指数如何计算? [英] How are exponents calculated?

问题描述

我试图确定我的一种算法的渐进运行时间，该算法使用指数，但是我不确定如何以编程方式计算指数.

I'm trying to determine the asymptotic run-time of one of my algorithms, which uses exponents, but I'm not sure of how exponents are calculated programmatically.

我正在专门寻找用于双精度浮点数的pow()算法.

I'm specifically looking for the pow() algorithm used for double-precision, floating point numbers.

推荐答案

我有机会了解fdlibm的实现.注释描述了所使用的算法:

I've had a chance to look at fdlibm's implementation. The comments describe the algorithm used:

 *                    n
 * Method:  Let x =  2   * (1+f)
 *      1. Compute and return log2(x) in two pieces:
 *              log2(x) = w1 + w2,
 *         where w1 has 53-24 = 29 bit trailing zeros.
 *      2. Perform y*log2(x) = n+y' by simulating muti-precision
 *         arithmetic, where |y'|<=0.5.
 *      3. Return x**y = 2**n*exp(y'*log2)

其后列出所有已处理的特殊情况(0、1，inf，nan).

followed by a listing of all the special cases handled (0, 1, inf, nan).

在所有特殊情况下，代码中最密集的部分都涉及到log2和2**计算.在这两个循环中都没有循环.因此，尽管浮点图元很复杂，但它看起来像一个渐近恒定时间算法.

The most intense sections of the code, after all the special-case handling, involve the log2 and 2** calculations. And there are no loops in either of those. So, the complexity of floating-point primitives notwithstanding, it looks like a asymptotically constant-time algorithm.

浮点专家(我不是其中的一员)欢迎发表评论. :-)

Floating-point experts (of which I'm not one) are welcome to comment. :-)

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