man3/tgamma.3

   1 .\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
   2 .\" %%%LICENSE_START(GPL_NOVERSION_ONELINE)
   3 .\" Distributed under GPL
   4 .\" %%%LICENSE_END
   5 .\" Based on glibc infopages
   6 .\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
   7 .\"     <mtk.manpages@gmail.com>
   8 .\" Modified 2004-11-15, fixed error noted by Fabian Kreutz
   9 .\"      <kreutz@dbs.uni-hannover.de>
  10 .TH TGAMMA 3 2010-09-20 "GNU" "Linux Programmer's Manual"
  11 .SH NAME
  12 tgamma, tgammaf, tgammal \- true gamma function
  13 .SH SYNOPSIS
  14 .B #include <math.h>
  15 .sp
  16 .BI "double tgamma(double " x );
  17 .br
  18 .BI "float tgammaf(float " x );
  19 .br
  20 .BI "long double tgammal(long double " x );
  21 .sp
  22 Link with \fI\-lm\fP.
  23 .sp
  24 .in -4n
  25 Feature Test Macro Requirements for glibc (see
  26 .BR feature_test_macros (7)):
  27 .in
  28 .sp
  29 .ad l
  30 .BR tgamma (),
  31 .BR tgammaf (),
  32 .BR tgammal ():
  33 .RS 4
  34 _XOPEN_SOURCE\ >=\ 600 || _ISOC99_SOURCE ||
  35 _POSIX_C_SOURCE\ >=\ 200112L;
  36 .br
  37 or
  38 .I cc\ -std=c99
  39 .RE
  40 .ad
  41 .SH DESCRIPTION
  42 The Gamma function is defined by
  43 .sp
  44     Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt
  45 .sp
  46 It is defined for every real number except for nonpositive integers.
  47 For nonnegative integral \fIm\fP one has
  48 .sp
  49     Gamma(m+1) = m!
  50 .sp
  51 and, more generally, for all \fIx\fP:
  52 .sp
  53     Gamma(x+1) = x * Gamma(x)
  54 .sp
  55 Furthermore, the following is valid for all values of \fIx\fP
  56 outside the poles:
  57 .sp
  58     Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
  59 .PP
  60 .SH RETURN VALUE
  61 On success, these functions return Gamma(x).
  62
  63 If
  64 .I x
  65 is a NaN, a NaN is returned.
  66
  67 If
  68 .I x
  69 is positive infinity, positive infinity is returned.
  70
  71 If
  72 .I x
  73 is a negative integer, or is negative infinity,
  74 a domain error occurs,
  75 and a NaN is returned.
  76
  77 If the result overflows,
  78 a range error occurs,
  79 and the functions return
  80 .BR HUGE_VAL ,
  81 .BR HUGE_VALF ,
  82 or
  83 .BR HUGE_VALL ,
  84 respectively, with the correct mathematical sign.
  85
  86 If the result underflows,
  87 a range error occurs,
  88 and the functions return 0, with the correct mathematical sign.
  89
  90 If
  91 .I x
  92 is \-0 or +0,
  93 a pole error occurs,
  94 and the functions return
  95 .BR HUGE_VAL ,
  96 .BR HUGE_VALF ,
  97 or
  98 .BR HUGE_VALL ,
  99 respectively, with the same sign as the 0.
 100 .SH ERRORS
 101 See
 102 .BR math_error (7)
 103 for information on how to determine whether an error has occurred
 104 when calling these functions.
 105 .PP
 106 The following errors can occur:
 107 .TP
 108 Domain error: \fIx\fP is a negative integer, or negative infinity
 109 .\" FIXME . errno is not set to EDOM for x == -inf
 110 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
 111 .I errno
 112 is set to
 113 .BR EDOM .
 114 An invalid floating-point exception
 115 .RB ( FE_INVALID )
 116 is raised (but see BUGS).
 117 .TP
 118 Pole error: \fIx\fP is +0 or \-0
 119 .I errno
 120 is set to
 121 .BR ERANGE .
 122 A divide-by-zero floating-point exception
 123 .RB ( FE_DIVBYZERO )
 124 is raised.
 125 .TP
 126 Range error: result overflow
 127 .I errno
 128 is set to
 129 .BR ERANGE .
 130 An overflow floating-point exception
 131 .RB ( FE_OVERFLOW )
 132 is raised.
 133 .PP
 134 glibc also gives the following error which is not specified
 135 in C99 or POSIX.1-2001.
 136 .TP
 137 Range error: result underflow
 138 .\" e.g., tgamma(-172.5) on glibc 2.8/x86-32
 139 .\" .I errno
 140 .\" is set to
 141 .\" .BR ERANGE .
 142 An underflow floating-point exception
 143 .RB ( FE_UNDERFLOW )
 144 is raised.
 145 .IP
 146 .I errno
 147 is not set for this case.
 148 .\" FIXME . Is it intentional that errno is not set:
 149 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6810
 150 .\"
 151 .\" glibc (as at 2.8) also supports and an inexact
 152 .\" exception for various cases.
 153 .SH VERSIONS
 154 These functions first appeared in glibc in version 2.1.
 155 .SH CONFORMING TO
 156 C99, POSIX.1-2001.
 157 .SH NOTES
 158 This function had to be called "true gamma function"
 159 since there is already a function
 160 .BR gamma (3)
 161 that returns something else (see
 162 .BR gamma (3)
 163 for details).
 164 .SH BUGS
 165 If
 166 .I x
 167 is negative infinity,
 168 .I errno
 169 is not set (it should be set to
 170 .BR EDOM ).
 171 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
 172
 173 In glibc versions 2.3.3 and earlier,
 174 an argument of +0 or \-0 incorrectly produced a domain error
 175 .RI ( errno
 176 set to
 177 .B EDOM
 178 and an
 179 .B FE_INVALID
 180 exception raised), rather than a pole error.
 181 .SH SEE ALSO
 182 .BR gamma (3),
 183 .BR lgamma (3)