X-Git-Url: https://git.njae.me.uk/?a=blobdiff_plain;f=07-interpreter%2Fmachine-code-4-reg.ipynb;fp=07-interpreter%2Fmachine-code-4-reg.ipynb;h=3d000c680b6344f206666891898f50585ccfa669;hb=e405461a789315af95c5ae0e90d63d9fd7d81d37;hp=0000000000000000000000000000000000000000;hpb=08e0c316beac066037ece028bf687379819fc409;p=ou-summer-of-code-2017.git

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Machine interpreter\n",
+    "\n",
+    "## Instructions\n",
+    "\n",
+    "Four registers, `a`, `b`, `c`, and `d`.\n",
+    "Program counter, `pc`.\n",
+    "\n",
+    "Each register can hold 8-byte integers (Java `long`s).\n",
+    "\n",
+    "Machine carries out the instruction at location `pc`. After it's executed, `pc` increments by 1.\n",
+    "\n",
+    "`jmp` and `jpz` override this normal change in `pc`.\n",
+    "\n",
+    "| Instruction | Description |\n",
+    "|:------------|:------------|\n",
+    "| `inc r`     | increment contents of register `r` |\n",
+    "| `dec r`     | decrement contents of register `r` |\n",
+    "| `set r i`   | set contents of register `r` to literal value `i` |\n",
+    "| `cpy r s`   | copy contents of register `r` into register `s` | \n",
+    "| `jmp i`     | jump to instruction `i` places forward |\n",
+    "| `jpz r i`   | jump to instruction `i` places forward if<br>register `r` contains zero, otherwise continue to next instruction |\n",
+    "\n",
+    "For `jmp` and `jpz`, `i` is relative to the current instruction. `i` can be negative to jump to earlier places in the program. `i`=1 is a no-op, `i`=0 causes an infinite loop."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def new_machine():\n",
+    "    return {'pc': 0, \n",
+    "            'a': 0,\n",
+    "            'b': 0, \n",
+    "            'c': 0,\n",
+    "            'd': 0,\n",
+    "            'instructions': []}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def show_machine(machine):\n",
+    "    return ', '.join('{}: {}'.format(sk, machine[int(sk) if sk.isnumeric() else sk]) \n",
+    "                     for sk in sorted(str(k) for k in machine)\n",
+    "                     if sk != 'instructions')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def inc(reg, machine):\n",
+    "    machine[reg] += 1\n",
+    "    machine['pc'] += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def dec(reg, machine):\n",
+    "    machine[reg] -= 1\n",
+    "    machine['pc'] += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def jmp(addr, machine):\n",
+    "    machine['pc'] += addr"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def jpz(reg, addr, machine):\n",
+    "    if machine[reg] == 0:\n",
+    "        machine['pc'] += addr\n",
+    "    else:\n",
+    "        machine['pc'] += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def set_literal(reg, literal, machine):\n",
+    "    machine[reg] = literal\n",
+    "    machine['pc'] += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def cpy(from_reg, to_reg, machine):\n",
+    "    machine[to_reg] = machine[from_reg]\n",
+    "    machine['pc'] += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "instruction_table = {'inc': inc, 'dec': dec, 'jmp': jmp,\n",
+    "                    'jpz': jpz, 'set': set_literal, 'cpy': cpy}\n",
+    "numeric_args_table = {'jmp': [0], 'jpz': [1], 'set': [1], 'sto': [1], 'ld': [1]}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def parse(instruction):\n",
+    "    words = instruction.split()\n",
+    "    instr = words[0]\n",
+    "    args = words[1:]\n",
+    "    if instr in numeric_args_table:\n",
+    "        for p in numeric_args_table[instr]:\n",
+    "            args[p] = int(args[p])\n",
+    "    return instruction_table[instr], args"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'a': 2, 'b': 1, 'c': 0, 'd': 0, 'instructions': [], 'pc': 3}"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "m = new_machine()\n",
+    "inc('a', m)\n",
+    "cargs = ['a', 'b']\n",
+    "cpy(*cargs, m)\n",
+    "inc('a', m)\n",
+    "m"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def program_from_instructions(prog, machine):\n",
+    "    machine['instructions'] = [parse(instr) for instr in prog]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def program_from_listing(listing, machine):\n",
+    "    labelled_instructions = [i.strip() for i in listing.split('\\n') \n",
+    "                             if i.strip() \n",
+    "                             if not i.strip().startswith('#')]\n",
+    "    instructions = replace_labels(labelled_instructions)\n",
+    "    program_from_instructions(instructions, machine)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def replace_labels(listing):\n",
+    "    locations = {}\n",
+    "    for n, i in enumerate(listing):\n",
+    "        if ':' in i:\n",
+    "            locations[i.split(':')[0]] = n\n",
+    "\n",
+    "    unlabelled_listing = []\n",
+    "    for n, i in enumerate(listing):\n",
+    "        instr = i.split()\n",
+    "        if ':' in i:\n",
+    "            instr = i.split(':')[1].split()\n",
+    "        else:\n",
+    "            instr = i.split()\n",
+    "        terms = []\n",
+    "        for term in instr:\n",
+    "            if term in locations:\n",
+    "                terms += [str(locations[term] - n)]\n",
+    "            else:\n",
+    "                terms += [term]\n",
+    "        transformed_instr = ' '.join(terms)\n",
+    "        unlabelled_listing += [transformed_instr]\n",
+    "        \n",
+    "    return unlabelled_listing    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['inc', 'a']"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "'fred: inc a'.split(':')[1].split()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "set a 10\n",
+      "dec a\n",
+      "inc b\n",
+      "jpz a 2\n",
+      "jmp -3\n"
+     ]
+    }
+   ],
+   "source": [
+    "program = \"\"\"\n",
+    "      set a 10\n",
+    "      # comment line\n",
+    "      \n",
+    "loop: dec a\n",
+    "      inc b\n",
+    "      jpz a 2\n",
+    "      jmp loop\n",
+    "\"\"\"\n",
+    "labelled_instructions = [i.strip() for i in program.split('\\n') if i.strip() if not i.strip().startswith('#')]\n",
+    "instructions = replace_labels(labelled_instructions)\n",
+    "print('\\n'.join(instructions))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def run(machine, initial_state=None, trace=False):\n",
+    "    if initial_state:\n",
+    "        machine.update(initial_state)\n",
+    "    while machine['pc'] < len(machine['instructions']):\n",
+    "        if trace:\n",
+    "            print(show_machine(machine))\n",
+    "        cmd, args = machine['instructions'][machine['pc']]\n",
+    "        cmd(*args, machine)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def execute(listing, initial_state=None, trace=False):\n",
+    "    m = new_machine()\n",
+    "    program_from_listing(listing, m)\n",
+    "    run(m, initial_state=initial_state, trace=trace)\n",
+    "    return m"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'a': 3,\n",
+       " 'b': 2,\n",
+       " 'c': 0,\n",
+       " 'd': 0,\n",
+       " 'instructions': [(<function __main__.inc>, ['a']),\n",
+       "  (<function __main__.inc>, ['a']),\n",
+       "  (<function __main__.cpy>, ['a', 'b']),\n",
+       "  (<function __main__.inc>, ['a'])],\n",
+       " 'pc': 4}"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "program = \"\"\"\n",
+    "inc a\n",
+    "inc a\n",
+    "cpy a b\n",
+    "inc a\n",
+    "\"\"\"\n",
+    "execute(program)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'a': 0,\n",
+       " 'b': 10,\n",
+       " 'c': 20,\n",
+       " 'd': 0,\n",
+       " 'instructions': [(<function __main__.set_literal>, ['a', 10]),\n",
+       "  (<function __main__.dec>, ['a']),\n",
+       "  (<function __main__.inc>, ['b']),\n",
+       "  (<function __main__.jpz>, ['a', 2]),\n",
+       "  (<function __main__.jmp>, [-3])],\n",
+       " 'pc': 5}"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "program = \"\"\"\n",
+    "set a 10\n",
+    "dec a\n",
+    "inc b\n",
+    "jpz a 2\n",
+    "jmp -3\n",
+    "\"\"\"\n",
+    "# m = new_machine()\n",
+    "# program_from_listing(program, m)\n",
+    "# run(m)\n",
+    "execute(program, initial_state={'c': 20})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'a': 0,\n",
+       " 'b': 10,\n",
+       " 'c': 20,\n",
+       " 'd': 0,\n",
+       " 'instructions': [(<function __main__.set_literal>, ['a', 10]),\n",
+       "  (<function __main__.dec>, ['a']),\n",
+       "  (<function __main__.inc>, ['b']),\n",
+       "  (<function __main__.jpz>, ['a', 2]),\n",
+       "  (<function __main__.jmp>, [-3])],\n",
+       " 'pc': 5}"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "program = \"\"\"\n",
+    "      set a 10\n",
+    "loop: dec a\n",
+    "      inc b\n",
+    "      jpz a 2\n",
+    "      jmp loop\n",
+    "\"\"\"\n",
+    "execute(program, initial_state={'c': 20})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'a': 0,\n",
+       " 'b': 1,\n",
+       " 'c': 5,\n",
+       " 'd': 0,\n",
+       " 'instructions': [(<function __main__.cpy>, ['c', 'a']),\n",
+       "  (<function __main__.set_literal>, ['b', 0]),\n",
+       "  (<function __main__.dec>, ['a']),\n",
+       "  (<function __main__.jpz>, ['b', 3]),\n",
+       "  (<function __main__.dec>, ['b']),\n",
+       "  (<function __main__.jmp>, [2]),\n",
+       "  (<function __main__.inc>, ['b']),\n",
+       "  (<function __main__.jpz>, ['a', 3]),\n",
+       "  (<function __main__.jmp>, [-6])],\n",
+       " 'pc': 10}"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "program = \"\"\"\n",
+    "cpy c a\n",
+    "set b 0\n",
+    "dec a\n",
+    "jpz b 3\n",
+    "dec b\n",
+    "jmp 2\n",
+    "inc b\n",
+    "jpz a 3\n",
+    "jmp -6\n",
+    "\"\"\"\n",
+    "# m = new_machine()\n",
+    "# program_from_listing(program, m)\n",
+    "# run(m)\n",
+    "execute(program, initial_state={'c': 5})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'a': 0,\n",
+       " 'b': 1,\n",
+       " 'c': 5,\n",
+       " 'd': 0,\n",
+       " 'instructions': [(<function __main__.cpy>, ['c', 'a']),\n",
+       "  (<function __main__.set_literal>, ['b', 0]),\n",
+       "  (<function __main__.dec>, ['a']),\n",
+       "  (<function __main__.jpz>, ['b', 3]),\n",
+       "  (<function __main__.dec>, ['b']),\n",
+       "  (<function __main__.jmp>, [2]),\n",
+       "  (<function __main__.inc>, ['b']),\n",
+       "  (<function __main__.jpz>, ['a', 2]),\n",
+       "  (<function __main__.jmp>, [-6])],\n",
+       " 'pc': 9}"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# b holds parity of number in c: (c % 2)\n",
+    "program = \"\"\"\n",
+    "      cpy c a\n",
+    "      set b 0\n",
+    "loop: dec a\n",
+    "      jpz b odd\n",
+    "      dec b\n",
+    "      jmp end\n",
+    "odd:  inc b\n",
+    "end:  jpz a 2\n",
+    "      jmp loop\n",
+    "\"\"\"\n",
+    "# m = new_machine()\n",
+    "# program_from_listing(program, m)\n",
+    "# run(m)\n",
+    "execute(program, initial_state={'c': 5})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'a: 0, b: 1, c: 8, d: 0, pc: 10'"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# c holds floor(a/2)\n",
+    "program = \"\"\"\n",
+    "      set c 0\n",
+    "      set b 0\n",
+    "loop: dec a\n",
+    "      jpz b odd\n",
+    "      dec b\n",
+    "      inc c\n",
+    "      jmp end\n",
+    "odd:  inc b\n",
+    "end:  jpz a 2\n",
+    "      jmp loop\n",
+    "\"\"\"\n",
+    "# m = new_machine()\n",
+    "# program_from_listing(program, m)\n",
+    "# run(m)\n",
+    "show_machine(execute(program, initial_state={'a': 17}))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'a: 4, b: 0, c: 12, d: 0, pc: 9'"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# c holds a * 3\n",
+    "program = \"\"\"\n",
+    "      set c 0\n",
+    "      cpy a b\n",
+    "      # start of main loop\n",
+    "loop: jpz b end\n",
+    "      dec b\n",
+    "      inc c\n",
+    "      inc c\n",
+    "      inc c\n",
+    "      jmp loop\n",
+    "      \n",
+    "      # end of program \n",
+    "      \n",
+    "end:  jmp 1\n",
+    "\"\"\"\n",
+    "# m = new_machine()\n",
+    "# program_from_listing(program, m)\n",
+    "# run(m)\n",
+    "show_machine(execute(program, initial_state={'a': 4}))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'a: 0, b: 0, c: 27, d: 0, pc: 11'"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# c holds a * b\n",
+    "program = \"\"\"\n",
+    "      set c 0\n",
+    "      cpy a d\n",
+    "loop: jpz b end      \n",
+    "      dec b\n",
+    "      cpy d a\n",
+    "smul: jpz a emul\n",
+    "      inc c\n",
+    "      dec a\n",
+    "      jmp smul\n",
+    "emul: jmp loop \n",
+    "      \n",
+    "end:  set d 0\n",
+    "\"\"\"\n",
+    "m = new_machine()\n",
+    "program_from_listing(program, m)\n",
+    "run(m)\n",
+    "show_machine(execute(program, initial_state={'a': 9, 'b': 3}))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "set c 0\n",
+      "cpy a d\n",
+      "jpz b 8\n",
+      "dec b\n",
+      "cpy d a\n",
+      "jpz a 4\n",
+      "inc c\n",
+      "dec a\n",
+      "jmp -3\n",
+      "jmp -7\n",
+      "set d 0\n"
+     ]
+    }
+   ],
+   "source": [
+    "labelled_instructions = [i.strip() for i in program.split('\\n') if i.strip() if not i.strip().startswith('#')]\n",
+    "instructions = replace_labels(labelled_instructions)\n",
+    "print('\\n'.join(instructions))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'a: 2, b: 0, c: 10, d: 2, pc: 13'"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# c holds a * b\n",
+    "program = \"\"\"\n",
+    "      set a 2\n",
+    "      set b 5\n",
+    "      set c 0\n",
+    "      cpy a d\n",
+    "loop: jpz b end      \n",
+    "      dec b\n",
+    "      cpy d a\n",
+    "smul: jpz a emul\n",
+    "      inc c\n",
+    "      dec a\n",
+    "      jmp smul\n",
+    "emul: jmp loop \n",
+    "      \n",
+    "end:  cpy d a\n",
+    "\"\"\"\n",
+    "m = new_machine()\n",
+    "program_from_listing(program, m)\n",
+    "run(m)\n",
+    "show_machine(execute(program, initial_state={'a': 9, 'b': 3}))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "set a 2\n",
+      "set b 5\n",
+      "set c 0\n",
+      "cpy a d\n",
+      "jpz b 8\n",
+      "dec b\n",
+      "cpy d a\n",
+      "jpz a 4\n",
+      "inc c\n",
+      "dec a\n",
+      "jmp -3\n",
+      "jmp -7\n",
+      "cpy d a\n"
+     ]
+    }
+   ],
+   "source": [
+    "labelled_instructions = [i.strip() for i in program.split('\\n') \n",
+    "                             if i.strip() \n",
+    "                             if not i.strip().startswith('#')]\n",
+    "instructions = replace_labels(labelled_instructions)\n",
+    "print('\\n'.join(instructions))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'a: 52, b: 0, c: 0, d: 0, pc: 48'"
+      ]
+     },
+     "execution_count": 33,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Collatz. a initially holds value, but location 1 is used to store the current value as we're going along.\n",
+    "# Location 2 holds number of steps taken\n",
+    "# Location 3 holds max value reached\n",
+    "program = \"\"\"\n",
+    "      cpy a d\n",
+    "      \n",
+    "      set b 0\n",
+    "      \n",
+    "      # if a is one, finish, \n",
+    "main: dec a\n",
+    "      jpz a end\n",
+    "      inc a\n",
+    "      \n",
+    "      # find parity of a\n",
+    "      cpy a c\n",
+    "      set b 0\n",
+    "prty: dec c\n",
+    "      jpz b odd\n",
+    "      dec b\n",
+    "      jmp prte\n",
+    "odd:  inc b\n",
+    "prte: jpz c 2\n",
+    "      jmp prty\n",
+    "      \n",
+    "      # b == 0 means a even; b == 1 means a odd\n",
+    "      jpz b isev\n",
+    "\n",
+    "      # c holds a * 3 + 1\n",
+    "      cpy a b\n",
+    "mul:  jpz b emul\n",
+    "      dec b\n",
+    "      inc c\n",
+    "      inc c\n",
+    "      inc c\n",
+    "      jmp mul\n",
+    "emul: inc c\n",
+    "      cpy c a\n",
+    "      jmp fin\n",
+    "      \n",
+    "      \n",
+    "isev: set c 0\n",
+    "      set b 0\n",
+    "hlvl: dec a\n",
+    "      jpz b oddh\n",
+    "      dec b\n",
+    "      inc c\n",
+    "      jmp endh\n",
+    "oddh: inc b\n",
+    "endh: jpz a 2\n",
+    "      jmp hlvl\n",
+    "      cpy c a\n",
+    "\n",
+    "fin:  cpy a b\n",
+    "      cpy d c\n",
+    "maxc: jpz c this\n",
+    "      jpz b othr\n",
+    "      dec b\n",
+    "      dec c\n",
+    "      jmp maxc\n",
+    "this: cpy a d\n",
+    "othr: jmp main\n",
+    "      \n",
+    "      # end of program \n",
+    "      \n",
+    "end:  cpy d a\n",
+    "      set c 0\n",
+    "      set d 0\n",
+    "\"\"\"\n",
+    "# m = new_machine()\n",
+    "# program_from_listing(program, m)\n",
+    "# run(m)\n",
+    "show_machine(execute(program, initial_state={'a': 7}))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "40"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "13*3+1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def max_collatz(start):\n",
+    "    mc = start\n",
+    "    i = start\n",
+    "    while i != 1:\n",
+    "        if i % 2 == 0:\n",
+    "            i = i // 2\n",
+    "        else:\n",
+    "            i = 3 * i + 1\n",
+    "        if i > mc:\n",
+    "            mc = i\n",
+    "    return mc"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "52"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max_collatz(7)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(250504, 937)"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max([(max_collatz(i), i) for i in range(1, 1000)])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(1, 0, 1),\n",
+       " (2, 0, 2),\n",
+       " (3, 0, 16),\n",
+       " (4, 0, 4),\n",
+       " (5, 0, 16),\n",
+       " (6, 0, 16),\n",
+       " (7, 0, 52),\n",
+       " (8, 0, 8),\n",
+       " (9, 0, 52),\n",
+       " (10, 0, 16),\n",
+       " (11, 0, 52),\n",
+       " (12, 0, 16),\n",
+       " (13, 0, 40),\n",
+       " (14, 0, 52),\n",
+       " (15, 0, 160),\n",
+       " (16, 0, 16),\n",
+       " (17, 0, 52),\n",
+       " (18, 0, 52),\n",
+       " (19, 0, 88),\n",
+       " (20, 0, 20),\n",
+       " (21, 0, 64),\n",
+       " (22, 0, 52),\n",
+       " (23, 0, 160),\n",
+       " (24, 0, 24),\n",
+       " (25, 0, 88),\n",
+       " (26, 0, 40),\n",
+       " (27, 0, 9232),\n",
+       " (28, 0, 52),\n",
+       " (29, 0, 88),\n",
+       " (30, 0, 160),\n",
+       " (31, 0, 9232),\n",
+       " (32, 0, 32),\n",
+       " (33, 0, 100),\n",
+       " (34, 0, 52),\n",
+       " (35, 0, 160),\n",
+       " (36, 0, 52),\n",
+       " (37, 0, 112),\n",
+       " (38, 0, 88),\n",
+       " (39, 0, 304),\n",
+       " (40, 0, 40),\n",
+       " (41, 0, 9232),\n",
+       " (42, 0, 64),\n",
+       " (43, 0, 196),\n",
+       " (44, 0, 52),\n",
+       " (45, 0, 136),\n",
+       " (46, 0, 160),\n",
+       " (47, 0, 9232),\n",
+       " (48, 0, 48),\n",
+       " (49, 0, 148),\n",
+       " (50, 0, 88),\n",
+       " (51, 0, 232),\n",
+       " (52, 0, 52),\n",
+       " (53, 0, 160),\n",
+       " (54, 0, 9232),\n",
+       " (55, 0, 9232),\n",
+       " (56, 0, 56),\n",
+       " (57, 0, 196),\n",
+       " (58, 0, 88),\n",
+       " (59, 0, 304),\n",
+       " (60, 0, 160),\n",
+       " (61, 0, 184),\n",
+       " (62, 0, 9232),\n",
+       " (63, 0, 9232),\n",
+       " (64, 0, 64),\n",
+       " (65, 0, 196),\n",
+       " (66, 0, 100),\n",
+       " (67, 0, 304),\n",
+       " (68, 0, 68),\n",
+       " (69, 0, 208),\n",
+       " (70, 0, 160),\n",
+       " (71, 0, 9232),\n",
+       " (72, 0, 72),\n",
+       " (73, 0, 9232),\n",
+       " (74, 0, 112),\n",
+       " (75, 0, 340),\n",
+       " (76, 0, 88),\n",
+       " (77, 0, 232),\n",
+       " (78, 0, 304),\n",
+       " (79, 0, 808),\n",
+       " (80, 0, 80),\n",
+       " (81, 0, 244),\n",
+       " (82, 0, 9232),\n",
+       " (83, 0, 9232),\n",
+       " (84, 0, 84),\n",
+       " (85, 0, 256),\n",
+       " (86, 0, 196),\n",
+       " (87, 0, 592),\n",
+       " (88, 0, 88),\n",
+       " (89, 0, 304),\n",
+       " (90, 0, 136),\n",
+       " (91, 0, 9232),\n",
+       " (92, 0, 160),\n",
+       " (93, 0, 280),\n",
+       " (94, 0, 9232),\n",
+       " (95, 0, 9232),\n",
+       " (96, 0, 96),\n",
+       " (97, 0, 9232),\n",
+       " (98, 0, 148),\n",
+       " (99, 0, 448)]"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ans = []\n",
+    "for i in range(1, 100):\n",
+    "    m = execute(program, initial_state={'a': i})\n",
+    "    c = max_collatz(i)\n",
+    "    if m[1] != c:\n",
+    "        ans += [(i, m[1], c)]\n",
+    "ans"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'a: 250504, b: 0, c: 0, d: 0, pc: 48'"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "show_machine(execute(program, initial_state={'a': 937}))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "cpy a d\n",
+      "set b 0\n",
+      "dec a\n",
+      "jpz a 42\n",
+      "inc a\n",
+      "cpy a c\n",
+      "set b 0\n",
+      "dec c\n",
+      "jpz b 3\n",
+      "dec b\n",
+      "jmp 2\n",
+      "inc b\n",
+      "jpz c 2\n",
+      "jmp -6\n",
+      "jpz b 11\n",
+      "cpy a b\n",
+      "jpz b 6\n",
+      "dec b\n",
+      "inc c\n",
+      "inc c\n",
+      "inc c\n",
+      "jmp -5\n",
+      "inc c\n",
+      "cpy c a\n",
+      "jmp 12\n",
+      "set c 0\n",
+      "set b 0\n",
+      "dec a\n",
+      "jpz b 4\n",
+      "dec b\n",
+      "inc c\n",
+      "jmp 2\n",
+      "inc b\n",
+      "jpz a 2\n",
+      "jmp -7\n",
+      "cpy c a\n",
+      "cpy a b\n",
+      "cpy d c\n",
+      "jpz c 5\n",
+      "jpz b 5\n",
+      "dec b\n",
+      "dec c\n",
+      "jmp -4\n",
+      "cpy a d\n",
+      "jmp -42\n",
+      "cpy d a\n",
+      "set c 0\n",
+      "set d 0\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "344"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "labelled_instructions = [i.strip() for i in program.split('\\n') \n",
+    "                             if i.strip() \n",
+    "                             if not i.strip().startswith('#')]\n",
+    "instructions = replace_labels(labelled_instructions)\n",
+    "print('\\n'.join(instructions))\n",
+    "open('07-program.txt', 'w').write('\\n'.join(instructions))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}