Generated by Cython 0.21
Raw output: quicktions.c
001: # cython: language_level=3, 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
020:
021:
+022: __all__ = ['Fraction']
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023:
+024: __version__ = '0.1'
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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 object Rational, Decimal, math, numbers, sys, re, operator
031:
+032: from numbers import Rational
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+033: from decimal import Decimal
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+034: import math
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+035: import numbers
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+036: import operator
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+037: import re
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+038: import sys
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039:
040:
+041: cpdef _gcd(a, b):
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042: """Calculate the Greatest Common Divisor of a and b.
043:
044: Unless b == 0, the result will have the same sign as b (so that when
045: b is divided by it, the result comes out positive).
046: """
047: # Try doing all computation in C space. If the numbers are too
048: # large at the beginning, retry after each iteration until they
049: # are small enough.
050: cdef long long ai, bi
+051: while b:
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056: else:
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062:
063:
064: # Constants related to the hash implementation; hash(x) is based
065: # on the reduction of x modulo the prime _PyHASH_MODULUS.
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073:
074:
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PyObject_HEAD
struct __pyx_vtabstruct_10quicktions_Fraction *__pyx_vtab;
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PyObject *(*_eq)(struct __pyx_obj_10quicktions_Fraction *, PyObject *);
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100: """A Rational number.
101:
102: Takes a string like '3/2' or '1.5', another Rational instance, a
103: numerator/denominator pair, or a float.
104:
105: Examples
106: --------
107:
108: >>> Fraction(10, -8)
109: Fraction(-5, 4)
110: >>> Fraction(Fraction(1, 7), 5)
111: Fraction(1, 35)
112: >>> Fraction(Fraction(1, 7), Fraction(2, 3))
113: Fraction(3, 14)
114: >>> Fraction('314')
115: Fraction(314, 1)
116: >>> Fraction('-35/4')
117: Fraction(-35, 4)
118: >>> Fraction('3.1415') # conversion from numeric string
119: Fraction(6283, 2000)
120: >>> Fraction('-47e-2') # string may include a decimal exponent
121: Fraction(-47, 100)
122: >>> Fraction(1.47) # direct construction from float (exact conversion)
123: Fraction(6620291452234629, 4503599627370496)
124: >>> Fraction(2.25)
125: Fraction(9, 4)
126: >>> from decimal import Decimal
127: >>> Fraction(Decimal('1.47'))
128: Fraction(147, 100)
129:
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155: # Handle construction from strings.
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__Pyx_INCREF(__pyx_v_10quicktions__parse_rational); __pyx_t_5 = __pyx_v_10quicktions__parse_rational; __pyx_t_7 = NULL; if (CYTHON_COMPILING_IN_CPYTHON && unlikely(PyMethod_Check(__pyx_t_5))) { __pyx_t_7 = PyMethod_GET_SELF(__pyx_t_5); if (likely(__pyx_t_7)) { PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_5); __Pyx_INCREF(__pyx_t_7); __Pyx_INCREF(function); __Pyx_DECREF_SET(__pyx_t_5, function); } } if (!__pyx_t_7) { __pyx_t_4 = __Pyx_PyObject_CallOneArg(__pyx_t_5, __pyx_v_numerator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 156; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); } else { __pyx_t_6 = PyTuple_New(1+1); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 156; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_7); __Pyx_GIVEREF(__pyx_t_7); __pyx_t_7 = NULL; __Pyx_INCREF(__pyx_v_numerator); PyTuple_SET_ITEM(__pyx_t_6, 0+1, __pyx_v_numerator); __Pyx_GIVEREF(__pyx_v_numerator); __pyx_t_4 = __Pyx_PyObject_Call(__pyx_t_5, __pyx_t_6, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 156; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; } __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_v_m = __pyx_t_4; __pyx_t_4 = 0;
+157: if m is None:
__pyx_t_1 = (__pyx_v_m == Py_None);
__pyx_t_2 = (__pyx_t_1 != 0);
if (__pyx_t_2) {
+158: raise ValueError('Invalid literal for Fraction: %r' %
__pyx_t_4 = PyUnicode_Format(__pyx_kp_u_Invalid_literal_for_Fraction_r, __pyx_v_numerator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 158; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_t_5 = PyTuple_New(1); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 158; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_4); __Pyx_GIVEREF(__pyx_t_4); __pyx_t_4 = 0; __pyx_t_4 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_t_5, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 158; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __Pyx_Raise(__pyx_t_4, 0, 0, 0); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; {__pyx_filename = __pyx_f[0]; __pyx_lineno = 158; __pyx_clineno = __LINE__; goto __pyx_L1_error;} }
159: 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 = 160; __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 = 160; __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 = 160; __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_u_0); __pyx_t_4 = __pyx_kp_u_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 = 160; __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_u_num); if (unlikely(!__pyx_tuple_)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 160; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple_); __Pyx_GIVEREF(__pyx_tuple_);
+161: denom = m.group('denom')
__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 = 161; __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 = 161; __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_u_denom); if (unlikely(!__pyx_tuple__2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 161; __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 = 162; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) {
+163: denominator = int(denom)
__pyx_t_4 = PyNumber_Int(__pyx_v_denom); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 163; __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*/ {
164: 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 = 166; __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 = 166; __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_u_decimal); if (unlikely(!__pyx_tuple__3)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 166; __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 = 167; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) {
+168: scale = 10**len(decimal)
__pyx_t_8 = PyObject_Length(__pyx_v_decimal); if (unlikely(__pyx_t_8 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 168; __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 = 168; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_v_scale = __pyx_t_6; __pyx_t_6 = 0;
+169: numerator = numerator * scale + int(decimal)
__pyx_t_6 = PyNumber_Multiply(__pyx_v_numerator, __pyx_v_scale); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 169; __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 = 169; __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 = 169; __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;
+170: denominator *= scale
__pyx_t_5 = PyNumber_InPlaceMultiply(__pyx_v_denominator, __pyx_v_scale); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 170; __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 = 171; __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 = 171; __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_u_exp); if (unlikely(!__pyx_tuple__4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 171; __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 = 172; __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 = 173; __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 = 174; __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 = 174; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; if (__pyx_t_2) {
+175: numerator *= 10**exp
__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 = 175; __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 = 175; __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*/ {
176: 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 = 177; __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 = 177; __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 = 177; __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 = 178; __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 = 178; __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_PyUnicode_Equals(__pyx_t_4, __pyx_kp_u__6, Py_EQ)); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 178; __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_u_sign); if (unlikely(!__pyx_tuple__5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 178; __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 = 179; __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; }
180: # fall through to normalisation below
181:
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__pyx_t_4 = PyTuple_New(2); 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_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 = 182; __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) {
+183: 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 = 183; __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;
+184: self._denominator = numerator.denominator
__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 = 184; __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;
}
186:
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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 = 187; __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) {
+188: 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 = 188; __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 = 188; __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 = 188; __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 = 188; __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 = 188; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_v_value = ((struct __pyx_obj_10quicktions_Fraction *)__pyx_t_4); __pyx_t_4 = 0;
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__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);
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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;
}
/*else*/ {
192:
193: else:
+194: 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 = 194; __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 = 194; __pyx_clineno = __LINE__; goto __pyx_L1_error;} } __pyx_L4:; goto __pyx_L3; } /* … */ __pyx_tuple__7 = PyTuple_Pack(1, __pyx_kp_u_argument_should_be_a_string_or_a); if (unlikely(!__pyx_tuple__7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 194; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple__7); __Pyx_GIVEREF(__pyx_tuple__7);
195: "or a Rational instance")
196:
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__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;
}
198: pass # *very* normal case
199:
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__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;
}
201: pass # *very* normal case
202:
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__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) {
204: numerator, denominator = (
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+206: (<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 = 206; __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; }
207: )
208:
+209: elif (isinstance(numerator, (Fraction, Rational)) and
__pyx_t_5 = PyTuple_New(2); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 209; __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 = 209; __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:;
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__pyx_t_5 = PyTuple_New(2); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 210; __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 = 210; __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) {
211: numerator, denominator = (
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__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 = 212; __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 = 212; __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 = 212; __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;
+213: 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 = 213; __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 = 213; __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 = 213; __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*/ {
214: )
215:
216: else:
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__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 = 217; __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 = 217; __pyx_clineno = __LINE__; goto __pyx_L1_error;} } __pyx_L3:; /* … */ __pyx_tuple__8 = PyTuple_Pack(1, __pyx_kp_u_both_arguments_should_be_Rationa); if (unlikely(!__pyx_tuple__8)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 217; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple__8); __Pyx_GIVEREF(__pyx_tuple__8);
218: "Rational instances")
219:
+220: 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 = 220; __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 = 220; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; if (__pyx_t_3) {
+221: raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
__pyx_t_6 = PyUnicode_Format(__pyx_kp_u_Fraction_s_0, __pyx_v_numerator); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 221; __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 = 221; __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 = 221; __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 = 221; __pyx_clineno = __LINE__; goto __pyx_L1_error;} }
+222: if _normalize:
__pyx_t_3 = __Pyx_PyObject_IsTrue(__pyx_v__normalize); if (unlikely(__pyx_t_3 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 222; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_3) {
+223: 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 = 223; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_v_g = __pyx_t_6; __pyx_t_6 = 0;
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+225: 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 = 225; __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_L20; } __pyx_L20:;
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__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;
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__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;
228:
+229: @classmethod
__pyx_t_2 = __Pyx_Method_ClassMethod(__pyx_t_8); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 229; __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 = 230; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0; PyType_Modified(__pyx_ptype_10quicktions_Fraction);
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/* 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) {
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__Pyx_RefNannySetupContext("from_float (wrapper)", 0);
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__Pyx_RefNannyDeclarations
__Pyx_RefNannySetupContext("from_float", 0);
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/* function exit code */
__pyx_L1_error:;
__Pyx_XDECREF(__pyx_t_1);
__Pyx_XDECREF(__pyx_t_4);
__Pyx_XDECREF(__pyx_t_5);
__Pyx_XDECREF(__pyx_t_6);
__Pyx_AddTraceback("quicktions.Fraction.from_float", __pyx_clineno, __pyx_lineno, __pyx_filename);
__pyx_r = NULL;
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__Pyx_XGIVEREF(__pyx_r);
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/* … */
__pyx_t_8 = __Pyx_GetNameInClass((PyObject *)__pyx_ptype_10quicktions_Fraction, __pyx_n_s_from_float); if (unlikely(!__pyx_t_8)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 230; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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231: """Converts a finite float to a rational number, exactly.
232:
233: Beware that Fraction.from_float(0.3) != Fraction(3, 10).
234:
235: """
+236: if isinstance(f, numbers.Integral):
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__pyx_t_4 = PyNumber_Int(__pyx_v_dec); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 251; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_INCREF(__pyx_v_10quicktions_Decimal); __pyx_t_5 = __pyx_v_10quicktions_Decimal; __pyx_t_6 = NULL; if (CYTHON_COMPILING_IN_CPYTHON && unlikely(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_1 = __Pyx_PyObject_CallOneArg(__pyx_t_5, __pyx_t_4); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 251; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __Pyx_GOTREF(__pyx_t_1); } else { __pyx_t_7 = PyTuple_New(1+1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 251; __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; PyTuple_SET_ITEM(__pyx_t_7, 0+1, __pyx_t_4); __Pyx_GIVEREF(__pyx_t_4); __pyx_t_4 = 0; __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_5, __pyx_t_7, NULL); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 251; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_1); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; } __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __Pyx_DECREF_SET(__pyx_v_dec, __pyx_t_1); __pyx_t_1 = 0; goto __pyx_L3; }
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__pyx_t_1 = __pyx_v_10quicktions_Decimal; __Pyx_INCREF(__pyx_t_1); __pyx_t_3 = PyObject_IsInstance(__pyx_v_dec, __pyx_t_1); if (unlikely(__pyx_t_3 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 252; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; __pyx_t_2 = ((!(__pyx_t_3 != 0)) != 0); if (__pyx_t_2) {
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+254: "%s.from_decimal() only takes Decimals, not %r (%s)" %
__pyx_t_5 = PyUnicode_Format(__pyx_kp_u_s_from_decimal_only_takes_Decim, __pyx_t_7); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 254; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
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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 = 256; __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 = 256; __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 = 256; __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 = 256; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; if (__pyx_t_2) {
+257: raise OverflowError(
__pyx_t_7 = PyTuple_New(1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 257; __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 = 257; __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 = 257; __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 = 258; __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 = 258; __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 = PyUnicode_Format(__pyx_kp_u_Cannot_convert_s_to_s, __pyx_t_7); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 258; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
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__pyx_t_7 = __Pyx_PyObject_GetAttrStr(__pyx_v_dec, __pyx_n_s_is_nan); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 259; __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 = 259; __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 = 259; __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 = 259; __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_5 = __Pyx_PyObject_GetAttrStr(((PyObject *)__pyx_v_cls), __pyx_n_s_name); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 260; __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 = 260; __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 = PyUnicode_Format(__pyx_kp_u_Cannot_convert_s_to_s, __pyx_t_7); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 260; __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 = 260; __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 = 260; __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 = 260; __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 = 261; __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 = 261; __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 = 261; __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 = 261; __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 = 261; __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 = 261; __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 = 261; __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 = 261; __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 = 261; __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 = 261; __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;
+262: digits = int(''.join(map(str, digits)))
__pyx_t_5 = PyTuple_New(2); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 262; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_INCREF(((PyObject *)((PyObject*)(&PyUnicode_Type)))); PyTuple_SET_ITEM(__pyx_t_5, 0, ((PyObject *)((PyObject*)(&PyUnicode_Type)))); __Pyx_GIVEREF(((PyObject *)((PyObject*)(&PyUnicode_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 = 262; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_5 = PyUnicode_Join(__pyx_kp_u__9, __pyx_t_4); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 262; __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 = 262; __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;
+263: if sign:
__pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_v_sign); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 263; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) {
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269:
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static char __pyx_doc_10quicktions_8Fraction_6limit_denominator[] = "Closest Fraction to self with denominator at most max_denominator.\n\n >>> Fraction('3.141592653589793').limit_denominator(10)\n Fraction(22, 7)\n >>> Fraction('3.141592653589793').limit_denominator(100)\n Fraction(311, 99)\n >>> Fraction(4321, 8765).limit_denominator(10000)\n Fraction(4321, 8765)\n\n ";
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271: """Closest Fraction to self with denominator at most max_denominator.
272:
273: >>> Fraction('3.141592653589793').limit_denominator(10)
274: Fraction(22, 7)
275: >>> Fraction('3.141592653589793').limit_denominator(100)
276: Fraction(311, 99)
277: >>> Fraction(4321, 8765).limit_denominator(10000)
278: Fraction(4321, 8765)
279:
280: """
281: # Algorithm notes: For any real number x, define a *best upper
282: # approximation* to x to be a rational number p/q such that:
283: #
284: # (1) p/q >= x, and
285: # (2) if p/q > r/s >= x then s > q, for any rational r/s.
286: #
287: # Define *best lower approximation* similarly. Then it can be
288: # proved that a rational number is a best upper or lower
289: # approximation to x if, and only if, it is a convergent or
290: # semiconvergent of the (unique shortest) continued fraction
291: # associated to x.
292: #
293: # To find a best rational approximation with denominator <= M,
294: # we find the best upper and lower approximations with
295: # denominator <= M and take whichever of these is closer to x.
296: # In the event of a tie, the bound with smaller denominator is
297: # chosen. If both denominators are equal (which can happen
298: # only when max_denominator == 1 and self is midway between
299: # two integers) the lower bound---i.e., the floor of self, is
300: # taken.
301:
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306:
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316:
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629:
630:
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641: else:
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643: # irrational number.
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645:
646:
647: """
648: In general, we want to implement the arithmetic operations so
649: that mixed-mode operations either call an implementation whose
650: author knew about the types of both arguments, or convert both
651: to the nearest built in type and do the operation there. In
652: Fraction, that means that we define __add__ and __radd__ as:
653:
654: def __add__(self, other):
655: # Both types have numerators/denominator attributes,
656: # so do the operation directly
657: if isinstance(other, (int, Fraction)):
658: return Fraction(self.numerator * other.denominator +
659: other.numerator * self.denominator,
660: self.denominator * other.denominator)
661: # float and complex don't have those operations, but we
662: # know about those types, so special case them.
663: elif isinstance(other, float):
664: return float(self) + other
665: elif isinstance(other, complex):
666: return complex(self) + other
667: # Let the other type take over.
668: return NotImplemented
669:
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671: # radd handles more types than add because there's
672: # nothing left to fall back to.
673: if isinstance(other, Rational):
674: return Fraction(self.numerator * other.denominator +
675: other.numerator * self.denominator,
676: self.denominator * other.denominator)
677: elif isinstance(other, Real):
678: return float(other) + float(self)
679: elif isinstance(other, Complex):
680: return complex(other) + complex(self)
681: return NotImplemented
682:
683:
684: There are 5 different cases for a mixed-type addition on
685: Fraction. I'll refer to all of the above code that doesn't
686: refer to Fraction, float, or complex as "boilerplate". 'r'
687: will be an instance of Fraction, which is a subtype of
688: Rational (r : Fraction <: Rational), and b : B <:
689: Complex. The first three involve 'r + b':
690:
691: 1. If B <: Fraction, int, float, or complex, we handle
692: that specially, and all is well.
693: 2. If Fraction falls back to the boilerplate code, and it
694: were to return a value from __add__, we'd miss the
695: possibility that B defines a more intelligent __radd__,
696: so the boilerplate should return NotImplemented from
697: __add__. In particular, we don't handle Rational
698: here, even though we could get an exact answer, in case
699: the other type wants to do something special.
700: 3. If B <: Fraction, Python tries B.__radd__ before
701: Fraction.__add__. This is ok, because it was
702: implemented with knowledge of Fraction, so it can
703: handle those instances before delegating to Real or
704: Complex.
705:
706: The next two situations describe 'b + r'. We assume that b
707: didn't know about Fraction in its implementation, and that it
708: uses similar boilerplate code:
709:
710: 4. If B <: Rational, then __radd_ converts both to the
711: builtin rational type (hey look, that's us) and
712: proceeds.
713: 5. Otherwise, __radd__ tries to find the nearest common
714: base ABC, and fall back to its builtin type. Since this
715: class doesn't subclass a concrete type, there's no
716: implementation to fall back to, so we need to try as
717: hard as possible to return an actual value, or the user
718: will get a TypeError.
719: """
720:
721:
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