SimpleUnums_old.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "immutable Unum\n",
    "    s::Int    # sign\n",
    "    e::Int    # exponent\n",
    "    f::Int    # fraction\n",
    "    u::Int    # ubit\n",
    "    esm1::Int   # exponent size - 1\n",
    "    fsm1::Int   # fraction size - 1\n",
    "    ########\n",
    "    es::Int\n",
    "    fs::Int\n",
    "    bias::Int\n",
    "\n",
    "    \n",
    "    Unum(s, e, f, u, esm1, fsm1, bias) = new(s, e, f, u, esm1, fsm1, esm1+1, fsm1+1, (1<<bias)-1)\n",
    "    Unum(s, e, f, u, esm1, fsm1) = new(s, e, f, u, esm1, fsm1, esm1+1, fsm1+1, esm1)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sign (generic function with 8 methods)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Base.sign(u::Unum) = u.s == 0 ? +1 : -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2,2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "esizesize,fsizesize = 2, 2  # utag = [esizesize, fsizesize]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Unum(0,0,0,0,0,0,1,1,0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = Unum(0, 0, 0, 0, 0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "convert (generic function with 535 methods)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function call(::Type{Float64}, u::Unum)\n",
    "    denominator = 1 << u.fs\n",
    "    \n",
    "    if u.e == 0 \n",
    "        sign(u) * 2.0^(1-u.bias) * u.f / denominator  # assumes u.s is 0 or 1\n",
    "        \n",
    "    elseif u.e == 1<<u.es-1 && u.f==1<<u.fs-1 && es==(1<<esizesize) && fs==(1<<fsizesize)\n",
    "        # not efficient!\n",
    "        sign(u) * Inf\n",
    "        \n",
    "    else\n",
    "        sign(u) * 2.0^(u.e-u.bias) * (1.0 + u.f/denominator)\n",
    "    end\n",
    "    \n",
    "end\n",
    "\n",
    "Base.convert(::Type{Float64}, u::Unum) = Float64(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.375"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "convert(Float64,Unum(0,1,1,0,2,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.375"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Float64(Unum(0,1,1,0,2,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0//"
     ]
    }
   ],
   "source": [
    "esizesize, fsizesize = 2, 2\n",
    "es = 1 << esizesize\n",
    "fs = 1 << fsizesize\n",
    "\n",
    "unums = vec([Unum(0, e, f, 0, es-1, fs-1) for e=0:2^es-1, f=0:2^fs-1])\n",
    "\n",
    "nums = map(Float64, unums)\n",
    "sort!(nums)\n",
    "\n",
    "for z in nums\n",
    "    print(rationalize(z), \", \")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "256"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(nums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1, 1//1024, 1//512, 3//1024, 1//256, 5//1024, 3//512, 7//1024, 1//128, 9//1024, 5//512, 11//1024, 3//256, 13//1024, 7//512, 15//1024, 1//64, 17//1024, 9//512, 19//1024, 5//256, 21//1024, 11//512, 23//1024, 3//128, 25//1024, 13//512, 27//1024, 7//256, 29//1024, 15//512, 31//1024, 1//32, 17//512, 9//256, 19//512, 5//128, 21//512, 11//256, 23//512, 3//64, 25//512, 13//256, 27//512, 7//128, 29//512, 15//256, 31//512, 1//16, 17//256, 9//128, 19//256, 5//64, 21//256, 11//128, 23//256, 3//32, 25//256, 13//128, 27//256, 7//64, 29//256, 15//128, 31//256, 1//8, 17//128, 9//64, 19//128, 5//32, 21//128, 11//64, 23//128, 3//16, 25//128, 13//64, 27//128, 7//32, 29//128, 15//64, 31//128, 1//4, 17//64, 9//32, 19//64, 5//16, 21//64, 11//32, 23//64, 3//8, 25//64, 13//32, 27//64, 7//16, 29//64, 15//32, 31//64, 1//2, 17//32, 9//16, 19//32, 5//8, 21//32, 11//16, 23//32, 3//4, 25//32, 13//16, 27//32, 7//8, 29//32, 15//16, 31//32, 1//1, 17//16, 9//8, 19//16, 5//4, 21//16, 11//8, 23//16, 3//2, 25//16, 13//8, 27//16, 7//4, 29//16, 15//8, 31//16, 2//1, 17//8, 9//4, 19//8, 5//2, 21//8, 11//4, 23//8, 3//1, 25//8, 13//4, 27//8, 7//2, 29//8, 15//4, 31//8, 4//1, 17//4, 9//2, 19//4, 5//1, 21//4, 11//2, 23//4, 6//1, 25//4, 13//2, 27//4, 7//1, 29//4, 15//2, 31//4, 8//1, 17//2, 9//1, 19//2, 10//1, 21//2, 11//1, 23//2, 12//1, 25//2, 13//1, 27//2, 14//1, 29//2, 15//1, 31//2, 16//1, 17//1, 18//1, 19//1, 20//1, 21//1, 22//1, 23//1, 24//1, 25//1, 26//1, 27//1, 28//1, 29//1, 30//1, 31//1, 32//1, 34//1, 36//1, 38//1, 40//1, 42//1, 44//1, 46//1, 48//1, 50//1, 52//1, 54//1, 56//1, 58//1, 60//1, 62//1, 64//1, 68//1, 72//1, 76//1, 80//1, 84//1, 88//1, 92//1, 96//1, 100//1, 104//1, 108//1, 112//1, 116//1, 120//1, 124//1, 128//1, 136//1, 144//1, 152//1, 160//1, 168//1, 176//1, 184//1, 192//1, 200//1, 208//1, 216//1, 224//1, 232//1, 240//1, 248//1, 256//1, 272//1, 288//1, 304//1, 320//1, 336//1, 352//1, 368//1, 384//1, 400//1, 416//1, 432//1, 448//1, 464//1, 480//1, 1//0, "
     ]
    },
    {
     "data": {
      "text/plain": [
       "16-element Array{Any,1}:\n",
       " Rational{Int64}[0//1,1//1024,1//512,3//1024,1//256,5//1024,3//512,7//1024,1//128,9//1024,5//512,11//1024,3//256,13//1024,7//512,15//1024]         \n",
       " Rational{Int64}[1//64,17//1024,9//512,19//1024,5//256,21//1024,11//512,23//1024,3//128,25//1024,13//512,27//1024,7//256,29//1024,15//512,31//1024]\n",
       " Rational{Int64}[1//32,17//512,9//256,19//512,5//128,21//512,11//256,23//512,3//64,25//512,13//256,27//512,7//128,29//512,15//256,31//512]         \n",
       " Rational{Int64}[1//16,17//256,9//128,19//256,5//64,21//256,11//128,23//256,3//32,25//256,13//128,27//256,7//64,29//256,15//128,31//256]           \n",
       " Rational{Int64}[1//8,17//128,9//64,19//128,5//32,21//128,11//64,23//128,3//16,25//128,13//64,27//128,7//32,29//128,15//64,31//128]                \n",
       " Rational{Int64}[1//4,17//64,9//32,19//64,5//16,21//64,11//32,23//64,3//8,25//64,13//32,27//64,7//16,29//64,15//32,31//64]                         \n",
       " Rational{Int64}[1//2,17//32,9//16,19//32,5//8,21//32,11//16,23//32,3//4,25//32,13//16,27//32,7//8,29//32,15//16,31//32]                           \n",
       " Rational{Int64}[1//1,17//16,9//8,19//16,5//4,21//16,11//8,23//16,3//2,25//16,13//8,27//16,7//4,29//16,15//8,31//16]                               \n",
       " Rational{Int64}[2//1,17//8,9//4,19//8,5//2,21//8,11//4,23//8,3//1,25//8,13//4,27//8,7//2,29//8,15//4,31//8]                                       \n",
       " Rational{Int64}[4//1,17//4,9//2,19//4,5//1,21//4,11//2,23//4,6//1,25//4,13//2,27//4,7//1,29//4,15//2,31//4]                                       \n",
       " Rational{Int64}[8//1,17//2,9//1,19//2,10//1,21//2,11//1,23//2,12//1,25//2,13//1,27//2,14//1,29//2,15//1,31//2]                                    \n",
       " Rational{Int64}[16//1,17//1,18//1,19//1,20//1,21//1,22//1,23//1,24//1,25//1,26//1,27//1,28//1,29//1,30//1,31//1]                                  \n",
       " Rational{Int64}[32//1,34//1,36//1,38//1,40//1,42//1,44//1,46//1,48//1,50//1,52//1,54//1,56//1,58//1,60//1,62//1]                                  \n",
       " Rational{Int64}[64//1,68//1,72//1,76//1,80//1,84//1,88//1,92//1,96//1,100//1,104//1,108//1,112//1,116//1,120//1,124//1]                           \n",
       " Rational{Int64}[128//1,136//1,144//1,152//1,160//1,168//1,176//1,184//1,192//1,200//1,208//1,216//1,224//1,232//1,240//1,248//1]                  \n",
       " Rational{Int64}[256//1,272//1,288//1,304//1,320//1,336//1,352//1,368//1,384//1,400//1,416//1,432//1,448//1,464//1,480//1,1//0]                    "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = Vector{Float64}[]\n",
    "for e in 0 : 2^es-1\n",
    "    push!(table, [Float64(Unum(0, e, f, 0, es-1, fs-1)) for f in 0 : 2^fs-1])\n",
    "end\n",
    "[map(rationalize, x) for x in table]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "256"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(nums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 in nums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: using PyPlot.table in module Main conflicts with an existing identifier.\n"
     ]
    }
   ],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31f0baa50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x31f5f1250>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(nums, \"*\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31f59aa50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.collections.LineCollection object at 0x31f5a8dd0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(log2(nums), \"*\", markersize=2)\n",
    "hlines([0], 0, length(nums))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(256,)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(nums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "integer_indices = Bool[isinteger(zz) for zz in nums];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0"
     ]
    }
   ],
   "source": [
    "showall(map(Int, nums[integer_indices]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extract bits from Float64 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.125"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 0.125"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0011111111000000000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ",1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,128,136,144,152,160,168,176,184,192,200,208,216,224,232,240,248,256,272,288,304,320,336,352,368,384,400,416,432,448,464,480]"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-3"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exponent(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "exponent<i>{T<:AbstractFloat}</i>(x::<b>T<:AbstractFloat</b>) at <a href=\"https://github.com/JuliaLang/julia/tree/0ff703b40afddf9b705bd6a06d3a59cb4c089ea5/base/math.jl#L199\" target=\"_blank\">math.jl:199</a>"
      ],
      "text/plain": [
       "exponent{T<:AbstractFloat}(x::T<:AbstractFloat) at math.jl:199"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@which exponent(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "significand(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: MethodError: `significand_bits` has no method matching significand_bits(::Float64)\nwhile loading In[24], in expression starting on line 1",
     "output_type": "error",
     "traceback": [
      "LoadError: MethodError: `significand_bits` has no method matching significand_bits(::Float64)\nwhile loading In[24], in expression starting on line 1",
      ""
     ]
    }
   ],
   "source": [
    "Base.significand_bits(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0x000fffffffffffff"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Base.significand_mask(Float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0x0000000000000000"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reinterpret(Int64, x) & Base.significand_mask(Float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.625"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = 2.0^(-1) + 2.0^(-3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.25,-1)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "significand(y), exponent(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "significand(y) * 2.0^(exponent(y)) == y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldexp(significand(y), exponent(y)) == y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0000000000000100000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(reinterpret(Int64, y) & Base.significand_mask(Float64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trailing_zeros(reinterpret(Int64, y) & Base.significand_mask(Float64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Base.significand_bits(Float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import Base: significand_bits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "significand_bits (generic function with 2 methods)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "significand_bits(x::Float64) = reinterpret(Int64, x) & Base.significand_mask(Float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "2 methods for generic function <b>significand_bits</b>:<ul><li> significand_bits<i>{T<:AbstractFloat}</i>(::<b>Type{T<:AbstractFloat}</b>) at <a href=\"https://github.com/JuliaLang/julia/tree/0ff703b40afddf9b705bd6a06d3a59cb4c089ea5/base/float.jl#L452\" target=\"_blank\">float.jl:452</a><li> significand_bits(x::<b>Float64</b>) at In[35]:1</ul>"
      ],
      "text/plain": [
       "# 2 methods for generic function \"significand_bits\":\n",
       "significand_bits{T<:AbstractFloat}(::Type{T<:AbstractFloat}) at float.jl:452\n",
       "significand_bits(x::Float64) at In[35]:1"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "methods(significand_bits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "num_significand_bits (generic function with 1 method)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function num_significand_bits(x::Float64) \n",
    "    \n",
    "    trailing = trailing_zeros(significand_bits(x))\n",
    "    \n",
    "    trailing < 64 ? 53-trailing : 0   # trailing is 64 for e.g. 8.0\n",
    "end\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_significand_bits(0.625)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_significand_bits(4.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_exponent_size = 1 << esizesize\n",
    "max_exponent = 1 << max_exponent_size\n",
    "\n",
    "maxbias = 1 << (max_exponent_size-1)\n",
    "\n",
    "min_exponent = 0 - maxbias\n",
    "max_exponent = max_exponent - maxbias\n",
    "\n",
    "min_exponent, max_exponent\n",
    "\n",
    "max_num_bits_significand = 1 << fsizesize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "is_unum_representable (generic function with 1 method)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function is_unum_representable(x::Float64)\n",
    "    @show num_sig_bits = num_significand_bits(x)\n",
    "    @show expo = exponent(x)\n",
    "    \n",
    "    num_sig_bits < (1 << fsizesize) && min_exponent < expo < max_exponent\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "num_sig_bits = num_significand_bits(x) = 3"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_unum_representable(0.625)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_unum_representable(8.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_unum_representable(float(pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0100000000001001001000011111101101010100010001000010110100011000\""
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(float(pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Unum"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "expo = exponent(x) = -1\n",
      "num_sig_bits = num_significand_bits(x) = 0\n",
      "expo = exponent(x) = 3\n",
      "num_sig_bits = num_significand_bits(x) = 50\n",
      "expo = exponent(x) = 1\n"
     ]
    }
   ],
   "source": [
    "function Unum(x::Float64)\n",
    "    \n",
    "    @show num_sig_bits = num_significand_bits(x)\n",
    "    @show expo = exponent(x)\n",
    "    \n",
    "    if min_exponent < expo < max_exponent\n",
    "        e = expo  # change this to use min number of bits\n",
    "        \n",
    "    else \n",
    "        error(\"Exponent out of bounds\")  # too big or too small -- CHANGE to 0+ or Inf\n",
    "    end\n",
    "    \n",
    "    signif = reinterpret(UInt64, significand(x))\n",
    "    if num_sig_bits <= (1 << fsizesize)\n",
    "        u = 0\n",
    "    else\n",
    "        u = 1\n",
    "\n",
    "    end\n",
    "    \n",
    "    f = signif >> (52 - max_num_bits_significand)  # change this to use minimum\n",
    "\n",
    "    s = sign(x)    # sign\n",
    "\n",
    "    esm1 = (1 << esizesize) - 1   # CHANGE!\n",
    "    fsm1 = (1 << fsizesize) - 1   # CHANGE!\n",
    "    \n",
    "    Unum(s, e, f, u, esm1, fsm1)\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "num_sig_bits = num_significand_bits(x) = 3"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Unum(1,-1,16372,0,3,3,4,4,7)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "expo = exponent(x) = -1\n"
     ]
    }
   ],
   "source": [
    "Unum(0.625)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.0009765625"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Float64(ans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "shift (generic function with 1 method)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"Shift value in `x` represented in `from` bits to value represented in `to` bits\"\"\"\n",
    "function shift(x, from, to)\n",
    "    if to < from\n",
    "        x >> (from - to)\n",
    "    else\n",
    "        x << (to - from)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "search: "
     ]
    },
    {
     "data": {
      "text/latex": [
       "Shift value in \\texttt{x} represented in \\texttt{from} bits to value represented in \\texttt{to} bits\n"
      ],
      "text/markdown": [
       "Shift value in `x` represented in `from` bits to value represented in `to` bits\n"
      ],
      "text/plain": [
       "Shift value in `x` represented in `from` bits to value represented in `to` bits\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shift shift! unshift! fftshift ifftshift circshift\n",
      "\n"
     ]
    }
   ],
   "source": [
    "?shift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bits (generic function with 6 methods)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Base.bits(x, n) = \"[1_]\"*bits(x)[end-n+1:end]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 2.0^(-1.0) + 2.0^(-3.0)\n",
    "y = reinterpret(UInt64, x)\n",
    "bits(x) == bits(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0011111111100100000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exponent(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.25"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "significand(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"[1_]0100000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = y & Base.significand_mask(Float64)\n",
    "bits(y, 52)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0x0000000000000001"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shift(y, 52, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"[1_]01\""
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(ans, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.562684646268003e-309"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reinterpret(Float64, shift(1, 2, 52))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0000000000000100000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(ans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0111111111110000000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(Base.exponent_mask(Float64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.25"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "significand(0.625)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0011111111110100000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(ans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0011111111100100000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(0.625)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0000000000000100000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(reinterpret(UInt64,0.625) & Base.significand_mask(Float64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"0000000000000100000000000000000000000000000000000000000000000000\""
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bits(reinterpret(Float64, shift(1, 2, 52)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0x01"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0b01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "UInt8"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(ans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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