1LGAMMA(3P)                 POSIX Programmer's Manual                LGAMMA(3P)
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PROLOG

6       This  manual  page is part of the POSIX Programmer's Manual.  The Linux
7       implementation of this interface may differ (consult the  corresponding
8       Linux  manual page for details of Linux behavior), or the interface may
9       not be implemented on Linux.
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11       delim $$
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NAME

14       lgamma, lgammaf, lgammal, signgam — log gamma function
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SYNOPSIS

17       #include <math.h>
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19       double lgamma(double x);
20       float lgammaf(float x);
21       long double lgammal(long double x);
22       extern int signgam;
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DESCRIPTION

25       The functionality described on this reference page is aligned with  the
26       ISO C  standard.  Any  conflict between the requirements described here
27       and the ISO C standard is unintentional. This  volume  of  POSIX.1‐2008
28       defers to the ISO C standard.
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30       These  functions shall compute $log_ e" " │ Γ ( ^ x ) │$ where $Γ ( ^ x
31       )$ is defined as $int from 0 to inf e"^" " "{ - t } t"^" " "{ x -  1  }
32       dt$.   The argument x need not be a non-positive integer ($Γ( ^ x )$ is
33       defined over the reals, except the non-positive integers).
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35       If x is NaN, −Inf, or a negative  integer,  the  value  of  signgam  is
36       unspecified.
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38       These functions need not be thread-safe.
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40       An  application  wishing to check for error situations should set errno
41       to zero and  call  feclearexcept(FE_ALL_EXCEPT)  before  calling  these
42       functions. On return, if errno is non-zero or fetestexcept(FE_INVALID |
43       FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero,  an  error  has
44       occurred.
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RETURN VALUE

47       Upon  successful completion, these functions shall return the logarith‐
48       mic gamma of x.
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50       If x is a non-positive integer, a pole error shall occur and  lgamma(),
51       lgammaf(),  and  lgammal()  shall  return  +HUGE_VAL,  +HUGE_VALF,  and
52       +HUGE_VALL, respectively.
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54       If the correct value would cause overflow, a range  error  shall  occur
55       and   lgamma(),   lgammaf(),  and  lgammal()  shall  return  ±HUGE_VAL,
56       ±HUGE_VALF, and ±HUGE_VALL (having the same sign as the correct value),
57       respectively.
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59       If x is NaN, a NaN shall be returned.
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61       If x is 1 or 2, +0 shall be returned.
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63       If x is ±Inf, +Inf shall be returned.
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ERRORS

66       These functions shall fail if:
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68       Pole Error  The x argument is a negative integer or zero.
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70                   If  the  integer expression (math_errhandling & MATH_ERRNO)
71                   is non-zero, then errno shall be set to [ERANGE].   If  the
72                   integer  expression  (math_errhandling & MATH_ERREXCEPT) is
73                   non-zero, then the divide-by-zero floating-point  exception
74                   shall be raised.
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76       Range Error The result overflows.
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78                   If  the  integer expression (math_errhandling & MATH_ERRNO)
79                   is non-zero, then errno shall be set to [ERANGE].   If  the
80                   integer  expression  (math_errhandling & MATH_ERREXCEPT) is
81                   non-zero, then the overflow floating-point exception  shall
82                   be raised.
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84       The following sections are informative.
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EXAMPLES

87       None.
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APPLICATION USAGE

90       On   error,   the   expressions  (math_errhandling  &  MATH_ERRNO)  and
91       (math_errhandling & MATH_ERREXCEPT) are independent of each other,  but
92       at least one of them must be non-zero.
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RATIONALE

95       None.
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FUTURE DIRECTIONS

98       None.
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SEE ALSO

101       exp(), feclearexcept(), fetestexcept(), isnan()
102
103       The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of
104       Error Conditions for Mathematical Functions, <math.h>
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107       Portions of this text are reprinted and reproduced in  electronic  form
108       from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
109       -- Portable Operating System Interface (POSIX),  The  Open  Group  Base
110       Specifications Issue 7, Copyright (C) 2013 by the Institute of Electri‐
111       cal and Electronics Engineers,  Inc  and  The  Open  Group.   (This  is
112       POSIX.1-2008  with  the  2013  Technical Corrigendum 1 applied.) In the
113       event of any discrepancy between this version and the original IEEE and
114       The  Open Group Standard, the original IEEE and The Open Group Standard
115       is the referee document. The original Standard can be  obtained  online
116       at http://www.unix.org/online.html .
117
118       Any  typographical  or  formatting  errors that appear in this page are
119       most likely to have been introduced during the conversion of the source
120       files  to  man page format. To report such errors, see https://www.ker‐
121       nel.org/doc/man-pages/reporting_bugs.html .
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125IEEE/The Open Group                  2013                           LGAMMA(3P)
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