//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));
}