{
 "metadata": {
  "name": "conversion_profile"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import pandas as pd\nfrom cStringIO import StringIO\nimport random\nfrom decimal import Decimal\nimport numpy as np\nimport matplotlib.pyplot as plt\n%matplotlib inline",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def xstrtod(s):\n    return pd.read_csv(StringIO(s), header=None)[0][0]",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def randnum(length):\n    s = '1.'\n    for i in range(length):\n        s += random.choice('0123456789')\n    return s",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def ulp(s):\n    num = Decimal(s)\n    f = np.float64(s)\n    a = f.view((np.uint8, 8))\n    # Since this is uint8 make sure the result doesn't accidentally wrap\n    if a[0] == 0:\n        a[0] = 1\n    elif a[0] == 255:\n        a[0] = 254\n    elif Decimal(f) < num:\n        a[0] += 1\n    elif Decimal(f) > num:\n        a[0] -= 1\n    f2 = a.view(np.float64)[0]\n    return abs(f2 - f)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def test_conversion(sig_figs):\n    y = []\n    diffs = []\n    great_vals = 0\n    good_vals = 0\n\n    for i in range(1000):\n        val = randnum(sig_figs)\n        guess = xstrtod(val)\n        decimal_diff = abs(Decimal(val) - Decimal(guess))\n        ulp_diff = decimal_diff / Decimal(ulp(val))\n        y.append(float(ulp_diff))\n        diffs.append(float(decimal_diff))\n        if float(ulp_diff) < 1.0:\n            good_vals += 1\n        if float(ulp_diff) < 0.5:\n            great_vals += 1\n\n    return (great_vals, good_vals, y, diffs)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def graph_results(sig_figs):\n    great_vals, good_vals, y, diffs = test_conversion(sig_figs)\n    print('{0}% of values within 0.5 ULP'.format(great_vals * 100.0 / 1000))\n    print('{0}% of values within 1.0 ULP'.format(good_vals * 100.0 / 1000))\n    plt.hist(y, bins=30, log=True)\n    plt.xlabel('Conversion error in ULP')\n    plt.ylabel('Logarithm of frequency')\n    plt.show()\n    plt.hist(diffs, bins=50, log=True)\n    plt.xlabel('Decimal conversion error')\n    plt.ylabel('Logarithm of frequency')\n    plt.show()",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "graph_results(5)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "100.0% of values within 0.5 ULP\n100.0% of values within 1.0 ULP\n"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0x7fde76e05ad0>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HTb6+bqbYqKgo9OnTB97e3mjbti1atGgBg8GAmpoazJgxAzqdDomJifj1119N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\nQmCC\n",
       "text": "<matplotlib.figure.Figure at 0x7fde76c2bb50>"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "graph_results(10)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "100.0% of values within 0.5 ULP\n100.0% of values within 1.0 ULP\n"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0x7fde76990e50>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8XlVVVYmWLVtavX4eSZDdffXVV1i/fj2ioqLw1FNPobCwEBcuXMD+/fuRkpKC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\n",
       "text": "<matplotlib.figure.Figure at 0x7fde76bfc350>"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "graph_results(15)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "100.0% of values within 0.5 ULP\n100.0% of values within 1.0 ULP\n"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0x7fde76cc4350>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YGDz55JMoLS3FmTNnsHfvXqSnp6N169YAgIceesjo8xtGio2MjETv3r3h7u6O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\nQUREkv4Pdjs+mtI2nxMAAAAASUVORK5CYII=\n",
       "text": "<matplotlib.figure.Figure at 0x7fde76cc4810>"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "graph_results(20)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "59.8% of values within 0.5 ULP\n91.6% of values within 1.0 ULP\n"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0x7fde76ba2350>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
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TUVFR4sqVK6KyslIEBgYKIZo3ZKqurhZCCFFZWSnCw8PbjeuXX34Rd999t7TB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\nTApERCRhUiAiIgmTAhERSZgUiIhI8n/gZaChL90otAAAAABJRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0x7fde7696a290>"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "graph_results(45)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "57.8% of values within 0.5 ULP\n90.4% of values within 1.0 ULP\n"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0x7fde769143d0>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8efNEUlKSqK6ublYX2Xfy5EnRq1cvIUTD//HNN9/cpvOZzWYxbNgwq7IePXpI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\n",
       "text": "<matplotlib.figure.Figure at 0x7fde76ac3650>"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "graph_results(100)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "61.0% of values within 0.5 ULP\n90.6% of values within 1.0 ULP\n"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bjz/++CXXs3XrVi1atEhffvmlNmzYoICAAC1YsECSVFlZqZtvvlnFxcXq3bt3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\nRAEAMEWiAACY+n8hctTQjVUQTAAAAABJRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0x7fde76c6ca90>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0x7fde76d19150>"
      }
     ],
     "prompt_number": 12
    }
   ],
   "metadata": {}
  }
 ]
}