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std::lerp(3)		      C++ Standard Libary		  std::lerp(3)

NAME
       std::lerp - std::lerp

Synopsis
	  Defined in header <cmath>
	  constexpr  float  lerp(  float  a,  float  b,	 float	t  ) noexcept;
       (1) (since C++20)
	  constexpr double lerp( double	a, double  b,  double  t  )  noexcept;
       (2) (since C++20)
	  constexpr  long  double  lerp(  long	double	a, long	double b, long
       (3) (since C++20)
	  double t ) noexcept;
	  constexpr Promoted lerp( Arithmetic1 a, Arithmetic2  b,  Arithmetic3
       (4) (since C++20)
	  t ) noexcept;

	  1-3) Computes	the linear interpolation between a and b, if the para-
       meter t is inside
	  [0, 1] (the linear extrapolation otherwise), i.e. the	result of
	  \(a+t(ba)\)a+t(ba)  with  accounting	for floating-point calculation
       imprecision.
	  4) A set of overloads	or a function template for all combinations of
       arguments of
	  arithmetic type not covered by 1-3). If any  argument	 has  integral
       type, it	is cast
	  to  double.  If  any	other argument is long double, then the	return
       type is long
	  double, otherwise it is double.

Parameters
	  a, b,	t - values of floating-point or	integral types

Return value
	  \(a+t(ba)\)a+t(ba)

	  When isfinite(a) and isfinite(b), the	following properties are guar-
       anteed:

	    * 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 isfinite(t) &&	a == b,	the result is equal to a.
	    * If isfinite(t) ||	(b - a != 0 and	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(lerp(a,  b,	t2), lerp(a, b,	t1)), CMP(t2, t1), and
       CMP(b, a) is
	  non-negative.	(That is, lerp is monotonic.)

Notes
	  lerp is available in the global namespace when <math.h> is included,
       even if it is
	  not a	part of	C.

	  Feature-test macro: __cpp_lib_interpolate

Example
       // Run this code

	#include <cmath>
	#include <cassert>
	#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)

http://cppreference.com		  2022.07.31			  std::lerp(3)

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