IEEE Std 1003.1-2008, 2016 Edition

Copyright © 2001-2016 The IEEE and The Open Group

lgamma, lgammaf, lgammal, signgam - log gamma function

#include <math.h>

double lgamma(doublex);

float lgammaf(floatx);

long double lgammal(long doublex);

^{[XSI]}extern int signgam;

^{[CX]}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

The argumentxneed not be a non-positive integer (Γ(x) is defined over the reals, except the non-positive integers).

^{[XSI]}Ifxis NaN, -Inf, or a negative integer, the value ofsigngamis unspecified.

^{[CX]}These functions need not be thread-safe.An application wishing to check for error situations should set

errnoto zero and callfeclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, iferrnois non-zero orfetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

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

x.If

xis a non-positive integer, a pole error shall occur andlgamma(),lgammaf(), andlgammal() 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(), andlgammal() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL (having the same sign as the correct value), respectively.

^{[MX]}Ifxis NaN, a NaN shall be returned.If

xis 1 or 2, +0 shall be returned.If

xis ±Inf, +Inf shall be returned.

These functions shall fail if:

- Pole Error
- The
xargument is a negative integer or zero.If the integer expression (

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

None.

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.

None.

None.

exp,feclearexcept,fetestexcept,isnanXBD

Treatment of Error Conditions for Mathematical Functions,<math.h>

First released in Issue 3.

The DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in the APPLICATION USAGE section.

A note indicating that this function need not be reentrant is added to the DESCRIPTION.

The

lgamma() function is no longer marked as an extension.The

lgammaf() andlgammal() functions are added for alignment with the ISO/IEC 9899:1999 standard.The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999 standard.

IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.

Functionality relating to the XSI option is marked.

Austin Group Interpretation 1003.1-2001 #156 is applied.

The DESCRIPTION is clarified regarding the value of

signgamwhenxis Nan, -Inf, or a negative integer.

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