# tgamma

## 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



           tgamma, tgammaf, tgammal — compute gamma() function
    


## SYNOPSIS



           #include <math.h>
    
           double tgamma(double _x_);
           float tgammaf(float _x_);
           long double tgammal(long double _x_);
    


## 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 Γ(_x_) where Γ(_x_) is defined as ∞0∫ _e^_
           − _tt^ x_ −1 _dt_.
    
           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 gamma
           of _x_.
    
           If _x_ is a negative integer, a domain error may occur and either a
           NaN (if supported) or an implementation-defined value shall be
           returned.  On systems that support the IEC 60559 Floating-Point
           option, a domain error shall occur and a NaN shall be returned.
    
           If _x_ is ±0, _tgamma_(), _tgammaf_(), and _tgammal_() shall return
           ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively.  On systems
           that support the IEC 60559 Floating-Point option, a pole error
           shall occur; otherwise, a pole error may occur.
    
           If the correct value would cause overflow, a range error shall
           occur and _tgamma_(), _tgammaf_(), and _tgammal_() shall return
           ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL, respectively, with the same
           sign as the correct value of the function.
    
           If the correct value would cause underflow, and is not
           representable, a range error may occur, and _tgamma_(), _tgammaf_(),
           and _tgammal_() shall return 0.0, or (if IEC 60559 Floating-Point is
           not supported) an implementation-defined value no greater in
           magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
    
           If the correct value would cause underflow, and is representable,
           a range error may occur and the correct value shall be returned.
    
           If _x_ is subnormal and 1/_x_ is representable, 1/_x_ should be
           returned.
    
           If _x_ is NaN, a NaN shall be returned.
    
           If _x_ is +Inf, _x_ shall be returned.
    
           If _x_ is -Inf, a domain error shall occur, and a NaN shall be
           returned.
    


## ERRORS



           These functions shall fail if:
    
           Domain Error
                       The value of _x_ is a negative integer, or _x_ is -Inf.
    
                       If the integer expression (_math_errhandling_ &
                       MATH_ERRNO) is non-zero, then _errno_ shall be set to
                       **[EDOM]**.  If the integer expression (_math_errhandling_ &
                       MATH_ERREXCEPT) is non-zero, then the invalid
                       floating-point exception shall be raised.
    
           Pole Error  The value of _x_ is 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 value 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.
    
           These functions may fail if:
    
           Domain Error
                       The value of _x_ is a negative integer.
    
                       If the integer expression (_math_errhandling_ &
                       MATH_ERRNO) is non-zero, then _errno_ shall be set to
                       **[EDOM]**.  If the integer expression (_math_errhandling_ &
                       MATH_ERREXCEPT) is non-zero, then the invalid
                       floating-point exception shall be raised.
    
           Pole Error  The value of _x_ is 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 underflows.
    
                       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 underflow
                       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



           This function is named _tgamma_() in order to avoid conflicts with
           the historical _gamma_() and _lgamma_() functions.
    


## FUTURE DIRECTIONS



           It is possible that the error response for a negative integer
           argument may be changed to a pole error and a return value of
           ±Inf.
    


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