ベクトルの正規化を高速化するために、Java にFast Inverse Square Rootを実装しようとしています。ただし、Java で単精度バージョンを実装すると1F / (float)Math.sqrt()、最初とほぼ同じ速度が得られますが、すぐに半分の速度に低下します。これは興味深いことです。なぜなら、Math.sqrt は (私が推測するに) ネイティブな方法を使用していますが、これには浮動小数点除算が含まれており、非常に遅いと聞いています。数値を計算するための私のコードは次のとおりです。
public static float fastInverseSquareRoot(float x){
float xHalf = 0.5F * x;
int temp = Float.floatToRawIntBits(x);
temp = 0x5F3759DF - (temp >> 1);
float newX = Float.intBitsToFloat(temp);
newX = newX * (1.5F - xHalf * newX * newX);
return newX;
}
私が書いた短いプログラムを使用して、1,600 万回ごとに反復し、結果を集計して繰り返すと、次のような結果が得られます。
1F / Math.sqrt() took 65209490 nanoseconds.
Fast Inverse Square Root took 65456128 nanoseconds.
Fast Inverse Square Root was 0.378224 percent slower than 1F / Math.sqrt()
1F / Math.sqrt() took 64131293 nanoseconds.
Fast Inverse Square Root took 26214534 nanoseconds.
Fast Inverse Square Root was 59.123647 percent faster than 1F / Math.sqrt()
1F / Math.sqrt() took 27312205 nanoseconds.
Fast Inverse Square Root took 56234714 nanoseconds.
Fast Inverse Square Root was 105.895914 percent slower than 1F / Math.sqrt()
1F / Math.sqrt() took 26493281 nanoseconds.
Fast Inverse Square Root took 56004783 nanoseconds.
Fast Inverse Square Root was 111.392402 percent slower than 1F / Math.sqrt()
両方でほぼ同じ速度の数値を一貫して取得し、続いて高速逆平方根が必要な時間の約 60% を節約する反復が1F / Math.sqrt()続き、続いて高速逆平方根が実行されるのに約 2 倍の時間がかかる反復が続きます。制御。なぜ FISR が同じ -> 60% 速い -> 100% 遅くなるのか、私は混乱しています。これは、プログラムを実行するたびに発生します。
編集:上記のデータは、Eclipseで実行したときのものです。プログラムを実行すると、javac/javaまったく異なるデータが得られます。
1F / Math.sqrt() took 57870498 nanoseconds.
Fast Inverse Square Root took 88206794 nanoseconds.
Fast Inverse Square Root was 52.421004 percent slower than 1F / Math.sqrt()
1F / Math.sqrt() took 54982400 nanoseconds.
Fast Inverse Square Root took 83777562 nanoseconds.
Fast Inverse Square Root was 52.371599 percent slower than 1F / Math.sqrt()
1F / Math.sqrt() took 21115822 nanoseconds.
Fast Inverse Square Root took 76705152 nanoseconds.
Fast Inverse Square Root was 263.259133 percent slower than 1F / Math.sqrt()
1F / Math.sqrt() took 20159210 nanoseconds.
Fast Inverse Square Root took 80745616 nanoseconds.
Fast Inverse Square Root was 300.539585 percent slower than 1F / Math.sqrt()
1F / Math.sqrt() took 21814675 nanoseconds.
Fast Inverse Square Root took 85261648 nanoseconds.
Fast Inverse Square Root was 290.845374 percent slower than 1F / Math.sqrt()
EDIT2:いくつかの応答の後、数回の反復後に速度が安定するように見えますが、安定する数は非常に不安定です。誰でも理由がわかりますか？
これが私のコードです（正確には簡潔ではありませんが、ここにすべてがあります）：
public class FastInverseSquareRootTest {
public static FastInverseSquareRootTest conductTest() {
float result = 0F;
long startTime, endTime, midTime;
startTime = System.nanoTime();
for (float x = 1F; x < 4_000_000F; x += 0.25F) {
result = 1F / (float) Math.sqrt(x);
}
midTime = System.nanoTime();
for (float x = 1F; x < 4_000_000F; x += 0.25F) {
result = fastInverseSquareRoot(x);
}
endTime = System.nanoTime();
return new FastInverseSquareRootTest(midTime - startTime, endTime
- midTime);
}
public static float fastInverseSquareRoot(float x) {
float xHalf = 0.5F * x;
int temp = Float.floatToRawIntBits(x);
temp = 0x5F3759DF - (temp >> 1);
float newX = Float.intBitsToFloat(temp);
newX = newX * (1.5F - xHalf * newX * newX);
return newX;
}
public static void main(String[] args) throws Exception {
for (int i = 0; i < 7; i++) {
System.out.println(conductTest().toString());
}
}
private long controlDiff;
private long experimentalDiff;
private double percentError;
public FastInverseSquareRootTest(long controlDiff, long experimentalDiff) {
this.experimentalDiff = experimentalDiff;
this.controlDiff = controlDiff;
this.percentError = 100D * (experimentalDiff - controlDiff)
/ controlDiff;
}
@Override
public String toString() {
StringBuilder sb = new StringBuilder();
sb.append(String.format("1F / Math.sqrt() took %d nanoseconds.%n",
controlDiff));
sb.append(String.format(
"Fast Inverse Square Root took %d nanoseconds.%n",
experimentalDiff));
sb.append(String
.format("Fast Inverse Square Root was %f percent %s than 1F / Math.sqrt()%n",
Math.abs(percentError), percentError > 0D ? "slower"
: "faster"));
return sb.toString();
}
}