lgamma

Name

lgamma, lgamma_r, lgammaf, lgammal, lgammaf_r
gamma, gamma_r, gammaf, gammal, gammaf_r

- log gamma function

Library

libm.lib

Synopsis

#include <math.h>

extern int signgam;

double lgamma (double x);

double lgamma_r (double x, int *signgamp);

float lgammaf (float x);

long double lgammal (long double x);

float lgammaf_r (float x, int *signgamp);

double gamma (double x);

double gamma_r (double x, int *signgamp);

float gammaf (float x);

long double gammal (long double x);

float gammaf_r (float x, int *signgamp);

Return values

gamma, gamma_r, gammaf, gammaf_r, lgamma, lgamma_r, lgammaf, and lgammaf_r return appropriate values unless an argument is out of range. Overflow will occur for sufficiently large positive values, and non-positive integers. For large non-integer negative values, tgamma will underflow.

Detailed description

lgamma (x);
and lgammaf (x);
return ln||^_(x)| where |^_(x) = I₀₀^oo0 t^x-10 e^-t0 dt for x > 0 and |^_(x) = pi/(|^_(1-x)sin(pix)) for x < 1. return ln||^_(x)|.

The external integer signgam returns the sign of |^_(x).

lgamma_r (x, signgamp);
and lgammaf_r (x, signgamp);
provide the same functionality as lgamma (x);
and lgammaf (x);
but the caller must provide an integer to store the sign of |^_(x).

gamma, gammaf, gamma_r, and gammaf_r are deprecated aliases for lgamma, lgammaf, lgamma_r, and lgammaf_r, respectively. lgammal (and);
gammal (are, just, alias, to, the, functions);
lgamma (and);
gamma respectively.

Idiosyncrasies

Do not use the expression "signgam*exp(lgamma(x))" to compute g := |^_(x). Instead use a program like this (in C):

lg = lgamma(x); g = signgam*exp(lg);

Only after lgamma or lgammaf has returned can signgam be correct.

Examples

#include <math.h>
int main( void )
{
   double x1 = 0.0,  y;
   y = lgamma( 0.0 );
   printf( "lgamma(%f) = %f and signgam = %d\n", x1, signgam, y );
   y = lgammaf( 0.0 );
   printf( "lgammaf(%f) = %f and signgam = %d\n", x1, signgam, y );
   y = lgammal( 0.0 );
   printf( "lgammal(%f) = %f and signgam = %d\n", x1, signgam, y );
   y = gamma( 0.0 );
   printf( "gamma(%f) = %f and signgam = %d\n", x1, signgam, y );
   y = gammaf( 0.0 );
   printf( "gammaf(%f) = %f and signgam = %d\n", x1, signgam, y );
   y = gammal( 0.0 );
   printf( "gammal(%f) = %f and signgam = %d\n", x1, signgam, y );
}

Output

lgamma ( 0.0) = Inf and signgam = 1
lgammaf( 0.0 ) = Inf and signgam = 1
lgammal( 0.0 ) = Inf and signgam = 1
gamma ( 0.0 ) = Inf and signgam = 1
gammaf( 0.0 ) = Inf and signgam = 1
gammal( 0.0 ) = Inf and signgam = 1

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