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.1-2024 defers to the ISO C standard.

These functions shall compute \( \log _e \mid \Gamma(x) \mid \text { where } \Gamma(x) \text { is defined as } \int_0^{\infty} e^{-t} t^{x-1} d t \text {. } \) The argument \(x\) need not be a non-positive integer \( (\Gamma(x) \) is defined over the reals, except the non-positive integers).

^[XSI] The sign of \( \Gamma(x) \) shall be returned in the external integer signgam. If \(x\) is NaN, -Inf, or a negative integer, the value of signgam is unspecified.

If concurrent calls are made to these functions, the value of signgam is indeterminate.

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.

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.

If the value of signgam will be obtained after a call to lgamma(), lgammaf(), or lgammal(), in order to ensure that the value will not be altered by another call in a different thread, applications should either restrict calls to these functions to be from a single thread or use a lock such as a mutex or spin lock to protect a critical section starting before the function call and ending after the value of signgam has been obtained.

RATIONALE

Earlier versions of this standard did not require lgamma(), lgammaf(), and lgammal() to be thread-safe because signgam was a global variable. They are now required to be thread-safe to align with the ISO C standard (which, since the introduction of threads in 2011, requires that they avoid data races), with the exception that they need not avoid data races when storing a value in the signgam variable. Since signgam is not specified by the ISO C standard, this exception is not a conflict with that standard.

FUTURE DIRECTIONS

None.

SEE ALSO

exp, feclearexcept, fetestexcept, isnan

XBD 4.23 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.

Issue 8

Austin Group Defect 1002 is applied, reinstating the requirement for the sign of \( \Gamma(x) \) to be returned in signgam, which had been accidentally removed in Issue 7.

Austin Group Defect 1302 is applied, aligning these functions with the ISO/IEC 9899:2018 standard.