# std::sub_sat

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< cpp‎ | numeric

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

Computes the saturating subtraction 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::sub_sat<int>(INT_MIN + 4, 3) == INT_MIN + 1) // not saturated
        && (std::sub_sat<int>(INT_MIN + 4, 5) == INT_MIN) // saturated
        && (std::sub_sat<int>(INT_MAX - 4, -3) == INT_MAX - 1) // not saturated
        && (std::sub_sat<int>(INT_MAX - 4, -5) == INT_MAX) // saturated
        && (std::sub_sat<unsigned>(4, 3) == 1) // not saturated
        && (std::sub_sat<unsigned>(4, 5) == 0) // saturated
    );

    int main() {}

### See also

add_sat (C++26) | saturating addition 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 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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