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r r r r �__le__" s zDummyFloat.__le__c C s | j | t j � S)N)r r �lt)r
r r r r �__lt__# s zDummyFloat.__lt__c C s | j | t j � S)N)r r �ge)r
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r r r r �__gt__% s zDummyFloat.__gt__c C s d s t d � � d S)NFz/__float__ should not be invoked for comparisons)�AssertionError)r
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r r r r r F s zDummyRational.__le__c C s | j | j | j | j k S)N)r. r4 r/ r3 )r
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DummyFractionz6Dummy Fraction subclass for copy and deepcopy testing.N)r& r' r( r) r r r r r5 Q s r5 c @ s e Z d Z d d � Z d S)�GcdTestc C s� | j t d � � t d d � Wd QRXt j � ��t j d d t � | j d t d d � � | j d t d d � � | j d t d d � � | j d t d d � � | j d t d d � � | j d t d d � � | j d t d d � � | j d t d d � � | j d t d d
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r r r �testMiscV s&
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ZexpectedZactualr r r �assertTypedEqualss s z FractionTest.assertTypedEqualsc O sg y | | | � Wn; | k
rN } z | j | t | � � WYd d } ~ Xn X| j d | j � d S)z@Asserts that callable(*args, **kwargs) raises exc_type(message).Nz
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r; r: r? � � � � � ic �q zFraction(12, 0)r< g �?y @z3/2y y �?)r r7 )r9 r7 )r9 rW rA )rA r7 rA rA )rA r7 rA )r7 r7 ���ra )r7 rX )r9 r; � m+?�R )rb r7 l m+?�R )rW r? ���)rc rY i����)r] r^ y �? @)rF rK r rV �ZeroDivisionError� assertRaisesr )r
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� � | j t t t d � � | j t t t d � � d S)NrY rX g @r r7 g � �L�33f � g�������?�nan�infz-inf)rY rX )r r7 g �)rg rh )rF rK r re �
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r r r �testInitFromFloat� s z FractionTest.testInitFromFloatc C s� | j d t t t d � � � � | j d t t t d � � � � | j d t t t d � � � � | j t t t d
� � | j t t t d � � | j t t t d � � | j t t t d
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r r r �testInitFromDecimal� s z FractionTest.testInitFromDecimalc C sh | j d- t t d � � � | j d. t t d � � � | j d/ t t d � � � | j d1 t t d � � � | j d2 t t d
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� � � | j d7 t t d � � � | j d8 t t d � � � | j d9 t t d � � � | j d: t t d � � � | j d< t t d � � � | j d= t t d � � � | j d> t t d � � � | j t d t d � | j t d t d � | j t d t d � | j t d t d � | j t d! t d" � | j t d# t d$ � | j t d% t d& � | j t d' t d( � | j t d) t d* � | j t d+ t d, � d S)?NrY r7 �5rW rX z3/2z
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� z 3.2 z -3.2 z -3. z .6 �5 z32.e-5�@B z1E+06i 0 z-1.23e4r z .0e+0 z-0.000e0zFraction(3, 0)z3/0z"Invalid literal for Fraction: '3/'z3/z"Invalid literal for Fraction: '/2'z/2z$Invalid literal for Fraction: '3 /2'z3 /2z$Invalid literal for Fraction: '3/+2'z3/+2z%Invalid literal for Fraction: '+ 3/2'z+ 3/2z#Invalid literal for Fraction: '3a2'Z3a2z%Invalid literal for Fraction: '3/7.2'z3/7.2z%Invalid literal for Fraction: '3.2/7'z3.2/7z!Invalid literal for Fraction: '.'�.)rY r7 )rW rX )rW rX ���)rw rX )rr rX )rs rY ��)rx rY rw )rw r7 )rW rY )r7 rt )ru r7 ����)ry r7 )r r7 )r r7 )rF rK r rV rd rk )r
r r r �testFromString� sX
zFractionTest.testFromStringc C s� t d d � } | j d d � | j d
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testImmutable� s zFractionTest.testImmutablec C s� | j t t j d � | j d t t j d � � � d } | j | d f t t j | � � � | j d t t j d � � � | j d t t j d � � � | j d t t j d � � � | j d t t j d
� � � | j t d � t t j d
� � � | j d t t j d � � � | j d t t j d � � � d } | | } | j t d t j | � | j t d t j | � | j t d t j | � d S)!NrW y @rZ r7 l �{�C r g g $@rY rX g @� l+?�R g�J��-�Dr: � �L�33f � g������ @g �z Cannot convert inf to Fraction.z Cannot convert -inf to Fraction.z Cannot convert nan to Fraction.y @ @)rZ r7 )r r7 g �)rZ r7 ���)r� rX g �)r� r7 l m+?�R )r� r� )
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zFractionTest.testFromFloatc C s� | j t t j d � | j t d d � t j d � � | j t d � t j t d � � � | j t d d � t j t d � � � | j t d d � t j t d
� � � | j t d � t j t d � � � | j d t d d � t j t d d d
� � � | j t d t j t d � � | j t d t j t d � � | j t d t j t d � � | j t d t j t d � � d S)NrW y @rZ r7 r z-0rY z0.5i� z5e-3i� Z5e3� z0.�9z$Cannot convert Infinity to Fraction.rj z%Cannot convert -Infinity to Fraction.z-infz Cannot convert NaN to Fraction.ri z Cannot convert sNaN to Fraction.ro y @ @l �7�3M�e') re r r Z from_decimalrF r rV rl rk )r
r r r �testFromDecimal s( "%((% z FractionTest.testFromDecimalc C sA t d � } | j | j d � t d d � � | j | j d � t d d � � | j | j d � t d d � � | j | j d � t d d � � | j t d d � j d
� t d � � | j t d d � j d � t d
d � � | j t d � j d � t d � � x- d D]% } | j t d t d � j | � qWd S)Nz3.1415926535897932i' ic r` �p iM �j �� rn �d r7 �e �f r z$max_denominator should be at least 1i����rA )r rA )r rF Zlimit_denominatorrV rk )r
Zrpi�ir r r �testLimitDenominator+ s "#""(+%
z!FractionTest.testLimitDenominatorc C s! | j d t j t d d � � � | j d t j t d d � � � | j d t j t d d � � � | j d t j t d d � � � | j d t j t d d � � � | j d t t d d � � � | j d t t d d � � � | j d t t d d � � � | j d t t d! d � � � | j d" t t d# d � � � | j d t t d d � � � | j d
t t d d � � � | j d t
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r r r �testConversions9 s" """"" ! 2z FractionTest.testConversionsc C s� | j t d � t t d
� d � � | j t d � t t d � d � � | j t d � t t d � d � � | j t d d � t t d d
� d � � | j t d d � t t d d
� d � � d S)Nrn � rX � r� � r7 rZ r; r� � i8���ij���ra i8���i���ra rA ra i�ra i��)rN r r� )r
r r r � testRoundQ s
%%%+zFractionTest.testRoundc C s | j t d d � t d d � t d d � � | j t d d � t d d � t d d � � | j t d d � t d d � t d d � � | j t d d � t d d � t d d � � | j d t d d � t d d � � | j d t d d � t d � � | j t d d � t d d � t d d � � | j t d d � t d d � t d � � | j t d d � t d d � t d � � | j d
t d � t d d � � | j t d d � t d d �
� t t d � t d d � � } | j | j d � | j | j d � t d d � d } | j | t d d � � | j | j d � | j | j d � t d d � d } | j | t d d � � | j | j d � | j | j d � t d d � d } | j | t d d � � | j | j d � | j | j d � d S) Nr7 rX rZ rY rW r� r| r\ r: r9 � � g @r rw l m+?�R l m+?�R i����rw rA rA rA rA ra ra rA ra ) rF r rN �powr� �real�imagrH rI )r
�z�pr r r �testArithmeticX s4 ////&#/,,## zFractionTest.testArithmeticc C s� | j t d d � t d d � d � | j d t d d � d � | j d t d d � d � | j t d d � d t d d � � | j d d t d d � � | j d d t d d � � | j t d d � t d d � d � | j d t d d � d � | j d t d d � d � | j t d d � d t d d � � | j d d t d d � � | j d d t d d � � | j t d d � t d d � d � | j d t d d � d � | j d t d d � d � | j t d d � d t d d � � | j d d t d d � � | j d! d" t d d � � | j t d d � t d d � d � | j d t d d � d � | j d# t d d � d$ � | j t d d � d t d d � � | j d
d t d d � � | j d% d& t d d � � | j d t d d � d � | j d t d d � d � | j d d t d d � � | j d' d( t d d � � | j d d t d d � � | j t d d � t d d � d � | j d t d d � d � | j t d d � d t d d � � | j d d t d d � � | j t d d � t d d � d) � | j t d d � t d d � d � | j d t d d � d � | j d* t d d � d+ � | j d d t d d � � t d, t d d � � } | j d | j � | j d | j � | j t d d � d t d- d � � | j d d t d d � � | j d d t d. d � � | j d/ d0 t d d � � | j t t j t d d � d1 � d S)2Nr[ rZ r7 g�������?g �?y r\ g�������?g�������?g $@r r: r_ g r� rX r| g @g �?y�������? y �? y�������? y �? i����g�������g�������y������� y �? y�������? y �? y�������? y �? y�������? y �? y�������? y �? y $@ y �? l m+?�R l �d�&O�!ra y�������? y �? rA ra ra y �? y �? ra )
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r� r r r �testMixedArithmeticu s^ & & & & & & & & & & && & z FractionTest.testMixedArithmeticc C sT | j t t j t d d � t d � � | j t t j t d � t d d � � d S)NrW r[ z 3.1415926)re r r �addr r )r
r r r �testMixingWithDecimal� s z"FractionTest.testMixingWithDecimalc C sQ | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � d S)Nr7 rX rW )�
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r r r �testComparisons� s %%%%%%%%z FractionTest.testComparisonsc C s | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � | j t d d � t d d � k � d S)Nr7 rX rW r| r9 )r� r r+ r� )r
r r r � testComparisonsDummyRational� s8 %%%%%%%%%%%%%%%%%%%%%%%%%%%z)FractionTest.testComparisonsDummyRationalc C s� t d � } t d d � } | j | | k � | j | | k pI | | k � | j | | k � | j | | k o{ | | k � | j | | k � | j | | k p� | | k � | j | | k � | j | | k o� | | k � d S)Ng �?g @r7 rW gUUUUUU�?)r r r� r� )r
�x�yr r r �testComparisonsDummyFloat� s z&FractionTest.testComparisonsDummyFloatc C s� | j d t d d � k � | j d t d d � k � | j t d d � d k � | j t d d � d k � | j t d d � d k � | j t d d � d k � | j d t d d � k � | j d t d d � k � | j t d � t d d � k � | j t d
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testMixedLess� s """""zFractionTest.testMixedLessc C s� | j d t d d � k � | j d t d d � k � | j t d d � d k � | j t d d � d k � | j d t d d � k � | j d t d d � k � | j t d d � d k � | j t d d � d k � | j t d � t d d � k � | j t d
� t d d � k � | j t d
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r r r �testMixedLessEqual� s """""z FractionTest.testMixedLessEqualc C s� | j t d � t d � k � | j d t t t j d � d � � k � | j d t t j d � d � k � | j d t t j d � d � k � | j d t t j d � d � k � | j d t t j d � d � k � d S)NrZ r: g�J��-�Dr7 l m+?�R l m+?�R )r� r r
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r r r �testBigFloatComparisons s ,&&&z$FractionTest.testBigFloatComparisonsc C sg | j t d � t d � k � | j t t j t d
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