NAME¶

std::add_sat - std::add_sat

Synopsis¶

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

Computes the saturating addition 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.

Exceptions¶

Throws no exceptions.

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 <limits>
#include <numeric>

static_assert(CHAR_BIT == 8);
static_assert(UCHAR_MAX == 255);

int main()
{
constexpr int a = std::add_sat(3, 4); // no saturation occurs, T = int
static_assert(a == 7);

constexpr unsigned char b = std::add_sat<unsigned char>(UCHAR_MAX, 4); // saturated
static_assert(b == UCHAR_MAX);

constexpr unsigned char c = std::add_sat(UCHAR_MAX, 4); // not saturated, T = int
// add_sat(int, int) returns int tmp == 259,
// then assignment truncates 259 % 256 == 3
static_assert(c == 3);

// unsigned char d = std::add_sat(252, c); // Error: inconsistent deductions for T

constexpr unsigned char e = std::add_sat<unsigned char>(251, a); // saturated
static_assert(e == UCHAR_MAX);
// 251 is of type T = unsigned char, `a` is converted to unsigned char value;
// might yield an int -> unsigned char conversion warning for `a`

constexpr signed char f = std::add_sat<signed char>(-123, -3); // not saturated
static_assert(f == -126);

constexpr signed char g = std::add_sat<signed char>(-123, -13); // saturated
static_assert(g == std::numeric_limits<signed char>::min()); // g == -128
}

See also¶

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

External links¶

1. A branch-free implementation of saturation arithmetic — Locklessinc.com, 2012