profiling-cython-numba.ipynb

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   "source": [
    "# Profiling, Cython, and Numba 🚀\n",
    "### Zbyszek & Jakob\n",
    "### ASPP 2022, Bilbao, Spain"
   ]
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   "source": [
    "## Outline\n",
    "\n",
    "* Introduction\n",
    "* Profiling\n",
    "* Speed up Python code using Cython\n",
    " * Basic principles\n",
    " * Interacting with NumPy arrays\n",
    "* Using Numba to speed up Python code"
   ]
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   "source": [
    "## Introduction\n",
    "\n",
    "* By now you are the *Master of Research*(tm).\n",
    "![Master of research](figures/mor.png)\n",
    "* Using your newly gained skills you can confidently transform any idea into a great manuscript."
   ]
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    "* It seems like the only thing that's holding you back is the **execution speed** of your scripts!\n",
    "* Both Cython and Numba are tools to make your code faster -> **optimization**."
   ]
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   "source": [
    "## Exercise\n",
    "\n",
    "Who thinks that they would benefit from reduced execution time?\n",
    "\n",
    "Please raise your hand."
   ]
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   "source": [
    "## The three rules of optimization\n",
    "(adapted from Sebastian Witowski, EuroPython 2016)"
   ]
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   "source": [
    "#### 1. Don't.\n",
    " * Likely you don't need it.\n",
    " * Optimization comes with costs."
   ]
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   "source": [
    "## Exercise\n",
    "\n",
    "What are costs associated with optimization?"
   ]
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   "source": [
    "#### 2. Don't yet.\n",
    " * Is your code finished?\n",
    " * Did you write tests?\n",
    " * Are you sure it's worth the investment?"
   ]
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   "source": [
    "#### 3. Profile\n",
    "* Don't guess which part of your code you should optimize!\n",
    "* Measure. Measure. Measure."
   ]
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    "## Runtime profilers\n",
    "\n",
    "- profilers monitor the execution of your script and record, for example, how much time is spent in each function\n",
    "- here we consider [py-spy](https://github.com/benfred/py-spy), a sampling-based profiler for Python\n",
    "  - simply speaking `py-spy` examines your program at regular intervals and records which part is currently executed\n",
    "- you can apply it to your script with `py-spy record -o profile.svg python myprogram.py`\n",
    "  - to make timings accurate it needs to collect enough of data; you can control the \"sampling rate\" using the `-r` argument\n",
    "- after measuring `py-spy` will produce a \"flamegraph\" like the following\n",
    "![flamegraph](./figures/flamegraph.svg)"
   ]
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   "source": [
    "## Demo\n",
    "\n",
    "Using a simple script, Jakob will explain how to read flamegraphs."
   ]
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    "## Example: numerical integration\n",
    "\n",
    "![RiemannSum](figures/MidRiemann2.svg)\n",
    "\n",
    "Riemann sum: $\\int_a^b dx f(x) \\approx \\sum_{i = 0}^{n - 1} f(a + (i + 0.5) \\Delta x) \\Delta x$ with $\\Delta x = (b - a)/n$\n",
    "\n",
    "here $a=0, b=2, n=4$"
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   "source": [
    "### Example implementation\n",
    "(see [./profiling/numerical_integration.py](./profiling/numerical_integration.py))\n",
    "\n",
    "Where do you think the bottlenecks are? *(don't do this at home!)*"
   ]
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   "source": [
    "## Demo\n",
    "\n",
    "With your help, Jakob will demonstrate a typical profiling/optimization workflow based on this script."
   ]
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   "source": [
    "## Exercise\n",
    "\n",
    "It's time to put theory into practice. We have prepared an example script (see [./profiling/count_words.py](./profiling/count_words.py)) which counts the number of occurences of words in a text.\n",
    "\n",
    "0. Fork & clone this repository.\n",
    "1. Familarize yourself with the script.\n",
    "2. Guess which functions are slow and should be optimized. *(don't do this at home.)*\n",
    "3. Use the workflow (time -> py-spy- > timeit/lprun -> time) we have just demonstrated to reduce the script's execution time. **Make sure not to break the tests.**\n",
    "4. Commit your changes in a new branch and create a PR. Include the duration before/after optimization in the PR message.\n",
    "\n",
    "Afterwards we will discuss the exercise jointly."
   ]
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   "source": [
    "## Exercise discussion\n",
    "\n",
    "What did we learn?\n",
    "- ..."
   ]
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   "source": [
    "## Profiling conclusion\n",
    "\n",
    "- Before optimizing, first finish your code & write tests!\n",
    "- Then *measure* to find slow functions. **Profiling is easy!**\n",
    "- Only optimize the slowest functions & *know when to stop*!\n",
    "- Most profilers can be invoked stand-alone and within ipython\n",
    "  - `time` (commandline)\n",
    "  - `%timeit`\n",
    "  - `import timeit; timeit.time('some_func()')`\n",
    "- [py-spy](https://github.com/benfred/py-spy) is just one of many profilers; alternatives:\n",
    "  - [cProfile](https://docs.python.org/3/library/profile.html) + [snakeviz](https://github.com/jiffyclub/snakeviz)\n",
    "  - [pyinstrument](https://github.com/joerick/pyinstrument)\n",
    "- Here we focus on profiling *runtime*, but maybe you are limited by *memory*\n",
    "  - [memray](https://github.com/bloomberg/memray)"
   ]
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   "source": [
    "### Optimization: what to do (in order of increasing complexity)\n",
    "\n",
    "- Do nothing\n",
    "- Vectorization (`numpy`!!)\n",
    "- Data structures and algorithms\n",
    "- Memoization / caching\n",
    "- Non-Python libraries (`blas` vs. `openblas` vs. `atlas` vs. Intel `mkl`)\n",
    "- Buy better hardware\n",
    "- **Cython / Numba** / pythran\n",
    "- **Parallelization** (->tomorrow)\n",
    "- GPUs\n",
    "- Low-level code\n"
   ]
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   "source": [
    "## Cython"
   ]
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    "# We start with our optimized Python implementation.\n",
    "# Parameter 'f' has been renamed to 'func', to distinguish it from the 'f' function.\n",
    "\n",
    "def f(x):\n",
    "    return x**4 - 3 * x\n",
    "\n",
    "def integrate_f(func, a, b, n):\n",
    "    dx = (b - a) / n\n",
    "    s = 0.0\n",
    "    for i in range(n):\n",
    "        s += func(a + (i + 0.5) * dx) * dx\n",
    "    return s"
   ]
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   "source": [
    "# We increase the number of points (from 5k to 1M) for easier measurement.\n",
    "\n",
    "integrate_f(f, -10, +10, 1_000_000)"
   ]
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     "text": [
      "328 ms ± 21.5 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit integrate_f(f, -10, +10, 1_000_000)"
   ]
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   "source": [
    "Our first step is to load the 'cython' extension and apply '%%cython' magic to the whole cell.\n",
    "\n",
    "'f', 'integrate_f' are renamed to 'f2', 'integrate_f2'.\n",
    "\n",
    "The code is otherwise unchanged."
   ]
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   "source": [
    "%load_ext cython"
   ]
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   "execution_count": 40,
   "id": "67093028",
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   "source": [
    "%%cython\n",
    "\n",
    "def f2(x):\n",
    "    return x**4 - 3 * x\n",
    "\n",
    "def integrate_f2(func, a, b, n):\n",
    "    dx = (b - a) / n\n",
    "    s = 0.0\n",
    "    for i in range(n):\n",
    "        s += func(a + (i + 0.5) * dx) * dx\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "f04b36a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "225 ms ± 15.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit integrate_f2(f2, -10, +10, 1_000_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d161a055",
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       "(<function _cython_magic_9a59b8cb490d86577a5bc789129b6c05.f2>,\n",
       " <function _cython_magic_9a59b8cb490d86577a5bc789129b6c05.integrate_f2>)"
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   "source": [
    "# f2 and integrate_f2 are now compiled functions\n",
    "\n",
    "f2, integrate_f2"
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    "Our next step is to set types of the function parameters.\n",
    "\n",
    "This is called \"type specialiation\".\n",
    "\n",
    "Our code is not valid Python anymore, only Cython can understand it."
   ]
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   "id": "d122ce72",
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   "source": [
    "%%cython\n",
    "\n",
    "def f3(double x):\n",
    "    return x**4 - 3 * x\n",
    "\n",
    "def integrate_f3(func, double a, double b, int n):\n",
    "    dx = (b - a) / n\n",
    "    s = 0.0\n",
    "    for i in range(n):\n",
    "        s += func(a + (i + 0.5) * dx) * dx\n",
    "    return s"
   ]
  },
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   "execution_count": 9,
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      ]
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     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "integrate_f3(f3, -10, +10, 1_000_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9c98e661",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "157 ms ± 9.94 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit integrate_f3(f3, -10, +10, 1_000_000)"
   ]
  },
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   "cell_type": "markdown",
   "id": "fdee555d",
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   "source": [
    "Our next step is to also provide types of internal variables.\n",
    "\n",
    "We also use '-a' to tell '%%cython' to generate annotated output with hints about Python ↔ C-code interation."
   ]
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       "<pre class='cython code score-6 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  __pyx_t_1 = <span class='py_c_api'>PyFloat_FromDouble</span>((pow(__pyx_v_x, 4.0) - (3.0 * __pyx_v_x)));<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 3, __pyx_L1_error)</span>\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">04</span>: </pre>\n",
       "<pre class=\"cython line score-81\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">05</span>: <span class=\"k\">def</span> <span class=\"nf\">integrate_f4</span><span class=\"p\">(</span><span class=\"n\">func</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">b</span><span class=\"p\">,</span> <span class=\"nb\">int</span> <span class=\"n\">n</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-81 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_4996f8bbcb067733c4e8fc5e0a70c4b0_3integrate_f4(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_4996f8bbcb067733c4e8fc5e0a70c4b0_3integrate_f4 = {\"integrate_f4\", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_46_cython_magic_4996f8bbcb067733c4e8fc5e0a70c4b0_3integrate_f4, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_4996f8bbcb067733c4e8fc5e0a70c4b0_3integrate_f4(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
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       "\n",
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       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_4996f8bbcb067733c4e8fc5e0a70c4b0.integrate_f4\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
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       "<pre class='cython code score-5 '>  __pyx_t_1 = (__pyx_v_b - __pyx_v_a);\n",
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       "</pre></div></body></html>"
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       "<IPython.core.display.HTML object>"
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     },
     "execution_count": 11,
     "metadata": {},
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    }
   ],
   "source": [
    "%%cython -a\n",
    "\n",
    "def f4(double x):\n",
    "    return x**4 - 3 * x\n",
    "\n",
    "def integrate_f4(func, double a, double b, int n):\n",
    "    cdef:\n",
    "        double dx = (b - a) / n\n",
    "        double s = 0.0\n",
    "        int i\n",
    "    \n",
    "    for i in range(n):\n",
    "        s += func(a + (i + 0.5) * dx) * dx\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3846893f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39999.999999868494"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate_f4(f4, -10, +10, 1_000_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ed522072",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "92.2 ms ± 2.16 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit integrate_f4(f4, -10, +10, 1_000_000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fe70695",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Exercise 01-cython-primes\n",
    "\n",
    "Please open [01-cython-primes/exercise.ipynb](01-cython-primes/exercise.ipynb) and follow instructions therein."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b29f03e",
   "metadata": {},
   "source": [
    "### Cython function type specialization\n",
    "\n",
    "We see strong yellow in the internal loop:\n",
    "\n",
    "every time we call 'f', which is a Python function, conversion from Python types to c types and back must be done. \n",
    "\n",
    "This is slow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fe6ee4ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%cython\n",
    "\n",
    "# We do \"function specialization\", by changing 'f5' to be a C function.\n",
    "#\n",
    "# On the first attempt we get a warning, because the generated C function is not used.\n",
    "\n",
    "cdef double f5(double x):\n",
    "    return x**4 - 3 * x\n",
    "\n",
    "def integrate_f5(func, double a, double b, int n):\n",
    "    cdef:\n",
    "        double dx = (b - a) / n\n",
    "        double s = 0.0\n",
    "        int i\n",
    "    \n",
    "    for i in range(n):\n",
    "        s += func(a + (i + 0.5) * dx) * dx\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ca74954f",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%cython\n",
    "\n",
    "# In the second attempt, integrate_f5 hardcodes the function to call.\n",
    "# We can rename it to just 'f', because it'll not be visible anywhere.\n",
    "\n",
    "cdef double f(double x):\n",
    "    return x**4 - 3 * x\n",
    "\n",
    "def integrate_f5(double a, double b, int n):\n",
    "    cdef:\n",
    "        double dx = (b - a) / n\n",
    "        double s = 0.0\n",
    "        int i\n",
    "    \n",
    "    for i in range(n):\n",
    "        s += f(a + (i + 0.5) * dx) * dx\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5b22a312",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25.8 ms ± 1.26 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit integrate_f5(-10, +10, 1_000_000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdbe9245",
   "metadata": {},
   "source": [
    "### Cython formula optimization\n",
    "\n",
    "As a final optimization step, we can replace the call to `x**4`,\n",
    "which generates a call to the C function `pow()`, with a series of multiplications.\n",
    "\n",
    "We can also reorder the expression a bit to save one multiplication."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9990b21c",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%cython\n",
    "\n",
    "cdef double f(double x):\n",
    "    # This is the same as x**4 - 3*x, and also the same as x*x*x*x - 3*x\n",
    "    return (x*x*x - 3) * x\n",
    "\n",
    "def integrate_f6(double a, double b, int n):\n",
    "    cdef:\n",
    "        double dx = (b - a) / n\n",
    "        double s = 0.0\n",
    "        int i\n",
    "    \n",
    "    for i in range(n):\n",
    "        s += f(a + (i + 0.5) * dx) * dx\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "679c0282",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39999.999999868494"
      ]
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     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate_f6(-10, +10, 1_000_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b9d04e5c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.97 ms ± 130 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit integrate_f6(10, +10, 1_000_000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52768b44",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Exercise: 02-cython-distrib\n",
    "\n",
    " Please open a terminal, `cd` to `02-cython-distrib/`, and follow the instructions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "eb773961",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "This is a very simple package that uses Cython.\n",
       "It shows how to \"package\" a Python package with compiled sources.\n",
       "\n",
       "The source code is just the `.pyx` file (`integrate_f6.pyx`).\n",
       "\n",
       "The other files are \"metadata\":\n",
       "\n",
       "- [pyproject.toml](02-cython-distrib/pyproject.toml)\n",
       "- [meson.build](02-cython-distrib/meson.build)\n",
       "- [setup.py](02-cython-distrib/setup.py)\n",
       "\n",
       "Exercise:\n",
       "    0) have a look at the different files\n",
       "    1) install the module\n",
       "    2) make sure it can be imported from anywhere:\n",
       "\n",
       "    cd /\n",
       "    python -c 'import integrate_f6; print(integrate_f6)'\n",
       "    \n",
       "    3) call the `integrate_f6` function from the Python interpreter after importing the module\n",
       "\n",
       "--\n",
       "\n",
       "How to install:\n",
       "\n",
       "The \"new\" way is to use `pip`:\n",
       "\n",
       "    pip install --user .\n",
       "\n",
       "To just build a distributable bundle:\n",
       "\n",
       "    pip wheel .\n",
       "\n",
       "This creates a binary \"wheel\" (zip archive) in dist/ .\n",
       "\n",
       "--\n",
       "\n",
       "The \"old\" way is to use setup.py:\n",
       "\n",
       "    python setup.py build\n",
       "\n",
       "or\n",
       "\n",
       "    python setup.py build_ext --inplace\n",
       "\n",
       "to compile the code.\n",
       "\n",
       "--\n",
       "\n",
       "Optionally:\n",
       "\n",
       "`meson` can also be invoked without `pip`:\n",
       "\n",
       "    meson build-meson\n",
       "    meson compile -C build-meson\n",
       "\n",
       "This builds a module (underneath `build-meson/`), but does not put it the Python module search path.\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython import display\n",
    "display.display(display.Markdown(open('02-cython-distrib/README.md').read()))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5afbe2d3",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "### When `setup.py` and when `meson.build`?\n",
    "\n",
    "[<img src=\"images/logo-over-white.svg\" width=\"100\"/>](images/logo-over-white.svg)\n",
    "\n",
    "- setuptools is (still) the standard in the Python ecosystem\n",
    "- excellent integration with PyPI and other Python packages\n",
    "- automatic downloads from PyPI\n",
    "- clumsy integration with non-Python libraries\n",
    "- weak support for optional dependencies and partial rebuilds\n",
    "\n",
    "[<img src=\"images/Meson_(software)_logo_2019.svg\" width=\"180\"/>](images/Meson_(software)_logo_2019.svg)\n",
    "\n",
    "- Meson is arguably the best available build system for compiled code\n",
    "- excellent integration with pkgconfig and other system libraries\n",
    "- integration with PyPI via pip, somewhat clumsy\n",
    "- excellent support for user configuration, optional dependencies, and partial rebuilds\n",
    "\n",
    "Thus, if setuptools is a good solution for Python projects with some Cython code, and no dependencies on system libraries. Meson is a good solution for some self-contained Python and/or Cython code, possibly alongside other non-Python libraries and executables."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8e77134",
   "metadata": {},
   "source": [
    "# Cython and Numpy Arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8cbf32a",
   "metadata": {},
   "source": [
    "## Array summing\n",
    "\n",
    "Let's start by summing up an array.\n",
    "\n",
    "`const double [:]` means that the parameter is a immutable 1D memoryview.\n",
    "\n",
    "We can use this function on numpy arrays."
   ]
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       "<pre class='cython code score-16 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_Import</span>(__pyx_n_s_numpy, 0, 0);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 2, __pyx_L1_error)</span>\n",
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    "%%cython -a\n",
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    "        ssize_t i, n = A.shape[A.ndim - 1]\n",
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       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">20</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\">n</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_4 = __pyx_v_n;\n",
       "  __pyx_t_5 = __pyx_t_4;\n",
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       "<pre class='cython code score-0 '>    __pyx_t_7 = __pyx_v_i;\n",
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   "source": [
    "%%cython -a\n",
    "\n",
    "# From the yellow output above, we see that in line 11 a check\n",
    "# is performed to optionally throw BufferIndexError.\n",
    "# We know that this cannot happen, so we can tell cython to\n",
    "# disable the check with 'boundscheck(False)'.\n",
    "#\n",
    "# While at it, let's disable support for negative indices with\n",
    "# 'wraparound(False)'. We don't use those.\n",
    "\n",
    "import numpy as np\n",
    "import cython\n",
    "\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def mysum(const double [:] A):\n",
    "    cdef:\n",
    "        double s = 0.0\n",
    "        ssize_t i, n = A.shape[A.ndim - 1]\n",
    "    \n",
    "    for i in range(n):\n",
    "        s += A[i]\n",
    "    return s"
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  {
   "cell_type": "markdown",
   "id": "a54ef430",
   "metadata": {},
   "source": [
    "## `mean3filter`\n",
    "\n",
    "Let's write a \"mean filter\", i.e. a function that calculates a local\n",
    "average for every 3 points.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ffbd9ca",
   "metadata": {},
   "source": [
    "$$ \\{ x_0, x_1, ...  , x_{n-2}, x_n \\} \\longrightarrow \\{ \\frac{x_0 + x_1}{2}, \\frac{x_0 + x_1 + x_2}{3}, \\frac{x_1 + x_2 + x_3}{3}, ... , \\frac{x_{i-1} + x_i + x_{i+1}}{3}, ... , \\frac{x_{n-3} + x_{n-2} + x_{n-1}}{3}, \\frac{x_{n-2} + x_{n-1}}{2} \\} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "9fddfb85",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def mean3filter_p(arr):\n",
    "    arr_out = np.empty_like(arr)\n",
    "    \n",
    "    arr_out[0] =  (arr[0] + arr[1]) / 2\n",
    "    for i in range(1, arr.shape[0] - 1):\n",
    "        arr_out[i] = arr[i-1:i+2].sum() / 3\n",
    "    arr_out[-1] = (arr[-2] + arr[-1]) / 2\n",
    "\n",
    "    return arr_out"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2825e05",
   "metadata": {},
   "source": [
    "## Exercise 03-cython-mean3filter\n",
    "\n",
    "Please open [03-cython-mean3filter/exercise.ipynb](03-cython-mean3filter/exercise.ipynb) and follow instructions therein."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c4e1ed16",
   "metadata": {},
   "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": 26,
   "id": "6248b20e",
   "metadata": {},
   "outputs": [
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    "%%cython -a\n",
    "\n",
    "# This is a naive cythonized version.\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "def mean3filter_c1(const double [:] arr):\n",
    "    cdef double [:] arr_out = np.empty_like(arr)\n",
    "    cdef ssize_t i, N = arr.size\n",
    "    \n",
    "    arr_out[0] =  (arr[0] + arr[1]) / 2\n",
    "    for i in range(1, N - 1):\n",
    "        arr_out[i] = (arr[i-1] + arr[i] + arr[i+1]) / 3\n",
    "    arr_out[-1] = (arr[-2] + arr[-1]) / 2\n",
    "\n",
    "    return arr_out"
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       "</pre><pre class=\"cython line score-14\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">14</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">ssize_t</span> <span class=\"nf\">i</span><span class=\"p\">,</span> <span class=\"nf\">N</span> <span class=\"o\">=</span> <span class=\"n\">arr</span><span class=\"o\">.</span><span class=\"n\">size</span></pre>\n",
       "<pre class='cython code score-14 '>  __pyx_t_1 = __pyx_memoryview_fromslice(__pyx_v_arr, 1, (PyObject *(*)(char *)) __pyx_memview_get_double__const__, (int (*)(char *, PyObject *)) NULL, 0);;<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 14, __pyx_L1_error)</span>\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">15</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">16</span>:     <span class=\"n\">arr_out</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span> <span class=\"o\">=</span>  <span class=\"p\">(</span><span class=\"n\">arr</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">arr</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">])</span> <span class=\"o\">/</span> <span class=\"mf\">2</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_6 = 0;\n",
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       "  __pyx_t_8 = 0;\n",
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       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">17</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=\"mf\">1</span><span class=\"p\">,</span> <span class=\"n\">N</span> <span class=\"o\">-</span> <span class=\"mf\">1</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_7 = (__pyx_v_N - 1);\n",
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       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">18</span>:         <span class=\"n\">arr_out</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"n\">arr</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"o\">-</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">arr</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">arr</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"o\">+</span><span class=\"mf\">1</span><span class=\"p\">])</span> <span class=\"o\">/</span> <span class=\"mf\">3</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_9 = (__pyx_v_i - 1);\n",
       "    __pyx_t_10 = __pyx_v_i;\n",
       "    __pyx_t_11 = (__pyx_v_i + 1);\n",
       "    __pyx_t_12 = __pyx_v_i;\n",
       "    *((double *) ( /* dim=0 */ (__pyx_v_arr_out.data + __pyx_t_12 * __pyx_v_arr_out.strides[0]) )) = ((((*((double const  *) ( /* dim=0 */ (__pyx_v_arr.data + __pyx_t_9 * __pyx_v_arr.strides[0]) ))) + (*((double const  *) ( /* dim=0 */ (__pyx_v_arr.data + __pyx_t_10 * __pyx_v_arr.strides[0]) )))) + (*((double const  *) ( /* dim=0 */ (__pyx_v_arr.data + __pyx_t_11 * __pyx_v_arr.strides[0]) )))) / 3.0);\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">19</span>:     <span class=\"n\">arr_out</span><span class=\"p\">[</span><span class=\"n\">N</span><span class=\"o\">-</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"n\">arr</span><span class=\"p\">[</span><span class=\"n\">N</span><span class=\"o\">-</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">arr</span><span class=\"p\">[</span><span class=\"n\">N</span><span class=\"o\">-</span><span class=\"mf\">1</span><span class=\"p\">])</span> <span class=\"o\">/</span> <span class=\"mf\">2</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_7 = (__pyx_v_N - 2);\n",
       "  __pyx_t_6 = (__pyx_v_N - 1);\n",
       "  __pyx_t_8 = (__pyx_v_N - 1);\n",
       "  *((double *) ( /* dim=0 */ (__pyx_v_arr_out.data + __pyx_t_8 * __pyx_v_arr_out.strides[0]) )) = (((*((double const  *) ( /* dim=0 */ (__pyx_v_arr.data + __pyx_t_7 * __pyx_v_arr.strides[0]) ))) + (*((double const  *) ( /* dim=0 */ (__pyx_v_arr.data + __pyx_t_6 * __pyx_v_arr.strides[0]) )))) / 2.0);\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">20</span>: </pre>\n",
       "<pre class=\"cython line score-1\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">21</span>:     <span class=\"k\">return</span> <span class=\"n\">arr_out</span></pre>\n",
       "<pre class='cython code score-1 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  __pyx_t_3 = __pyx_memoryview_fromslice(__pyx_v_arr_out, 1, (PyObject *(*)(char *)) __pyx_memview_get_double, (int (*)(char *, PyObject *)) __pyx_memview_set_double, 0);;<span class='error_goto'> if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 21, __pyx_L1_error)</span>\n",
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       "</pre></div></body></html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%cython -a\n",
    "\n",
    "# Similarly to 'mysum', we don't need the bounds checks.\n",
    "# But we are using negative indices. We can do get rid of\n",
    "# this by changing '-1' to 'N-1' and '-2' to 'N-2'.\n",
    "# With that change, we can also disable wraparound support.\n",
    "\n",
    "import numpy as np\n",
    "import cython\n",
    "\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def mean3filter_c2(const double [:] arr):\n",
    "    cdef double [:] arr_out = np.empty_like(arr)\n",
    "    cdef ssize_t i, N = arr.size\n",
    "    \n",
    "    arr_out[0] =  (arr[0] + arr[1]) / 2\n",
    "    for i in range(1, N - 1):\n",
    "        arr_out[i] = (arr[i-1] + arr[i] + arr[i+1]) / 3\n",
    "    arr_out[N-1] = (arr[N-2] + arr[N-1]) / 2\n",
    "\n",
    "    return arr_out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "569f6e34",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.rand(1_000_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "340c4f69",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.09 s ± 41.7 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit mean3filter_p(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "48acb163",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.43 ms ± 47 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit mean3filter_c1(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "fdf61242",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.48 ms ± 56.2 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit mean3filter_c2(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66055d28",
   "metadata": {},
   "source": [
    "It turns out the cythonized versions are statistically indistinguishable.\n",
    "\n",
    "Cython is about 750 times faster."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2f2fee8",
   "metadata": {},
   "source": [
    "http://docs.cython.org/en/stable/src/userguide/memoryviews.html"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbc3581f",
   "metadata": {},
   "source": [
    "# Wrapping external code in Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "73670ba0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function _cython_magic_8333d4130183217cee6a930dacf6f59a.f3>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3b35b39",
   "metadata": {},
   "source": [
    "# Numba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "8ab556b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numba\n",
    "\n",
    "# We apply the numba decorator to 'f' and 'integrate_f'\n",
    "# to let numba genenerate optimized versions of those funtions.\n",
    "#\n",
    "# 'numba.njit' is the same as 'numba.jit(nopython=True)',\n",
    "# and it means that numba should throw an exception instead of\n",
    "# falling back to the python version, in cases where it cannot generate\n",
    "# the optimized version.\n",
    "\n",
    "@numba.njit\n",
    "def f(x):\n",
    "    return x**4 - 3 * x\n",
    "\n",
    "@numba.njit\n",
    "def integrate_f(func, a, b, n):\n",
    "    dx = (b - a) / n\n",
    "    s = 0.0\n",
    "    for i in range(n):\n",
    "        s += func(a + (i + 0.5) * dx) * dx\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "b5414daa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.11 ms ± 44.3 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit integrate_f(f, -10, +10, 1_000_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "1dace462",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numba\n",
    "\n",
    "# Here we repeat the optimization of the formula to replace\n",
    "# pow() by a multiplications. It turns out that this doesn't\n",
    "# provide any speedup, so we can conclude that numba\n",
    "# (or the compiler backend, llvm) were smart enough to do this\n",
    "# step automatically.\n",
    "\n",
    "@numba.njit\n",
    "def f(x):\n",
    "    return (x*x*x - 3) * x\n",
    "\n",
    "@numba.njit\n",
    "def integrate_f(func, a, b, n):\n",
    "    dx = (b - a) / n\n",
    "    s = 0.0\n",
    "    for i in range(n):\n",
    "        s += func(a + (i + 0.5) * dx) * dx\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "f02c48b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.01 ms ± 62.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit integrate_f(f, -10, +10, 1_000_000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd411fdb",
   "metadata": {},
   "source": [
    "[<img src=\"images/whiteboard.jpeg\" width=\"200\"/>](images/whiteboard.jpeg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90ec12ac",
   "metadata": {},
   "source": [
    "### Summary of Python vs. Cython vs. Numba\n",
    "\n",
    "(Timings on my laptop, 64-bit amd-compatible cpu, 2.5 GHz)\n",
    "\n",
    "\n",
    "```\n",
    "original python version:      74   ms / 5000 iterations  = 14800 ns / iteration\n",
    "with [].append                 3.7 ms / 5000 iterations  =   740 ns / iteration\n",
    "no list                        3.3 ms / 5000 iterations  =   660\n",
    "constant moved outside loop    3.0 ms / 5000 iterations  =   600\n",
    "----\n",
    "pure python:                  335    ms / 10⁶ iterations =   335 ns / iteration\n",
    "python-compatible cython:     225    ms / 10⁶ iterations =   225 ns / iteration\n",
    "typing of arguments:          157    ms / 10⁶ iterations =   157 ns / iteration\n",
    "typing of variables:           92    ms / 10⁶ iterations =    92 ns / iteration\n",
    "c-only function:               25    ms / 10⁶ iterations =    25 ns / iteration\n",
    "simplified expression form:     2.11 ms / 10⁶ iterations =     2 ns / iteration\n",
    "\n",
    "numba jit:                      2.01 ms / 10⁶ iterations =     2 ns / iteration\n",
    "```\n",
    "\n",
    "We made a speed-up of approximately 7400 times.\n",
    "\n",
    "14800 ns × 2.5 × 10⁹ cycles/s = 37000 cycles\n",
    "2 ns × 2.5 × 10⁹ cycles/s = 5 cycles\n",
    "\n",
    "Our original versions was using about 40k CPU cycles (steps) to calculate a single iteration of the loop.\n",
    "The final version requires 5 cycles. This is what we should expect for four multiplications,\n",
    "a subtraction and an addition, and some overhead to manage the loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a06e8b13",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c28b54ad",
   "metadata": {},
   "source": [
    "# Architecture of Cython and Numba"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2b1fff5",
   "metadata": {},
   "source": [
    "[<img src=\"images/cython_architecture.png\" width=\"400\"/>](images/cython_architecture.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f12364b",
   "metadata": {},
   "source": [
    "[<img src=\"images/numba_architecture.png\" width=\"400\" />](images/numba_architecture.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a80eab14",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "6c8bb11f",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    " * ~Release the GIL and parallelize easily~ *(moved to parallel lecture)*\n",
    " * ~Wrap C/C++ code~ *(not relevant enough)*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12da18df",
   "metadata": {},
   "source": [
    "https://cython.readthedocs.io/en/latest/src/userguide/parallelism.html"
   ]
  }
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