03_higherperf_demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"blue\"> Demo, *just-in-time* compilation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from numba import jit, vectorize, float64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@jit(nopython=True)\n",
    "def step_numba():\n",
    "    return 1. if random.random() > .5 else -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@jit(nopython=True)\n",
    "def walk_numba(n):\n",
    "    x = np.zeros(n)\n",
    "    dx = 1. / n\n",
    "    for i in range(n - 1):\n",
    "        x_new = x[i] + dx * step_numba()\n",
    "        if x_new > 5e-3:\n",
    "            x[i + 1] = 0.\n",
    "        else:\n",
    "            x[i + 1] = x_new\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 100000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 86.08 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "1 loop, best of 3: 2.42 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "walk_numba(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@jit\n",
    "def primes_jit(kmax):  \n",
    "    p = []\n",
    "    result = []  \n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p.append(n)\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 2221.95 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 64.9 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "p = primes_jit(100)\n",
    "#print p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"blue\"> Demo: the Mandelbrot fractal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "size = 200\n",
    "iterations = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### First cython attempt\n",
    "\n",
    "First just add the cython magic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html>\n",
       "<!-- Generated by Cython 0.24 -->\n",
       "<html>\n",
       "<head>\n",
       "    <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\" />\n",
       "    <title>Cython: _cython_magic_c02047f89c226b574aa7bb3dae4c73eb.pyx</title>\n",
       "    <style type=\"text/css\">\n",
       "    \n",
       "body.cython { font-family: courier; font-size: 12; }\n",
       "\n",
       ".cython.tag  {  }\n",
       ".cython.line { margin: 0em }\n",
       ".cython.code { font-size: 9; color: #444444; display: none; margin: 0px 0px 0px 8px; border-left: 8px none; }\n",
       "\n",
       ".cython.line .run { background-color: #B0FFB0; }\n",
       ".cython.line .mis { background-color: #FFB0B0; }\n",
       ".cython.code.run  { border-left: 8px solid #B0FFB0; }\n",
       ".cython.code.mis  { border-left: 8px solid #FFB0B0; }\n",
       "\n",
       ".cython.code .py_c_api  { color: red; }\n",
       ".cython.code .py_macro_api  { color: #FF7000; }\n",
       ".cython.code .pyx_c_api  { color: #FF3000; }\n",
       ".cython.code .pyx_macro_api  { color: #FF7000; }\n",
       ".cython.code .refnanny  { color: #FFA000; }\n",
       ".cython.code .trace  { color: #FFA000; }\n",
       ".cython.code .error_goto  { color: #FFA000; }\n",
       "\n",
       ".cython.code .coerce  { color: #008000; border: 1px dotted #008000 }\n",
       ".cython.code .py_attr { color: #FF0000; font-weight: bold; }\n",
       ".cython.code .c_attr  { color: #0000FF; }\n",
       ".cython.code .py_call { color: #FF0000; font-weight: bold; }\n",
       ".cython.code .c_call  { color: #0000FF; }\n",
       "\n",
       ".cython.score-0 {background-color: #FFFFff;}\n",
       ".cython.score-1 {background-color: #FFFFe7;}\n",
       ".cython.score-2 {background-color: #FFFFd4;}\n",
       ".cython.score-3 {background-color: #FFFFc4;}\n",
       ".cython.score-4 {background-color: #FFFFb6;}\n",
       ".cython.score-5 {background-color: #FFFFaa;}\n",
       ".cython.score-6 {background-color: #FFFF9f;}\n",
       ".cython.score-7 {background-color: #FFFF96;}\n",
       ".cython.score-8 {background-color: #FFFF8d;}\n",
       ".cython.score-9 {background-color: #FFFF86;}\n",
       ".cython.score-10 {background-color: #FFFF7f;}\n",
       ".cython.score-11 {background-color: #FFFF79;}\n",
       ".cython.score-12 {background-color: #FFFF73;}\n",
       ".cython.score-13 {background-color: #FFFF6e;}\n",
       ".cython.score-14 {background-color: #FFFF6a;}\n",
       ".cython.score-15 {background-color: #FFFF66;}\n",
       ".cython.score-16 {background-color: #FFFF62;}\n",
       ".cython.score-17 {background-color: #FFFF5e;}\n",
       ".cython.score-18 {background-color: #FFFF5b;}\n",
       ".cython.score-19 {background-color: #FFFF57;}\n",
       ".cython.score-20 {background-color: #FFFF55;}\n",
       ".cython.score-21 {background-color: #FFFF52;}\n",
       ".cython.score-22 {background-color: #FFFF4f;}\n",
       ".cython.score-23 {background-color: #FFFF4d;}\n",
       ".cython.score-24 {background-color: #FFFF4b;}\n",
       ".cython.score-25 {background-color: #FFFF48;}\n",
       ".cython.score-26 {background-color: #FFFF46;}\n",
       ".cython.score-27 {background-color: #FFFF44;}\n",
       ".cython.score-28 {background-color: #FFFF43;}\n",
       ".cython.score-29 {background-color: #FFFF41;}\n",
       ".cython.score-30 {background-color: #FFFF3f;}\n",
       ".cython.score-31 {background-color: #FFFF3e;}\n",
       ".cython.score-32 {background-color: #FFFF3c;}\n",
       ".cython.score-33 {background-color: #FFFF3b;}\n",
       ".cython.score-34 {background-color: #FFFF39;}\n",
       ".cython.score-35 {background-color: #FFFF38;}\n",
       ".cython.score-36 {background-color: #FFFF37;}\n",
       ".cython.score-37 {background-color: #FFFF36;}\n",
       ".cython.score-38 {background-color: #FFFF35;}\n",
       ".cython.score-39 {background-color: #FFFF34;}\n",
       ".cython.score-40 {background-color: #FFFF33;}\n",
       ".cython.score-41 {background-color: #FFFF32;}\n",
       ".cython.score-42 {background-color: #FFFF31;}\n",
       ".cython.score-43 {background-color: #FFFF30;}\n",
       ".cython.score-44 {background-color: #FFFF2f;}\n",
       ".cython.score-45 {background-color: #FFFF2e;}\n",
       ".cython.score-46 {background-color: #FFFF2d;}\n",
       ".cython.score-47 {background-color: #FFFF2c;}\n",
       ".cython.score-48 {background-color: #FFFF2b;}\n",
       ".cython.score-49 {background-color: #FFFF2b;}\n",
       ".cython.score-50 {background-color: #FFFF2a;}\n",
       ".cython.score-51 {background-color: #FFFF29;}\n",
       ".cython.score-52 {background-color: #FFFF29;}\n",
       ".cython.score-53 {background-color: #FFFF28;}\n",
       ".cython.score-54 {background-color: #FFFF27;}\n",
       ".cython.score-55 {background-color: #FFFF27;}\n",
       ".cython.score-56 {background-color: #FFFF26;}\n",
       ".cython.score-57 {background-color: #FFFF26;}\n",
       ".cython.score-58 {background-color: #FFFF25;}\n",
       ".cython.score-59 {background-color: #FFFF24;}\n",
       ".cython.score-60 {background-color: #FFFF24;}\n",
       ".cython.score-61 {background-color: #FFFF23;}\n",
       ".cython.score-62 {background-color: #FFFF23;}\n",
       ".cython.score-63 {background-color: #FFFF22;}\n",
       ".cython.score-64 {background-color: #FFFF22;}\n",
       ".cython.score-65 {background-color: #FFFF22;}\n",
       ".cython.score-66 {background-color: #FFFF21;}\n",
       ".cython.score-67 {background-color: #FFFF21;}\n",
       ".cython.score-68 {background-color: #FFFF20;}\n",
       ".cython.score-69 {background-color: #FFFF20;}\n",
       ".cython.score-70 {background-color: #FFFF1f;}\n",
       ".cython.score-71 {background-color: #FFFF1f;}\n",
       ".cython.score-72 {background-color: #FFFF1f;}\n",
       ".cython.score-73 {background-color: #FFFF1e;}\n",
       ".cython.score-74 {background-color: #FFFF1e;}\n",
       ".cython.score-75 {background-color: #FFFF1e;}\n",
       ".cython.score-76 {background-color: #FFFF1d;}\n",
       ".cython.score-77 {background-color: #FFFF1d;}\n",
       ".cython.score-78 {background-color: #FFFF1c;}\n",
       ".cython.score-79 {background-color: #FFFF1c;}\n",
       ".cython.score-80 {background-color: #FFFF1c;}\n",
       ".cython.score-81 {background-color: #FFFF1c;}\n",
       ".cython.score-82 {background-color: #FFFF1b;}\n",
       ".cython.score-83 {background-color: #FFFF1b;}\n",
       ".cython.score-84 {background-color: #FFFF1b;}\n",
       ".cython.score-85 {background-color: #FFFF1a;}\n",
       ".cython.score-86 {background-color: #FFFF1a;}\n",
       ".cython.score-87 {background-color: #FFFF1a;}\n",
       ".cython.score-88 {background-color: #FFFF1a;}\n",
       ".cython.score-89 {background-color: #FFFF19;}\n",
       ".cython.score-90 {background-color: #FFFF19;}\n",
       ".cython.score-91 {background-color: #FFFF19;}\n",
       ".cython.score-92 {background-color: #FFFF19;}\n",
       ".cython.score-93 {background-color: #FFFF18;}\n",
       ".cython.score-94 {background-color: #FFFF18;}\n",
       ".cython.score-95 {background-color: #FFFF18;}\n",
       ".cython.score-96 {background-color: #FFFF18;}\n",
       ".cython.score-97 {background-color: #FFFF17;}\n",
       ".cython.score-98 {background-color: #FFFF17;}\n",
       ".cython.score-99 {background-color: #FFFF17;}\n",
       ".cython.score-100 {background-color: #FFFF17;}\n",
       ".cython.score-101 {background-color: #FFFF16;}\n",
       ".cython.score-102 {background-color: #FFFF16;}\n",
       ".cython.score-103 {background-color: #FFFF16;}\n",
       ".cython.score-104 {background-color: #FFFF16;}\n",
       ".cython.score-105 {background-color: #FFFF16;}\n",
       ".cython.score-106 {background-color: #FFFF15;}\n",
       ".cython.score-107 {background-color: #FFFF15;}\n",
       ".cython.score-108 {background-color: #FFFF15;}\n",
       ".cython.score-109 {background-color: #FFFF15;}\n",
       ".cython.score-110 {background-color: #FFFF15;}\n",
       ".cython.score-111 {background-color: #FFFF15;}\n",
       ".cython.score-112 {background-color: #FFFF14;}\n",
       ".cython.score-113 {background-color: #FFFF14;}\n",
       ".cython.score-114 {background-color: #FFFF14;}\n",
       ".cython.score-115 {background-color: #FFFF14;}\n",
       ".cython.score-116 {background-color: #FFFF14;}\n",
       ".cython.score-117 {background-color: #FFFF14;}\n",
       ".cython.score-118 {background-color: #FFFF13;}\n",
       ".cython.score-119 {background-color: #FFFF13;}\n",
       ".cython.score-120 {background-color: #FFFF13;}\n",
       ".cython.score-121 {background-color: #FFFF13;}\n",
       ".cython.score-122 {background-color: #FFFF13;}\n",
       ".cython.score-123 {background-color: #FFFF13;}\n",
       ".cython.score-124 {background-color: #FFFF13;}\n",
       ".cython.score-125 {background-color: #FFFF12;}\n",
       ".cython.score-126 {background-color: #FFFF12;}\n",
       ".cython.score-127 {background-color: #FFFF12;}\n",
       ".cython.score-128 {background-color: #FFFF12;}\n",
       ".cython.score-129 {background-color: #FFFF12;}\n",
       ".cython.score-130 {background-color: #FFFF12;}\n",
       ".cython.score-131 {background-color: #FFFF12;}\n",
       ".cython.score-132 {background-color: #FFFF11;}\n",
       ".cython.score-133 {background-color: #FFFF11;}\n",
       ".cython.score-134 {background-color: #FFFF11;}\n",
       ".cython.score-135 {background-color: #FFFF11;}\n",
       ".cython.score-136 {background-color: #FFFF11;}\n",
       ".cython.score-137 {background-color: #FFFF11;}\n",
       ".cython.score-138 {background-color: #FFFF11;}\n",
       ".cython.score-139 {background-color: #FFFF11;}\n",
       ".cython.score-140 {background-color: #FFFF11;}\n",
       ".cython.score-141 {background-color: #FFFF10;}\n",
       ".cython.score-142 {background-color: #FFFF10;}\n",
       ".cython.score-143 {background-color: #FFFF10;}\n",
       ".cython.score-144 {background-color: #FFFF10;}\n",
       ".cython.score-145 {background-color: #FFFF10;}\n",
       ".cython.score-146 {background-color: #FFFF10;}\n",
       ".cython.score-147 {background-color: #FFFF10;}\n",
       ".cython.score-148 {background-color: #FFFF10;}\n",
       ".cython.score-149 {background-color: #FFFF10;}\n",
       ".cython.score-150 {background-color: #FFFF0f;}\n",
       ".cython.score-151 {background-color: #FFFF0f;}\n",
       ".cython.score-152 {background-color: #FFFF0f;}\n",
       ".cython.score-153 {background-color: #FFFF0f;}\n",
       ".cython.score-154 {background-color: #FFFF0f;}\n",
       ".cython.score-155 {background-color: #FFFF0f;}\n",
       ".cython.score-156 {background-color: #FFFF0f;}\n",
       ".cython.score-157 {background-color: #FFFF0f;}\n",
       ".cython.score-158 {background-color: #FFFF0f;}\n",
       ".cython.score-159 {background-color: #FFFF0f;}\n",
       ".cython.score-160 {background-color: #FFFF0f;}\n",
       ".cython.score-161 {background-color: #FFFF0e;}\n",
       ".cython.score-162 {background-color: #FFFF0e;}\n",
       ".cython.score-163 {background-color: #FFFF0e;}\n",
       ".cython.score-164 {background-color: #FFFF0e;}\n",
       ".cython.score-165 {background-color: #FFFF0e;}\n",
       ".cython.score-166 {background-color: #FFFF0e;}\n",
       ".cython.score-167 {background-color: #FFFF0e;}\n",
       ".cython.score-168 {background-color: #FFFF0e;}\n",
       ".cython.score-169 {background-color: #FFFF0e;}\n",
       ".cython.score-170 {background-color: #FFFF0e;}\n",
       ".cython.score-171 {background-color: #FFFF0e;}\n",
       ".cython.score-172 {background-color: #FFFF0e;}\n",
       ".cython.score-173 {background-color: #FFFF0d;}\n",
       ".cython.score-174 {background-color: #FFFF0d;}\n",
       ".cython.score-175 {background-color: #FFFF0d;}\n",
       ".cython.score-176 {background-color: #FFFF0d;}\n",
       ".cython.score-177 {background-color: #FFFF0d;}\n",
       ".cython.score-178 {background-color: #FFFF0d;}\n",
       ".cython.score-179 {background-color: #FFFF0d;}\n",
       ".cython.score-180 {background-color: #FFFF0d;}\n",
       ".cython.score-181 {background-color: #FFFF0d;}\n",
       ".cython.score-182 {background-color: #FFFF0d;}\n",
       ".cython.score-183 {background-color: #FFFF0d;}\n",
       ".cython.score-184 {background-color: #FFFF0d;}\n",
       ".cython.score-185 {background-color: #FFFF0d;}\n",
       ".cython.score-186 {background-color: #FFFF0d;}\n",
       ".cython.score-187 {background-color: #FFFF0c;}\n",
       ".cython.score-188 {background-color: #FFFF0c;}\n",
       ".cython.score-189 {background-color: #FFFF0c;}\n",
       ".cython.score-190 {background-color: #FFFF0c;}\n",
       ".cython.score-191 {background-color: #FFFF0c;}\n",
       ".cython.score-192 {background-color: #FFFF0c;}\n",
       ".cython.score-193 {background-color: #FFFF0c;}\n",
       ".cython.score-194 {background-color: #FFFF0c;}\n",
       ".cython.score-195 {background-color: #FFFF0c;}\n",
       ".cython.score-196 {background-color: #FFFF0c;}\n",
       ".cython.score-197 {background-color: #FFFF0c;}\n",
       ".cython.score-198 {background-color: #FFFF0c;}\n",
       ".cython.score-199 {background-color: #FFFF0c;}\n",
       ".cython.score-200 {background-color: #FFFF0c;}\n",
       ".cython.score-201 {background-color: #FFFF0c;}\n",
       ".cython.score-202 {background-color: #FFFF0c;}\n",
       ".cython.score-203 {background-color: #FFFF0b;}\n",
       ".cython.score-204 {background-color: #FFFF0b;}\n",
       ".cython.score-205 {background-color: #FFFF0b;}\n",
       ".cython.score-206 {background-color: #FFFF0b;}\n",
       ".cython.score-207 {background-color: #FFFF0b;}\n",
       ".cython.score-208 {background-color: #FFFF0b;}\n",
       ".cython.score-209 {background-color: #FFFF0b;}\n",
       ".cython.score-210 {background-color: #FFFF0b;}\n",
       ".cython.score-211 {background-color: #FFFF0b;}\n",
       ".cython.score-212 {background-color: #FFFF0b;}\n",
       ".cython.score-213 {background-color: #FFFF0b;}\n",
       ".cython.score-214 {background-color: #FFFF0b;}\n",
       ".cython.score-215 {background-color: #FFFF0b;}\n",
       ".cython.score-216 {background-color: #FFFF0b;}\n",
       ".cython.score-217 {background-color: #FFFF0b;}\n",
       ".cython.score-218 {background-color: #FFFF0b;}\n",
       ".cython.score-219 {background-color: #FFFF0b;}\n",
       ".cython.score-220 {background-color: #FFFF0b;}\n",
       ".cython.score-221 {background-color: #FFFF0b;}\n",
       ".cython.score-222 {background-color: #FFFF0a;}\n",
       ".cython.score-223 {background-color: #FFFF0a;}\n",
       ".cython.score-224 {background-color: #FFFF0a;}\n",
       ".cython.score-225 {background-color: #FFFF0a;}\n",
       ".cython.score-226 {background-color: #FFFF0a;}\n",
       ".cython.score-227 {background-color: #FFFF0a;}\n",
       ".cython.score-228 {background-color: #FFFF0a;}\n",
       ".cython.score-229 {background-color: #FFFF0a;}\n",
       ".cython.score-230 {background-color: #FFFF0a;}\n",
       ".cython.score-231 {background-color: #FFFF0a;}\n",
       ".cython.score-232 {background-color: #FFFF0a;}\n",
       ".cython.score-233 {background-color: #FFFF0a;}\n",
       ".cython.score-234 {background-color: #FFFF0a;}\n",
       ".cython.score-235 {background-color: #FFFF0a;}\n",
       ".cython.score-236 {background-color: #FFFF0a;}\n",
       ".cython.score-237 {background-color: #FFFF0a;}\n",
       ".cython.score-238 {background-color: #FFFF0a;}\n",
       ".cython.score-239 {background-color: #FFFF0a;}\n",
       ".cython.score-240 {background-color: #FFFF0a;}\n",
       ".cython.score-241 {background-color: #FFFF0a;}\n",
       ".cython.score-242 {background-color: #FFFF0a;}\n",
       ".cython.score-243 {background-color: #FFFF0a;}\n",
       ".cython.score-244 {background-color: #FFFF0a;}\n",
       ".cython.score-245 {background-color: #FFFF0a;}\n",
       ".cython.score-246 {background-color: #FFFF09;}\n",
       ".cython.score-247 {background-color: #FFFF09;}\n",
       ".cython.score-248 {background-color: #FFFF09;}\n",
       ".cython.score-249 {background-color: #FFFF09;}\n",
       ".cython.score-250 {background-color: #FFFF09;}\n",
       ".cython.score-251 {background-color: #FFFF09;}\n",
       ".cython.score-252 {background-color: #FFFF09;}\n",
       ".cython.score-253 {background-color: #FFFF09;}\n",
       ".cython.score-254 {background-color: #FFFF09;}\n",
       ".cython .hll { background-color: #ffffcc }\n",
       ".cython  { background: #f8f8f8; }\n",
       ".cython .c { color: #408080; font-style: italic } /* Comment */\n",
       ".cython .err { border: 1px solid #FF0000 } /* Error */\n",
       ".cython .k { color: #008000; font-weight: bold } /* Keyword */\n",
       ".cython .o { color: #666666 } /* Operator */\n",
       ".cython .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       ".cython .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       ".cython .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       ".cython .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       ".cython .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       ".cython .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       ".cython .gd { color: #A00000 } /* Generic.Deleted */\n",
       ".cython .ge { font-style: italic } /* Generic.Emph */\n",
       ".cython .gr { color: #FF0000 } /* Generic.Error */\n",
       ".cython .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       ".cython .gi { color: #00A000 } /* Generic.Inserted */\n",
       ".cython .go { color: #888888 } /* Generic.Output */\n",
       ".cython .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       ".cython .gs { font-weight: bold } /* Generic.Strong */\n",
       ".cython .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       ".cython .gt { color: #0044DD } /* Generic.Traceback */\n",
       ".cython .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       ".cython .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       ".cython .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       ".cython .kp { color: #008000 } /* Keyword.Pseudo */\n",
       ".cython .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       ".cython .kt { color: #B00040 } /* Keyword.Type */\n",
       ".cython .m { color: #666666 } /* Literal.Number */\n",
       ".cython .s { color: #BA2121 } /* Literal.String */\n",
       ".cython .na { color: #7D9029 } /* Name.Attribute */\n",
       ".cython .nb { color: #008000 } /* Name.Builtin */\n",
       ".cython .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       ".cython .no { color: #880000 } /* Name.Constant */\n",
       ".cython .nd { color: #AA22FF } /* Name.Decorator */\n",
       ".cython .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       ".cython .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       ".cython .nf { color: #0000FF } /* Name.Function */\n",
       ".cython .nl { color: #A0A000 } /* Name.Label */\n",
       ".cython .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       ".cython .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       ".cython .nv { color: #19177C } /* Name.Variable */\n",
       ".cython .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       ".cython .w { color: #bbbbbb } /* Text.Whitespace */\n",
       ".cython .mb { color: #666666 } /* Literal.Number.Bin */\n",
       ".cython .mf { color: #666666 } /* Literal.Number.Float */\n",
       ".cython .mh { color: #666666 } /* Literal.Number.Hex */\n",
       ".cython .mi { color: #666666 } /* Literal.Number.Integer */\n",
       ".cython .mo { color: #666666 } /* Literal.Number.Oct */\n",
       ".cython .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       ".cython .sc { color: #BA2121 } /* Literal.String.Char */\n",
       ".cython .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       ".cython .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       ".cython .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       ".cython .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       ".cython .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       ".cython .sx { color: #008000 } /* Literal.String.Other */\n",
       ".cython .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       ".cython .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       ".cython .ss { color: #19177C } /* Literal.String.Symbol */\n",
       ".cython .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       ".cython .vc { color: #19177C } /* Name.Variable.Class */\n",
       ".cython .vg { color: #19177C } /* Name.Variable.Global */\n",
       ".cython .vi { color: #19177C } /* Name.Variable.Instance */\n",
       ".cython .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
       "    </style>\n",
       "    <script>\n",
       "    function toggleDiv(id) {\n",
       "        theDiv = id.nextElementSibling\n",
       "        if (theDiv.style.display != 'block') theDiv.style.display = 'block';\n",
       "        else theDiv.style.display = 'none';\n",
       "    }\n",
       "    </script>\n",
       "</head>\n",
       "<body class=\"cython\">\n",
       "<p><span style=\"border-bottom: solid 1px grey;\">Generated by Cython 0.24</span></p>\n",
       "<p>\n",
       "    <span style=\"background-color: #FFFF00\">Yellow lines</span> hint at Python interaction.<br />\n",
       "    Click on a line that starts with a \"<code>+</code>\" to see the C code that Cython generated for it.\n",
       "</p>\n",
       "<div class=\"cython\"><pre class=\"cython line score-8\" onclick='toggleDiv(this)'>+<span class=\"\">01</span>: <span class=\"k\">import</span> <span class=\"nn\">numpy</span> <span class=\"k\">as</span> <span class=\"nn\">np</span></pre>\n",
       "<pre class='cython code score-8 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_Import</span>(__pyx_n_s_numpy, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_np, __pyx_t_1) &lt; 0) __PYX_ERR(0, 1, __pyx_L1_error)\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">02</span>: </pre>\n",
       "<pre class=\"cython line score-65\" onclick='toggleDiv(this)'>+<span class=\"\">03</span>: <span class=\"k\">def</span> <span class=\"nf\">mandelbrot_cython</span><span class=\"p\">(</span><span class=\"n\">m</span><span class=\"p\">,</span> <span class=\"n\">size</span><span class=\"p\">,</span> <span class=\"n\">iterations</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-65 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_c02047f89c226b574aa7bb3dae4c73eb_1mandelbrot_cython(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_c02047f89c226b574aa7bb3dae4c73eb_1mandelbrot_cython = {\"mandelbrot_cython\", (PyCFunction)__pyx_pw_46_cython_magic_c02047f89c226b574aa7bb3dae4c73eb_1mandelbrot_cython, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_c02047f89c226b574aa7bb3dae4c73eb_1mandelbrot_cython(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  PyObject *__pyx_v_m = 0;\n",
       "  PyObject *__pyx_v_size = 0;\n",
       "  PyObject *__pyx_v_iterations = 0;\n",
       "  PyObject *__pyx_r = 0;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"mandelbrot_cython (wrapper)\", 0);\n",
       "  {\n",
       "    static PyObject **__pyx_pyargnames[] = {&amp;__pyx_n_s_m,&amp;__pyx_n_s_size,&amp;__pyx_n_s_iterations,0};\n",
       "    PyObject* values[3] = {0,0,0};\n",
       "    if (unlikely(__pyx_kwds)) {\n",
       "      Py_ssize_t kw_args;\n",
       "      const Py_ssize_t pos_args = <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args);\n",
       "      switch (pos_args) {\n",
       "        case  3: values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "        case  2: values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "        case  1: values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "        case  0: break;\n",
       "        default: goto __pyx_L5_argtuple_error;\n",
       "      }\n",
       "      kw_args = <span class='py_c_api'>PyDict_Size</span>(__pyx_kwds);\n",
       "      switch (pos_args) {\n",
       "        case  0:\n",
       "        if (likely((values[0] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_m)) != 0)) kw_args--;\n",
       "        else goto __pyx_L5_argtuple_error;\n",
       "        case  1:\n",
       "        if (likely((values[1] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_size)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"mandelbrot_cython\", 1, 3, 3, 1); __PYX_ERR(0, 3, __pyx_L3_error)\n",
       "        }\n",
       "        case  2:\n",
       "        if (likely((values[2] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_iterations)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"mandelbrot_cython\", 1, 3, 3, 2); __PYX_ERR(0, 3, __pyx_L3_error)\n",
       "        }\n",
       "      }\n",
       "      if (unlikely(kw_args &gt; 0)) {\n",
       "        if (unlikely(<span class='pyx_c_api'>__Pyx_ParseOptionalKeywords</span>(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, \"mandelbrot_cython\") &lt; 0)) __PYX_ERR(0, 3, __pyx_L3_error)\n",
       "      }\n",
       "    } else if (<span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args) != 3) {\n",
       "      goto __pyx_L5_argtuple_error;\n",
       "    } else {\n",
       "      values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "      values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "    }\n",
       "    __pyx_v_m = values[0];\n",
       "    __pyx_v_size = values[1];\n",
       "    __pyx_v_iterations = values[2];\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"mandelbrot_cython\", 1, 3, 3, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); __PYX_ERR(0, 3, __pyx_L3_error)\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_c02047f89c226b574aa7bb3dae4c73eb.mandelbrot_cython\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return NULL;\n",
       "  __pyx_L4_argument_unpacking_done:;\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_c02047f89c226b574aa7bb3dae4c73eb_mandelbrot_cython(__pyx_self, __pyx_v_m, __pyx_v_size, __pyx_v_iterations);\n",
       "\n",
       "  /* function exit code */\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_c02047f89c226b574aa7bb3dae4c73eb_mandelbrot_cython(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_m, PyObject *__pyx_v_size, PyObject *__pyx_v_iterations) {\n",
       "  PyObject *__pyx_v_i = NULL;\n",
       "  PyObject *__pyx_v_j = NULL;\n",
       "  PyObject *__pyx_v_c = NULL;\n",
       "  PyObject *__pyx_v_z = NULL;\n",
       "  PyObject *__pyx_v_n = NULL;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"mandelbrot_cython\", 0);\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_r = Py_None; <span class='pyx_macro_api'>__Pyx_INCREF</span>(Py_None);\n",
       "  goto __pyx_L0;\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_2);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_5);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_8);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_9);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_10);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_13);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_c02047f89c226b574aa7bb3dae4c73eb.mandelbrot_cython\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_v_i);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_v_j);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_v_c);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_v_z);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_v_n);\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple_ = <span class='py_c_api'>PyTuple_Pack</span>(8, __pyx_n_s_m, __pyx_n_s_size, __pyx_n_s_iterations, __pyx_n_s_i, __pyx_n_s_j, __pyx_n_s_c, __pyx_n_s_z, __pyx_n_s_n); if (unlikely(!__pyx_tuple_)) __PYX_ERR(0, 3, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple_);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple_);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_c02047f89c226b574aa7bb3dae4c73eb_1mandelbrot_cython, NULL, __pyx_n_s_cython_magic_c02047f89c226b574a); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 3, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_mandelbrot_cython, __pyx_t_1) &lt; 0) __PYX_ERR(0, 3, __pyx_L1_error)\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-57\" onclick='toggleDiv(this)'>+<span class=\"\">04</span>:     <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-57 '>  __pyx_t_1 = <span class='py_c_api'>PyTuple_New</span>(1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 4, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_size);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_v_size);\n",
       "  <span class='py_macro_api'>PyTuple_SET_ITEM</span>(__pyx_t_1, 0, __pyx_v_size);\n",
       "  __pyx_t_2 = <span class='pyx_c_api'>__Pyx_PyObject_Call</span>(__pyx_builtin_range, __pyx_t_1, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 4, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_2);\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "  if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_2)) || <span class='py_c_api'>PyTuple_CheckExact</span>(__pyx_t_2)) {\n",
       "    __pyx_t_1 = __pyx_t_2; <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_1); __pyx_t_3 = 0;\n",
       "    __pyx_t_4 = NULL;\n",
       "  } else {\n",
       "    __pyx_t_3 = -1; __pyx_t_1 = <span class='py_c_api'>PyObject_GetIter</span>(__pyx_t_2); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 4, __pyx_L1_error)\n",
       "    <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "    __pyx_t_4 = Py_TYPE(__pyx_t_1)-&gt;tp_iternext; if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 4, __pyx_L1_error)\n",
       "  }\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_2); __pyx_t_2 = 0;\n",
       "  for (;;) {\n",
       "    if (likely(!__pyx_t_4)) {\n",
       "      if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_1))) {\n",
       "        if (__pyx_t_3 &gt;= <span class='py_macro_api'>PyList_GET_SIZE</span>(__pyx_t_1)) break;\n",
       "        #if CYTHON_COMPILING_IN_CPYTHON\n",
       "        __pyx_t_2 = <span class='py_macro_api'>PyList_GET_ITEM</span>(__pyx_t_1, __pyx_t_3); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_2); __pyx_t_3++; if (unlikely(0 &lt; 0)) __PYX_ERR(0, 4, __pyx_L1_error)\n",
       "        #else\n",
       "        __pyx_t_2 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_1, __pyx_t_3); __pyx_t_3++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 4, __pyx_L1_error)\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_2);\n",
       "        #endif\n",
       "      } else {\n",
       "        if (__pyx_t_3 &gt;= <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_t_1)) break;\n",
       "        #if CYTHON_COMPILING_IN_CPYTHON\n",
       "        __pyx_t_2 = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_t_1, __pyx_t_3); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_2); __pyx_t_3++; if (unlikely(0 &lt; 0)) __PYX_ERR(0, 4, __pyx_L1_error)\n",
       "        #else\n",
       "        __pyx_t_2 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_1, __pyx_t_3); __pyx_t_3++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 4, __pyx_L1_error)\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_2);\n",
       "        #endif\n",
       "      }\n",
       "    } else {\n",
       "      __pyx_t_2 = __pyx_t_4(__pyx_t_1);\n",
       "      if (unlikely(!__pyx_t_2)) {\n",
       "        PyObject* exc_type = <span class='py_c_api'>PyErr_Occurred</span>();\n",
       "        if (exc_type) {\n",
       "          if (likely(exc_type == PyExc_StopIteration || <span class='py_c_api'>PyErr_GivenExceptionMatches</span>(exc_type, PyExc_StopIteration))) <span class='py_c_api'>PyErr_Clear</span>();\n",
       "          else __PYX_ERR(0, 4, __pyx_L1_error)\n",
       "        }\n",
       "        break;\n",
       "      }\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_2);\n",
       "    }\n",
       "    <span class='pyx_macro_api'>__Pyx_XDECREF_SET</span>(__pyx_v_i, __pyx_t_2);\n",
       "    __pyx_t_2 = 0;\n",
       "/* … */\n",
       "  }\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-57\" onclick='toggleDiv(this)'>+<span class=\"\">05</span>:         <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-57 '>    __pyx_t_2 = <span class='py_c_api'>PyTuple_New</span>(1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 5, __pyx_L1_error)\n",
       "    <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_2);\n",
       "    <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_size);\n",
       "    <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_v_size);\n",
       "    <span class='py_macro_api'>PyTuple_SET_ITEM</span>(__pyx_t_2, 0, __pyx_v_size);\n",
       "    __pyx_t_5 = <span class='pyx_c_api'>__Pyx_PyObject_Call</span>(__pyx_builtin_range, __pyx_t_2, NULL); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 5, __pyx_L1_error)\n",
       "    <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_5);\n",
       "    <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_2); __pyx_t_2 = 0;\n",
       "    if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_5)) || <span class='py_c_api'>PyTuple_CheckExact</span>(__pyx_t_5)) {\n",
       "      __pyx_t_2 = __pyx_t_5; <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_2); __pyx_t_6 = 0;\n",
       "      __pyx_t_7 = NULL;\n",
       "    } else {\n",
       "      __pyx_t_6 = -1; __pyx_t_2 = <span class='py_c_api'>PyObject_GetIter</span>(__pyx_t_5); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 5, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_2);\n",
       "      __pyx_t_7 = Py_TYPE(__pyx_t_2)-&gt;tp_iternext; if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 5, __pyx_L1_error)\n",
       "    }\n",
       "    <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_5); __pyx_t_5 = 0;\n",
       "    for (;;) {\n",
       "      if (likely(!__pyx_t_7)) {\n",
       "        if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_2))) {\n",
       "          if (__pyx_t_6 &gt;= <span class='py_macro_api'>PyList_GET_SIZE</span>(__pyx_t_2)) break;\n",
       "          #if CYTHON_COMPILING_IN_CPYTHON\n",
       "          __pyx_t_5 = <span class='py_macro_api'>PyList_GET_ITEM</span>(__pyx_t_2, __pyx_t_6); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_5); __pyx_t_6++; if (unlikely(0 &lt; 0)) __PYX_ERR(0, 5, __pyx_L1_error)\n",
       "          #else\n",
       "          __pyx_t_5 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_2, __pyx_t_6); __pyx_t_6++; if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 5, __pyx_L1_error)\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_5);\n",
       "          #endif\n",
       "        } else {\n",
       "          if (__pyx_t_6 &gt;= <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_t_2)) break;\n",
       "          #if CYTHON_COMPILING_IN_CPYTHON\n",
       "          __pyx_t_5 = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_t_2, __pyx_t_6); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_5); __pyx_t_6++; if (unlikely(0 &lt; 0)) __PYX_ERR(0, 5, __pyx_L1_error)\n",
       "          #else\n",
       "          __pyx_t_5 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_2, __pyx_t_6); __pyx_t_6++; if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 5, __pyx_L1_error)\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_5);\n",
       "          #endif\n",
       "        }\n",
       "      } else {\n",
       "        __pyx_t_5 = __pyx_t_7(__pyx_t_2);\n",
       "        if (unlikely(!__pyx_t_5)) {\n",
       "          PyObject* exc_type = <span class='py_c_api'>PyErr_Occurred</span>();\n",
       "          if (exc_type) {\n",
       "            if (likely(exc_type == PyExc_StopIteration || <span class='py_c_api'>PyErr_GivenExceptionMatches</span>(exc_type, PyExc_StopIteration))) <span class='py_c_api'>PyErr_Clear</span>();\n",
       "            else __PYX_ERR(0, 5, __pyx_L1_error)\n",
       "          }\n",
       "          break;\n",
       "        }\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_5);\n",
       "      }\n",
       "      <span class='pyx_macro_api'>__Pyx_XDECREF_SET</span>(__pyx_v_j, __pyx_t_5);\n",
       "      __pyx_t_5 = 0;\n",
       "/* … */\n",
       "    }\n",
       "    <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_2); __pyx_t_2 = 0;\n",
       "</pre><pre class=\"cython line score-42\" onclick='toggleDiv(this)'>+<span class=\"\">06</span>:             <span class=\"n\">c</span> <span class=\"o\">=</span> <span class=\"o\">-</span><span class=\"mf\">2</span> <span class=\"o\">+</span> <span class=\"mf\">3.</span><span class=\"o\">/</span><span class=\"n\">size</span><span class=\"o\">*</span><span class=\"n\">j</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"n\">j</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">1.5</span><span class=\"o\">-</span><span class=\"mf\">3.</span><span class=\"o\">/</span><span class=\"n\">size</span><span class=\"o\">*</span><span class=\"n\">i</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-42 '>      __pyx_t_5 = <span class='pyx_c_api'>__Pyx_PyFloat_DivideCObj</span>(__pyx_float_3_, __pyx_v_size, 3., 0); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_5);\n",
       "      __pyx_t_8 = <span class='py_c_api'>PyNumber_Multiply</span>(__pyx_t_5, __pyx_v_j); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_8);\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_5); __pyx_t_5 = 0;\n",
       "      __pyx_t_5 = <span class='pyx_c_api'>__Pyx_PyInt_AddCObj</span>(__pyx_int_neg_2, __pyx_t_8, -2L, 0); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_5);\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_8); __pyx_t_8 = 0;\n",
       "      __pyx_t_8 = <span class='py_c_api'>PyComplex_FromDoubles</span>(0.0, 1.0); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_8);\n",
       "      __pyx_t_9 = <span class='pyx_c_api'>__Pyx_PyFloat_DivideCObj</span>(__pyx_float_3_, __pyx_v_size, 3., 0); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_9);\n",
       "      __pyx_t_10 = <span class='py_c_api'>PyNumber_Multiply</span>(__pyx_t_9, __pyx_v_i); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_9); __pyx_t_9 = 0;\n",
       "      __pyx_t_9 = <span class='pyx_c_api'>__Pyx_PyFloat_SubtractCObj</span>(__pyx_float_1_5, __pyx_t_10, 1.5, 0); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_9);\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_10); __pyx_t_10 = 0;\n",
       "      __pyx_t_10 = <span class='py_c_api'>PyNumber_Multiply</span>(__pyx_t_8, __pyx_t_9); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_8); __pyx_t_8 = 0;\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_9); __pyx_t_9 = 0;\n",
       "      __pyx_t_9 = <span class='py_c_api'>PyNumber_Add</span>(__pyx_t_5, __pyx_t_10); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_9);\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_5); __pyx_t_5 = 0;\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_10); __pyx_t_10 = 0;\n",
       "      <span class='pyx_macro_api'>__Pyx_XDECREF_SET</span>(__pyx_v_c, __pyx_t_9);\n",
       "      __pyx_t_9 = 0;\n",
       "</pre><pre class=\"cython line score-2\" onclick='toggleDiv(this)'>+<span class=\"\">07</span>:             <span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-2 '>      <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_int_0);\n",
       "      <span class='pyx_macro_api'>__Pyx_XDECREF_SET</span>(__pyx_v_z, __pyx_int_0);\n",
       "</pre><pre class=\"cython line score-57\" onclick='toggleDiv(this)'>+<span class=\"\">08</span>:             <span class=\"k\">for</span> <span class=\"n\">n</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">iterations</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-57 '>      __pyx_t_9 = <span class='py_c_api'>PyTuple_New</span>(1); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 8, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_9);\n",
       "      <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_iterations);\n",
       "      <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_v_iterations);\n",
       "      <span class='py_macro_api'>PyTuple_SET_ITEM</span>(__pyx_t_9, 0, __pyx_v_iterations);\n",
       "      __pyx_t_10 = <span class='pyx_c_api'>__Pyx_PyObject_Call</span>(__pyx_builtin_range, __pyx_t_9, NULL); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 8, __pyx_L1_error)\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_9); __pyx_t_9 = 0;\n",
       "      if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_10)) || <span class='py_c_api'>PyTuple_CheckExact</span>(__pyx_t_10)) {\n",
       "        __pyx_t_9 = __pyx_t_10; <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_9); __pyx_t_11 = 0;\n",
       "        __pyx_t_12 = NULL;\n",
       "      } else {\n",
       "        __pyx_t_11 = -1; __pyx_t_9 = <span class='py_c_api'>PyObject_GetIter</span>(__pyx_t_10); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 8, __pyx_L1_error)\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_9);\n",
       "        __pyx_t_12 = Py_TYPE(__pyx_t_9)-&gt;tp_iternext; if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 8, __pyx_L1_error)\n",
       "      }\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_10); __pyx_t_10 = 0;\n",
       "      for (;;) {\n",
       "        if (likely(!__pyx_t_12)) {\n",
       "          if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_9))) {\n",
       "            if (__pyx_t_11 &gt;= <span class='py_macro_api'>PyList_GET_SIZE</span>(__pyx_t_9)) break;\n",
       "            #if CYTHON_COMPILING_IN_CPYTHON\n",
       "            __pyx_t_10 = <span class='py_macro_api'>PyList_GET_ITEM</span>(__pyx_t_9, __pyx_t_11); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_10); __pyx_t_11++; if (unlikely(0 &lt; 0)) __PYX_ERR(0, 8, __pyx_L1_error)\n",
       "            #else\n",
       "            __pyx_t_10 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_9, __pyx_t_11); __pyx_t_11++; if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 8, __pyx_L1_error)\n",
       "            <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "            #endif\n",
       "          } else {\n",
       "            if (__pyx_t_11 &gt;= <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_t_9)) break;\n",
       "            #if CYTHON_COMPILING_IN_CPYTHON\n",
       "            __pyx_t_10 = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_t_9, __pyx_t_11); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_10); __pyx_t_11++; if (unlikely(0 &lt; 0)) __PYX_ERR(0, 8, __pyx_L1_error)\n",
       "            #else\n",
       "            __pyx_t_10 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_9, __pyx_t_11); __pyx_t_11++; if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 8, __pyx_L1_error)\n",
       "            <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "            #endif\n",
       "          }\n",
       "        } else {\n",
       "          __pyx_t_10 = __pyx_t_12(__pyx_t_9);\n",
       "          if (unlikely(!__pyx_t_10)) {\n",
       "            PyObject* exc_type = <span class='py_c_api'>PyErr_Occurred</span>();\n",
       "            if (exc_type) {\n",
       "              if (likely(exc_type == PyExc_StopIteration || <span class='py_c_api'>PyErr_GivenExceptionMatches</span>(exc_type, PyExc_StopIteration))) <span class='py_c_api'>PyErr_Clear</span>();\n",
       "              else __PYX_ERR(0, 8, __pyx_L1_error)\n",
       "            }\n",
       "            break;\n",
       "          }\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "        }\n",
       "        <span class='pyx_macro_api'>__Pyx_XDECREF_SET</span>(__pyx_v_n, __pyx_t_10);\n",
       "        __pyx_t_10 = 0;\n",
       "/* … */\n",
       "      }\n",
       "      __pyx_L8_break:;\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_9); __pyx_t_9 = 0;\n",
       "</pre><pre class=\"cython line score-38\" onclick='toggleDiv(this)'>+<span class=\"\">09</span>:                 <span class=\"k\">if</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">abs</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"p\">)</span> <span class=\"o\">&lt;=</span> <span class=\"mf\">10</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-38 '>        __pyx_t_5 = <span class='pyx_c_api'>__Pyx_GetModuleGlobalName</span>(__pyx_n_s_np); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 9, __pyx_L1_error)\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_5);\n",
       "        __pyx_t_8 = <span class='pyx_c_api'>__Pyx_PyObject_GetAttrStr</span>(__pyx_t_5, __pyx_n_s_abs); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 9, __pyx_L1_error)\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_8);\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_5); __pyx_t_5 = 0;\n",
       "        __pyx_t_5 = NULL;\n",
       "        if (CYTHON_COMPILING_IN_CPYTHON &amp;&amp; unlikely(<span class='py_c_api'>PyMethod_Check</span>(__pyx_t_8))) {\n",
       "          __pyx_t_5 = <span class='py_macro_api'>PyMethod_GET_SELF</span>(__pyx_t_8);\n",
       "          if (likely(__pyx_t_5)) {\n",
       "            PyObject* function = <span class='py_macro_api'>PyMethod_GET_FUNCTION</span>(__pyx_t_8);\n",
       "            <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_5);\n",
       "            <span class='pyx_macro_api'>__Pyx_INCREF</span>(function);\n",
       "            <span class='pyx_macro_api'>__Pyx_DECREF_SET</span>(__pyx_t_8, function);\n",
       "          }\n",
       "        }\n",
       "        if (!__pyx_t_5) {\n",
       "          __pyx_t_10 = <span class='pyx_c_api'>__Pyx_PyObject_CallOneArg</span>(__pyx_t_8, __pyx_v_z); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 9, __pyx_L1_error)\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "        } else {\n",
       "          __pyx_t_13 = <span class='py_c_api'>PyTuple_New</span>(1+1); if (unlikely(!__pyx_t_13)) __PYX_ERR(0, 9, __pyx_L1_error)\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_13);\n",
       "          <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_t_5); <span class='py_macro_api'>PyTuple_SET_ITEM</span>(__pyx_t_13, 0, __pyx_t_5); __pyx_t_5 = NULL;\n",
       "          <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_z);\n",
       "          <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_v_z);\n",
       "          <span class='py_macro_api'>PyTuple_SET_ITEM</span>(__pyx_t_13, 0+1, __pyx_v_z);\n",
       "          __pyx_t_10 = <span class='pyx_c_api'>__Pyx_PyObject_Call</span>(__pyx_t_8, __pyx_t_13, NULL); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 9, __pyx_L1_error)\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "          <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_13); __pyx_t_13 = 0;\n",
       "        }\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_8); __pyx_t_8 = 0;\n",
       "        __pyx_t_8 = <span class='py_c_api'>PyObject_RichCompare</span>(__pyx_t_10, __pyx_int_10, Py_LE); <span class='refnanny'>__Pyx_XGOTREF</span>(__pyx_t_8); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 9, __pyx_L1_error)\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_10); __pyx_t_10 = 0;\n",
       "        __pyx_t_14 = <span class='pyx_c_api'>__Pyx_PyObject_IsTrue</span>(__pyx_t_8); if (unlikely(__pyx_t_14 &lt; 0)) __PYX_ERR(0, 9, __pyx_L1_error)\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_8); __pyx_t_8 = 0;\n",
       "        if (__pyx_t_14) {\n",
       "/* … */\n",
       "          goto __pyx_L9;\n",
       "        }\n",
       "</pre><pre class=\"cython line score-12\" onclick='toggleDiv(this)'>+<span class=\"\">10</span>:                     <span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"n\">z</span><span class=\"o\">*</span><span class=\"n\">z</span> <span class=\"o\">+</span> <span class=\"n\">c</span></pre>\n",
       "<pre class='cython code score-12 '>          __pyx_t_8 = <span class='py_c_api'>PyNumber_Multiply</span>(__pyx_v_z, __pyx_v_z); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 10, __pyx_L1_error)\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_8);\n",
       "          __pyx_t_10 = <span class='py_c_api'>PyNumber_Add</span>(__pyx_t_8, __pyx_v_c); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 10, __pyx_L1_error)\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "          <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_8); __pyx_t_8 = 0;\n",
       "          <span class='pyx_macro_api'>__Pyx_DECREF_SET</span>(__pyx_v_z, __pyx_t_10);\n",
       "          __pyx_t_10 = 0;\n",
       "</pre><pre class=\"cython line score-15\" onclick='toggleDiv(this)'>+<span class=\"\">11</span>:                     <span class=\"n\">m</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">n</span></pre>\n",
       "<pre class='cython code score-15 '>          __pyx_t_10 = <span class='py_c_api'>PyTuple_New</span>(2); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 11, __pyx_L1_error)\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "          <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_i);\n",
       "          <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_v_i);\n",
       "          <span class='py_macro_api'>PyTuple_SET_ITEM</span>(__pyx_t_10, 0, __pyx_v_i);\n",
       "          <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_j);\n",
       "          <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_v_j);\n",
       "          <span class='py_macro_api'>PyTuple_SET_ITEM</span>(__pyx_t_10, 1, __pyx_v_j);\n",
       "          if (unlikely(<span class='py_c_api'>PyObject_SetItem</span>(__pyx_v_m, __pyx_t_10, __pyx_v_n) &lt; 0)) __PYX_ERR(0, 11, __pyx_L1_error)\n",
       "          <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_10); __pyx_t_10 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">12</span>:                 <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">13</span>:                     <span class=\"k\">break</span></pre>\n",
       "<pre class='cython code score-0 '>        /*else*/ {\n",
       "          goto __pyx_L8_break;\n",
       "        }\n",
       "        __pyx_L9:;\n",
       "</pre></div></body></html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%cython -a\n",
    "import numpy as np\n",
    "\n",
    "def mandelbrot_cython(m, size, iterations):\n",
    "    for i in range(size):\n",
    "        for j in range(size):\n",
    "            c = -2 + 3./size*j + 1j*(1.5-3./size*i)\n",
    "            z = 0\n",
    "            for n in range(iterations):\n",
    "                if np.abs(z) <= 10:\n",
    "                    z = z*z + c\n",
    "                    m[i, j] = n\n",
    "                else:\n",
    "                    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 1: 1.76 s per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n1 -r1 \n",
    "m = np.zeros((size, size), dtype=np.int32)\n",
    "mandelbrot_cython(m, size, iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Small speedup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Second attempt\n",
    "\n",
    "Now add type information, use *memory views* for NumPy arrays, and replace `np.dot()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html>\n",
       "<!-- Generated by Cython 0.24 -->\n",
       "<html>\n",
       "<head>\n",
       "    <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\" />\n",
       "    <title>Cython: _cython_magic_b0c2988919ca09cab5abf1036708bff3.pyx</title>\n",
       "    <style type=\"text/css\">\n",
       "    \n",
       "body.cython { font-family: courier; font-size: 12; }\n",
       "\n",
       ".cython.tag  {  }\n",
       ".cython.line { margin: 0em }\n",
       ".cython.code { font-size: 9; color: #444444; display: none; margin: 0px 0px 0px 8px; border-left: 8px none; }\n",
       "\n",
       ".cython.line .run { background-color: #B0FFB0; }\n",
       ".cython.line .mis { background-color: #FFB0B0; }\n",
       ".cython.code.run  { border-left: 8px solid #B0FFB0; }\n",
       ".cython.code.mis  { border-left: 8px solid #FFB0B0; }\n",
       "\n",
       ".cython.code .py_c_api  { color: red; }\n",
       ".cython.code .py_macro_api  { color: #FF7000; }\n",
       ".cython.code .pyx_c_api  { color: #FF3000; }\n",
       ".cython.code .pyx_macro_api  { color: #FF7000; }\n",
       ".cython.code .refnanny  { color: #FFA000; }\n",
       ".cython.code .trace  { color: #FFA000; }\n",
       ".cython.code .error_goto  { color: #FFA000; }\n",
       "\n",
       ".cython.code .coerce  { color: #008000; border: 1px dotted #008000 }\n",
       ".cython.code .py_attr { color: #FF0000; font-weight: bold; }\n",
       ".cython.code .c_attr  { color: #0000FF; }\n",
       ".cython.code .py_call { color: #FF0000; font-weight: bold; }\n",
       ".cython.code .c_call  { color: #0000FF; }\n",
       "\n",
       ".cython.score-0 {background-color: #FFFFff;}\n",
       ".cython.score-1 {background-color: #FFFFe7;}\n",
       ".cython.score-2 {background-color: #FFFFd4;}\n",
       ".cython.score-3 {background-color: #FFFFc4;}\n",
       ".cython.score-4 {background-color: #FFFFb6;}\n",
       ".cython.score-5 {background-color: #FFFFaa;}\n",
       ".cython.score-6 {background-color: #FFFF9f;}\n",
       ".cython.score-7 {background-color: #FFFF96;}\n",
       ".cython.score-8 {background-color: #FFFF8d;}\n",
       ".cython.score-9 {background-color: #FFFF86;}\n",
       ".cython.score-10 {background-color: #FFFF7f;}\n",
       ".cython.score-11 {background-color: #FFFF79;}\n",
       ".cython.score-12 {background-color: #FFFF73;}\n",
       ".cython.score-13 {background-color: #FFFF6e;}\n",
       ".cython.score-14 {background-color: #FFFF6a;}\n",
       ".cython.score-15 {background-color: #FFFF66;}\n",
       ".cython.score-16 {background-color: #FFFF62;}\n",
       ".cython.score-17 {background-color: #FFFF5e;}\n",
       ".cython.score-18 {background-color: #FFFF5b;}\n",
       ".cython.score-19 {background-color: #FFFF57;}\n",
       ".cython.score-20 {background-color: #FFFF55;}\n",
       ".cython.score-21 {background-color: #FFFF52;}\n",
       ".cython.score-22 {background-color: #FFFF4f;}\n",
       ".cython.score-23 {background-color: #FFFF4d;}\n",
       ".cython.score-24 {background-color: #FFFF4b;}\n",
       ".cython.score-25 {background-color: #FFFF48;}\n",
       ".cython.score-26 {background-color: #FFFF46;}\n",
       ".cython.score-27 {background-color: #FFFF44;}\n",
       ".cython.score-28 {background-color: #FFFF43;}\n",
       ".cython.score-29 {background-color: #FFFF41;}\n",
       ".cython.score-30 {background-color: #FFFF3f;}\n",
       ".cython.score-31 {background-color: #FFFF3e;}\n",
       ".cython.score-32 {background-color: #FFFF3c;}\n",
       ".cython.score-33 {background-color: #FFFF3b;}\n",
       ".cython.score-34 {background-color: #FFFF39;}\n",
       ".cython.score-35 {background-color: #FFFF38;}\n",
       ".cython.score-36 {background-color: #FFFF37;}\n",
       ".cython.score-37 {background-color: #FFFF36;}\n",
       ".cython.score-38 {background-color: #FFFF35;}\n",
       ".cython.score-39 {background-color: #FFFF34;}\n",
       ".cython.score-40 {background-color: #FFFF33;}\n",
       ".cython.score-41 {background-color: #FFFF32;}\n",
       ".cython.score-42 {background-color: #FFFF31;}\n",
       ".cython.score-43 {background-color: #FFFF30;}\n",
       ".cython.score-44 {background-color: #FFFF2f;}\n",
       ".cython.score-45 {background-color: #FFFF2e;}\n",
       ".cython.score-46 {background-color: #FFFF2d;}\n",
       ".cython.score-47 {background-color: #FFFF2c;}\n",
       ".cython.score-48 {background-color: #FFFF2b;}\n",
       ".cython.score-49 {background-color: #FFFF2b;}\n",
       ".cython.score-50 {background-color: #FFFF2a;}\n",
       ".cython.score-51 {background-color: #FFFF29;}\n",
       ".cython.score-52 {background-color: #FFFF29;}\n",
       ".cython.score-53 {background-color: #FFFF28;}\n",
       ".cython.score-54 {background-color: #FFFF27;}\n",
       ".cython.score-55 {background-color: #FFFF27;}\n",
       ".cython.score-56 {background-color: #FFFF26;}\n",
       ".cython.score-57 {background-color: #FFFF26;}\n",
       ".cython.score-58 {background-color: #FFFF25;}\n",
       ".cython.score-59 {background-color: #FFFF24;}\n",
       ".cython.score-60 {background-color: #FFFF24;}\n",
       ".cython.score-61 {background-color: #FFFF23;}\n",
       ".cython.score-62 {background-color: #FFFF23;}\n",
       ".cython.score-63 {background-color: #FFFF22;}\n",
       ".cython.score-64 {background-color: #FFFF22;}\n",
       ".cython.score-65 {background-color: #FFFF22;}\n",
       ".cython.score-66 {background-color: #FFFF21;}\n",
       ".cython.score-67 {background-color: #FFFF21;}\n",
       ".cython.score-68 {background-color: #FFFF20;}\n",
       ".cython.score-69 {background-color: #FFFF20;}\n",
       ".cython.score-70 {background-color: #FFFF1f;}\n",
       ".cython.score-71 {background-color: #FFFF1f;}\n",
       ".cython.score-72 {background-color: #FFFF1f;}\n",
       ".cython.score-73 {background-color: #FFFF1e;}\n",
       ".cython.score-74 {background-color: #FFFF1e;}\n",
       ".cython.score-75 {background-color: #FFFF1e;}\n",
       ".cython.score-76 {background-color: #FFFF1d;}\n",
       ".cython.score-77 {background-color: #FFFF1d;}\n",
       ".cython.score-78 {background-color: #FFFF1c;}\n",
       ".cython.score-79 {background-color: #FFFF1c;}\n",
       ".cython.score-80 {background-color: #FFFF1c;}\n",
       ".cython.score-81 {background-color: #FFFF1c;}\n",
       ".cython.score-82 {background-color: #FFFF1b;}\n",
       ".cython.score-83 {background-color: #FFFF1b;}\n",
       ".cython.score-84 {background-color: #FFFF1b;}\n",
       ".cython.score-85 {background-color: #FFFF1a;}\n",
       ".cython.score-86 {background-color: #FFFF1a;}\n",
       ".cython.score-87 {background-color: #FFFF1a;}\n",
       ".cython.score-88 {background-color: #FFFF1a;}\n",
       ".cython.score-89 {background-color: #FFFF19;}\n",
       ".cython.score-90 {background-color: #FFFF19;}\n",
       ".cython.score-91 {background-color: #FFFF19;}\n",
       ".cython.score-92 {background-color: #FFFF19;}\n",
       ".cython.score-93 {background-color: #FFFF18;}\n",
       ".cython.score-94 {background-color: #FFFF18;}\n",
       ".cython.score-95 {background-color: #FFFF18;}\n",
       ".cython.score-96 {background-color: #FFFF18;}\n",
       ".cython.score-97 {background-color: #FFFF17;}\n",
       ".cython.score-98 {background-color: #FFFF17;}\n",
       ".cython.score-99 {background-color: #FFFF17;}\n",
       ".cython.score-100 {background-color: #FFFF17;}\n",
       ".cython.score-101 {background-color: #FFFF16;}\n",
       ".cython.score-102 {background-color: #FFFF16;}\n",
       ".cython.score-103 {background-color: #FFFF16;}\n",
       ".cython.score-104 {background-color: #FFFF16;}\n",
       ".cython.score-105 {background-color: #FFFF16;}\n",
       ".cython.score-106 {background-color: #FFFF15;}\n",
       ".cython.score-107 {background-color: #FFFF15;}\n",
       ".cython.score-108 {background-color: #FFFF15;}\n",
       ".cython.score-109 {background-color: #FFFF15;}\n",
       ".cython.score-110 {background-color: #FFFF15;}\n",
       ".cython.score-111 {background-color: #FFFF15;}\n",
       ".cython.score-112 {background-color: #FFFF14;}\n",
       ".cython.score-113 {background-color: #FFFF14;}\n",
       ".cython.score-114 {background-color: #FFFF14;}\n",
       ".cython.score-115 {background-color: #FFFF14;}\n",
       ".cython.score-116 {background-color: #FFFF14;}\n",
       ".cython.score-117 {background-color: #FFFF14;}\n",
       ".cython.score-118 {background-color: #FFFF13;}\n",
       ".cython.score-119 {background-color: #FFFF13;}\n",
       ".cython.score-120 {background-color: #FFFF13;}\n",
       ".cython.score-121 {background-color: #FFFF13;}\n",
       ".cython.score-122 {background-color: #FFFF13;}\n",
       ".cython.score-123 {background-color: #FFFF13;}\n",
       ".cython.score-124 {background-color: #FFFF13;}\n",
       ".cython.score-125 {background-color: #FFFF12;}\n",
       ".cython.score-126 {background-color: #FFFF12;}\n",
       ".cython.score-127 {background-color: #FFFF12;}\n",
       ".cython.score-128 {background-color: #FFFF12;}\n",
       ".cython.score-129 {background-color: #FFFF12;}\n",
       ".cython.score-130 {background-color: #FFFF12;}\n",
       ".cython.score-131 {background-color: #FFFF12;}\n",
       ".cython.score-132 {background-color: #FFFF11;}\n",
       ".cython.score-133 {background-color: #FFFF11;}\n",
       ".cython.score-134 {background-color: #FFFF11;}\n",
       ".cython.score-135 {background-color: #FFFF11;}\n",
       ".cython.score-136 {background-color: #FFFF11;}\n",
       ".cython.score-137 {background-color: #FFFF11;}\n",
       ".cython.score-138 {background-color: #FFFF11;}\n",
       ".cython.score-139 {background-color: #FFFF11;}\n",
       ".cython.score-140 {background-color: #FFFF11;}\n",
       ".cython.score-141 {background-color: #FFFF10;}\n",
       ".cython.score-142 {background-color: #FFFF10;}\n",
       ".cython.score-143 {background-color: #FFFF10;}\n",
       ".cython.score-144 {background-color: #FFFF10;}\n",
       ".cython.score-145 {background-color: #FFFF10;}\n",
       ".cython.score-146 {background-color: #FFFF10;}\n",
       ".cython.score-147 {background-color: #FFFF10;}\n",
       ".cython.score-148 {background-color: #FFFF10;}\n",
       ".cython.score-149 {background-color: #FFFF10;}\n",
       ".cython.score-150 {background-color: #FFFF0f;}\n",
       ".cython.score-151 {background-color: #FFFF0f;}\n",
       ".cython.score-152 {background-color: #FFFF0f;}\n",
       ".cython.score-153 {background-color: #FFFF0f;}\n",
       ".cython.score-154 {background-color: #FFFF0f;}\n",
       ".cython.score-155 {background-color: #FFFF0f;}\n",
       ".cython.score-156 {background-color: #FFFF0f;}\n",
       ".cython.score-157 {background-color: #FFFF0f;}\n",
       ".cython.score-158 {background-color: #FFFF0f;}\n",
       ".cython.score-159 {background-color: #FFFF0f;}\n",
       ".cython.score-160 {background-color: #FFFF0f;}\n",
       ".cython.score-161 {background-color: #FFFF0e;}\n",
       ".cython.score-162 {background-color: #FFFF0e;}\n",
       ".cython.score-163 {background-color: #FFFF0e;}\n",
       ".cython.score-164 {background-color: #FFFF0e;}\n",
       ".cython.score-165 {background-color: #FFFF0e;}\n",
       ".cython.score-166 {background-color: #FFFF0e;}\n",
       ".cython.score-167 {background-color: #FFFF0e;}\n",
       ".cython.score-168 {background-color: #FFFF0e;}\n",
       ".cython.score-169 {background-color: #FFFF0e;}\n",
       ".cython.score-170 {background-color: #FFFF0e;}\n",
       ".cython.score-171 {background-color: #FFFF0e;}\n",
       ".cython.score-172 {background-color: #FFFF0e;}\n",
       ".cython.score-173 {background-color: #FFFF0d;}\n",
       ".cython.score-174 {background-color: #FFFF0d;}\n",
       ".cython.score-175 {background-color: #FFFF0d;}\n",
       ".cython.score-176 {background-color: #FFFF0d;}\n",
       ".cython.score-177 {background-color: #FFFF0d;}\n",
       ".cython.score-178 {background-color: #FFFF0d;}\n",
       ".cython.score-179 {background-color: #FFFF0d;}\n",
       ".cython.score-180 {background-color: #FFFF0d;}\n",
       ".cython.score-181 {background-color: #FFFF0d;}\n",
       ".cython.score-182 {background-color: #FFFF0d;}\n",
       ".cython.score-183 {background-color: #FFFF0d;}\n",
       ".cython.score-184 {background-color: #FFFF0d;}\n",
       ".cython.score-185 {background-color: #FFFF0d;}\n",
       ".cython.score-186 {background-color: #FFFF0d;}\n",
       ".cython.score-187 {background-color: #FFFF0c;}\n",
       ".cython.score-188 {background-color: #FFFF0c;}\n",
       ".cython.score-189 {background-color: #FFFF0c;}\n",
       ".cython.score-190 {background-color: #FFFF0c;}\n",
       ".cython.score-191 {background-color: #FFFF0c;}\n",
       ".cython.score-192 {background-color: #FFFF0c;}\n",
       ".cython.score-193 {background-color: #FFFF0c;}\n",
       ".cython.score-194 {background-color: #FFFF0c;}\n",
       ".cython.score-195 {background-color: #FFFF0c;}\n",
       ".cython.score-196 {background-color: #FFFF0c;}\n",
       ".cython.score-197 {background-color: #FFFF0c;}\n",
       ".cython.score-198 {background-color: #FFFF0c;}\n",
       ".cython.score-199 {background-color: #FFFF0c;}\n",
       ".cython.score-200 {background-color: #FFFF0c;}\n",
       ".cython.score-201 {background-color: #FFFF0c;}\n",
       ".cython.score-202 {background-color: #FFFF0c;}\n",
       ".cython.score-203 {background-color: #FFFF0b;}\n",
       ".cython.score-204 {background-color: #FFFF0b;}\n",
       ".cython.score-205 {background-color: #FFFF0b;}\n",
       ".cython.score-206 {background-color: #FFFF0b;}\n",
       ".cython.score-207 {background-color: #FFFF0b;}\n",
       ".cython.score-208 {background-color: #FFFF0b;}\n",
       ".cython.score-209 {background-color: #FFFF0b;}\n",
       ".cython.score-210 {background-color: #FFFF0b;}\n",
       ".cython.score-211 {background-color: #FFFF0b;}\n",
       ".cython.score-212 {background-color: #FFFF0b;}\n",
       ".cython.score-213 {background-color: #FFFF0b;}\n",
       ".cython.score-214 {background-color: #FFFF0b;}\n",
       ".cython.score-215 {background-color: #FFFF0b;}\n",
       ".cython.score-216 {background-color: #FFFF0b;}\n",
       ".cython.score-217 {background-color: #FFFF0b;}\n",
       ".cython.score-218 {background-color: #FFFF0b;}\n",
       ".cython.score-219 {background-color: #FFFF0b;}\n",
       ".cython.score-220 {background-color: #FFFF0b;}\n",
       ".cython.score-221 {background-color: #FFFF0b;}\n",
       ".cython.score-222 {background-color: #FFFF0a;}\n",
       ".cython.score-223 {background-color: #FFFF0a;}\n",
       ".cython.score-224 {background-color: #FFFF0a;}\n",
       ".cython.score-225 {background-color: #FFFF0a;}\n",
       ".cython.score-226 {background-color: #FFFF0a;}\n",
       ".cython.score-227 {background-color: #FFFF0a;}\n",
       ".cython.score-228 {background-color: #FFFF0a;}\n",
       ".cython.score-229 {background-color: #FFFF0a;}\n",
       ".cython.score-230 {background-color: #FFFF0a;}\n",
       ".cython.score-231 {background-color: #FFFF0a;}\n",
       ".cython.score-232 {background-color: #FFFF0a;}\n",
       ".cython.score-233 {background-color: #FFFF0a;}\n",
       ".cython.score-234 {background-color: #FFFF0a;}\n",
       ".cython.score-235 {background-color: #FFFF0a;}\n",
       ".cython.score-236 {background-color: #FFFF0a;}\n",
       ".cython.score-237 {background-color: #FFFF0a;}\n",
       ".cython.score-238 {background-color: #FFFF0a;}\n",
       ".cython.score-239 {background-color: #FFFF0a;}\n",
       ".cython.score-240 {background-color: #FFFF0a;}\n",
       ".cython.score-241 {background-color: #FFFF0a;}\n",
       ".cython.score-242 {background-color: #FFFF0a;}\n",
       ".cython.score-243 {background-color: #FFFF0a;}\n",
       ".cython.score-244 {background-color: #FFFF0a;}\n",
       ".cython.score-245 {background-color: #FFFF0a;}\n",
       ".cython.score-246 {background-color: #FFFF09;}\n",
       ".cython.score-247 {background-color: #FFFF09;}\n",
       ".cython.score-248 {background-color: #FFFF09;}\n",
       ".cython.score-249 {background-color: #FFFF09;}\n",
       ".cython.score-250 {background-color: #FFFF09;}\n",
       ".cython.score-251 {background-color: #FFFF09;}\n",
       ".cython.score-252 {background-color: #FFFF09;}\n",
       ".cython.score-253 {background-color: #FFFF09;}\n",
       ".cython.score-254 {background-color: #FFFF09;}\n",
       ".cython .hll { background-color: #ffffcc }\n",
       ".cython  { background: #f8f8f8; }\n",
       ".cython .c { color: #408080; font-style: italic } /* Comment */\n",
       ".cython .err { border: 1px solid #FF0000 } /* Error */\n",
       ".cython .k { color: #008000; font-weight: bold } /* Keyword */\n",
       ".cython .o { color: #666666 } /* Operator */\n",
       ".cython .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       ".cython .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       ".cython .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       ".cython .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       ".cython .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       ".cython .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       ".cython .gd { color: #A00000 } /* Generic.Deleted */\n",
       ".cython .ge { font-style: italic } /* Generic.Emph */\n",
       ".cython .gr { color: #FF0000 } /* Generic.Error */\n",
       ".cython .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       ".cython .gi { color: #00A000 } /* Generic.Inserted */\n",
       ".cython .go { color: #888888 } /* Generic.Output */\n",
       ".cython .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       ".cython .gs { font-weight: bold } /* Generic.Strong */\n",
       ".cython .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       ".cython .gt { color: #0044DD } /* Generic.Traceback */\n",
       ".cython .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       ".cython .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       ".cython .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       ".cython .kp { color: #008000 } /* Keyword.Pseudo */\n",
       ".cython .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       ".cython .kt { color: #B00040 } /* Keyword.Type */\n",
       ".cython .m { color: #666666 } /* Literal.Number */\n",
       ".cython .s { color: #BA2121 } /* Literal.String */\n",
       ".cython .na { color: #7D9029 } /* Name.Attribute */\n",
       ".cython .nb { color: #008000 } /* Name.Builtin */\n",
       ".cython .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       ".cython .no { color: #880000 } /* Name.Constant */\n",
       ".cython .nd { color: #AA22FF } /* Name.Decorator */\n",
       ".cython .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       ".cython .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       ".cython .nf { color: #0000FF } /* Name.Function */\n",
       ".cython .nl { color: #A0A000 } /* Name.Label */\n",
       ".cython .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       ".cython .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       ".cython .nv { color: #19177C } /* Name.Variable */\n",
       ".cython .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       ".cython .w { color: #bbbbbb } /* Text.Whitespace */\n",
       ".cython .mb { color: #666666 } /* Literal.Number.Bin */\n",
       ".cython .mf { color: #666666 } /* Literal.Number.Float */\n",
       ".cython .mh { color: #666666 } /* Literal.Number.Hex */\n",
       ".cython .mi { color: #666666 } /* Literal.Number.Integer */\n",
       ".cython .mo { color: #666666 } /* Literal.Number.Oct */\n",
       ".cython .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       ".cython .sc { color: #BA2121 } /* Literal.String.Char */\n",
       ".cython .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       ".cython .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       ".cython .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       ".cython .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       ".cython .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       ".cython .sx { color: #008000 } /* Literal.String.Other */\n",
       ".cython .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       ".cython .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       ".cython .ss { color: #19177C } /* Literal.String.Symbol */\n",
       ".cython .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       ".cython .vc { color: #19177C } /* Name.Variable.Class */\n",
       ".cython .vg { color: #19177C } /* Name.Variable.Global */\n",
       ".cython .vi { color: #19177C } /* Name.Variable.Instance */\n",
       ".cython .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
       "    </style>\n",
       "    <script>\n",
       "    function toggleDiv(id) {\n",
       "        theDiv = id.nextElementSibling\n",
       "        if (theDiv.style.display != 'block') theDiv.style.display = 'block';\n",
       "        else theDiv.style.display = 'none';\n",
       "    }\n",
       "    </script>\n",
       "</head>\n",
       "<body class=\"cython\">\n",
       "<p><span style=\"border-bottom: solid 1px grey;\">Generated by Cython 0.24</span></p>\n",
       "<p>\n",
       "    <span style=\"background-color: #FFFF00\">Yellow lines</span> hint at Python interaction.<br />\n",
       "    Click on a line that starts with a \"<code>+</code>\" to see the C code that Cython generated for it.\n",
       "</p>\n",
       "<div class=\"cython\"><pre class=\"cython line score-19\" onclick='toggleDiv(this)'>+<span class=\"\">01</span>: <span class=\"k\">import</span> <span class=\"nn\">numpy</span> <span class=\"k\">as</span> <span class=\"nn\">np</span></pre>\n",
       "<pre class='cython code score-19 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_Import</span>(__pyx_n_s_numpy, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_np, __pyx_t_1) &lt; 0) __PYX_ERR(0, 1, __pyx_L1_error)\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "/* … */\n",
       "  __pyx_t_1 = <span class='py_c_api'>PyDict_New</span>(); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_test, __pyx_t_1) &lt; 0) __PYX_ERR(0, 1, __pyx_L1_error)\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">02</span>: </pre>\n",
       "<pre class=\"cython line score-71\" onclick='toggleDiv(this)'>+<span class=\"\">03</span>: <span class=\"k\">def</span> <span class=\"nf\">mandelbrot_cython</span><span class=\"p\">(</span><span class=\"nb\">int</span><span class=\"p\">[:,::</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"n\">m</span><span class=\"p\">,</span></pre>\n",
       "<pre class='cython code score-71 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_b0c2988919ca09cab5abf1036708bff3_1mandelbrot_cython(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_b0c2988919ca09cab5abf1036708bff3_1mandelbrot_cython = {\"mandelbrot_cython\", (PyCFunction)__pyx_pw_46_cython_magic_b0c2988919ca09cab5abf1036708bff3_1mandelbrot_cython, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_b0c2988919ca09cab5abf1036708bff3_1mandelbrot_cython(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  __Pyx_memviewslice __pyx_v_m = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
       "  int __pyx_v_size;\n",
       "  int __pyx_v_iterations;\n",
       "  PyObject *__pyx_r = 0;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"mandelbrot_cython (wrapper)\", 0);\n",
       "  {\n",
       "    static PyObject **__pyx_pyargnames[] = {&amp;__pyx_n_s_m,&amp;__pyx_n_s_size,&amp;__pyx_n_s_iterations,0};\n",
       "    PyObject* values[3] = {0,0,0};\n",
       "    if (unlikely(__pyx_kwds)) {\n",
       "      Py_ssize_t kw_args;\n",
       "      const Py_ssize_t pos_args = <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args);\n",
       "      switch (pos_args) {\n",
       "        case  3: values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "        case  2: values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "        case  1: values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "        case  0: break;\n",
       "        default: goto __pyx_L5_argtuple_error;\n",
       "      }\n",
       "      kw_args = <span class='py_c_api'>PyDict_Size</span>(__pyx_kwds);\n",
       "      switch (pos_args) {\n",
       "        case  0:\n",
       "        if (likely((values[0] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_m)) != 0)) kw_args--;\n",
       "        else goto __pyx_L5_argtuple_error;\n",
       "        case  1:\n",
       "        if (likely((values[1] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_size)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"mandelbrot_cython\", 1, 3, 3, 1); __PYX_ERR(0, 3, __pyx_L3_error)\n",
       "        }\n",
       "        case  2:\n",
       "        if (likely((values[2] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_iterations)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"mandelbrot_cython\", 1, 3, 3, 2); __PYX_ERR(0, 3, __pyx_L3_error)\n",
       "        }\n",
       "      }\n",
       "      if (unlikely(kw_args &gt; 0)) {\n",
       "        if (unlikely(<span class='pyx_c_api'>__Pyx_ParseOptionalKeywords</span>(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, \"mandelbrot_cython\") &lt; 0)) __PYX_ERR(0, 3, __pyx_L3_error)\n",
       "      }\n",
       "    } else if (<span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args) != 3) {\n",
       "      goto __pyx_L5_argtuple_error;\n",
       "    } else {\n",
       "      values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "      values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "    }\n",
       "    __pyx_v_m = <span class='pyx_c_api'>__Pyx_PyObject_to_MemoryviewSlice_d_dc_int</span>(values[0]); if (unlikely(!__pyx_v_m.memview)) __PYX_ERR(0, 3, __pyx_L3_error)\n",
       "    __pyx_v_size = <span class='pyx_c_api'>__Pyx_PyInt_As_int</span>(values[1]); if (unlikely((__pyx_v_size == (int)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) __PYX_ERR(0, 4, __pyx_L3_error)\n",
       "    __pyx_v_iterations = <span class='pyx_c_api'>__Pyx_PyInt_As_int</span>(values[2]); if (unlikely((__pyx_v_iterations == (int)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) __PYX_ERR(0, 5, __pyx_L3_error)\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"mandelbrot_cython\", 1, 3, 3, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); __PYX_ERR(0, 3, __pyx_L3_error)\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_b0c2988919ca09cab5abf1036708bff3.mandelbrot_cython\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return NULL;\n",
       "  __pyx_L4_argument_unpacking_done:;\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_b0c2988919ca09cab5abf1036708bff3_mandelbrot_cython(__pyx_self, __pyx_v_m, __pyx_v_size, __pyx_v_iterations);\n",
       "\n",
       "  /* function exit code */\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_b0c2988919ca09cab5abf1036708bff3_mandelbrot_cython(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_m, int __pyx_v_size, int __pyx_v_iterations) {\n",
       "  int __pyx_v_i;\n",
       "  int __pyx_v_j;\n",
       "  int __pyx_v_n;\n",
       "  __pyx_t_double_complex __pyx_v_z;\n",
       "  __pyx_t_double_complex __pyx_v_c;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"mandelbrot_cython\", 0);\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_r = Py_None; <span class='pyx_macro_api'>__Pyx_INCREF</span>(Py_None);\n",
       "  goto __pyx_L0;\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_b0c2988919ca09cab5abf1036708bff3.mandelbrot_cython\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  __PYX_XDEC_MEMVIEW(&amp;__pyx_v_m, 1);\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple__14 = <span class='py_c_api'>PyTuple_Pack</span>(8, __pyx_n_s_m, __pyx_n_s_size, __pyx_n_s_iterations, __pyx_n_s_i, __pyx_n_s_j, __pyx_n_s_n, __pyx_n_s_z, __pyx_n_s_c); if (unlikely(!__pyx_tuple__14)) __PYX_ERR(0, 3, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple__14);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple__14);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_b0c2988919ca09cab5abf1036708bff3_1mandelbrot_cython, NULL, __pyx_n_s_cython_magic_b0c2988919ca09cab5); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 3, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_mandelbrot_cython, __pyx_t_1) &lt; 0) __PYX_ERR(0, 3, __pyx_L1_error)\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "  __pyx_codeobj__15 = (PyObject*)<span class='pyx_c_api'>__Pyx_PyCode_New</span>(3, 0, 8, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__14, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_Users_ktw_ipython_cython__cytho, __pyx_n_s_mandelbrot_cython, 3, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__15)) __PYX_ERR(0, 3, __pyx_L1_error)\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">04</span>:                       <span class=\"nb\">int</span> <span class=\"n\">size</span><span class=\"p\">,</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">05</span>:                       <span class=\"nb\">int</span> <span class=\"n\">iterations</span><span class=\"p\">):</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">06</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">i</span><span class=\"p\">,</span> <span class=\"nf\">j</span><span class=\"p\">,</span> <span class=\"nf\">n</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">07</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">complex</span> <span class=\"nf\">z</span><span class=\"p\">,</span> <span class=\"nf\">c</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">08</span>:     <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_1 = __pyx_v_size;\n",
       "  for (__pyx_t_2 = 0; __pyx_t_2 &lt; __pyx_t_1; __pyx_t_2+=1) {\n",
       "    __pyx_v_i = __pyx_t_2;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">09</span>:         <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_3 = __pyx_v_size;\n",
       "    for (__pyx_t_4 = 0; __pyx_t_4 &lt; __pyx_t_3; __pyx_t_4+=1) {\n",
       "      __pyx_v_j = __pyx_t_4;\n",
       "</pre><pre class=\"cython line score-10\" onclick='toggleDiv(this)'>+<span class=\"\">10</span>:             <span class=\"n\">c</span> <span class=\"o\">=</span> <span class=\"o\">-</span><span class=\"mf\">2</span> <span class=\"o\">+</span> <span class=\"mf\">3.</span><span class=\"o\">/</span><span class=\"n\">size</span><span class=\"o\">*</span><span class=\"n\">j</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"n\">j</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">1.5</span><span class=\"o\">-</span><span class=\"mf\">3.</span><span class=\"o\">/</span><span class=\"n\">size</span><span class=\"o\">*</span><span class=\"n\">i</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-10 '>      if (unlikely(__pyx_v_size == 0)) {\n",
       "        <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "        __PYX_ERR(0, 10, __pyx_L1_error)\n",
       "      }\n",
       "      if (unlikely(__pyx_v_size == 0)) {\n",
       "        <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "        __PYX_ERR(0, 10, __pyx_L1_error)\n",
       "      }\n",
       "      __pyx_v_c = __Pyx_c_sum(__pyx_t_double_complex_from_parts((-2.0 + ((3. / __pyx_v_size) * __pyx_v_j)), 0), __Pyx_c_prod(__pyx_t_double_complex_from_parts(0, 1.0), __pyx_t_double_complex_from_parts((1.5 - ((3. / __pyx_v_size) * __pyx_v_i)), 0)));\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">11</span>:             <span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_z = __pyx_t_double_complex_from_parts(0, 0);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">12</span>:             <span class=\"k\">for</span> <span class=\"n\">n</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">iterations</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_t_5 = __pyx_v_iterations;\n",
       "      for (__pyx_t_6 = 0; __pyx_t_6 &lt; __pyx_t_5; __pyx_t_6+=1) {\n",
       "        __pyx_v_n = __pyx_t_6;\n",
       "</pre><pre class=\"cython line score-2\" onclick='toggleDiv(this)'>+<span class=\"\">13</span>:                 <span class=\"k\">if</span> <span class=\"n\">z</span><span class=\"o\">.</span><span class=\"n\">real</span><span class=\"o\">**</span><span class=\"mf\">2</span> <span class=\"o\">+</span> <span class=\"n\">z</span><span class=\"o\">.</span><span class=\"n\">imag</span><span class=\"o\">**</span><span class=\"mf\">2</span> <span class=\"o\">&lt;=</span> <span class=\"mf\">100</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-2 '>        __pyx_t_7 = (((pow(<span class='pyx_macro_api'>__Pyx_CREAL</span>(__pyx_v_z), 2.0) + pow(<span class='pyx_macro_api'>__Pyx_CIMAG</span>(__pyx_v_z), 2.0)) &lt;= 100.0) != 0);\n",
       "        if (__pyx_t_7) {\n",
       "/* … */\n",
       "          goto __pyx_L9;\n",
       "        }\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">14</span>:                     <span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"n\">z</span><span class=\"o\">*</span><span class=\"n\">z</span> <span class=\"o\">+</span> <span class=\"n\">c</span></pre>\n",
       "<pre class='cython code score-0 '>          __pyx_v_z = __Pyx_c_sum(__Pyx_c_prod(__pyx_v_z, __pyx_v_z), __pyx_v_c);\n",
       "</pre><pre class=\"cython line score-2\" onclick='toggleDiv(this)'>+<span class=\"\">15</span>:                     <span class=\"n\">m</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">n</span></pre>\n",
       "<pre class='cython code score-2 '>          __pyx_t_8 = __pyx_v_i;\n",
       "          __pyx_t_9 = __pyx_v_j;\n",
       "          __pyx_t_10 = -1;\n",
       "          if (__pyx_t_8 &lt; 0) {\n",
       "            __pyx_t_8 += __pyx_v_m.shape[0];\n",
       "            if (unlikely(__pyx_t_8 &lt; 0)) __pyx_t_10 = 0;\n",
       "          } else if (unlikely(__pyx_t_8 &gt;= __pyx_v_m.shape[0])) __pyx_t_10 = 0;\n",
       "          if (__pyx_t_9 &lt; 0) {\n",
       "            __pyx_t_9 += __pyx_v_m.shape[1];\n",
       "            if (unlikely(__pyx_t_9 &lt; 0)) __pyx_t_10 = 1;\n",
       "          } else if (unlikely(__pyx_t_9 &gt;= __pyx_v_m.shape[1])) __pyx_t_10 = 1;\n",
       "          if (unlikely(__pyx_t_10 != -1)) {\n",
       "            <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_10);\n",
       "            __PYX_ERR(0, 15, __pyx_L1_error)\n",
       "          }\n",
       "          *((int *) ( /* dim=1 */ ((char *) (((int *) ( /* dim=0 */ (__pyx_v_m.data + __pyx_t_8 * __pyx_v_m.strides[0]) )) + __pyx_t_9)) )) = __pyx_v_n;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">16</span>:                 <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">17</span>:                     <span class=\"k\">break</span></pre>\n",
       "<pre class='cython code score-0 '>        /*else*/ {\n",
       "          goto __pyx_L8_break;\n",
       "        }\n",
       "        __pyx_L9:;\n",
       "      }\n",
       "      __pyx_L8_break:;\n",
       "    }\n",
       "  }\n",
       "</pre></div></body></html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%cython -a\n",
    "import numpy as np\n",
    "\n",
    "def mandelbrot_cython(int[:,::1] m, \n",
    "                      int size, \n",
    "                      int iterations):\n",
    "    cdef int i, j, n\n",
    "    cdef complex z, c\n",
    "    for i in range(size):\n",
    "        for j in range(size):\n",
    "            c = -2 + 3./size*j + 1j*(1.5-3./size*i)\n",
    "            z = 0\n",
    "            for n in range(iterations):\n",
    "                if z.real**2 + z.imag**2 <= 100:\n",
    "                    z = z*z + c\n",
    "                    m[i, j] = n\n",
    "                else:\n",
    "                    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 1: 3.31 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n1 -r1 m = np.zeros((size, size), dtype=np.int32)\n",
    "mandelbrot_cython(m, size, iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Huge speedup!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"red\"> *Exercise: calculate primes*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def primes(kmax):  \n",
    "    p = []\n",
    "    result = []  \n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p.append(n)\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 2.13 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "p = primes(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Cython extension is already loaded. To reload it, use:\n",
      "  %reload_ext Cython\n"
     ]
    }
   ],
   "source": [
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "def primes_simplecython(kmax):  \n",
    "    p = []\n",
    "    result = []  \n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p.append(n)\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 387 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "p = primes_simplecython(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "#%%cython --compile-args=-fopenmp --link-args=-fopenmp\n",
    "def primes_cython(int kmax):  # The argument will be converted to int or raise a TypeError.\n",
    "    cdef int n, k, i  # These variables are declared with C types.\n",
    "    cdef int p[1000]  # Another C type\n",
    "    result = []  # A Python type\n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p[k] = n\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000 loops, best of 3: 31.8 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "p = primes_cython(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@jit\n",
    "def primes_jit(kmax):  \n",
    "    p = []\n",
    "    result = []  \n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p.append(n)\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 1489.29 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 80.4 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "p = primes_jit(100)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`cache=True` stores the compiled function in a file and avoids re-compilation on re-running a Python program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@jit(cache=True)\n",
    "def primes_jit2(kmax):  \n",
    "    p = []\n",
    "    result = []  \n",
    "    if kmax > 1000:\n",
    "        kmax = 1000\n",
    "    k = 0\n",
    "    n = 2\n",
    "    while k < kmax:\n",
    "        i = 0\n",
    "        while i < k and n % p[i] != 0:\n",
    "            i = i + 1\n",
    "        if i == k:\n",
    "            p.append(n)\n",
    "            k = k + 1\n",
    "            result.append(n)\n",
    "        n = n + 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 178.45 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 65.2 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "p = primes_jit2(100)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}