LGAMMA(3M)                           BSD                            LGAMMA(3M)



NAME
     lgamma - log gamma function

SYNOPSIS
     #include <math.h>

     double lgamma(x)
     double x;

DESCRIPTION
     lgamma returns ln|Γ(x)|.

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

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 has returned can signgam be correct.  Note too that
     Γ(x) must overflow when x is large enough, underflow when -x is large
     enough, and spawn a division by 0 when x is a nonpositive integer.

     Only in the UNIX math library for C was the name "gamma" ever attached to
     lnΓ.  Elsewhere, for instance in IBM*'s FORTRAN library, the name GAMMA
     belongs to Γ and the name ALGAMA to lnΓ 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(Γ(|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 Γ(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:

     ⊕  Use the old math library, libom.

     ⊕  Add the following program to your others:

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

SEE ALSO
     math(3M)

NOTES
     *IBM is a registered trademark of International Business Machines Corp.