Pseudo_aleatoriedade.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Pseudo aleatoriedade",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZlO2lOh3N0Tg",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "46264a67-172f-4f81-a332-127f5e353daf"
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "np.random.rand()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.2565472028882839"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 1
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q1bQCtj1WMr1"
      },
      "source": [
        "Von Neumann - Middle-square method"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bq-ohAXOPIC6"
      },
      "source": [
        "# semente = 5 # momoento que o primeiro rand é rodado\n",
        "# formula(x) = x * 3 / 2\n",
        "# formula(5) = 7.5\n",
        "# formula(7.5) = 11.25"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iLk0cfiBQpkQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c0a4bc11-17b0-4d96-d083-1f3394bf2004"
      },
      "source": [
        "5*3/2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7.5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BPpK-g0gQqdm",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4721dbcc-f9e2-4cff-8d86-207d5a807001"
      },
      "source": [
        "7.5*3/2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "11.25"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RUxgeL6TQrT5"
      },
      "source": [
        "seed = 150\n",
        "# 12345\n",
        "# 90000*90000\n",
        "# 8100000000\n",
        "\n",
        "def middle_square():\n",
        "  global seed\n",
        "  result = seed * seed\n",
        "  result = \"{0:08d}\".format(result)\n",
        "  result = result[2:6]\n",
        "  # print(result)\n",
        "  result = int(result)\n",
        "  seed = result\n",
        "  return result"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oihDkv4zRk66",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3b95e424-bee4-4168-e071-814572af829a"
      },
      "source": [
        "print(middle_square())\n",
        "print(middle_square())\n",
        "print(middle_square())\n",
        "print(middle_square())\n",
        "print(middle_square())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "225\n",
            "506\n",
            "2560\n",
            "5536\n",
            "6472\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HzHl4iz-RrpZ"
      },
      "source": [
        "from tqdm import tqdm\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def test_random(pseudo_random_generator):\n",
        "  results = np.array([pseudo_random_generator() for i in tqdm(range(10000000))])\n",
        "  results = pd.DataFrame(np.array([results]).T, columns=[\"middle_square\"])\n",
        "  print(results.mean())\n",
        "  results.plot(kind='hist')\n",
        "  plt.show()\n",
        "  display(results.value_counts().head())"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1BF-aR0aaWK4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "outputId": "ddaf71a8-0b59-4da7-a1ef-8ec7d30af46e"
      },
      "source": [
        "seed = 150\n",
        "\n",
        "test_random(middle_square)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 10000000/10000000 [00:10<00:00, 953302.45it/s]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "middle_square    5099.997823\n",
            "dtype: float64\n"
          ],
          "name": "stdout"
        },
        {
          "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"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "middle_square\n",
              "4100             2499987\n",
              "6100             2499987\n",
              "8100             2499987\n",
              "2100             2499986\n",
              "3388                   1\n",
              "dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8Vi30jb6To1K",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5285b2d7-932b-4cf0-91c0-42b53b974de5"
      },
      "source": [
        "# From https://en.wikipedia.org/wiki/Middle-square_method\n",
        "\n",
        "seed_number = 150\n",
        "\n",
        "number = seed_number\n",
        "already_seen = set()\n",
        "counter = 0\n",
        "\n",
        "while number not in already_seen:\n",
        "    counter += 1\n",
        "    already_seen.add(number)\n",
        "    number = int(str(number * number).zfill(8)[2:6])  # zfill adds padding of zeroes\n",
        "    print(f\"#{counter}: {number}\")\n",
        "\n",
        "print(f\"We began with {seed_number}, and\"\n",
        "      f\" have repeated ourselves after {counter} steps\"\n",
        "      f\" with {number}.\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "#1: 225\n",
            "#2: 506\n",
            "#3: 2560\n",
            "#4: 5536\n",
            "#5: 6472\n",
            "#6: 8867\n",
            "#7: 6236\n",
            "#8: 8876\n",
            "#9: 7833\n",
            "#10: 3558\n",
            "#11: 6593\n",
            "#12: 4676\n",
            "#13: 8649\n",
            "#14: 8052\n",
            "#15: 8347\n",
            "#16: 6724\n",
            "#17: 2121\n",
            "#18: 4986\n",
            "#19: 8601\n",
            "#20: 9772\n",
            "#21: 4919\n",
            "#22: 1965\n",
            "#23: 8612\n",
            "#24: 1665\n",
            "#25: 7722\n",
            "#26: 6292\n",
            "#27: 5892\n",
            "#28: 7156\n",
            "#29: 2083\n",
            "#30: 3388\n",
            "#31: 4785\n",
            "#32: 8962\n",
            "#33: 3174\n",
            "#34: 742\n",
            "#35: 5505\n",
            "#36: 3050\n",
            "#37: 3025\n",
            "#38: 1506\n",
            "#39: 2680\n",
            "#40: 1824\n",
            "#41: 3269\n",
            "#42: 6863\n",
            "#43: 1007\n",
            "#44: 140\n",
            "#45: 196\n",
            "#46: 384\n",
            "#47: 1474\n",
            "#48: 1726\n",
            "#49: 9790\n",
            "#50: 8441\n",
            "#51: 2504\n",
            "#52: 2700\n",
            "#53: 2900\n",
            "#54: 4100\n",
            "#55: 8100\n",
            "#56: 6100\n",
            "#57: 2100\n",
            "#58: 4100\n",
            "We began with 150, and have repeated ourselves after 58 steps with 4100.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QuDRIHhjU0Q8"
      },
      "source": [
        "x = 0\n",
        "weil_counter = 0\n",
        "k = int(\"0xb5ad4eceda1ce2a9\", 0)\n",
        "\n",
        "def msws():\n",
        "  global x, weil_counter, k\n",
        "  result = x * x\n",
        "  weil_counter += k\n",
        "  result += weil_counter\n",
        "  result = str(result).zfill(8)\n",
        "  result = result[2:6]\n",
        "  # print(result)\n",
        "  result = int(result)\n",
        "  x = result\n",
        "  return result"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4lbYR9QPZ65C",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c9d3b62b-944d-43d5-b287-1822eb53a62b"
      },
      "source": [
        "k"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "13091206342165455529"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 82
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7OcZoJFIaDPr",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "outputId": "c842f056-b6ef-4b90-c414-21f0bb66479b"
      },
      "source": [
        "test_random(msws)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 10000000/10000000 [00:11<00:00, 844851.86it/s]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "middle_square    4967.842999\n",
            "dtype: float64\n"
          ],
          "name": "stdout"
        },
        {
          "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"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "middle_square\n",
              "776              1079\n",
              "658              1078\n",
              "632              1077\n",
              "552              1077\n",
              "493              1077\n",
              "dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xf1_5EF_aizz"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}