pavelzw/RaceConditionDensity.ipynb

## RaceConditionDensity.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "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": "3.8.5"
    },
    "colab": {
      "name": "a93bd3ff77c8116fa7c21fd070ef2c93",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/pavelzw/a93bd3ff77c8116fa7c21fd070ef2c93\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V7_Q2Rl_j6Ja"
      },
      "source": [
        "This notebook plots the probability density of the result of a race condition. The first thread increments a counter `c` `inner_loop_size` times and the second thread decrements this counter. \n",
        "\n",
        "Due to the race condition, `c` can take values from `-inner_loop_size` to `inner_loop_size`. This density is plotted below with a sample size of `n = 1000`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kefe4s6Wj6Jb"
      },
      "source": [
        "import threading\n",
        "import numpy as np"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DbUWCl72j6Jb",
        "outputId": "d75e6816-ae24-4355-b0c5-7b9eb2f26aaa"
      },
      "source": [
        "inner_loop_size = int(1e7)\n",
        "\n",
        "class RaceCondition:\n",
        "    def __init__(self):\n",
        "        self.c = 0\n",
        "    \n",
        "    def increment(self):\n",
        "        for i in range(inner_loop_size):\n",
        "            self.c += 1\n",
        "    \n",
        "    def decrement(self):\n",
        "        for i in range(inner_loop_size):\n",
        "            self.c -= 1\n",
        "\n",
        "n = 1000\n",
        "values = np.empty(n)\n",
        "racecond = RaceCondition()\n",
        "from tqdm import tqdm\n",
        "for i in tqdm(range(n)):\n",
        "    increment = threading.Thread(target=racecond.increment)\n",
        "    decrement = threading.Thread(target=racecond.decrement)\n",
        "\n",
        "    increment.start()\n",
        "    decrement.start()\n",
        "    increment.join()\n",
        "    decrement.join()\n",
        "    \n",
        "    values[i] = racecond.c\n",
        "    racecond.c = 0"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 1000/1000 [35:34<00:00,  2.13s/it]\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PBXQsgWzj6Jc"
      },
      "source": [
        "Let's check out the histogram with the estimated density."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "i4dibaltj6Jc",
        "outputId": "9adc78de-5804-4640-86a9-de31491fee38"
      },
      "source": [
        "import seaborn as sns\n",
        "\n",
        "sns.histplot(values, bins=100, binrange=(-inner_loop_size, inner_loop_size), kde=True)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fb89da187f0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}
	{
	"nbformat": 4,
	"nbformat_minor": 0,
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"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": "3.8.5"
	},
	"colab": {
	"name": "a93bd3ff77c8116fa7c21fd070ef2c93",
	"provenance": [],
	"include_colab_link": true
	}
	},
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "view-in-github",
	"colab_type": "text"
	},
	"source": [
	"<a href=\"https://colab.research.google.com/gist/pavelzw/a93bd3ff77c8116fa7c21fd070ef2c93\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "V7_Q2Rl_j6Ja"
	},
	"source": [
	"This notebook plots the probability density of the result of a race condition. The first thread increments a counter `c` `inner_loop_size` times and the second thread decrements this counter. \n",
	"\n",
	"Due to the race condition, `c` can take values from `-inner_loop_size` to `inner_loop_size`. This density is plotted below with a sample size of `n = 1000`."
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "kefe4s6Wj6Jb"
	},
	"source": [
	"import threading\n",
	"import numpy as np"
	],
	"execution_count": 1,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "DbUWCl72j6Jb",
	"outputId": "d75e6816-ae24-4355-b0c5-7b9eb2f26aaa"
	},
	"source": [
	"inner_loop_size = int(1e7)\n",
	"\n",
	"class RaceCondition:\n",
	" def __init__(self):\n",
	" self.c = 0\n",
	" \n",
	" def increment(self):\n",
	" for i in range(inner_loop_size):\n",
	" self.c += 1\n",
	" \n",
	" def decrement(self):\n",
	" for i in range(inner_loop_size):\n",
	" self.c -= 1\n",
	"\n",
	"n = 1000\n",
	"values = np.empty(n)\n",
	"racecond = RaceCondition()\n",
	"from tqdm import tqdm\n",
	"for i in tqdm(range(n)):\n",
	" increment = threading.Thread(target=racecond.increment)\n",
	" decrement = threading.Thread(target=racecond.decrement)\n",
	"\n",
	" increment.start()\n",
	" decrement.start()\n",
	" increment.join()\n",
	" decrement.join()\n",
	" \n",
	" values[i] = racecond.c\n",
	" racecond.c = 0"
	],
	"execution_count": 2,
	"outputs": [
	{
	"output_type": "stream",
	"text": [
	"100%\|██████████\| 1000/1000 [35:34<00:00, 2.13s/it]\n"
	],
	"name": "stderr"
	}
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "PBXQsgWzj6Jc"
	},
	"source": [
	"Let's check out the histogram with the estimated density."
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 295
	},
	"id": "i4dibaltj6Jc",
	"outputId": "9adc78de-5804-4640-86a9-de31491fee38"
	},
	"source": [
	"import seaborn as sns\n",
	"\n",
	"sns.histplot(values, bins=100, binrange=(-inner_loop_size, inner_loop_size), kde=True)"
	],
	"execution_count": 3,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"<matplotlib.axes._subplots.AxesSubplot at 0x7fb89da187f0>"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 3
	},
	{
	"output_type": "display_data",
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"tags": [],
	"needs_background": "light"
	}
	}
	]
	}
	]
	}