/C

# log2, log2f, log2l

float       log2f( float arg );
(1) (since C99)
double      log2( double arg );
(2) (since C99)
long double log2l( long double arg );
(3) (since C99)
#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.

### Parameters

 arg - floating point value

### 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

#include <stdio.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <fenv.h>
// #pragma STDC FENV_ACCESS ON
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

### References

• C17 standard (ISO/IEC 9899:2018):
• 7.12.6.10 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):
• 7.12.6.10 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):
• 7.12.6.10 The log2 functions (p: 226)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• F.9.3.10 The log2 functions (p: 459)

 loglogflogl (C99)(C99) computes natural (base-e) logarithm ($${\small \ln{x} }$$ln(x)) (function) log10log10flog10l (C99)(C99) computes common (base-10) logarithm ($${\small \log_{10}{x} }$$log10(x)) (function) log1plog1pflog1pl (C99)(C99)(C99) computes natural (base-e) logarithm of 1 plus the given number ($${\small \ln{(1+x)} }$$ln(1+x)) (function) exp2exp2fexp2l (C99)(C99)(C99) computes 2 raised to the given power ($${\small 2^x}$$2x) (function) C++ documentation for log2