如何自己写一个电源功能？ [英] How can I write a power function myself?

问题描述

我一直想知道如何使用一个函数来计算权力（例如2 ³ ）。在大多数语言中，这些都包含在标准库中，主要是 pow（double x，double y），但是如何自己写？

我在考虑 for循环，但它认为我的大脑进入了一个循环（当我想用一个非整数指数，像5 ^4.5 或负面2 ^-21 ），我疯了;）

我写了一个函数来计算实数的幂？感谢

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哦，可能要注意：我不能使用使用权力的函数（例如 exp

解决方案

负权力不是一个问题，只需要正的幂的倒数（ 1 / x ）。

浮点数只是一点点更复杂;因为你知道小数幂等于一个根（例如 x ^（1/2）== sqrt（x）），你也知道，

分解整数部分和理性部分中的指数

使用循环计算整数幂（您可以根据因素优化其分解并重复使用部分计算）。

如果指数为负，则应用任何算法（任何迭代近似，如二分法或牛顿法）。

示例：

I was always wondering how I can make a function which calculates the power (e.g. 2³) myself. In most languages these are included in the standard library, mostly as pow(double x, double y), but how can I write it myself?

I was thinking about for loops, but it think my brain got in a loop (when I wanted to do a power with a non-integer exponent, like 5^4.5 or negatives 2^-21) and I went crazy ;)

So, how can I write a function which calculates the power of a real number? Thanks

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Oh, maybe important to note: I cannot use functions which use powers (e.g. exp), which would make this ultimately useless.

解决方案

Negative powers are not a problem, they're just the inverse (1/x) of the positive power.

Floating point powers are just a little bit more complicated; as you know a fractional power is equivalent to a root (e.g. x^(1/2) == sqrt(x)) and you also know that multiplying powers with the same base is equivalent to add their exponents.

With all the above, you can:

• Decompose the exponent in a integer part and a rational part.
• Calculate the integer power with a loop (you can optimise it decomposing in factors and reusing partial calculations).
• Calculate the root with any algorithm you like (any iterative approximation like bisection or Newton method could work).
• Multiply the result.
• If the exponent was negative, apply the inverse.

Example:

2^(-3.5) = (2^3 * 2^(1/2)))^-1 = 1 / (2*2*2 * sqrt(2))

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