quant_method_explain.ipynb

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    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from math import log, log2, floor\n",
    "from pprint import pprint\n",
    "\n",
    "dat = np.arange(0.0, 1, 0.00001)\n",
    "num_bits = 2.0"
   ]
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  {
   "source": [
    "## Linear quant, linear scale: quantizing the given range linearly"
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def linearQuantMidVal(data, bits, quant_range=(0.0, 1.0)):\n",
    "    base = (quant_range[1] - quant_range[0]) / (2.0**bits)\n",
    "    cutpoints = [quant_range[0]] + [(i+1)*base for i in range(int(2.0**bits))]\n",
    "    offset_val = (cutpoints[0] + cutpoints[1]) / 2\n",
    "    res = np.floor(data / base) * base + offset_val\n",
    "    res[data < cutpoints[1]] = 0.0\n",
    "    return res\n",
    "\n",
    "linear_quant_dat = linearQuantMidVal(dat, num_bits)\n",
    "\n",
    "plt.plot(dat, linear_quant_dat, 'r-')\n",
    "plt.grid(linestyle='--', color='grey', alpha=0.6)\n",
    "# plt.xticks(np.arange(0, 1, step=0.1))\n",
    "# plt.yticks(np.arange(0, 1, step=0.1))\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 1)\n",
    "plt.xlabel('input value')\n",
    "plt.ylabel('quantized value')\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(5, 5)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "source": [
    "## Linear quant, linear scale with pruning"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[0.0, 0.24975, 0.4995, 0.74925, 0.999]\n"
     ]
    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def linearQuantClampedMidVal(att, bits, quant_range=(0.0, 1.0)):\n",
    "    min_val = 1e-3\n",
    "    base = (quant_range[1] - min_val) / (2.0**bits)\n",
    "    cutpoints = [quant_range[0]] + [(i+1)*base for i in range(int(2.0**bits))]\n",
    "    print(cutpoints)\n",
    "    offset_val = (cutpoints[0] + cutpoints[1]) / 2\n",
    "    res = np.floor((att-min_val) / base) * base + offset_val + min_val\n",
    "    res[att < cutpoints[1]+min_val] = 0.0\n",
    "    return res\n",
    "\n",
    "linear_quant_dat = linearQuantClampedMidVal(dat, 2)\n",
    "\n",
    "plt.plot(dat, linear_quant_dat, 'r-')\n",
    "plt.grid(linestyle='--', color='grey', alpha=0.6)\n",
    "# plt.xticks(np.arange(0, 1, step=0.1))\n",
    "# plt.yticks(np.arange(0, 1, step=0.1))\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 1)\n",
    "plt.xlabel('input value')\n",
    "plt.ylabel('quantized value')\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(5, 5)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "source": [
    "## Linear quant log scale: quantizing on log base, the num_bits affects the minimum value"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[1.e-08 1.e-06 1.e-04 1.e-02 1.e+00]\n"
     ]
    },
    {
     "output_type": "display_data",
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am9kETJ89y8ne3tvm/RTz63SrbLmRO8kJ36845z6e3P4NAOfcU4u2+QPgB8657yS3XwU+Rr4hvOica05+3gM86Zz75Ps9Z2trqxscHLy5f5H8iLfffpu77747dIzUUD09uXwZSko4/5u/yYbf/d3QaVLBzAaccx03u38xh4n6gayZbTazEuAhYM+SbfYAjySjiu4HZpxzk865N4GTZvbjyXY/BQwv94QaWuqPzr/4pXr6pUPC8Vi2GTjnrgCPAy+QHwn0Xefcy2b2mJk9lmz2PPAacAz4I+BXFz3EE8BfmNkQ0Ar8x+WeU284fxa+/oofqqcnyS98C4daJLxizhngnHue/Af+4p89s+jvDvjCe+w7CNz0VxcRSTEtbhONKK9A1uRV/jQ0NISOkCqqp19azyAeagYpV1NTEzpCqqieft2plc6iEWUz0NhjfxaGyIkfqqdfb2hxm2hE2QxERGRlRdkMtLiNP+Xl5aEjpIrq6UkymqiktDRwEFkQ5aeuFrfxp7W1NXSEVFE9/br33ntDR5BElM3g3LlzoSOkxr59+0JHSBXV06+xsbHQESQRZTMQf7R4iF+qp19XNdtANNQMREQkzmagscf+7Nq1K3SEVFE9PUm+ETQ3NQUOIguibAYXLlwIHSE1FqYZFj9UT7+mpqZCR5BElM1Ax2X90URgfqmefp3XL37RiLIZiIjIyoqyGaxfvz50hNTYunVr6Aiponr6tWnTptARJBFlM9BhIn98LYkneaqnX1q7JB5RNoOF9Url1i2syyp+qJ6eJKOJpqenAweRBVE2AxERWVlRNoOSkpLQEVKjsbExdIRUUT392lhZGTqCJKJsBplMJnSE1KjUm80r1dMvDRaJR5TNQBed+XP48OHQEVJF9fRrcnIydARJRNkMRERkZUXZDHSYyJ+KiorQEVJF9fQkGU1UVlYWOIgsiLIZ6DiiP9u2bQsdIVVUT7/q6upCR5BElM1Ai9v409vbGzpCqqiefr2u6zaiEWUzEBGRlaVmICIicTYDLW7jT09PT+gIqaJ6+rV58+bQESQRZTPQdQb+DA0NhY6QKqqnJ8loIl1nEI8om4FmLfVnZmYmdIRUUT39unjxYugIkoiyGYjI6uDMQkeQRJTNQNcZ+LN9+/bQEVJF9fTrXl1nEI2imoGZPWBmr5rZMTN78jr3m5l9Lbl/yMzaltyfMbOXzOyvi3k+HSbyR/PF+6V6+qXzg/FYthmYWQb4OvAgkAMeNrPcks0eBLLJn0eBbyy5/0vAK8WG0uI2/pw4cSJ0hFRRPf2aPns2dARJFPPNoBM45px7zTl3CXgW2L1km93At1zei8BGM6sDMLMG4JPAH3vMLSK3s2Q0kcRjbRHb1AMnF90eB7qK2KYemAT+C/DrQPn7PYmZPUr+WwWbNm0qXPbf3NxMeXk5R44cAaCqqopcLsfevXuB/KR2O3fuZHBwsLA+bVtbG1NTU4yPjwOwZcsWSktLGR4eBqC6uppsNsv+/fuB/GI6XV1dDAwMcP78eQA6OjqYmJgoDH3LZrNkMhmOHj0KQG1tLU1NTRw4cADIT7i1Y8cO+vv7CyMkOjs7GRsb49SpUwC0tLQwPz/PyMgIkJ+Xpb6+noMHDwKwYcMG2tvb6evrK3w76u7uZmRkhNOnTwOQy+WYm5vj+PHjADQ0NFBTU8OhQ4cAKC8vp7W1lX379jE/P8/MzAzOOYaHhzlz5gyQX9R9dna2sIRjY2MjlZWVhemZKyoq2LZt249MvdDT08PQ0FBhNM327duZnp4u/Ka8Wl6nmZkZBgYGvL9OALt27Vo1r9OP3XsvteRHE/X29t4276eYX6dbZW6ZDm1mnwI+7pz7fHL7s0Cnc+6JRdt8H3jKObc3uf135BtAHfAJ59yvmtnHgF9zzv3scqE+8pGPuJdeeunm/kXyI86ePcvGjRtDx0gN1dOTc+egvJwLv/M7rP+t3wqdJhXMbMA513Gz+xdzmGgcuG/R7QbgjSK3+Ung58xslPzhpX9uZt9e7gl1Usmfhd8sxA/V0y9ddBaPYppBP5A1s81mVgI8BOxZss0e4JFkVNH9wIxzbtI59xvOuQbnXHOy3/9xzn3G5z9ARERu3bLnDJxzV8zsceAFIAN80zn3spk9ltz/DPA88AngGHAe+KVbCaXFbfypqqoKHSFVVE+/NmzYEDqCJIo5gYxz7nnyH/iLf/bMor874AvLPMYPgB8U83y66MyfXG7pKGC5FaqnJ8m5ytra2sBBZEGUVyBrcRt/FkYfiB+qp1+vv/566AiSiLIZiMgqobmJoqFmkHI6/+KX6unXmjX6CIpFlK+EFrfxZ+fOnaEjpIrq6Vdzc3PoCJKIshksXLUot25wcDB0hFRRPf2amJgIHUESUTaDq1evho6QGr4uVZc81dOTZDTR3Nxc4CCyIMpmICIiKyvKZqALUfxpa2tbfiMpmurpV/199y2/kayIKJvB5cuXQ0dIjampqdARUkX19OucDrtFQ80g5RamHRY/VE+/FqZwlvCibAYiIrKyomwGpaWloSOkxpYtW0JHSBXV05NkNNHdd98dOIgsiLIZmC5R90aN1S/V06+1a4uaK1NWQJTNYGGZO7l1C0sTih+qp19v6oR8NKJsBiIisrKibAb66uhPdXV16Aiponr6decdd4SOIIkom4GOy/qTzWZDR0gV1dMvNdd4RNkM3n333dARUmP//v2hI6SK6ulJMppodGwscBBZEGUzEBGRlRVlM9DQUn9KSkpCR0gV1dMvnR+MR5TN4A6dVPKmq6srdIRUUT39ampqCh1BElE2Ay1u48/AwEDoCKmievp18uTJ0BEkEWUz0OI2/qix+qV6+nXp0qXQESQRZTMQkZRLRhNJPKJsBlrcxp+Ojo7QEVJF9fTrPp0ziEaUzUDrGfijBcf9Uj39mjl7NnQESagZpNzk5GToCKmievr1zjvvhI4giSibgYiIrKwom4HmJvJHc+n4pXr6dc8994SOIIkom4GuQPYnk8mEjpAqqqcnyWiiNWui/AhalYp6JczsATN71cyOmdmT17nfzOxryf1DZtaW/Pw+M/u/ZvaKmb1sZl8q5vm0uI0/R48eDR0hVVRPv05pcZtoLNsMzCwDfB14EMgBD5tZbslmDwLZ5M+jwDeSn18B/p1z7p8A9wNfuM6+IiISWDHfDDqBY86515xzl4Bngd1LttkNfMvlvQhsNLM659ykc+4QgHNuFngFqF/uCTV5lT+1tbWhI6SK6ulXeXl56AiSKKYZ1AOLJxAZ59oP9GW3MbNm4CNA33JPqBPI/mgiML9UT7+qqqpCR5BEMb+CX+9s7tJryd93GzO7E/ge8GXn3HUHFpvZo+QPMXHPPffQ29sLQHNzM+Xl5Rw5cgTI/+fJ5XLs3bsXyJ/Q27lzJ4ODg8zOzgLQ1tbG1NQU4+PjAGzZsoXS0tLCYubV1dVks9nCQiUlJSV0dXUxMDBQmHumo6ODiYmJwrjybDZLJpMpHDOura2lqamJAwcOAFBWVsaOHTvo7+8vnPPo7OxkbGyMU6dOAdDS0sL8/DwjIyMA1NXVUV9fz8GDB4H8ldft7e309fUV5mzp7u5mZGSE06dPA5DL5Zibm+P48eMANDQ0UFNTw6FDh4D8b1qtra3s27eP+fl5RkdH+cxnPsPw8DBnzpwBYOvWrczOzjI6OgpAY2MjlZWVHD58GICKigq2bdtWeA0Aenp6GBoaYmZmBoDt27czPT3NiRMnVtXrNDo6Si6X8/46AezatWvVvE4/dvfd1AIvvfQSF3t7b5v3U8yv060yt8wcIWbWDXzFOffx5PZvADjnnlq0zR8AP3DOfSe5/SrwMefcpJmtA/4aeME595+LCdXS0uJ0os6P3t5eenp6QsdIDdXTk7ffhupqjn/xi2x5+unQaVLBzAacczc9X0oxh4n6gayZbTazEuAhYM+SbfYAjySjiu4HZpJGYMCfAK8U2whAQ0t9KisrCx0hVVRPv9auWxc6giSWPUzknLtiZo8DLwAZ4JvOuZfN7LHk/meA54FPAMeA88AvJbv/JPBZ4IiZDSY/+03n3PPv95xa3MafHTt2hI6QKqqnXzoHE4+ihu0kH97PL/nZM4v+7oAvXGe/vVz/fML7evfdd290F3kP/f39+gDzSPX0a2xsDLWDOER5+d9y5zGkeLqAzy/V068rV66EjiCJKJuBiKScfuGLTpTNQOcM/Ons7AwdIVVUT78adc4gGlE2g7m5udARUmNsbCx0hFRRPf2anp4OHUESUTYDHUf0Z+ECHfFD9fRLi9vEI8pmICIiKyvKZqALe/xpaWkJHSFVVE+/ajdtCh1BElE2Aw0t9WdhPhXxQ/X0JHmPu6tXAweRBVE2A51A9mdhEi/xQ/X0a0qL20QjymYgIquE5iGLRpTNYJ0mr/Kmrq4udIRUUT39qqioCB1BEmoGKVdfv+zCcnIDVE+/1AziEWUzWFgQQ27dwkIf4ofq6dfCYi4SXpTNQERSTiMGoxNlM1izJspYt6UNGzaEjpAqqqdfJSUloSNIIspPXb3h/Glvbw8dIVVUT780UV08omwGWtzGn76+vtARUkX19Ov1118PHUESUTYDXYHsz6VLl0JHSBXV0y9d0R2PKJuBiIisrCibgRa38ae7uzt0hFRRPT1Jvv1v3rw5cBBZEGUz0NxE/mguHb9UT7/eeuut0BEkEWUz0OI2/pw+fTp0hFRRPf06p8Ei0YiyGYiIyMqKshlocRt/crlc6Aiponr6tUmL20QjymagoaX+6PyLX6qnXzokHI8om4HecP4cP348dIRUUT09SX7h0zmYeETZDEREZGVF2Qy0noE/DQ0NoSOkiurp18bKytARJKFmkHI1NTWhI6SK6ulXeXl56AiSiLIZaHEbfw4dOhQ6Qqqonn6dOHkydARJRNkMRERkZa0tZiMzewB4GsgAf+yc++qS+y25/xPAeeAXnXOHitn3erS4jT/6Gu7Rt79N7nvfgz//89BJbn/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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def logQuantMidval(att, bits):\n",
    "    min_val = 1e-8\n",
    "    min_exp = log2(min_val)\n",
    "    base = (0-min_exp) / (2.0**bits)\n",
    "    cutpoints = np.array([0.0] + [(i+1)*base for i in range(int(2.0**bits))])\n",
    "    print(2**(min_exp+cutpoints))\n",
    "    offset_val = (cutpoints[2]-cutpoints[1])/2\n",
    "    res = np.floor((np.log2(att)-min_exp) / base) * base + offset_val + min_exp\n",
    "    res[att < 2**(min_exp + cutpoints[1])] = float('-Inf')\n",
    "    return 2**res\n",
    "\n",
    "log_quant_dat = logQuantMidval(dat, 2)\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlim(1e-8,1)\n",
    "ax.set_xscale('log', basex=10)\n",
    "# ax.set_yscale('log', basey=10)\n",
    "# ax.set_ylim(1e-6, 1)\n",
    "ax.plot(dat, log_quant_dat, 'r-')\n",
    "ax.grid(linestyle='--', color='grey', alpha=0.6)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "source": [
    "## Linear quant log scale with pruning: quantizing only the selecting range evenly on log base."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "<ipython-input-3-0f204339c42b>:8: RuntimeWarning: divide by zero encountered in log2\n  res = np.floor((np.log2(att)-min_exp) / base) * base + offset_val + min_exp\n<ipython-input-3-0f204339c42b>:15: MatplotlibDeprecationWarning: The 'basex' parameter of __init__() has been renamed 'base' since Matplotlib 3.3; support for the old name will be dropped two minor releases later.\n  ax.set_xscale('log', basex=10)\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def clampedLogQuantMidval(att, bits):\n",
    "    min_val = 1e-3\n",
    "    min_exp = log2(min_val)\n",
    "    base = (0-min_exp) / (2.0**bits-1)\n",
    "    cutpoints = np.array([0.0] + [(i+1)*base for i in range(int(2.0**bits-1))])\n",
    "    offset_val = np.array([(i+j)/2 for i, j in zip(cutpoints[0:-1], cutpoints[1:])])\n",
    "    offset_val = (cutpoints[0]+cutpoints[1])/2\n",
    "    res = np.floor((np.log2(att)-min_exp) / base) * base + offset_val + min_exp\n",
    "    res[att < min_val] = float('-Inf')\n",
    "    return 2**res\n",
    "\n",
    "clamped_log_quant_dat = clampedLogQuantMidval(dat, 2)\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlim(0.0001,1)\n",
    "ax.set_xscale('log', basex=10)\n",
    "# ax.set_yscale('log', basey=10)\n",
    "ax.plot(dat, clamped_log_quant_dat, 'r-')\n",
    "ax.grid(linestyle='--', color='grey', alpha=0.6)\n",
    "plt.show()\n",
    "plt.close()\n"
   ]
  },
  {
   "source": [
    "## Binarization"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    " def binQuant(att, bits):\n",
    "     thres = 0.5\n",
    "     res_att = att.copy()\n",
    "     res_att[att <= thres] = 0.0\n",
    "     unpruned_elements = float(np.sum(att > thres))\n",
    "     res_att[att > thres] = 1.0 / unpruned_elements\n",
    "\n",
    "     return res_att\n",
    "\n",
    "bin_quant_dat = binQuant(dat, num_bits)\n",
    "fig, ax = plt.subplots()\n",
    "# ax.set_xscale('log', basex=2)\n",
    "ax.plot(dat, bin_quant_dat, 'r-')\n",
    "ax.grid(linestyle='--', color='grey', alpha=0.6)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "source": [
    "## Uniform quant log scale: uniform quantization on the distribution"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "def uniform_slog_clamped_quant(att, bits):\n",
    "    from math import log\n",
    "    min_val = 0.001\n",
    "\n",
    "    att_std = np.copy(att).astype('float64')\n",
    "    att_std = np.sort(att_std[att_std>min_val])\n",
    "    num_ranks = int(2.0**bits)\n",
    "    log_threshs = [min_val,]\n",
    "\n",
    "    log_steps = np.array([len(att_std)//np.power(2, i) for i in range(1, num_ranks)] + [len(att_std)//np.power(2, num_ranks), ])\n",
    "    log_steps = np.cumsum(log_steps)[:-1]\n",
    "\n",
    "    log_threshs += [ att_std[i] for i in log_steps]\n",
    "\n",
    "    log_steps = np.insert(log_steps, 0, 0.0, axis=0)\n",
    "    # value_clamp_to = [(start+end)/2.0 for start, end in zip(log_threshs[:-1], log_threshs[1:])]\n",
    "    value_clamp_to = []\n",
    "    for start, end in zip(log_steps[:-1], log_steps[1:]):\n",
    "        value_clamp_to.append(np.mean(att_std[start:end]) if start < end else value_clamp_to[-1])\n",
    "\n",
    "    value_clamp_to = np.array(value_clamp_to)\n",
    "    ranking_map = log_threshs[1:]\n",
    "\n",
    "    if np.isnan(value_clamp_to[-1]): \n",
    "        print(\"break here\")\n",
    "\n",
    "    #zero_mask for vals < 1e-3, compare_done_mask for labelling values that are quantized so far.\n",
    "    zero_masks, compare_done_mask = np.ones(att.shape), np.ones(att.shape)\n",
    "    zero_masks[att<min_val] = 0.0\n",
    "    quant_att = np.zeros(att.shape)\n",
    "    for thres, val in zip(ranking_map, value_clamp_to):\n",
    "        quant_att += (att < thres) * val * compare_done_mask\n",
    "        compare_done_mask = att >= thres\n",
    "\n",
    "    quant_att += (att < 1.0) * value_clamp_to[-1] * compare_done_mask \n",
    "    #^this shouldn't ideally affect anything. Comment it.\n",
    "    quant_att = quant_att * zero_masks\n",
    "\n",
    "    return quant_att\n",
    "\n",
    "uniform_quant_dat = uniform_slog_clamped_quant(dat, 2)\n",
    "fig, ax = plt.subplots()\n",
    "# ax.set_xscale('log', basex=10)\n",
    "ax.plot(dat, uniform_quant_dat, 'r-')\n",
    "ax.grid(linestyle='--', color='grey', alpha=0.6)\n",
    "plt.show()\n",
    "plt.close()"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": 3,
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def uniform_slog_quant(att, bits):\n",
    "    from math import log\n",
    "\n",
    "    att_std = np.copy(att).astype('float64')\n",
    "    att_std = np.sort(att_std)\n",
    "    num_ranks = int(2.0**bits)\n",
    "    log_threshs = [0.0,]\n",
    "\n",
    "    log_steps = np.array([len(att_std)//np.power(2, i) for i in range(1, num_ranks+1)] + [len(att_std)//np.power(2, num_ranks), ])\n",
    "    log_steps = np.cumsum(log_steps)[:-1]\n",
    "\n",
    "    log_threshs += [ att_std[i] for i in log_steps]\n",
    "\n",
    "    log_steps = np.insert(log_steps, 0, 0.0, axis=0)\n",
    "    # value_clamp_to = [(start+end)/2.0 for start, end in zip(log_threshs[:-1], log_threshs[1:])]\n",
    "    value_clamp_to = []\n",
    "    for start, end in zip(log_steps[:-1], log_steps[1:]):\n",
    "        value_clamp_to.append(np.mean(att_std[start:end]) if start < end else value_clamp_to[-1])\n",
    "\n",
    "    value_clamp_to = np.array(value_clamp_to)\n",
    "    ranking_map = log_threshs[1:]\n",
    "\n",
    "    if np.isnan(value_clamp_to[-1]): \n",
    "        print(\"break here\")\n",
    "\n",
    "    # fixed ranking position based on histogram\n",
    "    compare_done_mask = np.ones(att.shape)\n",
    "    quant_att = np.zeros(att.shape)\n",
    "    for thres, val in zip(ranking_map, value_clamp_to):\n",
    "        quant_att += (att < thres) * val * compare_done_mask\n",
    "        compare_done_mask = (att >= thres) & (att > 0.0)\n",
    "\n",
    "    quant_att += (att < 1.0) * value_clamp_to[-1] * compare_done_mask \n",
    "\n",
    "    return quant_att\n",
    "\n",
    "uniform_quant_dat = uniform_slog_quant(dat, 2)\n",
    "fig, ax = plt.subplots()\n",
    "# ax.set_xscale('log', basex=10)\n",
    "ax.plot(dat, uniform_quant_dat, 'r-')\n",
    "ax.grid(linestyle='--', color='grey', alpha=0.6)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "source": [
    "## Quant 8"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def quant_8_linear(att, bits, min_val, max_val):\n",
    "    base = (max_val - min_val) / (2**int(bits)-1)\n",
    "    cutpoints = [0.0] + [(i+1)*base for i in range(int(2.0**bits-1))]\n",
    "    res = np.floor((att - min_val) / base) * base + min_val\n",
    "    res[att < (cutpoints[1] + min_val)] = 0\n",
    "    res[att > max_val] = max_val\n",
    "    return res\n",
    "\n",
    "res = quant_8_linear(dat, 2, 0.2, 0.6)\n",
    "fig, ax = plt.subplots()\n",
    "# ax.set_xscale('log', basex=10)\n",
    "ax.plot(dat, res, 'r-')\n",
    "ax.grid(linestyle='--', color='grey', alpha=0.6)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[0.0, 1.3184026700708402, 2.6368053401416804, 3.9552080102125204, 5.273610680283361, 6.592013350354201, 7.910416020425041, 9.228818690495881]\n",
      "[       -inf        -inf        -inf ... -0.73696559 -0.73696559\n",
      " -0.73696559]\n",
      "<ipython-input-26-d7c7121e5e3b>:6: RuntimeWarning: divide by zero encountered in log2\n",
      "  res = np.floor((np.log2(att)-min_exp) / base) * base + min_exp\n",
      "<ipython-input-26-d7c7121e5e3b>:14: MatplotlibDeprecationWarning: The 'basex' parameter of __init__() has been renamed 'base' since Matplotlib 3.3; support for the old name will be dropped two minor releases later.\n",
      "  ax.set_xscale('log', basex=2)\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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xpcWXDrDYosfo7UqfP6PYaYd7fGnxpQP8agkq0gt9+qRHxU473ONLiy8d4ECLHqNXSilVKJFe6BOJd10/pShph3t8afGlAyy26DF6u1ZWVmyPEArtcI8vLb50gF8tQUV6oU9fMKLYaYd7fGnxpQMcaNFj9EoppQol0gt9Y2Oj7RFCoR3u8aXFlw6w2KLH6O2qra21PUIotMM9vrT40gF+tQQV6YU+fXHgYqcd7vGlxZcOcKBFj9ErpZQqlEgv9BUVFbZHCIV2uMeXFl86wGKLHqO3q6ury/YIodAO9/jS4ksH+NUSVKQX+pGREdsjhEI73ONLiy8d4ECLHqO3I5VK2R4hFNrhHl9afOkAv1qCivRCr5RSBefAMXoxlobo7e01x48ft/K504wxiMVvp8KiHe7xpcWXDrDY8s1vwsc/DmNj0Nub992JyLgxJtAdRfoZ/dTUlO0RQqEd7vGlxZcOcKDF9WP0InKfiHxfRM6IyOM3+PgDIjIpIhMiclxEBsMfNXyXL1+2PUIotMM9vrT40gF+tQS1e7sNRCQGPAl8GJgDxkTkWWNM9pfH54FnjTFGRDqArwJthRhYKaWKigPH6HN5Rt8PnDHGvGKMWQWeAR7I3sAY86Z5+2D/DwH2y3LQ3t5ue4RQaId7fGnxpQP8aglq22f0QAPwWtbtOWBg60Yi8tPA7wG1wMdudEcichA4CNDQ0MDw8DAALS0tVFRUcOrUKQCqq6tJJBIcOXIEgFgsxoEDB5iYmGB5eRmA7u5uFhYWmJubA6C1tZXS0tLMcbiamhri8ThHjx4FoKSkhIGBAcbHx7l69SoA9fX1XLp0ifPnzwMQj8eJxWKcPn0agLq6Opqbmzl27BgAZWVl9PX1MTY2xrVr1wDo7+9nZmaGixcvAtDW1kYqlcpciLi+vp6GhgbSP3guLy+np6eH0dFRVldXgY2r009PT2euaZlIJFhZWcmcP7uxsZHa2trMuToqKiro6upiZGSEVCrF0tISH/vYx5iamsp8e9re3s7y8jLJZBKApqYmqqqqOHnyJACVlZV0dHRk9gHA0NAQk5OTLC0tAdDZ2cni4iKzs7O3ZT8tLS1x9913v2s/9fb2Mj8/X1T7aWlpicbGxnfsJ4DBwcGi2k9Hjx6lsrIyp8eT6/vpxIkTVFZWbvt4Cns/xV56iR8D3rxyhR/MzOS9n3bEGHPLN+BB4EtZtx8GvnCL7X8C+Lvt7renp8fYdvjwYdsjhEI73ONLiy8dxlhs+cY3jAFjxsdDuTvguNlmfd36lsuhmzngnqzbjcC5W3zhOAy0ikjNjr7yKKWUT4rkGP0YEBeRvSJSAjwEPJu9gYjsk80XqIpIN1AC/CDsYcPW1NRke4RQaId7fGnxpQP8aglq22P0xph1EXkMeA6IAU8bY14SkUc3P/4U8C+BT4nIGvAW8HOb32I4raqqyvYIodAO9/jS4ksHONDi+uvojTGHjDH3GmNajTGf3fyzpzYXeYwxnzPG/JgxpssYs98Yc6SQQ4cl/YOUYqcd7vGlxZcO8KslqEj/ZqxSShWcAwc3Ir3QV1ZW2h4hFNrhHl9afOkAv1qCivRC39HRYXuEUGiHe3xp8aUDHGhx/Ri9r7J/uaGYaYd7fGnxpQP8agkq0gu9UkoVnB6jV0opVWiRvvCIUkoV3F/+JfzMz8DEBHR25n13euGRgCYnJ22PEArtcI8vLb50gF8tQUV6oU+f/a/YaYd7fGnxpQP8agkq0gu9UkoVnP4w1q7OEI6XuUA73ONLiy8d4ECLvo7ejsXFRdsjhEI73ONLiy8d4FdLUJFe6NNXeil22uEeX1p86QC/WoLK5VKCSilVnA4fhk99CtbW6F9dhZKS2z/DW29t/NfioZtIL/QtLS22RwiFdrjHl5ai75iYgJkZePhh1tbWKL3jDjtzVFVBW5udz03EF/qKigrbI4RCO9zjS0vRd6Rf8fLEE6yLwJ13Wh3Hlkgfo09ffb3YaYd7fGnxpQP8agkq0gu9Uspz6Wf0Fo+PuyDSC311dbXtEUKhHe7xpaXoO7IW+qJvyUOkF/pEImF7hFBoh3t8afGlA/xqCSrSC/2RI0VxDfNtaYd7fGkp+o6sZ/RF35KHSC/0SikVBZFe6GOxmO0RQqEd7vGlpeg7sp7RF31LHvTCI0opf33+8/BrvwbLy2Drl6VCVrALj4jIfSLyfRE5IyKP3+DjPy8ik5tvIyJSFKe8m5iYsD1CKLTDPb60+NIBfrUEte1CLyIx4Engo0AC+ISIbP3x9avAPzHGdAD/FfijsActhOXlZdsjhEI73ONLS9F3ZB26KfqWPOTyjL4fOGOMecUYswo8AzyQvYExZsQYkz4H6HeBxnDHVEoptVO5nOumAXgt6/YcMHCL7X8Z+OsbfUBEDgIHARoaGhgeHgY2TpxUUVGR+RXl6upqEolE5uVQsViMAwcOMDExkfmq3N3dzcLCAnNzcwC0trZSWlrK1NQUADU1NcTjcY4ePQpASUkJAwMDjI+Pc/XqVWDjdbVnzpzh/PnzAMTjcWKxGKdPnwagrq6O5uZmjh07BkBZWRl9fX2MjY1x7do1APr7+5mZmeHixYsAtLW1kUqlmJ6eBqC+vp6GhgbSP48oLy+np6eH0dFRVldXAdi/fz/T09NcunQpM9fKygpnz54FoLGxkdraWk6cOAFsnH+kq6uLkZERUqkUq6urGGOYmpri8uXLALS3t7O8vEwymQSgqamJqqoqTp48CUBlZSUdHR2ZfQAwNDTE5ORk5pJrnZ2dLC4uZk7vWuj9tLq6yujo6Lv2U29vL/Pz80W1n1ZXV5mYmHjHfgIYHBwsqv20urrK8PBwTo8nF/dT4yuvsBc4f+FCpmW7x5Pr+2kntv1hrIg8CHzEGPPpzdsPA/3GmM/cYNsPAX8IDBpjfnCr+3Xhh7Gvvvoqe/futTpDGLTDPb60FH3H5z4Hjz8OV6/y6oULxd2yqVA/jJ0D7sm63Qicu8En7wC+BDyw3SLvivSzl2KnHe7xpcWXDvCrJahcFvoxIC4ie0WkBHgIeDZ7AxFpAr4OPGyMeTn8MZVSagf0pGZADsfojTHrIvIY8BwQA542xrwkIo9ufvwp4DeBu4A/lI1/0PWg31rY0NraanuEUGiHe3xp8aUD/GoJKqcLjxhjDgGHtvzZU1nvfxr4dLijFV5paantEUKhHe7xpaXoO7Ke0Rd9Sx4ifQqE9Cs/ip12uMeXlqLvyFroi74lD5Fe6JVSKgoivdDX1NTYHiEU2uEeX1qKviPrGX3Rt+Qh0gt9PB63PUIotMM9vrT40gF+tQQV6YU+/Vt+xU473ONLS9F3ZD2jL/qWPER6oVdKeU5fRw9EfKEvKSmxPUIotMM9vrT40gF+tQSlFx5RSvnrd34Hfuu3IJWCXX48ry3YhUd8NT4+bnuEUGiHe3xp8aUD/GoJKtILffr0qsVOO9zjS0vRd2Qdoy/6ljxEeqFXSnlOfxgLRHyh7+11/rxrOdEO9/jS4ksH+NUSVKQX+vn5edsjhEI73ONLS9F3ZL3YpOhb8hDphT59ybNipx3u8aXFlw7wqyWoSC/0SinPGRP54/MQ8YXel3NfaId7fGkp+o6shb7oW/IQ6YU+FovZHiEU2uEeX1p86QC/WoKK9EJ/+vRp2yOEQjvc40tL0XdkPaMv+pY8RHqhV0qpKIj0Ql9XV2d7hFBoh3t8aSn6jqxn9EXfkodIL/TNzc22RwiFdrjHl5ai78ha6Iu+JQ+RXuiPHTtme4RQaId7fGnxpQP8agkq0gu9Uspz+jp6IOILfVlZme0RQqEd7vGlxZcO8KslqJwWehG5T0S+LyJnROTxG3y8TUSOisiKiPxq+GMWRl9fn+0RQqEd7vGlpeg7sp7RF31LHrZd6EUkBjwJfBRIAJ8QkcSWzS4D/w74fOgTFtDY2JjtEUKhHe7xpaXoO7IW+qJvyUMuz+j7gTPGmFeMMavAM8AD2RsYYxaMMWPAWgFmLJhr167ZHiEU2uEeX1p86QC/WoLancM2DcBrWbfngIGdfDIROQgcBGhoaGB4eBiAlpYWKioqOHXqFADV1dUkEgmOHDkCbPzq8oEDB5iYmGB5eRmA7u5uFhYWmJubA6C1tZXS0lKmpqYAqKmpIR6Pc/ToUWDjwsADAwOMj49nrjSztrbGmTNnMme1i8fjxGKxzG/Q1dXV0dzcnPlpfVlZGX19fYyNjWX+p+nv72dmZoaLFy8C0NbWRiqVYnp6GoD6+noaGhpIXx+3vLycnp4eRkdHWV1dBWD//v1MT09z6dIlABKJBCsrK5w9exaAxsZGamtrOXHiBAAVFRV0dXUxMjJCKpUimUwyODjI1NQUly9fBqC9vZ3l5WWSySQATU1NVFVVcfLkSQAqKyvp6OjI7AOAoaEhJicnWVpaAqCzs5PFxUVmZ2dvy35KJpM33E+9vb3Mz88X1X5KJpPv2k9A0e2n9Fy5PJ627qe2khLK/uEfMv/mFe99L9XV1cxs3ueePXtobm5mZmaGtbWN54jNLS1cvnyZ5TfeyOxbYwwLCwuZf4/KyspMa0lJCU1NTSSTSdbX1wHYu3cvr7/+Om+++SZ3HTnCnSKcP3cu07Ld48n1/bQT214cXEQeBD5ijPn05u2HgX5jzGdusO1vA28aY7Y9hOPCxcFXVlYoLS21OkMYtMM9vrTk1fHII/DlL4c6z47E4/Dyy97sk51cHDyXZ/RzwD1ZtxuBc0E+iatmZma49957bY+RN+1wjy8teXWsrMD73w/f/W64QwX13vcC/uyTnchloR8D4iKyF5gHHgI+WdCpbpOLFy96seO1wz2+tOTVcf067NkDd98d7lA75Ms+2YltF3pjzLqIPAY8B8SAp40xL4nIo5sff0pEfhg4DrwXuC4ivwIkjDFvFG50pZTTjIFdkf5VHWfk8oweY8wh4NCWP3sq6/0LbBzSKSptbW22RwiFdrjHl5a8Oq5fd+q3Un3ZJzsR6S+36Z+wFzvtcI8vLXl1OPaM3pd9shPu7AUL0i+tK3ba4R5fWvLquH7dqYXel32yE+7sBaWUX/SEYs6I9EJfX19ve4RQaId7fGnJq8OxZ/S+7JOdcGcvWNDQ0GB7hFBoh3t8acmrw7Fn9L7sk52I9EJv+zdzw6Id7vGlJa8Ox57R+7JPdsKdvaCU8otjz+ijLNILfXl5ue0RQqEd7vGlJa8Ox57R+7JPdmLbk5oVigsnNVNKFdBHPgJvvAGbZ7xU4djJSc3c+XJrwejoqO0RQqEd7vGlJa8Ox57R+7JPdsKdvWBB+jzjxU473ONLS14djh2j92Wf7ESkF3qlVAE59ow+yiJ9jH59fZ3du3M6r5vTtMM9vrTk1fGhD20s9i+8EO5QO+TLPinUhUe8NT09zY/+6I/aHiNv2uEe6y0vvggTE3nfzcK5c7zvfe/b2V8+dw52+ncLwPo+sSjSC3362p/FTjvcY73lk5+EzWvq5iPvZXqH1zgtBOv7xKJIL/RKeevKFXjwQfiDP8jrbo4dO0Z/f//O78ChZ/RRFumFPpFI2B4hFNrhHust6+tw553Q3JzX3bTecQfcdVc4M1lmfZ9YFOkfia+srNgeIRTa4R7rLakUxGJ53431jhD51BJUpBf6s2fP2h4hFNrhHust6+sQwitMrHeEyKeWoCK90CvlrZAWeuWHSC/0jY1Fdz3zG9IO91hvCWmht94RIp9agor0l/za2lrbI4RCOxySSsEv/iJNMzOhHCPfsbfeCuXze7FPNvnUElSkn9GfOHHC9gih0A6HXLwIX/kKq2fPbjyrtvX2Ez8B99+fd44X+2STTy1BRfoZvVKhu3oVgNlHHuFHfvd3LQ+j1IacFnoRuQ94AogBXzLG/P6Wj8vmx+8HrgKPGGOc//JZUVFhe4RQaMem2Vn49V8Hmy+je+MNAEruvNPeDCHy5f8t8KslqG1PaiYiMeBl4MPAHDAGfMIYM5W1zf3AZ9hY6AeAJ4wxA7e6XxdOaqZCNDsLX/3qxqlpbRkbg699DRIJu684KS+HP/sz2LvX3gzKW4U6qVk/cMYY88rmJ3kGeACYytrmAeBPzMZXje+KyJ0iUm+MOX/Te331VfjUp4LMGrqF11+n9u67rc4QBic6vvIVu58/7X3v2ziZ1549VscYGRnhgAcL/cjICAcOHLA9Rih8agkql4W+AXgt6/YcG8/at9umAXjHQi8iB4GDAF2xGG/93d8BsGf3bmTXrsyFAWKxGHv27OHatWvpv0dZaSkrq6tcv34dgNLSUlKpFOvr6xv3sWcPIhLoPiqAtViM9VTq7fsAVtfW3r6P3bu5tnkoIH0f11ZWSH8nVFZaytr6OqnN+yjZswcDrG3ex+5YjNju3Znfytu1axelJSXvvI+yMtbW1t6+j5ISjDFv38fu3cRisZvex3vW1zF33PHu+7h+nbXNf5/du3cT27WLlc1/n/R9vLX57wPwnrKyd/4bl5SQun797X/jW+2n+nqWBgb44T/9UyYnJ1leXgagq6uL119/nfn5eQDe//73U1JSwunNE27ddddd7Nu3j9HRUWZnZ9m3bx99fX28+OKLXN083t3d3c25c+e4cOECAPv27WPXrl28/PLLwMarKZqamjh+/DjX9+yhbGKCvr4+xsbGMvu/v7+fmZkZLl68CEBbWxupVIrp6WkA6uvraWhoIP1dZnl5OT09PYyOjmZ69+/fz/T0dObkWIlEgpWVlcwv4jQ2NlJbW8uJEydIJpOUl5fT1dXFyMhIZr8MDg4yNTXF5cuXAWhvb2d5eZlkMglAU1MTVVVVnDx5EoDKyko6OjoYHh7O7KehoSEmJydZWloCoLOzk8XFRWZnZwFoaWmhoqKCU6dOAVBdXU0ikeDIkSOZ/XbgwAEmJiYy+6m7u5uFhQXm5uYAaG1tpbS0lLNnz5JKpaipqSEej3N087KAJSUlDAwMMD4+ntlPvb29zM/Pc/78xsM+Ho8Ti8Uy+7quro7m5maOHTuW+f/+du+nVCr1jv0EG4d0imk/7Ygx5pZvwINsHJdP334Y+MKWbb4FDGbdfh7oudX99vT0GNsOHz5se4RQaId7fGnxpcMYf1qA42abdXvrWy4vr5wD7sm63Qic28E2zhkcHLQ9Qii0wz2+tPjSAX61BJXLQj8GxEVkr4iUAA8Bz27Z5lngU7LhA8CSudXxeUdMTU1tv1ER0A73+NLiSwf41RLUtsfojTHrIvIY8BwbL6982hjzkog8uvnxp4BDbLzi5gwbL6/8xcKNHJ708bdipx3u8aXFlw7wqyWonF6DZow5xMZinv1nT2W9b4B/G+5oSimlwhDpUyC0t7fbHiEU2uEeX1p86QC/WoKK9EKffslSsdMO9/jS4ksH+NUSVKQX+vRrYouddrjHlxZfOsCvlqAivdArpVQUbHuum4J9YpHXgRkrn/xtNcAlyzOEQTvc40uLLx3gT8uPGGMCnaHN2pmfjDHWTzIjIsdNwJMDuUg73ONLiy8d4E+LiAQ+G6QeulFKKc/pQq+UUp6L+kL/R7YHCIl2uMeXFl86wJ+WwB3WfhirlFLq9oj6M3qllPKeLvRKKeU5XeiVUspzkV/oReT9IvI/ReTPN2//CxH5HyLyDRH557bnC+IGLT8kIl/e7Pl52/MFJSJNIvKsiDwtIo/bnicfIrJLRD4rIl8QkX9le558bP5/NS4iP2V7lnwU+WM90GPbu4VeRO4RkX8Qke+JyEsi8u9vtb0x5hVjzC9n3f4rY8y/Bh4Bfq7A495Svi3AzwB/vtnz8YIOm4OgPcC9wLeMMb8EJG7DiDnbQcsDbFxHeY2NK7I5YQcdAP8R+GqhZwtqB48XZx7rN3OLpkCPbWu/GVtA68B/MMacEJEKYFxEvs3GRVN+b8u2v2SMWbjJ/fwX4MkCzpmLfFsagVOb76cKO2pOAvUALwK/ISI/B3zl9o66raAtPwIcNcb8983vuJ6/vePeVNCODmAKKLu9Y+Zkp48XFx7rN3OzpkCPbe8W+s1LGJ7ffH9ZRL4HNBhjvg1s+62miAjw+8BfG2NOFHTYbeTbwsYzx0ZgAge+ewvaIyK/CvyWMebw5uL4v27rwLewg5Y5YHXzpgtfdIEddXwI+CE2vsN6S0QOGWOu386Zb2YHLc481m/mZk0EfGx7t9BnE5EW4MeB0VtscxfwWeDHReQ/AVeAnwQqRWRf9pW0bNphy38DvigiHwO+eTvmzFUuPcDfAL8tIp8EkrdhrB3JseXrwBdEZAg4fDvmCiqXDmPMb2xu+whwyZVFfqsc98lncPCxfjNbmlIEeGx7+wtTInIH8ALwWWPM123Pkw+fWsCvHl9afOkAv1rS8m2y/u18IYjIHuAvgP9d7Dvapxbwq8eXFl86wK+WtDCavHtGv3nc7cvAZWPMr1geJy8+tYBfPb60+NIBfrWkhdXk40I/CAyz8RPp9PHD/2yMOWRvqp3xqQX86vGlxZcO8KslLawm7xZ6pZRS7+TlMXqllFJv04VeKaU8pwu9Ukp5Thd6pZTynC70SinlOV3olVLKc7rQK6WU53ShV0opz+lCr5RSnvv/VFseRCccHbUAAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def quant_8_log(att, bits, min_val, max_val):\n",
    "    min_exp, max_exp = log2(min_val), log2(max_val)\n",
    "    base = (max_exp-min_exp) / (2.0**bits - 1)\n",
    "    cutpoints = [0.0] + [(i+1)*base for i in range(int(2.0**bits-1))]\n",
    "    print(cutpoints)\n",
    "    res = np.floor((np.log2(att)-min_exp) / base) * base + min_exp\n",
    "    res[att < 2**(cutpoints[1]+min_exp)] = float('-Inf')\n",
    "    res[att > max_val] = max_exp\n",
    "    print(res)\n",
    "    return 2**res\n",
    "\n",
    "res = quant_8_log(dat, 3, 0.001, 0.6)\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xscale('log', basex=2)\n",
    "ax.set_xlim(0.0001, 1)\n",
    "ax.plot(dat, res, 'r-')\n",
    "ax.grid(linestyle='--', color='grey', alpha=0.6)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}