doc/notebooks/integer_bit_fiddling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Integer logic and bit fiddling\n",
    "## Preliminaries\n",
    "\n",
    "Let us load the mp++ runtime, include the ``integer.hpp`` header and import the user-defined literals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#pragma cling add_include_path(\"$CONDA_PREFIX/include\")\n",
    "#pragma cling add_library_path(\"$CONDA_PREFIX/lib\")\n",
    "#pragma cling load(\"mp++\")\n",
    "\n",
    "#include <mp++/integer.hpp>\n",
    "\n",
    "using namespace mppp::literals;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us also include a few useful bits from the standard library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#include <iostream>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logic and bit fiddling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multiprecision integers support the standard bitwise operators, such as the bitwise NOT operator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "~(0_z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-124"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "~(123_z1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Negative integers are treated as-if they were represented using two’s complement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "~(-1_z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "123"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "~(-124_z1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bitwise OR, AND and XOR operators:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11011110"
     ]
    }
   ],
   "source": [
    "std::cout << (0b01001010_z1 | 0b10010100_z1).to_string(2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000000"
     ]
    }
   ],
   "source": [
    "std::cout << (0b11001010_z1 & 0b10010100_z1).to_string(2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1011110"
     ]
    }
   ],
   "source": [
    "std::cout << (0b11001010_z1 ^ 0b10010100_z1).to_string(2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multiprecision integer arguments can be mixed with C++ integral arguments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1101111"
     ]
    }
   ],
   "source": [
    "std::cout << (0b01001010_z1 | 45).to_string(2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000100"
     ]
    }
   ],
   "source": [
    "std::cout << (-123ll & 0b10010100_z1).to_string(2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1101011"
     ]
    }
   ],
   "source": [
    "std::cout << (255u ^ 0b10010100_z1).to_string(2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The in-place variants are supported as well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    }
   ],
   "source": [
    "{\n",
    "    auto n = 0b001_z1;\n",
    "    n |= 0b111_z1;\n",
    "    std::cout << n << '\\n';\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    }
   ],
   "source": [
    "{\n",
    "    int n = -0b101010;\n",
    "    n &= 0b111_z1;\n",
    "    std::cout << n << '\\n';\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "{\n",
    "    auto n = 0b001_z1;\n",
    "    n ^= 0b111_z1;\n",
    "    std::cout << n << '\\n';\n",
    "}"
   ]
  }
 ],
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