OT : Approximate / fast math libraries ?

[Mogens Kjaer]

Mogens Kjaer wrote:
...
> Padé approximation:
> 
> http://list.dprg.org/archive/2007-January/030202.html

You could try this piece of code:

static double atan2x(double y, double x)
{
   double z;
   if(x==0)
   {
     if(y<0) return -M_PI_2;
     else if(y>0) return M_PI_2;
     else return 0;
   }
   else
   {
     z = y/x;
     if(z>=-1 && z<=1)
     {
       z=z*(15.0+4.0*z*z)/(15.0+9.0*z*z);
       if(x>0) return z;
       else
       {
         if(y>=0) return M_PI+z;
         else return z-M_PI;
       }
     }
     else
     {
       z=x/y;
       z=M_PI_2-z*(15.0+4.0*z*z)/(15.0+9.0*z*z);
       if(y<=0) return z-M_PI;
       else return z;
     }
   }
}

Testing it with:

   maxe=0;

   for(i=0;i<10001;i++)
     for(j=0;j<10001;j++)
     {
       x=0.0001*i-0.5;
       y=0.0001*j-0.5;
       a1=atan2(y,x);
       a2=atan2x(y,x);
       e=fabs(a1-a2);
       if(e>maxe) maxe=e;
     }
   printf("maxe: %g\n", maxe);

gives maxe: 0.0062685

Timing (Xeon 5160 3 GHz) for the loop with only one function call:

atan2:	7.028u
atan2x:	1.586u

I'm not an expert on this, so use it at your own risk :-)

Mogens

-- 
Mogens Kjaer, Carlsberg A/S, Computer Department
Gamle Carlsberg Vej 10, DK-2500 Valby, Denmark
Phone: +45 33 27 53 25, Fax: +45 33 27 47 08
Email: mk at crc.dk Homepage: http://www.crc.dk