java在BigDecimal#divide（）中的“scale”越高，速度越快？

Question

我提出了一个问题，最初是一个问答式的问题

原来的问题是：

在BigDecimal#divide()中较高的scale对性能有多大影响

所以，我创建了这个SSCCE：

import java.math.BigDecimal;
import java.math.RoundingMode;
import java.util.concurrent.TimeUnit;

public class Test {

    public static void main(String args[]) {
        int[] scales = new int[] {1, 10, 50, 100, 500, 1000, 5000, 100000, 1000000};
        for(Integer scale : scales) {
            long start = System.nanoTime();
            BigDecimal.ONE.divide(BigDecimal.valueOf(7), scale, RoundingMode.HALF_UP);
            long end = System.nanoTime();
            long elapsed = end - start;
            String elapsed_str = String.format("%d mins, %d secs, %d millis, %d nanos", 
                TimeUnit.NANOSECONDS.toMinutes(elapsed),
                TimeUnit.NANOSECONDS.toSeconds(elapsed) - TimeUnit.MINUTES.toSeconds(TimeUnit.NANOSECONDS.toMinutes(elapsed)),
                TimeUnit.NANOSECONDS.toMillis(elapsed) - TimeUnit.SECONDS.toMillis(TimeUnit.NANOSECONDS.toSeconds(elapsed)),
                elapsed - TimeUnit.MILLISECONDS.toNanos(TimeUnit.NANOSECONDS.toMillis(elapsed))
            );
            System.out.println("Time for scale = " + scale + ": " + elapsed_str);
        }
    }
}

结果是：

Time for scale = 1: 0 mins, 0 secs, 2 millis, 883903 nanos
Time for scale = 10: 0 mins, 0 secs, 0 millis, 13995 nanos
Time for scale = 50: 0 mins, 0 secs, 1 millis, 138727 nanos
Time for scale = 100: 0 mins, 0 secs, 0 millis, 645636 nanos
Time for scale = 500: 0 mins, 0 secs, 1 millis, 250220 nanos
Time for scale = 1000: 0 mins, 0 secs, 4 millis, 38957 nanos
Time for scale = 5000: 0 mins, 0 secs, 15 millis, 66549 nanos
Time for scale = 100000: 0 mins, 0 secs, 500 millis, 873987 nanos
Time for scale = 1000000: 0 mins, 50 secs, 183 millis, 686684 nanos

随着数量级的增加，性能会受到指数级的影响。但让我挠头的是这些台词：

Time for scale = 1: 0 mins, 0 secs, 2 millis, 883903 nanos
Time for scale = 10: 0 mins, 0 secs, 0 millis, 13995 nanos
Time for scale = 50: 0 mins, 0 secs, 1 millis, 138727 nanos
Time for scale = 100: 0 mins, 0 secs, 0 millis, 645636 nanos
Time for scale = 500: 0 mins, 0 secs, 1 millis, 250220 nano

看来10的尺度对于BigDecimal#divide()来说是最佳的？而且100的规模比50快？我认为这可能只是一个异常，所以我再次运行它（这次，省略了最高的两个刻度，因为我不想等待50秒：），结果如下：

Time for scale = 1: 0 mins, 0 secs, 3 millis, 440903 nanos
Time for scale = 10: 0 mins, 0 secs, 0 millis, 10263 nanos
Time for scale = 50: 0 mins, 0 secs, 0 millis, 833169 nanos
Time for scale = 100: 0 mins, 0 secs, 0 millis, 487492 nanos
Time for scale = 500: 0 mins, 0 secs, 0 millis, 802846 nanos
Time for scale = 1000: 0 mins, 0 secs, 2 millis, 475715 nanos
Time for scale = 5000: 0 mins, 0 secs, 16 millis, 646117 nanos

同样地，10比1快得多，100比50快得多

我试了一次又一次，结果100总是比50快。而且1的尺度总是比小于1000的任何事物都慢

有人有解释吗