std::mul_sat

Defined in header `<numeric>`
template< class T > constexpr T mul_sat( T x, T y ) noexcept;		(since C++26)

Computes the saturating multiplication x × y. This operation (unlike built-in arithmetic operations on integers) behaves as-if it is a mathematical operation with an infinite range. Let q denote the result of such operation. Returns:

q, if q is representable as a value of type T. Otherwise,
the largest or smallest value of type T, whichever is closer to the q.

This overload participates in overload resolution only if T is an integer type, that is: signed char, short, int, long, long long, an extended signed integer type, or an unsigned version of such types. In particular, T must not be (possibly cv-qualified) bool, char, wchar_t, char8_t, char16_t, and char32_t, as these types are not intended for arithmetic.

Parameters

x, y

-

integer values

Return value

Saturated x × y.

Notes

Unlike the built-in arithmetic operators on integers, the integral promotion does not apply to the x and y arguments.

If two arguments of different type are passed, the call fails to compile, i.e. the behavior relative to template argument deduction is the same as for std::min or std::max.

Most modern hardware architectures have efficient support for saturation arithmetic on SIMD vectors, including SSE2 for x86 and NEON for ARM.

Feature-test macro	Value	Std	Feature
`__cpp_lib_saturation_arithmetic`	`202311L`	(C++26)	Saturation arithmetic

Possible implementation

See libstdc++ (gcc).

Example

Can be previewed on Compiler Explorer.

Run this code

#include <climits>
#include <numeric>
 
static_assert
(""
    && (std::mul_sat<int>(2, 3) == 6) // not saturated
    && (std::mul_sat<int>(INT_MAX / 2, 3) == INT_MAX) // saturated
    && (std::mul_sat<int>(-2, 3) == -6) // not saturated
    && (std::mul_sat<int>(INT_MIN / -2, -3) == INT_MIN) // saturated
    && (std::mul_sat<unsigned>(2, 3) == 6) // not saturated
    && (std::mul_sat<unsigned>(UINT_MAX / 2, 3) == UINT_MAX) // saturated
);
 
int main() {}

add_sat (C++26)	saturating addition operation on two integers (function template)
sub_sat (C++26)	saturating subtraction operation on two integers (function template)
div_sat (C++26)	saturating division operation on two integers (function template)
saturate_cast (C++26)	returns an integer value clamped to the range of another integer type (function template)
clamp (C++17)	clamps a value between a pair of boundary values (function template)
in_range (C++20)	checks if an integer value is in the range of a given integer type (function template)
min [static]	returns the smallest finite value of the given non-floating-point type, or the smallest positive normal value of the given floating-point type (public static member function of `std::numeric_limits<T>`)
max [static]	returns the largest finite value of the given type (public static member function of `std::numeric_limits<T>`)

External links

1.	A branch-free implementation of saturation arithmetic — Locklessinc.com, 2012
2.	C++ Weekly - Ep 459 - C++26's Saturating Math Operations — Youtube.com, 2024-12-16

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