log2, log2f, log2l

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< c‎ | numeric‎ | math
Common mathematical functions
Basic operations
Exponential functions
Power functions
Trigonometric and hyperbolic functions
Error and gamma functions
Nearest integer floating point operations
Floating point manipulation functions
Macro constants
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
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


  • 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 (ln(x))
computes common (base-10) logarithm (log10(x))
computes natural (base-e) logarithm of 1 plus the given number (ln(1+x))
computes 2 raised to the given power (2x)