{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 10**4\n",
      "x = np.abs(np.random.rand(n).astype(np.float32))\n",
      "\n",
      "sum0 = np.sum(x)\n",
      "\n",
      "b = x.astype(np.float64)\n",
      "sum1 = np.sum(b)\n",
      "\n",
      "# https://en.wikipedia.org/wiki/Kahan_summation_algorithm\n",
      "sum2 = x[0]\n",
      "c = np.single(0.0)\n",
      "for i in range(1,n):\n",
      "    y = x[i] - c           # assume c is zero.\n",
      "    t = sum2 + y           # sum2 is big, y is small\n",
      "    c = (t - sum2) - y     # c should still be zero--but isn't. Why?\n",
      "    sum2 = t\n",
      "\n",
      "# large to smallest\n",
      "d = np.sort(x)\n",
      "d = d[::-1]\n",
      "sum3 = d.sum()\n",
      "\n",
      "# smallest to largest\n",
      "e = np.sort(x)\n",
      "sum4 = e.sum()\n",
      "\n",
      "print \"single =         %.20g\"%sum0\n",
      "print \"double =         %.20g\"%sum1\n",
      "print \"Kahan =          %.20g\"%sum2\n",
      "print \"large to small = %.20g\"%sum3\n",
      "print \"small to large = %.20g\"%sum4"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "single =         4993.818359375\n",
        "double =         4993.8146699111312046\n",
        "Kahan =          4993.814453125\n",
        "large to small = 4993.80126953125\n",
        "small to large = 4993.81787109375\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Which of these is going to do well, which poorly?"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}