Classical Pell Equations Outperform math.sqrt in float64…
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Classical Pell Equations Outperform math.sqrt in float64 by up to 2.5×
I've been exploring whether the Pell equation x²−Dy²=1 can be used to compute square roots of primes faster than Python's math.sqrt(). The continued-fraction convergents turn out to give rational approximations that are 1.5–2.5× faster in float64 for repeated calculations, and scale up to 33–36 digit precision for primes as large as 15 million. Full write-up with benchmarks here;
https://musingsofvsmv.blogspot.com/2025/08/from-pell-to-precision-classical-math.html
#technology
I've been exploring whether the Pell equation x²−Dy²=1 can be used to compute square roots of primes faster than Python's math.sqrt(). The continued-fraction convergents turn out to give rational approximations that are 1.5–2.5× faster in float64 for repeated calculations, and scale up to 33–36 digit precision for primes as large as 15 million. Full write-up with benchmarks here;
https://musingsofvsmv.blogspot.com/2025/08/from-pell-to-precision-classical-math.html
#technology
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