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GAMMA(3M)							     GAMMA(3M)

NAME    [Toc]    [Back]

     lgamma, gamma, lgammal, gammal - log gamma	function

SYNOPSIS    [Toc]    [Back]

     #include <math.h>

     double gamma(double x);
     double lgamma(double x);
     long double gammal(long double x);
     long double lgammal(long double x);

     extern int	signgam;
     extern int	signgaml;

DESCRIPTION    [Toc]    [Back]

     lgamma and	gamma return ln|(GAMMA(x))|, where GAMMA is the
     mathematical gamma	function.

     gammal and	lgammal	are the	long double versions of	the log	gamma

     gamma and lgamma are identical, as	are gammal and lgammal.

     The external integer signgam returns the sign of GAMMA(x),	and the
     external integer signgaml returns the sign	of GAMMAL(x).

IDIOSYNCRASIES    [Toc]    [Back]

     Do	not use	the expression signgam*exp(gamma(x)) to	compute	g := GAMMA(x).
     Instead use a program like	this (in C):
	  lg = gamma(x); g = signgam*exp(lg);

     Only after	gamma has returned can signgam be correct.  Note too that
     GAMMA(x) must overflow when x is large enough, and	is undefined when x is
     a nonpositive integer.

     Analogous rules apply to gammal and signgaml.

     The following C program fragment might be used to calculate G if the
     overflow needs to be detected:
	   if ((y = gamma(x)) >	LN_MAXDOUBLE)
	   y = signgam * exp(y);

     where LN_MAXDOUBLE	is the least value that	causes exp(3M) to overflow and
     is	defined	in the <values.h> header file.

     Only in the UNIX math library for C was the name gamma ever attached to
     ln	G.   Elsewhere (in some	FORTRAN	libraries) the name GAMMA belongs to G
     and the name ALGAMMA to ln	G in single precision;	in double the usual
     names are DGAMMA and DLGAMMA in FORTRAN.  Why should C be different?

									Page 1

GAMMA(3M)							     GAMMA(3M)

     Archeological records suggest that	C's gamma originally delivered	ln(G
     (x)).  Later, the program gamma was changed to cope with negative
     arguments in a more conventional way, but the documentation did not
     reflect that change correctly.  The most recent change corrects
     inaccurate	values when x is almost	a negative integer.

     Some math libraries have changed the name of this function	to lgamma() to
     suggest its real functionality.
     On	SGI systems, the name gamma is currently maintained as a synonym to
     lgamma for	compatibility.	It may disappear in a future release.

NOTES    [Toc]    [Back]

     lgamma and	gamma are not ANSI-C functions.	 If you	compile	with flag
     -ansi or -ansiposix, you must supply your own prototypes for these
     functions or you will get incorrect results. (See the prototypes defined
     in	/usr/include/math.h)

DIAGNOSTICS    [Toc]    [Back]

     In	the diagnostics	below, functions in the	standard math library libm.a,
     are referred to as	-lm versions, those in math library libmx.a are
     referred to as -lmx versions, and those in	the the	BSD math library
     libm43.a are referred to as -lm43 versions.  The -lm and -lmx versions
     always return the default Quiet NaN and set errno to EDOM when a NaN is
     used as an	argument.  A NaN argument usually causes the -lm43 versions to
     return the	same argument.	The -lm43 versions never set errno.  The value
     of	HUGE_VAL is IEEE Infinity.

     The gamma functions return	HUGE_VAL when the argument is zero or a
     negative integer. The -lm and -lmx	versions also set errno	to EDOM.
     When the correct value would overflow, the	gamma functions	return
     HUGE_VAL. The -lm and -lmx	versions also set errno	to ERANGE.

     See matherr(3M) for a description of error	handling for -lmx functions.

SEE ALSO    [Toc]    [Back]

     math(3M), matherr(3M)

									PPPPaaaaggggeeee 2222
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