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/* @(#)w_gamma.c 5.1 93/09/24 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 *

 */

/* BUG:  FIXME?

     According to Linux man pages for tgamma, lgamma, and gamma, the gamma

function was originally defined in BSD as implemented here--the log of the gamma

function.  BSD 4.3 changed the name to lgamma, apparently removing gamma.  BSD

4.4 re-introduced the gamma name with the more intuitive, without logarithm,

plain gamma function.  The C99 standard apparently wanted to avoid a problem

with the poorly-named earlier gamma and used tgamma when adding a plain

gamma function.

     So the current gamma is matching an old, bad definition, and not

matching a newer, better definition.  */

/*

FUNCTION

        <<gamma>>, <<gammaf>>, <<lgamma>>, <<lgammaf>>, <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, <<lgammaf_r>>, <<tgamma>>, and <<tgammaf>>--logarithmic and plain gamma functions

INDEX

gamma

INDEX

gammaf

INDEX

lgamma

INDEX

lgammaf

INDEX

gamma_r

INDEX

gammaf_r

INDEX

lgamma_r

INDEX

lgammaf_r

INDEX

tgamma

INDEX

tgammaf

ANSI_SYNOPSIS

#include <math.h>

double gamma(double <[x]>);

float gammaf(float <[x]>);

double lgamma(double <[x]>);

float lgammaf(float <[x]>);

double gamma_r(double <[x]>, int *<[signgamp]>);

float gammaf_r(float <[x]>, int *<[signgamp]>);

double lgamma_r(double <[x]>, int *<[signgamp]>);

float lgammaf_r(float <[x]>, int *<[signgamp]>);

double tgamma(double <[x]>);

float tgammaf(float <[x]>);

TRAD_SYNOPSIS

#include <math.h>

double gamma(<[x]>)

double <[x]>;

float gammaf(<[x]>)

float <[x]>;

double lgamma(<[x]>)

double <[x]>;

float lgammaf(<[x]>)

float <[x]>;

double gamma_r(<[x]>, <[signgamp]>)

double <[x]>;

int <[signgamp]>;

float gammaf_r(<[x]>, <[signgamp]>)

float <[x]>;

int <[signgamp]>;

double lgamma_r(<[x]>, <[signgamp]>)

double <[x]>;

int <[signgamp]>;

float lgammaf_r(<[x]>, <[signgamp]>)

float <[x]>;

int <[signgamp]>;

double tgamma(<[x]>)

double <[x]>;

float tgammaf(<[x]>)

float <[x]>;

DESCRIPTION

<<gamma>> calculates

@tex

$\mit ln\bigl(\Gamma(x)\bigr)$,

@end tex

the natural logarithm of the gamma function of <[x]>.  The gamma function

(<<exp(gamma(<[x]>))>>) is a generalization of factorial, and retains

the property that

@ifnottex

<<exp(gamma(N))>> is equivalent to <<N*exp(gamma(N-1))>>.

@end ifnottex

@tex

$\mit \Gamma(N)\equiv N\times\Gamma(N-1)$.

@end tex

Accordingly, the results of the gamma function itself grow very

quickly.  <<gamma>> is defined as

@tex

$\mit ln\bigl(\Gamma(x)\bigr)$ rather than simply $\mit \Gamma(x)$

@end tex

@ifnottex

the natural log of the gamma function, rather than the gamma function

itself,

@end ifnottex

to extend the useful range of results representable.

The sign of the result is returned in the global variable <<signgam>>,

which is declared in math.h.

<<gammaf>> performs the same calculation as <<gamma>>, but uses and

returns <<float>> values.

<<lgamma>> and <<lgammaf>> are alternate names for <<gamma>> and

<<gammaf>>.  The use of <<lgamma>> instead of <<gamma>> is a reminder

that these functions compute the log of the gamma function, rather

than the gamma function itself.

The functions <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, and

<<lgammaf_r>> are just like <<gamma>>, <<gammaf>>, <<lgamma>>, and

<<lgammaf>>, respectively, but take an additional argument.  This

additional argument is a pointer to an integer.  This additional

argument is used to return the sign of the result, and the global

variable <<signgam>> is not used.  These functions may be used for

reentrant calls (but they will still set the global variable <<errno>>

if an error occurs).

<<tgamma>> and <<tgammaf>> are the "true gamma" functions, returning

@tex

$\mit \Gamma(x)$,

@end tex

the gamma function of <[x]>--without a logarithm.

(They are apparently so named because of the prior existence of the old,

poorly-named <<gamma>> functions which returned the log of gamma up

through BSD 4.2.)

RETURNS

Normally, the computed result is returned.

When <[x]> is a nonpositive integer, <<gamma>> returns <<HUGE_VAL>>

and <<errno>> is set to <<EDOM>>.  If the result overflows, <<gamma>>

returns <<HUGE_VAL>> and <<errno>> is set to <<ERANGE>>.

You can modify this error treatment using <<matherr>>.

PORTABILITY

Neither <<gamma>> nor <<gammaf>> is ANSI C.  It is better not to use either

of these; use <<lgamma>> or <<tgamma>> instead.@*

<<lgamma>>, <<lgammaf>>, <<tgamma>>, and <<tgammaf>> are nominally C standard

in terms of the base return values, although the <<matherr>> error-handling

is not standard, nor is the <[signgam]> global for <<lgamma>>.

*/

/* double gamma(double x)

 * Return the logarithm of the Gamma function of x.

 *

 * Method: call gamma_r

 */

#include "fdlibm.h"

#include <reent.h>

#include <errno.h>

#ifndef _DOUBLE_IS_32BITS

#ifdef __STDC__

        double gamma(double x)

#else

        double gamma(x)

        double x;

#endif

{

#ifdef _IEEE_LIBM

        return __ieee754_gamma_r(x,&(_REENT_SIGNGAM(_REENT)));

#else

        double y;

        struct exception exc;

        y = __ieee754_gamma_r(x,&(_REENT_SIGNGAM(_REENT)));

        if(_LIB_VERSION == _IEEE_) return y;

        if(!finite(y)&&finite(x)) {

#ifndef HUGE_VAL 

#define HUGE_VAL inf

            double inf = 0.0;

            SET_HIGH_WORD(inf,0x7ff00000);      /* set inf to infinite */

#endif

            exc.name = "gamma";

            exc.err = 0;

            exc.arg1 = exc.arg2 = x;

            if (_LIB_VERSION == _SVID_)

                exc.retval = HUGE;

            else

                exc.retval = HUGE_VAL;

            if(floor(x)==x&&x<=0.0) {

                /* gamma(-integer) or gamma(0) */

                exc.type = SING;

                if (_LIB_VERSION == _POSIX_)

                  errno = EDOM;

                else if (!matherr(&exc)) {

                  errno = EDOM;

                }

            } else {

                /* gamma(finite) overflow */

                exc.type = OVERFLOW;

                if (_LIB_VERSION == _POSIX_)

                  errno = ERANGE;

                else if (!matherr(&exc)) {

                  errno = ERANGE;

                }

            }

            if (exc.err != 0)

               errno = exc.err;

            return exc.retval;

        } else

            return y;

#endif

}

#endif /* defined(_DOUBLE_IS_32BITS) */