CoCalc -- prime.c

Harvard Workshop: Distribution of modular symbols and L-values
code / alex / psage / psage / number_fields / sqrt5 / prime.c
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#define __PYX_ERR(f_index, lineno, Ln_error) \
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#define __PYX_HAVE__code__alex__psage__psage__number_fields__sqrt5__prime
431
#define __PYX_HAVE_API__code__alex__psage__psage__number_fields__sqrt5__prime
432
#include "struct_signals.h"
433
#include "pxi.h"
434
#include <string.h>
435
#include <stdlib.h>
436
#include <stdio.h>
437
#include "pari/pari.h"
438
#ifdef _OPENMP
439
#include <omp.h>
440
#endif /* _OPENMP */
441

442
#ifdef PYREX_WITHOUT_ASSERTIONS
443
#define CYTHON_WITHOUT_ASSERTIONS
444
#endif
445

446
typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
447
                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
448

449
#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
450
#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
451
#define __PYX_DEFAULT_STRING_ENCODING ""
452
#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
453
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
454
#define __Pyx_uchar_cast(c) ((unsigned char)c)
455
#define __Pyx_long_cast(x) ((long)x)
456
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
457
    (sizeof(type) < sizeof(Py_ssize_t))  ||\
458
    (sizeof(type) > sizeof(Py_ssize_t) &&\
459
          likely(v < (type)PY_SSIZE_T_MAX ||\
460
                 v == (type)PY_SSIZE_T_MAX)  &&\
461
          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
462
                                v == (type)PY_SSIZE_T_MIN)))  ||\
463
    (sizeof(type) == sizeof(Py_ssize_t) &&\
464
          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
465
                               v == (type)PY_SSIZE_T_MAX)))  )
466
#if defined (__cplusplus) && __cplusplus >= 201103L
467
    #include <cstdlib>
468
    #define __Pyx_sst_abs(value) std::abs(value)
469
#elif SIZEOF_INT >= SIZEOF_SIZE_T
470
    #define __Pyx_sst_abs(value) abs(value)
471
#elif SIZEOF_LONG >= SIZEOF_SIZE_T
472
    #define __Pyx_sst_abs(value) labs(value)
473
#elif defined (_MSC_VER) && defined (_M_X64)
474
    #define __Pyx_sst_abs(value) _abs64(value)
475
#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
476
    #define __Pyx_sst_abs(value) llabs(value)
477
#elif defined (__GNUC__)
478
    #define __Pyx_sst_abs(value) __builtin_llabs(value)
479
#else
480
    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
481
#endif
482
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject*);
483
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
484
#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
485
#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
486
#define __Pyx_PyBytes_FromString        PyBytes_FromString
487
#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
488
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
489
#if PY_MAJOR_VERSION < 3
490
    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
491
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
492
#else
493
    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
494
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
495
#endif
496
#define __Pyx_PyObject_AsSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
497
#define __Pyx_PyObject_AsUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
498
#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
499
#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
500
#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
501
#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
502
#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
503
#if PY_MAJOR_VERSION < 3
504
static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u)
505
{
506
    const Py_UNICODE *u_end = u;
507
    while (*u_end++) ;
508
    return (size_t)(u_end - u - 1);
509
}
510
#else
511
#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen
512
#endif
513
#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
514
#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
515
#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
516
#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
517
#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
518
#define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False))
519
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
520
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
521
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
522
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
523
#if CYTHON_ASSUME_SAFE_MACROS
524
#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
525
#else
526
#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
527
#endif
528
#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
529
#if PY_MAJOR_VERSION >= 3
530
#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
531
#else
532
#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
533
#endif
534
#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
535
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
536
static int __Pyx_sys_getdefaultencoding_not_ascii;
537
static int __Pyx_init_sys_getdefaultencoding_params(void) {
538
    PyObject* sys;
539
    PyObject* default_encoding = NULL;
540
    PyObject* ascii_chars_u = NULL;
541
    PyObject* ascii_chars_b = NULL;
542
    const char* default_encoding_c;
543
    sys = PyImport_ImportModule("sys");
544
    if (!sys) goto bad;
545
    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
546
    Py_DECREF(sys);
547
    if (!default_encoding) goto bad;
548
    default_encoding_c = PyBytes_AsString(default_encoding);
549
    if (!default_encoding_c) goto bad;
550
    if (strcmp(default_encoding_c, "ascii") == 0) {
551
        __Pyx_sys_getdefaultencoding_not_ascii = 0;
552
    } else {
553
        char ascii_chars[128];
554
        int c;
555
        for (c = 0; c < 128; c++) {
556
            ascii_chars[c] = c;
557
        }
558
        __Pyx_sys_getdefaultencoding_not_ascii = 1;
559
        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
560
        if (!ascii_chars_u) goto bad;
561
        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
562
        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
563
            PyErr_Format(
564
                PyExc_ValueError,
565
                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
566
                default_encoding_c);
567
            goto bad;
568
        }
569
        Py_DECREF(ascii_chars_u);
570
        Py_DECREF(ascii_chars_b);
571
    }
572
    Py_DECREF(default_encoding);
573
    return 0;
574
bad:
575
    Py_XDECREF(default_encoding);
576
    Py_XDECREF(ascii_chars_u);
577
    Py_XDECREF(ascii_chars_b);
578
    return -1;
579
}
580
#endif
581
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
582
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
583
#else
584
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
585
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
586
static char* __PYX_DEFAULT_STRING_ENCODING;
587
static int __Pyx_init_sys_getdefaultencoding_params(void) {
588
    PyObject* sys;
589
    PyObject* default_encoding = NULL;
590
    char* default_encoding_c;
591
    sys = PyImport_ImportModule("sys");
592
    if (!sys) goto bad;
593
    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
594
    Py_DECREF(sys);
595
    if (!default_encoding) goto bad;
596
    default_encoding_c = PyBytes_AsString(default_encoding);
597
    if (!default_encoding_c) goto bad;
598
    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));
599
    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
600
    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
601
    Py_DECREF(default_encoding);
602
    return 0;
603
bad:
604
    Py_XDECREF(default_encoding);
605
    return -1;
606
}
607
#endif
608
#endif
609

610

611
/* Test for GCC > 2.95 */
612
#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
613
  #define likely(x)   __builtin_expect(!!(x), 1)
614
  #define unlikely(x) __builtin_expect(!!(x), 0)
615
#else /* !__GNUC__ or GCC < 2.95 */
616
  #define likely(x)   (x)
617
  #define unlikely(x) (x)
618
#endif /* __GNUC__ */
619

620
static PyObject *__pyx_m;
621
static PyObject *__pyx_d;
622
static PyObject *__pyx_b;
623
static PyObject *__pyx_empty_tuple;
624
static PyObject *__pyx_empty_bytes;
625
static PyObject *__pyx_empty_unicode;
626
static int __pyx_lineno;
627
static int __pyx_clineno = 0;
628
static const char * __pyx_cfilenm= __FILE__;
629
static const char *__pyx_filename;
630

631

632
static const char *__pyx_f[] = {
633
  "code/alex/psage/psage/number_fields/sqrt5/prime.pyx",
634
  "code/alex/psage/psage/number_fields/sqrt5/prime.pxd",
635
  "memory.pxd",
636
  "stdsage.pxd",
637
  "type.pxd",
638
  "signals.pxi",
639
  "stdsage.pxi",
640
  "interrupt.pxi",
641
};
642

643
/*--- Type declarations ---*/
644
struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime;
645

646
/* "code/alex/psage/psage/number_fields/sqrt5/prime.pxd":22
647
 * #################################################################################
648
 * 
649
 * cdef class Prime:             # <<<<<<<<<<<<<<
650
 *     cdef public long p, r
651
 *     cdef bint first
652
 */
653
struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime {
654
  PyObject_HEAD
655
  struct __pyx_vtabstruct_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_vtab;
656
  long p;
657
  long r;
658
  int first;
659
};
660

661

662

663
/* "code/alex/psage/psage/number_fields/sqrt5/prime.pyx":56
664
 * from sage.rings.number_field.number_field_ideal import NumberFieldFractionalIdeal
665
 * 
666
 * cdef class Prime:             # <<<<<<<<<<<<<<
667
 *     """
668
 *     Nonzero prime ideal of the ring of integers of Q(sqrt(5)).  This
669
 */
670

671
struct __pyx_vtabstruct_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime {
672
  long (*norm)(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *, int __pyx_skip_dispatch);
673
  int (*is_split)(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *, int __pyx_skip_dispatch);
674
  int (*is_inert)(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *, int __pyx_skip_dispatch);
675
  int (*is_ramified)(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *, int __pyx_skip_dispatch);
676
};
677
static struct __pyx_vtabstruct_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_vtabptr_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime;
678

679
/* --- Runtime support code (head) --- */
680
/* Refnanny.proto */
681
#ifndef CYTHON_REFNANNY
682
  #define CYTHON_REFNANNY 0
683
#endif
684
#if CYTHON_REFNANNY
685
  typedef struct {
686
    void (*INCREF)(void*, PyObject*, int);
687
    void (*DECREF)(void*, PyObject*, int);
688
    void (*GOTREF)(void*, PyObject*, int);
689
    void (*GIVEREF)(void*, PyObject*, int);
690
    void* (*SetupContext)(const char*, int, const char*);
691
    void (*FinishContext)(void**);
692
  } __Pyx_RefNannyAPIStruct;
693
  static __Pyx_RefNannyAPIStruct *__Pyx_RefNanny = NULL;
694
  static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname);
695
  #define __Pyx_RefNannyDeclarations void *__pyx_refnanny = NULL;
696
#ifdef WITH_THREAD
697
  #define __Pyx_RefNannySetupContext(name, acquire_gil)\
698
          if (acquire_gil) {\
699
              PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\
700
              __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\
701
              PyGILState_Release(__pyx_gilstate_save);\
702
          } else {\
703
              __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\
704
          }
705
#else
706
  #define __Pyx_RefNannySetupContext(name, acquire_gil)\
707
          __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__)
708
#endif
709
  #define __Pyx_RefNannyFinishContext()\
710
          __Pyx_RefNanny->FinishContext(&__pyx_refnanny)
711
  #define __Pyx_INCREF(r)  __Pyx_RefNanny->INCREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
712
  #define __Pyx_DECREF(r)  __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
713
  #define __Pyx_GOTREF(r)  __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
714
  #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
715
  #define __Pyx_XINCREF(r)  do { if((r) != NULL) {__Pyx_INCREF(r); }} while(0)
716
  #define __Pyx_XDECREF(r)  do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0)
717
  #define __Pyx_XGOTREF(r)  do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0)
718
  #define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);}} while(0)
719
#else
720
  #define __Pyx_RefNannyDeclarations
721
  #define __Pyx_RefNannySetupContext(name, acquire_gil)
722
  #define __Pyx_RefNannyFinishContext()
723
  #define __Pyx_INCREF(r) Py_INCREF(r)
724
  #define __Pyx_DECREF(r) Py_DECREF(r)
725
  #define __Pyx_GOTREF(r)
726
  #define __Pyx_GIVEREF(r)
727
  #define __Pyx_XINCREF(r) Py_XINCREF(r)
728
  #define __Pyx_XDECREF(r) Py_XDECREF(r)
729
  #define __Pyx_XGOTREF(r)
730
  #define __Pyx_XGIVEREF(r)
731
#endif
732
#define __Pyx_XDECREF_SET(r, v) do {\
733
        PyObject *tmp = (PyObject *) r;\
734
        r = v; __Pyx_XDECREF(tmp);\
735
    } while (0)
736
#define __Pyx_DECREF_SET(r, v) do {\
737
        PyObject *tmp = (PyObject *) r;\
738
        r = v; __Pyx_DECREF(tmp);\
739
    } while (0)
740
#define __Pyx_CLEAR(r)    do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
741
#define __Pyx_XCLEAR(r)   do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)
742

743
/* PyObjectGetAttrStr.proto */
744
#if CYTHON_USE_TYPE_SLOTS
745
static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
746
    PyTypeObject* tp = Py_TYPE(obj);
747
    if (likely(tp->tp_getattro))
748
        return tp->tp_getattro(obj, attr_name);
749
#if PY_MAJOR_VERSION < 3
750
    if (likely(tp->tp_getattr))
751
        return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
752
#endif
753
    return PyObject_GetAttr(obj, attr_name);
754
}
755
#else
756
#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
757
#endif
758

759
/* GetBuiltinName.proto */
760
static PyObject *__Pyx_GetBuiltinName(PyObject *name);
761

762
/* RaiseDoubleKeywords.proto */
763
static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
764

765
/* ParseKeywords.proto */
766
static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
767
    PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
768
    const char* function_name);
769

770
/* RaiseArgTupleInvalid.proto */
771
static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
772
    Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);
773

774
/* GetModuleGlobalName.proto */
775
static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);
776

777
/* PyCFunctionFastCall.proto */
778
#if CYTHON_FAST_PYCCALL
779
static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
780
#else
781
#define __Pyx_PyCFunction_FastCall(func, args, nargs)  (assert(0), NULL)
782
#endif
783

784
/* PyFunctionFastCall.proto */
785
#if CYTHON_FAST_PYCALL
786
#define __Pyx_PyFunction_FastCall(func, args, nargs)\
787
    __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
788
#if 1 || PY_VERSION_HEX < 0x030600B1
789
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs);
790
#else
791
#define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
792
#endif
793
#endif
794

795
/* PyObjectCall.proto */
796
#if CYTHON_COMPILING_IN_CPYTHON
797
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
798
#else
799
#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
800
#endif
801

802
/* PyObjectCallMethO.proto */
803
#if CYTHON_COMPILING_IN_CPYTHON
804
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
805
#endif
806

807
/* PyObjectCallOneArg.proto */
808
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
809

810
/* PyObjectCallNoArg.proto */
811
#if CYTHON_COMPILING_IN_CPYTHON
812
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
813
#else
814
#define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
815
#endif
816

817
/* None.proto */
818
static CYTHON_INLINE long __Pyx_mod_long(long, long);
819

820
/* PyThreadStateGet.proto */
821
#if CYTHON_FAST_THREAD_STATE
822
#define __Pyx_PyThreadState_declare  PyThreadState *__pyx_tstate;
823
#define __Pyx_PyThreadState_assign  __pyx_tstate = PyThreadState_GET();
824
#else
825
#define __Pyx_PyThreadState_declare
826
#define __Pyx_PyThreadState_assign
827
#endif
828

829
/* PyErrFetchRestore.proto */
830
#if CYTHON_FAST_THREAD_STATE
831
#define __Pyx_ErrRestoreWithState(type, value, tb)  __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
832
#define __Pyx_ErrFetchWithState(type, value, tb)    __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
833
#define __Pyx_ErrRestore(type, value, tb)  __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
834
#define __Pyx_ErrFetch(type, value, tb)    __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
835
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
836
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
837
#else
838
#define __Pyx_ErrRestoreWithState(type, value, tb)  PyErr_Restore(type, value, tb)
839
#define __Pyx_ErrFetchWithState(type, value, tb)  PyErr_Fetch(type, value, tb)
840
#define __Pyx_ErrRestore(type, value, tb)  PyErr_Restore(type, value, tb)
841
#define __Pyx_ErrFetch(type, value, tb)  PyErr_Fetch(type, value, tb)
842
#endif
843

844
/* WriteUnraisableException.proto */
845
static void __Pyx_WriteUnraisable(const char *name, int clineno,
846
                                  int lineno, const char *filename,
847
                                  int full_traceback, int nogil);
848

849
/* ArgTypeTest.proto */
850
static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
851
    const char *name, int exact);
852

853
/* Import.proto */
854
static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
855

856
/* ImportFrom.proto */
857
static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name);
858

859
/* RaiseException.proto */
860
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
861

862
/* ExtTypeTest.proto */
863
static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);
864

865
/* ListAppend.proto */
866
#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
867
static CYTHON_INLINE int __Pyx_PyList_Append(PyObject* list, PyObject* x) {
868
    PyListObject* L = (PyListObject*) list;
869
    Py_ssize_t len = Py_SIZE(list);
870
    if (likely(L->allocated > len) & likely(len > (L->allocated >> 1))) {
871
        Py_INCREF(x);
872
        PyList_SET_ITEM(list, len, x);
873
        Py_SIZE(list) = len+1;
874
        return 0;
875
    }
876
    return PyList_Append(list, x);
877
}
878
#else
879
#define __Pyx_PyList_Append(L,x) PyList_Append(L,x)
880
#endif
881

882
/* SetVTable.proto */
883
static int __Pyx_SetVtable(PyObject *dict, void *vtable);
884

885
/* CodeObjectCache.proto */
886
typedef struct {
887
    PyCodeObject* code_object;
888
    int code_line;
889
} __Pyx_CodeObjectCacheEntry;
890
struct __Pyx_CodeObjectCache {
891
    int count;
892
    int max_count;
893
    __Pyx_CodeObjectCacheEntry* entries;
894
};
895
static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
896
static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
897
static PyCodeObject *__pyx_find_code_object(int code_line);
898
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
899

900
/* AddTraceback.proto */
901
static void __Pyx_AddTraceback(const char *funcname, int c_line,
902
                               int py_line, const char *filename);
903

904
/* CIntToPy.proto */
905
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
906

907
/* CIntFromPy.proto */
908
static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
909

910
/* CIntFromPy.proto */
911
static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
912

913
/* CheckBinaryVersion.proto */
914
static int __Pyx_check_binary_version(void);
915

916
/* PyIdentifierFromString.proto */
917
#if !defined(__Pyx_PyIdentifier_FromString)
918
#if PY_MAJOR_VERSION < 3
919
  #define __Pyx_PyIdentifier_FromString(s) PyString_FromString(s)
920
#else
921
  #define __Pyx_PyIdentifier_FromString(s) PyUnicode_FromString(s)
922
#endif
923
#endif
924

925
/* ModuleImport.proto */
926
static PyObject *__Pyx_ImportModule(const char *name);
927

928
/* TypeImport.proto */
929
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, size_t size, int strict);
930

931
/* VoidPtrImport.proto */
932
static int __Pyx_ImportVoidPtr(PyObject *module, const char *name, void **p, const char *sig);
933

934
/* InitStrings.proto */
935
static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
936

937
static int __pyx_f_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_is_split(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
938
static int __pyx_f_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_is_inert(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
939
static int __pyx_f_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_is_ramified(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
940
static long __pyx_f_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_norm(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self, int __pyx_skip_dispatch); /* proto*/
941

942
/* Module declarations from 'cysignals.__init__' */
943

944
/* Module declarations from 'cysignals' */
945

946
/* Module declarations from 'cysignals.signals' */
947
static cysigs_t *__pyx_vp_9cysignals_7signals_cysigs = 0;
948
#define cysigs (*__pyx_vp_9cysignals_7signals_cysigs)
949
static void (*__pyx_f_9cysignals_7signals_print_backtrace)(void); /*proto*/
950
static void (*__pyx_f_9cysignals_7signals__sig_on_interrupt_received)(void); /*proto*/
951
static void (*__pyx_f_9cysignals_7signals__sig_on_recover)(void); /*proto*/
952
static void (*__pyx_f_9cysignals_7signals__sig_off_warning)(char const *, int); /*proto*/
953

954
/* Module declarations from 'cython' */
955

956
/* Module declarations from 'libc.string' */
957

958
/* Module declarations from 'libc.stdlib' */
959

960
/* Module declarations from 'cysignals.memory' */
961
static CYTHON_INLINE void *sig_malloc(size_t); /*proto*/
962
static CYTHON_INLINE void *sig_realloc(void *, size_t); /*proto*/
963
static CYTHON_INLINE void *sig_calloc(size_t, size_t); /*proto*/
964
static CYTHON_INLINE void sig_free(void *); /*proto*/
965
static CYTHON_INLINE size_t __pyx_f_9cysignals_6memory_mul_overflowcheck(size_t, size_t); /*proto*/
966
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_allocarray(size_t, size_t); /*proto*/
967
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_reallocarray(void *, size_t, size_t); /*proto*/
968
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_malloc(size_t); /*proto*/
969
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_realloc(void *, size_t); /*proto*/
970
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_calloc(size_t, size_t); /*proto*/
971

972
/* Module declarations from 'libc.stdio' */
973

974
/* Module declarations from '__builtin__' */
975

976
/* Module declarations from 'cpython.type' */
977
static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;
978

979
/* Module declarations from 'cpython' */
980

981
/* Module declarations from 'cpython.object' */
982

983
/* Module declarations from 'sage.ext.stdsage' */
984
static CYTHON_INLINE PyObject *__pyx_f_4sage_3ext_7stdsage_PY_NEW(PyTypeObject *); /*proto*/
985
static CYTHON_INLINE int __pyx_f_4sage_3ext_7stdsage_HAS_DICTIONARY(PyObject *); /*proto*/
986

987
/* Module declarations from 'code.alex.psage.psage.number_fields.sqrt5.prime' */
988
static PyTypeObject *__pyx_ptype_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime = 0;
989
#define __Pyx_MODULE_NAME "code.alex.psage.psage.number_fields.sqrt5.prime"
990
int __pyx_module_is_main_code__alex__psage__psage__number_fields__sqrt5__prime = 0;
991

992
/* Implementation of 'code.alex.psage.psage.number_fields.sqrt5.prime' */
993
static PyObject *__pyx_builtin_ValueError;
994
static PyObject *__pyx_builtin_MemoryError;
995
static const char __pyx_k_F[] = "F";
996
static const char __pyx_k_P[] = "P";
997
static const char __pyx_k_a[] = "a";
998
static const char __pyx_k_b[] = "b";
999
static const char __pyx_k_p[] = "p";
1000
static const char __pyx_k_r[] = "r";
1001
static const char __pyx_k_s[] = "%s";
1002
static const char __pyx_k_t[] = "t";
1003
static const char __pyx_k_v[] = "v";
1004
static const char __pyx_k_p2[] = "p2";
1005
static const char __pyx_k_r0[] = "r0";
1006
static const char __pyx_k_r1[] = "r1";
1007
static const char __pyx_k_sr[] = "sr";
1008
static const char __pyx_k_gen[] = "gen";
1009
static const char __pyx_k_s_s[] = "%s%s";
1010
static const char __pyx_k_main[] = "__main__";
1011
static const char __pyx_k_misc[] = "misc";
1012
static const char __pyx_k_norm[] = "norm";
1013
static const char __pyx_k_repr[] = "__repr__";
1014
static const char __pyx_k_stop[] = "stop";
1015
static const char __pyx_k_test[] = "__test__";
1016
static const char __pyx_k_bound[] = "bound";
1017
static const char __pyx_k_check[] = "check";
1018
static const char __pyx_k_first[] = "first";
1019
static const char __pyx_k_ideal[] = "ideal";
1020
static const char __pyx_k_start[] = "start";
1021
static const char __pyx_k_import[] = "__import__";
1022
static const char __pyx_k_Integer[] = "Integer";
1023
static const char __pyx_k_py_ints[] = "py_ints";
1024
static const char __pyx_k_is_inert[] = "is_inert";
1025
static const char __pyx_k_is_split[] = "is_split";
1026
static const char __pyx_k_pari_hnf[] = "pari_hnf";
1027
static const char __pyx_k_sage_all[] = "sage.all";
1028
static const char __pyx_k_ValueError[] = "ValueError";
1029
static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
1030
static const char __pyx_k_MemoryError[] = "MemoryError";
1031
static const char __pyx_k_deprecation[] = "deprecation";
1032
static const char __pyx_k_is_ramified[] = "is_ramified";
1033
static const char __pyx_k_prime_range[] = "prime_range";
1034
static const char __pyx_k_primes_above[] = "primes_above";
1035
static const char __pyx_k_Factorization[] = "Factorization";
1036
static const char __pyx_k_is_pseudoprime[] = "is_pseudoprime";
1037
static const char __pyx_k_prime_range_ZZ[] = "prime_range_ZZ";
1038
static const char __pyx_k_sage_ext_memory[] = "sage.ext.memory";
1039
static const char __pyx_k_p_must_be_a_prime[] = "p must be a prime";
1040
static const char __pyx_k_sage_rings_integer[] = "sage.rings.integer";
1041
static const char __pyx_k_sage_misc_superseded[] = "sage.misc.superseded";
1042
static const char __pyx_k_init_memory_functions[] = "init_memory_functions";
1043
static const char __pyx_k_primes_of_bounded_norm[] = "primes_of_bounded_norm";
1044
static const char __pyx_k_NumberFieldFractionalIdeal[] = "NumberFieldFractionalIdeal";
1045
static const char __pyx_k_failed_to_allocate_s_bytes[] = "failed to allocate %s bytes";
1046
static const char __pyx_k_bound_must_be_less_than_2_31[] = "bound must be less than 2^31";
1047
static const char __pyx_k_failed_to_allocate_s_s_bytes[] = "failed to allocate %s * %s bytes";
1048
static const char __pyx_k_sage_structure_factorization[] = "sage.structure.factorization";
1049
static const char __pyx_k_File_prime_pyx_starting_at_line[] = "File: prime.pyx (starting at line 1)\n\nFast prime ideals of the ring R of integers of Q(sqrt(5)).\n\nThis module implements Cython classes for prime ideals of R, and their\nenumeration.  The main entry function is primes_of_bounded_norm::\n\n    sage: from psage.number_fields.sqrt5 import primes_of_bounded_norm\n    sage: v = primes_of_bounded_norm(50); v\n    [2, 5a, 3, 11a, 11b, 19a, 19b, 29a, 29b, 31a, 31b, 41a, 41b, 7]\n\nNote that the output of primes_of_bounded_norm is a list.  Each entry\nis a prime ideal, which prints using a simple label consisting of the\ncharacteristic of the prime then \"a\" or \"b\", where \"b\" only appears for\nthe second split prime.::\n\n    sage: type(v[8])\n    <type 'psage.number_fields.sqrt5.prime.Prime'>\n    sage: v[8].sage_ideal()\n    Fractional ideal (a + 5)\n\nAUTHOR:\n    - William Stein \n";
1050
static const char __pyx_k_projects_68c8b2b8_03ba_44d4_a0d[] = "/projects/68c8b2b8-03ba-44d4-a0d1-5d771c8cb465/code/alex/psage/psage/number_fields/sqrt5/prime.pyx";
1051
static const char __pyx_k_code_alex_psage_psage_number_fie[] = "code.alex.psage.psage.number_fields.sqrt5.prime";
1052
static const char __pyx_k_import_cysignals_signals_pxi_ins[] = "import \"cysignals/signals.pxi\" instead of \"sage/ext/interrupt.pxi\"";
1053
static const char __pyx_k_sage_rings_number_field_number_f[] = "sage.rings.number_field.number_field_ideal";
1054
static PyObject *__pyx_n_s_F;
1055
static PyObject *__pyx_n_s_Factorization;
1056
static PyObject *__pyx_n_s_Integer;
1057
static PyObject *__pyx_n_s_MemoryError;
1058
static PyObject *__pyx_n_s_NumberFieldFractionalIdeal;
1059
static PyObject *__pyx_n_s_P;
1060
static PyObject *__pyx_n_s_ValueError;
1061
static PyObject *__pyx_n_s_a;
1062
static PyObject *__pyx_n_s_b;
1063
static PyObject *__pyx_n_s_bound;
1064
static PyObject *__pyx_kp_s_bound_must_be_less_than_2_31;
1065
static PyObject *__pyx_n_s_check;
1066
static PyObject *__pyx_n_s_code_alex_psage_psage_number_fie;
1067
static PyObject *__pyx_n_s_deprecation;
1068
static PyObject *__pyx_kp_s_failed_to_allocate_s_bytes;
1069
static PyObject *__pyx_kp_s_failed_to_allocate_s_s_bytes;
1070
static PyObject *__pyx_n_s_first;
1071
static PyObject *__pyx_n_s_gen;
1072
static PyObject *__pyx_n_s_ideal;
1073
static PyObject *__pyx_n_s_import;
1074
static PyObject *__pyx_kp_s_import_cysignals_signals_pxi_ins;
1075
static PyObject *__pyx_n_s_init_memory_functions;
1076
static PyObject *__pyx_n_s_is_inert;
1077
static PyObject *__pyx_n_s_is_pseudoprime;
1078
static PyObject *__pyx_n_s_is_ramified;
1079
static PyObject *__pyx_n_s_is_split;
1080
static PyObject *__pyx_n_s_main;
1081
static PyObject *__pyx_n_s_misc;
1082
static PyObject *__pyx_n_s_norm;
1083
static PyObject *__pyx_n_s_p;
1084
static PyObject *__pyx_n_s_p2;
1085
static PyObject *__pyx_kp_s_p_must_be_a_prime;
1086
static PyObject *__pyx_n_s_pari_hnf;
1087
static PyObject *__pyx_n_s_prime_range;
1088
static PyObject *__pyx_n_s_prime_range_ZZ;
1089
static PyObject *__pyx_n_s_primes_above;
1090
static PyObject *__pyx_n_s_primes_of_bounded_norm;
1091
static PyObject *__pyx_kp_s_projects_68c8b2b8_03ba_44d4_a0d;
1092
static PyObject *__pyx_n_s_py_ints;
1093
static PyObject *__pyx_n_s_pyx_vtable;
1094
static PyObject *__pyx_n_s_r;
1095
static PyObject *__pyx_n_s_r0;
1096
static PyObject *__pyx_n_s_r1;
1097
static PyObject *__pyx_n_s_repr;
1098
static PyObject *__pyx_kp_s_s;
1099
static PyObject *__pyx_kp_s_s_s;
1100
static PyObject *__pyx_n_s_sage_all;
1101
static PyObject *__pyx_n_s_sage_ext_memory;
1102
static PyObject *__pyx_n_s_sage_misc_superseded;
1103
static PyObject *__pyx_n_s_sage_rings_integer;
1104
static PyObject *__pyx_n_s_sage_rings_number_field_number_f;
1105
static PyObject *__pyx_n_s_sage_structure_factorization;
1106
static PyObject *__pyx_n_s_sr;
1107
static PyObject *__pyx_n_s_start;
1108
static PyObject *__pyx_n_s_stop;
1109
static PyObject *__pyx_n_s_t;
1110
static PyObject *__pyx_n_s_test;
1111
static PyObject *__pyx_n_s_v;
1112
static int __pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime___init__(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self, PyObject *__pyx_v_p, long __pyx_v_r, int __pyx_v_first); /* proto */
1113
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_2__repr__(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1114
static Py_hash_t __pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_4__hash__(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1115
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_6_latex_(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1116
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_8is_split(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1117
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_10is_inert(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1118
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_12is_ramified(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1119
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_14norm(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1120
#if PY_MAJOR_VERSION < 3
1121
static int __pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_16__cmp__(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self, struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_right); /* proto */
1122
#endif
1123
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_18sage_ideal(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1124
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_1p___get__(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1125
static int __pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_1p_2__set__(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
1126
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_1r___get__(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self); /* proto */
1127
static int __pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_1r_2__set__(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
1128
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_primes_above(CYTHON_UNUSED PyObject *__pyx_self, long __pyx_v_p, int __pyx_v_check); /* proto */
1129
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1130
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1131
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1132
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1133
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1134
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1135
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1136
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1137
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1138
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1140
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1141
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1142
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1143
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1144
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1145
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1146

1147
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1148
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1149
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1150
 *     def __init__(self, p, long r=0, bint first=True):             # <<<<<<<<<<<<<<
1151
 *         """
1152
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1153
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1154

1155
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1156
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1157
static char __pyx_doc_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime___init__[] = "File: prime.pyx (starting at line 62)\n\n        Create Prime ideal with given residue characteristic, root,\n        and first or not with that characterstic.\n\n        INPUT form 1:\n            - `p` -- prime\n            - `r` -- root (or 0)\n            - ``first`` -- boolean: True if first prime over p\n\n        INPUT form 2:\n            - p -- prime ideal of integers of Q(sqrt(5)); validity of the\n              input is not checked in any way!\n\n        NOTE: No checking is done to verify that the input is valid.\n        \n        EXAMPLES::\n\n            sage: from psage.number_fields.sqrt5.prime import Prime\n            sage: P = Prime(2,0,True); P\n            2\n            sage: type(P)\n            <type 'psage.number_fields.sqrt5.prime.Prime'>\n            sage: P = Prime(5,3,True); P\n            5a\n            sage: P = Prime(11,8,True); P\n            11a\n            sage: P = Prime(11,4,False); P\n            11b\n\n        We can also set P using a prime ideal of the ring of integers::\n\n            sage: from psage.number_fields.sqrt5.prime import Prime; K.<a> = NumberField(x^2-x-1)\n            sage: P1 = Prime(K.primes_above(11)[0]); P2 = Prime(K.primes_above(11)[1]); P1, P2\n            (11b, 11a)\n            sage: P1 > P2\n            True\n            sage: Prime(K.prime_above(2))\n            2\n            sage: P = Prime(K.prime_above(5)); P, P.r\n            (5a, 3)\n            sage: Prime(K.prime_above(3))\n            3\n\n        Test that conversion both ways works for primes up to norm `10^5`::\n        \n            sage: from psage.number_fields.sqrt5.prime import primes_of_bounded_norm, Prime\n            sage: v = primes_of_bounded_norm(10^5)\n            sage: w = [Prime(z.sage_ideal()) for z in v]\n            sage: v == w\n            True\n        ";
1158
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1159
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1160
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1161
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1162
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1163
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1170
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1175
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1177
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1180
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1193
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1251
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1252
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1253
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1254
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1255
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1265
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1266
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1267
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1268
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1269
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1294
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1295
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1296
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1297
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1298
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1299
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1300
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1301
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1307
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1308
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1309
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1310
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1311
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1312
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1314
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1316
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1317
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1318
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1319
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1320
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1323
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1325
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1326
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1327
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1328
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1329
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1330
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1332
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1333
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1334
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1335

1336
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1337
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1338
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1339
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1340
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1342
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1346
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1348
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1353
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1355
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1356
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1357
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1358
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1359
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1360
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1361
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1362
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1363

1364
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1365
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1366
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1367
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1368
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1369
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1370
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1371
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1372
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1373

1374
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1375
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1376
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1377
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1378
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1379
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1380
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1381
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1382

1383
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1384
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1385
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1386
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1387
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1388
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1389
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1390
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1391

1392
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1393
 *             self.first = True
1394
 *             t = self.p % 5
1395
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1396
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1397
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1398
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1399
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1400

1401
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1402
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1403
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1404
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1405
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1406
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1407
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1408
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1409

1410
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1411
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1412
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1413
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1414
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1415
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1416
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1417
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1418

1419
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1420
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1421
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1422
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1423
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1424
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1425
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1426
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1427
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1428

1429
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1430
 *                 self.r = 3
1431
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1432
 *                 self.r = 0             # <<<<<<<<<<<<<<
1433
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1434
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1435
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1436
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1437
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1438
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1439

1440
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1441
 *         """
1442
 *         cdef long t, r1
1443
 *         if isinstance(p, NumberFieldFractionalIdeal):             # <<<<<<<<<<<<<<
1444
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1445
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1446
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1447
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1448
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1449

1450
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1451
 *                 self.r = 0
1452
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1453
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1454
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1455
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1456
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1457
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1458
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1459
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1460

1461
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1462
 *         else:
1463
 *             self.p = p
1464
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1465
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1466
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1467
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1468
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1469

1470
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1471
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1472
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1473
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1474
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1475
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1476
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1477
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2168
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2169
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2170
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2171
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2174
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2220
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2221
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2222
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2223
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2224
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2234
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2235
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2236
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2237
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2281
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2292
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2293
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2294
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2295
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2296
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2297
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2298
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2300
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2301
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2302
static int __pyx_pw_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_17__cmp__(PyObject *__pyx_v_self, PyObject *__pyx_v_right); /*proto*/
2303
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2306
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2314
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2324
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2325
static int __pyx_pf_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_5Prime_16__cmp__(struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_self, struct __pyx_obj_4code_4alex_5psage_5psage_13number_fields_5sqrt5_5prime_Prime *__pyx_v_right) {
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2336
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2337
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2338
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2339
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2340
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2341
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2342

2343
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2344
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2345
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2346
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2348
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2349
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2354
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2355

2356
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2357
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2358
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2359
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2360
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2361
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2365
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2369
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2370
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2371
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2372
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2373
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2374
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2378
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2379
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2380
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2382
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2383
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2384
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2385
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2388
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2391
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2395
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2396
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2397
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2398
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2399
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2400
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2401
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2402
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2403
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2404
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2405
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2407
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2409
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2410
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2411
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2412
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2424
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2425
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2426
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2427
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2428
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2430
/* Python wrapper */
2431
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2876
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2877
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3165
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3209
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3210
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3233
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3234
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3235
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3236
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3377
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3378
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3379
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3380
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3381
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3386
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3387
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3388
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3389
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3390
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3391
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3399
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3400
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3408
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3410
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3413
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3414
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3415
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3416
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3417
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3418
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3419
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3420
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3421
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3422
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3430
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3431
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3432
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3433
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3434
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3435
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3436
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3438
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3439
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3440
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3441
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3443
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3453
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3454
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3455
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3461
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3462
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3467
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3469
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3470
 *     """
3471
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3472
 *         raise ValueError, "bound must be less than 2^31"             # <<<<<<<<<<<<<<
3473
 * 
3474
 *     cdef long p, p2, sr, r0, r1, t, bound
3475
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3476
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3477
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3480
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3481
 *     """
3482
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3483
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3484
 * 
3485
 */
3486
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3487

3488
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3489
 *     cdef long p, p2, sr, r0, r1, t, bound
3490
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3491
 *     cdef list v = []             # <<<<<<<<<<<<<<
3492
 * 
3493
 *     if stop is None:
3494
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3495
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3498
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3499

3500
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3501
 *     cdef list v = []
3502
 * 
3503
 *     if stop is None:             # <<<<<<<<<<<<<<
3504
 *         bound = start
3505
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3506
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3507
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3508
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3509
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3510

3511
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3512
 * 
3513
 *     if stop is None:
3514
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3515
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3516
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3517
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3518
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3519

3520
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3521
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3522
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3523
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3524
 *     else:
3525
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3526
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3527
    __pyx_v_start = 2;
3528

3529
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3530
 *     cdef list v = []
3531
 * 
3532
 *     if stop is None:             # <<<<<<<<<<<<<<
3533
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3534
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3535
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3536
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3537
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3538

3539
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3540
 *         start = 2
3541
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3542
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3543
 * 
3544
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3545
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3552
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3553
 *         bound = stop
3554
 * 
3555
 *     from sage.all import prime_range as prime_range_ZZ             # <<<<<<<<<<<<<<
3556
 * 
3557
 *     for p in prime_range_ZZ(bound, py_ints=True):
3558
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3574
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3575
 *     from sage.all import prime_range as prime_range_ZZ
3576
 * 
3577
 *     for p in prime_range_ZZ(bound, py_ints=True):             # <<<<<<<<<<<<<<
3578
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3579
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3607
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3620
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3639
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3640
 * 
3641
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3642
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3648
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3649
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3650
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3651
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3656
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3657
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3658
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3659
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3660
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3661
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3662
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3663
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3664
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3665

3666
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3667
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3668
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3674
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3675

3676
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3677
 *             if p >= start:
3678
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3679
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3680
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3681
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3685
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3686
 *                 sr = Fl_sqrt(5, p)
3687
 *                 # Find the two values of (1+sqrt(5))/2.
3688
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3689
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3690
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3694
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3695
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3696
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3697
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3700
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3703
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3704
 *                 r1 = p+1-r0
3705
 *                 # Sort
3706
 *                 if r0 > r1: r0, r1 = r1, r0             # <<<<<<<<<<<<<<
3707
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3708
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3709
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3712
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3715
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3716
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3718
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3719
 *                 if r0 > r1: r0, r1 = r1, r0
3720
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3721
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3722
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3723
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3724
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3725
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3728
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3729
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3730
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3731
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3732
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3733
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3734

3735
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3736
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3737
 *                 P = PY_NEW(Prime); P.p = p; P.r = r0; P.first = True; v.append(P)
3738
 *                 P = PY_NEW(Prime); P.p = p; P.r = r1; P.first = False; v.append(P)             # <<<<<<<<<<<<<<
3739
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3740
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3741
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3742
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3743
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3744
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3745
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3746
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3747
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3748
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3749
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3750
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3751

3752
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3753
 *         t = p % 5
3754
 *         if t == 1 or t == 4:   # split
3755
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3756
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3757
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3758
 */
3759
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3760

3761
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3762
 *     for p in prime_range_ZZ(bound, py_ints=True):
3763
 *         t = p % 5
3764
 *         if t == 1 or t == 4:   # split             # <<<<<<<<<<<<<<
3765
 *             if p >= start:
3766
 *                 # Compute a square root of 5 modulo p.
3767
 */
3768
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3769
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3770

3771
    /* "code/alex/psage/psage/number_fields/sqrt5/prime.pyx":478
3772
 *                 P = PY_NEW(Prime); P.p = p; P.r = r0; P.first = True; v.append(P)
3773
 *                 P = PY_NEW(Prime); P.p = p; P.r = r1; P.first = False; v.append(P)
3774
 *         elif p == 5:   # ramified             # <<<<<<<<<<<<<<
3775
 *             if p >= start:
3776
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3777
 */
3778
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3779
    if (__pyx_t_4) {
3780

3781
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3782
 *                 P = PY_NEW(Prime); P.p = p; P.r = r1; P.first = False; v.append(P)
3783
 *         elif p == 5:   # ramified
3784
 *             if p >= start:             # <<<<<<<<<<<<<<
3785
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3786
 *         else:
3787
 */
3788
      __pyx_t_4 = ((__pyx_v_p >= __pyx_v_start) != 0);
3789
      if (__pyx_t_4) {
3790

3791
        /* "code/alex/psage/psage/number_fields/sqrt5/prime.pyx":480
3792
 *         elif p == 5:   # ramified
3793
 *             if p >= start:
3794
 *                 v.append(Prime(p, 3, True))             # <<<<<<<<<<<<<<
3795
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3796
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3797
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3798
        __pyx_t_6 = __Pyx_PyInt_From_long(__pyx_v_p); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 480, __pyx_L1_error)
3799
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3800
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3801
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3802
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3803
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3804
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3805
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3806
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3807
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3808
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3809
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3810
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3811
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3812
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3813
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3814
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3815
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3816

3817
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3818
 *                 P = PY_NEW(Prime); P.p = p; P.r = r1; P.first = False; v.append(P)
3819
 *         elif p == 5:   # ramified
3820
 *             if p >= start:             # <<<<<<<<<<<<<<
3821
 *                 v.append(Prime(p, 3, True))
3822
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3823
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3824
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3825

3826
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3827
 *                 P = PY_NEW(Prime); P.p = p; P.r = r0; P.first = True; v.append(P)
3828
 *                 P = PY_NEW(Prime); P.p = p; P.r = r1; P.first = False; v.append(P)
3829
 *         elif p == 5:   # ramified             # <<<<<<<<<<<<<<
3830
 *             if p >= start:
3831
 *                 v.append(Prime(p, 3, True))
3832
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3833
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3834
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3835

3836
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3837
 *                 v.append(Prime(p, 3, True))
3838
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3839
 *             p2 = p*p             # <<<<<<<<<<<<<<
3840
 *             if p2 < bound and p2 >= start:
3841
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3842
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3843
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3844
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3845

3846
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3847
 *         else:
3848
 *             p2 = p*p
3849
 *             if p2 < bound and p2 >= start:             # <<<<<<<<<<<<<<
3850
 *                 v.append(Prime(p, 0, True))
3851
 * 
3852
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3853
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3854
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3855
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3856
        __pyx_t_4 = __pyx_t_1;
3857
        goto __pyx_L15_bool_binop_done;
3858
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3859
      __pyx_t_1 = ((__pyx_v_p2 >= __pyx_v_start) != 0);
3860
      __pyx_t_4 = __pyx_t_1;
3861
      __pyx_L15_bool_binop_done:;
3862
      if (__pyx_t_4) {
3863

3864
        /* "code/alex/psage/psage/number_fields/sqrt5/prime.pyx":484
3865
 *             p2 = p*p
3866
 *             if p2 < bound and p2 >= start:
3867
 *                 v.append(Prime(p, 0, True))             # <<<<<<<<<<<<<<
3868
 * 
3869
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3870
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3871
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3872
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3873
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3874
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3875
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3876
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3877
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3878
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3879
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3880
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3881
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3882
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3883
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3884
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3885
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3886
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3887
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3888
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3889

3890
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3891
 *         else:
3892
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3893
 *             if p2 < bound and p2 >= start:             # <<<<<<<<<<<<<<
3894
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3895
 * 
3896
 */
3897
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3898
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3899
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3900

3901
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3902
 *     from sage.all import prime_range as prime_range_ZZ
3903
 * 
3904
 *     for p in prime_range_ZZ(bound, py_ints=True):             # <<<<<<<<<<<<<<
3905
 *         t = p % 5
3906
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3907
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3908
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3909
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3910

3911
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3912
 *                 v.append(Prime(p, 0, True))
3913
 * 
3914
 *     v.sort()             # <<<<<<<<<<<<<<
3915
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3916
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3917
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3918
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3919

3920
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3921
 * 
3922
 *     v.sort()
3923
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3924
 * 
3925
 * 
3926
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3927
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3928
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3929
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3930
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3931

3932
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3933
 *     return prime_range(bound)
3934
 * 
3935
 * def prime_range(long start, stop=None):             # <<<<<<<<<<<<<<
3936
 *     """
3937
 *     Return ordered list of all prime ideals of the ring of integers of
3938
 */
3939

3940
  /* function exit code */
3941
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3942
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3943
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3944
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3946
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3947
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3948
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3949
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3951
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3952
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3953
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3955

3956
/* "cysignals/memory.pxd":40
3957
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3958
 * 
3959
 * cdef inline void* sig_malloc "sig_malloc"(size_t n) nogil:             # <<<<<<<<<<<<<<
3960
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3961
 *     cdef void* ret = malloc(n)
3962
 */
3963

3964
static CYTHON_INLINE void *sig_malloc(size_t __pyx_v_n) {
3965
  void *__pyx_v_ret;
3966
  void *__pyx_r;
3967

3968
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3969
 * 
3970
 * cdef inline void* sig_malloc "sig_malloc"(size_t n) nogil:
3971
 *     sig_block()             # <<<<<<<<<<<<<<
3972
 *     cdef void* ret = malloc(n)
3973
 *     sig_unblock()
3974
 */
3975
  sig_block();
3976

3977
  /* "cysignals/memory.pxd":42
3978
 * cdef inline void* sig_malloc "sig_malloc"(size_t n) nogil:
3979
 *     sig_block()
3980
 *     cdef void* ret = malloc(n)             # <<<<<<<<<<<<<<
3981
 *     sig_unblock()
3982
 *     return ret
3983
 */
3984
  __pyx_v_ret = malloc(__pyx_v_n);
3985

3986
  /* "cysignals/memory.pxd":43
3987
 *     sig_block()
3988
 *     cdef void* ret = malloc(n)
3989
 *     sig_unblock()             # <<<<<<<<<<<<<<
3990
 *     return ret
3991
 * 
3992
 */
3993
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3994

3995
  /* "cysignals/memory.pxd":44
3996
 *     cdef void* ret = malloc(n)
3997
 *     sig_unblock()
3998
 *     return ret             # <<<<<<<<<<<<<<
3999
 * 
4000
 * 
4001
 */
4002
  __pyx_r = __pyx_v_ret;
4003
  goto __pyx_L0;
4004

4005
  /* "cysignals/memory.pxd":40
4006
 * 
4007
 * 
4008
 * cdef inline void* sig_malloc "sig_malloc"(size_t n) nogil:             # <<<<<<<<<<<<<<
4009
 *     sig_block()
4010
 *     cdef void* ret = malloc(n)
4011
 */
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4013
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4014
  __pyx_L0:;
4015
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4016
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4017

4018
/* "cysignals/memory.pxd":47
4019
 * 
4020
 * 
4021
 * cdef inline void* sig_realloc "sig_realloc"(void* ptr, size_t size) nogil:             # <<<<<<<<<<<<<<
4022
 *     sig_block()
4023
 *     cdef void* ret = realloc(ptr, size)
4024
 */
4025

4026
static CYTHON_INLINE void *sig_realloc(void *__pyx_v_ptr, size_t __pyx_v_size) {
4027
  void *__pyx_v_ret;
4028
  void *__pyx_r;
4029

4030
  /* "cysignals/memory.pxd":48
4031
 * 
4032
 * cdef inline void* sig_realloc "sig_realloc"(void* ptr, size_t size) nogil:
4033
 *     sig_block()             # <<<<<<<<<<<<<<
4034
 *     cdef void* ret = realloc(ptr, size)
4035
 *     sig_unblock()
4036
 */
4037
  sig_block();
4038

4039
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4040
 * cdef inline void* sig_realloc "sig_realloc"(void* ptr, size_t size) nogil:
4041
 *     sig_block()
4042
 *     cdef void* ret = realloc(ptr, size)             # <<<<<<<<<<<<<<
4043
 *     sig_unblock()
4044
 *     return ret
4045
 */
4046
  __pyx_v_ret = realloc(__pyx_v_ptr, __pyx_v_size);
4047

4048
  /* "cysignals/memory.pxd":50
4049
 *     sig_block()
4050
 *     cdef void* ret = realloc(ptr, size)
4051
 *     sig_unblock()             # <<<<<<<<<<<<<<
4052
 *     return ret
4053
 * 
4054
 */
4055
  sig_unblock();
4056

4057
  /* "cysignals/memory.pxd":51
4058
 *     cdef void* ret = realloc(ptr, size)
4059
 *     sig_unblock()
4060
 *     return ret             # <<<<<<<<<<<<<<
4061
 * 
4062
 * 
4063
 */
4064
  __pyx_r = __pyx_v_ret;
4065
  goto __pyx_L0;
4066

4067
  /* "cysignals/memory.pxd":47
4068
 * 
4069
 * 
4070
 * cdef inline void* sig_realloc "sig_realloc"(void* ptr, size_t size) nogil:             # <<<<<<<<<<<<<<
4071
 *     sig_block()
4072
 *     cdef void* ret = realloc(ptr, size)
4073
 */
4074

4075
  /* function exit code */
4076
  __pyx_L0:;
4077
  return __pyx_r;
4078
}
4079

4080
/* "cysignals/memory.pxd":54
4081
 * 
4082
 * 
4083
 * cdef inline void* sig_calloc "sig_calloc"(size_t nmemb, size_t size) nogil:             # <<<<<<<<<<<<<<
4084
 *     sig_block()
4085
 *     cdef void* ret = calloc(nmemb, size)
4086
 */
4087

4088
static CYTHON_INLINE void *sig_calloc(size_t __pyx_v_nmemb, size_t __pyx_v_size) {
4089
  void *__pyx_v_ret;
4090
  void *__pyx_r;
4091

4092
  /* "cysignals/memory.pxd":55
4093
 * 
4094
 * cdef inline void* sig_calloc "sig_calloc"(size_t nmemb, size_t size) nogil:
4095
 *     sig_block()             # <<<<<<<<<<<<<<
4096
 *     cdef void* ret = calloc(nmemb, size)
4097
 *     sig_unblock()
4098
 */
4099
  sig_block();
4100

4101
  /* "cysignals/memory.pxd":56
4102
 * cdef inline void* sig_calloc "sig_calloc"(size_t nmemb, size_t size) nogil:
4103
 *     sig_block()
4104
 *     cdef void* ret = calloc(nmemb, size)             # <<<<<<<<<<<<<<
4105
 *     sig_unblock()
4106
 *     return ret
4107
 */
4108
  __pyx_v_ret = calloc(__pyx_v_nmemb, __pyx_v_size);
4109

4110
  /* "cysignals/memory.pxd":57
4111
 *     sig_block()
4112
 *     cdef void* ret = calloc(nmemb, size)
4113
 *     sig_unblock()             # <<<<<<<<<<<<<<
4114
 *     return ret
4115
 * 
4116
 */
4117
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4118

4119
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4120
 *     cdef void* ret = calloc(nmemb, size)
4121
 *     sig_unblock()
4122
 *     return ret             # <<<<<<<<<<<<<<
4123
 * 
4124
 * 
4125
 */
4126
  __pyx_r = __pyx_v_ret;
4127
  goto __pyx_L0;
4128

4129
  /* "cysignals/memory.pxd":54
4130
 * 
4131
 * 
4132
 * cdef inline void* sig_calloc "sig_calloc"(size_t nmemb, size_t size) nogil:             # <<<<<<<<<<<<<<
4133
 *     sig_block()
4134
 *     cdef void* ret = calloc(nmemb, size)
4135
 */
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4137
  /* function exit code */
4138
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4139
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4140
}
4141

4142
/* "cysignals/memory.pxd":61
4143
 * 
4144
 * 
4145
 * cdef inline void sig_free "sig_free"(void* ptr) nogil:             # <<<<<<<<<<<<<<
4146
 *     sig_block()
4147
 *     free(ptr)
4148
 */
4149

4150
static CYTHON_INLINE void sig_free(void *__pyx_v_ptr) {
4151

4152
  /* "cysignals/memory.pxd":62
4153
 * 
4154
 * cdef inline void sig_free "sig_free"(void* ptr) nogil:
4155
 *     sig_block()             # <<<<<<<<<<<<<<
4156
 *     free(ptr)
4157
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4158
 */
4159
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4160

4161
  /* "cysignals/memory.pxd":63
4162
 * cdef inline void sig_free "sig_free"(void* ptr) nogil:
4163
 *     sig_block()
4164
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4165
 *     sig_unblock()
4166
 * 
4167
 */
4168
  free(__pyx_v_ptr);
4169

4170
  /* "cysignals/memory.pxd":64
4171
 *     sig_block()
4172
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4173
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4174
 * 
4175
 * 
4176
 */
4177
  sig_unblock();
4178

4179
  /* "cysignals/memory.pxd":61
4180
 * 
4181
 * 
4182
 * cdef inline void sig_free "sig_free"(void* ptr) nogil:             # <<<<<<<<<<<<<<
4183
 *     sig_block()
4184
 *     free(ptr)
4185
 */
4186

4187
  /* function exit code */
4188
}
4189

4190
/* "cysignals/memory.pxd":68
4191
 * 
4192
 * @cython.cdivision(True)
4193
 * cdef inline size_t mul_overflowcheck(size_t a, size_t b) nogil:             # <<<<<<<<<<<<<<
4194
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4195
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4196
 */
4197

4198
static CYTHON_INLINE size_t __pyx_f_9cysignals_6memory_mul_overflowcheck(size_t __pyx_v_a, size_t __pyx_v_b) {
4199
  size_t __pyx_v_MUL_NO_OVERFLOW;
4200
  size_t __pyx_r;
4201
  int __pyx_t_1;
4202
  int __pyx_t_2;
4203

4204
  /* "cysignals/memory.pxd":75
4205
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4206
 *     # If a and b both less than MUL_NO_OVERFLOW, no overflow can occur
4207
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4208
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4209
 *         if unlikely(b > (<size_t>-1) // a):
4210
 */
4211
  __pyx_v_MUL_NO_OVERFLOW = (((size_t)1) << (4 * (sizeof(size_t))));
4212

4213
  /* "cysignals/memory.pxd":76
4214
 *     # If a and b both less than MUL_NO_OVERFLOW, no overflow can occur
4215
 *     cdef size_t MUL_NO_OVERFLOW = ((<size_t>1) << (4*sizeof(size_t)))
4216
 *     if a >= MUL_NO_OVERFLOW or b >= MUL_NO_OVERFLOW:             # <<<<<<<<<<<<<<
4217
 *         if unlikely(b > (<size_t>-1) // a):
4218
 *             return <size_t>(-1)
4219
 */
4220
  __pyx_t_2 = ((__pyx_v_a >= __pyx_v_MUL_NO_OVERFLOW) != 0);
4221
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4222
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4223
    __pyx_t_1 = __pyx_t_2;
4224
    goto __pyx_L4_bool_binop_done;
4225
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4226
  __pyx_t_2 = ((__pyx_v_b >= __pyx_v_MUL_NO_OVERFLOW) != 0);
4227
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4228
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4229
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4230

4231
    /* "cysignals/memory.pxd":77
4232
 *     cdef size_t MUL_NO_OVERFLOW = ((<size_t>1) << (4*sizeof(size_t)))
4233
 *     if a >= MUL_NO_OVERFLOW or b >= MUL_NO_OVERFLOW:
4234
 *         if unlikely(b > (<size_t>-1) // a):             # <<<<<<<<<<<<<<
4235
 *             return <size_t>(-1)
4236
 *     return a*b
4237
 */
4238
    __pyx_t_1 = (unlikely((__pyx_v_b > (((size_t)-1L) / __pyx_v_a))) != 0);
4239
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4240

4241
      /* "cysignals/memory.pxd":78
4242
 *     if a >= MUL_NO_OVERFLOW or b >= MUL_NO_OVERFLOW:
4243
 *         if unlikely(b > (<size_t>-1) // a):
4244
 *             return <size_t>(-1)             # <<<<<<<<<<<<<<
4245
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4246
 * 
4247
 */
4248
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4249
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4250

4251
      /* "cysignals/memory.pxd":77
4252
 *     cdef size_t MUL_NO_OVERFLOW = ((<size_t>1) << (4*sizeof(size_t)))
4253
 *     if a >= MUL_NO_OVERFLOW or b >= MUL_NO_OVERFLOW:
4254
 *         if unlikely(b > (<size_t>-1) // a):             # <<<<<<<<<<<<<<
4255
 *             return <size_t>(-1)
4256
 *     return a*b
4257
 */
4258
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4259

4260
    /* "cysignals/memory.pxd":76
4261
 *     # If a and b both less than MUL_NO_OVERFLOW, no overflow can occur
4262
 *     cdef size_t MUL_NO_OVERFLOW = ((<size_t>1) << (4*sizeof(size_t)))
4263
 *     if a >= MUL_NO_OVERFLOW or b >= MUL_NO_OVERFLOW:             # <<<<<<<<<<<<<<
4264
 *         if unlikely(b > (<size_t>-1) // a):
4265
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4266
 */
4267
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4268

4269
  /* "cysignals/memory.pxd":79
4270
 *         if unlikely(b > (<size_t>-1) // a):
4271
 *             return <size_t>(-1)
4272
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4273
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4274
 * 
4275
 */
4276
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4277
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4278

4279
  /* "cysignals/memory.pxd":68
4280
 * 
4281
 * @cython.cdivision(True)
4282
 * cdef inline size_t mul_overflowcheck(size_t a, size_t b) nogil:             # <<<<<<<<<<<<<<
4283
 *     """
4284
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4285
 */
4286

4287
  /* function exit code */
4288
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4289
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4290
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4291

4292
/* "cysignals/memory.pxd":82
4293
 * 
4294
 * 
4295
 * cdef inline void* check_allocarray(size_t nmemb, size_t size) except? NULL:             # <<<<<<<<<<<<<<
4296
 *     """
4297
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4298
 */
4299

4300
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_allocarray(size_t __pyx_v_nmemb, size_t __pyx_v_size) {
4301
  size_t __pyx_v_n;
4302
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4303
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4304
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4305
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4306
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4307
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4308
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4309
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4310

4311
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4312
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4313
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4314
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4315
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4316
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4317
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4318
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4319
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4320

4321
    /* "cysignals/memory.pxd":87
4322
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4323
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4324
 *         return NULL             # <<<<<<<<<<<<<<
4325
 *     cdef size_t n = mul_overflowcheck(nmemb, size)
4326
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4327
 */
4328
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4329
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4330

4331
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4332
 *     Allocate memory for ``nmemb`` elements of size ``size``.
4333
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4334
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4335
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4336
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4337
 */
4338
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4339

4340
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4341
 *     if nmemb == 0:
4342
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4343
 *     cdef size_t n = mul_overflowcheck(nmemb, size)             # <<<<<<<<<<<<<<
4344
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4345
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4346
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4347
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4348

4349
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4350
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4351
 *     cdef size_t n = mul_overflowcheck(nmemb, size)
4352
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4353
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4354
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4355
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4356
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4357

4358
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4359
 *     cdef size_t n = mul_overflowcheck(nmemb, size)
4360
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4361
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4362
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4363
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4364
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4365
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4366
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4367

4368
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4369
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4370
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4371
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4372
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4373
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4374
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4375
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4376
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4380
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4383
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4384
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4385
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4386
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4387
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4388
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4389
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4390
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4391
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4392
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4394
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4395
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4396
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4397
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4398
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4399
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4400
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4401

4402
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4403
 *     cdef size_t n = mul_overflowcheck(nmemb, size)
4404
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4405
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4406
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4407
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4408
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4409
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4410

4411
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4412
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4413
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4414
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4415
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4416
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4417
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4418
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4419
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4420

4421
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4422
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4423
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4424
 * cdef inline void* check_allocarray(size_t nmemb, size_t size) except? NULL:             # <<<<<<<<<<<<<<
4425
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4426
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4427
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4428

4429
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4430
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4431
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4432
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4433
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4434
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4435
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4436
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4437
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4438
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4439
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4440

4441
/* "cysignals/memory.pxd":95
4442
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4443
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4444
 * cdef inline void* check_reallocarray(void* ptr, size_t nmemb, size_t size) except? NULL:             # <<<<<<<<<<<<<<
4445
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4446
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4447
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4448

4449
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_reallocarray(void *__pyx_v_ptr, size_t __pyx_v_nmemb, size_t __pyx_v_size) {
4450
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4451
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4452
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4453
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4454
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4455
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4456
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4457
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4458
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4460
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4461
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4462
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4463
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4464
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4465
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4466
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4467
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4468
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4469

4470
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4471
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4472
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4473
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4474
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4475
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4476
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4477
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4478

4479
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4480
 *     if nmemb == 0:
4481
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4482
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4483
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4484
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4485
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4486
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4487
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4488

4489
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4490
 *     When ``nmemb`` equals 0, then free the memory at ``ptr``.
4491
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4492
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4493
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4494
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4495
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4496
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4497

4498
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4499
 *         sig_free(ptr)
4500
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4501
 *     cdef size_t n = mul_overflowcheck(nmemb, size)             # <<<<<<<<<<<<<<
4502
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4503
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4504
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4505
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4506

4507
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4508
 *         return NULL
4509
 *     cdef size_t n = mul_overflowcheck(nmemb, size)
4510
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4511
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4512
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4513
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4514
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4515

4516
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4517
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4518
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4519
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4520
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4521
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4522
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4523
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4524
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4525

4526
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4527
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4528
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4529
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4530
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4531
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4532
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4533
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4546
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4549
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4550
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4551
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4554
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4557
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4558
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4560
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4561
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4562
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4563
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4564
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4565
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4566
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4567
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4568

4569
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4570
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4571
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4572
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4573
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4574
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4575
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4576
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5168
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5170
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5577
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5581
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5593
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5594
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5595
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5596
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5599
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5600
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5601
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5602
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5603
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5609
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5613
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5615
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5617

5618
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5619
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5620
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5621
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5622
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5624
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5626
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5634
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5635
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5636

5637
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5638
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5639
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5640
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5641
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5642
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5643
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5646
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5647
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5648
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5649

5650
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5651
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5652
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5653
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5654
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5655
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5656

5657
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5658
 *     unsigned long Fl_div(unsigned long, unsigned long, unsigned long)
5659
 * 
5660
 * from sage.rings.number_field.number_field_ideal import NumberFieldFractionalIdeal             # <<<<<<<<<<<<<<
5661
 * 
5662
 * cdef class Prime:
5663
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5664
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5665
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5666
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5667
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5670
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5676
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5677

5678
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5679
 *         return I
5680
 * 
5681
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5682
 * 
5683
 * def primes_above(long p, bint check=True):
5684
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5685
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5686
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5688
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5694
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5695
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5697
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5698

5699
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5700
 * from sage.rings.integer import Integer
5701
 * 
5702
 * def primes_above(long p, bint check=True):             # <<<<<<<<<<<<<<
5703
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5704
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5705
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5706
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5707
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5709
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5710

5711
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5712
 *         return [Prime(p, 0, True)]
5713
 * 
5714
 * def primes_of_bounded_norm(bound):             # <<<<<<<<<<<<<<
5715
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5716
 *     Return ordered list of all prime ideals of the ring of integers of
5717
 */
5718
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5719
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5721
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5722

5723
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5724
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5725
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5726
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5727
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5728
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5729
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5730
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5734

5735
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5736
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5737
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5738
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5739
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5743
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5744

5745
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5746
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5747
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5748
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5749
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5750
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5751
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5752

5753
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5754

5755
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5756
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5757
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5758
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5759
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5760
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5761
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5762
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5763
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5764
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5766
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5767
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5768
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5769
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5770
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5771
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5772
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5773
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5774
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5775
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5776

5777
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5778
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5779
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5780
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5781
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5782
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5785
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5786
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5787
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5790
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5791
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5792
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5793
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5795
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5796
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5797
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5798
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5799
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5800
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5801
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5802
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5803
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5804
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5805
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5806
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5807
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5808

5809
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5810
static void __Pyx_RaiseDoubleKeywordsError(
5811
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5812
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5813
{
5814
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5815
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5816
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5817
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5818
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5819
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5820
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5821
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5822

5823
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5824
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5825
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5826
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5827
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5828
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5829
    Py_ssize_t num_pos_args,
5830
    const char* function_name)
5831
{
5832
    PyObject *key = 0, *value = 0;
5833
    Py_ssize_t pos = 0;
5834
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5835
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5836
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5837
        name = first_kw_arg;
5838
        while (*name && (**name != key)) name++;
5839
        if (*name) {
5840
            values[name-argnames] = value;
5841
            continue;
5842
        }
5843
        name = first_kw_arg;
5844
        #if PY_MAJOR_VERSION < 3
5845
        if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
5846
            while (*name) {
5847
                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
5848
                        && _PyString_Eq(**name, key)) {
5849
                    values[name-argnames] = value;
5850
                    break;
5851
                }
5852
                name++;
5853
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5854
            if (*name) continue;
5855
            else {
5856
                PyObject*** argname = argnames;
5857
                while (argname != first_kw_arg) {
5858
                    if ((**argname == key) || (
5859
                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
5860
                             && _PyString_Eq(**argname, key))) {
5861
                        goto arg_passed_twice;
5862
                    }
5863
                    argname++;
5864
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5865
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5866
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5867
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5868
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5869
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5870
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5871
                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
5872
                    (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
5873
                #endif
5874
                    PyUnicode_Compare(**name, key);
5875
                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
5876
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5877
                    values[name-argnames] = value;
5878
                    break;
5879
                }
5880
                name++;
5881
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5882
            if (*name) continue;
5883
            else {
5884
                PyObject*** argname = argnames;
5885
                while (argname != first_kw_arg) {
5886
                    int cmp = (**argname == key) ? 0 :
5887
                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
5888
                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
5889
                    #endif
5890
                        PyUnicode_Compare(**argname, key);
5891
                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
5892
                    if (cmp == 0) goto arg_passed_twice;
5893
                    argname++;
5894
                }
5895
            }
5896
        } else
5897
            goto invalid_keyword_type;
5898
        if (kwds2) {
5899
            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
5900
        } else {
5901
            goto invalid_keyword;
5902
        }
5903
    }
5904
    return 0;
5905
arg_passed_twice:
5906
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
5907
    goto bad;
5908
invalid_keyword_type:
5909
    PyErr_Format(PyExc_TypeError,
5910
        "%.200s() keywords must be strings", function_name);
5911
    goto bad;
5912
invalid_keyword:
5913
    PyErr_Format(PyExc_TypeError,
5914
    #if PY_MAJOR_VERSION < 3
5915
        "%.200s() got an unexpected keyword argument '%.200s'",
5916
        function_name, PyString_AsString(key));
5917
    #else
5918
        "%s() got an unexpected keyword argument '%U'",
5919
        function_name, key);
5920
    #endif
5921
bad:
5922
    return -1;
5923
}
5924

5925
/* RaiseArgTupleInvalid */
5926
static void __Pyx_RaiseArgtupleInvalid(
5927
    const char* func_name,
5928
    int exact,
5929
    Py_ssize_t num_min,
5930
    Py_ssize_t num_max,
5931
    Py_ssize_t num_found)
5932
{
5933
    Py_ssize_t num_expected;
5934
    const char *more_or_less;
5935
    if (num_found < num_min) {
5936
        num_expected = num_min;
5937
        more_or_less = "at least";
5938
    } else {
5939
        num_expected = num_max;
5940
        more_or_less = "at most";
5941
    }
5942
    if (exact) {
5943
        more_or_less = "exactly";
5944
    }
5945
    PyErr_Format(PyExc_TypeError,
5946
                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
5947
                 func_name, more_or_less, num_expected,
5948
                 (num_expected == 1) ? "" : "s", num_found);
5949
}
5950

5951
/* GetModuleGlobalName */
5952
static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
5953
    PyObject *result;
5954
#if !CYTHON_AVOID_BORROWED_REFS
5955
    result = PyDict_GetItem(__pyx_d, name);
5956
    if (likely(result)) {
5957
        Py_INCREF(result);
5958
    } else {
5959
#else
5960
    result = PyObject_GetItem(__pyx_d, name);
5961
    if (!result) {
5962
        PyErr_Clear();
5963
#endif
5964
        result = __Pyx_GetBuiltinName(name);
5965
    }
5966
    return result;
5967
}
5968

5969
/* PyCFunctionFastCall */
5970
  #if CYTHON_FAST_PYCCALL
5971
static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
5972
    PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
5973
    PyCFunction meth = PyCFunction_GET_FUNCTION(func);
5974
    PyObject *self = PyCFunction_GET_SELF(func);
5975
    assert(PyCFunction_Check(func));
5976
    assert(METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST)));
5977
    assert(nargs >= 0);
5978
    assert(nargs == 0 || args != NULL);
5979
    /* _PyCFunction_FastCallDict() must not be called with an exception set,
5980
       because it may clear it (directly or indirectly) and so the
5981
       caller loses its exception */
5982
    assert(!PyErr_Occurred());
5983
    return (*((__Pyx_PyCFunctionFast)meth)) (self, args, nargs, NULL);
5984
}
5985
#endif  // CYTHON_FAST_PYCCALL
5986

5987
/* PyFunctionFastCall */
5988
  #if CYTHON_FAST_PYCALL
5989
#include "frameobject.h"
5990
static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
5991
                                               PyObject *globals) {
5992
    PyFrameObject *f;
5993
    PyThreadState *tstate = PyThreadState_GET();
5994
    PyObject **fastlocals;
5995
    Py_ssize_t i;
5996
    PyObject *result;
5997
    assert(globals != NULL);
5998
    /* XXX Perhaps we should create a specialized
5999
       PyFrame_New() that doesn't take locals, but does
6000
       take builtins without sanity checking them.
6001
       */
6002
    assert(tstate != NULL);
6003
    f = PyFrame_New(tstate, co, globals, NULL);
6004
    if (f == NULL) {
6005
        return NULL;
6006
    }
6007
    fastlocals = f->f_localsplus;
6008
    for (i = 0; i < na; i++) {
6009
        Py_INCREF(*args);
6010
        fastlocals[i] = *args++;
6011
    }
6012
    result = PyEval_EvalFrameEx(f,0);
6013
    ++tstate->recursion_depth;
6014
    Py_DECREF(f);
6015
    --tstate->recursion_depth;
6016
    return result;
6017
}
6018
#if 1 || PY_VERSION_HEX < 0x030600B1
6019
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) {
6020
    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
6021
    PyObject *globals = PyFunction_GET_GLOBALS(func);
6022
    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
6023
    PyObject *closure;
6024
#if PY_MAJOR_VERSION >= 3
6025
    PyObject *kwdefs;
6026
#endif
6027
    PyObject *kwtuple, **k;
6028
    PyObject **d;
6029
    Py_ssize_t nd;
6030
    Py_ssize_t nk;
6031
    PyObject *result;
6032
    assert(kwargs == NULL || PyDict_Check(kwargs));
6033
    nk = kwargs ? PyDict_Size(kwargs) : 0;
6034
    if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
6035
        return NULL;
6036
    }
6037
    if (
6038
#if PY_MAJOR_VERSION >= 3
6039
            co->co_kwonlyargcount == 0 &&
6040
#endif
6041
            likely(kwargs == NULL || nk == 0) &&
6042
            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
6043
        if (argdefs == NULL && co->co_argcount == nargs) {
6044
            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
6045
            goto done;
6046
        }
6047
        else if (nargs == 0 && argdefs != NULL
6048
                 && co->co_argcount == Py_SIZE(argdefs)) {
6049
            /* function called with no arguments, but all parameters have
6050
               a default value: use default values as arguments .*/
6051
            args = &PyTuple_GET_ITEM(argdefs, 0);
6052
            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
6053
            goto done;
6054
        }
6055
    }
6056
    if (kwargs != NULL) {
6057
        Py_ssize_t pos, i;
6058
        kwtuple = PyTuple_New(2 * nk);
6059
        if (kwtuple == NULL) {
6060
            result = NULL;
6061
            goto done;
6062
        }
6063
        k = &PyTuple_GET_ITEM(kwtuple, 0);
6064
        pos = i = 0;
6065
        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
6066
            Py_INCREF(k[i]);
6067
            Py_INCREF(k[i+1]);
6068
            i += 2;
6069
        }
6070
        nk = i / 2;
6071
    }
6072
    else {
6073
        kwtuple = NULL;
6074
        k = NULL;
6075
    }
6076
    closure = PyFunction_GET_CLOSURE(func);
6077
#if PY_MAJOR_VERSION >= 3
6078
    kwdefs = PyFunction_GET_KW_DEFAULTS(func);
6079
#endif
6080
    if (argdefs != NULL) {
6081
        d = &PyTuple_GET_ITEM(argdefs, 0);
6082
        nd = Py_SIZE(argdefs);
6083
    }
6084
    else {
6085
        d = NULL;
6086
        nd = 0;
6087
    }
6088
#if PY_MAJOR_VERSION >= 3
6089
    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
6090
                               args, nargs,
6091
                               k, (int)nk,
6092
                               d, (int)nd, kwdefs, closure);
6093
#else
6094
    result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
6095
                               args, nargs,
6096
                               k, (int)nk,
6097
                               d, (int)nd, closure);
6098
#endif
6099
    Py_XDECREF(kwtuple);
6100
done:
6101
    Py_LeaveRecursiveCall();
6102
    return result;
6103
}
6104
#endif  // CPython < 3.6
6105
#endif  // CYTHON_FAST_PYCALL
6106

6107
/* PyObjectCall */
6108
  #if CYTHON_COMPILING_IN_CPYTHON
6109
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
6110
    PyObject *result;
6111
    ternaryfunc call = func->ob_type->tp_call;
6112
    if (unlikely(!call))
6113
        return PyObject_Call(func, arg, kw);
6114
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
6115
        return NULL;
6116
    result = (*call)(func, arg, kw);
6117
    Py_LeaveRecursiveCall();
6118
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
6119
        PyErr_SetString(
6120
            PyExc_SystemError,
6121
            "NULL result without error in PyObject_Call");
6122
    }
6123
    return result;
6124
}
6125
#endif
6126

6127
/* PyObjectCallMethO */
6128
  #if CYTHON_COMPILING_IN_CPYTHON
6129
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
6130
    PyObject *self, *result;
6131
    PyCFunction cfunc;
6132
    cfunc = PyCFunction_GET_FUNCTION(func);
6133
    self = PyCFunction_GET_SELF(func);
6134
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
6135
        return NULL;
6136
    result = cfunc(self, arg);
6137
    Py_LeaveRecursiveCall();
6138
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
6139
        PyErr_SetString(
6140
            PyExc_SystemError,
6141
            "NULL result without error in PyObject_Call");
6142
    }
6143
    return result;
6144
}
6145
#endif
6146

6147
/* PyObjectCallOneArg */
6148
  #if CYTHON_COMPILING_IN_CPYTHON
6149
static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
6150
    PyObject *result;
6151
    PyObject *args = PyTuple_New(1);
6152
    if (unlikely(!args)) return NULL;
6153
    Py_INCREF(arg);
6154
    PyTuple_SET_ITEM(args, 0, arg);
6155
    result = __Pyx_PyObject_Call(func, args, NULL);
6156
    Py_DECREF(args);
6157
    return result;
6158
}
6159
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
6160
#if CYTHON_FAST_PYCALL
6161
    if (PyFunction_Check(func)) {
6162
        return __Pyx_PyFunction_FastCall(func, &arg, 1);
6163
    }
6164
#endif
6165
#ifdef __Pyx_CyFunction_USED
6166
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
6167
#else
6168
    if (likely(PyCFunction_Check(func))) {
6169
#endif
6170
        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
6171
            return __Pyx_PyObject_CallMethO(func, arg);
6172
#if CYTHON_FAST_PYCCALL
6173
        } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
6174
            return __Pyx_PyCFunction_FastCall(func, &arg, 1);
6175
#endif
6176
        }
6177
    }
6178
    return __Pyx__PyObject_CallOneArg(func, arg);
6179
}
6180
#else
6181
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
6182
    PyObject *result;
6183
    PyObject *args = PyTuple_Pack(1, arg);
6184
    if (unlikely(!args)) return NULL;
6185
    result = __Pyx_PyObject_Call(func, args, NULL);
6186
    Py_DECREF(args);
6187
    return result;
6188
}
6189
#endif
6190

6191
/* PyObjectCallNoArg */
6192
    #if CYTHON_COMPILING_IN_CPYTHON
6193
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
6194
#if CYTHON_FAST_PYCALL
6195
    if (PyFunction_Check(func)) {
6196
        return __Pyx_PyFunction_FastCall(func, NULL, 0);
6197
    }
6198
#endif
6199
#ifdef __Pyx_CyFunction_USED
6200
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
6201
#else
6202
    if (likely(PyCFunction_Check(func))) {
6203
#endif
6204
        if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
6205
            return __Pyx_PyObject_CallMethO(func, NULL);
6206
        }
6207
    }
6208
    return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
6209
}
6210
#endif
6211

6212
/* None */
6213
      static CYTHON_INLINE long __Pyx_mod_long(long a, long b) {
6214
    long r = a % b;
6215
    r += ((r != 0) & ((r ^ b) < 0)) * b;
6216
    return r;
6217
}
6218

6219
/* PyErrFetchRestore */
6220
      #if CYTHON_FAST_THREAD_STATE
6221
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
6222
    PyObject *tmp_type, *tmp_value, *tmp_tb;
6223
    tmp_type = tstate->curexc_type;
6224
    tmp_value = tstate->curexc_value;
6225
    tmp_tb = tstate->curexc_traceback;
6226
    tstate->curexc_type = type;
6227
    tstate->curexc_value = value;
6228
    tstate->curexc_traceback = tb;
6229
    Py_XDECREF(tmp_type);
6230
    Py_XDECREF(tmp_value);
6231
    Py_XDECREF(tmp_tb);
6232
}
6233
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
6234
    *type = tstate->curexc_type;
6235
    *value = tstate->curexc_value;
6236
    *tb = tstate->curexc_traceback;
6237
    tstate->curexc_type = 0;
6238
    tstate->curexc_value = 0;
6239
    tstate->curexc_traceback = 0;
6240
}
6241
#endif
6242

6243
/* WriteUnraisableException */
6244
      static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno,
6245
                                  CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename,
6246
                                  int full_traceback, CYTHON_UNUSED int nogil) {
6247
    PyObject *old_exc, *old_val, *old_tb;
6248
    PyObject *ctx;
6249
    __Pyx_PyThreadState_declare
6250
#ifdef WITH_THREAD
6251
    PyGILState_STATE state;
6252
    if (nogil)
6253
        state = PyGILState_Ensure();
6254
#ifdef _MSC_VER
6255
    else state = (PyGILState_STATE)-1;
6256
#endif
6257
#endif
6258
    __Pyx_PyThreadState_assign
6259
    __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
6260
    if (full_traceback) {
6261
        Py_XINCREF(old_exc);
6262
        Py_XINCREF(old_val);
6263
        Py_XINCREF(old_tb);
6264
        __Pyx_ErrRestore(old_exc, old_val, old_tb);
6265
        PyErr_PrintEx(1);
6266
    }
6267
    #if PY_MAJOR_VERSION < 3
6268
    ctx = PyString_FromString(name);
6269
    #else
6270
    ctx = PyUnicode_FromString(name);
6271
    #endif
6272
    __Pyx_ErrRestore(old_exc, old_val, old_tb);
6273
    if (!ctx) {
6274
        PyErr_WriteUnraisable(Py_None);
6275
    } else {
6276
        PyErr_WriteUnraisable(ctx);
6277
        Py_DECREF(ctx);
6278
    }
6279
#ifdef WITH_THREAD
6280
    if (nogil)
6281
        PyGILState_Release(state);
6282
#endif
6283
}
6284

6285
/* ArgTypeTest */
6286
      static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) {
6287
    PyErr_Format(PyExc_TypeError,
6288
        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
6289
        name, type->tp_name, Py_TYPE(obj)->tp_name);
6290
}
6291
static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
6292
    const char *name, int exact)
6293
{
6294
    if (unlikely(!type)) {
6295
        PyErr_SetString(PyExc_SystemError, "Missing type object");
6296
        return 0;
6297
    }
6298
    if (none_allowed && obj == Py_None) return 1;
6299
    else if (exact) {
6300
        if (likely(Py_TYPE(obj) == type)) return 1;
6301
        #if PY_MAJOR_VERSION == 2
6302
        else if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
6303
        #endif
6304
    }
6305
    else {
6306
        if (likely(PyObject_TypeCheck(obj, type))) return 1;
6307
    }
6308
    __Pyx_RaiseArgumentTypeInvalid(name, obj, type);
6309
    return 0;
6310
}
6311

6312
/* Import */
6313
      static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
6314
    PyObject *empty_list = 0;
6315
    PyObject *module = 0;
6316
    PyObject *global_dict = 0;
6317
    PyObject *empty_dict = 0;
6318
    PyObject *list;
6319
    #if PY_VERSION_HEX < 0x03030000
6320
    PyObject *py_import;
6321
    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
6322
    if (!py_import)
6323
        goto bad;
6324
    #endif
6325
    if (from_list)
6326
        list = from_list;
6327
    else {
6328
        empty_list = PyList_New(0);
6329
        if (!empty_list)
6330
            goto bad;
6331
        list = empty_list;
6332
    }
6333
    global_dict = PyModule_GetDict(__pyx_m);
6334
    if (!global_dict)
6335
        goto bad;
6336
    empty_dict = PyDict_New();
6337
    if (!empty_dict)
6338
        goto bad;
6339
    {
6340
        #if PY_MAJOR_VERSION >= 3
6341
        if (level == -1) {
6342
            if (strchr(__Pyx_MODULE_NAME, '.')) {
6343
                #if PY_VERSION_HEX < 0x03030000
6344
                PyObject *py_level = PyInt_FromLong(1);
6345
                if (!py_level)
6346
                    goto bad;
6347
                module = PyObject_CallFunctionObjArgs(py_import,
6348
                    name, global_dict, empty_dict, list, py_level, NULL);
6349
                Py_DECREF(py_level);
6350
                #else
6351
                module = PyImport_ImportModuleLevelObject(
6352
                    name, global_dict, empty_dict, list, 1);
6353
                #endif
6354
                if (!module) {
6355
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
6356
                        goto bad;
6357
                    PyErr_Clear();
6358
                }
6359
            }
6360
            level = 0;
6361
        }
6362
        #endif
6363
        if (!module) {
6364
            #if PY_VERSION_HEX < 0x03030000
6365
            PyObject *py_level = PyInt_FromLong(level);
6366
            if (!py_level)
6367
                goto bad;
6368
            module = PyObject_CallFunctionObjArgs(py_import,
6369
                name, global_dict, empty_dict, list, py_level, NULL);
6370
            Py_DECREF(py_level);
6371
            #else
6372
            module = PyImport_ImportModuleLevelObject(
6373
                name, global_dict, empty_dict, list, level);
6374
            #endif
6375
        }
6376
    }
6377
bad:
6378
    #if PY_VERSION_HEX < 0x03030000
6379
    Py_XDECREF(py_import);
6380
    #endif
6381
    Py_XDECREF(empty_list);
6382
    Py_XDECREF(empty_dict);
6383
    return module;
6384
}
6385

6386
/* ImportFrom */
6387
      static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
6388
    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
6389
    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
6390
        PyErr_Format(PyExc_ImportError,
6391
        #if PY_MAJOR_VERSION < 3
6392
            "cannot import name %.230s", PyString_AS_STRING(name));
6393
        #else
6394
            "cannot import name %S", name);
6395
        #endif
6396
    }
6397
    return value;
6398
}
6399

6400
/* RaiseException */
6401
      #if PY_MAJOR_VERSION < 3
6402
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
6403
                        CYTHON_UNUSED PyObject *cause) {
6404
    __Pyx_PyThreadState_declare
6405
    Py_XINCREF(type);
6406
    if (!value || value == Py_None)
6407
        value = NULL;
6408
    else
6409
        Py_INCREF(value);
6410
    if (!tb || tb == Py_None)
6411
        tb = NULL;
6412
    else {
6413
        Py_INCREF(tb);
6414
        if (!PyTraceBack_Check(tb)) {
6415
            PyErr_SetString(PyExc_TypeError,
6416
                "raise: arg 3 must be a traceback or None");
6417
            goto raise_error;
6418
        }
6419
    }
6420
    if (PyType_Check(type)) {
6421
#if CYTHON_COMPILING_IN_PYPY
6422
        if (!value) {
6423
            Py_INCREF(Py_None);
6424
            value = Py_None;
6425
        }
6426
#endif
6427
        PyErr_NormalizeException(&type, &value, &tb);
6428
    } else {
6429
        if (value) {
6430
            PyErr_SetString(PyExc_TypeError,
6431
                "instance exception may not have a separate value");
6432
            goto raise_error;
6433
        }
6434
        value = type;
6435
        type = (PyObject*) Py_TYPE(type);
6436
        Py_INCREF(type);
6437
        if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
6438
            PyErr_SetString(PyExc_TypeError,
6439
                "raise: exception class must be a subclass of BaseException");
6440
            goto raise_error;
6441
        }
6442
    }
6443
    __Pyx_PyThreadState_assign
6444
    __Pyx_ErrRestore(type, value, tb);
6445
    return;
6446
raise_error:
6447
    Py_XDECREF(value);
6448
    Py_XDECREF(type);
6449
    Py_XDECREF(tb);
6450
    return;
6451
}
6452
#else
6453
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
6454
    PyObject* owned_instance = NULL;
6455
    if (tb == Py_None) {
6456
        tb = 0;
6457
    } else if (tb && !PyTraceBack_Check(tb)) {
6458
        PyErr_SetString(PyExc_TypeError,
6459
            "raise: arg 3 must be a traceback or None");
6460
        goto bad;
6461
    }
6462
    if (value == Py_None)
6463
        value = 0;
6464
    if (PyExceptionInstance_Check(type)) {
6465
        if (value) {
6466
            PyErr_SetString(PyExc_TypeError,
6467
                "instance exception may not have a separate value");
6468
            goto bad;
6469
        }
6470
        value = type;
6471
        type = (PyObject*) Py_TYPE(value);
6472
    } else if (PyExceptionClass_Check(type)) {
6473
        PyObject *instance_class = NULL;
6474
        if (value && PyExceptionInstance_Check(value)) {
6475
            instance_class = (PyObject*) Py_TYPE(value);
6476
            if (instance_class != type) {
6477
                int is_subclass = PyObject_IsSubclass(instance_class, type);
6478
                if (!is_subclass) {
6479
                    instance_class = NULL;
6480
                } else if (unlikely(is_subclass == -1)) {
6481
                    goto bad;
6482
                } else {
6483
                    type = instance_class;
6484
                }
6485
            }
6486
        }
6487
        if (!instance_class) {
6488
            PyObject *args;
6489
            if (!value)
6490
                args = PyTuple_New(0);
6491
            else if (PyTuple_Check(value)) {
6492
                Py_INCREF(value);
6493
                args = value;
6494
            } else
6495
                args = PyTuple_Pack(1, value);
6496
            if (!args)
6497
                goto bad;
6498
            owned_instance = PyObject_Call(type, args, NULL);
6499
            Py_DECREF(args);
6500
            if (!owned_instance)
6501
                goto bad;
6502
            value = owned_instance;
6503
            if (!PyExceptionInstance_Check(value)) {
6504
                PyErr_Format(PyExc_TypeError,
6505
                             "calling %R should have returned an instance of "
6506
                             "BaseException, not %R",
6507
                             type, Py_TYPE(value));
6508
                goto bad;
6509
            }
6510
        }
6511
    } else {
6512
        PyErr_SetString(PyExc_TypeError,
6513
            "raise: exception class must be a subclass of BaseException");
6514
        goto bad;
6515
    }
6516
#if PY_VERSION_HEX >= 0x03030000
6517
    if (cause) {
6518
#else
6519
    if (cause && cause != Py_None) {
6520
#endif
6521
        PyObject *fixed_cause;
6522
        if (cause == Py_None) {
6523
            fixed_cause = NULL;
6524
        } else if (PyExceptionClass_Check(cause)) {
6525
            fixed_cause = PyObject_CallObject(cause, NULL);
6526
            if (fixed_cause == NULL)
6527
                goto bad;
6528
        } else if (PyExceptionInstance_Check(cause)) {
6529
            fixed_cause = cause;
6530
            Py_INCREF(fixed_cause);
6531
        } else {
6532
            PyErr_SetString(PyExc_TypeError,
6533
                            "exception causes must derive from "
6534
                            "BaseException");
6535
            goto bad;
6536
        }
6537
        PyException_SetCause(value, fixed_cause);
6538
    }
6539
    PyErr_SetObject(type, value);
6540
    if (tb) {
6541
#if CYTHON_COMPILING_IN_PYPY
6542
        PyObject *tmp_type, *tmp_value, *tmp_tb;
6543
        PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
6544
        Py_INCREF(tb);
6545
        PyErr_Restore(tmp_type, tmp_value, tb);
6546
        Py_XDECREF(tmp_tb);
6547
#else
6548
        PyThreadState *tstate = PyThreadState_GET();
6549
        PyObject* tmp_tb = tstate->curexc_traceback;
6550
        if (tb != tmp_tb) {
6551
            Py_INCREF(tb);
6552
            tstate->curexc_traceback = tb;
6553
            Py_XDECREF(tmp_tb);
6554
        }
6555
#endif
6556
    }
6557
bad:
6558
    Py_XDECREF(owned_instance);
6559
    return;
6560
}
6561
#endif
6562

6563
/* ExtTypeTest */
6564
        static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
6565
    if (unlikely(!type)) {
6566
        PyErr_SetString(PyExc_SystemError, "Missing type object");
6567
        return 0;
6568
    }
6569
    if (likely(PyObject_TypeCheck(obj, type)))
6570
        return 1;
6571
    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
6572
                 Py_TYPE(obj)->tp_name, type->tp_name);
6573
    return 0;
6574
}
6575

6576
/* SetVTable */
6577
        static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
6578
#if PY_VERSION_HEX >= 0x02070000
6579
    PyObject *ob = PyCapsule_New(vtable, 0, 0);
6580
#else
6581
    PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
6582
#endif
6583
    if (!ob)
6584
        goto bad;
6585
    if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0)
6586
        goto bad;
6587
    Py_DECREF(ob);
6588
    return 0;
6589
bad:
6590
    Py_XDECREF(ob);
6591
    return -1;
6592
}
6593

6594
/* CodeObjectCache */
6595
        static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
6596
    int start = 0, mid = 0, end = count - 1;
6597
    if (end >= 0 && code_line > entries[end].code_line) {
6598
        return count;
6599
    }
6600
    while (start < end) {
6601
        mid = start + (end - start) / 2;
6602
        if (code_line < entries[mid].code_line) {
6603
            end = mid;
6604
        } else if (code_line > entries[mid].code_line) {
6605
             start = mid + 1;
6606
        } else {
6607
            return mid;
6608
        }
6609
    }
6610
    if (code_line <= entries[mid].code_line) {
6611
        return mid;
6612
    } else {
6613
        return mid + 1;
6614
    }
6615
}
6616
static PyCodeObject *__pyx_find_code_object(int code_line) {
6617
    PyCodeObject* code_object;
6618
    int pos;
6619
    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
6620
        return NULL;
6621
    }
6622
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
6623
    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
6624
        return NULL;
6625
    }
6626
    code_object = __pyx_code_cache.entries[pos].code_object;
6627
    Py_INCREF(code_object);
6628
    return code_object;
6629
}
6630
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
6631
    int pos, i;
6632
    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
6633
    if (unlikely(!code_line)) {
6634
        return;
6635
    }
6636
    if (unlikely(!entries)) {
6637
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
6638
        if (likely(entries)) {
6639
            __pyx_code_cache.entries = entries;
6640
            __pyx_code_cache.max_count = 64;
6641
            __pyx_code_cache.count = 1;
6642
            entries[0].code_line = code_line;
6643
            entries[0].code_object = code_object;
6644
            Py_INCREF(code_object);
6645
        }
6646
        return;
6647
    }
6648
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
6649
    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
6650
        PyCodeObject* tmp = entries[pos].code_object;
6651
        entries[pos].code_object = code_object;
6652
        Py_DECREF(tmp);
6653
        return;
6654
    }
6655
    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
6656
        int new_max = __pyx_code_cache.max_count + 64;
6657
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
6658
            __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
6659
        if (unlikely(!entries)) {
6660
            return;
6661
        }
6662
        __pyx_code_cache.entries = entries;
6663
        __pyx_code_cache.max_count = new_max;
6664
    }
6665
    for (i=__pyx_code_cache.count; i>pos; i--) {
6666
        entries[i] = entries[i-1];
6667
    }
6668
    entries[pos].code_line = code_line;
6669
    entries[pos].code_object = code_object;
6670
    __pyx_code_cache.count++;
6671
    Py_INCREF(code_object);
6672
}
6673

6674
/* AddTraceback */
6675
        #include "compile.h"
6676
#include "frameobject.h"
6677
#include "traceback.h"
6678
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
6679
            const char *funcname, int c_line,
6680
            int py_line, const char *filename) {
6681
    PyCodeObject *py_code = 0;
6682
    PyObject *py_srcfile = 0;
6683
    PyObject *py_funcname = 0;
6684
    #if PY_MAJOR_VERSION < 3
6685
    py_srcfile = PyString_FromString(filename);
6686
    #else
6687
    py_srcfile = PyUnicode_FromString(filename);
6688
    #endif
6689
    if (!py_srcfile) goto bad;
6690
    if (c_line) {
6691
        #if PY_MAJOR_VERSION < 3
6692
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
6693
        #else
6694
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
6695
        #endif
6696
    }
6697
    else {
6698
        #if PY_MAJOR_VERSION < 3
6699
        py_funcname = PyString_FromString(funcname);
6700
        #else
6701
        py_funcname = PyUnicode_FromString(funcname);
6702
        #endif
6703
    }
6704
    if (!py_funcname) goto bad;
6705
    py_code = __Pyx_PyCode_New(
6706
        0,
6707
        0,
6708
        0,
6709
        0,
6710
        0,
6711
        __pyx_empty_bytes, /*PyObject *code,*/
6712
        __pyx_empty_tuple, /*PyObject *consts,*/
6713
        __pyx_empty_tuple, /*PyObject *names,*/
6714
        __pyx_empty_tuple, /*PyObject *varnames,*/
6715
        __pyx_empty_tuple, /*PyObject *freevars,*/
6716
        __pyx_empty_tuple, /*PyObject *cellvars,*/
6717
        py_srcfile,   /*PyObject *filename,*/
6718
        py_funcname,  /*PyObject *name,*/
6719
        py_line,
6720
        __pyx_empty_bytes  /*PyObject *lnotab*/
6721
    );
6722
    Py_DECREF(py_srcfile);
6723
    Py_DECREF(py_funcname);
6724
    return py_code;
6725
bad:
6726
    Py_XDECREF(py_srcfile);
6727
    Py_XDECREF(py_funcname);
6728
    return NULL;
6729
}
6730
static void __Pyx_AddTraceback(const char *funcname, int c_line,
6731
                               int py_line, const char *filename) {
6732
    PyCodeObject *py_code = 0;
6733
    PyFrameObject *py_frame = 0;
6734
    py_code = __pyx_find_code_object(c_line ? c_line : py_line);
6735
    if (!py_code) {
6736
        py_code = __Pyx_CreateCodeObjectForTraceback(
6737
            funcname, c_line, py_line, filename);
6738
        if (!py_code) goto bad;
6739
        __pyx_insert_code_object(c_line ? c_line : py_line, py_code);
6740
    }
6741
    py_frame = PyFrame_New(
6742
        PyThreadState_GET(), /*PyThreadState *tstate,*/
6743
        py_code,             /*PyCodeObject *code,*/
6744
        __pyx_d,      /*PyObject *globals,*/
6745
        0                    /*PyObject *locals*/
6746
    );
6747
    if (!py_frame) goto bad;
6748
    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
6749
    PyTraceBack_Here(py_frame);
6750
bad:
6751
    Py_XDECREF(py_code);
6752
    Py_XDECREF(py_frame);
6753
}
6754

6755
/* CIntFromPyVerify */
6756
        #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
6757
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
6758
#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
6759
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
6760
#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
6761
    {\
6762
        func_type value = func_value;\
6763
        if (sizeof(target_type) < sizeof(func_type)) {\
6764
            if (unlikely(value != (func_type) (target_type) value)) {\
6765
                func_type zero = 0;\
6766
                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
6767
                    return (target_type) -1;\
6768
                if (is_unsigned && unlikely(value < zero))\
6769
                    goto raise_neg_overflow;\
6770
                else\
6771
                    goto raise_overflow;\
6772
            }\
6773
        }\
6774
        return (target_type) value;\
6775
    }
6776

6777
/* CIntToPy */
6778
        static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
6779
    const long neg_one = (long) -1, const_zero = (long) 0;
6780
    const int is_unsigned = neg_one > const_zero;
6781
    if (is_unsigned) {
6782
        if (sizeof(long) < sizeof(long)) {
6783
            return PyInt_FromLong((long) value);
6784
        } else if (sizeof(long) <= sizeof(unsigned long)) {
6785
            return PyLong_FromUnsignedLong((unsigned long) value);
6786
#ifdef HAVE_LONG_LONG
6787
        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
6788
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
6789
#endif
6790
        }
6791
    } else {
6792
        if (sizeof(long) <= sizeof(long)) {
6793
            return PyInt_FromLong((long) value);
6794
#ifdef HAVE_LONG_LONG
6795
        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
6796
            return PyLong_FromLongLong((PY_LONG_LONG) value);
6797
#endif
6798
        }
6799
    }
6800
    {
6801
        int one = 1; int little = (int)*(unsigned char *)&one;
6802
        unsigned char *bytes = (unsigned char *)&value;
6803
        return _PyLong_FromByteArray(bytes, sizeof(long),
6804
                                     little, !is_unsigned);
6805
    }
6806
}
6807

6808
/* CIntFromPy */
6809
        static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
6810
    const long neg_one = (long) -1, const_zero = (long) 0;
6811
    const int is_unsigned = neg_one > const_zero;
6812
#if PY_MAJOR_VERSION < 3
6813
    if (likely(PyInt_Check(x))) {
6814
        if (sizeof(long) < sizeof(long)) {
6815
            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
6816
        } else {
6817
            long val = PyInt_AS_LONG(x);
6818
            if (is_unsigned && unlikely(val < 0)) {
6819
                goto raise_neg_overflow;
6820
            }
6821
            return (long) val;
6822
        }
6823
    } else
6824
#endif
6825
    if (likely(PyLong_Check(x))) {
6826
        if (is_unsigned) {
6827
#if CYTHON_USE_PYLONG_INTERNALS
6828
            const digit* digits = ((PyLongObject*)x)->ob_digit;
6829
            switch (Py_SIZE(x)) {
6830
                case  0: return (long) 0;
6831
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
6832
                case 2:
6833
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
6834
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
6835
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
6836
                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
6837
                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
6838
                        }
6839
                    }
6840
                    break;
6841
                case 3:
6842
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
6843
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
6844
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
6845
                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
6846
                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
6847
                        }
6848
                    }
6849
                    break;
6850
                case 4:
6851
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
6852
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
6853
                            __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])))
6854
                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
6855
                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
6856
                        }
6857
                    }
6858
                    break;
6859
            }
6860
#endif
6861
#if CYTHON_COMPILING_IN_CPYTHON
6862
            if (unlikely(Py_SIZE(x) < 0)) {
6863
                goto raise_neg_overflow;
6864
            }
6865
#else
6866
            {
6867
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
6868
                if (unlikely(result < 0))
6869
                    return (long) -1;
6870
                if (unlikely(result == 1))
6871
                    goto raise_neg_overflow;
6872
            }
6873
#endif
6874
            if (sizeof(long) <= sizeof(unsigned long)) {
6875
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
6876
#ifdef HAVE_LONG_LONG
6877
            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
6878
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
6879
#endif
6880
            }
6881
        } else {
6882
#if CYTHON_USE_PYLONG_INTERNALS
6883
            const digit* digits = ((PyLongObject*)x)->ob_digit;
6884
            switch (Py_SIZE(x)) {
6885
                case  0: return (long) 0;
6886
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
6887
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
6888
                case -2:
6889
                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
6890
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
6891
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
6892
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
6893
                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
6894
                        }
6895
                    }
6896
                    break;
6897
                case 2:
6898
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
6899
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
6900
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
6901
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
6902
                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
6903
                        }
6904
                    }
6905
                    break;
6906
                case -3:
6907
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
6908
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
6909
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
6910
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
6911
                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
6912
                        }
6913
                    }
6914
                    break;
6915
                case 3:
6916
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
6917
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
6918
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
6919
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
6920
                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
6921
                        }
6922
                    }
6923
                    break;
6924
                case -4:
6925
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
6926
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
6927
                            __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])))
6928
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
6929
                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
6930
                        }
6931
                    }
6932
                    break;
6933
                case 4:
6934
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
6935
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
6936
                            __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])))
6937
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
6938
                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
6939
                        }
6940
                    }
6941
                    break;
6942
            }
6943
#endif
6944
            if (sizeof(long) <= sizeof(long)) {
6945
                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
6946
#ifdef HAVE_LONG_LONG
6947
            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
6948
                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
6949
#endif
6950
            }
6951
        }
6952
        {
6953
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
6954
            PyErr_SetString(PyExc_RuntimeError,
6955
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
6956
#else
6957
            long val;
6958
            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
6959
 #if PY_MAJOR_VERSION < 3
6960
            if (likely(v) && !PyLong_Check(v)) {
6961
                PyObject *tmp = v;
6962
                v = PyNumber_Long(tmp);
6963
                Py_DECREF(tmp);
6964
            }
6965
 #endif
6966
            if (likely(v)) {
6967
                int one = 1; int is_little = (int)*(unsigned char *)&one;
6968
                unsigned char *bytes = (unsigned char *)&val;
6969
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
6970
                                              bytes, sizeof(val),
6971
                                              is_little, !is_unsigned);
6972
                Py_DECREF(v);
6973
                if (likely(!ret))
6974
                    return val;
6975
            }
6976
#endif
6977
            return (long) -1;
6978
        }
6979
    } else {
6980
        long val;
6981
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
6982
        if (!tmp) return (long) -1;
6983
        val = __Pyx_PyInt_As_long(tmp);
6984
        Py_DECREF(tmp);
6985
        return val;
6986
    }
6987
raise_overflow:
6988
    PyErr_SetString(PyExc_OverflowError,
6989
        "value too large to convert to long");
6990
    return (long) -1;
6991
raise_neg_overflow:
6992
    PyErr_SetString(PyExc_OverflowError,
6993
        "can't convert negative value to long");
6994
    return (long) -1;
6995
}
6996

6997
/* CIntFromPy */
6998
        static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
6999
    const int neg_one = (int) -1, const_zero = (int) 0;
7000
    const int is_unsigned = neg_one > const_zero;
7001
#if PY_MAJOR_VERSION < 3
7002
    if (likely(PyInt_Check(x))) {
7003
        if (sizeof(int) < sizeof(long)) {
7004
            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
7005
        } else {
7006
            long val = PyInt_AS_LONG(x);
7007
            if (is_unsigned && unlikely(val < 0)) {
7008
                goto raise_neg_overflow;
7009
            }
7010
            return (int) val;
7011
        }
7012
    } else
7013
#endif
7014
    if (likely(PyLong_Check(x))) {
7015
        if (is_unsigned) {
7016
#if CYTHON_USE_PYLONG_INTERNALS
7017
            const digit* digits = ((PyLongObject*)x)->ob_digit;
7018
            switch (Py_SIZE(x)) {
7019
                case  0: return (int) 0;
7020
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
7021
                case 2:
7022
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
7023
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
7024
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
7025
                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
7026
                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
7027
                        }
7028
                    }
7029
                    break;
7030
                case 3:
7031
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
7032
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
7033
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
7034
                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
7035
                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
7036
                        }
7037
                    }
7038
                    break;
7039
                case 4:
7040
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
7041
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
7042
                            __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])))
7043
                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
7044
                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
7045
                        }
7046
                    }
7047
                    break;
7048
            }
7049
#endif
7050
#if CYTHON_COMPILING_IN_CPYTHON
7051
            if (unlikely(Py_SIZE(x) < 0)) {
7052
                goto raise_neg_overflow;
7053
            }
7054
#else
7055
            {
7056
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
7057
                if (unlikely(result < 0))
7058
                    return (int) -1;
7059
                if (unlikely(result == 1))
7060
                    goto raise_neg_overflow;
7061
            }
7062
#endif
7063
            if (sizeof(int) <= sizeof(unsigned long)) {
7064
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
7065
#ifdef HAVE_LONG_LONG
7066
            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
7067
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
7068
#endif
7069
            }
7070
        } else {
7071
#if CYTHON_USE_PYLONG_INTERNALS
7072
            const digit* digits = ((PyLongObject*)x)->ob_digit;
7073
            switch (Py_SIZE(x)) {
7074
                case  0: return (int) 0;
7075
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
7076
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
7077
                case -2:
7078
                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
7079
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
7080
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
7081
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
7082
                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
7083
                        }
7084
                    }
7085
                    break;
7086
                case 2:
7087
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
7088
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
7089
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
7090
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
7091
                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
7092
                        }
7093
                    }
7094
                    break;
7095
                case -3:
7096
                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
7097
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
7098
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
7099
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
7100
                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
7101
                        }
7102
                    }
7103
                    break;
7104
                case 3:
7105
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
7106
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
7107
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
7108
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
7109
                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
7110
                        }
7111
                    }
7112
                    break;
7113
                case -4:
7114
                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
7115
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
7116
                            __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])))
7117
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
7118
                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
7119
                        }
7120
                    }
7121
                    break;
7122
                case 4:
7123
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
7124
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
7125
                            __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])))
7126
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
7127
                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
7128
                        }
7129
                    }
7130
                    break;
7131
            }
7132
#endif
7133
            if (sizeof(int) <= sizeof(long)) {
7134
                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
7135
#ifdef HAVE_LONG_LONG
7136
            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
7137
                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
7138
#endif
7139
            }
7140
        }
7141
        {
7142
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
7143
            PyErr_SetString(PyExc_RuntimeError,
7144
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
7145
#else
7146
            int val;
7147
            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
7148
 #if PY_MAJOR_VERSION < 3
7149
            if (likely(v) && !PyLong_Check(v)) {
7150
                PyObject *tmp = v;
7151
                v = PyNumber_Long(tmp);
7152
                Py_DECREF(tmp);
7153
            }
7154
 #endif
7155
            if (likely(v)) {
7156
                int one = 1; int is_little = (int)*(unsigned char *)&one;
7157
                unsigned char *bytes = (unsigned char *)&val;
7158
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
7159
                                              bytes, sizeof(val),
7160
                                              is_little, !is_unsigned);
7161
                Py_DECREF(v);
7162
                if (likely(!ret))
7163
                    return val;
7164
            }
7165
#endif
7166
            return (int) -1;
7167
        }
7168
    } else {
7169
        int val;
7170
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
7171
        if (!tmp) return (int) -1;
7172
        val = __Pyx_PyInt_As_int(tmp);
7173
        Py_DECREF(tmp);
7174
        return val;
7175
    }
7176
raise_overflow:
7177
    PyErr_SetString(PyExc_OverflowError,
7178
        "value too large to convert to int");
7179
    return (int) -1;
7180
raise_neg_overflow:
7181
    PyErr_SetString(PyExc_OverflowError,
7182
        "can't convert negative value to int");
7183
    return (int) -1;
7184
}
7185

7186
/* CheckBinaryVersion */
7187
        static int __Pyx_check_binary_version(void) {
7188
    char ctversion[4], rtversion[4];
7189
    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
7190
    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
7191
    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
7192
        char message[200];
7193
        PyOS_snprintf(message, sizeof(message),
7194
                      "compiletime version %s of module '%.100s' "
7195
                      "does not match runtime version %s",
7196
                      ctversion, __Pyx_MODULE_NAME, rtversion);
7197
        return PyErr_WarnEx(NULL, message, 1);
7198
    }
7199
    return 0;
7200
}
7201

7202
/* ModuleImport */
7203
        #ifndef __PYX_HAVE_RT_ImportModule
7204
#define __PYX_HAVE_RT_ImportModule
7205
static PyObject *__Pyx_ImportModule(const char *name) {
7206
    PyObject *py_name = 0;
7207
    PyObject *py_module = 0;
7208
    py_name = __Pyx_PyIdentifier_FromString(name);
7209
    if (!py_name)
7210
        goto bad;
7211
    py_module = PyImport_Import(py_name);
7212
    Py_DECREF(py_name);
7213
    return py_module;
7214
bad:
7215
    Py_XDECREF(py_name);
7216
    return 0;
7217
}
7218
#endif
7219

7220
/* TypeImport */
7221
        #ifndef __PYX_HAVE_RT_ImportType
7222
#define __PYX_HAVE_RT_ImportType
7223
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
7224
    size_t size, int strict)
7225
{
7226
    PyObject *py_module = 0;
7227
    PyObject *result = 0;
7228
    PyObject *py_name = 0;
7229
    char warning[200];
7230
    Py_ssize_t basicsize;
7231
#ifdef Py_LIMITED_API
7232
    PyObject *py_basicsize;
7233
#endif
7234
    py_module = __Pyx_ImportModule(module_name);
7235
    if (!py_module)
7236
        goto bad;
7237
    py_name = __Pyx_PyIdentifier_FromString(class_name);
7238
    if (!py_name)
7239
        goto bad;
7240
    result = PyObject_GetAttr(py_module, py_name);
7241
    Py_DECREF(py_name);
7242
    py_name = 0;
7243
    Py_DECREF(py_module);
7244
    py_module = 0;
7245
    if (!result)
7246
        goto bad;
7247
    if (!PyType_Check(result)) {
7248
        PyErr_Format(PyExc_TypeError,
7249
            "%.200s.%.200s is not a type object",
7250
            module_name, class_name);
7251
        goto bad;
7252
    }
7253
#ifndef Py_LIMITED_API
7254
    basicsize = ((PyTypeObject *)result)->tp_basicsize;
7255
#else
7256
    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
7257
    if (!py_basicsize)
7258
        goto bad;
7259
    basicsize = PyLong_AsSsize_t(py_basicsize);
7260
    Py_DECREF(py_basicsize);
7261
    py_basicsize = 0;
7262
    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
7263
        goto bad;
7264
#endif
7265
    if (!strict && (size_t)basicsize > size) {
7266
        PyOS_snprintf(warning, sizeof(warning),
7267
            "%s.%s size changed, may indicate binary incompatibility. Expected %zd, got %zd",
7268
            module_name, class_name, basicsize, size);
7269
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
7270
    }
7271
    else if ((size_t)basicsize != size) {
7272
        PyErr_Format(PyExc_ValueError,
7273
            "%.200s.%.200s has the wrong size, try recompiling. Expected %zd, got %zd",
7274
            module_name, class_name, basicsize, size);
7275
        goto bad;
7276
    }
7277
    return (PyTypeObject *)result;
7278
bad:
7279
    Py_XDECREF(py_module);
7280
    Py_XDECREF(result);
7281
    return NULL;
7282
}
7283
#endif
7284

7285
/* VoidPtrImport */
7286
        #ifndef __PYX_HAVE_RT_ImportVoidPtr
7287
#define __PYX_HAVE_RT_ImportVoidPtr
7288
static int __Pyx_ImportVoidPtr(PyObject *module, const char *name, void **p, const char *sig) {
7289
    PyObject *d = 0;
7290
    PyObject *cobj = 0;
7291
    d = PyObject_GetAttrString(module, (char *)"__pyx_capi__");
7292
    if (!d)
7293
        goto bad;
7294
    cobj = PyDict_GetItemString(d, name);
7295
    if (!cobj) {
7296
        PyErr_Format(PyExc_ImportError,
7297
            "%.200s does not export expected C variable %.200s",
7298
                PyModule_GetName(module), name);
7299
        goto bad;
7300
    }
7301
#if PY_VERSION_HEX >= 0x02070000
7302
    if (!PyCapsule_IsValid(cobj, sig)) {
7303
        PyErr_Format(PyExc_TypeError,
7304
            "C variable %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
7305
             PyModule_GetName(module), name, sig, PyCapsule_GetName(cobj));
7306
        goto bad;
7307
    }
7308
    *p = PyCapsule_GetPointer(cobj, sig);
7309
#else
7310
    {const char *desc, *s1, *s2;
7311
    desc = (const char *)PyCObject_GetDesc(cobj);
7312
    if (!desc)
7313
        goto bad;
7314
    s1 = desc; s2 = sig;
7315
    while (*s1 != '\0' && *s1 == *s2) { s1++; s2++; }
7316
    if (*s1 != *s2) {
7317
        PyErr_Format(PyExc_TypeError,
7318
            "C variable %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
7319
             PyModule_GetName(module), name, sig, desc);
7320
        goto bad;
7321
    }
7322
    *p = PyCObject_AsVoidPtr(cobj);}
7323
#endif
7324
    if (!(*p))
7325
        goto bad;
7326
    Py_DECREF(d);
7327
    return 0;
7328
bad:
7329
    Py_XDECREF(d);
7330
    return -1;
7331
}
7332
#endif
7333

7334
/* InitStrings */
7335
        static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
7336
    while (t->p) {
7337
        #if PY_MAJOR_VERSION < 3
7338
        if (t->is_unicode) {
7339
            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
7340
        } else if (t->intern) {
7341
            *t->p = PyString_InternFromString(t->s);
7342
        } else {
7343
            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
7344
        }
7345
        #else
7346
        if (t->is_unicode | t->is_str) {
7347
            if (t->intern) {
7348
                *t->p = PyUnicode_InternFromString(t->s);
7349
            } else if (t->encoding) {
7350
                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
7351
            } else {
7352
                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
7353
            }
7354
        } else {
7355
            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
7356
        }
7357
        #endif
7358
        if (!*t->p)
7359
            return -1;
7360
        ++t;
7361
    }
7362
    return 0;
7363
}
7364

7365
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
7366
    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
7367
}
7368
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {
7369
    Py_ssize_t ignore;
7370
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
7371
}
7372
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
7373
#if CYTHON_COMPILING_IN_CPYTHON && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)
7374
    if (
7375
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
7376
            __Pyx_sys_getdefaultencoding_not_ascii &&
7377
#endif
7378
            PyUnicode_Check(o)) {
7379
#if PY_VERSION_HEX < 0x03030000
7380
        char* defenc_c;
7381
        PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
7382
        if (!defenc) return NULL;
7383
        defenc_c = PyBytes_AS_STRING(defenc);
7384
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
7385
        {
7386
            char* end = defenc_c + PyBytes_GET_SIZE(defenc);
7387
            char* c;
7388
            for (c = defenc_c; c < end; c++) {
7389
                if ((unsigned char) (*c) >= 128) {
7390
                    PyUnicode_AsASCIIString(o);
7391
                    return NULL;
7392
                }
7393
            }
7394
        }
7395
#endif
7396
        *length = PyBytes_GET_SIZE(defenc);
7397
        return defenc_c;
7398
#else
7399
        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
7400
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
7401
        if (PyUnicode_IS_ASCII(o)) {
7402
            *length = PyUnicode_GET_LENGTH(o);
7403
            return PyUnicode_AsUTF8(o);
7404
        } else {
7405
            PyUnicode_AsASCIIString(o);
7406
            return NULL;
7407
        }
7408
#else
7409
        return PyUnicode_AsUTF8AndSize(o, length);
7410
#endif
7411
#endif
7412
    } else
7413
#endif
7414
#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
7415
    if (PyByteArray_Check(o)) {
7416
        *length = PyByteArray_GET_SIZE(o);
7417
        return PyByteArray_AS_STRING(o);
7418
    } else
7419
#endif
7420
    {
7421
        char* result;
7422
        int r = PyBytes_AsStringAndSize(o, &result, length);
7423
        if (unlikely(r < 0)) {
7424
            return NULL;
7425
        } else {
7426
            return result;
7427
        }
7428
    }
7429
}
7430
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
7431
   int is_true = x == Py_True;
7432
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
7433
   else return PyObject_IsTrue(x);
7434
}
7435
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
7436
#if CYTHON_USE_TYPE_SLOTS
7437
  PyNumberMethods *m;
7438
#endif
7439
  const char *name = NULL;
7440
  PyObject *res = NULL;
7441
#if PY_MAJOR_VERSION < 3
7442
  if (PyInt_Check(x) || PyLong_Check(x))
7443
#else
7444
  if (PyLong_Check(x))
7445
#endif
7446
    return __Pyx_NewRef(x);
7447
#if CYTHON_USE_TYPE_SLOTS
7448
  m = Py_TYPE(x)->tp_as_number;
7449
  #if PY_MAJOR_VERSION < 3
7450
  if (m && m->nb_int) {
7451
    name = "int";
7452
    res = PyNumber_Int(x);
7453
  }
7454
  else if (m && m->nb_long) {
7455
    name = "long";
7456
    res = PyNumber_Long(x);
7457
  }
7458
  #else
7459
  if (m && m->nb_int) {
7460
    name = "int";
7461
    res = PyNumber_Long(x);
7462
  }
7463
  #endif
7464
#else
7465
  res = PyNumber_Int(x);
7466
#endif
7467
  if (res) {
7468
#if PY_MAJOR_VERSION < 3
7469
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
7470
#else
7471
    if (!PyLong_Check(res)) {
7472
#endif
7473
      PyErr_Format(PyExc_TypeError,
7474
                   "__%.4s__ returned non-%.4s (type %.200s)",
7475
                   name, name, Py_TYPE(res)->tp_name);
7476
      Py_DECREF(res);
7477
      return NULL;
7478
    }
7479
  }
7480
  else if (!PyErr_Occurred()) {
7481
    PyErr_SetString(PyExc_TypeError,
7482
                    "an integer is required");
7483
  }
7484
  return res;
7485
}
7486
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
7487
  Py_ssize_t ival;
7488
  PyObject *x;
7489
#if PY_MAJOR_VERSION < 3
7490
  if (likely(PyInt_CheckExact(b))) {
7491
    if (sizeof(Py_ssize_t) >= sizeof(long))
7492
        return PyInt_AS_LONG(b);
7493
    else
7494
        return PyInt_AsSsize_t(x);
7495
  }
7496
#endif
7497
  if (likely(PyLong_CheckExact(b))) {
7498
    #if CYTHON_USE_PYLONG_INTERNALS
7499
    const digit* digits = ((PyLongObject*)b)->ob_digit;
7500
    const Py_ssize_t size = Py_SIZE(b);
7501
    if (likely(__Pyx_sst_abs(size) <= 1)) {
7502
        ival = likely(size) ? digits[0] : 0;
7503
        if (size == -1) ival = -ival;
7504
        return ival;
7505
    } else {
7506
      switch (size) {
7507
         case 2:
7508
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
7509
             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
7510
           }
7511
           break;
7512
         case -2:
7513
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
7514
             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
7515
           }
7516
           break;
7517
         case 3:
7518
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
7519
             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
7520
           }
7521
           break;
7522
         case -3:
7523
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
7524
             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
7525
           }
7526
           break;
7527
         case 4:
7528
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
7529
             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]));
7530
           }
7531
           break;
7532
         case -4:
7533
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
7534
             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]));
7535
           }
7536
           break;
7537
      }
7538
    }
7539
    #endif
7540
    return PyLong_AsSsize_t(b);
7541
  }
7542
  x = PyNumber_Index(b);
7543
  if (!x) return -1;
7544
  ival = PyInt_AsSsize_t(x);
7545
  Py_DECREF(x);
7546
  return ival;
7547
}
7548
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
7549
    return PyInt_FromSize_t(ival);
7550
}
7551

7552

7553
#endif /* Py_PYTHON_H */
7554

7555
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