{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "# ^^ what's this about?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def pretty_print_fp(x):\n",
      "    print \"---------------------------------------------\"\n",
      "    print \"Floating point structure for %r\" % x\n",
      "    print \"---------------------------------------------\"\n",
      "    import struct\n",
      "    s = struct.pack(\"d\", x)\n",
      "    print \"Hex pattern:\", \" \".join(\"%02x\" % ord(i) for i in s[::-1])\n",
      "\n",
      "    def get_bit(i):\n",
      "        byte_nr, bit_nr = divmod(i, 8)\n",
      "        return int(bool(\n",
      "            ord(s[byte_nr]) & (1 << bit_nr)\n",
      "            ))\n",
      "\n",
      "    def get_bits(lsb, count):\n",
      "        return sum(get_bit(i+lsb)*2**i for i in xrange(count))\n",
      "\n",
      "    # https://en.wikipedia.org/wiki/Double_precision_floating-point_format\n",
      "\n",
      "    print \"Sign bit (1:negative):\", get_bit(63)\n",
      "    exponent = get_bits(52, 11)\n",
      "    print \"Exponent: %d (unshifted: %d = 0x%x)\" % (exponent - 1023, exponent, exponent)\n",
      "    fraction = get_bits(0, 52)\n",
      "    print \"Fraction:\", hex(fraction)\n",
      "    significand = fraction + 2**52\n",
      "    print \"Significand:\", hex(significand)\n",
      "    print \"Shifted significand:\", repr(significand / (2**52))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pretty_print_fp(1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "---------------------------------------------\n",
        "Floating point structure for 1\n",
        "---------------------------------------------\n",
        "Hex pattern: 3f f0 00 00 00 00 00 00\n",
        "Sign bit (1:negative): 0\n",
        "Exponent: 0 (unshifted: 1023 = 0x3ff)\n",
        "Fraction: 0x0\n",
        "Significand: 0x10000000000000\n",
        "Shifted significand: 1.0\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Examples to try:\n",
      "\n",
      "- 1\n",
      "- 1+2**-52\n",
      "- 0\n",
      "- 1+2**-53\n",
      "- 1-2**-52\n",
      "- 1-2**-53\n",
      "- NaN\n",
      "- What value should we try to see a denormal?\n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}