The Open Group Base Specifications Issue 7
IEEE Std 1003.1-2008, 2016 Edition
Copyright © 2001-2016 The IEEE and The Open Group

#### 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`);
> ``

> ``[XSI] extern int signgam;``
> `
> `

#### DESCRIPTION

> [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 loge|Γ(x)| where Γ(x) is defined as
> The argument x need not be a non-positive integer (Γ(x) is defined over the reals, except the non-positive integers).

> [XSI] If x is NaN, -Inf, or a negative integer, the value of signgam is unspecified.

> [CX] 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.

> [MX] 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

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

#### CHANGE HISTORY

> First released in Issue 3.

#### Issue 5

> 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.

#### Issue 6

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

> The lgammaf() and lgammal() 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.

#### Issue 7

> Austin Group Interpretation 1003.1-2001 #156 is applied.

> The DESCRIPTION is clarified regarding the value of signgam when x is Nan, -Inf, or a negative integer.

End of informative text.

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