/*
 * 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 (该Email地址已收到反垃圾邮件插件保护。要显示它您需要在浏览器中启用JavaScript。)
     * 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: 该Email地址已收到反垃圾邮件插件保护。要显示它您需要在浏览器中启用JavaScript。
     * 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;
       }
     */
}