lgamma man page
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.
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.12008 defers to the ISO C standard.
These functions shall compute $log\_e\text{}\│\Gamma \left(\text{}x\right)\│$ where $\Gamma \left(\text{}x\right)$ is defined as $\underset{0}{\overset{\infty}{\int}}e\text{^}\text{}tt\text{^}\text{}x1dt$. The argument x need not be a nonpositive integer ($\Gamma \left(\text{}x\right)$ is defined over the reals, except the nonpositive integers).
If x is NaN, Inf, or a negative integer, the value of signgam is unspecified.
These functions need not be threadsafe.
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 nonzero or fetestexcept(FE_INVALID  FE_DIVBYZERO  FE_OVERFLOW  FE_UNDERFLOW) is nonzero, an error has occurred.
Return Value
Upon successful completion, these functions shall return the logarithmic gamma of x.
If x is a nonpositive 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 nonzero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero, then the dividebyzero floatingpoint exception shall be raised.
 Range Error

The result overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is nonzero, then the overflow floatingpoint 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 nonzero.
Rationale
None.
Future Directions
None.
See Also
exp(), feclearexcept(), fetestexcept(), isnan()
The Base Definitions volume of POSIX.12008, 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.12008 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/manpages/reporting_bugs.html .