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static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
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static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, long level); /*proto*/

#define __pyx_PyComplex_FromComplex(z) \
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static CYTHON_INLINE signed long __Pyx_PyInt_AsSignedLong(PyObject *);

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static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb); /*proto*/
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static void __Pyx_WriteUnraisable(const char *name, int clineno,
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static int __Pyx_check_binary_version(void);

static void __Pyx_AddTraceback(const char *funcname, int __pyx_clineno,
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/* Module declarations from 'cython.cython.view' */

/* Module declarations from 'cython' */

/* Module declarations from 'scipy.special.lambertw' */
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static void *__pyx_v_5scipy_7special_8lambertw_the_func_to_apply[1];
static CYTHON_INLINE int __pyx_f_5scipy_7special_8lambertw_zisnan(__pyx_t_double_complex); /*proto*/
static CYTHON_INLINE double __pyx_f_5scipy_7special_8lambertw_zabs(__pyx_t_double_complex); /*proto*/
static CYTHON_INLINE __pyx_t_double_complex __pyx_f_5scipy_7special_8lambertw_zlog(__pyx_t_double_complex); /*proto*/
static CYTHON_INLINE __pyx_t_double_complex __pyx_f_5scipy_7special_8lambertw_zexp(__pyx_t_double_complex); /*proto*/
static void __pyx_f_5scipy_7special_8lambertw_lambertw_raise_warning(__pyx_t_double_complex); /*proto*/
static __pyx_t_double_complex __pyx_f_5scipy_7special_8lambertw_lambertw_scalar(__pyx_t_double_complex, long, double); /*proto*/
static void __pyx_f_5scipy_7special_8lambertw__apply_func_to_1d_vec(char **, npy_intp *, npy_intp *, void *); /*proto*/
#define __Pyx_MODULE_NAME "scipy.special.lambertw"
int __pyx_module_is_main_scipy__special__lambertw = 0;

/* Implementation of 'scipy.special.lambertw' */
static PyObject *__pyx_builtin_range;
static char __pyx_k_1[] = "Lambert W iteration failed to converge: %r";
static char __pyx_k_3[] = "";
static char __pyx_k_4[] = "scipy.special.lambertw";
static char __pyx_k_5[] = "lambertw (line 193)";
static char __pyx_k_6[] = "\n    lambertw(z, k=0, tol=1e-8)\n\n    Lambert W function.\n\n    The Lambert W function `W(z)` is defined as the inverse function\n    of :math:`w \\exp(w)`. In other words, the value of :math:`W(z)` is\n    such that :math:`z = W(z) \\exp(W(z))` for any complex number\n    :math:`z`.\n\n    The Lambert W function is a multivalued function with infinitely\n    many branches. Each branch gives a separate solution of the\n    equation :math:`w \\exp(w)`. Here, the branches are indexed by the\n    integer `k`.\n    \n    Parameters\n    ----------\n    z : array_like\n        Input argument\n    k : integer, optional\n        Branch index\n    tol : float\n        Evaluation tolerance\n\n    Notes\n    -----\n    All branches are supported by `lambertw`:\n\n    * ``lambertw(z)`` gives the principal solution (branch 0)\n    * ``lambertw(z, k)`` gives the solution on branch `k`\n\n    The Lambert W function has two partially real branches: the\n    principal branch (`k = 0`) is real for real `z > -1/e`, and the\n    `k = -1` branch is real for `-1/e < z < 0`. All branches except\n    `k = 0` have a logarithmic singularity at `z = 0`.\n\n    .. rubric:: Possible issues\n    \n    The evaluation can become inaccurate very close to the branch point\n    at `-1/e`. In some corner cases, :func:`lambertw` might currently\n    fail to converge, or can end up on the wrong branch.\n\n    .. rubric:: Algorithm\n\n    Halley's iteration is used to invert `w \\exp(w)`, using a first-order\n    asymptotic approximation (`O(\\log(w))` or `O(w)`) as the initial\n    estimate.\n\n    The definition, implementation and choice of branches is based\n    on Corless et al, \"On the Lambert W function\", Adv. Comp. Math. 5\n    (1996) 329-359, available online here:\n    http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf\n    \n    TODO: use a series expansion when extremely close to the branch point\n    at `-1/e` and make sure that the proper branch is chosen there\n\n    Examples""\n    --------\n    The Lambert W function is the inverse of `w \\exp(w)`::\n\n    >>> from scipy.special import lambertw\n    >>> w = lambertw(1)\n    >>> w\n    0.56714329040978387299996866221035555\n    >>> w*exp(w)\n    1.0\n\n    Any branch gives a valid inverse::\n\n    >>> w = lambertw(1, k=3)\n    >>> w\n    (-2.8535817554090378072068187234910812 +\n    17.113535539412145912607826671159289j)\n    >>> w*exp(w)\n    (1.0 + 3.5075477124212226194278700785075126e-36j)\n\n    .. rubric:: Applications to equation-solving\n\n    The Lambert W function may be used to solve various kinds of\n    equations, such as finding the value of the infinite power\n    tower `z^{z^{z^{\\ldots}}}`::\n\n    >>> def tower(z, n):\n    ... if n == 0:\n    ... return z\n    ... return z ** tower(z, n-1)\n    ...\n    >>> tower(0.5, 100)\n    0.641185744504986\n    >>> -lambertw(-log(0.5))/log(0.5)\n    0.6411857445049859844862004821148236665628209571911\n\n    .. rubric:: Properties\n\n    The Lambert W function grows roughly like the natural logarithm\n    for large arguments::\n\n    >>> lambertw(1000)\n    5.2496028524016\n    >>> log(1000)\n    6.90775527898214\n    >>> lambertw(10**100)\n    224.843106445119\n    >>> log(10**100)\n    230.258509299405\n    \n    The principal branch of the Lambert W function has a rational\n    Taylor series expansion around `z = 0`::\n    \n    >>> nprint(taylor(lambertw, 0, 6), 10)\n    [0.0, 1.0, -1.0, 1.5, -2.666666667, 5.208333333, -10.8]\n    \n    Some special values and limits are::\n    \n    >>> lambertw(0)\n    0.0\n    >>> lambertw(1)\n    0.567143290409784\n    >>> lambertw(e)\n    1.0\n    >>> lambertw(inf)\n    +inf\n    >>> lambertw(0, k=-1)\n    -inf\n    >>> lambertw(0, k=3)\n    -inf\n    >>> lambertw(inf, k=3)\n    (+inf + 18.8495559215388j)\n\n    The `k = 0` and `k = -1` branches join at `z = -1/e` where\n    `W(z) = -1` for both branches. Since `-1/e` can only be represented\n    approximately with mpmath numbers, evaluatin""g the Lambert W function\n    at this point only gives `-1` approximately::\n\n    >>> lambertw(-1/e, 0)\n    -0.999999999999837133022867\n    >>> lambertw(-1/e, -1)\n    -1.00000000000016286697718\n    \n    If `-1/e` happens to round in the negative direction, there might be\n    a small imaginary part::\n    \n    >>> lambertw(-1/e)\n    (-1.0 + 8.22007971511612e-9j)\n\n    ";
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static PyObject *__pyx_n_s__tol;
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/* "scipy/special/lambertw.pyx":44
 *     double NPY_PI
 * 
 * cdef inline bint zisnan(double complex x) nogil:             # <<<<<<<<<<<<<<
 *     return npy_isnan(x.real) or npy_isnan(x.imag)
 * 
 */

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  int __pyx_t_2;
  int __pyx_t_3;

  /* "scipy/special/lambertw.pyx":45
 * 
 * cdef inline bint zisnan(double complex x) nogil:
 *     return npy_isnan(x.real) or npy_isnan(x.imag)             # <<<<<<<<<<<<<<
 * 
 * cdef inline double zabs(double complex x) nogil:
 */
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/* "scipy/special/lambertw.pyx":47
 *     return npy_isnan(x.real) or npy_isnan(x.imag)
 * 
 * cdef inline double zabs(double complex x) nogil:             # <<<<<<<<<<<<<<
 *     cdef double r
 *     r = npy_cabs((<npy_cdouble*>&x)[0])
 */

static CYTHON_INLINE double __pyx_f_5scipy_7special_8lambertw_zabs(__pyx_t_double_complex __pyx_v_x) {
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  double __pyx_r;

  /* "scipy/special/lambertw.pyx":49
 * cdef inline double zabs(double complex x) nogil:
 *     cdef double r
 *     r = npy_cabs((<npy_cdouble*>&x)[0])             # <<<<<<<<<<<<<<
 *     return r
 * 
 */
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  /* "scipy/special/lambertw.pyx":50
 *     cdef double r
 *     r = npy_cabs((<npy_cdouble*>&x)[0])
 *     return r             # <<<<<<<<<<<<<<
 * 
 * cdef inline double complex zlog(double complex x) nogil:
 */
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/* "scipy/special/lambertw.pyx":52
 *     return r
 * 
 * cdef inline double complex zlog(double complex x) nogil:             # <<<<<<<<<<<<<<
 *     cdef npy_cdouble r
 *     r = npy_clog((<npy_cdouble*>&x)[0])
 */

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  __pyx_t_double_complex __pyx_r;

  /* "scipy/special/lambertw.pyx":54
 * cdef inline double complex zlog(double complex x) nogil:
 *     cdef npy_cdouble r
 *     r = npy_clog((<npy_cdouble*>&x)[0])             # <<<<<<<<<<<<<<
 *     return (<double complex*>&r)[0]
 * 
 */
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  /* "scipy/special/lambertw.pyx":55
 *     cdef npy_cdouble r
 *     r = npy_clog((<npy_cdouble*>&x)[0])
 *     return (<double complex*>&r)[0]             # <<<<<<<<<<<<<<
 * 
 * cdef inline double complex zexp(double complex x) nogil:
 */
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  __pyx_L0:;
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}

/* "scipy/special/lambertw.pyx":57
 *     return (<double complex*>&r)[0]
 * 
 * cdef inline double complex zexp(double complex x) nogil:             # <<<<<<<<<<<<<<
 *     cdef npy_cdouble r
 *     r = npy_cexp((<npy_cdouble*>&x)[0])
 */

static CYTHON_INLINE __pyx_t_double_complex __pyx_f_5scipy_7special_8lambertw_zexp(__pyx_t_double_complex __pyx_v_x) {
  npy_cdouble __pyx_v_r;
  __pyx_t_double_complex __pyx_r;

  /* "scipy/special/lambertw.pyx":59
 * cdef inline double complex zexp(double complex x) nogil:
 *     cdef npy_cdouble r
 *     r = npy_cexp((<npy_cdouble*>&x)[0])             # <<<<<<<<<<<<<<
 *     return (<double complex*>&r)[0]
 * 
 */
  __pyx_v_r = npy_cexp((((npy_cdouble *)(&__pyx_v_x))[0]));

  /* "scipy/special/lambertw.pyx":60
 *     cdef npy_cdouble r
 *     r = npy_cexp((<npy_cdouble*>&x)[0])
 *     return (<double complex*>&r)[0]             # <<<<<<<<<<<<<<
 * 
 * cdef void lambertw_raise_warning(double complex z) with gil:
 */
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  goto __pyx_L0;

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  __pyx_L0:;
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}

/* "scipy/special/lambertw.pyx":62
 *     return (<double complex*>&r)[0]
 * 
 * cdef void lambertw_raise_warning(double complex z) with gil:             # <<<<<<<<<<<<<<
 *     warnings.warn("Lambert W iteration failed to converge: %r" % z)
 * 
 */

static void __pyx_f_5scipy_7special_8lambertw_lambertw_raise_warning(__pyx_t_double_complex __pyx_v_z) {
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 * 
 * cdef void lambertw_raise_warning(double complex z) with gil:
 *     warnings.warn("Lambert W iteration failed to converge: %r" % z)             # <<<<<<<<<<<<<<
 * 
 * # Heavy lifting is here:
 */
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/* "scipy/special/lambertw.pyx":68
 * 
 * @cython.cdivision(True)
 * cdef double complex lambertw_scalar(double complex z, long k, double tol) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     This is just the implementation of W for a single input z.
 */

static __pyx_t_double_complex __pyx_f_5scipy_7special_8lambertw_lambertw_scalar(__pyx_t_double_complex __pyx_v_z, long __pyx_v_k, double __pyx_v_tol) {
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  __pyx_t_double_complex __pyx_v_wn;
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  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;
  int __pyx_t_4;
  int __pyx_t_5;

  /* "scipy/special/lambertw.pyx":74
 *     """
 *     # Comments copied verbatim from [2] are marked with '>'
 *     if zisnan(z):             # <<<<<<<<<<<<<<
 *         return z
 * 
 */
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    /* "scipy/special/lambertw.pyx":75
 *     # Comments copied verbatim from [2] are marked with '>'
 *     if zisnan(z):
 *         return z             # <<<<<<<<<<<<<<
 * 
 *     # Return value:
 */
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    goto __pyx_L3;
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  /* "scipy/special/lambertw.pyx":82
 *     #> We must be extremely careful near the singularities at -1/e and 0
 *     cdef double u
 *     u = exp(-1)             # <<<<<<<<<<<<<<
 * 
 *     cdef double absz
 */
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  /* "scipy/special/lambertw.pyx":85
 * 
 *     cdef double absz
 *     absz = zabs(z)             # <<<<<<<<<<<<<<
 *     if absz <= u:
 *         if z == 0:
 */
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  /* "scipy/special/lambertw.pyx":86
 *     cdef double absz
 *     absz = zabs(z)
 *     if absz <= u:             # <<<<<<<<<<<<<<
 *         if z == 0:
 *             #> w(0,0) = 0; for all other branches we hit the pole
 */
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    /* "scipy/special/lambertw.pyx":87
 *     absz = zabs(z)
 *     if absz <= u:
 *         if z == 0:             # <<<<<<<<<<<<<<
 *             #> w(0,0) = 0; for all other branches we hit the pole
 *             if k == 0:
 */
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 *         if z == 0:
 *             #> w(0,0) = 0; for all other branches we hit the pole
 *             if k == 0:             # <<<<<<<<<<<<<<
 *                 return z
 *             return -NPY_INFINITY
 */
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        /* "scipy/special/lambertw.pyx":90
 *             #> w(0,0) = 0; for all other branches we hit the pole
 *             if k == 0:
 *                 return z             # <<<<<<<<<<<<<<
 *             return -NPY_INFINITY
 * 
 */
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      /* "scipy/special/lambertw.pyx":91
 *             if k == 0:
 *                 return z
 *             return -NPY_INFINITY             # <<<<<<<<<<<<<<
 * 
 *         if k == 0:
 */
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      goto __pyx_L5;
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    __pyx_L5:;

    /* "scipy/special/lambertw.pyx":93
 *             return -NPY_INFINITY
 * 
 *         if k == 0:             # <<<<<<<<<<<<<<
 *             w = z # Initial guess for iteration
 *         #> For small real z < 0, the -1 branch beaves roughly like log(-z)
 */
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      /* "scipy/special/lambertw.pyx":94
 * 
 *         if k == 0:
 *             w = z # Initial guess for iteration             # <<<<<<<<<<<<<<
 *         #> For small real z < 0, the -1 branch beaves roughly like log(-z)
 *         elif k == -1 and z.imag ==0 and z.real < 0:
 */
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    /* "scipy/special/lambertw.pyx":96
 *             w = z # Initial guess for iteration
 *         #> For small real z < 0, the -1 branch beaves roughly like log(-z)
 *         elif k == -1 and z.imag ==0 and z.real < 0:             # <<<<<<<<<<<<<<
 *             w = log(-z.real)
 *         #> Use a simple asymptotic approximation.
 */
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      /* "scipy/special/lambertw.pyx":97
 *         #> For small real z < 0, the -1 branch beaves roughly like log(-z)
 *         elif k == -1 and z.imag ==0 and z.real < 0:
 *             w = log(-z.real)             # <<<<<<<<<<<<<<
 *         #> Use a simple asymptotic approximation.
 *         else:
 */
      __pyx_v_w = __pyx_t_double_complex_from_parts(log((-__Pyx_CREAL(__pyx_v_z))), 0);
      goto __pyx_L7;
    }
    /*else*/ {

      /* "scipy/special/lambertw.pyx":100
 *         #> Use a simple asymptotic approximation.
 *         else:
 *             w = zlog(z)             # <<<<<<<<<<<<<<
 *             #> The branches are roughly logarithmic. This approximation
 *             #> gets better for large |k|; need to check that this always
 */
      __pyx_v_w = __pyx_f_5scipy_7special_8lambertw_zlog(__pyx_v_z);

      /* "scipy/special/lambertw.pyx":104
 *             #> gets better for large |k|; need to check that this always
 *             #> works for k ~= -1, 0, 1.
 *             if k: w = w + k*2*NPY_PI*1j             # <<<<<<<<<<<<<<
 * 
 *     elif k == 0 and z.imag and zabs(z) <= 0.7:
 */
      if (__pyx_v_k) {
        __pyx_v_w = __Pyx_c_sum(__pyx_v_w, __Pyx_c_prod(__pyx_t_double_complex_from_parts(((__pyx_v_k * 2) * NPY_PI), 0), __pyx_t_double_complex_from_parts(0, 1.0)));
        goto __pyx_L8;
      }
      __pyx_L8:;
    }
    __pyx_L7:;
    goto __pyx_L4;
  }

  /* "scipy/special/lambertw.pyx":106
 *             if k: w = w + k*2*NPY_PI*1j
 * 
 *     elif k == 0 and z.imag and zabs(z) <= 0.7:             # <<<<<<<<<<<<<<
 *         #> Both the W(z) ~= z and W(z) ~= ln(z) approximations break
 *         #> down around z ~= -0.5 (converging to the wrong branch), so patch
 */
  __pyx_t_2 = (__pyx_v_k == 0);
  if (__pyx_t_2) {
    if ((__Pyx_CIMAG(__pyx_v_z) != 0)) {
      __pyx_t_1 = (__pyx_f_5scipy_7special_8lambertw_zabs(__pyx_v_z) <= 0.7);
      __pyx_t_4 = __pyx_t_1;
    } else {
      __pyx_t_4 = (__Pyx_CIMAG(__pyx_v_z) != 0);
    }
    __pyx_t_1 = __pyx_t_4;
  } else {
    __pyx_t_1 = __pyx_t_2;
  }
  if (__pyx_t_1) {

    /* "scipy/special/lambertw.pyx":110
 *         #> down around z ~= -0.5 (converging to the wrong branch), so patch
 *         #> with a constant approximation (adjusted for sign)
 *         if zabs(z+0.5) < 0.1:             # <<<<<<<<<<<<<<
 *             if z.imag > 0:
 *                 w = 0.7 + 0.7j
 */
    __pyx_t_1 = (__pyx_f_5scipy_7special_8lambertw_zabs(__Pyx_c_sum(__pyx_v_z, __pyx_t_double_complex_from_parts(0.5, 0))) < 0.1);
    if (__pyx_t_1) {

      /* "scipy/special/lambertw.pyx":111
 *         #> with a constant approximation (adjusted for sign)
 *         if zabs(z+0.5) < 0.1:
 *             if z.imag > 0:             # <<<<<<<<<<<<<<
 *                 w = 0.7 + 0.7j
 *             else:
 */
      __pyx_t_1 = (__Pyx_CIMAG(__pyx_v_z) > 0.0);
      if (__pyx_t_1) {

        /* "scipy/special/lambertw.pyx":112
 *         if zabs(z+0.5) < 0.1:
 *             if z.imag > 0:
 *                 w = 0.7 + 0.7j             # <<<<<<<<<<<<<<
 *             else:
 *                 w = 0.7 - 0.7j
 */
        __pyx_v_w = __Pyx_c_sum(__pyx_t_double_complex_from_parts(0.7, 0), __pyx_t_double_complex_from_parts(0, 0.69999999999999996));
        goto __pyx_L10;
      }
      /*else*/ {

        /* "scipy/special/lambertw.pyx":114
 *                 w = 0.7 + 0.7j
 *             else:
 *                 w = 0.7 - 0.7j             # <<<<<<<<<<<<<<
 *         else:
 *             w = z
 */
        __pyx_v_w = __Pyx_c_diff(__pyx_t_double_complex_from_parts(0.7, 0), __pyx_t_double_complex_from_parts(0, 0.69999999999999996));
      }
      __pyx_L10:;
      goto __pyx_L9;
    }
    /*else*/ {

      /* "scipy/special/lambertw.pyx":116
 *                 w = 0.7 - 0.7j
 *         else:
 *             w = z             # <<<<<<<<<<<<<<
 * 
 *     else:
 */
      __pyx_v_w = __pyx_v_z;
    }
    __pyx_L9:;
    goto __pyx_L4;
  }
  /*else*/ {

    /* "scipy/special/lambertw.pyx":119
 * 
 *     else:
 *         if z.real == NPY_INFINITY:             # <<<<<<<<<<<<<<
 *             if k == 0:
 *                 return z
 */
    __pyx_t_1 = (__Pyx_CREAL(__pyx_v_z) == NPY_INFINITY);
    if (__pyx_t_1) {

      /* "scipy/special/lambertw.pyx":120
 *     else:
 *         if z.real == NPY_INFINITY:
 *             if k == 0:             # <<<<<<<<<<<<<<
 *                 return z
 *             else:
 */
      __pyx_t_1 = (__pyx_v_k == 0);
      if (__pyx_t_1) {

        /* "scipy/special/lambertw.pyx":121
 *         if z.real == NPY_INFINITY:
 *             if k == 0:
 *                 return z             # <<<<<<<<<<<<<<
 *             else:
 *                 return z + 2*k*NPY_PI*1j
 */
        __pyx_r = __pyx_v_z;
        goto __pyx_L0;
        goto __pyx_L12;
      }
      /*else*/ {

        /* "scipy/special/lambertw.pyx":123
 *                 return z
 *             else:
 *                 return z + 2*k*NPY_PI*1j             # <<<<<<<<<<<<<<
 * 
 *         if z.real == -NPY_INFINITY:
 */
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        goto __pyx_L0;
      }
      __pyx_L12:;
      goto __pyx_L11;
    }
    __pyx_L11:;

    /* "scipy/special/lambertw.pyx":125
 *                 return z + 2*k*NPY_PI*1j
 * 
 *         if z.real == -NPY_INFINITY:             # <<<<<<<<<<<<<<
 *             return (-z) + (2*k+1)*NPY_PI*1j
 * 
 */
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    if (__pyx_t_1) {

      /* "scipy/special/lambertw.pyx":126
 * 
 *         if z.real == -NPY_INFINITY:
 *             return (-z) + (2*k+1)*NPY_PI*1j             # <<<<<<<<<<<<<<
 * 
 *         #> Simple asymptotic approximation as above
 */
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      goto __pyx_L0;
      goto __pyx_L13;
    }
    __pyx_L13:;

    /* "scipy/special/lambertw.pyx":129
 * 
 *         #> Simple asymptotic approximation as above
 *         w = zlog(z)             # <<<<<<<<<<<<<<
 *         if k: w = w + k*2*NPY_PI*1j
 * 
 */
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    /* "scipy/special/lambertw.pyx":130
 *         #> Simple asymptotic approximation as above
 *         w = zlog(z)
 *         if k: w = w + k*2*NPY_PI*1j             # <<<<<<<<<<<<<<
 * 
 *     #> Use Halley iteration to solve w*exp(w) = z
 */
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      __pyx_v_w = __Pyx_c_sum(__pyx_v_w, __Pyx_c_prod(__pyx_t_double_complex_from_parts(((__pyx_v_k * 2) * NPY_PI), 0), __pyx_t_double_complex_from_parts(0, 1.0)));
      goto __pyx_L14;
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    __pyx_L14:;
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  __pyx_L4:;

  /* "scipy/special/lambertw.pyx":135
 *     cdef double complex ew, wew, wewz, wn
 *     cdef int i
 *     for i in range(100):             # <<<<<<<<<<<<<<
 *         ew = zexp(w)
 *         wew = w*ew
 */
  for (__pyx_t_5 = 0; __pyx_t_5 < 100; __pyx_t_5+=1) {
    __pyx_v_i = __pyx_t_5;

    /* "scipy/special/lambertw.pyx":136
 *     cdef int i
 *     for i in range(100):
 *         ew = zexp(w)             # <<<<<<<<<<<<<<
 *         wew = w*ew
 *         wewz = wew-z
 */
    __pyx_v_ew = __pyx_f_5scipy_7special_8lambertw_zexp(__pyx_v_w);

    /* "scipy/special/lambertw.pyx":137
 *     for i in range(100):
 *         ew = zexp(w)
 *         wew = w*ew             # <<<<<<<<<<<<<<
 *         wewz = wew-z
 *         wn = w - wewz / (wew + ew - (w + 2)*wewz/(2*w + 2))
 */
    __pyx_v_wew = __Pyx_c_prod(__pyx_v_w, __pyx_v_ew);

    /* "scipy/special/lambertw.pyx":138
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 *         wew = w*ew
 *         wewz = wew-z             # <<<<<<<<<<<<<<
 *         wn = w - wewz / (wew + ew - (w + 2)*wewz/(2*w + 2))
 *         if zabs(wn-w) < tol*zabs(wn):
 */
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    /* "scipy/special/lambertw.pyx":139
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 *         wewz = wew-z
 *         wn = w - wewz / (wew + ew - (w + 2)*wewz/(2*w + 2))             # <<<<<<<<<<<<<<
 *         if zabs(wn-w) < tol*zabs(wn):
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    /* "scipy/special/lambertw.pyx":140
 *         wewz = wew-z
 *         wn = w - wewz / (wew + ew - (w + 2)*wewz/(2*w + 2))
 *         if zabs(wn-w) < tol*zabs(wn):             # <<<<<<<<<<<<<<
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 *         else:
 */
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      /* "scipy/special/lambertw.pyx":141
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 *         if zabs(wn-w) < tol*zabs(wn):
 *             return wn             # <<<<<<<<<<<<<<
 *         else:
 *             w = wn
 */
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      goto __pyx_L17;
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      /* "scipy/special/lambertw.pyx":143
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 *         else:
 *             w = wn             # <<<<<<<<<<<<<<
 * 
 *     lambertw_raise_warning(z)
 */
      __pyx_v_w = __pyx_v_wn;
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    __pyx_L17:;
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  /* "scipy/special/lambertw.pyx":145
 *             w = wn
 * 
 *     lambertw_raise_warning(z)             # <<<<<<<<<<<<<<
 *     return wn
 * 
 */
  __pyx_f_5scipy_7special_8lambertw_lambertw_raise_warning(__pyx_v_z);

  /* "scipy/special/lambertw.pyx":146
 * 
 *     lambertw_raise_warning(z)
 *     return wn             # <<<<<<<<<<<<<<
 * 
 * 
 */
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  goto __pyx_L0;

  __pyx_r = __pyx_t_double_complex_from_parts(0, 0);
  __pyx_L0:;
  return __pyx_r;
}

/* "scipy/special/lambertw.pyx":166
 *         int identity, char* name, char* doc, int c)
 * 
 * cdef void _apply_func_to_1d_vec(char **args, npy_intp *dimensions, npy_intp *steps,             # <<<<<<<<<<<<<<
 *                      void *func) nogil:
 *     cdef npy_intp i
 */

static void __pyx_f_5scipy_7special_8lambertw__apply_func_to_1d_vec(char **__pyx_v_args, npy_intp *__pyx_v_dimensions, npy_intp *__pyx_v_steps, void *__pyx_v_func) {
  npy_intp __pyx_v_i;
  char *__pyx_v_ip1;
  char *__pyx_v_ip2;
  char *__pyx_v_ip3;
  char *__pyx_v_op;
  npy_intp __pyx_t_1;
  npy_intp __pyx_t_2;

  /* "scipy/special/lambertw.pyx":169
 *                      void *func) nogil:
 *     cdef npy_intp i
 *     cdef char *ip1=args[0], *ip2=args[1], *ip3=args[2], *op=args[3]             # <<<<<<<<<<<<<<
 *     for i in range(0, dimensions[0]):
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 */
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  __pyx_v_op = (__pyx_v_args[3]);

  /* "scipy/special/lambertw.pyx":170
 *     cdef npy_intp i
 *     cdef char *ip1=args[0], *ip2=args[1], *ip3=args[2], *op=args[3]
 *     for i in range(0, dimensions[0]):             # <<<<<<<<<<<<<<
 *         (<double complex*>op)[0] = (<double complex(*)(double complex, long, double) nogil>func)(
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 */
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    /* "scipy/special/lambertw.pyx":171
 *     cdef char *ip1=args[0], *ip2=args[1], *ip3=args[2], *op=args[3]
 *     for i in range(0, dimensions[0]):
 *         (<double complex*>op)[0] = (<double complex(*)(double complex, long, double) nogil>func)(             # <<<<<<<<<<<<<<
 *             (<double complex*>ip1)[0], (<long*>ip2)[0], (<double*>ip3)[0])
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 */
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    /* "scipy/special/lambertw.pyx":173
 *         (<double complex*>op)[0] = (<double complex(*)(double complex, long, double) nogil>func)(
 *             (<double complex*>ip1)[0], (<long*>ip2)[0], (<double*>ip3)[0])
 *         ip1 += steps[0]; ip2 += steps[1]; ip3 += steps[2]; op += steps[3]             # <<<<<<<<<<<<<<
 * 
 * cdef PyUFuncGenericFunction _loop_funcs[1]
 */
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}

/* "scipy/special/lambertw.pyx":193
 *     _inp_outp_types, 1, 3, 1, 0, "", "", 0)
 * 
 * def lambertw(z, k=0, tol=1e-8):             # <<<<<<<<<<<<<<
 *     r"""
 *     lambertw(z, k=0, tol=1e-8)
 */

static PyObject *__pyx_pf_5scipy_7special_8lambertw_lambertw(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static char __pyx_doc_5scipy_7special_8lambertw_lambertw[] = "\n    lambertw(z, k=0, tol=1e-8)\n\n    Lambert W function.\n\n    The Lambert W function `W(z)` is defined as the inverse function\n    of :math:`w \\exp(w)`. In other words, the value of :math:`W(z)` is\n    such that :math:`z = W(z) \\exp(W(z))` for any complex number\n    :math:`z`.\n\n    The Lambert W function is a multivalued function with infinitely\n    many branches. Each branch gives a separate solution of the\n    equation :math:`w \\exp(w)`. Here, the branches are indexed by the\n    integer `k`.\n    \n    Parameters\n    ----------\n    z : array_like\n        Input argument\n    k : integer, optional\n        Branch index\n    tol : float\n        Evaluation tolerance\n\n    Notes\n    -----\n    All branches are supported by `lambertw`:\n\n    * ``lambertw(z)`` gives the principal solution (branch 0)\n    * ``lambertw(z, k)`` gives the solution on branch `k`\n\n    The Lambert W function has two partially real branches: the\n    principal branch (`k = 0`) is real for real `z > -1/e`, and the\n    `k = -1` branch is real for `-1/e < z < 0`. All branches except\n    `k = 0` have a logarithmic singularity at `z = 0`.\n\n    .. rubric:: Possible issues\n    \n    The evaluation can become inaccurate very close to the branch point\n    at `-1/e`. In some corner cases, :func:`lambertw` might currently\n    fail to converge, or can end up on the wrong branch.\n\n    .. rubric:: Algorithm\n\n    Halley's iteration is used to invert `w \\exp(w)`, using a first-order\n    asymptotic approximation (`O(\\log(w))` or `O(w)`) as the initial\n    estimate.\n\n    The definition, implementation and choice of branches is based\n    on Corless et al, \"On the Lambert W function\", Adv. Comp. Math. 5\n    (1996) 329-359, available online here:\n    http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf\n    \n    TODO: use a series expansion when extremely close to the branch point\n    at `-1/e` and make sure that the proper branch is chosen there\n\n    Examples""\n    --------\n    The Lambert W function is the inverse of `w \\exp(w)`::\n\n    >>> from scipy.special import lambertw\n    >>> w = lambertw(1)\n    >>> w\n    0.56714329040978387299996866221035555\n    >>> w*exp(w)\n    1.0\n\n    Any branch gives a valid inverse::\n\n    >>> w = lambertw(1, k=3)\n    >>> w\n    (-2.8535817554090378072068187234910812 +\n    17.113535539412145912607826671159289j)\n    >>> w*exp(w)\n    (1.0 + 3.5075477124212226194278700785075126e-36j)\n\n    .. rubric:: Applications to equation-solving\n\n    The Lambert W function may be used to solve various kinds of\n    equations, such as finding the value of the infinite power\n    tower `z^{z^{z^{\\ldots}}}`::\n\n    >>> def tower(z, n):\n    ... if n == 0:\n    ... return z\n    ... return z ** tower(z, n-1)\n    ...\n    >>> tower(0.5, 100)\n    0.641185744504986\n    >>> -lambertw(-log(0.5))/log(0.5)\n    0.6411857445049859844862004821148236665628209571911\n\n    .. rubric:: Properties\n\n    The Lambert W function grows roughly like the natural logarithm\n    for large arguments::\n\n    >>> lambertw(1000)\n    5.2496028524016\n    >>> log(1000)\n    6.90775527898214\n    >>> lambertw(10**100)\n    224.843106445119\n    >>> log(10**100)\n    230.258509299405\n    \n    The principal branch of the Lambert W function has a rational\n    Taylor series expansion around `z = 0`::\n    \n    >>> nprint(taylor(lambertw, 0, 6), 10)\n    [0.0, 1.0, -1.0, 1.5, -2.666666667, 5.208333333, -10.8]\n    \n    Some special values and limits are::\n    \n    >>> lambertw(0)\n    0.0\n    >>> lambertw(1)\n    0.567143290409784\n    >>> lambertw(e)\n    1.0\n    >>> lambertw(inf)\n    +inf\n    >>> lambertw(0, k=-1)\n    -inf\n    >>> lambertw(0, k=3)\n    -inf\n    >>> lambertw(inf, k=3)\n    (+inf + 18.8495559215388j)\n\n    The `k = 0` and `k = -1` branches join at `z = -1/e` where\n    `W(z) = -1` for both branches. Since `-1/e` can only be represented\n    approximately with mpmath numbers, evaluatin""g the Lambert W function\n    at this point only gives `-1` approximately::\n\n    >>> lambertw(-1/e, 0)\n    -0.999999999999837133022867\n    >>> lambertw(-1/e, -1)\n    -1.00000000000016286697718\n    \n    If `-1/e` happens to round in the negative direction, there might be\n    a small imaginary part::\n    \n    >>> lambertw(-1/e)\n    (-1.0 + 8.22007971511612e-9j)\n\n    ";
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            if (unlikely(!PyUnicode_CheckExact(key)) && unlikely(!PyUnicode_Check(key))) {
            #endif
                goto invalid_keyword_type;
            } else {
                for (name = first_kw_arg; *name; name++) {
                    #if PY_MAJOR_VERSION >= 3
                    if (PyUnicode_GET_SIZE(**name) == PyUnicode_GET_SIZE(key) &&
                        PyUnicode_Compare(**name, key) == 0) break;
                    #else
                    if (PyString_GET_SIZE(**name) == PyString_GET_SIZE(key) &&
                        _PyString_Eq(**name, key)) break;
                    #endif
                }
                if (*name) {
                    values[name-argnames] = value;
                } else {
                    /* unexpected keyword found */
                    for (name=argnames; name != first_kw_arg; name++) {
                        if (**name == key) goto arg_passed_twice;
                        #if PY_MAJOR_VERSION >= 3
                        if (PyUnicode_GET_SIZE(**name) == PyUnicode_GET_SIZE(key) &&
                            PyUnicode_Compare(**name, key) == 0) goto arg_passed_twice;
                        #else
                        if (PyString_GET_SIZE(**name) == PyString_GET_SIZE(key) &&
                            _PyString_Eq(**name, key)) goto arg_passed_twice;
                        #endif
                    }
                    if (kwds2) {
                        if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
                    } else {
                        goto invalid_keyword;
                    }
                }
            }
        }
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, **name);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%s() keywords must be strings", function_name);
    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%s() got an unexpected keyword argument '%s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
bad:
    return -1;
}

static void __Pyx_RaiseArgtupleInvalid(
    const char* func_name,
    int exact,
    Py_ssize_t num_min,
    Py_ssize_t num_max,
    Py_ssize_t num_found)
{
    Py_ssize_t num_expected;
    const char *more_or_less;

    if (num_found < num_min) {
        num_expected = num_min;
        more_or_less = "at least";
    } else {
        num_expected = num_max;
        more_or_less = "at most";
    }
    if (exact) {
        more_or_less = "exactly";
    }
    PyErr_Format(PyExc_TypeError,
                 "%s() takes %s %"PY_FORMAT_SIZE_T"d positional argument%s (%"PY_FORMAT_SIZE_T"d given)",
                 func_name, more_or_less, num_expected,
                 (num_expected == 1) ? "" : "s", num_found);
}

#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;
    }
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrt(z.real*z.real + z.imag*z.imag);
          #else
            return hypot(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow(__pyx_t_double_complex a, __pyx_t_double_complex b) {
            __pyx_t_double_complex z;
            double r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    double denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(a, a);
                    case 3:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, a);
                    case 4:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_abs(a);
                theta = atan2(a.imag, a.real);
            }
            lnr = log(r);
            z_r = exp(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cos(z_theta);
            z.imag = z_r * sin(z_theta);
            return z;
        }
    #endif
#endif

static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, long level) {
    PyObject *py_import = 0;
    PyObject *empty_list = 0;
    PyObject *module = 0;
    PyObject *global_dict = 0;
    PyObject *empty_dict = 0;
    PyObject *list;
    py_import = __Pyx_GetAttrString(__pyx_b, "__import__");
    if (!py_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;
    #if PY_VERSION_HEX >= 0x02050000
    {
        PyObject *py_level = PyInt_FromLong(level);
        if (!py_level)
            goto bad;
        module = PyObject_CallFunctionObjArgs(py_import,
            name, global_dict, empty_dict, list, py_level, NULL);
        Py_DECREF(py_level);
    }
    #else
    if (level>0) {
        PyErr_SetString(PyExc_RuntimeError, "Relative import is not supported for Python <=2.4.");
        goto bad;
    }
    module = PyObject_CallFunctionObjArgs(py_import,
        name, global_dict, empty_dict, list, NULL);
    #endif
bad:
    Py_XDECREF(empty_list);
    Py_XDECREF(py_import);
    Py_XDECREF(empty_dict);
    return module;
}

static CYTHON_INLINE PyObject *__Pyx_PyInt_to_py_npy_intp(npy_intp val) {
    const npy_intp neg_one = (npy_intp)-1, const_zero = (npy_intp)0;
    const int is_unsigned = const_zero < neg_one;
    if ((sizeof(npy_intp) == sizeof(char))  ||
        (sizeof(npy_intp) == sizeof(short))) {
        return PyInt_FromLong((long)val);
    } else if ((sizeof(npy_intp) == sizeof(int)) ||
               (sizeof(npy_intp) == sizeof(long))) {
        if (is_unsigned)
            return PyLong_FromUnsignedLong((unsigned long)val);
        else
            return PyInt_FromLong((long)val);
    } else if (sizeof(npy_intp) == sizeof(PY_LONG_LONG)) {
        if (is_unsigned)
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG)val);
        else
            return PyLong_FromLongLong((PY_LONG_LONG)val);
    } else {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&val;
        return _PyLong_FromByteArray(bytes, sizeof(npy_intp),
                                     little, !is_unsigned);
    }
}

static CYTHON_INLINE npy_intp __Pyx_PyInt_from_py_npy_intp(PyObject* x) {
    const npy_intp neg_one = (npy_intp)-1, const_zero = (npy_intp)0;
    const int is_unsigned = const_zero < neg_one;
    if (sizeof(npy_intp) == sizeof(char)) {
        if (is_unsigned)
            return (npy_intp)__Pyx_PyInt_AsUnsignedChar(x);
        else
            return (npy_intp)__Pyx_PyInt_AsSignedChar(x);
    } else if (sizeof(npy_intp) == sizeof(short)) {
        if (is_unsigned)
            return (npy_intp)__Pyx_PyInt_AsUnsignedShort(x);
        else
            return (npy_intp)__Pyx_PyInt_AsSignedShort(x);
    } else if (sizeof(npy_intp) == sizeof(int)) {
        if (is_unsigned)
            return (npy_intp)__Pyx_PyInt_AsUnsignedInt(x);
        else
            return (npy_intp)__Pyx_PyInt_AsSignedInt(x);
    } else if (sizeof(npy_intp) == sizeof(long)) {
        if (is_unsigned)
            return (npy_intp)__Pyx_PyInt_AsUnsignedLong(x);
        else
            return (npy_intp)__Pyx_PyInt_AsSignedLong(x);
    } else if (sizeof(npy_intp) == sizeof(PY_LONG_LONG)) {
        if (is_unsigned)
            return (npy_intp)__Pyx_PyInt_AsUnsignedLongLong(x);
        else
            return (npy_intp)__Pyx_PyInt_AsSignedLongLong(x);
    }  else {
        npy_intp val;
        PyObject *v = __Pyx_PyNumber_Int(x);
        #if PY_VERSION_HEX < 0x03000000
        if (likely(v) && !PyLong_Check(v)) {
            PyObject *tmp = v;
            v = PyNumber_Long(tmp);
            Py_DECREF(tmp);
        }
        #endif
        if (likely(v)) {
            int one = 1; int is_little = (int)*(unsigned char *)&one;
            unsigned char *bytes = (unsigned char *)&val;
            int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                          bytes, sizeof(val),
                                          is_little, !is_unsigned);
            Py_DECREF(v);
            if (likely(!ret))
                return val;
        }
        return (npy_intp)-1;
    }
}

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 int __Pyx_PyInt_AsLongDouble(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 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 (unsigned long)PyLong_AsUnsignedLong(x);
        } else {
            return (unsigned long)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 (unsigned PY_LONG_LONG)PyLong_AsUnsignedLongLong(x);
        } else {
            return (unsigned PY_LONG_LONG)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 (long)PyLong_AsUnsignedLong(x);
        } else {
            return (long)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 (PY_LONG_LONG)PyLong_AsUnsignedLongLong(x);
        } else {
            return (PY_LONG_LONG)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 (signed long)PyLong_AsUnsignedLong(x);
        } else {
            return (signed long)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 (signed PY_LONG_LONG)PyLong_AsUnsignedLongLong(x);
        } else {
            return (signed PY_LONG_LONG)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;
    }
}

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 void __Pyx_WriteUnraisable(const char *name, int clineno,
                                  int lineno, const char *filename) {
    PyObject *old_exc, *old_val, *old_tb;
    PyObject *ctx;
    __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
    #if PY_MAJOR_VERSION < 3
    ctx = PyString_FromString(name);
    #else
    ctx = PyUnicode_FromString(name);
    #endif
    __Pyx_ErrRestore(old_exc, old_val, old_tb);
    if (!ctx) {
        PyErr_WriteUnraisable(Py_None);
    } else {
        PyErr_WriteUnraisable(ctx);
        Py_DECREF(ctx);
    }
}

static int __Pyx_check_binary_version(void) {
    char ctversion[4], rtversion[4];
    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
        char message[200];
        PyOS_snprintf(message, sizeof(message),
                      "compiletime version %s of module '%.100s' "
                      "does not match runtime version %s",
                      ctversion, __Pyx_MODULE_NAME, rtversion);
        #if PY_VERSION_HEX < 0x02050000
        return PyErr_Warn(NULL, message);
        #else
        return PyErr_WarnEx(NULL, message, 1);
        #endif
    }
    return 0;
}

#include "compile.h"
#include "frameobject.h"
#include "traceback.h"

static void __Pyx_AddTraceback(const char *funcname, int __pyx_clineno,
                               int __pyx_lineno, const char *__pyx_filename) {
    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) {
   int is_true = x == Py_True;
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
   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 */