Category Archives: sage

An even speedier gamma function

Posted on February 27, 2013 by Fredrik

I’ve just pushed some new code to the Arb git repository for computing numerical rising factorials ($x (x+1) (x+2)\cdots (x+n-1)$) faster. It works by expanding subproducts as symbolic polynomials, and evaluating them using the rectangular splitting algorithm mentioned in the … Continue reading →

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Partitions into the quintillions

Posted on March 31, 2012 by Fredrik

One of my biggest undertakings last year was to implement the partition function $p(n)$ in FLINT. With this code, I was able to set a record by computing the number of partitions of $10^{19}$, or 10,000,000,000,000,000,000 (ten quintillion). The number … Continue reading →

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Some FLINT 2.2 highlights

Posted on June 8, 2011 by Fredrik

Version 2.2 of FLINT (Fast Library for Number Theory) was released last weekend. Some updated benchmarks are available. In this blog post, I’m going to talk a bit about features I contributed in this version. With apologies to Sebastian Pancratz … Continue reading →

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100 mpmath one-liners for pi

Posted on March 14, 2011 by Fredrik

Since it’s pi day today, I thought I’d share a list of mpmath one-liners for computing the value of pi to high precision using various representations in terms of special functions, infinite series, integrals, etc. Most of them can already … Continue reading →

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