docs/source/02-value-stats.ipynb

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   "source": [
    "<!-- # Copyright (c) 2024 Graphcore Ltd. All rights reserved. -->\n",
    "\n",
    "# Collect value statistics for formats\n",
    "\n",
    "This notebook presents various statistics for a variety of float formats.\n",
    "Some of these are present on the `FormatInfo` class, and are presented for all formats.\n",
    "Others are obtained by enumerating all values (only for the =16 bit formats). \n",
    "\n",
    "## Statistics obtained from FormatInfo\n",
    "\n",
    " - name: Format\n",
    " - B: Bits in the format\n",
    " - P: Precision in bits\n",
    " - E: Exponent field width in bits\n",
    " - T: Trailing significand field width in bits\n",
    " - max: Largest finite value\n",
    " - min: Most negative value (typically the same, unless twos complement)\n",
    " - smallest: Smallest positive value\n",
    " - smallest_normal: Smallest positive normal value, NaN if all finite values are subnormal\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
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       "      <th id=\"T_my_id_level0_col4\" class=\"col_heading level0 col4\" >smallest</th>\n",
       "      <th id=\"T_my_id_level0_col5\" class=\"col_heading level0 col5\" >smallest_normal</th>\n",
       "      <th id=\"T_my_id_level0_col6\" class=\"col_heading level0 col6\" >max</th>\n",
       "      <th id=\"T_my_id_level0_col7\" class=\"col_heading level0 col7\" >num_nans</th>\n",
       "      <th id=\"T_my_id_level0_col8\" class=\"col_heading level0 col8\" >infs</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <td id=\"T_my_id_row0_col1\" class=\"data row0 col1\" >4</td>\n",
       "      <td id=\"T_my_id_row0_col2\" class=\"data row0 col2\" >2</td>\n",
       "      <td id=\"T_my_id_row0_col3\" class=\"data row0 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row0_col4\" class=\"data row0 col4\" >     0.5</td>\n",
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       "      <td id=\"T_my_id_row0_col6\" class=\"data row0 col6\" >       6</td>\n",
       "      <td id=\"T_my_id_row0_col7\" class=\"data row0 col7\" >       0</td>\n",
       "      <td id=\"T_my_id_row0_col8\" class=\"data row0 col8\" >0</td>\n",
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       "      <td id=\"T_my_id_row1_col1\" class=\"data row1 col1\" >4</td>\n",
       "      <td id=\"T_my_id_row1_col2\" class=\"data row1 col2\" >2</td>\n",
       "      <td id=\"T_my_id_row1_col3\" class=\"data row1 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row1_col4\" class=\"data row1 col4\" >    0.25</td>\n",
       "      <td id=\"T_my_id_row1_col5\" class=\"data row1 col5\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row1_col6\" class=\"data row1 col6\" >       2</td>\n",
       "      <td id=\"T_my_id_row1_col7\" class=\"data row1 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row1_col8\" class=\"data row1 col8\" >2</td>\n",
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       "    <tr>\n",
       "      <td id=\"T_my_id_row2_col0\" class=\"data row2 col0\" >ocp_e2m3</td>\n",
       "      <td id=\"T_my_id_row2_col1\" class=\"data row2 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row2_col2\" class=\"data row2 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row2_col3\" class=\"data row2 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row2_col4\" class=\"data row2 col4\" >   0.125</td>\n",
       "      <td id=\"T_my_id_row2_col5\" class=\"data row2 col5\" >       1</td>\n",
       "      <td id=\"T_my_id_row2_col6\" class=\"data row2 col6\" >     7.5</td>\n",
       "      <td id=\"T_my_id_row2_col7\" class=\"data row2 col7\" >       0</td>\n",
       "      <td id=\"T_my_id_row2_col8\" class=\"data row2 col8\" >0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row3_col0\" class=\"data row3 col0\" >ocp_e3m2</td>\n",
       "      <td id=\"T_my_id_row3_col1\" class=\"data row3 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row3_col2\" class=\"data row3 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row3_col3\" class=\"data row3 col3\" >3</td>\n",
       "      <td id=\"T_my_id_row3_col4\" class=\"data row3 col4\" >  0.0625</td>\n",
       "      <td id=\"T_my_id_row3_col5\" class=\"data row3 col5\" >    0.25</td>\n",
       "      <td id=\"T_my_id_row3_col6\" class=\"data row3 col6\" >      28</td>\n",
       "      <td id=\"T_my_id_row3_col7\" class=\"data row3 col7\" >       0</td>\n",
       "      <td id=\"T_my_id_row3_col8\" class=\"data row3 col8\" >0</td>\n",
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       "    <tr>\n",
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       "      <td id=\"T_my_id_row4_col1\" class=\"data row4 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row4_col2\" class=\"data row4 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row4_col3\" class=\"data row4 col3\" >3</td>\n",
       "      <td id=\"T_my_id_row4_col4\" class=\"data row4 col4\" > 0.03125</td>\n",
       "      <td id=\"T_my_id_row4_col5\" class=\"data row4 col5\" >   0.125</td>\n",
       "      <td id=\"T_my_id_row4_col6\" class=\"data row4 col6\" >      12</td>\n",
       "      <td id=\"T_my_id_row4_col7\" class=\"data row4 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row4_col8\" class=\"data row4 col8\" >2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row5_col0\" class=\"data row5 col0\" >p3109_6p4</td>\n",
       "      <td id=\"T_my_id_row5_col1\" class=\"data row5 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row5_col2\" class=\"data row5 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row5_col3\" class=\"data row5 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row5_col4\" class=\"data row5 col4\" >  0.0625</td>\n",
       "      <td id=\"T_my_id_row5_col5\" class=\"data row5 col5\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row5_col6\" class=\"data row5 col6\" >     3.5</td>\n",
       "      <td id=\"T_my_id_row5_col7\" class=\"data row5 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row5_col8\" class=\"data row5 col8\" >2</td>\n",
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       "    <tr>\n",
       "      <td id=\"T_my_id_row6_col0\" class=\"data row6 col0\" >ocp_e4m3</td>\n",
       "      <td id=\"T_my_id_row6_col1\" class=\"data row6 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row6_col2\" class=\"data row6 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row6_col3\" class=\"data row6 col3\" >4</td>\n",
       "      <td id=\"T_my_id_row6_col4\" class=\"data row6 col4\" >≈0.0019531</td>\n",
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       "      <td id=\"T_my_id_row6_col7\" class=\"data row6 col7\" >       2</td>\n",
       "      <td id=\"T_my_id_row6_col8\" class=\"data row6 col8\" >0</td>\n",
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       "      <td id=\"T_my_id_row7_col2\" class=\"data row7 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row7_col3\" class=\"data row7 col3\" >5</td>\n",
       "      <td id=\"T_my_id_row7_col4\" class=\"data row7 col4\" >≈1.5259e-05</td>\n",
       "      <td id=\"T_my_id_row7_col5\" class=\"data row7 col5\" >≈6.1035e-05</td>\n",
       "      <td id=\"T_my_id_row7_col6\" class=\"data row7 col6\" >   57344</td>\n",
       "      <td id=\"T_my_id_row7_col7\" class=\"data row7 col7\" >       6</td>\n",
       "      <td id=\"T_my_id_row7_col8\" class=\"data row7 col8\" >2</td>\n",
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       "      <td id=\"T_my_id_row8_col1\" class=\"data row8 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row8_col2\" class=\"data row8 col2\" >1</td>\n",
       "      <td id=\"T_my_id_row8_col3\" class=\"data row8 col3\" >7</td>\n",
       "      <td id=\"T_my_id_row8_col4\" class=\"data row8 col4\" >≈2.1684e-19</td>\n",
       "      <td id=\"T_my_id_row8_col5\" class=\"data row8 col5\" >≈2.1684e-19</td>\n",
       "      <td id=\"T_my_id_row8_col6\" class=\"data row8 col6\" >≈9.2234e+18</td>\n",
       "      <td id=\"T_my_id_row8_col7\" class=\"data row8 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row8_col8\" class=\"data row8 col8\" >2</td>\n",
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       "      <td id=\"T_my_id_row9_col2\" class=\"data row9 col2\" >2</td>\n",
       "      <td id=\"T_my_id_row9_col3\" class=\"data row9 col3\" >6</td>\n",
       "      <td id=\"T_my_id_row9_col4\" class=\"data row9 col4\" >≈2.3283e-10</td>\n",
       "      <td id=\"T_my_id_row9_col5\" class=\"data row9 col5\" >≈4.6566e-10</td>\n",
       "      <td id=\"T_my_id_row9_col6\" class=\"data row9 col6\" >≈2.1475e+09</td>\n",
       "      <td id=\"T_my_id_row9_col7\" class=\"data row9 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row9_col8\" class=\"data row9 col8\" >2</td>\n",
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       "      <td id=\"T_my_id_row10_col0\" class=\"data row10 col0\" >p3109_8p3</td>\n",
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       "      <td id=\"T_my_id_row10_col2\" class=\"data row10 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row10_col3\" class=\"data row10 col3\" >5</td>\n",
       "      <td id=\"T_my_id_row10_col4\" class=\"data row10 col4\" >≈7.6294e-06</td>\n",
       "      <td id=\"T_my_id_row10_col5\" class=\"data row10 col5\" >≈3.0518e-05</td>\n",
       "      <td id=\"T_my_id_row10_col6\" class=\"data row10 col6\" >   49152</td>\n",
       "      <td id=\"T_my_id_row10_col7\" class=\"data row10 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row10_col8\" class=\"data row10 col8\" >2</td>\n",
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       "      <td id=\"T_my_id_row11_col1\" class=\"data row11 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row11_col2\" class=\"data row11 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row11_col3\" class=\"data row11 col3\" >4</td>\n",
       "      <td id=\"T_my_id_row11_col4\" class=\"data row11 col4\" >≈0.00097656</td>\n",
       "      <td id=\"T_my_id_row11_col5\" class=\"data row11 col5\" >0.0078125</td>\n",
       "      <td id=\"T_my_id_row11_col6\" class=\"data row11 col6\" >     224</td>\n",
       "      <td id=\"T_my_id_row11_col7\" class=\"data row11 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row11_col8\" class=\"data row11 col8\" >2</td>\n",
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       "    <tr>\n",
       "      <td id=\"T_my_id_row12_col0\" class=\"data row12 col0\" >p3109_8p5</td>\n",
       "      <td id=\"T_my_id_row12_col1\" class=\"data row12 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row12_col2\" class=\"data row12 col2\" >5</td>\n",
       "      <td id=\"T_my_id_row12_col3\" class=\"data row12 col3\" >3</td>\n",
       "      <td id=\"T_my_id_row12_col4\" class=\"data row12 col4\" >0.0078125</td>\n",
       "      <td id=\"T_my_id_row12_col5\" class=\"data row12 col5\" >   0.125</td>\n",
       "      <td id=\"T_my_id_row12_col6\" class=\"data row12 col6\" >      15</td>\n",
       "      <td id=\"T_my_id_row12_col7\" class=\"data row12 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row12_col8\" class=\"data row12 col8\" >2</td>\n",
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       "      <td id=\"T_my_id_row13_col2\" class=\"data row13 col2\" >6</td>\n",
       "      <td id=\"T_my_id_row13_col3\" class=\"data row13 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row13_col4\" class=\"data row13 col4\" >0.015625</td>\n",
       "      <td id=\"T_my_id_row13_col5\" class=\"data row13 col5\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row13_col6\" class=\"data row13 col6\" >   3.875</td>\n",
       "      <td id=\"T_my_id_row13_col7\" class=\"data row13 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row13_col8\" class=\"data row13 col8\" >2</td>\n",
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       "      <td id=\"T_my_id_row14_col0\" class=\"data row14 col0\" >binary16</td>\n",
       "      <td id=\"T_my_id_row14_col1\" class=\"data row14 col1\" >16</td>\n",
       "      <td id=\"T_my_id_row14_col2\" class=\"data row14 col2\" >11</td>\n",
       "      <td id=\"T_my_id_row14_col3\" class=\"data row14 col3\" >5</td>\n",
       "      <td id=\"T_my_id_row14_col4\" class=\"data row14 col4\" >≈5.9605e-08</td>\n",
       "      <td id=\"T_my_id_row14_col5\" class=\"data row14 col5\" >≈6.1035e-05</td>\n",
       "      <td id=\"T_my_id_row14_col6\" class=\"data row14 col6\" >   65504</td>\n",
       "      <td id=\"T_my_id_row14_col7\" class=\"data row14 col7\" >    2046</td>\n",
       "      <td id=\"T_my_id_row14_col8\" class=\"data row14 col8\" >2</td>\n",
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       "      <td id=\"T_my_id_row15_col0\" class=\"data row15 col0\" >bfloat16</td>\n",
       "      <td id=\"T_my_id_row15_col1\" class=\"data row15 col1\" >16</td>\n",
       "      <td id=\"T_my_id_row15_col2\" class=\"data row15 col2\" >8</td>\n",
       "      <td id=\"T_my_id_row15_col3\" class=\"data row15 col3\" >8</td>\n",
       "      <td id=\"T_my_id_row15_col4\" class=\"data row15 col4\" >≈9.1835e-41</td>\n",
       "      <td id=\"T_my_id_row15_col5\" class=\"data row15 col5\" >≈1.1755e-38</td>\n",
       "      <td id=\"T_my_id_row15_col6\" class=\"data row15 col6\" >≈3.3895e+38</td>\n",
       "      <td id=\"T_my_id_row15_col7\" class=\"data row15 col7\" >     254</td>\n",
       "      <td id=\"T_my_id_row15_col8\" class=\"data row15 col8\" >2</td>\n",
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       "      <td id=\"T_my_id_row16_col1\" class=\"data row16 col1\" >32</td>\n",
       "      <td id=\"T_my_id_row16_col2\" class=\"data row16 col2\" >24</td>\n",
       "      <td id=\"T_my_id_row16_col3\" class=\"data row16 col3\" >8</td>\n",
       "      <td id=\"T_my_id_row16_col4\" class=\"data row16 col4\" >≈1.4013e-45</td>\n",
       "      <td id=\"T_my_id_row16_col5\" class=\"data row16 col5\" >≈1.1755e-38</td>\n",
       "      <td id=\"T_my_id_row16_col6\" class=\"data row16 col6\" >≈3.4028e+38</td>\n",
       "      <td id=\"T_my_id_row16_col7\" class=\"data row16 col7\" >≈1.6777e+07</td>\n",
       "      <td id=\"T_my_id_row16_col8\" class=\"data row16 col8\" >2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row17_col0\" class=\"data row17 col0\" >binary64</td>\n",
       "      <td id=\"T_my_id_row17_col1\" class=\"data row17 col1\" >64</td>\n",
       "      <td id=\"T_my_id_row17_col2\" class=\"data row17 col2\" >53</td>\n",
       "      <td id=\"T_my_id_row17_col3\" class=\"data row17 col3\" >11</td>\n",
       "      <td id=\"T_my_id_row17_col4\" class=\"data row17 col4\" >4.9407e-324</td>\n",
       "      <td id=\"T_my_id_row17_col5\" class=\"data row17 col5\" >≈2.2251e-308</td>\n",
       "      <td id=\"T_my_id_row17_col6\" class=\"data row17 col6\" >≈1.7977e+308</td>\n",
       "      <td id=\"T_my_id_row17_col7\" class=\"data row17 col7\" >≈9.0072e+15</td>\n",
       "      <td id=\"T_my_id_row17_col8\" class=\"data row17 col8\" >2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row18_col0\" class=\"data row18 col0\" >ocp_e8m0</td>\n",
       "      <td id=\"T_my_id_row18_col1\" class=\"data row18 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row18_col2\" class=\"data row18 col2\" >1</td>\n",
       "      <td id=\"T_my_id_row18_col3\" class=\"data row18 col3\" >8</td>\n",
       "      <td id=\"T_my_id_row18_col4\" class=\"data row18 col4\" >≈5.8775e-39</td>\n",
       "      <td id=\"T_my_id_row18_col5\" class=\"data row18 col5\" >≈5.8775e-39</td>\n",
       "      <td id=\"T_my_id_row18_col6\" class=\"data row18 col6\" >≈1.7014e+38</td>\n",
       "      <td id=\"T_my_id_row18_col7\" class=\"data row18 col7\" >       1</td>\n",
       "      <td id=\"T_my_id_row18_col8\" class=\"data row18 col8\" >0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row19_col0\" class=\"data row19 col0\" >ocp_int8</td>\n",
       "      <td id=\"T_my_id_row19_col1\" class=\"data row19 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row19_col2\" class=\"data row19 col2\" >8</td>\n",
       "      <td id=\"T_my_id_row19_col3\" class=\"data row19 col3\" >0</td>\n",
       "      <td id=\"T_my_id_row19_col4\" class=\"data row19 col4\" >0.015625</td>\n",
       "      <td id=\"T_my_id_row19_col5\" class=\"data row19 col5\" >n/a</td>\n",
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       "      <td id=\"T_my_id_row19_col7\" class=\"data row19 col7\" >       0</td>\n",
       "      <td id=\"T_my_id_row19_col8\" class=\"data row19 col8\" >0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%run utils.py\n",
    "D = pandas_render  # from utils\n",
    "import pandas\n",
    "from functools import partial\n",
    "from gfloat import *\n",
    "from gfloat.formats import *\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "# Special rendering for float values -\n",
    "# if they don't round-trip in 8.5g, prepend with \"≈\", or render as rational\n",
    "def render_float(approx: bool, v):\n",
    "    if not isinstance(v, float):\n",
    "        return str(v)\n",
    "\n",
    "    if np.isnan(v):\n",
    "        return \"n/a\"\n",
    "\n",
    "    s = f\"{v:8.5g}\"\n",
    "    if float(s) == v:\n",
    "        return s\n",
    "\n",
    "    if approx:\n",
    "        return \"≈\" + s\n",
    "    else:\n",
    "        return float_pow2str(v)\n",
    "\n",
    "\n",
    "def collect_stats(fi: FormatInfo):\n",
    "    return dict(\n",
    "        name=fi.name,\n",
    "        B=fi.bits,\n",
    "        P=fi.precision,\n",
    "        E=fi.expBits,\n",
    "        smallest=fi.smallest,\n",
    "        smallest_normal=fi.smallest_normal if not fi.is_all_subnormal else np.nan,\n",
    "        max=fi.max,\n",
    "        num_nans=float(fi.num_nans),\n",
    "        infs=2 if fi.has_infs else 0,\n",
    "    )\n",
    "\n",
    "\n",
    "stats = [collect_stats(fi) for fi in all_formats]\n",
    "df = pandas.DataFrame(stats)\n",
    "D(df, format=partial(render_float, True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Statistics computed by exhaustive inspection\n",
    "\n",
    " - lt1: Number of values x such that `0 < x < 1`\n",
    " - gt1: Number of values x such that `1 < x < Inf`\n",
    " - rt16: True if all values are exactly representable in IEEE binary16\n",
    " - min/maxSubnormal: Smallest/largest subnormal value, \"n/a\" if no values are subnormal\n",
    " - min/maxNormal: Smallest/largest normal value, \"n/a\" if no values are normal\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "</style>\n",
       "<table id=\"T_my_id\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th id=\"T_my_id_level0_col0\" class=\"col_heading level0 col0\" >name</th>\n",
       "      <th id=\"T_my_id_level0_col1\" class=\"col_heading level0 col1\" >B</th>\n",
       "      <th id=\"T_my_id_level0_col2\" class=\"col_heading level0 col2\" >P</th>\n",
       "      <th id=\"T_my_id_level0_col3\" class=\"col_heading level0 col3\" >E</th>\n",
       "      <th id=\"T_my_id_level0_col4\" class=\"col_heading level0 col4\" >rt16</th>\n",
       "      <th id=\"T_my_id_level0_col5\" class=\"col_heading level0 col5\" >lt1</th>\n",
       "      <th id=\"T_my_id_level0_col6\" class=\"col_heading level0 col6\" >gt1</th>\n",
       "      <th id=\"T_my_id_level0_col7\" class=\"col_heading level0 col7\" >minSubnormal</th>\n",
       "      <th id=\"T_my_id_level0_col8\" class=\"col_heading level0 col8\" >maxSubnormal</th>\n",
       "      <th id=\"T_my_id_level0_col9\" class=\"col_heading level0 col9\" >minNormal</th>\n",
       "      <th id=\"T_my_id_level0_col10\" class=\"col_heading level0 col10\" >maxNormal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row0_col0\" class=\"data row0 col0\" >ocp_e2m1</td>\n",
       "      <td id=\"T_my_id_row0_col1\" class=\"data row0 col1\" >4</td>\n",
       "      <td id=\"T_my_id_row0_col2\" class=\"data row0 col2\" >2</td>\n",
       "      <td id=\"T_my_id_row0_col3\" class=\"data row0 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row0_col4\" class=\"data row0 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row0_col5\" class=\"data row0 col5\" >1</td>\n",
       "      <td id=\"T_my_id_row0_col6\" class=\"data row0 col6\" >5</td>\n",
       "      <td id=\"T_my_id_row0_col7\" class=\"data row0 col7\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row0_col8\" class=\"data row0 col8\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row0_col9\" class=\"data row0 col9\" >       1</td>\n",
       "      <td id=\"T_my_id_row0_col10\" class=\"data row0 col10\" >       6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row1_col0\" class=\"data row1 col0\" >p3109_4p2</td>\n",
       "      <td id=\"T_my_id_row1_col1\" class=\"data row1 col1\" >4</td>\n",
       "      <td id=\"T_my_id_row1_col2\" class=\"data row1 col2\" >2</td>\n",
       "      <td id=\"T_my_id_row1_col3\" class=\"data row1 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row1_col4\" class=\"data row1 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row1_col5\" class=\"data row1 col5\" >3</td>\n",
       "      <td id=\"T_my_id_row1_col6\" class=\"data row1 col6\" >2</td>\n",
       "      <td id=\"T_my_id_row1_col7\" class=\"data row1 col7\" >    0.25</td>\n",
       "      <td id=\"T_my_id_row1_col8\" class=\"data row1 col8\" >    0.25</td>\n",
       "      <td id=\"T_my_id_row1_col9\" class=\"data row1 col9\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row1_col10\" class=\"data row1 col10\" >       2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row2_col0\" class=\"data row2 col0\" >ocp_e2m3</td>\n",
       "      <td id=\"T_my_id_row2_col1\" class=\"data row2 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row2_col2\" class=\"data row2 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row2_col3\" class=\"data row2 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row2_col4\" class=\"data row2 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row2_col5\" class=\"data row2 col5\" >7</td>\n",
       "      <td id=\"T_my_id_row2_col6\" class=\"data row2 col6\" >23</td>\n",
       "      <td id=\"T_my_id_row2_col7\" class=\"data row2 col7\" >   0.125</td>\n",
       "      <td id=\"T_my_id_row2_col8\" class=\"data row2 col8\" >   0.875</td>\n",
       "      <td id=\"T_my_id_row2_col9\" class=\"data row2 col9\" >       1</td>\n",
       "      <td id=\"T_my_id_row2_col10\" class=\"data row2 col10\" >     7.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row3_col0\" class=\"data row3 col0\" >ocp_e3m2</td>\n",
       "      <td id=\"T_my_id_row3_col1\" class=\"data row3 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row3_col2\" class=\"data row3 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row3_col3\" class=\"data row3 col3\" >3</td>\n",
       "      <td id=\"T_my_id_row3_col4\" class=\"data row3 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row3_col5\" class=\"data row3 col5\" >11</td>\n",
       "      <td id=\"T_my_id_row3_col6\" class=\"data row3 col6\" >19</td>\n",
       "      <td id=\"T_my_id_row3_col7\" class=\"data row3 col7\" >  0.0625</td>\n",
       "      <td id=\"T_my_id_row3_col8\" class=\"data row3 col8\" >  0.1875</td>\n",
       "      <td id=\"T_my_id_row3_col9\" class=\"data row3 col9\" >    0.25</td>\n",
       "      <td id=\"T_my_id_row3_col10\" class=\"data row3 col10\" >      28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row4_col0\" class=\"data row4 col0\" >p3109_6p3</td>\n",
       "      <td id=\"T_my_id_row4_col1\" class=\"data row4 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row4_col2\" class=\"data row4 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row4_col3\" class=\"data row4 col3\" >3</td>\n",
       "      <td id=\"T_my_id_row4_col4\" class=\"data row4 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row4_col5\" class=\"data row4 col5\" >15</td>\n",
       "      <td id=\"T_my_id_row4_col6\" class=\"data row4 col6\" >14</td>\n",
       "      <td id=\"T_my_id_row4_col7\" class=\"data row4 col7\" > 0.03125</td>\n",
       "      <td id=\"T_my_id_row4_col8\" class=\"data row4 col8\" > 0.09375</td>\n",
       "      <td id=\"T_my_id_row4_col9\" class=\"data row4 col9\" >   0.125</td>\n",
       "      <td id=\"T_my_id_row4_col10\" class=\"data row4 col10\" >      12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row5_col0\" class=\"data row5 col0\" >p3109_6p4</td>\n",
       "      <td id=\"T_my_id_row5_col1\" class=\"data row5 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row5_col2\" class=\"data row5 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row5_col3\" class=\"data row5 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row5_col4\" class=\"data row5 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row5_col5\" class=\"data row5 col5\" >15</td>\n",
       "      <td id=\"T_my_id_row5_col6\" class=\"data row5 col6\" >14</td>\n",
       "      <td id=\"T_my_id_row5_col7\" class=\"data row5 col7\" >  0.0625</td>\n",
       "      <td id=\"T_my_id_row5_col8\" class=\"data row5 col8\" >  0.4375</td>\n",
       "      <td id=\"T_my_id_row5_col9\" class=\"data row5 col9\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row5_col10\" class=\"data row5 col10\" >     3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row6_col0\" class=\"data row6 col0\" >ocp_e4m3</td>\n",
       "      <td id=\"T_my_id_row6_col1\" class=\"data row6 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row6_col2\" class=\"data row6 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row6_col3\" class=\"data row6 col3\" >4</td>\n",
       "      <td id=\"T_my_id_row6_col4\" class=\"data row6 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row6_col5\" class=\"data row6 col5\" >55</td>\n",
       "      <td id=\"T_my_id_row6_col6\" class=\"data row6 col6\" >70</td>\n",
       "      <td id=\"T_my_id_row6_col7\" class=\"data row6 col7\" >≈0.0019531</td>\n",
       "      <td id=\"T_my_id_row6_col8\" class=\"data row6 col8\" >≈0.013672</td>\n",
       "      <td id=\"T_my_id_row6_col9\" class=\"data row6 col9\" >0.015625</td>\n",
       "      <td id=\"T_my_id_row6_col10\" class=\"data row6 col10\" >     448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row7_col0\" class=\"data row7 col0\" >ocp_e5m2</td>\n",
       "      <td id=\"T_my_id_row7_col1\" class=\"data row7 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row7_col2\" class=\"data row7 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row7_col3\" class=\"data row7 col3\" >5</td>\n",
       "      <td id=\"T_my_id_row7_col4\" class=\"data row7 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row7_col5\" class=\"data row7 col5\" >59</td>\n",
       "      <td id=\"T_my_id_row7_col6\" class=\"data row7 col6\" >63</td>\n",
       "      <td id=\"T_my_id_row7_col7\" class=\"data row7 col7\" >≈1.5259e-05</td>\n",
       "      <td id=\"T_my_id_row7_col8\" class=\"data row7 col8\" >≈4.5776e-05</td>\n",
       "      <td id=\"T_my_id_row7_col9\" class=\"data row7 col9\" >≈6.1035e-05</td>\n",
       "      <td id=\"T_my_id_row7_col10\" class=\"data row7 col10\" >   57344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row8_col0\" class=\"data row8 col0\" >p3109_8p1</td>\n",
       "      <td id=\"T_my_id_row8_col1\" class=\"data row8 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row8_col2\" class=\"data row8 col2\" >1</td>\n",
       "      <td id=\"T_my_id_row8_col3\" class=\"data row8 col3\" >7</td>\n",
       "      <td id=\"T_my_id_row8_col4\" class=\"data row8 col4\" >False</td>\n",
       "      <td id=\"T_my_id_row8_col5\" class=\"data row8 col5\" >62</td>\n",
       "      <td id=\"T_my_id_row8_col6\" class=\"data row8 col6\" >63</td>\n",
       "      <td id=\"T_my_id_row8_col7\" class=\"data row8 col7\" >n/a</td>\n",
       "      <td id=\"T_my_id_row8_col8\" class=\"data row8 col8\" >n/a</td>\n",
       "      <td id=\"T_my_id_row8_col9\" class=\"data row8 col9\" >≈2.1684e-19</td>\n",
       "      <td id=\"T_my_id_row8_col10\" class=\"data row8 col10\" >≈9.2234e+18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row9_col0\" class=\"data row9 col0\" >p3109_8p2</td>\n",
       "      <td id=\"T_my_id_row9_col1\" class=\"data row9 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row9_col2\" class=\"data row9 col2\" >2</td>\n",
       "      <td id=\"T_my_id_row9_col3\" class=\"data row9 col3\" >6</td>\n",
       "      <td id=\"T_my_id_row9_col4\" class=\"data row9 col4\" >False</td>\n",
       "      <td id=\"T_my_id_row9_col5\" class=\"data row9 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row9_col6\" class=\"data row9 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row9_col7\" class=\"data row9 col7\" >≈2.3283e-10</td>\n",
       "      <td id=\"T_my_id_row9_col8\" class=\"data row9 col8\" >≈2.3283e-10</td>\n",
       "      <td id=\"T_my_id_row9_col9\" class=\"data row9 col9\" >≈4.6566e-10</td>\n",
       "      <td id=\"T_my_id_row9_col10\" class=\"data row9 col10\" >≈2.1475e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row10_col0\" class=\"data row10 col0\" >p3109_8p3</td>\n",
       "      <td id=\"T_my_id_row10_col1\" class=\"data row10 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row10_col2\" class=\"data row10 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row10_col3\" class=\"data row10 col3\" >5</td>\n",
       "      <td id=\"T_my_id_row10_col4\" class=\"data row10 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row10_col5\" class=\"data row10 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row10_col6\" class=\"data row10 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row10_col7\" class=\"data row10 col7\" >≈7.6294e-06</td>\n",
       "      <td id=\"T_my_id_row10_col8\" class=\"data row10 col8\" >≈2.2888e-05</td>\n",
       "      <td id=\"T_my_id_row10_col9\" class=\"data row10 col9\" >≈3.0518e-05</td>\n",
       "      <td id=\"T_my_id_row10_col10\" class=\"data row10 col10\" >   49152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row11_col0\" class=\"data row11 col0\" >p3109_8p4</td>\n",
       "      <td id=\"T_my_id_row11_col1\" class=\"data row11 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row11_col2\" class=\"data row11 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row11_col3\" class=\"data row11 col3\" >4</td>\n",
       "      <td id=\"T_my_id_row11_col4\" class=\"data row11 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row11_col5\" class=\"data row11 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row11_col6\" class=\"data row11 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row11_col7\" class=\"data row11 col7\" >≈0.00097656</td>\n",
       "      <td id=\"T_my_id_row11_col8\" class=\"data row11 col8\" >≈0.0068359</td>\n",
       "      <td id=\"T_my_id_row11_col9\" class=\"data row11 col9\" >0.0078125</td>\n",
       "      <td id=\"T_my_id_row11_col10\" class=\"data row11 col10\" >     224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row12_col0\" class=\"data row12 col0\" >p3109_8p5</td>\n",
       "      <td id=\"T_my_id_row12_col1\" class=\"data row12 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row12_col2\" class=\"data row12 col2\" >5</td>\n",
       "      <td id=\"T_my_id_row12_col3\" class=\"data row12 col3\" >3</td>\n",
       "      <td id=\"T_my_id_row12_col4\" class=\"data row12 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row12_col5\" class=\"data row12 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row12_col6\" class=\"data row12 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row12_col7\" class=\"data row12 col7\" >0.0078125</td>\n",
       "      <td id=\"T_my_id_row12_col8\" class=\"data row12 col8\" >≈ 0.11719</td>\n",
       "      <td id=\"T_my_id_row12_col9\" class=\"data row12 col9\" >   0.125</td>\n",
       "      <td id=\"T_my_id_row12_col10\" class=\"data row12 col10\" >      15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row13_col0\" class=\"data row13 col0\" >p3109_8p6</td>\n",
       "      <td id=\"T_my_id_row13_col1\" class=\"data row13 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row13_col2\" class=\"data row13 col2\" >6</td>\n",
       "      <td id=\"T_my_id_row13_col3\" class=\"data row13 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row13_col4\" class=\"data row13 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row13_col5\" class=\"data row13 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row13_col6\" class=\"data row13 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row13_col7\" class=\"data row13 col7\" >0.015625</td>\n",
       "      <td id=\"T_my_id_row13_col8\" class=\"data row13 col8\" >≈ 0.48438</td>\n",
       "      <td id=\"T_my_id_row13_col9\" class=\"data row13 col9\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row13_col10\" class=\"data row13 col10\" >   3.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row14_col0\" class=\"data row14 col0\" >binary16</td>\n",
       "      <td id=\"T_my_id_row14_col1\" class=\"data row14 col1\" >16</td>\n",
       "      <td id=\"T_my_id_row14_col2\" class=\"data row14 col2\" >11</td>\n",
       "      <td id=\"T_my_id_row14_col3\" class=\"data row14 col3\" >5</td>\n",
       "      <td id=\"T_my_id_row14_col4\" class=\"data row14 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row14_col5\" class=\"data row14 col5\" >15359</td>\n",
       "      <td id=\"T_my_id_row14_col6\" class=\"data row14 col6\" >16383</td>\n",
       "      <td id=\"T_my_id_row14_col7\" class=\"data row14 col7\" >≈5.9605e-08</td>\n",
       "      <td id=\"T_my_id_row14_col8\" class=\"data row14 col8\" >≈6.0976e-05</td>\n",
       "      <td id=\"T_my_id_row14_col9\" class=\"data row14 col9\" >≈6.1035e-05</td>\n",
       "      <td id=\"T_my_id_row14_col10\" class=\"data row14 col10\" >   65504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row15_col0\" class=\"data row15 col0\" >bfloat16</td>\n",
       "      <td id=\"T_my_id_row15_col1\" class=\"data row15 col1\" >16</td>\n",
       "      <td id=\"T_my_id_row15_col2\" class=\"data row15 col2\" >8</td>\n",
       "      <td id=\"T_my_id_row15_col3\" class=\"data row15 col3\" >8</td>\n",
       "      <td id=\"T_my_id_row15_col4\" class=\"data row15 col4\" >False</td>\n",
       "      <td id=\"T_my_id_row15_col5\" class=\"data row15 col5\" >16255</td>\n",
       "      <td id=\"T_my_id_row15_col6\" class=\"data row15 col6\" >16383</td>\n",
       "      <td id=\"T_my_id_row15_col7\" class=\"data row15 col7\" >≈9.1835e-41</td>\n",
       "      <td id=\"T_my_id_row15_col8\" class=\"data row15 col8\" >≈1.1663e-38</td>\n",
       "      <td id=\"T_my_id_row15_col9\" class=\"data row15 col9\" >≈1.1755e-38</td>\n",
       "      <td id=\"T_my_id_row15_col10\" class=\"data row15 col10\" >≈3.3895e+38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row16_col0\" class=\"data row16 col0\" >ocp_e8m0</td>\n",
       "      <td id=\"T_my_id_row16_col1\" class=\"data row16 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row16_col2\" class=\"data row16 col2\" >1</td>\n",
       "      <td id=\"T_my_id_row16_col3\" class=\"data row16 col3\" >8</td>\n",
       "      <td id=\"T_my_id_row16_col4\" class=\"data row16 col4\" >False</td>\n",
       "      <td id=\"T_my_id_row16_col5\" class=\"data row16 col5\" >127</td>\n",
       "      <td id=\"T_my_id_row16_col6\" class=\"data row16 col6\" >127</td>\n",
       "      <td id=\"T_my_id_row16_col7\" class=\"data row16 col7\" >n/a</td>\n",
       "      <td id=\"T_my_id_row16_col8\" class=\"data row16 col8\" >n/a</td>\n",
       "      <td id=\"T_my_id_row16_col9\" class=\"data row16 col9\" >≈5.8775e-39</td>\n",
       "      <td id=\"T_my_id_row16_col10\" class=\"data row16 col10\" >≈1.7014e+38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row17_col0\" class=\"data row17 col0\" >ocp_int8</td>\n",
       "      <td id=\"T_my_id_row17_col1\" class=\"data row17 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row17_col2\" class=\"data row17 col2\" >8</td>\n",
       "      <td id=\"T_my_id_row17_col3\" class=\"data row17 col3\" >0</td>\n",
       "      <td id=\"T_my_id_row17_col4\" class=\"data row17 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row17_col5\" class=\"data row17 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row17_col6\" class=\"data row17 col6\" >63</td>\n",
       "      <td id=\"T_my_id_row17_col7\" class=\"data row17 col7\" >0.015625</td>\n",
       "      <td id=\"T_my_id_row17_col8\" class=\"data row17 col8\" >≈  1.9844</td>\n",
       "      <td id=\"T_my_id_row17_col9\" class=\"data row17 col9\" >n/a</td>\n",
       "      <td id=\"T_my_id_row17_col10\" class=\"data row17 col10\" >n/a</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def compute_stats(fi: FormatInfo):\n",
    "    # Generate all values\n",
    "    values = [decode_float(fi, i) for i in range(2**fi.bits)]\n",
    "    df = pandas.DataFrame(values)\n",
    "\n",
    "    # Compute statistics: lt1,gt1\n",
    "    fval = df[\"fval\"]\n",
    "    total_01 = fval.between(0, 1, inclusive=\"neither\").sum()\n",
    "    total_1Inf = fval.between(1, np.inf, inclusive=\"neither\").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",
    "    assert maxFinite == fi.max\n",
    "    assert minFinite == fi.min\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",
    "    assert np.isnan(maxNormal) or maxNormal == fi.max\n",
    "    assert np.isnan(minNormal) or minNormal == fi.smallest_normal\n",
    "\n",
    "    # Compute statistics: minSubnormal\n",
    "    pos_subnormal = fval[(df[\"fclass\"] == FloatClass.SUBNORMAL) & (fval > 0)]\n",
    "    maxSubnormal = (\n",
    "        pos_subnormal.loc[pos_subnormal.idxmax()] if pos_subnormal.any() else np.nan\n",
    "    )\n",
    "    minSubnormal = (\n",
    "        pos_subnormal.loc[pos_subnormal.idxmin()] if pos_subnormal.any() else np.nan\n",
    "    )\n",
    "    assert np.isnan(minSubnormal) or minSubnormal == fi.smallest_subnormal\n",
    "\n",
    "    assert np.nanmin([minSubnormal, minNormal]) == fi.smallest\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(\n",
    "        name=fi.name,\n",
    "        B=fi.bits,\n",
    "        P=fi.precision,\n",
    "        E=fi.expBits,\n",
    "        rt16=rt16,\n",
    "        lt1=total_01,\n",
    "        gt1=total_1Inf,\n",
    "        minSubnormal=minSubnormal,\n",
    "        maxSubnormal=maxSubnormal,\n",
    "        minNormal=minNormal,\n",
    "        maxNormal=maxNormal,\n",
    "    )\n",
    "\n",
    "\n",
    "stats = [compute_stats(fi) for fi in all_formats if fi.bits <= 16]\n",
    "df2 = pandas.DataFrame(stats)\n",
    "D(df2, format=partial(render_float, True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Emit the same table, but with exact values\n",
    "\n",
    "In this table, float values are printed as decimals, unless the decimals are not an\n",
    "exact representation of the value, in which case, they are printed as rationals (between 1 and 2) times 2^E."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "</style>\n",
       "<table id=\"T_my_id\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th id=\"T_my_id_level0_col0\" class=\"col_heading level0 col0\" >name</th>\n",
       "      <th id=\"T_my_id_level0_col1\" class=\"col_heading level0 col1\" >B</th>\n",
       "      <th id=\"T_my_id_level0_col2\" class=\"col_heading level0 col2\" >P</th>\n",
       "      <th id=\"T_my_id_level0_col3\" class=\"col_heading level0 col3\" >E</th>\n",
       "      <th id=\"T_my_id_level0_col4\" class=\"col_heading level0 col4\" >rt16</th>\n",
       "      <th id=\"T_my_id_level0_col5\" class=\"col_heading level0 col5\" >lt1</th>\n",
       "      <th id=\"T_my_id_level0_col6\" class=\"col_heading level0 col6\" >gt1</th>\n",
       "      <th id=\"T_my_id_level0_col7\" class=\"col_heading level0 col7\" >minSubnormal</th>\n",
       "      <th id=\"T_my_id_level0_col8\" class=\"col_heading level0 col8\" >maxSubnormal</th>\n",
       "      <th id=\"T_my_id_level0_col9\" class=\"col_heading level0 col9\" >minNormal</th>\n",
       "      <th id=\"T_my_id_level0_col10\" class=\"col_heading level0 col10\" >maxNormal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row0_col0\" class=\"data row0 col0\" >ocp_e2m1</td>\n",
       "      <td id=\"T_my_id_row0_col1\" class=\"data row0 col1\" >4</td>\n",
       "      <td id=\"T_my_id_row0_col2\" class=\"data row0 col2\" >2</td>\n",
       "      <td id=\"T_my_id_row0_col3\" class=\"data row0 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row0_col4\" class=\"data row0 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row0_col5\" class=\"data row0 col5\" >1</td>\n",
       "      <td id=\"T_my_id_row0_col6\" class=\"data row0 col6\" >5</td>\n",
       "      <td id=\"T_my_id_row0_col7\" class=\"data row0 col7\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row0_col8\" class=\"data row0 col8\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row0_col9\" class=\"data row0 col9\" >       1</td>\n",
       "      <td id=\"T_my_id_row0_col10\" class=\"data row0 col10\" >       6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row1_col0\" class=\"data row1 col0\" >p3109_4p2</td>\n",
       "      <td id=\"T_my_id_row1_col1\" class=\"data row1 col1\" >4</td>\n",
       "      <td id=\"T_my_id_row1_col2\" class=\"data row1 col2\" >2</td>\n",
       "      <td id=\"T_my_id_row1_col3\" class=\"data row1 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row1_col4\" class=\"data row1 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row1_col5\" class=\"data row1 col5\" >3</td>\n",
       "      <td id=\"T_my_id_row1_col6\" class=\"data row1 col6\" >2</td>\n",
       "      <td id=\"T_my_id_row1_col7\" class=\"data row1 col7\" >    0.25</td>\n",
       "      <td id=\"T_my_id_row1_col8\" class=\"data row1 col8\" >    0.25</td>\n",
       "      <td id=\"T_my_id_row1_col9\" class=\"data row1 col9\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row1_col10\" class=\"data row1 col10\" >       2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row2_col0\" class=\"data row2 col0\" >ocp_e2m3</td>\n",
       "      <td id=\"T_my_id_row2_col1\" class=\"data row2 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row2_col2\" class=\"data row2 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row2_col3\" class=\"data row2 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row2_col4\" class=\"data row2 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row2_col5\" class=\"data row2 col5\" >7</td>\n",
       "      <td id=\"T_my_id_row2_col6\" class=\"data row2 col6\" >23</td>\n",
       "      <td id=\"T_my_id_row2_col7\" class=\"data row2 col7\" >   0.125</td>\n",
       "      <td id=\"T_my_id_row2_col8\" class=\"data row2 col8\" >   0.875</td>\n",
       "      <td id=\"T_my_id_row2_col9\" class=\"data row2 col9\" >       1</td>\n",
       "      <td id=\"T_my_id_row2_col10\" class=\"data row2 col10\" >     7.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row3_col0\" class=\"data row3 col0\" >ocp_e3m2</td>\n",
       "      <td id=\"T_my_id_row3_col1\" class=\"data row3 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row3_col2\" class=\"data row3 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row3_col3\" class=\"data row3 col3\" >3</td>\n",
       "      <td id=\"T_my_id_row3_col4\" class=\"data row3 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row3_col5\" class=\"data row3 col5\" >11</td>\n",
       "      <td id=\"T_my_id_row3_col6\" class=\"data row3 col6\" >19</td>\n",
       "      <td id=\"T_my_id_row3_col7\" class=\"data row3 col7\" >  0.0625</td>\n",
       "      <td id=\"T_my_id_row3_col8\" class=\"data row3 col8\" >  0.1875</td>\n",
       "      <td id=\"T_my_id_row3_col9\" class=\"data row3 col9\" >    0.25</td>\n",
       "      <td id=\"T_my_id_row3_col10\" class=\"data row3 col10\" >      28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row4_col0\" class=\"data row4 col0\" >p3109_6p3</td>\n",
       "      <td id=\"T_my_id_row4_col1\" class=\"data row4 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row4_col2\" class=\"data row4 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row4_col3\" class=\"data row4 col3\" >3</td>\n",
       "      <td id=\"T_my_id_row4_col4\" class=\"data row4 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row4_col5\" class=\"data row4 col5\" >15</td>\n",
       "      <td id=\"T_my_id_row4_col6\" class=\"data row4 col6\" >14</td>\n",
       "      <td id=\"T_my_id_row4_col7\" class=\"data row4 col7\" > 0.03125</td>\n",
       "      <td id=\"T_my_id_row4_col8\" class=\"data row4 col8\" > 0.09375</td>\n",
       "      <td id=\"T_my_id_row4_col9\" class=\"data row4 col9\" >   0.125</td>\n",
       "      <td id=\"T_my_id_row4_col10\" class=\"data row4 col10\" >      12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row5_col0\" class=\"data row5 col0\" >p3109_6p4</td>\n",
       "      <td id=\"T_my_id_row5_col1\" class=\"data row5 col1\" >6</td>\n",
       "      <td id=\"T_my_id_row5_col2\" class=\"data row5 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row5_col3\" class=\"data row5 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row5_col4\" class=\"data row5 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row5_col5\" class=\"data row5 col5\" >15</td>\n",
       "      <td id=\"T_my_id_row5_col6\" class=\"data row5 col6\" >14</td>\n",
       "      <td id=\"T_my_id_row5_col7\" class=\"data row5 col7\" >  0.0625</td>\n",
       "      <td id=\"T_my_id_row5_col8\" class=\"data row5 col8\" >  0.4375</td>\n",
       "      <td id=\"T_my_id_row5_col9\" class=\"data row5 col9\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row5_col10\" class=\"data row5 col10\" >     3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row6_col0\" class=\"data row6 col0\" >ocp_e4m3</td>\n",
       "      <td id=\"T_my_id_row6_col1\" class=\"data row6 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row6_col2\" class=\"data row6 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row6_col3\" class=\"data row6 col3\" >4</td>\n",
       "      <td id=\"T_my_id_row6_col4\" class=\"data row6 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row6_col5\" class=\"data row6 col5\" >55</td>\n",
       "      <td id=\"T_my_id_row6_col6\" class=\"data row6 col6\" >70</td>\n",
       "      <td id=\"T_my_id_row6_col7\" class=\"data row6 col7\" >2^-9</td>\n",
       "      <td id=\"T_my_id_row6_col8\" class=\"data row6 col8\" >7/4*2^-7</td>\n",
       "      <td id=\"T_my_id_row6_col9\" class=\"data row6 col9\" >0.015625</td>\n",
       "      <td id=\"T_my_id_row6_col10\" class=\"data row6 col10\" >     448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row7_col0\" class=\"data row7 col0\" >ocp_e5m2</td>\n",
       "      <td id=\"T_my_id_row7_col1\" class=\"data row7 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row7_col2\" class=\"data row7 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row7_col3\" class=\"data row7 col3\" >5</td>\n",
       "      <td id=\"T_my_id_row7_col4\" class=\"data row7 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row7_col5\" class=\"data row7 col5\" >59</td>\n",
       "      <td id=\"T_my_id_row7_col6\" class=\"data row7 col6\" >63</td>\n",
       "      <td id=\"T_my_id_row7_col7\" class=\"data row7 col7\" >2^-16</td>\n",
       "      <td id=\"T_my_id_row7_col8\" class=\"data row7 col8\" >3/2*2^-15</td>\n",
       "      <td id=\"T_my_id_row7_col9\" class=\"data row7 col9\" >2^-14</td>\n",
       "      <td id=\"T_my_id_row7_col10\" class=\"data row7 col10\" >   57344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row8_col0\" class=\"data row8 col0\" >p3109_8p1</td>\n",
       "      <td id=\"T_my_id_row8_col1\" class=\"data row8 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row8_col2\" class=\"data row8 col2\" >1</td>\n",
       "      <td id=\"T_my_id_row8_col3\" class=\"data row8 col3\" >7</td>\n",
       "      <td id=\"T_my_id_row8_col4\" class=\"data row8 col4\" >False</td>\n",
       "      <td id=\"T_my_id_row8_col5\" class=\"data row8 col5\" >62</td>\n",
       "      <td id=\"T_my_id_row8_col6\" class=\"data row8 col6\" >63</td>\n",
       "      <td id=\"T_my_id_row8_col7\" class=\"data row8 col7\" >n/a</td>\n",
       "      <td id=\"T_my_id_row8_col8\" class=\"data row8 col8\" >n/a</td>\n",
       "      <td id=\"T_my_id_row8_col9\" class=\"data row8 col9\" >2^-62</td>\n",
       "      <td id=\"T_my_id_row8_col10\" class=\"data row8 col10\" >2^63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row9_col0\" class=\"data row9 col0\" >p3109_8p2</td>\n",
       "      <td id=\"T_my_id_row9_col1\" class=\"data row9 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row9_col2\" class=\"data row9 col2\" >2</td>\n",
       "      <td id=\"T_my_id_row9_col3\" class=\"data row9 col3\" >6</td>\n",
       "      <td id=\"T_my_id_row9_col4\" class=\"data row9 col4\" >False</td>\n",
       "      <td id=\"T_my_id_row9_col5\" class=\"data row9 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row9_col6\" class=\"data row9 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row9_col7\" class=\"data row9 col7\" >2^-32</td>\n",
       "      <td id=\"T_my_id_row9_col8\" class=\"data row9 col8\" >2^-32</td>\n",
       "      <td id=\"T_my_id_row9_col9\" class=\"data row9 col9\" >2^-31</td>\n",
       "      <td id=\"T_my_id_row9_col10\" class=\"data row9 col10\" >2^31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row10_col0\" class=\"data row10 col0\" >p3109_8p3</td>\n",
       "      <td id=\"T_my_id_row10_col1\" class=\"data row10 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row10_col2\" class=\"data row10 col2\" >3</td>\n",
       "      <td id=\"T_my_id_row10_col3\" class=\"data row10 col3\" >5</td>\n",
       "      <td id=\"T_my_id_row10_col4\" class=\"data row10 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row10_col5\" class=\"data row10 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row10_col6\" class=\"data row10 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row10_col7\" class=\"data row10 col7\" >2^-17</td>\n",
       "      <td id=\"T_my_id_row10_col8\" class=\"data row10 col8\" >3/2*2^-16</td>\n",
       "      <td id=\"T_my_id_row10_col9\" class=\"data row10 col9\" >2^-15</td>\n",
       "      <td id=\"T_my_id_row10_col10\" class=\"data row10 col10\" >   49152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row11_col0\" class=\"data row11 col0\" >p3109_8p4</td>\n",
       "      <td id=\"T_my_id_row11_col1\" class=\"data row11 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row11_col2\" class=\"data row11 col2\" >4</td>\n",
       "      <td id=\"T_my_id_row11_col3\" class=\"data row11 col3\" >4</td>\n",
       "      <td id=\"T_my_id_row11_col4\" class=\"data row11 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row11_col5\" class=\"data row11 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row11_col6\" class=\"data row11 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row11_col7\" class=\"data row11 col7\" >2^-10</td>\n",
       "      <td id=\"T_my_id_row11_col8\" class=\"data row11 col8\" >7/4*2^-8</td>\n",
       "      <td id=\"T_my_id_row11_col9\" class=\"data row11 col9\" >0.0078125</td>\n",
       "      <td id=\"T_my_id_row11_col10\" class=\"data row11 col10\" >     224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row12_col0\" class=\"data row12 col0\" >p3109_8p5</td>\n",
       "      <td id=\"T_my_id_row12_col1\" class=\"data row12 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row12_col2\" class=\"data row12 col2\" >5</td>\n",
       "      <td id=\"T_my_id_row12_col3\" class=\"data row12 col3\" >3</td>\n",
       "      <td id=\"T_my_id_row12_col4\" class=\"data row12 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row12_col5\" class=\"data row12 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row12_col6\" class=\"data row12 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row12_col7\" class=\"data row12 col7\" >0.0078125</td>\n",
       "      <td id=\"T_my_id_row12_col8\" class=\"data row12 col8\" >15/8*2^-4</td>\n",
       "      <td id=\"T_my_id_row12_col9\" class=\"data row12 col9\" >   0.125</td>\n",
       "      <td id=\"T_my_id_row12_col10\" class=\"data row12 col10\" >      15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row13_col0\" class=\"data row13 col0\" >p3109_8p6</td>\n",
       "      <td id=\"T_my_id_row13_col1\" class=\"data row13 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row13_col2\" class=\"data row13 col2\" >6</td>\n",
       "      <td id=\"T_my_id_row13_col3\" class=\"data row13 col3\" >2</td>\n",
       "      <td id=\"T_my_id_row13_col4\" class=\"data row13 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row13_col5\" class=\"data row13 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row13_col6\" class=\"data row13 col6\" >62</td>\n",
       "      <td id=\"T_my_id_row13_col7\" class=\"data row13 col7\" >0.015625</td>\n",
       "      <td id=\"T_my_id_row13_col8\" class=\"data row13 col8\" >31/16*2^-2</td>\n",
       "      <td id=\"T_my_id_row13_col9\" class=\"data row13 col9\" >     0.5</td>\n",
       "      <td id=\"T_my_id_row13_col10\" class=\"data row13 col10\" >   3.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row14_col0\" class=\"data row14 col0\" >binary16</td>\n",
       "      <td id=\"T_my_id_row14_col1\" class=\"data row14 col1\" >16</td>\n",
       "      <td id=\"T_my_id_row14_col2\" class=\"data row14 col2\" >11</td>\n",
       "      <td id=\"T_my_id_row14_col3\" class=\"data row14 col3\" >5</td>\n",
       "      <td id=\"T_my_id_row14_col4\" class=\"data row14 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row14_col5\" class=\"data row14 col5\" >15359</td>\n",
       "      <td id=\"T_my_id_row14_col6\" class=\"data row14 col6\" >16383</td>\n",
       "      <td id=\"T_my_id_row14_col7\" class=\"data row14 col7\" >2^-24</td>\n",
       "      <td id=\"T_my_id_row14_col8\" class=\"data row14 col8\" >1023/512*2^-15</td>\n",
       "      <td id=\"T_my_id_row14_col9\" class=\"data row14 col9\" >2^-14</td>\n",
       "      <td id=\"T_my_id_row14_col10\" class=\"data row14 col10\" >   65504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row15_col0\" class=\"data row15 col0\" >bfloat16</td>\n",
       "      <td id=\"T_my_id_row15_col1\" class=\"data row15 col1\" >16</td>\n",
       "      <td id=\"T_my_id_row15_col2\" class=\"data row15 col2\" >8</td>\n",
       "      <td id=\"T_my_id_row15_col3\" class=\"data row15 col3\" >8</td>\n",
       "      <td id=\"T_my_id_row15_col4\" class=\"data row15 col4\" >False</td>\n",
       "      <td id=\"T_my_id_row15_col5\" class=\"data row15 col5\" >16255</td>\n",
       "      <td id=\"T_my_id_row15_col6\" class=\"data row15 col6\" >16383</td>\n",
       "      <td id=\"T_my_id_row15_col7\" class=\"data row15 col7\" >2^-133</td>\n",
       "      <td id=\"T_my_id_row15_col8\" class=\"data row15 col8\" >127/64*2^-127</td>\n",
       "      <td id=\"T_my_id_row15_col9\" class=\"data row15 col9\" >2^-126</td>\n",
       "      <td id=\"T_my_id_row15_col10\" class=\"data row15 col10\" >255/128*2^127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row16_col0\" class=\"data row16 col0\" >ocp_e8m0</td>\n",
       "      <td id=\"T_my_id_row16_col1\" class=\"data row16 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row16_col2\" class=\"data row16 col2\" >1</td>\n",
       "      <td id=\"T_my_id_row16_col3\" class=\"data row16 col3\" >8</td>\n",
       "      <td id=\"T_my_id_row16_col4\" class=\"data row16 col4\" >False</td>\n",
       "      <td id=\"T_my_id_row16_col5\" class=\"data row16 col5\" >127</td>\n",
       "      <td id=\"T_my_id_row16_col6\" class=\"data row16 col6\" >127</td>\n",
       "      <td id=\"T_my_id_row16_col7\" class=\"data row16 col7\" >n/a</td>\n",
       "      <td id=\"T_my_id_row16_col8\" class=\"data row16 col8\" >n/a</td>\n",
       "      <td id=\"T_my_id_row16_col9\" class=\"data row16 col9\" >2^-127</td>\n",
       "      <td id=\"T_my_id_row16_col10\" class=\"data row16 col10\" >2^127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td id=\"T_my_id_row17_col0\" class=\"data row17 col0\" >ocp_int8</td>\n",
       "      <td id=\"T_my_id_row17_col1\" class=\"data row17 col1\" >8</td>\n",
       "      <td id=\"T_my_id_row17_col2\" class=\"data row17 col2\" >8</td>\n",
       "      <td id=\"T_my_id_row17_col3\" class=\"data row17 col3\" >0</td>\n",
       "      <td id=\"T_my_id_row17_col4\" class=\"data row17 col4\" >True</td>\n",
       "      <td id=\"T_my_id_row17_col5\" class=\"data row17 col5\" >63</td>\n",
       "      <td id=\"T_my_id_row17_col6\" class=\"data row17 col6\" >63</td>\n",
       "      <td id=\"T_my_id_row17_col7\" class=\"data row17 col7\" >0.015625</td>\n",
       "      <td id=\"T_my_id_row17_col8\" class=\"data row17 col8\" >127/64*2^0</td>\n",
       "      <td id=\"T_my_id_row17_col9\" class=\"data row17 col9\" >n/a</td>\n",
       "      <td id=\"T_my_id_row17_col10\" class=\"data row17 col10\" >n/a</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D(df2, format=partial(render_float, False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tables in RST/Markdown\n",
    "\n",
    "These are used to generate gfloat documentation, but may be of use in other\n",
    "contexts so left here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=========  ===  ===  ===  ===========  =================  ============  ===========  ======\n",
      "name         B    P    E  smallest     smallest_normal    max           num_nans       infs\n",
      "=========  ===  ===  ===  ===========  =================  ============  ===========  ======\n",
      "ocp_e2m1     4    2    2  0.5          1                  6             0                 0\n",
      "p3109_4p2    4    2    2  0.25         0.5                2             1                 2\n",
      "ocp_e2m3     6    4    2  0.125        1                  7.5           0                 0\n",
      "ocp_e3m2     6    3    3  0.0625       0.25               28            0                 0\n",
      "p3109_6p3    6    3    3  0.03125      0.125              12            1                 2\n",
      "p3109_6p4    6    4    2  0.0625       0.5                3.5           1                 2\n",
      "ocp_e4m3     8    4    4  ≈0.0019531   0.015625           448           2                 0\n",
      "ocp_e5m2     8    3    5  ≈1.5259e-05  ≈6.1035e-05        57344         6                 2\n",
      "p3109_8p1    8    1    7  ≈2.1684e-19  ≈2.1684e-19        ≈9.2234e+18   1                 2\n",
      "p3109_8p2    8    2    6  ≈2.3283e-10  ≈4.6566e-10        ≈2.1475e+09   1                 2\n",
      "p3109_8p3    8    3    5  ≈7.6294e-06  ≈3.0518e-05        49152         1                 2\n",
      "p3109_8p4    8    4    4  ≈0.00097656  0.0078125          224           1                 2\n",
      "p3109_8p5    8    5    3  0.0078125    0.125              15            1                 2\n",
      "p3109_8p6    8    6    2  0.015625     0.5                3.875         1                 2\n",
      "binary16    16   11    5  ≈5.9605e-08  ≈6.1035e-05        65504         2046              2\n",
      "bfloat16    16    8    8  ≈9.1835e-41  ≈1.1755e-38        ≈3.3895e+38   254               2\n",
      "binary32    32   24    8  ≈1.4013e-45  ≈1.1755e-38        ≈3.4028e+38   ≈1.6777e+07       2\n",
      "binary64    64   53   11  4.9407e-324  ≈2.2251e-308       ≈1.7977e+308  ≈9.0072e+15       2\n",
      "ocp_e8m0     8    1    8  ≈5.8775e-39  ≈5.8775e-39        ≈1.7014e+38   1                 0\n",
      "ocp_int8     8    8    0  0.015625     n/a                ≈  1.9844     0                 0\n",
      "=========  ===  ===  ===  ===========  =================  ============  ===========  ======\n"
     ]
    }
   ],
   "source": [
    "from tabulate import tabulate\n",
    "\n",
    "dfstr = df.map(lambda x: render_float(True, x))\n",
    "print(\n",
    "    tabulate(dfstr, df.columns, tablefmt=\"rst\", showindex=False).replace(\" nan\", \" n/a\")\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=========  ===  ===  ===  ===========  =================  ========================================  ======================================  ======\n",
      "name         B    P    E  smallest     smallest_normal    max                                       num_nans                                  infs\n",
      "=========  ===  ===  ===  ===========  =================  ========================================  ======================================  ======\n",
      "ocp_e2m1     4    2    2  0.5          1                  6                                         0                                            0\n",
      "p3109_4p2    4    2    2  0.25         0.5                2                                         1                                            2\n",
      "ocp_e2m3     6    4    2  0.125        1                  7.5                                       0                                            0\n",
      "ocp_e3m2     6    3    3  0.0625       0.25               28                                        0                                            0\n",
      "p3109_6p3    6    3    3  0.03125      0.125              12                                        1                                            2\n",
      "p3109_6p4    6    4    2  0.0625       0.5                3.5                                       1                                            2\n",
      "ocp_e4m3     8    4    4  2^-9         0.015625           448                                       2                                            0\n",
      "ocp_e5m2     8    3    5  2^-16        2^-14              57344                                     6                                            2\n",
      "p3109_8p1    8    1    7  2^-62        2^-62              2^63                                      1                                            2\n",
      "p3109_8p2    8    2    6  2^-32        2^-31              2^31                                      1                                            2\n",
      "p3109_8p3    8    3    5  2^-17        2^-15              49152                                     1                                            2\n",
      "p3109_8p4    8    4    4  2^-10        0.0078125          224                                       1                                            2\n",
      "p3109_8p5    8    5    3  0.0078125    0.125              15                                        1                                            2\n",
      "p3109_8p6    8    6    2  0.015625     0.5                3.875                                     1                                            2\n",
      "binary16    16   11    5  2^-24        2^-14              65504                                     2046                                         2\n",
      "bfloat16    16    8    8  2^-133       2^-126             255/128*2^127                             254                                          2\n",
      "binary32    32   24    8  2^-149       2^-126             16777215/8388608*2^127                    8388607/4194304*2^23                         2\n",
      "binary64    64   53   11  4.9407e-324  2^-1022            9007199254740991/9007199254740992*2^1024  4503599627370495/4503599627370496*2^53       2\n",
      "ocp_e8m0     8    1    8  2^-127       2^-127             2^127                                     1                                            0\n",
      "ocp_int8     8    8    0  0.015625     n/a                127/64*2^0                                0                                            0\n",
      "=========  ===  ===  ===  ===========  =================  ========================================  ======================================  ======\n"
     ]
    }
   ],
   "source": [
    "from tabulate import tabulate\n",
    "\n",
    "dfstr = df.map(lambda x: render_float(False, x))\n",
    "print(tabulate(dfstr, df.columns, tablefmt=\"rst\", showindex=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|    | name      |   B |   P |   E |     smallest |   smallest_normal |              max |       num_nans |   infs |\n",
      "|---:|:----------|----:|----:|----:|-------------:|------------------:|-----------------:|---------------:|-------:|\n",
      "|  0 | ocp_e2m1  |   4 |   2 |   2 | 0.5          |      1            |     6            |    0           |      0 |\n",
      "|  1 | p3109_4p2 |   4 |   2 |   2 | 0.25         |      0.5          |     2            |    1           |      2 |\n",
      "|  2 | ocp_e2m3  |   6 |   4 |   2 | 0.125        |      1            |     7.5          |    0           |      0 |\n",
      "|  3 | ocp_e3m2  |   6 |   3 |   3 | 0.0625       |      0.25         |    28            |    0           |      0 |\n",
      "|  4 | p3109_6p3 |   6 |   3 |   3 | 0.03125      |      0.125        |    12            |    1           |      2 |\n",
      "|  5 | p3109_6p4 |   6 |   4 |   2 | 0.0625       |      0.5          |     3.5          |    1           |      2 |\n",
      "|  6 | ocp_e4m3  |   8 |   4 |   4 | 0.00195312   |      0.015625     |   448            |    2           |      0 |\n",
      "|  7 | ocp_e5m2  |   8 |   3 |   5 | 1.52588e-05  |      6.10352e-05  | 57344            |    6           |      2 |\n",
      "|  8 | p3109_8p1 |   8 |   1 |   7 | 2.1684e-19   |      2.1684e-19   |     9.22337e+18  |    1           |      2 |\n",
      "|  9 | p3109_8p2 |   8 |   2 |   6 | 2.32831e-10  |      4.65661e-10  |     2.14748e+09  |    1           |      2 |\n",
      "| 10 | p3109_8p3 |   8 |   3 |   5 | 7.62939e-06  |      3.05176e-05  | 49152            |    1           |      2 |\n",
      "| 11 | p3109_8p4 |   8 |   4 |   4 | 0.000976562  |      0.0078125    |   224            |    1           |      2 |\n",
      "| 12 | p3109_8p5 |   8 |   5 |   3 | 0.0078125    |      0.125        |    15            |    1           |      2 |\n",
      "| 13 | p3109_8p6 |   8 |   6 |   2 | 0.015625     |      0.5          |     3.875        |    1           |      2 |\n",
      "| 14 | binary16  |  16 |  11 |   5 | 5.96046e-08  |      6.10352e-05  | 65504            | 2046           |      2 |\n",
      "| 15 | bfloat16  |  16 |   8 |   8 | 9.18355e-41  |      1.17549e-38  |     3.38953e+38  |  254           |      2 |\n",
      "| 16 | binary32  |  32 |  24 |   8 | 1.4013e-45   |      1.17549e-38  |     3.40282e+38  |    1.67772e+07 |      2 |\n",
      "| 17 | binary64  |  64 |  53 |  11 | 4.94066e-324 |      2.22507e-308 |     1.79769e+308 |    9.0072e+15  |      2 |\n",
      "| 18 | ocp_e8m0  |   8 |   1 |   8 | 5.87747e-39  |      5.87747e-39  |     1.70141e+38  |    1           |      0 |\n",
      "| 19 | ocp_int8  |   8 |   8 |   0 | 0.015625     |    nan            |     1.98438      |    0           |      0 |\n"
     ]
    }
   ],
   "source": [
    "print(df.to_markdown())"
   ]
  }
 ],
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   "display_name": "Python 3",
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