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    ".. _logical-xor:\n",
    "\n",
    "Logical Exclusive Or\n",
    "====================\n",
    "\n",
    "In this example, we will compute the elementwise logical XOR of secret shared bits.\n",
    "\n",
    "Note that the secret inputs to :meth:`~cicada.additive.AdditiveProtocolSuite.logical_xor` must be the field values :math:`0` or :math:`1`, producing similar outputs.  We use the :any:`Bits` encoding for our inputs and outputs because the default :any:`FixedPoint` encoding would produce unexpected results."
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:root:Player 0 x: [0 1 0 1]\n",
      "INFO:root:Player 1 y: [0 0 1 1]\n",
      "INFO:root:Player 0 x xor y: [0 1 1 0]\n",
      "INFO:root:Player 1 x xor y: [0 1 1 0]\n",
      "INFO:root:Player 2 x xor y: [0 1 1 0]\n"
     ]
    }
   ],
   "source": [
    "import logging\n",
    "\n",
    "import numpy\n",
    "\n",
    "from cicada.additive import AdditiveProtocolSuite\n",
    "from cicada.communicator import SocketCommunicator\n",
    "from cicada.encoding import Bits\n",
    "from cicada.logger import Logger\n",
    "\n",
    "logging.basicConfig(level=logging.INFO)\n",
    "\n",
    "def main(communicator):\n",
    "    log = Logger(logging.getLogger(), communicator)\n",
    "    protocol = AdditiveProtocolSuite(communicator)\n",
    "    \n",
    "    x = numpy.array([0, 1, 0, 1]) if communicator.rank == 0 else None\n",
    "    y = numpy.array([0, 0, 1, 1]) if communicator.rank == 1 else None\n",
    "    \n",
    "    x_share = protocol.share(src=0, secret=x, shape=(4,), encoding=Bits())\n",
    "    y_share = protocol.share(src=1, secret=y, shape=(4,), encoding=Bits())\n",
    "    xor_share = protocol.logical_xor(x_share, y_share)\n",
    "    xor = protocol.reveal(xor_share, encoding=Bits())\n",
    "    \n",
    "    log.info(f\"Player {communicator.rank} x: {x}\", src=0)\n",
    "    log.info(f\"Player {communicator.rank} y: {y}\", src=1)\n",
    "    log.info(f\"Player {communicator.rank} x xor y: {xor}\")\n",
    "\n",
    "SocketCommunicator.run(world_size=3, fn=main);"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. seealso:: :ref:`logical-not`"
   ]
  }
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