# Category Archives: sage

## An even speedier gamma function

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

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

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

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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