std::log, std::logf, std::logl

Defined in header <cmath>
float       log ( float arg );
float       logf( float arg );
(since C++11)
double      log ( double arg );
long double log ( long double arg );
long double logl( long double arg );
(since C++11)
double      log ( IntegralType arg );
(4) (since C++11)
1-3) Computes the natural (base e) logarithm of arg.
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (2) (the argument is cast to double).


arg - value of floating-point or Integral type

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 <iostream>
#include <cmath>
#include <cerrno>
#include <cstring>
#include <cfenv>
int main()
    std::cout << "log(1) = " << std::log(1) << '\n'
              << "base-5 logarithm of 125 = " << std::log(125)/std::log(5) << '\n';
    // special values
    std::cout << "log(1) = " << std::log(1) << '\n'
              << "log(+Inf) = " << std::log(INFINITY) << '\n';
    // error handling
    errno = 0;
    std::cout << "log(0) = " << std::log(0) << '\n';
    if (errno == ERANGE)
        std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_DIVBYZERO))
        std::cout << "    FE_DIVBYZERO raised\n";

Possible output:

log(1) = 0
base-5 logarithm of 125 = 3
log(1) = 0
log(+Inf) = inf
log(0) = -inf
    errno == ERANGE: Numerical result out of range
    FE_DIVBYZERO raised

See also

computes common (base 10) logarithm (\({\small \log_{10}{x} }\)log10(x))
base 2 logarithm of the given number (\({\small \log_{2}{x} }\)log2(x))
natural logarithm (to base e) of 1 plus the given number (\({\small \ln{(1+x)} }\)ln(1+x))
returns e raised to the given power (\({\small e^x}\)ex)
complex natural logarithm with the branch cuts along the negative real axis
(function template)
applies the function std::log to each element of valarray
(function template)
C documentation for log

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