qrsqrt.js

/**
 * References: 
 * [1] ftp://ftp.idsoftware.com/idstuff/source/quake3-1.32b-source.zip
 * [2] http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf
 * [3] http://en.wikipedia.org/wiki/Newton%27s_method
 * [4] https://developer.mozilla.org/en/JavaScript_typed_arrays
 * [5] http://en.wikipedia.org/wiki/Fast_inverse_square_root
 */

const QUAKEx32 = 0x5f3759df
const x32      = 0x5f375a86
const x64      = 0x5fe6eb50c7aa19f9

/**
 * Appearing in the Quake III Arena source code[1],
 * this strange algorithm uses integer operations
 * along with a 'magic number' to calculate floating point
 * approximation values of inverse square roots[5].
 * 
 * @param  {Number} n     Number
 * @param  {Number} p = 1 Number of iterations for performing Newton's method[3]
 * @return {Number}       Result
 */
function fisqrt( n, p ) {
  
  p = p || 1
  
  fisqrt.y[0] = n
  fisqrt.i[0] = 0x5f375a86 - ( fisqrt.i[0] >> 1 )
  
  while( p-- ) {
    fisqrt.y[0] = fisqrt.y[0] * ( 1.5 * ( ( n * 0.5 ) * fisqrt.y[0] * fisqrt.y[0] ) )
  }
  
  return y[0]
  
}

fisqrt.y = new Float32Array( 1 )
fisqrt.i = new Int32Array( y.buffer )