LGAMMA(3M)                                                          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 zero 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 inaccu‐
       rate  values when x is almost a negative integer, and lets Γ(x) be com‐
       puted without conditional expressions.  Programmers should  not  assume
       that lgamma has settled down.

       At  some  time  in the future, the name _g_a_m_m_a 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 _g_a_m_m_a in its former
       sense, for what is now _l_g_a_m_m_a, have two choices:

       1) Use the old math library, _l_i_b_o_m.

       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  argu‐
       ments, _e_r_r_n_o is set to ERANGE; for very large arguments over/underflows
       will occur inside the _l_g_a_m_m_a routine.

SEE ALSO
       math(3M), infnan(3M)



4.3 Berkeley Distribution        May 12, 1986                       LGAMMA(3M)