快速方形双倍 [英] Quickly square a double

问题描述

我正在寻找最方便的方法（ double d ）。到目前为止，我提出了两种方法：

I am looking for the fastest way to square a double (double d). So far I came up with two approaches:

1. d*d
2. Math.pow(d, 2)

测试性能我设置了三个测试用例，每个测试用例使用三个案例的相同种子生成随机数，然后计算循环中的平方数1000000次。

To test the performance I set up three test cases, in each I generate random numbers using the same seed for the three cases and just calculate the squared number in a loop 100 000 000 times.

在第一个测试案例中，使用 random.nextDouble（）生成数字，在第二种情况下使用 random.nextDouble（）* Double.MAX_VALUE 和第三个使用 random.nextDouble（）* Double.MIN_VALUE 。

In the first test case numbers are generated using random.nextDouble(), in the second case using random.nextDouble()*Double.MAX_VALUE and in the third one using random.nextDouble()*Double.MIN_VALUE.

一些运行的结果（近似结果，总是有一些变化，使用java 1.8运行，在Mac OSX Mavericks上为java 1.6编译）

The results of a couple of runs (approximate results, theres always some variation, run using java 1.8, compiled for java 1.6 on Mac OSX Mavericks)

Approach | Case 1 | Case 2 | Case 3
---------•--------•--------•-------
    1    | ~2.16s | ~2.16s | ~2.16s
    2    | ~9s    | ~30s   | ~60s

结论似乎是方法1更快但也 Math.pow 似乎表现得有些奇怪。

The conclusion seems to be that approach 1 is way faster but also that Math.pow seems to behave kind of weird.

所以我有两个问题：

1 为什么 Math.pow 这么慢，为什么它与>非常相应？ 1 ，甚至更糟糕的是< -1 数字？

1 Why is Math.pow so slow, and why does it cope badly with > 1 and even worse with < -1 numbers?

2 有没有办法提高性能超过我建议的方法1？我在想类似的事情：

2 Is there a way to improve the performance over what I suggested as approach 1? I was thinking about something like:

long l = Double.doubleToRawLongBits(d);
long sign = (l & (1 << 63));
Double.longBitsToDouble((l<<1)&sign);

但这是a）错误，b）与方法1的速度大致相同。

But that is a) wrong, and b) about the same speed as approach 1.

推荐答案

对数字求平方的最快方法是将其自身相乘。

The fastest way to square a number is to multiply it by itself.

为什么 Math.pow 这么慢？

实际上并非如此，但它正在执行取幂而不是简单的乘法。

It's really not, but it is performing exponentiation instead of simple multiplication.

为什么它严重处理> 1，更糟糕的是< -1个数字

and why does it cope badly with > 1 and even worse with < -1 numbers

首先，因为它算数学。来自 Javadoc 它还包含许多极端情况的测试。最后，我不会过分依赖你的微观基准。

First, because it does the math. From the Javadoc it also contains tests for many corner cases. Finally, I would not rely too much on your micro-benchmark.

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