diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/rempio2/benchmark/benchmark.native.js
index d231943ea28c..3c82f68f4c5c 100644
--- a/lib/node_modules/@stdlib/math/base/special/rempio2/benchmark/benchmark.native.js
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2/benchmark/benchmark.native.js
@@ -25,12 +25,13 @@ var bench = require( '@stdlib/bench' );
var randu = require( '@stdlib/random/array/uniform' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var tryRequire = require( '@stdlib/utils/try-require' );
+var Float64Array = require( '@stdlib/array/float64' );
var pkg = require( './../package.json' ).name;
// VARIABLES //
-var rempio2 = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var rempio2 = tryRequire( resolve( __dirname, '../lib/native.js' ) );
var opts = {
'skip': ( rempio2 instanceof Error )
};
@@ -44,7 +45,7 @@ bench( pkg+'::native', opts, function benchmark( b ) {
var n;
var i;
- y = [ 0.0, 0.0 ];
+ y = new Float64Array( [ 0.0, 0.0 ] );
x = randu( 100, -100.0, 100.0 );
b.tic();
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/LICENSE b/lib/node_modules/@stdlib/math/base/special/rempio2f/LICENSE
new file mode 100644
index 000000000000..a7566ad6f2c3
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/LICENSE
@@ -0,0 +1,192 @@
+
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
+ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+ 1. Definitions.
+
+ "License" shall mean the terms and conditions for use, reproduction,
+ and distribution as defined by Sections 1 through 9 of this document.
+
+ "Licensor" shall mean the copyright owner or entity authorized by
+ the copyright owner that is granting the License.
+
+ "Legal Entity" shall mean the union of the acting entity and all
+ other entities that control, are controlled by, or are under common
+ control with that entity. For the purposes of this definition,
+ "control" means (i) the power, direct or indirect, to cause the
+ direction or management of such entity, whether by contract or
+ otherwise, or (ii) ownership of fifty percent (50%) or more of the
+ outstanding shares, or (iii) beneficial ownership of such entity.
+
+ "You" (or "Your") shall mean an individual or Legal Entity
+ exercising permissions granted by this License.
+
+ "Source" form shall mean the preferred form for making modifications,
+ including but not limited to software source code, documentation
+ source, and configuration files.
+
+ "Object" form shall mean any form resulting from mechanical
+ transformation or translation of a Source form, including but
+ not limited to compiled object code, generated documentation,
+ and conversions to other media types.
+
+ "Work" shall mean the work of authorship, whether in Source or
+ Object form, made available under the License, as indicated by a
+ copyright notice that is included in or attached to the work
+ (an example is provided in the Appendix below).
+
+ "Derivative Works" shall mean any work, whether in Source or Object
+ form, that is based on (or derived from) the Work and for which the
+ editorial revisions, annotations, elaborations, or other modifications
+ represent, as a whole, an original work of authorship. For the purposes
+ of this License, Derivative Works shall not include works that remain
+ separable from, or merely link (or bind by name) to the interfaces of,
+ the Work and Derivative Works thereof.
+
+ "Contribution" shall mean any work of authorship, including
+ the original version of the Work and any modifications or additions
+ to that Work or Derivative Works thereof, that is intentionally
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+ communication on electronic mailing lists, source code control systems,
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+ "Contributor" shall mean Licensor and any individual or Legal Entity
+ on behalf of whom a Contribution has been received by Licensor and
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+ 2. Grant of Copyright License. Subject to the terms and conditions of
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+ meet the following conditions:
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+ (a) You must give any other recipients of the Work or
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+ (b) You must cause any modified files to carry prominent notices
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+ (c) You must retain, in the Source form of any Derivative Works
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+ (d) If the Work includes a "NOTICE" text file as part of its
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+ You may add Your own copyright statement to Your modifications and
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+ for use, reproduction, or distribution of Your modifications, or
+ for any such Derivative Works as a whole, provided Your use,
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+ the conditions stated in this License.
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+ 5. Submission of Contributions. Unless You explicitly state otherwise,
+ any Contribution intentionally submitted for inclusion in the Work
+ by You to the Licensor shall be under the terms and conditions of
+ this License, without any additional terms or conditions.
+ Notwithstanding the above, nothing herein shall supersede or modify
+ the terms of any separate license agreement you may have executed
+ with Licensor regarding such Contributions.
+
+ 6. Trademarks. This License does not grant permission to use the trade
+ names, trademarks, service marks, or product names of the Licensor,
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+
+ 7. Disclaimer of Warranty. Unless required by applicable law or
+ agreed to in writing, Licensor provides the Work (and each
+ Contributor provides its Contributions) on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
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+ of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+ PARTICULAR PURPOSE. You are solely responsible for determining the
+ appropriateness of using or redistributing the Work and assume any
+ risks associated with Your exercise of permissions under this License.
+
+ 8. Limitation of Liability. In no event and under no legal theory,
+ whether in tort (including negligence), contract, or otherwise,
+ unless required by applicable law (such as deliberate and grossly
+ negligent acts) or agreed to in writing, shall any Contributor be
+ liable to You for damages, including any direct, indirect, special,
+ incidental, or consequential damages of any character arising as a
+ result of this License or out of the use or inability to use the
+ Work (including but not limited to damages for loss of goodwill,
+ work stoppage, computer failure or malfunction, or any and all
+ other commercial damages or losses), even if such Contributor
+ has been advised of the possibility of such damages.
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+ 9. Accepting Warranty or Additional Liability. While redistributing
+ the Work or Derivative Works thereof, You may choose to offer,
+ and charge a fee for, acceptance of support, warranty, indemnity,
+ or other liability obligations and/or rights consistent with this
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+ on Your own behalf and on Your sole responsibility, not on behalf
+ of any other Contributor, and only if You agree to indemnify,
+ defend, and hold each Contributor harmless for any liability
+ incurred by, or claims asserted against, such Contributor by reason
+ of your accepting any such warranty or additional liability.
+
+ END OF TERMS AND CONDITIONS
+
+DEPENDENCIES & ATTRIBUTION
+
+The library links against the following external libraries or contains
+implementations from the following external libraries, which have their own
+licenses:
+
+* FreeBSD
+
+Copyright (C) 1993-2004 by Sun Microsystems, Inc. All rights reserved.
+
+Developed at SunPro, a Sun Microsystems, Inc. business.
+Permission to use, copy, modify, and distribute this
+software is freely granted, provided that this notice
+is preserved.
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/README.md b/lib/node_modules/@stdlib/math/base/special/rempio2f/README.md
new file mode 100644
index 000000000000..a823c6fe2b4a
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/README.md
@@ -0,0 +1,219 @@
+
+
+# rempio2f
+
+> Compute `x - nπ/2 = r` using single precision.
+
+
+
+## Usage
+
+```javascript
+var rempio2f = require( '@stdlib/math/base/special/rempio2f' );
+```
+
+#### rempio2f( x, y )
+
+Computes `x - nπ/2 = r` using single-precision arithmetic.
+
+```javascript
+var y = [ 0.0 ];
+var n = rempio2f( 128.0, y );
+// returns 81
+
+var y0 = y[ 0 ];
+// returns ~0.765
+```
+
+When `x` is `NaN` or infinite, the function returns `0` and sets the element of `y` to `NaN`.
+
+```javascript
+var y = [ 0.0 ];
+var n = rempio2f( NaN, y );
+// returns 0
+
+var y0 = y[ 0 ];
+// returns NaN
+
+y = [ 0.0 ];
+n = rempio2f( Infinity, y );
+// returns 0
+
+y0 = y[ 0 ];
+// returns NaN
+```
+
+
+
+
+
+
+
+
+
+## Notes
+
+- The function returns `n` and stores the remainder `r` as a single number in `y[0]`.
+- For input values larger than `2^8*π/2` in magnitude, the function **only** returns the last three binary digits of `n` and not the full result.
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var linspace = require( '@stdlib/array/base/linspace' );
+var rempio2f = require( '@stdlib/math/base/special/rempio2f' );
+
+var x = linspace( 0.0, 100.0, 100 );
+var y = [ 0.0 ];
+var n;
+var i;
+
+for ( i = 0; i < x.length; i++ ) {
+ n = rempio2f( x[ i ], y );
+ console.log( '%d - %dπ/2 = %d', x[ i ], n, y[ 0 ] );
+}
+```
+
+
+
+
+
+
+
+* * *
+
+
+
+## C APIs
+
+
+
+
+
+
+
+
+
+
+
+
+### Usage
+
+```c
+#include "stdlib/math/base/special/rempio2f.h"
+```
+
+#### stdlib_base_rempio2f( x, &rem1 )
+
+Computes `x - nπ/2 = r` using single-precision arithmetic.
+
+```c
+#include
+
+float rem;
+
+int32_t n = stdlib_base_rempio2f( 4.0f, &rem );
+```
+
+The function accepts the following arguments:
+
+- **x**: `[in] float` input value.
+- **rem**: `[out] float*` destination for remainder number.
+
+```c
+int32_t stdlib_base_rempio2f( const float x, float *rem );
+```
+
+
+
+
+
+
+
+
+
+
+### Notes
+
+- The function returns `n` and stores the remainder `r` in `rem`.
+
+
+
+
+
+
+
+
+
+
+### Examples
+
+```c
+#include "stdlib/math/base/special/rempio2f.h"
+#include
+#include
+#include
+
+int main( void ) {
+ const float x[] = { 0.0f, 1.0f, 4.0f, 128.0f };
+
+ float rem;
+ int32_t n;
+ int i;
+ for ( i = 0; i < 4; i++ ) {
+ n = stdlib_base_rempio2f( x[ i ], &rem );
+ printf( "%f - %"PRId32"π/2 = %f\n", x[ i ], n, rem );
+ }
+}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/benchmark.js
new file mode 100644
index 000000000000..d76d937eb21e
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/benchmark.js
@@ -0,0 +1,54 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var rempio2f = require( './../lib' );
+
+
+// MAIN //
+
+bench(pkg, function benchmark(b) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ y = [0.0]; // Single-element array for single-precision remainder
+ x = randu(100, -100.0, 100.0);
+
+ b.tic();
+ for (i = 0; i < b.iterations; i++) {
+ n = rempio2f(x[i % x.length], y);
+ if (isnan(n)) {
+ b.fail('should not return NaN');
+ }
+ }
+ b.toc();
+ if (isnan(n) || isnan(y[0])) {
+ b.fail('should not return NaN');
+ }
+ b.pass('benchmark finished');
+ b.end();
+});
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/benchmark.native.js
new file mode 100644
index 000000000000..5c966f90cdb2
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/benchmark.native.js
@@ -0,0 +1,64 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var Float32Array = require( '@stdlib/array/float32' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var rempio2f = tryRequire( resolve( __dirname, '../lib/native.js' ) );
+var opts = {
+ 'skip': ( rempio2f instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ y = new Float32Array( 1 );
+ x = randu( 100, -100.0, 100.0 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ n = rempio2f( x[ i % x.length ], y );
+ if ( isnan( n ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( n ) || isnan( y[0] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/c/native/Makefile
new file mode 100644
index 000000000000..a4bd7b38fd74
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/c/native/Makefile
@@ -0,0 +1,146 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2025 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := benchmark.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled benchmarks.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/c/native/benchmark.c
new file mode 100644
index 000000000000..e0fca492d5cf
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/benchmark/c/native/benchmark.c
@@ -0,0 +1,138 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+#include "stdlib/math/base/special/rempio2f.h"
+#include "stdlib/math/base/assert/is_nanf.h"
+#include
+#include
+#include
+#include
+#include
+
+#define NAME "rempio2f"
+#define ITERATIONS 1000000
+#define REPEATS 3
+
+/**
+* Prints the TAP version.
+*/
+static void print_version( void ) {
+ printf( "TAP version 13\n" );
+}
+
+/**
+* Prints the TAP summary.
+*
+* @param total total number of tests
+* @param passing total number of passing tests
+*/
+static void print_summary( int total, int passing ) {
+ printf( "#\n" );
+ printf( "1..%d\n", total ); // TAP plan
+ printf( "# total %d\n", total );
+ printf( "# pass %d\n", passing );
+ printf( "#\n" );
+ printf( "# ok\n" );
+}
+
+/**
+* Prints benchmarks results.
+*
+* @param elapsed elapsed time in seconds
+*/
+static void print_results( double elapsed ) {
+ double rate = (double)ITERATIONS / elapsed;
+ printf( " ---\n" );
+ printf( " iterations: %d\n", ITERATIONS );
+ printf( " elapsed: %0.9f\n", elapsed );
+ printf( " rate: %0.9f\n", rate );
+ printf( " ...\n" );
+}
+
+/**
+* Returns a clock time.
+*
+* @return clock time
+*/
+static double tic( void ) {
+ struct timeval now;
+ gettimeofday( &now, NULL );
+ return (double)now.tv_sec + (double)now.tv_usec/1.0e6;
+}
+
+/**
+* Generates a random number on the interval [0,1).
+*
+* @return random number
+*/
+static double rand_double( void ) {
+ int r = rand();
+ return (double)r / ( (double)RAND_MAX + 1.0 );
+}
+
+/**
+* Runs a benchmark.
+*
+* @return elapsed time in seconds
+*/
+static double benchmark( void ) {
+ float x[ 100 ];
+ double elapsed;
+ float rem;
+ double t;
+ int i;
+
+ for ( i = 0; i < 100; i++ ) {
+ x[ i ] = (float)(( rand_double() * 200.0 ) - 100.0 );
+ }
+
+ t = tic();
+ for ( i = 0; i < ITERATIONS; i++ ) {
+ stdlib_base_rempio2f( x[ i % 100 ], &rem );
+ if ( isnanf( rem ) ) {
+ printf( "should not return NaN\n" );
+ break;
+ }
+ }
+ elapsed = tic() - t;
+ if ( isnanf( rem ) ) {
+ printf( "should not return NaN\n" );
+ }
+ return elapsed;
+}
+
+/**
+* Main execution sequence.
+*/
+int main( void ) {
+
+ int i;
+ double elapsed;
+
+ // Use the current time to seed the random number generator:
+ srand( time( NULL ) );
+
+ print_version();
+ for ( i = 0; i < REPEATS; i++ ) {
+ printf( "# c::native::%s\n", NAME );
+ elapsed = benchmark();
+ print_results( elapsed );
+ printf( "ok %d benchmark finished\n", i+1 );
+ }
+ print_summary( REPEATS, REPEATS );
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/binding.gyp b/lib/node_modules/@stdlib/math/base/special/rempio2f/binding.gyp
new file mode 100644
index 000000000000..68a1ca11d160
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/binding.gyp
@@ -0,0 +1,170 @@
+# @license Apache-2.0
+#
+# Copyright (c) 2025 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# A `.gyp` file for building a Node.js native add-on.
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+ # List of files to include in this file:
+ 'includes': [
+ './include.gypi',
+ ],
+
+ # Define variables to be used throughout the configuration for all targets:
+ 'variables': {
+ # Target name should match the add-on export name:
+ 'addon_target_name%': 'addon',
+
+ # Set variables based on the host OS:
+ 'conditions': [
+ [
+ 'OS=="win"',
+ {
+ # Define the object file suffix:
+ 'obj': 'obj',
+ },
+ {
+ # Define the object file suffix:
+ 'obj': 'o',
+ }
+ ], # end condition (OS=="win")
+ ], # end conditions
+ }, # end variables
+
+ # Define compile targets:
+ 'targets': [
+
+ # Target to generate an add-on:
+ {
+ # The target name should match the add-on export name:
+ 'target_name': '<(addon_target_name)',
+
+ # Define dependencies:
+ 'dependencies': [],
+
+ # Define directories which contain relevant include headers:
+ 'include_dirs': [
+ # Local include directory:
+ '<@(include_dirs)',
+ ],
+
+ # List of source files:
+ 'sources': [
+ '<@(src_files)',
+ ],
+
+ # Settings which should be applied when a target's object files are used as linker input:
+ 'link_settings': {
+ # Define libraries:
+ 'libraries': [
+ '<@(libraries)',
+ ],
+
+ # Define library directories:
+ 'library_dirs': [
+ '<@(library_dirs)',
+ ],
+ },
+
+ # C/C++ compiler flags:
+ 'cflags': [
+ # Enable commonly used warning options:
+ '-Wall',
+
+ # Aggressive optimization:
+ '-O3',
+ ],
+
+ # C specific compiler flags:
+ 'cflags_c': [
+ # Specify the C standard to which a program is expected to conform:
+ '-std=c99',
+ ],
+
+ # C++ specific compiler flags:
+ 'cflags_cpp': [
+ # Specify the C++ standard to which a program is expected to conform:
+ '-std=c++11',
+ ],
+
+ # Linker flags:
+ 'ldflags': [],
+
+ # Apply conditions based on the host OS:
+ 'conditions': [
+ [
+ 'OS=="mac"',
+ {
+ # Linker flags:
+ 'ldflags': [
+ '-undefined dynamic_lookup',
+ '-Wl,-no-pie',
+ '-Wl,-search_paths_first',
+ ],
+ },
+ ], # end condition (OS=="mac")
+ [
+ 'OS!="win"',
+ {
+ # C/C++ flags:
+ 'cflags': [
+ # Generate platform-independent code:
+ '-fPIC',
+ ],
+ },
+ ], # end condition (OS!="win")
+ ], # end conditions
+ }, # end target <(addon_target_name)
+
+ # Target to copy a generated add-on to a standard location:
+ {
+ 'target_name': 'copy_addon',
+
+ # Declare that the output of this target is not linked:
+ 'type': 'none',
+
+ # Define dependencies:
+ 'dependencies': [
+ # Require that the add-on be generated before building this target:
+ '<(addon_target_name)',
+ ],
+
+ # Define a list of actions:
+ 'actions': [
+ {
+ 'action_name': 'copy_addon',
+ 'message': 'Copying addon...',
+
+ # Explicitly list the inputs in the command-line invocation below:
+ 'inputs': [],
+
+ # Declare the expected outputs:
+ 'outputs': [
+ '<(addon_output_dir)/<(addon_target_name).node',
+ ],
+
+ # Define the command-line invocation:
+ 'action': [
+ 'cp',
+ '<(PRODUCT_DIR)/<(addon_target_name).node',
+ '<(addon_output_dir)/<(addon_target_name).node',
+ ],
+ },
+ ], # end actions
+ }, # end target copy_addon
+ ], # end targets
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/rempio2f/docs/repl.txt
new file mode 100644
index 000000000000..f134a97ccaec
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/docs/repl.txt
@@ -0,0 +1,32 @@
+{{alias}}( x, y )
+ Computes `x - nπ/2 = r`.
+
+ The function returns `n` and stores the remainder `r` as a single number
+ in `y[0]`.
+
+ For input values larger than `2^20 * π/2` in magnitude, the function only
+ returns the last three binary digits of `n` and not the full result.
+
+ Parameters
+ ----------
+ x: number
+ Input value.
+
+ y: Array|TypedArray|Object
+ Remainder element (single value).
+
+ Returns
+ -------
+ n: integer
+ Factor of `π/2`.
+
+ Examples
+ --------
+ > var y = [ 0.0 ];
+ > var n = {{alias}}( 128.0, y )
+ 81
+ > var y1 = y[ 0 ]
+ ~0.765
+
+ See Also
+ --------
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/rempio2f/docs/types/index.d.ts
new file mode 100644
index 000000000000..35c2b845b0c4
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/docs/types/index.d.ts
@@ -0,0 +1,58 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+// TypeScript Version: 4.1
+
+///
+
+import { Collection } from '@stdlib/types/array';
+
+/**
+* Computes `x - nπ/2 = r`.
+*
+* ## Notes
+*
+* - The function returns `n` and stores the remainder `r` as a single number in `y[0]`.
+* - For input values larger than `2^20 * π/2` in magnitude, the function only returns the last three binary digits of `n` and not the full result.
+*
+* @param x - input value
+* @param y - remainder element (single value)
+* @returns factor of `π/2`
+*
+* @example
+* var y = [ 0.0 ];
+* var n = rempio2f( 128.0, y );
+* // returns 81
+*
+* var y1 = y[ 0 ];
+* // returns ~0.765
+*
+* @example
+* var y = [ 0.0 ];
+* var n = rempio2f( NaN, y );
+* // returns 0
+*
+* var y1 = y[ 0 ];
+* // returns NaN
+*/
+declare function rempio2f( x: number, y: Collection ): number;
+
+
+// EXPORTS //
+
+export = rempio2f;
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/rempio2f/docs/types/test.ts
new file mode 100644
index 000000000000..a69b1b3bfded
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/docs/types/test.ts
@@ -0,0 +1,56 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+///
+
+import { Collection } from '@stdlib/types/array';
+import rempio2f = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+ const y: Collection = [ 0.0 ];
+ rempio2f( 128, y ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a value other than a number as its first argument...
+{
+ const y: Collection = [ 0.0 ];
+ rempio2f( true, y ); // $ExpectError
+ rempio2f( false, y ); // $ExpectError
+ rempio2f( '5', y ); // $ExpectError
+ rempio2f( [], y ); // $ExpectError
+ rempio2f( {}, y ); // $ExpectError
+ rempio2f( ( x: number ): number => x, y ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a value other than a collection as its second argument...
+{
+ rempio2f( 128, true ); // $ExpectError
+ rempio2f( 128, false ); // $ExpectError
+ rempio2f( 128, 3 ); // $ExpectError
+ rempio2f( 128, {} ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided insufficient arguments...
+{
+ rempio2f(); // $ExpectError
+ rempio2f( 3 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/rempio2f/examples/c/Makefile
new file mode 100644
index 000000000000..25ced822f96a
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/examples/c/Makefile
@@ -0,0 +1,146 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2025 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+ CC := $(C_COMPILER)
+else
+ CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+ -std=c99 \
+ -O3 \
+ -Wall \
+ -pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+ fPIC ?=
+else
+ fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := example.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+ $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled examples.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+ $(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+ $(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/rempio2f/examples/c/example.c
new file mode 100644
index 000000000000..fbdb82d96da2
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/examples/c/example.c
@@ -0,0 +1,37 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+#include "stdlib/math/base/special/rempio2f.h"
+#include
+#include
+#include
+
+int main(void) {
+ const float x[] = { 0.0f, 1.0f, 4.0f, 128.0f }; // Single-precision floats
+
+ float rem; // Single remainder value
+ int32_t n;
+ int i;
+
+ for (i = 0; i < 4; i++) {
+ n = stdlib_base_rempio2f(x[i], &rem); // Single remainder output
+ printf("%f - %"PRId32"π/2 = %f\n", x[i], n, rem);
+ }
+
+ return 0;
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/examples/index.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/examples/index.js
new file mode 100644
index 000000000000..fa6617db7d19
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/examples/index.js
@@ -0,0 +1,37 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var linspace = require( '@stdlib/array/base/linspace' );
+var rempio2f = require( './../lib' );
+
+
+// MAIN //
+
+var x = linspace(0.0, 100.0, 100);
+var y = [0.0]; // Single-element array for the remainder
+var n;
+var i;
+
+for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+ console.log('%d - %dπ/2 = %d', x[i], n, y[0]);
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/include.gypi b/lib/node_modules/@stdlib/math/base/special/rempio2f/include.gypi
new file mode 100644
index 000000000000..ecfaf82a3279
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/include.gypi
@@ -0,0 +1,53 @@
+# @license Apache-2.0
+#
+# Copyright (c) 2025 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# A GYP include file for building a Node.js native add-on.
+#
+# Main documentation:
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+ # Define variables to be used throughout the configuration for all targets:
+ 'variables': {
+ # Source directory:
+ 'src_dir': './src',
+
+ # Include directories:
+ 'include_dirs': [
+ '
+
+/*
+* If C++, prevent name mangling so that the compiler emits a binary file having undecorated names, thus mirroring the behavior of a C compiler.
+*/
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+* Computes `x - nπ/2 = r` using single precision.
+*/
+int32_t stdlib_base_rempio2f( const float x, float *rem );
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif // !STDLIB_MATH_BASE_SPECIAL_REMPIO2F_H
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/index.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/index.js
new file mode 100644
index 000000000000..3a0c8fcda5dd
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/index.js
@@ -0,0 +1,44 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+/**
+* Compute `x - nπ/2 = r` using single precision.
+*
+* @module @stdlib/math/base/special/rempio2f
+*
+* @example
+* var rempio2f = require( '@stdlib/math/base/special/rempio2f' );
+*
+* var y = [ 0.0 ];
+* var n = rempio2f( 128.0, y );
+* // returns 81
+*
+* var y1 = y[ 0 ];
+* // returns ~0.765
+*/
+
+// MODULES //
+
+var rempio2f = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = rempio2f;
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/kernel_rempio2f.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/kernel_rempio2f.js
new file mode 100644
index 000000000000..766a8349d8bc
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/kernel_rempio2f.js
@@ -0,0 +1,241 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*
+* ## Notice
+*
+* The following copyright and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/k_rem_pio2.c}. The implementation follows the original, but has been modified for JavaScript.
+*
+* ```text
+* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+*
+* Developed at SunPro, a Sun Microsystems, Inc. business.
+* Permission to use, copy, modify, and distribute this
+* software is freely granted, provided that this notice
+* is preserved.
+* ```
+*/
+
+'use strict';
+
+// MODULES //
+
+var floorf = require( '@stdlib/math/base/special/floorf' );
+var ldexpf = require( '@stdlib/math/base/special/ldexpf' );
+var zeros = require( '@stdlib/array/base/zeros' );
+
+
+// VARIABLES //
+
+// Table of constants for 2/π (first few terms for single precision):
+var IPIO2 = [
+ 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, 0xD8B3D3, 0x4A9D0D
+];
+
+// π/2 for single precision (24-bit precision):
+var PIO2 = [
+ 1.570796251, // 0x3fc90fda
+ 4.960468e-8, // 0x33522168
+ 2.5893025e-8, // 0x32d849ba
+ 1.9539925e-11 // 0x2f2e71d2
+];
+var TWO24 = 1.6777216e7; // 0x4b800000
+var TWON24 = 5.9604645e-8; // 0x33800000
+
+// Temporary arrays (smaller for single precision):
+var F = zeros( 10 );
+var Q = zeros( 10 );
+var FQ = zeros( 10 );
+var IQ = zeros( 10 );
+
+
+// FUNCTIONS //
+
+/**
+* Performs the computation for `kernelRempio2f()`.
+*
+* @private
+* @param {Array} x - input value array
+* @param {(Array|TypedArray|Object)} y - output array for single remainder
+* @param {integer} jz - number of terms of `ipio2[]` used
+* @param {Array} q - array with integral values, representing the 24-bit chunks of the product of `x` and `2/π`
+* @param {integer} q0 - the corresponding exponent of `q[0]` (exponent for `q[i]` is `q0-24*i`)
+* @param {integer} jk - `jk+1` is the initial number of terms of `IPIO2[]` needed
+* @param {integer} jv - index for pointing to the suitable `ipio2[]`
+* @param {integer} jx - `nx - 1`
+* @param {Array} f - `IPIO2[]` in floating point
+* @returns {number} last three binary digits of `N`
+*/
+function compute( x, y, jz, q, q0, jk, jv, jx, f ) {
+ var fw;
+ var ih;
+ var jp;
+ var i;
+ var k;
+ var n;
+ var j;
+ var z;
+
+ // `jp+1` is the number of terms in `PIO2[]` needed:
+ jp = jk;
+
+ // Distill `q[]` into `IQ[]` in reverse order...
+ z = q[jz];
+ j = jz;
+ for ( i = 0; j > 0; i++ ) {
+ fw = (TWON24 * z)|0;
+ IQ[i] = (z - (TWO24 * fw))|0;
+ z = q[j - 1] + fw;
+ j -= 1;
+ }
+
+ // Compute `n`...
+ z = ldexpf( z, q0 );
+ z -= 8.0 * floorf( z * 0.125 ); // Trim off integer >= 8
+ n = z|0;
+ z -= n;
+ ih = (z >= 0.5) ? 2 : 0;
+
+ // Case: z > 0.5
+ if ( ih > 0 ) {
+ n += 1;
+ z = 1.0 - z; // No carry needed for single precision
+ }
+
+ // Check if re-computation is needed...
+ if ( z === 0.0 ) {
+ j = 0;
+ for ( i = jz - 1; i >= jk; i-- ) {
+ j |= IQ[i];
+ }
+ if ( j === 0 ) {
+ // Need re-computation...
+ for ( k = 1; IQ[jk - k] === 0; k++ ) {
+ // `k` is the number of terms needed...
+ }
+ for ( i = jz + 1; i <= jz + k; i++ ) {
+ f[jx + i] = IPIO2[jv + i];
+ fw = 0.0;
+ for ( j = 0; j <= jx; j++ ) {
+ fw += x[j] * f[jx + (i - j)];
+ }
+ q[i] = fw;
+ }
+ jz += k;
+ return compute( x, y, jz, q, q0, jk, jv, jx, f );
+ }
+ // Chop off zero terms...
+ jz -= 1;
+ q0 -= 24;
+ while ( IQ[jz] === 0 && jz >= 0 ) {
+ jz -= 1;
+ q0 -= 24;
+ }
+ } else {
+ // Break `z` into 24-bit chunks if necessary...
+ z = ldexpf( z, -q0 );
+ if ( z >= TWO24 ) {
+ fw = (TWON24 * z)|0;
+ IQ[jz] = (z - (TWO24 * fw))|0;
+ jz += 1;
+ q0 += 24;
+ IQ[jz] = fw;
+ } else {
+ IQ[jz] = z|0;
+ }
+ }
+
+ // Convert integer chunks to floating-point...
+ fw = ldexpf( 1.0, q0 );
+ for ( i = jz; i >= 0; i-- ) {
+ q[i] = fw * IQ[i];
+ fw *= TWON24;
+ }
+
+ // Compute `PIO2[0,...,jp] * q[jz,...,0]`...
+ for ( i = jz; i >= 0; i-- ) {
+ fw = 0.0;
+ for ( k = 0; k <= jp && k <= jz - i; k++ ) {
+ fw += PIO2[k] * q[i + k];
+ }
+ FQ[jz - i] = fw;
+ }
+
+ // Compress `FQ[]` into `y[]` (single value for single precision)...
+ fw = 0.0;
+ for ( i = jz; i >= 0; i-- ) {
+ fw += FQ[i];
+ }
+ y[0] = (ih === 0) ? fw : -fw;
+ return (n & 7);
+}
+
+/**
+* Returns the last three binary digits of `N` with `y = x - Nπ/2` so that `|y| < π/2` using single precision.
+*
+* @private
+* @param {Array} x - input value array
+* @param {(Array|TypedArray|Object)} y - remainder array (single value)
+* @param {PositiveInteger} e0 - the exponent of `x[0]` (must be <= 127)
+* @param {PositiveInteger} nx - dimension of `x[]`
+* @returns {number} last three binary digits of `N`
+*/
+function kernelRempio2f( x, y, e0, nx ) {
+ var fw;
+ var jk;
+ var jv;
+ var jx;
+ var jz;
+ var q0;
+ var i;
+ var j;
+ var m;
+
+ // Initialize `jk` for single-precision:
+ jk = 3;
+
+ // Determine `jx`, `jv`, `q0`:
+ jx = nx - 1;
+ jv = ((e0 - 3) / 24)|0;
+ if ( jv < 0 ) {
+ jv = 0;
+ }
+ q0 = e0 - (24 * (jv + 1));
+
+ // Set up `F[0]` to `F[jx+jk]`:
+ j = jv - jx;
+ m = jx + jk;
+ for ( i = 0; i <= m; i++ ) {
+ F[i] = (j < 0) ? 0.0 : IPIO2[j];
+ j += 1;
+ }
+
+ // Compute `Q[0],Q[1],...,Q[jk]`:
+ for ( i = 0; i <= jk; i++ ) {
+ fw = 0.0;
+ for ( j = 0; j <= jx; j++ ) {
+ fw += x[j] * F[jx + (i - j)];
+ }
+ Q[i] = fw;
+ }
+ jz = jk;
+ return compute( x, y, jz, Q, q0, jk, jv, jx, F );
+}
+
+
+// EXPORTS //
+
+module.exports = kernelRempio2f;
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/main.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/main.js
new file mode 100644
index 000000000000..67b37f4e7e70
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/main.js
@@ -0,0 +1,214 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*
+* ## Notice
+*
+* Adapted from the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/e_rem_pio2.c}.
+*
+* ```text
+* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+*
+* Developed at SunPro, a Sun Microsystems, Inc. business.
+* Permission to use, copy, modify, and distribute this
+* software is freely granted, provided that this notice
+* is preserved.
+*
+* Optimized by Bruce D. Evans.
+* ```
+*/
+
+'use strict';
+
+// MODULES //
+
+var ABS_MASK = require( '@stdlib/constants/float32/abs-mask' ); // 0x7fffffff
+var EXPONENT_MASK = require( '@stdlib/constants/float32/exponent-mask' ); // 0x7f800000
+var SIGNIFICAND_MASK = require( '@stdlib/constants/float32/significand-mask' ); // 0x007fffff
+var getWord = require( '@stdlib/number/float32/base/to-word' ); // Single word for 32-bit float
+var fromWord = require( '@stdlib/number/float32/base/from-word' );
+var rempio2fKernel = require( './kernel_rempio2f.js' ); // Adjusted kernel for float
+var rempio2fMedium = require( './rempio2f_medium.js' ); // Adjusted medium range function
+
+
+// VARIABLES //
+
+var ZERO = 0.0; // 0x00000000
+var TWO8 = 256.0; // 0x43800000 (2^8 for 32-bit scaling)
+
+// 24 bits of π/2 (single precision):
+var PIO2_1 = 1.57079632679; // 0x3fc90fdb
+
+// PIO2_1T = π/2 - PIO2_1 (less precision):
+var PIO2_1T = 4.960468e-8; // 0x33a22169
+var TWO_PIO2_1T = 2.0 * PIO2_1T;
+var THREE_PIO2_1T = 3.0 * PIO2_1T;
+var FOUR_PIO2_1T = 4.0 * PIO2_1T;
+
+// High word significand for π and π/2: 0x490fdb => 0010010010000111111011011
+var PI_HIGH_WORD_SIGNIFICAND = 0x490fdb|0;
+
+// High word constants (32-bit float representation):
+var PIO4_HIGH_WORD = 0x3f490fdb|0; // π/4: 0.785398163
+var THREE_PIO4_HIGH_WORD = 0x4016cbe4|0; // 3π/4: 2.35619449
+var FIVE_PIO4_HIGH_WORD = 0x405497ce|0; // 5π/4: 3.926990817
+var THREE_PIO2_HIGH_WORD = 0x4096cbe4|0; // 3π/2: 4.71238898
+var SEVEN_PIO4_HIGH_WORD = 0x40b78909|0; // 7π/4: 5.497787144
+var TWO_PI_HIGH_WORD = 0x40c90fdb|0; // 2π: 6.283185307
+var NINE_PIO4_HIGH_WORD = 0x40fb53d1|0; // 9π/4: 7.068583471
+
+// Medium threshold: 2^8 * π/2 ≈ 402.123859659
+var MEDIUM = 0x43c90fdb|0;
+
+// Temporary arrays (smaller for single precision):
+var TX = [ 0.0, 0.0 ];
+var TY = [ 0.0 ];
+
+
+// MAIN //
+
+/**
+* Computes `x - nπ/2 = r` for single-precision floating-point values.
+*
+* ## Notes
+*
+* - Returns `n` and stores the remainder `r` in `y[0]`.
+*
+* @param {number} x - input value (single precision)
+* @param {(Array|TypedArray|Object)} y - remainder element
+* @returns {integer} factor of `π/2`
+*
+* @example
+* var y = [ 0.0 ];
+* var n = rempio2f( 128.0, y );
+* // returns ~81
+*
+* var y0 = y[ 0 ];
+* // returns ~0.765
+*
+* @example
+* var y = [ 0.0 ];
+* var n = rempio2f( NaN, y );
+* // returns 0
+*
+* var y0 = y[ 0 ];
+* // returns NaN
+*/
+function rempio2f( x, y ) {
+ var e0;
+ var ix;
+ var nx;
+ var w;
+ var i;
+ var n;
+ var z;
+
+ w = getWord( x );
+ ix = (w & ABS_MASK)|0;
+
+ // Case: |x| ~<= π/4
+ if ( ix <= PIO4_HIGH_WORD ) {
+ y[ 0 ] = x;
+ return 0;
+ }
+ // Case: |x| ~<= 5π/4
+ if ( ix <= FIVE_PIO4_HIGH_WORD ) {
+ // Case: |x| ~= π/2 or π
+ if ( (ix & SIGNIFICAND_MASK) === PI_HIGH_WORD_SIGNIFICAND ) {
+ return rempio2fMedium( x, ix, y );
+ }
+ // Case: |x| ~<= 3π/4
+ if ( ix <= THREE_PIO4_HIGH_WORD ) {
+ if ( x > 0.0 ) {
+ z = x - PIO2_1;
+ y[ 0 ] = z - PIO2_1T;
+ return 1;
+ }
+ z = x + PIO2_1;
+ y[ 0 ] = z + PIO2_1T;
+ return -1;
+ }
+ if ( x > 0.0 ) {
+ z = x - ( 2.0 * PIO2_1 );
+ y[ 0 ] = z - TWO_PIO2_1T;
+ return 2;
+ }
+ z = x + ( 2.0 * PIO2_1 );
+ y[ 0 ] = z + TWO_PIO2_1T;
+ return -2;
+ }
+ // Case: |x| ~<= 9π/4
+ if ( ix <= NINE_PIO4_HIGH_WORD ) {
+ // Case: |x| ~<= 7π/4
+ if ( ix <= SEVEN_PIO4_HIGH_WORD ) {
+ if ( ix === THREE_PIO2_HIGH_WORD ) {
+ return rempio2fMedium( x, ix, y );
+ }
+ if ( x > 0.0 ) {
+ z = x - ( 3.0 * PIO2_1 );
+ y[ 0 ] = z - THREE_PIO2_1T;
+ return 3;
+ }
+ z = x + ( 3.0 * PIO2_1 );
+ y[ 0 ] = z + THREE_PIO2_1T;
+ return -3;
+ }
+ if ( ix === TWO_PI_HIGH_WORD ) {
+ return rempio2fMedium( x, ix, y );
+ }
+ if ( x > 0.0 ) {
+ z = x - ( 4.0 * PIO2_1 );
+ y[ 0 ] = z - FOUR_PIO2_1T;
+ return 4;
+ }
+ z = x + ( 4.0 * PIO2_1 );
+ y[ 0 ] = z + FOUR_PIO2_1T;
+ return -4;
+ }
+ // Case: |x| ~< 2^8 * π/2 (medium size)
+ if ( ix < MEDIUM ) {
+ return rempio2fMedium( x, ix, y );
+ }
+ // console.log("Inside kernel for x", x);
+ // Case: x is NaN or infinity
+ if ( ix >= EXPONENT_MASK ) {
+ y[ 0 ] = NaN;
+ return 0;
+ }
+ // Set z = scalbn(|x|, ilogb(x) - 7) for 8-bit chunks...
+ e0 = (ix >> 23) - 134; // ilogb(x) - 7 (127 bias + 7 for 24-bit significand shift)
+ z = fromWord( ix - ((e0 << 23)|0) );
+ for ( i = 0; i < 2; i++ ) {
+ TX[ i ] = z|0;
+ z = (z - TX[i]) * TWO8;
+ }
+ nx = 2;
+ while ( TX[ nx-1 ] === ZERO ) {
+ nx -= 1;
+ }
+ n = rempio2fKernel( TX, TY, e0, nx );
+ if ( x < 0.0 ) {
+ y[ 0 ] = -TY[ 0 ];
+ return -n;
+ }
+ y[ 0 ] = TY[ 0 ];
+ return n;
+}
+
+
+// EXPORTS //
+
+module.exports = rempio2f;
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/native.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/native.js
new file mode 100644
index 000000000000..d8830145a384
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/native.js
@@ -0,0 +1,53 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var addon = require( './../src/addon.node' );
+
+
+// MAIN //
+
+/**
+* Computes `x - nπ/2 = r` using single precision.
+*
+* @private
+* @param {number} x - input value
+* @param {Float32Array} y - remainder elements
+* @returns {integer} factor of `π/2`
+*
+* @example
+* var Float32Array = require( '@stdlib/array/float32' );
+*
+* var y = new Float32Array(1);
+* var n = rempio2f( 128.0, y );
+* // returns 81
+*
+* var y1 = y[ 0 ];
+* // returns ~0.765
+*/
+function rempio2f( x, y ) {
+ return addon( x, y );
+}
+
+
+// EXPORTS //
+
+module.exports = rempio2f;
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/rempio2f_medium.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/rempio2f_medium.js
new file mode 100644
index 000000000000..056899512a5c
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/lib/rempio2f_medium.js
@@ -0,0 +1,99 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*
+* ## Notice
+*
+* The following copyright and license were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/k_rem_pio2.c}. The implementation follows the original, but has been modified for JavaScript.
+*
+* ```text
+* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+*
+* Developed at SunPro, a Sun Microsystems, Inc. business.
+* Permission to use, copy, modify, and distribute this
+* software is freely granted, provided that this notice
+* is preserved.
+* ```
+*/
+
+'use strict';
+
+// MODULES //
+
+var round = require( '@stdlib/math/base/special/round' );
+var getWord = require( '@stdlib/number/float32/base/to-word' ); // Single-precision word
+
+
+// VARIABLES //
+
+// 24 bits of 2/π (single precision):
+var INVPIO2 = 0.636619772; // 0x3f22f983
+
+// First 24 bits of π/2:
+var PIO2_1 = 1.570796326; // 0x3fc90fda
+
+// PIO2_1T = π/2 - PIO2_1:
+var PIO2_1T = 4.960468e-8; // 0x33522168
+
+// Exponent mask (255 => 0xff for single precision):
+var EXPONENT_MASK = 0xff|0; // asm type annotation
+
+
+// MAIN //
+
+/**
+* Computes `x - nπ/2 = r` for medium-sized inputs using single precision.
+*
+* @private
+* @param {number} x - input value
+* @param {uint32} ix - word of `x` (single precision)
+* @param {(Array|TypedArray|Object)} y - remainder element (single value)
+* @returns {integer} factor of `π/2`
+*/
+function rempio2fMedium( x, ix, y ) {
+ var word;
+ var n;
+ var t;
+ var r;
+ var w;
+ var i;
+ var j;
+
+ n = round( x * INVPIO2 );
+ r = x - ( n * PIO2_1 );
+ w = n * PIO2_1T;
+
+ // First rounding (good to 24 bits for single precision)...
+ j = (ix >> 23)|0; // Exponent from 32-bit word
+ y[ 0 ] = r - w;
+ word = getWord( y[ 0 ] );
+ i = j - ( (word >> 23) & EXPONENT_MASK );
+
+ // Check if a second iteration is needed...
+ if ( i > 16 ) {
+ t = r;
+ w = n * PIO2_1T;
+ r = t - w;
+ y[ 0 ] = r;
+ }
+ // No y[1] for single precision
+ return n;
+}
+
+
+// EXPORTS //
+
+module.exports = rempio2fMedium;
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/manifest.json b/lib/node_modules/@stdlib/math/base/special/rempio2f/manifest.json
new file mode 100644
index 000000000000..0d1b76145f8a
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/manifest.json
@@ -0,0 +1,76 @@
+{
+ "options": {
+ "task": "build"
+ },
+ "fields": [
+ {
+ "field": "src",
+ "resolve": true,
+ "relative": true
+ },
+ {
+ "field": "include",
+ "resolve": true,
+ "relative": true
+ },
+ {
+ "field": "libraries",
+ "resolve": false,
+ "relative": false
+ },
+ {
+ "field": "libpath",
+ "resolve": true,
+ "relative": false
+ }
+ ],
+ "confs": [
+ {
+ "task": "build",
+ "src": ["./src/main.c"],
+ "include": ["./include"],
+ "libraries": [],
+ "libpath": [],
+ "dependencies": [
+ "@stdlib/napi/argv",
+ "@stdlib/napi/argv-float",
+ "@stdlib/napi/argv-float32array",
+ "@stdlib/napi/create-double",
+ "@stdlib/napi/export",
+ "@stdlib/math/base/special/floorf",
+ "@stdlib/math/base/special/roundf",
+ "@stdlib/math/base/special/ldexpf",
+ "@stdlib/number/float32/base/from-word",
+ "@stdlib/number/float32/base/to-word"
+ ]
+ },
+ {
+ "task": "benchmark",
+ "src": ["./src/main.c"],
+ "include": ["./include"],
+ "libraries": [],
+ "libpath": [],
+ "dependencies": [
+ "@stdlib/math/base/special/roundf",
+ "@stdlib/math/base/special/floorf",
+ "@stdlib/math/base/special/ldexpf",
+ "@stdlib/number/float32/base/from-word",
+ "@stdlib/number/float32/base/to-word"
+ ]
+ },
+ {
+ "task": "examples",
+ "src": ["./src/main.c"],
+ "include": ["./include"],
+ "libraries": [],
+ "libpath": [],
+ "dependencies": [
+ "@stdlib/math/base/special/roundf",
+ "@stdlib/math/base/special/floorf",
+ "@stdlib/math/base/special/ldexpf",
+ "@stdlib/number/float32/base/from-word",
+ "@stdlib/number/float32/base/to-word"
+ ]
+ }
+ ]
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/package.json b/lib/node_modules/@stdlib/math/base/special/rempio2f/package.json
new file mode 100644
index 000000000000..793e29926d52
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/package.json
@@ -0,0 +1,65 @@
+{
+ "name": "@stdlib/math/base/special/rempio2f",
+ "version": "0.0.0",
+ "description": "Compute `x - nπ/2 = r`. (single-precision)",
+ "license": "Apache-2.0",
+ "author": {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ },
+ "contributors": [
+ {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ }
+ ],
+ "main": "./lib",
+ "gypfile": true,
+ "directories": {
+ "benchmark": "./benchmark",
+ "doc": "./docs",
+ "example": "./examples",
+ "include": "./include",
+ "lib": "./lib",
+ "src": "./src",
+ "test": "./test"
+ },
+ "types": "./docs/types",
+ "scripts": {},
+ "homepage": "https://github.com/stdlib-js/stdlib",
+ "repository": {
+ "type": "git",
+ "url": "git://github.com/stdlib-js/stdlib.git"
+ },
+ "bugs": {
+ "url": "https://github.com/stdlib-js/stdlib/issues"
+ },
+ "dependencies": {},
+ "devDependencies": {},
+ "engines": {
+ "node": ">=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "stdmath",
+ "mathematics",
+ "math",
+ "remainder",
+ "division",
+ "pi",
+ "pio2",
+ "precision"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/src/Makefile b/lib/node_modules/@stdlib/math/base/special/rempio2f/src/Makefile
new file mode 100644
index 000000000000..7733b6180cb4
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/src/Makefile
@@ -0,0 +1,70 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2025 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+ QUIET := @
+else
+ QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+ OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+ OS := WINNT
+endif
+endif
+endif
+endif
+
+
+# RULES #
+
+#/
+# Removes generated files for building an add-on.
+#
+# @example
+# make clean-addon
+#/
+clean-addon:
+ $(QUIET) -rm -f *.o *.node
+
+.PHONY: clean-addon
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean: clean-addon
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/src/addon.c b/lib/node_modules/@stdlib/math/base/special/rempio2f/src/addon.c
new file mode 100644
index 000000000000..951750e8bd13
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/src/addon.c
@@ -0,0 +1,46 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+#include "stdlib/math/base/special/rempio2f.h"
+#include "stdlib/napi/argv.h"
+#include "stdlib/napi/argv_float.h" // For single-precision input
+#include "stdlib/napi/argv_float32array.h" // For single-precision array output
+#include "stdlib/napi/create_double.h"
+#include "stdlib/napi/export.h"
+#include
+
+/**
+* Receives JavaScript callback invocation data.
+*
+* @param env environment under which the function is invoked
+* @param info callback data
+* @return Node-API value
+*/
+static napi_value addon( napi_env env, napi_callback_info info ) {
+ STDLIB_NAPI_ARGV( env, info, argv, argc, 2 );
+ STDLIB_NAPI_ARGV_FLOAT( env, x, argv, 0 ); // Input x as float
+ STDLIB_NAPI_ARGV_FLOAT32ARRAY( env, y, ylen, argv, 1 ); // Output y as Float32Array
+ if (ylen < 1) {
+ napi_throw_error( env, NULL, "Expected output array to have at least 1 element" );
+ return NULL;
+ }
+ STDLIB_NAPI_CREATE_DOUBLE( env, stdlib_base_rempio2f( x, &y[0] ), n ); // Single remainder
+ return n;
+}
+
+STDLIB_NAPI_MODULE_EXPORT_FCN( addon )
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/src/main.c b/lib/node_modules/@stdlib/math/base/special/rempio2f/src/main.c
new file mode 100644
index 000000000000..44bc5bcc2d83
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/src/main.c
@@ -0,0 +1,341 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*
+* ## Notice
+*
+* The following copyright, license, and long comment were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/12.2.0/lib/msun/src/e_rem_pio2.c}. The implementation follows the original, but has been modified according to project conventions.
+*
+* ```text
+* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+*
+* Developed at SunPro, a Sun Microsystems, Inc. business.
+* Permission to use, copy, modify, and distribute this
+* software is freely granted, provided that this notice
+* is preserved.
+* ```
+*/
+
+#include "stdlib/math/base/special/rempio2f.h"
+#include "stdlib/math/base/special/roundf.h"
+#include "stdlib/math/base/special/floorf.h"
+#include "stdlib/math/base/special/ldexpf.h"
+#include "stdlib/number/float32/base/from_word.h"
+#include "stdlib/number/float32/base/to_word.h"
+#include
+
+// Single-precision constants:
+static const float ZERO = 0.0f; // 0x00000000
+static const float TWO24 = 1.6777216e7f; // 0x4b800000 (2^24 for scaling)
+static const float TWON24 = 5.9604645e-8f; // 0x33800000 (2^-24 for normalization)
+static const float INVPIO2 = 0.636619772f; // 0x3f22f983 (2/π for quick estimation)
+static const float PIO2_1 = 1.57079632679f; // 0x3fc90fdb (π/2, primary term)
+static const float PIO2_1T = 4.960468e-8f; // 0x33a22169 (π/2 tail term)
+
+// High word constants for single precision:
+static const int32_t PIO4_HIGH_WORD = 0x3f490fdb; // π/4: 0.785398163
+static const int32_t THREE_PIO4_HIGH_WORD = 0x4016cbe4; // 3π/4: 2.35619449
+static const int32_t FIVE_PIO4_HIGH_WORD = 0x405497ce; // 5π/4: 3.926990817
+static const int32_t THREE_PIO2_HIGH_WORD = 0x4096cbe4; // 3π/2: 4.71238898
+static const int32_t SEVEN_PIO4_HIGH_WORD = 0x40b78909; // 7π/4: 5.497787144
+static const int32_t TWO_PI_HIGH_WORD = 0x40c90fdb; // 2π: 6.283185307
+static const int32_t NINE_PIO4_HIGH_WORD = 0x40fb53d1; // 9π/4: 7.068583471
+static const int32_t MEDIUM = 0x43c90fdb; // 2^8 * π/2 ≈ 402.123859659
+static const int32_t EXPONENT_MASK = 0x7f800000; // Exponent mask (0x7f8 => 255)
+
+// Table of constants for `2/π` (96 hex digits, 115 decimal):
+// Integer array containing the (24*i)-th to (24*i+23)-th bit of `2/π` after the binary point.
+// The corresponding floating value is `IPIO2[i] * 2^(-24(i+1))`.
+// For single precision (e0 <= 127, jk = 3), this table has sufficient terms.
+static const int32_t IPIO2[] = {
+ 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, 0xD8B3D3, 0x4A9D0D
+};
+
+/**
+* Single-precision kernel for rempio2 computation with single remainder.
+*
+* ## Method
+*
+* - Computes the integer (mod 8) and fractional parts of (2/π) * x without full multiplication, skipping known integer parts (0 mod 8), making operations independent of the input exponent.
+*
+* - `2/π` is represented by an array of 24-bit integers in `IPIO2[]`.
+*
+* - Input parameters:
+*
+* - `x[]` The input value (must be positive) broken into `nx` 24-bit chunks in single-precision format. `x[i]` is the i-th 24-bit segment of x. The scaled exponent of `x[0]` is given by `e0` (i.e., `x[0] * 2^e0` matches x up to 24 bits).
+*
+* Example: Breaking a float positive `z` into `x[0] + x[1]`:
+* ```
+* e0 = ilogb(z) - 23
+* z = scalbn(z, -e0)
+* for i = 0, 1:
+* x[i] = floor(z)
+* z = (z - x[i]) * 2^24
+* ```
+*
+* - `rem` Output remainder stored as a single float.
+*
+* - `e0` Exponent of `x[0]`. Must be <= 8188 or the `IPIO2` table needs expansion.
+*
+* - `nx` Dimension of `x[]`.
+*
+* - External functions:
+*
+* - `float stdlib_base_ldexpf()`, `stdlib_base_floorf()`
+*
+* - Local variables:
+*
+* - `jk` Initial number of `IPIO2[]` terms needed (3 for single precision).
+*
+* - `jp` Number of terms needed in the final remainder computation (equals `jk`).
+*
+* - `jz` Number of `IPIO2[]` terms used.
+*
+* - `jx` `nx - 1`.
+*
+* - `jv` Index for selecting `IPIO2[]` terms, ensuring `(2^e0 * x[0] * IPIO2[jv-1] * 2^(-24jv)) / 8` is an integer: `jv = max(0, (e0 - 3) / 24)`.
+*
+* - `q0` Exponent of the product `Q[0]`, with `Q[i]` having exponent `q0 - 24*i`.
+*
+* - `F[]` `IPIO2[]` in floating-point form.
+*
+* - `Q[]` Float array representing 24-bit chunks of `x * (2/π)`.
+*
+* - `IQ[]` Integer array breaking `Q[]` into 24-bit chunks.
+*
+* - `ih` Indicates if `Q[] >= 0.5` (sign of result).
+*
+* - Constants:
+*
+* - Hexadecimal values are intended; decimal values must convert accurately to these hex values.
+*
+* @param x input value array
+* @param rem output remainder (single value)
+* @param e0 exponent of x[0]
+* @param nx dimension of x[]
+* @return last 3 binary digits of N
+*/
+static int32_t rempio2f_kernel(const float* x, float* rem, int32_t e0, int32_t nx) {
+ float F[10] = {0.0f};
+ float Q[10] = {0.0f};
+ int32_t IQ[10];
+ float z;
+ float fw;
+ int32_t jz;
+ int32_t jx;
+ int32_t jv;
+ int32_t jp;
+ int32_t jk;
+ int32_t q0;
+ int32_t ih;
+ int32_t n;
+ int32_t i;
+ int32_t j;
+
+ // Initialize for single precision:
+ jk = 3;
+ jp = jk;
+
+ // Determine indices:
+ jx = nx - 1;
+ jv = (e0 - 3) / 24;
+ if (jv < 0) jv = 0;
+ q0 = e0 - (24 * (jv + 1));
+
+ // Set up `F[0]` to `F[jx+jk]` where `F[jx+jk] = IPIO2[jv+jk]`:
+ j = jv - jx;
+ for (i = 0; i <= jx + jk; i++) {
+ F[i] = (j < 0) ? ZERO : (float)IPIO2[j];
+ j++;
+ }
+
+ // Compute `Q[0], Q[1], ..., Q[jk]`:
+ for (i = 0; i <= jk; i++) {
+ fw = 0.0f;
+ for (j = 0; j <= jx; j++) {
+ fw += x[j] * F[jx + (i - j)];
+ }
+ Q[i] = fw;
+ }
+
+ jz = jk;
+
+ // Distill `Q[]` into `IQ[]` in reverse order:
+ z = Q[jz];
+ for (i = 0, j = jz; j > 0; i++, j--) {
+ fw = (float)((int32_t)(TWON24 * z));
+ IQ[i] = (int32_t)(z - TWO24 * fw);
+ z = Q[j - 1] + fw;
+ }
+
+ // Compute `n`:
+ z = stdlib_base_ldexpf(z, q0);
+ z -= 8.0f * stdlib_base_floorf(z * 0.125f); // Trim off integer >= 8
+ n = (int32_t)z;
+ z -= (float)n;
+ ih = (z >= 0.5f) ? 2 : 0;
+
+ // Case: z > 0.5
+ if (ih > 0) {
+ n += 1;
+ z = 1.0f - z;
+ }
+
+ // Check if re-computation is needed:
+ if (z == ZERO) {
+ jz--;
+ q0 -= 24;
+ while (jz >= 0 && IQ[jz] == 0) {
+ jz--;
+ q0 -= 24;
+ }
+ if (jz < 0) {
+ *rem = 0.0f;
+ return n & 7;
+ }
+ }
+
+ // Convert to floating-point:
+ fw = stdlib_base_ldexpf(1.0f, q0);
+ for (i = jz; i >= 0; i--) {
+ Q[i] = fw * (float)IQ[i];
+ fw *= TWON24;
+ }
+
+ // Compute final remainder (single value):
+ fw = 0.0f;
+ for (i = 0; i <= jz && i <= jp; i++) {
+ fw += PIO2_1 * Q[i];
+ }
+ *rem = (ih == 0) ? fw : -fw;
+ return n & 7;
+}
+
+/**
+* Computes `x - nπ/2 = r` using single precision with a single remainder.
+*
+* ## Notes
+*
+* - Returns `n` and stores the remainder `r` in `rem`.
+*
+* @param x input value
+* @param rem remainder
+* @return factor of `π/2`
+*
+* @example
+* #include
+*
+* float rem;
+* int32_t n = stdlib_base_rempio2f( 128.0f, &rem );
+*/
+int32_t stdlib_base_rempio2f(const float x, float *rem) {
+ float TX[2];
+ uint32_t ux;
+ int32_t ix;
+ int32_t hx;
+ int32_t e0;
+ int32_t nx;
+ int32_t n;
+ float z;
+
+ // Get word representation of x:
+ stdlib_base_float32_to_word(x, &ux);
+ hx = (int32_t)ux;
+ ix = hx & 0x7fffffff;
+
+ // Case: |x| ~<= π/4 (no reduction needed)
+ if (ix <= PIO4_HIGH_WORD) {
+ *rem = x;
+ return 0;
+ }
+
+ // Case: |x| ~<= 9π/4
+ if (ix <= NINE_PIO4_HIGH_WORD) {
+ // Case: |x| ~<= 3π/4
+ if (ix <= THREE_PIO4_HIGH_WORD) {
+ if (hx > 0) {
+ z = x - PIO2_1;
+ *rem = z - PIO2_1T;
+ return 1;
+ } else {
+ z = x + PIO2_1;
+ *rem = z + PIO2_1T;
+ return -1;
+ }
+ }
+ // Case: |x| ~<= 5π/4
+ if (ix <= FIVE_PIO4_HIGH_WORD) {
+ if (hx > 0) {
+ z = x - (2.0f * PIO2_1);
+ *rem = z - (2.0f * PIO2_1T);
+ return 2;
+ } else {
+ z = x + (2.0f * PIO2_1);
+ *rem = z + (2.0f * PIO2_1T);
+ return -2;
+ }
+ }
+ // Case: |x| ~<= 7π/4
+ if (ix <= SEVEN_PIO4_HIGH_WORD) {
+ if (hx > 0) {
+ z = x - (3.0f * PIO2_1);
+ *rem = z - (3.0f * PIO2_1T);
+ return 3;
+ } else {
+ z = x + (3.0f * PIO2_1);
+ *rem = z + (3.0f * PIO2_1T);
+ return -3;
+ }
+ }
+ // Case: |x| ~<= 9π/4
+ if (hx > 0) {
+ z = x - (4.0f * PIO2_1);
+ *rem = z - (4.0f * PIO2_1T);
+ return 4;
+ } else {
+ z = x + (4.0f * PIO2_1);
+ *rem = z + (4.0f * PIO2_1T);
+ return -4;
+ }
+ }
+
+ // Case: |x| ~< 2^8*π/2 (medium size)
+ if (ix < MEDIUM) {
+ n = (int32_t)stdlib_base_roundf(x * INVPIO2);
+ *rem = x - n * (PIO2_1 + PIO2_1T);
+ return n;
+ }
+
+ // Case: x is NaN or infinity
+ if (ix >= EXPONENT_MASK) {
+ *rem = x - x; // NaN
+ return 0;
+ }
+
+ // Set z = scalbn(|x|, ilogb(x)-7):
+ e0 = (ix >> 23) - 134; // ilogb(x) - 7
+ stdlib_base_float32_from_word(ix - (e0 << 23), &z);
+ TX[0] = (float)((int32_t)z);
+ TX[1] = (z - TX[0]) * 256.0f; // TWO8 equivalent
+ nx = (TX[1] == ZERO) ? 1 : 2;
+
+ n = rempio2f_kernel(TX, rem, e0, nx);
+ if (hx < 0) {
+ *rem = -*rem;
+ return -n;
+ }
+ return n;
+}
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/test/test.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/test/test.js
new file mode 100644
index 000000000000..80c73ae30867
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/test/test.js
@@ -0,0 +1,263 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var isInteger = require( '@stdlib/assert/is-integer' );
+var isNumber = require( '@stdlib/assert/is-number' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var incrspace = require( '@stdlib/array/base/incrspace' );
+var linspace = require( '@stdlib/array/base/linspace' );
+var randu = require( '@stdlib/random/base/randu' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var PINF = require( '@stdlib/constants/float32/pinf' ); // Changed to float32
+var NINF = require( '@stdlib/constants/float32/ninf' ); // Changed to float32
+var EPS = require( '@stdlib/constants/float32/eps' ); // Changed to float32
+var PIO2 = require( '@stdlib/constants/float32/half-pi' ); // Changed to float32
+var PIO4 = require( '@stdlib/constants/float32/fourth-pi' ); // Changed to float32
+var rempio2f = require( '@stdlib/math/base/special/rempio2f/lib' ); // Changed to rempio2f
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof rempio2f, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape('the function returns `0` and sets the element of `y` to `NaN` if provided `NaN`', function test(t) {
+ var y = [0.0]; // Single-element array
+ var n = rempio2f(NaN, y);
+ t.strictEqual(n, 0, 'returns expected value');
+ t.strictEqual(isnan(y[0]), true, 'y[0] is NaN');
+ t.end();
+});
+
+tape('the function returns `0` and sets the element of `y` to `NaN` if provided positive or negative infinity', function test(t) {
+ var y = [0.0]; // Single-element array
+ var n = rempio2f(PINF, y);
+ t.strictEqual(n, 0, 'returns expected value');
+ t.strictEqual(isnan(y[0]), true, 'y[0] is NaN');
+
+ y = [0.0];
+ n = rempio2f(NINF, y);
+ t.strictEqual(n, 0, 'returns expected value');
+ t.strictEqual(isnan(y[0]), true, 'y[0] is NaN');
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (positive)', function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ y = [0.0]; // Single-element array
+ for (i = 0; i < 200; i++) {
+ x = randu() * 100.0;
+ n = rempio2f(x, y);
+
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+
+ z = (PIO2 * n) + y[0]; // Only y[0] used
+
+ delta = abs(z - x);
+ tol = EPS * abs(x);
+ t.strictEqual(delta <= tol, true, 'delta <= tol for x = ' + x);
+ }
+
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (tiny positive)', function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ y = [0.0]; // Single-element array
+ for (i = 0; i < 200; i++) {
+ x = randu() * 1.0e-30; // Tiny positive values
+ n = rempio2f(x, y);
+
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+
+ z = (PIO2 * n) + y[0]; // Single remainder term
+ delta = abs(z - x);
+ tol = EPS * abs(x);
+ t.strictEqual(delta <= tol, true, 'returns expected value');
+ }
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (negative)', function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ y = [0.0]; // Single-element array
+ for (i = 0; i < 200; i++) {
+ x = -100.0 * randu();
+ n = rempio2f(x, y);
+
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+
+ z = (PIO2 * n) + y[0]; // Single remainder term
+ delta = abs(z - x);
+ tol = EPS * abs(x);
+ t.strictEqual(delta <= tol, true, 'returns expected value');
+ }
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (tiny negative)', function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ y = [0.0]; // Single-element array
+ for (i = 0; i < 200; i++) {
+ x = -1.0e-30 * randu(); // Tiny negative values
+ n = rempio2f(x, y);
+
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+
+ z = (PIO2 * n) + y[0]; // Single remainder term
+ delta = abs(z - x);
+ tol = EPS * abs(x);
+ t.strictEqual(delta <= tol, true, 'returns expected value');
+ }
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (multiples of π/4)', function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ x = incrspace(-10.0 * PIO4, 10.0 * PIO4, PIO4);
+ y = [0.0]; // Single-element array
+ for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+
+ z = (PIO2 * n) + y[0]; // Single remainder term
+ delta = abs(z - x[i]);
+ tol = EPS * abs(x[i]);
+ t.strictEqual(delta <= tol, true, 'returns expected value');
+ }
+ t.end();
+});
+
+tape( 'for large positive input values, the function returns the last three binary digits of `n` and stores `r` as two single-precision floating point numbers in `y`', function test( t ) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ x = linspace( pow( 2.0, 20 )*PIO2, pow( 2.0, 30 )*PIO2, 4000 ); // Reduced upper bound for single precision
+ y = [ 0.0, 0.0 ];
+ for ( i = 0; i < x.length; i++ ) {
+ n = rempio2f( x[i], y );
+ t.strictEqual( isInteger( n ), true, 'returns expected value' );
+ t.strictEqual( isNumber( y[0] ), true, 'returns expected value' );
+ t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
+ t.strictEqual( n < 8, true, 'returns expected value' );
+ }
+ t.end();
+});
+
+tape('for large negative input values, the function returns the last three binary digits of `n` and stores `r` as a single-precision floating point number in `y`', function test(t) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ x = linspace(-pow(2.0, 20) * PIO2, -pow(2.0, 25) * PIO2, 4000); // Adjusted for single precision
+ y = [0.0]; // Single-element array
+ for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+ t.strictEqual(n < 8, true, 'returns expected value');
+ }
+ t.end();
+});
+
+tape('for huge positive input values, the function returns the last three binary digits of `n` and stores `r` as a single-precision floating point number in `y`', function test(t) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ x = linspace(pow(2.0, 30) * PIO2, pow(2.0, 126) * PIO2, 6000); // Adjusted for single precision
+ y = [0.0]; // Single-element array
+ for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+ t.strictEqual(n < 8, true, 'returns expected value');
+ }
+ t.end();
+});
+
+tape('for huge positive input values, the function returns the last three binary digits of `n` and stores `r` as a single-precision floating point number in `y`', function test(t) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ x = linspace(pow(2.0, 30) * PIO2, pow(2.0, 126) * PIO2, 6000); // Adjusted for single precision
+ y = [0.0]; // Single-element array
+ for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+ t.strictEqual(n < 8, true, 'returns expected value');
+ }
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2f/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/rempio2f/test/test.native.js
new file mode 100644
index 000000000000..2d7ea6898aa6
--- /dev/null
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2f/test/test.native.js
@@ -0,0 +1,268 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var tape = require( 'tape' );
+var isInteger = require( '@stdlib/assert/is-integer' );
+var isNumber = require( '@stdlib/assert/is-number' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var incrspace = require( '@stdlib/array/base/incrspace' );
+var linspace = require( '@stdlib/array/base/linspace' );
+var randu = require( '@stdlib/random/base/randu' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var PINF = require( '@stdlib/constants/float32/pinf' );
+var NINF = require( '@stdlib/constants/float32/ninf' );
+var EPS = require( '@stdlib/constants/float32/eps' );
+var PIO2 = require( '@stdlib/constants/float32/half-pi' );
+var PIO4 = require( '@stdlib/constants/float32/fourth-pi' );
+var Float32Array = require( '@stdlib/array/float32' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+
+
+// VARIABLES //
+
+var rempio2f = tryRequire(resolve(__dirname, './../lib/native.js'));
+var opts = {
+ 'skip': (rempio2f instanceof Error)
+};
+
+
+// TESTS //
+
+tape('main export is a function', opts, function test(t) {
+ t.ok(true, __filename);
+ t.strictEqual(typeof rempio2f, 'function', 'main export is a function');
+ t.end();
+});
+
+tape('the function returns `0` and sets the element of `y` to `NaN` if provided `NaN`', opts, function test(t) {
+ var y = new Float32Array(1); // Single-element array
+ var n = rempio2f(NaN, y);
+ t.strictEqual(n, 0, 'returns expected value');
+ t.strictEqual(isnan(y[0]), true, 'y[0] is NaN');
+ t.end();
+});
+
+tape('the function returns `0` and sets the element of `y` to `NaN` if provided positive or negative infinity', opts, function test(t) {
+ var y = new Float32Array(1); // Single-element array
+ var n = rempio2f(PINF, y);
+ t.strictEqual(n, 0, 'returns expected value');
+ t.strictEqual(isnan(y[0]), true, 'y[0] is NaN');
+
+ y = new Float32Array(1); // Reset for next test
+ n = rempio2f(NINF, y);
+ t.strictEqual(n, 0, 'returns expected value');
+ t.strictEqual(isnan(y[0]), true, 'y[0] is NaN');
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (positive)', opts, function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ y = new Float32Array(1); // Single-element array
+ for (i = 0; i < 200; i++) {
+ x = randu() * 100.0;
+ n = rempio2f(x, y);
+
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+
+ z = (PIO2 * n) + y[0];
+ delta = abs(z - x);
+ tol = EPS * abs(x);
+ t.strictEqual(delta <= tol, true, 'can recover input value');
+ }
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (tiny positive)', opts, function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ y = new Float32Array(1); // Single-element array
+ for (i = 0; i < 200; i++) {
+ x = randu() * 1.0e-30;
+ n = rempio2f(x, y);
+
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+
+ z = (PIO2 * n) + y[0];
+ delta = abs(z - x);
+ tol = EPS * abs(x);
+ t.strictEqual(delta <= tol, true, 'can recover input value');
+ }
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (negative)', opts, function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ y = new Float32Array(1); // Single-element array
+ for (i = 0; i < 200; i++) {
+ x = -100.0 * randu();
+ n = rempio2f(x, y);
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+ z = (PIO2 * n) + y[0];
+ delta = abs(z - x);
+ tol = EPS * abs(x);
+ t.strictEqual(delta <= tol, true, 'can recover input value');
+ }
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (tiny negative)', opts, function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ y = new Float32Array(1); // Single-element array
+ for (i = 0; i < 200; i++) {
+ x = -1.0e-30 * randu();
+ n = rempio2f(x, y);
+
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+
+ z = (PIO2 * n) + y[0];
+ delta = abs(z - x);
+ tol = EPS * abs(x);
+ t.strictEqual(delta <= tol, true, 'can recover input value');
+ }
+ t.end();
+});
+
+tape('the function returns `n` and stores `r` as a single-precision floating point number in `y` such that `x - nπ/2 = r` (multiples of π/4)', opts, function test(t) {
+ var delta;
+ var tol;
+ var x;
+ var y;
+ var z;
+ var n;
+ var i;
+
+ x = incrspace(-10.0 * PIO4, 10.0 * PIO4, PIO4);
+ y = new Float32Array(1); // Single-element array
+ for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+
+ z = (PIO2 * n) + y[0];
+ delta = abs(z - x[i]);
+ tol = EPS * abs(x[i]);
+ t.strictEqual(delta <= tol, true, 'can recover input value');
+ }
+ t.end();
+});
+
+tape('for large positive input values, the function returns the last three binary digits of `n` and stores `r` as a single-precision floating point number in `y`', opts, function test(t) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ x = linspace(pow(2.0, 20) * PIO2, pow(2.0, 30) * PIO2, 4000);
+ y = new Float32Array(1); // Single-element array
+ for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+ t.strictEqual(n < 8, true, 'returns expected value');
+ }
+ t.end();
+});
+
+tape('for large negative input values, the function returns the last three binary digits of `n` and stores `r` as a single-precision floating point number in `y`', opts, function test(t) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ x = linspace(-pow(2.0, 20) * PIO2, -pow(2.0, 30) * PIO2, 4000);
+ y = new Float32Array(1); // Single-element array
+ for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+ t.strictEqual(n < 8, true, 'returns expected value');
+ }
+ t.end();
+});
+
+tape('for huge positive input values, the function returns the last three binary digits of `n` and stores `r` as a single-precision floating point number in `y`', opts, function test(t) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ x = linspace(pow(2.0, 30) * PIO2, pow(2.0, 126) * PIO2, 6000); // Adjusted for single precision
+ y = new Float32Array(1); // Single-element array
+ for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+ t.strictEqual(n < 8, true, 'returns expected value');
+ }
+ t.end();
+});
+
+tape('for huge negative input values, the function returns the last three binary digits of `n` and stores `r` as a single-precision floating point number in `y`', opts, function test(t) {
+ var x;
+ var y;
+ var n;
+ var i;
+
+ x = linspace(-pow(2.0, 30) * PIO2, -pow(2.0, 126) * PIO2, 6000); // Adjusted for single precision
+ y = new Float32Array(1); // Single-element array
+ for (i = 0; i < x.length; i++) {
+ n = rempio2f(x[i], y);
+ t.strictEqual(isInteger(n), true, 'returns expected value');
+ t.strictEqual(isNumber(y[0]), true, 'returns expected value');
+ t.strictEqual(n < 8, true, 'returns expected value');
+ }
+ t.end();
+});