0001: # cython: language_level=3str

 0002: # cython: profile=True

 0003: 

 0004: # Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,

 0005: # 2011, 2012, 2013, 2014 Python Software Foundation; All Rights Reserved

 0006: #

 0007: # Based on the "fractions" module in CPython 3.4+.

 0008: # https://hg.python.org/cpython/file/b18288f24501/Lib/fractions.py

 0009: #

 0010: # Adapted for efficient Cython compilation by Stefan Behnel.

 0011: #

 0012: 

 0013: """

 0014: Fast fractions data type for rational numbers.

 0015: 

 0016: This is an almost-drop-in replacement for the standard library's

 0017: "fractions.Fraction".

 0018: """

 0019: 

 0020: from __future__ import division, absolute_import, print_function

 0021: 

 0022: 

+0023: __all__ = ['Fraction']

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 0027: cimport cython

 0028: from cpython.unicode cimport Py_UNICODE_TODECIMAL

 0029: from cpython.object cimport Py_LT, Py_LE, Py_EQ, Py_NE, Py_GT, Py_GE

 0030: from cpython.version cimport PY_MAJOR_VERSION

 0031: 

 0032: cdef extern from *:

 0033:     cdef long LONG_MAX, INT_MAX

 0034:     cdef long long PY_LLONG_MIN, PY_LLONG_MAX

 0035:     cdef long long MAX_SMALL_NUMBER "(PY_LLONG_MAX / 100)"

 0036: 

 0037: cdef object Rational, Integral, Real, Complex, Decimal, math, operator, sys

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 0221:     Examples

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 0235:     Fraction(6283, 2000)

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 0240:     >>> Fraction(2.25)

 0241:     Fraction(9, 4)

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 0302:             else:

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/* … */
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/* … */
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 0392:         """Closest Fraction to self with denominator at most max_denominator.

 0393: 

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 0395:         Fraction(22, 7)

 0396:         >>> Fraction('3.141592653589793').limit_denominator(100)

 0397:         Fraction(311, 99)

 0398:         >>> Fraction(4321, 8765).limit_denominator(10000)

 0399:         Fraction(4321, 8765)

 0400: 

 0401:         """

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 0404:         #

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 0417:         # In the event of a tie, the bound with smaller denominator is

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 0420:         # two integers) the lower bound---i.e., the floor of self, is

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 0793: 

 0794: 

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 0797: 

 0798: 

 0799: """

 0800: In general, we want to implement the arithmetic operations so

 0801: that mixed-mode operations either call an implementation whose

 0802: author knew about the types of both arguments, or convert both

 0803: to the nearest built in type and do the operation there. In

 0804: Fraction, that means that we define __add__ and __radd__ as:

 0805: 

 0806:     def __add__(self, other):

 0807:         # Both types have numerators/denominator attributes,

 0808:         # so do the operation directly

 0809:         if isinstance(other, (int, Fraction)):

 0810:             return Fraction(self.numerator * other.denominator +

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 0812:                             self.denominator * other.denominator)

 0813:         # float and complex don't have those operations, but we

 0814:         # know about those types, so special case them.

 0815:         elif isinstance(other, float):

 0816:             return float(self) + other

 0817:         elif isinstance(other, complex):

 0818:             return complex(self) + other

 0819:         # Let the other type take over.

 0820:         return NotImplemented

 0821: 

 0822:     def __radd__(self, other):

 0823:         # radd handles more types than add because there's

 0824:         # nothing left to fall back to.

 0825:         if isinstance(other, Rational):

 0826:             return Fraction(self.numerator * other.denominator +

 0827:                             other.numerator * self.denominator,

 0828:                             self.denominator * other.denominator)

 0829:         elif isinstance(other, Real):

 0830:             return float(other) + float(self)

 0831:         elif isinstance(other, Complex):

 0832:             return complex(other) + complex(self)

 0833:         return NotImplemented

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 0836: There are 5 different cases for a mixed-type addition on

 0837: Fraction. I'll refer to all of the above code that doesn't

 0838: refer to Fraction, float, or complex as "boilerplate". 'r'

 0839: will be an instance of Fraction, which is a subtype of

 0840: Rational (r : Fraction <: Rational), and b : B <:

 0841: Complex. The first three involve 'r + b':

 0842: 

 0843:     1. If B <: Fraction, int, float, or complex, we handle

 0844:        that specially, and all is well.

 0845:     2. If Fraction falls back to the boilerplate code, and it

 0846:        were to return a value from __add__, we'd miss the

 0847:        possibility that B defines a more intelligent __radd__,

 0848:        so the boilerplate should return NotImplemented from

 0849:        __add__. In particular, we don't handle Rational

 0850:        here, even though we could get an exact answer, in case

 0851:        the other type wants to do something special.

 0852:     3. If B <: Fraction, Python tries B.__radd__ before

 0853:        Fraction.__add__. This is ok, because it was

 0854:        implemented with knowledge of Fraction, so it can

 0855:        handle those instances before delegating to Real or

 0856:        Complex.

 0857: 

 0858: The next two situations describe 'b + r'. We assume that b

 0859: didn't know about Fraction in its implementation, and that it

 0860: uses similar boilerplate code:

 0861: 

 0862:     4. If B <: Rational, then __radd_ converts both to the

 0863:        builtin rational type (hey look, that's us) and

 0864:        proceeds.

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 1001:     """

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/* … */
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 1006:     cdef Py_UCS4 c

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/* … */
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/* … */
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/* … */
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 1013:     cdef ullong igcd

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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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 1025:                     pass

 1026:                 else:

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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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/* … */
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          __pyx_t_8 = __pyx_f_10quicktions__raise_invalid_input(__pyx_v_s); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1060, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_8);
          __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
          break;
        }
/* … */
          __pyx_t_10 = __pyx_f_10quicktions__raise_invalid_input(__pyx_v_s); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1060, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_10);
          __Pyx_DECREF(__pyx_t_10); __pyx_t_10 = 0;
          break;
        }

+1061:                 continue

        goto __pyx_L3_continue;
/* … */
        goto __pyx_L3_continue;

+1062:             elif c == u'_':

        break;
        default:
/* … */
        break;
        default:

+1063:                 if state == SMALL_NUM:

        switch (__pyx_v_state) {
          case __pyx_e_10quicktions_SMALL_NUM:
/* … */
          break;
          case __pyx_e_10quicktions_NUM:
/* … */
        switch (__pyx_v_state) {
          case __pyx_e_10quicktions_SMALL_NUM:
/* … */
          break;
          case __pyx_e_10quicktions_NUM:

+1064:                     state = SMALL_NUM_US

          __pyx_v_state = __pyx_e_10quicktions_SMALL_NUM_US;
/* … */
          __pyx_v_state = __pyx_e_10quicktions_SMALL_NUM_US;

+1065:                 elif state == NUM:

          break;
          case __pyx_e_10quicktions_SMALL_DECIMAL:
/* … */
          break;
          case __pyx_e_10quicktions_SMALL_DECIMAL:

+1066:                     state = NUM_US

          __pyx_v_state = __pyx_e_10quicktions_NUM_US;
/* … */
          __pyx_v_state = __pyx_e_10quicktions_NUM_US;

+1067:                 elif state == SMALL_DECIMAL:

          break;
          case __pyx_e_10quicktions_DECIMAL:
/* … */
          break;
          case __pyx_e_10quicktions_DECIMAL:

+1068:                     state = SMALL_DECIMAL_US

          __pyx_v_state = __pyx_e_10quicktions_SMALL_DECIMAL_US;
/* … */
          __pyx_v_state = __pyx_e_10quicktions_SMALL_DECIMAL_US;

+1069:                 elif state == DECIMAL:

          break;
          case __pyx_e_10quicktions_EXP:
/* … */
          break;
          case __pyx_e_10quicktions_EXP:

+1070:                     state = DECIMAL_US

          __pyx_v_state = __pyx_e_10quicktions_DECIMAL_US;
/* … */
          __pyx_v_state = __pyx_e_10quicktions_DECIMAL_US;

+1071:                 elif state == EXP:

          break;
          case __pyx_e_10quicktions_SMALL_DENOM:
/* … */
          break;
          case __pyx_e_10quicktions_SMALL_DENOM:

+1072:                     state = EXP_US

          __pyx_v_state = __pyx_e_10quicktions_EXP_US;
/* … */
          __pyx_v_state = __pyx_e_10quicktions_EXP_US;

+1073:                 elif state == SMALL_DENOM:

          break;
          case __pyx_e_10quicktions_DENOM:
/* … */
          break;
          case __pyx_e_10quicktions_DENOM:

+1074:                     state = SMALL_DENOM_US

          __pyx_v_state = __pyx_e_10quicktions_SMALL_DENOM_US;
/* … */
          __pyx_v_state = __pyx_e_10quicktions_SMALL_DENOM_US;

+1075:                 elif state == DENOM:

          break;
          default:
/* … */
          break;
          default:

+1076:                     state = DENOM_US

          __pyx_v_state = __pyx_e_10quicktions_DENOM_US;
/* … */
          __pyx_v_state = __pyx_e_10quicktions_DENOM_US;

 1077:                 else:

+1078:                     _raise_invalid_input(s)

          __pyx_t_8 = __pyx_f_10quicktions__raise_invalid_input(__pyx_v_s); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1078, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_8);
          __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
          break;
        }
/* … */
          __pyx_t_10 = __pyx_f_10quicktions__raise_invalid_input(__pyx_v_s); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1078, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_10);
          __Pyx_DECREF(__pyx_t_10); __pyx_t_10 = 0;
          break;
        }

+1079:                 continue

        goto __pyx_L3_continue;
/* … */
        goto __pyx_L3_continue;

 1080:             else:

+1081:                 if c.isspace():

        __pyx_t_7 = Py_UNICODE_ISSPACE(__pyx_v_c); 
        if ((__pyx_t_7 != 0)) {
/* … */
        }
        break;
      }
/* … */
        __pyx_t_9 = Py_UNICODE_ISSPACE(__pyx_v_c); 
        if ((__pyx_t_9 != 0)) {
/* … */
        }
        break;
      }

+1082:                     if state in (BEGIN_SPACE, NUM_SPACE, END_SPACE, SMALL_END_SPACE, DENOM_START, DENOM_SPACE):

          switch (__pyx_v_state) {
            case __pyx_e_10quicktions_BEGIN_SPACE:
            case __pyx_e_10quicktions_NUM_SPACE:
            case __pyx_e_10quicktions_END_SPACE:
            case __pyx_e_10quicktions_SMALL_END_SPACE:
            case __pyx_e_10quicktions_DENOM_START:
            case __pyx_e_10quicktions_DENOM_SPACE:
            break;
            case __pyx_e_10quicktions_SMALL_NUM:
/* … */
          switch (__pyx_v_state) {
            case __pyx_e_10quicktions_BEGIN_SPACE:
            case __pyx_e_10quicktions_NUM_SPACE:
            case __pyx_e_10quicktions_END_SPACE:
            case __pyx_e_10quicktions_SMALL_END_SPACE:
            case __pyx_e_10quicktions_DENOM_START:
            case __pyx_e_10quicktions_DENOM_SPACE:
            break;
            case __pyx_e_10quicktions_SMALL_NUM:

 1083:                         pass

+1084:                     elif state == SMALL_NUM:

            break;
            case __pyx_e_10quicktions_NUM:
/* … */
            break;
            case __pyx_e_10quicktions_NUM:

+1085:                         num = inum

            __pyx_t_8 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_inum); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1085, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_8);
            __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_8);
            __pyx_t_8 = 0;
/* … */
            __pyx_t_10 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_inum); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1085, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_10);
            __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_10);
            __pyx_t_10 = 0;

+1086:                         state = NUM_SPACE

            __pyx_v_state = __pyx_e_10quicktions_NUM_SPACE;
/* … */
            __pyx_v_state = __pyx_e_10quicktions_NUM_SPACE;

+1087:                     elif state == NUM:

            break;
            case __pyx_e_10quicktions_SMALL_DECIMAL:
/* … */
            break;
            case __pyx_e_10quicktions_SMALL_DECIMAL:

+1088:                         state = NUM_SPACE

            __pyx_v_state = __pyx_e_10quicktions_NUM_SPACE;
/* … */
            __pyx_v_state = __pyx_e_10quicktions_NUM_SPACE;

+1089:                     elif state in (SMALL_DECIMAL, SMALL_DECIMAL_DOT):

            case __pyx_e_10quicktions_SMALL_DECIMAL_DOT:
/* … */
            break;
            case __pyx_e_10quicktions_DECIMAL:
/* … */
            case __pyx_e_10quicktions_SMALL_DECIMAL_DOT:
/* … */
            break;
            case __pyx_e_10quicktions_DECIMAL:

+1090:                         num = inum

            __pyx_t_8 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_inum); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1090, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_8);
            __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_8);
            __pyx_t_8 = 0;
/* … */
            __pyx_t_10 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_inum); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1090, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_10);
            __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_10);
            __pyx_t_10 = 0;

+1091:                         state = SMALL_END_SPACE

            __pyx_v_state = __pyx_e_10quicktions_SMALL_END_SPACE;
/* … */
            __pyx_v_state = __pyx_e_10quicktions_SMALL_END_SPACE;

+1092:                     elif state in (DECIMAL, DECIMAL_DOT):

            case __pyx_e_10quicktions_DECIMAL_DOT:
/* … */
            break;
            case __pyx_e_10quicktions_EXP:
/* … */
            case __pyx_e_10quicktions_DECIMAL_DOT:
/* … */
            break;
            case __pyx_e_10quicktions_EXP:

+1093:                         state = END_SPACE

            __pyx_v_state = __pyx_e_10quicktions_END_SPACE;
/* … */
            __pyx_v_state = __pyx_e_10quicktions_END_SPACE;

+1094:                     elif state == EXP:

            break;
            case __pyx_e_10quicktions_SMALL_DENOM:
/* … */
            break;
            case __pyx_e_10quicktions_SMALL_DENOM:

+1095:                         state = END_SPACE

            __pyx_v_state = __pyx_e_10quicktions_END_SPACE;
/* … */
            __pyx_v_state = __pyx_e_10quicktions_END_SPACE;

+1096:                     elif state == SMALL_DENOM:

            break;
            case __pyx_e_10quicktions_DENOM:
/* … */
            break;
            case __pyx_e_10quicktions_DENOM:

+1097:                         denom = idenom

            __pyx_t_8 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_idenom); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1097, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_8);
            __Pyx_XDECREF_SET(__pyx_v_denom, __pyx_t_8);
            __pyx_t_8 = 0;
/* … */
            __pyx_t_10 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_idenom); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1097, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_10);
            __Pyx_XDECREF_SET(__pyx_v_denom, __pyx_t_10);
            __pyx_t_10 = 0;

+1098:                         state = DENOM_SPACE

            __pyx_v_state = __pyx_e_10quicktions_DENOM_SPACE;
/* … */
            __pyx_v_state = __pyx_e_10quicktions_DENOM_SPACE;

+1099:                     elif state == DENOM:

            break;
            default:
/* … */
            break;
            default:

+1100:                         state = DENOM_SPACE

            __pyx_v_state = __pyx_e_10quicktions_DENOM_SPACE;
/* … */
            __pyx_v_state = __pyx_e_10quicktions_DENOM_SPACE;

 1101:                     else:

+1102:                         _raise_invalid_input(s)

            __pyx_t_8 = __pyx_f_10quicktions__raise_invalid_input(__pyx_v_s); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1102, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_8);
            __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
            break;
          }
/* … */
            __pyx_t_10 = __pyx_f_10quicktions__raise_invalid_input(__pyx_v_s); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1102, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_10);
            __Pyx_DECREF(__pyx_t_10); __pyx_t_10 = 0;
            break;
          }

+1103:                     continue

          goto __pyx_L3_continue;
/* … */
          goto __pyx_L3_continue;

 1104: 

+1105:             digit = Py_UNICODE_TODECIMAL(c)

      __pyx_v_digit = Py_UNICODE_TODECIMAL(__pyx_v_c);
/* … */
      __pyx_v_digit = Py_UNICODE_TODECIMAL(__pyx_v_c);

+1106:             if digit == -1:

      __pyx_t_7 = ((__pyx_v_digit == -1L) != 0);
      if (__pyx_t_7) {
/* … */
      }
    }
    __pyx_L5:;
/* … */
      __pyx_t_9 = ((__pyx_v_digit == -1L) != 0);
      if (__pyx_t_9) {
/* … */
      }
    }
    __pyx_L5:;

+1107:                 _raise_invalid_input(s)

        __pyx_t_8 = __pyx_f_10quicktions__raise_invalid_input(__pyx_v_s); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1107, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_8);
        __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
/* … */
        __pyx_t_10 = __pyx_f_10quicktions__raise_invalid_input(__pyx_v_s); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1107, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_10);
        __Pyx_DECREF(__pyx_t_10); __pyx_t_10 = 0;

+1108:                 continue

        goto __pyx_L3_continue;
/* … */
        goto __pyx_L3_continue;

 1109: 

 1110:         # normal digit found

+1111:         if state in (BEGIN_SPACE, BEGIN_SIGN, SMALL_NUM, SMALL_NUM_US):

    switch (__pyx_v_state) {
      case __pyx_e_10quicktions_BEGIN_SPACE:
      case __pyx_e_10quicktions_BEGIN_SIGN:
      case __pyx_e_10quicktions_SMALL_NUM:
      case __pyx_e_10quicktions_SMALL_NUM_US:
/* … */
      break;
      case __pyx_e_10quicktions_NUM:
/* … */
    switch (__pyx_v_state) {
      case __pyx_e_10quicktions_BEGIN_SPACE:
      case __pyx_e_10quicktions_BEGIN_SIGN:
      case __pyx_e_10quicktions_SMALL_NUM:
      case __pyx_e_10quicktions_SMALL_NUM_US:
/* … */
      break;
      case __pyx_e_10quicktions_NUM:

+1112:             inum = inum * 10 + digit

      __pyx_v_inum = ((__pyx_v_inum * 10) + __pyx_v_digit);
/* … */
      __pyx_v_inum = ((__pyx_v_inum * 10) + __pyx_v_digit);

+1113:             state = SMALL_NUM

      __pyx_v_state = __pyx_e_10quicktions_SMALL_NUM;
/* … */
      __pyx_v_state = __pyx_e_10quicktions_SMALL_NUM;

+1114:             if inum > MAX_SMALL_NUMBER:

      __pyx_t_7 = ((__pyx_v_inum > (PY_LLONG_MAX / 100)) != 0);
      if (__pyx_t_7) {
/* … */
      }
/* … */
      __pyx_t_9 = ((__pyx_v_inum > (PY_LLONG_MAX / 100)) != 0);
      if (__pyx_t_9) {
/* … */
      }

+1115:                 num = inum

        __pyx_t_8 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_inum); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1115, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_8);
        __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_8);
        __pyx_t_8 = 0;
/* … */
        __pyx_t_10 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_inum); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1115, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_10);
        __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_10);
        __pyx_t_10 = 0;

+1116:                 state = NUM

        __pyx_v_state = __pyx_e_10quicktions_NUM;
/* … */
        __pyx_v_state = __pyx_e_10quicktions_NUM;

+1117:         elif state in (NUM, NUM_US):

      case __pyx_e_10quicktions_NUM_US:
/* … */
      break;
      case __pyx_e_10quicktions_START_DECIMAL_DOT:
/* … */
      case __pyx_e_10quicktions_NUM_US:
/* … */
      break;
      case __pyx_e_10quicktions_START_DECIMAL_DOT:

+1118:             num = num * 10 + digit

      __pyx_t_8 = PyNumber_Multiply(__pyx_v_num, __pyx_int_10); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1118, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_8);
      __pyx_t_9 = __Pyx_PyInt_From_int(__pyx_v_digit); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 1118, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_9);
      __pyx_t_10 = PyNumber_Add(__pyx_t_8, __pyx_t_9); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1118, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_10);
      __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
      __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0;
      __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_10);
      __pyx_t_10 = 0;
/* … */
      __pyx_t_10 = PyNumber_Multiply(__pyx_v_num, __pyx_int_10); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1118, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_10);
      __pyx_t_11 = __Pyx_PyInt_From_int(__pyx_v_digit); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 1118, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_11);
      __pyx_t_12 = PyNumber_Add(__pyx_t_10, __pyx_t_11); if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 1118, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_12);
      __Pyx_DECREF(__pyx_t_10); __pyx_t_10 = 0;
      __Pyx_DECREF(__pyx_t_11); __pyx_t_11 = 0;
      __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_12);
      __pyx_t_12 = 0;

+1119:             state = NUM

      __pyx_v_state = __pyx_e_10quicktions_NUM;
/* … */
      __pyx_v_state = __pyx_e_10quicktions_NUM;

+1120:         elif state in (START_DECIMAL_DOT, SMALL_DECIMAL_DOT, SMALL_DECIMAL, SMALL_DECIMAL_US):

      case __pyx_e_10quicktions_SMALL_DECIMAL_DOT:
      case __pyx_e_10quicktions_SMALL_DECIMAL:
      case __pyx_e_10quicktions_SMALL_DECIMAL_US:
/* … */
      break;
      case __pyx_e_10quicktions_DECIMAL_DOT:
/* … */
      case __pyx_e_10quicktions_SMALL_DECIMAL_DOT:
      case __pyx_e_10quicktions_SMALL_DECIMAL:
      case __pyx_e_10quicktions_SMALL_DECIMAL_US:
/* … */
      break;
      case __pyx_e_10quicktions_DECIMAL_DOT:

+1121:             decimal_len += 1

      __pyx_v_decimal_len = (__pyx_v_decimal_len + 1);
/* … */
      __pyx_v_decimal_len = (__pyx_v_decimal_len + 1);

+1122:             inum = inum * 10 + digit

      __pyx_v_inum = ((__pyx_v_inum * 10) + __pyx_v_digit);
/* … */
      __pyx_v_inum = ((__pyx_v_inum * 10) + __pyx_v_digit);

+1123:             state = SMALL_DECIMAL

      __pyx_v_state = __pyx_e_10quicktions_SMALL_DECIMAL;
/* … */
      __pyx_v_state = __pyx_e_10quicktions_SMALL_DECIMAL;

+1124:             if inum > MAX_SMALL_NUMBER:

      __pyx_t_7 = ((__pyx_v_inum > (PY_LLONG_MAX / 100)) != 0);
      if (__pyx_t_7) {
/* … */
      }
/* … */
      __pyx_t_9 = ((__pyx_v_inum > (PY_LLONG_MAX / 100)) != 0);
      if (__pyx_t_9) {
/* … */
      }

+1125:                 num = inum

        __pyx_t_10 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_inum); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1125, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_10);
        __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_10);
        __pyx_t_10 = 0;
/* … */
        __pyx_t_12 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_inum); if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 1125, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_12);
        __Pyx_DECREF_SET(__pyx_v_num, __pyx_t_12);
        __pyx_t_12 = 0;

+1126:                 state = DECIMAL

        __pyx_v_state = __pyx_e_10quicktions_DECIMAL;
/* … */
        __pyx_v_state = __pyx_e_10quicktions_DECIMAL;

+1127:         elif state in (DECIMAL_DOT, DECIMAL, DECIMAL_US):

      case __pyx_e_10quicktions_DECIMAL:
      case __pyx_e_10quicktions_DECIMAL_US:
/* … */
      break;
      case __pyx_e_10quicktions_EXP_E:
/* … */
      case __pyx_e_10quicktions_DECIMAL:
      case __pyx_e_10quicktions_DECIMAL_US:
/* … */
      break;
      case __pyx_e_10quicktions_EXP_E:

+1128:             decimal_len += 1

      __pyx_v_decimal_len = (__pyx_v_decimal_len + 1);
/* … */
      __pyx_v_decimal_len = (__pyx_v_decimal_len + 1);

+1129:             num = num * 10 + digit

      __pyx_t_10 = PyNumber_Multiply(__pyx_v_num, __pyx_int_10); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1129, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_10);
      __pyx_t_9 = __Pyx_PyInt_From_int(__pyx_v_digit); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 1129, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_9);
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      __Pyx_GOTREF(__pyx_t_8);
      __Pyx_DECREF(__pyx_t_10); __pyx_t_10 = 0;
      __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0;
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      __pyx_t_8 = 0;
/* … */
      __pyx_t_12 = PyNumber_Multiply(__pyx_v_num, __pyx_int_10); if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 1129, __pyx_L1_error)
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      __Pyx_GOTREF(__pyx_t_11);
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      __Pyx_GOTREF(__pyx_t_10);
      __Pyx_DECREF(__pyx_t_12); __pyx_t_12 = 0;
      __Pyx_DECREF(__pyx_t_11); __pyx_t_11 = 0;
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+1130:             state = DECIMAL

      __pyx_v_state = __pyx_e_10quicktions_DECIMAL;
/* … */
      __pyx_v_state = __pyx_e_10quicktions_DECIMAL;

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      case __pyx_e_10quicktions_EXP_SIGN:
      case __pyx_e_10quicktions_EXP:
      case __pyx_e_10quicktions_EXP_US:
/* … */
      break;
      case __pyx_e_10quicktions_DENOM_START:
/* … */
      case __pyx_e_10quicktions_EXP_SIGN:
      case __pyx_e_10quicktions_EXP:
      case __pyx_e_10quicktions_EXP_US:
/* … */
      break;
      case __pyx_e_10quicktions_DENOM_START:

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/* … */
      __pyx_v_iexp = ((__pyx_v_iexp * 10) + __pyx_v_digit);

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/* … */
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/* … */
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/* … */
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+1134:                 _raise_parse_overflow(s)

        __pyx_t_8 = __pyx_f_10quicktions__raise_parse_overflow(__pyx_v_s); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 1134, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_8);
        __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
/* … */
        __pyx_t_10 = __pyx_f_10quicktions__raise_parse_overflow(__pyx_v_s); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1134, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_10);
        __Pyx_DECREF(__pyx_t_10); __pyx_t_10 = 0;

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      __pyx_v_state = __pyx_e_10quicktions_EXP;
/* … */
      __pyx_v_state = __pyx_e_10quicktions_EXP;

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      case __pyx_e_10quicktions_DENOM_SIGN:
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      case __pyx_e_10quicktions_SMALL_DENOM_US:
/* … */
      break;
      case __pyx_e_10quicktions_DENOM:
/* … */
      case __pyx_e_10quicktions_DENOM_SIGN:
      case __pyx_e_10quicktions_SMALL_DENOM:
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/* … */
      break;
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/* … */
      __pyx_v_idenom = ((__pyx_v_idenom * 10) + __pyx_v_digit);

+1138:             state = SMALL_DENOM

      __pyx_v_state = __pyx_e_10quicktions_SMALL_DENOM;
/* … */
      __pyx_v_state = __pyx_e_10quicktions_SMALL_DENOM;

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/* … */
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/* … */
      __pyx_t_9 = ((__pyx_v_idenom > (PY_LLONG_MAX / 100)) != 0);
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/* … */
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        __Pyx_GOTREF(__pyx_t_8);
        __Pyx_XDECREF_SET(__pyx_v_denom, __pyx_t_8);
        __pyx_t_8 = 0;
/* … */
        __pyx_t_10 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_idenom); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1140, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_10);
        __Pyx_XDECREF_SET(__pyx_v_denom, __pyx_t_10);
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+1141:                 state = DENOM

        __pyx_v_state = __pyx_e_10quicktions_DENOM;
/* … */
        __pyx_v_state = __pyx_e_10quicktions_DENOM;

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      case __pyx_e_10quicktions_DENOM_US:
/* … */
      break;
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/* … */
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/* … */
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      __Pyx_GOTREF(__pyx_t_8);
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      __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0;
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/* … */
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      __Pyx_GOTREF(__pyx_t_10);
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      __Pyx_XDECREF_SET(__pyx_v_denom, __pyx_t_12);
      __pyx_t_12 = 0;

+1144:             state = DENOM

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/* … */
      __pyx_v_state = __pyx_e_10quicktions_DENOM;

 1145:         else:

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/* … */
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      __Pyx_GOTREF(__pyx_t_12);
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+1148:     is_normalised = False

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/* … */
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/* … */
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/* … */
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/* … */
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 1150:         # Special case for 'small' numbers: normalise directly in C space.

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/* … */
      goto __pyx_L12;
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/* … */
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    __pyx_t_13 = (__pyx_v_decimal_len != 0);
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/* … */
      goto __pyx_L12;
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      __Pyx_GOTREF(__pyx_t_10);
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      __pyx_t_10 = 0;
/* … */
      __pyx_t_12 = __pyx_f_10quicktions_pow10(__pyx_v_decimal_len); if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 1152, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_12);
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      __pyx_t_12 = 0;

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      __pyx_v_igcd = __pyx_fuse_0__pyx_f_10quicktions__ibgcd(__pyx_v_inum, __pyx_t_12);
/* … */
      __pyx_t_14 = __Pyx_PyInt_As_unsigned_PY_LONG_LONG(__pyx_v_denom); if (unlikely((__pyx_t_14 == (unsigned PY_LONG_LONG)-1) && PyErr_Occurred())) __PYX_ERR(0, 1153, __pyx_L1_error)
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/* … */
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/* … */
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/* … */
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/* … */
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          PyErr_SetString(PyExc_ZeroDivisionError, "integer division or modulo by zero");
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        __Pyx_GOTREF(__pyx_t_10);
        __pyx_t_9 = PyNumber_InPlaceFloorDivide(__pyx_v_denom, __pyx_t_10); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 1156, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_9);
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        __pyx_t_9 = 0;
/* … */
        __pyx_t_12 = __Pyx_PyInt_From_unsigned_PY_LONG_LONG(__pyx_v_igcd); if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 1156, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_12);
        __pyx_t_11 = PyNumber_InPlaceFloorDivide(__pyx_v_denom, __pyx_t_12); if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 1156, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_11);
        __Pyx_DECREF(__pyx_t_12); __pyx_t_12 = 0;
        __Pyx_DECREF_SET(__pyx_v_denom, __pyx_t_11);
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 1157:         else:

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    /*else*/ {
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/* … */
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/* … */
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/* … */
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    if (__pyx_t_9) {
/* … */
    }

+1160:             inum = -inum

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/* … */
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    __Pyx_GOTREF(__pyx_t_9);
    __pyx_t_10 = PyTuple_New(3); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1161, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_10);
    __Pyx_GIVEREF(__pyx_t_9);
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    __Pyx_INCREF(__pyx_v_denom);
    __Pyx_GIVEREF(__pyx_v_denom);
    PyTuple_SET_ITEM(__pyx_t_10, 1, __pyx_v_denom);
    __Pyx_INCREF(Py_True);
    __Pyx_GIVEREF(Py_True);
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    goto __pyx_L0;
/* … */
    __Pyx_XDECREF(__pyx_r);
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    __Pyx_GOTREF(__pyx_t_11);
    __pyx_t_12 = PyTuple_New(3); if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 1161, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_12);
    __Pyx_GIVEREF(__pyx_t_11);
    PyTuple_SET_ITEM(__pyx_t_12, 0, __pyx_t_11);
    __Pyx_INCREF(__pyx_v_denom);
    __Pyx_GIVEREF(__pyx_v_denom);
    PyTuple_SET_ITEM(__pyx_t_12, 1, __pyx_v_denom);
    __Pyx_INCREF(Py_True);
    __Pyx_GIVEREF(Py_True);
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    goto __pyx_L0;

 1162: 

+1163:     elif state in (NUM, NUM_SPACE, DECIMAL_DOT, DECIMAL, EXP, END_SPACE):

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    case __pyx_e_10quicktions_EXP:
    case __pyx_e_10quicktions_END_SPACE:
/* … */
    break;
    case __pyx_e_10quicktions_SMALL_DENOM:
/* … */
    case __pyx_e_10quicktions_NUM_SPACE:
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    case __pyx_e_10quicktions_EXP:
    case __pyx_e_10quicktions_END_SPACE:
/* … */
    break;
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/* … */
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+1165:         denom = 1

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/* … */
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    break;
    case __pyx_e_10quicktions_DENOM:
/* … */
    break;
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    __pyx_t_10 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_idenom); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 1167, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_10);
    __Pyx_XDECREF_SET(__pyx_v_denom, __pyx_t_10);
    __pyx_t_10 = 0;
/* … */
    __pyx_t_12 = __Pyx_PyInt_From_PY_LONG_LONG(__pyx_v_idenom); if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 1167, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_12);
    __Pyx_XDECREF_SET(__pyx_v_denom, __pyx_t_12);
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+1168:     elif state in (DENOM, DENOM_SPACE):

    case __pyx_e_10quicktions_DENOM_SPACE:
    break;
    default:
/* … */
    case __pyx_e_10quicktions_DENOM_SPACE:
    break;
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 1169:         pass

 1170:     else:

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    __Pyx_GOTREF(__pyx_t_10);
    __Pyx_DECREF(__pyx_t_10); __pyx_t_10 = 0;
    break;
  }
/* … */
    __pyx_t_12 = __pyx_f_10quicktions__raise_invalid_input(__pyx_v_s); if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 1171, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_12);
    __Pyx_DECREF(__pyx_t_12); __pyx_t_12 = 0;
    break;
  }

 1172: 

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