Log2

Defined in header <cmath>.

Description

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 num.

Declarations

C++23

// 1)
/* floating-point-type */ log2( /* floating-point-type */ num );
// 2)
float log2f( float num );
// 3)
long double log2l( long double num );

Additional Overloads

// 4)
template< class Integer >
double log2 ( Integer num );

C++11

// 1)
float log2 ( float num );
// 2)
double log2 ( double num );
// 3)
long double log2 ( long double num );
// 4)
float log2f( float num );
// 5)
long double log2l( long double num );

Additional Overloads

// 6)
template< class Integer >
double log2 ( Integer num );

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 Additional Overloads. 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)).

Examples

#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 Result

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