Generated by Cython 0.23.1
Yellow lines hint at Python interaction.
Click on a line that starts with a "+" to see the C code that Cython generated for it.
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: cdef object Rational, Decimal, math, numbers, sys, re, operator
034:
+035: from numbers import Rational
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+036: from decimal import Decimal
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+037: import math
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+038: import numbers
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+039: import operator
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+040: import re
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+041: import sys
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042:
043:
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045: """Calculate the Greatest Common Divisor of a and b as a non-negative number.
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 unsigned long long au, bu
051: cdef long long ai, bi
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080:
081:
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104:
105:
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PyObject_HEAD
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107: """A Rational number.
108:
109: Takes a string like '3/2' or '1.5', another Rational instance, a
110: numerator/denominator pair, or a float.
111:
112: Examples
113: --------
114:
115: >>> Fraction(10, -8)
116: Fraction(-5, 4)
117: >>> Fraction(Fraction(1, 7), 5)
118: Fraction(1, 35)
119: >>> Fraction(Fraction(1, 7), Fraction(2, 3))
120: Fraction(3, 14)
121: >>> Fraction('314')
122: Fraction(314, 1)
123: >>> Fraction('-35/4')
124: Fraction(-35, 4)
125: >>> Fraction('3.1415') # conversion from numeric string
126: Fraction(6283, 2000)
127: >>> Fraction('-47e-2') # string may include a decimal exponent
128: Fraction(-47, 100)
129: >>> Fraction(1.47) # direct construction from float (exact conversion)
130: Fraction(6620291452234629, 4503599627370496)
131: >>> Fraction(2.25)
132: Fraction(9, 4)
133: >>> from decimal import Decimal
134: >>> Fraction(Decimal('1.47'))
135: Fraction(147, 100)
136:
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157: # Exact conversion from float
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__pyx_t_5 = __Pyx_PyObject_GetAttrStr(((PyObject *)__pyx_ptype_10quicktions_Fraction), __pyx_n_s_from_float); 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); __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 = 158; __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 = 158; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_6); __pyx_t_6 = NULL; __Pyx_INCREF(__pyx_v_numerator); __Pyx_GIVEREF(__pyx_v_numerator); PyTuple_SET_ITEM(__pyx_t_7, 0+1, __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 = 158; __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 = 158; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_v_value = ((struct __pyx_obj_10quicktions_Fraction *)__pyx_t_4); __pyx_t_4 = 0;
+159: self._numerator = 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;
+160: self._denominator = 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;
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__pyx_r = 0;
goto __pyx_L0;
162:
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__pyx_t_2 = __Pyx_PyBaseString_Check(__pyx_v_numerator);
__pyx_t_1 = (__pyx_t_2 != 0);
if (__pyx_t_1) {
/* … */
goto __pyx_L4;
}
164: # 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 = 165; __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 = 165; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_GIVEREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_7); __pyx_t_7 = NULL; __Pyx_INCREF(__pyx_v_numerator); __Pyx_GIVEREF(__pyx_v_numerator); PyTuple_SET_ITEM(__pyx_t_6, 0+1, __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 = 165; __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;
+166: if m is None:
__pyx_t_1 = (__pyx_v_m == Py_None);
__pyx_t_2 = (__pyx_t_1 != 0);
if (__pyx_t_2) {
/* … */
}
+167: raise ValueError('Invalid literal for Fraction: %r' %
__pyx_t_4 = __Pyx_PyString_Format(__pyx_kp_s_Invalid_literal_for_Fraction_r, __pyx_v_numerator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 167; __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 = 167; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_5, 0, __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 = 167; __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 = 167; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
168: numerator)
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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 = 169; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_v_group = __pyx_t_4; __pyx_t_4 = 0;
+170: numerator = int(group('num') or 0)
__pyx_t_5 = __Pyx_PyObject_Call(__pyx_v_group, __pyx_tuple_, NULL); 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_t_2 = __Pyx_PyObject_IsTrue(__pyx_t_5); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 170; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (!__pyx_t_2) { __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; } else { __Pyx_INCREF(__pyx_t_5); __pyx_t_4 = __pyx_t_5; __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; goto __pyx_L8_bool_binop_done; } __pyx_t_5 = __Pyx_PyInt_From_long(0); 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_t_4 = __pyx_t_5; __pyx_t_5 = 0; __pyx_L8_bool_binop_done:; __pyx_t_5 = PyNumber_Int(__pyx_t_4); 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(__pyx_t_4); __pyx_t_4 = 0; __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_5); __pyx_t_5 = 0; /* … */ __pyx_tuple_ = PyTuple_Pack(1, __pyx_n_s_num); if (unlikely(!__pyx_tuple_)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 170; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple_); __Pyx_GIVEREF(__pyx_tuple_);
+171: denom = group('denom')
__pyx_t_5 = __Pyx_PyObject_Call(__pyx_v_group, __pyx_tuple__2, NULL); 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_v_denom = __pyx_t_5; __pyx_t_5 = 0; /* … */ __pyx_tuple__2 = PyTuple_Pack(1, __pyx_n_s_denom); if (unlikely(!__pyx_tuple__2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 171; __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 = 172; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) { /* … */ goto __pyx_L10; }
+173: denominator = int(denom)
__pyx_t_5 = PyNumber_Int(__pyx_v_denom); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 173; __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;
174: else:
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/*else*/ {
__pyx_t_5 = __Pyx_PyObject_Call(__pyx_v_group, __pyx_tuple__3, NULL); 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_v_decimal = __pyx_t_5;
__pyx_t_5 = 0;
/* … */
__pyx_tuple__3 = PyTuple_Pack(1, __pyx_n_s_decimal); if (unlikely(!__pyx_tuple__3)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 175; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_tuple__3);
__Pyx_GIVEREF(__pyx_tuple__3);
+176: if decimal:
__pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_v_decimal); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 176; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) { /* … */ goto __pyx_L11; }
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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 = 177; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_5 = PyInt_FromSsize_t(__pyx_t_8); 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_v_scale = __pyx_t_4; __pyx_t_4 = 0;
+178: numerator = numerator * scale + int(decimal)
__pyx_t_4 = PyNumber_Multiply(__pyx_v_numerator, __pyx_v_scale); 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_t_5 = PyNumber_Int(__pyx_v_decimal); 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_6 = PyNumber_Add(__pyx_t_4, __pyx_t_5); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 178; __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_6); __pyx_t_6 = 0;
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__Pyx_INCREF(__pyx_v_scale); __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_v_scale);
180: 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_6 = __Pyx_PyObject_Call(__pyx_v_group, __pyx_tuple__4, NULL); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 182; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_v_exp = __pyx_t_6; __pyx_t_6 = 0; /* … */ __pyx_tuple__4 = PyTuple_Pack(1, __pyx_n_s_exp); if (unlikely(!__pyx_tuple__4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 182; __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 = 183; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) { /* … */ } } __pyx_L10:;
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__pyx_t_6 = PyNumber_Int(__pyx_v_exp); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 184; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF_SET(__pyx_v_exp, __pyx_t_6); __pyx_t_6 = 0;
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__pyx_t_6 = PyObject_RichCompare(__pyx_v_exp, __pyx_int_0, Py_GE); __Pyx_XGOTREF(__pyx_t_6); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 185; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_t_6); 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_6); __pyx_t_6 = 0; if (__pyx_t_2) { /* … */ goto __pyx_L13; }
+186: numerator *= 10**exp
__pyx_t_6 = PyNumber_Power(__pyx_int_10, __pyx_v_exp, Py_None); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 186; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_t_5 = PyNumber_InPlaceMultiply(__pyx_v_numerator, __pyx_t_6); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 186; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_5); __pyx_t_5 = 0;
187: else:
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/*else*/ {
__pyx_t_5 = PyNumber_Negative(__pyx_v_exp); 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 = PyNumber_Power(__pyx_int_10, __pyx_t_5, Py_None); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 188; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_6);
__Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
__pyx_t_5 = PyNumber_InPlaceMultiply(__pyx_v_denominator, __pyx_t_6); 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_DECREF(__pyx_t_6); __pyx_t_6 = 0;
__Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_5);
__pyx_t_5 = 0;
}
__pyx_L13:;
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__pyx_t_5 = __Pyx_PyObject_Call(__pyx_v_group, __pyx_tuple__5, NULL); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 189; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_2 = (__Pyx_PyString_Equals(__pyx_t_5, __pyx_kp_s__6, Py_EQ)); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 189; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 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 = 189; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_tuple__5); __Pyx_GIVEREF(__pyx_tuple__5);
+190: numerator = -numerator
__pyx_t_5 = PyNumber_Negative(__pyx_v_numerator); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 190; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_5); __pyx_t_5 = 0;
191: # fall through to normalisation below
192:
+193: elif isinstance(numerator, (Fraction, Rational)):
__Pyx_INCREF(__pyx_v_10quicktions_Rational); __pyx_t_5 = __pyx_v_10quicktions_Rational; __pyx_t_1 = __Pyx_TypeCheck(__pyx_v_numerator, __pyx_ptype_10quicktions_Fraction); __pyx_t_3 = (__pyx_t_1 != 0); if (!__pyx_t_3) { } else { __pyx_t_2 = __pyx_t_3; goto __pyx_L15_bool_binop_done; } __pyx_t_3 = PyObject_IsInstance(__pyx_v_numerator, __pyx_t_5); __pyx_t_1 = (__pyx_t_3 != 0); __pyx_t_2 = __pyx_t_1; __pyx_L15_bool_binop_done:; __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __pyx_t_1 = (__pyx_t_2 != 0); if (__pyx_t_1) { /* … */ }
+194: self._numerator = numerator.numerator
__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 = 194; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_GIVEREF(__pyx_t_5); __Pyx_GOTREF(__pyx_v_self->_numerator); __Pyx_DECREF(__pyx_v_self->_numerator); __pyx_v_self->_numerator = __pyx_t_5; __pyx_t_5 = 0;
+195: self._denominator = numerator.denominator
__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 = 195; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_GIVEREF(__pyx_t_5); __Pyx_GOTREF(__pyx_v_self->_denominator); __Pyx_DECREF(__pyx_v_self->_denominator); __pyx_v_self->_denominator = __pyx_t_5; __pyx_t_5 = 0;
+196: return
__pyx_r = 0;
goto __pyx_L0;
197:
+198: elif isinstance(numerator, Decimal):
__pyx_t_5 = __pyx_v_10quicktions_Decimal;
__Pyx_INCREF(__pyx_t_5);
__pyx_t_1 = PyObject_IsInstance(__pyx_v_numerator, __pyx_t_5); if (unlikely(__pyx_t_1 == -1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 198; __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) {
/* … */
}
+199: value = Fraction.from_decimal(numerator)
__pyx_t_6 = __Pyx_PyObject_GetAttrStr(((PyObject *)__pyx_ptype_10quicktions_Fraction), __pyx_n_s_from_decimal); if (unlikely(!__pyx_t_6)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 199; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_6); __pyx_t_4 = NULL; if (CYTHON_COMPILING_IN_CPYTHON && likely(PyMethod_Check(__pyx_t_6))) { __pyx_t_4 = PyMethod_GET_SELF(__pyx_t_6); if (likely(__pyx_t_4)) { PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_6); __Pyx_INCREF(__pyx_t_4); __Pyx_INCREF(function); __Pyx_DECREF_SET(__pyx_t_6, function); } } if (!__pyx_t_4) { __pyx_t_5 = __Pyx_PyObject_CallOneArg(__pyx_t_6, __pyx_v_numerator); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 199; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); } else { __pyx_t_7 = PyTuple_New(1+1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 199; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_4); __pyx_t_4 = NULL; __Pyx_INCREF(__pyx_v_numerator); __Pyx_GIVEREF(__pyx_v_numerator); PyTuple_SET_ITEM(__pyx_t_7, 0+1, __pyx_v_numerator); __pyx_t_5 = __Pyx_PyObject_Call(__pyx_t_6, __pyx_t_7, NULL); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 199; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; } __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; if (!(likely(((__pyx_t_5) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_5, __pyx_ptype_10quicktions_Fraction))))) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 199; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_v_value = ((struct __pyx_obj_10quicktions_Fraction *)__pyx_t_5); __pyx_t_5 = 0;
+200: self._numerator = (<Fraction>value)._numerator
__pyx_t_5 = __pyx_v_value->_numerator;
__Pyx_INCREF(__pyx_t_5);
__Pyx_GIVEREF(__pyx_t_5);
__Pyx_GOTREF(__pyx_v_self->_numerator);
__Pyx_DECREF(__pyx_v_self->_numerator);
__pyx_v_self->_numerator = __pyx_t_5;
__pyx_t_5 = 0;
+201: self._denominator = (<Fraction>value)._denominator
__pyx_t_5 = __pyx_v_value->_denominator;
__Pyx_INCREF(__pyx_t_5);
__Pyx_GIVEREF(__pyx_t_5);
__Pyx_GOTREF(__pyx_v_self->_denominator);
__Pyx_DECREF(__pyx_v_self->_denominator);
__pyx_v_self->_denominator = __pyx_t_5;
__pyx_t_5 = 0;
+202: return
__pyx_r = 0;
goto __pyx_L0;
203:
204: else:
+205: raise TypeError("argument should be a string "
/*else*/ {
__pyx_t_5 = __Pyx_PyObject_Call(__pyx_builtin_TypeError, __pyx_tuple__7, NULL); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 205; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_5);
__Pyx_Raise(__pyx_t_5, 0, 0, 0);
__Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
{__pyx_filename = __pyx_f[0]; __pyx_lineno = 205; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}
__pyx_L4:;
/* … */
__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 = 205; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_tuple__7);
__Pyx_GIVEREF(__pyx_tuple__7);
206: "or a Rational instance")
207:
+208: elif type(numerator) is int is type(denominator):
__pyx_t_2 = (((PyObject *)Py_TYPE(__pyx_v_numerator)) == ((PyObject *)(&PyInt_Type)));
if (__pyx_t_2) {
__pyx_t_2 = ((&PyInt_Type) == ((PyTypeObject*)((PyObject *)Py_TYPE(__pyx_v_denominator))));
}
__pyx_t_1 = (__pyx_t_2 != 0);
if (__pyx_t_1) {
goto __pyx_L3;
}
209: pass # *very* normal case
210:
+211: 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) {
} else {
__pyx_t_1 = __pyx_t_2;
goto __pyx_L17_bool_binop_done;
}
__pyx_t_2 = (((PyObject *)Py_TYPE(__pyx_v_numerator)) == ((PyObject *)(&PyLong_Type)));
if (__pyx_t_2) {
__pyx_t_2 = ((&PyLong_Type) == ((PyTypeObject*)((PyObject *)Py_TYPE(__pyx_v_denominator))));
}
__pyx_t_3 = (__pyx_t_2 != 0);
__pyx_t_1 = __pyx_t_3;
__pyx_L17_bool_binop_done:;
if (__pyx_t_1) {
goto __pyx_L3;
}
212: pass # *very* normal case
213:
+214: elif type(numerator) is Fraction is type(denominator):
__pyx_t_1 = (((PyObject *)Py_TYPE(__pyx_v_numerator)) == ((PyObject *)__pyx_ptype_10quicktions_Fraction));
if (__pyx_t_1) {
__pyx_t_1 = (__pyx_ptype_10quicktions_Fraction == ((PyTypeObject*)((PyObject *)Py_TYPE(__pyx_v_denominator))));
}
__pyx_t_3 = (__pyx_t_1 != 0);
if (__pyx_t_3) {
/* … */
goto __pyx_L3;
}
215: numerator, denominator = (
+216: (<Fraction>numerator)._numerator * (<Fraction>denominator)._denominator,
__pyx_t_5 = PyNumber_Multiply(((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_numerator)->_numerator, ((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_denominator)->_denominator); 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);
+217: (<Fraction>denominator)._numerator * (<Fraction>numerator)._denominator
__pyx_t_6 = PyNumber_Multiply(((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_denominator)->_numerator, ((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_numerator)->_denominator); 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_DECREF_SET(__pyx_v_numerator, __pyx_t_5); __pyx_t_5 = 0; __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_6); __pyx_t_6 = 0;
218: )
219:
+220: elif (isinstance(numerator, (Fraction, Rational)) and
__Pyx_INCREF(__pyx_v_10quicktions_Rational); __pyx_t_6 = __pyx_v_10quicktions_Rational; __pyx_t_2 = __Pyx_TypeCheck(__pyx_v_numerator, __pyx_ptype_10quicktions_Fraction); __pyx_t_9 = (__pyx_t_2 != 0); if (!__pyx_t_9) { } else { __pyx_t_1 = __pyx_t_9; goto __pyx_L21_bool_binop_done; } __pyx_t_9 = PyObject_IsInstance(__pyx_v_numerator, __pyx_t_6); __pyx_t_2 = (__pyx_t_9 != 0); __pyx_t_1 = __pyx_t_2; __pyx_L21_bool_binop_done:; __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __pyx_t_2 = (__pyx_t_1 != 0); if (__pyx_t_2) { } else { __pyx_t_3 = __pyx_t_2; goto __pyx_L19_bool_binop_done; } /* … */ if (__pyx_t_3) { /* … */ goto __pyx_L3; }
+221: isinstance(denominator, (Fraction, Rational))):
__Pyx_INCREF(__pyx_v_10quicktions_Rational); __pyx_t_6 = __pyx_v_10quicktions_Rational; __pyx_t_1 = __Pyx_TypeCheck(__pyx_v_denominator, __pyx_ptype_10quicktions_Fraction); __pyx_t_9 = (__pyx_t_1 != 0); if (!__pyx_t_9) { } else { __pyx_t_2 = __pyx_t_9; goto __pyx_L23_bool_binop_done; } __pyx_t_9 = PyObject_IsInstance(__pyx_v_denominator, __pyx_t_6); __pyx_t_1 = (__pyx_t_9 != 0); __pyx_t_2 = __pyx_t_1; __pyx_L23_bool_binop_done:; __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __pyx_t_1 = (__pyx_t_2 != 0); __pyx_t_3 = __pyx_t_1; __pyx_L19_bool_binop_done:;
222: numerator, denominator = (
+223: numerator.numerator * denominator.denominator,
__pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_numerator); 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_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_denominator, __pyx_n_s_denominator); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 223; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_7 = PyNumber_Multiply(__pyx_t_6, __pyx_t_5); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 223; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
+224: denominator.numerator * numerator.denominator
__pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_denominator, __pyx_n_s_numerator); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 224; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_denominator); 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_t_4 = PyNumber_Multiply(__pyx_t_5, __pyx_t_6); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 224; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_7); __pyx_t_7 = 0; __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_4); __pyx_t_4 = 0;
225: )
226:
227: else:
+228: raise TypeError("both arguments should be "
/*else*/ {
__pyx_t_4 = __Pyx_PyObject_Call(__pyx_builtin_TypeError, __pyx_tuple__8, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 228; __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 = 228; __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 = 228; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_tuple__8);
__Pyx_GIVEREF(__pyx_tuple__8);
229: "Rational instances")
230:
+231: if denominator == 0:
__pyx_t_4 = __Pyx_PyInt_EqObjC(__pyx_v_denominator, __pyx_int_0, 0, 0); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 231; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_t_3 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_3 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 231; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; if (__pyx_t_3) { /* … */ }
+232: raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
__pyx_t_4 = __Pyx_PyString_Format(__pyx_kp_s_Fraction_s_0, __pyx_v_numerator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 232; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_t_7 = PyTuple_New(1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 232; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_4); __pyx_t_4 = 0; __pyx_t_4 = __Pyx_PyObject_Call(__pyx_builtin_ZeroDivisionError, __pyx_t_7, NULL); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 232; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 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 = 232; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
+233: if _normalize:
__pyx_t_3 = (__pyx_v__normalize != 0);
if (__pyx_t_3) {
/* … */
}
+234: g = _gcd(numerator, denominator)
__pyx_t_4 = __pyx_f_10quicktions__gcd(__pyx_v_numerator, __pyx_v_denominator, 0); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 234; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_4); __pyx_v_g = __pyx_t_4; __pyx_t_4 = 0;
235: # NOTE: 'is' tests on integers are generally a bad idea, but
236: # they are fast and if they fail here, it'll still be correct
+237: if denominator < 0:
__pyx_t_4 = PyObject_RichCompare(__pyx_v_denominator, __pyx_int_0, Py_LT); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 237; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_3 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_3 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 237; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; if (__pyx_t_3) { /* … */ }
+238: if g is 1:
__pyx_t_3 = (__pyx_v_g == __pyx_int_1);
__pyx_t_1 = (__pyx_t_3 != 0);
if (__pyx_t_1) {
/* … */
goto __pyx_L28;
}
+239: numerator = -numerator
__pyx_t_4 = PyNumber_Negative(__pyx_v_numerator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 239; __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;
+240: denominator = -denominator
__pyx_t_4 = PyNumber_Negative(__pyx_v_denominator); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 240; __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;
241: else:
+242: g = -g
/*else*/ {
__pyx_t_4 = PyNumber_Negative(__pyx_v_g); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 242; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_4);
__Pyx_DECREF_SET(__pyx_v_g, __pyx_t_4);
__pyx_t_4 = 0;
}
__pyx_L28:;
+243: 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) {
/* … */
}
+244: numerator //= g
__pyx_t_4 = PyNumber_InPlaceFloorDivide(__pyx_v_numerator, __pyx_v_g); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 244; __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;
+245: denominator //= g
__pyx_t_4 = PyNumber_InPlaceFloorDivide(__pyx_v_denominator, __pyx_v_g); if (unlikely(!__pyx_t_4)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 245; __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;
+246: 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;
+247: 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;
248:
+249: @classmethod
__pyx_t_2 = __Pyx_Method_ClassMethod(__pyx_t_8); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 249; __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 = 250; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0; PyType_Modified(__pyx_ptype_10quicktions_Fraction);
+250: 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(((PyTypeObject*)__pyx_v_cls), ((PyObject *)__pyx_v_f));
/* function exit code */
__Pyx_RefNannyFinishContext();
return __pyx_r;
}
static PyObject *__pyx_pf_10quicktions_8Fraction_2from_float(PyTypeObject *__pyx_v_cls, PyObject *__pyx_v_f) {
PyObject *__pyx_v_ratio = NULL;
PyObject *__pyx_r = NULL;
__Pyx_TraceDeclarations
__Pyx_RefNannyDeclarations
__Pyx_RefNannySetupContext("from_float", 0);
__Pyx_TraceCall("from_float", __pyx_f[0], 250, 0, {__pyx_filename = __pyx_f[0]; __pyx_lineno = 250; __pyx_clineno = __LINE__; goto __pyx_L1_error;});
/* … */
/* function exit code */
__pyx_L1_error:;
__Pyx_XDECREF(__pyx_t_4);
__Pyx_XDECREF(__pyx_t_5);
__Pyx_XDECREF(__pyx_t_6);
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__pyx_t_5 = __Pyx_PyString_Format(__pyx_kp_s_s_from_decimal_only_takes_Decim, __pyx_t_7); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 279; __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 = 281; __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 = 281; __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 = 281; __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 = 281; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; if (__pyx_t_2) { /* … */ }
+282: raise OverflowError(
__pyx_t_7 = PyTuple_New(1); if (unlikely(!__pyx_t_7)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 282; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_7, 0, __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 = 282; __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 = 282; __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 = 283; __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 = 283; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_INCREF(__pyx_v_dec); __Pyx_GIVEREF(__pyx_v_dec); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_v_dec); __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_7, 1, __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 = 283; __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_5 = __Pyx_PyObject_GetAttrStr(((PyObject *)__pyx_v_cls), __pyx_n_s_name); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 285; __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 = 285; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_INCREF(__pyx_v_dec); __Pyx_GIVEREF(__pyx_v_dec); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_v_dec); __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_7, 1, __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 = 285; __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 = 285; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_7); __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_7, 0, __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 = 285; __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 = 285; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
+286: sign, digits, exp = dec.as_tuple()
__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 = 286; __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 = 286; __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 = 286; __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 = 286; __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 = 286; __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 = 286; __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 = 286; __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 = 286; __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 = 286; __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 = 286; __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;
+287: digits = int(''.join(map(str, digits)))
__pyx_t_5 = PyTuple_New(2); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 287; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_GOTREF(__pyx_t_5); __Pyx_INCREF(((PyObject *)(&PyString_Type))); __Pyx_GIVEREF(((PyObject *)(&PyString_Type))); PyTuple_SET_ITEM(__pyx_t_5, 0, ((PyObject *)(&PyString_Type))); __Pyx_INCREF(__pyx_v_digits); __Pyx_GIVEREF(__pyx_v_digits); PyTuple_SET_ITEM(__pyx_t_5, 1, __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 = 287; __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 = 287; __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 = 287; __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;
+288: if sign:
__pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_v_sign); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 288; __pyx_clineno = __LINE__; goto __pyx_L1_error;} if (__pyx_t_2) { /* … */ }
+289: digits = -digits
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296: """Closest Fraction to self with denominator at most max_denominator.
297:
298: >>> Fraction('3.141592653589793').limit_denominator(10)
299: Fraction(22, 7)
300: >>> Fraction('3.141592653589793').limit_denominator(100)
301: Fraction(311, 99)
302: >>> Fraction(4321, 8765).limit_denominator(10000)
303: Fraction(4321, 8765)
304:
305: """
306: # Algorithm notes: For any real number x, define a *best upper
307: # approximation* to x to be a rational number p/q such that:
308: #
309: # (1) p/q >= x, and
310: # (2) if p/q > r/s >= x then s > q, for any rational r/s.
311: #
312: # Define *best lower approximation* similarly. Then it can be
313: # proved that a rational number is a best upper or lower
314: # approximation to x if, and only if, it is a convergent or
315: # semiconvergent of the (unique shortest) continued fraction
316: # associated to x.
317: #
318: # To find a best rational approximation with denominator <= M,
319: # we find the best upper and lower approximations with
320: # denominator <= M and take whichever of these is closer to x.
321: # In the event of a tie, the bound with smaller denominator is
322: # chosen. If both denominators are equal (which can happen
323: # only when max_denominator == 1 and self is midway between
324: # two integers) the lower bound---i.e., the floor of self, is
325: # taken.
326:
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__pyx_t_1 = PyObject_RichCompare(__pyx_v_max_denominator, __pyx_int_1, Py_LT); __Pyx_XGOTREF(__pyx_t_1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 327; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_t_1); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 327; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; if (__pyx_t_2) { /* … */ }
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__pyx_t_1 = PyObject_RichCompare(__pyx_v_self->_denominator, __pyx_v_max_denominator, Py_LE); __Pyx_XGOTREF(__pyx_t_1); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 329; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_t_1); if (unlikely(__pyx_t_2 < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 329; __pyx_clineno = __LINE__; goto __pyx_L1_error;} __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; if (__pyx_t_2) { /* … */ }
+330: return Fraction(self)
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331:
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341:
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680:
681:
682: """
683: In general, we want to implement the arithmetic operations so
684: that mixed-mode operations either call an implementation whose
685: author knew about the types of both arguments, or convert both
686: to the nearest built in type and do the operation there. In
687: Fraction, that means that we define __add__ and __radd__ as:
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689: def __add__(self, other):
690: # Both types have numerators/denominator attributes,
691: # so do the operation directly
692: if isinstance(other, (int, Fraction)):
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694: other.numerator * self.denominator,
695: self.denominator * other.denominator)
696: # float and complex don't have those operations, but we
697: # know about those types, so special case them.
698: elif isinstance(other, float):
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700: elif isinstance(other, complex):
701: return complex(self) + other
702: # Let the other type take over.
703: return NotImplemented
704:
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707: # nothing left to fall back to.
708: if isinstance(other, Rational):
709: return Fraction(self.numerator * other.denominator +
710: other.numerator * self.denominator,
711: self.denominator * other.denominator)
712: elif isinstance(other, Real):
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714: elif isinstance(other, Complex):
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716: return NotImplemented
717:
718:
719: There are 5 different cases for a mixed-type addition on
720: Fraction. I'll refer to all of the above code that doesn't
721: refer to Fraction, float, or complex as "boilerplate". 'r'
722: will be an instance of Fraction, which is a subtype of
723: Rational (r : Fraction <: Rational), and b : B <:
724: Complex. The first three involve 'r + b':
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726: 1. If B <: Fraction, int, float, or complex, we handle
727: that specially, and all is well.
728: 2. If Fraction falls back to the boilerplate code, and it
729: were to return a value from __add__, we'd miss the
730: possibility that B defines a more intelligent __radd__,
731: so the boilerplate should return NotImplemented from
732: __add__. In particular, we don't handle Rational
733: here, even though we could get an exact answer, in case
734: the other type wants to do something special.
735: 3. If B <: Fraction, Python tries B.__radd__ before
736: Fraction.__add__. This is ok, because it was
737: implemented with knowledge of Fraction, so it can
738: handle those instances before delegating to Real or
739: Complex.
740:
741: The next two situations describe 'b + r'. We assume that b
742: didn't know about Fraction in its implementation, and that it
743: uses similar boilerplate code:
744:
745: 4. If B <: Rational, then __radd_ converts both to the
746: builtin rational type (hey look, that's us) and
747: proceeds.
748: 5. Otherwise, __radd__ tries to find the nearest common
749: base ABC, and fall back to its builtin type. Since this
750: class doesn't subclass a concrete type, there's no
751: implementation to fall back to, so we need to try as
752: hard as possible to return an actual value, or the user
753: will get a TypeError.
754: """
755:
756:
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