testing_loops.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "45e2eb4e",
   "metadata": {},
   "source": [
    "# Testing how function declarations can slow down loops"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa383891",
   "metadata": {},
   "source": [
    "I wanted to know how much slower a loop runs if an operation is abstracted into a function. I tested this by creating a function that does nothing but return the input, and then running a loop that calls that function.\n",
    "\n",
    "It seems that the function call is not a not a significant overhead for this simple case. But what about nested functions in nested loops?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ee25c373",
   "metadata": {},
   "outputs": [],
   "source": [
    "import timeit\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "65409417",
   "metadata": {},
   "outputs": [],
   "source": [
    "def busy_work(num):\n",
    "    return num + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38fcaf15",
   "metadata": {},
   "source": [
    "Initialise the input arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9faae284",
   "metadata": {},
   "outputs": [],
   "source": [
    "results_loop = []\n",
    "results_loop_with_function = []\n",
    "\n",
    "max_num = 100000\n",
    "div = max_num // 10\n",
    "x = range(0,max_num,div)\n",
    "\n",
    "timeit_iterations = 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccf1ab1b",
   "metadata": {},
   "source": [
    "Crunch the numbers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "51937a67",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loop size: 0 / 100000   normal loop is 1.014394672378432 times faster than loop with function\n",
      "Loop size: 10000 / 100000   normal loop is 2.244825457863768 times faster than loop with function\n",
      "Loop size: 20000 / 100000   normal loop is 2.291423466231766 times faster than loop with function\n",
      "Loop size: 30000 / 100000   normal loop is 2.226239632730982 times faster than loop with function\n",
      "Loop size: 40000 / 100000   normal loop is 2.332858294755286 times faster than loop with function\n",
      "Loop size: 50000 / 100000   normal loop is 2.3388644538480703 times faster than loop with function\n",
      "Loop size: 60000 / 100000   normal loop is 2.3610812693882512 times faster than loop with function\n",
      "Loop size: 70000 / 100000   normal loop is 2.3533071776357475 times faster than loop with function\n",
      "Loop size: 80000 / 100000   normal loop is 2.325384993566371 times faster than loop with function\n",
      "Loop size: 90000 / 100000   normal loop is 2.424588137210641 times faster than loop with function\n"
     ]
    }
   ],
   "source": [
    "for i in x:\n",
    "    results_loop.append(timeit.timeit(\"for num in range(0,\"+str(i)+\"): a = a + 1\", number=timeit_iterations, setup=\"a = 0\"))\n",
    "    results_loop_with_function.append(timeit.timeit(\"for num in range(0,\"+str(i)+\"): a = busy_work(a)\", number=timeit_iterations, setup=\"from __main__ import busy_work; a = 0\"))\n",
    "    print(\"Loop size: \" + str(i) + \" / \" + str(max_num) + \"   normal loop is {} times faster than loop with function\".format(results_loop_with_function[-1]/results_loop[-1]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08ad1350",
   "metadata": {},
   "source": [
    "Graph the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "37c86e51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y1 = results_loop\n",
    "y2 = results_loop_with_function\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(2)\n",
    "fig.suptitle('Loop vs Loop with Function')\n",
    "ax1.plot(x,y1, 'r.', label=\"loop\")\n",
    "ax1.set(xlabel='input size', ylabel='time (s)')\n",
    "ax1.legend()\n",
    "ax2.plot(x,y2, 'r.', label=\"loop with function\")\n",
    "ax2.set(xlabel='input size', ylabel='time (s)')\n",
    "ax2.legend()\n",
    "\n",
    "# space the plots out a bit\n",
    "fig.tight_layout(pad=2.0)\n",
    "\n",
    "# annotate the points with their values\n",
    "for x,y in zip(x,y1):\n",
    "    label = \"{:f}\".format(y)\n",
    "    ax1.annotate(label, # this is the text\n",
    "                 (x,y), # these are the coordinates to position the label\n",
    "                 textcoords=\"offset points\", # how to position the text\n",
    "                 xytext=(0,10), # distance from text to points (x,y)\n",
    "                 ha='center') # horizontal alignment can be left, right or center\n",
    "\n",
    "# reset x iterator\n",
    "x = range(0,max_num,div)\n",
    "\n",
    "for x,y in zip(x,y2):\n",
    "    label = \"{:f}\".format(y)\n",
    "    ax2.annotate(label, # this is the text\n",
    "                 (x,y), # these are the coordinates to position the label\n",
    "                 textcoords=\"offset points\", # how to position the text\n",
    "                 xytext=(0,10), # distance from text to points (x,y)\n",
    "                 ha='center') # horizontal alignment can be left, right or center\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.1 64-bit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.1"
  },
  "vscode": {
   "interpreter": {
    "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}