# std::log2, std::log2f, std::log2l

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float log2 ( float num ); double log2 ( double num ); long double log2 ( long double num ); |  | (until C++23)
/* floating-point-type */ log2 ( /* floating-point-type */ num ); |  | (since C++23) (constexpr since C++26)
float log2f( float num ); | (2) | (since C++11) (constexpr since C++26)
long double log2l( long double num ); | (3) | (since C++11) (constexpr since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Integer > double log2 ( Integer num ); | (A) | (constexpr since C++26)

1-3) Computes the binary (base-2) logarithm of num. The library provides overloads of `std::log2` for all cv-unqualified floating-point types as the type of the parameter. (since C++23)

A) Additional overloads are provided for all integer types, which are treated as double. | (since C++11)

### Parameters

num | - | floating-point or integer value

### Return value

If no errors occur, the base-2 logarithm of num (log
2(num) or lb(num)) is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a pole error occurs, -HUGE_VAL, `-HUGE_VALF`, or `-HUGE_VALL` is returned.

### Error handling

Errors are reported as specified in math_errhandling.

Domain error occurs if num is less than zero.

Pole error may occur if num is zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- If the argument is ±0, -∞ is returned and FE_DIVBYZERO is raised
- If the argument is 1, +0 is returned
- If the argument is negative, NaN is returned and FE_INVALID is raised
- If the argument is +∞, +∞ is returned
- If the argument is NaN, NaN is returned

### Notes

For integer num, the binary logarithm can be interpreted as the zero-based index of the most significant 1 bit in the input.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::log2(num) has the same effect as std::log2(static_cast<double>(num)).

### Example

Run this code

    #include <cerrno>
    #include <cfenv>
    #include <cstring>
    #include <cmath>
    #include <iostream>

    // #pragma STDC FENV_ACCESS ON

    int main()
    {
        std::cout << "log2(65536) = " << std::log2(65536) << '\n'
                  << "log2(0.125) = " << std::log2(0.125) << '\n'
                  << "log2(0x020f) = " << std::log2(0x020f)
                  << " (highest set bit is in position 9)\n"
                  << "base-5 logarithm of 125 = "
                  << std::log2(125) / std::log2(5) << '\n';

        // special values
        std::cout << "log2(1) = " << std::log2(1) << '\n'
                  << "log2(+Inf) = " << std::log2(INFINITY) << '\n';

        // error handling
        errno = 0;
        std::feclearexcept(FE_ALL_EXCEPT);

        std::cout << "log2(0) = " << std::log2(0) << '\n';

        if (errno == ERANGE)
            std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
        if (std::fetestexcept(FE_DIVBYZERO))
            std::cout << "    FE_DIVBYZERO raised\n";
    }

Possible output:

    log2(65536) = 16
    log2(0.125) = -3
    log2(0x020f) = 9.04166 (highest set bit is in position 9)
    base-5 logarithm of 125 = 3
    log2(1) = 0
    log2(+Inf) = inf
    log2(0) = -inf
        errno == ERANGE: Numerical result out of range
        FE_DIVBYZERO raised

### See also

log logf logl (C++11)(C++11) | computes natural (base e) logarithm (\({\small \ln{x} }\)ln(x)) (function)
log10 log10f log10l (C++11)(C++11) | computes common (base 10) logarithm (\({\small \log_{10}{x} }\)log10(x)) (function)
log1p log1pf log1pl (C++11)(C++11)(C++11) | natural logarithm (to base e) of 1 plus the given number (\({\small \ln{(1+x)} }\)ln(1+x)) (function)
exp2 exp2f exp2l (C++11)(C++11)(C++11) | returns 2 raised to the given power (\({\small 2^x}\)2x) (function)

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