lgamma(3) - OpenBSD manual pages

NAME

lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, tgamma, tgammaf, tgammal, gamma, gammaf — log gamma functions

SYNOPSIS

#include <math.h>

extern int signgam;

double
lgamma(double x);

float
lgammaf(float x);

long double
lgammal(long double x);

double
lgamma_r(double x, int *signgamp);

float
lgammaf_r(float x, int *signgamp);

long double
lgammal_r(long double x, int *signgamp);

double
tgamma(double x);

float
tgammaf(float x);

long double
tgammal(long double x);

DESCRIPTION

lgamma(x) returns ln|Γ(x)| where

Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} dt

for x > 0 and

Γ (x) = \frac{π}{Γ (1 - x) \sin (π x)}

for x < 1.

The external integer signgam returns the sign of Γ(x). The lgammaf() function is a single precision version of lgamma(). The lgammal() function is an extended precision version of lgamma().

The lgamma_r(), lgammaf_r(), and lgammal_r() functions are thread-safe versions of lgamma(), lgammaf(), and lgammal() that return the sign via the signgamp pointer instead of modifying signgam.

The tgamma(x), tgammaf(x) and tgammal(x) functions return Γ(x), with no effect on signgam.

IDIOSYNCRASIES

Do not use the expression ‘signgam*exp(lgamma(x))’ to compute g := Γ(x). Instead use a program like this (in C):

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

Only after lgamma() has returned can signgam be correct.

For arguments in its range, tgamma() is preferred, as for positive arguments it is accurate to within one unit in the last place.

RETURN VALUES

lgamma() returns 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.

STANDARDS

The lgamma(), lgammaf(), lgammal(), tgamma(), tgammaf(), and tgammal() functions are expected to conform to ISO/IEC 9899:1999 (“ISO C99”).

The lgamma_r(), lgammaf_r(), and lgammal_r() functions are BSD extensions.

gamma() and gammaf() are deprecated aliases for lgamma() and lgammaf(), respectively.

HISTORY

A gamma() function first appeared in Version 5 AT&T UNIX. The lgamma() function first appeared in 4.3BSD. The tgamma() function first appeared in OpenBSD 4.4, and is based on the gamma() function that appeared in 4.4BSD as a function to compute Γ(x).