From Python To Cython

This longer post will show you some of the coding skills you’ll need for turning your existing Python code into the Python-C hybrid we call Cython. In doing so, we’ll be digging into some C static data types, to see how much faster Python code will run, and restructuring some Python code along the way for maximum speed.

With Cython, all the benefits of Python are still yours – easily readable code, fast development cycles, powerful high level commands, maintainability, a suite of web development frameworks, a huge standard library for data science, machine learning, imaging, databases and security, plus easy manipulation of files, documents and strings. You should still use Python for all these things – these are what Python does best. But you should also consider combining them with Cython to speed up the computationally intensive Python functions that needs to be fast. Continue reading “From Python To Cython”

Parallel Python – 1: Prime Numbers

With the impending demise of Moore’s Law, multiple cores are a common manufacturers’ workaround for improving hardware performance, whether or not your installed apps can use the parallel architecture.

And with each new release of Python, parallel programming gets even easier. But the degree to which your code can use your multiple cores will depend on the kind of problem you are trying to solve, on the implementation of Python you are running and, as it turns out, how truly parallel the underlying architecture of your system actually is.

The goal of this series of posts is to see how adaptable some of my existing code is to take advantage of multi-core hardware, to see what changes need be made to scale it, and to measure the performance improvements from the exercise. Continue reading “Parallel Python – 1: Prime Numbers”

Eratosthenes 2: Swifter, Further, Cooler

Human & alien hands

 

This post describes the process I used to design an algorithm that allows you to implement a modified Sieve of Eratosthenes to bypass the memory limitations of your computer and, in the process, to find big primes well beyond your 64-bit computer’s supposed numerical limit of 2.0e63 (9.223e18). Beyond that, with this algorithm, the only limitation is the speed of your CPU.

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A Faster Sieve of Eratosthenes

SievePic

The Sieve of Eratosthenes is a beautifully elegant way of finding all the prime numbers up to any limit. The goal of this post is to implement the algorithm as efficiently as possible in standard Python 3.5, without resorting to importing any modules, or to running it on faster hardware.

Eratosthenes was a Greek scholar who lived in Alexandria (276BC to 194BC) in the so-called Hellenistic period. He was working about a century after Alexander, and about a century before the Romans arrived to impose their cultural desert and call it peace. And then do nothing with the body of knowledge they discovered. Literally. For over 1,600 years, if you count Constantinople. Not a damn thing.

So much for overly religious, centralised, bureaucratic superstates, obsessed with conquest. But I digress.

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Finding Primes Using Complex Numbers

Pythagoras In LegoWith complex numbers, I always feel as if I’m getting a glimpse of something truly awesome that lies hidden within mathematics. The first time I understood how they worked, I thought it was some form of magic.

I get the same feeling with prime numbers. Like many, I’ve looked at them from all angles – prime gaps, large primes, prime densities, prime sieves – and they continue to fascinate. A few months ago I was thumbing through Henry Warren’s programmers cookbook Hacker’s Delight (A) and discovered a whole chapter on the various formulas for (some of) them. Mind-bending stuff.

Continue reading “Finding Primes Using Complex Numbers”