Generated by Cython 0.21
Raw output: quicktions.c
001: # cython: profile=True
002:
003: # Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
004: # 2011, 2012, 2013, 2014 Python Software Foundation; All Rights Reserved
005: #
006: # Based on the "fractions" module in CPython 3.4.
007: # https://hg.python.org/cpython/file/b18288f24501/Lib/fractions.py
008: #
009: # Adapted for efficient Cython compilation by Stefan Behnel.
010: #
011:
012: """
013: Fast fractions data type for rational numbers.
014:
015: This is an almost-drop-in replacement for the standard library's
016: "fractions.Fraction".
017: """
018:
019: from __future__ import division, absolute_import, print_function
020:
021:
+022: __all__ = ['Fraction']
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023:
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025:
026: cimport cython
027: from cpython.object cimport Py_LT, Py_LE, Py_EQ, Py_NE, Py_GT, Py_GE
028: from cpython.version cimport PY_MAJOR_VERSION
029:
030: cdef extern from *:
031: ctypedef long Py_hash_t
032:
033:
034: cdef object Rational, Decimal, math, numbers, sys, re, operator
035:
+036: from numbers import Rational
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+037: from decimal import Decimal
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+038: import math
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+039: import numbers
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+040: import operator
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+041: import re
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+042: import sys
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043:
044:
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046: """Calculate the Greatest Common Divisor of a and b as a non-negative number.
047: """
048: # Try doing all computation in C space. If the numbers are too
049: # large at the beginning, retry after each iteration until they
050: # are small enough.
051: cdef unsigned long long au, bu
052: cdef long long ai, bi
+053: while b:
while (1) {
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067:
068:
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070: # on the reduction of x modulo the prime _PyHASH_MODULUS.
071:
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078:
079:
080: # Value to be used for rationals that reduce to infinity modulo
081: # _PyHASH_MODULUS.
082: cdef Py_hash_t _PyHASH_INF
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102:
103:
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struct __pyx_obj_10quicktions_Fraction {
PyObject_HEAD
struct __pyx_vtabstruct_10quicktions_Fraction *__pyx_vtab;
PyObject *_numerator;
PyObject *_denominator;
Py_hash_t _hash;
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PyObject *(*_eq)(struct __pyx_obj_10quicktions_Fraction *, PyObject *);
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105: """A Rational number.
106:
107: Takes a string like '3/2' or '1.5', another Rational instance, a
108: numerator/denominator pair, or a float.
109:
110: Examples
111: --------
112:
113: >>> Fraction(10, -8)
114: Fraction(-5, 4)
115: >>> Fraction(Fraction(1, 7), 5)
116: Fraction(1, 35)
117: >>> Fraction(Fraction(1, 7), Fraction(2, 3))
118: Fraction(3, 14)
119: >>> Fraction('314')
120: Fraction(314, 1)
121: >>> Fraction('-35/4')
122: Fraction(-35, 4)
123: >>> Fraction('3.1415') # conversion from numeric string
124: Fraction(6283, 2000)
125: >>> Fraction('-47e-2') # string may include a decimal exponent
126: Fraction(-47, 100)
127: >>> Fraction(1.47) # direct construction from float (exact conversion)
128: Fraction(6620291452234629, 4503599627370496)
129: >>> Fraction(2.25)
130: Fraction(9, 4)
131: >>> from decimal import Decimal
132: >>> Fraction(Decimal('1.47'))
133: Fraction(147, 100)
134:
135: """
136: cdef _numerator
137: cdef _denominator
138: cdef Py_hash_t _hash
139:
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__Pyx_INCREF(__pyx_t_4);
__Pyx_GIVEREF(__pyx_t_4);
__Pyx_GOTREF(__pyx_v_self->_denominator);
__Pyx_DECREF(__pyx_v_self->_denominator);
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goto __pyx_L0;
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160:
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__pyx_t_2 = __Pyx_PyBaseString_Check(__pyx_v_numerator);
__pyx_t_1 = (__pyx_t_2 != 0);
if (__pyx_t_1) {
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__pyx_t_1 = (__pyx_v_m == Py_None);
__pyx_t_2 = (__pyx_t_1 != 0);
if (__pyx_t_2) {
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166: numerator)
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__pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_m, __pyx_n_s_group); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 167; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_6 = __Pyx_PyObject_Call(__pyx_t_5, __pyx_tuple_, NULL); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 167; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_t_6); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 167; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (!__pyx_t_2) { __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; goto __pyx_L9_next_or; } else { __Pyx_INCREF(__pyx_t_6); __pyx_t_4 = __pyx_t_6; __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; goto __pyx_L8_bool_binop_done; } __pyx_L9_next_or:; __Pyx_INCREF(__pyx_kp_s_0); __pyx_t_4 = __pyx_kp_s_0; __pyx_L8_bool_binop_done:; __pyx_t_6 = PyNumber_Int(__pyx_t_4); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 167; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_6); __pyx_t_6 = 0; /* … */ __pyx_tuple_ = PyTuple_Pack(1, __pyx_n_s_num); if (unlikely(!__pyx_tuple_)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 167; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple_); __Pyx_GIVEREF(__pyx_tuple_);
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__pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_m, __pyx_n_s_group); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 168; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_t_4 = __Pyx_PyObject_Call(__pyx_t_6, __pyx_tuple__2, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 168; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __pyx_v_denom = __pyx_t_4; __pyx_t_4 = 0; /* … */ __pyx_tuple__2 = PyTuple_Pack(1, __pyx_n_s_denom); if (unlikely(!__pyx_tuple__2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 168; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple__2); __Pyx_GIVEREF(__pyx_tuple__2);
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__pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_v_denom); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 169; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) {
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__pyx_t_4 = PyNumber_Int(__pyx_v_denom); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 170; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_4); __pyx_t_4 = 0; goto __pyx_L10; } /*else*/ {
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__Pyx_INCREF(__pyx_int_1); __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_int_1);
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__pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_m, __pyx_n_s_group); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 173; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_t_6 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_tuple__3, NULL); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 173; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __pyx_v_decimal = __pyx_t_6; __pyx_t_6 = 0; /* … */ __pyx_tuple__3 = PyTuple_Pack(1, __pyx_n_s_decimal); if (unlikely(!__pyx_tuple__3)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 173; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple__3); __Pyx_GIVEREF(__pyx_tuple__3);
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__pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_v_decimal); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 174; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) {
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__pyx_t_8 = PyObject_Length(__pyx_v_decimal); if (unlikely(__pyx_t_8 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 175; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_6 = PyInt_FromSsize_t(__Pyx_pow_Py_ssize_t(10, __pyx_t_8)); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 175; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_v_scale = __pyx_t_6; __pyx_t_6 = 0;
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__pyx_t_6 = PyNumber_Multiply(__pyx_v_numerator, __pyx_v_scale); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 176; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_t_4 = PyNumber_Int(__pyx_v_decimal); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 176; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_t_5 = PyNumber_Add(__pyx_t_6, __pyx_t_4); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 176; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_5); __pyx_t_5 = 0;
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__pyx_t_5 = PyNumber_InPlaceMultiply(__pyx_v_denominator, __pyx_v_scale); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 177; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_5); __pyx_t_5 = 0; goto __pyx_L11; } __pyx_L11:;
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__pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_m, __pyx_n_s_group); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 178; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_4 = __Pyx_PyObject_Call(__pyx_t_5, __pyx_tuple__4, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 178; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_v_exp = __pyx_t_4; __pyx_t_4 = 0; /* … */ __pyx_tuple__4 = PyTuple_Pack(1, __pyx_n_s_exp); if (unlikely(!__pyx_tuple__4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 178; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple__4); __Pyx_GIVEREF(__pyx_tuple__4);
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__pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_v_exp); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 179; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) {
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__pyx_t_4 = PyNumber_Int(__pyx_v_exp); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 180; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF_SET(__pyx_v_exp, __pyx_t_4); __pyx_t_4 = 0;
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__pyx_t_4 = PyObject_RichCompare(__pyx_v_exp, __pyx_int_0, Py_GE); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 181; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 181; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; if (__pyx_t_2) {
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__pyx_t_4 = PyNumber_Power(__pyx_int_10, __pyx_v_exp, Py_None); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 182; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_t_5 = PyNumber_InPlaceMultiply(__pyx_v_numerator, __pyx_t_4); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 182; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_5); __pyx_t_5 = 0; goto __pyx_L13; } /*else*/ {
183: else:
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__pyx_t_5 = PyNumber_Negative(__pyx_v_exp); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 184; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_4 = PyNumber_Power(__pyx_int_10, __pyx_t_5, Py_None); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 184; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_5 = PyNumber_InPlaceMultiply(__pyx_v_denominator, __pyx_t_4); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 184; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_5); __pyx_t_5 = 0; } __pyx_L13:; goto __pyx_L12; } __pyx_L12:; } __pyx_L10:;
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__pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_m, __pyx_n_s_group); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 185; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_4 = __Pyx_PyObject_Call(__pyx_t_5, __pyx_tuple__5, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 185; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_2 = (__Pyx_PyString_Equals(__pyx_t_4, __pyx_kp_s__6, Py_EQ)); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 185; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; if (__pyx_t_2) { /* … */ __pyx_tuple__5 = PyTuple_Pack(1, __pyx_n_s_sign); if (unlikely(!__pyx_tuple__5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 185; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple__5); __Pyx_GIVEREF(__pyx_tuple__5);
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__pyx_t_4 = PyNumber_Negative(__pyx_v_numerator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 186; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_4); __pyx_t_4 = 0; goto __pyx_L14; } __pyx_L14:; goto __pyx_L4; }
187: # fall through to normalisation below
188:
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__pyx_t_4 = PyTuple_New(2); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 189; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_INCREF(((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction))); PyTuple_SET_ITEM(__pyx_t_4, 0, ((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction))); __Pyx_GIVEREF(((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction))); __Pyx_INCREF(__pyx_v_10quicktions_Rational); PyTuple_SET_ITEM(__pyx_t_4, 1, __pyx_v_10quicktions_Rational); __Pyx_GIVEREF(__pyx_v_10quicktions_Rational); __pyx_t_2 = PyObject_IsInstance(__pyx_v_numerator, __pyx_t_4); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 189; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __pyx_t_1 = (__pyx_t_2 != 0); if (__pyx_t_1) {
+190: self._numerator = numerator.numerator
__pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_numerator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 190; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_GIVEREF(__pyx_t_4); __Pyx_GOTREF(__pyx_v_self->_numerator); __Pyx_DECREF(__pyx_v_self->_numerator); __pyx_v_self->_numerator = __pyx_t_4; __pyx_t_4 = 0;
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__pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_denominator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 191; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_GIVEREF(__pyx_t_4); __Pyx_GOTREF(__pyx_v_self->_denominator); __Pyx_DECREF(__pyx_v_self->_denominator); __pyx_v_self->_denominator = __pyx_t_4; __pyx_t_4 = 0;
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__pyx_r = 0;
goto __pyx_L0;
}
193:
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__pyx_t_4 = __pyx_v_10quicktions_Decimal;
__Pyx_INCREF(__pyx_t_4);
__pyx_t_1 = PyObject_IsInstance(__pyx_v_numerator, __pyx_t_4); if (unlikely(__pyx_t_1 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 194; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
__pyx_t_2 = (__pyx_t_1 != 0);
if (__pyx_t_2) {
+195: value = Fraction.from_decimal(numerator)
__pyx_t_5 = __Pyx_PyObject_GetAttrStr(((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction)), __pyx_n_s_from_decimal); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 195; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_6 = NULL; if (CYTHON_COMPILING_IN_CPYTHON && likely(PyMethod_Check(__pyx_t_5))) { __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_5); if (likely(__pyx_t_6)) { PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_5); __Pyx_INCREF(__pyx_t_6); __Pyx_INCREF(function); __Pyx_DECREF_SET(__pyx_t_5, function); } } if (!__pyx_t_6) { __pyx_t_4 = __Pyx_PyObject_CallOneArg(__pyx_t_5, __pyx_v_numerator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 195; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); } else { __pyx_t_7 = PyTuple_New(1+1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 195; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_6); __Pyx_GIVEREF(__pyx_t_6); __pyx_t_6 = NULL; __Pyx_INCREF(__pyx_v_numerator); PyTuple_SET_ITEM(__pyx_t_7, 0+1, __pyx_v_numerator); __Pyx_GIVEREF(__pyx_v_numerator); __pyx_t_4 = __Pyx_PyObject_Call(__pyx_t_5, __pyx_t_7, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 195; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; } __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; if (!(likely(((__pyx_t_4) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_4, __pyx_ptype_10quicktions_Fraction))))) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 195; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_v_value = ((struct __pyx_obj_10quicktions_Fraction *)__pyx_t_4); __pyx_t_4 = 0;
+196: self._numerator = (<Fraction>value)._numerator
__pyx_t_4 = __pyx_v_value->_numerator;
__Pyx_INCREF(__pyx_t_4);
__Pyx_GIVEREF(__pyx_t_4);
__Pyx_GOTREF(__pyx_v_self->_numerator);
__Pyx_DECREF(__pyx_v_self->_numerator);
__pyx_v_self->_numerator = __pyx_t_4;
__pyx_t_4 = 0;
+197: self._denominator = (<Fraction>value)._denominator
__pyx_t_4 = __pyx_v_value->_denominator;
__Pyx_INCREF(__pyx_t_4);
__Pyx_GIVEREF(__pyx_t_4);
__Pyx_GOTREF(__pyx_v_self->_denominator);
__Pyx_DECREF(__pyx_v_self->_denominator);
__pyx_v_self->_denominator = __pyx_t_4;
__pyx_t_4 = 0;
+198: return
__pyx_r = 0;
goto __pyx_L0;
}
/*else*/ {
199:
200: else:
+201: raise TypeError("argument should be a string "
__pyx_t_4 = __Pyx_PyObject_Call(__pyx_builtin_TypeError, __pyx_tuple__7, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 201; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_Raise(__pyx_t_4, 0, 0, 0); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; {__pyx_filename = __pyx_f[0]; __pyx_lineno = 201; __pyx_clineno = __LINE__; goto __pyx_L1_error;} } __pyx_L4:; goto __pyx_L3; } /* … */ __pyx_tuple__7 = PyTuple_Pack(1, __pyx_kp_s_argument_should_be_a_string_or_a); if (unlikely(!__pyx_tuple__7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 201; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple__7); __Pyx_GIVEREF(__pyx_tuple__7);
202: "or a Rational instance")
203:
+204: elif type(numerator) is int is type(denominator):
__pyx_t_2 = (((PyObject *)Py_TYPE(__pyx_v_numerator)) == ((PyObject *)((PyObject*)(&PyInt_Type))));
if (__pyx_t_2) {
__pyx_t_2 = (((PyObject*)(&PyInt_Type)) == ((PyObject*)((PyObject *)Py_TYPE(__pyx_v_denominator))));
}
__pyx_t_1 = (__pyx_t_2 != 0);
if (__pyx_t_1) {
goto __pyx_L3;
}
205: pass # *very* normal case
206:
+207: elif PY_MAJOR_VERSION < 3 and type(numerator) is long is type(denominator):
__pyx_t_2 = ((PY_MAJOR_VERSION < 3) != 0);
if (__pyx_t_2) {
goto __pyx_L16_next_and;
} else {
__pyx_t_1 = __pyx_t_2;
goto __pyx_L15_bool_binop_done;
}
__pyx_L16_next_and:;
__pyx_t_2 = (((PyObject *)Py_TYPE(__pyx_v_numerator)) == ((PyObject *)((PyObject*)(&PyLong_Type))));
if (__pyx_t_2) {
__pyx_t_2 = (((PyObject*)(&PyLong_Type)) == ((PyObject*)((PyObject *)Py_TYPE(__pyx_v_denominator))));
}
__pyx_t_3 = (__pyx_t_2 != 0);
__pyx_t_1 = __pyx_t_3;
__pyx_L15_bool_binop_done:;
if (__pyx_t_1) {
goto __pyx_L3;
}
208: pass # *very* normal case
209:
+210: elif type(numerator) is Fraction is type(denominator):
__pyx_t_1 = (((PyObject *)Py_TYPE(__pyx_v_numerator)) == ((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction)));
if (__pyx_t_1) {
__pyx_t_1 = (((PyObject*)__pyx_ptype_10quicktions_Fraction) == ((PyObject*)((PyObject *)Py_TYPE(__pyx_v_denominator))));
}
__pyx_t_3 = (__pyx_t_1 != 0);
if (__pyx_t_3) {
211: numerator, denominator = (
+212: (<Fraction>numerator)._numerator * (<Fraction>denominator)._denominator,
__pyx_t_4 = PyNumber_Multiply(((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_numerator)->_numerator, ((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_denominator)->_denominator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 212; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4);
+213: (<Fraction>denominator)._numerator * (<Fraction>numerator)._denominator
__pyx_t_5 = PyNumber_Multiply(((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_denominator)->_numerator, ((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_numerator)->_denominator); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 213; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_4); __pyx_t_4 = 0; __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_5); __pyx_t_5 = 0; goto __pyx_L3; }
214: )
215:
+216: elif (isinstance(numerator, (Fraction, Rational)) and
__pyx_t_5 = PyTuple_New(2); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 216; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_INCREF(((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction))); PyTuple_SET_ITEM(__pyx_t_5, 0, ((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction))); __Pyx_GIVEREF(((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction))); __Pyx_INCREF(__pyx_v_10quicktions_Rational); PyTuple_SET_ITEM(__pyx_t_5, 1, __pyx_v_10quicktions_Rational); __Pyx_GIVEREF(__pyx_v_10quicktions_Rational); __pyx_t_1 = PyObject_IsInstance(__pyx_v_numerator, __pyx_t_5); if (unlikely(__pyx_t_1 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 216; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_2 = (__pyx_t_1 != 0); if (__pyx_t_2) { goto __pyx_L18_next_and; } else { __pyx_t_3 = __pyx_t_2; goto __pyx_L17_bool_binop_done; } __pyx_L18_next_and:;
+217: isinstance(denominator, (Fraction, Rational))):
__pyx_t_5 = PyTuple_New(2); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 217; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_INCREF(((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction))); PyTuple_SET_ITEM(__pyx_t_5, 0, ((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction))); __Pyx_GIVEREF(((PyObject *)((PyObject*)__pyx_ptype_10quicktions_Fraction))); __Pyx_INCREF(__pyx_v_10quicktions_Rational); PyTuple_SET_ITEM(__pyx_t_5, 1, __pyx_v_10quicktions_Rational); __Pyx_GIVEREF(__pyx_v_10quicktions_Rational); __pyx_t_2 = PyObject_IsInstance(__pyx_v_denominator, __pyx_t_5); if (unlikely(__pyx_t_2 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 217; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_1 = (__pyx_t_2 != 0); __pyx_t_3 = __pyx_t_1; __pyx_L17_bool_binop_done:; if (__pyx_t_3) {
218: numerator, denominator = (
+219: numerator.numerator * denominator.denominator,
__pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_numerator); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 219; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_denominator, __pyx_n_s_denominator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 219; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_t_7 = PyNumber_Multiply(__pyx_t_5, __pyx_t_4); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 219; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
+220: denominator.numerator * numerator.denominator
__pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_denominator, __pyx_n_s_numerator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 220; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_denominator); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 220; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_6 = PyNumber_Multiply(__pyx_t_4, __pyx_t_5); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 220; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_7); __pyx_t_7 = 0; __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_6); __pyx_t_6 = 0; goto __pyx_L3; } /*else*/ {
221: )
222:
223: else:
+224: raise TypeError("both arguments should be "
__pyx_t_6 = __Pyx_PyObject_Call(__pyx_builtin_TypeError, __pyx_tuple__8, NULL); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 224; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_Raise(__pyx_t_6, 0, 0, 0); __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; {__pyx_filename = __pyx_f[0]; __pyx_lineno = 224; __pyx_clineno = __LINE__; goto __pyx_L1_error;} } __pyx_L3:; /* … */ __pyx_tuple__8 = PyTuple_Pack(1, __pyx_kp_s_both_arguments_should_be_Rationa); if (unlikely(!__pyx_tuple__8)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 224; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple__8); __Pyx_GIVEREF(__pyx_tuple__8);
225: "Rational instances")
226:
+227: if denominator == 0:
__pyx_t_6 = PyObject_RichCompare(__pyx_v_denominator, __pyx_int_0, Py_EQ); __Pyx_XGOTREF(__pyx_t_6); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 227; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_3 = __Pyx_PyObject_IsTrue(__pyx_t_6); if (unlikely(__pyx_t_3 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 227; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; if (__pyx_t_3) {
+228: raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
__pyx_t_6 = __Pyx_PyString_Format(__pyx_kp_s_Fraction_s_0, __pyx_v_numerator); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 228; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_t_7 = PyTuple_New(1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 228; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_6); __Pyx_GIVEREF(__pyx_t_6); __pyx_t_6 = 0; __pyx_t_6 = __Pyx_PyObject_Call(__pyx_builtin_ZeroDivisionError, __pyx_t_7, NULL); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 228; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; __Pyx_Raise(__pyx_t_6, 0, 0, 0); __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; {__pyx_filename = __pyx_f[0]; __pyx_lineno = 228; __pyx_clineno = __LINE__; goto __pyx_L1_error;} }
+229: if _normalize:
__pyx_t_3 = (__pyx_v__normalize != 0);
if (__pyx_t_3) {
+230: g = _gcd(numerator, denominator)
__pyx_t_6 = __pyx_f_10quicktions__gcd(__pyx_v_numerator, __pyx_v_denominator, 0); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 230; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_v_g = __pyx_t_6; __pyx_t_6 = 0;
231: # NOTE: 'is' tests on integers are generally a bad idea, but
232: # they are fast and if they fail here, it'll still be correct
+233: if denominator < 0:
__pyx_t_6 = PyObject_RichCompare(__pyx_v_denominator, __pyx_int_0, Py_LT); __Pyx_XGOTREF(__pyx_t_6); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 233; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_3 = __Pyx_PyObject_IsTrue(__pyx_t_6); if (unlikely(__pyx_t_3 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 233; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; if (__pyx_t_3) {
+234: if g is 1:
__pyx_t_3 = (__pyx_v_g == __pyx_int_1);
__pyx_t_1 = (__pyx_t_3 != 0);
if (__pyx_t_1) {
+235: numerator = -numerator
__pyx_t_6 = PyNumber_Negative(__pyx_v_numerator); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 235; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_6); __pyx_t_6 = 0;
+236: denominator = -denominator
__pyx_t_6 = PyNumber_Negative(__pyx_v_denominator); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 236; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_6); __pyx_t_6 = 0; goto __pyx_L22; } /*else*/ {
237: else:
+238: g = -g
__pyx_t_6 = PyNumber_Negative(__pyx_v_g); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 238; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF_SET(__pyx_v_g, __pyx_t_6); __pyx_t_6 = 0; } __pyx_L22:; goto __pyx_L21; } __pyx_L21:;
+239: if g is not 1:
__pyx_t_1 = (__pyx_v_g != __pyx_int_1);
__pyx_t_3 = (__pyx_t_1 != 0);
if (__pyx_t_3) {
+240: numerator //= g
__pyx_t_6 = PyNumber_InPlaceFloorDivide(__pyx_v_numerator, __pyx_v_g); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 240; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_6); __pyx_t_6 = 0;
+241: denominator //= g
__pyx_t_6 = PyNumber_InPlaceFloorDivide(__pyx_v_denominator, __pyx_v_g); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 241; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_6); __pyx_t_6 = 0; goto __pyx_L23; } __pyx_L23:; goto __pyx_L20; } __pyx_L20:;
+242: self._numerator = numerator
__Pyx_INCREF(__pyx_v_numerator); __Pyx_GIVEREF(__pyx_v_numerator); __Pyx_GOTREF(__pyx_v_self->_numerator); __Pyx_DECREF(__pyx_v_self->_numerator); __pyx_v_self->_numerator = __pyx_v_numerator;
+243: self._denominator = denominator
__Pyx_INCREF(__pyx_v_denominator); __Pyx_GIVEREF(__pyx_v_denominator); __Pyx_GOTREF(__pyx_v_self->_denominator); __Pyx_DECREF(__pyx_v_self->_denominator); __pyx_v_self->_denominator = __pyx_v_denominator;
244:
+245: @classmethod
__pyx_t_2 = __Pyx_Method_ClassMethod(__pyx_t_8); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 245; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_2); __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0; if (PyDict_SetItem((PyObject *)__pyx_ptype_10quicktions_Fraction->tp_dict, __pyx_n_s_from_float, __pyx_t_2) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 246; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0; PyType_Modified(__pyx_ptype_10quicktions_Fraction);
+246: def from_float(cls, f):
/* Python wrapper */
static PyObject *__pyx_pw_10quicktions_8Fraction_3from_float(PyObject *__pyx_v_cls, PyObject *__pyx_v_f); /*proto*/
static char __pyx_doc_10quicktions_8Fraction_2from_float[] = "Converts a finite float to a rational number, exactly.\n\n Beware that Fraction.from_float(0.3) != Fraction(3, 10).\n\n ";
static PyObject *__pyx_pw_10quicktions_8Fraction_3from_float(PyObject *__pyx_v_cls, PyObject *__pyx_v_f) {
PyObject *__pyx_r = 0;
__Pyx_RefNannyDeclarations
__Pyx_RefNannySetupContext("from_float (wrapper)", 0);
__pyx_r = __pyx_pf_10quicktions_8Fraction_2from_float(((PyObject*)__pyx_v_cls), ((PyObject *)__pyx_v_f));
/* function exit code */
__Pyx_RefNannyFinishContext();
return __pyx_r;
}
static PyObject *__pyx_pf_10quicktions_8Fraction_2from_float(PyObject *__pyx_v_cls, PyObject *__pyx_v_f) {
PyObject *__pyx_r = NULL;
__Pyx_TraceDeclarations
__Pyx_RefNannyDeclarations
__Pyx_RefNannySetupContext("from_float", 0);
__Pyx_TraceCall("from_float", __pyx_f[0], 246);
/* … */
/* function exit code */
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__pyx_t_7 = __Pyx_PyObject_GetAttrStr(__pyx_v_dec, __pyx_n_s_is_infinite); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 272; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __pyx_t_1 = NULL; if (CYTHON_COMPILING_IN_CPYTHON && likely(PyMethod_Check(__pyx_t_7))) { __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_7); if (likely(__pyx_t_1)) { PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_7); __Pyx_INCREF(__pyx_t_1); __Pyx_INCREF(function); __Pyx_DECREF_SET(__pyx_t_7, function); } } if (__pyx_t_1) { __pyx_t_5 = __Pyx_PyObject_CallOneArg(__pyx_t_7, __pyx_t_1); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 272; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; } else { __pyx_t_5 = __Pyx_PyObject_CallNoArg(__pyx_t_7); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 272; __pyx_clineno = __LINE__; goto __pyx_L1_error;} } __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; __pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_t_5); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 272; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; if (__pyx_t_2) {
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__pyx_t_7 = PyTuple_New(1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 273; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_5); __Pyx_GIVEREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_5 = __Pyx_PyObject_Call(__pyx_builtin_OverflowError, __pyx_t_7, NULL); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 273; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; __Pyx_Raise(__pyx_t_5, 0, 0, 0); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; {__pyx_filename = __pyx_f[0]; __pyx_lineno = 273; __pyx_clineno = __LINE__; goto __pyx_L1_error;} }
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__pyx_t_5 = __Pyx_PyObject_GetAttrStr(((PyObject *)__pyx_v_cls), __pyx_n_s_name); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 276; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_7 = PyTuple_New(2); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 276; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_INCREF(__pyx_v_dec); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_v_dec); __Pyx_GIVEREF(__pyx_v_dec); PyTuple_SET_ITEM(__pyx_t_7, 1, __pyx_t_5); __Pyx_GIVEREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_5 = __Pyx_PyString_Format(__pyx_kp_s_Cannot_convert_s_to_s, __pyx_t_7); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 276; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; __pyx_t_7 = PyTuple_New(1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 276; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_5); __Pyx_GIVEREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_5 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_t_7, NULL); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 276; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; __Pyx_Raise(__pyx_t_5, 0, 0, 0); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; {__pyx_filename = __pyx_f[0]; __pyx_lineno = 276; __pyx_clineno = __LINE__; goto __pyx_L1_error;} }
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__pyx_t_7 = __Pyx_PyObject_GetAttrStr(__pyx_v_dec, __pyx_n_s_as_tuple); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __pyx_t_1 = NULL; if (CYTHON_COMPILING_IN_CPYTHON && likely(PyMethod_Check(__pyx_t_7))) { __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_7); if (likely(__pyx_t_1)) { PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_7); __Pyx_INCREF(__pyx_t_1); __Pyx_INCREF(function); __Pyx_DECREF_SET(__pyx_t_7, function); } } if (__pyx_t_1) { __pyx_t_5 = __Pyx_PyObject_CallOneArg(__pyx_t_7, __pyx_t_1); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; } else { __pyx_t_5 = __Pyx_PyObject_CallNoArg(__pyx_t_7); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} } __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; if ((likely(PyTuple_CheckExact(__pyx_t_5))) || (PyList_CheckExact(__pyx_t_5))) { PyObject* sequence = __pyx_t_5; #if CYTHON_COMPILING_IN_CPYTHON Py_ssize_t size = Py_SIZE(sequence); #else Py_ssize_t size = PySequence_Size(sequence); #endif if (unlikely(size != 3)) { if (size > 3) __Pyx_RaiseTooManyValuesError(3); else if (size >= 0) __Pyx_RaiseNeedMoreValuesError(size); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} } #if CYTHON_COMPILING_IN_CPYTHON if (likely(PyTuple_CheckExact(sequence))) { __pyx_t_7 = PyTuple_GET_ITEM(sequence, 0); __pyx_t_1 = PyTuple_GET_ITEM(sequence, 1); __pyx_t_4 = PyTuple_GET_ITEM(sequence, 2); } else { __pyx_t_7 = PyList_GET_ITEM(sequence, 0); __pyx_t_1 = PyList_GET_ITEM(sequence, 1); __pyx_t_4 = PyList_GET_ITEM(sequence, 2); } __Pyx_INCREF(__pyx_t_7); __Pyx_INCREF(__pyx_t_1); __Pyx_INCREF(__pyx_t_4); #else __pyx_t_7 = PySequence_ITEM(sequence, 0); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __pyx_t_1 = PySequence_ITEM(sequence, 1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __pyx_t_4 = PySequence_ITEM(sequence, 2); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); #endif __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; } else { Py_ssize_t index = -1; __pyx_t_6 = PyObject_GetIter(__pyx_t_5); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_8 = Py_TYPE(__pyx_t_6)->tp_iternext; index = 0; __pyx_t_7 = __pyx_t_8(__pyx_t_6); if (unlikely(!__pyx_t_7)) goto __pyx_L6_unpacking_failed; __Pyx_GOTREF(__pyx_t_7); index = 1; __pyx_t_1 = __pyx_t_8(__pyx_t_6); if (unlikely(!__pyx_t_1)) goto __pyx_L6_unpacking_failed; __Pyx_GOTREF(__pyx_t_1); index = 2; __pyx_t_4 = __pyx_t_8(__pyx_t_6); if (unlikely(!__pyx_t_4)) goto __pyx_L6_unpacking_failed; __Pyx_GOTREF(__pyx_t_4); if (__Pyx_IternextUnpackEndCheck(__pyx_t_8(__pyx_t_6), 3) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_8 = NULL; __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; goto __pyx_L7_unpacking_done; __pyx_L6_unpacking_failed:; __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __pyx_t_8 = NULL; if (__Pyx_IterFinish() == 0) __Pyx_RaiseNeedMoreValuesError(index); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 277; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_L7_unpacking_done:; } __pyx_v_sign = __pyx_t_7; __pyx_t_7 = 0; __pyx_v_digits = __pyx_t_1; __pyx_t_1 = 0; __pyx_v_exp = __pyx_t_4; __pyx_t_4 = 0;
+278: digits = int(''.join(map(str, digits)))
__pyx_t_5 = PyTuple_New(2); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 278; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_INCREF(((PyObject *)((PyObject*)(&PyString_Type)))); PyTuple_SET_ITEM(__pyx_t_5, 0, ((PyObject *)((PyObject*)(&PyString_Type)))); __Pyx_GIVEREF(((PyObject *)((PyObject*)(&PyString_Type)))); __Pyx_INCREF(__pyx_v_digits); PyTuple_SET_ITEM(__pyx_t_5, 1, __pyx_v_digits); __Pyx_GIVEREF(__pyx_v_digits); __pyx_t_4 = __Pyx_PyObject_Call(__pyx_builtin_map, __pyx_t_5, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 278; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_5 = __Pyx_PyString_Join(__pyx_kp_s__9, __pyx_t_4); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 278; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __pyx_t_4 = PyNumber_Int(__pyx_t_5); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 278; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __Pyx_DECREF_SET(__pyx_v_digits, __pyx_t_4); __pyx_t_4 = 0;
+279: if sign:
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287: """Closest Fraction to self with denominator at most max_denominator.
288:
289: >>> Fraction('3.141592653589793').limit_denominator(10)
290: Fraction(22, 7)
291: >>> Fraction('3.141592653589793').limit_denominator(100)
292: Fraction(311, 99)
293: >>> Fraction(4321, 8765).limit_denominator(10000)
294: Fraction(4321, 8765)
295:
296: """
297: # Algorithm notes: For any real number x, define a *best upper
298: # approximation* to x to be a rational number p/q such that:
299: #
300: # (1) p/q >= x, and
301: # (2) if p/q > r/s >= x then s > q, for any rational r/s.
302: #
303: # Define *best lower approximation* similarly. Then it can be
304: # proved that a rational number is a best upper or lower
305: # approximation to x if, and only if, it is a convergent or
306: # semiconvergent of the (unique shortest) continued fraction
307: # associated to x.
308: #
309: # To find a best rational approximation with denominator <= M,
310: # we find the best upper and lower approximations with
311: # denominator <= M and take whichever of these is closer to x.
312: # In the event of a tie, the bound with smaller denominator is
313: # chosen. If both denominators are equal (which can happen
314: # only when max_denominator == 1 and self is midway between
315: # two integers) the lower bound---i.e., the floor of self, is
316: # taken.
317:
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322:
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332:
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407: """a ** b
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657: else:
658: # A fractional power will generally produce an
659: # irrational number.
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664:
665:
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668:
669:
670: """
671: In general, we want to implement the arithmetic operations so
672: that mixed-mode operations either call an implementation whose
673: author knew about the types of both arguments, or convert both
674: to the nearest built in type and do the operation there. In
675: Fraction, that means that we define __add__ and __radd__ as:
676:
677: def __add__(self, other):
678: # Both types have numerators/denominator attributes,
679: # so do the operation directly
680: if isinstance(other, (int, Fraction)):
681: return Fraction(self.numerator * other.denominator +
682: other.numerator * self.denominator,
683: self.denominator * other.denominator)
684: # float and complex don't have those operations, but we
685: # know about those types, so special case them.
686: elif isinstance(other, float):
687: return float(self) + other
688: elif isinstance(other, complex):
689: return complex(self) + other
690: # Let the other type take over.
691: return NotImplemented
692:
693: def __radd__(self, other):
694: # radd handles more types than add because there's
695: # nothing left to fall back to.
696: if isinstance(other, Rational):
697: return Fraction(self.numerator * other.denominator +
698: other.numerator * self.denominator,
699: self.denominator * other.denominator)
700: elif isinstance(other, Real):
701: return float(other) + float(self)
702: elif isinstance(other, Complex):
703: return complex(other) + complex(self)
704: return NotImplemented
705:
706:
707: There are 5 different cases for a mixed-type addition on
708: Fraction. I'll refer to all of the above code that doesn't
709: refer to Fraction, float, or complex as "boilerplate". 'r'
710: will be an instance of Fraction, which is a subtype of
711: Rational (r : Fraction <: Rational), and b : B <:
712: Complex. The first three involve 'r + b':
713:
714: 1. If B <: Fraction, int, float, or complex, we handle
715: that specially, and all is well.
716: 2. If Fraction falls back to the boilerplate code, and it
717: were to return a value from __add__, we'd miss the
718: possibility that B defines a more intelligent __radd__,
719: so the boilerplate should return NotImplemented from
720: __add__. In particular, we don't handle Rational
721: here, even though we could get an exact answer, in case
722: the other type wants to do something special.
723: 3. If B <: Fraction, Python tries B.__radd__ before
724: Fraction.__add__. This is ok, because it was
725: implemented with knowledge of Fraction, so it can
726: handle those instances before delegating to Real or
727: Complex.
728:
729: The next two situations describe 'b + r'. We assume that b
730: didn't know about Fraction in its implementation, and that it
731: uses similar boilerplate code:
732:
733: 4. If B <: Rational, then __radd_ converts both to the
734: builtin rational type (hey look, that's us) and
735: proceeds.
736: 5. Otherwise, __radd__ tries to find the nearest common
737: base ABC, and fall back to its builtin type. Since this
738: class doesn't subclass a concrete type, there's no
739: implementation to fall back to, so we need to try as
740: hard as possible to return an actual value, or the user
741: will get a TypeError.
742: """
743:
744:
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750: """a - b"""
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752:
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