Quantization.ipynb

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  "cells": [
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      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/MrDevCop/Quantization/blob/main/Quantization.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EZtTshKerZIW"
      },
      "source": [
        "#Quantization & De-quantization"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cduhorRurt2B"
      },
      "source": [
        "\n",
        "\n",
        "What is quantization?\n",
        "\n",
        " \n",
        "\n",
        "1.   It means given a range of values,  𝑋={𝑥1,𝑥2,…𝑥𝑛}  and a desired precision of 𝑘  bits.\n",
        "2.   Find the minimum and maximum values of X,  𝑥𝑚𝑎𝑥  and  𝑥𝑚𝑖𝑛 .\n",
        "3.   Find the minimum and maximum value of the bits, namely  𝑞𝑚𝑖𝑛=0  and  𝑞𝑚𝑎𝑥=2𝑘−1 .\n",
        "4.   Set  𝑠𝑐𝑎𝑙𝑒=(𝑥𝑚𝑎𝑥−𝑥𝑚𝑖𝑛)/𝑞𝑚𝑎𝑥 .\n",
        "5.   Note that besides scaling, we also have to consider the bias , or what  0  will map to. Set  𝑧𝑒𝑟𝑜𝑝𝑜𝑖𝑛𝑡  as follows:\n",
        "\n",
        "     a. If  𝑥𝑚𝑖𝑛≥0 ,  𝑧𝑒𝑟𝑜𝑝𝑜𝑖𝑛𝑡=0  \\ b. Else if  𝑥𝑚𝑎𝑥<0        𝑧𝑒𝑟𝑜𝑝𝑜𝑖𝑛𝑡=𝑞𝑚𝑎𝑥 .\n",
        "c. Else  𝑧𝑒𝑟𝑜𝑝𝑜𝑖𝑛𝑡=−𝑥𝑚𝑖𝑛/𝑠𝑐𝑎𝑙𝑒 . \\ d. https://docs.openvinotoolkit.org/latest/pot_compression_algorithms_quantization_README.html\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "6.   The formula for quantization of  𝑥  then becomes:  \n",
        "𝑄(𝑥,𝑏𝑖𝑡𝑠)=𝑟𝑜𝑢𝑛𝑑(𝑥𝑠𝑐𝑎𝑙𝑒+𝑧𝑒𝑟𝑜𝑝𝑜𝑖𝑛𝑡) .\n",
        "7.   The formula to dequantize becomes:  \n",
        "𝐷𝑄(𝑥,𝑠𝑐𝑎𝑙𝑒,𝑧𝑒𝑟𝑜𝑝𝑜𝑖𝑛𝑡,𝑛𝑢𝑚−𝑏𝑖𝑡𝑠)=𝑠𝑐𝑎𝑙𝑒∗(𝑓𝑙𝑜𝑎(𝑥)−𝑧𝑒𝑟𝑜𝑝𝑜𝑖𝑛𝑡) .\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K9DhHu_ktec9"
      },
      "source": [
        "We work through a quick example. Consider the values 𝑋=[1,3,4,14], 𝑘=4. \\ Then 𝑞𝑚𝑎𝑥=15 and 𝑠𝑐𝑎𝑙𝑒=13/15. 𝑧𝑒𝑟𝑜𝑝𝑜𝑖𝑛𝑡=0. \\ The quantization becomes: 𝑟𝑜𝑢𝑛𝑑([0,30/13,45/13,195/13])=[0,2,3,15].\n",
        "\n",
        "The dequantization becomes 1315∗([0,2,3,15])=[0,1.733,2.6,13].\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zJhl6qVZQuzc"
      },
      "source": [
        "import torch\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import tensorflow as tf\n",
        "from collections import namedtuple\n",
        "from torch import tensor\n",
        "\n",
        "QTensor = namedtuple('QTensor', ['tensor', 'scale', 'zero_point'])"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qI_y7qufQ-0x"
      },
      "source": [
        "def calcScaleZeroPoint(min_val, max_val, num_bits):\n",
        "    \n",
        "    qmax = 2**num_bits - 1\n",
        "    scale = (max_val - min_val)/qmax\n",
        "    \n",
        "    if min_val >=0:\n",
        "        zero_point = 0\n",
        "    elif max_val < 0:\n",
        "        zero_point = qmax\n",
        "    else:\n",
        "        zero_point = -min_val/scale\n",
        "    \n",
        "    \n",
        "        \n",
        "    return (scale, zero_point)    \n",
        "  #pass\n",
        "  # Return scale and zero point.\n",
        "  # Use formulas 3 and 4 above.\n",
        "\n",
        "def quantize_tensor(float_x: tensor, num_bits: int):\n",
        "    \n",
        "    maximum = torch.max(float_x)\n",
        "    minimum = torch.min(float_x)\n",
        "    scale , zeropoint = calcScaleZeroPoint(minimum, maximum, num_bits)\n",
        "\n",
        "    q_tensor = (float_x/scale) + zeropoint\n",
        "    q_tensor = q_tensor.clamp_(minimum, maximum)\n",
        "    q_tensor = torch.round(q_tensor)\n",
        "    q_tensor = q_tensor.float()\n",
        "    \n",
        "    #QTensor = namedtuple('QTensor', ['tensor', 'scale', 'zero_point'])\n",
        "    Q_T = QTensor(q_tensor, scale, zeropoint)\n",
        "    \n",
        "    return (Q_T)\n",
        "  #pass\n",
        "  # Return a QTensor tuple, with the quantized tensor, scale and zero point as described above.\n",
        "  # Use calcScaleZeroPoint and formula 6 above.\n",
        "\n",
        "\n",
        "def dequantize_tensor(quantized_x: tensor, scale: float, zero_point: float):\n",
        "    \n",
        "    dq_tensor = scale * (quantized_x.float() - zero_point)\n",
        "    return (dq_tensor)\n",
        "#  pass\n",
        "  # Return float_tensor. "
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lqd-XudED06l"
      },
      "source": [
        "Verification of `quantize_tensor` and `dequantize_tensor`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yvT-DOdMtuk6",
        "outputId": "b1f5587c-f88b-4aef-fd93-709aaeb4c4c3"
      },
      "source": [
        "# Defining a random tensor\n",
        "a = torch.tensor([2,0.9,41,52])\n",
        "\n",
        "# Checking quantize_tensor function\n",
        "tup = quantize_tensor(a,4)\n",
        "tup.tensor"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 1.,  1., 12., 15.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "B8Xo_0FluuVc",
        "outputId": "e3b57940-319f-4005-9637-266dfba87907"
      },
      "source": [
        "tup.scale"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(3.4067)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "B5HmYbnxESTZ",
        "outputId": "6a5a0729-d5fc-4824-ef48-8ac04348e295"
      },
      "source": [
        "tup.zero_point"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JR0AaZBPucSR",
        "outputId": "59b8a268-3152-4e97-b192-171f675feddf"
      },
      "source": [
        "# Checking dequantize_tensor function\n",
        "d_a = dequantize_tensor(tup.tensor, tup.scale, tup.zero_point)\n",
        "d_a"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 3.4067,  3.4067, 40.8800, 51.1000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BAcSeAasfkTS"
      },
      "source": [
        "MNIST\n",
        "\n",
        "We now train a basic MNIST model. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UuthHEA0fixZ"
      },
      "source": [
        "# You don't need to edit any of this code.\n",
        "from __future__ import print_function\n",
        "import argparse\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import torch.optim as optim\n",
        "from torchvision import datasets, transforms\n",
        "\n",
        "\n",
        "class Net(nn.Module):\n",
        "    def __init__(self, mnist=True):\n",
        "      \n",
        "        super(Net, self).__init__()\n",
        "        if mnist:\n",
        "          num_channels = 1\n",
        "        else:\n",
        "          num_channels = 3\n",
        "          \n",
        "        self.conv1 = nn.Conv2d(num_channels, 20, 5, 1)\n",
        "        self.conv2 = nn.Conv2d(20, 50, 5, 1)\n",
        "        self.fc1 = nn.Linear(4*4*50, 500)\n",
        "        self.fc2 = nn.Linear(500, 10)\n",
        "        \n",
        "      \n",
        "    def forward(self, x):\n",
        "        \n",
        "        x = F.relu(self.conv1(x))\n",
        "        x = F.max_pool2d(x, 2, 2)\n",
        "        x = F.relu(self.conv2(x))\n",
        "        x = F.max_pool2d(x, 2, 2)  \n",
        "        x = x.view(-1, 4*4*50)\n",
        "        x = F.relu(self.fc1(x))\n",
        "        x = self.fc2(x)\n",
        "        return F.log_softmax(x, dim=1)"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000,
          "referenced_widgets": [
            "563a1bdf20034087834874955911930c",
            "5d4db3fb423247e3a25079c24b01bddf",
            "4f5e6a2c64554dffb3d990ce47400b62",
            "44e8d4d40f8b468aa9dcc36f1a832200",
            "3cbca58d1c574a6f8e604617fa0b0fee",
            "8973fc9c88d6458886c83234ac358800",
            "96701b7d220e4b0a8a84c31f3e72bd3f",
            "0098cbe3accb40d0b55c81312b1d1f10",
            "05efc8b7274441279a8a5aa6cf3c6307",
            "e8437f560d594b6a8785507b14347ea7",
            "ead0e615984d4515a2a55c7e425f955a",
            "22094f2550e047528c391b00e8a02f70",
            "0ff57d0672244e4d89f80b9036f00162",
            "a484324a26f741888b11e5bf84c828f3",
            "74f06389ce584f33bcbea88928ff0423",
            "88e091c1b99e4a51825f75fe5eb5ccff",
            "cf6492b795ac4c2a9fff70da3e2cabe6",
            "63b56710d3e244c9b25cfdaedf14c232",
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            "124f1fd998df4980b939a86ecca11ece",
            "f98ac22a8b6748ae9be0f4e5d2e45f22",
            "b91d0b1849ad4230919aea48d0d3f499",
            "ed34881722284b0ab7fed772e4f95e4a",
            "017619d37956492e91fc568dadac0969",
            "f215adb5966844c399a8e9d6a5400a6e",
            "9e1d36aefa3a4e10a6db8b472eba7718",
            "894e49ec37f341c0a1e18de7fd914040",
            "fd82dec6033e4e218df4f8024d85c237",
            "cd0d5c6c0d664dbdbc6e9ff78e44231b",
            "ffe434c7cd874995931018a92193db82"
          ]
        },
        "id": "8M-c-V5Vf-MC",
        "outputId": "246eda8c-6e52-422e-f721-6ebc2960ef2d"
      },
      "source": [
        "\n",
        "def train(args, model, device, train_loader, optimizer, epoch):\n",
        "    model.train()\n",
        "    for batch_idx, (data, target) in enumerate(train_loader):\n",
        "        data, target = data.to(device), target.to(device)\n",
        "        optimizer.zero_grad()\n",
        "        output = model(data)\n",
        "        loss = F.nll_loss(output, target)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "        \n",
        "   \n",
        "        if batch_idx % args[\"log_interval\"] == 0:\n",
        "            print('Train Epoch: {} [{}/{} ({:.0f}%)]\\tLoss: {:.6f}'.format(\n",
        "                epoch, batch_idx * len(data), len(train_loader.dataset),\n",
        "                100. * batch_idx / len(train_loader), loss.item()))\n",
        "\n",
        "def test(args, model, device, test_loader):\n",
        "    model.eval()\n",
        "    test_loss = 0\n",
        "    correct = 0\n",
        "    with torch.no_grad():\n",
        "        for data, target in test_loader:\n",
        "            data, target = data.to(device), target.to(device)\n",
        "            output = model(data)\n",
        "            test_loss += F.nll_loss(output, target, reduction='sum').item() # sum up batch loss\n",
        "            pred = output.argmax(dim=1, keepdim=True) # get the index of the max log-probability\n",
        "            correct += pred.eq(target.view_as(pred)).sum().item()\n",
        "\n",
        "    test_loss /= len(test_loader.dataset)\n",
        "\n",
        "    print('\\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\\n'.format(\n",
        "        test_loss, correct, len(test_loader.dataset),\n",
        "        100. * correct / len(test_loader.dataset)))\n",
        "\n",
        "def main():\n",
        " \n",
        "    batch_size = 64\n",
        "    test_batch_size = 64\n",
        "    epochs = 5\n",
        "    lr = 0.01\n",
        "    momentum = 0.5\n",
        "    seed = 1\n",
        "    log_interval = 500\n",
        "    save_model = False\n",
        "    no_cuda = False\n",
        "    \n",
        "    use_cuda = not no_cuda and torch.cuda.is_available()\n",
        "\n",
        "    torch.manual_seed(seed)\n",
        "\n",
        "    device = torch.device(\"cuda\" if use_cuda else \"cpu\")\n",
        "\n",
        "    kwargs = {'num_workers': 1, 'pin_memory': True} if use_cuda else {}\n",
        "    train_loader = torch.utils.data.DataLoader(\n",
        "        datasets.MNIST('../data', train=True, download=True,\n",
        "                       transform=transforms.Compose([\n",
        "                           transforms.ToTensor(),\n",
        "                           transforms.Normalize((0.1307,), (0.3081,))\n",
        "                       ])),\n",
        "        batch_size=batch_size, shuffle=True, **kwargs)\n",
        "    \n",
        "    test_loader = torch.utils.data.DataLoader(\n",
        "        datasets.MNIST('../data', train=False, transform=transforms.Compose([\n",
        "                           transforms.ToTensor(),\n",
        "                           transforms.Normalize((0.1307,), (0.3081,))\n",
        "                       ])),\n",
        "        batch_size=test_batch_size, shuffle=True, **kwargs)\n",
        "    \n",
        "  \n",
        "    model = Net().to(device)\n",
        "    optimizer = optim.SGD(model.parameters(), lr=lr, momentum=momentum)\n",
        "    args = {}\n",
        "    args[\"log_interval\"] = log_interval\n",
        "    for epoch in range(1, epochs + 1):\n",
        "        train(args, model, device, train_loader, optimizer, epoch)\n",
        "        test(args, model, device, test_loader)\n",
        "\n",
        "    if (save_model):\n",
        "        torch.save(model.state_dict(),\"mnist_cnn.pt\")\n",
        "    \n",
        "    return model\n",
        "\n",
        "model = main()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ../data/MNIST/raw/train-images-idx3-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 503: Service Unavailable\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz to ../data/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "563a1bdf20034087834874955911930c",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=9912422.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Extracting ../data/MNIST/raw/train-images-idx3-ubyte.gz to ../data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ../data/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "05efc8b7274441279a8a5aa6cf3c6307",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=28881.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Extracting ../data/MNIST/raw/train-labels-idx1-ubyte.gz to ../data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 503: Service Unavailable\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz to ../data/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "cf6492b795ac4c2a9fff70da3e2cabe6",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=1648877.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Extracting ../data/MNIST/raw/t10k-images-idx3-ubyte.gz to ../data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ../data/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "ed34881722284b0ab7fed772e4f95e4a",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=4542.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Extracting ../data/MNIST/raw/t10k-labels-idx1-ubyte.gz to ../data/MNIST/raw\n",
            "\n",
            "Processing...\n",
            "Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/torchvision/datasets/mnist.py:502: UserWarning: The given NumPy array is not writeable, and PyTorch does not support non-writeable tensors. This means you can write to the underlying (supposedly non-writeable) NumPy array using the tensor. You may want to copy the array to protect its data or make it writeable before converting it to a tensor. This type of warning will be suppressed for the rest of this program. (Triggered internally at  /pytorch/torch/csrc/utils/tensor_numpy.cpp:143.)\n",
            "  return torch.from_numpy(parsed.astype(m[2], copy=False)).view(*s)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Train Epoch: 1 [0/60000 (0%)]\tLoss: 2.292215\n",
            "Train Epoch: 1 [32000/60000 (53%)]\tLoss: 0.255719\n",
            "\n",
            "Test set: Average loss: 0.1194, Accuracy: 9627/10000 (96%)\n",
            "\n",
            "Train Epoch: 2 [0/60000 (0%)]\tLoss: 0.132260\n",
            "Train Epoch: 2 [32000/60000 (53%)]\tLoss: 0.055792\n",
            "\n",
            "Test set: Average loss: 0.0755, Accuracy: 9749/10000 (97%)\n",
            "\n",
            "Train Epoch: 3 [0/60000 (0%)]\tLoss: 0.056983\n",
            "Train Epoch: 3 [32000/60000 (53%)]\tLoss: 0.026856\n",
            "\n",
            "Test set: Average loss: 0.0511, Accuracy: 9845/10000 (98%)\n",
            "\n",
            "Train Epoch: 4 [0/60000 (0%)]\tLoss: 0.040046\n",
            "Train Epoch: 4 [32000/60000 (53%)]\tLoss: 0.019234\n",
            "\n",
            "Test set: Average loss: 0.0459, Accuracy: 9837/10000 (98%)\n",
            "\n",
            "Train Epoch: 5 [0/60000 (0%)]\tLoss: 0.023508\n",
            "Train Epoch: 5 [32000/60000 (53%)]\tLoss: 0.009386\n",
            "\n",
            "Test set: Average loss: 0.0323, Accuracy: 9889/10000 (99%)\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0rjnP_YlgKLV"
      },
      "source": [
        "# These are driver functions for your code. You do not need to edit.\n",
        "def quantForward(model, input, num_bits):\n",
        "  quantized_input = quantize_tensor(input, num_bits)\n",
        "  output_1  = F.relu(model.conv1(quantized_input.tensor))\n",
        "  output_2 = F.max_pool2d(quantize_tensor(output_1, num_bits).tensor, 2, 2)\n",
        "  output_3 = F.relu(model.conv2(quantize_tensor(output_2, num_bits).tensor))\n",
        "  output_4 = F.max_pool2d(quantize_tensor(output_3, num_bits).tensor, 2, 2)\n",
        "  output_5 = output_4.view(-1, 4*4*50)\n",
        "  output_6 = F.relu(model.fc1(quantize_tensor(output_5, num_bits).tensor))\n",
        "  output_7 = model.fc2(quantize_tensor(output_6, num_bits).tensor)\n",
        "  return F.log_softmax(quantize_tensor(output_7, num_bits).tensor, dim=1)\n",
        "\n",
        "def testQuant(model, test_loader, quant=False, num_bits=8):\n",
        "    device = 'cuda'\n",
        "    \n",
        "    model.eval()\n",
        "    test_loss = 0\n",
        "    correct = 0\n",
        "    with torch.no_grad():\n",
        "        for data, target in test_loader:\n",
        "            data, target = data.to(device), target.to(device)\n",
        "            if quant:\n",
        "              output = quantForward(model, data, num_bits)\n",
        "            else:\n",
        "              output = model(data)\n",
        "            test_loss += F.nll_loss(output, target, reduction='sum').item() # sum up batch loss\n",
        "            pred = output.argmax(dim=1, keepdim=True) # get the index of the max log-probability\n",
        "            correct += pred.eq(target.view_as(pred)).sum().item()\n",
        "\n",
        "    test_loss /= len(test_loader.dataset)\n",
        "\n",
        "    print('\\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\\n'.format(\n",
        "        test_loss, correct, len(test_loader.dataset),\n",
        "        100. * correct / len(test_loader.dataset)))\n",
        "    return (round(100*correct/len(test_loader.dataset)))"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jjelU3HjgPxU"
      },
      "source": [
        "kwargs = {'num_workers': 1, 'pin_memory': True}\n",
        "test_loader = torch.utils.data.DataLoader(\n",
        "    datasets.MNIST('../data', train=False, transform=transforms.Compose([\n",
        "                       transforms.ToTensor(),\n",
        "                       transforms.Normalize((0.1307,), (0.3081,))\n",
        "                   ])),\n",
        "    batch_size=64, shuffle=True, **kwargs)"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-6im_6VdgTgT",
        "outputId": "193d87aa-183a-401f-e26d-65365034514c"
      },
      "source": [
        "acc = testQuant(model, test_loader, quant=True, num_bits=16)\n"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Test set: Average loss: 2.3166, Accuracy: 980/10000 (10%)\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_IC0GotcLcJz"
      },
      "source": [
        "##Checking the realtion between `number of bits` and `accuracy`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "k5sK8RXelHJ6",
        "outputId": "fa83e0d7-21c8-4d72-98fb-25531e891d24"
      },
      "source": [
        "bits = 16\n",
        "acc_list = []\n",
        "no_bits = []\n",
        "for b in range(bits):\n",
        "  temp =  testQuant(model, test_loader, quant=True, num_bits=b+1)\n",
        "  print(\"\\nNumber of bits are {} and accuracy is {}%\".format(b+1,temp))\n",
        "  no_bits.append(b+1)\n",
        "  acc_list.append(temp)\n",
        "  #eprint(b)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Test set: Average loss: 2.2356, Accuracy: 1294/10000 (13%)\n",
            "\n",
            "\n",
            "Number of bits are 1 and accuracy is 13%\n",
            "\n",
            "Test set: Average loss: 1.4614, Accuracy: 6828/10000 (68%)\n",
            "\n",
            "\n",
            "Number of bits are 2 and accuracy is 68%\n",
            "\n",
            "Test set: Average loss: 0.6779, Accuracy: 9636/10000 (96%)\n",
            "\n",
            "\n",
            "Number of bits are 3 and accuracy is 96%\n",
            "\n",
            "Test set: Average loss: 0.2353, Accuracy: 9688/10000 (97%)\n",
            "\n",
            "\n",
            "Number of bits are 4 and accuracy is 97%\n",
            "\n",
            "Test set: Average loss: 5.3073, Accuracy: 3241/10000 (32%)\n",
            "\n",
            "\n",
            "Number of bits are 5 and accuracy is 32%\n",
            "\n",
            "Test set: Average loss: 21.5271, Accuracy: 1289/10000 (13%)\n",
            "\n",
            "\n",
            "Number of bits are 6 and accuracy is 13%\n",
            "\n",
            "Test set: Average loss: 49.1244, Accuracy: 1055/10000 (11%)\n",
            "\n",
            "\n",
            "Number of bits are 7 and accuracy is 11%\n",
            "\n",
            "Test set: Average loss: 51.3691, Accuracy: 1215/10000 (12%)\n",
            "\n",
            "\n",
            "Number of bits are 8 and accuracy is 12%\n",
            "\n",
            "Test set: Average loss: 16.0480, Accuracy: 1419/10000 (14%)\n",
            "\n",
            "\n",
            "Number of bits are 9 and accuracy is 14%\n",
            "\n",
            "Test set: Average loss: 3.9928, Accuracy: 1132/10000 (11%)\n",
            "\n",
            "\n",
            "Number of bits are 10 and accuracy is 11%\n",
            "\n",
            "Test set: Average loss: 2.7072, Accuracy: 980/10000 (10%)\n",
            "\n",
            "\n",
            "Number of bits are 11 and accuracy is 10%\n",
            "\n",
            "Test set: Average loss: 2.4369, Accuracy: 980/10000 (10%)\n",
            "\n",
            "\n",
            "Number of bits are 12 and accuracy is 10%\n",
            "\n",
            "Test set: Average loss: 2.3872, Accuracy: 980/10000 (10%)\n",
            "\n",
            "\n",
            "Number of bits are 13 and accuracy is 10%\n",
            "\n",
            "Test set: Average loss: 2.3270, Accuracy: 980/10000 (10%)\n",
            "\n",
            "\n",
            "Number of bits are 14 and accuracy is 10%\n",
            "\n",
            "Test set: Average loss: 2.3232, Accuracy: 980/10000 (10%)\n",
            "\n",
            "\n",
            "Number of bits are 15 and accuracy is 10%\n",
            "\n",
            "Test set: Average loss: 2.3302, Accuracy: 980/10000 (10%)\n",
            "\n",
            "\n",
            "Number of bits are 16 and accuracy is 10%\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xBL5Y3vzn1nL",
        "outputId": "65e8f719-1c68-4f0b-f63a-3184ef40c4e8"
      },
      "source": [
        "print(acc_list) # Prints a list of accuracy measures for different number of bits\n",
        "print(no_bits) # Prints the number of bits\n"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[14, 67, 96, 97, 33, 13, 11, 12, 14, 11, 10, 10, 10, 10, 10, 10]\n",
            "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "FjNoHz44n7c2",
        "outputId": "afe2cb08-de0a-442e-a8a8-8271e888da4f"
      },
      "source": [
        " \n",
        "plt.plot(no_bits, acc_list)\n",
        "  \n",
        "plt.xlabel('Number of Bits')\n",
        "\n",
        "plt.ylabel('Accuracy (%)')\n",
        "  \n",
        "\n",
        "plt.title('No of Bits VS Accuracy')\n",
        "  \n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "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"
          }
        }
      ]
    }
  ]
}