Fast, Fixed Point Square Root Computation ?

I did test your magic_sqrt but the time to execute sqrt() and magic_sqrt() are almost the same with my environment:

Linux, RHEL 4., x64, Xeon 3.2G x 2, 4MB memory gcc (GCC) 3.4.6 20060404 (Red Hat 3.4.6-3), glib 2.3.4.

Here is the code:

[vuhung@ g++]$gcc -lm sqrt.c
[vuhung@ g++]$./a.out
     sqrt time = 0.025689
magic sqrt time = 0.026223
[vuhung@ g++]$cat sqrt.c
#include 
#include 
#include 
#include 

float magic_sqrt (float number)
{
  long i;
  float f = 1.5, x = number/2, y = number;
  i  = * ( unsigned long * ) &y;
  i   = 0x5f3759df - ( i >> 1 );
  y = * ( float * ) &i;
  y = y * (f - x*y*y);
  return number * y;

}

int main()
{
       long i;

       long NUM  = 1000000;
       float x;

   double real, real_begin;
   struct timeval tv;
   gettimeofday (&tv, NULL);
   real_begin = tv.tv_sec + (double) tv.tv_usec * 1e-6;

       for(i = 0; i < NUM; i++)
               x =sqrt(i + 0.01);

   gettimeofday (&tv, NULL);
   real = (tv.tv_sec + (double) tv.tv_usec * 1e-6);     
       printf ("      sqrt time = %f\n", real - real_begin);


   gettimeofday (&tv, NULL);   
       real_begin = tv.tv_sec + (double) tv.tv_usec * 1e-6;

   for(i = 0; i < NUM; i++)
       x = magic_sqrt(i + 0.01);
   gettimeofday (&tv, NULL);   
       real = (tv.tv_sec + (double) tv.tv_usec * 1e-6);       
   printf ("magic sqrt time = %f\n", real - real_begin);

       return 0;

}
http://www.qoheleth.uklinux.net/blog/?p=139
http://themanaworld.org/tmwservdox/mathutils_8cpp-source.html