Math.sqrt()函数将double作为参数并返回double。我正在使用一个在所有情况下都使用完美方格的程序，我需要以整数形式获得平方根。唯一的方法是将此参数转换为int，然后返回int - 铸造的双倍？
答案 0 :(得分：24)
施法技术比初看起来要好得多。
从int到double的转换是准确的。
对于正常正数，指定Math.sqrt返回“最接近参数值的真数学平方根的双精度值”。如果输入是一个完美的方形int，则结果将是一个整数值的double，它在int范围内。
类似地，将整数值double转换回int也是准确的。
净效果是施法技术不会在您的情况下引入任何舍入误差。
如果您的程序会因使用Guava intMath API而受益，您可以使用它来执行平方根，但我不会为了避免强制转换而添加对API的依赖。
答案 1 :(得分：10)
您始终可以使用Google Guava IntMath API。
final int sqrtX = IntMath.sqrt(x, RoundingMode.HALF_EVEN);
答案 2 :(得分：1)
如果您只计算完美正方形的平方根，您是否考虑过将它们预先计算到表格中的选项？存在有限数量的整数完美正方形，并且大多数JVM可以毫不费力地同时保存所有这些正方形。如果空间非常宝贵，我相信在这方面会有其他选择。
虽然它们有65535个，但如果它太多，你可以存储一个或许四个并计算其中的一个。毕竟（x + 1）^ 2 =（x + 1）（x + 1）= x ^ 2 + 2x + 1.
答案 3 :(得分：1)
也许有人感兴趣，找到了一个链接：
http://atoms.alife.co.uk/sqrt/index.html
/*
ATOMS
Fast integer square roots in Java
Here are several fast integer square root methods, written in Java, including:
sqrt(x) agrees completely with (int)(java.lang.Math.sqrt(x)) for x < 2147483648 (i.e. 2^31), while executing about three times faster than it1.
fast_sqrt(x) agrees completely with (int)(java.lang.Math.sqrt(x)) for x < 289 (and provides a reasonable approximation thereafter), while executing about five times faster than it1.
SquareRoot.java - fast integer square root class;
SquareRootTest.java - basic speed and accuracy test class.
Thanks to Paul Hsieh's square root page for the accurate algorithm.
This code has been placed in the public domain.
Can you improve on the speed or accuracy of these methods (without chewing an "unreasonable" quantity of cache with a huge look-up table)?
If so, drop us a line, and hopefully we'll put your name up in lights.
[1: your mileage may vary]
tim@tt1.org | http://atoms.org.uk/
*/
/*
* 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;
}
*/
}
/*
* Test Integer Square Root function
*/
public class SquareRootTest {
public static void main(String args[]) {
int x = -2;
debug("" + (x == -2L));
// perform timings...
//testSpeed();
// accuracy test...
testAccuracy();
// hang...
do {} while (true);
}
static void testSpeed() {
int i;
long newtime;
long oldtime;
int N = 10000000;
int mask = (1 << 16) - 1;
// SquareRoot.fast_sqrt()...
oldtime = System.currentTimeMillis();
for (i = 0; i < N; i++) {
int temp = SquareRoot.fastSqrt(i & mask);
}
newtime = System.currentTimeMillis();
debug("SquareRoot.fast_sqrt:" + (newtime - oldtime));
// SquareRoot.sqrt()...
oldtime = System.currentTimeMillis();
for (i = 0; i < N; i++) {
int temp = SquareRoot.sqrt(i & mask);
}
newtime = System.currentTimeMillis();
debug("SquareRoot.sqrt:" + (newtime - oldtime));
/*
// SquareRoot.mborg_sqrt()...
oldtime = System.currentTimeMillis();
for (i = 0; i < N; i++) {
temp = SquareRoot.mborg_sqrt(i & mask);
}
newtime = System.currentTimeMillis();
debug("SquareRoot.mborg_sqrt:" + (newtime - oldtime));
// SquareRoot.test_sqrt()...
oldtime = System.currentTimeMillis();
for (i = 0; i < N; i++) {
temp = SquareRoot.test_sqrt(i & mask);
}
newtime = System.currentTimeMillis();
debug("SquareRoot.test_sqrt:" + (newtime - oldtime));
*/
// java.lang.Math.sqrt()...
oldtime = System.currentTimeMillis();
for (i = 0; i < N; i++) {
int temp = (int) (java.lang.Math.sqrt(i & mask));
}
newtime = System.currentTimeMillis();
debug("java.lang.Math.sqrt:" + (newtime - oldtime));
}
static void testAccuracy() {
int i;
int a;
int b;
int c;
int d;
int e;
int start = 0;
int last_wrong_value = 0;
for (i = start; ; i++) {
a = (int) (java.lang.Math.sqrt(i));
b = (int) (java.lang.Math.sqrt(i) + 0.5);
c = SquareRoot.sqrt(i);
d = SquareRoot.fastSqrt(i);
e = SquareRoot.accurateSqrt(i);
// e = SquareRoot.mborg_sqrt(i);
// f = SquareRoot.test_sqrt(i);
if (b != e) {
//if (a > (last_wrong_value * 1.05)) { // don't print too many wrong values - just a sample...
last_wrong_value = a;
debug("N:" + i + " - Math.sqrt:" + a + " - Math.sqrt+:" + b + " - accurateSqrt:" + e + " - sqrt:" + c);
}
//}
}
}
final static void debug(String o) {
System.out.println(o);
}
}
;