# log2, log2f, log2l

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< c‎ | numeric‎ | math

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.

### Parameters

arg | - | floating point value

### Return value

If no errors occur, the base-2 logarithm of `arg` (log2(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 <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)

### See also

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

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