//精度 private final static double accuracy= 1e-6; /** * 暴力求解 */ public static double bruteSqrt(double x) { assert(x>=0); double ans=0.0; while (Math.abs(x - ans * ans) > accuracy)ans += accuracy; return ans; } /** * 牛顿法求解 */ public static double newtonSqrt(double x) { assert(x>=0); double avg = x; double last_avg = Double.MAX_VALUE; while (Math.abs(avg - last_avg) > accuracy) { last_avg = avg; avg = (avg + x / avg) / 2; } return avg; } /** * 二分法求解 */ public static double binarySqrt(double x) { assert(x>=0); double low = 0; double high = x; double mid = Double.MAX_VALUE; double last_mid = Double.MIN_VALUE; while (Math.abs(mid - last_mid) > accuracy) { last_mid = mid; mid = (low + high)/2; if (mid*mid>x)high = mid; if (mid*mid<x)low = mid; } return mid; } private final static int[] LUT = { 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 }; /** * 查表法求解 */ public static int intLutSqrt(int x) { int xn; if (x >= 0x10000) { if (x >= 0x1000000) { if (x >= 0x10000000) { if (x >= 0x40000000) { xn = LUT[x >> 24] << 8; } else { xn = LUT[x >> 22] << 7; } } else { if (x >= 0x4000000) { xn = LUT[x >> 20] << 6; } else { xn = LUT[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 = LUT[x >> 16] << 4; } else { xn = LUT[x >> 14] << 3; } } else { if (x >= 0x40000) { xn = LUT[x >> 12] << 2; } else { xn = LUT[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 = (LUT[x >> 8]) + 1; } else { xn = (LUT[x >> 6] >> 1) + 1; } } else { if (x >= 0x400) { xn = (LUT[x >> 4] >> 2) + 1; } else { xn = (LUT[x >> 2] >> 3) + 1; } } return ((xn * xn) > x) ? --xn : xn; } else { if (x >= 0) { return LUT[x] >> 4; } } } return -1; } /** * Quake III中快速求解平方根倒数的方法 */ public static float fastInvSqrt(float x) { float xhalf = 0.5f*x; int f2i = Float.floatToRawIntBits(x); f2i = 0x5f375a86-(f2i>>1); x = Float.intBitsToFloat(f2i); x = x*(1.5f-xhalf*x*x); x = x*(1.5f-xhalf*x*x); return x; } /** * Quake III中快速求解平方根方法 */ public static float fastSqrt(float x) { float y=x; float xhalf = 0.5f*x; int f2i = Float.floatToRawIntBits(x); f2i = 0x5f3759df-(f2i>>1); x = Float.intBitsToFloat(f2i); x = x * (1.5f-(xhalf*x*x)); x = x * (1.5f-(xhalf*x*x)); return y*x; } public static void main(String[] args) { System.out.println(bruteSqrt(3)); System.out.println(newtonSqrt(3)); System.out.println(binarySqrt(3)); System.out.println(intLutSqrt(64)); System.out.println(1/fastInvSqrt(3)); System.out.println(fastSqrt(3)); }