哪种方法来实现EXP函数在C？ [英] which method to implement exp function in c?

问题描述

我要计算在有限precision EXP函数的错误（数据类型是双）。是泰勒级数或其他特殊的算法？

I want to calculate the error of exp function under finite precision(data type is double). Is taylor series or other special algorithm?

推荐答案

一般情况下，实施电子最好的办法^{的 X 的}是通过调用 EXP 您计算平台提供的功能。

Generally, the best way to implement e^x is by calling the exp function provided by your computing platform.

如果做不到这一点，实施 EXP 功能复杂，需要几个深奥的技巧。实施通常涉及：

Failing this, implementing the exp function is complicated and requires several esoteric skills. An implementation typically involves:

• 测试输入各种特殊情况下，如NaN。


• 将日志 ₂ E的专门prepared重新presentation乘以投入，改造从电子^{的 X 的 2 的是的，其中的是 = X 的•登录 ₂ 即}


• 移动的是的整数部分为一个浮点编码的指数字段。


• 评估的小数部分的指数的是的有极小多项式。


• 这两个结果结合以上。

• Testing the input for various special cases, such as NaNs.
• Multiplying the input by a specially prepared representation of log₂e, to transform the problem from e^x to 2^y, where y = x • log₂e.
• Moving the integer part of y into the exponent field of a floating-point encoding.
• Evaluating the exponential of the fractional part of y with a minimax polynomial.
• Combining the two results above.

此外：

• 极小极大多项式工程，常有特殊的软件，使用雷米兹算法或类似的东西。


• 的工作必须有一些扩展precision这样做的最终结果，可以计算precisely。

• The minimax polynomial is engineered, often with special software, using the Remez algorithm or something similar.
• The work must be done with some extended precision so that the final result can be calculated precisely.

泰勒级数不适合，因为它们是不准确的，从它们的中心点距离评估功能。这意味着它们把太多的术语收敛于必要precision。有太多的方面，不仅需要时间，而且也难以准确地做算术。

Taylor series are inappropriate for evaluating functions because they are inaccurate away from their center points. This means they take too many terms to converge to the necessary precision. Having too many terms not only takes time but also makes it difficult to do the arithmetic accurately.

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