std::lerp(3)

NAME
std::lerp - std::lerp

Synopsis
   Defined in header <cmath>
   constexpr float lerp( float a, float b, float t )
   noexcept;
   constexpr double lerp( double a, double b, double t ) (since C++20)
   noexcept; (until C++23)
   constexpr long double lerp( long double a, long double b,
                        long double t ) noexcept;
   constexpr /* floating-point-type */
       lerp( /* floating-point-type */ a, (since C++23)
             /* floating-point-type */ b, (1)
             /* floating-point-type */ t ) noexcept;
   Additional overloads
   Defined in header <cmath>
   template< class Arithmetic1, class Arithmetic2, class
   Arithmetic3 >
   constexpr /* common-floating-point-type */ (A) (since C++20)
       lerp( Arithmetic1 a, Arithmetic2 b, Arithmetic3 t )
   noexcept;
   1) Computes the linear interpolation between a and b, if the parameter t is inside
   [0, 1) (the linear extrapolation otherwise), i.e. the result of \(a+t(b−a)\)a+t(b−a)
   with accounting for floating-point calculation imprecision.
   The library provides overloads for all cv-unqualified floating-point types as the
   type of the parameters a, b and t.
   (since C++23)
   A) Additional overloads are provided for all other combinations of arithmetic types.

Parameters
   a, b, t - floating-point or integer values

Return value
   \(a + t(b − a)\)a + t(b − a)
   When std::isfinite(a) && std::isfinite(b) is true, the following properties are
   guaranteed:
     * If t == 0, the result is equal to a.
     * If t == 1, the result is equal to b.
     * If t >= 0 && t <= 1, the result is finite.
     * If std::isfinite(t) && a == b, the result is equal to a.
     * If std::isfinite(t) || (b - a != 0 && std::isinf(t)), the result is not NaN.
   Let CMP(x, y) be 1 if x > y, -1 if x < y, and 0 otherwise. For any t1 and t2, the
   product of
     * CMP(std::lerp(a, b, t2), std::lerp(a, b, t1)),
     * CMP(t2, t1), and
     * CMP(b, a)
   is non-negative. (That is, std::lerp is monotonic.)

Notes
   The additional overloads are not required to be provided exactly as (A). They only
   need to be sufficient to ensure that for their first argument num1, second argument
   num2 and third argument num3:
     * If num1, num2 or num3 has type long double, then std::lerp(num1,
       num2, num3) has the same effect as std::lerp(static_cast<long
       double>(num1),
                 static_cast<long double>(num2),
                 static_cast<long double>(num3)).
     * Otherwise, if num1, num2 and/or num3 has type double or an integer
       type, then std::lerp(num1, num2, num3) has the same effect as
       std::lerp(static_cast<double>(num1), (until C++23)
                 static_cast<double>(num2),
                 static_cast<double>(num3)).
     * Otherwise, if num1, num2 or num3 has type float, then
       std::lerp(num1, num2, num3) has the same effect as
       std::lerp(static_cast<float>(num1),
                 static_cast<float>(num2),
                 static_cast<float>(num3)).
   If num1, num2 and num3 have arithmetic types, then std::lerp(num1,
   num2, num3) has the same effect as std::lerp(static_cast</*
   common-floating-point-type */>(num1),
             static_cast</* common-floating-point-type */>(num2),
             static_cast</* common-floating-point-type */>(num3)), where
   /* common-floating-point-type */ is the floating-point type with the
   greatest floating-point conversion rank and greatest floating-point (since C++23)
   conversion subrank among the types of num1, num2 and num3, arguments
   of integer type are considered to have the same floating-point
   conversion rank as double.
   If no such floating-point type with the greatest rank and subrank
   exists, then overload resolution does not result in a usable candidate
   from the overloads provided.
    Feature-test macro Value Std Feature
   __cpp_lib_interpolate 201902L (C++20) std::lerp, std::midpoint

Example
// Run this code
 #include <cassert>
 #include <cmath>
 #include <iostream>
 float naive_lerp(float a, float b, float t)
 {
     return a + t * (b - a);
 }
 int main()
 {
     std::cout << std::boolalpha;
     const float a = 1e8f, b = 1.0f;
     const float midpoint = std::lerp(a, b, 0.5f);
     std::cout << "a = " << a << ", " << "b = " << b << '\n'
               << "midpoint = " << midpoint << '\n';
     std::cout << "std::lerp is exact: "
               << (a == std::lerp(a, b, 0.0f)) << ' '
               << (b == std::lerp(a, b, 1.0f)) << '\n';
     std::cout << "naive_lerp is exact: "
               << (a == naive_lerp(a, b, 0.0f)) << ' '
               << (b == naive_lerp(a, b, 1.0f)) << '\n';
     std::cout << "std::lerp(a, b, 1.0f) = " << std::lerp(a, b, 1.0f) << '\n'
               << "naive_lerp(a, b, 1.0f) = " << naive_lerp(a, b, 1.0f) << '\n';
     assert(not std::isnan(std::lerp(a, b, INFINITY))); // lerp here can be -inf
     std::cout << "Extrapolation demo, given std::lerp(5, 10, t):\n";
     for (auto t{-2.0}; t <= 2.0; t += 0.5)
         std::cout << std::lerp(5.0, 10.0, t) << ' ';
     std::cout << '\n';
 }

Possible output:
 a = 1e+08, b = 1
 midpoint = 5e+07
 std::lerp is exact?: true true
 naive_lerp is exact?: true false
 std::lerp(a, b, 1.0f) = 1
 naive_lerp(a, b, 1.0f) = 0
 Extrapolation demo, given std::lerp(5, 10, t):
 -5 -2.5 0 2.5 5 7.5 10 12.5 15

See also
   midpoint midpoint between two numbers or pointers
   (C++20) (function template)