tgamma(3)

1tgamma(3)                  Library Functions Manual                  tgamma(3)
2
3
4

NAME

6       tgamma, tgammaf, tgammal - true gamma function
7

LIBRARY

9       Math library (libm, -lm)
10

SYNOPSIS

12       #include <math.h>
13
14       double tgamma(double x);
15       float tgammaf(float x);
16       long double tgammal(long double x);
17
18   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
19
20       tgamma(), tgammaf(), tgammal():
21           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
22

DESCRIPTION

24       These functions calculate the Gamma function of x.
25
26       The Gamma function is defined by
27
28              Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt
29
30       It  is  defined  for every real number except for nonpositive integers.
31       For nonnegative integral m one has
32
33              Gamma(m+1) = m!
34
35       and, more generally, for all x:
36
37              Gamma(x+1) = x * Gamma(x)
38
39       Furthermore, the following is valid for all values  of  x  outside  the
40       poles:
41
42              Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)
43

RETURN VALUE

45       On success, these functions return Gamma(x).
46
47       If x is a NaN, a NaN is returned.
48
49       If x is positive infinity, positive infinity is returned.
50
51       If x is a negative integer, or is negative infinity, a domain error oc‐
52       curs, and a NaN is returned.
53
54       If the result overflows, a range error occurs, and the functions return
55       HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct math‐
56       ematical sign.
57
58       If the result underflows, a range error occurs, and the  functions  re‐
59       turn 0, with the correct mathematical sign.
60
61       If  x  is  -0  or  +0,  a  pole  error occurs, and the functions return
62       HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign  as
63       the 0.
64

ERRORS

66       See  math_error(7) for information on how to determine whether an error
67       has occurred when calling these functions.
68
69       The following errors can occur:
70
71       Domain error: x is a negative integer, or negative infinity
72              errno is set  to  EDOM.   An  invalid  floating-point  exception
73              (FE_INVALID) is raised (but see BUGS).
74
75       Pole error: x is +0 or -0
76              errno  is set to ERANGE.  A divide-by-zero floating-point excep‐
77              tion (FE_DIVBYZERO) is raised.
78
79       Range error: result overflow
80              errno is set to ERANGE.  An  overflow  floating-point  exception
81              (FE_OVERFLOW) is raised.
82
83       glibc  also  gives the following error which is not specified in C99 or
84       POSIX.1-2001.
85
86       Range error: result underflow
87              An underflow floating-point exception (FE_UNDERFLOW) is  raised,
88              and errno is set to ERANGE.
89

ATTRIBUTES

91       For  an  explanation  of  the  terms  used  in  this  section,  see at‐
92       tributes(7).
93
94       ┌────────────────────────────────────────────┬───────────────┬─────────┐
95       │Interface                                   │ Attribute     │ Value   │
96       ├────────────────────────────────────────────┼───────────────┼─────────┤
97       │tgamma(), tgammaf(), tgammal()              │ Thread safety │ MT-Safe │
98       └────────────────────────────────────────────┴───────────────┴─────────┘
99

STANDARDS

101       C11, POSIX.1-2008.
102

HISTORY

104       glibc 2.1.  C99, POSIX.1-2001.
105

NOTES

107       This function had to be called "true gamma  function"  since  there  is
108       already  a  function gamma(3) that returns something else (see gamma(3)
109       for details).
110

BUGS

112       Before glibc 2.18, the glibc implementation of these functions did  not
113       set errno to EDOM when x is negative infinity.
114
115       Before  glibc 2.19, the glibc implementation of these functions did not
116       set errno to ERANGE on an underflow range error.
117
118       In  glibc  versions  2.3.3  and  earlier,  an  argument  of  +0  or  -0
119       incorrectly  produced  a  domain  error  (errno  set  to  EDOM  and  an
120       FE_INVALID exception raised), rather than a pole error.
121