lgamma, lgammaf, lgammal - cppreference.com (original) (raw)

Defined in header <math.h>
float lgammaf( float arg ); (1) (since C99)
double lgamma( double arg ); (2) (since C99)
long double lgammal( long double arg ); (3) (since C99)
Defined in header <tgmath.h>
#define lgamma( arg ) (4) (since C99)

1-3) Computes the natural logarithm of the absolute value of the gamma function of arg.

  1. Type-generic macro: If arg has type long double, lgammal is called. Otherwise, if arg has integer type or the type double, lgamma is called. Otherwise, lgammaf is called.

Contents

[edit] Parameters

arg - floating-point value

[edit] Return value

If no errors occur, the value of the logarithm of the gamma function of arg, that is \(\log_{e}|{\int_0^\infty t^{arg-1} e^{-t} \mathsf{d}t}|\)loge|∫∞
0_t_arg-1
e_-t d_t|, is returned.

If a pole error occurs, +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL is returned.

If a range error due to overflow occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned.

[edit] Error handling

Errors are reported as specified in math_errhandling.

If arg is zero or is an integer less than zero, a pole error may occur.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

[edit] Notes

If arg is a natural number, lgamma(arg) is the logarithm of the factorial of arg - 1.

The POSIX version of lgamma is not thread-safe: each execution of the function stores the sign of the gamma function of arg in the static external variable signgam. Some implementations provide lgamma_r, which takes a pointer to user-provided storage for singgam as the second parameter, and is thread-safe.

There is a non-standard function named gamma in various implementations, but its definition is inconsistent. For example, glibc and 4.2BSD version of gamma executes lgamma, but 4.4BSD version of gamma executes tgamma.

[edit] Example

#include <errno.h> #include <fenv.h> #include <float.h> #include <math.h> #include <stdio.h> // #pragma STDC FENV_ACCESS ON   int main(void) { printf("lgamma(10) = %f, log(9!) = %f\n", lgamma(10), log(2 * 3 * 4 * 5 * 6 * 7 * 8 * 9)); const double pi = acos(-1); printf("lgamma(0.5) = %f, log(sqrt(pi)) = %f\n", log(sqrt(pi)), lgamma(0.5)); // special values printf("lgamma(1) = %f\n", lgamma(1)); printf("lgamma(+Inf) = %f\n", lgamma(INFINITY));   // error handling errno = 0; feclearexcept(FE_ALL_EXCEPT); printf("lgamma(0) = %f\n", lgamma(0)); if (errno == ERANGE) perror(" errno == ERANGE"); if (fetestexcept(FE_DIVBYZERO)) puts(" FE_DIVBYZERO raised"); }

Possible output:

lgamma(10) = 12.801827, log(9!) = 12.801827 lgamma(0.5) = 0.572365, log(sqrt(pi)) = 0.572365 lgamma(1) = 0.000000 lgamma(+Inf) = inf lgamma(0) = inf errno == ERANGE: Numerical result out of range FE_DIVBYZERO raised

[edit] References

[edit] See also