[2023-04-07] Understanding float64

understanding_float64.ipynb

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   "source": [
    "import struct\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "_ = np.seterr(divide=\"ignore\", invalid=\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9b7cead3",
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   "source": [
    "def show_bits(value):\n",
    "    float_bytes = struct.pack(\">d\", value)\n",
    "    float_bits = ''.join([f\"{digit:08b}\" for digit in float_bytes])\n",
    "    switches = float_bits.replace(\"0\", \"-\").replace(\"1\", \"+\")\n",
    "    return switches[0] + \"|\" + switches[1:12] + \"|\" + switches[12:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f365a06e",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|-++++++++++|----------------------------------------------------'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7f94a9d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|-++++++++++|+---------------------------------------------------'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a2ece44e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|-++++++++++|++--------------------------------------------------'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(1.75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a0b6f8d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+----------|----------------------------------------------------'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(2.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dc6e7a47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+---------+|----------------------------------------------------'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(4.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f3def30e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+--------+-|----------------------------------------------------'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(8.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "546074bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+--------++|----------------------------------------------------'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(16.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b6d7db70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+-------+--|----------------------------------------------------'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(32.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c11e9dd7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+-------+-+|----------------------------------------------------'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(64.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "32a6b237",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+----------|+---------------------------------------------------'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(3.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2e2270a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+---------+|+---------------------------------------------------'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(6.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "08d72016",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|-----------|----------------------------------------------------'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4323d6e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'+|-----------|----------------------------------------------------'"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(-0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "438180cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+++++++++++|----------------------------------------------------'"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(float(\"inf\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d039b6fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+++++++++++|+---------------------------------------------------'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(float(\"nan\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d6d1486e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_ones, = struct.unpack(\">d\", b\"\\xff\\xff\\xff\\xff\\xff\\xff\\xff\\xff\")\n",
    "all_ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a82b4e71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'+|+++++++++++|++++++++++++++++++++++++++++++++++++++++++++++++++++'"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(all_ones)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4937ec26",
   "metadata": {},
   "outputs": [
    {
     "ename": "ZeroDivisionError",
     "evalue": "float division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[20], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;241;43m0.0\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m/\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0.0\u001b[39;49m\n",
      "\u001b[0;31mZeroDivisionError\u001b[0m: float division by zero"
     ]
    }
   ],
   "source": [
    "0.0 / 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1ed2b2e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.float64(0.0) / np.float64(0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ce2d7f6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.float64(1.0) / np.float64(0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "63b60c87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-inf"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.float64(-1.0) / np.float64(0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "05b28470",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-|+++++++++++|----------------------------------------------------'"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(float(\"inf\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "374824e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'+|+++++++++++|----------------------------------------------------'"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_bits(float(\"-inf\"))"
   ]
  }
 ],
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