log, logf, logl

Defined in header <math.h>
float       logf( float arg );
(1) (since C99)
double      log( double arg );
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).


arg - floating point value

Return value

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


#include <stdio.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <fenv.h>
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");


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


  • C17 standard (ISO/IEC 9899:2018):
    • The log functions (p: 178-179)
    • 7.25 Type-generic math <tgmath.h> (p: 272-273)
    • F.10.3.7 The log functions (p: 380)
  • C11 standard (ISO/IEC 9899:2011):
    • 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):
    • 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):
    • The log function

See also

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

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