/*
 * Integer Square Root function
 * Contributors include Arne Steinarson for the basic approximation idea, Dann 
 * Corbit and Mathew Hendry for the first cut at the algorithm, Lawrence Kirby 
 * for the rearrangement, improvments and range optimization, Paul Hsieh 
 * for the round-then-adjust idea, Tim Tyler, for the Java port
 * and Jeff Lawson for a bug-fix and some code to improve accuracy.
 * 
 * 
 * v0.02 - 2003/09/07
 */

/**
 * Faster replacements for (int)(java.lang.Math.sqrt(integer))
 */
public class SquareRoot {
  final static int[] table = {
     0,    16,  22,  27,  32,  35,  39,  42,  45,  48,  50,  53,  55,  57,
     59,   61,  64,  65,  67,  69,  71,  73,  75,  76,  78,  80,  81,  83,
     84,   86,  87,  89,  90,  91,  93,  94,  96,  97,  98,  99, 101, 102,
     103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118,
     119, 120, 121, 122, 123, 124, 125, 126, 128, 128, 129, 130, 131, 132,
     133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 144, 145,
     146, 147, 148, 149, 150, 150, 151, 152, 153, 154, 155, 155, 156, 157,
     158, 159, 160, 160, 161, 162, 163, 163, 164, 165, 166, 167, 167, 168,
     169, 170, 170, 171, 172, 173, 173, 174, 175, 176, 176, 177, 178, 178,
     179, 180, 181, 181, 182, 183, 183, 184, 185, 185, 186, 187, 187, 188,
     189, 189, 190, 191, 192, 192, 193, 193, 194, 195, 195, 196, 197, 197,
     198, 199, 199, 200, 201, 201, 202, 203, 203, 204, 204, 205, 206, 206,
     207, 208, 208, 209, 209, 210, 211, 211, 212, 212, 213, 214, 214, 215,
     215, 216, 217, 217, 218, 218, 219, 219, 220, 221, 221, 222, 222, 223,
     224, 224, 225, 225, 226, 226, 227, 227, 228, 229, 229, 230, 230, 231,
     231, 232, 232, 233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238,
     239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 245, 246,
     246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253,
     253, 254, 254, 255
  };

  /**
   * A faster replacement for (int)(java.lang.Math.sqrt(x)).  Completely accurate for x < 2147483648 (i.e. 2^31)...
   */
  static int sqrt(int x) {
    int xn;

    if (x >= 0x10000) {
      if (x >= 0x1000000) {
        if (x >= 0x10000000) {
          if (x >= 0x40000000) {
            xn = table[x >> 24] << 8;
          } else {
            xn = table[x >> 22] << 7;
          }
        } else {
          if (x >= 0x4000000) {
            xn = table[x >> 20] << 6;
          } else {
            xn = table[x >> 18] << 5;
          }
        }

        xn = (xn + 1 + (x / xn)) >> 1;
        xn = (xn + 1 + (x / xn)) >> 1;
        return ((xn * xn) > x) ? --xn : xn;
      } else {
        if (x >= 0x100000) {
          if (x >= 0x400000) {
            xn = table[x >> 16] << 4;
          } else {
            xn = table[x >> 14] << 3;
          }
        } else {
          if (x >= 0x40000) {
            xn = table[x >> 12] << 2;
          } else {
            xn = table[x >> 10] << 1;
          }
        }

        xn = (xn + 1 + (x / xn)) >> 1;

        return ((xn * xn) > x) ? --xn : xn;
      }
    } else {
      if (x >= 0x100) {
        if (x >= 0x1000) {
          if (x >= 0x4000) {
            xn = (table[x >> 8]) + 1;
          } else {
            xn = (table[x >> 6] >> 1) + 1;
          }
        } else {
          if (x >= 0x400) {
            xn = (table[x >> 4] >> 2) + 1;
          } else {
            xn = (table[x >> 2] >> 3) + 1;
          }
        }

        return ((xn * xn) > x) ? --xn : xn;
      } else {
        if (x >= 0) {
          return table[x] >> 4;
        }
      }
    }
    
    illegalArgument();
    return -1;
  }

  /**
   * A faster replacement for (int)(java.lang.Math.sqrt(x)).  Completely accurate for x < 2147483648 (i.e. 2^31)...
   * Adjusted to more closely approximate 
   * "(int)(java.lang.Math.sqrt(x) + 0.5)"
   * by Jeff Lawson.
   */
  static int accurateSqrt(int x) {
    int xn;

    if (x >= 0x10000) {
      if (x >= 0x1000000) {
        if (x >= 0x10000000) {
          if (x >= 0x40000000) {
            xn = table[x >> 24] << 8;
          } else {
            xn = table[x >> 22] << 7;
          }
        } else {
          if (x >= 0x4000000) {
            xn = table[x >> 20] << 6;
          } else {
            xn = table[x >> 18] << 5;
          }
        }

        xn = (xn + 1 + (x / xn)) >> 1;
        xn = (xn + 1 + (x / xn)) >> 1;
        return adjustment(x, xn);
      } else {
        if (x >= 0x100000) {
          if (x >= 0x400000) {
            xn = table[x >> 16] << 4;
          } else {
            xn = table[x >> 14] << 3;
          }
        } else {
          if (x >= 0x40000) {
            xn = table[x >> 12] << 2;
          } else {
            xn = table[x >> 10] << 1;
          }
        }

        xn = (xn + 1 + (x / xn)) >> 1;

         return adjustment(x, xn);
      }
    } else {
      if (x >= 0x100) {
        if (x >= 0x1000) {
          if (x >= 0x4000) {
            xn = (table[x >> 8]) + 1;
          } else {
            xn = (table[x >> 6] >> 1) + 1;
          }
        } else {
          if (x >= 0x400) {
            xn = (table[x >> 4] >> 2) + 1;
          } else {
            xn = (table[x >> 2] >> 3) + 1;
          }
        }

        return adjustment(x, xn);
      } else {
        if (x >= 0) {
          return adjustment(x, table[x] >> 4);
        }
      }
    }
    
    illegalArgument();
    return -1;
  }
  
  private static int adjustment(int x, int xn) {
    // Added by Jeff Lawson:
    // need to test:
    //   if  |xn * xn - x|  >  |x - (xn-1) * (xn-1)|  then xn-1 is more accurate
    //   if  |xn * xn - x|  >  |(xn+1) * (xn+1) - x|  then xn+1 is more accurate
    // or, for all cases except x == 0:
    //    if  |xn * xn - x|  >  x - xn * xn + 2 * xn - 1 then xn-1 is more accurate
    //    if  |xn * xn - x|  >  xn * xn + 2 * xn + 1 - x then xn+1 is more accurate
    int xn2 = xn * xn;
            
    // |xn * xn - x|
    int comparitor0 = xn2 - x;
    if (comparitor0 < 0) {
      comparitor0 = -comparitor0;
    }
    
    int twice_xn = xn << 1;
    
    // |x - (xn-1) * (xn-1)|
    int comparitor1 = x - xn2 + twice_xn - 1;
    if (comparitor1 < 0) { // need to correct for x == 0 case?
      comparitor1 = -comparitor1; // only gets here when x == 0
    }
            
    // |(xn+1) * (xn+1) - x|
    int comparitor2 = xn2 + twice_xn + 1 - x;
            
    if (comparitor0 > comparitor1) {
      return (comparitor1 > comparitor2) ? ++xn : --xn;
    }
            
    return (comparitor0 > comparitor2) ? ++xn : xn;
  }

  /**
  * A *much* faster replacement for (int)(java.lang.Math.sqrt(x)).  Completely accurate for x < 289...
  */
  static int fastSqrt(int x) {
    if (x >= 0x10000) {
      if (x >= 0x1000000) {
        if (x >= 0x10000000) {
          if (x >= 0x40000000) {
            return (table[x >> 24] << 8);
          } else {
            return (table[x >> 22] << 7);
          }
        } else if (x >= 0x4000000) {
          return (table[x >> 20] << 6);
        } else {
          return (table[x >> 18] << 5);
        }
      } else if (x >= 0x100000) {
        if (x >= 0x400000) {
          return (table[x >> 16] << 4);
        } else {
          return (table[x >> 14] << 3);
        }
      } else if (x >= 0x40000) {
        return (table[x >> 12] << 2);
      } else {
        return (table[x >> 10] << 1);
      }
    } else if (x >= 0x100) {
      if (x >= 0x1000) {
        if (x >= 0x4000) {
          return (table[x >> 8]);
        } else {
          return (table[x >> 6] >> 1);
        }
      } else if (x >= 0x400) {
        return (table[x >> 4] >> 2);
      } else {
        return (table[x >> 2] >> 3);
      }
    } else if (x >= 0) {
      return table[x] >> 4;
    }
    illegalArgument();
    return -1;
  }

  private static void illegalArgument() {
    throw new IllegalArgumentException("Attemt to take the square root of negative number");
  }

  /** From http://research.microsoft.com/~hollasch/cgindex/math/introot.html
     * where it is presented by Ben Discoe (rodent@netcom.COM)
     * Not terribly speedy...
     */

  /*
     static int unrolled_sqrt(int x) {
        int v;
        int t = 1<<30;
        int r = 0;
        int s;
     
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;} t >>= 2;
        s = t + r; r>>= 1; 
        if (s <= x) { x -= s; r |= t;}
     
        return r;
     }
  */

  /**
   * Mark Borgerding's algorithm...
   * Not terribly speedy...
   */

  /*
     static int mborg_sqrt(int val) {
        int guess=0;
        int bit = 1 << 15;
        do {
           guess ^= bit;  
           // check to see if we can set this bit without going over sqrt(val)...
           if (guess * guess > val )
              guess ^= bit;  // it was too much, unset the bit...
        } while ((bit >>= 1) != 0);
     
        return guess;
     }
  	*/

  /** 
   * Taken from http://www.jjj.de/isqrt.cc
   * Code not tested well...
   * Attributed to: http://www.tu-chemnitz.de/~arndt/joerg.html / email: arndt@physik.tu-chemnitz.de
   * Slow.
   */

  /*
     final static int BITS = 32;
     final static int NN = 0;  // range: 0...BITSPERLONG/2
  
     final static int test_sqrt(int x) {
        int i;
        int a = 0;                   // accumulator...
        int e = 0;                   // trial product...
        int r;
     
        r=0;                         // remainder...
     
        for (i=0; i < (BITS/2) + NN; i++)
        {
           r <<= 2;
           r +=  (x >> (BITS - 2));
           x <<= 2;
        
           a <<= 1;
           e = (a << 1)+1;
        
           if(r >= e)
           {
              r -= e;
              a++;
           }
        }
     
        return a;
     }
  */

  /*
  // Totally hopeless performance...
     static int test_sqrt(int n) {
        float r = 2.0F;
        float s = 0.0F;
        for(; r < (float)n / r; r *= 2.0F);
        for(s = (r + (float)n / r) / 2.0F; r - s > 1.0F; s = (r + (float)n / r) / 2.0F) {
           r = s;
        }
     
        return (int)s;
     }
  	*/
}