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  /* "/Users/rgommers/Code/scipy/scipy/signal/spectral.pyx":16
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  static char __pyx_doc_5scipy_6signal_8spectral_lombscargle[] = "Computes the Lomb-Scargle periodogram.\n""    \n""    The Lomb-Scargle periodogram was developed by Lomb [1]_ and further\n""    extended by Scargle [2]_ to find, and test the significance of weak\n""    periodic signals with uneven temporal sampling.\n""\n""    The computed periodogram is unnormalized, it takes the value\n""    ``(A**2) * N/4`` for a harmonic signal with amplitude A for sufficiently\n""    large N.\n""\n""    Parameters\n""    ----------\n""    x : array_like\n""        Sample times.\n""    y : array_like\n""        Measurement values.\n""    freqs : array_like\n""        Angular frequencies for output periodogram.\n""\n""    Returns\n""    -------\n""    pgram : array_like\n""        Lomb-Scargle periodogram.\n""\n""    Raises\n""    ------\n""    ValueError\n""        If the input arrays `x` and `y` do not have the same shape.\n""\n""    Notes\n""    -----\n""    This subroutine calculates the periodogram using a slightly\n""    modified algorithm due to Townsend [3]_ which allows the\n""    periodogram to be calculated using only a single pass through\n""    the input arrays for each frequency.\n""\n""    The algorithm running time scales roughly as O(x * freqs) or O(N^2)\n""    for a large number of samples and frequencies.\n""\n""    References\n""    ----------\n""    .. [1] N.R. Lomb \"Least-squares frequency analysis of unequally spaced\n""    data\", Astrophysics and Space Science, vol 39, pp. 447-462, 1976\n""\n""    .. [2] J.D. Scargle \"Studies in astronomical time series analysis. II - \n""    Statistical aspects of spectral analysis of unevenly spaced data\",\n""    The Astrophysical Journal, vol 263, pp. 835-853, 1982\n""\n""    .. [3] R.H.D. Townsend, \"Fast calculation of the Lomb-Scargle\n""    periodogram using graphics processing units.\", The Astrophysical\n""    Journal Supplement Series, vol 191, pp. 247-253, 2010\n""\n""    Examples\n""    --------\n""    >>> import scipy.signal\n""\n""    First define some input parameters for the signal:\n""\n""    >>> A = 2.\n""    >>> w = 1.\n""    >>> phi = 0.5 * np.pi\n""    >>> nin = 1000\n""    >>> nout = 100000\n""    >>> frac_points = 0.9 # Fraction of points to select\n""     \n""    Randomly select a fraction of an array with timesteps:\n""\n""    >>> r = np.random.rand(nin)\n""    >>> x = np.linspace(0.01, 10*np.pi, nin)\n""    >>> x = x[r >= frac_points]\n""    >>> normval = x.shape[0] # For normalization of the periodogram\n""     \n""    Plot a sine wave for the selected times:\n""\n""    >>> y = A * np.sin(w*x+phi)\n""\n""    Define the array of frequencies for which to compute the periodogram:\n""    \n""    >>> f = np.linspace(0.01, 10, nout)\n""     \n""    Calculate Lomb-Scargle periodogram:\n""\n""    >>> pgram = sp.signal.lombscargle(x, y, f)\n""\n""    Now make a plot of the input data:\n""\n""    >>> plt.subplot(2, 1, 1)\n""    <matplotlib.axes.AxesSubplot object at 0x102154f50>\n""    >>> plt.plot(x, y, 'b+')\n""    [<matplotlib.lines.Line2D object at 0x102154a10>]\n""\n""    Then plot the normalized periodogram:\n""\n""    >>> plt.subplot(2, 1, 2)\n""    <matplotlib.axes.AxesSubplot object at 0x104b0a990>\n""    >>> plt.plot(f, np.sqrt(4*(pgram/normval)))\n""    [<matplotlib.lines.Line2D object at 0x104b2f910>]\n""    >>> plt.show()\n""    \n""    ";
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   *         tau = atan(2 * cs / (cc - ss)) / (2 * freqs[i])             # <<<<<<<<<<<<<<
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    /* "/Library/Frameworks/Python.framework/Versions/2.6/lib/python2.6/site-packages/Cython-0.12.1-py2.6-macosx-10.3-fat.egg/Cython/Includes/stdlib.pxd":2
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                          if (PyUnicode_GET_SIZE(**name) == PyUnicode_GET_SIZE(key) &&
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  typedef struct { char c; short x; } __Pyx_st_short;
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  static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, int is_complex) {
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          }
          ++ts;
          ctx->new_count = 1;
          got_Z = 0;
          break;
        default:
          {
            ctx->new_count = __Pyx_BufFmt_ParseNumber(&ts);
            if (ctx->new_count == -1) { /* First char was not a digit */
              char msg[2] = { *ts, 0 };
              PyErr_Format(PyExc_ValueError,
                           "Does not understand character buffer dtype format string ('%s')", msg);
              return NULL;
            }
          }
        
      }
    }
  }
  
  static CYTHON_INLINE void __Pyx_ZeroBuffer(Py_buffer* buf) {
    buf->buf = NULL;
    buf->obj = NULL;
    buf->strides = __Pyx_zeros;
    buf->shape = __Pyx_zeros;
    buf->suboffsets = __Pyx_minusones;
  }
  
  static int __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj, __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack) {
    if (obj == Py_None) {
      __Pyx_ZeroBuffer(buf);
      return 0;
    }
    buf->buf = NULL;
    if (__Pyx_GetBuffer(obj, buf, flags) == -1) goto fail;
    if (buf->ndim != nd) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer has wrong number of dimensions (expected %d, got %d)",
                   nd, buf->ndim);
      goto fail;
    }
    if (!cast) {
      __Pyx_BufFmt_Context ctx;
      __Pyx_BufFmt_Init(&ctx, stack, dtype);
      if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
    }
    if ((unsigned)buf->itemsize != dtype->size) {
      PyErr_Format(PyExc_ValueError,
        "Item size of buffer (%"PY_FORMAT_SIZE_T"d byte%s) does not match size of '%s' (%"PY_FORMAT_SIZE_T"d byte%s)",
        buf->itemsize, (buf->itemsize > 1) ? "s" : "",
        dtype->name,
        dtype->size, (dtype->size > 1) ? "s" : "");
      goto fail;
    }
    if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
    return 0;
  fail:;
    __Pyx_ZeroBuffer(buf);
    return -1;
  }
  
  static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
    if (info->buf == NULL) return;
    if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
    __Pyx_ReleaseBuffer(info);
  }
  
  
  static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb) {
      PyObject *tmp_type, *tmp_value, *tmp_tb;
      PyThreadState *tstate = PyThreadState_GET();
  
      tmp_type = tstate->curexc_type;
      tmp_value = tstate->curexc_value;
      tmp_tb = tstate->curexc_traceback;
      tstate->curexc_type = type;
      tstate->curexc_value = value;
      tstate->curexc_traceback = tb;
      Py_XDECREF(tmp_type);
      Py_XDECREF(tmp_value);
      Py_XDECREF(tmp_tb);
  }
  
  static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb) {
      PyThreadState *tstate = PyThreadState_GET();
      *type = tstate->curexc_type;
      *value = tstate->curexc_value;
      *tb = tstate->curexc_traceback;
  
      tstate->curexc_type = 0;
      tstate->curexc_value = 0;
      tstate->curexc_traceback = 0;
  }
  
  
  static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
      PyErr_Format(PyExc_ValueError,
          #if PY_VERSION_HEX < 0x02050000
                   "need more than %d value%s to unpack", (int)index,
          #else
                   "need more than %zd value%s to unpack", index,
          #endif
                   (index == 1) ? "" : "s");
  }
  
  static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(void) {
      PyErr_SetString(PyExc_ValueError, "too many values to unpack");
  }
  
  static PyObject *__Pyx_UnpackItem(PyObject *iter, Py_ssize_t index) {
      PyObject *item;
      if (!(item = PyIter_Next(iter))) {
          if (!PyErr_Occurred()) {
              __Pyx_RaiseNeedMoreValuesError(index);
          }
      }
      return item;
  }
  
  static int __Pyx_EndUnpack(PyObject *iter) {
      PyObject *item;
      if ((item = PyIter_Next(iter))) {
          Py_DECREF(item);
          __Pyx_RaiseTooManyValuesError();
          return -1;
      }
      else if (!PyErr_Occurred())
          return 0;
      else
          return -1;
  }
  
  static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
      if (unlikely(!type)) {
          PyErr_Format(PyExc_SystemError, "Missing type object");
          return 0;
      }
      if (likely(PyObject_TypeCheck(obj, type)))
          return 1;
      PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
                   Py_TYPE(obj)->tp_name, type->tp_name);
      return 0;
  }
  
  static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
      PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
  }
  
  static void __Pyx_UnpackTupleError(PyObject *t, Py_ssize_t index) {
      if (t == Py_None) {
        __Pyx_RaiseNoneNotIterableError();
      } else if (PyTuple_GET_SIZE(t) < index) {
        __Pyx_RaiseNeedMoreValuesError(PyTuple_GET_SIZE(t));
      } else {
        __Pyx_RaiseTooManyValuesError();
      }
  }
  
  static int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
      const char *name, int exact)
  {
      if (!type) {
          PyErr_Format(PyExc_SystemError, "Missing type object");
          return 0;
      }
      if (none_allowed && obj == Py_None) return 1;
      else if (exact) {
          if (Py_TYPE(obj) == type) return 1;
      }
      else {
          if (PyObject_TypeCheck(obj, type)) return 1;
      }
      PyErr_Format(PyExc_TypeError,
          "Argument '%s' has incorrect type (expected %s, got %s)",
          name, type->tp_name, Py_TYPE(obj)->tp_name);
      return 0;
  }
  
  #if PY_MAJOR_VERSION < 3
  static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
    #if PY_VERSION_HEX >= 0x02060000
    if (Py_TYPE(obj)->tp_flags & Py_TPFLAGS_HAVE_NEWBUFFER)
        return PyObject_GetBuffer(obj, view, flags);
    #endif
    if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pf_5numpy_7ndarray___getbuffer__(obj, view, flags);
    else {
    PyErr_Format(PyExc_TypeError, "'%100s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
    return -1;
      }
  }
  
  static void __Pyx_ReleaseBuffer(Py_buffer *view) {
    PyObject* obj = view->obj;
    if (obj) {
  if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) __pyx_pf_5numpy_7ndarray___releasebuffer__(obj, view);
      Py_DECREF(obj);
      view->obj = NULL;
    }
  }
  
  #endif
  
  static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list) {
      PyObject *__import__ = 0;
      PyObject *empty_list = 0;
      PyObject *module = 0;
      PyObject *global_dict = 0;
      PyObject *empty_dict = 0;
      PyObject *list;
      __import__ = __Pyx_GetAttrString(__pyx_b, "__import__");
      if (!__import__)
          goto bad;
      if (from_list)
          list = from_list;
      else {
          empty_list = PyList_New(0);
          if (!empty_list)
              goto bad;
          list = empty_list;
      }
      global_dict = PyModule_GetDict(__pyx_m);
      if (!global_dict)
          goto bad;
      empty_dict = PyDict_New();
      if (!empty_dict)
          goto bad;
      module = PyObject_CallFunctionObjArgs(__import__,
          name, global_dict, empty_dict, list, NULL);
  bad:
      Py_XDECREF(empty_list);
      Py_XDECREF(__import__);
      Py_XDECREF(empty_dict);
      return module;
  }
  
  static PyObject *__Pyx_GetName(PyObject *dict, PyObject *name) {
      PyObject *result;
      result = PyObject_GetAttr(dict, name);
      if (!result)
          PyErr_SetObject(PyExc_NameError, name);
      return result;
  }
  
  #if PY_MAJOR_VERSION < 3
  static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb) {
      Py_XINCREF(type);
      Py_XINCREF(value);
      Py_XINCREF(tb);
      /* First, check the traceback argument, replacing None with NULL. */
      if (tb == Py_None) {
          Py_DECREF(tb);
          tb = 0;
      }
      else if (tb != NULL && !PyTraceBack_Check(tb)) {
          PyErr_SetString(PyExc_TypeError,
              "raise: arg 3 must be a traceback or None");
          goto raise_error;
      }
      /* Next, replace a missing value with None */
      if (value == NULL) {
          value = Py_None;
          Py_INCREF(value);
      }
      #if PY_VERSION_HEX < 0x02050000
      if (!PyClass_Check(type))
      #else
      if (!PyType_Check(type))
      #endif
      {
          /* Raising an instance.  The value should be a dummy. */
          if (value != Py_None) {
              PyErr_SetString(PyExc_TypeError,
                  "instance exception may not have a separate value");
              goto raise_error;
          }
          /* Normalize to raise <class>, <instance> */
          Py_DECREF(value);
          value = type;
          #if PY_VERSION_HEX < 0x02050000
              if (PyInstance_Check(type)) {
                  type = (PyObject*) ((PyInstanceObject*)type)->in_class;
                  Py_INCREF(type);
              }
              else {
                  type = 0;
                  PyErr_SetString(PyExc_TypeError,
                      "raise: exception must be an old-style class or instance");
                  goto raise_error;
              }
          #else
              type = (PyObject*) Py_TYPE(type);
              Py_INCREF(type);
              if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
                  PyErr_SetString(PyExc_TypeError,
                      "raise: exception class must be a subclass of BaseException");
                  goto raise_error;
              }
          #endif
      }
  
      __Pyx_ErrRestore(type, value, tb);
      return;
  raise_error:
      Py_XDECREF(value);
      Py_XDECREF(type);
      Py_XDECREF(tb);
      return;
  }
  
  #else /* Python 3+ */
  
  static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb) {
      if (tb == Py_None) {
          tb = 0;
      } else if (tb && !PyTraceBack_Check(tb)) {
          PyErr_SetString(PyExc_TypeError,
              "raise: arg 3 must be a traceback or None");
          goto bad;
      }
      if (value == Py_None)
          value = 0;
  
      if (PyExceptionInstance_Check(type)) {
          if (value) {
              PyErr_SetString(PyExc_TypeError,
                  "instance exception may not have a separate value");
              goto bad;
          }
          value = type;
          type = (PyObject*) Py_TYPE(value);
      } else if (!PyExceptionClass_Check(type)) {
          PyErr_SetString(PyExc_TypeError,
              "raise: exception class must be a subclass of BaseException");
          goto bad;
      }
  
      PyErr_SetObject(type, value);
  
      if (tb) {
          PyThreadState *tstate = PyThreadState_GET();
          PyObject* tmp_tb = tstate->curexc_traceback;
          if (tb != tmp_tb) {
              Py_INCREF(tb);
              tstate->curexc_traceback = tb;
              Py_XDECREF(tmp_tb);
          }
      }
  
  bad:
      return;
  }
  #endif
  
  static CYTHON_INLINE PyObject *__Pyx_PyInt_to_py_npy_intp(npy_intp val) {
      const npy_intp neg_one = (npy_intp)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(npy_intp) <  sizeof(long)) {
          return PyInt_FromLong((long)val);
      } else if (sizeof(npy_intp) == sizeof(long)) {
          if (is_unsigned)
              return PyLong_FromUnsignedLong((unsigned long)val);
          else
              return PyInt_FromLong((long)val);
      } else { /* (sizeof(npy_intp) > sizeof(long)) */
          if (is_unsigned)
              return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG)val);
          else
              return PyLong_FromLongLong((PY_LONG_LONG)val);
      }
  }
  
  #if CYTHON_CCOMPLEX
    #ifdef __cplusplus
      static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
        return ::std::complex< float >(x, y);
      }
    #else
      static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
        return x + y*(__pyx_t_float_complex)_Complex_I;
      }
    #endif
  #else
      static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
        __pyx_t_float_complex z;
        z.real = x;
        z.imag = y;
        return z;
      }
  #endif
  
  #if CYTHON_CCOMPLEX
  #else
      static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
         return (a.real == b.real) && (a.imag == b.imag);
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
          __pyx_t_float_complex z;
          z.real = a.real + b.real;
          z.imag = a.imag + b.imag;
          return z;
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex a, __pyx_t_float_complex b) {
          __pyx_t_float_complex z;
          z.real = a.real - b.real;
          z.imag = a.imag - b.imag;
          return z;
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
          __pyx_t_float_complex z;
          z.real = a.real * b.real - a.imag * b.imag;
          z.imag = a.real * b.imag + a.imag * b.real;
          return z;
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
          __pyx_t_float_complex z;
          float denom = b.real * b.real + b.imag * b.imag;
          z.real = (a.real * b.real + a.imag * b.imag) / denom;
          z.imag = (a.imag * b.real - a.real * b.imag) / denom;
          return z;
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex a) {
          __pyx_t_float_complex z;
          z.real = -a.real;
          z.imag = -a.imag;
          return z;
      }
      static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex a) {
         return (a.real == 0) && (a.imag == 0);
      }
      static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex a) {
          __pyx_t_float_complex z;
          z.real =  a.real;
          z.imag = -a.imag;
          return z;
      }
  /*
      static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex z) {
  #if HAVE_HYPOT
          return hypotf(z.real, z.imag);
  #else
          return sqrtf(z.real*z.real + z.imag*z.imag);
  #endif
      }
  */
  #endif
  
  #if CYTHON_CCOMPLEX
    #ifdef __cplusplus
      static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
        return ::std::complex< double >(x, y);
      }
    #else
      static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
        return x + y*(__pyx_t_double_complex)_Complex_I;
      }
    #endif
  #else
      static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
        __pyx_t_double_complex z;
        z.real = x;
        z.imag = y;
        return z;
      }
  #endif
  
  #if CYTHON_CCOMPLEX
  #else
      static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex a, __pyx_t_double_complex b) {
         return (a.real == b.real) && (a.imag == b.imag);
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex a, __pyx_t_double_complex b) {
          __pyx_t_double_complex z;
          z.real = a.real + b.real;
          z.imag = a.imag + b.imag;
          return z;
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex a, __pyx_t_double_complex b) {
          __pyx_t_double_complex z;
          z.real = a.real - b.real;
          z.imag = a.imag - b.imag;
          return z;
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex a, __pyx_t_double_complex b) {
          __pyx_t_double_complex z;
          z.real = a.real * b.real - a.imag * b.imag;
          z.imag = a.real * b.imag + a.imag * b.real;
          return z;
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex a, __pyx_t_double_complex b) {
          __pyx_t_double_complex z;
          double denom = b.real * b.real + b.imag * b.imag;
          z.real = (a.real * b.real + a.imag * b.imag) / denom;
          z.imag = (a.imag * b.real - a.real * b.imag) / denom;
          return z;
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex a) {
          __pyx_t_double_complex z;
          z.real = -a.real;
          z.imag = -a.imag;
          return z;
      }
      static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex a) {
         return (a.real == 0) && (a.imag == 0);
      }
      static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex a) {
          __pyx_t_double_complex z;
          z.real =  a.real;
          z.imag = -a.imag;
          return z;
      }
  /*
      static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex z) {
  #if HAVE_HYPOT
          return hypot(z.real, z.imag);
  #else
          return sqrt(z.real*z.real + z.imag*z.imag);
  #endif
      }
  */
  #endif
  
  static CYTHON_INLINE unsigned char __Pyx_PyInt_AsUnsignedChar(PyObject* x) {
      const unsigned char neg_one = (unsigned char)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(unsigned char) < sizeof(long)) {
          long val = __Pyx_PyInt_AsLong(x);
          if (unlikely(val != (long)(unsigned char)val)) {
              if (!unlikely(val == -1 && PyErr_Occurred())) {
                  PyErr_SetString(PyExc_OverflowError,
                      (is_unsigned && unlikely(val < 0)) ?
                      "can't convert negative value to unsigned char" :
                      "value too large to convert to unsigned char");
              }
              return (unsigned char)-1;
          }
          return (unsigned char)val;
      }
      return (unsigned char)__Pyx_PyInt_AsUnsignedLong(x);
  }
  
  static CYTHON_INLINE unsigned short __Pyx_PyInt_AsUnsignedShort(PyObject* x) {
      const unsigned short neg_one = (unsigned short)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(unsigned short) < sizeof(long)) {
          long val = __Pyx_PyInt_AsLong(x);
          if (unlikely(val != (long)(unsigned short)val)) {
              if (!unlikely(val == -1 && PyErr_Occurred())) {
                  PyErr_SetString(PyExc_OverflowError,
                      (is_unsigned && unlikely(val < 0)) ?
                      "can't convert negative value to unsigned short" :
                      "value too large to convert to unsigned short");
              }
              return (unsigned short)-1;
          }
          return (unsigned short)val;
      }
      return (unsigned short)__Pyx_PyInt_AsUnsignedLong(x);
  }
  
  static CYTHON_INLINE unsigned int __Pyx_PyInt_AsUnsignedInt(PyObject* x) {
      const unsigned int neg_one = (unsigned int)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(unsigned int) < sizeof(long)) {
          long val = __Pyx_PyInt_AsLong(x);
          if (unlikely(val != (long)(unsigned int)val)) {
              if (!unlikely(val == -1 && PyErr_Occurred())) {
                  PyErr_SetString(PyExc_OverflowError,
                      (is_unsigned && unlikely(val < 0)) ?
                      "can't convert negative value to unsigned int" :
                      "value too large to convert to unsigned int");
              }
              return (unsigned int)-1;
          }
          return (unsigned int)val;
      }
      return (unsigned int)__Pyx_PyInt_AsUnsignedLong(x);
  }
  
  static CYTHON_INLINE char __Pyx_PyInt_AsChar(PyObject* x) {
      const char neg_one = (char)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(char) < sizeof(long)) {
          long val = __Pyx_PyInt_AsLong(x);
          if (unlikely(val != (long)(char)val)) {
              if (!unlikely(val == -1 && PyErr_Occurred())) {
                  PyErr_SetString(PyExc_OverflowError,
                      (is_unsigned && unlikely(val < 0)) ?
                      "can't convert negative value to char" :
                      "value too large to convert to char");
              }
              return (char)-1;
          }
          return (char)val;
      }
      return (char)__Pyx_PyInt_AsLong(x);
  }
  
  static CYTHON_INLINE short __Pyx_PyInt_AsShort(PyObject* x) {
      const short neg_one = (short)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(short) < sizeof(long)) {
          long val = __Pyx_PyInt_AsLong(x);
          if (unlikely(val != (long)(short)val)) {
              if (!unlikely(val == -1 && PyErr_Occurred())) {
                  PyErr_SetString(PyExc_OverflowError,
                      (is_unsigned && unlikely(val < 0)) ?
                      "can't convert negative value to short" :
                      "value too large to convert to short");
              }
              return (short)-1;
          }
          return (short)val;
      }
      return (short)__Pyx_PyInt_AsLong(x);
  }
  
  static CYTHON_INLINE int __Pyx_PyInt_AsInt(PyObject* x) {
      const int neg_one = (int)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(int) < sizeof(long)) {
          long val = __Pyx_PyInt_AsLong(x);
          if (unlikely(val != (long)(int)val)) {
              if (!unlikely(val == -1 && PyErr_Occurred())) {
                  PyErr_SetString(PyExc_OverflowError,
                      (is_unsigned && unlikely(val < 0)) ?
                      "can't convert negative value to int" :
                      "value too large to convert to int");
              }
              return (int)-1;
          }
          return (int)val;
      }
      return (int)__Pyx_PyInt_AsLong(x);
  }
  
  static CYTHON_INLINE signed char __Pyx_PyInt_AsSignedChar(PyObject* x) {
      const signed char neg_one = (signed char)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(signed char) < sizeof(long)) {
          long val = __Pyx_PyInt_AsLong(x);
          if (unlikely(val != (long)(signed char)val)) {
              if (!unlikely(val == -1 && PyErr_Occurred())) {
                  PyErr_SetString(PyExc_OverflowError,
                      (is_unsigned && unlikely(val < 0)) ?
                      "can't convert negative value to signed char" :
                      "value too large to convert to signed char");
              }
              return (signed char)-1;
          }
          return (signed char)val;
      }
      return (signed char)__Pyx_PyInt_AsSignedLong(x);
  }
  
  static CYTHON_INLINE signed short __Pyx_PyInt_AsSignedShort(PyObject* x) {
      const signed short neg_one = (signed short)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(signed short) < sizeof(long)) {
          long val = __Pyx_PyInt_AsLong(x);
          if (unlikely(val != (long)(signed short)val)) {
              if (!unlikely(val == -1 && PyErr_Occurred())) {
                  PyErr_SetString(PyExc_OverflowError,
                      (is_unsigned && unlikely(val < 0)) ?
                      "can't convert negative value to signed short" :
                      "value too large to convert to signed short");
              }
              return (signed short)-1;
          }
          return (signed short)val;
      }
      return (signed short)__Pyx_PyInt_AsSignedLong(x);
  }
  
  static CYTHON_INLINE signed int __Pyx_PyInt_AsSignedInt(PyObject* x) {
      const signed int neg_one = (signed int)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
      if (sizeof(signed int) < sizeof(long)) {
          long val = __Pyx_PyInt_AsLong(x);
          if (unlikely(val != (long)(signed int)val)) {
              if (!unlikely(val == -1 && PyErr_Occurred())) {
                  PyErr_SetString(PyExc_OverflowError,
                      (is_unsigned && unlikely(val < 0)) ?
                      "can't convert negative value to signed int" :
                      "value too large to convert to signed int");
              }
              return (signed int)-1;
          }
          return (signed int)val;
      }
      return (signed int)__Pyx_PyInt_AsSignedLong(x);
  }
  
  static CYTHON_INLINE unsigned long __Pyx_PyInt_AsUnsignedLong(PyObject* x) {
      const unsigned long neg_one = (unsigned long)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
  #if PY_VERSION_HEX < 0x03000000
      if (likely(PyInt_Check(x))) {
          long val = PyInt_AS_LONG(x);
          if (is_unsigned && unlikely(val < 0)) {
              PyErr_SetString(PyExc_OverflowError,
                              "can't convert negative value to unsigned long");
              return (unsigned long)-1;
          }
          return (unsigned long)val;
      } else
  #endif
      if (likely(PyLong_Check(x))) {
          if (is_unsigned) {
              if (unlikely(Py_SIZE(x) < 0)) {
                  PyErr_SetString(PyExc_OverflowError,
                                  "can't convert negative value to unsigned long");
                  return (unsigned long)-1;
              }
              return PyLong_AsUnsignedLong(x);
          } else {
              return PyLong_AsLong(x);
          }
      } else {
          unsigned long val;
          PyObject *tmp = __Pyx_PyNumber_Int(x);
          if (!tmp) return (unsigned long)-1;
          val = __Pyx_PyInt_AsUnsignedLong(tmp);
          Py_DECREF(tmp);
          return val;
      }
  }
  
  static CYTHON_INLINE unsigned PY_LONG_LONG __Pyx_PyInt_AsUnsignedLongLong(PyObject* x) {
      const unsigned PY_LONG_LONG neg_one = (unsigned PY_LONG_LONG)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
  #if PY_VERSION_HEX < 0x03000000
      if (likely(PyInt_Check(x))) {
          long val = PyInt_AS_LONG(x);
          if (is_unsigned && unlikely(val < 0)) {
              PyErr_SetString(PyExc_OverflowError,
                              "can't convert negative value to unsigned PY_LONG_LONG");
              return (unsigned PY_LONG_LONG)-1;
          }
          return (unsigned PY_LONG_LONG)val;
      } else
  #endif
      if (likely(PyLong_Check(x))) {
          if (is_unsigned) {
              if (unlikely(Py_SIZE(x) < 0)) {
                  PyErr_SetString(PyExc_OverflowError,
                                  "can't convert negative value to unsigned PY_LONG_LONG");
                  return (unsigned PY_LONG_LONG)-1;
              }
              return PyLong_AsUnsignedLongLong(x);
          } else {
              return PyLong_AsLongLong(x);
          }
      } else {
          unsigned PY_LONG_LONG val;
          PyObject *tmp = __Pyx_PyNumber_Int(x);
          if (!tmp) return (unsigned PY_LONG_LONG)-1;
          val = __Pyx_PyInt_AsUnsignedLongLong(tmp);
          Py_DECREF(tmp);
          return val;
      }
  }
  
  static CYTHON_INLINE long __Pyx_PyInt_AsLong(PyObject* x) {
      const long neg_one = (long)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
  #if PY_VERSION_HEX < 0x03000000
      if (likely(PyInt_Check(x))) {
          long val = PyInt_AS_LONG(x);
          if (is_unsigned && unlikely(val < 0)) {
              PyErr_SetString(PyExc_OverflowError,
                              "can't convert negative value to long");
              return (long)-1;
          }
          return (long)val;
      } else
  #endif
      if (likely(PyLong_Check(x))) {
          if (is_unsigned) {
              if (unlikely(Py_SIZE(x) < 0)) {
                  PyErr_SetString(PyExc_OverflowError,
                                  "can't convert negative value to long");
                  return (long)-1;
              }
              return PyLong_AsUnsignedLong(x);
          } else {
              return PyLong_AsLong(x);
          }
      } else {
          long val;
          PyObject *tmp = __Pyx_PyNumber_Int(x);
          if (!tmp) return (long)-1;
          val = __Pyx_PyInt_AsLong(tmp);
          Py_DECREF(tmp);
          return val;
      }
  }
  
  static CYTHON_INLINE PY_LONG_LONG __Pyx_PyInt_AsLongLong(PyObject* x) {
      const PY_LONG_LONG neg_one = (PY_LONG_LONG)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
  #if PY_VERSION_HEX < 0x03000000
      if (likely(PyInt_Check(x))) {
          long val = PyInt_AS_LONG(x);
          if (is_unsigned && unlikely(val < 0)) {
              PyErr_SetString(PyExc_OverflowError,
                              "can't convert negative value to PY_LONG_LONG");
              return (PY_LONG_LONG)-1;
          }
          return (PY_LONG_LONG)val;
      } else
  #endif
      if (likely(PyLong_Check(x))) {
          if (is_unsigned) {
              if (unlikely(Py_SIZE(x) < 0)) {
                  PyErr_SetString(PyExc_OverflowError,
                                  "can't convert negative value to PY_LONG_LONG");
                  return (PY_LONG_LONG)-1;
              }
              return PyLong_AsUnsignedLongLong(x);
          } else {
              return PyLong_AsLongLong(x);
          }
      } else {
          PY_LONG_LONG val;
          PyObject *tmp = __Pyx_PyNumber_Int(x);
          if (!tmp) return (PY_LONG_LONG)-1;
          val = __Pyx_PyInt_AsLongLong(tmp);
          Py_DECREF(tmp);
          return val;
      }
  }
  
  static CYTHON_INLINE signed long __Pyx_PyInt_AsSignedLong(PyObject* x) {
      const signed long neg_one = (signed long)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
  #if PY_VERSION_HEX < 0x03000000
      if (likely(PyInt_Check(x))) {
          long val = PyInt_AS_LONG(x);
          if (is_unsigned && unlikely(val < 0)) {
              PyErr_SetString(PyExc_OverflowError,
                              "can't convert negative value to signed long");
              return (signed long)-1;
          }
          return (signed long)val;
      } else
  #endif
      if (likely(PyLong_Check(x))) {
          if (is_unsigned) {
              if (unlikely(Py_SIZE(x) < 0)) {
                  PyErr_SetString(PyExc_OverflowError,
                                  "can't convert negative value to signed long");
                  return (signed long)-1;
              }
              return PyLong_AsUnsignedLong(x);
          } else {
              return PyLong_AsLong(x);
          }
      } else {
          signed long val;
          PyObject *tmp = __Pyx_PyNumber_Int(x);
          if (!tmp) return (signed long)-1;
          val = __Pyx_PyInt_AsSignedLong(tmp);
          Py_DECREF(tmp);
          return val;
      }
  }
  
  static CYTHON_INLINE signed PY_LONG_LONG __Pyx_PyInt_AsSignedLongLong(PyObject* x) {
      const signed PY_LONG_LONG neg_one = (signed PY_LONG_LONG)-1, const_zero = 0;
      const int is_unsigned = neg_one > const_zero;
  #if PY_VERSION_HEX < 0x03000000
      if (likely(PyInt_Check(x))) {
          long val = PyInt_AS_LONG(x);
          if (is_unsigned && unlikely(val < 0)) {
              PyErr_SetString(PyExc_OverflowError,
                              "can't convert negative value to signed PY_LONG_LONG");
              return (signed PY_LONG_LONG)-1;
          }
          return (signed PY_LONG_LONG)val;
      } else
  #endif
      if (likely(PyLong_Check(x))) {
          if (is_unsigned) {
              if (unlikely(Py_SIZE(x) < 0)) {
                  PyErr_SetString(PyExc_OverflowError,
                                  "can't convert negative value to signed PY_LONG_LONG");
                  return (signed PY_LONG_LONG)-1;
              }
              return PyLong_AsUnsignedLongLong(x);
          } else {
              return PyLong_AsLongLong(x);
          }
      } else {
          signed PY_LONG_LONG val;
          PyObject *tmp = __Pyx_PyNumber_Int(x);
          if (!tmp) return (signed PY_LONG_LONG)-1;
          val = __Pyx_PyInt_AsSignedLongLong(tmp);
          Py_DECREF(tmp);
          return val;
      }
  }
  
  #ifndef __PYX_HAVE_RT_ImportType
  #define __PYX_HAVE_RT_ImportType
  static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
      long size, int strict)
  {
      PyObject *py_module = 0;
      PyObject *result = 0;
      PyObject *py_name = 0;
      char warning[200];
  
      py_module = __Pyx_ImportModule(module_name);
      if (!py_module)
          goto bad;
      #if PY_MAJOR_VERSION < 3
      py_name = PyString_FromString(class_name);
      #else
      py_name = PyUnicode_FromString(class_name);
      #endif
      if (!py_name)
          goto bad;
      result = PyObject_GetAttr(py_module, py_name);
      Py_DECREF(py_name);
      py_name = 0;
      Py_DECREF(py_module);
      py_module = 0;
      if (!result)
          goto bad;
      if (!PyType_Check(result)) {
          PyErr_Format(PyExc_TypeError, 
              "%s.%s is not a type object",
              module_name, class_name);
          goto bad;
      }
      if (!strict && ((PyTypeObject *)result)->tp_basicsize > size) {
          PyOS_snprintf(warning, sizeof(warning), 
              "%s.%s size changed, may indicate binary incompatibility",
              module_name, class_name);
          PyErr_WarnEx(NULL, warning, 0);
      }
      else if (((PyTypeObject *)result)->tp_basicsize != size) {
          PyErr_Format(PyExc_ValueError, 
              "%s.%s has the wrong size, try recompiling",
              module_name, class_name);
          goto bad;
      }
      return (PyTypeObject *)result;
  bad:
      Py_XDECREF(py_module);
      Py_XDECREF(result);
      return 0;
  }
  #endif
  
  #ifndef __PYX_HAVE_RT_ImportModule
  #define __PYX_HAVE_RT_ImportModule
  static PyObject *__Pyx_ImportModule(const char *name) {
      PyObject *py_name = 0;
      PyObject *py_module = 0;
  
      #if PY_MAJOR_VERSION < 3
      py_name = PyString_FromString(name);
      #else
      py_name = PyUnicode_FromString(name);
      #endif
      if (!py_name)
          goto bad;
      py_module = PyImport_Import(py_name);
      Py_DECREF(py_name);
      return py_module;
  bad:
      Py_XDECREF(py_name);
      return 0;
  }
  #endif
  
  #include "compile.h"
  #include "frameobject.h"
  #include "traceback.h"
  
  static void __Pyx_AddTraceback(const char *funcname) {
      PyObject *py_srcfile = 0;
      PyObject *py_funcname = 0;
      PyObject *py_globals = 0;
      PyCodeObject *py_code = 0;
      PyFrameObject *py_frame = 0;
  
      #if PY_MAJOR_VERSION < 3
      py_srcfile = PyString_FromString(__pyx_filename);
      #else
      py_srcfile = PyUnicode_FromString(__pyx_filename);
      #endif
      if (!py_srcfile) goto bad;
      if (__pyx_clineno) {
          #if PY_MAJOR_VERSION < 3
          py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, __pyx_clineno);
          #else
          py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, __pyx_clineno);
          #endif
      }
      else {
          #if PY_MAJOR_VERSION < 3
          py_funcname = PyString_FromString(funcname);
          #else
          py_funcname = PyUnicode_FromString(funcname);
          #endif
      }
      if (!py_funcname) goto bad;
      py_globals = PyModule_GetDict(__pyx_m);
      if (!py_globals) goto bad;
      py_code = PyCode_New(
          0,            /*int argcount,*/
          #if PY_MAJOR_VERSION >= 3
          0,            /*int kwonlyargcount,*/
          #endif
          0,            /*int nlocals,*/
          0,            /*int stacksize,*/
          0,            /*int flags,*/
          __pyx_empty_bytes, /*PyObject *code,*/
          __pyx_empty_tuple,  /*PyObject *consts,*/
          __pyx_empty_tuple,  /*PyObject *names,*/
          __pyx_empty_tuple,  /*PyObject *varnames,*/
          __pyx_empty_tuple,  /*PyObject *freevars,*/
          __pyx_empty_tuple,  /*PyObject *cellvars,*/
          py_srcfile,   /*PyObject *filename,*/
          py_funcname,  /*PyObject *name,*/
          __pyx_lineno,   /*int firstlineno,*/
          __pyx_empty_bytes  /*PyObject *lnotab*/
      );
      if (!py_code) goto bad;
      py_frame = PyFrame_New(
          PyThreadState_GET(), /*PyThreadState *tstate,*/
          py_code,             /*PyCodeObject *code,*/
          py_globals,          /*PyObject *globals,*/
          0                    /*PyObject *locals*/
      );
      if (!py_frame) goto bad;
      py_frame->f_lineno = __pyx_lineno;
      PyTraceBack_Here(py_frame);
  bad:
      Py_XDECREF(py_srcfile);
      Py_XDECREF(py_funcname);
      Py_XDECREF(py_code);
      Py_XDECREF(py_frame);
  }
  
  static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
      while (t->p) {
          #if PY_MAJOR_VERSION < 3
          if (t->is_unicode) {
              *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
          } else if (t->intern) {
              *t->p = PyString_InternFromString(t->s);
          } else {
              *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
          }
          #else  /* Python 3+ has unicode identifiers */
          if (t->is_unicode | t->is_str) {
              if (t->intern) {
                  *t->p = PyUnicode_InternFromString(t->s);
              } else if (t->encoding) {
                  *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
              } else {
                  *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
              }
          } else {
              *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
          }
          #endif
          if (!*t->p)
              return -1;
          ++t;
      }
      return 0;
  }
  
  /* Type Conversion Functions */
  
  static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
     if (x == Py_True) return 1;
     else if ((x == Py_False) | (x == Py_None)) return 0;
     else return PyObject_IsTrue(x);
  }
  
  static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x) {
    PyNumberMethods *m;
    const char *name = NULL;
    PyObject *res = NULL;
  #if PY_VERSION_HEX < 0x03000000
    if (PyInt_Check(x) || PyLong_Check(x))
  #else
    if (PyLong_Check(x))
  #endif
      return Py_INCREF(x), x;
    m = Py_TYPE(x)->tp_as_number;
  #if PY_VERSION_HEX < 0x03000000
    if (m && m->nb_int) {
      name = "int";
      res = PyNumber_Int(x);
    }
    else if (m && m->nb_long) {
      name = "long";
      res = PyNumber_Long(x);
    }
  #else
    if (m && m->nb_int) {
      name = "int";
      res = PyNumber_Long(x);
    }
  #endif
    if (res) {
  #if PY_VERSION_HEX < 0x03000000
      if (!PyInt_Check(res) && !PyLong_Check(res)) {
  #else
      if (!PyLong_Check(res)) {
  #endif
        PyErr_Format(PyExc_TypeError,
                     "__%s__ returned non-%s (type %.200s)",
                     name, name, Py_TYPE(res)->tp_name);
        Py_DECREF(res);
        return NULL;
      }
    }
    else if (!PyErr_Occurred()) {
      PyErr_SetString(PyExc_TypeError,
                      "an integer is required");
    }
    return res;
  }
  
  static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
    Py_ssize_t ival;
    PyObject* x = PyNumber_Index(b);
    if (!x) return -1;
    ival = PyInt_AsSsize_t(x);
    Py_DECREF(x);
    return ival;
  }
  
  static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
  #if PY_VERSION_HEX < 0x02050000
     if (ival <= LONG_MAX)
         return PyInt_FromLong((long)ival);
     else {
         unsigned char *bytes = (unsigned char *) &ival;
         int one = 1; int little = (int)*(unsigned char*)&one;
         return _PyLong_FromByteArray(bytes, sizeof(size_t), little, 0);
     }
  #else
     return PyInt_FromSize_t(ival);
  #endif
  }
  
  static CYTHON_INLINE size_t __Pyx_PyInt_AsSize_t(PyObject* x) {
     unsigned PY_LONG_LONG val = __Pyx_PyInt_AsUnsignedLongLong(x);
     if (unlikely(val == (unsigned PY_LONG_LONG)-1 && PyErr_Occurred())) {
         return (size_t)-1;
     } else if (unlikely(val != (unsigned PY_LONG_LONG)(size_t)val)) {
         PyErr_SetString(PyExc_OverflowError,
                         "value too large to convert to size_t");
         return (size_t)-1;
     }
     return (size_t)val;
  }
  
  
  #endif /* Py_PYTHON_H */
  