lgamma(), lgammaf(), lgammal() — Log gamma function

Standards

Standards / Extensions	C or C++	Dependencies
XPG4 XPG4.2 C99 Single UNIX Specification, Version 3 C++ TR1 C99	both

Format

#define _XOPEN_SOURCE
#include <math.h>

double lgamma(double x);
extern int signgam;
int *__signgam(void);

C99:

#define _ISOC99_SOURCE
#include <math.h>

double lgamma(double x);
float lgammaf(float x);
long double lgammal(long double x);

C++ TR1 C99:

#define _TR1_C99
#include <math.h>

float lgamma(float x); 
long double lgamma(long double x);

General description

The lgamma() function computes the

where

is defined as

The sign of

is returned in the external integer signgam. The argument x may not be a non-positive integer.

In a multithreaded process, each thread has its own instance of the signgam variable. Threads access their instances of the variable by calling the __signgam() function. See __signgam() — Return signgam reference. The math.h header (see math.h) redefines the string “signgam” to an invocation of the __signham function. The actual signgam external variable is used to store the signgam value for the IPT.

Note: The following table shows the viable formats for these functions. See IEEE binary floating-point for more information about IEEE Binary Floating-Point.

Function	Hex	IEEE
lgamma	X	X
lgammaf	X	X
lgammal	X	X

Returned value

If successful, lgamma() returns the above function of its argument.

lgamma() will fail under the following conditions:

If the result overflows, the function will return HUGE_VAL and set errno to ERANGE.
If x is a non-positive integer and _XOPEN_SOURCE is defined, lgamma() returns HUGE_VAL and sets errno to EDOM.
If x is a non-positive integer and _ISOC99_SOURCE is defined, lgamma() returns HUGE_VAL and sets errno to ERANGE.

Note: If both _XOPEN_SOURCE and _ISOC99_SOURCE are defined, the _ISOC99_SOURCE behavior will take precedence.

Special behavior for IEEE: Even when _XOPEN_SOURCE is defined and _ISOC99_SOURCE not, lgamma() returns HUGE_VAL and sets errno to ERANGE.

Example

/*
   This example uses lgamma() to calculate ln(|G(x)|), where x = 42.
 */
#include <math.h>
#include <stdio.h>

int main(void)
{
   double x=42, g_at_x;

   g_at_x = exp(lgamma(x));       /* g_at_x = 3.345253e+49 */
   printf ("The value of G(%4.2f) is %7.2e\n", x, g_at_x);
}

Output

The value of G(42.00) is 3.35e+49