Add Replicated Sqrt operation

[yanndupis]

One more for the road. When working on a PyMoose example, I realized that sqrt was missing to compute pearson correlation. So here it is.

• Add replicated sqrt. We compute the square root using log2 and pow2. There are other algorithm which could much more efficient but it should be good enough for the initial implementation.
• Add sqrt to logical dialect.
• Add sqrt to the edsl.

[rdragos]

This looks good to me, Yann! One small request, could you test a bit the bounds that this sqrt function provides accurate results? This way we would know how to calibrate the magnitude of our inputs when we operate with sqrt

[kkloberdanz]

Looks good! Perhaps a small proof in the comments would help a future reader?

2^(0.5 * log_2 x) = (2^log_2 x)^0.5 = x^0.5 = sqrt(x)

[rdragos]

We should add a followup issue to implement the square root as we've described in our whitepaper.

[yanndupis]

Thank you both for the review.

@rdragos good question. I checked the bounds. With 10 fractional precision, we get accurate result for [0.001, 1000] with error threshold set to 0.1 and for 20 fractional precision we get accurate result [0.01, 500000] for error threshold set to 0.001.

Sounds good, I will open a follow up issue to implement sqrt as described in the whitepaper.

Thanks

[yanndupis]

#1058