rusthm.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2500-element Array{Array{Int64,1},1}:\n",
       " [515819847,334175522]\n",
       " [288677522,93249963] \n",
       " [241299425,76127148] \n",
       " [196762596,64982528] \n",
       " [159898357,57019509] \n",
       " [129947120,50983453] \n",
       " [105641455,46207826] \n",
       " [85897560,42314923]  \n",
       " [69844214,39065785]  \n",
       " [56783248,36301485]  \n",
       " [46161041,33917695]  \n",
       " [37514250,31837054]  \n",
       " [30472652,29998070]  \n",
       " ⋮                    \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                \n",
       " [0,0]                "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8874368e8"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats_buckets = floor(100 * 2^21 * 0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f0429c08a10>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-140.0,2940.0,1.8115345980826792e-9,32.49582025415666)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats_dist_without_sum = map(x -> x[2], stats[1:2500])\n",
    "stats_distribution = map(idx -> sum(stats_dist_without_sum[idx:2500]) / stats_buckets, 1:2500)\n",
    "p1_x = 300\n",
    "p_dx = 900\n",
    "p2_x = p1_x + p_dx\n",
    "extrapolate_dx = 2500\n",
    "extrapolate_x = p1_x + extrapolate_dx\n",
    "p1 = stats_distribution[p1_x]\n",
    "p2 = stats_distribution[p1_x + p_dx]\n",
    "extrapolated = [p2, p1 * (p2 / p1)^(extrapolate_dx / p_dx)]\n",
    "\n",
    "using PyPlot\n",
    "figure(0)\n",
    "plot(stats_distribution, linewidth=1.5, linestyle=\"-\", label=\"Real insertion cost\")\n",
    "plot([p2_x, extrapolate_x], extrapolated, linewidth=1.5, linestyle=\"--\", label=\"Extrapolated\")\n",
    "semilogy()\n",
    "title(\"Probability distribution of insertion forward shift cost higher than k at load factor=0.9\")\n",
    "legend(loc=\"lower right\")\n",
    "xlabel(\"k\")\n",
    "ylabel(\"probability\")\n",
    "grid(true)\n",
    "(x1, x2, y1, y2) = axis()\n",
    "axis((x1, x2, max(y1, 10e-40), y2))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.5.0",
   "language": "julia",
   "name": "julia-0.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}