Rework URBG requirements for clarity and simplicitly

... by removing the redundance between the URBG concept and the URBG requirements.

Author: CaseyCarter

source/numerics.tex

@@ -1869,82 +1869,6 @@
  is often determined statistically.
 \end{note}
 
-\pnum
-A class \tcode{G}
-satisfies the requirements
-of a \term{uniform random bit generator}
-if the expressions shown
-in \tref{UniformRandomBitGenerator}
-are valid and have the indicated semantics,
-and if \tcode{G} also satisfies all other requirements
-of this subclause \ref{rand.req.urng}.
-In that Table and throughout this subclause:
-\begin{enumeratea}
-  \item
-    \tcode{T} is the type named by
-    \tcode{G}'s associated \tcode{result_type},
-  and
-  \item
-    \tcode{g} is a value of \tcode{G}.
-\end{enumeratea}
-
-\begin{libreqtab4d}
-  {Uniform random bit generator requirements}
-  {tab:UniformRandomBitGenerator}
-\\ \topline
-\lhdr{Expression}
-  & \chdr{Return type}
-  & \chdr{Pre/post-condition}
-  & \rhdr{Complexity}
-  \\ \capsep
-\endfirsthead
-\hline
-\lhdr{Expression}
-  & \chdr{Return type}
-  & \chdr{Pre/post-condition}
-  & \rhdr{Complexity}
-  \\ \capsep
-\endhead
-\indextext{\idxcode{result_type}!uniform random bit generator requirement}%
-\tcode{G::result_type}
-  & \tcode{T}
-  & \tcode{T} is an unsigned integer type\iref{basic.fundamental}.
-  & compile-time
-  \\ \rowsep
-\tcode{g()}%
-\indextext{\idxcode{operator()}!uniform random bit generator requirement}
-  & \tcode{T}
-  & Returns a value in the closed interval
-    $[$\tcode{G::min()}, \tcode{G::max()}$]$.
-  & amortized constant
-  \\ \rowsep
-\tcode{G::min()}%
-\indextext{\idxcode{min}!uniform random bit generator requirement}
-  & \tcode{T}
-  & Denotes the least value potentially returned
-    by \tcode{operator()}.
-  & compile-time
-  \\ \rowsep
-\tcode{G::max()}
-\indextext{\idxcode{max}!uniform random bit generator requirement}
-  & \tcode{T}
-  & Denotes the greatest value potentially returned
-    by \tcode{operator()}.
-  & compile-time
-  \\
-\end{libreqtab4d}
-
-\pnum
-The following relation shall hold:
-\tcode{G::min() < G::max()}.
-\indextext{requirements!uniform random bit generator|)}%
-\indextext{uniform random bit generator!requirements|)}
-
-\pnum
-The \libconcept{UniformRandomBitGenerator} concept is a slight relaxation of the
-uniform random bit generator requirements, in that it does not require a nested
-\grammarterm{typedef-name} \tcode{result_type}.
-
 \begin{codeblock}
 template <class G>
 concept UniformRandomBitGenerator =
@@ -1956,8 +1880,8 @@
 \end{codeblock}
 
 \pnum
-Let \tcode{g} be an object of type \tcode{G}.
-\tcode{UniformRandomBitGenerator<G>} is satisfied only if
+Let \tcode{g} be an object of type \tcode{G}. \tcode{G} models
+\libconcept{UniformRandomBitGenerator} only if
 
 \begin{itemize}
 \item Both \tcode{G::min()} and \tcode{G::max()} are constant
@@ -1968,6 +1892,17 @@
 \item \tcode{g()} has amortized constant complexity.
 \end{itemize}
 
+\indextext{requirements!uniform random bit generator|)}%
+\indextext{uniform random bit generator!requirements|)}%
+\pnum
+A class \tcode{G} meets the \term{uniform random bit generator} requirements if
+\tcode{G} models \libconcept{UniformRandomBitGenerator},
+\tcode{invoke_result_t<G\&>} is an unsigned integer type\iref{basic.fundamental},
+and
+\tcode{G} provides a nested \grammarterm{typedef-name} \tcode{result_type}
+that denotes the same type as \tcode{invoke_result_t<G\&>}.
+
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Random Number Engine requirements:
 
@@ -2142,7 +2077,7 @@
       \state{e}{i+1} $= \mathsf{TA}($\state{e}{i}$)$
     and returns
       $\mathsf{GA}($\state{e}{i}$)$.
-  & per \tref{UniformRandomBitGenerator}
+  & per \ref{rand.req.urng}
   \\ \rowsep
 \tcode{e.discard(z)}%
 \indextext{\idxcode{discard}!random number engine requirement}