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

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

Compiler support
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Feature test macros (C++20)
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Diagnostics library
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Technical specifications
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Common mathematical functions
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Mathematical constants (C++20)
Floating-point environment (C++11)
Complex numbers
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gcd (C++17)
lcm (C++17)
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midpoint (C++20)
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iota (C++11)
ranges::iota (C++23)
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transform_exclusive_scan (C++17)
Bit operations
bit_cast (C++20)
byteswap (C++23)
has_single_bit (C++20)
bit_ceil (C++20)
bit_floor (C++20)
bit_width (C++20)
rotl (C++20)
rotr (C++20)
countl_zero (C++20)
countl_one (C++20)
countr_zero (C++20)
countr_one (C++20)
popcount (C++20)
endian (C++20)

loglogflogl (C++11)(C++11)	computes natural (base e) logarithm (\({\small \ln{x} }\) $ln(x)$ ) (function)
log10log10flog10l (C++11)(C++11)	computes common (base 10) logarithm (\({\small \log_{10}{x} }\) $log 10 (x)$ ) (function)
log1plog1pflog1pl (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)
exp2exp2fexp2l (C++11)(C++11)(C++11)	returns 2 raised to the given power (\({\small 2^x}\) $2 x$ ) (function)