⚡️ Golf sqrt and cbrt by getting a better initial estimate and removing an iteration#1515
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…moving an iteration (#1515) * ⚡️Golf `sqrt` and `cbrt` by getting a better initial estimate and removing an iteration * ⚡️Golf `cbrt` a little bit more by cutting corners during initialization
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* rebase with origin/main * T * Added test * T * T * ⚡️ Golf `sqrt` and `cbrt` by getting a better initial estimate and removing an iteration (#1515) * ⚡️Golf `sqrt` and `cbrt` by getting a better initial estimate and removing an iteration * ⚡️Golf `cbrt` a little bit more by cutting corners during initialization * ⚡️ Golf `cbrt` by using a small table for an even better initial estimate and removing another iteration (#1523) * ⚡️ Golf `cbrt` by using a small table for an even better initial estimate and removing another iteration * Formatting * T --------- Co-authored-by: duncancmt <1207590+duncancmt@users.noreply.github.com>
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Description
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sqrtandcbrtcan be gas optimized.sqrtonly needs 6 Babylonian steps. A better initial estimate incbrtallows us to shave a Newton-Raphson iteration later; also going down to 6.Implementation by a meatbag. Formal proof of correctness is vibe coded.
Checklist
Ensure you completed all of the steps below before submitting your pull request:
forge fmt?forge test?