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Annotation of 43BSDReno/lib/libm/common_source/lgamma.3, revision 1.1.1.1

1.1       root        1: .\" Copyright (c) 1985 Regents of the University of California.
                      2: .\" All rights reserved.  The Berkeley software License Agreement
                      3: .\" specifies the terms and conditions for redistribution.
                      4: .\"
                      5: .\"    @(#)lgamma.3    6.2 (Berkeley) 5/12/86
                      6: .\"
                      7: .TH LGAMMA 3M  "May 12, 1986"
                      8: .UC 6
                      9: .SH NAME
                     10: lgamma \- log gamma function
                     11: .SH SYNOPSIS
                     12: .nf
                     13: .B #include <math.h>
                     14: .PP
                     15: .B double lgamma(x)
                     16: .B double x;
                     17: .fi
                     18: .SH DESCRIPTION
                     19: .nf
                     20: .ta \w'Lgamma returns ln\||\(*G(x)| where'u+1n +1.7i
                     21: .if t \{\
                     22: Lgamma returns ln\||\(*G(x)| where     \(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt for x > 0 and
                     23: .br
                     24:        \(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.  \}
                     25: .if n \
                     26: Lgamma returns ln\||\(*G(x)|.
                     27: .ta
                     28: .fi
                     29: .PP
                     30: The external integer signgam returns the sign of
                     31: \(*G(x) .
                     32: .SH IDIOSYNCRASIES
                     33: Do \fBnot\fR use the expression signgam\(**exp(lgamma(x))
                     34: to compute g := \(*G(x).  Instead use a program like this (in C):
                     35: .RS
                     36: lg = lgamma(x); g = signgam\(**exp(lg);
                     37: .RE
                     38: .PP
                     39: Only after lgamma has returned can signgam be correct.
                     40: Note too that \(*G(x) must overflow when x is large enough,
                     41: underflow when \-x is large enough, and spawn a division by zero
                     42: when x is a nonpositive integer.
                     43: .PP
                     44: Only in the UNIX math library for C was the name gamma ever attached
                     45: to ln\(*G.  Elsewhere, for instance in IBM's FORTRAN library, the name
                     46: GAMMA belongs to \(*G and the name ALGAMA to ln\(*G in single precision;
                     47: in double the names are DGAMMA and DLGAMA.  Why should C be different?
                     48: .PP
                     49: Archaeological records suggest that C's gamma originally delivered
                     50: ln(\(*G(|x|)).  Later, the program gamma was changed to
                     51: cope with negative arguments x in a more conventional way, but
                     52: the documentation did not reflect that change correctly.  The most
                     53: recent change corrects inaccurate values when x is almost a
                     54: negative integer, and lets \(*G(x) be computed without
                     55: conditional expressions.  Programmers should not assume that
                     56: lgamma has settled down.
                     57: .PP
                     58: At some time in the future, the name \fIgamma\fR will be rehabilitated
                     59: and used for the gamma function, just as is done in FORTRAN.
                     60: The reason for this is not so much compatibility with FORTRAN as a
                     61: desire to achieve greater speed for smaller values of |x| and greater
                     62: accuracy for larger values.
                     63: .PP
                     64: Meanwhile, programmers who have to use the name \fIgamma\fR in its former
                     65: sense, for what is now \fIlgamma\fR, have two choices:
                     66: .IP 1) \w'1)\0'u
                     67: Use the old math library, \fIlibom\fR.
                     68: .IP 2) \w'1)\0'u
                     69: Add the following program to your others:
                     70: .RS
                     71: .nf
                     72: \fB#include <math.h>
                     73: double gamma(x)
                     74: double x;
                     75: {
                     76: .RS
                     77: \fBreturn (lgamma(x));
                     78: .RE
                     79: }\fR
                     80: .RE
                     81: .fi
                     82: .SH DIAGNOSTICS
                     83: The reserved operand is returned on a VAX for negative integer arguments,
                     84: \fIerrno\fR is set to ERANGE; for very large arguments over/underflows will
                     85: occur inside the \fIlgamma\fP routine.
                     86: .SH SEE ALSO
                     87: math(3M), infnan(3M)

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