# log, logf, logl

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float logf( float arg ); | (1) | (since C99)
double log( double arg ); | (2) |
long double logl( long double arg ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define log( arg ) | (4) | (since C99)

1-3) Computes the natural (base e) logarithm of `arg`.
4) Type-generic macro: If `arg` has type long double, `logl` is called. Otherwise, if `arg` has integer type or the type double, `log` is called. Otherwise, `logf` is called. If `arg` is complex or imaginary, then the macro invokes the corresponding complex function (clogf, clog, clogl).

### Parameters

arg | - | floating point value

### Return value

If no errors occur, the natural (base-e) logarithm of `arg` (ln(arg) or log
e(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

### 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("log(1) = %f\n", log(1));
        printf("base-5 logarithm of 125 = %f\n", log(125)/log(5));
        // special values
        printf("log(1) = %f\n", log(1));
        printf("log(+Inf) = %f\n", log(INFINITY));
        //error handling
        errno = 0; feclearexcept(FE_ALL_EXCEPT);
        printf("log(0) = %f\n", log(0));
        if(errno == ERANGE) perror("    errno == ERANGE");
        if(fetestexcept(FE_DIVBYZERO)) puts("    FE_DIVBYZERO raised");
    }

Output:

    log(1) = 0.000000
    base-5 logarithm of 125 = 3.000000
    log(1) = 0.000000
    log(+Inf) = inf
    log(0) = -inf
        errno == ERANGE: Numerical result out of range
        FE_DIVBYZERO raised

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.6.7 The log functions (p: 244-245)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.3.7 The log functions (p: 522)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.6.7 The log functions (p: 225)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.3.7 The log functions (p: 459)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5.4.4 The log function

### See also

log10 log10f log10l (C99)(C99) | computes common (base-10) logarithm (log10(x)) (function)
log2 log2f log2l (C99)(C99)(C99) | computes base-2 logarithm (log2(x)) (function)
log1p log1pf log1pl (C99)(C99)(C99) | computes natural (base-e) logarithm of 1 plus the given number (ln(1+x)) (function)
exp expf expl (C99)(C99) | computes e raised to the given power (ex) (function)
clog clogf clogl (C99)(C99)(C99) | computes the complex natural logarithm (function)

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