/* Generated by Cython 0.25 */

/* BEGIN: Cython Metadata
{
    "distutils": {
        "depends": [
            "yt/utilities/lib/platform_dep.h"
        ], 
        "libraries": [
            "m"
        ]
    }, 
    "module_name": "yt.utilities.lib.element_mappings"
}
END: Cython Metadata */

#define PY_SSIZE_T_CLEAN
#include "Python.h"
#ifndef Py_PYTHON_H
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#define CYTHON_ABI "0_25"
#include <stddef.h>
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#ifndef Py_HUGE_VAL
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  #define CYTHON_USE_UNICODE_INTERNALS 0
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  #define CYTHON_USE_UNICODE_WRITER 0
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  #define CYTHON_USE_PYLONG_INTERNALS 0
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  #define CYTHON_UNPACK_METHODS 0
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  #define __Pyx_PyCode_HasFreeVars(co)  PyCode_HasFreeVars(co)
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#if PY_MAJOR_VERSION >= 3
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#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)

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#if defined(WIN32) || defined(MS_WINDOWS)
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#include <math.h>
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#define __PYX_NAN() ((float) NAN)
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static CYTHON_INLINE float __PYX_NAN() {
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#if PY_MAJOR_VERSION >= 3
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#define __PYX_HAVE__yt__utilities__lib__element_mappings
#define __PYX_HAVE_API__yt__utilities__lib__element_mappings
#include <string.h>
#include <stdio.h>
#include <stdlib.h>
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include <math.h>
#include "platform_dep.h"
#ifdef _OPENMP
#include <omp.h>
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#ifdef PYREX_WITHOUT_ASSERTIONS
#define CYTHON_WITHOUT_ASSERTIONS
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#ifndef CYTHON_UNUSED
# if defined(__GNUC__)
#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
#     define CYTHON_UNUSED __attribute__ ((__unused__))
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#     define CYTHON_UNUSED
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# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
#   define CYTHON_UNUSED __attribute__ ((__unused__))
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#   define CYTHON_UNUSED
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#ifndef CYTHON_NCP_UNUSED
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typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
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#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
#define __PYX_DEFAULT_STRING_ENCODING ""
#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#define __Pyx_uchar_cast(c) ((unsigned char)c)
#define __Pyx_long_cast(x) ((long)x)
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
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#elif defined (_MSC_VER) && defined (_M_X64)
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#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
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#elif defined (__GNUC__)
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    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
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static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
#define __Pyx_PyBytes_FromString        PyBytes_FromString
#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
#if PY_MAJOR_VERSION < 3
    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
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    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
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#define __Pyx_PyObject_AsSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
#if PY_MAJOR_VERSION < 3
static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u)
{
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}
#else
#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen
#endif
#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
#define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False))
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
#if CYTHON_ASSUME_SAFE_MACROS
#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
#else
#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
#endif
#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
#if PY_MAJOR_VERSION >= 3
#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
#else
#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
#endif
#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
static int __Pyx_sys_getdefaultencoding_not_ascii;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
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    PyObject* ascii_chars_b = NULL;
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    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
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    if (strcmp(default_encoding_c, "ascii") == 0) {
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    } else {
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        }
        __Pyx_sys_getdefaultencoding_not_ascii = 1;
        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
        if (!ascii_chars_u) goto bad;
        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
            PyErr_Format(
                PyExc_ValueError,
                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
                default_encoding_c);
            goto bad;
        }
        Py_DECREF(ascii_chars_u);
        Py_DECREF(ascii_chars_b);
    }
    Py_DECREF(default_encoding);
    return 0;
bad:
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    Py_XDECREF(ascii_chars_u);
    Py_XDECREF(ascii_chars_b);
    return -1;
}
#endif
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
#else
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
static char* __PYX_DEFAULT_STRING_ENCODING;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
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    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));
    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    return -1;
}
#endif
#endif


/* Test for GCC > 2.95 */
#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
  #define likely(x)   __builtin_expect(!!(x), 1)
  #define unlikely(x) __builtin_expect(!!(x), 0)
#else /* !__GNUC__ or GCC < 2.95 */
  #define likely(x)   (x)
  #define unlikely(x) (x)
#endif /* __GNUC__ */

static PyObject *__pyx_m;
static PyObject *__pyx_d;
static PyObject *__pyx_b;
static PyObject *__pyx_empty_tuple;
static PyObject *__pyx_empty_bytes;
static PyObject *__pyx_empty_unicode;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;

/* Header.proto */
#if !defined(CYTHON_CCOMPLEX)
  #if defined(__cplusplus)
    #define CYTHON_CCOMPLEX 1
  #elif defined(_Complex_I)
    #define CYTHON_CCOMPLEX 1
  #else
    #define CYTHON_CCOMPLEX 0
  #endif
#endif
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    #include <complex>
  #else
    #include <complex.h>
  #endif
#endif
#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
  #undef _Complex_I
  #define _Complex_I 1.0fj
#endif


static const char *__pyx_f[] = {
  "yt/utilities/lib/element_mappings.pyx",
  "__init__.pxd",
  "type.pxd",
};
/* BufferFormatStructs.proto */
#define IS_UNSIGNED(type) (((type) -1) > 0)
struct __Pyx_StructField_;
#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
typedef struct {
  const char* name;
  struct __Pyx_StructField_* fields;
  size_t size;
  size_t arraysize[8];
  int ndim;
  char typegroup;
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} __Pyx_TypeInfo;
typedef struct __Pyx_StructField_ {
  __Pyx_TypeInfo* type;
  const char* name;
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} __Pyx_StructField;
typedef struct {
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typedef struct {
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/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":725
 * # in Cython to enable them only on the right systems.
 * 
 * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 */
typedef npy_int8 __pyx_t_5numpy_int8_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":726
 * 
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t
 */
typedef npy_int16 __pyx_t_5numpy_int16_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":727
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int64      int64_t
 * #ctypedef npy_int96      int96_t
 */
typedef npy_int32 __pyx_t_5numpy_int32_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":728
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_int96      int96_t
 * #ctypedef npy_int128     int128_t
 */
typedef npy_int64 __pyx_t_5numpy_int64_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":732
 * #ctypedef npy_int128     int128_t
 * 
 * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 */
typedef npy_uint8 __pyx_t_5numpy_uint8_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":733
 * 
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t
 */
typedef npy_uint16 __pyx_t_5numpy_uint16_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":734
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint64     uint64_t
 * #ctypedef npy_uint96     uint96_t
 */
typedef npy_uint32 __pyx_t_5numpy_uint32_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":735
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_uint96     uint96_t
 * #ctypedef npy_uint128    uint128_t
 */
typedef npy_uint64 __pyx_t_5numpy_uint64_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":739
 * #ctypedef npy_uint128    uint128_t
 * 
 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float64    float64_t
 * #ctypedef npy_float80    float80_t
 */
typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":740
 * 
 * ctypedef npy_float32    float32_t
 * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_float80    float80_t
 * #ctypedef npy_float128   float128_t
 */
typedef npy_float64 __pyx_t_5numpy_float64_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":749
 * # The int types are mapped a bit surprising --
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t
 */
typedef npy_long __pyx_t_5numpy_int_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":750
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   longlong_t
 * 
 */
typedef npy_longlong __pyx_t_5numpy_long_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":751
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_ulong      uint_t
 */
typedef npy_longlong __pyx_t_5numpy_longlong_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":753
 * ctypedef npy_longlong   longlong_t
 * 
 * ctypedef npy_ulong      uint_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t
 */
typedef npy_ulong __pyx_t_5numpy_uint_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":754
 * 
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 */
typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":755
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_intp       intp_t
 */
typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":757
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uintp      uintp_t
 * 
 */
typedef npy_intp __pyx_t_5numpy_intp_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":758
 * 
 * ctypedef npy_intp       intp_t
 * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_double     float_t
 */
typedef npy_uintp __pyx_t_5numpy_uintp_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":760
 * ctypedef npy_uintp      uintp_t
 * 
 * ctypedef npy_double     float_t             # <<<<<<<<<<<<<<
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t
 */
typedef npy_double __pyx_t_5numpy_float_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":761
 * 
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longdouble longdouble_t
 * 
 */
typedef npy_double __pyx_t_5numpy_double_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":762
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cfloat      cfloat_t
 */
typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
/* Declarations.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< float > __pyx_t_float_complex;
  #else
    typedef float _Complex __pyx_t_float_complex;
  #endif
#else
    typedef struct { float real, imag; } __pyx_t_float_complex;
#endif
static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);

/* Declarations.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< double > __pyx_t_double_complex;
  #else
    typedef double _Complex __pyx_t_double_complex;
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#else
    typedef struct { double real, imag; } __pyx_t_double_complex;
#endif
static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);


/*--- Type declarations ---*/
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":764
 * ctypedef npy_longdouble longdouble_t
 * 
 * ctypedef npy_cfloat      cfloat_t             # <<<<<<<<<<<<<<
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t
 */
typedef npy_cfloat __pyx_t_5numpy_cfloat_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":765
 * 
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t             # <<<<<<<<<<<<<<
 * ctypedef npy_clongdouble clongdouble_t
 * 
 */
typedef npy_cdouble __pyx_t_5numpy_cdouble_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":766
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cdouble     complex_t
 */
typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;

/* "../../../../usr/local/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":768
 * ctypedef npy_clongdouble clongdouble_t
 * 
 * ctypedef npy_cdouble     complex_t             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew1(a):
 */
typedef npy_cdouble __pyx_t_5numpy_complex_t;

/* "yt/utilities/lib/element_mappings.pxd":81
 * #          once it is converged.
 * #
 * ctypedef void (*func_type)(double* fx,             # <<<<<<<<<<<<<<
 *                            double* x,
 *                            double* vertices,
 */
typedef void (*__pyx_t_2yt_9utilities_3lib_16element_mappings_func_type)(double *, double *, double *, double *);

/* "yt/utilities/lib/element_mappings.pxd":101
 * #     tcol     - the third column of the jaocobian
 * #
 * ctypedef void (*jac_type3D)(double* rcol,             # <<<<<<<<<<<<<<
 *                             double* scol,
 *                             double* tcol,
 */
typedef void (*__pyx_t_2yt_9utilities_3lib_16element_mappings_jac_type3D)(double *, double *, double *, double *, double *, double *);

/* "yt/utilities/lib/element_mappings.pxd":123
 * #                The order of this array is [J11, J12, J21, J22]
 * #
 * ctypedef void (*jac_type2D)(double* A,             # <<<<<<<<<<<<<<
 *                             double* x,
 *                             double* vertices,
 */
typedef void (*__pyx_t_2yt_9utilities_3lib_16element_mappings_jac_type2D)(double *, double *, double *, double *);

/* "yt/utilities/lib/element_mappings.pxd":7
 * from libc.math cimport fabs, fmax
 * 
 * cdef class ElementSampler:             # <<<<<<<<<<<<<<
 * 
 *     # how close a point has to be to the element
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler {
  PyObject_HEAD
  struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_vtab;
  __pyx_t_5numpy_float64_t inclusion_tol;
  int num_mapped_coords;
};


/* "yt/utilities/lib/element_mappings.pxd":36
 * 
 * 
 * cdef class P1Sampler2D(ElementSampler):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler __pyx_base;
};


/* "yt/utilities/lib/element_mappings.pxd":51
 * 
 * 
 * cdef class P1Sampler3D(ElementSampler):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler __pyx_base;
};


/* "yt/utilities/lib/element_mappings.pxd":129
 * 
 * 
 * cdef class NonlinearSolveSampler3D(ElementSampler):             # <<<<<<<<<<<<<<
 * 
 *     cdef int dim
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler __pyx_base;
  int dim;
  int max_iter;
  __pyx_t_5numpy_float64_t tolerance;
  __pyx_t_2yt_9utilities_3lib_16element_mappings_func_type func;
  __pyx_t_2yt_9utilities_3lib_16element_mappings_jac_type3D jac;
};


/* "yt/utilities/lib/element_mappings.pxd":143
 * 
 * 
 * cdef class Q1Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D __pyx_base;
};


/* "yt/utilities/lib/element_mappings.pxd":160
 * 
 * 
 * cdef class W1Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D __pyx_base;
};


/* "yt/utilities/lib/element_mappings.pxd":178
 * 
 * 
 * cdef class S2Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D {
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};


/* "yt/utilities/lib/element_mappings.pxd":196
 * 
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 * 
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struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D {
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};


/* "yt/utilities/lib/element_mappings.pxd":210
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 * 
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 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D {
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/* "yt/utilities/lib/element_mappings.pyx":49
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 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler {
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  double (*sample_at_real_point)(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *, double *, double *, double *);
  int (*check_inside)(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *, double *);
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/* "yt/utilities/lib/element_mappings.pyx":107
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 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler2D {
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/* "yt/utilities/lib/element_mappings.pyx":177
 * 
 * 
 * cdef class P1Sampler3D(ElementSampler):             # <<<<<<<<<<<<<<
 *     '''
 * 
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler3D {
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/* "yt/utilities/lib/element_mappings.pyx":271
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 * 
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 * 
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 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D {
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static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D;


/* "yt/utilities/lib/element_mappings.pyx":334
 * 
 * 
 * cdef class Q1Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
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 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D {
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/* "yt/utilities/lib/element_mappings.pyx":674
 * 
 * 
 * cdef class W1Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
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 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_W1Sampler3D {
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/* "yt/utilities/lib/element_mappings.pyx":459
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 * 
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 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_S2Sampler3D {
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/* "yt/utilities/lib/element_mappings.pyx":794
 * 
 * 
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 * 
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 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D {
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static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D;


/* "yt/utilities/lib/element_mappings.pyx":856
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 * 
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 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D {
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static void __pyx_f_2yt_9utilities_3lib_16element_mappings_14ElementSampler_map_real_to_unit(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_v_self, CYTHON_UNUSED double *__pyx_v_mapped_x, CYTHON_UNUSED double *__pyx_v_vertices, CYTHON_UNUSED double *__pyx_v_physical_x); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_14ElementSampler_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_v_self, CYTHON_UNUSED double *__pyx_v_coord, CYTHON_UNUSED double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_14ElementSampler_check_inside(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_v_self, CYTHON_UNUSED double *__pyx_v_mapped_coord); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_14ElementSampler_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_v_self, CYTHON_UNUSED double *__pyx_v_mapped_coord); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_14ElementSampler_sample_at_real_point(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_v_self, double *__pyx_v_vertices, double *__pyx_v_field_values, double *__pyx_v_physical_x); /* proto*/
static void __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D_map_real_to_unit(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *__pyx_v_self, double *__pyx_v_mapped_x, double *__pyx_v_vertices, double *__pyx_v_physical_x); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static void __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_map_real_to_unit(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_x, double *__pyx_v_vertices, double *__pyx_v_physical_x); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static void __pyx_f_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler3D_map_real_to_unit(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D *__pyx_v_self, double *__pyx_v_mapped_x, double *__pyx_v_vertices, double *__pyx_v_physical_x); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static void __pyx_f_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler2D_map_real_to_unit(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D *__pyx_v_self, double *__pyx_v_mapped_x, double *__pyx_v_vertices, double *__pyx_v_physical_x); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q1Sampler2D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q1Sampler2D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/

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/* Module declarations from 'yt.utilities.lib.element_mappings' */
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_ElementSampler = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_P1Sampler2D = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_P1Sampler3D = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_W1Sampler3D = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_S2Sampler3D = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D = 0;
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_determinant_3x3(double *, double *, double *); /*proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_maxnorm(double *, int); /*proto*/
static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_Q1Function3D(double *, double *, double *, double *); /*proto*/
static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_Q1Jacobian3D(double *, double *, double *, double *, double *, double *); /*proto*/
static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_S2Function3D(double *, double *, double *, double *); /*proto*/
static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_S2Jacobian3D(double *, double *, double *, double *, double *, double *); /*proto*/
static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_W1Function3D(double *, double *, double *, double *); /*proto*/
static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_W1Jacobian3D(double *, double *, double *, double *, double *, double *); /*proto*/
static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_Q1Jacobian2D(double *, double *, double *, double *); /*proto*/
static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_Q1Function2D(double *, double *, double *, double *); /*proto*/
static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_float64_t = { "float64_t", NULL, sizeof(__pyx_t_5numpy_float64_t), { 0 }, 0, 'R', 0, 0 };
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static const char __pyx_k_sampler[] = "sampler";
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static const char __pyx_k_ValueError[] = "ValueError";
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static const char __pyx_k_ImportError[] = "ImportError";
static const char __pyx_k_RuntimeError[] = "RuntimeError";
static const char __pyx_k_field_values[] = "field_values";
static const char __pyx_k_test_hex_sampler[] = "test_hex_sampler";
static const char __pyx_k_test_tri_sampler[] = "test_tri_sampler";
static const char __pyx_k_test_quad_sampler[] = "test_quad_sampler";
static const char __pyx_k_test_hex20_sampler[] = "test_hex20_sampler";
static const char __pyx_k_test_tetra_sampler[] = "test_tetra_sampler";
static const char __pyx_k_test_wedge_sampler[] = "test_wedge_sampler";
static const char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static const char __pyx_k_Users_goldbaum_Documents_yt_hg[] = "/Users/goldbaum/Documents/yt-hg/yt/utilities/lib/element_mappings.pyx";
static const char __pyx_k_This_file_contains_coordinate_m[] = "\nThis file contains coordinate mappings between physical coordinates and those\ndefined on unit elements, as well as doing the corresponding intracell \ninterpolation on finite element data.\n\n\n";
static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import";
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static const char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
static const char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import";
static const char __pyx_k_yt_utilities_lib_element_mapping[] = "yt.utilities.lib.element_mappings";
static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;
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static PyObject *__pyx_kp_s_Users_goldbaum_Documents_yt_hg;
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static PyObject *__pyx_n_s_numpy;
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static PyObject *__pyx_kp_s_numpy_core_umath_failed_to_impor;
static PyObject *__pyx_n_s_physical_x;
static PyObject *__pyx_n_s_pyx_vtable;
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static PyObject *__pyx_n_s_test;
static PyObject *__pyx_n_s_test_hex20_sampler;
static PyObject *__pyx_n_s_test_hex_sampler;
static PyObject *__pyx_n_s_test_quad_sampler;
static PyObject *__pyx_n_s_test_tetra_sampler;
static PyObject *__pyx_n_s_test_tri_sampler;
static PyObject *__pyx_n_s_test_wedge_sampler;
static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
static PyObject *__pyx_n_s_val;
static PyObject *__pyx_n_s_vertices;
static PyObject *__pyx_n_s_yt_utilities_lib_element_mapping;
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_14ElementSampler___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_v_self); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *__pyx_v_self); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler3D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D *__pyx_v_self); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *__pyx_v_self); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *__pyx_v_self); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_v_self); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler2D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D *__pyx_v_self); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_11Q1Sampler2D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_test_hex_sampler(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_vertices, PyArrayObject *__pyx_v_field_values, PyArrayObject *__pyx_v_physical_x); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_2test_hex20_sampler(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_vertices, PyArrayObject *__pyx_v_field_values, PyArrayObject *__pyx_v_physical_x); /* proto */
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/* "yt/utilities/lib/element_mappings.pyx":40
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/* "yt/utilities/lib/element_mappings.pyx":158
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 * 
 */
  (__pyx_v_mapped_x[2]) = (__pyx_f_2yt_9utilities_3lib_16element_mappings_determinant_3x3(__pyx_v_col0, __pyx_v_col1, __pyx_v_bvec) / __pyx_v_d);

  /* "yt/utilities/lib/element_mappings.pyx":215
 *         mapped_x[1] = determinant_3x3(col0, bvec, col2)/d
 *         mapped_x[2] = determinant_3x3(col0, col1, bvec)/d
 *         mapped_x[3] = 1.0 - mapped_x[0] - mapped_x[1] - mapped_x[2]             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  (__pyx_v_mapped_x[3]) = (((1.0 - (__pyx_v_mapped_x[0])) - (__pyx_v_mapped_x[1])) - (__pyx_v_mapped_x[2]));

  /* "yt/utilities/lib/element_mappings.pyx":193
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef void map_real_to_unit(self, double* mapped_x,             # <<<<<<<<<<<<<<
 *                                double* vertices, double* physical_x) nogil:
 * 
 */

  /* function exit code */
}

/* "yt/utilities/lib/element_mappings.pyx":220
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef double sample_at_unit_point(self,             # <<<<<<<<<<<<<<
 *                                      double* coord,
 *                                      double* vals) nogil:
 */

static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals) {
  double __pyx_r;

  /* "yt/utilities/lib/element_mappings.pyx":224
 *                                      double* vals) nogil:
 *         return vals[0]*coord[0] + vals[1]*coord[1] + \
 *             vals[2]*coord[2] + vals[3]*coord[3]             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  __pyx_r = (((((__pyx_v_vals[0]) * (__pyx_v_coord[0])) + ((__pyx_v_vals[1]) * (__pyx_v_coord[1]))) + ((__pyx_v_vals[2]) * (__pyx_v_coord[2]))) + ((__pyx_v_vals[3]) * (__pyx_v_coord[3])));
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":220
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef double sample_at_unit_point(self,             # <<<<<<<<<<<<<<
 *                                      double* coord,
 *                                      double* vals) nogil:
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":229
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         # for tetrahedra, we check whether all mapped coordinates
 *         # are within 0 and 1, to within the inclusion tolerance
 */

static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord) {
  int __pyx_v_i;
  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;

  /* "yt/utilities/lib/element_mappings.pyx":233
 *         # are within 0 and 1, to within the inclusion tolerance
 *         cdef int i
 *         for i in range(4):             # <<<<<<<<<<<<<<
 *             if (mapped_coord[i] < -self.inclusion_tol or
 *                 mapped_coord[i] - 1.0 > self.inclusion_tol):
 */
  for (__pyx_t_1 = 0; __pyx_t_1 < 4; __pyx_t_1+=1) {
    __pyx_v_i = __pyx_t_1;

    /* "yt/utilities/lib/element_mappings.pyx":234
 *         cdef int i
 *         for i in range(4):
 *             if (mapped_coord[i] < -self.inclusion_tol or             # <<<<<<<<<<<<<<
 *                 mapped_coord[i] - 1.0 > self.inclusion_tol):
 *                 return 0
 */
    __pyx_t_3 = (((__pyx_v_mapped_coord[__pyx_v_i]) < (-__pyx_v_self->__pyx_base.inclusion_tol)) != 0);
    if (!__pyx_t_3) {
    } else {
      __pyx_t_2 = __pyx_t_3;
      goto __pyx_L6_bool_binop_done;
    }

    /* "yt/utilities/lib/element_mappings.pyx":235
 *         for i in range(4):
 *             if (mapped_coord[i] < -self.inclusion_tol or
 *                 mapped_coord[i] - 1.0 > self.inclusion_tol):             # <<<<<<<<<<<<<<
 *                 return 0
 *         return 1
 */
    __pyx_t_3 = ((((__pyx_v_mapped_coord[__pyx_v_i]) - 1.0) > __pyx_v_self->__pyx_base.inclusion_tol) != 0);
    __pyx_t_2 = __pyx_t_3;
    __pyx_L6_bool_binop_done:;

    /* "yt/utilities/lib/element_mappings.pyx":234
 *         cdef int i
 *         for i in range(4):
 *             if (mapped_coord[i] < -self.inclusion_tol or             # <<<<<<<<<<<<<<
 *                 mapped_coord[i] - 1.0 > self.inclusion_tol):
 *                 return 0
 */
    if (__pyx_t_2) {

      /* "yt/utilities/lib/element_mappings.pyx":236
 *             if (mapped_coord[i] < -self.inclusion_tol or
 *                 mapped_coord[i] - 1.0 > self.inclusion_tol):
 *                 return 0             # <<<<<<<<<<<<<<
 *         return 1
 * 
 */
      __pyx_r = 0;
      goto __pyx_L0;

      /* "yt/utilities/lib/element_mappings.pyx":234
 *         cdef int i
 *         for i in range(4):
 *             if (mapped_coord[i] < -self.inclusion_tol or             # <<<<<<<<<<<<<<
 *                 mapped_coord[i] - 1.0 > self.inclusion_tol):
 *                 return 0
 */
    }
  }

  /* "yt/utilities/lib/element_mappings.pyx":237
 *                 mapped_coord[i] - 1.0 > self.inclusion_tol):
 *                 return 0
 *         return 1             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  __pyx_r = 1;
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":229
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         # for tetrahedra, we check whether all mapped coordinates
 *         # are within 0 and 1, to within the inclusion tolerance
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":242
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         cdef double u, v, w
 *         cdef double thresh = 2.0e-2
 */

static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord) {
  double __pyx_v_u;
  double __pyx_v_v;
  double __pyx_v_w;
  double __pyx_v_thresh;
  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "yt/utilities/lib/element_mappings.pyx":244
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         cdef double u, v, w
 *         cdef double thresh = 2.0e-2             # <<<<<<<<<<<<<<
 *         if mapped_coord[0] == 0:
 *             u = mapped_coord[1]
 */
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  /* "yt/utilities/lib/element_mappings.pyx":245
 *         cdef double u, v, w
 *         cdef double thresh = 2.0e-2
 *         if mapped_coord[0] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[1]
 *             v = mapped_coord[2]
 */
  __pyx_t_1 = (((__pyx_v_mapped_coord[0]) == 0.0) != 0);
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":246
 *         cdef double thresh = 2.0e-2
 *         if mapped_coord[0] == 0:
 *             u = mapped_coord[1]             # <<<<<<<<<<<<<<
 *             v = mapped_coord[2]
 *             w = mapped_coord[3]
 */
    __pyx_v_u = (__pyx_v_mapped_coord[1]);

    /* "yt/utilities/lib/element_mappings.pyx":247
 *         if mapped_coord[0] == 0:
 *             u = mapped_coord[1]
 *             v = mapped_coord[2]             # <<<<<<<<<<<<<<
 *             w = mapped_coord[3]
 *         elif mapped_coord[1] == 0:
 */
    __pyx_v_v = (__pyx_v_mapped_coord[2]);

    /* "yt/utilities/lib/element_mappings.pyx":248
 *             u = mapped_coord[1]
 *             v = mapped_coord[2]
 *             w = mapped_coord[3]             # <<<<<<<<<<<<<<
 *         elif mapped_coord[1] == 0:
 *             u = mapped_coord[2]
 */
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    /* "yt/utilities/lib/element_mappings.pyx":245
 *         cdef double u, v, w
 *         cdef double thresh = 2.0e-2
 *         if mapped_coord[0] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[1]
 *             v = mapped_coord[2]
 */
    goto __pyx_L3;
  }

  /* "yt/utilities/lib/element_mappings.pyx":249
 *             v = mapped_coord[2]
 *             w = mapped_coord[3]
 *         elif mapped_coord[1] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[2]
 *             v = mapped_coord[3]
 */
  __pyx_t_1 = (((__pyx_v_mapped_coord[1]) == 0.0) != 0);
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":250
 *             w = mapped_coord[3]
 *         elif mapped_coord[1] == 0:
 *             u = mapped_coord[2]             # <<<<<<<<<<<<<<
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]
 */
    __pyx_v_u = (__pyx_v_mapped_coord[2]);

    /* "yt/utilities/lib/element_mappings.pyx":251
 *         elif mapped_coord[1] == 0:
 *             u = mapped_coord[2]
 *             v = mapped_coord[3]             # <<<<<<<<<<<<<<
 *             w = mapped_coord[0]
 *         elif mapped_coord[2] == 0:
 */
    __pyx_v_v = (__pyx_v_mapped_coord[3]);

    /* "yt/utilities/lib/element_mappings.pyx":252
 *             u = mapped_coord[2]
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]             # <<<<<<<<<<<<<<
 *         elif mapped_coord[2] == 0:
 *             u = mapped_coord[1]
 */
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    /* "yt/utilities/lib/element_mappings.pyx":249
 *             v = mapped_coord[2]
 *             w = mapped_coord[3]
 *         elif mapped_coord[1] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[2]
 *             v = mapped_coord[3]
 */
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  /* "yt/utilities/lib/element_mappings.pyx":253
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]
 *         elif mapped_coord[2] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[1]
 *             v = mapped_coord[3]
 */
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    /* "yt/utilities/lib/element_mappings.pyx":254
 *             w = mapped_coord[0]
 *         elif mapped_coord[2] == 0:
 *             u = mapped_coord[1]             # <<<<<<<<<<<<<<
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]
 */
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    /* "yt/utilities/lib/element_mappings.pyx":255
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 *             u = mapped_coord[1]
 *             v = mapped_coord[3]             # <<<<<<<<<<<<<<
 *             w = mapped_coord[0]
 *         else:
 */
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    /* "yt/utilities/lib/element_mappings.pyx":256
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 *             v = mapped_coord[3]
 *             w = mapped_coord[0]             # <<<<<<<<<<<<<<
 *         else:
 *             u = mapped_coord[1]
 */
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    /* "yt/utilities/lib/element_mappings.pyx":253
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]
 *         elif mapped_coord[2] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[1]
 *             v = mapped_coord[3]
 */
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  /* "yt/utilities/lib/element_mappings.pyx":258
 *             w = mapped_coord[0]
 *         else:
 *             u = mapped_coord[1]             # <<<<<<<<<<<<<<
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 *             w = mapped_coord[0]
 */
  /*else*/ {
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    /* "yt/utilities/lib/element_mappings.pyx":259
 *         else:
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 *             v = mapped_coord[2]             # <<<<<<<<<<<<<<
 *             w = mapped_coord[0]
 *         if ((u < thresh) or
 */
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    /* "yt/utilities/lib/element_mappings.pyx":260
 *             u = mapped_coord[1]
 *             v = mapped_coord[2]
 *             w = mapped_coord[0]             # <<<<<<<<<<<<<<
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 */
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  __pyx_L3:;

  /* "yt/utilities/lib/element_mappings.pyx":261
 *             v = mapped_coord[2]
 *             w = mapped_coord[0]
 *         if ((u < thresh) or             # <<<<<<<<<<<<<<
 *             (v < thresh) or
 *             (w < thresh) or
 */
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  } else {
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  /* "yt/utilities/lib/element_mappings.pyx":262
 *             w = mapped_coord[0]
 *         if ((u < thresh) or
 *             (v < thresh) or             # <<<<<<<<<<<<<<
 *             (w < thresh) or
 *             (fabs(u - 1) < thresh) or
 */
  __pyx_t_2 = ((__pyx_v_v < __pyx_v_thresh) != 0);
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  } else {
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  }

  /* "yt/utilities/lib/element_mappings.pyx":263
 *         if ((u < thresh) or
 *             (v < thresh) or
 *             (w < thresh) or             # <<<<<<<<<<<<<<
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 */
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  /* "yt/utilities/lib/element_mappings.pyx":264
 *             (v < thresh) or
 *             (w < thresh) or
 *             (fabs(u - 1) < thresh) or             # <<<<<<<<<<<<<<
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  /* "yt/utilities/lib/element_mappings.pyx":265
 *             (w < thresh) or
 *             (fabs(u - 1) < thresh) or
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 *             (fabs(u - 1) < thresh) or
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 */
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 */
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 *         if ((u < thresh) or             # <<<<<<<<<<<<<<
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 */
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 * 
 */
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 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
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  /* "yt/utilities/lib/element_mappings.pyx":363
 * 
 *         F = vals[0]*rm*sm*tm + vals[1]*rp*sm*tm + vals[2]*rp*sp*tm + vals[3]*rm*sp*tm + \
 *             vals[4]*rm*sm*tp + vals[5]*rp*sm*tp + vals[6]*rp*sp*tp + vals[7]*rm*sp*tp             # <<<<<<<<<<<<<<
 *         return 0.125*F
 * 
 */
  __pyx_v_F = (((((((((((__pyx_v_vals[0]) * __pyx_v_rm) * __pyx_v_sm) * __pyx_v_tm) + ((((__pyx_v_vals[1]) * __pyx_v_rp) * __pyx_v_sm) * __pyx_v_tm)) + ((((__pyx_v_vals[2]) * __pyx_v_rp) * __pyx_v_sp) * __pyx_v_tm)) + ((((__pyx_v_vals[3]) * __pyx_v_rm) * __pyx_v_sp) * __pyx_v_tm)) + ((((__pyx_v_vals[4]) * __pyx_v_rm) * __pyx_v_sm) * __pyx_v_tp)) + ((((__pyx_v_vals[5]) * __pyx_v_rp) * __pyx_v_sm) * __pyx_v_tp)) + ((((__pyx_v_vals[6]) * __pyx_v_rp) * __pyx_v_sp) * __pyx_v_tp)) + ((((__pyx_v_vals[7]) * __pyx_v_rm) * __pyx_v_sp) * __pyx_v_tp));

  /* "yt/utilities/lib/element_mappings.pyx":364
 *         F = vals[0]*rm*sm*tm + vals[1]*rp*sm*tm + vals[2]*rp*sp*tm + vals[3]*rm*sp*tm + \
 *             vals[4]*rm*sm*tp + vals[5]*rp*sm*tp + vals[6]*rp*sp*tp + vals[7]*rm*sp*tp
 *         return 0.125*F             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  __pyx_r = (0.125 * __pyx_v_F);
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":352
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef double sample_at_unit_point(self, double* coord, double* vals) nogil:             # <<<<<<<<<<<<<<
 *         cdef double F, rm, rp, sm, sp, tm, tp
 * 
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":369
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         # for hexes, the mapped coordinates all go from -1 to 1
 *         # if we are inside the element.
 */

static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord) {
  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "yt/utilities/lib/element_mappings.pyx":372
 *         # for hexes, the mapped coordinates all go from -1 to 1
 *         # if we are inside the element.
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 */
  __pyx_t_2 = (((fabs((__pyx_v_mapped_coord[0])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":373
 *         # if we are inside the element.
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0
 */
  __pyx_t_2 = (((fabs((__pyx_v_mapped_coord[1])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":374
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):             # <<<<<<<<<<<<<<
 *             return 0
 *         return 1
 */
  __pyx_t_2 = (((fabs((__pyx_v_mapped_coord[2])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":372
 *         # for hexes, the mapped coordinates all go from -1 to 1
 *         # if we are inside the element.
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":375
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0             # <<<<<<<<<<<<<<
 *         return 1
 * 
 */
    __pyx_r = 0;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":372
 *         # for hexes, the mapped coordinates all go from -1 to 1
 *         # if we are inside the element.
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":376
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0
 *         return 1             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  __pyx_r = 1;
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":369
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         # for hexes, the mapped coordinates all go from -1 to 1
 *         # if we are inside the element.
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":381
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 */

static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord) {
  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "yt/utilities/lib/element_mappings.pyx":382
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[0])) - 1.0)) < 1e-1) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":383
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):             # <<<<<<<<<<<<<<
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[1])) - 1.0)) < 1e-1) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":382
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":384
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1             # <<<<<<<<<<<<<<
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 */
    __pyx_r = 1;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":382
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":385
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[0])) - 1.0)) < 1e-1) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":386
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):             # <<<<<<<<<<<<<<
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[2])) - 1.0)) < 1e-1) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":385
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":387
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1             # <<<<<<<<<<<<<<
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 */
    __pyx_r = 1;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":385
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":388
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[1])) - 1.0)) < 1e-1) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":389
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):             # <<<<<<<<<<<<<<
 *             return 1
 *         else:
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[2])) - 1.0)) < 1e-1) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":388
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":390
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1             # <<<<<<<<<<<<<<
 *         else:
 *             return -1
 */
    __pyx_r = 1;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":388
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":392
 *             return 1
 *         else:
 *             return -1             # <<<<<<<<<<<<<<
 * 
 * 
 */
  /*else*/ {
    __pyx_r = -1;
    goto __pyx_L0;
  }

  /* "yt/utilities/lib/element_mappings.pyx":381
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":399
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void Q1Function3D(double* fx,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_Q1Function3D(double *__pyx_v_fx, double *__pyx_v_x, double *__pyx_v_vertices, double *__pyx_v_phys_x) {
  int __pyx_v_i;
  double __pyx_v_rm;
  double __pyx_v_rp;
  double __pyx_v_sm;
  double __pyx_v_sp;
  double __pyx_v_tm;
  double __pyx_v_tp;
  int __pyx_t_1;

  /* "yt/utilities/lib/element_mappings.pyx":406
 *     cdef double rm, rp, sm, sp, tm, tp
 * 
 *     rm = 1.0 - x[0]             # <<<<<<<<<<<<<<
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]
 */
  __pyx_v_rm = (1.0 - (__pyx_v_x[0]));

  /* "yt/utilities/lib/element_mappings.pyx":407
 * 
 *     rm = 1.0 - x[0]
 *     rp = 1.0 + x[0]             # <<<<<<<<<<<<<<
 *     sm = 1.0 - x[1]
 *     sp = 1.0 + x[1]
 */
  __pyx_v_rp = (1.0 + (__pyx_v_x[0]));

  /* "yt/utilities/lib/element_mappings.pyx":408
 *     rm = 1.0 - x[0]
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]             # <<<<<<<<<<<<<<
 *     sp = 1.0 + x[1]
 *     tm = 1.0 - x[2]
 */
  __pyx_v_sm = (1.0 - (__pyx_v_x[1]));

  /* "yt/utilities/lib/element_mappings.pyx":409
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]
 *     sp = 1.0 + x[1]             # <<<<<<<<<<<<<<
 *     tm = 1.0 - x[2]
 *     tp = 1.0 + x[2]
 */
  __pyx_v_sp = (1.0 + (__pyx_v_x[1]));

  /* "yt/utilities/lib/element_mappings.pyx":410
 *     sm = 1.0 - x[1]
 *     sp = 1.0 + x[1]
 *     tm = 1.0 - x[2]             # <<<<<<<<<<<<<<
 *     tp = 1.0 + x[2]
 * 
 */
  __pyx_v_tm = (1.0 - (__pyx_v_x[2]));

  /* "yt/utilities/lib/element_mappings.pyx":411
 *     sp = 1.0 + x[1]
 *     tm = 1.0 - x[2]
 *     tp = 1.0 + x[2]             # <<<<<<<<<<<<<<
 * 
 *     for i in range(3):
 */
  __pyx_v_tp = (1.0 + (__pyx_v_x[2]));

  /* "yt/utilities/lib/element_mappings.pyx":413
 *     tp = 1.0 + x[2]
 * 
 *     for i in range(3):             # <<<<<<<<<<<<<<
 *         fx[i] = vertices[0 + i]*rm*sm*tm \
 *               + vertices[3 + i]*rp*sm*tm \
 */
  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
    __pyx_v_i = __pyx_t_1;

    /* "yt/utilities/lib/element_mappings.pyx":414
 * 
 *     for i in range(3):
 *         fx[i] = vertices[0 + i]*rm*sm*tm \             # <<<<<<<<<<<<<<
 *               + vertices[3 + i]*rp*sm*tm \
 *               + vertices[6 + i]*rp*sp*tm \
 */
    (__pyx_v_fx[__pyx_v_i]) = ((((((((((((__pyx_v_vertices[(0 + __pyx_v_i)]) * __pyx_v_rm) * __pyx_v_sm) * __pyx_v_tm) + ((((__pyx_v_vertices[(3 + __pyx_v_i)]) * __pyx_v_rp) * __pyx_v_sm) * __pyx_v_tm)) + ((((__pyx_v_vertices[(6 + __pyx_v_i)]) * __pyx_v_rp) * __pyx_v_sp) * __pyx_v_tm)) + ((((__pyx_v_vertices[(9 + __pyx_v_i)]) * __pyx_v_rm) * __pyx_v_sp) * __pyx_v_tm)) + ((((__pyx_v_vertices[(12 + __pyx_v_i)]) * __pyx_v_rm) * __pyx_v_sm) * __pyx_v_tp)) + ((((__pyx_v_vertices[(15 + __pyx_v_i)]) * __pyx_v_rp) * __pyx_v_sm) * __pyx_v_tp)) + ((((__pyx_v_vertices[(18 + __pyx_v_i)]) * __pyx_v_rp) * __pyx_v_sp) * __pyx_v_tp)) + ((((__pyx_v_vertices[(21 + __pyx_v_i)]) * __pyx_v_rm) * __pyx_v_sp) * __pyx_v_tp)) - (8.0 * (__pyx_v_phys_x[__pyx_v_i])));
  }

  /* "yt/utilities/lib/element_mappings.pyx":399
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void Q1Function3D(double* fx,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

  /* function exit code */
}

/* "yt/utilities/lib/element_mappings.pyx":428
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void Q1Jacobian3D(double* rcol,             # <<<<<<<<<<<<<<
 *                               double* scol,
 *                               double* tcol,
 */

static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_Q1Jacobian3D(double *__pyx_v_rcol, double *__pyx_v_scol, double *__pyx_v_tcol, double *__pyx_v_x, double *__pyx_v_vertices, CYTHON_UNUSED double *__pyx_v_phys_x) {
  int __pyx_v_i;
  double __pyx_v_rm;
  double __pyx_v_rp;
  double __pyx_v_sm;
  double __pyx_v_sp;
  double __pyx_v_tm;
  double __pyx_v_tp;
  int __pyx_t_1;

  /* "yt/utilities/lib/element_mappings.pyx":437
 *     cdef double rm, rp, sm, sp, tm, tp
 * 
 *     rm = 1.0 - x[0]             # <<<<<<<<<<<<<<
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]
 */
  __pyx_v_rm = (1.0 - (__pyx_v_x[0]));

  /* "yt/utilities/lib/element_mappings.pyx":438
 * 
 *     rm = 1.0 - x[0]
 *     rp = 1.0 + x[0]             # <<<<<<<<<<<<<<
 *     sm = 1.0 - x[1]
 *     sp = 1.0 + x[1]
 */
  __pyx_v_rp = (1.0 + (__pyx_v_x[0]));

  /* "yt/utilities/lib/element_mappings.pyx":439
 *     rm = 1.0 - x[0]
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]             # <<<<<<<<<<<<<<
 *     sp = 1.0 + x[1]
 *     tm = 1.0 - x[2]
 */
  __pyx_v_sm = (1.0 - (__pyx_v_x[1]));

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 *     @cython.cdivision(True)
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  __pyx_t_2 = (((fabs((__pyx_v_mapped_coord[0])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":519
 *     cdef int check_inside(self, double* mapped_coord) nogil:
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0
 */
  __pyx_t_2 = (((fabs((__pyx_v_mapped_coord[1])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":520
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):             # <<<<<<<<<<<<<<
 *             return 0
 *         return 1
 */
  __pyx_t_2 = (((fabs((__pyx_v_mapped_coord[2])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":518
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":521
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0             # <<<<<<<<<<<<<<
 *         return 1
 * 
 */
    __pyx_r = 0;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":518
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":522
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0
 *         return 1             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  __pyx_r = 1;
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":517
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol or
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":527
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 */

static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord) {
  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "yt/utilities/lib/element_mappings.pyx":528
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[0])) - 1.0)) < 1e-1) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":529
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):             # <<<<<<<<<<<<<<
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[1])) - 1.0)) < 1e-1) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":528
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":530
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1             # <<<<<<<<<<<<<<
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 */
    __pyx_r = 1;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":528
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":531
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[0])) - 1.0)) < 1e-1) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":532
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):             # <<<<<<<<<<<<<<
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[2])) - 1.0)) < 1e-1) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":531
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":533
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1             # <<<<<<<<<<<<<<
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 */
    __pyx_r = 1;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":531
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":534
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[1])) - 1.0)) < 1e-1) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":535
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):             # <<<<<<<<<<<<<<
 *             return 1
 *         else:
 */
  __pyx_t_2 = ((fabs((fabs((__pyx_v_mapped_coord[2])) - 1.0)) < 1e-1) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":534
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":536
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1             # <<<<<<<<<<<<<<
 *         else:
 *             return -1
 */
    __pyx_r = 1;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":534
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
 *             return 1
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":538
 *             return 1
 *         else:
 *             return -1             # <<<<<<<<<<<<<<
 * 
 * 
 */
  /*else*/ {
    __pyx_r = -1;
    goto __pyx_L0;
  }

  /* "yt/utilities/lib/element_mappings.pyx":527
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         if (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *             fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1):
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":544
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void S2Function3D(double* fx,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_S2Function3D(double *__pyx_v_fx, double *__pyx_v_x, double *__pyx_v_vertices, double *__pyx_v_phys_x) {
  int __pyx_v_i;
  double __pyx_v_r;
  double __pyx_v_s;
  double __pyx_v_t;
  double __pyx_v_rm;
  double __pyx_v_rp;
  double __pyx_v_sm;
  double __pyx_v_sp;
  double __pyx_v_tm;
  double __pyx_v_tp;
  int __pyx_t_1;

  /* "yt/utilities/lib/element_mappings.pyx":551
 *         cdef double r, s, t, rm, rp, sm, sp, tm, tp
 * 
 *         r = x[0]             # <<<<<<<<<<<<<<
 *         rm = 1.0 - r
 *         rp = 1.0 + r
 */
  __pyx_v_r = (__pyx_v_x[0]);

  /* "yt/utilities/lib/element_mappings.pyx":552
 * 
 *         r = x[0]
 *         rm = 1.0 - r             # <<<<<<<<<<<<<<
 *         rp = 1.0 + r
 * 
 */
  __pyx_v_rm = (1.0 - __pyx_v_r);

  /* "yt/utilities/lib/element_mappings.pyx":553
 *         r = x[0]
 *         rm = 1.0 - r
 *         rp = 1.0 + r             # <<<<<<<<<<<<<<
 * 
 *         s = x[1]
 */
  __pyx_v_rp = (1.0 + __pyx_v_r);

  /* "yt/utilities/lib/element_mappings.pyx":555
 *         rp = 1.0 + r
 * 
 *         s = x[1]             # <<<<<<<<<<<<<<
 *         sm = 1.0 - s
 *         sp = 1.0 + s
 */
  __pyx_v_s = (__pyx_v_x[1]);

  /* "yt/utilities/lib/element_mappings.pyx":556
 * 
 *         s = x[1]
 *         sm = 1.0 - s             # <<<<<<<<<<<<<<
 *         sp = 1.0 + s
 * 
 */
  __pyx_v_sm = (1.0 - __pyx_v_s);

  /* "yt/utilities/lib/element_mappings.pyx":557
 *         s = x[1]
 *         sm = 1.0 - s
 *         sp = 1.0 + s             # <<<<<<<<<<<<<<
 * 
 *         t = x[2]
 */
  __pyx_v_sp = (1.0 + __pyx_v_s);

  /* "yt/utilities/lib/element_mappings.pyx":559
 *         sp = 1.0 + s
 * 
 *         t = x[2]             # <<<<<<<<<<<<<<
 *         tm = 1.0 - t
 *         tp = 1.0 + t
 */
  __pyx_v_t = (__pyx_v_x[2]);

  /* "yt/utilities/lib/element_mappings.pyx":560
 * 
 *         t = x[2]
 *         tm = 1.0 - t             # <<<<<<<<<<<<<<
 *         tp = 1.0 + t
 * 
 */
  __pyx_v_tm = (1.0 - __pyx_v_t);

  /* "yt/utilities/lib/element_mappings.pyx":561
 *         t = x[2]
 *         tm = 1.0 - t
 *         tp = 1.0 + t             # <<<<<<<<<<<<<<
 * 
 *         for i in range(3):
 */
  __pyx_v_tp = (1.0 + __pyx_v_t);

  /* "yt/utilities/lib/element_mappings.pyx":563
 *         tp = 1.0 + t
 * 
 *         for i in range(3):             # <<<<<<<<<<<<<<
 *             fx[i] = rm*sm*tm*(-r - s - t - 2.0)*vertices[0 + i]  \
 *                   + rp*sm*tm*( r - s - t - 2.0)*vertices[3 + i]  \
 */
  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
    __pyx_v_i = __pyx_t_1;

    /* "yt/utilities/lib/element_mappings.pyx":564
 * 
 *         for i in range(3):
 *             fx[i] = rm*sm*tm*(-r - s - t - 2.0)*vertices[0 + i]  \             # <<<<<<<<<<<<<<
 *                   + rp*sm*tm*( r - s - t - 2.0)*vertices[3 + i]  \
 *                   + rp*sp*tm*( r + s - t - 2.0)*vertices[6 + i]  \
 */
    (__pyx_v_fx[__pyx_v_i]) = ((((((((((((((((((((((((__pyx_v_rm * __pyx_v_sm) * __pyx_v_tm) * ((((-__pyx_v_r) - __pyx_v_s) - __pyx_v_t) - 2.0)) * (__pyx_v_vertices[(0 + __pyx_v_i)])) + ((((__pyx_v_rp * __pyx_v_sm) * __pyx_v_tm) * (((__pyx_v_r - __pyx_v_s) - __pyx_v_t) - 2.0)) * (__pyx_v_vertices[(3 + __pyx_v_i)]))) + ((((__pyx_v_rp * __pyx_v_sp) * __pyx_v_tm) * (((__pyx_v_r + __pyx_v_s) - __pyx_v_t) - 2.0)) * (__pyx_v_vertices[(6 + __pyx_v_i)]))) + ((((__pyx_v_rm * __pyx_v_sp) * __pyx_v_tm) * ((((-__pyx_v_r) + __pyx_v_s) - __pyx_v_t) - 2.0)) * (__pyx_v_vertices[(9 + __pyx_v_i)]))) + ((((__pyx_v_rm * __pyx_v_sm) * __pyx_v_tp) * ((((-__pyx_v_r) - __pyx_v_s) + __pyx_v_t) - 2.0)) * (__pyx_v_vertices[(12 + __pyx_v_i)]))) + ((((__pyx_v_rp * __pyx_v_sm) * __pyx_v_tp) * (((__pyx_v_r - __pyx_v_s) + __pyx_v_t) - 2.0)) * (__pyx_v_vertices[(15 + __pyx_v_i)]))) + ((((__pyx_v_rp * __pyx_v_sp) * __pyx_v_tp) * (((__pyx_v_r + __pyx_v_s) + __pyx_v_t) - 2.0)) * (__pyx_v_vertices[(18 + __pyx_v_i)]))) + ((((__pyx_v_rm * __pyx_v_sp) * __pyx_v_tp) * ((((-__pyx_v_r) + __pyx_v_s) + __pyx_v_t) - 2.0)) * (__pyx_v_vertices[(21 + __pyx_v_i)]))) + ((((2.0 * (1.0 - pow(__pyx_v_r, 2.0))) * __pyx_v_sm) * __pyx_v_tm) * (__pyx_v_vertices[(24 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rp) * (1.0 - pow(__pyx_v_s, 2.0))) * __pyx_v_tm) * (__pyx_v_vertices[(27 + __pyx_v_i)]))) + ((((2.0 * (1.0 - pow(__pyx_v_r, 2.0))) * __pyx_v_sp) * __pyx_v_tm) * (__pyx_v_vertices[(30 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rm) * (1.0 - pow(__pyx_v_s, 2.0))) * __pyx_v_tm) * (__pyx_v_vertices[(33 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rm) * __pyx_v_sm) * (1.0 - pow(__pyx_v_t, 2.0))) * (__pyx_v_vertices[(36 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rp) * __pyx_v_sm) * (1.0 - pow(__pyx_v_t, 2.0))) * (__pyx_v_vertices[(39 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rp) * __pyx_v_sp) * (1.0 - pow(__pyx_v_t, 2.0))) * (__pyx_v_vertices[(42 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rm) * __pyx_v_sp) * (1.0 - pow(__pyx_v_t, 2.0))) * (__pyx_v_vertices[(45 + __pyx_v_i)]))) + ((((2.0 * (1.0 - pow(__pyx_v_r, 2.0))) * __pyx_v_sm) * __pyx_v_tp) * (__pyx_v_vertices[(48 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rp) * (1.0 - pow(__pyx_v_s, 2.0))) * __pyx_v_tp) * (__pyx_v_vertices[(51 + __pyx_v_i)]))) + ((((2.0 * (1.0 - pow(__pyx_v_r, 2.0))) * __pyx_v_sp) * __pyx_v_tp) * (__pyx_v_vertices[(54 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rm) * (1.0 - pow(__pyx_v_s, 2.0))) * __pyx_v_tp) * (__pyx_v_vertices[(57 + __pyx_v_i)]))) - (8.0 * (__pyx_v_phys_x[__pyx_v_i])));
  }

  /* "yt/utilities/lib/element_mappings.pyx":544
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void S2Function3D(double* fx,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

  /* function exit code */
}

/* "yt/utilities/lib/element_mappings.pyx":590
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void S2Jacobian3D(double* rcol,             # <<<<<<<<<<<<<<
 *                               double* scol,
 *                               double* tcol,
 */

static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_S2Jacobian3D(double *__pyx_v_rcol, double *__pyx_v_scol, double *__pyx_v_tcol, double *__pyx_v_x, double *__pyx_v_vertices, CYTHON_UNUSED double *__pyx_v_phys_x) {
  int __pyx_v_i;
  double __pyx_v_r;
  double __pyx_v_s;
  double __pyx_v_t;
  double __pyx_v_rm;
  double __pyx_v_rp;
  double __pyx_v_sm;
  double __pyx_v_sp;
  double __pyx_v_tm;
  double __pyx_v_tp;
  int __pyx_t_1;

  /* "yt/utilities/lib/element_mappings.pyx":599
 *         cdef double r, s, t, rm, rp, sm, sp, tm, tp
 * 
 *         r = x[0]             # <<<<<<<<<<<<<<
 *         rm = 1.0 - r
 *         rp = 1.0 + r
 */
  __pyx_v_r = (__pyx_v_x[0]);

  /* "yt/utilities/lib/element_mappings.pyx":600
 * 
 *         r = x[0]
 *         rm = 1.0 - r             # <<<<<<<<<<<<<<
 *         rp = 1.0 + r
 * 
 */
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 *     @cython.boundscheck(False)
 */
  __pyx_v_self->__pyx_base.jac = __pyx_f_2yt_9utilities_3lib_16element_mappings_W1Jacobian3D;

  /* "yt/utilities/lib/element_mappings.pyx":682
 *     '''
 * 
 *     def __init__(self):             # <<<<<<<<<<<<<<
 *         super(W1Sampler3D, self).__init__()
 *         self.num_mapped_coords = 3
 */

  /* function exit code */
  __pyx_r = 0;
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_AddTraceback("yt.utilities.lib.element_mappings.W1Sampler3D.__init__", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __pyx_L0:;
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":692
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef double sample_at_unit_point(self, double* coord, double* vals) nogil:             # <<<<<<<<<<<<<<
 *         cdef double F
 * 
 */

static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals) {
  double __pyx_v_F;
  double __pyx_r;

  /* "yt/utilities/lib/element_mappings.pyx":699
 *             vals[2]*coord[1]*(1.0 - coord[2]) + \
 *             vals[3]*(1.0 - coord[0] - coord[1])*(1.0 + coord[2]) + \
 *             vals[4]*coord[0]*(1.0 + coord[2]) + \             # <<<<<<<<<<<<<<
 *             vals[5]*coord[1]*(1.0 + coord[2])
 * 
 */
  __pyx_v_F = ((((((((__pyx_v_vals[0]) * ((1.0 - (__pyx_v_coord[0])) - (__pyx_v_coord[1]))) * (1.0 - (__pyx_v_coord[2]))) + (((__pyx_v_vals[1]) * (__pyx_v_coord[0])) * (1.0 - (__pyx_v_coord[2])))) + (((__pyx_v_vals[2]) * (__pyx_v_coord[1])) * (1.0 - (__pyx_v_coord[2])))) + (((__pyx_v_vals[3]) * ((1.0 - (__pyx_v_coord[0])) - (__pyx_v_coord[1]))) * (1.0 + (__pyx_v_coord[2])))) + (((__pyx_v_vals[4]) * (__pyx_v_coord[0])) * (1.0 + (__pyx_v_coord[2])))) + (((__pyx_v_vals[5]) * (__pyx_v_coord[1])) * (1.0 + (__pyx_v_coord[2]))));

  /* "yt/utilities/lib/element_mappings.pyx":702
 *             vals[5]*coord[1]*(1.0 + coord[2])
 * 
 *         return F / 2.0             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  __pyx_r = (__pyx_v_F / 2.0);
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":692
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef double sample_at_unit_point(self, double* coord, double* vals) nogil:             # <<<<<<<<<<<<<<
 *         cdef double F
 * 
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":707
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         # for wedges the bounds of the mapped coordinates are:
 *         #     0 <= mapped_coord[0] <= 1 - mapped_coord[1]
 */

static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord) {
  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "yt/utilities/lib/element_mappings.pyx":712
 *         #     0 <= mapped_coord[1]
 *         #    -1 <= mapped_coord[2] <= 1
 *         if (mapped_coord[0] < -self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             mapped_coord[0] + mapped_coord[1] - 1.0 > self.inclusion_tol):
 *             return 0
 */
  __pyx_t_2 = (((__pyx_v_mapped_coord[0]) < (-__pyx_v_self->__pyx_base.__pyx_base.inclusion_tol)) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":713
 *         #    -1 <= mapped_coord[2] <= 1
 *         if (mapped_coord[0] < -self.inclusion_tol or
 *             mapped_coord[0] + mapped_coord[1] - 1.0 > self.inclusion_tol):             # <<<<<<<<<<<<<<
 *             return 0
 *         if (mapped_coord[1] < -self.inclusion_tol):
 */
  __pyx_t_2 = (((((__pyx_v_mapped_coord[0]) + (__pyx_v_mapped_coord[1])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":712
 *         #     0 <= mapped_coord[1]
 *         #    -1 <= mapped_coord[2] <= 1
 *         if (mapped_coord[0] < -self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             mapped_coord[0] + mapped_coord[1] - 1.0 > self.inclusion_tol):
 *             return 0
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":714
 *         if (mapped_coord[0] < -self.inclusion_tol or
 *             mapped_coord[0] + mapped_coord[1] - 1.0 > self.inclusion_tol):
 *             return 0             # <<<<<<<<<<<<<<
 *         if (mapped_coord[1] < -self.inclusion_tol):
 *             return 0
 */
    __pyx_r = 0;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":712
 *         #     0 <= mapped_coord[1]
 *         #    -1 <= mapped_coord[2] <= 1
 *         if (mapped_coord[0] < -self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             mapped_coord[0] + mapped_coord[1] - 1.0 > self.inclusion_tol):
 *             return 0
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":715
 *             mapped_coord[0] + mapped_coord[1] - 1.0 > self.inclusion_tol):
 *             return 0
 *         if (mapped_coord[1] < -self.inclusion_tol):             # <<<<<<<<<<<<<<
 *             return 0
 *         if (fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 */
  __pyx_t_1 = (((__pyx_v_mapped_coord[1]) < (-__pyx_v_self->__pyx_base.__pyx_base.inclusion_tol)) != 0);
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":716
 *             return 0
 *         if (mapped_coord[1] < -self.inclusion_tol):
 *             return 0             # <<<<<<<<<<<<<<
 *         if (fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0
 */
    __pyx_r = 0;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":715
 *             mapped_coord[0] + mapped_coord[1] - 1.0 > self.inclusion_tol):
 *             return 0
 *         if (mapped_coord[1] < -self.inclusion_tol):             # <<<<<<<<<<<<<<
 *             return 0
 *         if (fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":717
 *         if (mapped_coord[1] < -self.inclusion_tol):
 *             return 0
 *         if (fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):             # <<<<<<<<<<<<<<
 *             return 0
 *         return 1
 */
  __pyx_t_1 = (((fabs((__pyx_v_mapped_coord[2])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":718
 *             return 0
 *         if (fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0             # <<<<<<<<<<<<<<
 *         return 1
 * 
 */
    __pyx_r = 0;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":717
 *         if (mapped_coord[1] < -self.inclusion_tol):
 *             return 0
 *         if (fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):             # <<<<<<<<<<<<<<
 *             return 0
 *         return 1
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":719
 *         if (fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0
 *         return 1             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  __pyx_r = 1;
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":707
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         # for wedges the bounds of the mapped coordinates are:
 *         #     0 <= mapped_coord[0] <= 1 - mapped_coord[1]
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":724
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         cdef double r, s, t
 *         cdef double thresh = 5.0e-2
 */

static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord) {
  double __pyx_v_r;
  double __pyx_v_s;
  CYTHON_UNUSED double __pyx_v_t;
  double __pyx_v_thresh;
  int __pyx_v_near_edge_r;
  int __pyx_v_near_edge_s;
  int __pyx_v_near_edge_t;
  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;

  /* "yt/utilities/lib/element_mappings.pyx":726
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         cdef double r, s, t
 *         cdef double thresh = 5.0e-2             # <<<<<<<<<<<<<<
 *         r = mapped_coord[0]
 *         s = mapped_coord[1]
 */
  __pyx_v_thresh = 5.0e-2;

  /* "yt/utilities/lib/element_mappings.pyx":727
 *         cdef double r, s, t
 *         cdef double thresh = 5.0e-2
 *         r = mapped_coord[0]             # <<<<<<<<<<<<<<
 *         s = mapped_coord[1]
 *         t = mapped_coord[2]
 */
  __pyx_v_r = (__pyx_v_mapped_coord[0]);

  /* "yt/utilities/lib/element_mappings.pyx":728
 *         cdef double thresh = 5.0e-2
 *         r = mapped_coord[0]
 *         s = mapped_coord[1]             # <<<<<<<<<<<<<<
 *         t = mapped_coord[2]
 * 
 */
  __pyx_v_s = (__pyx_v_mapped_coord[1]);

  /* "yt/utilities/lib/element_mappings.pyx":729
 *         r = mapped_coord[0]
 *         s = mapped_coord[1]
 *         t = mapped_coord[2]             # <<<<<<<<<<<<<<
 * 
 *         cdef int near_edge_r, near_edge_s, near_edge_t
 */
  __pyx_v_t = (__pyx_v_mapped_coord[2]);

  /* "yt/utilities/lib/element_mappings.pyx":732
 * 
 *         cdef int near_edge_r, near_edge_s, near_edge_t
 *         near_edge_r = (r < thresh) or (fabs(r + s - 1.0) < thresh)             # <<<<<<<<<<<<<<
 *         near_edge_s = (s < thresh)
 *         near_edge_t = fabs(fabs(mapped_coord[2]) - 1.0) < thresh
 */
  __pyx_t_2 = (__pyx_v_r < __pyx_v_thresh);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L3_bool_binop_done;
  }
  __pyx_t_2 = (fabs(((__pyx_v_r + __pyx_v_s) - 1.0)) < __pyx_v_thresh);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L3_bool_binop_done:;
  __pyx_v_near_edge_r = __pyx_t_1;

  /* "yt/utilities/lib/element_mappings.pyx":733
 *         cdef int near_edge_r, near_edge_s, near_edge_t
 *         near_edge_r = (r < thresh) or (fabs(r + s - 1.0) < thresh)
 *         near_edge_s = (s < thresh)             # <<<<<<<<<<<<<<
 *         near_edge_t = fabs(fabs(mapped_coord[2]) - 1.0) < thresh
 * 
 */
  __pyx_v_near_edge_s = (__pyx_v_s < __pyx_v_thresh);

  /* "yt/utilities/lib/element_mappings.pyx":734
 *         near_edge_r = (r < thresh) or (fabs(r + s - 1.0) < thresh)
 *         near_edge_s = (s < thresh)
 *         near_edge_t = fabs(fabs(mapped_coord[2]) - 1.0) < thresh             # <<<<<<<<<<<<<<
 * 
 *         # we use ray.instID to pass back whether the ray is near the
 */
  __pyx_v_near_edge_t = (fabs((fabs((__pyx_v_mapped_coord[2])) - 1.0)) < __pyx_v_thresh);

  /* "yt/utilities/lib/element_mappings.pyx":738
 *         # we use ray.instID to pass back whether the ray is near the
 *         # element boundary or not (used to annotate mesh lines)
 *         if (near_edge_r and near_edge_s):             # <<<<<<<<<<<<<<
 *             return 1
 *         elif (near_edge_r and near_edge_t):
 */
  __pyx_t_3 = (__pyx_v_near_edge_r != 0);
  if (__pyx_t_3) {
  } else {
    __pyx_t_2 = __pyx_t_3;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_3 = (__pyx_v_near_edge_s != 0);
  __pyx_t_2 = __pyx_t_3;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_2) {

    /* "yt/utilities/lib/element_mappings.pyx":739
 *         # element boundary or not (used to annotate mesh lines)
 *         if (near_edge_r and near_edge_s):
 *             return 1             # <<<<<<<<<<<<<<
 *         elif (near_edge_r and near_edge_t):
 *             return 1
 */
    __pyx_r = 1;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":738
 *         # we use ray.instID to pass back whether the ray is near the
 *         # element boundary or not (used to annotate mesh lines)
 *         if (near_edge_r and near_edge_s):             # <<<<<<<<<<<<<<
 *             return 1
 *         elif (near_edge_r and near_edge_t):
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":740
 *         if (near_edge_r and near_edge_s):
 *             return 1
 *         elif (near_edge_r and near_edge_t):             # <<<<<<<<<<<<<<
 *             return 1
 *         elif (near_edge_s and near_edge_t):
 */
  __pyx_t_3 = (__pyx_v_near_edge_r != 0);
  if (__pyx_t_3) {
  } else {
    __pyx_t_2 = __pyx_t_3;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_3 = (__pyx_v_near_edge_t != 0);
  __pyx_t_2 = __pyx_t_3;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_2) {

    /* "yt/utilities/lib/element_mappings.pyx":741
 *             return 1
 *         elif (near_edge_r and near_edge_t):
 *             return 1             # <<<<<<<<<<<<<<
 *         elif (near_edge_s and near_edge_t):
 *             return 1
 */
    __pyx_r = 1;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":740
 *         if (near_edge_r and near_edge_s):
 *             return 1
 *         elif (near_edge_r and near_edge_t):             # <<<<<<<<<<<<<<
 *             return 1
 *         elif (near_edge_s and near_edge_t):
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":742
 *         elif (near_edge_r and near_edge_t):
 *             return 1
 *         elif (near_edge_s and near_edge_t):             # <<<<<<<<<<<<<<
 *             return 1
 *         else:
 */
  __pyx_t_3 = (__pyx_v_near_edge_s != 0);
  if (__pyx_t_3) {
  } else {
    __pyx_t_2 = __pyx_t_3;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_3 = (__pyx_v_near_edge_t != 0);
  __pyx_t_2 = __pyx_t_3;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_2) {

    /* "yt/utilities/lib/element_mappings.pyx":743
 *             return 1
 *         elif (near_edge_s and near_edge_t):
 *             return 1             # <<<<<<<<<<<<<<
 *         else:
 *             return -1
 */
    __pyx_r = 1;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":742
 *         elif (near_edge_r and near_edge_t):
 *             return 1
 *         elif (near_edge_s and near_edge_t):             # <<<<<<<<<<<<<<
 *             return 1
 *         else:
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":745
 *             return 1
 *         else:
 *             return -1             # <<<<<<<<<<<<<<
 * 
 * 
 */
  /*else*/ {
    __pyx_r = -1;
    goto __pyx_L0;
  }

  /* "yt/utilities/lib/element_mappings.pyx":724
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         cdef double r, s, t
 *         cdef double thresh = 5.0e-2
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":751
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void W1Function3D(double* fx,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_W1Function3D(double *__pyx_v_fx, double *__pyx_v_x, double *__pyx_v_vertices, double *__pyx_v_phys_x) {
  int __pyx_v_i;
  int __pyx_t_1;

  /* "yt/utilities/lib/element_mappings.pyx":756
 *                               double* phys_x) nogil:
 *     cdef int i
 *     for i in range(3):             # <<<<<<<<<<<<<<
 *         fx[i] = vertices[0 + i]*(1.0 - x[0] - x[1])*(1.0 - x[2]) \
 *               + vertices[3 + i]*x[0]*(1.0 - x[2]) \
 */
  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
    __pyx_v_i = __pyx_t_1;

    /* "yt/utilities/lib/element_mappings.pyx":757
 *     cdef int i
 *     for i in range(3):
 *         fx[i] = vertices[0 + i]*(1.0 - x[0] - x[1])*(1.0 - x[2]) \             # <<<<<<<<<<<<<<
 *               + vertices[3 + i]*x[0]*(1.0 - x[2]) \
 *               + vertices[6 + i]*x[1]*(1.0 - x[2]) \
 */
    (__pyx_v_fx[__pyx_v_i]) = (((((((((__pyx_v_vertices[(0 + __pyx_v_i)]) * ((1.0 - (__pyx_v_x[0])) - (__pyx_v_x[1]))) * (1.0 - (__pyx_v_x[2]))) + (((__pyx_v_vertices[(3 + __pyx_v_i)]) * (__pyx_v_x[0])) * (1.0 - (__pyx_v_x[2])))) + (((__pyx_v_vertices[(6 + __pyx_v_i)]) * (__pyx_v_x[1])) * (1.0 - (__pyx_v_x[2])))) + (((__pyx_v_vertices[(9 + __pyx_v_i)]) * ((1.0 - (__pyx_v_x[0])) - (__pyx_v_x[1]))) * (1.0 + (__pyx_v_x[2])))) + (((__pyx_v_vertices[(12 + __pyx_v_i)]) * (__pyx_v_x[0])) * (1.0 + (__pyx_v_x[2])))) + (((__pyx_v_vertices[(15 + __pyx_v_i)]) * (__pyx_v_x[1])) * (1.0 + (__pyx_v_x[2])))) - (2.0 * (__pyx_v_phys_x[__pyx_v_i])));
  }

  /* "yt/utilities/lib/element_mappings.pyx":751
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void W1Function3D(double* fx,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

  /* function exit code */
}

/* "yt/utilities/lib/element_mappings.pyx":769
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void W1Jacobian3D(double* rcol,             # <<<<<<<<<<<<<<
 *                               double* scol,
 *                               double* tcol,
 */

static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_W1Jacobian3D(double *__pyx_v_rcol, double *__pyx_v_scol, double *__pyx_v_tcol, double *__pyx_v_x, double *__pyx_v_vertices, CYTHON_UNUSED double *__pyx_v_phys_x) {
  int __pyx_v_i;
  int __pyx_t_1;

  /* "yt/utilities/lib/element_mappings.pyx":777
 * 
 *     cdef int i
 *     for i in range(3):             # <<<<<<<<<<<<<<
 *         rcol[i] = (x[2] - 1.0) * vertices[0 + i] \
 *                 - (x[2] - 1.0) * vertices[3 + i] \
 */
  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
    __pyx_v_i = __pyx_t_1;

    /* "yt/utilities/lib/element_mappings.pyx":778
 *     cdef int i
 *     for i in range(3):
 *         rcol[i] = (x[2] - 1.0) * vertices[0 + i] \             # <<<<<<<<<<<<<<
 *                 - (x[2] - 1.0) * vertices[3 + i] \
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 *     def __init__(self):
 *         super(Q1Sampler2D, self).__init__()
 *         self.num_mapped_coords = 2             # <<<<<<<<<<<<<<
 *         self.dim = 2
 *         self.func = Q1Function2D
 */
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  /* "yt/utilities/lib/element_mappings.pyx":867
 *         super(Q1Sampler2D, self).__init__()
 *         self.num_mapped_coords = 2
 *         self.dim = 2             # <<<<<<<<<<<<<<
 *         self.func = Q1Function2D
 *         self.jac = Q1Jacobian2D
 */
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  /* "yt/utilities/lib/element_mappings.pyx":868
 *         self.num_mapped_coords = 2
 *         self.dim = 2
 *         self.func = Q1Function2D             # <<<<<<<<<<<<<<
 *         self.jac = Q1Jacobian2D
 * 
 */
  __pyx_v_self->__pyx_base.func = __pyx_f_2yt_9utilities_3lib_16element_mappings_Q1Function2D;

  /* "yt/utilities/lib/element_mappings.pyx":869
 *         self.dim = 2
 *         self.func = Q1Function2D
 *         self.jac = Q1Jacobian2D             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
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 *     '''
 * 
 *     def __init__(self):             # <<<<<<<<<<<<<<
 *         super(Q1Sampler2D, self).__init__()
 *         self.num_mapped_coords = 2
 */

  /* function exit code */
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  __Pyx_XDECREF(__pyx_t_1);
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/* "yt/utilities/lib/element_mappings.pyx":874
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef double sample_at_unit_point(self, double* coord, double* vals) nogil:             # <<<<<<<<<<<<<<
 *         cdef double F, rm, rp, sm, sp
 * 
 */

static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q1Sampler2D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals) {
  double __pyx_v_F;
  double __pyx_v_rm;
  double __pyx_v_rp;
  double __pyx_v_sm;
  double __pyx_v_sp;
  double __pyx_r;

  /* "yt/utilities/lib/element_mappings.pyx":877
 *         cdef double F, rm, rp, sm, sp
 * 
 *         rm = 1.0 - coord[0]             # <<<<<<<<<<<<<<
 *         rp = 1.0 + coord[0]
 *         sm = 1.0 - coord[1]
 */
  __pyx_v_rm = (1.0 - (__pyx_v_coord[0]));

  /* "yt/utilities/lib/element_mappings.pyx":878
 * 
 *         rm = 1.0 - coord[0]
 *         rp = 1.0 + coord[0]             # <<<<<<<<<<<<<<
 *         sm = 1.0 - coord[1]
 *         sp = 1.0 + coord[1]
 */
  __pyx_v_rp = (1.0 + (__pyx_v_coord[0]));

  /* "yt/utilities/lib/element_mappings.pyx":879
 *         rm = 1.0 - coord[0]
 *         rp = 1.0 + coord[0]
 *         sm = 1.0 - coord[1]             # <<<<<<<<<<<<<<
 *         sp = 1.0 + coord[1]
 * 
 */
  __pyx_v_sm = (1.0 - (__pyx_v_coord[1]));

  /* "yt/utilities/lib/element_mappings.pyx":880
 *         rp = 1.0 + coord[0]
 *         sm = 1.0 - coord[1]
 *         sp = 1.0 + coord[1]             # <<<<<<<<<<<<<<
 * 
 *         F = vals[0]*rm*sm + vals[1]*rp*sm + vals[2]*rp*sp + vals[3]*rm*sp
 */
  __pyx_v_sp = (1.0 + (__pyx_v_coord[1]));

  /* "yt/utilities/lib/element_mappings.pyx":882
 *         sp = 1.0 + coord[1]
 * 
 *         F = vals[0]*rm*sm + vals[1]*rp*sm + vals[2]*rp*sp + vals[3]*rm*sp             # <<<<<<<<<<<<<<
 *         return 0.25*F
 * 
 */
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  /* "yt/utilities/lib/element_mappings.pyx":883
 * 
 *         F = vals[0]*rm*sm + vals[1]*rp*sm + vals[2]*rp*sp + vals[3]*rm*sp
 *         return 0.25*F             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  __pyx_r = (0.25 * __pyx_v_F);
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":874
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef double sample_at_unit_point(self, double* coord, double* vals) nogil:             # <<<<<<<<<<<<<<
 *         cdef double F, rm, rp, sm, sp
 * 
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":888
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         # for quads, we check whether the mapped_coord is between
 *         # -1 and 1 in both directions.
 */

static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q1Sampler2D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *__pyx_v_self, double *__pyx_v_mapped_coord) {
  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "yt/utilities/lib/element_mappings.pyx":891
 *         # for quads, we check whether the mapped_coord is between
 *         # -1 and 1 in both directions.
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol):
 *             return 0
 */
  __pyx_t_2 = (((fabs((__pyx_v_mapped_coord[0])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":892
 *         # -1 and 1 in both directions.
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol):             # <<<<<<<<<<<<<<
 *             return 0
 *         return 1
 */
  __pyx_t_2 = (((fabs((__pyx_v_mapped_coord[1])) - 1.0) > __pyx_v_self->__pyx_base.__pyx_base.inclusion_tol) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":891
 *         # for quads, we check whether the mapped_coord is between
 *         # -1 and 1 in both directions.
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol):
 *             return 0
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":893
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol):
 *             return 0             # <<<<<<<<<<<<<<
 *         return 1
 * 
 */
    __pyx_r = 0;
    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":891
 *         # for quads, we check whether the mapped_coord is between
 *         # -1 and 1 in both directions.
 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or             # <<<<<<<<<<<<<<
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol):
 *             return 0
 */
  }

  /* "yt/utilities/lib/element_mappings.pyx":894
 *             fabs(mapped_coord[1]) - 1.0 > self.inclusion_tol):
 *             return 0
 *         return 1             # <<<<<<<<<<<<<<
 * 
 * @cython.boundscheck(False)
 */
  __pyx_r = 1;
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":888
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
 *         # for quads, we check whether the mapped_coord is between
 *         # -1 and 1 in both directions.
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "yt/utilities/lib/element_mappings.pyx":899
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void Q1Jacobian2D(double* A,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_Q1Jacobian2D(double *__pyx_v_A, double *__pyx_v_x, double *__pyx_v_vertices, CYTHON_UNUSED double *__pyx_v_phys_x) {
  double __pyx_v_rm;
  double __pyx_v_rp;
  double __pyx_v_sm;
  double __pyx_v_sp;

  /* "yt/utilities/lib/element_mappings.pyx":905
 *     cdef double rm, rp, sm, sp
 * 
 *     rm = 1.0 - x[0]             # <<<<<<<<<<<<<<
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]
 */
  __pyx_v_rm = (1.0 - (__pyx_v_x[0]));

  /* "yt/utilities/lib/element_mappings.pyx":906
 * 
 *     rm = 1.0 - x[0]
 *     rp = 1.0 + x[0]             # <<<<<<<<<<<<<<
 *     sm = 1.0 - x[1]
 *     sp = 1.0 + x[1]
 */
  __pyx_v_rp = (1.0 + (__pyx_v_x[0]));

  /* "yt/utilities/lib/element_mappings.pyx":907
 *     rm = 1.0 - x[0]
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]             # <<<<<<<<<<<<<<
 *     sp = 1.0 + x[1]
 * 
 */
  __pyx_v_sm = (1.0 - (__pyx_v_x[1]));

  /* "yt/utilities/lib/element_mappings.pyx":908
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]
 *     sp = 1.0 + x[1]             # <<<<<<<<<<<<<<
 * 
 *     A[0] = -sm*vertices[0] + sm*vertices[2] + sp*vertices[4] - sp*vertices[6]
 */
  __pyx_v_sp = (1.0 + (__pyx_v_x[1]));

  /* "yt/utilities/lib/element_mappings.pyx":910
 *     sp = 1.0 + x[1]
 * 
 *     A[0] = -sm*vertices[0] + sm*vertices[2] + sp*vertices[4] - sp*vertices[6]             # <<<<<<<<<<<<<<
 *     A[1] = -rm*vertices[0] - rp*vertices[2] + rp*vertices[4] + rm*vertices[6]
 *     A[2] = -sm*vertices[1] + sm*vertices[3] + sp*vertices[5] - sp*vertices[7]
 */
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  /* "yt/utilities/lib/element_mappings.pyx":911
 * 
 *     A[0] = -sm*vertices[0] + sm*vertices[2] + sp*vertices[4] - sp*vertices[6]
 *     A[1] = -rm*vertices[0] - rp*vertices[2] + rp*vertices[4] + rm*vertices[6]             # <<<<<<<<<<<<<<
 *     A[2] = -sm*vertices[1] + sm*vertices[3] + sp*vertices[5] - sp*vertices[7]
 *     A[3] = -rm*vertices[1] - rp*vertices[3] + rp*vertices[5] + rm*vertices[7]
 */
  (__pyx_v_A[1]) = (((((-__pyx_v_rm) * (__pyx_v_vertices[0])) - (__pyx_v_rp * (__pyx_v_vertices[2]))) + (__pyx_v_rp * (__pyx_v_vertices[4]))) + (__pyx_v_rm * (__pyx_v_vertices[6])));

  /* "yt/utilities/lib/element_mappings.pyx":912
 *     A[0] = -sm*vertices[0] + sm*vertices[2] + sp*vertices[4] - sp*vertices[6]
 *     A[1] = -rm*vertices[0] - rp*vertices[2] + rp*vertices[4] + rm*vertices[6]
 *     A[2] = -sm*vertices[1] + sm*vertices[3] + sp*vertices[5] - sp*vertices[7]             # <<<<<<<<<<<<<<
 *     A[3] = -rm*vertices[1] - rp*vertices[3] + rp*vertices[5] + rm*vertices[7]
 * 
 */
  (__pyx_v_A[2]) = (((((-__pyx_v_sm) * (__pyx_v_vertices[1])) + (__pyx_v_sm * (__pyx_v_vertices[3]))) + (__pyx_v_sp * (__pyx_v_vertices[5]))) - (__pyx_v_sp * (__pyx_v_vertices[7])));

  /* "yt/utilities/lib/element_mappings.pyx":913
 *     A[1] = -rm*vertices[0] - rp*vertices[2] + rp*vertices[4] + rm*vertices[6]
 *     A[2] = -sm*vertices[1] + sm*vertices[3] + sp*vertices[5] - sp*vertices[7]
 *     A[3] = -rm*vertices[1] - rp*vertices[3] + rp*vertices[5] + rm*vertices[7]             # <<<<<<<<<<<<<<
 * 
 * 
 */
  (__pyx_v_A[3]) = (((((-__pyx_v_rm) * (__pyx_v_vertices[1])) - (__pyx_v_rp * (__pyx_v_vertices[3]))) + (__pyx_v_rp * (__pyx_v_vertices[5]))) + (__pyx_v_rm * (__pyx_v_vertices[7])));

  /* "yt/utilities/lib/element_mappings.pyx":899
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void Q1Jacobian2D(double* A,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

  /* function exit code */
}

/* "yt/utilities/lib/element_mappings.pyx":919
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void Q1Function2D(double* fx,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

static CYTHON_INLINE void __pyx_f_2yt_9utilities_3lib_16element_mappings_Q1Function2D(double *__pyx_v_fx, double *__pyx_v_x, double *__pyx_v_vertices, double *__pyx_v_phys_x) {
  int __pyx_v_i;
  double __pyx_v_rm;
  double __pyx_v_rp;
  double __pyx_v_sm;
  double __pyx_v_sp;
  int __pyx_t_1;

  /* "yt/utilities/lib/element_mappings.pyx":926
 *     cdef double rm, rp, sm, sp
 * 
 *     rm = 1.0 - x[0]             # <<<<<<<<<<<<<<
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]
 */
  __pyx_v_rm = (1.0 - (__pyx_v_x[0]));

  /* "yt/utilities/lib/element_mappings.pyx":927
 * 
 *     rm = 1.0 - x[0]
 *     rp = 1.0 + x[0]             # <<<<<<<<<<<<<<
 *     sm = 1.0 - x[1]
 *     sp = 1.0 + x[1]
 */
  __pyx_v_rp = (1.0 + (__pyx_v_x[0]));

  /* "yt/utilities/lib/element_mappings.pyx":928
 *     rm = 1.0 - x[0]
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]             # <<<<<<<<<<<<<<
 *     sp = 1.0 + x[1]
 * 
 */
  __pyx_v_sm = (1.0 - (__pyx_v_x[1]));

  /* "yt/utilities/lib/element_mappings.pyx":929
 *     rp = 1.0 + x[0]
 *     sm = 1.0 - x[1]
 *     sp = 1.0 + x[1]             # <<<<<<<<<<<<<<
 * 
 *     for i in range(2):
 */
  __pyx_v_sp = (1.0 + (__pyx_v_x[1]));

  /* "yt/utilities/lib/element_mappings.pyx":931
 *     sp = 1.0 + x[1]
 * 
 *     for i in range(2):             # <<<<<<<<<<<<<<
 *         fx[i] = vertices[0 + i]*rm*sm \
 *               + vertices[2 + i]*rp*sm \
 */
  for (__pyx_t_1 = 0; __pyx_t_1 < 2; __pyx_t_1+=1) {
    __pyx_v_i = __pyx_t_1;

    /* "yt/utilities/lib/element_mappings.pyx":932
 * 
 *     for i in range(2):
 *         fx[i] = vertices[0 + i]*rm*sm \             # <<<<<<<<<<<<<<
 *               + vertices[2 + i]*rp*sm \
 *               + vertices[4 + i]*rp*sp \
 */
    (__pyx_v_fx[__pyx_v_i]) = (((((((__pyx_v_vertices[(0 + __pyx_v_i)]) * __pyx_v_rm) * __pyx_v_sm) + (((__pyx_v_vertices[(2 + __pyx_v_i)]) * __pyx_v_rp) * __pyx_v_sm)) + (((__pyx_v_vertices[(4 + __pyx_v_i)]) * __pyx_v_rp) * __pyx_v_sp)) + (((__pyx_v_vertices[(6 + __pyx_v_i)]) * __pyx_v_rm) * __pyx_v_sp)) - (4.0 * (__pyx_v_phys_x[__pyx_v_i])));
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  /* "yt/utilities/lib/element_mappings.pyx":919
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef inline void Q1Function2D(double* fx,             # <<<<<<<<<<<<<<
 *                               double* x,
 *                               double* vertices,
 */

  /* function exit code */
}

/* "yt/utilities/lib/element_mappings.pyx":942
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * def test_hex_sampler(np.ndarray[np.float64_t, ndim=2] vertices,             # <<<<<<<<<<<<<<
 *                      np.ndarray[np.float64_t, ndim=1] field_values,
 *                      np.ndarray[np.float64_t, ndim=1] physical_x):
 */

/* Python wrapper */
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        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        case  0: break;
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_14ElementSampler_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_ElementSampler, /*tp_new*/
  0, /*tp_free*/
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  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler2D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_P1Sampler2D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler2D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *p;
  PyObject *o = __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_ElementSampler(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_P1Sampler2D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_P1Sampler2D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_P1Sampler2D = {
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  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_2yt_9utilities_3lib_16element_mappings_ElementSampler, /*tp_dealloc*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
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  #if PY_MAJOR_VERSION >= 3
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  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
  "\n\n    This implements sampling inside a linear, triangular mesh element.\n    This mapping is linear and can be inverted easily.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
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  0, /*tp_richcompare*/
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  __pyx_methods_2yt_9utilities_3lib_16element_mappings_P1Sampler2D, /*tp_methods*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D_1__init__, /*tp_init*/
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  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler2D, /*tp_new*/
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  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler3D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_P1Sampler3D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *p;
  PyObject *o = __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_ElementSampler(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_P1Sampler3D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_P1Sampler3D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_P1Sampler3D = {
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  "yt.utilities.lib.element_mappings.P1Sampler3D", /*tp_name*/
  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_2yt_9utilities_3lib_16element_mappings_ElementSampler, /*tp_dealloc*/
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  #if PY_MAJOR_VERSION < 3
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  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
  "\n\n    This implements sampling inside a linear, tetrahedral mesh element.\n    This mapping is linear and can be inverted easily.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
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  __pyx_methods_2yt_9utilities_3lib_16element_mappings_P1Sampler3D, /*tp_methods*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_1__init__, /*tp_init*/
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  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler3D, /*tp_new*/
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  #if PY_VERSION_HEX >= 0x030400a1
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};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D *p;
  PyObject *o = __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_ElementSampler(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D = {
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  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_2yt_9utilities_3lib_16element_mappings_ElementSampler, /*tp_dealloc*/
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  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
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  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
  "\n\n    This is a base class for handling element samplers that require\n    a nonlinear solve to invert the mapping between coordinate systems.\n    To do this, we perform Newton-Raphson iteration using a specified \n    system of equations with an analytic Jacobian matrix. This solver\n    is hard-coded for 3D for reasons of efficiency. This is not to be\n    used directly, use one of the subclasses instead.\n\n    ", /*tp_doc*/
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  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D, /*tp_new*/
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};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *p;
  PyObject *o = __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.Q1Sampler3D", /*tp_name*/
  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_2yt_9utilities_3lib_16element_mappings_ElementSampler, /*tp_dealloc*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
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  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
  " \n\n    This implements sampling inside a 3D, linear, hexahedral mesh element.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
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};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_W1Sampler3D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_W1Sampler3D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_W1Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *p;
  PyObject *o = __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_W1Sampler3D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_W1Sampler3D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_W1Sampler3D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.W1Sampler3D", /*tp_name*/
  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_2yt_9utilities_3lib_16element_mappings_ElementSampler, /*tp_dealloc*/
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  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
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  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
  " \n\n    This implements sampling inside a 3D, linear, wedge mesh element.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_1__init__, /*tp_init*/
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  0, /*tp_finalize*/
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};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_S2Sampler3D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_S2Sampler3D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_S2Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *p;
  PyObject *o = __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_S2Sampler3D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_S2Sampler3D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_S2Sampler3D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.S2Sampler3D", /*tp_name*/
  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_2yt_9utilities_3lib_16element_mappings_ElementSampler, /*tp_dealloc*/
  0, /*tp_print*/
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  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
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  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
  " \n\n    This implements sampling inside a 3D, 20-node hexahedral mesh element.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_1__init__, /*tp_init*/
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  0, /*tp_finalize*/
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};
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/* PyCFunctionFastCall */
#if CYTHON_FAST_PYCCALL
static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
    PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
    PyCFunction meth = PyCFunction_GET_FUNCTION(func);
    PyObject *self = PyCFunction_GET_SELF(func);
    PyObject *result;
    int flags;
    assert(PyCFunction_Check(func));
    assert(METH_FASTCALL == PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST));
    assert(nargs >= 0);
    assert(nargs == 0 || args != NULL);
    /* _PyCFunction_FastCallDict() must not be called with an exception set,
       because it may clear it (directly or indirectly) and so the
       caller loses its exception */
    assert(!PyErr_Occurred());
    return (*((__Pyx_PyCFunctionFast)meth)) (self, args, nargs, NULL);
}
#endif  // CYTHON_FAST_PYCCALL

/* PyFunctionFastCall */
#if CYTHON_FAST_PYCALL
#include "frameobject.h"
static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
                                               PyObject *globals) {
    PyFrameObject *f;
    PyThreadState *tstate = PyThreadState_GET();
    PyObject **fastlocals;
    Py_ssize_t i;
    PyObject *result;
    assert(globals != NULL);
    /* XXX Perhaps we should create a specialized
       PyFrame_New() that doesn't take locals, but does
       take builtins without sanity checking them.
       */
    assert(tstate != NULL);
    f = PyFrame_New(tstate, co, globals, NULL);
    if (f == NULL) {
        return NULL;
    }
    fastlocals = f->f_localsplus;
    for (i = 0; i < na; i++) {
        Py_INCREF(*args);
        fastlocals[i] = *args++;
    }
    result = PyEval_EvalFrameEx(f,0);
    ++tstate->recursion_depth;
    Py_DECREF(f);
    --tstate->recursion_depth;
    return result;
}
#if 1 || PY_VERSION_HEX < 0x030600B1
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) {
    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
    PyObject *globals = PyFunction_GET_GLOBALS(func);
    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
    PyObject *closure;
#if PY_MAJOR_VERSION >= 3
    PyObject *kwdefs;
#endif
    PyObject *kwtuple, **k;
    PyObject **d;
    Py_ssize_t nd;
    Py_ssize_t nk;
    PyObject *result;
    assert(kwargs == NULL || PyDict_Check(kwargs));
    nk = kwargs ? PyDict_Size(kwargs) : 0;
    if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
        return NULL;
    }
    if (
#if PY_MAJOR_VERSION >= 3
            co->co_kwonlyargcount == 0 &&
#endif
            likely(kwargs == NULL || nk == 0) &&
            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
        if (argdefs == NULL && co->co_argcount == nargs) {
            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
            goto done;
        }
        else if (nargs == 0 && argdefs != NULL
                 && co->co_argcount == Py_SIZE(argdefs)) {
            /* function called with no arguments, but all parameters have
               a default value: use default values as arguments .*/
            args = &PyTuple_GET_ITEM(argdefs, 0);
            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
            goto done;
        }
    }
    if (kwargs != NULL) {
        Py_ssize_t pos, i;
        kwtuple = PyTuple_New(2 * nk);
        if (kwtuple == NULL) {
            result = NULL;
            goto done;
        }
        k = &PyTuple_GET_ITEM(kwtuple, 0);
        pos = i = 0;
        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
            Py_INCREF(k[i]);
            Py_INCREF(k[i+1]);
            i += 2;
        }
        nk = i / 2;
    }
    else {
        kwtuple = NULL;
        k = NULL;
    }
    closure = PyFunction_GET_CLOSURE(func);
#if PY_MAJOR_VERSION >= 3
    kwdefs = PyFunction_GET_KW_DEFAULTS(func);
#endif
    if (argdefs != NULL) {
        d = &PyTuple_GET_ITEM(argdefs, 0);
        nd = Py_SIZE(argdefs);
    }
    else {
        d = NULL;
        nd = 0;
    }
#if PY_MAJOR_VERSION >= 3
    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
                               args, nargs,
                               k, (int)nk,
                               d, (int)nd, kwdefs, closure);
#else
    result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
                               args, nargs,
                               k, (int)nk,
                               d, (int)nd, closure);
#endif
    Py_XDECREF(kwtuple);
done:
    Py_LeaveRecursiveCall();
    return result;
}
#endif  // CPython < 3.6
#endif  // CYTHON_FAST_PYCALL

/* PyObjectCallMethO */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
    PyObject *self, *result;
    PyCFunction cfunc;
    cfunc = PyCFunction_GET_FUNCTION(func);
    self = PyCFunction_GET_SELF(func);
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
        return NULL;
    result = cfunc(self, arg);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

/* PyObjectCallOneArg */
#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_New(1);
    if (unlikely(!args)) return NULL;
    Py_INCREF(arg);
    PyTuple_SET_ITEM(args, 0, arg);
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
#if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCall(func, &arg, 1);
    }
#endif
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
            return __Pyx_PyObject_CallMethO(func, arg);
#if CYTHON_FAST_PYCCALL
        } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
            return __Pyx_PyCFunction_FastCall(func, &arg, 1);
#endif
        }
    }
    return __Pyx__PyObject_CallOneArg(func, arg);
}
#else
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_Pack(1, arg);
    if (unlikely(!args)) return NULL;
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
#endif

/* PyObjectCallNoArg */
  #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
#if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCall(func, NULL, 0);
    }
#endif
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
            return __Pyx_PyObject_CallMethO(func, NULL);
        }
    }
    return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
}
#endif

/* RaiseDoubleKeywords */
    static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name,
    PyObject* kw_name)
{
    PyErr_Format(PyExc_TypeError,
        #if PY_MAJOR_VERSION >= 3
        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
        #else
        "%s() got multiple values for keyword argument '%s'", func_name,
        PyString_AsString(kw_name));
        #endif
}

/* ParseKeywords */
    static int __Pyx_ParseOptionalKeywords(
    PyObject *kwds,
    PyObject **argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject *key = 0, *value = 0;
    Py_ssize_t pos = 0;
    PyObject*** name;
    PyObject*** first_kw_arg = argnames + num_pos_args;
    while (PyDict_Next(kwds, &pos, &key, &value)) {
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            values[name-argnames] = value;
            continue;
        }
        name = first_kw_arg;
        #if PY_MAJOR_VERSION < 3
        if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
            while (*name) {
                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
                        && _PyString_Eq(**name, key)) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    if ((**argname == key) || (
                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
                             && _PyString_Eq(**argname, key))) {
                        goto arg_passed_twice;
                    }
                    argname++;
                }
            }
        } else
        #endif
        if (likely(PyUnicode_Check(key))) {
            while (*name) {
                int cmp = (**name == key) ? 0 :
                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                    (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
                #endif
                    PyUnicode_Compare(**name, key);
                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                if (cmp == 0) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    int cmp = (**argname == key) ? 0 :
                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
                    #endif
                        PyUnicode_Compare(**argname, key);
                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                    if (cmp == 0) goto arg_passed_twice;
                    argname++;
                }
            }
        } else
            goto invalid_keyword_type;
        if (kwds2) {
            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
        } else {
            goto invalid_keyword;
        }
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%.200s() got an unexpected keyword argument '%.200s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
bad:
    return -1;
}

/* ArgTypeTest */
    static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) {
    PyErr_Format(PyExc_TypeError,
        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
        name, type->tp_name, Py_TYPE(obj)->tp_name);
}
static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
    const char *name, int exact)
{
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (none_allowed && obj == Py_None) return 1;
    else if (exact) {
        if (likely(Py_TYPE(obj) == type)) return 1;
        #if PY_MAJOR_VERSION == 2
        else if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
        #endif
    }
    else {
        if (likely(PyObject_TypeCheck(obj, type))) return 1;
    }
    __Pyx_RaiseArgumentTypeInvalid(name, obj, type);
    return 0;
}

/* BufferFormatCheck */
    static CYTHON_INLINE int __Pyx_IsLittleEndian(void) {
  unsigned int n = 1;
  return *(unsigned char*)(&n) != 0;
}
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              __Pyx_TypeInfo* type) {
  stack[0].field = &ctx->root;
  stack[0].parent_offset = 0;
  ctx->root.type = type;
  ctx->root.name = "buffer dtype";
  ctx->root.offset = 0;
  ctx->head = stack;
  ctx->head->field = &ctx->root;
  ctx->fmt_offset = 0;
  ctx->head->parent_offset = 0;
  ctx->new_packmode = '@';
  ctx->enc_packmode = '@';
  ctx->new_count = 1;
  ctx->enc_count = 0;
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  ctx->is_valid_array = 0;
  ctx->struct_alignment = 0;
  while (type->typegroup == 'S') {
    ++ctx->head;
    ctx->head->field = type->fields;
    ctx->head->parent_offset = 0;
    type = type->fields->type;
  }
}
static int __Pyx_BufFmt_ParseNumber(const char** ts) {
    int count;
    const char* t = *ts;
    if (*t < '0' || *t > '9') {
      return -1;
    } else {
        count = *t++ - '0';
        while (*t >= '0' && *t < '9') {
            count *= 10;
            count += *t++ - '0';
        }
    }
    *ts = t;
    return count;
}
static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
    int number = __Pyx_BufFmt_ParseNumber(ts);
    if (number == -1)
        PyErr_Format(PyExc_ValueError,\
                     "Does not understand character buffer dtype format string ('%c')", **ts);
    return number;
}
static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
  PyErr_Format(PyExc_ValueError,
               "Unexpected format string character: '%c'", ch);
}
static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
  switch (ch) {
    case 'c': return "'char'";
    case 'b': return "'signed char'";
    case 'B': return "'unsigned char'";
    case 'h': return "'short'";
    case 'H': return "'unsigned short'";
    case 'i': return "'int'";
    case 'I': return "'unsigned int'";
    case 'l': return "'long'";
    case 'L': return "'unsigned long'";
    case 'q': return "'long long'";
    case 'Q': return "'unsigned long long'";
    case 'f': return (is_complex ? "'complex float'" : "'float'");
    case 'd': return (is_complex ? "'complex double'" : "'double'");
    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
    case 'T': return "a struct";
    case 'O': return "Python object";
    case 'P': return "a pointer";
    case 's': case 'p': return "a string";
    case 0: return "end";
    default: return "unparseable format string";
  }
}
static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return 2;
    case 'i': case 'I': case 'l': case 'L': return 4;
    case 'q': case 'Q': return 8;
    case 'f': return (is_complex ? 8 : 4);
    case 'd': return (is_complex ? 16 : 8);
    case 'g': {
      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
      return 0;
    }
    case 'O': case 'P': return sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
  switch (ch) {
    case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(short);
    case 'i': case 'I': return sizeof(int);
    case 'l': case 'L': return sizeof(long);
    #ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
    #endif
    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
    case 'O': case 'P': return sizeof(void*);
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
typedef struct { char c; short x; } __Pyx_st_short;
typedef struct { char c; int x; } __Pyx_st_int;
typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
/* These are for computing the padding at the end of the struct to align
   on the first member of the struct. This will probably the same as above,
   but we don't have any guarantees.
 */
typedef struct { short x; char c; } __Pyx_pad_short;
typedef struct { int x; char c; } __Pyx_pad_int;
typedef struct { long x; char c; } __Pyx_pad_long;
typedef struct { float x; char c; } __Pyx_pad_float;
typedef struct { double x; char c; } __Pyx_pad_double;
typedef struct { long double x; char c; } __Pyx_pad_longdouble;
typedef struct { void *x; char c; } __Pyx_pad_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
  switch (ch) {
    case 'c':
        return 'H';
    case 'b': case 'h': case 'i':
    case 'l': case 'q': case 's': case 'p':
        return 'I';
    case 'B': case 'H': case 'I': case 'L': case 'Q':
        return 'U';
    case 'f': case 'd': case 'g':
        return (is_complex ? 'C' : 'R');
    case 'O':
        return 'O';
    case 'P':
        return 'P';
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
    const char* expected;
    const char* quote;
    if (ctx->head == NULL) {
      expected = "end";
      quote = "";
    } else {
      expected = ctx->head->field->type->name;
      quote = "'";
    }
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected %s%s%s but got %s",
                 quote, expected, quote,
                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
  } else {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_StructField* parent = (ctx->head - 1)->field;
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
                 parent->type->name, field->name);
  }
}
static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
  char group;
  size_t size, offset, arraysize = 1;
  if (ctx->enc_type == 0) return 0;
  if (ctx->head->field->type->arraysize[0]) {
    int i, ndim = 0;
    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
        ndim = 1;
        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
            PyErr_Format(PyExc_ValueError,
                         "Expected a dimension of size %zu, got %zu",
                         ctx->head->field->type->arraysize[0], ctx->enc_count);
            return -1;
        }
    }
    if (!ctx->is_valid_array) {
      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
                   ctx->head->field->type->ndim, ndim);
      return -1;
    }
    for (i = 0; i < ctx->head->field->type->ndim; i++) {
      arraysize *= ctx->head->field->type->arraysize[i];
    }
    ctx->is_valid_array = 0;
    ctx->enc_count = 1;
  }
  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
  do {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_TypeInfo* type = field->type;
    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
    } else {
      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
    }
    if (ctx->enc_packmode == '@') {
      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
      size_t align_mod_offset;
      if (align_at == 0) return -1;
      align_mod_offset = ctx->fmt_offset % align_at;
      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
      if (ctx->struct_alignment == 0)
          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
                                                                 ctx->is_complex);
    }
    if (type->size != size || type->typegroup != group) {
      if (type->typegroup == 'C' && type->fields != NULL) {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        ++ctx->head;
        ctx->head->field = type->fields;
        ctx->head->parent_offset = parent_offset;
        continue;
      }
      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
      } else {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
      }
    }
    offset = ctx->head->parent_offset + field->offset;
    if (ctx->fmt_offset != offset) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
      return -1;
    }
    ctx->fmt_offset += size;
    if (arraysize)
      ctx->fmt_offset += (arraysize - 1) * size;
    --ctx->enc_count;
    while (1) {
      if (field == &ctx->root) {
        ctx->head = NULL;
        if (ctx->enc_count != 0) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
        }
        break;
      }
      ctx->head->field = ++field;
      if (field->type == NULL) {
        --ctx->head;
        field = ctx->head->field;
        continue;
      } else if (field->type->typegroup == 'S') {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        if (field->type->fields->type == NULL) continue;
        field = field->type->fields;
        ++ctx->head;
        ctx->head->field = field;
        ctx->head->parent_offset = parent_offset;
        break;
      } else {
        break;
      }
    }
  } while (ctx->enc_count);
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  return 0;
}
static CYTHON_INLINE PyObject *
__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
{
    const char *ts = *tsp;
    int i = 0, number;
    int ndim = ctx->head->field->type->ndim;
;
    ++ts;
    if (ctx->new_count != 1) {
        PyErr_SetString(PyExc_ValueError,
                        "Cannot handle repeated arrays in format string");
        return NULL;
    }
    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
    while (*ts && *ts != ')') {
        switch (*ts) {
            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
            default:  break;
        }
        number = __Pyx_BufFmt_ExpectNumber(&ts);
        if (number == -1) return NULL;
        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
            return PyErr_Format(PyExc_ValueError,
                        "Expected a dimension of size %zu, got %d",
                        ctx->head->field->type->arraysize[i], number);
        if (*ts != ',' && *ts != ')')
            return PyErr_Format(PyExc_ValueError,
                                "Expected a comma in format string, got '%c'", *ts);
        if (*ts == ',') ts++;
        i++;
    }
    if (i != ndim)
        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
                            ctx->head->field->type->ndim, i);
    if (!*ts) {
        PyErr_SetString(PyExc_ValueError,
                        "Unexpected end of format string, expected ')'");
        return NULL;
    }
    ctx->is_valid_array = 1;
    ctx->new_count = 1;
    *tsp = ++ts;
    return Py_None;
}
static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
  int got_Z = 0;
  while (1) {
    switch(*ts) {
      case 0:
        if (ctx->enc_type != 0 && ctx->head == NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        if (ctx->head != NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        return ts;
      case ' ':
      case '\r':
      case '\n':
        ++ts;
        break;
      case '<':
        if (!__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '=':
      case '@':
      case '^':
        ctx->new_packmode = *ts++;
        break;
      case 'T':
        {
          const char* ts_after_sub;
          size_t i, struct_count = ctx->new_count;
          size_t struct_alignment = ctx->struct_alignment;
          ctx->new_count = 1;
          ++ts;
          if (*ts != '{') {
            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
            return NULL;
          }
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          ctx->enc_count = 0;
          ctx->struct_alignment = 0;
          ++ts;
          ts_after_sub = ts;
          for (i = 0; i != struct_count; ++i) {
            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
            if (!ts_after_sub) return NULL;
          }
          ts = ts_after_sub;
          if (struct_alignment) ctx->struct_alignment = struct_alignment;
        }
        break;
      case '}':
        {
          size_t alignment = ctx->struct_alignment;
          ++ts;
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          if (alignment && ctx->fmt_offset % alignment) {
            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
          }
        }
        return ts;
      case 'x':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->fmt_offset += ctx->new_count;
        ctx->new_count = 1;
        ctx->enc_count = 0;
        ctx->enc_type = 0;
        ctx->enc_packmode = ctx->new_packmode;
        ++ts;
        break;
      case 'Z':
        got_Z = 1;
        ++ts;
        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
          return NULL;
        }
      case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
      case 'l': case 'L': case 'q': case 'Q':
      case 'f': case 'd': case 'g':
      case 'O': case 'p':
        if (ctx->enc_type == *ts && got_Z == ctx->is_complex &&
            ctx->enc_packmode == ctx->new_packmode) {
          ctx->enc_count += ctx->new_count;
          ctx->new_count = 1;
          got_Z = 0;
          ++ts;
          break;
        }
      case 's':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->enc_count = ctx->new_count;
        ctx->enc_packmode = ctx->new_packmode;
        ctx->enc_type = *ts;
        ctx->is_complex = got_Z;
        ++ts;
        ctx->new_count = 1;
        got_Z = 0;
        break;
      case ':':
        ++ts;
        while(*ts != ':') ++ts;
        ++ts;
        break;
      case '(':
        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
        break;
      default:
        {
          int number = __Pyx_BufFmt_ExpectNumber(&ts);
          if (number == -1) return NULL;
          ctx->new_count = (size_t)number;
        }
    }
  }
}
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 CYTHON_INLINE 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 || obj == NULL) {
    __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 (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
      dtype->name, (Py_ssize_t)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);
}

/* PyErrFetchRestore */
      #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    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_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    *type = tstate->curexc_type;
    *value = tstate->curexc_value;
    *tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
}
#endif

/* RaiseException */
      #if PY_MAJOR_VERSION < 3
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
                        CYTHON_UNUSED PyObject *cause) {
    __Pyx_PyThreadState_declare
    Py_XINCREF(type);
    if (!value || value == Py_None)
        value = NULL;
    else
        Py_INCREF(value);
    if (!tb || tb == Py_None)
        tb = NULL;
    else {
        Py_INCREF(tb);
        if (!PyTraceBack_Check(tb)) {
            PyErr_SetString(PyExc_TypeError,
                "raise: arg 3 must be a traceback or None");
            goto raise_error;
        }
    }
    if (PyType_Check(type)) {
#if CYTHON_COMPILING_IN_PYPY
        if (!value) {
            Py_INCREF(Py_None);
            value = Py_None;
        }
#endif
        PyErr_NormalizeException(&type, &value, &tb);
    } else {
        if (value) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto raise_error;
        }
        value = type;
        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;
        }
    }
    __Pyx_PyThreadState_assign
    __Pyx_ErrRestore(type, value, tb);
    return;
raise_error:
    Py_XDECREF(value);
    Py_XDECREF(type);
    Py_XDECREF(tb);
    return;
}
#else
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
    PyObject* owned_instance = NULL;
    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)) {
        PyObject *instance_class = NULL;
        if (value && PyExceptionInstance_Check(value)) {
            instance_class = (PyObject*) Py_TYPE(value);
            if (instance_class != type) {
                int is_subclass = PyObject_IsSubclass(instance_class, type);
                if (!is_subclass) {
                    instance_class = NULL;
                } else if (unlikely(is_subclass == -1)) {
                    goto bad;
                } else {
                    type = instance_class;
                }
            }
        }
        if (!instance_class) {
            PyObject *args;
            if (!value)
                args = PyTuple_New(0);
            else if (PyTuple_Check(value)) {
                Py_INCREF(value);
                args = value;
            } else
                args = PyTuple_Pack(1, value);
            if (!args)
                goto bad;
            owned_instance = PyObject_Call(type, args, NULL);
            Py_DECREF(args);
            if (!owned_instance)
                goto bad;
            value = owned_instance;
            if (!PyExceptionInstance_Check(value)) {
                PyErr_Format(PyExc_TypeError,
                             "calling %R should have returned an instance of "
                             "BaseException, not %R",
                             type, Py_TYPE(value));
                goto bad;
            }
        }
    } else {
        PyErr_SetString(PyExc_TypeError,
            "raise: exception class must be a subclass of BaseException");
        goto bad;
    }
#if PY_VERSION_HEX >= 0x03030000
    if (cause) {
#else
    if (cause && cause != Py_None) {
#endif
        PyObject *fixed_cause;
        if (cause == Py_None) {
            fixed_cause = NULL;
        } else if (PyExceptionClass_Check(cause)) {
            fixed_cause = PyObject_CallObject(cause, NULL);
            if (fixed_cause == NULL)
                goto bad;
        } else if (PyExceptionInstance_Check(cause)) {
            fixed_cause = cause;
            Py_INCREF(fixed_cause);
        } else {
            PyErr_SetString(PyExc_TypeError,
                            "exception causes must derive from "
                            "BaseException");
            goto bad;
        }
        PyException_SetCause(value, fixed_cause);
    }
    PyErr_SetObject(type, value);
    if (tb) {
#if CYTHON_COMPILING_IN_PYPY
        PyObject *tmp_type, *tmp_value, *tmp_tb;
        PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
        Py_INCREF(tb);
        PyErr_Restore(tmp_type, tmp_value, tb);
        Py_XDECREF(tmp_tb);
#else
        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);
        }
#endif
    }
bad:
    Py_XDECREF(owned_instance);
    return;
}
#endif

/* RaiseTooManyValuesToUnpack */
        static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
    PyErr_Format(PyExc_ValueError,
                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
}

/* RaiseNeedMoreValuesToUnpack */
        static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
    PyErr_Format(PyExc_ValueError,
                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
                 index, (index == 1) ? "" : "s");
}

/* RaiseNoneIterError */
        static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
}

/* ExtTypeTest */
        static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
    if (unlikely(!type)) {
        PyErr_SetString(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;
}

/* SaveResetException */
        #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
}
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = type;
    tstate->exc_value = value;
    tstate->exc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}
#endif

/* PyErrExceptionMatches */
        #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
    PyObject *exc_type = tstate->curexc_type;
    if (exc_type == err) return 1;
    if (unlikely(!exc_type)) return 0;
    return PyErr_GivenExceptionMatches(exc_type, err);
}
#endif

/* GetException */
        #if CYTHON_FAST_THREAD_STATE
static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
#else
static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
#endif
    PyObject *local_type, *local_value, *local_tb;
#if CYTHON_FAST_THREAD_STATE
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    local_type = tstate->curexc_type;
    local_value = tstate->curexc_value;
    local_tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#else
    PyErr_Fetch(&local_type, &local_value, &local_tb);
#endif
    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
#if CYTHON_FAST_THREAD_STATE
    if (unlikely(tstate->curexc_type))
#else
    if (unlikely(PyErr_Occurred()))
#endif
        goto bad;
    #if PY_MAJOR_VERSION >= 3
    if (local_tb) {
        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
            goto bad;
    }
    #endif
    Py_XINCREF(local_tb);
    Py_XINCREF(local_type);
    Py_XINCREF(local_value);
    *type = local_type;
    *value = local_value;
    *tb = local_tb;
#if CYTHON_FAST_THREAD_STATE
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = local_type;
    tstate->exc_value = local_value;
    tstate->exc_traceback = local_tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#else
    PyErr_SetExcInfo(local_type, local_value, local_tb);
#endif
    return 0;
bad:
    *type = 0;
    *value = 0;
    *tb = 0;
    Py_XDECREF(local_type);
    Py_XDECREF(local_value);
    Py_XDECREF(local_tb);
    return -1;
}

/* SetVTable */
          static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
#if PY_VERSION_HEX >= 0x02070000
    PyObject *ob = PyCapsule_New(vtable, 0, 0);
#else
    PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
#endif
    if (!ob)
        goto bad;
    if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0)
        goto bad;
    Py_DECREF(ob);
    return 0;
bad:
    Py_XDECREF(ob);
    return -1;
}

/* Import */
          static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
    PyObject *empty_list = 0;
    PyObject *module = 0;
    PyObject *global_dict = 0;
    PyObject *empty_dict = 0;
    PyObject *list;
    #if PY_VERSION_HEX < 0x03030000
    PyObject *py_import;
    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
    if (!py_import)
        goto bad;
    #endif
    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_MAJOR_VERSION >= 3
        if (level == -1) {
            if (strchr(__Pyx_MODULE_NAME, '.')) {
                #if PY_VERSION_HEX < 0x03030000
                PyObject *py_level = PyInt_FromLong(1);
                if (!py_level)
                    goto bad;
                module = PyObject_CallFunctionObjArgs(py_import,
                    name, global_dict, empty_dict, list, py_level, NULL);
                Py_DECREF(py_level);
                #else
                module = PyImport_ImportModuleLevelObject(
                    name, global_dict, empty_dict, list, 1);
                #endif
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0;
        }
        #endif
        if (!module) {
            #if PY_VERSION_HEX < 0x03030000
            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
            module = PyImport_ImportModuleLevelObject(
                name, global_dict, empty_dict, list, level);
            #endif
        }
    }
bad:
    #if PY_VERSION_HEX < 0x03030000
    Py_XDECREF(py_import);
    #endif
    Py_XDECREF(empty_list);
    Py_XDECREF(empty_dict);
    return module;
}

/* CodeObjectCache */
          static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
    int start = 0, mid = 0, end = count - 1;
    if (end >= 0 && code_line > entries[end].code_line) {
        return count;
    }
    while (start < end) {
        mid = start + (end - start) / 2;
        if (code_line < entries[mid].code_line) {
            end = mid;
        } else if (code_line > entries[mid].code_line) {
             start = mid + 1;
        } else {
            return mid;
        }
    }
    if (code_line <= entries[mid].code_line) {
        return mid;
    } else {
        return mid + 1;
    }
}
static PyCodeObject *__pyx_find_code_object(int code_line) {
    PyCodeObject* code_object;
    int pos;
    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
        return NULL;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
        return NULL;
    }
    code_object = __pyx_code_cache.entries[pos].code_object;
    Py_INCREF(code_object);
    return code_object;
}
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
    int pos, i;
    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
    if (unlikely(!code_line)) {
        return;
    }
    if (unlikely(!entries)) {
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
        if (likely(entries)) {
            __pyx_code_cache.entries = entries;
            __pyx_code_cache.max_count = 64;
            __pyx_code_cache.count = 1;
            entries[0].code_line = code_line;
            entries[0].code_object = code_object;
            Py_INCREF(code_object);
        }
        return;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
        PyCodeObject* tmp = entries[pos].code_object;
        entries[pos].code_object = code_object;
        Py_DECREF(tmp);
        return;
    }
    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
        int new_max = __pyx_code_cache.max_count + 64;
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
            __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
        if (unlikely(!entries)) {
            return;
        }
        __pyx_code_cache.entries = entries;
        __pyx_code_cache.max_count = new_max;
    }
    for (i=__pyx_code_cache.count; i>pos; i--) {
        entries[i] = entries[i-1];
    }
    entries[pos].code_line = code_line;
    entries[pos].code_object = code_object;
    __pyx_code_cache.count++;
    Py_INCREF(code_object);
}

/* AddTraceback */
          #include "compile.h"
#include "frameobject.h"
#include "traceback.h"
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
            const char *funcname, int c_line,
            int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyObject *py_srcfile = 0;
    PyObject *py_funcname = 0;
    #if PY_MAJOR_VERSION < 3
    py_srcfile = PyString_FromString(filename);
    #else
    py_srcfile = PyUnicode_FromString(filename);
    #endif
    if (!py_srcfile) goto bad;
    if (c_line) {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #else
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #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_code = __Pyx_PyCode_New(
        0,
        0,
        0,
        0,
        0,
        __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,*/
        py_line,
        __pyx_empty_bytes  /*PyObject *lnotab*/
    );
    Py_DECREF(py_srcfile);
    Py_DECREF(py_funcname);
    return py_code;
bad:
    Py_XDECREF(py_srcfile);
    Py_XDECREF(py_funcname);
    return NULL;
}
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyFrameObject *py_frame = 0;
    py_code = __pyx_find_code_object(c_line ? c_line : py_line);
    if (!py_code) {
        py_code = __Pyx_CreateCodeObjectForTraceback(
            funcname, c_line, py_line, filename);
        if (!py_code) goto bad;
        __pyx_insert_code_object(c_line ? c_line : py_line, py_code);
    }
    py_frame = PyFrame_New(
        PyThreadState_GET(), /*PyThreadState *tstate,*/
        py_code,             /*PyCodeObject *code,*/
        __pyx_d,      /*PyObject *globals,*/
        0                    /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}

#if PY_MAJOR_VERSION < 3
static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pw_5numpy_7ndarray_1__getbuffer__(obj, view, flags);
    PyErr_Format(PyExc_TypeError, "'%.200s' 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) return;
    if (PyObject_CheckBuffer(obj)) {
        PyBuffer_Release(view);
        return;
    }
        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) { __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view); return; }
    Py_DECREF(obj);
    view->obj = NULL;
}
#endif


          /* CIntToPy */
          static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
    const int neg_one = (int) -1, const_zero = (int) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(int) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(int),
                                     little, !is_unsigned);
    }
}

/* CIntFromPyVerify */
          #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
    {\
        func_type value = func_value;\
        if (sizeof(target_type) < sizeof(func_type)) {\
            if (unlikely(value != (func_type) (target_type) value)) {\
                func_type zero = 0;\
                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
                    return (target_type) -1;\
                if (is_unsigned && unlikely(value < zero))\
                    goto raise_neg_overflow;\
                else\
                    goto raise_overflow;\
            }\
        }\
        return (target_type) value;\
    }

/* Declarations */
          #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

/* Arithmetic */
          #if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq_float(__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_sum_float(__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_diff_float(__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_prod_float(__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;
    }
    #if 1
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        if (b.imag == 0) {
            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else if (fabsf(b.real) >= fabsf(b.imag)) {
            if (b.real == 0 && b.imag == 0) {
                return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag);
            } else {
                float r = b.imag / b.real;
                float s = 1.0 / (b.real + b.imag * r);
                return __pyx_t_float_complex_from_parts(
                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
            }
        } else {
            float r = b.real / b.imag;
            float s = 1.0 / (b.imag + b.real * r);
            return __pyx_t_float_complex_from_parts(
                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
        }
    }
    #else
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        if (b.imag == 0) {
            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else {
            float denom = b.real * b.real + b.imag * b.imag;
            return __pyx_t_float_complex_from_parts(
                (a.real * b.real + a.imag * b.imag) / denom,
                (a.imag * b.real - a.real * b.imag) / denom);
        }
    }
    #endif
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__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_zero_float(__pyx_t_float_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) {
        __pyx_t_float_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrtf(z.real*z.real + z.imag*z.imag);
          #else
            return hypotf(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
            __pyx_t_float_complex z;
            float r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    float 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_float(a, a);
                        return __Pyx_c_prod_float(a, a);
                    case 3:
                        z = __Pyx_c_prod_float(a, a);
                        return __Pyx_c_prod_float(z, a);
                    case 4:
                        z = __Pyx_c_prod_float(a, a);
                        return __Pyx_c_prod_float(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_abs_float(a);
                theta = atan2f(a.imag, a.real);
            }
            lnr = logf(r);
            z_r = expf(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cosf(z_theta);
            z.imag = z_r * sinf(z_theta);
            return z;
        }
    #endif
#endif

/* Declarations */
          #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

/* Arithmetic */
          #if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq_double(__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_double(__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_double(__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_double(__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;
    }
    #if 1
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else if (fabs(b.real) >= fabs(b.imag)) {
            if (b.real == 0 && b.imag == 0) {
                return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
            } else {
                double r = b.imag / b.real;
                double s = 1.0 / (b.real + b.imag * r);
                return __pyx_t_double_complex_from_parts(
                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
            }
        } else {
            double r = b.real / b.imag;
            double s = 1.0 / (b.imag + b.real * r);
            return __pyx_t_double_complex_from_parts(
                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
        }
    }
    #else
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else {
            double denom = b.real * b.real + b.imag * b.imag;
            return __pyx_t_double_complex_from_parts(
                (a.real * b.real + a.imag * b.imag) / denom,
                (a.imag * b.real - a.real * b.imag) / denom);
        }
    }
    #endif
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__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_double(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__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_double(__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_double(__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_double(a, a);
                        return __Pyx_c_prod_double(a, a);
                    case 3:
                        z = __Pyx_c_prod_double(a, a);
                        return __Pyx_c_prod_double(z, a);
                    case 4:
                        z = __Pyx_c_prod_double(a, a);
                        return __Pyx_c_prod_double(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_abs_double(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

/* CIntToPy */
          static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value) {
    const enum NPY_TYPES neg_one = (enum NPY_TYPES) -1, const_zero = (enum NPY_TYPES) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(enum NPY_TYPES) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(enum NPY_TYPES) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(enum NPY_TYPES),
                                     little, !is_unsigned);
    }
}

/* CIntFromPy */
          static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) -1, const_zero = (int) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(int) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (int) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
                case 2:
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (int) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            int val;
            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
 #if PY_MAJOR_VERSION < 3
            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;
            }
#endif
            return (int) -1;
        }
    } else {
        int val;
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
        if (!tmp) return (int) -1;
        val = __Pyx_PyInt_As_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to int");
    return (int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to int");
    return (int) -1;
}

/* CIntToPy */
          static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) -1, const_zero = (long) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(long) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
    }
}

/* CIntFromPy */
          static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) -1, const_zero = (long) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(long) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (long) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
                case 2:
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (long) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(long) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(long) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            long val;
            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
 #if PY_MAJOR_VERSION < 3
            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;
            }
#endif
            return (long) -1;
        }
    } else {
        long val;
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
        if (!tmp) return (long) -1;
        val = __Pyx_PyInt_As_long(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to long");
    return (long) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to long");
    return (long) -1;
}

/* CheckBinaryVersion */
          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);
        return PyErr_WarnEx(NULL, message, 1);
    }
    return 0;
}

/* ModuleImport */
          #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;
    py_name = __Pyx_PyIdentifier_FromString(name);
    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

/* TypeImport */
          #ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    size_t size, int strict)
{
    PyObject *py_module = 0;
    PyObject *result = 0;
    PyObject *py_name = 0;
    char warning[200];
    Py_ssize_t basicsize;
#ifdef Py_LIMITED_API
    PyObject *py_basicsize;
#endif
    py_module = __Pyx_ImportModule(module_name);
    if (!py_module)
        goto bad;
    py_name = __Pyx_PyIdentifier_FromString(class_name);
    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,
            "%.200s.%.200s is not a type object",
            module_name, class_name);
        goto bad;
    }
#ifndef Py_LIMITED_API
    basicsize = ((PyTypeObject *)result)->tp_basicsize;
#else
    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
    if (!py_basicsize)
        goto bad;
    basicsize = PyLong_AsSsize_t(py_basicsize);
    Py_DECREF(py_basicsize);
    py_basicsize = 0;
    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
        goto bad;
#endif
    if (!strict && (size_t)basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
    }
    else if ((size_t)basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s has the wrong size, try recompiling. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

/* InitStrings */
          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
        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;
}

static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
}
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if CYTHON_COMPILING_IN_CPYTHON && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)
    if (
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
            __Pyx_sys_getdefaultencoding_not_ascii &&
#endif
            PyUnicode_Check(o)) {
#if PY_VERSION_HEX < 0x03030000
        char* defenc_c;
        PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
        if (!defenc) return NULL;
        defenc_c = PyBytes_AS_STRING(defenc);
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        {
            char* end = defenc_c + PyBytes_GET_SIZE(defenc);
            char* c;
            for (c = defenc_c; c < end; c++) {
                if ((unsigned char) (*c) >= 128) {
                    PyUnicode_AsASCIIString(o);
                    return NULL;
                }
            }
        }
#endif
        *length = PyBytes_GET_SIZE(defenc);
        return defenc_c;
#else
        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        if (PyUnicode_IS_ASCII(o)) {
            *length = PyUnicode_GET_LENGTH(o);
            return PyUnicode_AsUTF8(o);
        } else {
            PyUnicode_AsASCIIString(o);
            return NULL;
        }
#else
        return PyUnicode_AsUTF8AndSize(o, length);
#endif
#endif
    } else
#endif
#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
    if (PyByteArray_Check(o)) {
        *length = PyByteArray_GET_SIZE(o);
        return PyByteArray_AS_STRING(o);
    } else
#endif
    {
        char* result;
        int r = PyBytes_AsStringAndSize(o, &result, length);
        if (unlikely(r < 0)) {
            return NULL;
        } else {
            return result;
        }
    }
}
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_IntOrLong(PyObject* x) {
#if CYTHON_USE_TYPE_SLOTS
  PyNumberMethods *m;
#endif
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_MAJOR_VERSION < 3
  if (PyInt_Check(x) || PyLong_Check(x))
#else
  if (PyLong_Check(x))
#endif
    return __Pyx_NewRef(x);
#if CYTHON_USE_TYPE_SLOTS
  m = Py_TYPE(x)->tp_as_number;
  #if PY_MAJOR_VERSION < 3
  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
#else
  res = PyNumber_Int(x);
#endif
  if (res) {
#if PY_MAJOR_VERSION < 3
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
#else
    if (!PyLong_Check(res)) {
#endif
      PyErr_Format(PyExc_TypeError,
                   "__%.4s__ returned non-%.4s (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;
#if PY_MAJOR_VERSION < 3
  if (likely(PyInt_CheckExact(b))) {
    if (sizeof(Py_ssize_t) >= sizeof(long))
        return PyInt_AS_LONG(b);
    else
        return PyInt_AsSsize_t(x);
  }
#endif
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_USE_PYLONG_INTERNALS
    const digit* digits = ((PyLongObject*)b)->ob_digit;
    const Py_ssize_t size = Py_SIZE(b);
    if (likely(__Pyx_sst_abs(size) <= 1)) {
        ival = likely(size) ? digits[0] : 0;
        if (size == -1) ival = -ival;
        return ival;
    } else {
      switch (size) {
         case 2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
      }
    }
    #endif
    return PyLong_AsSsize_t(b);
  }
  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) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */
