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

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.


[edit] Parameters

x, y - integer values

[edit] Return value

Saturated x + y.

[edit] Exceptions

Throws no exceptions.

[edit] 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

[edit] Possible implementation

See libstdc++ (gcc).

[edit] Example

Can be previewed on Compiler Explorer.

#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

[edit] See also

saturating subtraction operation on two integers
(function template) [edit]
saturating multiplication operation on two integers
(function template) [edit]
saturating division operation on two integers
(function template) [edit]
returns an integer value clamped to the range of a another integer type
(function template) [edit]
clamps a value between a pair of boundary values
(function template) [edit]
checks if an integer value is in the range of a given integer type
(function template) [edit]
returns the smallest finite value of the given type
(public static member function of std::numeric_limits<T>) [edit]
returns the largest finite value of the given type
(public static member function of std::numeric_limits<T>) [edit]

[edit] External links

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