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)