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/* BEGIN: Cython Metadata
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#ifndef __Pyx_PyAsyncMethodsStruct
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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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  return value;
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#define __Pyx_truncl trunc
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#define __Pyx_truncl truncl
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#ifndef __PYX_EXTERN_C
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    #define __PYX_EXTERN_C extern "C"
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    #define __PYX_EXTERN_C extern
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#define __PYX_HAVE__yt__utilities__lib__element_mappings
#define __PYX_HAVE_API__yt__utilities__lib__element_mappings
/* Early includes */
#include <string.h>
#include <stdio.h>
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include <math.h>
#include "platform_dep.h"
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */

#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
#define CYTHON_WITHOUT_ASSERTIONS
#endif

typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;

#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)  (\
    (sizeof(type) < sizeof(Py_ssize_t))  ||\
    (sizeof(type) > sizeof(Py_ssize_t) &&\
          likely(v < (type)PY_SSIZE_T_MAX ||\
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          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
                                v == (type)PY_SSIZE_T_MIN)))  ||\
    (sizeof(type) == sizeof(Py_ssize_t) &&\
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                               v == (type)PY_SSIZE_T_MAX)))  )
#if defined (__cplusplus) && __cplusplus >= 201103L
    #include <cstdlib>
    #define __Pyx_sst_abs(value) std::abs(value)
#elif SIZEOF_INT >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) abs(value)
#elif SIZEOF_LONG >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) labs(value)
#elif defined (_MSC_VER)
    #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define __Pyx_sst_abs(value) llabs(value)
#elif defined (__GNUC__)
    #define __Pyx_sst_abs(value) __builtin_llabs(value)
#else
    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
#endif
static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE const 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
#else
    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
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#define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))
#define __Pyx_PyObject_AsWritableString(s)    ((char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsUString(s)    ((const 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)
static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
    const Py_UNICODE *u_end = u;
    while (*u_end++) ;
    return (size_t)(u_end - u - 1);
}
#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)
static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
#define __Pyx_PySequence_Tuple(obj)\
    (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
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;
    PyObject* default_encoding = NULL;
    PyObject* ascii_chars_u = NULL;
    PyObject* ascii_chars_b = NULL;
    const char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    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);
    if (!default_encoding_c) goto bad;
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        __Pyx_sys_getdefaultencoding_not_ascii = 0;
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        char ascii_chars[128];
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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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    char* default_encoding_c;
    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;
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    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    return -1;
}
#endif
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/* 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)
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  #define likely(x)   (x)
  #define unlikely(x) (x)
#endif /* __GNUC__ */
static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }

static PyObject *__pyx_m = NULL;
static PyObject *__pyx_d;
static PyObject *__pyx_b;
static PyObject *__pyx_cython_runtime = NULL;
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[] = {
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  "stringsource",
  "__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 {
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typedef struct __Pyx_StructField_ {
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typedef struct {
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typedef struct {
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  char enc_type;
  char new_packmode;
  char enc_packmode;
  char is_valid_array;
} __Pyx_BufFmt_Context;


/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":730
 * # 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":731
 * 
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":732
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":733
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":737
 * #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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":738
 * 
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":739
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":740
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":744
 * #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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":745
 * 
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":754
 * # 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":755
 * # 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":756
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":758
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":759
 * 
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 */
typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":760
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":762
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uintp      uintp_t
 * 
 */
typedef npy_intp __pyx_t_5numpy_intp_t;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":763
 * 
 * ctypedef npy_intp       intp_t
 * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_double     float_t
 */
typedef npy_uintp __pyx_t_5numpy_uintp_t;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":765
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":766
 * 
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longdouble longdouble_t
 * 
 */
typedef npy_double __pyx_t_5numpy_double_t;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":767
 * 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
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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_P1Sampler1D;
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;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D;
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":769
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":770
 * 
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t             # <<<<<<<<<<<<<<
 * ctypedef npy_clongdouble clongdouble_t
 * 
 */
typedef npy_cdouble __pyx_t_5numpy_cdouble_t;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":771
 * 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;

/* "../_h_env/lib/site-packages/Cython/Includes/numpy/__init__.pxd":773
 * 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":96
 * #          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":116
 * #     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":138
 * #     scol     - the second column of the jacobian
 * #
 * ctypedef void (*jac_type2D)(double* rcol,             # <<<<<<<<<<<<<<
 *                             double* scol,
 *                             double* x,
 */
typedef void (*__pyx_t_2yt_9utilities_3lib_16element_mappings_jac_type2D)(double *, 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 P1Sampler1D(ElementSampler):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler1D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler __pyx_base;
};


/* "yt/utilities/lib/element_mappings.pxd":51
 * 
 * 
 * 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":66
 * 
 * 
 * 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":145
 * 
 * 
 * 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":159
 * 
 * 
 * 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":176
 * 
 * 
 * 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":194
 * 
 * 
 * cdef class S2Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D __pyx_base;
};


/* "yt/utilities/lib/element_mappings.pxd":212
 * 
 * 
 * cdef class NonlinearSolveSampler2D(ElementSampler):             # <<<<<<<<<<<<<<
 * 
 *     cdef int dim
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D {
  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_type2D jac;
};


/* "yt/utilities/lib/element_mappings.pxd":226
 * 
 * 
 * cdef class Q1Sampler2D(NonlinearSolveSampler2D):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D __pyx_base;
};


/* "yt/utilities/lib/element_mappings.pxd":241
 * 
 * 
 * cdef class Q2Sampler2D(NonlinearSolveSampler2D):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D __pyx_base;
};


/* "yt/utilities/lib/element_mappings.pxd":256
 * 
 * 
 * cdef class T2Sampler2D(NonlinearSolveSampler2D):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D __pyx_base;
};


/* "yt/utilities/lib/element_mappings.pxd":270
 *     cdef int check_inside(self, double* mapped_coord) nogil
 * 
 * cdef class Tet2Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
 *     cdef void map_real_to_unit(self,
 */
struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D __pyx_base;
};



/* "yt/utilities/lib/element_mappings.pyx":62
 * 
 * 
 * cdef class ElementSampler:             # <<<<<<<<<<<<<<
 *     '''
 * 
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler {
  void (*map_real_to_unit)(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *, double *, double *, double *);
  double (*sample_at_unit_point)(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *, double *, double *);
  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 *);
  int (*check_mesh_lines)(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *, double *);
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_ElementSampler;


/* "yt/utilities/lib/element_mappings.pyx":120
 * 
 * 
 * cdef class P1Sampler1D(ElementSampler):             # <<<<<<<<<<<<<<
 *     '''
 * 
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler1D {
  struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler __pyx_base;
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler1D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_P1Sampler1D;


/* "yt/utilities/lib/element_mappings.pyx":155
 * 
 * 
 * cdef class P1Sampler2D(ElementSampler):             # <<<<<<<<<<<<<<
 *     '''
 * 
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler2D {
  struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler __pyx_base;
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_P1Sampler2D;


/* "yt/utilities/lib/element_mappings.pyx":226
 * 
 * 
 * cdef class P1Sampler3D(ElementSampler):             # <<<<<<<<<<<<<<
 *     '''
 * 
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler3D {
  struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler __pyx_base;
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_P1Sampler3D;


/* "yt/utilities/lib/element_mappings.pyx":320
 * 
 * 
 * cdef class NonlinearSolveSampler3D(ElementSampler):             # <<<<<<<<<<<<<<
 * 
 *     '''
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D {
  struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler __pyx_base;
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D;


/* "yt/utilities/lib/element_mappings.pyx":427
 * 
 * 
 * cdef class Q1Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
 *     '''
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D {
  struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D __pyx_base;
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D;


/* "yt/utilities/lib/element_mappings.pyx":703
 * 
 * 
 * cdef class W1Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
 *     '''
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_W1Sampler3D {
  struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D __pyx_base;
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_W1Sampler3D;


/* "yt/utilities/lib/element_mappings.pyx":488
 * 
 * 
 * cdef class S2Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
 *     '''
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_S2Sampler3D {
  struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D __pyx_base;
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_S2Sampler3D;


/* "yt/utilities/lib/element_mappings.pyx":777
 * 
 * 
 * cdef class NonlinearSolveSampler2D(ElementSampler):             # <<<<<<<<<<<<<<
 * 
 *     '''
 */

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":877
 * 
 * 
 * cdef class Q1Sampler2D(NonlinearSolveSampler2D):             # <<<<<<<<<<<<<<
 * 
 *     '''
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D {
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static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D;


/* "yt/utilities/lib/element_mappings.pyx":917
 *         return 1
 * 
 * cdef class Q2Sampler2D(NonlinearSolveSampler2D):             # <<<<<<<<<<<<<<
 * 
 *     '''
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D {
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static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D;


/* "yt/utilities/lib/element_mappings.pyx":974
 * 
 * 
 * cdef class T2Sampler2D(NonlinearSolveSampler2D):             # <<<<<<<<<<<<<<
 * 
 *     '''
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_T2Sampler2D {
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static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_T2Sampler2D *__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_T2Sampler2D;


/* "yt/utilities/lib/element_mappings.pyx":1023
 *         return 1
 * 
 * cdef class Tet2Sampler3D(NonlinearSolveSampler3D):             # <<<<<<<<<<<<<<
 * 
 *     '''
 */

struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D {
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#define __Pyx_PyThreadState_assign  __pyx_tstate = __Pyx_PyThreadState_Current;
#define __Pyx_PyErr_Occurred()  __pyx_tstate->curexc_type
#else
#define __Pyx_PyThreadState_declare
#define __Pyx_PyThreadState_assign
#define __Pyx_PyErr_Occurred()  PyErr_Occurred()
#endif

/* PyErrFetchRestore.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
#define __Pyx_ErrRestoreWithState(type, value, tb)  __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)    __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)    __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
#else
#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
#endif
#else
#define __Pyx_PyErr_Clear() PyErr_Clear()
#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
#define __Pyx_ErrRestoreWithState(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)  PyErr_Fetch(type, value, tb)
#define __Pyx_ErrRestoreInState(tstate, type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetchInState(tstate, type, value, tb)  PyErr_Fetch(type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)  PyErr_Fetch(type, value, tb)
#endif

/* GetAttr.proto */
static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *, PyObject *);

/* GetAttr3.proto */
static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *, PyObject *, PyObject *);

/* GetModuleGlobalName.proto */
static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);

/* PyObjectCall.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
#else
#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
#endif

/* PyCFunctionFastCall.proto */
#if CYTHON_FAST_PYCCALL
static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
#else
#define __Pyx_PyCFunction_FastCall(func, args, nargs)  (assert(0), NULL)
#endif

/* PyFunctionFastCall.proto */
#if CYTHON_FAST_PYCALL
#define __Pyx_PyFunction_FastCall(func, args, nargs)\
    __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
#if 1 || PY_VERSION_HEX < 0x030600B1
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs);
#else
#define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
#endif
#endif

/* PyObjectCallMethO.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
#endif

/* PyObjectCallOneArg.proto */
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);

/* PyObjectCallNoArg.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
#else
#define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
#endif

/* RaiseException.proto */
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);

/* RaiseDoubleKeywords.proto */
static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);

/* ParseKeywords.proto */
static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
    PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
    const char* function_name);

/* ArgTypeTest.proto */
#define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
    ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\
        __Pyx__ArgTypeTest(obj, type, name, exact))
static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);

/* IsLittleEndian.proto */
static CYTHON_INLINE int __Pyx_Is_Little_Endian(void);

/* BufferFormatCheck.proto */
static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts);
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              __Pyx_TypeInfo* type);

/* BufferGetAndValidate.proto */
#define __Pyx_GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack)\
    ((obj == Py_None || obj == NULL) ?\
    (__Pyx_ZeroBuffer(buf), 0) :\
    __Pyx__GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack))
static int  __Pyx__GetBufferAndValidate(Py_buffer* buf, PyObject* obj,
    __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack);
static void __Pyx_ZeroBuffer(Py_buffer* buf);
static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);
static Py_ssize_t __Pyx_minusones[] = { -1, -1, -1, -1, -1, -1, -1, -1 };
static Py_ssize_t __Pyx_zeros[] = { 0, 0, 0, 0, 0, 0, 0, 0 };

/* Import.proto */
static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);

/* ImportFrom.proto */
static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name);

/* GetItemInt.proto */
#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
    __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\
    (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) :\
               __Pyx_GetItemInt_Generic(o, to_py_func(i))))
#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
    __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
    (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL))
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck);
#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
    __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
    (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL))
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck);
static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
                                                     int is_list, int wraparound, int boundscheck);

/* HasAttr.proto */
static CYTHON_INLINE int __Pyx_HasAttr(PyObject *, PyObject *);

/* DictGetItem.proto */
#if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY
static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key);
#define __Pyx_PyObject_Dict_GetItem(obj, name)\
    (likely(PyDict_CheckExact(obj)) ?\
     __Pyx_PyDict_GetItem(obj, name) : PyObject_GetItem(obj, name))
#else
#define __Pyx_PyDict_GetItem(d, key) PyObject_GetItem(d, key)
#define __Pyx_PyObject_Dict_GetItem(obj, name)  PyObject_GetItem(obj, name)
#endif

/* RaiseTooManyValuesToUnpack.proto */
static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);

/* RaiseNeedMoreValuesToUnpack.proto */
static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);

/* RaiseNoneIterError.proto */
static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);

/* ExtTypeTest.proto */
static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);

/* SaveResetException.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
#else
#define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)
#define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)
#endif

/* GetException.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
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_GenericGetAttrNoDict.proto */
#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name);
#else
#define __Pyx_PyObject_GenericGetAttrNoDict PyObject_GenericGetAttr
#endif

/* PyObject_GenericGetAttr.proto */
#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name);
#else
#define __Pyx_PyObject_GenericGetAttr PyObject_GenericGetAttr
#endif

/* SetVTable.proto */
static int __Pyx_SetVtable(PyObject *dict, void *vtable);

/* SetupReduce.proto */
static int __Pyx_setup_reduce(PyObject* type_obj);

/* CLineInTraceback.proto */
#ifdef CYTHON_CLINE_IN_TRACEBACK
#define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
#else
static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
#endif

/* CodeObjectCache.proto */
typedef struct {
    PyCodeObject* code_object;
    int code_line;
} __Pyx_CodeObjectCacheEntry;
struct __Pyx_CodeObjectCache {
    int count;
    int max_count;
    __Pyx_CodeObjectCacheEntry* entries;
};
static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
static PyCodeObject *__pyx_find_code_object(int code_line);
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);

/* AddTraceback.proto */
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename);

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);

/* BufferStructDeclare.proto */
typedef struct {
  Py_ssize_t shape, strides, suboffsets;
} __Pyx_Buf_DimInfo;
typedef struct {
  size_t refcount;
  Py_buffer pybuffer;
} __Pyx_Buffer;
typedef struct {
  __Pyx_Buffer *rcbuffer;
  char *data;
  __Pyx_Buf_DimInfo diminfo[8];
} __Pyx_LocalBuf_ND;

#if PY_MAJOR_VERSION < 3
    static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
    static void __Pyx_ReleaseBuffer(Py_buffer *view);
#else
    #define __Pyx_GetBuffer PyObject_GetBuffer
    #define __Pyx_ReleaseBuffer PyBuffer_Release
#endif


/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);

/* RealImag.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    #define __Pyx_CREAL(z) ((z).real())
    #define __Pyx_CIMAG(z) ((z).imag())
  #else
    #define __Pyx_CREAL(z) (__real__(z))
    #define __Pyx_CIMAG(z) (__imag__(z))
  #endif
#else
    #define __Pyx_CREAL(z) ((z).real)
    #define __Pyx_CIMAG(z) ((z).imag)
#endif
#if defined(__cplusplus) && CYTHON_CCOMPLEX\
        && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)
    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
#else
    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
#endif

/* Arithmetic.proto */
#if CYTHON_CCOMPLEX
    #define __Pyx_c_eq_float(a, b)   ((a)==(b))
    #define __Pyx_c_sum_float(a, b)  ((a)+(b))
    #define __Pyx_c_diff_float(a, b) ((a)-(b))
    #define __Pyx_c_prod_float(a, b) ((a)*(b))
    #define __Pyx_c_quot_float(a, b) ((a)/(b))
    #define __Pyx_c_neg_float(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zero_float(z) ((z)==(float)0)
    #define __Pyx_c_conj_float(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_abs_float(z)     (::std::abs(z))
        #define __Pyx_c_pow_float(a, b)  (::std::pow(a, b))
    #endif
  #else
    #define __Pyx_c_is_zero_float(z) ((z)==0)
    #define __Pyx_c_conj_float(z)    (conjf(z))
    #if 1
        #define __Pyx_c_abs_float(z)     (cabsf(z))
        #define __Pyx_c_pow_float(a, b)  (cpowf(a, b))
    #endif
 #endif
#else
    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex);
    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex);
    #if 1
        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex);
        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex);
    #endif
#endif

/* Arithmetic.proto */
#if CYTHON_CCOMPLEX
    #define __Pyx_c_eq_double(a, b)   ((a)==(b))
    #define __Pyx_c_sum_double(a, b)  ((a)+(b))
    #define __Pyx_c_diff_double(a, b) ((a)-(b))
    #define __Pyx_c_prod_double(a, b) ((a)*(b))
    #define __Pyx_c_quot_double(a, b) ((a)/(b))
    #define __Pyx_c_neg_double(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zero_double(z) ((z)==(double)0)
    #define __Pyx_c_conj_double(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_abs_double(z)     (::std::abs(z))
        #define __Pyx_c_pow_double(a, b)  (::std::pow(a, b))
    #endif
  #else
    #define __Pyx_c_is_zero_double(z) ((z)==0)
    #define __Pyx_c_conj_double(z)    (conj(z))
    #if 1
        #define __Pyx_c_abs_double(z)     (cabs(z))
        #define __Pyx_c_pow_double(a, b)  (cpow(a, b))
    #endif
 #endif
#else
    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex);
    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex);
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex);
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex);
    #endif
#endif

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value);

/* CIntFromPy.proto */
static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);

/* CIntFromPy.proto */
static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);

/* FastTypeChecks.proto */
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
#else
#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
#endif
#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)

/* CheckBinaryVersion.proto */
static int __Pyx_check_binary_version(void);

/* PyIdentifierFromString.proto */
#if !defined(__Pyx_PyIdentifier_FromString)
#if PY_MAJOR_VERSION < 3
  #define __Pyx_PyIdentifier_FromString(s) PyString_FromString(s)
#else
  #define __Pyx_PyIdentifier_FromString(s) PyUnicode_FromString(s)
#endif
#endif

/* ModuleImport.proto */
static PyObject *__Pyx_ImportModule(const char *name);

/* TypeImport.proto */
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, size_t size, int strict);

/* FunctionImport.proto */
static int __Pyx_ImportFunction(PyObject *module, const char *funcname, void (**f)(void), const char *sig);

/* InitStrings.proto */
static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);

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_11P1Sampler1D_map_real_to_unit(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler1D *__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_11P1Sampler1D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler1D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11P1Sampler1D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler1D *__pyx_v_self, double *__pyx_v_mapped_coord); /* 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*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q2Sampler2D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11Q2Sampler2D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_11T2Sampler2D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_11T2Sampler2D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static double __pyx_f_2yt_9utilities_3lib_16element_mappings_13Tet2Sampler3D_sample_at_unit_point(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D *__pyx_v_self, double *__pyx_v_coord, double *__pyx_v_vals); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_13Tet2Sampler3D_check_inside(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/
static int __pyx_f_2yt_9utilities_3lib_16element_mappings_13Tet2Sampler3D_check_mesh_lines(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D *__pyx_v_self, double *__pyx_v_mapped_coord); /* proto*/

/* Module declarations from 'cpython.buffer' */

/* Module declarations from 'libc.string' */

/* Module declarations from 'libc.stdio' */

/* Module declarations from '__builtin__' */

/* Module declarations from 'cpython.type' */
static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;

/* Module declarations from 'cpython' */

/* Module declarations from 'cpython.object' */

/* Module declarations from 'cpython.ref' */

/* Module declarations from 'cpython.mem' */

/* Module declarations from 'numpy' */

/* Module declarations from 'numpy' */
static PyTypeObject *__pyx_ptype_5numpy_dtype = 0;
static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;
static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;
static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0;
static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;
static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/

/* Module declarations from 'cython' */

/* Module declarations from 'libc.math' */

/* Module declarations from 'yt.utilities.lib.autogenerated_element_samplers' */
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_Q1Function3D)(double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_Q1Jacobian3D)(double *, double *, double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_Q1Function2D)(double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_Q1Jacobian2D)(double *, double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_Q2Function2D)(double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_Q2Jacobian2D)(double *, double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_Tet2Function3D)(double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_Tet2Jacobian3D)(double *, double *, double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_T2Function2D)(double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_T2Jacobian2D)(double *, double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_W1Function3D)(double *, double *, double *, double *); /*proto*/
static void (*__pyx_f_2yt_9utilities_3lib_30autogenerated_element_samplers_W1Jacobian3D)(double *, double *, double *, double *, double *, double *); /*proto*/

/* 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_P1Sampler1D = 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 PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_T2Sampler2D = 0;
static PyTypeObject *__pyx_ptype_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D = 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_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 PyObject *__pyx_f_2yt_9utilities_3lib_16element_mappings___pyx_unpickle_ElementSampler__set_state(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *, PyObject *); /*proto*/
static PyObject *__pyx_f_2yt_9utilities_3lib_16element_mappings___pyx_unpickle_P1Sampler1D__set_state(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler1D *, PyObject *); /*proto*/
static PyObject *__pyx_f_2yt_9utilities_3lib_16element_mappings___pyx_unpickle_P1Sampler2D__set_state(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *, PyObject *); /*proto*/
static PyObject *__pyx_f_2yt_9utilities_3lib_16element_mappings___pyx_unpickle_P1Sampler3D__set_state(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *, PyObject *); /*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 };
#define __Pyx_MODULE_NAME "yt.utilities.lib.element_mappings"
extern int __pyx_module_is_main_yt__utilities__lib__element_mappings;
int __pyx_module_is_main_yt__utilities__lib__element_mappings = 0;

/* Implementation of 'yt.utilities.lib.element_mappings' */
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_super;
static PyObject *__pyx_builtin_TypeError;
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_RuntimeError;
static PyObject *__pyx_builtin_ImportError;
static const char __pyx_k_np[] = "np";
static const char __pyx_k_new[] = "__new__";
static const char __pyx_k_val[] = "val";
static const char __pyx_k_dict[] = "__dict__";
static const char __pyx_k_init[] = "__init__";
static const char __pyx_k_main[] = "__main__";
static const char __pyx_k_name[] = "__name__";
static const char __pyx_k_test[] = "__test__";
static const char __pyx_k_numpy[] = "numpy";
static const char __pyx_k_range[] = "range";
static const char __pyx_k_super[] = "super";
static const char __pyx_k_import[] = "__import__";
static const char __pyx_k_pickle[] = "pickle";
static const char __pyx_k_reduce[] = "__reduce__";
static const char __pyx_k_update[] = "update";
static const char __pyx_k_sampler[] = "sampler";
static const char __pyx_k_getstate[] = "__getstate__";
static const char __pyx_k_pyx_type[] = "__pyx_type";
static const char __pyx_k_setstate[] = "__setstate__";
static const char __pyx_k_vertices[] = "vertices";
static const char __pyx_k_TypeError[] = "TypeError";
static const char __pyx_k_pyx_state[] = "__pyx_state";
static const char __pyx_k_reduce_ex[] = "__reduce_ex__";
static const char __pyx_k_ValueError[] = "ValueError";
static const char __pyx_k_physical_x[] = "physical_x";
static const char __pyx_k_pyx_result[] = "__pyx_result";
static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
static const char __pyx_k_ImportError[] = "ImportError";
static const char __pyx_k_PickleError[] = "PickleError";
static const char __pyx_k_RuntimeError[] = "RuntimeError";
static const char __pyx_k_field_values[] = "field_values";
static const char __pyx_k_pyx_checksum[] = "__pyx_checksum";
static const char __pyx_k_stringsource[] = "stringsource";
static const char __pyx_k_reduce_cython[] = "__reduce_cython__";
static const char __pyx_k_pyx_PickleError[] = "__pyx_PickleError";
static const char __pyx_k_setstate_cython[] = "__setstate_cython__";
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_tet2_sampler[] = "test_tet2_sampler";
static const char __pyx_k_test_tri2_sampler[] = "test_tri2_sampler";
static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
static const char __pyx_k_test_hex20_sampler[] = "test_hex20_sampler";
static const char __pyx_k_test_quad2_sampler[] = "test_quad2_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_test_linear1D_sampler[] = "test_linear1D_sampler";
static const char __pyx_k_pyx_unpickle_P1Sampler1D[] = "__pyx_unpickle_P1Sampler1D";
static const char __pyx_k_pyx_unpickle_P1Sampler2D[] = "__pyx_unpickle_P1Sampler2D";
static const char __pyx_k_pyx_unpickle_P1Sampler3D[] = "__pyx_unpickle_P1Sampler3D";
static const char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static const char __pyx_k_pyx_unpickle_ElementSampler[] = "__pyx_unpickle_ElementSampler";
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";
static const char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
static const char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
static const char __pyx_k_Incompatible_checksums_s_vs_0xa3[] = "Incompatible checksums (%s vs 0xa37a4b3 = (inclusion_tol, num_mapped_coords))";
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_self_func_self_jac_cannot_be_con[] = "self.func,self.jac cannot be converted to a Python object for pickling";
static const char __pyx_k_yt_utilities_lib_element_mapping[] = "yt\\utilities\\lib\\element_mappings.pyx";
static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
static const char __pyx_k_yt_utilities_lib_element_mapping_2[] = "yt.utilities.lib.element_mappings";
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;
static PyObject *__pyx_n_s_ImportError;
static PyObject *__pyx_kp_s_Incompatible_checksums_s_vs_0xa3;
static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
static PyObject *__pyx_n_s_PickleError;
static PyObject *__pyx_n_s_RuntimeError;
static PyObject *__pyx_n_s_TypeError;
static PyObject *__pyx_n_s_ValueError;
static PyObject *__pyx_n_s_cline_in_traceback;
static PyObject *__pyx_n_s_dict;
static PyObject *__pyx_n_s_field_values;
static PyObject *__pyx_n_s_getstate;
static PyObject *__pyx_n_s_import;
static PyObject *__pyx_n_s_init;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_name;
static PyObject *__pyx_kp_u_ndarray_is_not_C_contiguous;
static PyObject *__pyx_kp_u_ndarray_is_not_Fortran_contiguou;
static PyObject *__pyx_n_s_new;
static PyObject *__pyx_n_s_np;
static PyObject *__pyx_n_s_numpy;
static PyObject *__pyx_kp_s_numpy_core_multiarray_failed_to;
static PyObject *__pyx_kp_s_numpy_core_umath_failed_to_impor;
static PyObject *__pyx_n_s_physical_x;
static PyObject *__pyx_n_s_pickle;
static PyObject *__pyx_n_s_pyx_PickleError;
static PyObject *__pyx_n_s_pyx_checksum;
static PyObject *__pyx_n_s_pyx_result;
static PyObject *__pyx_n_s_pyx_state;
static PyObject *__pyx_n_s_pyx_type;
static PyObject *__pyx_n_s_pyx_unpickle_ElementSampler;
static PyObject *__pyx_n_s_pyx_unpickle_P1Sampler1D;
static PyObject *__pyx_n_s_pyx_unpickle_P1Sampler2D;
static PyObject *__pyx_n_s_pyx_unpickle_P1Sampler3D;
static PyObject *__pyx_n_s_pyx_vtable;
static PyObject *__pyx_n_s_range;
static PyObject *__pyx_n_s_reduce;
static PyObject *__pyx_n_s_reduce_cython;
static PyObject *__pyx_n_s_reduce_ex;
static PyObject *__pyx_n_s_sampler;
static PyObject *__pyx_kp_s_self_func_self_jac_cannot_be_con;
static PyObject *__pyx_n_s_setstate;
static PyObject *__pyx_n_s_setstate_cython;
static PyObject *__pyx_kp_s_stringsource;
static PyObject *__pyx_n_s_super;
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_linear1D_sampler;
static PyObject *__pyx_n_s_test_quad2_sampler;
static PyObject *__pyx_n_s_test_quad_sampler;
static PyObject *__pyx_n_s_test_tet2_sampler;
static PyObject *__pyx_n_s_test_tetra_sampler;
static PyObject *__pyx_n_s_test_tri2_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_update;
static PyObject *__pyx_n_s_val;
static PyObject *__pyx_n_s_vertices;
static PyObject *__pyx_kp_s_yt_utilities_lib_element_mapping;
static PyObject *__pyx_n_s_yt_utilities_lib_element_mapping_2;
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 PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_14ElementSampler_2__reduce_cython__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_14ElementSampler_4__setstate_cython__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_ElementSampler *__pyx_v_self, PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_11P1Sampler1D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler1D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11P1Sampler1D_2__reduce_cython__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler1D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11P1Sampler1D_4__setstate_cython__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler1D *__pyx_v_self, PyObject *__pyx_v___pyx_state); /* 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 PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D_2__reduce_cython__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D_4__setstate_cython__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler2D *__pyx_v_self, PyObject *__pyx_v___pyx_state); /* 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 PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_2__reduce_cython__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_4__setstate_cython__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler3D *__pyx_v_self, PyObject *__pyx_v___pyx_state); /* 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 PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler3D_2__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler3D_4__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* 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 PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_2__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_4__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* 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 PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_2__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_4__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_S2Sampler3D *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* 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 PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_2__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_4__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_W1Sampler3D *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* 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 PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler2D_2__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler2D_4__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* 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_11Q1Sampler2D_2__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11Q1Sampler2D_4__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_11Q2Sampler2D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11Q2Sampler2D_2__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11Q2Sampler2D_4__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_11T2Sampler2D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11T2Sampler2D_2__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_11T2Sampler2D_4__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_2yt_9utilities_3lib_16element_mappings_13Tet2Sampler3D___init__(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_13Tet2Sampler3D_2__reduce_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_13Tet2Sampler3D_4__setstate_cython__(CYTHON_UNUSED struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* 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 */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_4test_tetra_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_6test_wedge_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_8test_linear1D_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_10test_tri_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_12test_quad_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_14test_quad2_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_16test_tri2_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_18test_tet2_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_20__pyx_unpickle_ElementSampler(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v___pyx_type, long __pyx_v___pyx_checksum, PyObject *__pyx_v___pyx_state); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_22__pyx_unpickle_P1Sampler1D(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v___pyx_type, long __pyx_v___pyx_checksum, PyObject *__pyx_v___pyx_state); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_24__pyx_unpickle_P1Sampler2D(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v___pyx_type, long __pyx_v___pyx_checksum, PyObject *__pyx_v___pyx_state); /* proto */
static PyObject *__pyx_pf_2yt_9utilities_3lib_16element_mappings_26__pyx_unpickle_P1Sampler3D(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v___pyx_type, long __pyx_v___pyx_checksum, PyObject *__pyx_v___pyx_state); /* proto */
static int __pyx_pf_5numpy_7ndarray___getbuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_ElementSampler(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler1D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_W1Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_S2Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_T2Sampler2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_int_171418803;
static PyObject *__pyx_tuple_;
static PyObject *__pyx_tuple__2;
static PyObject *__pyx_tuple__3;
static PyObject *__pyx_tuple__4;
static PyObject *__pyx_tuple__5;
static PyObject *__pyx_tuple__6;
static PyObject *__pyx_tuple__7;
static PyObject *__pyx_tuple__8;
static PyObject *__pyx_tuple__9;
static PyObject *__pyx_tuple__10;
static PyObject *__pyx_tuple__11;
static PyObject *__pyx_tuple__12;
static PyObject *__pyx_tuple__13;
static PyObject *__pyx_tuple__14;
static PyObject *__pyx_tuple__15;
static PyObject *__pyx_tuple__16;
static PyObject *__pyx_tuple__17;
static PyObject *__pyx_tuple__18;
static PyObject *__pyx_tuple__19;
static PyObject *__pyx_tuple__20;
static PyObject *__pyx_tuple__21;
static PyObject *__pyx_tuple__22;
static PyObject *__pyx_tuple__23;
static PyObject *__pyx_tuple__24;
static PyObject *__pyx_tuple__25;
static PyObject *__pyx_tuple__26;
static PyObject *__pyx_tuple__27;
static PyObject *__pyx_tuple__28;
static PyObject *__pyx_tuple__30;
static PyObject *__pyx_tuple__32;
static PyObject *__pyx_tuple__34;
static PyObject *__pyx_tuple__36;
static PyObject *__pyx_tuple__38;
static PyObject *__pyx_tuple__40;
static PyObject *__pyx_tuple__42;
static PyObject *__pyx_tuple__44;
static PyObject *__pyx_tuple__46;
static PyObject *__pyx_tuple__48;
static PyObject *__pyx_tuple__50;
static PyObject *__pyx_tuple__52;
static PyObject *__pyx_tuple__54;
static PyObject *__pyx_codeobj__29;
static PyObject *__pyx_codeobj__31;
static PyObject *__pyx_codeobj__33;
static PyObject *__pyx_codeobj__35;
static PyObject *__pyx_codeobj__37;
static PyObject *__pyx_codeobj__39;
static PyObject *__pyx_codeobj__41;
static PyObject *__pyx_codeobj__43;
static PyObject *__pyx_codeobj__45;
static PyObject *__pyx_codeobj__47;
static PyObject *__pyx_codeobj__49;
static PyObject *__pyx_codeobj__51;
static PyObject *__pyx_codeobj__53;
static PyObject *__pyx_codeobj__55;
/* Late includes */

/* "yt/utilities/lib/element_mappings.pyx":42
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef double determinant_3x3(double* col0,             # <<<<<<<<<<<<<<
 *                             double* col1,
 *                             double* col2) nogil:
 */

static double __pyx_f_2yt_9utilities_3lib_16element_mappings_determinant_3x3(double *__pyx_v_col0, double *__pyx_v_col1, double *__pyx_v_col2) {
  double __pyx_r;

  /* "yt/utilities/lib/element_mappings.pyx":47
 *     return col0[0]*col1[1]*col2[2] - col0[0]*col1[2]*col2[1] - \
 *            col0[1]*col1[0]*col2[2] + col0[1]*col1[2]*col2[0] + \
 *            col0[2]*col1[0]*col2[1] - col0[2]*col1[1]*col2[0]             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = ((((((((__pyx_v_col0[0]) * (__pyx_v_col1[1])) * (__pyx_v_col2[2])) - (((__pyx_v_col0[0]) * (__pyx_v_col1[2])) * (__pyx_v_col2[1]))) - (((__pyx_v_col0[1]) * (__pyx_v_col1[0])) * (__pyx_v_col2[2]))) + (((__pyx_v_col0[1]) * (__pyx_v_col1[2])) * (__pyx_v_col2[0]))) + (((__pyx_v_col0[2]) * (__pyx_v_col1[0])) * (__pyx_v_col2[1]))) - (((__pyx_v_col0[2]) * (__pyx_v_col1[1])) * (__pyx_v_col2[0])));
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":42
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef double determinant_3x3(double* col0,             # <<<<<<<<<<<<<<
 *                             double* col1,
 *                             double* col2) nogil:
 */

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

/* "yt/utilities/lib/element_mappings.pyx":53
 * @cython.wraparound(False)
 * @cython.cdivision(True)
 * cdef double maxnorm(double* f, int dim) nogil:             # <<<<<<<<<<<<<<
 *     cdef double err
 *     cdef int i
 */

static double __pyx_f_2yt_9utilities_3lib_16element_mappings_maxnorm(double *__pyx_v_f, int __pyx_v_dim) {
  double __pyx_v_err;
  int __pyx_v_i;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;

  /* "yt/utilities/lib/element_mappings.pyx":56
 *     cdef double err
 *     cdef int i
 *     err = fabs(f[0])             # <<<<<<<<<<<<<<
 *     for i in range(1, dim):
 *         err = fmax(err, fabs(f[i]))
 */
  __pyx_v_err = fabs((__pyx_v_f[0]));

  /* "yt/utilities/lib/element_mappings.pyx":57
 *     cdef int i
 *     err = fabs(f[0])
 *     for i in range(1, dim):             # <<<<<<<<<<<<<<
 *         err = fmax(err, fabs(f[i]))
 *     return err
 */
  __pyx_t_1 = __pyx_v_dim;
  __pyx_t_2 = __pyx_t_1;
  for (__pyx_t_3 = 1; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
    __pyx_v_i = __pyx_t_3;

    /* "yt/utilities/lib/element_mappings.pyx":58
 *     err = fabs(f[0])
 *     for i in range(1, dim):
 *         err = fmax(err, fabs(f[i]))             # <<<<<<<<<<<<<<
 *     return err
 * 
 */
    __pyx_v_err = fmax(__pyx_v_err, fabs((__pyx_v_f[__pyx_v_i])));
  }

  /* "yt/utilities/lib/element_mappings.pyx":59
 *     for i in range(1, dim):
 *         err = fmax(err, fabs(f[i]))
 *     return err             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = __pyx_v_err;
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  double __pyx_v_col2[3];
  int __pyx_t_1;

  /* "yt/utilities/lib/element_mappings.pyx":254
 *         # here, we express positions relative to the 4th element,
 *         # which is selected by vertices[9]
 *         for i in range(3):             # <<<<<<<<<<<<<<
 *             bvec[i] = physical_x[i]       - vertices[9 + i]
 *             col0[i] = vertices[0 + i]     - vertices[9 + 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":255
 *         # which is selected by vertices[9]
 *         for i in range(3):
 *             bvec[i] = physical_x[i]       - vertices[9 + i]             # <<<<<<<<<<<<<<
 *             col0[i] = vertices[0 + i]     - vertices[9 + i]
 *             col1[i] = vertices[3 + i]     - vertices[9 + i]
 */
    (__pyx_v_bvec[__pyx_v_i]) = ((__pyx_v_physical_x[__pyx_v_i]) - (__pyx_v_vertices[(9 + __pyx_v_i)]));

    /* "yt/utilities/lib/element_mappings.pyx":256
 *         for i in range(3):
 *             bvec[i] = physical_x[i]       - vertices[9 + i]
 *             col0[i] = vertices[0 + i]     - vertices[9 + i]             # <<<<<<<<<<<<<<
 *             col1[i] = vertices[3 + i]     - vertices[9 + i]
 *             col2[i] = vertices[6 + i]     - vertices[9 + i]
 */
    (__pyx_v_col0[__pyx_v_i]) = ((__pyx_v_vertices[(0 + __pyx_v_i)]) - (__pyx_v_vertices[(9 + __pyx_v_i)]));

    /* "yt/utilities/lib/element_mappings.pyx":257
 *             bvec[i] = physical_x[i]       - vertices[9 + i]
 *             col0[i] = vertices[0 + i]     - vertices[9 + i]
 *             col1[i] = vertices[3 + i]     - vertices[9 + i]             # <<<<<<<<<<<<<<
 *             col2[i] = vertices[6 + i]     - vertices[9 + i]
 * 
 */
    (__pyx_v_col1[__pyx_v_i]) = ((__pyx_v_vertices[(3 + __pyx_v_i)]) - (__pyx_v_vertices[(9 + __pyx_v_i)]));

    /* "yt/utilities/lib/element_mappings.pyx":258
 *             col0[i] = vertices[0 + i]     - vertices[9 + i]
 *             col1[i] = vertices[3 + i]     - vertices[9 + i]
 *             col2[i] = vertices[6 + i]     - vertices[9 + i]             # <<<<<<<<<<<<<<
 * 
 *         d = determinant_3x3(col0, col1, col2)
 */
    (__pyx_v_col2[__pyx_v_i]) = ((__pyx_v_vertices[(6 + __pyx_v_i)]) - (__pyx_v_vertices[(9 + __pyx_v_i)]));
  }

  /* "yt/utilities/lib/element_mappings.pyx":260
 *             col2[i] = vertices[6 + i]     - vertices[9 + i]
 * 
 *         d = determinant_3x3(col0, col1, col2)             # <<<<<<<<<<<<<<
 *         mapped_x[0] = determinant_3x3(bvec, col1, col2)/d
 *         mapped_x[1] = determinant_3x3(col0, bvec, col2)/d
 */
  __pyx_v_d = __pyx_f_2yt_9utilities_3lib_16element_mappings_determinant_3x3(__pyx_v_col0, __pyx_v_col1, __pyx_v_col2);

  /* "yt/utilities/lib/element_mappings.pyx":261
 * 
 *         d = determinant_3x3(col0, col1, col2)
 *         mapped_x[0] = determinant_3x3(bvec, col1, col2)/d             # <<<<<<<<<<<<<<
 *         mapped_x[1] = determinant_3x3(col0, bvec, col2)/d
 *         mapped_x[2] = determinant_3x3(col0, col1, bvec)/d
 */
  (__pyx_v_mapped_x[0]) = (__pyx_f_2yt_9utilities_3lib_16element_mappings_determinant_3x3(__pyx_v_bvec, __pyx_v_col1, __pyx_v_col2) / __pyx_v_d);

  /* "yt/utilities/lib/element_mappings.pyx":262
 *         d = determinant_3x3(col0, col1, col2)
 *         mapped_x[0] = determinant_3x3(bvec, col1, col2)/d
 *         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]
 */
  (__pyx_v_mapped_x[1]) = (__pyx_f_2yt_9utilities_3lib_16element_mappings_determinant_3x3(__pyx_v_col0, __pyx_v_bvec, __pyx_v_col2) / __pyx_v_d);

  /* "yt/utilities/lib/element_mappings.pyx":263
 *         mapped_x[0] = determinant_3x3(bvec, col1, col2)/d
 *         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]
 * 
 */
  (__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":264
 *         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":242
 *     @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":269
 *     @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":273
 *                                      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":269
 *     @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":278
 *     @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":282
 *         # 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":283
 *         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":284
 *         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":283
 *         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":285
 *             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":283
 *         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":286
 *                 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":278
 *     @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":291
 *     @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":293
 *     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]
 */
  __pyx_v_thresh = 2.0e-2;

  /* "yt/utilities/lib/element_mappings.pyx":294
 *         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":295
 *         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":296
 *         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":297
 *             u = mapped_coord[1]
 *             v = mapped_coord[2]
 *             w = mapped_coord[3]             # <<<<<<<<<<<<<<
 *         elif mapped_coord[1] == 0:
 *             u = mapped_coord[2]
 */
    __pyx_v_w = (__pyx_v_mapped_coord[3]);

    /* "yt/utilities/lib/element_mappings.pyx":294
 *         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":298
 *             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":299
 *             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":300
 *         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":301
 *             u = mapped_coord[2]
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]             # <<<<<<<<<<<<<<
 *         elif mapped_coord[2] == 0:
 *             u = mapped_coord[1]
 */
    __pyx_v_w = (__pyx_v_mapped_coord[0]);

    /* "yt/utilities/lib/element_mappings.pyx":298
 *             v = mapped_coord[2]
 *             w = mapped_coord[3]
 *         elif mapped_coord[1] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[2]
 *             v = mapped_coord[3]
 */
    goto __pyx_L3;
  }

  /* "yt/utilities/lib/element_mappings.pyx":302
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]
 *         elif mapped_coord[2] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[1]
 *             v = mapped_coord[3]
 */
  __pyx_t_1 = (((__pyx_v_mapped_coord[2]) == 0.0) != 0);
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":303
 *             w = mapped_coord[0]
 *         elif mapped_coord[2] == 0:
 *             u = mapped_coord[1]             # <<<<<<<<<<<<<<
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]
 */
    __pyx_v_u = (__pyx_v_mapped_coord[1]);

    /* "yt/utilities/lib/element_mappings.pyx":304
 *         elif mapped_coord[2] == 0:
 *             u = mapped_coord[1]
 *             v = mapped_coord[3]             # <<<<<<<<<<<<<<
 *             w = mapped_coord[0]
 *         else:
 */
    __pyx_v_v = (__pyx_v_mapped_coord[3]);

    /* "yt/utilities/lib/element_mappings.pyx":305
 *             u = mapped_coord[1]
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]             # <<<<<<<<<<<<<<
 *         else:
 *             u = mapped_coord[1]
 */
    __pyx_v_w = (__pyx_v_mapped_coord[0]);

    /* "yt/utilities/lib/element_mappings.pyx":302
 *             v = mapped_coord[3]
 *             w = mapped_coord[0]
 *         elif mapped_coord[2] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[1]
 *             v = mapped_coord[3]
 */
    goto __pyx_L3;
  }

  /* "yt/utilities/lib/element_mappings.pyx":307
 *             w = mapped_coord[0]
 *         else:
 *             u = mapped_coord[1]             # <<<<<<<<<<<<<<
 *             v = mapped_coord[2]
 *             w = mapped_coord[0]
 */
  /*else*/ {
    __pyx_v_u = (__pyx_v_mapped_coord[1]);

    /* "yt/utilities/lib/element_mappings.pyx":308
 *         else:
 *             u = mapped_coord[1]
 *             v = mapped_coord[2]             # <<<<<<<<<<<<<<
 *             w = mapped_coord[0]
 *         if ((u < thresh) or
 */
    __pyx_v_v = (__pyx_v_mapped_coord[2]);

    /* "yt/utilities/lib/element_mappings.pyx":309
 *             u = mapped_coord[1]
 *             v = mapped_coord[2]
 *             w = mapped_coord[0]             # <<<<<<<<<<<<<<
 *         if ((u < thresh) or
 *             (v < thresh) or
 */
    __pyx_v_w = (__pyx_v_mapped_coord[0]);
  }
  __pyx_L3:;

  /* "yt/utilities/lib/element_mappings.pyx":310
 *             v = mapped_coord[2]
 *             w = mapped_coord[0]
 *         if ((u < thresh) or             # <<<<<<<<<<<<<<
 *             (v < thresh) or
 *             (w < thresh) or
 */
  __pyx_t_2 = ((__pyx_v_u < __pyx_v_thresh) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L5_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":311
 *             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);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L5_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":312
 *         if ((u < thresh) or
 *             (v < thresh) or
 *             (w < thresh) or             # <<<<<<<<<<<<<<
 *             (fabs(u - 1) < thresh) or
 *             (fabs(v - 1) < thresh) or
 */
  __pyx_t_2 = ((__pyx_v_w < __pyx_v_thresh) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L5_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":313
 *             (v < thresh) or
 *             (w < thresh) or
 *             (fabs(u - 1) < thresh) or             # <<<<<<<<<<<<<<
 *             (fabs(v - 1) < thresh) or
 *             (fabs(w - 1) < thresh)):
 */
  __pyx_t_2 = ((fabs((__pyx_v_u - 1.0)) < __pyx_v_thresh) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L5_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":314
 *             (w < thresh) or
 *             (fabs(u - 1) < thresh) or
 *             (fabs(v - 1) < thresh) or             # <<<<<<<<<<<<<<
 *             (fabs(w - 1) < thresh)):
 *             return 1
 */
  __pyx_t_2 = ((fabs((__pyx_v_v - 1.0)) < __pyx_v_thresh) != 0);
  if (!__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L5_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":315
 *             (fabs(u - 1) < thresh) or
 *             (fabs(v - 1) < thresh) or
 *             (fabs(w - 1) < thresh)):             # <<<<<<<<<<<<<<
 *             return 1
 *         return -1
 */
  __pyx_t_2 = ((fabs((__pyx_v_w - 1.0)) < __pyx_v_thresh) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L5_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":310
 *             v = mapped_coord[2]
 *             w = mapped_coord[0]
 *         if ((u < thresh) or             # <<<<<<<<<<<<<<
 *             (v < thresh) or
 *             (w < thresh) or
 */
  if (__pyx_t_1) {

    /* "yt/utilities/lib/element_mappings.pyx":316
 *             (fabs(v - 1) < thresh) or
 *             (fabs(w - 1) < thresh)):
 *             return 1             # <<<<<<<<<<<<<<
 *         return -1
 * 
 */
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/* "yt/utilities/lib/element_mappings.pyx":341
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef void map_real_to_unit(self,             # <<<<<<<<<<<<<<
 *                                double* mapped_x,
 *                                double* vertices,
 */

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) {
  int __pyx_v_i;
  double __pyx_v_d;
  double __pyx_v_lam;
  double __pyx_v_f[3];
  double __pyx_v_r[3];
  double __pyx_v_s[3];
  double __pyx_v_t[3];
  double __pyx_v_x[3];
  double __pyx_v_xk[3];
  double __pyx_v_s_n[3];
  int __pyx_v_iterations;
  double __pyx_v_err_c;
  double __pyx_v_err_plus;
  double __pyx_v_alpha;
  double __pyx_v_min_lam;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;

  /* "yt/utilities/lib/element_mappings.pyx":376
 *         cdef double[3] t
 *         cdef double[3] x, xk, s_n
 *         cdef int iterations = 0             # <<<<<<<<<<<<<<
 *         cdef double err_c, err_plus
 *         cdef double alpha = 1e-4
 */
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  /* "yt/utilities/lib/element_mappings.pyx":378
 *         cdef int iterations = 0
 *         cdef double err_c, err_plus
 *         cdef double alpha = 1e-4             # <<<<<<<<<<<<<<
 *         cdef double min_lam = 1e-6
 * 
 */
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 *         cdef double err_c, err_plus
 *         cdef double alpha = 1e-4
 *         cdef double min_lam = 1e-6             # <<<<<<<<<<<<<<
 * 
 *         # initial guess
 */
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 * 
 *         # initial guess
 *         for i in range(3):             # <<<<<<<<<<<<<<
 *             x[i] = 0.0
 * 
 */
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 *         # initial guess
 *         for i in range(3):
 *             x[i] = 0.0             # <<<<<<<<<<<<<<
 * 
 *         # initial error norm
 */
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 * 
 *         # initial error norm
 *         self.func(f, x, vertices, physical_x)             # <<<<<<<<<<<<<<
 *         err_c = maxnorm(f, 3)
 * 
 */
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  /* "yt/utilities/lib/element_mappings.pyx":387
 *         # initial error norm
 *         self.func(f, x, vertices, physical_x)
 *         err_c = maxnorm(f, 3)             # <<<<<<<<<<<<<<
 * 
 *         # begin Newton iteration
 */
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 * 
 *         # begin Newton iteration
 *         while (err_c > self.tolerance and iterations < self.max_iter):             # <<<<<<<<<<<<<<
 *             self.jac(r, s, t, x, vertices, physical_x)
 *             d = determinant_3x3(r, s, t)
 */
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    } else {
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      goto __pyx_L7_bool_binop_done;
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    __pyx_t_2 = __pyx_t_3;
    __pyx_L7_bool_binop_done:;
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    /* "yt/utilities/lib/element_mappings.pyx":391
 *         # begin Newton iteration
 *         while (err_c > self.tolerance and iterations < self.max_iter):
 *             self.jac(r, s, t, x, vertices, physical_x)             # <<<<<<<<<<<<<<
 *             d = determinant_3x3(r, s, t)
 * 
 */
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 *         while (err_c > self.tolerance and iterations < self.max_iter):
 *             self.jac(r, s, t, x, vertices, physical_x)
 *             d = determinant_3x3(r, s, t)             # <<<<<<<<<<<<<<
 * 
 *             s_n[0] = - (determinant_3x3(f, s, t)/d)
 */
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 *             d = determinant_3x3(r, s, t)
 * 
 *             s_n[0] = - (determinant_3x3(f, s, t)/d)             # <<<<<<<<<<<<<<
 *             s_n[1] = - (determinant_3x3(r, f, t)/d)
 *             s_n[2] = - (determinant_3x3(r, s, f)/d)
 */
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    /* "yt/utilities/lib/element_mappings.pyx":395
 * 
 *             s_n[0] = - (determinant_3x3(f, s, t)/d)
 *             s_n[1] = - (determinant_3x3(r, f, t)/d)             # <<<<<<<<<<<<<<
 *             s_n[2] = - (determinant_3x3(r, s, f)/d)
 *             xk[0] = x[0] + s_n[0]
 */
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 *             s_n[0] = - (determinant_3x3(f, s, t)/d)
 *             s_n[1] = - (determinant_3x3(r, f, t)/d)
 *             s_n[2] = - (determinant_3x3(r, s, f)/d)             # <<<<<<<<<<<<<<
 *             xk[0] = x[0] + s_n[0]
 *             xk[1] = x[1] + s_n[1]
 */
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 *             s_n[1] = - (determinant_3x3(r, f, t)/d)
 *             s_n[2] = - (determinant_3x3(r, s, f)/d)
 *             xk[0] = x[0] + s_n[0]             # <<<<<<<<<<<<<<
 *             xk[1] = x[1] + s_n[1]
 *             xk[2] = x[2] + s_n[2]
 */
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 *             s_n[2] = - (determinant_3x3(r, s, f)/d)
 *             xk[0] = x[0] + s_n[0]
 *             xk[1] = x[1] + s_n[1]             # <<<<<<<<<<<<<<
 *             xk[2] = x[2] + s_n[2]
 *             self.func(f, xk, vertices, physical_x)
 */
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 *             xk[0] = x[0] + s_n[0]
 *             xk[1] = x[1] + s_n[1]
 *             xk[2] = x[2] + s_n[2]             # <<<<<<<<<<<<<<
 *             self.func(f, xk, vertices, physical_x)
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 */
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 *             xk[2] = x[2] + s_n[2]
 *             self.func(f, xk, vertices, physical_x)             # <<<<<<<<<<<<<<
 *             err_plus = maxnorm(f, 3)
 * 
 */
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 *             xk[2] = x[2] + s_n[2]
 *             self.func(f, xk, vertices, physical_x)
 *             err_plus = maxnorm(f, 3)             # <<<<<<<<<<<<<<
 * 
 *             lam = 1
 */
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 * 
 *             lam = 1             # <<<<<<<<<<<<<<
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 */
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 * 
 *             lam = 1
 *             while err_plus > err_c * (1. - alpha * lam) and lam > min_lam:             # <<<<<<<<<<<<<<
 *                 lam = lam / 2
 *                 xk[0] = x[0] + lam * s_n[0]
 */
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 *                 lam = lam / 2             # <<<<<<<<<<<<<<
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 */
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 *                 xk[2] = x[2] + lam * s_n[2]
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 *                 xk[2] = x[2] + lam * s_n[2]             # <<<<<<<<<<<<<<
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 *                 xk[2] = x[2] + lam * s_n[2]
 *                 self.func(f, xk, vertices, physical_x)             # <<<<<<<<<<<<<<
 *                 err_plus = maxnorm(f, 3)
 * 
 */
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 *                 xk[2] = x[2] + lam * s_n[2]
 *                 self.func(f, xk, vertices, physical_x)
 *                 err_plus = maxnorm(f, 3)             # <<<<<<<<<<<<<<
 * 
 *             x[0] = xk[0]
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 *                 err_plus = maxnorm(f, 3)
 * 
 *             x[0] = xk[0]             # <<<<<<<<<<<<<<
 *             x[1] = xk[1]
 *             x[2] = xk[2]
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 * 
 *             x[0] = xk[0]
 *             x[1] = xk[1]             # <<<<<<<<<<<<<<
 *             x[2] = xk[2]
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 *             x[2] = xk[2]             # <<<<<<<<<<<<<<
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 *             iterations += 1
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 *             x[2] = xk[2]
 *             err_c = err_plus             # <<<<<<<<<<<<<<
 *             iterations += 1
 * 
 */
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 *             iterations += 1             # <<<<<<<<<<<<<<
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 *         if (err_c > self.tolerance):
 */
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 * 
 *         if (err_c > self.tolerance):             # <<<<<<<<<<<<<<
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 *             for i in range(3):             # <<<<<<<<<<<<<<
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 * 
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/* "yt/utilities/lib/element_mappings.pyx":462
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 *         # if we are inside the element.
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 *         if (fabs(mapped_coord[0]) - 1.0 > self.inclusion_tol or
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 *         # for hexes, the mapped coordinates all go from -1 to 1
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 *         # for hexes, the mapped coordinates all go from -1 to 1
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/* "yt/utilities/lib/element_mappings.pyx":474
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 *     @cython.cdivision(True)
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  __pyx_v_F = (((((((((((((((((((((((__pyx_v_rm * __pyx_v_sm) * __pyx_v_tm) * ((((-__pyx_v_r) - __pyx_v_s) - __pyx_v_t) - 2.0)) * (__pyx_v_vals[0])) + ((((__pyx_v_rp * __pyx_v_sm) * __pyx_v_tm) * (((__pyx_v_r - __pyx_v_s) - __pyx_v_t) - 2.0)) * (__pyx_v_vals[1]))) + ((((__pyx_v_rp * __pyx_v_sp) * __pyx_v_tm) * (((__pyx_v_r + __pyx_v_s) - __pyx_v_t) - 2.0)) * (__pyx_v_vals[2]))) + ((((__pyx_v_rm * __pyx_v_sp) * __pyx_v_tm) * ((((-__pyx_v_r) + __pyx_v_s) - __pyx_v_t) - 2.0)) * (__pyx_v_vals[3]))) + ((((__pyx_v_rm * __pyx_v_sm) * __pyx_v_tp) * ((((-__pyx_v_r) - __pyx_v_s) + __pyx_v_t) - 2.0)) * (__pyx_v_vals[4]))) + ((((__pyx_v_rp * __pyx_v_sm) * __pyx_v_tp) * (((__pyx_v_r - __pyx_v_s) + __pyx_v_t) - 2.0)) * (__pyx_v_vals[5]))) + ((((__pyx_v_rp * __pyx_v_sp) * __pyx_v_tp) * (((__pyx_v_r + __pyx_v_s) + __pyx_v_t) - 2.0)) * (__pyx_v_vals[6]))) + ((((__pyx_v_rm * __pyx_v_sp) * __pyx_v_tp) * ((((-__pyx_v_r) + __pyx_v_s) + __pyx_v_t) - 2.0)) * (__pyx_v_vals[7]))) + ((((2.0 * (1.0 - (__pyx_v_r * __pyx_v_r))) * __pyx_v_sm) * __pyx_v_tm) * (__pyx_v_vals[8]))) + ((((2.0 * __pyx_v_rp) * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tm) * (__pyx_v_vals[9]))) + ((((2.0 * (1.0 - (__pyx_v_r * __pyx_v_r))) * __pyx_v_sp) * __pyx_v_tm) * (__pyx_v_vals[10]))) + ((((2.0 * __pyx_v_rm) * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tm) * (__pyx_v_vals[11]))) + ((((2.0 * __pyx_v_rm) * __pyx_v_sm) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vals[12]))) + ((((2.0 * __pyx_v_rp) * __pyx_v_sm) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vals[13]))) + ((((2.0 * __pyx_v_rp) * __pyx_v_sp) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vals[14]))) + ((((2.0 * __pyx_v_rm) * __pyx_v_sp) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vals[15]))) + ((((2.0 * (1.0 - (__pyx_v_r * __pyx_v_r))) * __pyx_v_sm) * __pyx_v_tp) * (__pyx_v_vals[16]))) + ((((2.0 * __pyx_v_rp) * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tp) * (__pyx_v_vals[17]))) + ((((2.0 * (1.0 - (__pyx_v_r * __pyx_v_r))) * __pyx_v_sp) * __pyx_v_tp) * (__pyx_v_vals[18]))) + ((((2.0 * __pyx_v_rm) * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tp) * (__pyx_v_vals[19])));

  /* "yt/utilities/lib/element_mappings.pyx":541
 *           + 2.0*(1.0 - r*r)*sp*tp*vals[18] \
 *           + 2.0*rm*(1.0 - s*s)*tp*vals[19]
 *         return 0.125*F             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
  __pyx_r = (0.125 * __pyx_v_F);
  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":506
 *     @cython.wraparound(False)
 *     @cython.cdivision(True)
 *     cdef double sample_at_unit_point(self, double* coord, double* vals) nogil:             # <<<<<<<<<<<<<<
 *         cdef double F, r, s, t, rm, rp, sm, sp, tm, tp
 * 
 */

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

/* "yt/utilities/lib/element_mappings.pyx":546
 *     @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
 */

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) {
  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "yt/utilities/lib/element_mappings.pyx":547
 *     @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):
 */
  __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":548
 *     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);
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  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
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  /* "yt/utilities/lib/element_mappings.pyx":549
 *         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":547
 *     @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":550
 *             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":547
 *     @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":551
 *             fabs(mapped_coord[2]) - 1.0 > self.inclusion_tol):
 *             return 0
 *         return 1             # <<<<<<<<<<<<<<
 * 
 *     @cython.boundscheck(False)
 */
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  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":546
 *     @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 */
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}

/* "yt/utilities/lib/element_mappings.pyx":556
 *     @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":557
 *     @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
 */
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  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }

  /* "yt/utilities/lib/element_mappings.pyx":558
 *     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):             # <<<<<<<<<<<<<<
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 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 */
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  /* "yt/utilities/lib/element_mappings.pyx":557
 *     @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
 */
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    /* "yt/utilities/lib/element_mappings.pyx":559
 *         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):
 */
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    /* "yt/utilities/lib/element_mappings.pyx":557
 *     @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
 */
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  /* "yt/utilities/lib/element_mappings.pyx":560
 *             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):
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 */
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 *             return 1
 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):             # <<<<<<<<<<<<<<
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 */
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  /* "yt/utilities/lib/element_mappings.pyx":560
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 *         elif (fabs(fabs(mapped_coord[0]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
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 */
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    /* "yt/utilities/lib/element_mappings.pyx":562
 *         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
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 */
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    /* "yt/utilities/lib/element_mappings.pyx":560
 *             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):
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 */
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  /* "yt/utilities/lib/element_mappings.pyx":563
 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
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 *         elif (fabs(fabs(mapped_coord[1]) - 1.0) < 1e-1 and             # <<<<<<<<<<<<<<
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  /* "yt/utilities/lib/element_mappings.pyx":564
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 *               fabs(fabs(mapped_coord[2]) - 1.0) < 1e-1):
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/* "yt/utilities/lib/element_mappings.pyx":573
 * @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":580
 *         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":581
 * 
 *         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":582
 *         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":584
 *         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":585
 * 
 *         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":586
 *         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":588
 *         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":589
 * 
 *         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":590
 *         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":592
 *         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":593
 * 
 *         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 - (__pyx_v_r * __pyx_v_r))) * __pyx_v_sm) * __pyx_v_tm) * (__pyx_v_vertices[(24 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rp) * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tm) * (__pyx_v_vertices[(27 + __pyx_v_i)]))) + ((((2.0 * (1.0 - (__pyx_v_r * __pyx_v_r))) * __pyx_v_sp) * __pyx_v_tm) * (__pyx_v_vertices[(30 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rm) * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tm) * (__pyx_v_vertices[(33 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rm) * __pyx_v_sm) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vertices[(36 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rp) * __pyx_v_sm) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vertices[(39 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rp) * __pyx_v_sp) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vertices[(42 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rm) * __pyx_v_sp) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vertices[(45 + __pyx_v_i)]))) + ((((2.0 * (1.0 - (__pyx_v_r * __pyx_v_r))) * __pyx_v_sm) * __pyx_v_tp) * (__pyx_v_vertices[(48 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rp) * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tp) * (__pyx_v_vertices[(51 + __pyx_v_i)]))) + ((((2.0 * (1.0 - (__pyx_v_r * __pyx_v_r))) * __pyx_v_sp) * __pyx_v_tp) * (__pyx_v_vertices[(54 + __pyx_v_i)]))) + ((((2.0 * __pyx_v_rm) * (1.0 - (__pyx_v_s * __pyx_v_s))) * __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":573
 * @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":619
 * @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":628
 *         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":629
 * 
 *         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":630
 *         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":632
 *         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":633
 * 
 *         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":634
 *         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":636
 *         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":637
 * 
 *         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":638
 *         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":640
 *         tp = 1.0 + t
 * 
 *         for i in range(3):             # <<<<<<<<<<<<<<
 *             rcol[i] = (sm*tm*(r + s + t + 2.0) - rm*sm*tm)*vertices[0  + i] \
 *                     + (sm*tm*(r - s - t - 2.0) + rp*sm*tm)*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":641
 * 
 *         for i in range(3):
 *             rcol[i] = (sm*tm*(r + s + t + 2.0) - rm*sm*tm)*vertices[0  + i] \             # <<<<<<<<<<<<<<
 *                     + (sm*tm*(r - s - t - 2.0) + rp*sm*tm)*vertices[3  + i] \
 *                     + (sp*tm*(r + s - t - 2.0) + rp*sp*tm)*vertices[6  + i] \
 */
    (__pyx_v_rcol[__pyx_v_i]) = (((((((((((((((((((((((__pyx_v_sm * __pyx_v_tm) * (((__pyx_v_r + __pyx_v_s) + __pyx_v_t) + 2.0)) - ((__pyx_v_rm * __pyx_v_sm) * __pyx_v_tm)) * (__pyx_v_vertices[(0 + __pyx_v_i)])) + ((((__pyx_v_sm * __pyx_v_tm) * (((__pyx_v_r - __pyx_v_s) - __pyx_v_t) - 2.0)) + ((__pyx_v_rp * __pyx_v_sm) * __pyx_v_tm)) * (__pyx_v_vertices[(3 + __pyx_v_i)]))) + ((((__pyx_v_sp * __pyx_v_tm) * (((__pyx_v_r + __pyx_v_s) - __pyx_v_t) - 2.0)) + ((__pyx_v_rp * __pyx_v_sp) * __pyx_v_tm)) * (__pyx_v_vertices[(6 + __pyx_v_i)]))) + ((((__pyx_v_sp * __pyx_v_tm) * (((__pyx_v_r - __pyx_v_s) + __pyx_v_t) + 2.0)) - ((__pyx_v_rm * __pyx_v_sp) * __pyx_v_tm)) * (__pyx_v_vertices[(9 + __pyx_v_i)]))) + ((((__pyx_v_sm * __pyx_v_tp) * (((__pyx_v_r + __pyx_v_s) - __pyx_v_t) + 2.0)) - ((__pyx_v_rm * __pyx_v_sm) * __pyx_v_tp)) * (__pyx_v_vertices[(12 + __pyx_v_i)]))) + ((((__pyx_v_sm * __pyx_v_tp) * (((__pyx_v_r - __pyx_v_s) + __pyx_v_t) - 2.0)) + ((__pyx_v_rp * __pyx_v_sm) * __pyx_v_tp)) * (__pyx_v_vertices[(15 + __pyx_v_i)]))) + ((((__pyx_v_sp * __pyx_v_tp) * (((__pyx_v_r + __pyx_v_s) + __pyx_v_t) - 2.0)) + ((__pyx_v_rp * __pyx_v_sp) * __pyx_v_tp)) * (__pyx_v_vertices[(18 + __pyx_v_i)]))) + ((((__pyx_v_sp * __pyx_v_tp) * (((__pyx_v_r - __pyx_v_s) - __pyx_v_t) + 2.0)) - ((__pyx_v_rm * __pyx_v_sp) * __pyx_v_tp)) * (__pyx_v_vertices[(21 + __pyx_v_i)]))) - ((((4.0 * __pyx_v_r) * __pyx_v_sm) * __pyx_v_tm) * (__pyx_v_vertices[(24 + __pyx_v_i)]))) + (((2.0 * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tm) * (__pyx_v_vertices[(27 + __pyx_v_i)]))) - ((((4.0 * __pyx_v_r) * __pyx_v_sp) * __pyx_v_tm) * (__pyx_v_vertices[(30 + __pyx_v_i)]))) - (((2.0 * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tm) * (__pyx_v_vertices[(33 + __pyx_v_i)]))) - (((2.0 * __pyx_v_sm) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vertices[(36 + __pyx_v_i)]))) + (((2.0 * __pyx_v_sm) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vertices[(39 + __pyx_v_i)]))) + (((2.0 * __pyx_v_sp) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vertices[(42 + __pyx_v_i)]))) - (((2.0 * __pyx_v_sp) * (1.0 - (__pyx_v_t * __pyx_v_t))) * (__pyx_v_vertices[(45 + __pyx_v_i)]))) - ((((4.0 * __pyx_v_r) * __pyx_v_sm) * __pyx_v_tp) * (__pyx_v_vertices[(48 + __pyx_v_i)]))) + (((2.0 * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tp) * (__pyx_v_vertices[(51 + __pyx_v_i)]))) - ((((4.0 * __pyx_v_r) * __pyx_v_sp) * __pyx_v_tp) * (__pyx_v_vertices[(54 + __pyx_v_i)]))) - (((2.0 * (1.0 - (__pyx_v_s * __pyx_v_s))) * __pyx_v_tp) * (__pyx_v_vertices[(57 + __pyx_v_i)])));

    /* "yt/utilities/lib/element_mappings.pyx":661
 *                     - 4.0*r*sp*tp*vertices[54 + i] \
 *                     - 2.0*(1.0 - s*s)*tp*vertices[57 + i]
 *             scol[i] = ( rm*tm*(r + s + t + 2.0) - rm*sm*tm)*vertices[0  + i] \             # <<<<<<<<<<<<<<
 *                     + (-rp*tm*(r - s - t - 2.0) - rp*sm*tm)*vertices[3  + i] \
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/* "yt/utilities/lib/element_mappings.pyx":736
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 *             mapped_coord[0] + mapped_coord[1] + mapped_coord[2] - 1.0 > \             # <<<<<<<<<<<<<<
 *             self.inclusion_tol):
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 */
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  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;

  /* "yt/utilities/lib/element_mappings.pyx":1079
 *         # for canonical tets, we check whether the mapped_coords are between
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 *         if (mapped_coord[0] < -self.inclusion_tol or \             # <<<<<<<<<<<<<<
 *             mapped_coord[1] < -self.inclusion_tol or \
 *             mapped_coord[2] < -self.inclusion_tol or \
 */
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    /* "yt/utilities/lib/element_mappings.pyx":1084
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 *         return 1
 * 
 */
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    goto __pyx_L0;

    /* "yt/utilities/lib/element_mappings.pyx":1079
 *         # for canonical tets, we check whether the mapped_coords are between
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 *             mapped_coord[1] < -self.inclusion_tol or \
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 */
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 * 
 *     @cython.boundscheck(False)
 */
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  goto __pyx_L0;

  /* "yt/utilities/lib/element_mappings.pyx":1076
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 *     @cython.cdivision(True)
 *     cdef int check_inside(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
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 */

  /* function exit code */
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/* "yt/utilities/lib/element_mappings.pyx":1090
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 *     @cython.cdivision(True)
 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:             # <<<<<<<<<<<<<<
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 */

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 *     cdef int check_mesh_lines(self, double* mapped_coord) nogil:
 *         cdef double u, v
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 *         if mapped_coord[0] == 0:
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 */
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  /* "yt/utilities/lib/element_mappings.pyx":1093
 *         cdef double u, v
 *         cdef double thresh = 2.0e-2
 *         if mapped_coord[0] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[1]
 *             v = mapped_coord[2]
 */
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    /* "yt/utilities/lib/element_mappings.pyx":1094
 *         cdef double thresh = 2.0e-2
 *         if mapped_coord[0] == 0:
 *             u = mapped_coord[1]             # <<<<<<<<<<<<<<
 *             v = mapped_coord[2]
 *         elif mapped_coord[1] == 0:
 */
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    /* "yt/utilities/lib/element_mappings.pyx":1095
 *         if mapped_coord[0] == 0:
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 *             v = mapped_coord[2]             # <<<<<<<<<<<<<<
 *         elif mapped_coord[1] == 0:
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 */
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 *         cdef double u, v
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 *             u = mapped_coord[1]
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 */
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 *         elif mapped_coord[1] == 0:             # <<<<<<<<<<<<<<
 *             u = mapped_coord[2]
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 */
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 *             v = mapped_coord[0]
 *         elif mapped_coord[2] == 0:
 */
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 *         elif mapped_coord[2] == 0:
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 */
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 */
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 *         elif mapped_coord[2] == 0:             # <<<<<<<<<<<<<<
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 */
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 *             v = mapped_coord[0]
 *         else:
 */
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 */
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 */
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 */
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 */
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  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_P1Sampler1D), /*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*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
  #endif
  0, /*tp_repr*/
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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, 1D element.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_2yt_9utilities_3lib_16element_mappings_P1Sampler1D, /*tp_methods*/
  0, /*tp_members*/
  0, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11P1Sampler1D_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler1D, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
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  0, /*tp_del*/
  0, /*tp_version_tag*/
  #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[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D_5__setstate_cython__, METH_O, 0},
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_P1Sampler2D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.P1Sampler2D", /*tp_name*/
  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*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
  #endif
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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. Note that this\n    implementation uses triangular (or barycentric) coordinates.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_2yt_9utilities_3lib_16element_mappings_P1Sampler2D, /*tp_methods*/
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  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11P1Sampler2D_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler2D, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
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  0, /*tp_cache*/
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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[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11P1Sampler3D_5__setstate_cython__, METH_O, 0},
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_P1Sampler3D = {
  PyVarObject_HEAD_INIT(0, 0)
  "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*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #endif
  #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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  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
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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*/
  0, /*tp_alloc*/
  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_P1Sampler3D, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
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  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
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[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler3D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler3D_5__setstate_cython__, METH_O, 0},
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.NonlinearSolveSampler3D", /*tp_name*/
  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*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
  #endif
  0, /*tp_repr*/
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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*/
  0, /*tp_traverse*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
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  __pyx_methods_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D, /*tp_methods*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler3D_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler3D, /*tp_new*/
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  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
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[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_5__setstate_cython__, METH_O, 0},
  {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*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
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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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  __pyx_methods_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D, /*tp_methods*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11Q1Sampler3D_1__init__, /*tp_init*/
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  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Q1Sampler3D, /*tp_new*/
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  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
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[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_5__setstate_cython__, METH_O, 0},
  {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*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
  #endif
  0, /*tp_repr*/
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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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  0, /*tp_iter*/
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  __pyx_methods_2yt_9utilities_3lib_16element_mappings_W1Sampler3D, /*tp_methods*/
  0, /*tp_members*/
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  0, /*tp_dictoffset*/
  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11W1Sampler3D_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_W1Sampler3D, /*tp_new*/
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  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
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[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_5__setstate_cython__, METH_O, 0},
  {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*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
  #endif
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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*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_2yt_9utilities_3lib_16element_mappings_S2Sampler3D, /*tp_methods*/
  0, /*tp_members*/
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  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11S2Sampler3D_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_S2Sampler3D, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D *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_NonlinearSolveSampler2D *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler2D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler2D_5__setstate_cython__, METH_O, 0},
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.NonlinearSolveSampler2D", /*tp_name*/
  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D), /*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*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
  #endif
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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 2D for reasons of efficiency. This is not to be\n    used directly, use one of the subclasses instead.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
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  0, /*tp_iter*/
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  __pyx_methods_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D, /*tp_methods*/
  0, /*tp_members*/
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  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  __pyx_pw_2yt_9utilities_3lib_16element_mappings_23NonlinearSolveSampler2D_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
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  0, /*tp_cache*/
  0, /*tp_subclasses*/
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  0, /*tp_version_tag*/
  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *p;
  PyObject *o = __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11Q1Sampler2D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11Q1Sampler2D_5__setstate_cython__, METH_O, 0},
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.Q1Sampler2D", /*tp_name*/
  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D), /*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*/
  #endif
  #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 2D, linear, quadrilateral mesh element.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
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  __pyx_methods_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D, /*tp_methods*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11Q1Sampler2D_1__init__, /*tp_init*/
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  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Q1Sampler2D, /*tp_new*/
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  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D *p;
  PyObject *o = __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11Q2Sampler2D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11Q2Sampler2D_5__setstate_cython__, METH_O, 0},
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.Q2Sampler2D", /*tp_name*/
  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D), /*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*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
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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 2D, quadratic, quadrilateral mesh element.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
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  __pyx_methods_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D, /*tp_methods*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11Q2Sampler2D_1__init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Q2Sampler2D, /*tp_new*/
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  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_T2Sampler2D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_T2Sampler2D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_T2Sampler2D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D *p;
  PyObject *o = __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_NonlinearSolveSampler2D(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_T2Sampler2D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_T2Sampler2D[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11T2Sampler2D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_11T2Sampler2D_5__setstate_cython__, METH_O, 0},
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_T2Sampler2D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.T2Sampler2D", /*tp_name*/
  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_T2Sampler2D), /*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*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
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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 2D, quadratic, triangular mesh\n    element. Note that this implementation uses canonical coordinates.\n\n    ", /*tp_doc*/
  0, /*tp_traverse*/
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  __pyx_methods_2yt_9utilities_3lib_16element_mappings_T2Sampler2D, /*tp_methods*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_11T2Sampler2D_1__init__, /*tp_init*/
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  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_T2Sampler2D, /*tp_new*/
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  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
static struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D __pyx_vtable_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D;

static PyObject *__pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D *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_Tet2Sampler3D *)o);
  p->__pyx_base.__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_2yt_9utilities_3lib_16element_mappings_ElementSampler*)__pyx_vtabptr_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D;
  return o;
}

static PyMethodDef __pyx_methods_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D[] = {
  {"__reduce_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_13Tet2Sampler3D_3__reduce_cython__, METH_NOARGS, 0},
  {"__setstate_cython__", (PyCFunction)__pyx_pw_2yt_9utilities_3lib_16element_mappings_13Tet2Sampler3D_5__setstate_cython__, METH_O, 0},
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D = {
  PyVarObject_HEAD_INIT(0, 0)
  "yt.utilities.lib.element_mappings.Tet2Sampler3D", /*tp_name*/
  sizeof(struct __pyx_obj_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_2yt_9utilities_3lib_16element_mappings_ElementSampler, /*tp_dealloc*/
  0, /*tp_print*/
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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, quadratic, tetrahedral mesh\n    element. Note that this implementation uses canonical coordinates.\n\n    ", /*tp_doc*/
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  __pyx_pw_2yt_9utilities_3lib_16element_mappings_13Tet2Sampler3D_1__init__, /*tp_init*/
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  __pyx_tp_new_2yt_9utilities_3lib_16element_mappings_Tet2Sampler3D, /*tp_new*/
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 *             info.buf = PyArray_DATA(self)
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 * 
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 *         if ((child.byteorder == c'>' and little_endian) or
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 * cdef inline int import_umath() except -1:
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 * @cython.wraparound(False)
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 * def test_hex_sampler(np.ndarray[np.float64_t, ndim=2] vertices,             # <<<<<<<<<<<<<<
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 * @cython.wraparound(False)
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 * def test_hex20_sampler(np.ndarray[np.float64_t, ndim=2] vertices,             # <<<<<<<<<<<<<<
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 * @cython.wraparound(False)
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 * @cython.wraparound(False)
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#if PY_MAJOR_VERSION < 3
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            "name '%.200s' is not defined", PyString_AS_STRING(name));
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#if CYTHON_COMPILING_IN_PYPY
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invalid_keyword_type:
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#endif
invalid_keyword:
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#if PY_MAJOR_VERSION >= 3
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}
#endif

/* PyErrFetchRestore */
#if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
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static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
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/* GetAttr */
static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *o, PyObject *n) {
#if CYTHON_USE_TYPE_SLOTS
#if PY_MAJOR_VERSION >= 3
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#else
    if (likely(PyString_Check(n)))
#endif
        return __Pyx_PyObject_GetAttrStr(o, n);
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static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *o, PyObject *n, PyObject *d) {
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/* GetModuleGlobalName */
static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
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#if !CYTHON_AVOID_BORROWED_REFS
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1
    result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);
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        Py_INCREF(result);
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        result = NULL;
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#else
    result = PyDict_GetItem(__pyx_d, name);
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        Py_INCREF(result);
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#endif
#else
    result = PyObject_GetItem(__pyx_d, name);
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/* PyObjectCall */
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static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
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    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
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    result = (*call)(func, arg, kw);
    Py_LeaveRecursiveCall();
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static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
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    PyCFunction meth = PyCFunction_GET_FUNCTION(func);
    PyObject *self = PyCFunction_GET_SELF(func);
    int flags = PyCFunction_GET_FLAGS(func);
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    assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS)));
    assert(nargs >= 0);
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    /* _PyCFunction_FastCallDict() must not be called with an exception set,
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    assert(!PyErr_Occurred());
    if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
        return (*((__Pyx_PyCFunctionFastWithKeywords)meth)) (self, args, nargs, NULL);
    } else {
        return (*((__Pyx_PyCFunctionFast)meth)) (self, args, nargs);
    }
}
#endif

/* 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 = __Pyx_PyThreadState_Current;
    PyObject **fastlocals;
    Py_ssize_t i;
    PyObject *result;
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    assert(tstate != NULL);
    f = PyFrame_New(tstate, co, globals, NULL);
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        return NULL;
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    fastlocals = f->f_localsplus;
    for (i = 0; i < na; i++) {
        Py_INCREF(*args);
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    result = PyEval_EvalFrameEx(f,0);
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#if 1 || PY_VERSION_HEX < 0x030600B1
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) {
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#if PY_MAJOR_VERSION >= 3
    PyObject *kwdefs;
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#if PY_MAJOR_VERSION >= 3
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#endif
            likely(kwargs == NULL || nk == 0) &&
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        if (argdefs == NULL && co->co_argcount == nargs) {
            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
            goto done;
        }
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            goto done;
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static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
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static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
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static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
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    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 (cause) {
        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 = __Pyx_PyThreadState_Current;
        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

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

/* IsLittleEndian */
      static CYTHON_INLINE int __Pyx_Is_Little_Endian(void)
{
  union {
    uint32_t u32;
    uint8_t u8[4];
  } S;
  S.u32 = 0x01020304;
  return S.u8[0] == 4;
}

/* BufferFormatCheck */
      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 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_Is_Little_Endian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_Is_Little_Endian()) {
          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;
        }
        CYTHON_FALLTHROUGH;
      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;
        }
        CYTHON_FALLTHROUGH;
      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;
        }
    }
  }
}

/* BufferGetAndValidate */
        static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
  if (unlikely(info->buf == NULL)) return;
  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
  __Pyx_ReleaseBuffer(info);
}
static void __Pyx_ZeroBuffer(Py_buffer* buf) {
  buf->buf = NULL;
  buf->obj = NULL;
  buf->strides = __Pyx_zeros;
  buf->shape = __Pyx_zeros;
  buf->suboffsets = __Pyx_minusones;
}
static int __Pyx__GetBufferAndValidate(
        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
{
  buf->buf = NULL;
  if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) {
    __Pyx_ZeroBuffer(buf);
    return -1;
  }
  if (unlikely(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 (unlikely((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_SafeReleaseBuffer(buf);
  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_MAJOR_VERSION < 3
    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, '.')) {
                module = PyImport_ImportModuleLevelObject(
                    name, global_dict, empty_dict, list, 1);
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0;
        }
        #endif
        if (!module) {
            #if PY_MAJOR_VERSION < 3
            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_MAJOR_VERSION < 3
    Py_XDECREF(py_import);
    #endif
    Py_XDECREF(empty_list);
    Py_XDECREF(empty_dict);
    return module;
}

/* ImportFrom */
        static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
        PyErr_Format(PyExc_ImportError,
        #if PY_MAJOR_VERSION < 3
            "cannot import name %.230s", PyString_AS_STRING(name));
        #else
            "cannot import name %S", name);
        #endif
    }
    return value;
}

/* GetItemInt */
        static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
    PyObject *r;
    if (!j) return NULL;
    r = PyObject_GetItem(o, j);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    Py_ssize_t wrapped_i = i;
    if (wraparound & unlikely(i < 0)) {
        wrapped_i += PyList_GET_SIZE(o);
    }
    if ((!boundscheck) || likely((0 <= wrapped_i) & (wrapped_i < PyList_GET_SIZE(o)))) {
        PyObject *r = PyList_GET_ITEM(o, wrapped_i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    Py_ssize_t wrapped_i = i;
    if (wraparound & unlikely(i < 0)) {
        wrapped_i += PyTuple_GET_SIZE(o);
    }
    if ((!boundscheck) || likely((0 <= wrapped_i) & (wrapped_i < PyTuple_GET_SIZE(o)))) {
        PyObject *r = PyTuple_GET_ITEM(o, wrapped_i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,
                                                     CYTHON_NCP_UNUSED int wraparound,
                                                     CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
        if ((!boundscheck) || (likely((n >= 0) & (n < PyList_GET_SIZE(o))))) {
            PyObject *r = PyList_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    }
    else if (PyTuple_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
        if ((!boundscheck) || likely((n >= 0) & (n < PyTuple_GET_SIZE(o)))) {
            PyObject *r = PyTuple_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    } else {
        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
        if (likely(m && m->sq_item)) {
            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
                Py_ssize_t l = m->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
                        return NULL;
                    PyErr_Clear();
                }
            }
            return m->sq_item(o, i);
        }
    }
#else
    if (is_list || PySequence_Check(o)) {
        return PySequence_GetItem(o, i);
    }
#endif
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
}

/* HasAttr */
        static CYTHON_INLINE int __Pyx_HasAttr(PyObject *o, PyObject *n) {
    PyObject *r;
    if (unlikely(!__Pyx_PyBaseString_Check(n))) {
        PyErr_SetString(PyExc_TypeError,
                        "hasattr(): attribute name must be string");
        return -1;
    }
    r = __Pyx_GetAttr(o, n);
    if (unlikely(!r)) {
        PyErr_Clear();
        return 0;
    } else {
        Py_DECREF(r);
        return 1;
    }
}

/* DictGetItem */
        #if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY
static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) {
    PyObject *value;
    value = PyDict_GetItemWithError(d, key);
    if (unlikely(!value)) {
        if (!PyErr_Occurred()) {
            PyObject* args = PyTuple_Pack(1, key);
            if (likely(args))
                PyErr_SetObject(PyExc_KeyError, args);
            Py_XDECREF(args);
        }
        return NULL;
    }
    Py_INCREF(value);
    return value;
}
#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(__Pyx_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) {
    #if PY_VERSION_HEX >= 0x030700A2
    *type = tstate->exc_state.exc_type;
    *value = tstate->exc_state.exc_value;
    *tb = tstate->exc_state.exc_traceback;
    #else
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    #endif
    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;
    #if PY_VERSION_HEX >= 0x030700A2
    tmp_type = tstate->exc_state.exc_type;
    tmp_value = tstate->exc_state.exc_value;
    tmp_tb = tstate->exc_state.exc_traceback;
    tstate->exc_state.exc_type = type;
    tstate->exc_state.exc_value = value;
    tstate->exc_state.exc_traceback = tb;
    #else
    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;
    #endif
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}
#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
    #if PY_VERSION_HEX >= 0x030700A2
    tmp_type = tstate->exc_state.exc_type;
    tmp_value = tstate->exc_state.exc_value;
    tmp_tb = tstate->exc_state.exc_traceback;
    tstate->exc_state.exc_type = local_type;
    tstate->exc_state.exc_value = local_value;
    tstate->exc_state.exc_traceback = local_tb;
    #else
    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;
    #endif
    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;
}

/* PyObject_GenericGetAttrNoDict */
          #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
static PyObject *__Pyx_RaiseGenericGetAttributeError(PyTypeObject *tp, PyObject *attr_name) {
    PyErr_Format(PyExc_AttributeError,
#if PY_MAJOR_VERSION >= 3
                 "'%.50s' object has no attribute '%U'",
                 tp->tp_name, attr_name);
#else
                 "'%.50s' object has no attribute '%.400s'",
                 tp->tp_name, PyString_AS_STRING(attr_name));
#endif
    return NULL;
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name) {
    PyObject *descr;
    PyTypeObject *tp = Py_TYPE(obj);
    if (unlikely(!PyString_Check(attr_name))) {
        return PyObject_GenericGetAttr(obj, attr_name);
    }
    assert(!tp->tp_dictoffset);
    descr = _PyType_Lookup(tp, attr_name);
    if (unlikely(!descr)) {
        return __Pyx_RaiseGenericGetAttributeError(tp, attr_name);
    }
    Py_INCREF(descr);
    #if PY_MAJOR_VERSION < 3
    if (likely(PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_HAVE_CLASS)))
    #endif
    {
        descrgetfunc f = Py_TYPE(descr)->tp_descr_get;
        if (unlikely(f)) {
            PyObject *res = f(descr, obj, (PyObject *)tp);
            Py_DECREF(descr);
            return res;
        }
    }
    return descr;
}
#endif

/* PyObject_GenericGetAttr */
          #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name) {
    if (unlikely(Py_TYPE(obj)->tp_dictoffset)) {
        return PyObject_GenericGetAttr(obj, attr_name);
    }
    return __Pyx_PyObject_GenericGetAttrNoDict(obj, attr_name);
}
#endif

/* 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;
}

/* SetupReduce */
          static int __Pyx_setup_reduce_is_named(PyObject* meth, PyObject* name) {
  int ret;
  PyObject *name_attr;
  name_attr = __Pyx_PyObject_GetAttrStr(meth, __pyx_n_s_name);
  if (likely(name_attr)) {
      ret = PyObject_RichCompareBool(name_attr, name, Py_EQ);
  } else {
      ret = -1;
  }
  if (unlikely(ret < 0)) {
      PyErr_Clear();
      ret = 0;
  }
  Py_XDECREF(name_attr);
  return ret;
}
static int __Pyx_setup_reduce(PyObject* type_obj) {
    int ret = 0;
    PyObject *object_reduce = NULL;
    PyObject *object_reduce_ex = NULL;
    PyObject *reduce = NULL;
    PyObject *reduce_ex = NULL;
    PyObject *reduce_cython = NULL;
    PyObject *setstate = NULL;
    PyObject *setstate_cython = NULL;
#if CYTHON_USE_PYTYPE_LOOKUP
    if (_PyType_Lookup((PyTypeObject*)type_obj, __pyx_n_s_getstate)) goto GOOD;
#else
    if (PyObject_HasAttr(type_obj, __pyx_n_s_getstate)) goto GOOD;
#endif
#if CYTHON_USE_PYTYPE_LOOKUP
    object_reduce_ex = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto BAD;
#else
    object_reduce_ex = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto BAD;
#endif
    reduce_ex = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_ex); if (unlikely(!reduce_ex)) goto BAD;
    if (reduce_ex == object_reduce_ex) {
#if CYTHON_USE_PYTYPE_LOOKUP
        object_reduce = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto BAD;
#else
        object_reduce = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto BAD;
#endif
        reduce = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce); if (unlikely(!reduce)) goto BAD;
        if (reduce == object_reduce || __Pyx_setup_reduce_is_named(reduce, __pyx_n_s_reduce_cython)) {
            reduce_cython = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_cython); if (unlikely(!reduce_cython)) goto BAD;
            ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce, reduce_cython); if (unlikely(ret < 0)) goto BAD;
            ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce_cython); if (unlikely(ret < 0)) goto BAD;
            setstate = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate);
            if (!setstate) PyErr_Clear();
            if (!setstate || __Pyx_setup_reduce_is_named(setstate, __pyx_n_s_setstate_cython)) {
                setstate_cython = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate_cython); if (unlikely(!setstate_cython)) goto BAD;
                ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate, setstate_cython); if (unlikely(ret < 0)) goto BAD;
                ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate_cython); if (unlikely(ret < 0)) goto BAD;
            }
            PyType_Modified((PyTypeObject*)type_obj);
        }
    }
    goto GOOD;
BAD:
    if (!PyErr_Occurred())
        PyErr_Format(PyExc_RuntimeError, "Unable to initialize pickling for %s", ((PyTypeObject*)type_obj)->tp_name);
    ret = -1;
GOOD:
#if !CYTHON_USE_PYTYPE_LOOKUP
    Py_XDECREF(object_reduce);
    Py_XDECREF(object_reduce_ex);
#endif
    Py_XDECREF(reduce);
    Py_XDECREF(reduce_ex);
    Py_XDECREF(reduce_cython);
    Py_XDECREF(setstate);
    Py_XDECREF(setstate_cython);
    return ret;
}

/* CLineInTraceback */
          #ifndef CYTHON_CLINE_IN_TRACEBACK
static int __Pyx_CLineForTraceback(CYTHON_UNUSED PyThreadState *tstate, int c_line) {
    PyObject *use_cline;
    PyObject *ptype, *pvalue, *ptraceback;
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject **cython_runtime_dict;
#endif
    if (unlikely(!__pyx_cython_runtime)) {
        return c_line;
    }
    __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
#if CYTHON_COMPILING_IN_CPYTHON
    cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
    if (likely(cython_runtime_dict)) {
      use_cline = __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback);
    } else
#endif
    {
      PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
      if (use_cline_obj) {
        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
        Py_DECREF(use_cline_obj);
      } else {
        PyErr_Clear();
        use_cline = NULL;
      }
    }
    if (!use_cline) {
        c_line = 0;
        PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
    }
    else if (PyObject_Not(use_cline) != 0) {
        c_line = 0;
    }
    __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
    return c_line;
}
#endif

/* 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;
    PyThreadState *tstate = __Pyx_PyThreadState_Current;
    if (c_line) {
        c_line = __Pyx_CLineForTraceback(tstate, c_line);
    }
    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(
        tstate,            /*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);
}

/* 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;\
    }

#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 (__Pyx_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 ((0)) {}
        else if (__Pyx_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view);
    view->obj = NULL;
    Py_DECREF(obj);
}
#endif


          /* 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);
    }
}

/* 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;
                } else if (b.imag == 0) {
                    z.real = powf(a.real, b.real);
                    z.imag = 0;
                    return z;
                } else if (a.real > 0) {
                    r = a.real;
                    theta = 0;
                } else {
                    r = -a.real;
                    theta = atan2f(0, -1);
                }
            } 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;
                } else if (b.imag == 0) {
                    z.real = pow(a.real, b.real);
                    z.imag = 0;
                    return z;
                } else if (a.real > 0) {
                    r = a.real;
                    theta = 0;
                } else {
                    r = -a.real;
                    theta = atan2(0, -1);
                }
            } 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;
}

/* 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;
}

/* FastTypeChecks */
          #if CYTHON_COMPILING_IN_CPYTHON
static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
    while (a) {
        a = a->tp_base;
        if (a == b)
            return 1;
    }
    return b == &PyBaseObject_Type;
}
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
    PyObject *mro;
    if (a == b) return 1;
    mro = a->tp_mro;
    if (likely(mro)) {
        Py_ssize_t i, n;
        n = PyTuple_GET_SIZE(mro);
        for (i = 0; i < n; i++) {
            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
                return 1;
        }
        return 0;
    }
    return __Pyx_InBases(a, b);
}
#if PY_MAJOR_VERSION == 2
static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
    PyObject *exception, *value, *tb;
    int res;
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    __Pyx_ErrFetch(&exception, &value, &tb);
    res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
    if (unlikely(res == -1)) {
        PyErr_WriteUnraisable(err);
        res = 0;
    }
    if (!res) {
        res = PyObject_IsSubclass(err, exc_type2);
        if (unlikely(res == -1)) {
            PyErr_WriteUnraisable(err);
            res = 0;
        }
    }
    __Pyx_ErrRestore(exception, value, tb);
    return res;
}
#else
static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
    int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
    if (!res) {
        res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
    }
    return res;
}
#endif
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
    if (likely(err == exc_type)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
    }
    return PyErr_GivenExceptionMatches(err, exc_type);
}
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
    if (likely(err == exc_type1 || err == exc_type2)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
    }
    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
}
#endif

/* 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

/* FunctionImport */
          #ifndef __PYX_HAVE_RT_ImportFunction
#define __PYX_HAVE_RT_ImportFunction
static int __Pyx_ImportFunction(PyObject *module, const char *funcname, void (**f)(void), const char *sig) {
    PyObject *d = 0;
    PyObject *cobj = 0;
    union {
        void (*fp)(void);
        void *p;
    } tmp;
    d = PyObject_GetAttrString(module, (char *)"__pyx_capi__");
    if (!d)
        goto bad;
    cobj = PyDict_GetItemString(d, funcname);
    if (!cobj) {
        PyErr_Format(PyExc_ImportError,
            "%.200s does not export expected C function %.200s",
                PyModule_GetName(module), funcname);
        goto bad;
    }
#if PY_VERSION_HEX >= 0x02070000
    if (!PyCapsule_IsValid(cobj, sig)) {
        PyErr_Format(PyExc_TypeError,
            "C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), funcname, sig, PyCapsule_GetName(cobj));
        goto bad;
    }
    tmp.p = PyCapsule_GetPointer(cobj, sig);
#else
    {const char *desc, *s1, *s2;
    desc = (const char *)PyCObject_GetDesc(cobj);
    if (!desc)
        goto bad;
    s1 = desc; s2 = sig;
    while (*s1 != '\0' && *s1 == *s2) { s1++; s2++; }
    if (*s1 != *s2) {
        PyErr_Format(PyExc_TypeError,
            "C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), funcname, sig, desc);
        goto bad;
    }
    tmp.p = PyCObject_AsVoidPtr(cobj);}
#endif
    *f = tmp.fp;
    if (!(*f))
        goto bad;
    Py_DECREF(d);
    return 0;
bad:
    Py_XDECREF(d);
    return -1;
}
#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;
        if (PyObject_Hash(*t->p) == -1)
            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 const char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
#if !CYTHON_PEP393_ENABLED
static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
    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
static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
    if (likely(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
#endif
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if __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)) {
        return __Pyx_PyUnicode_AsStringAndSize(o, length);
    } 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 PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
#if PY_MAJOR_VERSION >= 3
    if (PyLong_Check(result)) {
        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
                "__int__ returned non-int (type %.200s).  "
                "The ability to return an instance of a strict subclass of int "
                "is deprecated, and may be removed in a future version of Python.",
                Py_TYPE(result)->tp_name)) {
            Py_DECREF(result);
            return NULL;
        }
        return result;
    }
#endif
    PyErr_Format(PyExc_TypeError,
                 "__%.4s__ returned non-%.4s (type %.200s)",
                 type_name, type_name, Py_TYPE(result)->tp_name);
    Py_DECREF(result);
    return NULL;
}
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 (likely(PyInt_Check(x) || PyLong_Check(x)))
#else
  if (likely(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 = m->nb_int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = m->nb_long(x);
  }
  #else
  if (likely(m && m->nb_int)) {
    name = "int";
    res = m->nb_int(x);
  }
  #endif
#else
  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
    res = PyNumber_Int(x);
  }
#endif
  if (likely(res)) {
#if PY_MAJOR_VERSION < 3
    if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
#else
    if (unlikely(!PyLong_CheckExact(res))) {
#endif
        return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
    }
  }
  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_PyBool_FromLong(long b) {
  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
}
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */
