The most efficient way of implementing pow() function in floating point

Question

I am trying to implement my own version of pow() and sqrt() function as my custom library doesn't have pow()/sqrt() floating point support.

Can anyone help?

Answer 1

Yes, Sun can (Oracle now, I guess):

fdlibm, the "freely distributable math library", has sqrt and pow, along with many other math functions.

They're fairly high-tech implementations, though, and of course nothing is ever the "most efficient" implementation of something like this. Are you after source code to get it done, or are you really not so much looking for pow and sqrt, but actually looking for an education in floating-point algorithms programming?

Answer 2

Sure - it's easy if you have exponential and natural log functions.

Since y = x^n, you can take the natural log of both sides:

ln(y) = n*ln(x)

Then taking the exponential of both sides gives you what you want:

y = exp(n*ln(x))

If you want something better, the best place I know to look is Abramowitz and Stegun.