LGAMMA(3)                 386BSD Programmer's Manual                 LGAMMA(3)

NAME
     lgamma - log gamma function

SYNOPSIS
     #include <math.h>

     double
     lgamma(double x)

DESCRIPTION
     Lgamma returns ln|gamma(x)|.

     The external integer signgam returns the sign of gamma(x) .

IDIOSYNCRASIES
     Do not use the expression ``signgam*exp(lgamma(x))'' to compute g :=
     gamma(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.  Note too that
     gamma(x) must overflow when x is large enough, underflow when -x is large
     enough, and spawn a division by zero when x is a nonpositive integer.

     Only in the UNIX math library for C was the name gamma ever attached to
     lngamma.  Elsewhere, for instance in IBM's FORTRAN library, the name
     GAMMA belongs to gamma and the name ALGAMA to lngamma in single
     precision; in double the names are DGAMMA and DLGAMA. Why should C be
     different?

     Archaeological records suggest that C's gamma originally delivered
     ln(gamma(|x|)).  Later, the program gamma was changed to cope with
     negative arguments x 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, and lets gamma(x)
     be computed without conditional expressions.  Programmers should not
     assume that lgamma() has settled down.

     At some time in the future, the name gamma will be rehabilitated and used
     for the gamma function, just as is done in FORTRAN. The reason for this
     is not so much compatibility with FORTRAN as a desire to achieve greater
     speed for smaller values of |x| and greater accuracy for larger values.

     Meanwhile, programmers who have to use the name gamma in its former
     sense, for what is now lgamma(), have two choices:

     1.      Use the old math library, libom.

     2.      Add the following program to your others:

             #include <math.h>
             double gamma(x)
             double x;
             {
                     return (lgamma(x));
             }

DIAGNOSTICS
     The reserved operand is returned on a VAX for negative integer arguments,
     errno is set to ERANGE; for very large arguments over/underflows will
     occur inside the lgamma() routine.

SEE ALSO
     math(3),  infnan(3)

HISTORY
     The lgamma function appeared in 4.3BSD.

4.3 Berkeley Distribution         May 6, 1991                                2