Defined in header <cmath> | ||
|---|---|---|
| (1) | ||
constexpr float lerp( float a, float b, float t ) noexcept;
constexpr double lerp( double a, double b, double t ) noexcept;
constexpr long double lerp( long double a, long double b,
long double t ) noexcept;
| (since C++20) (until C++23) | |
constexpr /* floating-point-type */
lerp( /* floating-point-type */ a,
/* floating-point-type */ b,
/* floating-point-type */ t ) noexcept;
| (since C++23) | |
| Additional overloads | ||
Defined in header <cmath> | ||
template< class Arithmetic1, class Arithmetic2, class Arithmetic3 >
constexpr /* common-floating-point-type */
lerp( Arithmetic1 a, Arithmetic2 b, Arithmetic3 t ) noexcept;
| (A) | (since C++20) |
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, b, t | - | floating-point or integer values |
\(a+t(b−a)\)a+t(b−a).
When std::isfinite(a) && std::isfinite(b) is true, the following properties are guaranteed:
t == 0, the result is equal to a. t == 1, the result is equal to b. t >= 0 && t <= 1, the result is finite. std::isfinite(t) && a == b, the result is equal to a. 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.).
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:
| (until C++23) |
| If 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. | (since C++23) |
| Feature-test macro | Value | Std | Comment |
|---|---|---|---|
__cpp_lib_interpolate | 201902L | (C++20) |
std::lerp, std::midpoint |
#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
|
(C++20) | midpoint between two numbers or pointers (function template) |
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