quake_3_hack.cpp

#include <cmath>
#include <iostream>

using std::cout;
using std::endl;

float quake3_hack(float number) {
  float x2 = number * 0.5f;
  float y  = number;
  long i  = *(long*) & y;
  i  = 0x5f3759df - ( i >> 1 );
  y  = *(float*) & i;
  y  = y * (1.5f - (x2 * y * y));
  y  = y * (1.5f - (x2 * y * y));
  return y;
}

int main() {

  for (int i = 2; i < 100; i += 10) {

    cout << "i = " << i << ", std 1/sqrt(i) = " << (1.0/sqrtf(i));
    cout << ", quake3_hack 1/sqrt(i) = " << quake3_hack(i) << endl;

  }

  return 0;
}

Output:

i = 2, std 1/sqrt(i) = 0.707107, quake3_hack 1/sqrt(i) = 0.707107
i = 12, std 1/sqrt(i) = 0.288675, quake3_hack 1/sqrt(i) = 0.288675
i = 22, std 1/sqrt(i) = 0.213201, quake3_hack 1/sqrt(i) = 0.213201
i = 32, std 1/sqrt(i) = 0.176777, quake3_hack 1/sqrt(i) = 0.176777
i = 42, std 1/sqrt(i) = 0.154303, quake3_hack 1/sqrt(i) = 0.154303
i = 52, std 1/sqrt(i) = 0.138675, quake3_hack 1/sqrt(i) = 0.138675
i = 62, std 1/sqrt(i) = 0.127, quake3_hack 1/sqrt(i) = 0.127
i = 72, std 1/sqrt(i) = 0.117851, quake3_hack 1/sqrt(i) = 0.117851
i = 82, std 1/sqrt(i) = 0.110432, quake3_hack 1/sqrt(i) = 0.110432
i = 92, std 1/sqrt(i) = 0.104257, quake3_hack 1/sqrt(i) = 0.104257