# lgamma

## 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.
    


## 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_);
           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.1‐2017 defers to the ISO C standard.
    
           These functions shall compute _log_ __e_ │Γ(_x_)│ where Γ(_x_) is defined
           as ∞0∫ _e^_ − _tt^ x_ −1 _dt_.  The argument _x_ need not be a non-positive
           integer (Γ(_x_) is defined over the reals, except the non-positive
           integers).
    
           If _x_ is NaN, -Inf, or a negative integer, the value of _signgam_ is
           unspecified.
    
           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.
    
           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.
    


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