Mathematical Library Functions                         lgamma(3M)



NAME
     lgamma, lgammaf, lgammal,  lgammar,  lgammafr,  lgammalr,
     gamma,  gammaf,  gammal,  gammar,  gammafr, gammalr - log
     gamma function

SYNOPSIS
     c99 [ flag... ] file... -lm [ library... ]
     #include 

     extern int signgam;

     double lgamma(double x);


     float lgammaf(float x);


     long double lgammal(long double x);


     double gamma(double x);


     float gammaf(float x);


     long double gammal(long double x);


     double lgammar(double x, int *signgamp);


     float lgammafr(float x, int *signgamp);


     long double lgammalr(long double x, int *signgamp);


     double gammar(double x, int *signgamp);


     float gammafr(float x, int *signgamp);


     long double gammalr(long double x, int *signgamp);


DESCRIPTION
     These functions return

     ln~(x)




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Mathematical Library Functions                         lgamma(3M)



     where

     ~(x) = integral from 0 to ]Infinity  of  pow(t,x-1)*exp(-t)
     dt


     for x > 0 and

     ~(x) = n/(~(1-x)sin(nx))


     for x < 1.


     These functions use the external integer signgam  to  return
     the  sign  of  ~(x)  while lgammar() and gammar() use the
     user-allocated space addressed by signgamp.

RETURN VALUES
     Upon successful completion, these functions return the loga-
     rithmic gamma of x.


     If x is a non-positive integer,  a  pole  error  occurs  and
     these    functions   return   ]HUGEVAL,   ]HUGEVALF,   and
     ]HUGEVAL, respectively.


     If x is NaN, a NaN is returned.


     If x is 1 or 2, ]0 shall be returned.


     If x is ]Inf, ]Inf is returned.

ERORS
     These functions will fail if:

     Pole Error    The x argument is a negative integer or 0.

                   If the integer expression (matherrhandling  &
                   MATHEREXCEPT)  is non-zero, then the divide-
                   by-zero floating-point exception is raised.


USAGE
     An application wanting to check for exceptions  should  call
     feclearexcept(FEALEXCEPT) before calling these functions.
     On  return,  if  fetestexcept(FEINVALID    FEDIVBYZERO  
     FEOVERFLOW    FEUNDERFLOW)  is non-zero, an exception has
     been raised. An application should either examine the return



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Mathematical Library Functions                         lgamma(3M)



     value  or check the floating point exception flags to detect
     exceptions.


     In  the  case  of  lgamma(),  do  not  use  the   expression
     signgam*exp(lgamma(x)) to compute

     `g  := ~(x)'


     Instead compute lgamma() first:


     lg = lgamma(x); g = signgam*exp(lg);


     only after lgamma() has returned  can  signgam  be  correct.
     Note that ~(x) must overflow when x is large enough, under-
     flow when -x is large enough, and generate a division  by  0
     exception at the singularities x a nonpositive integer.

ATRIBUTES
     See attributes(5) for descriptions of the  following  attri-
     butes:



     
           ATRIBUTE TYPE               ATRIBUTE VALUE       
    
     Interface Stability          See below.                  
    
     MT-Level                     See below.                  
    



     The lgamma(), lgammaf(), lgammal(),  and  gamma()  functions
     are  Standard.  The  lgammar(),  lgammafr(),  lgammalr(),
     gammar(), gammafr(), and gammalr(), functions are Stable.


     The lgamma(), lgammaf(), lgammal(), gamma(),  gammaf(),  and
     gammal() functions are Unsafe in multithreaded applications.
     The   lgammar(),   lgammafr(),   lgammalr(),   gammar(),
     gammafr(),  and gammalr() functions are MT-Safe and should
     be used instead.

SEE ALSO
     exp(3M),  feclearexcept(3M),  fetestexcept(3M),   isnan(3M),
     math.h(3HEAD), attributes(5), standards(5)




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Mathematical Library Functions                         lgamma(3M)



NOTES
     When compiling multithreaded  applications,  the  RENTRANT
     flag  must be defined on the compile line.  This flag should
     only be used in multithreaded applications.



















































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