HP-UX Reference (11i v1 00/12) - 3 Library Functions A-M (vol 6)

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lgamma(3M) lgamma(3M)

NAME

lgamma(), lgamma_r(), gamma(), signgam() - log gamma function

SYNOPSIS

#include <math.h>

double lgamma(double x);

double gamma(double x);

(TO BE WITHDRAWN)

extern int signgam;

double lgamma_r(double x, int *sign);

DESCRIPTION

lgamma() and gamma() return ln(|Γ(x)|), where Γ(x) is deﬁned as the integral, as t goes from zero

to inﬁnity, of exp(−t) times t to the power (x−1).

The sign of Γ(x) is returned in the external integer signgam. The argument x must not be zero or a nega-

tive integer. (lgamma() is deﬁned over the reals excluding the non-positive integers.)

The following C program fragment can be used to calculate Γ(x):

if ((y = lgamma(x)) > LN_MAXDOUBLE)

error( );

y = signgam * exp(y);

where if y is greater than LN_MAXDOUBLE , as deﬁned in the <values.h> header ﬁle,

exp() returns a

range error (see exp(3M)).

The log gamma function

lgamma() is not reentrant because it uses the global variable signgam. The

function

lgamma_r() is a reentrant version of lgamma() that can be used in multi-threaded applica-

tions. The function lgamma_r() returns the sign of Γ(x) in its parameter list, through the pointer sign.

The value pointed to by sign is +1 if Γ(x) is positive, -1 if it is negative.

The

gamma() function is functionally equivalent to lgamma(), and in the XPG4.2 standard it is marked

TO BE WITHDRAWN. A true gamma() function has been approved for inclusion in the C9X draft stan-

dard.

The ISO/ANSI C committee has approved the

lgamma() function for inclusion in the C9X draft standard.

To use these functions, compile either with the default

-Ae option or with the -Aa

and

-D_HPUX_SOURCE options. Make sure your program includes <

math.h>. Link in the math library by

specifying

-lm on the compiler or linker command line.

RETURN VALUE

If x is a non-positive integer, lgamma() and gamma() return HUGE_VAL.

If the correct value would overﬂow, lgamma() and gamma() return HUGE_VAL.

If the correct value after rounding would be smaller in magnitude than MINDOUBLE, lgamma() and

gamma() return zero.

If x is NaN, lgamma() and gamma() return NaN.

ERRORS

No errors are deﬁned.

WARNINGS

lgamma() and gamma() are unsafe in multi-thread applications. lgamma_r() is MT-Safe and should

be used instead.