# std::mul_sat

< cpp‎ | numeric

Numerics library
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Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
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Pseudo-random number generation
Factor operations
 gcd(C++17)
 lcm(C++17)
Interpolations
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 lerp(C++20)
Saturation arithmetic
 mul_sat(C++26) div_sat(C++26)
Generic numeric operations
 iota(C++11) ranges::iota(C++23) accumulate inner_product adjacent_difference partial_sum
 reduce(C++17) transform_reduce(C++17) inclusive_scan(C++17) exclusive_scan(C++17) transform_inclusive_scan(C++17) transform_exclusive_scan(C++17)
Bit operations
 has_single_bit(C++20) bit_cast(C++20) bit_ceil(C++20) bit_floor(C++20) bit_width(C++20) rotl(C++20) rotr(C++20)
 popcount(C++20) countl_zero(C++20) countl_one(C++20) countr_zero(C++20) countr_one(C++20) byteswap(C++23) endian(C++20)

 Defined in header  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.

## Contents

### Parameters

 x, y - integer values

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.

#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 a 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 type (public static member function of std::numeric_limits)  max[static] returns the largest finite value of the given type (public static member function of std::numeric_limits)