{
"metadata": {
"name": "",
"signature": "sha256:8845296976cab33005a3bb80b31d57f89fff309b8284088e7846fb1067a7aacb"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Sebastian Raschka](http://sebastianraschka.com) \n",
"\n",
"last updated: 05/27/2014\n",
"\n",
"- [Open in IPython nbviewer](http://nbviewer.ipython.org/github/rasbt/One-Python-benchmark-per-day/blob/master/ipython_nbs/day8_sqrt_and_exp.ipynb?create=1) \n",
"\n",
"- [Link to this IPython notebook on Github](https://github.com/rasbt/One-Python-benchmark-per-day/blob/master/ipython_nbs/day8_sqrt_and_exp.ipynb) \n",
"\n",
"- [Link to the GitHub Repository One-Python-benchmark-per-day](https://github.com/rasbt/One-Python-benchmark-per-day)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Day 8 - One Python Benchmark per Day"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Calculating square roots and exponents"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"I would be happy to hear your comments and suggestions. \n",
"Please feel free to drop me a note via\n",
"[twitter](https://twitter.com/rasbt), [email](mailto:bluewoodtree@gmail.com), or [google+](https://plus.google.com/118404394130788869227).\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For this benchmark, I only want to focus on the simplest approaches that don't require any additional libraries or modules that are not part of Python's in-built functions or the standard library. \n",
"Why? Because in most simple Python scripts I often see people using the math module for those calculations and I was curious to see if we are not better off using ,e.g., the basic arithmetic operator $x^{0.5}$ and the in-built `pow` function for exponential functions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"**-> [skip to the results](#Results)**\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Square root functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- `math.sqrt(x)`\n",
"\n",
"- `x**0.5`\n",
"\n",
"\n",
"\n",
"**Note that we'll import the math.sqrt() and math.pow() functions into the global namespace to reduce the overhead:**"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from math import sqrt as math_sqrt\n",
"\n",
"x = 81\n",
"%timeit math_sqrt(x)\n",
"%timeit math.sqrt(x)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"10000000 loops, best of 3: 140 ns per loop\n",
"10000000 loops, best of 3: 177 ns per loop"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = 988\n",
"assert(math_sqrt(x) == x**0.5)\n",
"print('both functions produce similar results')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"both functions produce similar results\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Power *n* functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- `math.pow(x, n)`\n",
"\n",
"- `pow(x, n)`\n",
"\n",
"- `x**n`"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import pow as math_pow\n",
"\n",
"x = 3.3\n",
"n = 4\n",
"assert(math_pow(x, n) == pow(x, n) == x**n)\n",
"print('All functions produce similar results')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"All functions produce similar results\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Timing square root"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import timeit\n",
"\n",
"test_sqrt = [12345.54321, 54756, 23423422, 999999999999999]\n",
"\n",
"timings_sqrt = {'math_module':[], 'arithmetic':[]}\n",
"\n",
"for x in test_sqrt:\n",
" timings_sqrt['math_module'].append(min(timeit.Timer('math_sqrt(x)', \n",
" 'from __main__ import x, math_sqrt')\n",
" .repeat(repeat=100, number=1000)))\n",
" timings_sqrt['arithmetic'].append(min(timeit.Timer('x**0.5', \n",
" 'from __main__ import x')\n",
" .repeat(repeat=100, number=1000)))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Timing power *n*"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import timeit\n",
"\n",
"test_pow = list(range(1,13))\n",
"funcs_pow = ['math_module', 'inbuilt', 'arithmetic']\n",
"\n",
"timings_pow = {f:[] for f in funcs_pow}\n",
"\n",
"for n in test_pow:\n",
" timings_pow['math_module'].append(min(timeit.Timer('math_pow(n, n)', \n",
" 'from __main__ import n, math_pow')\n",
" .repeat(repeat=100, number=1000)))\n",
" timings_pow['inbuilt'].append(min(timeit.Timer('pow(n, n)', \n",
" 'from __main__ import n')\n",
" .repeat(repeat=100, number=1000)))\n",
" timings_pow['arithmetic'].append(min(timeit.Timer('n**n', \n",
" 'from __main__ import n')\n",
" .repeat(repeat=100, number=1000))) "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Setting up plots"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import platform\n",
"import multiprocessing\n",
"\n",
"def print_sysinfo():\n",
" print('\\nsystem :', platform.system())\n",
" print('release :', platform.release())\n",
" print('machine :', platform.machine())\n",
" print('processor:', platform.processor())\n",
" print('interpreter:', platform.architecture()[0])\n",
" print('CPU count :', multiprocessing.cpu_count())\n",
"\n",
" print('\\nPython version', platform.python_version())\n",
" print('compiler', platform.python_compiler())\n",
" print('\\n\\n')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt\n",
"\n",
"def plot_figures(): \n",
" \n",
" fig = plt.figure(figsize=(8,4))\n",
" plt.plot(range(len(test_sqrt)), timings_sqrt['math_module'], \n",
" alpha=0.5, label='math.sqrt(x)', marker='o', lw=2)\n",
" plt.plot(range(len(test_sqrt)), timings_sqrt['arithmetic'], \n",
" alpha=0.5, label='x**0.5', marker='o', lw=2)\n",
" plt.legend(loc='upper left')\n",
" plt.xticks(range(len(test_sqrt)), ['$\\sqrt{%s}$'%(x) for x in test_sqrt])\n",
" plt.grid()\n",
" plt.ylabel('time in milliseconds')\n",
" \n",
" plt.show()\n",
" \n",
" fig = plt.figure(figsize=(8,4))\n",
" plt.plot(range(len(test_pow)), timings_pow['math_module'], \n",
" alpha=0.5, label='math.pow(x, n)', marker='o', lw=2)\n",
" plt.plot(range(len(test_pow)), timings_pow['inbuilt'], \n",
" alpha=0.5, label='pow(x, n)', marker='o', lw=2)\n",
" plt.plot(range(len(test_pow)), timings_pow['arithmetic'], \n",
" alpha=0.5, label='x**n', marker='o', lw=2)\n",
" plt.legend(loc='upper left')\n",
" plt.xticks(range(len(test_pow)), ['$%s^{%s}$'%(x, x) for x in test_pow])\n",
" plt.grid()\n",
" plt.ylabel('time in milliseconds')\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Results"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print_sysinfo()\n",
"plot_figures()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"system : Darwin\n",
"release : 13.1.0\n",
"machine : x86_64\n",
"processor: i386\n",
"interpreter:"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 64bit\n",
"CPU count : 4\n",
"\n",
"Python version 3.4.0\n",
"compiler GCC 4.2.1 (Apple Inc. build 5577)\n",
"\n",
"\n",
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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KobOHcHN244kpT/A/8f/DYMNgelT1wPe0L4lTZUCwuHkx42KoP1rf4vddXWEd0WOjLdQU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\n8Q7C1uSaErampbbP7BiaXr16odfrWb9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"text": [
""
]
},
{
"metadata": {},
"output_type": "display_data",
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xxhvU19eze/duQ1svvfQSdnZ2DB06lOnTp5OSkmK0DkFLlOhfVJKm749/T9Hg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\nCywpKYkxxlhiYiJbt24dY4yx1tZWptfrGWOM1dTUsAkTJrC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"text": [
""
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Conclusion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Despite the **additional name-lookup** for the `math`-module functions, those approaches are still faster than the in-built `**` operator and `pow` function.\n",
"\n",
"**Why is the `math` module more efficient?** \n",
"The `math` module uses the C implementations of the square root and power functions which explains the better performance. \n",
"And `pow()` is really the same as the `**` operator but comes with an additional function call overhead.\n",
"\n",
"However, the math module comes with the disadvantage that it can't handle complex numbers. In those cases we'd need to use the `cmath` module.\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"(81+2j)**0.5"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 1,
"text": [
"(9.000685740426075+0.11110264582492375j)"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import cmath\n",
"cmath.sqrt(81+2j)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"(9.000685740426075+0.11110264582492377j)"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"math.sqrt(81+2j)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"ename": "TypeError",
"evalue": "can't convert complex to float",
"output_type": "pyerr",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m81\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m2j\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mTypeError\u001b[0m: can't convert complex to float"
]
}
],
"prompt_number": 4
}
],
"metadata": {}
}
]
}