通过将sqrt（-0.0）定义为-0.0来简化数值算法？ [英] What numerical algorithm is simplified by defining sqrt(-0.0) as -0.0?

问题描述

IEEE 754标准定义负零的平方根为负零。这个选择很容易理解，但是其他选择，比如定义 sqrt（-0.0）为 NaN ，可以也要合理化，并且在硬件上更容易实现。如果担心程序员会编写 if（x> = 0.0），那么sqrt（x）else 0.0 并被这个表达式咬住，计算结果为当 x 是 -0.0 ，那么 sqrt（ - 0.0）可以被定义为 +0.0 （实际上，对于这个特定的表达式，结果会更加一致）。

是否有一个数值算法，其中 sqrt（-0.0）定义为 -0.0 简化了算法本身的逻辑？


解决方案

唯一的数学上合理的结果是0.有一个合理的问题应该是+0还是-0。对于大多数计算来说，它根本没有什么区别，但是在-0约定下，有一些特定的复杂表达式使得结果更有意义。确切的细节超出了本网站的范围，但这是它的要义。

当我不在度假时，我可以解释一些，如果其他人我不会打我的。

The IEEE 754 standard defines the square root of negative zero as negative zero. This choice is easy enough to rationalize, but other choices, such as defining sqrt(-0.0) as NaN, can be rationalized too and are easier to implement in hardware. If the fear was that programmers would write if (x >= 0.0) then sqrt(x) else 0.0 and be bitten by this expression evaluating to NaN when x is -0.0, then sqrt(-0.0) could have been defined as +0.0 (actually, for this particular expression, the results would be even more consistent).

Is there a numerical algorithm in particular where having sqrt(-0.0) defined as -0.0 simplifies the logic of the algorithm itself?

解决方案

The only mathematically reasonable result is 0. There is a reasonable question of whether it should be +0 or -0. For most computations it makes no difference at all, but there are some specific complex expressions for which the result makes more sense under the -0 convention. The exact details are outside the scope of this site, but that's the gist of it.

I may explain some more when I'm not on vacation, if someone else doesn't beat me to it.

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