Merge 2019-02 LWG Motion 13

P0811R3 Well-behaved interpolation for numbers and pointers

Fixes #2704.

Author: zygoloid

source/algorithms.tex

@@ -8805,6 +8805,12 @@
   // \ref{numeric.ops.lcm}, least common multiple
   template<class M, class N>
     constexpr common_type_t<M,N> lcm(M m, N n);
+
+  // \ref{numeric.ops.midpoint}, midpoint
+  template<class T>
+    constexpr T midpoint(T a, T b) noexcept;
+  template<class T>
+    constexpr T* midpoint(T* a, T* b);
 }
 \end{codeblock}
 
@@ -9780,6 +9786,59 @@
 Nothing.
 \end{itemdescr}
 
+\rSec2[numeric.ops.midpoint]{Midpoint}
+
+\indexlibrary{\idxcode{midpoint}}%
+\begin{itemdecl}
+template<class T>
+  constexpr T midpoint(T a, T b) noexcept;
+\end{itemdecl}
+\begin{itemdescr}
+\pnum
+\constraints
+\tcode{T} is an arithmetic type other than \tcode{bool}.
+
+\pnum
+\returns
+Half the sum of \tcode{a} and \tcode{b}.
+If \tcode{T} is an integer type and the sum is odd,
+the result is rounded towards \tcode{a}.
+
+\pnum
+\remarks
+No overflow occurs.
+If \tcode{T} is a floating-point type, at most one inexact operation occurs.
+\end{itemdescr}
+
+\indexlibrary{\idxcode{midpoint}}%
+\begin{itemdecl}
+template<class T>
+  constexpr T* midpoint(T* a, T* b);
+\end{itemdecl}
+\begin{itemdescr}
+\pnum
+\constraints
+\tcode{T} is a complete object type.
+
+\pnum
+\expects
+\tcode{a} and \tcode{b} point to, respectively,
+elements $\tcode{x}[i]$ and $\tcode{x}[j]$ of the same array object \tcode{x}.
+\begin{note}
+An object that is not an array element is considered to belong
+to a single-element array for this purpose; see \ref{expr.unary.op}.
+A pointer past the last element of an array \tcode{x} of $n$ elements
+is considered to be equivalent to a pointer
+to a hypothetical element $\tcode{x}[n]$ for this purpose;
+see \ref{basic.compound}.
+\end{note}
+
+\pnum
+\returns
+A pointer to $\tcode{x}[i+\frac{j-i}{2}]$,
+where the result of the division is truncated towards zero.
+\end{itemdescr}
+
 \rSec1[alg.c.library]{C library algorithms}
 
 \pnum

source/numerics.tex

@@ -9119,6 +9119,11 @@
   float fmaf(float x, float y, float z);
   long double fmal(long double x, long double y, long double z);
 
+  // \ref{c.math.lerp}, linear interpolation
+  constexpr float lerp(float a, float b, float t);
+  constexpr double lerp(double a, double b, double t);
+  constexpr long double lerp(long double a, long double b, long double t);
+
   // \ref{c.math.fpclass}, classification / comparison functions
   int fpclassify(float x);
   int fpclassify(double x);
@@ -9375,6 +9380,39 @@
 \returns $\sqrt{x^2+y^2+z^2}$.
 \end{itemdescr}
 
+\rSec2[c.math.lerp]{Linear interpolation}
+
+\indexlibrary{\idxcode{lerp}}%
+\begin{itemdecl}
+constexpr float lerp(float a, float b, float t);
+constexpr double lerp(double a, double b, double t);
+constexpr long double lerp(long double a, long double b, long double t);
+\end{itemdecl}
+\begin{itemdescr}
+\pnum
+\returns
+$a+t(b-a)$.
+
+\pnum
+\remarks
+Let \tcode{r} be the value returned.
+If \tcode{isfinite(a) \&\& isfinite(b)}, then:
+\begin{itemize}
+\item If \tcode{t == 0}, then \tcode{r == a}.
+\item If \tcode{t == 1}, then \tcode{r == b}.
+\item If \tcode{t >= 0 \&\& t <= 1}, then \tcode{isfinite(r)}.
+\item If \tcode{isfinite(t) \&\& a == b}, then \tcode{r == a}.
+\item If \tcode{isfinite(t) || !isnan(t) \&\& b-a != 0}, then \tcode{!isnan(r)}.
+\end{itemize}
+Let \tcode{\placeholder{CMP}(x,y)} be \tcode{1} if \tcode{x > y},
+\tcode{-1} if \tcode{x < y}, and \tcode{0} otherwise.
+For any \tcode{t1} and \tcode{t2}, the product of
+\tcode{\placeholder{CMP}(lerp(a, b, t2), lerp(a, b, t1))},
+\tcode{\placeholder{CMP}(t2, t1)}, and
+\tcode{\placeholder{CMP}(b, a)}
+is non-negative.
+\end{itemdescr}
+
 \rSec2[c.math.fpclass]{Classification / comparison functions}
 
 \pnum

source/support.tex

@@ -610,6 +610,8 @@
   \tcode{<utility>} \\ \rowsep
 \defnlibxname{cpp_lib_integral_constant_callable}           & \tcode{201304L} &
   \tcode{<type_traits>} \\ \rowsep
+\defnlibxname{cpp_lib_interpolate}                          & \tcode{201902L} &
+  \tcode{<cmath>} \tcode{<numeric>} \\ \rowsep
 \defnlibxname{cpp_lib_invoke}                               & \tcode{201411L} &
   \tcode{<functional>} \\ \rowsep
 \defnlibxname{cpp_lib_is_aggregate}                         & \tcode{201703L} &