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< cpp‎ | numeric

Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric arrays
Pseudo-random number generation
Factor operations
(C++17)
(C++17)
Interpolations
(C++20)
(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 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.

## Contents

### Parameters

 x, y - integer values

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.

#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
}

 sub_sat(C++26) saturating subtraction operation on two integers (function template)  mul_sat(C++26) saturating multiplication 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)