log2, log2f, log2l

Defined in header <math.h>
float       log2f( float arg );
(1) (since C99)
double      log2( double arg );
(2) (since C99)
long double log2l( long double arg );
(3) (since C99)
Defined in header <tgmath.h>
#define log2( arg )
(4) (since C99)
1-3) Computes the base 2 logarithm of arg.
4) Type-generic macro: If arg has type long double, log2l is called. Otherwise, if arg has integer type or the type double, log2 is called. Otherwise, log2f is called.


arg - floating point value

Return value

If no errors occur, the base-2 logarithm of arg (log
(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


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


#include <stdio.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <fenv.h>
int main(void)
    printf("log2(65536) = %f\n", log2(65536));
    printf("log2(0.125) = %f\n", log2(0.125));
    printf("log2(0x020f) = %f (highest set bit is in position 9)\n", log2(0x020f));
    printf("base-5 logarithm of 125 = %f\n", log2(125)/log2(5));
    // special values
    printf("log2(1) = %f\n", log2(1));
    printf("log2(+Inf) = %f\n", log2(INFINITY));
    //error handling
    errno = 0; feclearexcept(FE_ALL_EXCEPT);
    printf("log2(0) = %f\n", log2(0));
    if(errno == ERANGE) perror("    errno == ERANGE");
    if(fetestexcept(FE_DIVBYZERO)) puts("    FE_DIVBYZERO raised");

Possible output:

log2(65536) = 16.000000
log2(0.125) = -3.000000
log2(0x020f) = 9.041659 (highest set bit is in position 9)
base-5 logarithm of 125 = 3.000000
log2(1) = 0.000000
log2(+Inf) = inf
log2(0) = -inf
    errno == ERANGE: Numerical result out of range
    FE_DIVBYZERO raised


  • C17 standard (ISO/IEC 9899:2018):
    • The log2 functions (p: 179)
    • 7.25 Type-generic math <tgmath.h> (p: 272-273)
    • F.10.3.10 The log2 functions (p: 381)
  • C11 standard (ISO/IEC 9899:2011):
    • The log2 functions (p: 246)
    • 7.25 Type-generic math <tgmath.h> (p: 373-375)
    • F.10.3.10 The log2 functions (p: 522)
  • C99 standard (ISO/IEC 9899:1999):
    • The log2 functions (p: 226)
    • 7.22 Type-generic math <tgmath.h> (p: 335-337)
    • F.9.3.10 The log2 functions (p: 459)

See also

computes natural (base-e) logarithm (\({\small \ln{x} }\)ln(x))
computes common (base-10) logarithm (\({\small \log_{10}{x} }\)log10(x))
computes natural (base-e) logarithm of 1 plus the given number (\({\small \ln{(1+x)} }\)ln(1+x))
computes 2 raised to the given power (\({\small 2^x}\)2x)
C++ documentation for log2

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