std::lerp

 

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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 double t ) noexcept;	(3)	(since C++20)
constexpr Promoted    lerp( Arithmetic1 a, Arithmetic2 b, Arithmetic3 t ) noexcept;	(4)	(since C++20)

1-3) 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.

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

\(a+t(b−a)\)a+t(b−a)

When isfinite(a) and isfinite(b), 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 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

Feature-test macro	Value	Std	Feature
__cpp_lib_interpolate	201902L	(C++20)	std::lerp, std::midpoint

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 (C++20)

midpoint between two numbers or pointers (function template)