# std::bit_width

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< cpp‎ | numeric

Defined in header `<bit>` |  |
template< class T > constexpr int bit_width( T x ) noexcept; |  | (since C++20)

If x is not zero, calculates the number of bits needed to store the value x, that is, \(1 + \lfloor \log_2(x) \rfloor\)1 + floor(log
2(x)). If x is zero, returns zero.

This overload participates in overload resolution only if `T` is an unsigned integer type (that is, unsigned char, unsigned short, unsigned int, unsigned long, unsigned long long, or an extended unsigned integer type).

### Parameters

x | - | unsigned integer value

### Return value

Zero if x is zero; otherwise, one plus the base-2 logarithm of x, with any fractional part discarded.

### Notes

This function is equivalent to return std::numeric_limits<T>::digits - std::countl_zero(x);.

Feature-test macro | Value | Std | Comment
--- | --- | --- | ---
`__cpp_lib_int_pow2` | 202002L | (C++20) | Integral power-of-2 operations

### Example

Run this code

    #include <bit>
    #include <bitset>
    #include <iostream>

    int main()
    {
        for (unsigned x{0}; x != 8; ++x)
        {
            std::cout
                << "bit_width( "
                << std::bitset<4>{x} << " ) = "
                << std::bit_width(x) << '\n';
        }
    }

Output:

    bit_width( 0000 ) = 0
    bit_width( 0001 ) = 1
    bit_width( 0010 ) = 2
    bit_width( 0011 ) = 2
    bit_width( 0100 ) = 3
    bit_width( 0101 ) = 3
    bit_width( 0110 ) = 3
    bit_width( 0111 ) = 3

### Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR | Applied to | Behavior as published | Correct behavior
--- | --- | --- | ---
LWG 3656 | C++20 | the return type of `bit_width` is the same as the type of its function argument | made it int

### See also

countl_zero (C++20) | counts the number of consecutive 0 bits, starting from the most significant bit (function template)

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