tutorial_solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# CNN Quantisation Tutorial\n",
    "\n",
    "This tutorial introduces basic ideas in the field of CNN quantisation.\n",
    "You will first learn how to wrap up fixed-point data objects and their arithmetic in Python.\n",
    "Then, after training a toy CNN model for MNIST, you can quantise it to a specific fixed-point format and inference it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "from __future__ import print_function\n",
    "from __future__ import absolute_import\n",
    "\n",
    "import math\n",
    "import time\n",
    "from collections import OrderedDict\n",
    "from itertools import product\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "from mnist_deep import deepnn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed-Point Arithmetic\n",
    "\n",
    "In this section, we will implement fixed-point number classes in Python, including their representation and arithmetic.\n",
    "These classes will be further used in later sections.\n",
    "\n",
    "A [**fixed-point** number](https://en.wikipedia.org/wiki/Fixed-point_arithmetic) has fixed number of digits before and after a **radix point**.\n",
    "Normally we represent a fixed-point number in Q format, which specifies the number of integer bits (m) and fractional bits (n) by Qm.n .\n",
    "The total number of bits is m + n + 1 and the signed bit is implicitly allocated.\n",
    "The representation of unsigned format is prefixed with **U**, e.g. UQm.n .\n",
    "\n",
    "You only need to implement signed Q format in this tutorial, and we restrict the total number of bits to be **8**.\n",
    "See `QInt8` for the fixed-point class definition and try to implement its member functions.\n",
    "\n",
    "You can check this [page](https://en.wikipedia.org/wiki/Q_(number_format)) for some hints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Implementation of the 8-bit Q format.\n",
    "\"\"\"\n",
    "\n",
    "class QInt8(object):\n",
    "    \n",
    "    def __init__(self, n, val):\n",
    "        \"\"\"\n",
    "        instance initialisation function\n",
    "        \n",
    "        :param n: number of fractional bits\n",
    "        :param val: initialise value, can be float or QInt8\n",
    "        :return: initialised object\n",
    "        \"\"\"\n",
    "        assert isinstance(n, int), \"n should be an integer\"\n",
    "        assert n >= 0 and n <= 7,  \"n should in range [0, 7]\"\n",
    "        assert isinstance(val, float) or isinstance(val, np.int8), \"val should be a float or int8\"\n",
    "        \n",
    "        \"\"\"\n",
    "        TODO: try to implement a initialisation function for QInt8\n",
    "        Note that it should handle both types of initial values (float or np.int8)\n",
    "        \"\"\"\n",
    "        self.n = n\n",
    "        self.m = 7 - self.n\n",
    "        self.max_val = (1 << self.m) - 1. / (1 << self.n)\n",
    "        self.min_val = - (1 << self.m - 1)\n",
    "        \n",
    "        # if initialise value is a float, we convert it to fixed-point format\n",
    "        if isinstance(val, float):\n",
    "            if val > self.max_val:\n",
    "                print('WARNING: Initial value overflow %.6f > %.6f'  % (val, self.max_val))\n",
    "                self.val = self.max_val\n",
    "            elif val < self.min_val:\n",
    "                print('WARNING: Initial value underflow %.6f < %.6f' % (val, self.min_val))\n",
    "                self.val = self.min_val\n",
    "            else:\n",
    "                self.val = val\n",
    "            # round to the nearest integer value and cast to int8 (char)\n",
    "            self.val = np.int8(round(val * (1 << self.n)))\n",
    "        # else we just assign\n",
    "        elif isinstance(val, np.int8):\n",
    "            self.val = val\n",
    "        else:\n",
    "            raise RuntimeError('Should never reach this point!')\n",
    "\n",
    "    def __repr__(self):\n",
    "        return 'QInt8(%d, %d) %s %f' % (7 - self.n, self.n, hex(self.val), float(self))\n",
    "    \n",
    "    @staticmethod\n",
    "    def sat8(val):\n",
    "        \"\"\"\n",
    "        TODO: Try to implement this saturation function.\n",
    "        You need to return the upperbound when overflow and lowerbound when underflow.\n",
    "        \"\"\"\n",
    "        if val > 0x7F:  return 0x7F\n",
    "        if val < -0x80: return -0x80\n",
    "        return val\n",
    "   \n",
    "    \"\"\"\n",
    "    TODO: Implement basic arithmetics between two QInt8 objects of the same precision\n",
    "    i.e. self.n == q.n\n",
    "\n",
    "    Could you also use the sat8 function you defined above?\n",
    "    \"\"\"\n",
    "    def __add__(self, q):\n",
    "        assert isinstance(q, QInt8), \"The other operand should be of QInt8 type\"\n",
    "        assert q.n == self.n, \"Number of fractional bits should match\"\n",
    "        \n",
    "        tmp = np.int16(self.val) + np.int16(q.val)\n",
    "        return QInt8(self.n, np.int8(self.sat8(tmp)))\n",
    "    \n",
    "    def __sub__(self, q):\n",
    "        assert isinstance(q, QInt8), \"The other operand should be of QInt8 type\"\n",
    "        assert q.n == self.n, \"Number of fractional bits should match\"\n",
    "        \n",
    "        tmp = np.int16(self.val) - np.int16(q.val)\n",
    "        return QInt8(self.n, np.int8(self.sat8(tmp)))\n",
    "    \n",
    "    def __mul__(self, q):\n",
    "        assert isinstance(q, QInt8), \"The other operand should be of QInt8 type\"\n",
    "        assert q.n == self.n, \"Number of fractional bits should match\"\n",
    "        \n",
    "        tmp = np.int16(self.val) * np.int16(q.val)\n",
    "        tmp = tmp + (1 << (self.n - 1))\n",
    "        tmp = tmp >> self.n\n",
    "        # print(hex(q.val))\n",
    "        return QInt8(self.n, np.int8(self.sat8(tmp)))\n",
    "    \n",
    "    def __truediv__(self, q):\n",
    "        assert isinstance(q, QInt8), \"The other operand should be of QInt8 type\"\n",
    "        assert q.n == self.n, \"Number of fractional bits should match\"\n",
    "        \n",
    "        tmp = np.int16(self.val) << self.n\n",
    "        if (tmp >= 0 and q.val >= 0) or (tmp < 0 and q.val < 0):\n",
    "            tmp = tmp + q.val / 2\n",
    "        else:\n",
    "            tmp = tmp - q.val / 2\n",
    "        return QInt8(self.n, np.int8(tmp / q.val))\n",
    "    \n",
    "    def __float__(self):\n",
    "        return float(self.val) / (1 << self.n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QInt8(3, 4) -0xe -0.875000\n",
      "QInt8(3, 4) 0x36 3.375000\n",
      "QInt8(3, 4) -0x2a -2.625000\n",
      "QInt8(3, 4) -0x9 -0.562500\n",
      "1.25\n"
     ]
    }
   ],
   "source": [
    "# Maybe you can try with some other examples to see whether you implemented correctly.\n",
    "q1 = QInt8(4, 1.26)\n",
    "q2 = QInt8(4, - 2.1)\n",
    "\n",
    "print(q1 + q2)\n",
    "print(q1 - q2)\n",
    "print(q1 * q2)\n",
    "print(q1 / q2)\n",
    "print(float(q1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Challenges (No Solution)\n",
    "\n",
    "1. Mixed-precision: Can you support arithmetic between operands in different precisions? (hint: use shift)\n",
    "2. Can you define and calculate a metric that evaluates the \"goodness\" of a precision on a given tensor?\n",
    "3. Can you provide a process that can search for the best precision, regarding the goodness metric defined above, of a given tensor?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MNIST in TensorFlow\n",
    "\n",
    "In this section, we build a CNN for MNIST classification in TensorFlow.\n",
    "The aim is to extract coefficients from the TensorFlow pre-trained model and convert them to quantised format.\n",
    "\n",
    "The code block below trains a CNN for MNIST classification. It has two convolution layers, two max-pooling layers, two fully-connected layers, and a dropout layer.\n",
    "You just need to run the code block below.\n",
    "Later we will try to extract coefficients from the model you trained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting mnist/train-images-idx3-ubyte.gz\n",
      "Extracting mnist/train-labels-idx1-ubyte.gz\n",
      "Extracting mnist/t10k-images-idx3-ubyte.gz\n",
      "Extracting mnist/t10k-labels-idx1-ubyte.gz\n",
      "step 0, training accuracy 0.18\n",
      "step 100, training accuracy 0.76\n",
      "step 200, training accuracy 0.94\n",
      "step 300, training accuracy 0.9\n",
      "step 400, training accuracy 0.94\n",
      "step 500, training accuracy 0.92\n",
      "step 600, training accuracy 0.92\n",
      "step 700, training accuracy 0.92\n",
      "step 800, training accuracy 0.98\n",
      "step 900, training accuracy 0.98\n",
      "test accuracy 0.9645\n",
      "INFO:tensorflow:Froze 8 variables.\n",
      "Converted 8 variables to const ops.\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "TODO: just run this code block\n",
    "\"\"\"\n",
    "tf.reset_default_graph()\n",
    "\n",
    "X = tf.placeholder(tf.float32, [None, 784])\n",
    "Y = tf.placeholder(tf.float32, [None, 10])\n",
    "\n",
    "mnist = input_data.read_data_sets('mnist', one_hot=True)\n",
    "\n",
    "Y_conv, keep_prob = deepnn(X)\n",
    "\n",
    "with tf.name_scope('loss'):\n",
    "    cross_entropy = tf.nn.softmax_cross_entropy_with_logits(labels=Y, logits=Y_conv)\n",
    "    cross_entropy = tf.reduce_mean(cross_entropy)\n",
    "with tf.name_scope('adam_optimizer'):\n",
    "    train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)\n",
    "with tf.name_scope('accuracy'):\n",
    "    correct_prediction = tf.equal(tf.argmax(Y_conv, 1), tf.argmax(Y, 1))\n",
    "    correct_prediction = tf.cast(correct_prediction, tf.float32)\n",
    "accuracy = tf.reduce_mean(correct_prediction)\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    for i in range(1000):\n",
    "        batch = mnist.train.next_batch(50)\n",
    "        if i % 100 == 0:\n",
    "            train_accuracy = accuracy.eval(feed_dict={\n",
    "                X: batch[0], Y: batch[1], keep_prob: 1.0})\n",
    "            print('step %d, training accuracy %g' % (i, train_accuracy))\n",
    "            \n",
    "        train_step.run(feed_dict={X: batch[0], Y: batch[1], keep_prob: 0.5})\n",
    "\n",
    "    print('test accuracy %g' % accuracy.eval(feed_dict={\n",
    "        X: mnist.test.images, Y: mnist.test.labels, keep_prob: 1.0}))\n",
    "    \n",
    "    graph = tf.get_default_graph()\n",
    "    graph_def = graph.as_graph_def()\n",
    "    graph_def = tf.graph_util.convert_variables_to_constants(sess,\n",
    "                                                             graph_def,\n",
    "                                                             output_node_names=[Y_conv.name.split(':')[0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Data Map\n",
    "\n",
    "From the trained CNN model we can build a data map.\n",
    "The code block below creates a `data_map` based on the model (i.e. `graph_def`) you have just trained.\n",
    "\n",
    "You can further quantise the `data_map` in later sections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_const_data(node_name, node_map):\n",
    "    tensor = node_map[node_name].attr['value'].tensor\n",
    "    return np.frombuffer(tensor.tensor_content,\n",
    "                         dtype=np.float32)\n",
    "\n",
    "data_map = OrderedDict()\n",
    "\n",
    "node_map = {}\n",
    "for node in graph_def.node:\n",
    "    node_map[node.name] = node\n",
    "    \n",
    "data_map['weights'] = OrderedDict()\n",
    "data_map['weights']['conv1'] = get_const_data('conv1/Variable', node_map).reshape((5, 5, 1, 32))\n",
    "data_map['weights']['conv2'] = get_const_data('conv2/Variable', node_map).reshape((5, 5, 32, 64))\n",
    "data_map['weights']['fc1'] = get_const_data('fc1/Variable', node_map).reshape((1024, 7 * 7 * 64))\n",
    "data_map['weights']['fc2'] = get_const_data('fc2/Variable', node_map).reshape((10, 1024))\n",
    "\n",
    "data_map['bias'] = OrderedDict()\n",
    "data_map['bias']['conv1'] = get_const_data('conv1/Variable_1', node_map)\n",
    "data_map['bias']['conv2'] = get_const_data('conv2/Variable_1', node_map)\n",
    "data_map['bias']['fc1'] = get_const_data('fc1/Variable_1', node_map)\n",
    "data_map['bias']['fc2'] = get_const_data('fc2/Variable_1', node_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can you implement the following functions that can convert a vector from `float` to `QInt8`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def convert_to_qint8(X, n):\n",
    "    \"\"\"\n",
    "    TODO: assign the converted vector from X to list_of_qint8.\n",
    "    n is the number of fractional bits.\n",
    "    \"\"\"\n",
    "    list_of_qint8 = [QInt8(n, float(x)) for x in X]\n",
    "    return np.array(list_of_qint8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_qint8_data_map(data_map, n_s):\n",
    "    qint8_data_map = OrderedDict()\n",
    "    for group in data_map:\n",
    "        qint8_data_map[group] = OrderedDict()\n",
    "        for idx, layer in enumerate(data_map[group].keys()):\n",
    "            shape = data_map[group][layer].shape\n",
    "            qint8_data_map[group][layer] = convert_to_qint8(\n",
    "                data_map[group][layer].reshape(-1), n_s[idx]).reshape(shape)\n",
    "    return qint8_data_map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you have the quantised `data_map` (`qint8_data_map`) of the trained MNIST CNN model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 10.4 s, sys: 164 ms, total: 10.5 s\n",
      "Wall time: 10.5 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# suppose we use 3 as the number of fractional bits for all layers\n",
    "qint8_data_map = create_qint8_data_map(data_map, [3, 3, 3, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Challenges (No Solution)\n",
    "\n",
    "1. Can you try to quantise the `data_map` with different precisions for different layers?\n",
    "2. Can you evaluate the goodness of your current precision setting?\n",
    "3. Can you search for the **best** precision setting for the current trained coefficients?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantised CNN Layers\n",
    "\n",
    "This section implements typical CNN layers with quantised data types.\n",
    "Coefficients are converted from pre-trained values in floating-point to fixed-point.\n",
    "We will show intermediate results to see how the quantised layers work.\n",
    "\n",
    "You don't need to implement these layers. We already provide the naive solutions. You can just re-run them and experience with \n",
    "other test images."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantised Input Images\n",
    "\n",
    "`images` is a numpy array contains quantised MNIST test images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MFSKG28HAHvKFPlbRpAvY+Xye6bimoTm5+3k7L607ycYqMLfSMn3r7AzbRWaz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\n4hkWtIQQ4pn/D25u4EfTP8W8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f02e7d0c978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NUM_TEST_IMAGES = 100\n",
    "\n",
    "# convert input images to quantised images\n",
    "images = np.array([\n",
    "    convert_to_qint8(X, 3).reshape(1, 28, 28)\n",
    "    for X in mnist.test.images[:NUM_TEST_IMAGES]])\n",
    "\n",
    "# show some samples\n",
    "f, axarr = plt.subplots(4, 4)\n",
    "for x, y in product(range(4), range(4)):\n",
    "    img = images[x * 4 + y].astype(float).reshape(28, 28)\n",
    "    axarr[x, y].imshow(img, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantised CNN Layers implementation\n",
    "\n",
    "Since we already have the definition of `QInt8`, we can straightforwardly implement each type of CNN layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def conv2d(X, W, b):\n",
    "    \"\"\"\n",
    "    naive implementation\n",
    "    \"\"\"\n",
    "    num_channels, height, width = X.shape[1:]\n",
    "    kernel_size, num_filters = W.shape[0], W.shape[3]\n",
    "    pad = int(math.floor(kernel_size / 2))\n",
    "    out_height = height - kernel_size + 1 + 2 * pad\n",
    "    out_width = width - kernel_size + 1 + 2 * pad\n",
    "    \n",
    "    Y = np.zeros((X.shape[0], num_filters, out_height, out_width), dtype=object)\n",
    "    \n",
    "    for idx in range(X.shape[0]):\n",
    "        image = X[idx]\n",
    "        for f in range(num_filters):\n",
    "            for h, w in product(range(out_height), range(out_width)): \n",
    "                result = b[f]\n",
    "                for c, kx, ky in product(range(num_channels), range(kernel_size), range(kernel_size)):\n",
    "                    x = h + kx - pad\n",
    "                    y = w + ky - pad\n",
    "\n",
    "                    if x < 0 or x >= height or y < 0 or y >= width:\n",
    "                        continue\n",
    "\n",
    "                    result = result + W[kx][ky][c][f] * image[c][x][y]\n",
    "                Y[idx][f][h][w] = QInt8(result.n, 0.0) if result.val < 0 else result\n",
    "    return Y\n",
    "        \n",
    "def max_pool_2x2(X):\n",
    "    num_channel, height, width = X.shape[1:]\n",
    "    out_height = int(height / 2)\n",
    "    out_width = int(width / 2)\n",
    "    Y = np.zeros((X.shape[0], num_channel, out_height, out_width), dtype=object)\n",
    "    for idx in range(X.shape[0]):\n",
    "        image = X[idx]\n",
    "        for c, x, y in product(range(num_channel), range(out_height), range(out_width)):\n",
    "            p1, p2, p3, p4 = image[c][2*x][2*y], image[c][2*x+1][2*y], image[c][2*x][2*y+1], image[c][2*x+1][2*y+1]\n",
    "            Y[idx][c][x][y] = QInt8(p1.n, max(max(p1.val, p2.val), max(p3.val, p4.val)))\n",
    "    return Y\n",
    "\n",
    "def fc(X, W, b):\n",
    "    return np.array([\n",
    "        list(map(lambda result: QInt8(result.n, 0.0) if result.val < 0 else result,\n",
    "                 np.dot(W, image) + b)) for image in X])\n",
    "\n",
    "def softmax(X):\n",
    "    \"\"\"\n",
    "    The final softmax is implemented in floating point\n",
    "    \"\"\"\n",
    "    X = X.astype(float)\n",
    "    X = np.exp(X)\n",
    "    return X / np.sum(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 7.03 s, sys: 0 ns, total: 7.03 s\n",
      "Wall time: 7.03 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "Y = conv2d(np.array([images[2]]),\n",
    "           qint8_data_map['weights']['conv1'],\n",
    "           qint8_data_map['bias']['conv1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3+tUbdu/erZMnT+ratWsTmYdcZ/XCCy808r2bbM9///3369VXX9WVK1eGKqtB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\nfF7ec+o2ilkV/d7zHiOr9p0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frm08qaAQHwAAAAASw4kaAAAAACSm+b62DcsroSsqaYyf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\nAIBiDDUAAIBiDDUAAIBinhvikM3M09BfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f02e45c25c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axarr = plt.subplots(4, 8, figsize=(15, 8))\n",
    "for x in range(4):\n",
    "    for y in range(8):\n",
    "        axarr[x, y].imshow(Y[0][x * 8 + y].astype(float), cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 32 ms, sys: 44 ms, total: 76 ms\n",
      "Wall time: 25.8 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "Y1 = max_pool_2x2(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cumjU3pb0+Q0/39VbGyXvmtkdktT781LH9fRDTuvIKg6yioOs4iCrOMgqjtyz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f02e3f6a278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axarr = plt.subplots(4, 8, figsize=(15, 8))\n",
    "for x in range(4):\n",
    "    for y in range(8):\n",
    "        axarr[x, y].imshow(Y1[0][x * 8 + y].astype(float), cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 42s, sys: 96 ms, total: 1min 42s\n",
      "Wall time: 1min 42s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "Y2 = conv2d(Y1, qint8_data_map['weights']['conv2'], qint8_data_map['bias']['conv2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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n5uq47dSpk1zjjTfknIFKRNOTmX681Nf2qFGj5LbUuWnEiBFurl7TNDfcKEdR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\nbqsKqtJT2uQ8dV5ZunRpLmu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CCy/IbVVT2Y6rzp07u/m6devc/Pbbb3fztMf3hhtucHPV\nVZcuXdxcvaZpDWXrycxs9OjRbn748GE3VxOK+/btK9dQUwYnTJjg5mU4rsrYlZqwqKYiPv30027+\n7W9/W66hJhWrtdXzmzrWW1MeY/Y/EkJgXnIc6CoedBUPuooHXcWDruJAT/Ggq4jwI44AAAAAUBIt\nvUALZvZEkiQLkiTxf5YMZUFX8aCreNBVPOgqHnQVB3qKB11FpqU/4jg5hLA5SZLeZvZkkiTLQwjz\nTrxB0xfCtKa/t3A5tABdxSNTVyhUalccU6Vy0l2hcBxXceC5Kh68BoxMi76DFkLY3PTnDjN70Mz+\n4TfUQwjTQwgTy/ALibUsa1ccnMWhq3g01xXnv/LI0hXHVLHoKg48V8Uja1d1dfwGVNEq/g5akiSd\nzawuhLC/6e9TzOw/ctuzZqjJOyofMGBApu3/8z//s/xYx44d3VxNK1PTg1avXp1pnypVdFdqKuPE\nif5r1i1btri5mgCYNvXxD3/4g5sfOHAg0+3VPuWt6K769+/v5uprPutkrOeee06uraY4qlytUa3p\njkV2lfV81qNHDzf//Oc/7+Zq8qyZntaoJkiqyVvVnOJYZFdqWuNbb73l5moSnLp9GjUBVW2roaHB\nzdUkytZQ9DnQ06tXLze//PLL3Xzo0KFuvn37drmGmhSpjsUdO3a4ebWmzRXdk3pe2LZtm5t/6lOf\nyrT9tMdRTUdV1MTAaim6qyFDhri5mtb4ta99zc2fffZZN1dTNc3Mxo8f7+ZqWuNDDz3k5osWLZJr\ntJaW/IhjHzN7sOn/iJxiZveFEPRsZhSJruJBV/Ggq3jQVTzoKg70FA+6ilDFF2ghhLVmdk6O+4JW\nQlfxoKt40FU86CoedBUHeooHXcWJHzIFAAAAgJLgAg0AAAAASoILNAAAAAAoiZa+D1ph1HQqlX/y\nk5908//6r/9yczW1zsxs8+bNbq4m2qnb1wo1GfCZZ57JtJ39+/e7+dVXXy0/Z+TIkW6uJkKqKY5p\nkyLVfpVV2te2moyoPuczn/mMmz/yyCNuvnTpUrn25MmTM61drWmNZaTONSNGjHDzl156yc3V5MXz\nzz9frq2mX6lpcz179nTzxYsXyzXakvbt27u5mow4depUNz/33HPd/Cc/+YlcW003U/ukpjuq27c1\napKimsqojhM1YTHtnNWnTx83X7JkifycWqamOKqvefXa8Morr3TzRx99VK49f/58N886rTFt+qDa\n31qmXjN+61vfkp+jnq/Utk4//fRsO9WK+A4aAAAAAJQEF2gAAAAAUBJcoAEAAABASXCBBgAAAAAl\nwQUaAAAAAJQEF2gAAAAAUBKlHrOfNg68vr7ezdXo1R/84AduvmnTJjf/1Kc+lXltlf/85z93czUq\nu63p16+fm6vR9SpfuXJl5rXV5/z4xz92czUyP7ZR+mnUMWKmx+wPGzbMzX/zm9+4+ZNPPunmZ555\nplx7y5YtmdZWamE8seqpR48ebn7o0CE3P+uss9x81qxZcm01Bl69ncjOnTvdvC2d/9TIfLPsY/Z7\n9erl5mPHjnXzhoYGufbGjRsz7VOtjNNX1Hj83r17Z9rOwYMH3fzyyy+Xn6Pe8kL55je/mWnttkY9\nj6l8yJAhbq7OpertgdKsX78+0+1r4bnKTL/9gHqbAdXVjBkz3PwLX/iCXFt9jhrNv3DhQjfP+hYK\neeA7aAAAAABQElygAQAAAEBJcIEGAAAAACXBBRoAAAAAlAQXaAAAAABQEtFOcRwxYoSbn3/++W4+\nYMAANz/jjDPcfM6cOZnXXrx4sfyctk5NXkxz3nnnufnWrVtz2Y6Z2YIFC9z86quvdvMf/ehHmdZu\na9REKzWJU026Wrt2rZunTa1SnTzwwAOZttWWpgMqnTp1cnM1lVad/wYNGuTmt912m1x74MCBbq7O\nmWpf25LTTjtNfqxnz55urqY4qvzee+9182eeeUaurSZCqq8TtXatT3e87LLL3PzFF19080svvdTN\nDxw4INdQEwBnzpyZeVu1QJ3/sz6HrVu3LvPaQ4cOdfPXXnst87baCjWR0UxPQLzuuusy3f6SSy5x\n8/Hjx8u11flRHW/79u2T26o2voMGAAAAACXBBRoAAAAAlAQXaAAAAABQElygAQAAAEBJcIEGAAAA\nACXR7BTHJEnuNrOrzGxHCGFcU1ZvZr8zsyFmtt7MPhtC2NN6u/mPdu/e7eZqgs/q1avdXE2h+9Sn\nPiXX/uMf/+jmanrc5s2b5bbyVGRX+/fvlx9T06bUhEWVT5s2zc3Tpj6qCT4qV9Mo0+5fJcp6XKnH\nfs8efzcmT57s5mryojrezPSxq1RrWmMZu1LnvyVLlrj517/+dTdXkxe/8Y1vyLVnzZrl5qtWrXJz\n9bXTGorqSk0/NNMTTdXkx6xTHNWkRjM9rVFNZazmtMYyHledO3d2c9XhsGHD3Fwdh9/97nfl2k89\n9VSmfWpoaJDbylMZezIzGzJkSKbbX3TRRW7+/PPPu/mjjz4qt7Vs2bJMa3fo0CHT7SsVW1dqkuJD\nDz3k5h/+8IfdXE13NE5T0isAACAASURBVEufLplln4pwMt9Bm2FmU9+T3WZmc0MII8xsbtO/UbwZ\nRlexmGF0FYsZRlexmGF0FYsZRlcxmGH0FIsZRldtRrMXaCGEeWb23v9de62Z3dP093vMzH8zA1QV\nXcWDruJBV/Ggq3jQVRzoKR501bZU+jtofUIIf/25sm1m1ien/UH+6CoedBUPuooHXcWDruJAT/Gg\nq0g1+ztozQkhhCRJgvp4kiTTzGxa099buhxagK7ikaUrFCutK46pcjnZrlA8jqs48FwVD14DxqXS\n76BtT5Kkn5lZ05871A1DCNNDCBNDCBMrXAstU1FXHJyFoKt4nFRXnP9KIXNXHFOFoas48FwVj4q6\nqqtjyHvRKv0O2mwzu8nMvt/058O57dEJ0qa07dq1y83V9CQ19UxtZ9CgQc3s3T968cUX3bxjx45u\nXqUpdFXpSk0/NDN75ZVXMn3O1VdfnWntfv36yY+lTQ305D2tMaOqdFXJVD01YVF1q77mL7/8crnG\nHXfc4ebVmtaYUVW6ymrnzp1u/tJLL7l5JZNnDx065Obq66oE/RXalZqM2LNnTzfft2+fm2/fvt3N\n16xZU9mOlVOhXamJmF26dHHzoUOHZtr+L3/5S/kx9frhL3/5S6Y1qqTw89+2bdvcfMyYMW6+d+9e\nN587d66bp02HLtOkv5NQla7U42umJylmncT57LPPuvknPvEJ+Tnjx4/PtEba/ai2Zi+RkySZaWYv\nmNmoJEk2JUlysx0v+ookSVaZ2eVN/0bB6CoedBUPuooHXcWDruJAT/Ggq7al2e+ghRCuFx+6LOd9\nQQvRVTzoKh50FQ+6igddxYGe4kFXbQs/ZAoAAAAAJcEFGgAAAACUBBdoAAAAAFASXKABAAAAQEm0\n+I2qW1PaeGY16lmN2Vfj9AcMGODmzzzzjFx71apVbt6hQwc3L8GY6VaXNp5ejbpXnzN9+nQ3nzbN\nf6/LmTNnyrX/8Ic/yI/VqsbGRvkxNVpYfc7YsWPdXL1VwtKlS+Xa6u0S1q5d6+aVvF1AW5E2Bt8z\nZ84cNz/77LPd/N5775XbUuc/9dYK6i1OaoV6jlE2bdrk5suWLXPz4cOHy221sRH8rU6N0z9w4ICb\nr1u3zs137PDfakptp9LPwT9Sr8P+7//+z83Vc9vy5cszr5H23FrL1NsSXHLJJW7etWtXN//CF77g\n5jNmzJBrf+1rX3PzX//61/JzyoLvoAEAAABASXCBBgAAAAAlwQUaAAAAAJQEF2gAAAAAUBJcoAEA\nAABASZR6iqOaClYJNUlsxIgRbq6mPprpKWa1PFUuzZYtW9x81KhRbq4mCarpjldddVVu+1QL1AQq\nM7Pu3bu7uZrEqY5RNT1Obd8s+wTJWqYmw9bX17v56tWr3bxHjx5unnbuVX2otbNOnGxrst7/nTt3\nunmvXr0yr60+56233sq8rVqQdWLi4sWL3VxNR02jJki+/vrrmbdVy9RkTfW8t3fvXjfv27dv5rVr\n+blKPY5mZuPHj3dz1dWGDRsyrT1kyBD5MTWtcdGiRZnWKALfQQMAAACAkuACDQAAAABKggs0AAAA\nACgJLtAAAAAAoCS4QAMAAACAkkhCCNVbLEkazOyv41l6mpk/rqpta637fXoIIfuYL4GuzKx17neu\nPZnRVZPSd0VPZsb5LyZ0FQ+6igddxaPQrqp6gfZ3CyfJKyGEiYUsXqAY73eM+5yHGO93jPuch9ju\nd2z7m5cY73eM+5yHGO93jPuchxjvd4z7nIcY73eM+5yHou83P+IIAAAAACXBBRoAAAAAlESRF2jT\nC1y7SDHe7xj3OQ8x3u8Y9zkPsd3v2PY3LzHe7xj3OQ8x3u8Y9zkPMd7vGPc5DzHe7xj3OQ+F3u/C\nfgcNAAAAAPD3+BFHAAAAACgJLtAAAAAAoCSqfoGWJMnUJElWJEmyOkmS26q9fjUlSXJ3kiQ7kiR5\n/YSsPkmSJ5MkWdX0Z/ci9zENXdFV2cTekxld0VX50FU86CoesXdVKz2ZlbOrql6gJUnSzsz+28w+\nZmZjzez6JEnGVnMfqmyGmU19T3abmc0NIYwws7lN/y4dujIzuiqjGRZpT2Z0ZXRVVjOMrmIxw+gq\nFjMs0q5qrCezEnZV7e+gTTKz1SGEtSGEo2Z2v5ldW+V9qJoQwjwz2/2e+Fozu6fp7/eY2XVV3amT\nR1d0VTqR92RGV3RVQnQVD7qKR+Rd1UxPZuXsqtoXaAPMbOMJ/97UlNWSPiGErU1/32ZmfYrcmRR0\nRVexiKUnM7qiq3jQVTzoKh6xdFXrPZkV3BVDQgoUjr/HAe9zEAG6igM9xYOu4kFX8aCreNBVPIro\nqtoXaJvNbNAJ/x7YlNWS7UmS9DMza/pzR8H7o9AVXcUilp7M6Iqu4kFX8aCreMTSVa33ZFZwV9W+\nQHvZzEYkSTI0SZJTzexzZja7yvtQtNlmdlPT328ys4cL3Jc0dEVXsYilJzO6oqt40FU86CoesXRV\n6z2ZFd1VCKGq/5nZlWa20szWmNnt1V6/yvd1ppltNbO37fjP795sZj3s+DSYVWb2JzOrL3o/6Yqu\nYvkv9p7oiq7K+B9dxfMfXcXzX+xd1UpPZe0qadoxAAAAAEDBWvQjjrX0Jnaxo6t40FU86CoedBUH\neooHXcWDruJT8XfQmt7EbqWZXWHHvx34spldH0J4I+VzQpIkFa3XWk499VQ3r6vT167Hjh3LtMbR\no0dbfY0Qws4QQi/vY5V2lWkHctShQwc3b2xsdHPVoZnZO++8k2kN1VVaHxV0JQ+CSrtK+1oqgupE\ndWhm1q1bNzc/5ZRT3PzAgQNurjo3y9bVsWPHcu2qyGMq69dH2jGljhHVk+ojbZ/SOhTk+c+ssq7K\n9lylzlnve9/75Oe8++67bt6uXTs3f/vttzPlaWsobem5Sj2O6jFJ60o9xupz1PGWdo6t4PVe7l0V\n9Vyl1lXPCR07dsxt7bTjR8l6Djx27FjuXRV1Dsz6NZL2vK62lfW8ledjkXYOPJF/hJ+cv72JnZlZ\nkiR/fRO7tMLlk0xRBgzw39ahc+fO8nMOHjyYaY3Nm/3BN2kngMOHD2da4/DhwxtSPpy5qyINGTLE\nzZcvX+7mffv2ldvauXOnm48ZM8bNN2zwH8ZDhw7JNdI+VoHMXdXV1ZXuuBo8eLCbqw7NzD7ykY+4\nea9e/nls3rx5bq46N8vWVdoLnSbRHFdZX2wMHTpUfmzdunVurnpqaGhw87Rz7I4dmYdlpZ3/zDJ2\nlSSJtW/fPus+tKpRo0a5eb9+/eTn7Nmzx827d+/u5lu3bnXzbdu2yTX27t0rP+ZpbGxsM89VXbt2\ndfPdu9/7frfH9emj30Zp06ZNmT6nR48ebr5y5Uq5RtbXFZZ+XFX0XJXnhU8W6nyjXs+NGzcut7W3\nb9+e+XPUeVM5ePBgrl0lSZL6P+paU9bXM2nP1Wpb+/bty7RGno/FkSNHmnu+MrOW/Ygjb2IXD7qK\nB13Fg67iQVdxoKd40FU86CpCLfkO2klJkmSamU1r+ntrL4cWOLErlBvHVRw4puJBV/Ggq3jwXBUP\njqtyackF2km9iV0IYbqZTTczq6urY2RkMTJ3VeTP9de4zF21a9eOrorRbFccU6WRqSueqwrDc1U8\neK6KB6/XI9SSC7S/vYmdHS/6c2Z2Qy571Qqy/tzzpZdeKj/21FNP5bIt9TPnZuk/R16BqLrKSv0+\nmZn+nbIbb7zRzdXvNb355ptyjQULFqTsXWZRdaV+10z9vL963M3MBg0a5OYbN250c6VTp07yYzn/\nvmA0XanfD+vSpYubX3DBBXJb6vfD1GNbye9yVPA7aM2Jpis1LKcS6ncJ1e9sqHNp1t8za4FoejLT\n5xr1u17nnHOO3Jb6XRl1XuzZs2cze/ePFi1alPlzUkTVVdbfNUv7vbHLL7/czdXxNnu2//7Oac9V\nWX8HrRlRdaXOgep3PtXrPDN9XE2aNCnT7VesWCHXSFu/JSq+QAshvJMkyVfN7HEza2dmd4cQlua2\nZ8gNXcWDruJBV/GgqzjQUzzoKh50FacW/Q5aCGGOmc3JaV/QiugqHnQVD7qKB13FgZ7iQVfxoKv4\nlOvNkwAAAACghnGBBgAAAAAlwQUaAAAAAJREq78PWlmoaTkTJkzIdHszs5EjR7r5rbfe6ub/8i//\n0sze1Sb1GKvpVF/72tfcPG2K486dO91cTZxT0wcrmZhVC9TjldaJ0rt3bzdXx88HP/hBN087dmuV\nmtZ42WWXubnqIu1zhgwZ4ubqWLvjjjvkGrVMPY79+vXLvC11LIwdO9bNt23b5uZqslmt69Gjh5uP\nGDHCzdPOTWpao8pznvTc5qlpjWpi7eLFi+W21FRc9Xx4zTXXuPmf/vQnuUYtU9MaR40alXlbanKq\nWkNN8t63b1/mtVuK76ABAAAAQElwgQYAAAAAJcEFGgAAAACUBBdoAAAAAFASXKABAAAAQElwgQYA\nAAAAJVEzY/bV2NvPfOYzbt6xY0e5LTVmf9GiRW5+1VVXufncuXPlGrVAja5Xo/FVrkbempk99thj\nbn777be7+bJly9x8w4YNco1apsbpq27Tupo6daqbq64UNeq4FqSNx/fccsstbn7ffffJz1Gj2K++\n+mo3v+uuu9w8raeDBw/Kj7V1jY2Nbr5u3To3v/nmm+W2+vfvn2mNp556qpm9q03q9YD6Oh04cKCb\nq7ecMDMbP368m1944YVu/sgjj7g5HfqGDRuW6fZf+tKXMm9rx44dbq7OgbVOvX1Ht27d3FyNxle3\nN9PnukmTJrm5GuX/n//5n3KN1sJ30AAAAACgJLhAAwAAAICS4AINAAAAAEqCCzQAAAAAKAku0AAA\nAACgJGpmiuOgQYPc/LLLLnPzXbt2yW1t3LjRzdXkpl/84hfN7F1tUhP91GQsNc0vbeLbd7/7XTd/\n5ZVX3FxNH5w4caJcY/ny5fJjbcXgwYPdXD1eH/rQh3Jbu1OnTm6upnqqyZJmekpnW6cmJqqpj+q4\nMTO744473FxNGVST69ImetbCFMchQ4a4+cc//nE3f/XVV91cPYeZmS1cuNDN1dQzNZ1ObadWDBgw\nwM3VcaVeb6jtmOnpcWo6tJriWF9fL9eoBaqT66+/3s1nzpzp5l26dJFrqGmN27dvz7S2OpfWOjWt\ncfHixW6eNnFz7969bj5lyhQ3f+CBB9xcTZxsTXwHDQAAAABKggs0AAAAACgJLtAAAAAAoCS4QAMA\nAACAkuACDQAAAABKokVTHJMkWW9m+83sXTN7J4SgR91VyciRI938qquucvO5c+e6eceOHeUaF110\nkZs///zzbq6mmKnpTK2hyK7UpL8NGza4+XnnnZfLdsz0RL+f/vSnbn766ae7uZr62BrKeFxlndao\nOlTHgplZQ0ODm997771u/sEPftDN33zzTblG3srWlZp4ecstt7h5JVMcDxw44OaXX365m991111u\nnjYlrTWUrauhQ4e6+bZt29x8z549bp42XUx9bOvWrW6+YMECN29sbJRrtIaydaWoiYlp0xqV8ePH\nu7ma1qimd1Zz4maRPalpjddcc42bv/DCC26+ZMkSN58+fbpce/369W4+e/ZsN1fHupr62BqK7Eqd\nh/r06ePmasqsOg+p7ZjpKY7q9bfqpNrnQLN8xux/JITgz7tG2dBVPOgqHnQVD7qKB13FgZ7iQVcR\n4UccAQAAAKAkWnqBFszsiSRJFiRJMi2PHUKroat40FU86CoedBUPuooDPcWDriLT0h9xnBxC2Jwk\nSW8zezJJkuUhhHkn3qDpC2Fa099buBxaIFNXKBTHVTxSu+KYKhW6igddxYHnqnjwGjAyLfoOWghh\nc9OfO8zsQTOb5NxmeghhYll/ybdW0FU8snbFk15xmuuKY6o8snTFMVUsjqs48FwVD7qKT8XfQUuS\npLOZ1YUQ9jf9fYqZ/Udue1ahc845x8179Ojh5mpy0muvvZZ57ayfkzYp8vDhw5nXV4ruSk1GVFP7\n1GTAWbNmZbq9mZ7EpKYJqgl1r776qlwjT0V3paYATpzovw56+eWXM21HfS2kGT16tJurDtOmeuap\nyK6GDBni5moyopr4pqjjoBKqp7SJnnkrsis1wUzl6nH59Kc/7eZqQpyZngipJqOqiWfVVGRXaiqj\nmuCmznOLFy928wceeECurSYLq9cCv//9791c3Ye8Ff1cdfDgQTdX0x3V641vfvObbv7000/LtdX0\nb2XHjh2Z9ilvRXeljBo1ys3V6wR1fko7b6lrgvbt27v5Sy+95OaxTXHsY2YPNl1ln2Jm94UQHstl\nr5A3uooHXcWDruJBV/GgqzjQUzzoKkIVX6CFENaamX9pilKhq3jQVTzoKh50FQ+6igM9xYOu4sSY\nfQAAAAAoCS7QAAAAAKAkuEADAAAAgJJo6fugFSZtAqJHTWt85JFH3HzkyJFyW2pao5rc9MILL7h5\nnpMay0x11atXLzdXk7F27tzp5j179pRrq20NGjTIzdW0RrUds+pOo2tt6rEcM2aMm6vH5aMf/aib\nL1iwQK6tpnGqNc4999xMtzdrW115rr76ajdXx9q6devcfP369XKNW265xc1/9rOfufmZZ57p5kuX\nLpVrtCXdunVz8/79+7u5OkbOO+88N3/qqafk2nPmzHHzsWPHuvmDDz7o5uo+mBUz3ay1qHPHwIED\nM23nwgsvdPO05/yNGze6uXotcsEFF7j5okWLmtm7tkGd084//3w3v+OOO9xcTUFV0x3NzL7zne+4\n+TXXXOPms2fPdnM1cdJMT6mMUZ8+fTLlTzzxhJtPmTLFzfv27Zt5n37zm99kun0R5zm+gwYAAAAA\nJcEFGgAAAACUBBdoAAAAAFASXKABAAAAQElwgQYAAAAAJcEFGgAAAACURLRj9tU4XJWr8dpqHO7c\nuXPl2pdddpmbr1y5MtM+taUx+2mjzd988003V6Pb1Tjp6dOnu/mf//xnufayZcvcXI3sV7LePlZq\nzL66/zfeeGOm2997772Z9+mTn/ykm+fVbYyyji1W57/bb7/dzdWoajOzX/7yl27epUsXN3/xxRfd\nvC2NkU6jRkCrsc3qbQluvvlmN08bs6/G4//2t7918w4dOsht1TL1OkE976mR+Wkj8H//+9+7+aWX\nXurm6vVDW3pdkUad65YsWeLmZ511lptff/31bq7OW2ZmvXv3dnM1Nl+d62rlHJjV9u3b3bx9+/Zu\nvnfvXrmtz3zmM26uRvlv2LChmb2rHr6DBgAAAAAlwQUa/h97dxpkV3Xe+/9ZEtaAJDS11ALNktGA\nJTPJQg6DwaAEDwzBsROlbsyNceRU4ir73tS9IcWLxFWOL5WKb+Kb4KrIhjSJbflvl6GQbTCWZBPZ\nGEkgBKg1gsbWPCChqSUBWv8XNImA57db+/Tus/fq8/1UqdR6zjl7rdO/s4el0/0cAAAAABXBAg0A\nAAAAKoIFGgAAAABUBAs0AAAAAKiIZLs4Xn755W5ddWx54YUX3LrqWvenf/qncuyvfvWrbn3MmDFu\nXXV06kmyujgqI0aMcOt5O84999xzcgy1reuvvz7XGI1CZaK+X6tWrXLrqjvV+PHjc8+pUTtgqY5g\nZnp/mzNnTq77q45nWV0cP//5z7v1L33pS25ddTxrbW2VYzSC3bt3u3XVnXTPnj1u/fnnn5djqO5m\nWV3PPKrjZE8zfPhwt75z5063rs75qvNi1rWAGls9phGuK7KoroyKymT//v256mZmM2bMcOtbt27N\nvS281+DBg3PdP+u64qWXXnLrixYtcut5j43diXfQAAAAAKAiWKABAAAAQEWwQAMAAACAimCBBgAA\nAAAVwQINAAAAACqi0y6OIYSHzOyTZrY/xjijozbMzP4/M5tgZtvM7DMxxsPdN833OnTokFu/4oor\n3LrqeDR27Fi3vnz5cjm26mil5tTe3i63VaSqZnXrrbe6ddV5R3WcmzZtmlvfvn27HFt1xvrZz34m\nH1MPVc1KdQ5U32OVrfr+/sM//IMcW+W7Y8cOt646dBatrKyyujjmfcz3v/99t666PmZ1SPv2t7/t\n1o8fP+7WDxw4ILdVtLKy6tevn7xt6NChbv3wYX8Kn/jEJ9z6xIkTc9XNzH70ox+59b1797r1rOdR\ntLKy6t+/f2HbUud21fXx4Ycfltsqcl5Fquq5Sr3uVcfE5uZmt6462X7ve9+TY48aNaqT2ZWjzKyy\njh2q6/qQIUPc+tSpU9366dOn3fqyZctyz0vNad++fW69jE625/MOWouZvfsq7F4zWxpjvNTMlnb8\nG+VrMbJKRYuRVSpajKxS0WJklYoWI6sUtBg5paLFyKrH6HSBFmNcZmavvqt8h5m9/V9BD5vZnQXP\nCzUgq3SQVTrIKh1klQ6ySgM5pYOsepZafwetOcb49qdm7jUz/71jVAFZpYOs0kFW6SCrdJBVGsgp\nHWSVqE5/B60zMcYYQojq9hDCfDOb3/F1V4dDF+TJCuViv0pHVlbsU9VCVukgqzRwrkoH14BpqfUd\ntH0hhIvNzDr+9n8r08xijAtijLNijLNqHAtdQ1bpqCkrTnqlOK+s2KcqIXdW7FOlYb9KA+eqdJBV\nomp9B22Rmd1tZvd3/P1YYTPqom9+85tu/bd+67fc+jPPPOPWx4wZI8f4zW9+49YPHjzYyexKUZes\nVOdFM7N169a5ddXFUfnHf/xHt57VwSdvp7+SMyx9v1Id99T35ZFHHnHrCxYscOuqI6OZ2bhx49y6\nep1kde+sg1Kzmjx5sltXXRxVZzN1f9XJykx3a1Rd1erZxVEoNSvV/euFF15w67/3e7/n1v/+7/8+\n1/bNzNavX9/J7N5JdTyrYwezUrPatGmTWx82bJhb/+xnP+vWVXdH1TXaTJ+rVP3VV9/9q0Z1VZec\nsjrZtra2unXVoVQZOXKkW886bn3wgx9061u2bHHrJ06cyDWngtUlq6xjhDpXq/PMlClT3Lq6Fjhy\n5IgcW10frly50q2X0a1R6fQdtBDCQjN7xsymhhB2hhDusbeCnhtCeNnMbun4N0pGVukgq3SQVTrI\nKh1klQZySgdZ9SydvoMWY5wnbrq54Lmgi8gqHWSVDrJKB1mlg6zSQE7pIKuepdbfQQMAAAAAFIwF\nGgAAAABUBAs0AAAAAKgIFmgAAAAAUBFd/qDqsvTv39+tqxaZX/3qV916U1OTW1dtPs3M2tra3HrJ\nbW9LldU+PW+re0W1vc3bStosu31vI8v7vZw+fbpbX7VqlVufNm2a3JbaF1WL/6JeV1WlWuObma1Z\ns8atL1q0yK0vX74813auueYaOfbWrVtz1Rvdnj173PqQIUPcet++fd262jdVa28z3X66Au30K0ld\nV6iP6VH7lWrXv3TpUjn25Zdf7tbV9UYjyGpPrz4iSV0nqNb46rj1+c9/Xo792GN+p/oKfKRIJeU9\nDqn2++r8NnXq1NxjZ7XmrwreQQMAAACAimCBBgAAAAAVwQINAAAAACqCBRoAAAAAVAQLNAAAAACo\niEp3cWxvb5e3/fKXv8z9GI/qkDRmzBj5GNXp6sILLyxkTj3N+PHj3br6vjzxxBNuXXWKVJ0EzXQX\nqOeff14+ppGp17DKcPv27W79uuuuyz226tao6j1dVqdR9bpW3a9Up7I/+ZM/ceu/+MUv5NgTJ050\n662trfIxPV0tHcEmTJiQ6/6q6+Phw4dzjw2fOv795Cc/cesf/ehH3frq1avd+rBhw+TYL7/8sls/\ndOiQfEwj27Ztm1sfOXKkW3/ppZdybV8dS810B+FG7mSrOjKa6e+luq5Q21q2bJlbV9chWVLoZMs7\naAAAAABQESzQAAAAAKAiWKABAAAAQEWwQAMAAACAimCBBgAAAAAVEWKM9RsshANm9na7lSYza8T2\nbN31vMfHGEcUtTGyMrPued6F5mRGVh0qnxU5mRnHv5SQVTrIKh1klY5Ss6rrAu0dA4fwXIxxVimD\nlyjF553inIuQ4vNOcc5FSO15pzbfoqT4vFOccxFSfN4pzrkIKT7vFOdchBSfd4pzLkLZz5sfcQQA\nAACAimCBBgAAAAAVUeYCbUGJY5cpxeed4pyLkOLzTnHORUjteac236Kk+LxTnHMRUnzeKc65CCk+\n7xTnXIQUn3eKcy5Cqc+7tN9BAwAAAAC8Ez/iCAAAAAAVwQINAAAAACqi7gu0EMKtIYSNIYRXQgj3\n1nv8egohPBRC2B9CaD2nNiyEsDiE8HLH30PLnGMWsiKrqkk9JzOyIqvqIat0kFU6Us+qUXIyq2ZW\ndV2ghRB6m9kDZvYxM7vMzOaFEC6r5xzqrMXMbn1X7V4zWxpjvNTMlnb8u3LIyszIqopaLNGczMjK\nyKqqWoysUtFiZJWKFks0qwbLyayCWdX7HbTZZvZKjHFLjPGMmX3fzO6o8xzqJsa4zMxefVf5DjN7\nuOPrh83szrpO6vyRFVlVTuI5mZEVWVUQWaWDrNKReFYNk5NZNbOq9wJttJm1nfPvnR21RtIcY9zT\n8fVeM2suczIZyIqsUpFKTmZkRVbpIKt0kFU6Usmq0XMyKzkrmoSUKL71GQd8zkECyCoN5JQOskoH\nWaWDrNJBVukoI6t6L9B2mdnYc/49pqPWSPaFEC42M+v4e3/J81HIiqxSkUpOZmRFVukgq3SQVTpS\nyarRczIrOat6L9CeNbNLQwgTQwh9zOwPzGxRnedQtkVmdnfH13eb2WMlziULWZFVKlLJyYysyCod\nZJUOskpHKlk1ek5mZWcVY6zrHzP7uJltMrPNZnZfvcev83NdaGZ7zOx1e+vnd+8xs+H2VjeYl81s\niZkNK3ueZEVWqfxJPSeyIqsq/iGrdP6QVTp/Us+qUXKqalahY2IAAAAAgJJ16UccG+lD7FJHVukg\nq3SQVTrIKg3klA6ySgdZpafmd9A6PsRuk5nNtbfeDnzWzObFGNdlPCb26lVO40g17htvvOHWBw4c\nKLd19uzZXGOfG9EP7wAAIABJREFUOnUq93byfp/Onj17MMY4wrut1qxCCLnmUJTevXu7dfU96dOn\nj9zW66+/7tbf97735bp/1n6iHqO2E2OU39jU9qsLLrggVz2L2h9UvkePHnXrWfvuyZMnc82nyKzK\nzElR88nKb/DgwW790KFDubaljr1m+Y+xWcc/s9qyKuv4p75fKqus15Tad86cOePW29vb3bo6Jpvl\nzyrGWPi5qqz9Kuvc48k6Nh08eNCt13LeU1TuSk+6rlDj1nIMVMeuvMe6rH0n77V5d+xXZWVV5P7c\nt29ft/7mm2/m2k6R56usrM6V/yrqv/znh9iZmYUQ3v4QOxl4r169rF+/fl0YsnYDBgxw6wcOHHDr\ns2bNkts6fvx4rrHXrfO/JVkXi3m/TydPntyecXPurEIINZ0AiqAuANX3ZNy4cXJbe/fudeujRo3K\ndf+sE9u+ffvkbXm20yGp/aqpqcmtjxjR6bHnPU6cOOHWx48f79affPJJt37FFVfIMZ5//vnzno/6\nj5Vz5MqqzJwUdVzMyu8Tn/iEW29pacm1LXXsNdOvBaWT459ZzqxCCJXbpy688EK33r9/f7ktdWzc\nsWOHW3/hhRfc+pAhQ+QYef7Tw8ysvb290HNVr169Mr8H3WnixIm57j9nzhx527e//W23rp5b3rHN\nzLZu3Zrr/idOnCj8ukL952h3Uxfqqq72QzO9mFaPUfc/ffq0HCPrNs+ZM2cKz0p9b7pbkfvz5MmT\n3frhw4dzbefVV9/9Gdb/Rf3HlnLq1KnOzldm1rUfceRD7NJBVukgq3SQVTrIKg3klA6ySgdZJagr\n76CdlxDCfDOb3/F1dw+HLjg3K1Qb+1UayCkdZJUOskoH1xXpIKtq6coC7bw+xC7GuMDMFpiZ9e7d\nm5aR5cidVa9evciqHOxX6eg0K3KqjFxZcfwrDce/dHBdkQ6ySlBXfsSRD7FLB1mlg6zSQVbpIKs0\nkFM6yCodZJWgmt9BizG+EUL4opk9aWa9zeyhGOPawmZWMPWL6uqX0T/+8Y/LbalftFW/KLh9+3n9\nPmC3qWpW6pfwX3vtNbc+ZcoUt66aipjp3NXY59EY4j3yNAnpTFWzykv9kq9qSmFmdvXVV+caQ92/\nlgYltegJWak8VEMKM90k6QMf+ECu+6tmI2ZmP/jBD+RttUgpq+HDh7t1ldXcuXPltqZOnerWH3zw\nwVz337hxoxyjyF/oTyknM52JukaYMWNG7jHUY9Q+qhpgZc2rFqllpRpeXHTRRW49q6HL8uXL3frI\nkSNz1ffv3y/H2LJli7wtr9SyyuuGG26Qtw0bNsytL1y40K3feeedbn3ZsmVyjLxNQs5Xl34HLcb4\nuJk9XtBc0I3IKh1klQ6ySgdZpYGc0kFW6SCr9FTrQ3kAAAAAoIGxQAMAAACAimCBBgAAAAAVwQIN\nAAAAACqi2z+ouipUx6PPfOYzbn327NlyW88++6xb/+///b+79aeeesqtZ3Wb27Ztm7ytp1AdE5ub\nm916Ld35Lr/88tyP8ajMkU9WhgcOHHDr48ePd+tNTU1uff369fkn1sOpLmLquHjTTTfJbanOdU88\n8YRb/7M/+zO3XmRHuZ6kra3NrU+bNs2t33777XJbixcvdutXXXWVW1f71MGDB+UYJ0+elLf1dGr/\nUR1NV6xYIbf1V3/1V2590qRJbl11oG70/Up1a1T1Pn36uHXV3dFMH09Hjx7t1lVHxg0bNsgx1Lwa\nWS0dY1UXVFVvbW1167t375ZjqK7gXcU7aAAAAABQESzQAAAAAKAiWKABAAAAQEWwQAMAAACAimCB\nBgAAAAAVwQINAAAAACqix7XZV+1PVSvgCRMmuHXVwtbM7BOf+IRb/+u//utc21ItehvF4MGDc91f\nffTB6dOn5WNUVt/85jfd+po1a9z6mTNnOpldz6bab99www257n/11VfLMdQ+mtXiO68dO3YUtq2U\nqGOQqmd9HII6Zt54441uvZHbsGdR+8jUqVPd+ty5c9161rlKnWPa29s7mR3OpVpyq9e2+uiD48eP\nyzFmzpzp1vfv3+/WVe7qGqhRqOuBQYMGuXX1kQhjxoyRY6iW/eqjYtT91THAzOzo0aPytp5Ctc0/\nfPiwW1cfY3DJJZfIMYYOHerWP/ShD7l19ZFKs2bNkmOo1vxdxTtoAAAAAFARLNAAAAAAoCJYoAEA\nAABARbBAAwAAAICKYIEGAAAAABXR47o45u2MqDovqi5/ZrrD2cSJE9266hbzxBNPdDK7nqFfv365\n7q86/akOfJ/61Kfktvbu3evWp0yZ4tZPnTrl1tva2uQY+/btk7c1KtXdcf369fIxqsPZ888/79a/\n8IUvuPVf/epXncyu51Jd5e6++263rrr5/a//9b/kGD/84Q/d+qc//Wm3vnbtWrdeZHfOFI0bN66Q\n+2d1Rh0wYIBbX7x4sVufNm2aW9+wYYMcY+PGjfK2nm7SpEluXV0LDBw4UG7rpptucuuqM+DSpUvd\n+i9+8Qs5RiNQ12fqOkRlmNUd+u/+7u/c+pw5c9y66uKo6o1CdXHM22V23rx58rb/+I//cOu/8zu/\n49ZVJ+8jR47kmlMReAcNAAAAACqCBRoAAAAAVAQLNAAAAACoCBZoAAAAAFARXWoSEkLYZmbHzOxN\nM3sjxjiriEmheGSVDrJKB1mlg6zSQVZpIKd0kFV6iujieFOMsTLtuFQXx8985jNuXXVIam1tlWP8\n8R//ca45qS4yJahUVhdddJFbHzVqlFtvbm5264MHD5ZjqM5njzzyiFs/evSoW1cdJLtRKVmp/UfV\nm5qa3LrqLKfub2a2YMECt37XXXe59e3bt7t1tU93o8rsVxMmTHDrzz77rFtX3ebU99ZMdwY8ceJE\n9uSqoe5ZqX1HdbFUHcnmzp3r1lVHxiyqK6Pq4njo0KHcYxSg7lmp1/bIkSNz1VesWOHWZ8yYIcdW\nHVjVtciWLVty1btRKce/vJ0Rp0+f7tavvPJKt5513bZw4UK3rjpIqjnt379fjtFN57HKnKvMzF59\n9VW3rrppq2Pg9ddfL8d49NFH3fqTTz7p1tXxmi6OAAAAANDAurpAi2b28xDCqhDC/CImhG5DVukg\nq3SQVTrIKh1klQZySgdZJaarP+J4XYxxVwhhpJktDiFsiDEuO/cOHS+E+R1fd3E4dEGurFAq9qt0\nZGZFTpVCVukgqzRwXZEOskpMl95BizHu6vh7v5k9amaznfssiDHOijHO4kBaHrJKB1mlo7OsyKk6\n8mRVxvzwX9iv0sC5Kh1klZ6aF2ghhAEhhEFvf21mv21murMGSkNW6SCrdJBVOsgqHWSVBnJKB1ml\nqSs/4thsZo92rLIvMLPvxRh/VsiszoPqVqZ84AMfcOuqu9k111wjt/XUU0+59a1btxYydjcoNSvV\nwahfv36FbCfLT3/6U7euOvKo7nWqq1A3KDUr1cFIUV2rVLfGVatWyW2pzo/btm1z6yV1ljtXqVl5\n1PdddY974IEH3PoPf/hDOYbKXFHdyNTxspuUlpXap1T3uOHDh+eqq+5/ZmZ33HGHW1dd6FavXu3W\n29ra5Bj9+/eXt9WotKxUV9Pjx4+7dbVfqc6Lc+bMkWOr/UGNPXDgwFxjd4NKXlfkPT5t3rzZrav9\n08zs9OnTueak1LHjZqlZqWPE4cOH3bo6bs2e/Z43/Tqlrt2GDRvm1tesWePW29vbc4/dVTUv0GKM\nW8zs8gLngm5CVukgq3SQVTrIKh1klQZySgdZpYk2+wAAAABQESzQAAAAAKAiWKABAAAAQEWwQAMA\nAACAiujqB1WXRnWuUh2zPv7xj7v1hx9+2K1/6EMfkmOrLo6qe9DatWvd+okTJ+QYqcnbkdHMbObM\nmW59ypQpbn3cuHFuXXXdMcvfVWnIkCFuPauLWU+i9qsbbrjBrav9TdXXr1+fe05qX/zbv/1bt37w\n4MHcY6Qmq3OfR3XRqqWTrHrMjTfemOv+eZ9DqtS+oI5n1157bSHbNzN7+umn3brqUKe6O44dO1aO\n0ZP2N/W9HDVqlFvfv3+/Wx85cmTusR977DG33tzc7Nbr3AW1ci666KJc9TFjxrj1devWufU//dM/\nlWP/6Ec/cut9+vRx66o7atb1ieoUmaK8XRxVZ03l5z//ubxNXT9885vfdOuqu+OuXbtyzakIvIMG\nAAAAABXBAg0AAAAAKoIFGgAAAABUBAs0AAAAAKgIFmgAAAAAUBEs0AAAAACgIpJts6+olpqqpfOK\nFSvcumqfa2b2gx/8INcY27Ztk9tqBKoF//jx4936pk2b3PqXv/xlt/7II4/IsXfs2OHWz5w549ZV\ny/5Tp07JMXqSpqamXPf/b//tv7n1BQsWuPWsrNS2Dhw4kKveCCZMmODWn3vuObc+Y8aMXNtRHw2S\nZeXKlW59+vTpue7f0+T9SBj18StLlizJtR0z3bpdtdlXHyfSKB+JoGzZssWtX3PNNW5dtcBX+6GZ\n/tgZ9XrI+niZnqKWNvSTJk1y6yorNUZWW3X1ehg0aJBbV9dAPamVfpbdu3cXsp33v//9bv1nP/uZ\nfIzKSm2rtbU1/8S6Ce+gAQAAAEBFsEADAAAAgIpggQYAAAAAFcECDQAAAAAqggUaAAAAAFREpbs4\njhw5Ut6mOoP9/u//vltXnZCam5vd+o033ijHVh2tfvKTn7h19TyyOkWmJqvL4eDBg936xo0b3fpt\nt93m1pcuXZp7XioT1VUJvquvvtqtq31h1apVbv3666+XY2R1o8M7qW6bqoutqo8YMcKtZ3XIVMfG\nBx54IPe2Gpnad9S5bfXq1W4961g2derUXNs6dOiQW+/fv78cIzUDBgyQt6lM5syZ49ZVl8w77rjD\nrWed89Vt+/btc+uqU2SjUN0XVX3x4sVu/SMf+YhbP3r0qBxbdWs8ePCgW9+8ebPcFt5r8uTJbv2S\nSy5x66NHj5bbUh0kly1b5tardKzjHTQAAAAAqAgWaAAAAABQESzQAAAAAKAiWKABAAAAQEV0ukAL\nITwUQtgfQmg9pzYshLA4hPByx99Du3eaOB9klQ6ySgdZpYOs0kFWaSCndJBVz3I+XRxbzOyfzezf\nzqnda2ZLY4z3hxDu7fj3XxY9OdV50Ux3X1SdkFauXOnWVXezZ599Vo69bds2t646QGU9j4K1WElZ\n1dIVMe9jXnvtNbeelVWFO2W2WElZZVFdqPJ2WFSd+6ZNmyYfozo/Kmqu3aDFKpaV6r6oOrupro8/\n/elP3brqHGemj3+qO16duzi2WMWyUq/T4cOHu3XVYVHdP2vfVF0ZN2zYkGsMdW7roharWFaKOof/\n4R/+oVu//fbb3XpWZ+oKa7EK5qSOgVdeeaVbV/vVFVdc4dZVlz8z3WVw/fr18jF10mIlZZXV/TCr\ny7dnxowZbl1d6x0+fFhuS3VxVBlmXU/WW6fvoMUYl5nZq+8q32FmD3d8/bCZ3VnwvFADskoHWaWD\nrNJBVukgqzSQUzrIqmep9XfQmmOMezq+3mtm/ttZqAKySgdZpYOs0kFW6SCrNJBTOsgqUV3+oOoY\nYwwhRHV7CGG+mc3v+Lqrw6EL8mSFcrFfpSMrK3KqFrJKB1mlgeuKdJBVWmp9B21fCOFiM7OOv+Uv\n+sQYF8QYZ8UYZ3EgLQVZpYOs0nFeWZFTJeTOqq6zw7nYr9LAuSodZJWoWhdoi8zs7o6v7zazx4qZ\nDroBWaWDrNJBVukgq3SQVRrIKR1klahOf8QxhLDQzG40s6YQwk4z+2szu9/MfhBCuMfMtpvZZ7pz\nkh7VSexf//Vf3Xp7e7tbV13PrrnmGjm26h6kupXVq4tjmVlldenp27evWx8yZIhbv/TSS9360qVL\n3fqaNWtyz0t1kMzbbahWVd2vxo8fn+v+6jWvullldYO76qqr3Pp3v/vdXHMqWlWzymPixIlu/Zvf\n/KZbP378uNyWOjaqLl7qWN0dysoqq5Oiuk11lXv66afd+rXXXuvWx40bJ8dWHSQ3btwoH1MvZWVV\ny/l4yZIlue6vOpp+4xvfkI+ZOXNmrrEb4bpCXTuYmU2aNMmtnz592q0fPXrUratujZs3b5Zjb9my\nxa2r6wc1p6JV9VylrreGDRvm1kePHu3Wb7jhBrf+5JNPyrHVtb/q7qjuX4ZOF2gxxnnippsLngu6\niKzSQVbpIKt0kFU6yCoN5JQOsupZav0RRwAAAABAwVigAQAAAEBFsEADAAAAgIpggQYAAAAAFcEC\nDQAAAAAqotMujmXKaiOrWjdPnz7drT/11FNufcKECW597dq1cuzW1la3rlqOZ7Vg7ilUG9XObvP8\n3//7f3NtJ6sFsmrZ39bWlmtOjU7tV6qNd1NTk1vP2hfI5PypY81nPuN3UFb3Vz70oQ/J29SxUR2T\n9++Xn4vaY2R9fMTYsWPdunq9q48rOHTokFtfvHixHHvatGnyNk/W8+gpVAv8LOpjKtRHvKgxsq5p\n1HmsETJRstrTHzt2zK2rdvqTJ0926+rYuHPnTjm2eszgwYPlYxqZOqapNvuq1f3Xv/51t571kQiv\nvvpqrnqV8A4aAAAAAFQECzQAAAAAqAgWaAAAAABQESzQAAAAAKAiWKABAAAAQEVUuotjFtUNTnV/\n+fSnP+3WVRfHffv25Z6T2lYjdDHLMnLkSLe+Y8cOt75x48Zc28/qnPTyyy+7ddUdqm/fvrnGbhSP\nPPKIW1ddHFV9w4YNcgzV+bGRu5gp27dvd+u//OUv3frAgQPd+ogRI3Ld30x3a1RzagRZ3UnV61rV\nVcezn//857m2Y6b3N7V/NoKsToqTJk1y60uXLnXr6tymXg9qfzPT3aHVGI0gq4ujuu2hhx5y6+r7\nOHr0aLe+a9cuOba6Tli9erV8TE+nrr2zDBkyxK0/++yzbl3tI1mdwg8fPpx7XlXBO2gAAAAAUBEs\n0AAAAACgIligAQAAAEBFsEADAAAAgIpggQYAAAAAFRFijPUbLIQDZvZ2q68mM2vEVlLd9bzHxxh1\ni6icyMrMuud5F5qTGVl1qHxW5GRmHP9SQlbpIKt0kFU6Ss2qrgu0dwwcwnMxxlmlDF6iFJ93inMu\nQorPO8U5FyG1553afIuS4vNOcc5FSPF5pzjnIqT4vFOccxFSfN4pzrkIZT9vfsQRAAAAACqCBRoA\nAAAAVESZC7QFJY5dphSfd4pzLkKKzzvFORchteed2nyLkuLzTnHORUjxeac45yKk+LxTnHMRUnze\nKc65CKU+79J+Bw0AAAAA8E78iCMAAAAAVETdF2ghhFtDCBtDCK+EEO6t9/j1FEJ4KISwP4TQek5t\nWAhhcQjh5Y6/h5Y5xyxkRVZVk3pOZmRFVtVDVukgq3SknlWj5GRWzazqukALIfQ2swfM7GNmdpmZ\nzQshXFbPOdRZi5nd+q7avWa2NMZ4qZkt7fh35ZCVmZFVFbVYojmZkZWRVVW1GFmlosXIKhUtlmhW\nDZaTWQWzqvc7aLPN7JUY45YY4xkz+76Z3VHnOdRNjHGZmb36rvIdZvZwx9cPm9mddZ3U+SMrsqqc\nxHMyIyuyqiCySgdZpSPxrBomJ7NqZlXvBdpoM2s75987O2qNpDnGuKfj671m1lzmZDKQFVmlIpWc\nzMiKrNJBVukgq3SkklWj52RWclY0CSlRfKuFJm00E0BWaSCndJBVOsgqHWSVDrJKRxlZ1XuBtsvM\nxp7z7zEdtUayL4RwsZlZx9/7S56PQlZklYpUcjIjK7JKB1mlg6zSkUpWjZ6TWclZ1XuB9qyZXRpC\nmBhC6GNmf2Bmi+o8h7ItMrO7O76+28weK3EuWciKrFKRSk5mZEVW6SCrdJBVOlLJqtFzMis7qxhj\nXf+Y2cfNbJOZbTaz++o9fp2f60Iz22Nmr9tbP797j5kNt7e6wbxsZkvMbFjZ8yQrskrlT+o5kRVZ\nVfEPWaXzh6zS+ZN6Vo2SU1WzCh0TAwAAAACUrEs/4thIH2KXOrJKB1mlg6zSQVZpIKd0kFU6yCo9\nNb+D1vEhdpvMbK699Xbgs2Y2L8a4LuMxMYRQ03hd1auXvxa94IIL3HrWPNX37H3ve59bP3v2rFtv\nb2+XY+QVYzwYYxzh3ZZaViqT119/Pfe2+vXr59bffPNNt/7GG2+4dfX6MdP5ejreupbf2Fqzyppf\nGdT3pJZ55t1WUVmdPXu20KzK3KeU3r17537MhRde6NZPnTrl1s+cOePW1b5pZnb69Olcc8o6/pnV\nllWuCdRBnz59cj9G7Qsqd/V9V8fFGvX4c5Wqq33HTO8n6jEHDx7sZHbvlef4Z9Y91xVlnavUa15d\nV2TNU13rqWOaGkNdh2Q9Rjl79myPyUod62o5Bqpj18mTJ9262nfz7jtZsrJ6x1y6MMZ/foidmVkI\n4e0PscsKPPOk3J369+/v1ocNG+bWs+apLkTGjBnj1tULYc2aNXKMvNrb27dn3FxTVn379i1sfnkM\nHTrUre/Zs8etZ5k0aZJbP3z4cK66ev2Y5Vton8eFZ+6sevXqlTm/Mpw4ccKt1zLPvNsaMGBA7m15\nziPXXFmVuU8pQ4YMyf2YK6+80q2vX7/erW/bts2tT5gwQY6hHqOcOnUq6/hnVsN+VTWXXHJJ7scM\nHDjQrat9ZOvWrW59//5Cm5cVfq4q67qiqanJrQ8fPtytq33HzKytrc2tX3XVVW79wQcf7GR276Wu\nRZSiryt69eqVuUjtToMGDXLr6roia55qX5wyZUquMY4dOybH2L17t7zNc/z48cKzKmu/GjdunFsf\nP3587m2p/8hYtWqVW1fnxLz7TpaTJ092dr4ys679iCMfYpcOskoHWaWDrNJBVmkgp3SQVTrIKkFd\neQftvIQQ5pvZ/I6vu3s4dMG5WaHa2K/SwD6VDrJKB8e/dJBVOsiqWrqyQDuvD7GLMS4wswVmZr16\n9arcz/U3CLJKR+6sevfuTVbl6DQr9qnKyJVVFX8HrUFwrkoH56p0kFWCuvIjjnyIXTrIKh1klQ6y\nSgdZpYGc0kFW6SCrBNX8DlqM8Y0QwhfN7Ekz621mD8UY1xY2s4KphgKXXnqpW1fNQ8zMrrnmGre+\nc+dOt75y5cpcczIrvMNjUlmpJizK1VdfLW/L2yRk7dr835ZGzkq56aab3PqoUaPkY2bMmOHWv/Wt\nb7n15uZmt571y91qX6xFSlmpX/ZWeUycOFFuS/2CvKqrfWrDhg1yjKKllJVq4FHL633y5Mlufd++\nfbnmNHLkSHlba2trrm1lSSmnLNOmTXPrtTQ5UPnefvvtbn3Rovpcd6eWlTo+TZ06Nfe2Nm7cmGtb\nqkFJlrxNQrJUNSv12lbHQNWIavr06XIMdZ39O7/zO259xAi/ueKyZcvkGLV0VD0fXfodtBjj42b2\neEFzQTciq3SQVTrIKh1klQZySgdZpYOs0lOtD08CAAAAgAbGAg0AAAAAKoIFGgAAAABUBAs0AAAA\nAKiIbv+g6qpQnVxeeuklt37//ffLbakOgKoj5FNPPeXWszpF7tr1no+oaHhDhw516yoPM7OLL744\n12P27Nnj1lUXvEanui0NHDgw97aWLFni1mfOnOnWVYfOpUuX5h67pxsyZIhbV/tU1rHpox/9qFt/\n/vnn3frTTz+da05mZnv37pW39XRqn5ozZ45b//a3vy23pR6jujiqzoBq32wUqttc3u5tWR0D1baG\nDx/u1h988EG3fvLkyVxzahSqk6I6V/3hH/6h3NamTZtybWvevHlufcGCBXKMRtbU1OTWVcfu7du3\ny22pLtsf+9jHcs3pxIkT8rYnn3wy17bOF++gAQAAAEBFsEADAAAAgIpggQYAAAAAFcECDQAAAAAq\nggUaAAAAAFQECzQAAAAAqIge12Y/qz2056677nLrqj2xmdny5cvdumrFq9rkvvLKK53MrjHlbaev\nWq+amc2aNSvXtpRLLrlE3rZ79+5c20qRajE7YsQIt97c3Jx7jA9+8INufeTIkW69tbXVrW/dujX3\n2D3dxIkTc93/z//8z+Vt69evd+unTp1y61deeaVbX716da45NYqbb77ZrauPj1i0aJHc1po1a9y6\naiGu7r927Vo5RiNQ53bVDnzatGm57m9m9k//9E9u/XOf+5xbv+WWW9x61uuhkVvwT5kyxa2r9vs3\n3nij3NaPf/xjt37bbbflmlMjXDtkGT9+vFvPey2ttmOmrw/VGOr8tmPHDjlGd+EdNAAAAACoCBZo\nAAAAAFARLNAAAAAAoCJYoAEAAABARbBAAwAAAICK6HFdHJV+/fq59fb2drc+evRouS3V/UVRY7z/\n/e+Xj1HdtHqS/v3757p/VrdGRXW6Ut2TPvnJT7r1devW5R67J1GdFOfNm+fWJ02a5NZVhzozsy99\n6UtuXXWQnDFjhlvP6mLW0w0ZMsStq2OQ2qeyuj6qDqhbtmxx61dddZVb/+UvfynHaAQDBgxw68eP\nH3frM2fOzD2G6vyo9k8l6/Wwf//+XNtKkep+eO2117r1sWPH5qqbmS1ZssStX3fddW79sccec+uq\ng6SZ2fPPPy9v6ymmTp3q1o8dO+bWVbfGVatWyTFUF1RFdYrctGlTru2kSl0zq3O72t8GDhzo1seN\nGyfH/o//+A+3/tnPftatHzx4UG6r3ngHDQAAAAAqggUaAAAAAFQECzQAAAAAqAgWaAAAAABQEV1q\nEhJC2GZmx8zsTTN7I8Y4q4hJoXhklQ6ySgdZpYOs0kFWaSCndJBVeoro4nhTjLHubU9UB0DVfVF1\nkfmTP/mT3GOrDjOqW4zqCnPq1KncY3dRKVkpeTtr/vrXv3bra9eulWOobanvfd4OdWb6eXRRpbJS\n1L6gujMtX75cbkt1eNy3b59b37p1ayezq5vKZKVei0OHDnXraj9Q3SDNzI4cOZJrbDWG2k4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koHWaWDrNKRSlaNnpNZyVnVe4H2rJldGkKYGELoY2Z/YGaL6jyHsi0ys7s7vr7bzB4rcS5ZyIqs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\nmJnt2bPHr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7vzJlcZAh+3UkdJc3T0JrU0dXxKZR8490Vzs2b/32nnzDXXeRxzfT8gjv9r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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f02e37708d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axarr = plt.subplots(8, 8, figsize=(15, 15))\n",
    "for x in range(8):\n",
    "    for y in range(8):\n",
    "        axarr[x, y].imshow(Y2[0][x * 8 + y].astype(float), cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 16 ms, sys: 8 ms, total: 24 ms\n",
      "Wall time: 14.1 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "Y3 = max_pool_2x2(Y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KeE/09+Vzn/tceMbcuXPDe/Bu0Y8/jY2N4RmzZ88OrV+3bl14hpqtW7eG96xf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\nsDVcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f02e13bbc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axarr = plt.subplots(8, 8, figsize=(15, 15))\n",
    "for x in range(8):\n",
    "    for y in range(8):\n",
    "        axarr[x, y].imshow(Y3[0][x * 8 + y].astype(float), cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 38.9 s, sys: 72 ms, total: 38.9 s\n",
      "Wall time: 38.9 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "Y4 = fc(Y3.reshape((Y3.shape[0], -1)),\n",
    "        qint8_data_map['weights']['fc1'],\n",
    "        qint8_data_map['bias']['fc1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 128 ms, sys: 0 ns, total: 128 ms\n",
      "Wall time: 125 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "Y5 = fc(Y4, qint8_data_map['weights']['fc2'], qint8_data_map['bias']['fc2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0.    10.     0.     0.     7.     0.     0.     0.     8.5    6.75]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(Y5.astype(float))\n",
    "np.argmax(softmax(Y5[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Challenges (No Solution)\n",
    "\n",
    "1. Can you give several reasons why the current layer implementations are quite slow? (hint: consider the nature of Python)\n",
    "2. Can you provide a performance optimised version?\n",
    "3. Can you try to run the inference on the original TensorFlow model and compare the intermediate results with the quantised version?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Quantised CNN for MNIST\n",
    "\n",
    "Maybe you can try to build a quantised MNIST CNN model from the examples given above!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q_mnist(images, data_map, n):\n",
    "    \"\"\"\n",
    "    TODO: implement quantised MNIST CNN model with a given batch of images, an original data_map\n",
    "    and a target number of fractional bits n.\n",
    "    The returned value should be the prediction result (a scalar)\n",
    "    \"\"\"\n",
    "    print('creating quantised images and data ')\n",
    "    q_img = np.array([convert_to_qint8(X, n).reshape(1, 28, 28)\n",
    "                      for X in images])\n",
    "    q_map = create_qint8_data_map(data_map, [n, n, n, n])\n",
    "    print('conv1/pool1')\n",
    "    Y0 = conv2d(q_img, q_map['weights']['conv1'], q_map['bias']['conv1'])\n",
    "    Y1 = max_pool_2x2(Y0)\n",
    "    print('conv2/pool2')\n",
    "    Y2 = conv2d(Y1, q_map['weights']['conv2'], q_map['bias']['conv2'])\n",
    "    Y3 = max_pool_2x2(Y2)\n",
    "    print('fc1/fc2')\n",
    "    Y4 = fc(Y3.reshape((Y3.shape[0], -1)), q_map['weights']['fc1'], q_map['bias']['fc1'])\n",
    "    Y5 = fc(Y4, q_map['weights']['fc2'], q_map['bias']['fc2'])\n",
    "    return [np.argmax(softmax(y)) for y in Y5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "creating quantised images and data \n",
      "conv1/pool1\n",
      "conv2/pool2\n",
      "fc1/fc2\n"
     ]
    }
   ],
   "source": [
    "# If you haven't optimised the performance yet, please just start with one test image \n",
    "q_mnist(mnist.test.images[:1], data_map, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Challenges (No Solution)\n",
    "\n",
    "1. Can you evaluate the accuracy of the quantised model?\n",
    "2. Can you search for a quantised model that has the best accuracy?"
   ]
  }
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