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

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
float log2 ( float arg ); float log2f( float arg ); | (1) | (since C++11)
double log2 ( double arg ); | (2) | (since C++11)
long double log2 ( long double arg ); long double log2l( long double arg ); | (3) | (since C++11)
double log2 ( IntegralType arg ); | (4) | (since C++11)

1-3) Computes the binary (base-2) logarithm of arg.
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to 2) (the argument is cast to double).

### Parameters

arg | - | value of floating-point or Integral type

### Return value

If no errors occur, the base-2 logarithm of `arg` (log
2(arg) or lb(arg)) 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 `arg` is less than zero.

Pole error may occur if `arg` 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 `arg`, the binary logarithm can be interpreted as the zero-based index of the most significant 1 bit in the input.

### Example

Run this code

    #include <iostream>
    #include <cmath>
    #include <cerrno>
    #include <cstring>
    #include <cfenv>
    #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 (ln(x)) (function)
log10 log10f log10l (C++11)(C++11) | computes common (base 10) logarithm (log10(x)) (function)
log1p log1pf log1pl (C++11)(C++11)(C++11) | natural logarithm (to base e) of 1 plus the given number (ln(1+x)) (function)
exp2 exp2f exp2l (C++11)(C++11)(C++11) | returns 2 raised to the given power (2x) (function)

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