How can I write a function to compute a^b when b could be negative or fractional?

Question

I want to make a exponent function that allows fractions and negatives. I have seen related questions but haven't really found what I'm looking for. I need a function that will be able to do something like this pow(5,1/2) and pow(7,-2). Is there anyone that can help me?

Note that, in C, `1/2` equals 0, so `pow(5, 1/2)` will be `pow(5, 0)`, which is 1. Consider using 1.0f/2 instead — luiscubal, Oct 07 '13 at 23:01
Have you tried [`pow`](http://en.cppreference.com/w/c/numeric/math/pow)? — Oliver Charlesworth, Oct 07 '13 at 23:02
@OliCharlesworth- I think the question is how to write a function like this from scratch. — templatetypedef, Oct 07 '13 at 23:03

score 1 · Answer 1 · answered Oct 07 '13 at 23:07

1

If you have the ability to compute e^x and ln x, then you can use the following identity to compute a^b:

a^b = e^{b ln a}

It looks like the x86 architecture has native support for computing logarithms; if you look at the x86 instruction listings, the FYL2X instruction can compute logs. You can probably approximate e^x using the Taylor series:

e^x = 1 + x + x² / 2! + x³ / 3! + x⁴ / 4! + ...

Hope this helps!

answered Oct 07 '13 at 23:07

templatetypedef

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Good implementations of math library routines use minimax polynomials or something similar, not Taylor series. Taylor series converge too slowly and have poor error properties. – Eric Postpischil Oct 07 '13 at 23:18
@EricPostpischil- Can you post a link to something about that? I'm aware Taylor series aren't the best option, but I haven't heard about minimax polynomials. – templatetypedef Oct 07 '13 at 23:22
Start with Wikipedia for background and introduction. There are links in [my answer here](http://stackoverflow.com/a/15351205/298225). I also recommend [Handbook of Floating-Point Arithmetic](http://www.amazon.com/Handbook-Floating-Point-Arithmetic-Jean-Michel-Muller/dp/081764704X). – Eric Postpischil Oct 07 '13 at 23:29

score 0 · Answer 2 · answered Oct 07 '13 at 23:07

0

if you would like to implement pow from scratch, then you might want to use Taylor's series.

http://en.wikipedia.org/wiki/Taylor_series

answered Oct 07 '13 at 23:07

Zac Wrangler

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Good implementations of math library routines use minimax polynomials or something similar, not Taylor series. Taylor series converge too slowly and have poor error properties. – Eric Postpischil Oct 07 '13 at 23:18

How can I write a function to compute a^b when b could be negative or fractional?

2 Answers2