kghose/dram-refresh.ipynb

## dram-refresh.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time domain analysis of memory read durations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline \n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import numpy.fft\n",
    "\n",
    "import pandas as pd\n",
    "fname = \"example-data.csv\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(fname, names=[\"timestamp\", \"delta\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time domain analysis\n",
    "Let's just plot interval histograms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 5))\n",
    "ax = plt.subplot(2,2,1)\n",
    "df.hist(\"delta\", bins=201, range=(0, 10000), log=True, ax=ax)\n",
    "ax = plt.subplot(2,2,2)\n",
    "df.hist(\"delta\", bins=101, range=(0, 4000), log=True, ax=ax)\n",
    "ax = plt.subplot(2,2,3)\n",
    "df.hist(\"delta\", bins=101, range=(0, 500), log=True, ax=ax)\n",
    "ax=plt.subplot(2,2,4)\n",
    "_ = df.hist(\"delta\", bins=101, range=(0, 200), log=True, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an inter-event-interval histogram. It is useful to get an idea of the periodicity of the events we are measuring. Note that the y-scale is logarithmic. The initial peak is about eighty times larger than the next largest peak. The four plots zoom in along the interval axis.\n",
    "\n",
    "The vast majority of loops seem to take 167 units of time (see detail plot below). There is some jitter around this, but the next clear cluster is at 350-ish units, possibly 167 * 2 units. But these intervals are far fewer. There are periodic peaks in the histogram, but these are dwarfed by the first peak.\n",
    "\n",
    "I gather that the unit of time is 100ns, making this interval 16,700 ns or 16.7 us"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = df.hist(\"delta\", bins=25, range=(160, 170))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = df.hist(\"delta\", bins=25, range=(160, 400))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frequency domain analysis with gaussian smoothing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23148014"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"timestamp\"].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "point_events = np.zeros(df[\"timestamp\"].max() + 1)\n",
    "point_events[df[\"timestamp\"]] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.plot(point_events[2000:2500])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll create a fairly narrow Gaussian window"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma = 5\n",
    "gx = np.arange(-5*sigma, 5*sigma, 1)\n",
    "gaussian = np.exp(-(gx/sigma)**2/2)\n",
    "_ = plt.plot(gaussian)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gaussian_smoothed = np.convolve(point_events, gaussian, mode=\"full\")\n",
    "_ = plt.plot(gaussian_smoothed[2000:2500])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a lag in the gaussians, but since we are going to do a fourier analysis, it doesn't matter (it's a fixed lag)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23148064"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaussian_smoothed.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It takes too long on my poor laptop to do the FFT of the whole trace, so I just do a part."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "UNIT = 100\n",
    "C = numpy.fft.fft(gaussian_smoothed[:int(1e6)])\n",
    "T = numpy.fft.fftfreq(len(gaussian_smoothed[:int(1e6)])) * (1000000000/UNIT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = T.size\n",
    "off = 1\n",
    "_ = plt.plot(T[:int(l/10)], np.abs(C[:int(l/10)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.plot(T[:int(l/40)], np.abs(C[:int(l/40)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.plot(T[:int(l/100)], np.abs(C[:int(l/100)]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first peak (ignoring the DC component) is 60000 Hz = 1/6e4 = 16.7 us\n",
    "\n",
    "There is some wisdom about the harmonics that I should know but have forgotten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}