Lab26-Performance-Cython1Lab.ipynb

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   "cell_type": "markdown",
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   "source": [
    "We'll go back to our Julia example for the lab. We re-produce our last step here..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
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     "name": "stdout",
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     "text": [
      "The Cython extension is already loaded. To reload it, use:\n",
      "  %reload_ext Cython\n"
     ]
    }
   ],
   "source": [
    "%load_ext Cython"
   ]
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  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
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   "source": [
    "from collections import namedtuple\n",
    "Box = namedtuple(\"Box\", \"x1 x2 y1 y2\")\n",
    "bounds = Box(-1.8, 1.8, -1.8, 1.8)\n",
    "focus=complex(-0.62772, -.42193)\n",
    "gridsize=1000\n",
    "iters=300\n",
    "\n",
    "def setup_grid(gridsize, box):\n",
    "    xstep = (box.x2 - box.x1)/(gridsize - 1.0)\n",
    "    ystep = (box.y2 - box.y1)/(gridsize - 1.0)\n",
    "    xs = (box.x1+ i* xstep for i in range(gridsize))\n",
    "    zs=[]\n",
    "    for x in xs:\n",
    "        ys = (box.y1+ i* ystep for i in range(gridsize))\n",
    "        for y in ys:\n",
    "            zs.append(complex(x,y))\n",
    "    return zs\n",
    "\n",
    "def zts1(maxiter, zs, c): \n",
    "    output = [0] * len(zs)\n",
    "    for i,z in enumerate(zs):\n",
    "        n=0\n",
    "        while n < maxiter and abs(z) < 2:\n",
    "            z=z*z+c\n",
    "            n+=1 \n",
    "        output[i] = n\n",
    "    return output\n",
    "\n",
    "def run1():\n",
    "    zs = setup_grid(gridsize, bounds)\n",
    "    out = zts1(iters, zs, focus)\n",
    "    return zs, out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you remember, profiling found that `zts1` needed speeding up..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 loops, best of 1: 9.97 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit -r 1 -n 5 run1()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q1\n",
    "\n",
    "What speedup do you get from simply cythonizing `zts1`, with no annotations at all?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
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       "<div class=\"cython\"><pre class=\"cython line score-60\" onclick='toggleDiv(this)'>+<span class=\"\">01</span>: <span class=\"k\">def</span> <span class=\"nf\">zts1_cython</span><span class=\"p\">(</span><span class=\"n\">maxiter</span><span class=\"p\">,</span> <span class=\"n\">zs</span><span class=\"p\">,</span> <span class=\"n\">c</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-60 '>/* Python wrapper */\n",
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       "static PyMethodDef __pyx_mdef_46_cython_magic_8c0a139ed8b716edd4ae7e5c03417be2_1zts1_cython = {\"zts1_cython\", (PyCFunction)__pyx_pw_46_cython_magic_8c0a139ed8b716edd4ae7e5c03417be2_1zts1_cython, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_8c0a139ed8b716edd4ae7e5c03417be2_1zts1_cython(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  PyObject *__pyx_v_maxiter = 0;\n",
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       "        case  1: values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
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    "%%cython --annotate\n",
    "def zts1_cython(maxiter, zs, c): \n",
    "    #your code here\n",
    "    output = [0] * len(zs)\n",
    "    for i,z in enumerate(zs):\n",
    "        n=0\n",
    "        while n < maxiter and abs(z) < 2:\n",
    "            z=z*z+c\n",
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   "metadata": {
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     "text": [
      "5 loops, best of 1: 9.86 s per loop\n"
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   "source": [
    "%timeit -r 1 -n 5 run1()"
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    "### Q2\n",
    "\n",
    "Keeping `zts1` a `def` function, and leaving out `output` and `zs`, type annotate as many variables as you can. For complex numbers, use the type `double complex`. Create the function `zts1_cython2`"
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       "    <span style=\"background-color: #FFFF00\">Yellow lines</span> hint at Python interaction.<br />\n",
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       "<div class=\"cython\"><pre class=\"cython line score-0\">&#xA0;<span class=\"\">01</span>: </pre>\n",
       "<pre class=\"cython line score-63\" onclick='toggleDiv(this)'>+<span class=\"\">02</span>: <span class=\"k\">def</span> <span class=\"nf\">zts1</span><span class=\"p\">(</span><span class=\"nb\">int</span> <span class=\"n\">maxiter</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"nb\">complex</span> <span class=\"n\">z</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"nb\">complex</span> <span class=\"n\">c</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-63 '>/* Python wrapper */\n",
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       "static PyMethodDef __pyx_mdef_46_cython_magic_da645186996be5522c140a834faf9ca4_1zts1 = {\"zts1\", (PyCFunction)__pyx_pw_46_cython_magic_da645186996be5522c140a834faf9ca4_1zts1, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_da645186996be5522c140a834faf9ca4_1zts1(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  int __pyx_v_maxiter;\n",
       "  __pyx_t_double_complex __pyx_v_z;\n",
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       "        if (likely((values[1] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_z)) != 0)) kw_args--;\n",
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       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"zts1\", 1, 3, 3, 1); <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\n",
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       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"zts1\", 1, 3, 3, 2); <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\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, \"zts1\") &lt; 0)) <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\n",
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       "    __pyx_v_z = <span class='pyx_c_api'>__Pyx_PyComplex_As___pyx_t_double_complex</span>(values[1]);<span class='error_goto'> if (unlikely(PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\n",
       "    __pyx_v_c = <span class='pyx_c_api'>__Pyx_PyComplex_As___pyx_t_double_complex</span>(values[2]);<span class='error_goto'> if (unlikely(PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"zts1\", 1, 3, 3, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_da645186996be5522c140a834faf9ca4.zts1\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
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       "  int __pyx_lineno = 0;\n",
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       "\n",
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       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_da645186996be5522c140a834faf9ca4_zts1(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_maxiter, __pyx_t_double_complex __pyx_v_z, __pyx_t_double_complex __pyx_v_c) {\n",
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       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
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       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_2);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_3);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_da645186996be5522c140a834faf9ca4.zts1\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\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>(4, __pyx_n_s_maxiter, __pyx_n_s_z, __pyx_n_s_c, __pyx_n_s_n);<span class='error_goto'> if (unlikely(!__pyx_tuple_)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\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_da645186996be5522c140a834faf9ca4_1zts1, NULL, __pyx_n_s_cython_magic_da645186996be5522c);<span class='error_goto'> if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
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       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
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       "</pre><pre class=\"cython line score-1\" onclick='toggleDiv(this)'>+<span class=\"\">03</span>:     <span class=\"n\">n</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
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    "%%cython --annotate\n",
    "\n",
    "def zts1(int maxiter, double complex z, double complex c):\n",
    "    n = 0\n",
    "    while n < maxiter and abs(z) < 2:\n",
    "        z = z*z+c\n",
    "        n += 1\n",
    "    return n\n",
    "\n",
    "#your code here\n",
    "def zts1_cython2(maxiter, zs, c): \n",
    "    #your code here\n",
    "    cdef unsigned int i\n",
    "    cdef double complex z\n",
    "    output = [0] * len(zs)\n",
    "    i = 0\n",
    "    for z in zs:\n",
    "        output[i] = zts1(maxiter, z, c)\n",
    "        i += 1\n",
    "    return output"
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    "def run2():\n",
    "    zs = setup_grid(gridsize, bounds)\n",
    "    out = zts1_cython2(iters, zs, focus)\n",
    "    return zs, out"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "%timeit -r 1 -n 5 run2()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q3.\n",
    "\n",
    "Replace the `abs` function in the `while` by an equivalent condition which does not require a square root (needed for `abs`. \n",
    "\n",
    "This equivalent but specialized code is called a **strength reduction**. You have lost flexibility and meaning in readability for faster speed."
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#your code here"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def run3():\n",
    "    zs = setup_grid(gridsize, bounds)\n",
    "    out = zts1_cython3(iters, zs, focus)\n",
    "    return zs, out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%timeit -r 1 -n 5 run3()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q4.\n",
    "\n",
    "Turn off bounds-checking (see cython docs for how). Does it make much of a difference? Why?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def run4():\n",
    "    zs = setup_grid(gridsize, bounds)\n",
    "    out = zts1_cython4(iters, zs, focus)\n",
    "    return zs, out\n",
    "%timeit -r 1 -n 5 run4()"
   ]
  }
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