Tim Peters <t...@python.org> added the comment:
Just FYI, if the "differential correction" step seems obscure to anyone, here's some insight, following a chain of mathematical equivalent respellings: result + x / (2 * result) = result + (sumsq - result**2) / (2 * result) = result + (sumsq - result**2) / result / 2 = result + (sumsq / result - result**2 / result) / 2 = result + (sumsq / result - result) / 2 = result + sumsq / result / 2 - result / 2 = result / 2 + sumsq / result / 2 = (result + sumsq / result) / 2 I hope the last line is an "aha!" for you then: it's one iteration of Newton's square root method, for improving a guess "result" for the square root of "sumsq". Which shouldn't be too surprising, since Newton's method is also derived from a first-order Taylor expansion around 0. Note an implication: the quality of the initial square root is pretty much irrelevant, since a Newton iteration basically doubles the number of "good bits". Pretty much the whole trick relies on computing "sumsq - result**2" to greater than basic machine precision. ---------- _______________________________________ Python tracker <rep...@bugs.python.org> <https://bugs.python.org/issue41513> _______________________________________ _______________________________________________ Python-bugs-list mailing list Unsubscribe: https://mail.python.org/mailman/options/python-bugs-list/archive%40mail-archive.com
