gistfile1.json

{
 "metadata": {
  "name": "Fibonacci"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": "Comparison between several implementations of the Fibonacci sequence"
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Simple solution"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "First, a basic imperative implementation."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def fib(n):\n    a, b = 0, 1\n    for i in range(n):\n        a, b = a+b, a\n    return a",
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "notes"
      }
     },
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Python > 3.2"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Then a recursive approach, with a Python 3 cache."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "from functools import lru_cache\n\n@lru_cache(maxsize=None)\ndef cached_fib(n):\n    if n < 2:\n        return n\n    return cached_fib(n-1) + cached_fib(n-2)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Cython"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Finally, we load Cython and reuse the imperative implementation, but with static typing.\nWe don't even try the recursive implementation as it will lead to a huge overflow."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%load_ext cythonmagic",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%%cython\n\ndef cython_fib(int n):\n    cdef unsigned long long int a, b, i\n    a, b = 0, 1\n    for i in range(n):\n        a, b = a+b, a\n    return a",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Performance test"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Let's look at the results\u2026"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "n = 50\nprint(fib(n))\nprint(cached_fib(n))\nprint(cython_fib(n))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "12586269025\n12586269025\n12586269025\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%timeit fib(50)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "100000 loops, best of 3: 3.01 \u00b5s per loop\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%timeit cached_fib(50)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "1000000 loops, best of 3: 739 ns per loop\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%timeit cython_fib(50)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "10000000 loops, best of 3: 103 ns per loop\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Warning"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Unfortunately, when the result exceeds `2**64 - 1` (the maximum value for an `unsigned long long int`), the Cython implementation is broken."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "n = 94\nprint(fib(n))\nprint(cached_fib(n))\nprint(cython_fib(n))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "19740274219868223167\n19740274219868223167\n1293530146158671551\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": "Conclusion"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "* If you want extreme speed with n < 94, use the Cython implementation.\n* Otherwise, if you're using Python > 3.2, use the simple and mathematical recursive approach with `@lru_cache`.\n* As a last resort, you can use the regular imperative implementation."
    }
   ],
   "metadata": {}
  }
 ]
}