Numba_Demo_001.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Numba Demo 1\n",
    "\n",
    "## Sum of first X integers\n",
    "\n",
    "Given this simple function:\n",
    "\n",
    "$$sum(x) = \\sum\\limits_{x=0}^X x$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Lets define $sum_p(x)$ in pure Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def sum_p(X):\n",
    "    y = 0\n",
    "    for x_i in range(int(X)):\n",
    "        y += x_i\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then we define $sum_j(x)$ that is identical but just with decorator `@jit` in the definition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from numba import jit\n",
    "\n",
    "@jit\n",
    "def sum_j(X):\n",
    "    y = 0\n",
    "    for x_i in range(int(X)):\n",
    "        y += x_i\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Lets benchmark them!\n",
    "\n",
    "Lets define a benchmark to study perfromances of our implementations of $sum(x)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import time\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "%matplotlib inline\n",
    "\n",
    "# Different platforms require different functions to properly measure current timestamp:\n",
    "if os.name == 'nt':\n",
    "    now = time.clock\n",
    "else:\n",
    "    now = time.time\n",
    "\n",
    "def run_benchmarks(functions, call_parameters, num_times,\n",
    "                   logy=False, logx=False):\n",
    "    \n",
    "    # Executes one function several times and measure performances:\n",
    "    def _apply_function(function, num_times):\n",
    "        for j in range(num_times):\n",
    "            t_0 = now()\n",
    "            y = function(*call_parameters)\n",
    "            duration = (now() - t_0)\n",
    "            yield float(duration)\n",
    "    \n",
    "    def _name(function):\n",
    "        return '${' + function.__name__ + '(x)}$'\n",
    "    \n",
    "    # Execute all functions the requested number of times and collects durations:\n",
    "    def _apply_functions(functions, num_times):\n",
    "        for function in functions:\n",
    "            yield pd.Series(_apply_function(function, num_times),\n",
    "                            name=_name(function))\n",
    "            \n",
    "            \n",
    "    # Collects and plots the results:\n",
    "    df = pd.concat(_apply_functions(functions, num_times),\n",
    "                   axis=1)\n",
    "    ax = df.plot(figsize=(10,5),\n",
    "                 logy=logy,\n",
    "                 logx=logx,\n",
    "                 title='$T[f(x)]$ in seconds',\n",
    "                 style='o-')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Benchmark results\n",
    "\n",
    "Lets measure them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
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5DcuuXkbXll0DjUtERESkvIQf6So24cQJ/OjUH5E2M40de3cEHY6IiIhIxMTVSFexmxbd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7922208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_benchmarks(functions=[sum_p, sum_j],\n",
    "               call_parameters=(10000000,),\n",
    "               num_times=5,\n",
    "               logy=True) # Logarithmic scale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Numba caching\n",
    "\n",
    "A second run to study `numba` caching mechanism"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa818d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_benchmarks(functions=[sum_j],\n",
    "               call_parameters=(1000000000000000.,),\n",
    "               num_times=5,\n",
    "               logy=True) # Logarithmic scale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Numba JIT functionality works in the following way:\n",
    "- At each call of a function $f(x)$, numba looks at the type $T$ of $x$.\n",
    "- If it is the first time that type have been used generates a native implementation $f_T(x)$.\n",
    "- If it is not  the first time that type have been used generates fetches the native implementation from a cache.\n",
    "- Numba executes $f_T(x)$ that is orders of magnitudes faster than a pure Python implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##And what about adding Cython to the game?\n",
    "\n",
    "Lets define the same functon, but tuned to operate with floats:\n",
    "\n",
    "$$sum(x) = \\sum\\limits_{x=0}^X x$$\n",
    "\n",
    "We redefine it using `numba` and `cython`, this time using float numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from numba import jit\n",
    "\n",
    "@jit\n",
    "def sum_j(x):\n",
    "    y = 0.\n",
    "    x_i = 0.\n",
    "    while x_i < x:\n",
    "        y += x_i\n",
    "        x_i += 1.\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "def sum_c(double x):\n",
    "    cdef double y = 0.\n",
    "    cdef double x_i = 0.\n",
    "    while x_i < x:\n",
    "        y += x_i\n",
    "        x_i += 1.\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "About Cython:\n",
    "- generates C code from a Python code.\n",
    "- allows to define low level C-types.\n",
    "- in this example we use C-type `double`.\n",
    "- C code is generated, compiled and executed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Benchmarks JIT vs Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hncjuxx9h2zaIjrY6Evc0diw0bWo2ee7e3epohJX274eRI2HjRlOT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\nMHKk2ccpLz/8AG++KasDhRBCWOeDD2D/fvjmG6s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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1126668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run_benchmarks(functions=[sum_j, sum_c],\n",
    "               call_parameters=(1000000000.,),\n",
    "               num_times=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The `numba` jitted function is comparable with the *cythonized* one, lets check what was the C code `cython` used, just to give us an idea of the efficiency of the code generated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html>\n",
       "<!-- Generated by Cython 0.22.1 -->\n",
       "<html>\n",
       "<head>\n",
       "    <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\" />\n",
       "    <title>Cython: _cython_magic_21008fbc7088ac68cab2b82581ff3eba.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 20px;  }\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 .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",
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       ".cython.score-5 {background-color: #FFFFaa;}\n",
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       ".cython.score-22 {background-color: #FFFF4f;}\n",
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       "static PyMethodDef __pyx_mdef_46_cython_magic_21008fbc7088ac68cab2b82581ff3eba_1sum_c = {\"sum_c\", (PyCFunction)__pyx_pw_46_cython_magic_21008fbc7088ac68cab2b82581ff3eba_1sum_c, METH_O, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_21008fbc7088ac68cab2b82581ff3eba_1sum_c(PyObject *__pyx_self, PyObject *__pyx_arg_x) {\n",
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    "%%cython --annotate\n",
    "def sum_c(double x):\n",
    "    cdef double y = 0.\n",
    "    cdef double x_i = 0.\n",
    "    while x_i < x:\n",
    "        y += x_i\n",
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   "metadata": {
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   },
   "source": [
    "The function is in order, we have Python overhead only during the call and the return value to convert values from/to Python."
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  },
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   "source": [
    "# Conclusions\n",
    "\n",
    "Pure Python code can be 2-3 order of magnitudes slower than native code, but cheap solutions exists to solve the issue by makeing native just the parts where going native matters.\n",
    "\n",
    "We have several ways of going native:"
   ]
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   "source": [
    "## Optiona A: C/C++ written Python extensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Write C/C++ code and use it from Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "It is sure the most powerful approach, but by far the more expensive."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
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   },
   "source": [
    "Who develops C/C++ knows what does it mean:\n",
    "- passing long hours waiting for a compiler to finish.\n",
    "- never ending discussions about how to better pass parameters to functions.\n",
    "- narrow set of 3rd party libraries, often complex to compile and integrate.\n",
    "- very complicated generic programming.\n",
    "\n",
    "In general, C++ is expensive and reserved to projects with a very big budget."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Option B: use Cython"
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  {
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    "- Cython can generate C++ code for us from some code that we can define as *Python with types*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "- Sure is much cheaper than option A, but still forces us to assign typize our code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
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   "source": [
    "- Choosing types requires some effort to understand what types we really need, and forces us to restrict the scope of our numerical functions."
   ]
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  {
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   "metadata": {
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   "source": [
    "- we have still something to compile again and again even if C is much faster than C++."
   ]
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   "metadata": {
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     "slide_type": "subslide"
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   },
   "source": [
    "## Option C: try Numba and compile on the fly"
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Numba allow us to have just in time code generation, and we can also omit types."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The native code is to be generated on demand *where* and *when* needed with all the necessary information in place (types, target CPU, algorithmical context...)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Another nice extra is to give to the user the Pythonic support for arbitrary big numbers."
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  }
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