lgamma - log gamma function
Lgamma returns ln|| (x)|.
The external integer signgam returns the sign of | (x) .
Do not use the expression signgam*exp(lgamma(x)) to compute g := | (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 | (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 m_th library for C was the na_e gamma ever attached to ln| . Elsewhere, for instance in IBM's FORTRAN library, the name
GAMMA belongs to | and the name ALGAMA to ln| 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(| (|x|)). Later, the program gamma was changed to cope with negative
arguments x in a more conventional way, but the documentation did _ot reflect that change correctly. The most recent change corrects inac-
curate values when x is almost a negative integer, and lets | (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
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:
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.
4.3 Berkeley Distribution May 12, 1986 LGAMMA(3M)