Question

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.

Answer 1

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))