lgamma, lgammaf, lgammal, signgam - log gamma function
double lgamma(double x);
float lgammaf(float x);
long double lgammal(long double x);
[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.1-2017 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.
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.
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.
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.
exp, feclearexcept, fetestexcept, isnan
XBD 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() 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.
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.
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