# std::midpoint

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< cpp‎ | numeric

Defined in header `<numeric>` |  |
template< class T > constexpr T midpoint( T a, T b ) noexcept; | (1) | (since C++20)
template< class T > constexpr T* midpoint( T* a, T* b ); | (2) | (since C++20)

Computes the midpoint of the integers, floating-points, or pointers a and b.

1) This overload participates in overload resolution only if `T` is an arithmetic type other than bool.
2) This overload participates in overload resolution only if `T` is an object type. Use of this overload is ill-formed if `T` is an incomplete type.

### Parameters

a, b | - | integers, floating-points, or pointer values

### Return value

1) Half the sum of a and b. No overflow occurs. If a and b have integer type and the sum is odd, the result is rounded towards a. If a and b have floating-point type, at most one inexact operation occurs.
2) If a and b point to, respectively, x[i] and x[j] of the same array object `x` (for the purpose of pointer arithmetic), returns a pointer to x[i + (j - i) / 2] (or, equivalently x[std::midpoint(i, j)]) where the division rounds towards zero. If a and b do not point to elements of the same array object, the behavior is undefined.

### Exceptions

Throws no exceptions.

### Notes

Overload (2) can be simply implemented as return a + (b - a) / 2; on common platforms. However, such implementation is not guaranteed to be portable, because there may be some platforms where creating an array with number of elements greater than PTRDIFF_MAX is possible, and b - a may result in undefined behavior even if both b and a point to elements in the same array.

Feature-test macro | Value | Std | Feature
--- | --- | --- | ---
`__cpp_lib_interpolate` | `201902L` | (C++20) | std::lerp, `std::midpoint`

### Example

Run this code

    #include <cstdint>
    #include <iostream>
    #include <limits>
    #include <numeric>

    int main()
    {
        std::uint32_t a = std::numeric_limits<std::uint32_t>::max();
        std::uint32_t b = std::numeric_limits<std::uint32_t>::max() - 2;

        std::cout << "a: " << a << '\n'
                  << "b: " << b << '\n'
                  << "Incorrect (overflow and wrapping): " << (a + b) / 2 << '\n'
                  << "Correct: " << std::midpoint(a, b) << "\n\n";

        auto on_pointers = [](int i, int j)
        {
            char const* text = "0123456789";
            char const* p = text + i;
            char const* q = text + j;
            std::cout << "std::midpoint('" << *p << "', '" << *q << "'): '"
                      << *std::midpoint(p, q) << "'\n";
        };

        on_pointers(2, 4);
        on_pointers(2, 5);
        on_pointers(5, 2);
        on_pointers(2, 6);
    }

Output:

    a: 4294967295
    b: 4294967293
    Incorrect (overflow and wrapping): 2147483646
    Correct: 4294967294

    std::midpoint('2', '4'): '3'
    std::midpoint('2', '5'): '3'
    std::midpoint('5', '2'): '4'
    std::midpoint('2', '6'): '4'

### References

- C++23 standard (ISO/IEC 14882:2024):

  - 27.10.16 Midpoint [numeric.ops.midpoint]

- C++20 standard (ISO/IEC 14882:2020):

  - 25.10.15 Midpoint [numeric.ops.midpoint]

### See also

lerp (C++20) | linear interpolation function (function)

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