lgamma, lgammaf, lgammal

float       lgammaf( float arg );

double      lgamma( double arg );

long double lgammal( long double arg );

#define lgamma( arg )

Parameters

Return value

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

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),

• If the argument is 1, +0 is returned
• If the argument is 2, +0 is returned
• If the argument is ±0, +∞ is returned and FE_DIVBYZERO is raised
• If the argument is a negative integer, +∞ is returned and FE_DIVBYZERO is raised
• If the argument is ±∞, +∞ is returned.
• If the argument is NaN, NaN is returned

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.

Example

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

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

References

• C17 standard (ISO/IEC 9899:2018):
• 7.12.8.3 The lgamma functions (p: 182)
• 7.25 Type-generic math <tgmath.h> (p: 272-273)
• F.10.5.3 The lgamma functions (p: 383)
• C11 standard (ISO/IEC 9899:2011):
• 7.12.8.3 The lgamma functions (p: 250)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• F.10.5.3 The lgamma functions (p: 525)
• C99 standard (ISO/IEC 9899:1999):
• 7.12.8.3 The lgamma functions (p: 231)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• F.9.5.3 The lgamma functions (p: 462)

See also

External links

Weisstein, Eric W. "Log Gamma Function." From MathWorld--A Wolfram Web Resource.