Merge 2018-06 LWG Motion 23

Fixes #2140

Author: zygoloid

source/numerics.tex

@@ -1377,6 +1377,16 @@
   // \ref{bit.cast}, \tcode{bit_cast}
   template<typename To, typename From>
     constexpr To bit_cast(const From& from) noexcept;
+
+  // \ref{bit.pow.two}, integral powers of 2
+  template <class T>
+    constexpr bool ispow2(T x) noexcept;
+  template <class T>
+    constexpr T ceil2(T x) noexcept;
+  template <class T>
+    constexpr T floor2(T x) noexcept;
+  template <class T>
+    constexpr T log2p1(T x) noexcept;
 }
 \end{codeblock}
 
@@ -1419,6 +1429,84 @@
 \end{itemize}
 \end{itemdescr}
 
+\rSec2[bit.pow.two]{Integral powers of 2}
+
+\indexlibrary{\idxcode{ispow2}}%
+\begin{itemdecl}
+template <class T>
+  constexpr bool ispow2(T x) noexcept;
+\end{itemdecl}
+
+\begin{itemdescr}
+\pnum
+\returns
+\tcode{true} if \tcode{x} is an integral power of two;
+\tcode{false} otherwise.
+
+\pnum
+\remarks
+This function shall not participate in overload resolution
+unless \tcode{T} is an unsigned integer type\iref{basic.fundamental}.
+\end{itemdescr}
+
+\indexlibrary{\idxcode{ceil2}}%
+\begin{itemdecl}
+template <class T>
+  constexpr T ceil2(T x) noexcept;
+\end{itemdecl}
+
+\begin{itemdescr}
+\pnum
+\returns
+The minimal value \tcode{y} such that
+\tcode{ispow2(y)} is \tcode{true} and \tcode{y >= x};
+if \tcode{y} is not representable as a value of type \tcode{T},
+the result is an unspecified value.
+
+\pnum
+\remarks
+This function shall not participate in overload resolution
+unless \tcode{T} is an unsigned integer type\iref{basic.fundamental}.
+\end{itemdescr}
+
+\indexlibrary{\idxcode{floor2}}%
+\begin{itemdecl}
+template <class T>
+  constexpr T floor2(T x) noexcept;
+\end{itemdecl}
+
+\begin{itemdescr}
+\pnum
+\returns
+If \tcode{x == 0}, \tcode{0};
+otherwise the maximal value \tcode{y}
+such that \tcode{ispow2(y)} is \tcode{true} and \tcode{y <= x}.
+
+\pnum
+\remarks
+This function shall not participate in overload resolution
+unless \tcode{T} is an unsigned integer type\iref{basic.fundamental}.
+\end{itemdescr}
+
+\indexlibrary{\idxcode{log2p1}}%
+\begin{itemdecl}
+template <class T>
+  constexpr T log2p1(T x) noexcept;
+\end{itemdecl}
+
+\begin{itemdescr}
+\pnum
+\returns
+If \tcode{x == 0}, \tcode{0};
+otherwise one plus the base-2 logarithm of \tcode{x},
+with any fractional part discarded.
+
+\pnum
+\remarks
+This function shall not participate in overload resolution
+unless \tcode{T} is an unsigned integer type\iref{basic.fundamental}.
+\end{itemdescr}
+
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