Re: OT : Approximate / fast math libraries ?

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@xxxxxx Homepage: http://www.crc.dk