PROLOG

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

       delim $$

NAME

       lgamma, lgammaf, lgammal, signgam — log gamma function

SYNOPSIS

       #include <math.h>

       double lgamma(double x);
       float lgammaf(float x);
       long double lgammal(long double x);
       extern int signgam;

DESCRIPTION

       The functionality described on this reference page is aligned with the ISO C standard. Any
       conflict between the requirements described here and the ISO C standard is  unintentional.
       This volume of POSIX.1‐2008 defers to the ISO C standard.

       These  functions  shall  compute $log_ e" " │ Γ ( ^ x ) │$ where $Γ ( ^ x )$ is defined as
       $int from 0 to inf e"^" " "{ - t } t"^" " "{ x - 1 } dt$.  The argument x need  not  be  a
       non-positive  integer  ($Γ(  ^  x  )$  is  defined over the reals, except the non-positive
       integers).

       If x is NaN, −Inf, or a negative integer, the value of signgam is unspecified.

       These functions need not be thread-safe.

       An application wishing to check for error situations should set errno  to  zero  and  call
       feclearexcept(FE_ALL_EXCEPT)  before  calling these functions. On return, if errno is non-
       zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is  non-zero,
       an error has occurred.

RETURN VALUE

       Upon successful completion, these functions shall return the logarithmic gamma of x.

       If  x  is  a  non-positive  integer, a pole error shall occur and lgamma(), lgammaf(), and
       lgammal() shall return +HUGE_VAL, +HUGE_VALF, and +HUGE_VALL, respectively.

       If the correct value would cause  overflow,  a  range  error  shall  occur  and  lgamma(),
       lgammaf(),  and  lgammal()  shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL (having the
       same sign as the correct value), respectively.

       If x is NaN, a NaN shall be returned.

       If x is 1 or 2, +0 shall be returned.

       If x is ±Inf, +Inf shall be returned.

ERRORS

       These functions shall fail if:

       Pole Error  The x argument is a negative integer or zero.

                   If the integer expression (math_errhandling & MATH_ERRNO)  is  non-zero,  then
                   errno shall be set to [ERANGE].  If the integer expression (math_errhandling &
                   MATH_ERREXCEPT) is non-zero, then the divide-by-zero floating-point  exception
                   shall be raised.

       Range Error The result overflows.

                   If  the  integer  expression (math_errhandling & MATH_ERRNO) is non-zero, then
                   errno shall be set to [ERANGE].  If the integer expression (math_errhandling &
                   MATH_ERREXCEPT)  is non-zero, then the overflow floating-point exception shall
                   be raised.

       The following sections are informative.

EXAMPLES

       None.

APPLICATION USAGE

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

RATIONALE

       None.

FUTURE DIRECTIONS

       None.

SEE ALSO

       exp(), feclearexcept(), fetestexcept(), isnan()

       The  Base  Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of Error Conditions
       for Mathematical Functions, <math.h>

COPYRIGHT

       Portions of this text are reprinted and  reproduced  in  electronic  form  from  IEEE  Std
       1003.1,  2013  Edition,  Standard  for Information Technology -- Portable Operating System
       Interface (POSIX), The Open Group Base Specifications Issue 7, Copyright (C) 2013  by  the
       Institute  of  Electrical  and  Electronics  Engineers,  Inc and The Open Group.  (This is
       POSIX.1-2008 with the  2013  Technical  Corrigendum  1  applied.)  In  the  event  of  any
       discrepancy  between  this  version and the original IEEE and The Open Group Standard, the
       original IEEE and The Open Group Standard is the referee document. The  original  Standard
       can be obtained online at http://www.unix.org/online.html .

       Any  typographical  or  formatting errors that appear in this page are most likely to have
       been introduced during the conversion of the source files to man page  format.  To  report
       such errors, see https://www.kernel.org/doc/man-pages/reporting_bugs.html .