n = n + 2; x = x << 2;} - if (x <= 0x7FFFFFFF) {n = n + 1;} - - return n; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0, - mpd_uint_t v) -{ - const mpd_uint_t b = 65536; - mpd_uint_t un1, un0, - vn1, vn0, - q1, q0, - un32, un21, un10, - rhat, t; - int s; - - assert(u1 < v); - - s = nlz(v); - v = v << s; - vn1 = v >> 16; - vn0 = v & 0xFFFF; - - t = (s == 0) ? 0 : u0 >> (32 - s); - un32 = (u1 << s) | t; - un10 = u0 << s; - - un1 = un10 >> 16; - un0 = un10 & 0xFFFF; - - q1 = un32 / vn1; - rhat = un32 - q1*vn1; -again1: - if (q1 >= b || q1*vn0 > b*rhat + un1) { - q1 = q1 - 1; - rhat = rhat + vn1; - if (rhat < b) goto again1; - } - - /* - * Before again1 we had: - * (1) q1*vn1 + rhat = un32 - * (2) q1*vn1*b + rhat*b + un1 = un32*b + un1 - * - * The statements inside the if-clause do not change the value - * of the left-hand side of (2), and the loop is only exited - * if q1*vn0 <= rhat*b + un1, so: - * - * (3) q1*vn1*b + q1*vn0 <= un32*b + un1 - * (4) q1*v <= un32*b + un1 - * (5) 0 <= un32*b + un1 - q1*v - * - * By (5) we are certain that the possible add-back step from - * Knuth's algorithm D is never required. - * - * Since the final quotient is less than 2**32, the following - * must be true: - * - * (6) un32*b + un1 - q1*v <= UINT32_MAX - * - * This means that in the following line, the high words - * of un32*b and q1*v can be discarded without any effect - * on the result. - */ - un21 = un32*b + un1 - q1*v; - - q0 = un21 / vn1; - rhat = un21 - q0*vn1; -again2: - if (q0 >= b || q0*vn0 > b*rhat + un0) { - q0 = q0 - 1; - rhat = rhat + vn1; - if (rhat < b) goto again2; - } - - *q = q1*b + q0; - *r = (un21*b + un0 - q0*v) >> s; -} -#endif /* END ANSI + LEGACY_COMPILER */ - -/* END ANSI */ -#elif defined(ASM) -static inline void -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - mpd_uint_t h, l; - - __asm__ ( "mull %3\n\t" - : "=d" (h), "=a" (l) - : "%a" (a), "rm" (b) - : "cc" - ); - - *hi = h; - *lo = l; -} - -static inline void -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - mpd_uint_t qq, rr; - - __asm__ ( "divl %4\n\t" - : "=a" (qq), "=d" (rr) - : "a" (lo), "d" (hi), "rm" (d) - : "cc" - ); - - *q = qq; - *r = rr; -} -/* END GCC ASM */ -#elif defined(MASM) -static inline void __cdecl -_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b) -{ - mpd_uint_t h, l; - - __asm { - mov eax, a - mul b - mov h, edx - mov l, eax - } - - *hi = h; - *lo = l; -} - -static inline void __cdecl -_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo, - mpd_uint_t d) -{ - mpd_uint_t qq, rr; - - __asm { - mov eax, lo - mov edx, hi - div d - mov qq, eax - mov rr, edx - } - - *q = qq; - *r = rr; -} -/* END MASM (_MSC_VER) */ -#else - #error "need platform specific 64 bit multiplication and division" -#endif - -#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d -static inline void -_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp) -{ - assert(exp <= 9); - - if (exp <= 4) { - switch (exp) { - case 0: *q = v; *r = 0; break; - case 1: DIVMOD(q, r, v, 10UL); break; - case 2: DIVMOD(q, r, v, 100UL); break; - case 3: DIVMOD(q, r, v, 1000UL); break; - case 4: DIVMOD(q, r, v, 10000UL); break; - } - } - else { - switch (exp) { - case 5: DIVMOD(q, r, v, 100000UL); break; - case 6: DIVMOD(q, r, v, 1000000UL); break; - case 7: DIVMOD(q, r, v, 10000000UL); break; - case 8: DIVMOD(q, r, v, 100000000UL); break; - case 9: DIVMOD(q, r, v, 1000000000UL); break; /* GCOV_NOT_REACHED */ - } - } -} -/* END CONFIG_32 */ - -/* NO CONFIG */ -#else - #error "define CONFIG_64 or CONFIG_32" -#endif /* CONFIG */ - - -static inline void -_mpd_div_word(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t d) -{ - *q = v / d; - *r = v - *q * d; -} - -static inline void -_mpd_idiv_word(mpd_ssize_t *q, mpd_ssize_t *r, mpd_ssize_t v, mpd_ssize_t d) -{ - *q = v / d; - *r = v - *q * d; -} - - -/** ------------------------------------------------------------ - ** Arithmetic with overflow checking - ** ------------------------------------------------------------ - */ - -/* The following macros do call exit() in case of an overflow. - If the library is used correctly (i.e. with valid context - parameters), such overflows cannot occur. The macros are used - as sanity checks in a couple of strategic places and should - be viewed as a handwritten version of gcc's -ftrapv option. */ - -static inline mpd_size_t -add_size_t(mpd_size_t a, mpd_size_t b) -{ - if (a > MPD_SIZE_MAX - b) { - mpd_err_fatal("add_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */ - } - return a + b; -} - -static inline mpd_size_t -sub_size_t(mpd_size_t a, mpd_size_t b) -{ - if (b > a) { - mpd_err_fatal("sub_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */ - } - return a - b; -} - -#if MPD_SIZE_MAX != MPD_UINT_MAX - #error "adapt mul_size_t() and mulmod_size_t()" -#endif - -static inline mpd_size_t -mul_size_t(mpd_size_t a, mpd_size_t b) -{ - mpd_uint_t hi, lo; - - _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b); - if (hi) { - mpd_err_fatal("mul_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */ - } - return lo; -} - -static inline mpd_size_t -add_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow) -{ - mpd_size_t ret; - - *overflow = 0; - ret = a + b; - if (ret < a) *overflow = 1; - return ret; -} - -static inline mpd_size_t -mul_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow) -{ - mpd_uint_t hi, lo; - - _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b); - *overflow = (mpd_size_t)hi; - return lo; -} - -static inline mpd_ssize_t -mod_mpd_ssize_t(mpd_ssize_t a, mpd_ssize_t m) -{ - mpd_ssize_t r = a % m; - return (r < 0) ? r + m : r; -} - -static inline mpd_size_t -mulmod_size_t(mpd_size_t a, mpd_size_t b, mpd_size_t m) -{ - mpd_uint_t hi, lo; - mpd_uint_t q, r; - - _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b); - _mpd_div_words(&q, &r, hi, lo, (mpd_uint_t)m); - - return r; -} - - -#endif /* LIBMPDEC_TYPEARITH_H_ */ diff --git a/Modules/_decimal/libmpdec/umodarith.h b/Modules/_decimal/libmpdec/umodarith.h deleted file mode 100644 index d7dbbbe6a7331a..00000000000000 --- a/Modules/_decimal/libmpdec/umodarith.h +++ /dev/null @@ -1,648 +0,0 @@ -/* - * Copyright (c) 2008-2020 Stefan Krah. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#ifndef LIBMPDEC_UMODARITH_H_ -#define LIBMPDEC_UMODARITH_H_ - - -#include "mpdecimal.h" - -#include "constants.h" -#include "typearith.h" - - -/* Bignum: Low level routines for unsigned modular arithmetic. These are - used in the fast convolution functions for very large coefficients. */ - - -/**************************************************************************/ -/* ANSI modular arithmetic */ -/**************************************************************************/ - - -/* - * Restrictions: a < m and b < m - * ACL2 proof: umodarith.lisp: addmod-correct - */ -static inline mpd_uint_t -addmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t s; - - s = a + b; - s = (s < a) ? s - m : s; - s = (s >= m) ? s - m : s; - - return s; -} - -/* - * Restrictions: a < m and b < m - * ACL2 proof: umodarith.lisp: submod-2-correct - */ -static inline mpd_uint_t -submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t d; - - d = a - b; - d = (a < b) ? d + m : d; - - return d; -} - -/* - * Restrictions: a < 2m and b < 2m - * ACL2 proof: umodarith.lisp: section ext-submod - */ -static inline mpd_uint_t -ext_submod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t d; - - a = (a >= m) ? a - m : a; - b = (b >= m) ? b - m : b; - - d = a - b; - d = (a < b) ? d + m : d; - - return d; -} - -/* - * Reduce double word modulo m. - * Restrictions: m != 0 - * ACL2 proof: umodarith.lisp: section dw-reduce - */ -static inline mpd_uint_t -dw_reduce(mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t m) -{ - mpd_uint_t r1, r2, w; - - _mpd_div_word(&w, &r1, hi, m); - _mpd_div_words(&w, &r2, r1, lo, m); - - return r2; -} - -/* - * Subtract double word from a. - * Restrictions: a < m - * ACL2 proof: umodarith.lisp: section dw-submod - */ -static inline mpd_uint_t -dw_submod(mpd_uint_t a, mpd_uint_t hi, mpd_uint_t lo, mpd_uint_t m) -{ - mpd_uint_t d, r; - - r = dw_reduce(hi, lo, m); - d = a - r; - d = (a < r) ? d + m : d; - - return d; -} - -#ifdef CONFIG_64 - -/**************************************************************************/ -/* 64-bit modular arithmetic */ -/**************************************************************************/ - -/* - * A proof of the algorithm is in literature/mulmod-64.txt. An ACL2 - * proof is in umodarith.lisp: section "Fast modular reduction". - * - * Algorithm: calculate (a * b) % p: - * - * a) hi, lo <- a * b # Calculate a * b. - * - * b) hi, lo <- R(hi, lo) # Reduce modulo p. - * - * c) Repeat step b) until 0 <= hi * 2**64 + lo < 2*p. - * - * d) If the result is less than p, return lo. Otherwise return lo - p. - */ - -static inline mpd_uint_t -x64_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t hi, lo, x, y; - - - _mpd_mul_words(&hi, &lo, a, b); - - if (m & (1ULL<<32)) { /* P1 */ - - /* first reduction */ - x = y = hi; - hi >>= 32; - - x = lo - x; - if (x > lo) hi--; - - y <<= 32; - lo = y + x; - if (lo < y) hi++; - - /* second reduction */ - x = y = hi; - hi >>= 32; - - x = lo - x; - if (x > lo) hi--; - - y <<= 32; - lo = y + x; - if (lo < y) hi++; - - return (hi || lo >= m ? lo - m : lo); - } - else if (m & (1ULL<<34)) { /* P2 */ - - /* first reduction */ - x = y = hi; - hi >>= 30; - - x = lo - x; - if (x > lo) hi--; - - y <<= 34; - lo = y + x; - if (lo < y) hi++; - - /* second reduction */ - x = y = hi; - hi >>= 30; - - x = lo - x; - if (x > lo) hi--; - - y <<= 34; - lo = y + x; - if (lo < y) hi++; - - /* third reduction */ - x = y = hi; - hi >>= 30; - - x = lo - x; - if (x > lo) hi--; - - y <<= 34; - lo = y + x; - if (lo < y) hi++; - - return (hi || lo >= m ? lo - m : lo); - } - else { /* P3 */ - - /* first reduction */ - x = y = hi; - hi >>= 24; - - x = lo - x; - if (x > lo) hi--; - - y <<= 40; - lo = y + x; - if (lo < y) hi++; - - /* second reduction */ - x = y = hi; - hi >>= 24; - - x = lo - x; - if (x > lo) hi--; - - y <<= 40; - lo = y + x; - if (lo < y) hi++; - - /* third reduction */ - x = y = hi; - hi >>= 24; - - x = lo - x; - if (x > lo) hi--; - - y <<= 40; - lo = y + x; - if (lo < y) hi++; - - return (hi || lo >= m ? lo - m : lo); - } -} - -static inline void -x64_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m) -{ - *a = x64_mulmod(*a, w, m); - *b = x64_mulmod(*b, w, m); -} - -static inline void -x64_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - mpd_uint_t m) -{ - *a0 = x64_mulmod(*a0, b0, m); - *a1 = x64_mulmod(*a1, b1, m); -} - -static inline mpd_uint_t -x64_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod) -{ - mpd_uint_t r = 1; - - while (exp > 0) { - if (exp & 1) - r = x64_mulmod(r, base, umod); - base = x64_mulmod(base, base, umod); - exp >>= 1; - } - - return r; -} - -/* END CONFIG_64 */ -#else /* CONFIG_32 */ - - -/**************************************************************************/ -/* 32-bit modular arithmetic */ -/**************************************************************************/ - -#if defined(ANSI) -#if !defined(LEGACY_COMPILER) -/* HAVE_UINT64_T */ -static inline mpd_uint_t -std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - return ((mpd_uuint_t) a * b) % m; -} - -static inline void -std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m) -{ - *a = ((mpd_uuint_t) *a * w) % m; - *b = ((mpd_uuint_t) *b * w) % m; -} - -static inline void -std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - mpd_uint_t m) -{ - *a0 = ((mpd_uuint_t) *a0 * b0) % m; - *a1 = ((mpd_uuint_t) *a1 * b1) % m; -} -/* END HAVE_UINT64_T */ -#else -/* LEGACY_COMPILER */ -static inline mpd_uint_t -std_mulmod(mpd_uint_t a, mpd_uint_t b, mpd_uint_t m) -{ - mpd_uint_t hi, lo, q, r; - _mpd_mul_words(&hi, &lo, a, b); - _mpd_div_words(&q, &r, hi, lo, m); - return r; -} - -static inline void -std_mulmod2c(mpd_uint_t *a, mpd_uint_t *b, mpd_uint_t w, mpd_uint_t m) -{ - *a = std_mulmod(*a, w, m); - *b = std_mulmod(*b, w, m); -} - -static inline void -std_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - mpd_uint_t m) -{ - *a0 = std_mulmod(*a0, b0, m); - *a1 = std_mulmod(*a1, b1, m); -} -/* END LEGACY_COMPILER */ -#endif - -static inline mpd_uint_t -std_powmod(mpd_uint_t base, mpd_uint_t exp, mpd_uint_t umod) -{ - mpd_uint_t r = 1; - - while (exp > 0) { - if (exp & 1) - r = std_mulmod(r, base, umod); - base = std_mulmod(base, base, umod); - exp >>= 1; - } - - return r; -} -#endif /* ANSI CONFIG_32 */ - - -/**************************************************************************/ -/* Pentium Pro modular arithmetic */ -/**************************************************************************/ - -/* - * A proof of the algorithm is in literature/mulmod-ppro.txt. The FPU - * control word must be set to 64-bit precision and truncation mode - * prior to using these functions. - * - * Algorithm: calculate (a * b) % p: - * - * p := prime < 2**31 - * pinv := (long double)1.0 / p (precalculated) - * - * a) n = a * b # Calculate exact product. - * b) qest = n * pinv # Calculate estimate for q = n / p. - * c) q = (qest+2**63)-2**63 # Truncate qest to the exact quotient. - * d) r = n - q * p # Calculate remainder. - * - * Remarks: - * - * - p = dmod and pinv = dinvmod. - * - dinvmod points to an array of three uint32_t, which is interpreted - * as an 80 bit long double by fldt. - * - Intel compilers prior to version 11 do not seem to handle the - * __GNUC__ inline assembly correctly. - * - random tests are provided in tests/extended/ppro_mulmod.c - */ - -#if defined(PPRO) -#if defined(ASM) - -/* Return (a * b) % dmod */ -static inline mpd_uint_t -ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod) -{ - mpd_uint_t retval; - - __asm__ ( - "fildl %2\n\t" - "fildl %1\n\t" - "fmulp %%st, %%st(1)\n\t" - "fldt (%4)\n\t" - "fmul %%st(1), %%st\n\t" - "flds %5\n\t" - "fadd %%st, %%st(1)\n\t" - "fsubrp %%st, %%st(1)\n\t" - "fldl (%3)\n\t" - "fmulp %%st, %%st(1)\n\t" - "fsubrp %%st, %%st(1)\n\t" - "fistpl %0\n\t" - : "=m" (retval) - : "m" (a), "m" (b), "r" (dmod), "r" (dinvmod), "m" (MPD_TWO63) - : "st", "memory" - ); - - return retval; -} - -/* - * Two modular multiplications in parallel: - * *a0 = (*a0 * w) % dmod - * *a1 = (*a1 * w) % dmod - */ -static inline void -ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w, - double *dmod, uint32_t *dinvmod) -{ - __asm__ ( - "fildl %2\n\t" - "fildl (%1)\n\t" - "fmul %%st(1), %%st\n\t" - "fxch %%st(1)\n\t" - "fildl (%0)\n\t" - "fmulp %%st, %%st(1) \n\t" - "fldt (%4)\n\t" - "flds %5\n\t" - "fld %%st(2)\n\t" - "fmul %%st(2)\n\t" - "fadd %%st(1)\n\t" - "fsub %%st(1)\n\t" - "fmull (%3)\n\t" - "fsubrp %%st, %%st(3)\n\t" - "fxch %%st(2)\n\t" - "fistpl (%0)\n\t" - "fmul %%st(2)\n\t" - "fadd %%st(1)\n\t" - "fsubp %%st, %%st(1)\n\t" - "fmull (%3)\n\t" - "fsubrp %%st, %%st(1)\n\t" - "fistpl (%1)\n\t" - : : "r" (a0), "r" (a1), "m" (w), - "r" (dmod), "r" (dinvmod), - "m" (MPD_TWO63) - : "st", "memory" - ); -} - -/* - * Two modular multiplications in parallel: - * *a0 = (*a0 * b0) % dmod - * *a1 = (*a1 * b1) % dmod - */ -static inline void -ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - double *dmod, uint32_t *dinvmod) -{ - __asm__ ( - "fildl %3\n\t" - "fildl (%2)\n\t" - "fmulp %%st, %%st(1)\n\t" - "fildl %1\n\t" - "fildl (%0)\n\t" - "fmulp %%st, %%st(1)\n\t" - "fldt (%5)\n\t" - "fld %%st(2)\n\t" - "fmul %%st(1), %%st\n\t" - "fxch %%st(1)\n\t" - "fmul %%st(2), %%st\n\t" - "flds %6\n\t" - "fldl (%4)\n\t" - "fxch %%st(3)\n\t" - "fadd %%st(1), %%st\n\t" - "fxch %%st(2)\n\t" - "fadd %%st(1), %%st\n\t" - "fxch %%st(2)\n\t" - "fsub %%st(1), %%st\n\t" - "fxch %%st(2)\n\t" - "fsubp %%st, %%st(1)\n\t" - "fxch %%st(1)\n\t" - "fmul %%st(2), %%st\n\t" - "fxch %%st(1)\n\t" - "fmulp %%st, %%st(2)\n\t" - "fsubrp %%st, %%st(3)\n\t" - "fsubrp %%st, %%st(1)\n\t" - "fxch %%st(1)\n\t" - "fistpl (%2)\n\t" - "fistpl (%0)\n\t" - : : "r" (a0), "m" (b0), "r" (a1), "m" (b1), - "r" (dmod), "r" (dinvmod), - "m" (MPD_TWO63) - : "st", "memory" - ); -} -/* END PPRO GCC ASM */ -#elif defined(MASM) - -/* Return (a * b) % dmod */ -static inline mpd_uint_t __cdecl -ppro_mulmod(mpd_uint_t a, mpd_uint_t b, double *dmod, uint32_t *dinvmod) -{ - mpd_uint_t retval; - - __asm { - mov eax, dinvmod - mov edx, dmod - fild b - fild a - fmulp st(1), st - fld TBYTE PTR [eax] - fmul st, st(1) - fld MPD_TWO63 - fadd st(1), st - fsubp st(1), st - fld QWORD PTR [edx] - fmulp st(1), st - fsubp st(1), st - fistp retval - } - - return retval; -} - -/* - * Two modular multiplications in parallel: - * *a0 = (*a0 * w) % dmod - * *a1 = (*a1 * w) % dmod - */ -static inline mpd_uint_t __cdecl -ppro_mulmod2c(mpd_uint_t *a0, mpd_uint_t *a1, mpd_uint_t w, - double *dmod, uint32_t *dinvmod) -{ - __asm { - mov ecx, dmod - mov edx, a1 - mov ebx, dinvmod - mov eax, a0 - fild w - fild DWORD PTR [edx] - fmul st, st(1) - fxch st(1) - fild DWORD PTR [eax] - fmulp st(1), st - fld TBYTE PTR [ebx] - fld MPD_TWO63 - fld st(2) - fmul st, st(2) - fadd st, st(1) - fsub st, st(1) - fmul QWORD PTR [ecx] - fsubp st(3), st - fxch st(2) - fistp DWORD PTR [eax] - fmul st, st(2) - fadd st, st(1) - fsubrp st(1), st - fmul QWORD PTR [ecx] - fsubp st(1), st - fistp DWORD PTR [edx] - } -} - -/* - * Two modular multiplications in parallel: - * *a0 = (*a0 * b0) % dmod - * *a1 = (*a1 * b1) % dmod - */ -static inline void __cdecl -ppro_mulmod2(mpd_uint_t *a0, mpd_uint_t b0, mpd_uint_t *a1, mpd_uint_t b1, - double *dmod, uint32_t *dinvmod) -{ - __asm { - mov ecx, dmod - mov edx, a1 - mov ebx, dinvmod - mov eax, a0 - fild b1 - fild DWORD PTR [edx] - fmulp st(1), st - fild b0 - fild DWORD PTR [eax] - fmulp st(1), st - fld TBYTE PTR [ebx] - fld st(2) - fmul st, st(1) - fxch st(1) - fmul st, st(2) - fld DWORD PTR MPD_TWO63 - fld QWORD PTR [ecx] - fxch st(3) - fadd st, st(1) - fxch st(2) - fadd st, st(1) - fxch st(2) - fsub st, st(1) - fxch st(2) - fsubrp st(1), st - fxch st(1) - fmul st, st(2) - fxch st(1) - fmulp st(2), st - fsubp st(3), st - fsubp st(1), st - fxch st(1) - fistp DWORD PTR [edx] - fistp DWORD PTR [eax] - } -} -#endif /* PPRO MASM (_MSC_VER) */ - - -/* Return (base ** exp) % dmod */ -static inline mpd_uint_t -ppro_powmod(mpd_uint_t base, mpd_uint_t exp, double *dmod, uint32_t *dinvmod) -{ - mpd_uint_t r = 1; - - while (exp > 0) { - if (exp & 1) - r = ppro_mulmod(r, base, dmod, dinvmod); - base = ppro_mulmod(base, base, dmod, dinvmod); - exp >>= 1; - } - - return r; -} -#endif /* PPRO */ -#endif /* CONFIG_32 */ - - -#endif /* LIBMPDEC_UMODARITH_H_ */ diff --git a/Modules/_decimal/libmpdec/vcdiv64.asm b/Modules/_decimal/libmpdec/vcdiv64.asm deleted file mode 100644 index 597e9ba9352c8f..00000000000000 --- a/Modules/_decimal/libmpdec/vcdiv64.asm +++ /dev/null @@ -1,46 +0,0 @@ -; -; Copyright (c) 2008-2020 Stefan Krah. All rights reserved. -; -; Redistribution and use in source and binary forms, with or without -; modification, are permitted provided that the following conditions -; are met: -; -; 1. Redistributions of source code must retain the above copyright -; notice, this list of conditions and the following disclaimer. -; -; 2. Redistributions in binary form must reproduce the above copyright -; notice, this list of conditions and the following disclaimer in the -; documentation and/or other materials provided with the distribution. -; -; THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND -; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE -; ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE -; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS -; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) -; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY -; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF -; SUCH DAMAGE. -; - - -PUBLIC _mpd_div_words -_TEXT SEGMENT -q$ = 8 -r$ = 16 -hi$ = 24 -lo$ = 32 -d$ = 40 -_mpd_div_words PROC - mov r10, rdx - mov rdx, r8 - mov rax, r9 - div QWORD PTR d$[rsp] - mov QWORD PTR [r10], rdx - mov QWORD PTR [rcx], rax - ret 0 -_mpd_div_words ENDP -_TEXT ENDS -END diff --git a/Modules/makesetup b/Modules/makesetup index f6cf695b457cbf..d87793392aa83c 100755 --- a/Modules/makesetup +++ b/Modules/makesetup @@ -248,7 +248,7 @@ sed -e 's/[ ]*#.*//' -e '/^[ ]*$/d' | \$*) ;; *) src='$(srcdir)/'"$srcdir/$src";; esac - # custom flags first, PY_STDMODULE_CFLAGS may contain -I with system libmpdec + # custom flags first, PY_STDMODULE_CFLAGS may contain -I for system libmpdec case $doconfig in no) cc="$cc $cpps \$(PY_STDMODULE_CFLAGS) \$(CCSHARED)" diff --git a/Tools/build/generate_sbom.py b/Tools/build/generate_sbom.py index df52f8de762a01..ad87a046216819 100644 --- a/Tools/build/generate_sbom.py +++ b/Tools/build/generate_sbom.py @@ -56,9 +56,6 @@ class PackageFiles(typing.NamedTuple): # values to 'exclude' if we create new files within tracked # directories that aren't sourced from third-party packages. PACKAGE_TO_FILES = { - "mpdecimal": PackageFiles( - include=["Modules/_decimal/libmpdec/**"] - ), "expat": PackageFiles( include=["Modules/expat/**"], exclude=[ diff --git a/Tools/c-analyzer/cpython/_parser.py b/Tools/c-analyzer/cpython/_parser.py index 037fe11ea223c7..d7bdf7ce9e56bd 100644 --- a/Tools/c-analyzer/cpython/_parser.py +++ b/Tools/c-analyzer/cpython/_parser.py @@ -115,7 +115,6 @@ def clean_lines(text): * ./Include/internal * ./Include/internal/mimalloc -Modules/_decimal/**/*.c Modules/_decimal/libmpdec Modules/_elementtree.c Modules/expat Modules/_hacl/*.c Modules/_hacl/include Modules/_hacl/*.c Modules/_hacl/ diff --git a/configure b/configure index b0dc18d5cea749..4df17ad417105a 100755 --- a/configure +++ b/configure @@ -882,7 +882,6 @@ TCLTK_LIBS TCLTK_CFLAGS LIBSQLITE3_LIBS LIBSQLITE3_CFLAGS -LIBMPDEC_INTERNAL LIBMPDEC_LIBS LIBMPDEC_CFLAGS MODULE__CTYPES_MALLOC_CLOSURE @@ -1112,7 +1111,6 @@ with_hash_algorithm with_tzpath with_libs with_system_expat -with_system_libmpdec with_decimal_contextvar enable_loadable_sqlite_extensions with_dbmliborder @@ -1909,9 +1907,6 @@ Optional Packages: --with-libs='lib1 ...' link against additional libs (default is no) --with-system-expat build pyexpat module using an installed expat library, see Doc/library/pyexpat.rst (default is no) - --with-system-libmpdec build _decimal module using an installed mpdecimal - library, see Doc/library/decimal.rst (default is - yes) --with-decimal-contextvar build _decimal module using a coroutine-local rather than a thread-local context (default is yes) @@ -15753,26 +15748,6 @@ printf "%s\n" "#define Py_FFI_SUPPORT_C_COMPLEX 1" >>confdefs.h fi -# Check for use of the system libmpdec library -{ printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for --with-system-libmpdec" >&5 -printf %s "checking for --with-system-libmpdec... " >&6; } - -# Check whether --with-system_libmpdec was given. -if test ${with_system_libmpdec+y} -then : - withval=$with_system_libmpdec; -else case e in #( - e) with_system_libmpdec="yes" ;; -esac -fi - -{ printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $with_system_libmpdec" >&5 -printf "%s\n" "$with_system_libmpdec" >&6; } - - - -if test "x$with_system_libmpdec" = xyes -then : pkg_failed=no { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for libmpdec >= 2.5.0" >&5 @@ -15832,33 +15807,63 @@ fi # Put the nasty error message in config.log where it belongs echo "$LIBMPDEC_PKG_ERRORS" >&5 - LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""} - LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"} - LIBMPDEC_INTERNAL= -elif test $pkg_failed = untried; then - { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 -printf "%s\n" "no" >&6; } - LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""} - LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"} - LIBMPDEC_INTERNAL= -else - LIBMPDEC_CFLAGS=$pkg_cv_LIBMPDEC_CFLAGS - LIBMPDEC_LIBS=$pkg_cv_LIBMPDEC_LIBS - { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: yes" >&5 -printf "%s\n" "yes" >&6; } -fi + save_CFLAGS=$CFLAGS +save_CPPFLAGS=$CPPFLAGS +save_LDFLAGS=$LDFLAGS +save_LIBS=$LIBS + + + CPPFLAGS="$CPPFLAGS $LIBMPDEC_CFLAGS" + LIBS="$LIBS $LIBMPDEC_LIBS" + + cat confdefs.h - <<_ACEOF >conftest.$ac_ext +/* end confdefs.h. */ + + + #include + #if MPD_VERSION_HEX < 0x02050000 + # error "mpdecimal 2.5.0 or higher required" + #endif + +int +main (void) +{ +const char *x = mpd_version(); + ; + return 0; +} + +_ACEOF +if ac_fn_c_try_link "$LINENO" +then : + have_mpdec=yes else case e in #( - e) LIBMPDEC_CFLAGS="-I\$(srcdir)/Modules/_decimal/libmpdec" - LIBMPDEC_LIBS="-lm \$(LIBMPDEC_A)" - LIBMPDEC_INTERNAL="\$(LIBMPDEC_HEADERS) \$(LIBMPDEC_A)" - have_mpdec=yes - with_system_libmpdec=no ;; + e) have_mpdec=no ;; esac fi +rm -f core conftest.err conftest.$ac_objext conftest.beam \ + conftest$ac_exeext conftest.$ac_ext -if test "x$with_system_libmpdec" = xyes + if test "x$have_mpdec" = xyes then : + + LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""} + LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"} + +fi + +CFLAGS=$save_CFLAGS +CPPFLAGS=$save_CPPFLAGS +LDFLAGS=$save_LDFLAGS +LIBS=$save_LIBS + + + +elif test $pkg_failed = untried; then + { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: no" >&5 +printf "%s\n" "no" >&6; } + save_CFLAGS=$CFLAGS save_CPPFLAGS=$CPPFLAGS save_LDFLAGS=$LDFLAGS @@ -15884,6 +15889,7 @@ const char *x = mpd_version(); ; return 0; } + _ACEOF if ac_fn_c_try_link "$LINENO" then : @@ -15895,27 +15901,27 @@ fi rm -f core conftest.err conftest.$ac_objext conftest.beam \ conftest$ac_exeext conftest.$ac_ext + if test "x$have_mpdec" = xyes +then : + + LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""} + LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"} + +fi + CFLAGS=$save_CFLAGS CPPFLAGS=$save_CPPFLAGS LDFLAGS=$save_LDFLAGS LIBS=$save_LIBS -else case e in #( - e) { printf "%s\n" "$as_me:${as_lineno-$LINENO}: WARNING: the bundled copy of libmpdecimal is scheduled for removal in Python 3.15; consider using a system installed mpdecimal library." >&5 -printf "%s\n" "$as_me: WARNING: the bundled copy of libmpdecimal is scheduled for removal in Python 3.15; consider using a system installed mpdecimal library." >&2;} ;; -esac -fi -if test "$with_system_libmpdec" = "yes" && test "$have_mpdec" = "no" -then : - { printf "%s\n" "$as_me:${as_lineno-$LINENO}: WARNING: no system libmpdecimal found; falling back to bundled libmpdecimal (deprecated and scheduled for removal in Python 3.15)" >&5 -printf "%s\n" "$as_me: WARNING: no system libmpdecimal found; falling back to bundled libmpdecimal (deprecated and scheduled for removal in Python 3.15)" >&2;} - LIBMPDEC_CFLAGS="-I\$(srcdir)/Modules/_decimal/libmpdec" - LIBMPDEC_LIBS="-lm \$(LIBMPDEC_A)" - LIBMPDEC_INTERNAL="\$(LIBMPDEC_HEADERS) \$(LIBMPDEC_A)" - have_mpdec=yes - with_system_libmpdec=no +else + LIBMPDEC_CFLAGS=$pkg_cv_LIBMPDEC_CFLAGS + LIBMPDEC_LIBS=$pkg_cv_LIBMPDEC_LIBS + { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: yes" >&5 +printf "%s\n" "yes" >&6; } + have_mpdec=yes fi # Disable forced inlining in debug builds, see GH-94847 @@ -15924,6 +15930,21 @@ then : as_fn_append LIBMPDEC_CFLAGS " -DTEST_COVERAGE" fi +if test "$have_ipa_pure_const_bug" = yes; then + # Some versions of gcc miscompile inline asm: + # https://gcc.gnu.org/bugzilla/show_bug.cgi?id=46491 + # https://gcc.gnu.org/ml/gcc/2010-11/msg00366.html + as_fn_append LIBMPDEC_CFLAGS " -fno-ipa-pure-const" +fi + +if test "$have_glibc_memmove_bug" = yes; then + # _FORTIFY_SOURCE wrappers for memmove and bcopy are incorrect: + # https://sourceware.org/ml/libc-alpha/2010-12/msg00009.html + as_fn_append LIBMPDEC_CFLAGS " -U_FORTIFY_SOURCE" +fi + + + # Check whether _decimal should use a coroutine-local or thread-local context { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for --with-decimal-contextvar" >&5 printf %s "checking for --with-decimal-contextvar... " >&6; } @@ -15944,94 +15965,9 @@ then printf "%s\n" "#define WITH_DECIMAL_CONTEXTVAR 1" >>confdefs.h fi - { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $with_decimal_contextvar" >&5 printf "%s\n" "$with_decimal_contextvar" >&6; } -if test "x$with_system_libmpdec" = xno -then : - # Check for libmpdec machine flavor - { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for decimal libmpdec machine" >&5 -printf %s "checking for decimal libmpdec machine... " >&6; } - case $ac_sys_system in #( - Darwin*) : - libmpdec_system=Darwin ;; #( - SunOS*) : - libmpdec_system=sunos ;; #( - *) : - libmpdec_system=other - ;; -esac - - libmpdec_machine=unknown - if test "$libmpdec_system" = Darwin; then - # universal here means: build libmpdec with the same arch options - # the python interpreter was built with - libmpdec_machine=universal - elif test $ac_cv_sizeof_size_t -eq 8; then - if test "$ac_cv_gcc_asm_for_x64" = yes; then - libmpdec_machine=x64 - elif test "$ac_cv_type___uint128_t" = yes; then - libmpdec_machine=uint128 - else - libmpdec_machine=ansi64 - fi - elif test $ac_cv_sizeof_size_t -eq 4; then - if test "$ac_cv_gcc_asm_for_x87" = yes -a "$libmpdec_system" != sunos; then - case $ac_cv_cc_name in #( - *gcc*) : - libmpdec_machine=ppro ;; #( - *clang*) : - libmpdec_machine=ppro ;; #( - *) : - libmpdec_machine=ansi32 - ;; -esac - else - libmpdec_machine=ansi32 - fi - fi - { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $libmpdec_machine" >&5 -printf "%s\n" "$libmpdec_machine" >&6; } - - case $libmpdec_machine in #( - x64) : - as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_64=1 -DASM=1" ;; #( - uint128) : - as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_64=1 -DANSI=1 -DHAVE_UINT128_T=1" ;; #( - ansi64) : - as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_64=1 -DANSI=1" ;; #( - ppro) : - as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_32=1 -DANSI=1 -DASM=1 -Wno-unknown-pragmas" ;; #( - ansi32) : - as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_32=1 -DANSI=1" ;; #( - ansi-legacy) : - as_fn_append LIBMPDEC_CFLAGS " -DCONFIG_32=1 -DANSI=1 -DLEGACY_COMPILER=1" ;; #( - universal) : - as_fn_append LIBMPDEC_CFLAGS " -DUNIVERSAL=1" ;; #( - *) : - as_fn_error $? "_decimal: unsupported architecture" "$LINENO" 5 - ;; -esac -fi - -if test "$have_ipa_pure_const_bug" = yes; then - # Some versions of gcc miscompile inline asm: - # https://gcc.gnu.org/bugzilla/show_bug.cgi?id=46491 - # https://gcc.gnu.org/ml/gcc/2010-11/msg00366.html - as_fn_append LIBMPDEC_CFLAGS " -fno-ipa-pure-const" -fi - -if test "$have_glibc_memmove_bug" = yes; then - # _FORTIFY_SOURCE wrappers for memmove and bcopy are incorrect: - # https://sourceware.org/ml/libc-alpha/2010-12/msg00009.html - as_fn_append LIBMPDEC_CFLAGS " -U_FORTIFY_SOURCE" -fi - - - - - @@ -29935,7 +29871,6 @@ SRCDIRS="\ Modules \ Modules/_ctypes \ Modules/_decimal \ - Modules/_decimal/libmpdec \ Modules/_hacl \ Modules/_io \ Modules/_multiprocessing \ @@ -33130,6 +33065,10 @@ fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: result: $py_cv_module__curses_panel" >&5 printf "%s\n" "$py_cv_module__curses_panel" >&6; } +if test "$have_mpdec" = "no" +then + py_cv_module__decimal=n/a +fi { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking for stdlib extension module _decimal" >&5 printf %s "checking for stdlib extension module _decimal... " >&6; } diff --git a/configure.ac b/configure.ac index 70ad6da86719c6..425fb0876dc861 100644 --- a/configure.ac +++ b/configure.ac @@ -4171,36 +4171,9 @@ if test "$ac_cv_ffi_complex_double_supported" = "yes"; then [Defined if _Complex C type can be used with libffi.]) fi -# Check for use of the system libmpdec library -AC_MSG_CHECKING([for --with-system-libmpdec]) -AC_ARG_WITH( - [system_libmpdec], - [AS_HELP_STRING( - [--with-system-libmpdec], - [build _decimal module using an installed mpdecimal library, see Doc/library/decimal.rst (default is yes)] - )], - [], - [with_system_libmpdec="yes"]) -AC_MSG_RESULT([$with_system_libmpdec]) - -AC_DEFUN([USE_BUNDLED_LIBMPDEC], - [LIBMPDEC_CFLAGS="-I\$(srcdir)/Modules/_decimal/libmpdec" - LIBMPDEC_LIBS="-lm \$(LIBMPDEC_A)" - LIBMPDEC_INTERNAL="\$(LIBMPDEC_HEADERS) \$(LIBMPDEC_A)" - have_mpdec=yes - with_system_libmpdec=no]) - -AS_VAR_IF( - [with_system_libmpdec], [yes], - [PKG_CHECK_MODULES( - [LIBMPDEC], [libmpdec >= 2.5.0], [], - [LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""} - LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"} - LIBMPDEC_INTERNAL=])], - [USE_BUNDLED_LIBMPDEC()]) - -AS_VAR_IF([with_system_libmpdec], [yes], - [WITH_SAVE_ENV([ +dnl Check for libmpdec >= 2.5.0 +PKG_CHECK_MODULES([LIBMPDEC], [libmpdec >= 2.5.0], [have_mpdec=yes], [ + WITH_SAVE_ENV([ CPPFLAGS="$CPPFLAGS $LIBMPDEC_CFLAGS" LIBS="$LIBS $LIBMPDEC_LIBS" @@ -4210,25 +4183,36 @@ AS_VAR_IF([with_system_libmpdec], [yes], #if MPD_VERSION_HEX < 0x02050000 # error "mpdecimal 2.5.0 or higher required" #endif - ], [const char *x = mpd_version();])], - [have_mpdec=yes], - [have_mpdec=no]) - ])], - [AC_MSG_WARN([m4_normalize([ - the bundled copy of libmpdecimal is scheduled for removal in Python 3.15; - consider using a system installed mpdecimal library.])])]) - -AS_IF([test "$with_system_libmpdec" = "yes" && test "$have_mpdec" = "no"], - [AC_MSG_WARN([m4_normalize([ - no system libmpdecimal found; falling back to bundled libmpdecimal - (deprecated and scheduled for removal in Python 3.15)])]) - USE_BUNDLED_LIBMPDEC()]) + ], [const char *x = mpd_version();]) + ], [have_mpdec=yes], [have_mpdec=no]) + + AS_VAR_IF([have_mpdec], [yes], [ + LIBMPDEC_CFLAGS=${LIBMPDEC_CFLAGS-""} + LIBMPDEC_LIBS=${LIBMPDEC_LIBS-"-lmpdec -lm"} + ]) + ]) +]) # Disable forced inlining in debug builds, see GH-94847 AS_VAR_IF( [with_pydebug], [yes], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DTEST_COVERAGE"])]) +if test "$have_ipa_pure_const_bug" = yes; then + # Some versions of gcc miscompile inline asm: + # https://gcc.gnu.org/bugzilla/show_bug.cgi?id=46491 + # https://gcc.gnu.org/ml/gcc/2010-11/msg00366.html + AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -fno-ipa-pure-const"]) +fi + +if test "$have_glibc_memmove_bug" = yes; then + # _FORTIFY_SOURCE wrappers for memmove and bcopy are incorrect: + # https://sourceware.org/ml/libc-alpha/2010-12/msg00009.html + AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -U_FORTIFY_SOURCE"]) +fi + +AC_SUBST([LIBMPDEC_CFLAGS]) + # Check whether _decimal should use a coroutine-local or thread-local context AC_MSG_CHECKING([for --with-decimal-contextvar]) AC_ARG_WITH( @@ -4245,73 +4229,8 @@ then AC_DEFINE([WITH_DECIMAL_CONTEXTVAR], [1], [Define if you want build the _decimal module using a coroutine-local rather than a thread-local context]) fi - AC_MSG_RESULT([$with_decimal_contextvar]) -AS_VAR_IF( - [with_system_libmpdec], [no], - [# Check for libmpdec machine flavor - AC_MSG_CHECKING([for decimal libmpdec machine]) - AS_CASE([$ac_sys_system], - [Darwin*], [libmpdec_system=Darwin], - [SunOS*], [libmpdec_system=sunos], - [libmpdec_system=other] - ) - - libmpdec_machine=unknown - if test "$libmpdec_system" = Darwin; then - # universal here means: build libmpdec with the same arch options - # the python interpreter was built with - libmpdec_machine=universal - elif test $ac_cv_sizeof_size_t -eq 8; then - if test "$ac_cv_gcc_asm_for_x64" = yes; then - libmpdec_machine=x64 - elif test "$ac_cv_type___uint128_t" = yes; then - libmpdec_machine=uint128 - else - libmpdec_machine=ansi64 - fi - elif test $ac_cv_sizeof_size_t -eq 4; then - if test "$ac_cv_gcc_asm_for_x87" = yes -a "$libmpdec_system" != sunos; then - AS_CASE([$ac_cv_cc_name], - [*gcc*], [libmpdec_machine=ppro], - [*clang*], [libmpdec_machine=ppro], - [libmpdec_machine=ansi32] - ) - else - libmpdec_machine=ansi32 - fi - fi - AC_MSG_RESULT([$libmpdec_machine]) - - AS_CASE([$libmpdec_machine], - [x64], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_64=1 -DASM=1"])], - [uint128], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_64=1 -DANSI=1 -DHAVE_UINT128_T=1"])], - [ansi64], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_64=1 -DANSI=1"])], - [ppro], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_32=1 -DANSI=1 -DASM=1 -Wno-unknown-pragmas"])], - [ansi32], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_32=1 -DANSI=1"])], - [ansi-legacy], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DCONFIG_32=1 -DANSI=1 -DLEGACY_COMPILER=1"])], - [universal], [AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -DUNIVERSAL=1"])], - [AC_MSG_ERROR([_decimal: unsupported architecture])] - )]) - -if test "$have_ipa_pure_const_bug" = yes; then - # Some versions of gcc miscompile inline asm: - # https://gcc.gnu.org/bugzilla/show_bug.cgi?id=46491 - # https://gcc.gnu.org/ml/gcc/2010-11/msg00366.html - AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -fno-ipa-pure-const"]) -fi - -if test "$have_glibc_memmove_bug" = yes; then - # _FORTIFY_SOURCE wrappers for memmove and bcopy are incorrect: - # https://sourceware.org/ml/libc-alpha/2010-12/msg00009.html - AS_VAR_APPEND([LIBMPDEC_CFLAGS], [" -U_FORTIFY_SOURCE"]) -fi - -AC_SUBST([LIBMPDEC_CFLAGS]) -AC_SUBST([LIBMPDEC_INTERNAL]) - - dnl detect sqlite3 from Emscripten emport PY_CHECK_EMSCRIPTEN_PORT([LIBSQLITE3], [-sUSE_SQLITE3]) @@ -7185,7 +7104,6 @@ SRCDIRS="\ Modules \ Modules/_ctypes \ Modules/_decimal \ - Modules/_decimal/libmpdec \ Modules/_hacl \ Modules/_io \ Modules/_multiprocessing \ @@ -8125,6 +8043,10 @@ PY_STDLIB_MOD([_curses_panel], [], [test "$have_curses" = "yes" && test "$have_panel" = "yes"], [$PANEL_CFLAGS $CURSES_CFLAGS], [$PANEL_LIBS $CURSES_LIBS] ) +if test "$have_mpdec" = "no" +then + AS_VAR_SET([py_cv_module_]_decimal, [n/a]) +fi PY_STDLIB_MOD([_decimal], [], [test "$have_mpdec" = "yes"], [$LIBMPDEC_CFLAGS], [$LIBMPDEC_LIBS])