Value Tables/make-value-tables.ipynb

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    "<a href=\"https://colab.research.google.com/github/P3109/Public/blob/main/Value%20Tables/make-value-tables.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    "## Value tables of 8-bit floating point formats\n",
    "\n",
    "This code allows the reader to experiment with properties of FP8 formats, and is produced in conjunction with the work of the IEEE P3109 working group on\n",
    "floating point formats for machine learning, although is *not* an official output of that group.\n",
    "\n",
    "The public outputs of of the group are available at https://github.com/P3109/Public and the interim report is at [PDF](https://github.com/P3109/Public/blob/main/Shared%20Reports/P3109%20WG%20Interim%20report.pdf)\n"
   ]
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    "outputId": "a155fc78-0d3a-40a2-ccbe-cf13207a3411"
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     "text": [
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      "Note: you may need to restart the kernel to use updated packages.\n"
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   "source": [
    "%pip install pandas jinja2 airium ipytest gfloat==0.3"
   ]
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  {
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    "id": "eZn-CPStHLCS"
   },
   "source": [
    "## FormatInfo\n",
    "\n",
    "A small dataclass holding format information.  \n",
    "See https://gfloat.readthedocs.io/en/latest/#gfloat.FormatInfo\n"
   ]
  },
  {
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   "id": "5615abc8",
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     "height": 363
    },
    "id": "H35Ojl9gHhUn",
    "outputId": "8d5500e8-c7dc-4c01-801b-799922e3538d"
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    {
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     "text": [
      "name: Short name for the format, e.g. binary32, bfloat16\n",
      "k: Number of bits in the format\n",
      "precision: Number of significand bits (including implicit leading bit encoded by exponent>0)\n",
      "emax: Largest exponent, emax, which shall equal floor(log_2(maxFinite))\n",
      "has_nz: Has negative zero (following e.g. LLVM Float8E5M2FNUZ)\n",
      "has_infs: Set if format includes +/- Infinity\n",
      "num_high_nans: Number of NaNs that are encoded in the highest encodings for each sign\n",
      "has_subnormals: Set if format encodes subnormals\n",
      "is_signed: Set if the format has a sign bit\n",
      "is_twos_complement: Set if the format uses twos complement encoding for the significand\n"
     ]
    },
    {
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       "      <td id=\"T_b33ba_row3_col5\" class=\"data row3 col5\" >0</td>\n",
       "      <td id=\"T_b33ba_row3_col6\" class=\"data row3 col6\" >True</td>\n",
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       "      <td id=\"T_b33ba_row3_col8\" class=\"data row3 col8\" >False</td>\n",
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       "      <td id=\"T_b33ba_row4_col1\" class=\"data row4 col1\" >5</td>\n",
       "      <td id=\"T_b33ba_row4_col2\" class=\"data row4 col2\" >3</td>\n",
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       "      <td id=\"T_b33ba_row6_col2\" class=\"data row6 col2\" >0</td>\n",
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       "    <tr>\n",
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       "      <td id=\"T_b33ba_row10_col3\" class=\"data row10 col3\" >True</td>\n",
       "      <td id=\"T_b33ba_row10_col4\" class=\"data row10 col4\" >True</td>\n",
       "      <td id=\"T_b33ba_row10_col5\" class=\"data row10 col5\" >127</td>\n",
       "      <td id=\"T_b33ba_row10_col6\" class=\"data row10 col6\" >True</td>\n",
       "      <td id=\"T_b33ba_row10_col7\" class=\"data row10 col7\" >True</td>\n",
       "      <td id=\"T_b33ba_row10_col8\" class=\"data row10 col8\" >False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b33ba_level0_row11\" class=\"row_heading level0 row11\" >binary32</th>\n",
       "      <td id=\"T_b33ba_row11_col0\" class=\"data row11 col0\" >32</td>\n",
       "      <td id=\"T_b33ba_row11_col1\" class=\"data row11 col1\" >24</td>\n",
       "      <td id=\"T_b33ba_row11_col2\" class=\"data row11 col2\" >127</td>\n",
       "      <td id=\"T_b33ba_row11_col3\" class=\"data row11 col3\" >True</td>\n",
       "      <td id=\"T_b33ba_row11_col4\" class=\"data row11 col4\" >True</td>\n",
       "      <td id=\"T_b33ba_row11_col5\" class=\"data row11 col5\" >8388607</td>\n",
       "      <td id=\"T_b33ba_row11_col6\" class=\"data row11 col6\" >True</td>\n",
       "      <td id=\"T_b33ba_row11_col7\" class=\"data row11 col7\" >True</td>\n",
       "      <td id=\"T_b33ba_row11_col8\" class=\"data row11 col8\" >False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x7f760e7e10f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas\n",
    "import numpy as np\n",
    "import gfloat\n",
    "from gfloat import FloatClass, FormatInfo, FloatValue, decode_float \n",
    "from gfloat.formats import *\n",
    "\n",
    "def df_left_align(df):\n",
    "  \"\"\"\n",
    "  Left-align dataframe for display\n",
    "  \"\"\"\n",
    "  return df.style.set_table_styles([dict(selector = 'th', props=[('text-align', 'left')])])\n",
    "\n",
    "other_formats = [format_info_ocp_e5m2, format_info_ocp_e4m3]\n",
    "p3109_formats = [format_info_p3109(i) for i in range(1,8)]\n",
    "p3109_and_ocp_formats = p3109_formats + other_formats\n",
    "sub32_formats = p3109_and_ocp_formats + [format_info_binary16, format_info_bfloat16, format_info_binary32]\n",
    "\n",
    "# hacky fix to names - can be removed after https://github.com/graphcore-research/gfloat/pull/22 is released\n",
    "for fi in sub32_formats:\n",
    "  fi.name = fi.name.replace('format_info_','')\n",
    "\n",
    "df = pandas.DataFrame(sub32_formats).set_index('name')\n",
    "\n",
    "\n",
    "print('name: Short name for the format, e.g. binary32, bfloat16')\n",
    "print('k: Number of bits in the format')\n",
    "print('precision: Number of significand bits (including implicit leading bit encoded by exponent>0)')\n",
    "print('emax: Largest exponent, emax, which shall equal floor(log_2(maxFinite))')\n",
    "print('has_nz: Has negative zero (following e.g. LLVM Float8E5M2FNUZ)')\n",
    "print('has_infs: Set if format includes +/- Infinity')\n",
    "print('num_high_nans: Number of NaNs that are encoded in the highest encodings for each sign')\n",
    "print('has_subnormals: Set if format encodes subnormals')\n",
    "print('is_signed: Set if the format has a sign bit')\n",
    "print('is_twos_complement: Set if the format uses two''s complement encoding for the significand')\n",
    "display(df_left_align(df))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "381d6969",
   "metadata": {},
   "source": [
    "## Enumerate all values for a given format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ba3737e1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "code:Integer code point\n",
      "fval:Value (as python float)\n",
      "exp:Raw exponent without bias\n",
      "expval:Exponent, bias subtracted\n",
      "significand:Significand as an integer\n",
      "fsignificand:Significand as a float in the range [0,2)\n",
      "signbit:1 => negative, 0 => positive\n",
      "fclass: ZERO, SUBNORMAL, NORMAL, INFINITE, NAN\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_3a5aa th {\n",
       "  text-align: left;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_3a5aa\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th id=\"T_3a5aa_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_3a5aa_level0_col1\" class=\"col_heading level0 col1\" >fval</th>\n",
       "      <th id=\"T_3a5aa_level0_col2\" class=\"col_heading level0 col2\" >exp</th>\n",
       "      <th id=\"T_3a5aa_level0_col3\" class=\"col_heading level0 col3\" >expval</th>\n",
       "      <th id=\"T_3a5aa_level0_col4\" class=\"col_heading level0 col4\" >significand</th>\n",
       "      <th id=\"T_3a5aa_level0_col5\" class=\"col_heading level0 col5\" >fsignificand</th>\n",
       "      <th id=\"T_3a5aa_level0_col6\" class=\"col_heading level0 col6\" >signbit</th>\n",
       "      <th id=\"T_3a5aa_level0_col7\" class=\"col_heading level0 col7\" >fclass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td id=\"T_3a5aa_row0_col0\" class=\"data row0 col0\" >0</td>\n",
       "      <td id=\"T_3a5aa_row0_col1\" class=\"data row0 col1\" >0.000000</td>\n",
       "      <td id=\"T_3a5aa_row0_col2\" class=\"data row0 col2\" >0</td>\n",
       "      <td id=\"T_3a5aa_row0_col3\" class=\"data row0 col3\" >-15</td>\n",
       "      <td id=\"T_3a5aa_row0_col4\" class=\"data row0 col4\" >0</td>\n",
       "      <td id=\"T_3a5aa_row0_col5\" class=\"data row0 col5\" >0.000000</td>\n",
       "      <td id=\"T_3a5aa_row0_col6\" class=\"data row0 col6\" >0</td>\n",
       "      <td id=\"T_3a5aa_row0_col7\" class=\"data row0 col7\" >FloatClass.ZERO</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_3a5aa_row1_col0\" class=\"data row1 col0\" >1</td>\n",
       "      <td id=\"T_3a5aa_row1_col1\" class=\"data row1 col1\" >0.000008</td>\n",
       "      <td id=\"T_3a5aa_row1_col2\" class=\"data row1 col2\" >0</td>\n",
       "      <td id=\"T_3a5aa_row1_col3\" class=\"data row1 col3\" >-15</td>\n",
       "      <td id=\"T_3a5aa_row1_col4\" class=\"data row1 col4\" >1</td>\n",
       "      <td id=\"T_3a5aa_row1_col5\" class=\"data row1 col5\" >0.250000</td>\n",
       "      <td id=\"T_3a5aa_row1_col6\" class=\"data row1 col6\" >0</td>\n",
       "      <td id=\"T_3a5aa_row1_col7\" class=\"data row1 col7\" >FloatClass.SUBNORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_3a5aa_row2_col0\" class=\"data row2 col0\" >2</td>\n",
       "      <td id=\"T_3a5aa_row2_col1\" class=\"data row2 col1\" >0.000015</td>\n",
       "      <td id=\"T_3a5aa_row2_col2\" class=\"data row2 col2\" >0</td>\n",
       "      <td id=\"T_3a5aa_row2_col3\" class=\"data row2 col3\" >-15</td>\n",
       "      <td id=\"T_3a5aa_row2_col4\" class=\"data row2 col4\" >2</td>\n",
       "      <td id=\"T_3a5aa_row2_col5\" class=\"data row2 col5\" >0.500000</td>\n",
       "      <td id=\"T_3a5aa_row2_col6\" class=\"data row2 col6\" >0</td>\n",
       "      <td id=\"T_3a5aa_row2_col7\" class=\"data row2 col7\" >FloatClass.SUBNORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_3a5aa_row3_col0\" class=\"data row3 col0\" >3</td>\n",
       "      <td id=\"T_3a5aa_row3_col1\" class=\"data row3 col1\" >0.000023</td>\n",
       "      <td id=\"T_3a5aa_row3_col2\" class=\"data row3 col2\" >0</td>\n",
       "      <td id=\"T_3a5aa_row3_col3\" class=\"data row3 col3\" >-15</td>\n",
       "      <td id=\"T_3a5aa_row3_col4\" class=\"data row3 col4\" >3</td>\n",
       "      <td id=\"T_3a5aa_row3_col5\" class=\"data row3 col5\" >0.750000</td>\n",
       "      <td id=\"T_3a5aa_row3_col6\" class=\"data row3 col6\" >0</td>\n",
       "      <td id=\"T_3a5aa_row3_col7\" class=\"data row3 col7\" >FloatClass.SUBNORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_3a5aa_row4_col0\" class=\"data row4 col0\" >4</td>\n",
       "      <td id=\"T_3a5aa_row4_col1\" class=\"data row4 col1\" >0.000031</td>\n",
       "      <td id=\"T_3a5aa_row4_col2\" class=\"data row4 col2\" >1</td>\n",
       "      <td id=\"T_3a5aa_row4_col3\" class=\"data row4 col3\" >-15</td>\n",
       "      <td id=\"T_3a5aa_row4_col4\" class=\"data row4 col4\" >0</td>\n",
       "      <td id=\"T_3a5aa_row4_col5\" class=\"data row4 col5\" >1.000000</td>\n",
       "      <td id=\"T_3a5aa_row4_col6\" class=\"data row4 col6\" >0</td>\n",
       "      <td id=\"T_3a5aa_row4_col7\" class=\"data row4 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_3a5aa_row5_col0\" class=\"data row5 col0\" >5</td>\n",
       "      <td id=\"T_3a5aa_row5_col1\" class=\"data row5 col1\" >0.000038</td>\n",
       "      <td id=\"T_3a5aa_row5_col2\" class=\"data row5 col2\" >1</td>\n",
       "      <td id=\"T_3a5aa_row5_col3\" class=\"data row5 col3\" >-15</td>\n",
       "      <td id=\"T_3a5aa_row5_col4\" class=\"data row5 col4\" >1</td>\n",
       "      <td id=\"T_3a5aa_row5_col5\" class=\"data row5 col5\" >1.250000</td>\n",
       "      <td id=\"T_3a5aa_row5_col6\" class=\"data row5 col6\" >0</td>\n",
       "      <td id=\"T_3a5aa_row5_col7\" class=\"data row5 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_3a5aa_row6_col0\" class=\"data row6 col0\" >6</td>\n",
       "      <td id=\"T_3a5aa_row6_col1\" class=\"data row6 col1\" >0.000046</td>\n",
       "      <td id=\"T_3a5aa_row6_col2\" class=\"data row6 col2\" >1</td>\n",
       "      <td id=\"T_3a5aa_row6_col3\" class=\"data row6 col3\" >-15</td>\n",
       "      <td id=\"T_3a5aa_row6_col4\" class=\"data row6 col4\" >2</td>\n",
       "      <td id=\"T_3a5aa_row6_col5\" class=\"data row6 col5\" >1.500000</td>\n",
       "      <td id=\"T_3a5aa_row6_col6\" class=\"data row6 col6\" >0</td>\n",
       "      <td id=\"T_3a5aa_row6_col7\" class=\"data row6 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_3a5aa_row7_col0\" class=\"data row7 col0\" >7</td>\n",
       "      <td id=\"T_3a5aa_row7_col1\" class=\"data row7 col1\" >0.000053</td>\n",
       "      <td id=\"T_3a5aa_row7_col2\" class=\"data row7 col2\" >1</td>\n",
       "      <td id=\"T_3a5aa_row7_col3\" class=\"data row7 col3\" >-15</td>\n",
       "      <td id=\"T_3a5aa_row7_col4\" class=\"data row7 col4\" >3</td>\n",
       "      <td id=\"T_3a5aa_row7_col5\" class=\"data row7 col5\" >1.750000</td>\n",
       "      <td id=\"T_3a5aa_row7_col6\" class=\"data row7 col6\" >0</td>\n",
       "      <td id=\"T_3a5aa_row7_col7\" class=\"data row7 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x7f75bf821ab0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_67d37 th {\n",
       "  text-align: left;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_67d37\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th id=\"T_67d37_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_67d37_level0_col1\" class=\"col_heading level0 col1\" >fval</th>\n",
       "      <th id=\"T_67d37_level0_col2\" class=\"col_heading level0 col2\" >exp</th>\n",
       "      <th id=\"T_67d37_level0_col3\" class=\"col_heading level0 col3\" >expval</th>\n",
       "      <th id=\"T_67d37_level0_col4\" class=\"col_heading level0 col4\" >significand</th>\n",
       "      <th id=\"T_67d37_level0_col5\" class=\"col_heading level0 col5\" >fsignificand</th>\n",
       "      <th id=\"T_67d37_level0_col6\" class=\"col_heading level0 col6\" >signbit</th>\n",
       "      <th id=\"T_67d37_level0_col7\" class=\"col_heading level0 col7\" >fclass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td id=\"T_67d37_row0_col0\" class=\"data row0 col0\" >124</td>\n",
       "      <td id=\"T_67d37_row0_col1\" class=\"data row0 col1\" >32768.000000</td>\n",
       "      <td id=\"T_67d37_row0_col2\" class=\"data row0 col2\" >31</td>\n",
       "      <td id=\"T_67d37_row0_col3\" class=\"data row0 col3\" >15</td>\n",
       "      <td id=\"T_67d37_row0_col4\" class=\"data row0 col4\" >0</td>\n",
       "      <td id=\"T_67d37_row0_col5\" class=\"data row0 col5\" >1.000000</td>\n",
       "      <td id=\"T_67d37_row0_col6\" class=\"data row0 col6\" >0</td>\n",
       "      <td id=\"T_67d37_row0_col7\" class=\"data row0 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_67d37_row1_col0\" class=\"data row1 col0\" >125</td>\n",
       "      <td id=\"T_67d37_row1_col1\" class=\"data row1 col1\" >40960.000000</td>\n",
       "      <td id=\"T_67d37_row1_col2\" class=\"data row1 col2\" >31</td>\n",
       "      <td id=\"T_67d37_row1_col3\" class=\"data row1 col3\" >15</td>\n",
       "      <td id=\"T_67d37_row1_col4\" class=\"data row1 col4\" >1</td>\n",
       "      <td id=\"T_67d37_row1_col5\" class=\"data row1 col5\" >1.250000</td>\n",
       "      <td id=\"T_67d37_row1_col6\" class=\"data row1 col6\" >0</td>\n",
       "      <td id=\"T_67d37_row1_col7\" class=\"data row1 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_67d37_row2_col0\" class=\"data row2 col0\" >126</td>\n",
       "      <td id=\"T_67d37_row2_col1\" class=\"data row2 col1\" >49152.000000</td>\n",
       "      <td id=\"T_67d37_row2_col2\" class=\"data row2 col2\" >31</td>\n",
       "      <td id=\"T_67d37_row2_col3\" class=\"data row2 col3\" >15</td>\n",
       "      <td id=\"T_67d37_row2_col4\" class=\"data row2 col4\" >2</td>\n",
       "      <td id=\"T_67d37_row2_col5\" class=\"data row2 col5\" >1.500000</td>\n",
       "      <td id=\"T_67d37_row2_col6\" class=\"data row2 col6\" >0</td>\n",
       "      <td id=\"T_67d37_row2_col7\" class=\"data row2 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_67d37_row3_col0\" class=\"data row3 col0\" >127</td>\n",
       "      <td id=\"T_67d37_row3_col1\" class=\"data row3 col1\" >inf</td>\n",
       "      <td id=\"T_67d37_row3_col2\" class=\"data row3 col2\" >31</td>\n",
       "      <td id=\"T_67d37_row3_col3\" class=\"data row3 col3\" >15</td>\n",
       "      <td id=\"T_67d37_row3_col4\" class=\"data row3 col4\" >3</td>\n",
       "      <td id=\"T_67d37_row3_col5\" class=\"data row3 col5\" >1.750000</td>\n",
       "      <td id=\"T_67d37_row3_col6\" class=\"data row3 col6\" >0</td>\n",
       "      <td id=\"T_67d37_row3_col7\" class=\"data row3 col7\" >FloatClass.INFINITE</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_67d37_row4_col0\" class=\"data row4 col0\" >128</td>\n",
       "      <td id=\"T_67d37_row4_col1\" class=\"data row4 col1\" >nan</td>\n",
       "      <td id=\"T_67d37_row4_col2\" class=\"data row4 col2\" >0</td>\n",
       "      <td id=\"T_67d37_row4_col3\" class=\"data row4 col3\" >-15</td>\n",
       "      <td id=\"T_67d37_row4_col4\" class=\"data row4 col4\" >0</td>\n",
       "      <td id=\"T_67d37_row4_col5\" class=\"data row4 col5\" >0.000000</td>\n",
       "      <td id=\"T_67d37_row4_col6\" class=\"data row4 col6\" >1</td>\n",
       "      <td id=\"T_67d37_row4_col7\" class=\"data row4 col7\" >FloatClass.NAN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_67d37_row5_col0\" class=\"data row5 col0\" >129</td>\n",
       "      <td id=\"T_67d37_row5_col1\" class=\"data row5 col1\" >-0.000008</td>\n",
       "      <td id=\"T_67d37_row5_col2\" class=\"data row5 col2\" >0</td>\n",
       "      <td id=\"T_67d37_row5_col3\" class=\"data row5 col3\" >-15</td>\n",
       "      <td id=\"T_67d37_row5_col4\" class=\"data row5 col4\" >1</td>\n",
       "      <td id=\"T_67d37_row5_col5\" class=\"data row5 col5\" >0.250000</td>\n",
       "      <td id=\"T_67d37_row5_col6\" class=\"data row5 col6\" >1</td>\n",
       "      <td id=\"T_67d37_row5_col7\" class=\"data row5 col7\" >FloatClass.SUBNORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_67d37_row6_col0\" class=\"data row6 col0\" >130</td>\n",
       "      <td id=\"T_67d37_row6_col1\" class=\"data row6 col1\" >-0.000015</td>\n",
       "      <td id=\"T_67d37_row6_col2\" class=\"data row6 col2\" >0</td>\n",
       "      <td id=\"T_67d37_row6_col3\" class=\"data row6 col3\" >-15</td>\n",
       "      <td id=\"T_67d37_row6_col4\" class=\"data row6 col4\" >2</td>\n",
       "      <td id=\"T_67d37_row6_col5\" class=\"data row6 col5\" >0.500000</td>\n",
       "      <td id=\"T_67d37_row6_col6\" class=\"data row6 col6\" >1</td>\n",
       "      <td id=\"T_67d37_row6_col7\" class=\"data row6 col7\" >FloatClass.SUBNORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_67d37_row7_col0\" class=\"data row7 col0\" >131</td>\n",
       "      <td id=\"T_67d37_row7_col1\" class=\"data row7 col1\" >-0.000023</td>\n",
       "      <td id=\"T_67d37_row7_col2\" class=\"data row7 col2\" >0</td>\n",
       "      <td id=\"T_67d37_row7_col3\" class=\"data row7 col3\" >-15</td>\n",
       "      <td id=\"T_67d37_row7_col4\" class=\"data row7 col4\" >3</td>\n",
       "      <td id=\"T_67d37_row7_col5\" class=\"data row7 col5\" >0.750000</td>\n",
       "      <td id=\"T_67d37_row7_col6\" class=\"data row7 col6\" >1</td>\n",
       "      <td id=\"T_67d37_row7_col7\" class=\"data row7 col7\" >FloatClass.SUBNORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_67d37_row8_col0\" class=\"data row8 col0\" >132</td>\n",
       "      <td id=\"T_67d37_row8_col1\" class=\"data row8 col1\" >-0.000031</td>\n",
       "      <td id=\"T_67d37_row8_col2\" class=\"data row8 col2\" >1</td>\n",
       "      <td id=\"T_67d37_row8_col3\" class=\"data row8 col3\" >-15</td>\n",
       "      <td id=\"T_67d37_row8_col4\" class=\"data row8 col4\" >0</td>\n",
       "      <td id=\"T_67d37_row8_col5\" class=\"data row8 col5\" >1.000000</td>\n",
       "      <td id=\"T_67d37_row8_col6\" class=\"data row8 col6\" >1</td>\n",
       "      <td id=\"T_67d37_row8_col7\" class=\"data row8 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td class=\"data col0 row_trim\" >...</td>\n",
       "      <td class=\"data col1 row_trim\" >...</td>\n",
       "      <td class=\"data col2 row_trim\" >...</td>\n",
       "      <td class=\"data col3 row_trim\" >...</td>\n",
       "      <td class=\"data col4 row_trim\" >...</td>\n",
       "      <td class=\"data col5 row_trim\" >...</td>\n",
       "      <td class=\"data col6 row_trim\" >...</td>\n",
       "      <td class=\"data col7 row_trim\" >...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x7f75bf821f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
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       "}\n",
       "</style>\n",
       "<table id=\"T_b6e56\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th id=\"T_b6e56_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_b6e56_level0_col1\" class=\"col_heading level0 col1\" >fval</th>\n",
       "      <th id=\"T_b6e56_level0_col2\" class=\"col_heading level0 col2\" >exp</th>\n",
       "      <th id=\"T_b6e56_level0_col3\" class=\"col_heading level0 col3\" >expval</th>\n",
       "      <th id=\"T_b6e56_level0_col4\" class=\"col_heading level0 col4\" >significand</th>\n",
       "      <th id=\"T_b6e56_level0_col5\" class=\"col_heading level0 col5\" >fsignificand</th>\n",
       "      <th id=\"T_b6e56_level0_col6\" class=\"col_heading level0 col6\" >signbit</th>\n",
       "      <th id=\"T_b6e56_level0_col7\" class=\"col_heading level0 col7\" >fclass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td id=\"T_b6e56_row0_col0\" class=\"data row0 col0\" >249</td>\n",
       "      <td id=\"T_b6e56_row0_col1\" class=\"data row0 col1\" >-20480.000000</td>\n",
       "      <td id=\"T_b6e56_row0_col2\" class=\"data row0 col2\" >30</td>\n",
       "      <td id=\"T_b6e56_row0_col3\" class=\"data row0 col3\" >14</td>\n",
       "      <td id=\"T_b6e56_row0_col4\" class=\"data row0 col4\" >1</td>\n",
       "      <td id=\"T_b6e56_row0_col5\" class=\"data row0 col5\" >1.250000</td>\n",
       "      <td id=\"T_b6e56_row0_col6\" class=\"data row0 col6\" >1</td>\n",
       "      <td id=\"T_b6e56_row0_col7\" class=\"data row0 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_b6e56_row1_col0\" class=\"data row1 col0\" >250</td>\n",
       "      <td id=\"T_b6e56_row1_col1\" class=\"data row1 col1\" >-24576.000000</td>\n",
       "      <td id=\"T_b6e56_row1_col2\" class=\"data row1 col2\" >30</td>\n",
       "      <td id=\"T_b6e56_row1_col3\" class=\"data row1 col3\" >14</td>\n",
       "      <td id=\"T_b6e56_row1_col4\" class=\"data row1 col4\" >2</td>\n",
       "      <td id=\"T_b6e56_row1_col5\" class=\"data row1 col5\" >1.500000</td>\n",
       "      <td id=\"T_b6e56_row1_col6\" class=\"data row1 col6\" >1</td>\n",
       "      <td id=\"T_b6e56_row1_col7\" class=\"data row1 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_b6e56_row2_col0\" class=\"data row2 col0\" >251</td>\n",
       "      <td id=\"T_b6e56_row2_col1\" class=\"data row2 col1\" >-28672.000000</td>\n",
       "      <td id=\"T_b6e56_row2_col2\" class=\"data row2 col2\" >30</td>\n",
       "      <td id=\"T_b6e56_row2_col3\" class=\"data row2 col3\" >14</td>\n",
       "      <td id=\"T_b6e56_row2_col4\" class=\"data row2 col4\" >3</td>\n",
       "      <td id=\"T_b6e56_row2_col5\" class=\"data row2 col5\" >1.750000</td>\n",
       "      <td id=\"T_b6e56_row2_col6\" class=\"data row2 col6\" >1</td>\n",
       "      <td id=\"T_b6e56_row2_col7\" class=\"data row2 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_b6e56_row3_col0\" class=\"data row3 col0\" >252</td>\n",
       "      <td id=\"T_b6e56_row3_col1\" class=\"data row3 col1\" >-32768.000000</td>\n",
       "      <td id=\"T_b6e56_row3_col2\" class=\"data row3 col2\" >31</td>\n",
       "      <td id=\"T_b6e56_row3_col3\" class=\"data row3 col3\" >15</td>\n",
       "      <td id=\"T_b6e56_row3_col4\" class=\"data row3 col4\" >0</td>\n",
       "      <td id=\"T_b6e56_row3_col5\" class=\"data row3 col5\" >1.000000</td>\n",
       "      <td id=\"T_b6e56_row3_col6\" class=\"data row3 col6\" >1</td>\n",
       "      <td id=\"T_b6e56_row3_col7\" class=\"data row3 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_b6e56_row4_col0\" class=\"data row4 col0\" >253</td>\n",
       "      <td id=\"T_b6e56_row4_col1\" class=\"data row4 col1\" >-40960.000000</td>\n",
       "      <td id=\"T_b6e56_row4_col2\" class=\"data row4 col2\" >31</td>\n",
       "      <td id=\"T_b6e56_row4_col3\" class=\"data row4 col3\" >15</td>\n",
       "      <td id=\"T_b6e56_row4_col4\" class=\"data row4 col4\" >1</td>\n",
       "      <td id=\"T_b6e56_row4_col5\" class=\"data row4 col5\" >1.250000</td>\n",
       "      <td id=\"T_b6e56_row4_col6\" class=\"data row4 col6\" >1</td>\n",
       "      <td id=\"T_b6e56_row4_col7\" class=\"data row4 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_b6e56_row5_col0\" class=\"data row5 col0\" >254</td>\n",
       "      <td id=\"T_b6e56_row5_col1\" class=\"data row5 col1\" >-49152.000000</td>\n",
       "      <td id=\"T_b6e56_row5_col2\" class=\"data row5 col2\" >31</td>\n",
       "      <td id=\"T_b6e56_row5_col3\" class=\"data row5 col3\" >15</td>\n",
       "      <td id=\"T_b6e56_row5_col4\" class=\"data row5 col4\" >2</td>\n",
       "      <td id=\"T_b6e56_row5_col5\" class=\"data row5 col5\" >1.500000</td>\n",
       "      <td id=\"T_b6e56_row5_col6\" class=\"data row5 col6\" >1</td>\n",
       "      <td id=\"T_b6e56_row5_col7\" class=\"data row5 col7\" >FloatClass.NORMAL</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_b6e56_row6_col0\" class=\"data row6 col0\" >255</td>\n",
       "      <td id=\"T_b6e56_row6_col1\" class=\"data row6 col1\" >-inf</td>\n",
       "      <td id=\"T_b6e56_row6_col2\" class=\"data row6 col2\" >31</td>\n",
       "      <td id=\"T_b6e56_row6_col3\" class=\"data row6 col3\" >15</td>\n",
       "      <td id=\"T_b6e56_row6_col4\" class=\"data row6 col4\" >3</td>\n",
       "      <td id=\"T_b6e56_row6_col5\" class=\"data row6 col5\" >1.750000</td>\n",
       "      <td id=\"T_b6e56_row6_col6\" class=\"data row6 col6\" >1</td>\n",
       "      <td id=\"T_b6e56_row6_col7\" class=\"data row6 col7\" >FloatClass.INFINITE</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x7f75bf821c90>"
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   ],
   "source": [
    "# Get the FormatInfo\n",
    "fi = format_info_p3109(precision=3)\n",
    "\n",
    "# Generate values as a list of FloatValues\n",
    "values = [decode_float(fi, i) for i in range(256)]\n",
    "\n",
    "# Convert to dataframe (and hide the FormatInfo)\n",
    "df_left_align(pandas.DataFrame(values)).hide().hide(subset=[*range(9,120), *range(131,251)])\n",
    "\n",
    "\n",
    "print('code:Integer code point')\n",
    "print('fval:Value (as python float)')\n",
    "print('exp:Raw exponent without bias')\n",
    "print('expval:Exponent, bias subtracted')\n",
    "print('significand:Significand as an integer')\n",
    "print('fsignificand:Significand as a float in the range [0,2)')\n",
    "print('signbit:1 => negative, 0 => positive')\n",
    "print('fclass: ZERO, SUBNORMAL, NORMAL, INFINITE, NAN')\n",
    "\n",
    "\n",
    "with pandas.option_context(\"render.max_rows\", 9):\n",
    "  df = pandas.DataFrame(values)\n",
    "  display(df_left_align(df[0:8]).hide())\n",
    "  display(df_left_align(df[124:134]).hide())\n",
    "  display(df_left_align(df[249:]).hide())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed5b767e",
   "metadata": {},
   "source": [
    "## Collect value statistics for formats\n",
    "\n",
    "Stats collected are:\n",
    " - lt1: Number of values with `0 < x < 1`\n",
    " - gt1: Number of values with `1<=x<Inf`\n",
    " - rt16: Round-trips to IEEE binary16\n",
    " - rt32: Round-trips to IEEE binary32 (True for all current formats, would not be true if emax(8) were 2**(-1/2).\n",
    " - maxNormal: Largest finite normal value, NaN if all finite values are subnormal\n",
    " - minSubnormal: Smallest positive subnormal value, NaN if no finite values are subnormal\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d1e909c7",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 540
    },
    "id": "Klbai4Hi0Pb6",
    "outputId": "ad103803-8eca-48a8-ac15-249ca93d180a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P: Precision\n",
      "E: Exponent field width in bits\n",
      "T: Trailing significand field width in bits\n",
      "lt1: Number of values <code>x</code> such that <code>0 < x < 1</code>\n",
      "ge1: Number of values <code>x</code> such that <code>1 <= x < Inf</code>\n",
      "rt16: Round-trips to IEEE binary16\n",
      "maxFinite: Largest finite value\n",
      "minFinite: Smallest finite value\n",
      "maxNormal: Largest finite normal value, NaN if all finite values are subnormal\n",
      "minNormal: Smallest positive normal value, NaN if all finite values are subnormal\n",
      "minSubnormal: Smallest positive subnormal value, NaN if no finite values are subnormal\n",
      "maxSubnormal: Largest subnormal value, NaN if no finite values are subnormal\n"
     ]
    },
    {
     "data": {
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       "#T_8b636 th {\n",
       "  text-align: left;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_8b636\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th id=\"T_8b636_level0_col0\" class=\"col_heading level0 col0\" >name</th>\n",
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       "      <th id=\"T_8b636_level0_col2\" class=\"col_heading level0 col2\" >E</th>\n",
       "      <th id=\"T_8b636_level0_col3\" class=\"col_heading level0 col3\" >T</th>\n",
       "      <th id=\"T_8b636_level0_col4\" class=\"col_heading level0 col4\" >lt1</th>\n",
       "      <th id=\"T_8b636_level0_col5\" class=\"col_heading level0 col5\" >ge1</th>\n",
       "      <th id=\"T_8b636_level0_col6\" class=\"col_heading level0 col6\" >rt16</th>\n",
       "      <th id=\"T_8b636_level0_col7\" class=\"col_heading level0 col7\" >maxFinite</th>\n",
       "      <th id=\"T_8b636_level0_col8\" class=\"col_heading level0 col8\" >minFinite</th>\n",
       "      <th id=\"T_8b636_level0_col9\" class=\"col_heading level0 col9\" >maxNormal</th>\n",
       "      <th id=\"T_8b636_level0_col10\" class=\"col_heading level0 col10\" >minNormal</th>\n",
       "      <th id=\"T_8b636_level0_col11\" class=\"col_heading level0 col11\" >minSubnormal</th>\n",
       "      <th id=\"T_8b636_level0_col12\" class=\"col_heading level0 col12\" >maxSubnormal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td id=\"T_8b636_row0_col0\" class=\"data row0 col0\" >p3109_p1</td>\n",
       "      <td id=\"T_8b636_row0_col1\" class=\"data row0 col1\" >1</td>\n",
       "      <td id=\"T_8b636_row0_col2\" class=\"data row0 col2\" >7</td>\n",
       "      <td id=\"T_8b636_row0_col3\" class=\"data row0 col3\" >0</td>\n",
       "      <td id=\"T_8b636_row0_col4\" class=\"data row0 col4\" >62</td>\n",
       "      <td id=\"T_8b636_row0_col5\" class=\"data row0 col5\" >64</td>\n",
       "      <td id=\"T_8b636_row0_col6\" class=\"data row0 col6\" >False</td>\n",
       "      <td id=\"T_8b636_row0_col7\" class=\"data row0 col7\" >9223372036854775808.000000</td>\n",
       "      <td id=\"T_8b636_row0_col8\" class=\"data row0 col8\" >-9223372036854775808.000000</td>\n",
       "      <td id=\"T_8b636_row0_col9\" class=\"data row0 col9\" >9223372036854775808.000000</td>\n",
       "      <td id=\"T_8b636_row0_col10\" class=\"data row0 col10\" >0.000000</td>\n",
       "      <td id=\"T_8b636_row0_col11\" class=\"data row0 col11\" >nan</td>\n",
       "      <td id=\"T_8b636_row0_col12\" class=\"data row0 col12\" >nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_8b636_row1_col0\" class=\"data row1 col0\" >p3109_p2</td>\n",
       "      <td id=\"T_8b636_row1_col1\" class=\"data row1 col1\" >2</td>\n",
       "      <td id=\"T_8b636_row1_col2\" class=\"data row1 col2\" >6</td>\n",
       "      <td id=\"T_8b636_row1_col3\" class=\"data row1 col3\" >1</td>\n",
       "      <td id=\"T_8b636_row1_col4\" class=\"data row1 col4\" >63</td>\n",
       "      <td id=\"T_8b636_row1_col5\" class=\"data row1 col5\" >63</td>\n",
       "      <td id=\"T_8b636_row1_col6\" class=\"data row1 col6\" >False</td>\n",
       "      <td id=\"T_8b636_row1_col7\" class=\"data row1 col7\" >2147483648.000000</td>\n",
       "      <td id=\"T_8b636_row1_col8\" class=\"data row1 col8\" >-2147483648.000000</td>\n",
       "      <td id=\"T_8b636_row1_col9\" class=\"data row1 col9\" >2147483648.000000</td>\n",
       "      <td id=\"T_8b636_row1_col10\" class=\"data row1 col10\" >0.000000</td>\n",
       "      <td id=\"T_8b636_row1_col11\" class=\"data row1 col11\" >0.000000</td>\n",
       "      <td id=\"T_8b636_row1_col12\" class=\"data row1 col12\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_8b636_row2_col0\" class=\"data row2 col0\" >p3109_p3</td>\n",
       "      <td id=\"T_8b636_row2_col1\" class=\"data row2 col1\" >3</td>\n",
       "      <td id=\"T_8b636_row2_col2\" class=\"data row2 col2\" >5</td>\n",
       "      <td id=\"T_8b636_row2_col3\" class=\"data row2 col3\" >2</td>\n",
       "      <td id=\"T_8b636_row2_col4\" class=\"data row2 col4\" >63</td>\n",
       "      <td id=\"T_8b636_row2_col5\" class=\"data row2 col5\" >63</td>\n",
       "      <td id=\"T_8b636_row2_col6\" class=\"data row2 col6\" >True</td>\n",
       "      <td id=\"T_8b636_row2_col7\" class=\"data row2 col7\" >49152.000000</td>\n",
       "      <td id=\"T_8b636_row2_col8\" class=\"data row2 col8\" >-49152.000000</td>\n",
       "      <td id=\"T_8b636_row2_col9\" class=\"data row2 col9\" >49152.000000</td>\n",
       "      <td id=\"T_8b636_row2_col10\" class=\"data row2 col10\" >0.000031</td>\n",
       "      <td id=\"T_8b636_row2_col11\" class=\"data row2 col11\" >0.000008</td>\n",
       "      <td id=\"T_8b636_row2_col12\" class=\"data row2 col12\" >0.000023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_8b636_row3_col0\" class=\"data row3 col0\" >p3109_p4</td>\n",
       "      <td id=\"T_8b636_row3_col1\" class=\"data row3 col1\" >4</td>\n",
       "      <td id=\"T_8b636_row3_col2\" class=\"data row3 col2\" >4</td>\n",
       "      <td id=\"T_8b636_row3_col3\" class=\"data row3 col3\" >3</td>\n",
       "      <td id=\"T_8b636_row3_col4\" class=\"data row3 col4\" >63</td>\n",
       "      <td id=\"T_8b636_row3_col5\" class=\"data row3 col5\" >63</td>\n",
       "      <td id=\"T_8b636_row3_col6\" class=\"data row3 col6\" >True</td>\n",
       "      <td id=\"T_8b636_row3_col7\" class=\"data row3 col7\" >224.000000</td>\n",
       "      <td id=\"T_8b636_row3_col8\" class=\"data row3 col8\" >-224.000000</td>\n",
       "      <td id=\"T_8b636_row3_col9\" class=\"data row3 col9\" >224.000000</td>\n",
       "      <td id=\"T_8b636_row3_col10\" class=\"data row3 col10\" >0.007812</td>\n",
       "      <td id=\"T_8b636_row3_col11\" class=\"data row3 col11\" >0.000977</td>\n",
       "      <td id=\"T_8b636_row3_col12\" class=\"data row3 col12\" >0.006836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_8b636_row4_col0\" class=\"data row4 col0\" >p3109_p5</td>\n",
       "      <td id=\"T_8b636_row4_col1\" class=\"data row4 col1\" >5</td>\n",
       "      <td id=\"T_8b636_row4_col2\" class=\"data row4 col2\" >3</td>\n",
       "      <td id=\"T_8b636_row4_col3\" class=\"data row4 col3\" >4</td>\n",
       "      <td id=\"T_8b636_row4_col4\" class=\"data row4 col4\" >63</td>\n",
       "      <td id=\"T_8b636_row4_col5\" class=\"data row4 col5\" >63</td>\n",
       "      <td id=\"T_8b636_row4_col6\" class=\"data row4 col6\" >True</td>\n",
       "      <td id=\"T_8b636_row4_col7\" class=\"data row4 col7\" >15.000000</td>\n",
       "      <td id=\"T_8b636_row4_col8\" class=\"data row4 col8\" >-15.000000</td>\n",
       "      <td id=\"T_8b636_row4_col9\" class=\"data row4 col9\" >15.000000</td>\n",
       "      <td id=\"T_8b636_row4_col10\" class=\"data row4 col10\" >0.125000</td>\n",
       "      <td id=\"T_8b636_row4_col11\" class=\"data row4 col11\" >0.007812</td>\n",
       "      <td id=\"T_8b636_row4_col12\" class=\"data row4 col12\" >0.117188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_8b636_row5_col0\" class=\"data row5 col0\" >p3109_p6</td>\n",
       "      <td id=\"T_8b636_row5_col1\" class=\"data row5 col1\" >6</td>\n",
       "      <td id=\"T_8b636_row5_col2\" class=\"data row5 col2\" >2</td>\n",
       "      <td id=\"T_8b636_row5_col3\" class=\"data row5 col3\" >5</td>\n",
       "      <td id=\"T_8b636_row5_col4\" class=\"data row5 col4\" >63</td>\n",
       "      <td id=\"T_8b636_row5_col5\" class=\"data row5 col5\" >63</td>\n",
       "      <td id=\"T_8b636_row5_col6\" class=\"data row5 col6\" >True</td>\n",
       "      <td id=\"T_8b636_row5_col7\" class=\"data row5 col7\" >3.875000</td>\n",
       "      <td id=\"T_8b636_row5_col8\" class=\"data row5 col8\" >-3.875000</td>\n",
       "      <td id=\"T_8b636_row5_col9\" class=\"data row5 col9\" >3.875000</td>\n",
       "      <td id=\"T_8b636_row5_col10\" class=\"data row5 col10\" >0.500000</td>\n",
       "      <td id=\"T_8b636_row5_col11\" class=\"data row5 col11\" >0.015625</td>\n",
       "      <td id=\"T_8b636_row5_col12\" class=\"data row5 col12\" >0.484375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_8b636_row6_col0\" class=\"data row6 col0\" >p3109_p7</td>\n",
       "      <td id=\"T_8b636_row6_col1\" class=\"data row6 col1\" >7</td>\n",
       "      <td id=\"T_8b636_row6_col2\" class=\"data row6 col2\" >1</td>\n",
       "      <td id=\"T_8b636_row6_col3\" class=\"data row6 col3\" >6</td>\n",
       "      <td id=\"T_8b636_row6_col4\" class=\"data row6 col4\" >63</td>\n",
       "      <td id=\"T_8b636_row6_col5\" class=\"data row6 col5\" >63</td>\n",
       "      <td id=\"T_8b636_row6_col6\" class=\"data row6 col6\" >True</td>\n",
       "      <td id=\"T_8b636_row6_col7\" class=\"data row6 col7\" >1.968750</td>\n",
       "      <td id=\"T_8b636_row6_col8\" class=\"data row6 col8\" >-1.968750</td>\n",
       "      <td id=\"T_8b636_row6_col9\" class=\"data row6 col9\" >1.968750</td>\n",
       "      <td id=\"T_8b636_row6_col10\" class=\"data row6 col10\" >1.000000</td>\n",
       "      <td id=\"T_8b636_row6_col11\" class=\"data row6 col11\" >0.015625</td>\n",
       "      <td id=\"T_8b636_row6_col12\" class=\"data row6 col12\" >0.984375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_8b636_row7_col0\" class=\"data row7 col0\" >ocp_e5m2</td>\n",
       "      <td id=\"T_8b636_row7_col1\" class=\"data row7 col1\" >3</td>\n",
       "      <td id=\"T_8b636_row7_col2\" class=\"data row7 col2\" >5</td>\n",
       "      <td id=\"T_8b636_row7_col3\" class=\"data row7 col3\" >2</td>\n",
       "      <td id=\"T_8b636_row7_col4\" class=\"data row7 col4\" >59</td>\n",
       "      <td id=\"T_8b636_row7_col5\" class=\"data row7 col5\" >64</td>\n",
       "      <td id=\"T_8b636_row7_col6\" class=\"data row7 col6\" >True</td>\n",
       "      <td id=\"T_8b636_row7_col7\" class=\"data row7 col7\" >57344.000000</td>\n",
       "      <td id=\"T_8b636_row7_col8\" class=\"data row7 col8\" >-57344.000000</td>\n",
       "      <td id=\"T_8b636_row7_col9\" class=\"data row7 col9\" >57344.000000</td>\n",
       "      <td id=\"T_8b636_row7_col10\" class=\"data row7 col10\" >0.000061</td>\n",
       "      <td id=\"T_8b636_row7_col11\" class=\"data row7 col11\" >0.000015</td>\n",
       "      <td id=\"T_8b636_row7_col12\" class=\"data row7 col12\" >0.000046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_8b636_row8_col0\" class=\"data row8 col0\" >ocp_e4m3</td>\n",
       "      <td id=\"T_8b636_row8_col1\" class=\"data row8 col1\" >4</td>\n",
       "      <td id=\"T_8b636_row8_col2\" class=\"data row8 col2\" >4</td>\n",
       "      <td id=\"T_8b636_row8_col3\" class=\"data row8 col3\" >3</td>\n",
       "      <td id=\"T_8b636_row8_col4\" class=\"data row8 col4\" >55</td>\n",
       "      <td id=\"T_8b636_row8_col5\" class=\"data row8 col5\" >71</td>\n",
       "      <td id=\"T_8b636_row8_col6\" class=\"data row8 col6\" >True</td>\n",
       "      <td id=\"T_8b636_row8_col7\" class=\"data row8 col7\" >448.000000</td>\n",
       "      <td id=\"T_8b636_row8_col8\" class=\"data row8 col8\" >-448.000000</td>\n",
       "      <td id=\"T_8b636_row8_col9\" class=\"data row8 col9\" >448.000000</td>\n",
       "      <td id=\"T_8b636_row8_col10\" class=\"data row8 col10\" >0.015625</td>\n",
       "      <td id=\"T_8b636_row8_col11\" class=\"data row8 col11\" >0.001953</td>\n",
       "      <td id=\"T_8b636_row8_col12\" class=\"data row8 col12\" >0.013672</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x7f760fe074c0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "def collect_stats(fi : FormatInfo):\n",
    "  # Generate all values\n",
    "  values = [decode_float(fi, i) for i in range(256)]\n",
    "  df = pandas.DataFrame(values)\n",
    "  \n",
    "  # Extract format information parameters\n",
    "  E=fi.expBits\n",
    "  S=fi.tSignificandBits\n",
    "\n",
    "  # Compute statistics: lt1,ge1\n",
    "  fval = df['fval']\n",
    "  total_01 = fval.between(0, 1, inclusive='neither').sum()\n",
    "  total_1Inf = fval.between(1, np.inf, inclusive='left').sum()\n",
    "\n",
    "  # Compute statistics: maxFinite,minFinite\n",
    "  finite_vals = fval[np.isfinite(fval)]\n",
    "  maxFinite = finite_vals.loc[finite_vals.idxmax()]\n",
    "  minFinite = finite_vals.loc[finite_vals.idxmin()]\n",
    "\n",
    "  # Compute statistics: maxNormal,minNormal\n",
    "  normal_vals = fval[(df['fclass'] == FloatClass.NORMAL) & (fval>0)]\n",
    "  maxNormal = normal_vals.loc[normal_vals.idxmax()] if normal_vals.any() else np.nan\n",
    "  minNormal = normal_vals.loc[normal_vals.idxmin()] if normal_vals.any() else np.nan\n",
    "\n",
    "  # Compute statistics: minSubnormal\n",
    "  pos_subnormal = fval[(df['fclass'] == FloatClass.SUBNORMAL) & (fval>0)]\n",
    "  maxSubnormal = pos_subnormal.loc[pos_subnormal.idxmax()] if pos_subnormal.any() else np.nan\n",
    "  minSubnormal = pos_subnormal.loc[pos_subnormal.idxmin()] if pos_subnormal.any() else np.nan\n",
    "\n",
    "  # Compute roundtrips: rt16, rt32\n",
    "  with np.errstate(over='ignore'):\n",
    "    rt16 = (np.float64(np.float16(fval)) == np.float64(fval)) | ~np.isfinite(fval)\n",
    "    rt32 = (np.float64(np.float32(fval)) == np.float64(fval)) | ~np.isfinite(fval)\n",
    "\n",
    "  rt16 = rt16.all()\n",
    "  rt32 = rt32.all()\n",
    "  assert rt32 # If not, we should include rt32 in the table\n",
    "  \n",
    "  # Assemble tuple\n",
    "  return dict(name=fi.name,P=fi.precision,E=E,T=S,\n",
    "            lt1=total_01,ge1=total_1Inf,\n",
    "            rt16=rt16,\n",
    "            maxFinite=maxFinite,minFinite=minFinite,\n",
    "            maxNormal=maxNormal,minNormal=minNormal,\n",
    "            minSubnormal=minSubnormal,maxSubnormal=maxSubnormal)\n",
    "\n",
    "print('P: Precision')\n",
    "print('E: Exponent field width in bits')\n",
    "print('T: Trailing significand field width in bits')\n",
    "print('lt1: Number of values <code>x</code> such that <code>0 < x < 1</code>')\n",
    "print('ge1: Number of values <code>x</code> such that <code>1 <= x < Inf</code>')\n",
    "print('rt16: Round-trips to IEEE binary16')\n",
    "print('maxFinite: Largest finite value')\n",
    "print('minFinite: Smallest finite value')\n",
    "print('maxNormal: Largest finite normal value, NaN if all finite values are subnormal')\n",
    "print('minNormal: Smallest positive normal value, NaN if all finite values are subnormal')\n",
    "print('minSubnormal: Smallest positive subnormal value, NaN if no finite values are subnormal')\n",
    "print('maxSubnormal: Largest subnormal value, NaN if no finite values are subnormal')\n",
    "\n",
    "stats = [collect_stats(fi) for fi in p3109_and_ocp_formats]\n",
    "df = pandas.DataFrame(stats)\n",
    "df_left_align(df).hide()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59de1636",
   "metadata": {},
   "source": [
    "## Value statistics as exact fractions * 2^e\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1d4d7737",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 540
    },
    "id": "-xdGU0pInm0d",
    "outputId": "1dc03db2-a5b4-4565-c95b-6d81d86eec81"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_d53c2 th {\n",
       "  text-align: left;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_d53c2\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th id=\"T_d53c2_level0_col0\" class=\"col_heading level0 col0\" >name</th>\n",
       "      <th id=\"T_d53c2_level0_col1\" class=\"col_heading level0 col1\" >P</th>\n",
       "      <th id=\"T_d53c2_level0_col2\" class=\"col_heading level0 col2\" >E</th>\n",
       "      <th id=\"T_d53c2_level0_col3\" class=\"col_heading level0 col3\" >T</th>\n",
       "      <th id=\"T_d53c2_level0_col4\" class=\"col_heading level0 col4\" >lt1</th>\n",
       "      <th id=\"T_d53c2_level0_col5\" class=\"col_heading level0 col5\" >ge1</th>\n",
       "      <th id=\"T_d53c2_level0_col6\" class=\"col_heading level0 col6\" >rt16</th>\n",
       "      <th id=\"T_d53c2_level0_col7\" class=\"col_heading level0 col7\" >maxFinite</th>\n",
       "      <th id=\"T_d53c2_level0_col8\" class=\"col_heading level0 col8\" >minFinite</th>\n",
       "      <th id=\"T_d53c2_level0_col9\" class=\"col_heading level0 col9\" >maxNormal</th>\n",
       "      <th id=\"T_d53c2_level0_col10\" class=\"col_heading level0 col10\" >minNormal</th>\n",
       "      <th id=\"T_d53c2_level0_col11\" class=\"col_heading level0 col11\" >minSubnormal</th>\n",
       "      <th id=\"T_d53c2_level0_col12\" class=\"col_heading level0 col12\" >maxSubnormal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td id=\"T_d53c2_row0_col0\" class=\"data row0 col0\" >p3109_p1</td>\n",
       "      <td id=\"T_d53c2_row0_col1\" class=\"data row0 col1\" >1</td>\n",
       "      <td id=\"T_d53c2_row0_col2\" class=\"data row0 col2\" >7</td>\n",
       "      <td id=\"T_d53c2_row0_col3\" class=\"data row0 col3\" >0</td>\n",
       "      <td id=\"T_d53c2_row0_col4\" class=\"data row0 col4\" >62</td>\n",
       "      <td id=\"T_d53c2_row0_col5\" class=\"data row0 col5\" >64</td>\n",
       "      <td id=\"T_d53c2_row0_col6\" class=\"data row0 col6\" >False</td>\n",
       "      <td id=\"T_d53c2_row0_col7\" class=\"data row0 col7\" >1*2^63</td>\n",
       "      <td id=\"T_d53c2_row0_col8\" class=\"data row0 col8\" >-1*2^63</td>\n",
       "      <td id=\"T_d53c2_row0_col9\" class=\"data row0 col9\" >1*2^63</td>\n",
       "      <td id=\"T_d53c2_row0_col10\" class=\"data row0 col10\" >1*2^-62</td>\n",
       "      <td id=\"T_d53c2_row0_col11\" class=\"data row0 col11\" >nan</td>\n",
       "      <td id=\"T_d53c2_row0_col12\" class=\"data row0 col12\" >nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_d53c2_row1_col0\" class=\"data row1 col0\" >p3109_p2</td>\n",
       "      <td id=\"T_d53c2_row1_col1\" class=\"data row1 col1\" >2</td>\n",
       "      <td id=\"T_d53c2_row1_col2\" class=\"data row1 col2\" >6</td>\n",
       "      <td id=\"T_d53c2_row1_col3\" class=\"data row1 col3\" >1</td>\n",
       "      <td id=\"T_d53c2_row1_col4\" class=\"data row1 col4\" >63</td>\n",
       "      <td id=\"T_d53c2_row1_col5\" class=\"data row1 col5\" >63</td>\n",
       "      <td id=\"T_d53c2_row1_col6\" class=\"data row1 col6\" >False</td>\n",
       "      <td id=\"T_d53c2_row1_col7\" class=\"data row1 col7\" >1*2^31</td>\n",
       "      <td id=\"T_d53c2_row1_col8\" class=\"data row1 col8\" >-1*2^31</td>\n",
       "      <td id=\"T_d53c2_row1_col9\" class=\"data row1 col9\" >1*2^31</td>\n",
       "      <td id=\"T_d53c2_row1_col10\" class=\"data row1 col10\" >1*2^-31</td>\n",
       "      <td id=\"T_d53c2_row1_col11\" class=\"data row1 col11\" >1*2^-32</td>\n",
       "      <td id=\"T_d53c2_row1_col12\" class=\"data row1 col12\" >1*2^-32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_d53c2_row2_col0\" class=\"data row2 col0\" >p3109_p3</td>\n",
       "      <td id=\"T_d53c2_row2_col1\" class=\"data row2 col1\" >3</td>\n",
       "      <td id=\"T_d53c2_row2_col2\" class=\"data row2 col2\" >5</td>\n",
       "      <td id=\"T_d53c2_row2_col3\" class=\"data row2 col3\" >2</td>\n",
       "      <td id=\"T_d53c2_row2_col4\" class=\"data row2 col4\" >63</td>\n",
       "      <td id=\"T_d53c2_row2_col5\" class=\"data row2 col5\" >63</td>\n",
       "      <td id=\"T_d53c2_row2_col6\" class=\"data row2 col6\" >True</td>\n",
       "      <td id=\"T_d53c2_row2_col7\" class=\"data row2 col7\" >3/2*2^15</td>\n",
       "      <td id=\"T_d53c2_row2_col8\" class=\"data row2 col8\" >-3/2*2^15</td>\n",
       "      <td id=\"T_d53c2_row2_col9\" class=\"data row2 col9\" >3/2*2^15</td>\n",
       "      <td id=\"T_d53c2_row2_col10\" class=\"data row2 col10\" >1*2^-15</td>\n",
       "      <td id=\"T_d53c2_row2_col11\" class=\"data row2 col11\" >1*2^-17</td>\n",
       "      <td id=\"T_d53c2_row2_col12\" class=\"data row2 col12\" >3/2*2^-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_d53c2_row3_col0\" class=\"data row3 col0\" >p3109_p4</td>\n",
       "      <td id=\"T_d53c2_row3_col1\" class=\"data row3 col1\" >4</td>\n",
       "      <td id=\"T_d53c2_row3_col2\" class=\"data row3 col2\" >4</td>\n",
       "      <td id=\"T_d53c2_row3_col3\" class=\"data row3 col3\" >3</td>\n",
       "      <td id=\"T_d53c2_row3_col4\" class=\"data row3 col4\" >63</td>\n",
       "      <td id=\"T_d53c2_row3_col5\" class=\"data row3 col5\" >63</td>\n",
       "      <td id=\"T_d53c2_row3_col6\" class=\"data row3 col6\" >True</td>\n",
       "      <td id=\"T_d53c2_row3_col7\" class=\"data row3 col7\" >7/4*2^7</td>\n",
       "      <td id=\"T_d53c2_row3_col8\" class=\"data row3 col8\" >-7/4*2^7</td>\n",
       "      <td id=\"T_d53c2_row3_col9\" class=\"data row3 col9\" >7/4*2^7</td>\n",
       "      <td id=\"T_d53c2_row3_col10\" class=\"data row3 col10\" >1*2^-7</td>\n",
       "      <td id=\"T_d53c2_row3_col11\" class=\"data row3 col11\" >1*2^-10</td>\n",
       "      <td id=\"T_d53c2_row3_col12\" class=\"data row3 col12\" >7/4*2^-8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_d53c2_row4_col0\" class=\"data row4 col0\" >p3109_p5</td>\n",
       "      <td id=\"T_d53c2_row4_col1\" class=\"data row4 col1\" >5</td>\n",
       "      <td id=\"T_d53c2_row4_col2\" class=\"data row4 col2\" >3</td>\n",
       "      <td id=\"T_d53c2_row4_col3\" class=\"data row4 col3\" >4</td>\n",
       "      <td id=\"T_d53c2_row4_col4\" class=\"data row4 col4\" >63</td>\n",
       "      <td id=\"T_d53c2_row4_col5\" class=\"data row4 col5\" >63</td>\n",
       "      <td id=\"T_d53c2_row4_col6\" class=\"data row4 col6\" >True</td>\n",
       "      <td id=\"T_d53c2_row4_col7\" class=\"data row4 col7\" >15/8*2^3</td>\n",
       "      <td id=\"T_d53c2_row4_col8\" class=\"data row4 col8\" >-15/8*2^3</td>\n",
       "      <td id=\"T_d53c2_row4_col9\" class=\"data row4 col9\" >15/8*2^3</td>\n",
       "      <td id=\"T_d53c2_row4_col10\" class=\"data row4 col10\" >1*2^-3</td>\n",
       "      <td id=\"T_d53c2_row4_col11\" class=\"data row4 col11\" >1*2^-7</td>\n",
       "      <td id=\"T_d53c2_row4_col12\" class=\"data row4 col12\" >15/8*2^-4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_d53c2_row5_col0\" class=\"data row5 col0\" >p3109_p6</td>\n",
       "      <td id=\"T_d53c2_row5_col1\" class=\"data row5 col1\" >6</td>\n",
       "      <td id=\"T_d53c2_row5_col2\" class=\"data row5 col2\" >2</td>\n",
       "      <td id=\"T_d53c2_row5_col3\" class=\"data row5 col3\" >5</td>\n",
       "      <td id=\"T_d53c2_row5_col4\" class=\"data row5 col4\" >63</td>\n",
       "      <td id=\"T_d53c2_row5_col5\" class=\"data row5 col5\" >63</td>\n",
       "      <td id=\"T_d53c2_row5_col6\" class=\"data row5 col6\" >True</td>\n",
       "      <td id=\"T_d53c2_row5_col7\" class=\"data row5 col7\" >31/16*2^1</td>\n",
       "      <td id=\"T_d53c2_row5_col8\" class=\"data row5 col8\" >-31/16*2^1</td>\n",
       "      <td id=\"T_d53c2_row5_col9\" class=\"data row5 col9\" >31/16*2^1</td>\n",
       "      <td id=\"T_d53c2_row5_col10\" class=\"data row5 col10\" >1*2^-1</td>\n",
       "      <td id=\"T_d53c2_row5_col11\" class=\"data row5 col11\" >1*2^-6</td>\n",
       "      <td id=\"T_d53c2_row5_col12\" class=\"data row5 col12\" >31/16*2^-2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_d53c2_row6_col0\" class=\"data row6 col0\" >p3109_p7</td>\n",
       "      <td id=\"T_d53c2_row6_col1\" class=\"data row6 col1\" >7</td>\n",
       "      <td id=\"T_d53c2_row6_col2\" class=\"data row6 col2\" >1</td>\n",
       "      <td id=\"T_d53c2_row6_col3\" class=\"data row6 col3\" >6</td>\n",
       "      <td id=\"T_d53c2_row6_col4\" class=\"data row6 col4\" >63</td>\n",
       "      <td id=\"T_d53c2_row6_col5\" class=\"data row6 col5\" >63</td>\n",
       "      <td id=\"T_d53c2_row6_col6\" class=\"data row6 col6\" >True</td>\n",
       "      <td id=\"T_d53c2_row6_col7\" class=\"data row6 col7\" >63/32*2^0</td>\n",
       "      <td id=\"T_d53c2_row6_col8\" class=\"data row6 col8\" >-63/32*2^0</td>\n",
       "      <td id=\"T_d53c2_row6_col9\" class=\"data row6 col9\" >63/32*2^0</td>\n",
       "      <td id=\"T_d53c2_row6_col10\" class=\"data row6 col10\" >1*2^0</td>\n",
       "      <td id=\"T_d53c2_row6_col11\" class=\"data row6 col11\" >1*2^-6</td>\n",
       "      <td id=\"T_d53c2_row6_col12\" class=\"data row6 col12\" >63/32*2^-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_d53c2_row7_col0\" class=\"data row7 col0\" >ocp_e5m2</td>\n",
       "      <td id=\"T_d53c2_row7_col1\" class=\"data row7 col1\" >3</td>\n",
       "      <td id=\"T_d53c2_row7_col2\" class=\"data row7 col2\" >5</td>\n",
       "      <td id=\"T_d53c2_row7_col3\" class=\"data row7 col3\" >2</td>\n",
       "      <td id=\"T_d53c2_row7_col4\" class=\"data row7 col4\" >59</td>\n",
       "      <td id=\"T_d53c2_row7_col5\" class=\"data row7 col5\" >64</td>\n",
       "      <td id=\"T_d53c2_row7_col6\" class=\"data row7 col6\" >True</td>\n",
       "      <td id=\"T_d53c2_row7_col7\" class=\"data row7 col7\" >7/4*2^15</td>\n",
       "      <td id=\"T_d53c2_row7_col8\" class=\"data row7 col8\" >-7/4*2^15</td>\n",
       "      <td id=\"T_d53c2_row7_col9\" class=\"data row7 col9\" >7/4*2^15</td>\n",
       "      <td id=\"T_d53c2_row7_col10\" class=\"data row7 col10\" >1*2^-14</td>\n",
       "      <td id=\"T_d53c2_row7_col11\" class=\"data row7 col11\" >1*2^-16</td>\n",
       "      <td id=\"T_d53c2_row7_col12\" class=\"data row7 col12\" >3/2*2^-15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_d53c2_row8_col0\" class=\"data row8 col0\" >ocp_e4m3</td>\n",
       "      <td id=\"T_d53c2_row8_col1\" class=\"data row8 col1\" >4</td>\n",
       "      <td id=\"T_d53c2_row8_col2\" class=\"data row8 col2\" >4</td>\n",
       "      <td id=\"T_d53c2_row8_col3\" class=\"data row8 col3\" >3</td>\n",
       "      <td id=\"T_d53c2_row8_col4\" class=\"data row8 col4\" >55</td>\n",
       "      <td id=\"T_d53c2_row8_col5\" class=\"data row8 col5\" >71</td>\n",
       "      <td id=\"T_d53c2_row8_col6\" class=\"data row8 col6\" >True</td>\n",
       "      <td id=\"T_d53c2_row8_col7\" class=\"data row8 col7\" >7/4*2^8</td>\n",
       "      <td id=\"T_d53c2_row8_col8\" class=\"data row8 col8\" >-7/4*2^8</td>\n",
       "      <td id=\"T_d53c2_row8_col9\" class=\"data row8 col9\" >7/4*2^8</td>\n",
       "      <td id=\"T_d53c2_row8_col10\" class=\"data row8 col10\" >1*2^-6</td>\n",
       "      <td id=\"T_d53c2_row8_col11\" class=\"data row8 col11\" >1*2^-9</td>\n",
       "      <td id=\"T_d53c2_row8_col12\" class=\"data row8 col12\" >7/4*2^-7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x7f760e81d990>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_pow2 = df.copy()\n",
    "for field in (\"maxFinite\",\"minFinite\",\"maxNormal\",\"minNormal\",\"minSubnormal\",\"maxSubnormal\"):\n",
    "  df_pow2[field] = df_pow2[field].map(gfloat.printing.float_pow2str)\n",
    "df_left_align(df_pow2).hide()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7f06edd",
   "metadata": {},
   "source": [
    "## Value Tables\n",
    "\n",
    "Print one-line summaries of each float value in the form\n",
    "```text\n",
    "Code Binary     = Exact binary E  = Float Value\n",
    "0x21 0_0100_001 = +0b1.001*2^-4   = ~0.0703\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9ce24b75",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ocp_e5m2\n",
      "0x00 0_00000_00 = 0.0\n",
      "0x01 0_00000_01 = +0b0.01*2^-14 ≈ 1.526e-05\n",
      "0x07 0_00001_11 = +0b1.11*2^-14 ≈ 0.0001\n",
      "0x21 0_01000_01 = +0b1.01*2^-7  ≈ 0.0098\n",
      "0x40 0_10000_00 = +0b1.00*2^1   = 2.0\n",
      "0x41 0_10000_01 = +0b1.01*2^1   = 2.5\n",
      "0x7e 0_11111_10 = nan\n",
      "0x7f 0_11111_11 = nan\n",
      "0x80 1_00000_00 = -0.0\n",
      "0x81 1_00000_01 = -0b0.01*2^-14 ≈ -1.526e-05\n",
      "0xe6 1_11001_10 = -0b1.10*2^10  = -1536.0\n",
      "0xfe 1_11111_10 = nan\n",
      "0xff 1_11111_11 = nan\n",
      "\n",
      "p3109_p3\n",
      "0x00 0_00000_00 = 0.0\n",
      "0x01 0_00000_01 = +0b0.01*2^-15 ≈ 7.629e-06\n",
      "0x07 0_00001_11 = +0b1.11*2^-15 ≈ 5.341e-05\n",
      "0x21 0_01000_01 = +0b1.01*2^-8  ≈ 0.0049\n",
      "0x40 0_10000_00 = +0b1.00*2^0   = 1.0\n",
      "0x41 0_10000_01 = +0b1.01*2^0   = 1.25\n",
      "0x7e 0_11111_10 = +0b1.10*2^15  = 49152.0\n",
      "0x7f 0_11111_11 = inf\n",
      "0x80 1_00000_00 = nan\n",
      "0x81 1_00000_01 = -0b0.01*2^-15 ≈ -7.629e-06\n",
      "0xe6 1_11001_10 = -0b1.10*2^9   = -768.0\n",
      "0xfe 1_11111_10 = -0b1.10*2^15  = -49152.0\n",
      "0xff 1_11111_11 = -inf\n"
     ]
    }
   ],
   "source": [
    "from gfloat import float_tilde_unless_roundtrip_str\n",
    "\n",
    "def str_bits_with_underscores(fi, fv):\n",
    "    # 0_1011110_\n",
    "    if fi.tSignificandBits == 0:\n",
    "        return f\"{fv.signbit}_{fv.exp:0{fi.expBits}b}_\"\n",
    "\n",
    "    # 0__1011110\n",
    "    if fi.expBits == 0:\n",
    "        return f\"{fv.signbit}__{fv.significand:0{fi.tSignificandBits}b}\"\n",
    "\n",
    "    # 0_101_1110\n",
    "    return (\n",
    "        f\"{fv.signbit}_{fv.exp:0{fi.expBits}b}_{fv.significand:0{fi.tSignificandBits}b}\"\n",
    "    )\n",
    "\n",
    "def str_tablerow(fi : FormatInfo, fv : FloatValue, vs_width=14, vs_d=8):\n",
    "  \"\"\"\n",
    "  Create a string of the form\n",
    "    0x41 0_10000_01 = +0b1.01*2^0   = 1.25\n",
    "  \"\"\"\n",
    "  text = []\n",
    "\n",
    "  # 0x45 0_1000_101\n",
    "  text.append(f'0x{fv.code:02x} {str_bits_with_underscores(fi,fv)}')\n",
    "  \n",
    "  finite_nonzero = np.isfinite(fv.fval) and fv.fval != 0\n",
    "  \n",
    "  #  = +0b1.101*2^-7 =\n",
    "  if finite_nonzero:\n",
    "    b = '0' if fv.fclass == FloatClass.SUBNORMAL else '1'\n",
    "    signstr = \"-\" if fv.signbit else \"+\"\n",
    "    binary_pow2 = f'{signstr}0b{b}.{fv.significand:0{fi.tSignificandBits}b}*2^{fv.expval:<3}'\n",
    "    text.append(binary_pow2)\n",
    "\n",
    "  # 1.125\n",
    "  text.append(float_tilde_unless_roundtrip_str(fv.fval, width=vs_width, d=vs_d))\n",
    "\n",
    "  ret = \" = \".join(text)\n",
    "  # Replace \"= ~\" with \"≈\"\n",
    "  return ret.replace('= ~','≈ ')\n",
    "\n",
    "\n",
    "for fi in (format_info_ocp_e5m2, format_info_p3109(3)):\n",
    "  print()\n",
    "  print(fi.name)\n",
    "  for i in (0x00, 0x01, 0x07, 0x21, 0x40, 0x41, 0x7e, 0x7f, 0x80, 0x81, 0xe6, 0xfe,0xff):\n",
    "    print(str_tablerow(fi, decode_float(fi, i), vs_width=8, vs_d=4))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c374cc7",
   "metadata": {},
   "source": [
    "## Generate HTML Value Tables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7a2717ea",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 143
    },
    "id": "ZgGpbJaeR-tM",
    "outputId": "f433e2ce-378a-48a3-8f3f-573e7106753c"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html>\n",
       "<html>\n",
       "  <head>\n",
       "    <meta charset=\"utf-8\" />\n",
       "    <title>FP8 Value Table, p3109_p4</title>\n",
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       "    height: 4ex;\n",
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       "  td {\n",
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       "    margin: 1pt 1pt 1pt 13pt;\n",
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       "</style>\n",
       "  </head>\n",
       "  <body>\n",
       "    <h3>FP8 Value Table, p3109_p4</h3>\n",
       "    <table>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x00 0_0000_000 = 0.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x40 0_1000_000 = +0b1.000*2^0   = 1.0</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x80 1_0000_000 = nan</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc0 1_1000_000 = -0b1.000*2^0   = -1.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x01 0_0000_001 = +0b0.001*2^-7  ≈ 0.0010</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x41 0_1000_001 = +0b1.001*2^0   = 1.125</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x81 1_0000_001 = -0b0.001*2^-7  ≈ -0.0010</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc1 1_1000_001 = -0b1.001*2^0   = -1.125</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x02 0_0000_010 = +0b0.010*2^-7  ≈ 0.0020</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x42 0_1000_010 = +0b1.010*2^0   = 1.25</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x82 1_0000_010 = -0b0.010*2^-7  ≈ -0.0020</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc2 1_1000_010 = -0b1.010*2^0   = -1.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x03 0_0000_011 = +0b0.011*2^-7  ≈ 0.0029</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x43 0_1000_011 = +0b1.011*2^0   = 1.375</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x83 1_0000_011 = -0b0.011*2^-7  ≈ -0.0029</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc3 1_1000_011 = -0b1.011*2^0   = -1.375</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x04 0_0000_100 = +0b0.100*2^-7  ≈ 0.0039</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x44 0_1000_100 = +0b1.100*2^0   = 1.5</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x84 1_0000_100 = -0b0.100*2^-7  ≈ -0.0039</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc4 1_1000_100 = -0b1.100*2^0   = -1.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x05 0_0000_101 = +0b0.101*2^-7  ≈ 0.0049</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x45 0_1000_101 = +0b1.101*2^0   = 1.625</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x85 1_0000_101 = -0b0.101*2^-7  ≈ -0.0049</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc5 1_1000_101 = -0b1.101*2^0   = -1.625</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x06 0_0000_110 = +0b0.110*2^-7  ≈ 0.0059</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x46 0_1000_110 = +0b1.110*2^0   = 1.75</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x86 1_0000_110 = -0b0.110*2^-7  ≈ -0.0059</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc6 1_1000_110 = -0b1.110*2^0   = -1.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x07 0_0000_111 = +0b0.111*2^-7  ≈ 0.0068</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x47 0_1000_111 = +0b1.111*2^0   = 1.875</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x87 1_0000_111 = -0b0.111*2^-7  ≈ -0.0068</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc7 1_1000_111 = -0b1.111*2^0   = -1.875</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x08 0_0001_000 = +0b1.000*2^-7  ≈ 0.0078</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x48 0_1001_000 = +0b1.000*2^1   = 2.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x88 1_0001_000 = -0b1.000*2^-7  ≈ -0.0078</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc8 1_1001_000 = -0b1.000*2^1   = -2.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x09 0_0001_001 = +0b1.001*2^-7  ≈ 0.0088</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x49 0_1001_001 = +0b1.001*2^1   = 2.25</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x89 1_0001_001 = -0b1.001*2^-7  ≈ -0.0088</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc9 1_1001_001 = -0b1.001*2^1   = -2.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0a 0_0001_010 = +0b1.010*2^-7  ≈ 0.0098</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4a 0_1001_010 = +0b1.010*2^1   = 2.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8a 1_0001_010 = -0b1.010*2^-7  ≈ -0.0098</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xca 1_1001_010 = -0b1.010*2^1   = -2.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0b 0_0001_011 = +0b1.011*2^-7  ≈ 0.0107</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4b 0_1001_011 = +0b1.011*2^1   = 2.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8b 1_0001_011 = -0b1.011*2^-7  ≈ -0.0107</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcb 1_1001_011 = -0b1.011*2^1   = -2.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0c 0_0001_100 = +0b1.100*2^-7  ≈ 0.0117</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4c 0_1001_100 = +0b1.100*2^1   = 3.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8c 1_0001_100 = -0b1.100*2^-7  ≈ -0.0117</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcc 1_1001_100 = -0b1.100*2^1   = -3.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0d 0_0001_101 = +0b1.101*2^-7  ≈ 0.0127</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4d 0_1001_101 = +0b1.101*2^1   = 3.25</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8d 1_0001_101 = -0b1.101*2^-7  ≈ -0.0127</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcd 1_1001_101 = -0b1.101*2^1   = -3.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0e 0_0001_110 = +0b1.110*2^-7  ≈ 0.0137</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4e 0_1001_110 = +0b1.110*2^1   = 3.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8e 1_0001_110 = -0b1.110*2^-7  ≈ -0.0137</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xce 1_1001_110 = -0b1.110*2^1   = -3.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0f 0_0001_111 = +0b1.111*2^-7  ≈ 0.0146</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4f 0_1001_111 = +0b1.111*2^1   = 3.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8f 1_0001_111 = -0b1.111*2^-7  ≈ -0.0146</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcf 1_1001_111 = -0b1.111*2^1   = -3.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"blankrow\">\n",
       "        <td ...></td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3c 0_0111_100 = +0b1.100*2^-1  = 0.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7c 0_1111_100 = +0b1.100*2^7   = 192.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbc 1_0111_100 = -0b1.100*2^-1  = -0.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfc 1_1111_100 = -0b1.100*2^7   = -192.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3d 0_0111_101 = +0b1.101*2^-1  = 0.8125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7d 0_1111_101 = +0b1.101*2^7   = 208.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbd 1_0111_101 = -0b1.101*2^-1  = -0.8125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfd 1_1111_101 = -0b1.101*2^7   = -208.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3e 0_0111_110 = +0b1.110*2^-1  = 0.875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7e 0_1111_110 = +0b1.110*2^7   = 224.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbe 1_0111_110 = -0b1.110*2^-1  = -0.875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfe 1_1111_110 = -0b1.110*2^7   = -224.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3f 0_0111_111 = +0b1.111*2^-1  = 0.9375</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x7f 0_1111_111 = inf</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbf 1_0111_111 = -0b1.111*2^-1  = -0.9375</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0xff 1_1111_111 = -inf</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "    </table>\n",
       "  </body>\n",
       "</html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import airium\n",
    "from IPython.display import HTML\n",
    "\n",
    "def table_style(fv):\n",
    "    \"\"\"\n",
    "    Select from the table entry styles defined in CSS below.\n",
    "    \"\"\"\n",
    "    if fv.fclass == FloatClass.SUBNORMAL:\n",
    "        return \"subnormal\"\n",
    "\n",
    "    if fv.fclass == FloatClass.NORMAL:\n",
    "        return \"normal\"\n",
    "\n",
    "    if fv.fclass == FloatClass.ZERO and not fv.signbit:\n",
    "        return \"normal\"\n",
    "\n",
    "    # Everyting else is special\n",
    "    return \"special\"\n",
    "\n",
    "def mktbl(fi : FormatInfo, short=False, **kw):\n",
    "  # Make tables\n",
    "  cols = 4\n",
    "  rows = 256//cols\n",
    "\n",
    "  style = f'''\n",
    "  body {{\n",
    "  }}\n",
    "  table {{\n",
    "    width:100%;\n",
    "    margin: 0pt;\n",
    "    font-family: monospace;\n",
    "    font-size: small;\n",
    "    font-weight: bold;\n",
    "    border-collapse: collapse;\n",
    "  }}\n",
    "\n",
    "  tr.blankrow {{\n",
    "    height: 4ex;\n",
    "    vertical-align: top;\n",
    "  }}\n",
    "  \n",
    "  td {{\n",
    "    text-align: left;\n",
    "    border: solid 2px #ccc;\n",
    "    width: {98/cols}%;\n",
    "  }}\n",
    "  \n",
    "  .special {{\n",
    "    color: #874723;\n",
    "  }}\n",
    "  \n",
    "  .subnormal {{\n",
    "    color: #0121a7;\n",
    "  }}\n",
    "  \n",
    "  .normal {{\n",
    "  }}\n",
    "  \n",
    "  pre {{\n",
    "    margin: 1pt 1pt 1pt 13pt;\n",
    "    display: inline;\n",
    "  }}\n",
    "'''\n",
    "\n",
    "  title = f\"FP8 Value Table, {fi.name}\"\n",
    "  a = airium.Airium()\n",
    "  a('<!DOCTYPE html>')\n",
    "  with a.html():\n",
    "    with a.head():\n",
    "        # a.meta('http-equiv=\"refresh\" content=\"1\"') # for rapid testing\n",
    "        a.meta(charset=\"utf-8\")\n",
    "        a.title(_t=title)\n",
    "        a.style(_t=style)\n",
    "\n",
    "    with a.body():\n",
    "        a.h3(_t=title)\n",
    "\n",
    "        with a.table():\n",
    "          for i in range(0,rows):\n",
    "            if short and (16 <= i < 60):\n",
    "              if i == 16:\n",
    "                a.tr(klass='blankrow').td('...')\n",
    "              continue\n",
    "            trklass='blankrow' if i > 0 and i%16 == 0 else ''\n",
    "            with a.tr(klass=trklass):\n",
    "              for n in range(i,256,rows):\n",
    "                fv = decode_float(fi, n)\n",
    "                text = str_tablerow(fi, fv, **kw)\n",
    "                a.td(klass=table_style(fv)).pre(_t=text)\n",
    "\n",
    "  return str(a)\n",
    "\n",
    "HTML(mktbl(format_info_p3109(4), short=True, vs_width=8, vs_d=4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "dd784087",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html>\n",
       "<html>\n",
       "  <head>\n",
       "    <meta charset=\"utf-8\" />\n",
       "    <title>FP8 Value Table, p3109_p4 [without subnormals]</title>\n",
       "    <style>\n",
       "  body {\n",
       "  }\n",
       "  table {\n",
       "    width:100%;\n",
       "    margin: 0pt;\n",
       "    font-family: monospace;\n",
       "    font-size: small;\n",
       "    font-weight: bold;\n",
       "    border-collapse: collapse;\n",
       "  }\n",
       "\n",
       "  tr.blankrow {\n",
       "    height: 4ex;\n",
       "    vertical-align: top;\n",
       "  }\n",
       "  \n",
       "  td {\n",
       "    text-align: left;\n",
       "    border: solid 2px #ccc;\n",
       "    width: 24.5%;\n",
       "  }\n",
       "  \n",
       "  .special {\n",
       "    color: #874723;\n",
       "  }\n",
       "  \n",
       "  .subnormal {\n",
       "    color: #0121a7;\n",
       "  }\n",
       "  \n",
       "  .normal {\n",
       "  }\n",
       "  \n",
       "  pre {\n",
       "    margin: 1pt 1pt 1pt 13pt;\n",
       "    display: inline;\n",
       "  }\n",
       "</style>\n",
       "  </head>\n",
       "  <body>\n",
       "    <h3>FP8 Value Table, p3109_p4 [without subnormals]</h3>\n",
       "    <table>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x00 0_0000_000 = 0.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x40 0_1000_000 = +0b1.000*2^0   = 1.0</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x80 1_0000_000 = nan</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc0 1_1000_000 = -0b1.000*2^0   = -1.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x01 0_0000_001 = +0b1.001*2^-8  ≈ 0.0044</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x41 0_1000_001 = +0b1.001*2^0   = 1.125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x81 1_0000_001 = -0b1.001*2^-8  ≈ -0.0044</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc1 1_1000_001 = -0b1.001*2^0   = -1.125</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x02 0_0000_010 = +0b1.010*2^-8  ≈ 0.0049</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x42 0_1000_010 = +0b1.010*2^0   = 1.25</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x82 1_0000_010 = -0b1.010*2^-8  ≈ -0.0049</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc2 1_1000_010 = -0b1.010*2^0   = -1.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x03 0_0000_011 = +0b1.011*2^-8  ≈ 0.0054</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x43 0_1000_011 = +0b1.011*2^0   = 1.375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x83 1_0000_011 = -0b1.011*2^-8  ≈ -0.0054</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc3 1_1000_011 = -0b1.011*2^0   = -1.375</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x04 0_0000_100 = +0b1.100*2^-8  ≈ 0.0059</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x44 0_1000_100 = +0b1.100*2^0   = 1.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x84 1_0000_100 = -0b1.100*2^-8  ≈ -0.0059</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc4 1_1000_100 = -0b1.100*2^0   = -1.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x05 0_0000_101 = +0b1.101*2^-8  ≈ 0.0063</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x45 0_1000_101 = +0b1.101*2^0   = 1.625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x85 1_0000_101 = -0b1.101*2^-8  ≈ -0.0063</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc5 1_1000_101 = -0b1.101*2^0   = -1.625</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x06 0_0000_110 = +0b1.110*2^-8  ≈ 0.0068</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x46 0_1000_110 = +0b1.110*2^0   = 1.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x86 1_0000_110 = -0b1.110*2^-8  ≈ -0.0068</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc6 1_1000_110 = -0b1.110*2^0   = -1.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x07 0_0000_111 = +0b1.111*2^-8  ≈ 0.0073</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x47 0_1000_111 = +0b1.111*2^0   = 1.875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x87 1_0000_111 = -0b1.111*2^-8  ≈ -0.0073</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc7 1_1000_111 = -0b1.111*2^0   = -1.875</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x08 0_0001_000 = +0b1.000*2^-7  ≈ 0.0078</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x48 0_1001_000 = +0b1.000*2^1   = 2.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x88 1_0001_000 = -0b1.000*2^-7  ≈ -0.0078</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc8 1_1001_000 = -0b1.000*2^1   = -2.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x09 0_0001_001 = +0b1.001*2^-7  ≈ 0.0088</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x49 0_1001_001 = +0b1.001*2^1   = 2.25</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x89 1_0001_001 = -0b1.001*2^-7  ≈ -0.0088</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc9 1_1001_001 = -0b1.001*2^1   = -2.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0a 0_0001_010 = +0b1.010*2^-7  ≈ 0.0098</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4a 0_1001_010 = +0b1.010*2^1   = 2.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8a 1_0001_010 = -0b1.010*2^-7  ≈ -0.0098</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xca 1_1001_010 = -0b1.010*2^1   = -2.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0b 0_0001_011 = +0b1.011*2^-7  ≈ 0.0107</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4b 0_1001_011 = +0b1.011*2^1   = 2.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8b 1_0001_011 = -0b1.011*2^-7  ≈ -0.0107</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcb 1_1001_011 = -0b1.011*2^1   = -2.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0c 0_0001_100 = +0b1.100*2^-7  ≈ 0.0117</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4c 0_1001_100 = +0b1.100*2^1   = 3.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8c 1_0001_100 = -0b1.100*2^-7  ≈ -0.0117</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcc 1_1001_100 = -0b1.100*2^1   = -3.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0d 0_0001_101 = +0b1.101*2^-7  ≈ 0.0127</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4d 0_1001_101 = +0b1.101*2^1   = 3.25</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8d 1_0001_101 = -0b1.101*2^-7  ≈ -0.0127</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcd 1_1001_101 = -0b1.101*2^1   = -3.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0e 0_0001_110 = +0b1.110*2^-7  ≈ 0.0137</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4e 0_1001_110 = +0b1.110*2^1   = 3.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8e 1_0001_110 = -0b1.110*2^-7  ≈ -0.0137</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xce 1_1001_110 = -0b1.110*2^1   = -3.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0f 0_0001_111 = +0b1.111*2^-7  ≈ 0.0146</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4f 0_1001_111 = +0b1.111*2^1   = 3.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8f 1_0001_111 = -0b1.111*2^-7  ≈ -0.0146</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcf 1_1001_111 = -0b1.111*2^1   = -3.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"blankrow\">\n",
       "        <td ...></td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3c 0_0111_100 = +0b1.100*2^-1  = 0.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7c 0_1111_100 = +0b1.100*2^7   = 192.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbc 1_0111_100 = -0b1.100*2^-1  = -0.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfc 1_1111_100 = -0b1.100*2^7   = -192.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3d 0_0111_101 = +0b1.101*2^-1  = 0.8125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7d 0_1111_101 = +0b1.101*2^7   = 208.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbd 1_0111_101 = -0b1.101*2^-1  = -0.8125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfd 1_1111_101 = -0b1.101*2^7   = -208.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3e 0_0111_110 = +0b1.110*2^-1  = 0.875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7e 0_1111_110 = +0b1.110*2^7   = 224.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbe 1_0111_110 = -0b1.110*2^-1  = -0.875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfe 1_1111_110 = -0b1.110*2^7   = -224.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3f 0_0111_111 = +0b1.111*2^-1  = 0.9375</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x7f 0_1111_111 = inf</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbf 1_0111_111 = -0b1.111*2^-1  = -0.9375</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0xff 1_1111_111 = -inf</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "    </table>\n",
       "  </body>\n",
       "</html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What would the table look like without subnormals\n",
    "from copy import deepcopy\n",
    "fi = deepcopy(format_info_p3109(4))\n",
    "fi.name += ' [without subnormals]'\n",
    "fi.has_subnormals = False\n",
    "HTML(mktbl(fi, short=True, vs_width=8, vs_d=4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dee30c28",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving to html/value-table-p3109_p1.html\n",
      "Saving to html/value-table-p3109_p2.html\n",
      "Saving to html/value-table-p3109_p3.html\n",
      "Saving to html/value-table-p3109_p4.html\n",
      "Saving to html/value-table-p3109_p5.html\n",
      "Saving to html/value-table-p3109_p6.html\n",
      "Saving to html/value-table-p3109_p7.html\n",
      "Saving to html/value-table-ocp_e5m2.html\n",
      "Saving to html/value-table-ocp_e4m3.html\n",
      "Saving html/index.html\n"
     ]
    }
   ],
   "source": [
    "## Write HTML to disk\n",
    "import pathlib\n",
    "dir = pathlib.Path(\"html\")\n",
    "dir.mkdir(parents=True, exist_ok=True)\n",
    "\n",
    "a = airium.Airium()\n",
    "a('<!DOCTYPE html>')\n",
    "a('<!-- Autogenerated from make-value-tables.ipynb -->')\n",
    "a.head().title(_t='F8 value tables')\n",
    "with a.body():\n",
    "  a.h2(_t='F8 value tables')\n",
    "  with a.ol():\n",
    "    for fi in p3109_and_ocp_formats:\n",
    "      html_str = mktbl(fi)\n",
    "      filename = f\"value-table-{fi.name}.html\"\n",
    "      print(f'Saving to {dir / filename}')\n",
    "      a.li().a(href=filename).code(_t=fi.name)\n",
    "      with open(dir / filename, \"w\") as f:\n",
    "        f.write(html_str)\n",
    "\n",
    "index_filename = dir / 'index.html'\n",
    "print(f'Saving {index_filename}')\n",
    "with open(index_filename, \"w\") as index:\n",
    "  index.write(str(a))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20514fb3",
   "metadata": {},
   "source": [
    "## Show full table for p=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6ece5085",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "IJihmWKHkFwb",
    "outputId": "e6f31b52-c8b3-4bf7-b385-4d45548a8920"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html>\n",
       "<html>\n",
       "  <head>\n",
       "    <meta charset=\"utf-8\" />\n",
       "    <title>FP8 Value Table, p3109_p4</title>\n",
       "    <style>\n",
       "  body {\n",
       "  }\n",
       "  table {\n",
       "    width:100%;\n",
       "    margin: 0pt;\n",
       "    font-family: monospace;\n",
       "    font-size: small;\n",
       "    font-weight: bold;\n",
       "    border-collapse: collapse;\n",
       "  }\n",
       "\n",
       "  tr.blankrow {\n",
       "    height: 4ex;\n",
       "    vertical-align: top;\n",
       "  }\n",
       "  \n",
       "  td {\n",
       "    text-align: left;\n",
       "    border: solid 2px #ccc;\n",
       "    width: 24.5%;\n",
       "  }\n",
       "  \n",
       "  .special {\n",
       "    color: #874723;\n",
       "  }\n",
       "  \n",
       "  .subnormal {\n",
       "    color: #0121a7;\n",
       "  }\n",
       "  \n",
       "  .normal {\n",
       "  }\n",
       "  \n",
       "  pre {\n",
       "    margin: 1pt 1pt 1pt 13pt;\n",
       "    display: inline;\n",
       "  }\n",
       "</style>\n",
       "  </head>\n",
       "  <body>\n",
       "    <h3>FP8 Value Table, p3109_p4</h3>\n",
       "    <table>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x00 0_0000_000 = 0.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x40 0_1000_000 = +0b1.000*2^0   = 1.0</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x80 1_0000_000 = nan</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc0 1_1000_000 = -0b1.000*2^0   = -1.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x01 0_0000_001 = +0b0.001*2^-7  = 0.0009765625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x41 0_1000_001 = +0b1.001*2^0   = 1.125</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x81 1_0000_001 = -0b0.001*2^-7  = -0.0009765625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc1 1_1000_001 = -0b1.001*2^0   = -1.125</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x02 0_0000_010 = +0b0.010*2^-7  = 0.001953125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x42 0_1000_010 = +0b1.010*2^0   = 1.25</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x82 1_0000_010 = -0b0.010*2^-7  = -0.001953125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc2 1_1000_010 = -0b1.010*2^0   = -1.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x03 0_0000_011 = +0b0.011*2^-7  = 0.0029296875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x43 0_1000_011 = +0b1.011*2^0   = 1.375</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x83 1_0000_011 = -0b0.011*2^-7  = -0.0029296875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc3 1_1000_011 = -0b1.011*2^0   = -1.375</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x04 0_0000_100 = +0b0.100*2^-7  = 0.00390625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x44 0_1000_100 = +0b1.100*2^0   = 1.5</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x84 1_0000_100 = -0b0.100*2^-7  = -0.00390625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc4 1_1000_100 = -0b1.100*2^0   = -1.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x05 0_0000_101 = +0b0.101*2^-7  = 0.0048828125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x45 0_1000_101 = +0b1.101*2^0   = 1.625</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x85 1_0000_101 = -0b0.101*2^-7  = -0.0048828125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc5 1_1000_101 = -0b1.101*2^0   = -1.625</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x06 0_0000_110 = +0b0.110*2^-7  = 0.005859375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x46 0_1000_110 = +0b1.110*2^0   = 1.75</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x86 1_0000_110 = -0b0.110*2^-7  = -0.005859375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc6 1_1000_110 = -0b1.110*2^0   = -1.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x07 0_0000_111 = +0b0.111*2^-7  = 0.0068359375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x47 0_1000_111 = +0b1.111*2^0   = 1.875</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x87 1_0000_111 = -0b0.111*2^-7  = -0.0068359375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc7 1_1000_111 = -0b1.111*2^0   = -1.875</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x08 0_0001_000 = +0b1.000*2^-7  = 0.0078125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x48 0_1001_000 = +0b1.000*2^1   = 2.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x88 1_0001_000 = -0b1.000*2^-7  = -0.0078125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc8 1_1001_000 = -0b1.000*2^1   = -2.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x09 0_0001_001 = +0b1.001*2^-7  = 0.0087890625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x49 0_1001_001 = +0b1.001*2^1   = 2.25</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x89 1_0001_001 = -0b1.001*2^-7  = -0.0087890625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc9 1_1001_001 = -0b1.001*2^1   = -2.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0a 0_0001_010 = +0b1.010*2^-7  = 0.009765625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4a 0_1001_010 = +0b1.010*2^1   = 2.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8a 1_0001_010 = -0b1.010*2^-7  = -0.009765625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xca 1_1001_010 = -0b1.010*2^1   = -2.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0b 0_0001_011 = +0b1.011*2^-7  = 0.0107421875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4b 0_1001_011 = +0b1.011*2^1   = 2.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8b 1_0001_011 = -0b1.011*2^-7  = -0.0107421875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcb 1_1001_011 = -0b1.011*2^1   = -2.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0c 0_0001_100 = +0b1.100*2^-7  = 0.01171875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4c 0_1001_100 = +0b1.100*2^1   = 3.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8c 1_0001_100 = -0b1.100*2^-7  = -0.01171875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcc 1_1001_100 = -0b1.100*2^1   = -3.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0d 0_0001_101 = +0b1.101*2^-7  = 0.0126953125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4d 0_1001_101 = +0b1.101*2^1   = 3.25</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8d 1_0001_101 = -0b1.101*2^-7  = -0.0126953125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcd 1_1001_101 = -0b1.101*2^1   = -3.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0e 0_0001_110 = +0b1.110*2^-7  = 0.013671875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4e 0_1001_110 = +0b1.110*2^1   = 3.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8e 1_0001_110 = -0b1.110*2^-7  = -0.013671875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xce 1_1001_110 = -0b1.110*2^1   = -3.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0f 0_0001_111 = +0b1.111*2^-7  = 0.0146484375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4f 0_1001_111 = +0b1.111*2^1   = 3.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8f 1_0001_111 = -0b1.111*2^-7  = -0.0146484375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcf 1_1001_111 = -0b1.111*2^1   = -3.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"blankrow\">\n",
       "        <td ...></td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3c 0_0111_100 = +0b1.100*2^-1  = 0.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7c 0_1111_100 = +0b1.100*2^7   = 192.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbc 1_0111_100 = -0b1.100*2^-1  = -0.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfc 1_1111_100 = -0b1.100*2^7   = -192.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3d 0_0111_101 = +0b1.101*2^-1  = 0.8125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7d 0_1111_101 = +0b1.101*2^7   = 208.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbd 1_0111_101 = -0b1.101*2^-1  = -0.8125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfd 1_1111_101 = -0b1.101*2^7   = -208.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3e 0_0111_110 = +0b1.110*2^-1  = 0.875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7e 0_1111_110 = +0b1.110*2^7   = 224.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbe 1_0111_110 = -0b1.110*2^-1  = -0.875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfe 1_1111_110 = -0b1.110*2^7   = -224.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3f 0_0111_111 = +0b1.111*2^-1  = 0.9375</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x7f 0_1111_111 = inf</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbf 1_0111_111 = -0b1.111*2^-1  = -0.9375</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0xff 1_1111_111 = -inf</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "    </table>\n",
       "  </body>\n",
       "</html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(mktbl(format_info_p3109(4), short=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eebe2efb",
   "metadata": {
    "id": "gM6eilps3X-k"
   },
   "source": [
    "## Format tables: OCP formats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a894ac20",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "8GzhrKcf3Y1O",
    "outputId": "8b27f4cf-1c6e-409e-e3bd-18b07148f001"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html>\n",
       "<html>\n",
       "  <head>\n",
       "    <meta charset=\"utf-8\" />\n",
       "    <title>FP8 Value Table, ocp_e5m2</title>\n",
       "    <style>\n",
       "  body {\n",
       "  }\n",
       "  table {\n",
       "    width:100%;\n",
       "    margin: 0pt;\n",
       "    font-family: monospace;\n",
       "    font-size: small;\n",
       "    font-weight: bold;\n",
       "    border-collapse: collapse;\n",
       "  }\n",
       "\n",
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       "</style>\n",
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       "  <body>\n",
       "    <h3>FP8 Value Table, ocp_e5m2</h3>\n",
       "    <table>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x00 0_00000_00 = 0.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x40 0_10000_00 = +0b1.00*2^1   = 2.0</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x80 1_00000_00 = -0.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc0 1_10000_00 = -0b1.00*2^1   = -2.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x01 0_00000_01 = +0b0.01*2^-14 ≈ 1.5258789e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x41 0_10000_01 = +0b1.01*2^1   = 2.5</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x81 1_00000_01 = -0b0.01*2^-14 ≈ -1.5258789e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc1 1_10000_01 = -0b1.01*2^1   = -2.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x02 0_00000_10 = +0b0.10*2^-14 ≈ 3.0517578e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x42 0_10000_10 = +0b1.10*2^1   = 3.0</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x82 1_00000_10 = -0b0.10*2^-14 ≈ -3.0517578e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc2 1_10000_10 = -0b1.10*2^1   = -3.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x03 0_00000_11 = +0b0.11*2^-14 ≈ 4.5776367e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x43 0_10000_11 = +0b1.11*2^1   = 3.5</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x83 1_00000_11 = -0b0.11*2^-14 ≈ -4.5776367e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc3 1_10000_11 = -0b1.11*2^1   = -3.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x04 0_00001_00 = +0b1.00*2^-14 ≈ 6.1035156e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x44 0_10001_00 = +0b1.00*2^2   = 4.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x84 1_00001_00 = -0b1.00*2^-14 ≈ -6.1035156e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc4 1_10001_00 = -0b1.00*2^2   = -4.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x05 0_00001_01 = +0b1.01*2^-14 ≈ 7.6293945e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x45 0_10001_01 = +0b1.01*2^2   = 5.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x85 1_00001_01 = -0b1.01*2^-14 ≈ -7.6293945e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc5 1_10001_01 = -0b1.01*2^2   = -5.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x06 0_00001_10 = +0b1.10*2^-14 ≈ 9.1552734e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x46 0_10001_10 = +0b1.10*2^2   = 6.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x86 1_00001_10 = -0b1.10*2^-14 ≈ -9.1552734e-05</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc6 1_10001_10 = -0b1.10*2^2   = -6.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x07 0_00001_11 = +0b1.11*2^-14 ≈ 0.00010681</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x47 0_10001_11 = +0b1.11*2^2   = 7.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x87 1_00001_11 = -0b1.11*2^-14 ≈ -0.00010681</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc7 1_10001_11 = -0b1.11*2^2   = -7.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x08 0_00010_00 = +0b1.00*2^-13 ≈ 0.00012207</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x48 0_10010_00 = +0b1.00*2^3   = 8.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x88 1_00010_00 = -0b1.00*2^-13 ≈ -0.00012207</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc8 1_10010_00 = -0b1.00*2^3   = -8.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x09 0_00010_01 = +0b1.01*2^-13 ≈ 0.00015259</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x49 0_10010_01 = +0b1.01*2^3   = 10.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x89 1_00010_01 = -0b1.01*2^-13 ≈ -0.00015259</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc9 1_10010_01 = -0b1.01*2^3   = -10.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0a 0_00010_10 = +0b1.10*2^-13 ≈ 0.00018311</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4a 0_10010_10 = +0b1.10*2^3   = 12.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8a 1_00010_10 = -0b1.10*2^-13 ≈ -0.00018311</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xca 1_10010_10 = -0b1.10*2^3   = -12.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0b 0_00010_11 = +0b1.11*2^-13 ≈ 0.00021362</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4b 0_10010_11 = +0b1.11*2^3   = 14.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8b 1_00010_11 = -0b1.11*2^-13 ≈ -0.00021362</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcb 1_10010_11 = -0b1.11*2^3   = -14.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0c 0_00011_00 = +0b1.00*2^-12 = 0.000244140625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4c 0_10011_00 = +0b1.00*2^4   = 16.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8c 1_00011_00 = -0b1.00*2^-12 ≈ -0.00024414</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcc 1_10011_00 = -0b1.00*2^4   = -16.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0d 0_00011_01 = +0b1.01*2^-12 ≈ 0.00030518</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4d 0_10011_01 = +0b1.01*2^4   = 20.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8d 1_00011_01 = -0b1.01*2^-12 ≈ -0.00030518</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcd 1_10011_01 = -0b1.01*2^4   = -20.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0e 0_00011_10 = +0b1.10*2^-12 ≈ 0.00036621</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4e 0_10011_10 = +0b1.10*2^4   = 24.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8e 1_00011_10 = -0b1.10*2^-12 ≈ -0.00036621</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xce 1_10011_10 = -0b1.10*2^4   = -24.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0f 0_00011_11 = +0b1.11*2^-12 ≈ 0.00042725</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4f 0_10011_11 = +0b1.11*2^4   = 28.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8f 1_00011_11 = -0b1.11*2^-12 ≈ -0.00042725</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcf 1_10011_11 = -0b1.11*2^4   = -28.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"blankrow\">\n",
       "        <td ...></td>\n",
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       "        <td class=\"normal\">\n",
       "          <pre>0x3c 0_01111_00 = +0b1.00*2^0   = 1.0</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x7c 0_11111_00 = inf</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbc 1_01111_00 = -0b1.00*2^0   = -1.0</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0xfc 1_11111_00 = -inf</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3d 0_01111_01 = +0b1.01*2^0   = 1.25</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x7d 0_11111_01 = nan</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbd 1_01111_01 = -0b1.01*2^0   = -1.25</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0xfd 1_11111_01 = nan</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3e 0_01111_10 = +0b1.10*2^0   = 1.5</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x7e 0_11111_10 = nan</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbe 1_01111_10 = -0b1.10*2^0   = -1.5</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0xfe 1_11111_10 = nan</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3f 0_01111_11 = +0b1.11*2^0   = 1.75</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x7f 0_11111_11 = nan</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbf 1_01111_11 = -0b1.11*2^0   = -1.75</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0xff 1_11111_11 = nan</pre>\n",
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       "  <body>\n",
       "    <h3>FP8 Value Table, ocp_e4m3</h3>\n",
       "    <table>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x00 0_0000_000 = 0.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x40 0_1000_000 = +0b1.000*2^1   = 2.0</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x80 1_0000_000 = -0.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc0 1_1000_000 = -0b1.000*2^1   = -2.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x01 0_0000_001 = +0b0.001*2^-6  = 0.001953125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x41 0_1000_001 = +0b1.001*2^1   = 2.25</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x81 1_0000_001 = -0b0.001*2^-6  = -0.001953125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc1 1_1000_001 = -0b1.001*2^1   = -2.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x02 0_0000_010 = +0b0.010*2^-6  = 0.00390625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x42 0_1000_010 = +0b1.010*2^1   = 2.5</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x82 1_0000_010 = -0b0.010*2^-6  = -0.00390625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc2 1_1000_010 = -0b1.010*2^1   = -2.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x03 0_0000_011 = +0b0.011*2^-6  = 0.005859375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x43 0_1000_011 = +0b1.011*2^1   = 2.75</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x83 1_0000_011 = -0b0.011*2^-6  = -0.005859375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc3 1_1000_011 = -0b1.011*2^1   = -2.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x04 0_0000_100 = +0b0.100*2^-6  = 0.0078125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x44 0_1000_100 = +0b1.100*2^1   = 3.0</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x84 1_0000_100 = -0b0.100*2^-6  = -0.0078125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc4 1_1000_100 = -0b1.100*2^1   = -3.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x05 0_0000_101 = +0b0.101*2^-6  = 0.009765625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x45 0_1000_101 = +0b1.101*2^1   = 3.25</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x85 1_0000_101 = -0b0.101*2^-6  = -0.009765625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc5 1_1000_101 = -0b1.101*2^1   = -3.25</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x06 0_0000_110 = +0b0.110*2^-6  = 0.01171875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x46 0_1000_110 = +0b1.110*2^1   = 3.5</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x86 1_0000_110 = -0b0.110*2^-6  = -0.01171875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc6 1_1000_110 = -0b1.110*2^1   = -3.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x07 0_0000_111 = +0b0.111*2^-6  = 0.013671875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x47 0_1000_111 = +0b1.111*2^1   = 3.75</pre>\n",
       "        </td>\n",
       "        <td class=\"subnormal\">\n",
       "          <pre>0x87 1_0000_111 = -0b0.111*2^-6  = -0.013671875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc7 1_1000_111 = -0b1.111*2^1   = -3.75</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x08 0_0001_000 = +0b1.000*2^-6  = 0.015625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x48 0_1001_000 = +0b1.000*2^2   = 4.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x88 1_0001_000 = -0b1.000*2^-6  = -0.015625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc8 1_1001_000 = -0b1.000*2^2   = -4.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x09 0_0001_001 = +0b1.001*2^-6  = 0.017578125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x49 0_1001_001 = +0b1.001*2^2   = 4.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x89 1_0001_001 = -0b1.001*2^-6  = -0.017578125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xc9 1_1001_001 = -0b1.001*2^2   = -4.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0a 0_0001_010 = +0b1.010*2^-6  = 0.01953125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4a 0_1001_010 = +0b1.010*2^2   = 5.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8a 1_0001_010 = -0b1.010*2^-6  = -0.01953125</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xca 1_1001_010 = -0b1.010*2^2   = -5.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0b 0_0001_011 = +0b1.011*2^-6  = 0.021484375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4b 0_1001_011 = +0b1.011*2^2   = 5.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8b 1_0001_011 = -0b1.011*2^-6  = -0.021484375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcb 1_1001_011 = -0b1.011*2^2   = -5.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0c 0_0001_100 = +0b1.100*2^-6  = 0.0234375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4c 0_1001_100 = +0b1.100*2^2   = 6.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8c 1_0001_100 = -0b1.100*2^-6  = -0.0234375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcc 1_1001_100 = -0b1.100*2^2   = -6.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0d 0_0001_101 = +0b1.101*2^-6  = 0.025390625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4d 0_1001_101 = +0b1.101*2^2   = 6.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8d 1_0001_101 = -0b1.101*2^-6  = -0.025390625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcd 1_1001_101 = -0b1.101*2^2   = -6.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0e 0_0001_110 = +0b1.110*2^-6  = 0.02734375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4e 0_1001_110 = +0b1.110*2^2   = 7.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8e 1_0001_110 = -0b1.110*2^-6  = -0.02734375</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xce 1_1001_110 = -0b1.110*2^2   = -7.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x0f 0_0001_111 = +0b1.111*2^-6  = 0.029296875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x4f 0_1001_111 = +0b1.111*2^2   = 7.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x8f 1_0001_111 = -0b1.111*2^-6  = -0.029296875</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xcf 1_1001_111 = -0b1.111*2^2   = -7.5</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"blankrow\">\n",
       "        <td ...></td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3c 0_0111_100 = +0b1.100*2^0   = 1.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7c 0_1111_100 = +0b1.100*2^8   = 384.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbc 1_0111_100 = -0b1.100*2^0   = -1.5</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfc 1_1111_100 = -0b1.100*2^8   = -384.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3d 0_0111_101 = +0b1.101*2^0   = 1.625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7d 0_1111_101 = +0b1.101*2^8   = 416.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbd 1_0111_101 = -0b1.101*2^0   = -1.625</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfd 1_1111_101 = -0b1.101*2^8   = -416.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3e 0_0111_110 = +0b1.110*2^0   = 1.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x7e 0_1111_110 = +0b1.110*2^8   = 448.0</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbe 1_0111_110 = -0b1.110*2^0   = -1.75</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xfe 1_1111_110 = -0b1.110*2^8   = -448.0</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "      <tr class=\"\">\n",
       "        <td class=\"normal\">\n",
       "          <pre>0x3f 0_0111_111 = +0b1.111*2^0   = 1.875</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0x7f 0_1111_111 = nan</pre>\n",
       "        </td>\n",
       "        <td class=\"normal\">\n",
       "          <pre>0xbf 1_0111_111 = -0b1.111*2^0   = -1.875</pre>\n",
       "        </td>\n",
       "        <td class=\"special\">\n",
       "          <pre>0xff 1_1111_111 = nan</pre>\n",
       "        </td>\n",
       "      </tr>\n",
       "    </table>\n",
       "  </body>\n",
       "</html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(mktbl(format_info_ocp_e4m3, short=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c21c16c",
   "metadata": {},
   "source": [
    "## Generate LaTeX table of min/max values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3f5a38b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>minSubnormal</th>\n",
       "      <th>maxSubnormal</th>\n",
       "      <th>minNormal</th>\n",
       "      <th>maxNormal</th>\n",
       "      <th>maxFinite</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>1*2^-62</td>\n",
       "      <td>1*2^63</td>\n",
       "      <td>1*2^63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1*2^-32</td>\n",
       "      <td>1*2^-32</td>\n",
       "      <td>1*2^-31</td>\n",
       "      <td>1*2^31</td>\n",
       "      <td>1*2^31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1*2^-17</td>\n",
       "      <td>3/2*2^-16</td>\n",
       "      <td>1*2^-15</td>\n",
       "      <td>3/2*2^15</td>\n",
       "      <td>3/2*2^15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1*2^-10</td>\n",
       "      <td>7/4*2^-8</td>\n",
       "      <td>1*2^-7</td>\n",
       "      <td>7/4*2^7</td>\n",
       "      <td>7/4*2^7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1*2^-7</td>\n",
       "      <td>15/8*2^-4</td>\n",
       "      <td>1*2^-3</td>\n",
       "      <td>15/8*2^3</td>\n",
       "      <td>15/8*2^3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1*2^-6</td>\n",
       "      <td>31/16*2^-2</td>\n",
       "      <td>1*2^-1</td>\n",
       "      <td>31/16*2^1</td>\n",
       "      <td>31/16*2^1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1*2^-6</td>\n",
       "      <td>63/32*2^-1</td>\n",
       "      <td>1*2^0</td>\n",
       "      <td>63/32*2^0</td>\n",
       "      <td>63/32*2^0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1*2^-16</td>\n",
       "      <td>3/2*2^-15</td>\n",
       "      <td>1*2^-14</td>\n",
       "      <td>7/4*2^15</td>\n",
       "      <td>7/4*2^15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1*2^-9</td>\n",
       "      <td>7/4*2^-7</td>\n",
       "      <td>1*2^-6</td>\n",
       "      <td>7/4*2^8</td>\n",
       "      <td>7/4*2^8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  minSubnormal maxSubnormal minNormal  maxNormal  maxFinite\n",
       "0          nan          nan   1*2^-62     1*2^63     1*2^63\n",
       "1      1*2^-32      1*2^-32   1*2^-31     1*2^31     1*2^31\n",
       "2      1*2^-17    3/2*2^-16   1*2^-15   3/2*2^15   3/2*2^15\n",
       "3      1*2^-10     7/4*2^-8    1*2^-7    7/4*2^7    7/4*2^7\n",
       "4       1*2^-7    15/8*2^-4    1*2^-3   15/8*2^3   15/8*2^3\n",
       "5       1*2^-6   31/16*2^-2    1*2^-1  31/16*2^1  31/16*2^1\n",
       "6       1*2^-6   63/32*2^-1     1*2^0  63/32*2^0  63/32*2^0\n",
       "7      1*2^-16    3/2*2^-15   1*2^-14   7/4*2^15   7/4*2^15\n",
       "8       1*2^-9     7/4*2^-7    1*2^-6    7/4*2^8    7/4*2^8"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_pow2[[\"minSubnormal\",\"maxSubnormal\",\"minNormal\",\"maxNormal\",\"maxFinite\"]]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a54f96c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "latex/tbl-extremalvalues.tex:% File: tbl-extremalvalues.tex\n",
      "latex/tbl-extremalvalues.tex:% Generated from https://github.com/P3109/Public/blob/main/Value%20Tables/make-value-tables.ipynb\n",
      "latex/tbl-extremalvalues.tex:\\begin{tabular}{llllll}\n",
      "latex/tbl-extremalvalues.tex:\\toprule\n",
      "latex/tbl-extremalvalues.tex:Format & minSubnormal & maxSubnormal & minNormal & maxNormal & maxFinite \\\\\n",
      "latex/tbl-extremalvalues.tex:\\midrule\n",
      "latex/tbl-extremalvalues.tex:p1 & nan & nan & 1*2^-62 & 1*2^63 & 1*2^63 \\\\\n",
      "latex/tbl-extremalvalues.tex:p2 & 1*2^-32 & 1*2^-32 & 1*2^-31 & 1*2^31 & 1*2^31 \\\\\n",
      "latex/tbl-extremalvalues.tex:p3 & 1*2^-17 & 3/2*2^-16 & 1*2^-15 & 3/2*2^15 & 3/2*2^15 \\\\\n",
      "latex/tbl-extremalvalues.tex:p4 & 1*2^-10 & 7/4*2^-8 & 1*2^-7 & 7/4*2^7 & 7/4*2^7 \\\\\n",
      "latex/tbl-extremalvalues.tex:p5 & 1*2^-7 & 15/8*2^-4 & 1*2^-3 & 15/8*2^3 & 15/8*2^3 \\\\\n",
      "latex/tbl-extremalvalues.tex:p6 & 1*2^-6 & 31/16*2^-2 & 1*2^-1 & 31/16*2^1 & 31/16*2^1 \\\\\n",
      "latex/tbl-extremalvalues.tex:p7 & 1*2^-6 & 63/32*2^-1 & 1*2^0 & 63/32*2^0 & 63/32*2^0 \\\\\n",
      "latex/tbl-extremalvalues.tex:ocp\\_e5m2 & 1*2^-16 & 3/2*2^-15 & 1*2^-14 & 7/4*2^15 & 7/4*2^15 \\\\\n",
      "latex/tbl-extremalvalues.tex:ocp\\_e4m3 & 1*2^-9 & 7/4*2^-7 & 1*2^-6 & 7/4*2^8 & 7/4*2^8 \\\\\n",
      "latex/tbl-extremalvalues.tex:\\bottomrule\n",
      "latex/tbl-extremalvalues.tex:\\end{tabular}\n"
     ]
    }
   ],
   "source": [
    "import pathlib\n",
    "dir = pathlib.Path(\"latex\")\n",
    "dir.mkdir(parents=True, exist_ok=True)\n",
    "\n",
    "tbl3 = df_pow2[[\"name\", \"minSubnormal\",\"maxSubnormal\",\"minNormal\",\"maxNormal\",\"maxFinite\"]]\n",
    "header=[\"Format\", \"minSubnormal\",\"maxSubnormal\",\"minNormal\",\"maxNormal\",\"maxFinite\"]\n",
    "latex = tbl3.to_latex(header=header, index=False, float_format=gfloat.printing.float_pow2str, na_rep='N/A')\n",
    "\n",
    "import re \n",
    "latex = re.sub('([\\d./]+)\\*2.textasciicircum ([\\d-]+)','$\\\\\\\\binaryfloat{\\\\1}{\\\\2}$', latex)\n",
    "latex = latex.replace('p3109_p', 'p')\n",
    "latex = latex.replace('ocp_', 'ocp\\_')\n",
    "\n",
    "with open('latex/tbl-extremalvalues.tex', 'w') as f:\n",
    "  pr = lambda x: print(x,file=f)\n",
    "  pr('% File: tbl-extremalvalues.tex')\n",
    "  pr('% Generated from https://github.com/P3109/Public/blob/main/Value%20Tables/make-value-tables.ipynb')\n",
    "  pr(latex)\n",
    "\n",
    "!grep -H . latex/tbl-extremalvalues.tex"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a975be51",
   "metadata": {},
   "source": [
    "## LaTeX value tables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "08da03d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving to latex/value-table-p3109_p1.tex\n",
      "Saving to latex/value-table-p3109_p2.tex\n",
      "Saving to latex/value-table-p3109_p3.tex\n",
      "Saving to latex/value-table-p3109_p4.tex\n",
      "Saving to latex/value-table-p3109_p5.tex\n",
      "Saving to latex/value-table-p3109_p6.tex\n",
      "Saving to latex/value-table-p3109_p7.tex\n",
      "Saving to latex/value-table-ocp_e5m2.tex\n",
      "Saving to latex/value-table-ocp_e4m3.tex\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def mktbltex(fi : FormatInfo, file):\n",
    "  # Make tables\n",
    "  cols = 4\n",
    "  rows = 256//cols\n",
    "\n",
    "  for i in range(0,rows):\n",
    "    out_row = []\n",
    "    for n in range(i,256,rows):\n",
    "      fv = decode_float(fi, n)\n",
    "      text = str_tablerow(fi, fv)\n",
    "      style = table_style(fv)\n",
    "\n",
    "      # 2^-7  -> \\pow{-7}\n",
    "      text = re.sub(r'\\*2\\^([-0-9]+)', r'\\\\pow{\\1}', text)\n",
    "      # 1.234E7  -> \\e{1.234}{7}\n",
    "      text = re.sub(r'([0-9.+-]+)[eE]([0-9]+)', r'\\\\e{\\1}{\\2}', text)\n",
    "      # 1.234E-7  -> \\e{1.234}{-7}\n",
    "      text = re.sub(r'([0-9.+-]+)[eE]-([0-9]+)', r'\\\\e{\\1}{\\\\neg{\\2}}', text)\n",
    "      # -1.234 EOL  -> \\f{-1.234}\n",
    "      text = re.sub(r'([0-9.+-]+)$', r'\\\\f{\\1}', text)\n",
    "      #\\f{-1.234} -> \\f{\\neg{1.234}}\n",
    "      text = re.sub(r'\\\\(f|pow)\\{-([0-9.]+)\\}', r'\\\\\\1{\\\\neg{\\2}}', text)\n",
    "      \n",
    "      # ^0x44  -> 0x44~\n",
    "      text = re.sub('^(0x[0-9a-f]+) ', '\\\\1 = ', text)\n",
    "      text = text.replace('_', '\\_')\n",
    "      text = text.replace('≈ ', '\\\\approx ')\n",
    "      out_row += [f'\\\\{style}{{{text}}}']\n",
    "    print(*out_row, sep=\"&\\n\", end=r'\\\\'+\"\\n\", file=file)\n",
    "\n",
    "for fi in p3109_and_ocp_formats:\n",
    "  filename = f\"value-table-{fi.name}.tex\"\n",
    "  print(f'Saving to {dir / filename}')\n",
    "  with open(dir / filename, \"w\") as f:\n",
    "    print('% Autogenerated from make-value-tables.ipynb', file=f)\n",
    "    mktbltex(fi, f)\n"
   ]
  }
 ],
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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