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/* digamma and first  polygamma function
Adapted and CORRECTED! from:  C Mathematical Function Handbook by Louis Baker
Modified by M. Beeson for use in Mathpert, 9.17.92
In particular, 'abs' has to be changed to 'fabs' or you compute
very wrong values.
*/

#include <math.h>
#define BADVAL 2.0E300
#define pi 3.141592653589793238462643383279
#define  Egamma 0.577215664901532860606512090082402431

double pg1(double x)
{ int i;
  double sum,z,u,y;
  double b[10]={.4041138064,.1471100206,.0500956643,
  .0160671426,.004941886,.0014725602,.0004282353,
  .0001221952,.000034347,.0000095387};
  if( x<=0. && fabs((int)(x)-x) <1.e-8)
      return BADVAL;
  u=x-1.;
  if(u>0. && u<=.5)
     { sum=b[9];
       y=u*u;
       for(i=8;i>=0;i--)
         { sum= sum*y+b[i];
         }
       sum*=u;
       /*printf(" omega=%e\n",sum);*/
       z=1./(u+1.); /* z=1/x */
       sum-=.5*z*z;
       z=1./(1.-u);
       sum+=.5*z*z;
       z=sin(u*pi);
       return  pi*pi*.5/(z*z)-sum-.5/(u*u);
     }
  if(x>=2.)
     {  /* printf(" asymptotic x=%e\n",x);*/
        y=1./x;
        z=y*y;
             /*printf(" asymptotic z,y=%e %e\n",y,z);*/
             /* desmet blows up on underflow*/
        return(y+z*(.5+y*(1./6.+z*(-1./30./*+z*(1./42.-z/30.)*/))));
     }
  if(x<0.)
     {  z=sin(pi*x);
        return (-pg1(1.-x)-pi*pi/(z*z));
     }
   /*  .5<=x<2.*/
   /*if(x>1.)*/
  return(pg1(x+1.)+1./(x*x));
}

/*_________________________________________________________________*/
double digamma(double x)
{
static double digammin;
double q,y,z,sum;
q=x;
sum=0.;
if(q==0.)
  return BADVAL;
if(digammin<=0.)
   digammin=30.;
if(q<0.)
  { if( fabs((int)(q)-q) <1.e-8)
        return BADVAL;
    q=1.-x;sum=pi/tan(pi*x); /*note sum subtracted from final result*/
  }
while(q<digammin)
  { if(q==0.)
      return BADVAL;
    sum+=1./q;
    q++;
  }
y=1/q;
z=y*y;
/* logx-1/2x- sum n=1 to inf of  B[2n]z^-2n/2n*/
return log(q)-sum-.5*y-z*(1./12.-z*(1/120.-z*(1/252.-z/240.)));
}

#undef pi