GAMMA 3 "04 August 2000" "Version 1.00"

Table of contents


NAME

gamma - Single-precision Gamma(x)

SYNOPSIS

Fortran (77, 90, 95, HPF):
f77 [ flags ] file(s) ... -L/usr/local/lib -lgjl
REAL FUNCTION gamma(x)
REAL             x
C (K&R, 89, 99), C++ (98):
cc [ flags ] -I/usr/local/include file(s) ... -L/usr/local/lib -lgjl
Use
#include <gampsi.h>
to get this prototype:
fortran_real gamma(const fortran_real * x_);

NB: The definition of C/C++ data types fortran_ xxx, and the mapping of Fortran external names to C/C++ external names, is handled by the C/C++ header file. That way, the same function or subroutine name can be used in C, C++, and Fortran code, independent of compiler conventions for mangling of external names in these programming languages.

Last code modification: 04-Aug-2000


DESCRIPTION

Compute and return the value of the Gamma(x) function for single-precision x.

This code correctly handles the case where x is NaN, for which Gamma(NaN) is a NaN, and the case where x is sufficiently large and positive, or takes one of the integer values 0, -1, -2, -3, ..., for which Gamma(x) = +Infinity, a special value in IEEE 754 arithmetic.

This code is derived from code given by

W. J. Cody
Algorithm 715: SPECFUN --- A Portable FORTRAN
Package of Special Function Routines and Test Drivers
ACM Trans. Math. Software 19(1) 22--32, March 1993.

but has been augmented for support of IEEE 754 arithmetic, and extended with a new rational Pade approximation for x*Gamma(x) in [1,2], and new algorithms for argument reduction.


SEE ALSO

dgamma(3), dpsi(3), dpsiln(3), psi(3), psiln(3), qgamma(3), qpsi(3), qpsiln(3).

AUTHORS

The algorithms and code are described in detail in the paper
Algorithm xxx: Quadruple-Precision Gamma(x) and psi(x) Functions for Real Arguments
in ACM Transactions on Mathematical Software, Volume ??, Number ??, Pages ????--???? and ????--????, 2001, by
Nelson H. F. Beebe
Center for Scientific Computing
University of Utah
Department of Mathematics, 110 LCB
155 S 1400 E RM 233
Salt Lake City, UT 84112-0090
Tel: +1 801 581 5254
FAX: +1 801 581 4148
Email: beebe@math.utah.edu, beebe@acm.org, beebe@computer.org
WWW URL: http://www.math.utah.edu/~beebe
and
James S. Ball
University of Utah
Department of Physics
Salt Lake City, UT 84112-0830
USA
Tel: +1 801 581 8397
FAX: +1 801 581 6256
Email: ball@physics.utah.edu
WWW URL: http://www.physics.utah.edu/people/faculty/ball.html