NAME

lgamma, lgamma_r, lgammaf, lgammaf_r, gamma, gamma_r, gammaf, gammaf_r, tgamma, tgammaf — log gamma functions, gamma function

LIBRARY

Math Library (libm, -lm)

SYNOPSIS

#include < math.h>

extern int signgam;

double
lgamma( double x);

double
lgamma_r( double x, int *signgamp);

float
lgammaf( float x);

float
lgammaf_r( float x, int *signgamp);

double
gamma( double x);

double
gamma_r( double x, int *signgamp);

float
gammaf( float x);

float
gammaf_r( float x, int *signgamp);

double
tgamma( double x);

float
tgammaf( float x);

DESCRIPTION

lgamma( x) and lgammaf( x) return ln|Γ(x)|. The external integer signgam returns the sign of Γ(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 Γ(x).

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

gamma(), gammaf(), gamma_r(), and gammaf_r() are deprecated aliases for lgamma(), lgammaf(), lgamma_r(), and lgammaf_r(), respectively.

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() or lgammaf() 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. Exponentiation of lgamma() will lose up to 10 significant bits.

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.

SEE ALSO

math(3)

STANDARDS

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

HISTORY

The lgamma() function appeared in 4.3BSD. The gamma() function appeared in 4.4BSD as a function which computed Γ(x). This version was used in FreeBSD 1.1. The name gamma() was originally dedicated to the lgamma() function, and that usage was restored by switching to Sun's fdlibm in FreeBSD 1.1.5. The tgamma() function appeared in FreeBSD 5.0.