Generated by Cython 0.26.1
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 3.4/5.
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:
+024: __version__ = '1.4'
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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: cdef long LONG_MAX
033:
034: cdef object Rational, Decimal, math, numbers, sys, re, operator
035:
+036: from numbers import Rational
__pyx_t_1 = PyList_New(1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 36, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_1); __Pyx_INCREF(__pyx_n_s_Rational); __Pyx_GIVEREF(__pyx_n_s_Rational); PyList_SET_ITEM(__pyx_t_1, 0, __pyx_n_s_Rational); __pyx_t_2 = __Pyx_Import(__pyx_n_s_numbers, __pyx_t_1, 0); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 36, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_2); __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; __pyx_t_1 = __Pyx_ImportFrom(__pyx_t_2, __pyx_n_s_Rational); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 36, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_1); __Pyx_INCREF(__pyx_t_1); __Pyx_XGOTREF(__pyx_v_10quicktions_Rational); __Pyx_DECREF_SET(__pyx_v_10quicktions_Rational, __pyx_t_1); __Pyx_GIVEREF(__pyx_t_1); __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
+037: from decimal import Decimal
__pyx_t_2 = PyList_New(1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 37, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_2); __Pyx_INCREF(__pyx_n_s_Decimal); __Pyx_GIVEREF(__pyx_n_s_Decimal); PyList_SET_ITEM(__pyx_t_2, 0, __pyx_n_s_Decimal); __pyx_t_1 = __Pyx_Import(__pyx_n_s_decimal, __pyx_t_2, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 37, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_1); __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0; __pyx_t_2 = __Pyx_ImportFrom(__pyx_t_1, __pyx_n_s_Decimal); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 37, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_2); __Pyx_INCREF(__pyx_t_2); __Pyx_XGOTREF(__pyx_v_10quicktions_Decimal); __Pyx_DECREF_SET(__pyx_v_10quicktions_Decimal, __pyx_t_2); __Pyx_GIVEREF(__pyx_t_2); __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0; __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
+038: import math
__pyx_t_1 = __Pyx_Import(__pyx_n_s_math, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 38, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_1); __Pyx_XGOTREF(__pyx_v_10quicktions_math); __Pyx_DECREF_SET(__pyx_v_10quicktions_math, __pyx_t_1); __Pyx_GIVEREF(__pyx_t_1); __pyx_t_1 = 0;
+039: import numbers
__pyx_t_1 = __Pyx_Import(__pyx_n_s_numbers, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 39, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_1); __Pyx_XGOTREF(__pyx_v_10quicktions_numbers); __Pyx_DECREF_SET(__pyx_v_10quicktions_numbers, __pyx_t_1); __Pyx_GIVEREF(__pyx_t_1); __pyx_t_1 = 0;
+040: import operator
__pyx_t_1 = __Pyx_Import(__pyx_n_s_operator, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 40, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_1); __Pyx_XGOTREF(__pyx_v_10quicktions_operator); __Pyx_DECREF_SET(__pyx_v_10quicktions_operator, __pyx_t_1); __Pyx_GIVEREF(__pyx_t_1); __pyx_t_1 = 0;
+041: import re
__pyx_t_1 = __Pyx_Import(__pyx_n_s_re, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 41, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_1); __Pyx_XGOTREF(__pyx_v_10quicktions_re); __Pyx_DECREF_SET(__pyx_v_10quicktions_re, __pyx_t_1); __Pyx_GIVEREF(__pyx_t_1); __pyx_t_1 = 0;
+042: import sys
__pyx_t_1 = __Pyx_Import(__pyx_n_s_sys, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 42, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_1); __Pyx_XGOTREF(__pyx_v_10quicktions_sys); __Pyx_DECREF_SET(__pyx_v_10quicktions_sys, __pyx_t_1); __Pyx_GIVEREF(__pyx_t_1); __pyx_t_1 = 0;
043:
+044: cdef bint _decimal_supports_integer_ratio = hasattr(Decimal, "as_integer_ratio") # Py3.6+
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045:
046:
+047: cpdef _gcd(a, b):
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048: """Calculate the Greatest Common Divisor of a and b as a non-negative number.
049: """
050: # Try doing all computation in C space. If the numbers are too
051: # large at the beginning, retry after each iteration until they
052: # are small enough.
053: cdef unsigned long long au, bu
054: cdef long long ai, bi
+055: while b:
while (1) { __pyx_t_1 = __Pyx_PyObject_IsTrue(__pyx_v_b); if (unlikely(__pyx_t_1 < 0)) __PYX_ERR(0, 55, __pyx_L1_error) if (!__pyx_t_1) break;
+056: try:
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+057: ai, bi = a, b
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059: pass
060: else:
061: # switch to C space
+062: au = abs(ai)
/*else:*/ { __pyx_t_7 = __Pyx_abs_longlong(__pyx_v_ai); __pyx_v_au = __pyx_t_7;
+063: bu = abs(bi)
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+064: while bu:
while (1) { __pyx_t_1 = (__pyx_v_bu != 0); if (!__pyx_t_1) break;
+065: au, bu = bu, au%bu
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066: # try PyInt downcast in Py2
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+069: return au
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+070: a, b = b, a%b
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072:
073:
074: # Constants related to the hash implementation; hash(x) is based
075: # on the reduction of x modulo the prime _PyHASH_MODULUS.
076:
077: cdef Py_hash_t _PyHASH_MODULUS
+078: try:
{ /*try:*/ { /* … */ } __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0; __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0; __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0; goto __pyx_L7_try_end; __pyx_L2_error:; __Pyx_PyThreadState_assign __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0; __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0; /* … */ __Pyx_PyThreadState_assign __Pyx_XGIVEREF(__pyx_t_4); __Pyx_XGIVEREF(__pyx_t_5); __Pyx_XGIVEREF(__pyx_t_6); __Pyx_ExceptionReset(__pyx_t_4, __pyx_t_5, __pyx_t_6); goto __pyx_L1_error; __pyx_L3_exception_handled:; __Pyx_PyThreadState_assign __Pyx_XGIVEREF(__pyx_t_4); __Pyx_XGIVEREF(__pyx_t_5); __Pyx_XGIVEREF(__pyx_t_6); __Pyx_ExceptionReset(__pyx_t_4, __pyx_t_5, __pyx_t_6); __pyx_L7_try_end:; }
+079: _PyHASH_MODULUS = sys.hash_info.modulus
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if ((((sizeof(Py_hash_t)) >= 8) != 0)) { __pyx_t_10 = 61; } else { __pyx_t_10 = 31; } __pyx_v_10quicktions__PyHASH_MODULUS = (((Py_hash_t)1) << (__pyx_t_10 - 1)); __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0; __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0; goto __pyx_L3_exception_handled; } goto __pyx_L4_except_error; __pyx_L4_except_error:;
083:
084:
085: # Value to be used for rationals that reduce to infinity modulo
086: # _PyHASH_MODULUS.
087: cdef Py_hash_t _PyHASH_INF
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095: \A\s* # optional whitespace at the start, then
096: (?P<sign>[-+]?) # an optional sign, then
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098: (?P<num>\d*) # numerator (possibly empty)
099: (?: # followed by
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101: | # or
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108:
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110: """A Rational number.
111:
112: Takes a string like '3/2' or '1.5', another Rational instance, a
113: numerator/denominator pair, or a float.
114:
115: Examples
116: --------
117:
118: >>> Fraction(10, -8)
119: Fraction(-5, 4)
120: >>> Fraction(Fraction(1, 7), 5)
121: Fraction(1, 35)
122: >>> Fraction(Fraction(1, 7), Fraction(2, 3))
123: Fraction(3, 14)
124: >>> Fraction('314')
125: Fraction(314, 1)
126: >>> Fraction('-35/4')
127: Fraction(-35, 4)
128: >>> Fraction('3.1415') # conversion from numeric string
129: Fraction(6283, 2000)
130: >>> Fraction('-47e-2') # string may include a decimal exponent
131: Fraction(-47, 100)
132: >>> Fraction(1.47) # direct construction from float (exact conversion)
133: Fraction(6620291452234629, 4503599627370496)
134: >>> Fraction(2.25)
135: Fraction(9, 4)
136: >>> from decimal import Decimal
137: >>> Fraction(Decimal('1.47'))
138: Fraction(147, 100)
139:
140: """
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142: cdef _denominator
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144:
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163:
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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;
}
165: # Handle construction from strings.
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__pyx_t_1 = (__pyx_v_m == Py_None); __pyx_t_2 = (__pyx_t_1 != 0); if (__pyx_t_2) { /* … */ }
+168: raise ValueError('Invalid literal for Fraction: %r' %
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169: numerator)
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175: else:
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__pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_v_decimal); if (unlikely(__pyx_t_2 < 0)) __PYX_ERR(0, 177, __pyx_L1_error) if (__pyx_t_2) { /* … */ goto __pyx_L13; }
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__pyx_t_4 = PyNumber_Multiply(__pyx_v_numerator, __pyx_v_scale); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 179, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_4); __pyx_t_6 = __Pyx_PyNumber_Int(__pyx_v_decimal); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 179, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __pyx_t_7 = PyNumber_Add(__pyx_t_4, __pyx_t_6); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 179, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_7); __pyx_t_7 = 0;
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181: else:
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__pyx_t_7 = PyNumber_Power(__pyx_int_10, __pyx_v_exp, Py_None); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 187, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __pyx_t_6 = PyNumber_InPlaceMultiply(__pyx_v_numerator, __pyx_t_7); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 187, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_6); __pyx_t_6 = 0;
188: else:
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/*else*/ { __pyx_t_6 = PyNumber_Negative(__pyx_v_exp); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 189, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __pyx_t_7 = PyNumber_Power(__pyx_int_10, __pyx_t_6, Py_None); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 189, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __pyx_t_6 = PyNumber_InPlaceMultiply(__pyx_v_denominator, __pyx_t_7); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 189, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_6); __pyx_t_6 = 0; } __pyx_L15:;
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__pyx_t_6 = __Pyx_PyObject_Call(__pyx_v_group, __pyx_tuple__5, NULL); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 190, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __pyx_t_2 = (__Pyx_PyString_Equals(__pyx_t_6, __pyx_kp_s__6, Py_EQ)); if (unlikely(__pyx_t_2 < 0)) __PYX_ERR(0, 190, __pyx_L1_error) __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; if (__pyx_t_2) { /* … */ } /* … */ __pyx_tuple__5 = PyTuple_Pack(1, __pyx_n_s_sign); if (unlikely(!__pyx_tuple__5)) __PYX_ERR(0, 190, __pyx_L1_error) __Pyx_GOTREF(__pyx_tuple__5); __Pyx_GIVEREF(__pyx_tuple__5);
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__pyx_t_6 = PyNumber_Negative(__pyx_v_numerator); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 191, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_6); __pyx_t_6 = 0;
192: # fall through to normalisation below
193:
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__Pyx_INCREF(__pyx_v_10quicktions_Rational); __pyx_t_6 = __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_L17_bool_binop_done; } __pyx_t_3 = PyObject_IsInstance(__pyx_v_numerator, __pyx_t_6); __pyx_t_1 = (__pyx_t_3 != 0); __pyx_t_2 = __pyx_t_1; __pyx_L17_bool_binop_done:; __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __pyx_t_1 = (__pyx_t_2 != 0); if (__pyx_t_1) { /* … */ }
+195: self._numerator = numerator.numerator
__pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_numerator); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 195, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __Pyx_GIVEREF(__pyx_t_6); __Pyx_GOTREF(__pyx_v_self->_numerator); __Pyx_DECREF(__pyx_v_self->_numerator); __pyx_v_self->_numerator = __pyx_t_6; __pyx_t_6 = 0;
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__pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_denominator); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 196, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __Pyx_GIVEREF(__pyx_t_6); __Pyx_GOTREF(__pyx_v_self->_denominator); __Pyx_DECREF(__pyx_v_self->_denominator); __pyx_v_self->_denominator = __pyx_t_6; __pyx_t_6 = 0;
+197: return
__pyx_r = 0; goto __pyx_L0;
198:
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__pyx_t_6 = __pyx_v_10quicktions_Decimal; __Pyx_INCREF(__pyx_t_6); __pyx_t_1 = PyObject_IsInstance(__pyx_v_numerator, __pyx_t_6); if (unlikely(__pyx_t_1 == -1)) __PYX_ERR(0, 199, __pyx_L1_error) __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0; __pyx_t_2 = (__pyx_t_1 != 0); if (__pyx_t_2) { /* … */ }
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__pyx_t_2 = (__pyx_v_10quicktions__decimal_supports_integer_ratio != 0); if (__pyx_t_2) { /* … */ goto __pyx_L19; }
201: # Exact conversion
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203: else:
+204: value = Fraction.from_decimal(numerator)
/*else*/ { __pyx_t_4 = __Pyx_PyObject_GetAttrStr(((PyObject *)__pyx_ptype_10quicktions_Fraction), __pyx_n_s_from_decimal); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 204, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_4); __pyx_t_7 = NULL; if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_4))) { __pyx_t_7 = PyMethod_GET_SELF(__pyx_t_4); if (likely(__pyx_t_7)) { PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4); __Pyx_INCREF(__pyx_t_7); __Pyx_INCREF(function); __Pyx_DECREF_SET(__pyx_t_4, function); } } if (!__pyx_t_7) { __pyx_t_6 = __Pyx_PyObject_CallOneArg(__pyx_t_4, __pyx_v_numerator); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 204, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); } else { #if CYTHON_FAST_PYCALL if (PyFunction_Check(__pyx_t_4)) { PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_v_numerator}; __pyx_t_6 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 204, __pyx_L1_error) __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0; __Pyx_GOTREF(__pyx_t_6); } else #endif #if CYTHON_FAST_PYCCALL if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) { PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_v_numerator}; __pyx_t_6 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 204, __pyx_L1_error) __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0; __Pyx_GOTREF(__pyx_t_6); } else #endif { __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 204, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_5); __Pyx_GIVEREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_7); __pyx_t_7 = NULL; __Pyx_INCREF(__pyx_v_numerator); __Pyx_GIVEREF(__pyx_v_numerator); PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_v_numerator); __pyx_t_6 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_5, NULL); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 204, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; } } __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; if (!(likely(((__pyx_t_6) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_6, __pyx_ptype_10quicktions_Fraction))))) __PYX_ERR(0, 204, __pyx_L1_error) __pyx_v_value = ((struct __pyx_obj_10quicktions_Fraction *)__pyx_t_6); __pyx_t_6 = 0;
+205: self._numerator = (<Fraction>value)._numerator
__pyx_t_6 = __pyx_v_value->_numerator; __Pyx_INCREF(__pyx_t_6); __Pyx_GIVEREF(__pyx_t_6); __Pyx_GOTREF(__pyx_v_self->_numerator); __Pyx_DECREF(__pyx_v_self->_numerator); __pyx_v_self->_numerator = __pyx_t_6; __pyx_t_6 = 0;
+206: self._denominator = (<Fraction>value)._denominator
__pyx_t_6 = __pyx_v_value->_denominator; __Pyx_INCREF(__pyx_t_6); __Pyx_GIVEREF(__pyx_t_6); __Pyx_GOTREF(__pyx_v_self->_denominator); __Pyx_DECREF(__pyx_v_self->_denominator); __pyx_v_self->_denominator = __pyx_t_6; __pyx_t_6 = 0; } __pyx_L19:;
+207: return
__pyx_r = 0; goto __pyx_L0;
208:
209: else:
+210: raise TypeError("argument should be a string "
/*else*/ { __pyx_t_6 = __Pyx_PyObject_Call(__pyx_builtin_TypeError, __pyx_tuple__7, NULL); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 210, __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_ERR(0, 210, __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_ERR(0, 210, __pyx_L1_error) __Pyx_GOTREF(__pyx_tuple__7); __Pyx_GIVEREF(__pyx_tuple__7);
211: "or a Rational instance")
212:
+213: 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; }
214: pass # *very* normal case
215:
+216: 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_L22_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_L22_bool_binop_done:; if (__pyx_t_1) { goto __pyx_L3; }
217: pass # *very* normal case
218:
+219: 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; }
220: numerator, denominator = (
+221: (<Fraction>numerator)._numerator * (<Fraction>denominator)._denominator,
__pyx_t_6 = PyNumber_Multiply(((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_numerator)->_numerator, ((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_denominator)->_denominator); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 221, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6);
+222: (<Fraction>denominator)._numerator * (<Fraction>numerator)._denominator
__pyx_t_4 = PyNumber_Multiply(((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_denominator)->_numerator, ((struct __pyx_obj_10quicktions_Fraction *)__pyx_v_numerator)->_denominator); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 222, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_4); __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_6); __pyx_t_6 = 0; __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_4); __pyx_t_4 = 0;
223: )
224:
+225: elif (isinstance(numerator, (Fraction, Rational)) and
__Pyx_INCREF(__pyx_v_10quicktions_Rational); __pyx_t_4 = __pyx_v_10quicktions_Rational; __pyx_t_2 = __Pyx_TypeCheck(__pyx_v_numerator, __pyx_ptype_10quicktions_Fraction); __pyx_t_10 = (__pyx_t_2 != 0); if (!__pyx_t_10) { } else { __pyx_t_1 = __pyx_t_10; goto __pyx_L26_bool_binop_done; } __pyx_t_10 = PyObject_IsInstance(__pyx_v_numerator, __pyx_t_4); __pyx_t_2 = (__pyx_t_10 != 0); __pyx_t_1 = __pyx_t_2; __pyx_L26_bool_binop_done:; __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __pyx_t_2 = (__pyx_t_1 != 0); if (__pyx_t_2) { } else { __pyx_t_3 = __pyx_t_2; goto __pyx_L24_bool_binop_done; } /* … */ if (__pyx_t_3) { /* … */ goto __pyx_L3; }
+226: isinstance(denominator, (Fraction, Rational))):
__Pyx_INCREF(__pyx_v_10quicktions_Rational); __pyx_t_4 = __pyx_v_10quicktions_Rational; __pyx_t_1 = __Pyx_TypeCheck(__pyx_v_denominator, __pyx_ptype_10quicktions_Fraction); __pyx_t_10 = (__pyx_t_1 != 0); if (!__pyx_t_10) { } else { __pyx_t_2 = __pyx_t_10; goto __pyx_L28_bool_binop_done; } __pyx_t_10 = PyObject_IsInstance(__pyx_v_denominator, __pyx_t_4); __pyx_t_1 = (__pyx_t_10 != 0); __pyx_t_2 = __pyx_t_1; __pyx_L28_bool_binop_done:; __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __pyx_t_1 = (__pyx_t_2 != 0); __pyx_t_3 = __pyx_t_1; __pyx_L24_bool_binop_done:;
227: numerator, denominator = (
+228: numerator.numerator * denominator.denominator,
__pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_numerator); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 228, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_4); __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_denominator, __pyx_n_s_denominator); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 228, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __pyx_t_5 = PyNumber_Multiply(__pyx_t_4, __pyx_t_6); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 228, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_5); __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0; __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
+229: denominator.numerator * numerator.denominator
__pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_denominator, __pyx_n_s_numerator); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 229, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_6); __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_numerator, __pyx_n_s_denominator); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 229, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_4); __pyx_t_7 = PyNumber_Multiply(__pyx_t_6, __pyx_t_4); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 229, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __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; __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_7); __pyx_t_7 = 0;
230: )
231:
232: else:
+233: raise TypeError("both arguments should be "
/*else*/ { __pyx_t_7 = __Pyx_PyObject_Call(__pyx_builtin_TypeError, __pyx_tuple__8, NULL); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 233, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __Pyx_Raise(__pyx_t_7, 0, 0, 0); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; __PYX_ERR(0, 233, __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_ERR(0, 233, __pyx_L1_error) __Pyx_GOTREF(__pyx_tuple__8); __Pyx_GIVEREF(__pyx_tuple__8);
234: "Rational instances")
235:
+236: if denominator == 0:
__pyx_t_7 = __Pyx_PyInt_EqObjC(__pyx_v_denominator, __pyx_int_0, 0, 0); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 236, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __pyx_t_3 = __Pyx_PyObject_IsTrue(__pyx_t_7); if (unlikely(__pyx_t_3 < 0)) __PYX_ERR(0, 236, __pyx_L1_error) __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; if (__pyx_t_3) { /* … */ }
+237: raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
__pyx_t_7 = __Pyx_PyString_Format(__pyx_kp_s_Fraction_s_0, __pyx_v_numerator); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 237, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __pyx_t_5 = PyTuple_New(1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 237, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_5); __Pyx_GIVEREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_7); __pyx_t_7 = 0; __pyx_t_7 = __Pyx_PyObject_Call(__pyx_builtin_ZeroDivisionError, __pyx_t_5, NULL); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 237, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0; __Pyx_Raise(__pyx_t_7, 0, 0, 0); __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; __PYX_ERR(0, 237, __pyx_L1_error)
+238: if _normalize:
__pyx_t_3 = (__pyx_v__normalize != 0); if (__pyx_t_3) { /* … */ }
+239: g = _gcd(numerator, denominator)
__pyx_t_7 = __pyx_f_10quicktions__gcd(__pyx_v_numerator, __pyx_v_denominator, 0); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 239, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __pyx_v_g = __pyx_t_7; __pyx_t_7 = 0;
240: # NOTE: 'is' tests on integers are generally a bad idea, but
241: # they are fast and if they fail here, it'll still be correct
+242: if denominator < 0:
__pyx_t_7 = PyObject_RichCompare(__pyx_v_denominator, __pyx_int_0, Py_LT); __Pyx_XGOTREF(__pyx_t_7); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 242, __pyx_L1_error) __pyx_t_3 = __Pyx_PyObject_IsTrue(__pyx_t_7); if (unlikely(__pyx_t_3 < 0)) __PYX_ERR(0, 242, __pyx_L1_error) __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0; if (__pyx_t_3) { /* … */ }
+243: 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_L33; }
+244: numerator = -numerator
__pyx_t_7 = PyNumber_Negative(__pyx_v_numerator); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 244, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_7); __pyx_t_7 = 0;
+245: denominator = -denominator
__pyx_t_7 = PyNumber_Negative(__pyx_v_denominator); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 245, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_7); __pyx_t_7 = 0;
246: else:
+247: g = -g
/*else*/ { __pyx_t_7 = PyNumber_Negative(__pyx_v_g); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 247, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF_SET(__pyx_v_g, __pyx_t_7); __pyx_t_7 = 0; } __pyx_L33:;
+248: 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) { /* … */ }
+249: numerator //= g
__pyx_t_7 = PyNumber_InPlaceFloorDivide(__pyx_v_numerator, __pyx_v_g); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 249, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF_SET(__pyx_v_numerator, __pyx_t_7); __pyx_t_7 = 0;
+250: denominator //= g
__pyx_t_7 = PyNumber_InPlaceFloorDivide(__pyx_v_denominator, __pyx_v_g); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 250, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_7); __Pyx_DECREF_SET(__pyx_v_denominator, __pyx_t_7); __pyx_t_7 = 0;
+251: 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;
+252: 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;
253:
+254: @classmethod
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256: """Converts a finite float to a rational number, exactly.
257:
258: Beware that Fraction.from_float(0.3) != Fraction(3, 10).
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260: """
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297: else:
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299:
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301: """Closest Fraction to self with denominator at most max_denominator.
302:
303: >>> Fraction('3.141592653589793').limit_denominator(10)
304: Fraction(22, 7)
305: >>> Fraction('3.141592653589793').limit_denominator(100)
306: Fraction(311, 99)
307: >>> Fraction(4321, 8765).limit_denominator(10000)
308: Fraction(4321, 8765)
309:
310: """
311: # Algorithm notes: For any real number x, define a *best upper
312: # approximation* to x to be a rational number p/q such that:
313: #
314: # (1) p/q >= x, and
315: # (2) if p/q > r/s >= x then s > q, for any rational r/s.
316: #
317: # Define *best lower approximation* similarly. Then it can be
318: # proved that a rational number is a best upper or lower
319: # approximation to x if, and only if, it is a convergent or
320: # semiconvergent of the (unique shortest) continued fraction
321: # associated to x.
322: #
323: # To find a best rational approximation with denominator <= M,
324: # we find the best upper and lower approximations with
325: # denominator <= M and take whichever of these is closer to x.
326: # In the event of a tie, the bound with smaller denominator is
327: # chosen. If both denominators are equal (which can happen
328: # only when max_denominator == 1 and self is midway between
329: # two integers) the lower bound---i.e., the floor of self, is
330: # taken.
331:
+332: if max_denominator < 1:
__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_ERR(0, 332, __pyx_L1_error) __pyx_t_2 = __Pyx_PyObject_IsTrue(__pyx_t_1); if (unlikely(__pyx_t_2 < 0)) __PYX_ERR(0, 332, __pyx_L1_error) __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0; if (__pyx_t_2) { /* … */ }
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+335: return Fraction(self)
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336:
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346:
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354:
355: @property
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358:
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421: """a ** b
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423: If b is not an integer, the result will be a float or complex
424: since roots are generally irrational. If b is an integer, the
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/* … */
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433: else:
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436: # reversed call
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444:
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513:
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518:
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679:
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684:
685:
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696: else:
697: # A fractional power will generally produce an
698: # irrational number.
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703:
704:
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707:
708:
709: """
710: In general, we want to implement the arithmetic operations so
711: that mixed-mode operations either call an implementation whose
712: author knew about the types of both arguments, or convert both
713: to the nearest built in type and do the operation there. In
714: Fraction, that means that we define __add__ and __radd__ as:
715:
716: def __add__(self, other):
717: # Both types have numerators/denominator attributes,
718: # so do the operation directly
719: if isinstance(other, (int, Fraction)):
720: return Fraction(self.numerator * other.denominator +
721: other.numerator * self.denominator,
722: self.denominator * other.denominator)
723: # float and complex don't have those operations, but we
724: # know about those types, so special case them.
725: elif isinstance(other, float):
726: return float(self) + other
727: elif isinstance(other, complex):
728: return complex(self) + other
729: # Let the other type take over.
730: return NotImplemented
731:
732: def __radd__(self, other):
733: # radd handles more types than add because there's
734: # nothing left to fall back to.
735: if isinstance(other, Rational):
736: return Fraction(self.numerator * other.denominator +
737: other.numerator * self.denominator,
738: self.denominator * other.denominator)
739: elif isinstance(other, Real):
740: return float(other) + float(self)
741: elif isinstance(other, Complex):
742: return complex(other) + complex(self)
743: return NotImplemented
744:
745:
746: There are 5 different cases for a mixed-type addition on
747: Fraction. I'll refer to all of the above code that doesn't
748: refer to Fraction, float, or complex as "boilerplate". 'r'
749: will be an instance of Fraction, which is a subtype of
750: Rational (r : Fraction <: Rational), and b : B <:
751: Complex. The first three involve 'r + b':
752:
753: 1. If B <: Fraction, int, float, or complex, we handle
754: that specially, and all is well.
755: 2. If Fraction falls back to the boilerplate code, and it
756: were to return a value from __add__, we'd miss the
757: possibility that B defines a more intelligent __radd__,
758: so the boilerplate should return NotImplemented from
759: __add__. In particular, we don't handle Rational
760: here, even though we could get an exact answer, in case
761: the other type wants to do something special.
762: 3. If B <: Fraction, Python tries B.__radd__ before
763: Fraction.__add__. This is ok, because it was
764: implemented with knowledge of Fraction, so it can
765: handle those instances before delegating to Real or
766: Complex.
767:
768: The next two situations describe 'b + r'. We assume that b
769: didn't know about Fraction in its implementation, and that it
770: uses similar boilerplate code:
771:
772: 4. If B <: Rational, then __radd_ converts both to the
773: builtin rational type (hey look, that's us) and
774: proceeds.
775: 5. Otherwise, __radd__ tries to find the nearest common
776: base ABC, and fall back to its builtin type. Since this
777: class doesn't subclass a concrete type, there's no
778: implementation to fall back to, so we need to try as
779: hard as possible to return an actual value, or the user
780: will get a TypeError.
781: """
782:
783:
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