lgamma(3)

1LGAMMA(3)                  Linux Programmer's Manual                 LGAMMA(3)
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NAME

6       lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, signgam - log
7       gamma function
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SYNOPSIS

10       #include <math.h>
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12       double lgamma(double x);
13       float lgammaf(float x);
14       long double lgammal(long double x);
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16       double lgamma_r(double x, int *signp);
17       float lgammaf_r(float x, int *signp);
18       long double lgammal_r(long double x, int *signp);
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20       extern int signgam;
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22       Link with -lm.
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24   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
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26       lgamma():
27           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
28               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
29               || /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
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31       lgammaf(), lgammal():
32           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
33               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
34               || /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
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36       lgamma_r(), lgammaf_r(), lgammal_r():
37           /* Since glibc 2.19: */ _DEFAULT_SOURCE
38               || /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
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40       signgam:
41           _XOPEN_SOURCE
42               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
43               || /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
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DESCRIPTION

46       For the definition of the Gamma function, see tgamma(3).
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48       The lgamma(), lgammaf(), and lgammal()  functions  return  the  natural
49       logarithm of the absolute value of the Gamma function.  The sign of the
50       Gamma function is returned in the external integer signgam declared  in
51       <math.h>.  It is 1 when the Gamma function is positive or zero, -1 when
52       it is negative.
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54       Since using a constant location signgam is not thread-safe,  the  func‐
55       tions  lgamma_r(),  lgammaf_r(),  and lgammal_r() have been introduced;
56       they return the sign via the argument signp.
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RETURN VALUE

59       On success, these functions return the natural logarithm of Gamma(x).
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61       If x is a NaN, a NaN is returned.
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63       If x is 1 or 2, +0 is returned.
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65       If x is positive infinity or negative infinity,  positive  infinity  is
66       returned.
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68       If  x  is a nonpositive integer, a pole error occurs, and the functions
69       return +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL, respectively.
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71       If the result overflows, a range error occurs, and the functions return
72       HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct math‐
73       ematical sign.
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ERRORS

76       See math_error(7) for information on how to determine whether an  error
77       has occurred when calling these functions.
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79       The following errors can occur:
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81       Pole error: x is a nonpositive integer
82              errno  is set to ERANGE (but see BUGS).  A divide-by-zero float‐
83              ing-point exception (FE_DIVBYZERO) is raised.
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85       Range error: result overflow
86              errno is set to ERANGE.  An  overflow  floating-point  exception
87              (FE_OVERFLOW) is raised.
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CONFORMING TO

90       The   lgamma()  functions  are  specified  in  C99,  POSIX.1-2001,  and
91       POSIX.1-2008.  signgam is specified in POSIX.1-2001  and  POSIX.1-2008,
92       but  not in C99.  The lgamma_r() functions are nonstandard, but present
93       on several other systems.
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BUGS

96       In glibc 2.9 and earlier, when a pole error occurs,  errno  is  set  to
97       EDOM;  instead of the POSIX-mandated ERANGE.  Since version 2.10, glibc
98       does the right thing.
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COLOPHON

104       This page is part of release 5.12 of the Linux  man-pages  project.   A
105       description  of  the project, information about reporting bugs, and the
106       latest    version    of    this    page,    can     be     found     at
107       https://www.kernel.org/doc/man-pages/.
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111                                  2021-03-22                         LGAMMA(3)