02-cython-comparison.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How does Cython speed up Python?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reason 1: Interpreted -> Compiled\n",
    "\n",
    "## Cython version of trivial function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Cython extension is already loaded. To reload it, use:\n",
      "  %reload_ext Cython\n"
     ]
    }
   ],
   "source": [
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython -n cyfoo\n",
    "\n",
    "def cyfoo(a, b):\n",
    "    return a + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Profiling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "82.8 ns ± 3.08 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit cyfoo(1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'cyfoo' (/home/jovyan/.cache/ipython/cython/cyfoo.cpython-36m-x86_64-linux-gnu.so)>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sys\n",
    "sys.modules['cyfoo']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cython integer addition speedup: 29.5%\n"
     ]
    }
   ],
   "source": [
    "print(\"Cython integer addition speedup: {:0.1f}%\".format((112. - 79.) / 112. * 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "119 ns ± 3.74 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit cyfoo('a', 'b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cython string addition speedup: 16.4%\n"
     ]
    }
   ],
   "source": [
    "print(\"Cython string addition speedup: {:0.1f}%\".format((159. - 133.) / 159. * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For simple addition, Cython version gives consistent speedup\n",
    "\n",
    "* With all the caveats for microbenchmarks..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## We see the same `PyNumber_Add()` entry point as for interpreted Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     1\t/* Generated by Cython 0.25.2 */\r\n",
      "       \r\n",
      "     2\t/* BEGIN: Cython Metadata\r\n",
      "     3\t{\r\n",
      "     4\t    \"distutils\": {\r\n",
      "     5\t        \"language\": \"c\"\r\n",
      "     6\t    },\r\n",
      "     7\t    \"module_name\": \"cyfoo\"\r\n",
      "     8\t}\r\n",
      "     9\tEND: Cython Metadata */\r\n",
      "       \r\n",
      "    10\t#define PY_SSIZE_T_CLEAN\r\n",
      "    11\t#include \"Python.h\"\r\n",
      "    12\t#ifndef Py_PYTHON_H\r\n",
      "    13\t    #error Python headers needed to compile C extensions, please install development version of Python.\r\n",
      "    14\t#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03020000)\r\n",
      "    15\t    #error Cython requires Python 2.6+ or Python 3.2+.\r\n",
      "    16\t#else\r\n",
      "    17\t#define CYTHON_ABI \"0_25_2\"\r\n",
      "    18\t#include <stddef.h>\r\n",
      "    19\t#ifndef offsetof\r\n",
      "    20\t  #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )\r\n",
      "    21\t#endif\r\n",
      "    22\t#if !defined(WIN32) && !defined(MS_WINDOWS)\r\n",
      "    23\t  #ifndef __stdcall\r\n",
      "    24\t    #define __stdcall\r\n",
      "    25\t  #endif\r\n",
      "    26\t  #ifndef __cdecl\r\n",
      "    27\t    #define __cdecl\r\n",
      "    28\t  #endif\r\n",
      "    29\t  #ifndef __fastcall\r\n",
      "    30\t    #define __fastcall\r\n",
      "    31\t  #endif\r\n",
      "    32\t#endif\r\n",
      "    33\t#ifndef DL_IMPORT\r\n",
      "    34\t  #define DL_IMPORT(t) t\r\n",
      "    35\t#endif\r\n",
      "    36\t#ifndef DL_EXPORT\r\n",
      "    37\t  #define DL_EXPORT(t) t\r\n",
      "    38\t#endif\r\n",
      "    39\t#ifndef HAVE_LONG_LONG\r\n",
      "    40\t  #if PY_VERSION_HEX >= 0x03030000 || (PY_MAJOR_VERSION == 2 && PY_VERSION_HEX >= 0x02070000)\r\n",
      "    41\t    #define HAVE_LONG_LONG\r\n",
      "    42\t  #endif\r\n",
      "    43\t#endif\r\n",
      "    44\t#ifndef PY_LONG_LONG\r\n",
      "    45\t  #define PY_LONG_LONG LONG_LONG\r\n",
      "    46\t#endif\r\n",
      "    47\t#ifndef Py_HUGE_VAL\r\n",
      "    48\t  #define Py_HUGE_VAL HUGE_VAL\r\n",
      "    49\t#endif\r\n",
      "    50\t#ifdef PYPY_VERSION\r\n",
      "    51\t  #define CYTHON_COMPILING_IN_PYPY 1\r\n",
      "    52\t  #define CYTHON_COMPILING_IN_PYSTON 0\r\n",
      "    53\t  #define CYTHON_COMPILING_IN_CPYTHON 0\r\n",
      "    54\t  #undef CYTHON_USE_TYPE_SLOTS\r\n",
      "    55\t  #define CYTHON_USE_TYPE_SLOTS 0\r\n",
      "    56\t  #undef CYTHON_USE_ASYNC_SLOTS\r\n",
      "    57\t  #define CYTHON_USE_ASYNC_SLOTS 0\r\n",
      "    58\t  #undef CYTHON_USE_PYLIST_INTERNALS\r\n",
      "    59\t  #define CYTHON_USE_PYLIST_INTERNALS 0\r\n",
      "    60\t  #undef CYTHON_USE_UNICODE_INTERNALS\r\n",
      "    61\t  #define CYTHON_USE_UNICODE_INTERNALS 0\r\n",
      "    62\t  #undef CYTHON_USE_UNICODE_WRITER\r\n",
      "    63\t  #define CYTHON_USE_UNICODE_WRITER 0\r\n",
      "    64\t  #undef CYTHON_USE_PYLONG_INTERNALS\r\n",
      "    65\t  #define CYTHON_USE_PYLONG_INTERNALS 0\r\n",
      "    66\t  #undef CYTHON_AVOID_BORROWED_REFS\r\n",
      "    67\t  #define CYTHON_AVOID_BORROWED_REFS 1\r\n",
      "    68\t  #undef CYTHON_ASSUME_SAFE_MACROS\r\n",
      "    69\t  #define CYTHON_ASSUME_SAFE_MACROS 0\r\n",
      "    70\t  #undef CYTHON_UNPACK_METHODS\r\n",
      "    71\t  #define CYTHON_UNPACK_METHODS 0\r\n",
      "    72\t  #undef CYTHON_FAST_THREAD_STATE\r\n",
      "    73\t  #define CYTHON_FAST_THREAD_STATE 0\r\n",
      "    74\t  #undef CYTHON_FAST_PYCALL\r\n",
      "    75\t  #define CYTHON_FAST_PYCALL 0\r\n",
      "    76\t#elif defined(PYSTON_VERSION)\r\n",
      "    77\t  #define CYTHON_COMPILING_IN_PYPY 0\r\n",
      "    78\t  #define CYTHON_COMPILING_IN_PYSTON 1\r\n",
      "    79\t  #define CYTHON_COMPILING_IN_CPYTHON 0\r\n",
      "    80\t  #ifndef CYTHON_USE_TYPE_SLOTS\r\n",
      "    81\t    #define CYTHON_USE_TYPE_SLOTS 1\r\n",
      "    82\t  #endif\r\n",
      "    83\t  #undef CYTHON_USE_ASYNC_SLOTS\r\n",
      "    84\t  #define CYTHON_USE_ASYNC_SLOTS 0\r\n",
      "    85\t  #undef CYTHON_USE_PYLIST_INTERNALS\r\n",
      "    86\t  #define CYTHON_USE_PYLIST_INTERNALS 0\r\n",
      "    87\t  #ifndef CYTHON_USE_UNICODE_INTERNALS\r\n",
      "    88\t    #define CYTHON_USE_UNICODE_INTERNALS 1\r\n",
      "    89\t  #endif\r\n",
      "    90\t  #undef CYTHON_USE_UNICODE_WRITER\r\n",
      "    91\t  #define CYTHON_USE_UNICODE_WRITER 0\r\n",
      "    92\t  #undef CYTHON_USE_PYLONG_INTERNALS\r\n",
      "    93\t  #define CYTHON_USE_PYLONG_INTERNALS 0\r\n",
      "    94\t  #ifndef CYTHON_AVOID_BORROWED_REFS\r\n",
      "    95\t    #define CYTHON_AVOID_BORROWED_REFS 0\r\n",
      "    96\t  #endif\r\n",
      "    97\t  #ifndef CYTHON_ASSUME_SAFE_MACROS\r\n",
      "    98\t    #define CYTHON_ASSUME_SAFE_MACROS 1\r\n",
      "    99\t  #endif\r\n",
      "   100\t  #ifndef CYTHON_UNPACK_METHODS\r\n",
      "   101\t    #define CYTHON_UNPACK_METHODS 1\r\n",
      "   102\t  #endif\r\n",
      "   103\t  #undef CYTHON_FAST_THREAD_STATE\r\n",
      "   104\t  #define CYTHON_FAST_THREAD_STATE 0\r\n",
      "   105\t  #undef CYTHON_FAST_PYCALL\r\n",
      "   106\t  #define CYTHON_FAST_PYCALL 0\r\n",
      "   107\t#else\r\n",
      "   108\t  #define CYTHON_COMPILING_IN_PYPY 0\r\n",
      "   109\t  #define CYTHON_COMPILING_IN_PYSTON 0\r\n",
      "   110\t  #define CYTHON_COMPILING_IN_CPYTHON 1\r\n",
      "   111\t  #ifndef CYTHON_USE_TYPE_SLOTS\r\n",
      "   112\t    #define CYTHON_USE_TYPE_SLOTS 1\r\n",
      "   113\t  #endif\r\n",
      "   114\t  #if PY_MAJOR_VERSION < 3\r\n",
      "   115\t    #undef CYTHON_USE_ASYNC_SLOTS\r\n",
      "   116\t    #define CYTHON_USE_ASYNC_SLOTS 0\r\n",
      "   117\t  #elif !defined(CYTHON_USE_ASYNC_SLOTS)\r\n",
      "   118\t    #define CYTHON_USE_ASYNC_SLOTS 1\r\n",
      "   119\t  #endif\r\n",
      "   120\t  #if PY_VERSION_HEX < 0x02070000\r\n",
      "   121\t    #undef CYTHON_USE_PYLONG_INTERNALS\r\n",
      "   122\t    #define CYTHON_USE_PYLONG_INTERNALS 0\r\n",
      "   123\t  #elif !defined(CYTHON_USE_PYLONG_INTERNALS)\r\n",
      "   124\t    #define CYTHON_USE_PYLONG_INTERNALS 1\r\n",
      "   125\t  #endif\r\n",
      "   126\t  #ifndef CYTHON_USE_PYLIST_INTERNALS\r\n",
      "   127\t    #define CYTHON_USE_PYLIST_INTERNALS 1\r\n",
      "   128\t  #endif\r\n",
      "   129\t  #ifndef CYTHON_USE_UNICODE_INTERNALS\r\n",
      "   130\t    #define CYTHON_USE_UNICODE_INTERNALS 1\r\n",
      "   131\t  #endif\r\n",
      "   132\t  #if PY_VERSION_HEX < 0x030300F0\r\n",
      "   133\t    #undef CYTHON_USE_UNICODE_WRITER\r\n",
      "   134\t    #define CYTHON_USE_UNICODE_WRITER 0\r\n",
      "   135\t  #elif !defined(CYTHON_USE_UNICODE_WRITER)\r\n",
      "   136\t    #define CYTHON_USE_UNICODE_WRITER 1\r\n",
      "   137\t  #endif\r\n",
      "   138\t  #ifndef CYTHON_AVOID_BORROWED_REFS\r\n",
      "   139\t    #define CYTHON_AVOID_BORROWED_REFS 0\r\n",
      "   140\t  #endif\r\n",
      "   141\t  #ifndef CYTHON_ASSUME_SAFE_MACROS\r\n",
      "   142\t    #define CYTHON_ASSUME_SAFE_MACROS 1\r\n",
      "   143\t  #endif\r\n",
      "   144\t  #ifndef CYTHON_UNPACK_METHODS\r\n",
      "   145\t    #define CYTHON_UNPACK_METHODS 1\r\n",
      "   146\t  #endif\r\n",
      "   147\t  #ifndef CYTHON_FAST_THREAD_STATE\r\n",
      "   148\t    #define CYTHON_FAST_THREAD_STATE 1\r\n",
      "   149\t  #endif\r\n",
      "   150\t  #ifndef CYTHON_FAST_PYCALL\r\n",
      "   151\t    #define CYTHON_FAST_PYCALL 1\r\n",
      "   152\t  #endif\r\n",
      "   153\t#endif\r\n",
      "   154\t#if !defined(CYTHON_FAST_PYCCALL)\r\n",
      "   155\t#define CYTHON_FAST_PYCCALL  (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1)\r\n",
      "   156\t#endif\r\n",
      "   157\t#if CYTHON_USE_PYLONG_INTERNALS\r\n",
      "   158\t  #include \"longintrepr.h\"\r\n",
      "   159\t  #undef SHIFT\r\n",
      "   160\t  #undef BASE\r\n",
      "   161\t  #undef MASK\r\n",
      "   162\t#endif\r\n",
      "   163\t#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag)\r\n",
      "   164\t  #define Py_OptimizeFlag 0\r\n",
      "   165\t#endif\r\n",
      "   166\t#define __PYX_BUILD_PY_SSIZE_T \"n\"\r\n",
      "   167\t#define CYTHON_FORMAT_SSIZE_T \"z\"\r\n",
      "   168\t#if PY_MAJOR_VERSION < 3\r\n",
      "   169\t  #define __Pyx_BUILTIN_MODULE_NAME \"__builtin__\"\r\n",
      "   170\t  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\\\r\n",
      "   171\t          PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\r\n",
      "   172\t  #define __Pyx_DefaultClassType PyClass_Type\r\n",
      "   173\t#else\r\n",
      "   174\t  #define __Pyx_BUILTIN_MODULE_NAME \"builtins\"\r\n",
      "   175\t  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\\\r\n",
      "   176\t          PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\r\n",
      "   177\t  #define __Pyx_DefaultClassType PyType_Type\r\n",
      "   178\t#endif\r\n",
      "   179\t#ifndef Py_TPFLAGS_CHECKTYPES\r\n",
      "   180\t  #define Py_TPFLAGS_CHECKTYPES 0\r\n",
      "   181\t#endif\r\n",
      "   182\t#ifndef Py_TPFLAGS_HAVE_INDEX\r\n",
      "   183\t  #define Py_TPFLAGS_HAVE_INDEX 0\r\n",
      "   184\t#endif\r\n",
      "   185\t#ifndef Py_TPFLAGS_HAVE_NEWBUFFER\r\n",
      "   186\t  #define Py_TPFLAGS_HAVE_NEWBUFFER 0\r\n",
      "   187\t#endif\r\n",
      "   188\t#ifndef Py_TPFLAGS_HAVE_FINALIZE\r\n",
      "   189\t  #define Py_TPFLAGS_HAVE_FINALIZE 0\r\n",
      "   190\t#endif\r\n",
      "   191\t#ifndef METH_FASTCALL\r\n",
      "   192\t  #define METH_FASTCALL 0x80\r\n",
      "   193\t  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject **args,\r\n",
      "   194\t                                              Py_ssize_t nargs, PyObject *kwnames);\r\n",
      "   195\t#else\r\n",
      "   196\t  #define __Pyx_PyCFunctionFast _PyCFunctionFast\r\n",
      "   197\t#endif\r\n",
      "   198\t#if CYTHON_FAST_PYCCALL\r\n",
      "   199\t#define __Pyx_PyFastCFunction_Check(func)\\\r\n",
      "   200\t    ((PyCFunction_Check(func) && (METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST)))))\r\n",
      "   201\t#else\r\n",
      "   202\t#define __Pyx_PyFastCFunction_Check(func) 0\r\n",
      "   203\t#endif\r\n",
      "   204\t#if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)\r\n",
      "   205\t  #define CYTHON_PEP393_ENABLED 1\r\n",
      "   206\t  #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ?\\\r\n",
      "   207\t                                              0 : _PyUnicode_Ready((PyObject *)(op)))\r\n",
      "   208\t  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_LENGTH(u)\r\n",
      "   209\t  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)\r\n",
      "   210\t  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   PyUnicode_MAX_CHAR_VALUE(u)\r\n",
      "   211\t  #define __Pyx_PyUnicode_KIND(u)         PyUnicode_KIND(u)\r\n",
      "   212\t  #define __Pyx_PyUnicode_DATA(u)         PyUnicode_DATA(u)\r\n",
      "   213\t  #define __Pyx_PyUnicode_READ(k, d, i)   PyUnicode_READ(k, d, i)\r\n",
      "   214\t  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  PyUnicode_WRITE(k, d, i, ch)\r\n",
      "   215\t  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))\r\n",
      "   216\t#else\r\n",
      "   217\t  #define CYTHON_PEP393_ENABLED 0\r\n",
      "   218\t  #define PyUnicode_1BYTE_KIND  1\r\n",
      "   219\t  #define PyUnicode_2BYTE_KIND  2\r\n",
      "   220\t  #define PyUnicode_4BYTE_KIND  4\r\n",
      "   221\t  #define __Pyx_PyUnicode_READY(op)       (0)\r\n",
      "   222\t  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_SIZE(u)\r\n",
      "   223\t  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))\r\n",
      "   224\t  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111)\r\n",
      "   225\t  #define __Pyx_PyUnicode_KIND(u)         (sizeof(Py_UNICODE))\r\n",
      "   226\t  #define __Pyx_PyUnicode_DATA(u)         ((void*)PyUnicode_AS_UNICODE(u))\r\n",
      "   227\t  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))\r\n",
      "   228\t  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  (((void)(k)), ((Py_UNICODE*)d)[i] = ch)\r\n",
      "   229\t  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_SIZE(u))\r\n",
      "   230\t#endif\r\n",
      "   231\t#if CYTHON_COMPILING_IN_PYPY\r\n",
      "   232\t  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)\r\n",
      "   233\t  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)\r\n",
      "   234\t#else\r\n",
      "   235\t  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)\r\n",
      "   236\t  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\\\r\n",
      "   237\t      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))\r\n",
      "   238\t#endif\r\n",
      "   239\t#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)\r\n",
      "   240\t  #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)\r\n",
      "   241\t#endif\r\n",
      "   242\t#if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check)\r\n",
      "   243\t  #define PyByteArray_Check(obj)  PyObject_TypeCheck(obj, &PyByteArray_Type)\r\n",
      "   244\t#endif\r\n",
      "   245\t#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)\r\n",
      "   246\t  #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, \"__format__\", \"O\", fmt)\r\n",
      "   247\t#endif\r\n",
      "   248\t#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)\r\n",
      "   249\t  #define PyObject_Malloc(s)   PyMem_Malloc(s)\r\n",
      "   250\t  #define PyObject_Free(p)     PyMem_Free(p)\r\n",
      "   251\t  #define PyObject_Realloc(p)  PyMem_Realloc(p)\r\n",
      "   252\t#endif\r\n",
      "   253\t#if CYTHON_COMPILING_IN_PYSTON\r\n",
      "   254\t  #define __Pyx_PyCode_HasFreeVars(co)  PyCode_HasFreeVars(co)\r\n",
      "   255\t  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno)\r\n",
      "   256\t#else\r\n",
      "   257\t  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)\r\n",
      "   258\t  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)  (frame)->f_lineno = (lineno)\r\n",
      "   259\t#endif\r\n",
      "   260\t#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))\r\n",
      "   261\t#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))\r\n",
      "   262\t#if PY_MAJOR_VERSION >= 3\r\n",
      "   263\t  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)\r\n",
      "   264\t#else\r\n",
      "   265\t  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)\r\n",
      "   266\t#endif\r\n",
      "   267\t#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)\r\n",
      "   268\t  #define PyObject_ASCII(o)            PyObject_Repr(o)\r\n",
      "   269\t#endif\r\n",
      "   270\t#if PY_MAJOR_VERSION >= 3\r\n",
      "   271\t  #define PyBaseString_Type            PyUnicode_Type\r\n",
      "   272\t  #define PyStringObject               PyUnicodeObject\r\n",
      "   273\t  #define PyString_Type                PyUnicode_Type\r\n",
      "   274\t  #define PyString_Check               PyUnicode_Check\r\n",
      "   275\t  #define PyString_CheckExact          PyUnicode_CheckExact\r\n",
      "   276\t#endif\r\n",
      "   277\t#if PY_MAJOR_VERSION >= 3\r\n",
      "   278\t  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)\r\n",
      "   279\t  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)\r\n",
      "   280\t#else\r\n",
      "   281\t  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))\r\n",
      "   282\t  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))\r\n",
      "   283\t#endif\r\n",
      "   284\t#ifndef PySet_CheckExact\r\n",
      "   285\t  #define PySet_CheckExact(obj)        (Py_TYPE(obj) == &PySet_Type)\r\n",
      "   286\t#endif\r\n",
      "   287\t#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)\r\n",
      "   288\t#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)\r\n",
      "   289\t#if PY_MAJOR_VERSION >= 3\r\n",
      "   290\t  #define PyIntObject                  PyLongObject\r\n",
      "   291\t  #define PyInt_Type                   PyLong_Type\r\n",
      "   292\t  #define PyInt_Check(op)              PyLong_Check(op)\r\n",
      "   293\t  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)\r\n",
      "   294\t  #define PyInt_FromString             PyLong_FromString\r\n",
      "   295\t  #define PyInt_FromUnicode            PyLong_FromUnicode\r\n",
      "   296\t  #define PyInt_FromLong               PyLong_FromLong\r\n",
      "   297\t  #define PyInt_FromSize_t             PyLong_FromSize_t\r\n",
      "   298\t  #define PyInt_FromSsize_t            PyLong_FromSsize_t\r\n",
      "   299\t  #define PyInt_AsLong                 PyLong_AsLong\r\n",
      "   300\t  #define PyInt_AS_LONG                PyLong_AS_LONG\r\n",
      "   301\t  #define PyInt_AsSsize_t              PyLong_AsSsize_t\r\n",
      "   302\t  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask\r\n",
      "   303\t  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask\r\n",
      "   304\t  #define PyNumber_Int                 PyNumber_Long\r\n",
      "   305\t#endif\r\n",
      "   306\t#if PY_MAJOR_VERSION >= 3\r\n",
      "   307\t  #define PyBoolObject                 PyLongObject\r\n",
      "   308\t#endif\r\n",
      "   309\t#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY\r\n",
      "   310\t  #ifndef PyUnicode_InternFromString\r\n",
      "   311\t    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)\r\n",
      "   312\t  #endif\r\n",
      "   313\t#endif\r\n",
      "   314\t#if PY_VERSION_HEX < 0x030200A4\r\n",
      "   315\t  typedef long Py_hash_t;\r\n",
      "   316\t  #define __Pyx_PyInt_FromHash_t PyInt_FromLong\r\n",
      "   317\t  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong\r\n",
      "   318\t#else\r\n",
      "   319\t  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t\r\n",
      "   320\t  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t\r\n",
      "   321\t#endif\r\n",
      "   322\t#if PY_MAJOR_VERSION >= 3\r\n",
      "   323\t  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : PyInstanceMethod_New(func))\r\n",
      "   324\t#else\r\n",
      "   325\t  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)\r\n",
      "   326\t#endif\r\n",
      "   327\t#if CYTHON_USE_ASYNC_SLOTS\r\n",
      "   328\t  #if PY_VERSION_HEX >= 0x030500B1\r\n",
      "   329\t    #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods\r\n",
      "   330\t    #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)\r\n",
      "   331\t  #else\r\n",
      "   332\t    typedef struct {\r\n",
      "   333\t        unaryfunc am_await;\r\n",
      "   334\t        unaryfunc am_aiter;\r\n",
      "   335\t        unaryfunc am_anext;\r\n",
      "   336\t    } __Pyx_PyAsyncMethodsStruct;\r\n",
      "   337\t    #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))\r\n",
      "   338\t  #endif\r\n",
      "   339\t#else\r\n",
      "   340\t  #define __Pyx_PyType_AsAsync(obj) NULL\r\n",
      "   341\t#endif\r\n",
      "   342\t#ifndef CYTHON_RESTRICT\r\n",
      "   343\t  #if defined(__GNUC__)\r\n",
      "   344\t    #define CYTHON_RESTRICT __restrict__\r\n",
      "   345\t  #elif defined(_MSC_VER) && _MSC_VER >= 1400\r\n",
      "   346\t    #define CYTHON_RESTRICT __restrict\r\n",
      "   347\t  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L\r\n",
      "   348\t    #define CYTHON_RESTRICT restrict\r\n",
      "   349\t  #else\r\n",
      "   350\t    #define CYTHON_RESTRICT\r\n",
      "   351\t  #endif\r\n",
      "   352\t#endif\r\n",
      "   353\t#ifndef CYTHON_UNUSED\r\n",
      "   354\t# if defined(__GNUC__)\r\n",
      "   355\t#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))\r\n",
      "   356\t#     define CYTHON_UNUSED __attribute__ ((__unused__))\r\n",
      "   357\t#   else\r\n",
      "   358\t#     define CYTHON_UNUSED\r\n",
      "   359\t#   endif\r\n",
      "   360\t# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))\r\n",
      "   361\t#   define CYTHON_UNUSED __attribute__ ((__unused__))\r\n",
      "   362\t# else\r\n",
      "   363\t#   define CYTHON_UNUSED\r\n",
      "   364\t# endif\r\n",
      "   365\t#endif\r\n",
      "   366\t#ifndef CYTHON_MAYBE_UNUSED_VAR\r\n",
      "   367\t#  if defined(__cplusplus)\r\n",
      "   368\t     template<class T> void CYTHON_MAYBE_UNUSED_VAR( const T& ) { }\r\n",
      "   369\t#  else\r\n",
      "   370\t#    define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x)\r\n",
      "   371\t#  endif\r\n",
      "   372\t#endif\r\n",
      "   373\t#ifndef CYTHON_NCP_UNUSED\r\n",
      "   374\t# if CYTHON_COMPILING_IN_CPYTHON\r\n",
      "   375\t#  define CYTHON_NCP_UNUSED\r\n",
      "   376\t# else\r\n",
      "   377\t#  define CYTHON_NCP_UNUSED CYTHON_UNUSED\r\n",
      "   378\t# endif\r\n",
      "   379\t#endif\r\n",
      "   380\t#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)\r\n",
      "       \r\n",
      "   381\t#ifndef CYTHON_INLINE\r\n",
      "   382\t  #if defined(__clang__)\r\n",
      "   383\t    #define CYTHON_INLINE __inline__ __attribute__ ((__unused__))\r\n",
      "   384\t  #elif defined(__GNUC__)\r\n",
      "   385\t    #define CYTHON_INLINE __inline__\r\n",
      "   386\t  #elif defined(_MSC_VER)\r\n",
      "   387\t    #define CYTHON_INLINE __inline\r\n",
      "   388\t  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L\r\n",
      "   389\t    #define CYTHON_INLINE inline\r\n",
      "   390\t  #else\r\n",
      "   391\t    #define CYTHON_INLINE\r\n",
      "   392\t  #endif\r\n",
      "   393\t#endif\r\n",
      "       \r\n",
      "   394\t#if defined(WIN32) || defined(MS_WINDOWS)\r\n",
      "   395\t  #define _USE_MATH_DEFINES\r\n",
      "   396\t#endif\r\n",
      "   397\t#include <math.h>\r\n",
      "   398\t#ifdef NAN\r\n",
      "   399\t#define __PYX_NAN() ((float) NAN)\r\n",
      "   400\t#else\r\n",
      "   401\tstatic CYTHON_INLINE float __PYX_NAN() {\r\n",
      "   402\t  float value;\r\n",
      "   403\t  memset(&value, 0xFF, sizeof(value));\r\n",
      "   404\t  return value;\r\n",
      "   405\t}\r\n",
      "   406\t#endif\r\n",
      "   407\t#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)\r\n",
      "   408\t#define __Pyx_truncl trunc\r\n",
      "   409\t#else\r\n",
      "   410\t#define __Pyx_truncl truncl\r\n",
      "   411\t#endif\r\n",
      "       \r\n",
      "       \r\n",
      "   412\t#define __PYX_ERR(f_index, lineno, Ln_error) \\\r\n",
      "   413\t{ \\\r\n",
      "   414\t  __pyx_filename = __pyx_f[f_index]; __pyx_lineno = lineno; __pyx_clineno = __LINE__; goto Ln_error; \\\r\n",
      "   415\t}\r\n",
      "       \r\n",
      "   416\t#if PY_MAJOR_VERSION >= 3\r\n",
      "   417\t  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)\r\n",
      "   418\t  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)\r\n",
      "   419\t#else\r\n",
      "   420\t  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)\r\n",
      "   421\t  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)\r\n",
      "   422\t#endif\r\n",
      "       \r\n",
      "   423\t#ifndef __PYX_EXTERN_C\r\n",
      "   424\t  #ifdef __cplusplus\r\n",
      "   425\t    #define __PYX_EXTERN_C extern \"C\"\r\n",
      "   426\t  #else\r\n",
      "   427\t    #define __PYX_EXTERN_C extern\r\n",
      "   428\t  #endif\r\n",
      "   429\t#endif\r\n",
      "       \r\n",
      "   430\t#define __PYX_HAVE__cyfoo\r\n",
      "   431\t#define __PYX_HAVE_API__cyfoo\r\n",
      "   432\t#ifdef _OPENMP\r\n",
      "   433\t#include <omp.h>\r\n",
      "   434\t#endif /* _OPENMP */\r\n",
      "       \r\n",
      "   435\t#ifdef PYREX_WITHOUT_ASSERTIONS\r\n",
      "   436\t#define CYTHON_WITHOUT_ASSERTIONS\r\n",
      "   437\t#endif\r\n",
      "       \r\n",
      "   438\ttypedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;\r\n",
      "   439\t                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;\r\n",
      "       \r\n",
      "   440\t#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0\r\n",
      "   441\t#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0\r\n",
      "   442\t#define __PYX_DEFAULT_STRING_ENCODING \"\"\r\n",
      "   443\t#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString\r\n",
      "   444\t#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize\r\n",
      "   445\t#define __Pyx_uchar_cast(c) ((unsigned char)c)\r\n",
      "   446\t#define __Pyx_long_cast(x) ((long)x)\r\n",
      "   447\t#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\\\r\n",
      "   448\t    (sizeof(type) < sizeof(Py_ssize_t))  ||\\\r\n",
      "   449\t    (sizeof(type) > sizeof(Py_ssize_t) &&\\\r\n",
      "   450\t          likely(v < (type)PY_SSIZE_T_MAX ||\\\r\n",
      "   451\t                 v == (type)PY_SSIZE_T_MAX)  &&\\\r\n",
      "   452\t          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\\\r\n",
      "   453\t                                v == (type)PY_SSIZE_T_MIN)))  ||\\\r\n",
      "   454\t    (sizeof(type) == sizeof(Py_ssize_t) &&\\\r\n",
      "   455\t          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\\\r\n",
      "   456\t                               v == (type)PY_SSIZE_T_MAX)))  )\r\n",
      "   457\t#if defined (__cplusplus) && __cplusplus >= 201103L\r\n",
      "   458\t    #include <cstdlib>\r\n",
      "   459\t    #define __Pyx_sst_abs(value) std::abs(value)\r\n",
      "   460\t#elif SIZEOF_INT >= SIZEOF_SIZE_T\r\n",
      "   461\t    #define __Pyx_sst_abs(value) abs(value)\r\n",
      "   462\t#elif SIZEOF_LONG >= SIZEOF_SIZE_T\r\n",
      "   463\t    #define __Pyx_sst_abs(value) labs(value)\r\n",
      "   464\t#elif defined (_MSC_VER) && defined (_M_X64)\r\n",
      "   465\t    #define __Pyx_sst_abs(value) _abs64(value)\r\n",
      "   466\t#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L\r\n",
      "   467\t    #define __Pyx_sst_abs(value) llabs(value)\r\n",
      "   468\t#elif defined (__GNUC__)\r\n",
      "   469\t    #define __Pyx_sst_abs(value) __builtin_llabs(value)\r\n",
      "   470\t#else\r\n",
      "   471\t    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)\r\n",
      "   472\t#endif\r\n",
      "   473\tstatic CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject*);\r\n",
      "   474\tstatic CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);\r\n",
      "   475\t#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))\r\n",
      "   476\t#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)\r\n",
      "   477\t#define __Pyx_PyBytes_FromString        PyBytes_FromString\r\n",
      "   478\t#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize\r\n",
      "   479\tstatic CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);\r\n",
      "   480\t#if PY_MAJOR_VERSION < 3\r\n",
      "   481\t    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString\r\n",
      "   482\t    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize\r\n",
      "   483\t#else\r\n",
      "   484\t    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString\r\n",
      "   485\t    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize\r\n",
      "   486\t#endif\r\n",
      "   487\t#define __Pyx_PyObject_AsSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))\r\n",
      "   488\t#define __Pyx_PyObject_AsUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))\r\n",
      "   489\t#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)\r\n",
      "   490\t#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)\r\n",
      "   491\t#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)\r\n",
      "   492\t#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)\r\n",
      "   493\t#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)\r\n",
      "   494\t#if PY_MAJOR_VERSION < 3\r\n",
      "   495\tstatic CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u)\r\n",
      "   496\t{\r\n",
      "   497\t    const Py_UNICODE *u_end = u;\r\n",
      "   498\t    while (*u_end++) ;\r\n",
      "   499\t    return (size_t)(u_end - u - 1);\r\n",
      "   500\t}\r\n",
      "   501\t#else\r\n",
      "   502\t#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen\r\n",
      "   503\t#endif\r\n",
      "   504\t#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))\r\n",
      "   505\t#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode\r\n",
      "   506\t#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode\r\n",
      "   507\t#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)\r\n",
      "   508\t#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)\r\n",
      "   509\t#define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False))\r\n",
      "   510\tstatic CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);\r\n",
      "   511\tstatic CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);\r\n",
      "   512\tstatic CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);\r\n",
      "   513\tstatic CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);\r\n",
      "   514\t#if CYTHON_ASSUME_SAFE_MACROS\r\n",
      "   515\t#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))\r\n",
      "   516\t#else\r\n",
      "   517\t#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)\r\n",
      "   518\t#endif\r\n",
      "   519\t#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))\r\n",
      "   520\t#if PY_MAJOR_VERSION >= 3\r\n",
      "   521\t#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))\r\n",
      "   522\t#else\r\n",
      "   523\t#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))\r\n",
      "   524\t#endif\r\n",
      "   525\t#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))\r\n",
      "   526\t#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII\r\n",
      "   527\tstatic int __Pyx_sys_getdefaultencoding_not_ascii;\r\n",
      "   528\tstatic int __Pyx_init_sys_getdefaultencoding_params(void) {\r\n",
      "   529\t    PyObject* sys;\r\n",
      "   530\t    PyObject* default_encoding = NULL;\r\n",
      "   531\t    PyObject* ascii_chars_u = NULL;\r\n",
      "   532\t    PyObject* ascii_chars_b = NULL;\r\n",
      "   533\t    const char* default_encoding_c;\r\n",
      "   534\t    sys = PyImport_ImportModule(\"sys\");\r\n",
      "   535\t    if (!sys) goto bad;\r\n",
      "   536\t    default_encoding = PyObject_CallMethod(sys, (char*) \"getdefaultencoding\", NULL);\r\n",
      "   537\t    Py_DECREF(sys);\r\n",
      "   538\t    if (!default_encoding) goto bad;\r\n",
      "   539\t    default_encoding_c = PyBytes_AsString(default_encoding);\r\n",
      "   540\t    if (!default_encoding_c) goto bad;\r\n",
      "   541\t    if (strcmp(default_encoding_c, \"ascii\") == 0) {\r\n",
      "   542\t        __Pyx_sys_getdefaultencoding_not_ascii = 0;\r\n",
      "   543\t    } else {\r\n",
      "   544\t        char ascii_chars[128];\r\n",
      "   545\t        int c;\r\n",
      "   546\t        for (c = 0; c < 128; c++) {\r\n",
      "   547\t            ascii_chars[c] = c;\r\n",
      "   548\t        }\r\n",
      "   549\t        __Pyx_sys_getdefaultencoding_not_ascii = 1;\r\n",
      "   550\t        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);\r\n",
      "   551\t        if (!ascii_chars_u) goto bad;\r\n",
      "   552\t        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);\r\n",
      "   553\t        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {\r\n",
      "   554\t            PyErr_Format(\r\n",
      "   555\t                PyExc_ValueError,\r\n",
      "   556\t                \"This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.\",\r\n",
      "   557\t                default_encoding_c);\r\n",
      "   558\t            goto bad;\r\n",
      "   559\t        }\r\n",
      "   560\t        Py_DECREF(ascii_chars_u);\r\n",
      "   561\t        Py_DECREF(ascii_chars_b);\r\n",
      "   562\t    }\r\n",
      "   563\t    Py_DECREF(default_encoding);\r\n",
      "   564\t    return 0;\r\n",
      "   565\tbad:\r\n",
      "   566\t    Py_XDECREF(default_encoding);\r\n",
      "   567\t    Py_XDECREF(ascii_chars_u);\r\n",
      "   568\t    Py_XDECREF(ascii_chars_b);\r\n",
      "   569\t    return -1;\r\n",
      "   570\t}\r\n",
      "   571\t#endif\r\n",
      "   572\t#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3\r\n",
      "   573\t#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)\r\n",
      "   574\t#else\r\n",
      "   575\t#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)\r\n",
      "   576\t#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT\r\n",
      "   577\tstatic char* __PYX_DEFAULT_STRING_ENCODING;\r\n",
      "   578\tstatic int __Pyx_init_sys_getdefaultencoding_params(void) {\r\n",
      "   579\t    PyObject* sys;\r\n",
      "   580\t    PyObject* default_encoding = NULL;\r\n",
      "   581\t    char* default_encoding_c;\r\n",
      "   582\t    sys = PyImport_ImportModule(\"sys\");\r\n",
      "   583\t    if (!sys) goto bad;\r\n",
      "   584\t    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) \"getdefaultencoding\", NULL);\r\n",
      "   585\t    Py_DECREF(sys);\r\n",
      "   586\t    if (!default_encoding) goto bad;\r\n",
      "   587\t    default_encoding_c = PyBytes_AsString(default_encoding);\r\n",
      "   588\t    if (!default_encoding_c) goto bad;\r\n",
      "   589\t    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));\r\n",
      "   590\t    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;\r\n",
      "   591\t    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);\r\n",
      "   592\t    Py_DECREF(default_encoding);\r\n",
      "   593\t    return 0;\r\n",
      "   594\tbad:\r\n",
      "   595\t    Py_XDECREF(default_encoding);\r\n",
      "   596\t    return -1;\r\n",
      "   597\t}\r\n",
      "   598\t#endif\r\n",
      "   599\t#endif\r\n",
      "       \r\n",
      "       \r\n",
      "   600\t/* Test for GCC > 2.95 */\r\n",
      "   601\t#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))\r\n",
      "   602\t  #define likely(x)   __builtin_expect(!!(x), 1)\r\n",
      "   603\t  #define unlikely(x) __builtin_expect(!!(x), 0)\r\n",
      "   604\t#else /* !__GNUC__ or GCC < 2.95 */\r\n",
      "   605\t  #define likely(x)   (x)\r\n",
      "   606\t  #define unlikely(x) (x)\r\n",
      "   607\t#endif /* __GNUC__ */\r\n",
      "       \r\n",
      "   608\tstatic PyObject *__pyx_m;\r\n",
      "   609\tstatic PyObject *__pyx_d;\r\n",
      "   610\tstatic PyObject *__pyx_b;\r\n",
      "   611\tstatic PyObject *__pyx_empty_tuple;\r\n",
      "   612\tstatic PyObject *__pyx_empty_bytes;\r\n",
      "   613\tstatic PyObject *__pyx_empty_unicode;\r\n",
      "   614\tstatic int __pyx_lineno;\r\n",
      "   615\tstatic int __pyx_clineno = 0;\r\n",
      "   616\tstatic const char * __pyx_cfilenm= __FILE__;\r\n",
      "   617\tstatic const char *__pyx_filename;\r\n",
      "       \r\n",
      "       \r\n",
      "   618\tstatic const char *__pyx_f[] = {\r\n",
      "   619\t  \".cache/ipython/cython/cyfoo.pyx\",\r\n",
      "   620\t};\r\n",
      "       \r\n",
      "   621\t/*--- Type declarations ---*/\r\n",
      "       \r\n",
      "   622\t/* --- Runtime support code (head) --- */\r\n",
      "   623\t/* Refnanny.proto */\r\n",
      "   624\t#ifndef CYTHON_REFNANNY\r\n",
      "   625\t  #define CYTHON_REFNANNY 0\r\n",
      "   626\t#endif\r\n",
      "   627\t#if CYTHON_REFNANNY\r\n",
      "   628\t  typedef struct {\r\n",
      "   629\t    void (*INCREF)(void*, PyObject*, int);\r\n",
      "   630\t    void (*DECREF)(void*, PyObject*, int);\r\n",
      "   631\t    void (*GOTREF)(void*, PyObject*, int);\r\n",
      "   632\t    void (*GIVEREF)(void*, PyObject*, int);\r\n",
      "   633\t    void* (*SetupContext)(const char*, int, const char*);\r\n",
      "   634\t    void (*FinishContext)(void**);\r\n",
      "   635\t  } __Pyx_RefNannyAPIStruct;\r\n",
      "   636\t  static __Pyx_RefNannyAPIStruct *__Pyx_RefNanny = NULL;\r\n",
      "   637\t  static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname);\r\n",
      "   638\t  #define __Pyx_RefNannyDeclarations void *__pyx_refnanny = NULL;\r\n",
      "   639\t#ifdef WITH_THREAD\r\n",
      "   640\t  #define __Pyx_RefNannySetupContext(name, acquire_gil)\\\r\n",
      "   641\t          if (acquire_gil) {\\\r\n",
      "   642\t              PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\\\r\n",
      "   643\t              __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\\\r\n",
      "   644\t              PyGILState_Release(__pyx_gilstate_save);\\\r\n",
      "   645\t          } else {\\\r\n",
      "   646\t              __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\\\r\n",
      "   647\t          }\r\n",
      "   648\t#else\r\n",
      "   649\t  #define __Pyx_RefNannySetupContext(name, acquire_gil)\\\r\n",
      "   650\t          __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__)\r\n",
      "   651\t#endif\r\n",
      "   652\t  #define __Pyx_RefNannyFinishContext()\\\r\n",
      "   653\t          __Pyx_RefNanny->FinishContext(&__pyx_refnanny)\r\n",
      "   654\t  #define __Pyx_INCREF(r)  __Pyx_RefNanny->INCREF(__pyx_refnanny, (PyObject *)(r), __LINE__)\r\n",
      "   655\t  #define __Pyx_DECREF(r)  __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), __LINE__)\r\n",
      "   656\t  #define __Pyx_GOTREF(r)  __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__)\r\n",
      "   657\t  #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), __LINE__)\r\n",
      "   658\t  #define __Pyx_XINCREF(r)  do { if((r) != NULL) {__Pyx_INCREF(r); }} while(0)\r\n",
      "   659\t  #define __Pyx_XDECREF(r)  do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0)\r\n",
      "   660\t  #define __Pyx_XGOTREF(r)  do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0)\r\n",
      "   661\t  #define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);}} while(0)\r\n",
      "   662\t#else\r\n",
      "   663\t  #define __Pyx_RefNannyDeclarations\r\n",
      "   664\t  #define __Pyx_RefNannySetupContext(name, acquire_gil)\r\n",
      "   665\t  #define __Pyx_RefNannyFinishContext()\r\n",
      "   666\t  #define __Pyx_INCREF(r) Py_INCREF(r)\r\n",
      "   667\t  #define __Pyx_DECREF(r) Py_DECREF(r)\r\n",
      "   668\t  #define __Pyx_GOTREF(r)\r\n",
      "   669\t  #define __Pyx_GIVEREF(r)\r\n",
      "   670\t  #define __Pyx_XINCREF(r) Py_XINCREF(r)\r\n",
      "   671\t  #define __Pyx_XDECREF(r) Py_XDECREF(r)\r\n",
      "   672\t  #define __Pyx_XGOTREF(r)\r\n",
      "   673\t  #define __Pyx_XGIVEREF(r)\r\n",
      "   674\t#endif\r\n",
      "   675\t#define __Pyx_XDECREF_SET(r, v) do {\\\r\n",
      "   676\t        PyObject *tmp = (PyObject *) r;\\\r\n",
      "   677\t        r = v; __Pyx_XDECREF(tmp);\\\r\n",
      "   678\t    } while (0)\r\n",
      "   679\t#define __Pyx_DECREF_SET(r, v) do {\\\r\n",
      "   680\t        PyObject *tmp = (PyObject *) r;\\\r\n",
      "   681\t        r = v; __Pyx_DECREF(tmp);\\\r\n",
      "   682\t    } while (0)\r\n",
      "   683\t#define __Pyx_CLEAR(r)    do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)\r\n",
      "   684\t#define __Pyx_XCLEAR(r)   do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)\r\n",
      "       \r\n",
      "   685\t/* RaiseArgTupleInvalid.proto */\r\n",
      "   686\tstatic void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,\r\n",
      "   687\t    Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);\r\n",
      "       \r\n",
      "   688\t/* RaiseDoubleKeywords.proto */\r\n",
      "   689\tstatic void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);\r\n",
      "       \r\n",
      "   690\t/* ParseKeywords.proto */\r\n",
      "   691\tstatic int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\\\r\n",
      "   692\t    PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\\\r\n",
      "   693\t    const char* function_name);\r\n",
      "       \r\n",
      "   694\t/* CodeObjectCache.proto */\r\n",
      "   695\ttypedef struct {\r\n",
      "   696\t    PyCodeObject* code_object;\r\n",
      "   697\t    int code_line;\r\n",
      "   698\t} __Pyx_CodeObjectCacheEntry;\r\n",
      "   699\tstruct __Pyx_CodeObjectCache {\r\n",
      "   700\t    int count;\r\n",
      "   701\t    int max_count;\r\n",
      "   702\t    __Pyx_CodeObjectCacheEntry* entries;\r\n",
      "   703\t};\r\n",
      "   704\tstatic struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};\r\n",
      "   705\tstatic int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);\r\n",
      "   706\tstatic PyCodeObject *__pyx_find_code_object(int code_line);\r\n",
      "   707\tstatic void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);\r\n",
      "       \r\n",
      "   708\t/* AddTraceback.proto */\r\n",
      "   709\tstatic void __Pyx_AddTraceback(const char *funcname, int c_line,\r\n",
      "   710\t                               int py_line, const char *filename);\r\n",
      "       \r\n",
      "   711\t/* CIntToPy.proto */\r\n",
      "   712\tstatic CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);\r\n",
      "       \r\n",
      "   713\t/* CIntFromPy.proto */\r\n",
      "   714\tstatic CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);\r\n",
      "       \r\n",
      "   715\t/* CIntFromPy.proto */\r\n",
      "   716\tstatic CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);\r\n",
      "       \r\n",
      "   717\t/* CheckBinaryVersion.proto */\r\n",
      "   718\tstatic int __Pyx_check_binary_version(void);\r\n",
      "       \r\n",
      "   719\t/* InitStrings.proto */\r\n",
      "   720\tstatic int __Pyx_InitStrings(__Pyx_StringTabEntry *t);\r\n",
      "       \r\n",
      "       \r\n",
      "   721\t/* Module declarations from 'cyfoo' */\r\n",
      "   722\t#define __Pyx_MODULE_NAME \"cyfoo\"\r\n",
      "   723\tint __pyx_module_is_main_cyfoo = 0;\r\n",
      "       \r\n",
      "   724\t/* Implementation of 'cyfoo' */\r\n",
      "   725\tstatic const char __pyx_k_a[] = \"a\";\r\n",
      "   726\tstatic const char __pyx_k_b[] = \"b\";\r\n",
      "   727\tstatic const char __pyx_k_main[] = \"__main__\";\r\n",
      "   728\tstatic const char __pyx_k_test[] = \"__test__\";\r\n",
      "   729\tstatic const char __pyx_k_cyfoo[] = \"cyfoo\";\r\n",
      "   730\tstatic const char __pyx_k_home_jovyan_cache_ipython_cytho[] = \"/home/jovyan/.cache/ipython/cython/cyfoo.pyx\";\r\n",
      "   731\tstatic PyObject *__pyx_n_s_a;\r\n",
      "   732\tstatic PyObject *__pyx_n_s_b;\r\n",
      "   733\tstatic PyObject *__pyx_n_s_cyfoo;\r\n",
      "   734\tstatic PyObject *__pyx_kp_s_home_jovyan_cache_ipython_cytho;\r\n",
      "   735\tstatic PyObject *__pyx_n_s_main;\r\n",
      "   736\tstatic PyObject *__pyx_n_s_test;\r\n",
      "   737\tstatic PyObject *__pyx_pf_5cyfoo_cyfoo(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_a, PyObject *__pyx_v_b); /* proto */\r\n",
      "   738\tstatic PyObject *__pyx_tuple_;\r\n",
      "   739\tstatic PyObject *__pyx_codeobj__2;\r\n",
      "       \r\n",
      "   740\t/* \"cyfoo.pyx\":2\r\n",
      "   741\t * \r\n",
      "   742\t * def cyfoo(a, b):             # <<<<<<<<<<<<<<\r\n",
      "   743\t *     return a + b\r\n",
      "   744\t */\r\n",
      "       \r\n",
      "   745\t/* Python wrapper */\r\n",
      "   746\tstatic PyObject *__pyx_pw_5cyfoo_1cyfoo(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\r\n",
      "   747\tstatic PyMethodDef __pyx_mdef_5cyfoo_1cyfoo = {\"cyfoo\", (PyCFunction)__pyx_pw_5cyfoo_1cyfoo, METH_VARARGS|METH_KEYWORDS, 0};\r\n",
      "   748\tstatic PyObject *__pyx_pw_5cyfoo_1cyfoo(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\r\n",
      "   749\t  PyObject *__pyx_v_a = 0;\r\n",
      "   750\t  PyObject *__pyx_v_b = 0;\r\n",
      "   751\t  PyObject *__pyx_r = 0;\r\n",
      "   752\t  __Pyx_RefNannyDeclarations\r\n",
      "   753\t  __Pyx_RefNannySetupContext(\"cyfoo (wrapper)\", 0);\r\n",
      "   754\t  {\r\n",
      "   755\t    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_a,&__pyx_n_s_b,0};\r\n",
      "   756\t    PyObject* values[2] = {0,0};\r\n",
      "   757\t    if (unlikely(__pyx_kwds)) {\r\n",
      "   758\t      Py_ssize_t kw_args;\r\n",
      "   759\t      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);\r\n",
      "   760\t      switch (pos_args) {\r\n",
      "   761\t        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);\r\n",
      "   762\t        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);\r\n",
      "   763\t        case  0: break;\r\n",
      "   764\t        default: goto __pyx_L5_argtuple_error;\r\n",
      "   765\t      }\r\n",
      "   766\t      kw_args = PyDict_Size(__pyx_kwds);\r\n",
      "   767\t      switch (pos_args) {\r\n",
      "   768\t        case  0:\r\n",
      "   769\t        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_a)) != 0)) kw_args--;\r\n",
      "   770\t        else goto __pyx_L5_argtuple_error;\r\n",
      "   771\t        case  1:\r\n",
      "   772\t        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_b)) != 0)) kw_args--;\r\n",
      "   773\t        else {\r\n",
      "   774\t          __Pyx_RaiseArgtupleInvalid(\"cyfoo\", 1, 2, 2, 1); __PYX_ERR(0, 2, __pyx_L3_error)\r\n",
      "   775\t        }\r\n",
      "   776\t      }\r\n",
      "   777\t      if (unlikely(kw_args > 0)) {\r\n",
      "   778\t        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, \"cyfoo\") < 0)) __PYX_ERR(0, 2, __pyx_L3_error)\r\n",
      "   779\t      }\r\n",
      "   780\t    } else if (PyTuple_GET_SIZE(__pyx_args) != 2) {\r\n",
      "   781\t      goto __pyx_L5_argtuple_error;\r\n",
      "   782\t    } else {\r\n",
      "   783\t      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);\r\n",
      "   784\t      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);\r\n",
      "   785\t    }\r\n",
      "   786\t    __pyx_v_a = values[0];\r\n",
      "   787\t    __pyx_v_b = values[1];\r\n",
      "   788\t  }\r\n",
      "   789\t  goto __pyx_L4_argument_unpacking_done;\r\n",
      "   790\t  __pyx_L5_argtuple_error:;\r\n",
      "   791\t  __Pyx_RaiseArgtupleInvalid(\"cyfoo\", 1, 2, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 2, __pyx_L3_error)\r\n",
      "   792\t  __pyx_L3_error:;\r\n",
      "   793\t  __Pyx_AddTraceback(\"cyfoo.cyfoo\", __pyx_clineno, __pyx_lineno, __pyx_filename);\r\n",
      "   794\t  __Pyx_RefNannyFinishContext();\r\n",
      "   795\t  return NULL;\r\n",
      "   796\t  __pyx_L4_argument_unpacking_done:;\r\n",
      "   797\t  __pyx_r = __pyx_pf_5cyfoo_cyfoo(__pyx_self, __pyx_v_a, __pyx_v_b);\r\n",
      "       \r\n",
      "   798\t  /* function exit code */\r\n",
      "   799\t  __Pyx_RefNannyFinishContext();\r\n",
      "   800\t  return __pyx_r;\r\n",
      "   801\t}\r\n",
      "       \r\n",
      "   802\tstatic PyObject *__pyx_pf_5cyfoo_cyfoo(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_a, PyObject *__pyx_v_b) {\r\n",
      "   803\t  PyObject *__pyx_r = NULL;\r\n",
      "   804\t  __Pyx_RefNannyDeclarations\r\n",
      "   805\t  PyObject *__pyx_t_1 = NULL;\r\n",
      "   806\t  __Pyx_RefNannySetupContext(\"cyfoo\", 0);\r\n",
      "       \r\n",
      "   807\t  /* \"cyfoo.pyx\":3\r\n",
      "   808\t * \r\n",
      "   809\t * def cyfoo(a, b):\r\n",
      "   810\t *     return a + b             # <<<<<<<<<<<<<<\r\n",
      "   811\t */\r\n",
      "   812\t  __Pyx_XDECREF(__pyx_r);\r\n",
      "   813\t  __pyx_t_1 = PyNumber_Add(__pyx_v_a, __pyx_v_b); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 3, __pyx_L1_error)\r\n",
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      "   857\t  {&__pyx_kp_s_home_jovyan_cache_ipython_cytho, __pyx_k_home_jovyan_cache_ipython_cytho, sizeof(__pyx_k_home_jovyan_cache_ipython_cytho), 0, 0, 1, 0},\r\n",
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      "   877\t  __Pyx_RefNannyFinishContext();\r\n",
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      "   881\t  return -1;\r\n",
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      "       \r\n",
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      "   885\t  return 0;\r\n",
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      "   887\t  return -1;\r\n",
      "   888\t}\r\n",
      "       \r\n",
      "   889\t#if PY_MAJOR_VERSION < 3\r\n",
      "   890\tPyMODINIT_FUNC initcyfoo(void); /*proto*/\r\n",
      "   891\tPyMODINIT_FUNC initcyfoo(void)\r\n",
      "   892\t#else\r\n",
      "   893\tPyMODINIT_FUNC PyInit_cyfoo(void); /*proto*/\r\n",
      "   894\tPyMODINIT_FUNC PyInit_cyfoo(void)\r\n",
      "   895\t#endif\r\n",
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      "   930\t  #if defined(__PYX_FORCE_INIT_THREADS) && __PYX_FORCE_INIT_THREADS\r\n",
      "   931\t  #ifdef WITH_THREAD /* Python build with threading support? */\r\n",
      "   932\t  PyEval_InitThreads();\r\n",
      "   933\t  #endif\r\n",
      "   934\t  #endif\r\n",
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      "   936\t  #if PY_MAJOR_VERSION < 3\r\n",
      "   937\t  __pyx_m = Py_InitModule4(\"cyfoo\", __pyx_methods, 0, 0, PYTHON_API_VERSION); Py_XINCREF(__pyx_m);\r\n",
      "   938\t  #else\r\n",
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      "   943\t  Py_INCREF(__pyx_d);\r\n",
      "   944\t  __pyx_b = PyImport_AddModule(__Pyx_BUILTIN_MODULE_NAME); if (unlikely(!__pyx_b)) __PYX_ERR(0, 2, __pyx_L1_error)\r\n",
      "   945\t  #if CYTHON_COMPILING_IN_PYPY\r\n",
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      "   950\t  if (__Pyx_InitGlobals() < 0) __PYX_ERR(0, 2, __pyx_L1_error)\r\n",
      "   951\t  #if PY_MAJOR_VERSION < 3 && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)\r\n",
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      "   953\t  #endif\r\n",
      "   954\t  if (__pyx_module_is_main_cyfoo) {\r\n",
      "   955\t    if (PyObject_SetAttrString(__pyx_m, \"__name__\", __pyx_n_s_main) < 0) __PYX_ERR(0, 2, __pyx_L1_error)\r\n",
      "   956\t  }\r\n",
      "   957\t  #if PY_MAJOR_VERSION >= 3\r\n",
      "   958\t  {\r\n",
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      "   960\t    if (!PyDict_GetItemString(modules, \"cyfoo\")) {\r\n",
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      "   962\t    }\r\n",
      "   963\t  }\r\n",
      "   964\t  #endif\r\n",
      "   965\t  /*--- Builtin init code ---*/\r\n",
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      "   967\t  /*--- Constants init code ---*/\r\n",
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      "   969\t  /*--- Global init code ---*/\r\n",
      "   970\t  /*--- Variable export code ---*/\r\n",
      "   971\t  /*--- Function export code ---*/\r\n",
      "   972\t  /*--- Type init code ---*/\r\n",
      "   973\t  /*--- Type import code ---*/\r\n",
      "   974\t  /*--- Variable import code ---*/\r\n",
      "   975\t  /*--- Function import code ---*/\r\n",
      "   976\t  /*--- Execution code ---*/\r\n",
      "   977\t  #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)\r\n",
      "   978\t  if (__Pyx_patch_abc() < 0) __PYX_ERR(0, 2, __pyx_L1_error)\r\n",
      "   979\t  #endif\r\n",
      "       \r\n",
      "   980\t  /* \"cyfoo.pyx\":2\r\n",
      "   981\t * \r\n",
      "   982\t * def cyfoo(a, b):             # <<<<<<<<<<<<<<\r\n",
      "   983\t *     return a + b\r\n",
      "   984\t */\r\n",
      "   985\t  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_5cyfoo_1cyfoo, NULL, __pyx_n_s_cyfoo); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 2, __pyx_L1_error)\r\n",
      "   986\t  __Pyx_GOTREF(__pyx_t_1);\r\n",
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      "   988\t  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;\r\n",
      "   989\t  __pyx_t_1 = PyDict_New(); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 2, __pyx_L1_error)\r\n",
      "   990\t  __Pyx_GOTREF(__pyx_t_1);\r\n",
      "   991\t  if (PyDict_SetItem(__pyx_d, __pyx_n_s_test, __pyx_t_1) < 0) __PYX_ERR(0, 2, __pyx_L1_error)\r\n",
      "   992\t  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;\r\n",
      "       \r\n",
      "   993\t  /*--- Wrapped vars code ---*/\r\n",
      "       \r\n",
      "   994\t  goto __pyx_L0;\r\n",
      "   995\t  __pyx_L1_error:;\r\n",
      "   996\t  __Pyx_XDECREF(__pyx_t_1);\r\n",
      "   997\t  if (__pyx_m) {\r\n",
      "   998\t    if (__pyx_d) {\r\n",
      "   999\t      __Pyx_AddTraceback(\"init cyfoo\", __pyx_clineno, __pyx_lineno, __pyx_filename);\r\n",
      "  1000\t    }\r\n",
      "  1001\t    Py_DECREF(__pyx_m); __pyx_m = 0;\r\n",
      "  1002\t  } else if (!PyErr_Occurred()) {\r\n",
      "  1003\t    PyErr_SetString(PyExc_ImportError, \"init cyfoo\");\r\n",
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      "  1010\t  return __pyx_m;\r\n",
      "  1011\t  #endif\r\n",
      "  1012\t}\r\n",
      "       \r\n",
      "  1013\t/* --- Runtime support code --- */\r\n",
      "  1014\t/* Refnanny */\r\n",
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      "  1016\tstatic __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {\r\n",
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      "  1019\t    m = PyImport_ImportModule((char *)modname);\r\n",
      "  1020\t    if (!m) goto end;\r\n",
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      "  1033\t    int exact,\r\n",
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      "  1035\t    Py_ssize_t num_max,\r\n",
      "  1036\t    Py_ssize_t num_found)\r\n",
      "  1037\t{\r\n",
      "  1038\t    Py_ssize_t num_expected;\r\n",
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      "  1040\t    if (num_found < num_min) {\r\n",
      "  1041\t        num_expected = num_min;\r\n",
      "  1042\t        more_or_less = \"at least\";\r\n",
      "  1043\t    } else {\r\n",
      "  1044\t        num_expected = num_max;\r\n",
      "  1045\t        more_or_less = \"at most\";\r\n",
      "  1046\t    }\r\n",
      "  1047\t    if (exact) {\r\n",
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      "  1049\t    }\r\n",
      "  1050\t    PyErr_Format(PyExc_TypeError,\r\n",
      "  1051\t                 \"%.200s() takes %.8s %\" CYTHON_FORMAT_SSIZE_T \"d positional argument%.1s (%\" CYTHON_FORMAT_SSIZE_T \"d given)\",\r\n",
      "  1052\t                 func_name, more_or_less, num_expected,\r\n",
      "  1053\t                 (num_expected == 1) ? \"\" : \"s\", num_found);\r\n",
      "  1054\t}\r\n",
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      "  1055\t/* RaiseDoubleKeywords */\r\n",
      "  1056\tstatic void __Pyx_RaiseDoubleKeywordsError(\r\n",
      "  1057\t    const char* func_name,\r\n",
      "  1058\t    PyObject* kw_name)\r\n",
      "  1059\t{\r\n",
      "  1060\t    PyErr_Format(PyExc_TypeError,\r\n",
      "  1061\t        #if PY_MAJOR_VERSION >= 3\r\n",
      "  1062\t        \"%s() got multiple values for keyword argument '%U'\", func_name, kw_name);\r\n",
      "  1063\t        #else\r\n",
      "  1064\t        \"%s() got multiple values for keyword argument '%s'\", func_name,\r\n",
      "  1065\t        PyString_AsString(kw_name));\r\n",
      "  1066\t        #endif\r\n",
      "  1067\t}\r\n",
      "       \r\n",
      "  1068\t/* ParseKeywords */\r\n",
      "  1069\tstatic int __Pyx_ParseOptionalKeywords(\r\n",
      "  1070\t    PyObject *kwds,\r\n",
      "  1071\t    PyObject **argnames[],\r\n",
      "  1072\t    PyObject *kwds2,\r\n",
      "  1073\t    PyObject *values[],\r\n",
      "  1074\t    Py_ssize_t num_pos_args,\r\n",
      "  1075\t    const char* function_name)\r\n",
      "  1076\t{\r\n",
      "  1077\t    PyObject *key = 0, *value = 0;\r\n",
      "  1078\t    Py_ssize_t pos = 0;\r\n",
      "  1079\t    PyObject*** name;\r\n",
      "  1080\t    PyObject*** first_kw_arg = argnames + num_pos_args;\r\n",
      "  1081\t    while (PyDict_Next(kwds, &pos, &key, &value)) {\r\n",
      "  1082\t        name = first_kw_arg;\r\n",
      "  1083\t        while (*name && (**name != key)) name++;\r\n",
      "  1084\t        if (*name) {\r\n",
      "  1085\t            values[name-argnames] = value;\r\n",
      "  1086\t            continue;\r\n",
      "  1087\t        }\r\n",
      "  1088\t        name = first_kw_arg;\r\n",
      "  1089\t        #if PY_MAJOR_VERSION < 3\r\n",
      "  1090\t        if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {\r\n",
      "  1091\t            while (*name) {\r\n",
      "  1092\t                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))\r\n",
      "  1093\t                        && _PyString_Eq(**name, key)) {\r\n",
      "  1094\t                    values[name-argnames] = value;\r\n",
      "  1095\t                    break;\r\n",
      "  1096\t                }\r\n",
      "  1097\t                name++;\r\n",
      "  1098\t            }\r\n",
      "  1099\t            if (*name) continue;\r\n",
      "  1100\t            else {\r\n",
      "  1101\t                PyObject*** argname = argnames;\r\n",
      "  1102\t                while (argname != first_kw_arg) {\r\n",
      "  1103\t                    if ((**argname == key) || (\r\n",
      "  1104\t                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))\r\n",
      "  1105\t                             && _PyString_Eq(**argname, key))) {\r\n",
      "  1106\t                        goto arg_passed_twice;\r\n",
      "  1107\t                    }\r\n",
      "  1108\t                    argname++;\r\n",
      "  1109\t                }\r\n",
      "  1110\t            }\r\n",
      "  1111\t        } else\r\n",
      "  1112\t        #endif\r\n",
      "  1113\t        if (likely(PyUnicode_Check(key))) {\r\n",
      "  1114\t            while (*name) {\r\n",
      "  1115\t                int cmp = (**name == key) ? 0 :\r\n",
      "  1116\t                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3\r\n",
      "  1117\t                    (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :\r\n",
      "  1118\t                #endif\r\n",
      "  1119\t                    PyUnicode_Compare(**name, key);\r\n",
      "  1120\t                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;\r\n",
      "  1121\t                if (cmp == 0) {\r\n",
      "  1122\t                    values[name-argnames] = value;\r\n",
      "  1123\t                    break;\r\n",
      "  1124\t                }\r\n",
      "  1125\t                name++;\r\n",
      "  1126\t            }\r\n",
      "  1127\t            if (*name) continue;\r\n",
      "  1128\t            else {\r\n",
      "  1129\t                PyObject*** argname = argnames;\r\n",
      "  1130\t                while (argname != first_kw_arg) {\r\n",
      "  1131\t                    int cmp = (**argname == key) ? 0 :\r\n",
      "  1132\t                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3\r\n",
      "  1133\t                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :\r\n",
      "  1134\t                    #endif\r\n",
      "  1135\t                        PyUnicode_Compare(**argname, key);\r\n",
      "  1136\t                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;\r\n",
      "  1137\t                    if (cmp == 0) goto arg_passed_twice;\r\n",
      "  1138\t                    argname++;\r\n",
      "  1139\t                }\r\n",
      "  1140\t            }\r\n",
      "  1141\t        } else\r\n",
      "  1142\t            goto invalid_keyword_type;\r\n",
      "  1143\t        if (kwds2) {\r\n",
      "  1144\t            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;\r\n",
      "  1145\t        } else {\r\n",
      "  1146\t            goto invalid_keyword;\r\n",
      "  1147\t        }\r\n",
      "  1148\t    }\r\n",
      "  1149\t    return 0;\r\n",
      "  1150\targ_passed_twice:\r\n",
      "  1151\t    __Pyx_RaiseDoubleKeywordsError(function_name, key);\r\n",
      "  1152\t    goto bad;\r\n",
      "  1153\tinvalid_keyword_type:\r\n",
      "  1154\t    PyErr_Format(PyExc_TypeError,\r\n",
      "  1155\t        \"%.200s() keywords must be strings\", function_name);\r\n",
      "  1156\t    goto bad;\r\n",
      "  1157\tinvalid_keyword:\r\n",
      "  1158\t    PyErr_Format(PyExc_TypeError,\r\n",
      "  1159\t    #if PY_MAJOR_VERSION < 3\r\n",
      "  1160\t        \"%.200s() got an unexpected keyword argument '%.200s'\",\r\n",
      "  1161\t        function_name, PyString_AsString(key));\r\n",
      "  1162\t    #else\r\n",
      "  1163\t        \"%s() got an unexpected keyword argument '%U'\",\r\n",
      "  1164\t        function_name, key);\r\n",
      "  1165\t    #endif\r\n",
      "  1166\tbad:\r\n",
      "  1167\t    return -1;\r\n",
      "  1168\t}\r\n",
      "       \r\n",
      "  1169\t/* CodeObjectCache */\r\n",
      "  1170\tstatic int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {\r\n",
      "  1171\t    int start = 0, mid = 0, end = count - 1;\r\n",
      "  1172\t    if (end >= 0 && code_line > entries[end].code_line) {\r\n",
      "  1173\t        return count;\r\n",
      "  1174\t    }\r\n",
      "  1175\t    while (start < end) {\r\n",
      "  1176\t        mid = start + (end - start) / 2;\r\n",
      "  1177\t        if (code_line < entries[mid].code_line) {\r\n",
      "  1178\t            end = mid;\r\n",
      "  1179\t        } else if (code_line > entries[mid].code_line) {\r\n",
      "  1180\t             start = mid + 1;\r\n",
      "  1181\t        } else {\r\n",
      "  1182\t            return mid;\r\n",
      "  1183\t        }\r\n",
      "  1184\t    }\r\n",
      "  1185\t    if (code_line <= entries[mid].code_line) {\r\n",
      "  1186\t        return mid;\r\n",
      "  1187\t    } else {\r\n",
      "  1188\t        return mid + 1;\r\n",
      "  1189\t    }\r\n",
      "  1190\t}\r\n",
      "  1191\tstatic PyCodeObject *__pyx_find_code_object(int code_line) {\r\n",
      "  1192\t    PyCodeObject* code_object;\r\n",
      "  1193\t    int pos;\r\n",
      "  1194\t    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {\r\n",
      "  1195\t        return NULL;\r\n",
      "  1196\t    }\r\n",
      "  1197\t    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);\r\n",
      "  1198\t    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {\r\n",
      "  1199\t        return NULL;\r\n",
      "  1200\t    }\r\n",
      "  1201\t    code_object = __pyx_code_cache.entries[pos].code_object;\r\n",
      "  1202\t    Py_INCREF(code_object);\r\n",
      "  1203\t    return code_object;\r\n",
      "  1204\t}\r\n",
      "  1205\tstatic void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {\r\n",
      "  1206\t    int pos, i;\r\n",
      "  1207\t    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;\r\n",
      "  1208\t    if (unlikely(!code_line)) {\r\n",
      "  1209\t        return;\r\n",
      "  1210\t    }\r\n",
      "  1211\t    if (unlikely(!entries)) {\r\n",
      "  1212\t        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));\r\n",
      "  1213\t        if (likely(entries)) {\r\n",
      "  1214\t            __pyx_code_cache.entries = entries;\r\n",
      "  1215\t            __pyx_code_cache.max_count = 64;\r\n",
      "  1216\t            __pyx_code_cache.count = 1;\r\n",
      "  1217\t            entries[0].code_line = code_line;\r\n",
      "  1218\t            entries[0].code_object = code_object;\r\n",
      "  1219\t            Py_INCREF(code_object);\r\n",
      "  1220\t        }\r\n",
      "  1221\t        return;\r\n",
      "  1222\t    }\r\n",
      "  1223\t    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);\r\n",
      "  1224\t    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {\r\n",
      "  1225\t        PyCodeObject* tmp = entries[pos].code_object;\r\n",
      "  1226\t        entries[pos].code_object = code_object;\r\n",
      "  1227\t        Py_DECREF(tmp);\r\n",
      "  1228\t        return;\r\n",
      "  1229\t    }\r\n",
      "  1230\t    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {\r\n",
      "  1231\t        int new_max = __pyx_code_cache.max_count + 64;\r\n",
      "  1232\t        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(\r\n",
      "  1233\t            __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));\r\n",
      "  1234\t        if (unlikely(!entries)) {\r\n",
      "  1235\t            return;\r\n",
      "  1236\t        }\r\n",
      "  1237\t        __pyx_code_cache.entries = entries;\r\n",
      "  1238\t        __pyx_code_cache.max_count = new_max;\r\n",
      "  1239\t    }\r\n",
      "  1240\t    for (i=__pyx_code_cache.count; i>pos; i--) {\r\n",
      "  1241\t        entries[i] = entries[i-1];\r\n",
      "  1242\t    }\r\n",
      "  1243\t    entries[pos].code_line = code_line;\r\n",
      "  1244\t    entries[pos].code_object = code_object;\r\n",
      "  1245\t    __pyx_code_cache.count++;\r\n",
      "  1246\t    Py_INCREF(code_object);\r\n",
      "  1247\t}\r\n",
      "       \r\n",
      "  1248\t/* AddTraceback */\r\n",
      "  1249\t#include \"compile.h\"\r\n",
      "  1250\t#include \"frameobject.h\"\r\n",
      "  1251\t#include \"traceback.h\"\r\n",
      "  1252\tstatic PyCodeObject* __Pyx_CreateCodeObjectForTraceback(\r\n",
      "  1253\t            const char *funcname, int c_line,\r\n",
      "  1254\t            int py_line, const char *filename) {\r\n",
      "  1255\t    PyCodeObject *py_code = 0;\r\n",
      "  1256\t    PyObject *py_srcfile = 0;\r\n",
      "  1257\t    PyObject *py_funcname = 0;\r\n",
      "  1258\t    #if PY_MAJOR_VERSION < 3\r\n",
      "  1259\t    py_srcfile = PyString_FromString(filename);\r\n",
      "  1260\t    #else\r\n",
      "  1261\t    py_srcfile = PyUnicode_FromString(filename);\r\n",
      "  1262\t    #endif\r\n",
      "  1263\t    if (!py_srcfile) goto bad;\r\n",
      "  1264\t    if (c_line) {\r\n",
      "  1265\t        #if PY_MAJOR_VERSION < 3\r\n",
      "  1266\t        py_funcname = PyString_FromFormat( \"%s (%s:%d)\", funcname, __pyx_cfilenm, c_line);\r\n",
      "  1267\t        #else\r\n",
      "  1268\t        py_funcname = PyUnicode_FromFormat( \"%s (%s:%d)\", funcname, __pyx_cfilenm, c_line);\r\n",
      "  1269\t        #endif\r\n",
      "  1270\t    }\r\n",
      "  1271\t    else {\r\n",
      "  1272\t        #if PY_MAJOR_VERSION < 3\r\n",
      "  1273\t        py_funcname = PyString_FromString(funcname);\r\n",
      "  1274\t        #else\r\n",
      "  1275\t        py_funcname = PyUnicode_FromString(funcname);\r\n",
      "  1276\t        #endif\r\n",
      "  1277\t    }\r\n",
      "  1278\t    if (!py_funcname) goto bad;\r\n",
      "  1279\t    py_code = __Pyx_PyCode_New(\r\n",
      "  1280\t        0,\r\n",
      "  1281\t        0,\r\n",
      "  1282\t        0,\r\n",
      "  1283\t        0,\r\n",
      "  1284\t        0,\r\n",
      "  1285\t        __pyx_empty_bytes, /*PyObject *code,*/\r\n",
      "  1286\t        __pyx_empty_tuple, /*PyObject *consts,*/\r\n",
      "  1287\t        __pyx_empty_tuple, /*PyObject *names,*/\r\n",
      "  1288\t        __pyx_empty_tuple, /*PyObject *varnames,*/\r\n",
      "  1289\t        __pyx_empty_tuple, /*PyObject *freevars,*/\r\n",
      "  1290\t        __pyx_empty_tuple, /*PyObject *cellvars,*/\r\n",
      "  1291\t        py_srcfile,   /*PyObject *filename,*/\r\n",
      "  1292\t        py_funcname,  /*PyObject *name,*/\r\n",
      "  1293\t        py_line,\r\n",
      "  1294\t        __pyx_empty_bytes  /*PyObject *lnotab*/\r\n",
      "  1295\t    );\r\n",
      "  1296\t    Py_DECREF(py_srcfile);\r\n",
      "  1297\t    Py_DECREF(py_funcname);\r\n",
      "  1298\t    return py_code;\r\n",
      "  1299\tbad:\r\n",
      "  1300\t    Py_XDECREF(py_srcfile);\r\n",
      "  1301\t    Py_XDECREF(py_funcname);\r\n",
      "  1302\t    return NULL;\r\n",
      "  1303\t}\r\n",
      "  1304\tstatic void __Pyx_AddTraceback(const char *funcname, int c_line,\r\n",
      "  1305\t                               int py_line, const char *filename) {\r\n",
      "  1306\t    PyCodeObject *py_code = 0;\r\n",
      "  1307\t    PyFrameObject *py_frame = 0;\r\n",
      "  1308\t    py_code = __pyx_find_code_object(c_line ? c_line : py_line);\r\n",
      "  1309\t    if (!py_code) {\r\n",
      "  1310\t        py_code = __Pyx_CreateCodeObjectForTraceback(\r\n",
      "  1311\t            funcname, c_line, py_line, filename);\r\n",
      "  1312\t        if (!py_code) goto bad;\r\n",
      "  1313\t        __pyx_insert_code_object(c_line ? c_line : py_line, py_code);\r\n",
      "  1314\t    }\r\n",
      "  1315\t    py_frame = PyFrame_New(\r\n",
      "  1316\t        PyThreadState_GET(), /*PyThreadState *tstate,*/\r\n",
      "  1317\t        py_code,             /*PyCodeObject *code,*/\r\n",
      "  1318\t        __pyx_d,      /*PyObject *globals,*/\r\n",
      "  1319\t        0                    /*PyObject *locals*/\r\n",
      "  1320\t    );\r\n",
      "  1321\t    if (!py_frame) goto bad;\r\n",
      "  1322\t    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);\r\n",
      "  1323\t    PyTraceBack_Here(py_frame);\r\n",
      "  1324\tbad:\r\n",
      "  1325\t    Py_XDECREF(py_code);\r\n",
      "  1326\t    Py_XDECREF(py_frame);\r\n",
      "  1327\t}\r\n",
      "       \r\n",
      "  1328\t/* CIntToPy */\r\n",
      "  1329\tstatic CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {\r\n",
      "  1330\t    const long neg_one = (long) -1, const_zero = (long) 0;\r\n",
      "  1331\t    const int is_unsigned = neg_one > const_zero;\r\n",
      "  1332\t    if (is_unsigned) {\r\n",
      "  1333\t        if (sizeof(long) < sizeof(long)) {\r\n",
      "  1334\t            return PyInt_FromLong((long) value);\r\n",
      "  1335\t        } else if (sizeof(long) <= sizeof(unsigned long)) {\r\n",
      "  1336\t            return PyLong_FromUnsignedLong((unsigned long) value);\r\n",
      "  1337\t#ifdef HAVE_LONG_LONG\r\n",
      "  1338\t        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {\r\n",
      "  1339\t            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);\r\n",
      "  1340\t#endif\r\n",
      "  1341\t        }\r\n",
      "  1342\t    } else {\r\n",
      "  1343\t        if (sizeof(long) <= sizeof(long)) {\r\n",
      "  1344\t            return PyInt_FromLong((long) value);\r\n",
      "  1345\t#ifdef HAVE_LONG_LONG\r\n",
      "  1346\t        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {\r\n",
      "  1347\t            return PyLong_FromLongLong((PY_LONG_LONG) value);\r\n",
      "  1348\t#endif\r\n",
      "  1349\t        }\r\n",
      "  1350\t    }\r\n",
      "  1351\t    {\r\n",
      "  1352\t        int one = 1; int little = (int)*(unsigned char *)&one;\r\n",
      "  1353\t        unsigned char *bytes = (unsigned char *)&value;\r\n",
      "  1354\t        return _PyLong_FromByteArray(bytes, sizeof(long),\r\n",
      "  1355\t                                     little, !is_unsigned);\r\n",
      "  1356\t    }\r\n",
      "  1357\t}\r\n",
      "       \r\n",
      "  1358\t/* CIntFromPyVerify */\r\n",
      "  1359\t#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\\\r\n",
      "  1360\t    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)\r\n",
      "  1361\t#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\\\r\n",
      "  1362\t    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)\r\n",
      "  1363\t#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\\\r\n",
      "  1364\t    {\\\r\n",
      "  1365\t        func_type value = func_value;\\\r\n",
      "  1366\t        if (sizeof(target_type) < sizeof(func_type)) {\\\r\n",
      "  1367\t            if (unlikely(value != (func_type) (target_type) value)) {\\\r\n",
      "  1368\t                func_type zero = 0;\\\r\n",
      "  1369\t                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\\\r\n",
      "  1370\t                    return (target_type) -1;\\\r\n",
      "  1371\t                if (is_unsigned && unlikely(value < zero))\\\r\n",
      "  1372\t                    goto raise_neg_overflow;\\\r\n",
      "  1373\t                else\\\r\n",
      "  1374\t                    goto raise_overflow;\\\r\n",
      "  1375\t            }\\\r\n",
      "  1376\t        }\\\r\n",
      "  1377\t        return (target_type) value;\\\r\n",
      "  1378\t    }\r\n",
      "       \r\n",
      "  1379\t/* CIntFromPy */\r\n",
      "  1380\tstatic CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {\r\n",
      "  1381\t    const long neg_one = (long) -1, const_zero = (long) 0;\r\n",
      "  1382\t    const int is_unsigned = neg_one > const_zero;\r\n",
      "  1383\t#if PY_MAJOR_VERSION < 3\r\n",
      "  1384\t    if (likely(PyInt_Check(x))) {\r\n",
      "  1385\t        if (sizeof(long) < sizeof(long)) {\r\n",
      "  1386\t            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))\r\n",
      "  1387\t        } else {\r\n",
      "  1388\t            long val = PyInt_AS_LONG(x);\r\n",
      "  1389\t            if (is_unsigned && unlikely(val < 0)) {\r\n",
      "  1390\t                goto raise_neg_overflow;\r\n",
      "  1391\t            }\r\n",
      "  1392\t            return (long) val;\r\n",
      "  1393\t        }\r\n",
      "  1394\t    } else\r\n",
      "  1395\t#endif\r\n",
      "  1396\t    if (likely(PyLong_Check(x))) {\r\n",
      "  1397\t        if (is_unsigned) {\r\n",
      "  1398\t#if CYTHON_USE_PYLONG_INTERNALS\r\n",
      "  1399\t            const digit* digits = ((PyLongObject*)x)->ob_digit;\r\n",
      "  1400\t            switch (Py_SIZE(x)) {\r\n",
      "  1401\t                case  0: return (long) 0;\r\n",
      "  1402\t                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])\r\n",
      "  1403\t                case 2:\r\n",
      "  1404\t                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {\r\n",
      "  1405\t                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {\r\n",
      "  1406\t                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1407\t                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {\r\n",
      "  1408\t                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));\r\n",
      "  1409\t                        }\r\n",
      "  1410\t                    }\r\n",
      "  1411\t                    break;\r\n",
      "  1412\t                case 3:\r\n",
      "  1413\t                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {\r\n",
      "  1414\t                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {\r\n",
      "  1415\t                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1416\t                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {\r\n",
      "  1417\t                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));\r\n",
      "  1418\t                        }\r\n",
      "  1419\t                    }\r\n",
      "  1420\t                    break;\r\n",
      "  1421\t                case 4:\r\n",
      "  1422\t                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {\r\n",
      "  1423\t                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {\r\n",
      "  1424\t                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1425\t                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {\r\n",
      "  1426\t                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));\r\n",
      "  1427\t                        }\r\n",
      "  1428\t                    }\r\n",
      "  1429\t                    break;\r\n",
      "  1430\t            }\r\n",
      "  1431\t#endif\r\n",
      "  1432\t#if CYTHON_COMPILING_IN_CPYTHON\r\n",
      "  1433\t            if (unlikely(Py_SIZE(x) < 0)) {\r\n",
      "  1434\t                goto raise_neg_overflow;\r\n",
      "  1435\t            }\r\n",
      "  1436\t#else\r\n",
      "  1437\t            {\r\n",
      "  1438\t                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);\r\n",
      "  1439\t                if (unlikely(result < 0))\r\n",
      "  1440\t                    return (long) -1;\r\n",
      "  1441\t                if (unlikely(result == 1))\r\n",
      "  1442\t                    goto raise_neg_overflow;\r\n",
      "  1443\t            }\r\n",
      "  1444\t#endif\r\n",
      "  1445\t            if (sizeof(long) <= sizeof(unsigned long)) {\r\n",
      "  1446\t                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))\r\n",
      "  1447\t#ifdef HAVE_LONG_LONG\r\n",
      "  1448\t            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {\r\n",
      "  1449\t                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))\r\n",
      "  1450\t#endif\r\n",
      "  1451\t            }\r\n",
      "  1452\t        } else {\r\n",
      "  1453\t#if CYTHON_USE_PYLONG_INTERNALS\r\n",
      "  1454\t            const digit* digits = ((PyLongObject*)x)->ob_digit;\r\n",
      "  1455\t            switch (Py_SIZE(x)) {\r\n",
      "  1456\t                case  0: return (long) 0;\r\n",
      "  1457\t                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))\r\n",
      "  1458\t                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])\r\n",
      "  1459\t                case -2:\r\n",
      "  1460\t                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {\r\n",
      "  1461\t                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {\r\n",
      "  1462\t                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1463\t                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {\r\n",
      "  1464\t                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));\r\n",
      "  1465\t                        }\r\n",
      "  1466\t                    }\r\n",
      "  1467\t                    break;\r\n",
      "  1468\t                case 2:\r\n",
      "  1469\t                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {\r\n",
      "  1470\t                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {\r\n",
      "  1471\t                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1472\t                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {\r\n",
      "  1473\t                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));\r\n",
      "  1474\t                        }\r\n",
      "  1475\t                    }\r\n",
      "  1476\t                    break;\r\n",
      "  1477\t                case -3:\r\n",
      "  1478\t                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {\r\n",
      "  1479\t                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {\r\n",
      "  1480\t                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1481\t                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {\r\n",
      "  1482\t                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));\r\n",
      "  1483\t                        }\r\n",
      "  1484\t                    }\r\n",
      "  1485\t                    break;\r\n",
      "  1486\t                case 3:\r\n",
      "  1487\t                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {\r\n",
      "  1488\t                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {\r\n",
      "  1489\t                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1490\t                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {\r\n",
      "  1491\t                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));\r\n",
      "  1492\t                        }\r\n",
      "  1493\t                    }\r\n",
      "  1494\t                    break;\r\n",
      "  1495\t                case -4:\r\n",
      "  1496\t                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {\r\n",
      "  1497\t                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {\r\n",
      "  1498\t                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1499\t                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {\r\n",
      "  1500\t                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));\r\n",
      "  1501\t                        }\r\n",
      "  1502\t                    }\r\n",
      "  1503\t                    break;\r\n",
      "  1504\t                case 4:\r\n",
      "  1505\t                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {\r\n",
      "  1506\t                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {\r\n",
      "  1507\t                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1508\t                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {\r\n",
      "  1509\t                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));\r\n",
      "  1510\t                        }\r\n",
      "  1511\t                    }\r\n",
      "  1512\t                    break;\r\n",
      "  1513\t            }\r\n",
      "  1514\t#endif\r\n",
      "  1515\t            if (sizeof(long) <= sizeof(long)) {\r\n",
      "  1516\t                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))\r\n",
      "  1517\t#ifdef HAVE_LONG_LONG\r\n",
      "  1518\t            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {\r\n",
      "  1519\t                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))\r\n",
      "  1520\t#endif\r\n",
      "  1521\t            }\r\n",
      "  1522\t        }\r\n",
      "  1523\t        {\r\n",
      "  1524\t#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)\r\n",
      "  1525\t            PyErr_SetString(PyExc_RuntimeError,\r\n",
      "  1526\t                            \"_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers\");\r\n",
      "  1527\t#else\r\n",
      "  1528\t            long val;\r\n",
      "  1529\t            PyObject *v = __Pyx_PyNumber_IntOrLong(x);\r\n",
      "  1530\t #if PY_MAJOR_VERSION < 3\r\n",
      "  1531\t            if (likely(v) && !PyLong_Check(v)) {\r\n",
      "  1532\t                PyObject *tmp = v;\r\n",
      "  1533\t                v = PyNumber_Long(tmp);\r\n",
      "  1534\t                Py_DECREF(tmp);\r\n",
      "  1535\t            }\r\n",
      "  1536\t #endif\r\n",
      "  1537\t            if (likely(v)) {\r\n",
      "  1538\t                int one = 1; int is_little = (int)*(unsigned char *)&one;\r\n",
      "  1539\t                unsigned char *bytes = (unsigned char *)&val;\r\n",
      "  1540\t                int ret = _PyLong_AsByteArray((PyLongObject *)v,\r\n",
      "  1541\t                                              bytes, sizeof(val),\r\n",
      "  1542\t                                              is_little, !is_unsigned);\r\n",
      "  1543\t                Py_DECREF(v);\r\n",
      "  1544\t                if (likely(!ret))\r\n",
      "  1545\t                    return val;\r\n",
      "  1546\t            }\r\n",
      "  1547\t#endif\r\n",
      "  1548\t            return (long) -1;\r\n",
      "  1549\t        }\r\n",
      "  1550\t    } else {\r\n",
      "  1551\t        long val;\r\n",
      "  1552\t        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);\r\n",
      "  1553\t        if (!tmp) return (long) -1;\r\n",
      "  1554\t        val = __Pyx_PyInt_As_long(tmp);\r\n",
      "  1555\t        Py_DECREF(tmp);\r\n",
      "  1556\t        return val;\r\n",
      "  1557\t    }\r\n",
      "  1558\traise_overflow:\r\n",
      "  1559\t    PyErr_SetString(PyExc_OverflowError,\r\n",
      "  1560\t        \"value too large to convert to long\");\r\n",
      "  1561\t    return (long) -1;\r\n",
      "  1562\traise_neg_overflow:\r\n",
      "  1563\t    PyErr_SetString(PyExc_OverflowError,\r\n",
      "  1564\t        \"can't convert negative value to long\");\r\n",
      "  1565\t    return (long) -1;\r\n",
      "  1566\t}\r\n",
      "       \r\n",
      "  1567\t/* CIntFromPy */\r\n",
      "  1568\tstatic CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {\r\n",
      "  1569\t    const int neg_one = (int) -1, const_zero = (int) 0;\r\n",
      "  1570\t    const int is_unsigned = neg_one > const_zero;\r\n",
      "  1571\t#if PY_MAJOR_VERSION < 3\r\n",
      "  1572\t    if (likely(PyInt_Check(x))) {\r\n",
      "  1573\t        if (sizeof(int) < sizeof(long)) {\r\n",
      "  1574\t            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))\r\n",
      "  1575\t        } else {\r\n",
      "  1576\t            long val = PyInt_AS_LONG(x);\r\n",
      "  1577\t            if (is_unsigned && unlikely(val < 0)) {\r\n",
      "  1578\t                goto raise_neg_overflow;\r\n",
      "  1579\t            }\r\n",
      "  1580\t            return (int) val;\r\n",
      "  1581\t        }\r\n",
      "  1582\t    } else\r\n",
      "  1583\t#endif\r\n",
      "  1584\t    if (likely(PyLong_Check(x))) {\r\n",
      "  1585\t        if (is_unsigned) {\r\n",
      "  1586\t#if CYTHON_USE_PYLONG_INTERNALS\r\n",
      "  1587\t            const digit* digits = ((PyLongObject*)x)->ob_digit;\r\n",
      "  1588\t            switch (Py_SIZE(x)) {\r\n",
      "  1589\t                case  0: return (int) 0;\r\n",
      "  1590\t                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])\r\n",
      "  1591\t                case 2:\r\n",
      "  1592\t                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {\r\n",
      "  1593\t                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {\r\n",
      "  1594\t                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1595\t                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {\r\n",
      "  1596\t                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));\r\n",
      "  1597\t                        }\r\n",
      "  1598\t                    }\r\n",
      "  1599\t                    break;\r\n",
      "  1600\t                case 3:\r\n",
      "  1601\t                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {\r\n",
      "  1602\t                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {\r\n",
      "  1603\t                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1604\t                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {\r\n",
      "  1605\t                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));\r\n",
      "  1606\t                        }\r\n",
      "  1607\t                    }\r\n",
      "  1608\t                    break;\r\n",
      "  1609\t                case 4:\r\n",
      "  1610\t                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {\r\n",
      "  1611\t                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {\r\n",
      "  1612\t                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1613\t                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {\r\n",
      "  1614\t                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));\r\n",
      "  1615\t                        }\r\n",
      "  1616\t                    }\r\n",
      "  1617\t                    break;\r\n",
      "  1618\t            }\r\n",
      "  1619\t#endif\r\n",
      "  1620\t#if CYTHON_COMPILING_IN_CPYTHON\r\n",
      "  1621\t            if (unlikely(Py_SIZE(x) < 0)) {\r\n",
      "  1622\t                goto raise_neg_overflow;\r\n",
      "  1623\t            }\r\n",
      "  1624\t#else\r\n",
      "  1625\t            {\r\n",
      "  1626\t                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);\r\n",
      "  1627\t                if (unlikely(result < 0))\r\n",
      "  1628\t                    return (int) -1;\r\n",
      "  1629\t                if (unlikely(result == 1))\r\n",
      "  1630\t                    goto raise_neg_overflow;\r\n",
      "  1631\t            }\r\n",
      "  1632\t#endif\r\n",
      "  1633\t            if (sizeof(int) <= sizeof(unsigned long)) {\r\n",
      "  1634\t                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))\r\n",
      "  1635\t#ifdef HAVE_LONG_LONG\r\n",
      "  1636\t            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {\r\n",
      "  1637\t                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))\r\n",
      "  1638\t#endif\r\n",
      "  1639\t            }\r\n",
      "  1640\t        } else {\r\n",
      "  1641\t#if CYTHON_USE_PYLONG_INTERNALS\r\n",
      "  1642\t            const digit* digits = ((PyLongObject*)x)->ob_digit;\r\n",
      "  1643\t            switch (Py_SIZE(x)) {\r\n",
      "  1644\t                case  0: return (int) 0;\r\n",
      "  1645\t                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))\r\n",
      "  1646\t                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])\r\n",
      "  1647\t                case -2:\r\n",
      "  1648\t                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {\r\n",
      "  1649\t                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {\r\n",
      "  1650\t                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1651\t                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {\r\n",
      "  1652\t                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));\r\n",
      "  1653\t                        }\r\n",
      "  1654\t                    }\r\n",
      "  1655\t                    break;\r\n",
      "  1656\t                case 2:\r\n",
      "  1657\t                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {\r\n",
      "  1658\t                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {\r\n",
      "  1659\t                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1660\t                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {\r\n",
      "  1661\t                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));\r\n",
      "  1662\t                        }\r\n",
      "  1663\t                    }\r\n",
      "  1664\t                    break;\r\n",
      "  1665\t                case -3:\r\n",
      "  1666\t                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {\r\n",
      "  1667\t                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {\r\n",
      "  1668\t                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1669\t                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {\r\n",
      "  1670\t                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));\r\n",
      "  1671\t                        }\r\n",
      "  1672\t                    }\r\n",
      "  1673\t                    break;\r\n",
      "  1674\t                case 3:\r\n",
      "  1675\t                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {\r\n",
      "  1676\t                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {\r\n",
      "  1677\t                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1678\t                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {\r\n",
      "  1679\t                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));\r\n",
      "  1680\t                        }\r\n",
      "  1681\t                    }\r\n",
      "  1682\t                    break;\r\n",
      "  1683\t                case -4:\r\n",
      "  1684\t                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {\r\n",
      "  1685\t                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {\r\n",
      "  1686\t                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1687\t                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {\r\n",
      "  1688\t                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));\r\n",
      "  1689\t                        }\r\n",
      "  1690\t                    }\r\n",
      "  1691\t                    break;\r\n",
      "  1692\t                case 4:\r\n",
      "  1693\t                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {\r\n",
      "  1694\t                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {\r\n",
      "  1695\t                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))\r\n",
      "  1696\t                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {\r\n",
      "  1697\t                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));\r\n",
      "  1698\t                        }\r\n",
      "  1699\t                    }\r\n",
      "  1700\t                    break;\r\n",
      "  1701\t            }\r\n",
      "  1702\t#endif\r\n",
      "  1703\t            if (sizeof(int) <= sizeof(long)) {\r\n",
      "  1704\t                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))\r\n",
      "  1705\t#ifdef HAVE_LONG_LONG\r\n",
      "  1706\t            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {\r\n",
      "  1707\t                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))\r\n",
      "  1708\t#endif\r\n",
      "  1709\t            }\r\n",
      "  1710\t        }\r\n",
      "  1711\t        {\r\n",
      "  1712\t#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)\r\n",
      "  1713\t            PyErr_SetString(PyExc_RuntimeError,\r\n",
      "  1714\t                            \"_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers\");\r\n",
      "  1715\t#else\r\n",
      "  1716\t            int val;\r\n",
      "  1717\t            PyObject *v = __Pyx_PyNumber_IntOrLong(x);\r\n",
      "  1718\t #if PY_MAJOR_VERSION < 3\r\n",
      "  1719\t            if (likely(v) && !PyLong_Check(v)) {\r\n",
      "  1720\t                PyObject *tmp = v;\r\n",
      "  1721\t                v = PyNumber_Long(tmp);\r\n",
      "  1722\t                Py_DECREF(tmp);\r\n",
      "  1723\t            }\r\n",
      "  1724\t #endif\r\n",
      "  1725\t            if (likely(v)) {\r\n",
      "  1726\t                int one = 1; int is_little = (int)*(unsigned char *)&one;\r\n",
      "  1727\t                unsigned char *bytes = (unsigned char *)&val;\r\n",
      "  1728\t                int ret = _PyLong_AsByteArray((PyLongObject *)v,\r\n",
      "  1729\t                                              bytes, sizeof(val),\r\n",
      "  1730\t                                              is_little, !is_unsigned);\r\n",
      "  1731\t                Py_DECREF(v);\r\n",
      "  1732\t                if (likely(!ret))\r\n",
      "  1733\t                    return val;\r\n",
      "  1734\t            }\r\n",
      "  1735\t#endif\r\n",
      "  1736\t            return (int) -1;\r\n",
      "  1737\t        }\r\n",
      "  1738\t    } else {\r\n",
      "  1739\t        int val;\r\n",
      "  1740\t        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);\r\n",
      "  1741\t        if (!tmp) return (int) -1;\r\n",
      "  1742\t        val = __Pyx_PyInt_As_int(tmp);\r\n",
      "  1743\t        Py_DECREF(tmp);\r\n",
      "  1744\t        return val;\r\n",
      "  1745\t    }\r\n",
      "  1746\traise_overflow:\r\n",
      "  1747\t    PyErr_SetString(PyExc_OverflowError,\r\n",
      "  1748\t        \"value too large to convert to int\");\r\n",
      "  1749\t    return (int) -1;\r\n",
      "  1750\traise_neg_overflow:\r\n",
      "  1751\t    PyErr_SetString(PyExc_OverflowError,\r\n",
      "  1752\t        \"can't convert negative value to int\");\r\n",
      "  1753\t    return (int) -1;\r\n",
      "  1754\t}\r\n",
      "       \r\n",
      "  1755\t/* CheckBinaryVersion */\r\n",
      "  1756\tstatic int __Pyx_check_binary_version(void) {\r\n",
      "  1757\t    char ctversion[4], rtversion[4];\r\n",
      "  1758\t    PyOS_snprintf(ctversion, 4, \"%d.%d\", PY_MAJOR_VERSION, PY_MINOR_VERSION);\r\n",
      "  1759\t    PyOS_snprintf(rtversion, 4, \"%s\", Py_GetVersion());\r\n",
      "  1760\t    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {\r\n",
      "  1761\t        char message[200];\r\n",
      "  1762\t        PyOS_snprintf(message, sizeof(message),\r\n",
      "  1763\t                      \"compiletime version %s of module '%.100s' \"\r\n",
      "  1764\t                      \"does not match runtime version %s\",\r\n",
      "  1765\t                      ctversion, __Pyx_MODULE_NAME, rtversion);\r\n",
      "  1766\t        return PyErr_WarnEx(NULL, message, 1);\r\n",
      "  1767\t    }\r\n",
      "  1768\t    return 0;\r\n",
      "  1769\t}\r\n",
      "       \r\n",
      "  1770\t/* InitStrings */\r\n",
      "  1771\tstatic int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {\r\n",
      "  1772\t    while (t->p) {\r\n",
      "  1773\t        #if PY_MAJOR_VERSION < 3\r\n",
      "  1774\t        if (t->is_unicode) {\r\n",
      "  1775\t            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);\r\n",
      "  1776\t        } else if (t->intern) {\r\n",
      "  1777\t            *t->p = PyString_InternFromString(t->s);\r\n",
      "  1778\t        } else {\r\n",
      "  1779\t            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);\r\n",
      "  1780\t        }\r\n",
      "  1781\t        #else\r\n",
      "  1782\t        if (t->is_unicode | t->is_str) {\r\n",
      "  1783\t            if (t->intern) {\r\n",
      "  1784\t                *t->p = PyUnicode_InternFromString(t->s);\r\n",
      "  1785\t            } else if (t->encoding) {\r\n",
      "  1786\t                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);\r\n",
      "  1787\t            } else {\r\n",
      "  1788\t                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);\r\n",
      "  1789\t            }\r\n",
      "  1790\t        } else {\r\n",
      "  1791\t            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);\r\n",
      "  1792\t        }\r\n",
      "  1793\t        #endif\r\n",
      "  1794\t        if (!*t->p)\r\n",
      "  1795\t            return -1;\r\n",
      "  1796\t        ++t;\r\n",
      "  1797\t    }\r\n",
      "  1798\t    return 0;\r\n",
      "  1799\t}\r\n",
      "       \r\n",
      "  1800\tstatic CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {\r\n",
      "  1801\t    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));\r\n",
      "  1802\t}\r\n",
      "  1803\tstatic CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {\r\n",
      "  1804\t    Py_ssize_t ignore;\r\n",
      "  1805\t    return __Pyx_PyObject_AsStringAndSize(o, &ignore);\r\n",
      "  1806\t}\r\n",
      "  1807\tstatic CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {\r\n",
      "  1808\t#if CYTHON_COMPILING_IN_CPYTHON && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)\r\n",
      "  1809\t    if (\r\n",
      "  1810\t#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII\r\n",
      "  1811\t            __Pyx_sys_getdefaultencoding_not_ascii &&\r\n",
      "  1812\t#endif\r\n",
      "  1813\t            PyUnicode_Check(o)) {\r\n",
      "  1814\t#if PY_VERSION_HEX < 0x03030000\r\n",
      "  1815\t        char* defenc_c;\r\n",
      "  1816\t        PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);\r\n",
      "  1817\t        if (!defenc) return NULL;\r\n",
      "  1818\t        defenc_c = PyBytes_AS_STRING(defenc);\r\n",
      "  1819\t#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII\r\n",
      "  1820\t        {\r\n",
      "  1821\t            char* end = defenc_c + PyBytes_GET_SIZE(defenc);\r\n",
      "  1822\t            char* c;\r\n",
      "  1823\t            for (c = defenc_c; c < end; c++) {\r\n",
      "  1824\t                if ((unsigned char) (*c) >= 128) {\r\n",
      "  1825\t                    PyUnicode_AsASCIIString(o);\r\n",
      "  1826\t                    return NULL;\r\n",
      "  1827\t                }\r\n",
      "  1828\t            }\r\n",
      "  1829\t        }\r\n",
      "  1830\t#endif\r\n",
      "  1831\t        *length = PyBytes_GET_SIZE(defenc);\r\n",
      "  1832\t        return defenc_c;\r\n",
      "  1833\t#else\r\n",
      "  1834\t        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;\r\n",
      "  1835\t#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII\r\n",
      "  1836\t        if (PyUnicode_IS_ASCII(o)) {\r\n",
      "  1837\t            *length = PyUnicode_GET_LENGTH(o);\r\n",
      "  1838\t            return PyUnicode_AsUTF8(o);\r\n",
      "  1839\t        } else {\r\n",
      "  1840\t            PyUnicode_AsASCIIString(o);\r\n",
      "  1841\t            return NULL;\r\n",
      "  1842\t        }\r\n",
      "  1843\t#else\r\n",
      "  1844\t        return PyUnicode_AsUTF8AndSize(o, length);\r\n",
      "  1845\t#endif\r\n",
      "  1846\t#endif\r\n",
      "  1847\t    } else\r\n",
      "  1848\t#endif\r\n",
      "  1849\t#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))\r\n",
      "  1850\t    if (PyByteArray_Check(o)) {\r\n",
      "  1851\t        *length = PyByteArray_GET_SIZE(o);\r\n",
      "  1852\t        return PyByteArray_AS_STRING(o);\r\n",
      "  1853\t    } else\r\n",
      "  1854\t#endif\r\n",
      "  1855\t    {\r\n",
      "  1856\t        char* result;\r\n",
      "  1857\t        int r = PyBytes_AsStringAndSize(o, &result, length);\r\n",
      "  1858\t        if (unlikely(r < 0)) {\r\n",
      "  1859\t            return NULL;\r\n",
      "  1860\t        } else {\r\n",
      "  1861\t            return result;\r\n",
      "  1862\t        }\r\n",
      "  1863\t    }\r\n",
      "  1864\t}\r\n",
      "  1865\tstatic CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {\r\n",
      "  1866\t   int is_true = x == Py_True;\r\n",
      "  1867\t   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;\r\n",
      "  1868\t   else return PyObject_IsTrue(x);\r\n",
      "  1869\t}\r\n",
      "  1870\tstatic CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {\r\n",
      "  1871\t#if CYTHON_USE_TYPE_SLOTS\r\n",
      "  1872\t  PyNumberMethods *m;\r\n",
      "  1873\t#endif\r\n",
      "  1874\t  const char *name = NULL;\r\n",
      "  1875\t  PyObject *res = NULL;\r\n",
      "  1876\t#if PY_MAJOR_VERSION < 3\r\n",
      "  1877\t  if (PyInt_Check(x) || PyLong_Check(x))\r\n",
      "  1878\t#else\r\n",
      "  1879\t  if (PyLong_Check(x))\r\n",
      "  1880\t#endif\r\n",
      "  1881\t    return __Pyx_NewRef(x);\r\n",
      "  1882\t#if CYTHON_USE_TYPE_SLOTS\r\n",
      "  1883\t  m = Py_TYPE(x)->tp_as_number;\r\n",
      "  1884\t  #if PY_MAJOR_VERSION < 3\r\n",
      "  1885\t  if (m && m->nb_int) {\r\n",
      "  1886\t    name = \"int\";\r\n",
      "  1887\t    res = PyNumber_Int(x);\r\n",
      "  1888\t  }\r\n",
      "  1889\t  else if (m && m->nb_long) {\r\n",
      "  1890\t    name = \"long\";\r\n",
      "  1891\t    res = PyNumber_Long(x);\r\n",
      "  1892\t  }\r\n",
      "  1893\t  #else\r\n",
      "  1894\t  if (m && m->nb_int) {\r\n",
      "  1895\t    name = \"int\";\r\n",
      "  1896\t    res = PyNumber_Long(x);\r\n",
      "  1897\t  }\r\n",
      "  1898\t  #endif\r\n",
      "  1899\t#else\r\n",
      "  1900\t  res = PyNumber_Int(x);\r\n",
      "  1901\t#endif\r\n",
      "  1902\t  if (res) {\r\n",
      "  1903\t#if PY_MAJOR_VERSION < 3\r\n",
      "  1904\t    if (!PyInt_Check(res) && !PyLong_Check(res)) {\r\n",
      "  1905\t#else\r\n",
      "  1906\t    if (!PyLong_Check(res)) {\r\n",
      "  1907\t#endif\r\n",
      "  1908\t      PyErr_Format(PyExc_TypeError,\r\n",
      "  1909\t                   \"__%.4s__ returned non-%.4s (type %.200s)\",\r\n",
      "  1910\t                   name, name, Py_TYPE(res)->tp_name);\r\n",
      "  1911\t      Py_DECREF(res);\r\n",
      "  1912\t      return NULL;\r\n",
      "  1913\t    }\r\n",
      "  1914\t  }\r\n",
      "  1915\t  else if (!PyErr_Occurred()) {\r\n",
      "  1916\t    PyErr_SetString(PyExc_TypeError,\r\n",
      "  1917\t                    \"an integer is required\");\r\n",
      "  1918\t  }\r\n",
      "  1919\t  return res;\r\n",
      "  1920\t}\r\n",
      "  1921\tstatic CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {\r\n",
      "  1922\t  Py_ssize_t ival;\r\n",
      "  1923\t  PyObject *x;\r\n",
      "  1924\t#if PY_MAJOR_VERSION < 3\r\n",
      "  1925\t  if (likely(PyInt_CheckExact(b))) {\r\n",
      "  1926\t    if (sizeof(Py_ssize_t) >= sizeof(long))\r\n",
      "  1927\t        return PyInt_AS_LONG(b);\r\n",
      "  1928\t    else\r\n",
      "  1929\t        return PyInt_AsSsize_t(x);\r\n",
      "  1930\t  }\r\n",
      "  1931\t#endif\r\n",
      "  1932\t  if (likely(PyLong_CheckExact(b))) {\r\n",
      "  1933\t    #if CYTHON_USE_PYLONG_INTERNALS\r\n",
      "  1934\t    const digit* digits = ((PyLongObject*)b)->ob_digit;\r\n",
      "  1935\t    const Py_ssize_t size = Py_SIZE(b);\r\n",
      "  1936\t    if (likely(__Pyx_sst_abs(size) <= 1)) {\r\n",
      "  1937\t        ival = likely(size) ? digits[0] : 0;\r\n",
      "  1938\t        if (size == -1) ival = -ival;\r\n",
      "  1939\t        return ival;\r\n",
      "  1940\t    } else {\r\n",
      "  1941\t      switch (size) {\r\n",
      "  1942\t         case 2:\r\n",
      "  1943\t           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {\r\n",
      "  1944\t             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));\r\n",
      "  1945\t           }\r\n",
      "  1946\t           break;\r\n",
      "  1947\t         case -2:\r\n",
      "  1948\t           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {\r\n",
      "  1949\t             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));\r\n",
      "  1950\t           }\r\n",
      "  1951\t           break;\r\n",
      "  1952\t         case 3:\r\n",
      "  1953\t           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {\r\n",
      "  1954\t             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));\r\n",
      "  1955\t           }\r\n",
      "  1956\t           break;\r\n",
      "  1957\t         case -3:\r\n",
      "  1958\t           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {\r\n",
      "  1959\t             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));\r\n",
      "  1960\t           }\r\n",
      "  1961\t           break;\r\n",
      "  1962\t         case 4:\r\n",
      "  1963\t           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {\r\n",
      "  1964\t             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));\r\n",
      "  1965\t           }\r\n",
      "  1966\t           break;\r\n",
      "  1967\t         case -4:\r\n",
      "  1968\t           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {\r\n",
      "  1969\t             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));\r\n",
      "  1970\t           }\r\n",
      "  1971\t           break;\r\n",
      "  1972\t      }\r\n",
      "  1973\t    }\r\n",
      "  1974\t    #endif\r\n",
      "  1975\t    return PyLong_AsSsize_t(b);\r\n",
      "  1976\t  }\r\n",
      "  1977\t  x = PyNumber_Index(b);\r\n",
      "  1978\t  if (!x) return -1;\r\n",
      "  1979\t  ival = PyInt_AsSsize_t(x);\r\n",
      "  1980\t  Py_DECREF(x);\r\n",
      "  1981\t  return ival;\r\n",
      "  1982\t}\r\n",
      "  1983\tstatic CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {\r\n",
      "  1984\t    return PyInt_FromSize_t(ival);\r\n",
      "  1985\t}\r\n",
      "       \r\n",
      "       \r\n",
      "  1986\t#endif /* Py_PYTHON_H */\r\n"
     ]
    }
   ],
   "source": [
    "!cat /home/jovyan/.cache/ipython/cython/cyfoo.c | nl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "```c\n",
    "static PyObject \n",
    "*__pyx_pf_5cyfoo_cyfoo(CYTHON_UNUSED PyObject *__pyx_self,\n",
    "                       PyObject *__pyx_v_a,\n",
    "                       PyObject *__pyx_v_b) {\n",
    "[...]\n",
    "  /* \"cyfoo.pyx\":3\n",
    " * \n",
    " * def cyfoo(a, b):\n",
    " *     return a + b             # <<<<<<<<<<<<<<\n",
    " */\n",
    "  __pyx_t_1 = PyNumber_Add(__pyx_v_a, __pyx_v_b);\n",
    " [...]\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## We conclude: converting from interpreted to compiled code gives some speedup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reason 2: Dynamic -> Static Typing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def pyfac(n):\n",
    "    if n <= 1:\n",
    "        return 1\n",
    "    return n * pyfac(n - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.66 µs ± 35.9 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2.43290200817664e+18"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%timeit pyfac(20.0)\n",
    "pyfac(20.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "\n",
    "def cyfac(n):\n",
    "    if n <= 1:\n",
    "        return 1\n",
    "    return n * cyfac(n - 1)\n",
    "\n",
    "def cyfac_double(double n):\n",
    "    if n <= 1:\n",
    "        return 1.0\n",
    "    return n * cyfac_double(n - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.48 µs ± 44.3 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2.43290200817664e+18"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%timeit cyfac(20.0)\n",
    "cyfac(20.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "943 ns ± 9.14 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2.43290200817664e+18"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%timeit cyfac_double(20.0)\n",
    "cyfac_double(20.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimal Cython solution: up to 40x speedup\n",
    "\n",
    "* Optimal for *this* recursive implementation..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "\n",
    "cpdef double cyfac_double_fast(double n):\n",
    "    if n <= 1:\n",
    "        return 1.0\n",
    "    return n * cyfac_double_fast(n - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "89.4 ns ± 1.48 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2.43290200817664e+18"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%timeit cyfac_double_fast(20.0)\n",
    "cyfac_double_fast(20.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For the record: what about a loop-based version?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def pyfac_loop(n):\n",
    "    r = 1.0\n",
    "    for i in range(1, n+1):\n",
    "        r *= i\n",
    "    return r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.02 µs ± 13.4 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2.43290200817664e+18"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%timeit pyfac_loop(20)\n",
    "pyfac_loop(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
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    "%%cython -a\n",
    "\n",
    "cpdef double cyfac_loop(int n):\n",
    "    cdef double r = 1.0\n",
    "    cdef int i\n",
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   "metadata": {},
   "outputs": [
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     "text": [
      "69 ns ± 1.4 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)\n"
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    "%timeit cyfac_loop(20)\n",
    "cyfac_loop(20)"
   ]
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   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cython speedup factor--loop-based version: 29.2\n"
     ]
    }
   ],
   "source": [
    "print(\"Cython speedup factor--loop-based version: {:0.1f}\".format((1.81 / 0.062)))"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Excercises / questions\n",
    "\n",
    "* Why are we using `double` here instead of `long`?\n",
    "* Why are the `pyfac_loop()` and `cyfac_loop()` versions *better* from a robustness pov?\n",
    "* Write a trivial no-op function in Python and measure its performance w/ `timeit`.  Now, make a Cython no-op `def` function, and measure *it*.  How do they compare?  Conjecture why.  What does this imply for function call overhead between pure Python and Cython code?"
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   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "78 ns ± 0.942 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)\n"
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    "def pynoop(): pass\n",
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