ÿØÿà JFIF    ÿÛ „ !.%+&8&+/1555$;@;4?.451 4,$,44444444444414444444444444444444444444444444444444ÿÀ  á á" ÿÄ     ÿÄ ?    !1AQaq"2‘¡±ÁðBRbrÑá#‚’¢²3S CñÿÄ   ÿÄ !    !1QAa‘2ÿÚ   ? 5˜Z¯V¦cø)›t/? z¨±>Õ5€¶‹Á¤·¼z¼Ü¬+ñ®v¤¨_ˆR­BFn©—˜ý®ç̝P8gýt·ÉSTŦˆìät?þé¼íìN/Þa)ì–í6ô… Ï¿øÃj´¿KÇü]ÿ ªô¹-eKànëÕHTx}ýSÜ›ÿ ”7Ø×&µ<¦  ¥ÑO¶[Ù¯ä¨ÞÃÿ PZ-¬;#õ|•oaÿ ©CìÞz3˜öː/¤­ñTûIØ}š^ mÓ%ªxˆ¥ÉŸu=Z+ISe¿45™¼u;ú&WØ÷€æßQ™®{|íx*TC“#ZŠìZ§²‹ 6pv…³¿¡äª*áZÐ%ÒOáˆo"x«OHk w±æ+¬V(kMúŸ5Vö«$ ÁrÏbàb57/luR ¸ÑÛj Òµì`Ðœq­û žICÀÊ•©4€Âcà¨Ï€O´<èÐ:›ù(Ë^L8þ‘ÍÌ#¸Ð_Ì©ÙK(Öz 4¬û+¸;ü’V’84‘¬ÃŽ:[â‡ÔÌáõp¢~§ªlæ£ö{®G>J¼"°‡7¯ÆÉèßû ‹É‹§ÁòÃýâßî ^ƾÙõ‹×óH#«LP½ïX=xÑÍ$|W?•~• îëÔ©ª‹ {ÝT…Kÿ ”hûâá)J*ö˜–ÔU;iÇ€/ ÆþjóZ\ýwØ=Ìm ºèËL9 ýèÆð/¨’¥öo=nË.%Îì ŽÕ¯È|{Oj²ƒE6e/ßdÄõ²Ìâ1O®ò×TsəԸhOMýíMˆ¿¼H˜l²,7Â¥#MF/Úf°Ö½± ¸–dr‹NýÊ íjqx{œÉ ä-È ¦ øÄër¨q°ð †nцýÑÄÆ’mä…n<0È™;ÁÝá¯ÁZƒ7FÀmì­ É&9ˆîéi¶ùN§Y• ÃZãAâ?•‡©‰ , ó¾IŸŠc1 4â&y­&pŠ­6;M À 0¹qç»p.á …ŸÅáK@%6·y6ƒ‰3?”úºŽ‰éX5ªPT §µ!=Mž«Ú½‹ÅgÂSâÉaþÓoö–¯ÁÔìR>5éÿ üs¶ÆUcÌ kÇR ]ÿ ù¬¼«VŽ;Â|‡~¢¦”ÏÅ°æ {L™Õ°Óv¹ò¸írŽ¡×¢CÃ!íVÕ {¶»sŒNPg/ "uÕbkm²“$ďå¿é¹§°½æz¯6 †s¿!s–wÚÝ“™Œ °.ûj>·+™Òa…©Œ&rÝÎtÛë긪Ît’LAVp%c Úý[ÄzJ¾ÇàXXç@˜ó<êL]·T˜¾¥1Ó©V‡g´æ½¦Ý@¹óø!_@´ÞâSÁ —S3™•& ]@JHÚý©ZŽ €×æÔr»Áf!‡yÞ4Mv*èÓã_{‘åóUuљØ«Oïé*®EvÑ Œ÷‡U \"㪒ÍK+À 4“M¡ï:0¥5í!'<@î´”>Ç»&Z–ïCCV˜Ì5Šo&îhè.žû |ÓK©h$s6KìŒëã)¹hI¦GïOåóI;ììü#É$Š0…Ææ¥TØ.5­¾gn´ “ÂÖ\:hœ89G)J@„}œ:’Ò{/Š"¦_Æ×7Æ3VÇŠÊa]ÚŒÙ€Ä–=®uÁßâACZƒ§§£ Qnâ:«,×{tyø¬iÛcœÜÄ€H½ÄÍCk´÷šß .W'b¤Íåh]÷€=,Žv×cÚEÚHXJX¶îo¨FÒtèöŸ>ªª6[J®Fµ£sGÁeqõfe\íjÒÐïÄÐGˆe1Ø‹.Ø”‘Ëuø Y­ˆÜ ŽG|zùªüMpDnQWÄ”%JŠ™)â*p@Örš«ÕT2Ð%ˆG#ª„ ·¤!°ŸOTÂT¸aÚ%4&h™LµšØüÐ.F¿²ÐÞ_Ç‚¾ÅÃaÜ÷09Æ q€öy˜v‡85õN÷]¬äѼóS{°_MŽ¬úÔ#°Ç¸0åÞè2ëôPcvÆw9®ií1Ä8F™˜à‰´+‰Ik1òÝ7“Ñ×ÒsÝ\x‚h`ÞÑ`ó"|µEcý£n˜h`}GÞ !±ù²Ápü²ß6 0ïi󜵩SÈÇ7˜-ÕURO˜¦´f$ªž-Í6(œ}<„ éc øs]ŽŽ„*—¾ ìdŽ„)méª\¿êÎIg¾ØÞ~I#C/¼¼´EÁÈŽi8“©õådô·>euä ƒ'Ê×लR1ÉJE1ÐAát`t;ÇР%Ý<‡¥„ÍÆ`×Oyó)õiI€ñQaŸ4Ûù\áàaÃÔ¹HÃu¹*k€¦<„e S‡&õÏ B!ŽhüÞ`yj}mªf×\¿ Ç~æ­9‡û\՞Ǖg²1Žû5V7 !àöšm° c`ܬøÇìµÒ'P"?…´Ö,"§^•õŽ¨sÔ)6˜sæéÍR¼ ò|Sl”‹7 nPW Gòú÷½§O¯‡„l¡kSÞŒr½PÊ@æ¢pŽ-mÿ #Ÿ˜Àº¶Áä¦;ïÔæ$1££`“Õ>„—·ž)ßð³ñ#Ï Ô$¶œ‰ÊE‹À;÷º ¯«P:Ñ”8–IÊtpÞ3ª“>ê“þës4ò2OÏÕ­±zô†Õ§‰.÷ä¸;¿˜“'œ›žª}«Œ{ª±Ì 9ÔóÞÕ‡0 $íWV3Üì¬ —@kÝ4@¿r¼±½¬™›?øØæ´'Áé®CË3-g$˜ö‡×auÚi´Žp/êÛ æF›Ú2v‹ã¿¿,nB1̨ƃqÞa5͝@&Æû“él÷ \C²½UÍc ¯k×¢U ÖéQå™—-r wô ÞÏ<Ò=&=ÿ Ôê Òêˈt,i—;LîÜ á¸*ÚÃ1$êL•LÍ <É)ýÐà’ ;F™{ƒ™˜€&'}‚ãÄK`¡ÞT@I;®žZóè‚s’7®°›+§O­Åq©é»²9<Ô J ¼9O’HL»Ùïì¸rk¼Ž_ý‘TŸu[²ßÚŒ·ü÷B%¯E ŸÔX5êO´ Ç•€’I0 ÉJX` ñ¹õ%;µŸD‘«´€àwÒ™U ûئžÖö\×®×´8 ½‡ºÐÆÓ§?Àkmœ=;d5*@-ì0F Rªýš[Ü6âö̃ڸr*KA9· u*µæ£?U¸Âêí†8@¦X4 e-ò„0s{ HâUpU?¼mñRa°®a%Ð'tÉ×’\¾ÊÉ]t›h>·(Ë@R¼¡Ãt h}’O÷au<+nT…Ö…MӐ??Óe95 q>í/;&JSû °¯ÊéÞ øƒ*Ã2½Ài&:nôUl=¾¿5eˆ3”ñc|Ú2V”>„»&eE;«ÚäC p¢Û úy 9š[ŒÌx¼擼A&DåÒ¯ˆ¤ÀÌ;"˜ ÏQä¸åhÊ}Ûq«Û0WžÒ|»€ø®öCm5•\ÇÀ§Pe3£]0ÃàLDÉ‰1øªxjgwT‚÷¿LΨK‹›ùs—xˆÜ±µ kæ¸f‰‰ÜGk/LÛØ6d9ò¶ùA{ƒA3š/¬D¬khÓk‰`˜"㯒r¿±Óã jx‡°e}<Ñø\3y:'À•/h½Í€Ç4~g ?Û(¼]v‘ªlKÎâ~?O‚W%{Ì:“'©úNq¾›úo(X’¥¯ˆ nFê{Ç€ü?º'ë ø‹ì Þ09ŒÌç9Æ —ËC`j@ÓÄ(+a‹un¸#ÂꟋ{K`‘ÑÍÍ'à´»/Û,KW;Þ4²þð ï Nm|~fGÏ(…³Ã)«1ö­Õ ¥‡¨©ƒÃ™ü-s=à=U66Ï«Ýc蓦W¹íž®›nÔ%êÇìŒ<#Ü×84ån®Ð ÒåOC` ñânÑs‡¢ç 1õ%Îhì½Ã½® e:ݼUZo™`  ÅZŸŒÊ«ê1ÏÄo$q¹Þ€©ˆhÐÉä¯ñ[!…Ú˜àJ:x2$Íß&PåT£6ç— ‡Í*4Ýšçjÿ ‰É nófÐ ó(L5C•åÆ\rMÒ@ò }y-W}™üýVù—ú¢=Ù”c®‘< M ž ´Phr ¦©TD ‘ù.$´÷O‡‘V2Æò.=IUŒ=ž‡â¬i™aþÓåÙ?òUø'ØÖ•.~* šTŒ!•-×áºTâ®ä#õü'´ eýlYÅÓeÕKÂrT"CÚ@u!Óxƒ{š3€}1¿(r}%«nËamjÑ%ÑNEò v ˜à  σöK³,*º.àzù¨™Ó ÚçâU¦*¿ 9{%Ö¹ njûdaXöb) kÛƱûÓ\°M7ˆÂ=û›ç¿Ã‚­V»Cg–8ÙêE- j)k$º`Ã-ùEýeBÆÇ]c¡°ñty&Òd0nõ'¡W+ƒ*|–øµFa\GQªEAÔp5\Ǽ·¼Ç8·õ -â§Ú[ ‡ uZeÖ 3}×d'+¹:ð+K†Û®s!Ï$úe€<Û”x)1»a­¡LC]¸µík…ÚàA»AYº{†ªS[¦5HÒ7ù --,ísòDØ€èk ÞÀîÜ ò@â( ËNˆë›4ô½•/¦o‡€Û7 ê•ÆêòðÜy'Án½µ á˜ݦ ndeo…[ì¶Ê,¥R³Ä=À±—–ß;£™´ñSâ*g§”ïaið‘Jå~™ÓÞ ß³Õ¢»8x埒²52>AÊb&-÷\7´éÄù€T˜,w;3{ï˜k…à¹ÄqÀ«œ{€\ ˆ¾[´¨јr &Úé„Ívˆ±8†¿]|¬ņ4I×pÞS1ÈÖz‰#Ìv‡G!YNògñ:màTz¢Ý1ô©^O=~ë|5Bã™ç•¼µõ•bÆ@úÕS¬ÈŒ#¬zünrŸ û” Z²•ï›èðV"ÁHÚý©wÝ €7¼Ìu1hÑa3Éä û f$o¿É ™Ú›ÝçnpÒ3äÌ3†Í§,Äï]$‰/pê †«À¼¸e9­Æê_C]žƒ·ý·frÁN«, E=›Çq -‰öŒ:aÏ¿±í&£Í:-} 84‘ÿ eƒQÑeëSsuiA ³g㟥ú£?ÿ ʼn*”“÷aühe:ÊWa@ÒÞk±eØ] F Ô—r.åä˜ @ö¥ªZoÐýYL·¥S²G/‡ñ <~*ZÆ´è>JlòàÛƽÿ 窘ìGN¢:I®KšJp/`íIÁÀõ#Ä-€ö­šµŒoF4|ÆQØÆ@Ì|£Ô…¢À{9˜è½Üó›€ôYÒÎYsið;ís¤€à²ˆ‚4qÉVŒI$ ‰"° æµ8cXGjœˏ¡Aâý•ËÜ¢ûï e·çLx']á"oÅÎê3¯Ç—¹”ó0nå‚âg{Œñ> S´˜îè°g238‚ãköÝfÚd´6Ò€;ò÷±¢™¼›º ¢Æ'¥Ðx'e¬ç ]bÈÆV¢ó‹kýBO ðÊâ$Ÿ!×T 3Mýמ žìٍàÌü‘8÷€àæØ8æ©6‰©L´«…oãpð„~Çk‰!ñ;‹”ÛžÍ àž±z Ÿôû øŸÝužÏ;ÿ #|u6™Þ¬ÚˆÐõA4¶â|ôl|Ê2ŽÇ¤ÝÅÇY.<#Aí.k§hóF‚”Y; 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Þ'¯°ÌME[YéïĵÂCå½ Ué©Áû'Ê9%eÔðNU”ë‘ÌsD3/®+UI˜9h.WC”빓$#:pz:YÓ ¿xž* ³$Í +$kñAŠ‹†¢ Uê>¸)_š¬÷©ßAÂÔb9ÇU ¯¾á•9¯ÏÏ÷O÷¼¼Fähal1‰3Ì[Ïr•´UCksNÐ] R‘¸¥H+§Šé†c©vÖÞ0iÓ76s†î!§=ß ¼~Ô'°Ãmäoäš³ªøi1úÉ)³yV8 CLÄØÁ‘WYïi€H6ÖÑiámø^ÈY´°Ñ7¥Û*—Ñ©L«Qƒï—Ùrÿ ›£Ð*š¸ˆL©ˆ$ˆ ÷¾D§9È®«qbqC)–ˆïv´çñsÑVT­Ø, <àïºÀO«Jý·õ àfPìð .wFšir´þ’2_Y *Æ€x\« ì€9š@ Ž|F⇥ˆkZ@hÖÄ0t¿-<“‹qµ¾*ZL¤Ú)&BJpÓF5=$„at*Zš$’ÑtdûÝRI1 2Ž‰$€$I$#‰SÞ’Hë¬ï;Á$¡t$’`<(ñÇt)$‡Ð.Êf¢X’Kt=Éé$‚ˆªè¢oÝëòI%Rgcª÷ŠyI%¡‰ÿ !ñ)´õ $¤ Ô’IIGÿÙ"""Tests for Lib/fractions.py.""" from decimal import Decimal from test.support import requires_IEEE_754 import math import numbers import operator import fractions import functools import sys import unittest from copy import copy, deepcopy from pickle import dumps, loads F = fractions.Fraction class DummyFloat(object): """Dummy float class for testing comparisons with Fractions""" def __init__(self, value): if not isinstance(value, float): raise TypeError("DummyFloat can only be initialized from float") self.value = value def _richcmp(self, other, op): if isinstance(other, numbers.Rational): return op(F.from_float(self.value), other) elif isinstance(other, DummyFloat): return op(self.value, other.value) else: return NotImplemented def __eq__(self, other): return self._richcmp(other, operator.eq) def __le__(self, other): return self._richcmp(other, operator.le) def __lt__(self, other): return self._richcmp(other, operator.lt) def __ge__(self, other): return self._richcmp(other, operator.ge) def __gt__(self, other): return self._richcmp(other, operator.gt) # shouldn't be calling __float__ at all when doing comparisons def __float__(self): assert False, "__float__ should not be invoked for comparisons" # same goes for subtraction def __sub__(self, other): assert False, "__sub__ should not be invoked for comparisons" __rsub__ = __sub__ class DummyRational(object): """Test comparison of Fraction with a naive rational implementation.""" def __init__(self, num, den): g = math.gcd(num, den) self.num = num // g self.den = den // g def __eq__(self, other): if isinstance(other, fractions.Fraction): return (self.num == other._numerator and self.den == other._denominator) else: return NotImplemented def __lt__(self, other): return(self.num * other._denominator < self.den * other._numerator) def __gt__(self, other): return(self.num * other._denominator > self.den * other._numerator) def __le__(self, other): return(self.num * other._denominator <= self.den * other._numerator) def __ge__(self, other): return(self.num * other._denominator >= self.den * other._numerator) # this class is for testing comparisons; conversion to float # should never be used for a comparison, since it loses accuracy def __float__(self): assert False, "__float__ should not be invoked" class DummyFraction(fractions.Fraction): """Dummy Fraction subclass for copy and deepcopy testing.""" def _components(r): return (r.numerator, r.denominator) class FractionTest(unittest.TestCase): def assertTypedEquals(self, expected, actual): """Asserts that both the types and values are the same.""" self.assertEqual(type(expected), type(actual)) self.assertEqual(expected, actual) def assertTypedTupleEquals(self, expected, actual): """Asserts that both the types and values in the tuples are the same.""" self.assertTupleEqual(expected, actual) self.assertListEqual(list(map(type, expected)), list(map(type, actual))) def assertRaisesMessage(self, exc_type, message, callable, *args, **kwargs): """Asserts that callable(*args, **kwargs) raises exc_type(message).""" try: callable(*args, **kwargs) except exc_type as e: self.assertEqual(message, str(e)) else: self.fail("%s not raised" % exc_type.__name__) def testInit(self): self.assertEqual((0, 1), _components(F())) self.assertEqual((7, 1), _components(F(7))) self.assertEqual((7, 3), _components(F(F(7, 3)))) self.assertEqual((-1, 1), _components(F(-1, 1))) self.assertEqual((-1, 1), _components(F(1, -1))) self.assertEqual((1, 1), _components(F(-2, -2))) self.assertEqual((1, 2), _components(F(5, 10))) self.assertEqual((7, 15), _components(F(7, 15))) self.assertEqual((10**23, 1), _components(F(10**23))) self.assertEqual((3, 77), _components(F(F(3, 7), 11))) self.assertEqual((-9, 5), _components(F(2, F(-10, 9)))) self.assertEqual((2486, 2485), _components(F(F(22, 7), F(355, 113)))) self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)", F, 12, 0) self.assertRaises(TypeError, F, 1.5 + 3j) self.assertRaises(TypeError, F, "3/2", 3) self.assertRaises(TypeError, F, 3, 0j) self.assertRaises(TypeError, F, 3, 1j) self.assertRaises(TypeError, F, 1, 2, 3) @requires_IEEE_754 def testInitFromFloat(self): self.assertEqual((5, 2), _components(F(2.5))) self.assertEqual((0, 1), _components(F(-0.0))) self.assertEqual((3602879701896397, 36028797018963968), _components(F(0.1))) # bug 16469: error types should be consistent with float -> int self.assertRaises(ValueError, F, float('nan')) self.assertRaises(OverflowError, F, float('inf')) self.assertRaises(OverflowError, F, float('-inf')) def testInitFromDecimal(self): self.assertEqual((11, 10), _components(F(Decimal('1.1')))) self.assertEqual((7, 200), _components(F(Decimal('3.5e-2')))) self.assertEqual((0, 1), _components(F(Decimal('.000e20')))) # bug 16469: error types should be consistent with decimal -> int self.assertRaises(ValueError, F, Decimal('nan')) self.assertRaises(ValueError, F, Decimal('snan')) self.assertRaises(OverflowError, F, Decimal('inf')) self.assertRaises(OverflowError, F, Decimal('-inf')) def testFromString(self): self.assertEqual((5, 1), _components(F("5"))) self.assertEqual((3, 2), _components(F("3/2"))) self.assertEqual((3, 2), _components(F(" \n +3/2"))) self.assertEqual((-3, 2), _components(F("-3/2 "))) self.assertEqual((13, 2), _components(F(" 013/02 \n "))) self.assertEqual((16, 5), _components(F(" 3.2 "))) self.assertEqual((-16, 5), _components(F(" -3.2 "))) self.assertEqual((-3, 1), _components(F(" -3. "))) self.assertEqual((3, 5), _components(F(" .6 "))) self.assertEqual((1, 3125), _components(F("32.e-5"))) self.assertEqual((1000000, 1), _components(F("1E+06"))) self.assertEqual((-12300, 1), _components(F("-1.23e4"))) self.assertEqual((0, 1), _components(F(" .0e+0\t"))) self.assertEqual((0, 1), _components(F("-0.000e0"))) self.assertRaisesMessage( ZeroDivisionError, "Fraction(3, 0)", F, "3/0") self.assertRaisesMessage( ValueError, "Invalid literal for Fraction: '3/'", F, "3/") self.assertRaisesMessage( ValueError, "Invalid literal for Fraction: '/2'", F, "/2") self.assertRaisesMessage( ValueError, "Invalid literal for Fraction: '3 /2'", F, "3 /2") self.assertRaisesMessage( # Denominators don't need a sign. ValueError, "Invalid literal for Fraction: '3/+2'", F, "3/+2") self.assertRaisesMessage( # Imitate float's parsing. ValueError, "Invalid literal for Fraction: '+ 3/2'", F, "+ 3/2") self.assertRaisesMessage( # Avoid treating '.' as a regex special character. ValueError, "Invalid literal for Fraction: '3a2'", F, "3a2") self.assertRaisesMessage( # Don't accept combinations of decimals and rationals. ValueError, "Invalid literal for Fraction: '3/7.2'", F, "3/7.2") self.assertRaisesMessage( # Don't accept combinations of decimals and rationals. ValueError, "Invalid literal for Fraction: '3.2/7'", F, "3.2/7") self.assertRaisesMessage( # Allow 3. and .3, but not . ValueError, "Invalid literal for Fraction: '.'", F, ".") def testImmutable(self): r = F(7, 3) r.__init__(2, 15) self.assertEqual((7, 3), _components(r)) self.assertRaises(AttributeError, setattr, r, 'numerator', 12) self.assertRaises(AttributeError, setattr, r, 'denominator', 6) self.assertEqual((7, 3), _components(r)) # But if you _really_ need to: r._numerator = 4 r._denominator = 2 self.assertEqual((4, 2), _components(r)) # Which breaks some important operations: self.assertNotEqual(F(4, 2), r) def testFromFloat(self): self.assertRaises(TypeError, F.from_float, 3+4j) self.assertEqual((10, 1), _components(F.from_float(10))) bigint = 1234567890123456789 self.assertEqual((bigint, 1), _components(F.from_float(bigint))) self.assertEqual((0, 1), _components(F.from_float(-0.0))) self.assertEqual((10, 1), _components(F.from_float(10.0))) self.assertEqual((-5, 2), _components(F.from_float(-2.5))) self.assertEqual((99999999999999991611392, 1), _components(F.from_float(1e23))) self.assertEqual(float(10**23), float(F.from_float(1e23))) self.assertEqual((3602879701896397, 1125899906842624), _components(F.from_float(3.2))) self.assertEqual(3.2, float(F.from_float(3.2))) inf = 1e1000 nan = inf - inf # bug 16469: error types should be consistent with float -> int self.assertRaisesMessage( OverflowError, "cannot convert Infinity to integer ratio", F.from_float, inf) self.assertRaisesMessage( OverflowError, "cannot convert Infinity to integer ratio", F.from_float, -inf) self.assertRaisesMessage( ValueError, "cannot convert NaN to integer ratio", F.from_float, nan) def testFromDecimal(self): self.assertRaises(TypeError, F.from_decimal, 3+4j) self.assertEqual(F(10, 1), F.from_decimal(10)) self.assertEqual(F(0), F.from_decimal(Decimal("-0"))) self.assertEqual(F(5, 10), F.from_decimal(Decimal("0.5"))) self.assertEqual(F(5, 1000), F.from_decimal(Decimal("5e-3"))) self.assertEqual(F(5000), F.from_decimal(Decimal("5e3"))) self.assertEqual(1 - F(1, 10**30), F.from_decimal(Decimal("0." + "9" * 30))) # bug 16469: error types should be consistent with decimal -> int self.assertRaisesMessage( OverflowError, "cannot convert Infinity to integer ratio", F.from_decimal, Decimal("inf")) self.assertRaisesMessage( OverflowError, "cannot convert Infinity to integer ratio", F.from_decimal, Decimal("-inf")) self.assertRaisesMessage( ValueError, "cannot convert NaN to integer ratio", F.from_decimal, Decimal("nan")) self.assertRaisesMessage( ValueError, "cannot convert NaN to integer ratio", F.from_decimal, Decimal("snan")) def test_as_integer_ratio(self): self.assertEqual(F(4, 6).as_integer_ratio(), (2, 3)) self.assertEqual(F(-4, 6).as_integer_ratio(), (-2, 3)) self.assertEqual(F(4, -6).as_integer_ratio(), (-2, 3)) self.assertEqual(F(0, 6).as_integer_ratio(), (0, 1)) def testLimitDenominator(self): rpi = F('3.1415926535897932') self.assertEqual(rpi.limit_denominator(10000), F(355, 113)) self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113)) self.assertEqual(rpi.limit_denominator(113), F(355, 113)) self.assertEqual(rpi.limit_denominator(112), F(333, 106)) self.assertEqual(F(201, 200).limit_denominator(100), F(1)) self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101)) self.assertEqual(F(0).limit_denominator(10000), F(0)) for i in (0, -1): self.assertRaisesMessage( ValueError, "max_denominator should be at least 1", F(1).limit_denominator, i) def testConversions(self): self.assertTypedEquals(-1, math.trunc(F(-11, 10))) self.assertTypedEquals(1, math.trunc(F(11, 10))) self.assertTypedEquals(-2, math.floor(F(-11, 10))) self.assertTypedEquals(-1, math.ceil(F(-11, 10))) self.assertTypedEquals(-1, math.ceil(F(-10, 10))) self.assertTypedEquals(-1, int(F(-11, 10))) self.assertTypedEquals(0, round(F(-1, 10))) self.assertTypedEquals(0, round(F(-5, 10))) self.assertTypedEquals(-2, round(F(-15, 10))) self.assertTypedEquals(-1, round(F(-7, 10))) self.assertEqual(False, bool(F(0, 1))) self.assertEqual(True, bool(F(3, 2))) self.assertTypedEquals(0.1, float(F(1, 10))) # Check that __float__ isn't implemented by converting the # numerator and denominator to float before dividing. self.assertRaises(OverflowError, float, int('2'*400+'7')) self.assertAlmostEqual(2.0/3, float(F(int('2'*400+'7'), int('3'*400+'1')))) self.assertTypedEquals(0.1+0j, complex(F(1,10))) def testBoolGuarateesBoolReturn(self): # Ensure that __bool__ is used on numerator which guarantees a bool # return. See also bpo-39274. @functools.total_ordering class CustomValue: denominator = 1 def __init__(self, value): self.value = value def __bool__(self): return bool(self.value) @property def numerator(self): # required to preserve `self` during instantiation return self def __eq__(self, other): raise AssertionError("Avoid comparisons in Fraction.__bool__") __lt__ = __eq__ # We did not implement all abstract methods, so register: numbers.Rational.register(CustomValue) numerator = CustomValue(1) r = F(numerator) # ensure the numerator was not lost during instantiation: self.assertIs(r.numerator, numerator) self.assertIs(bool(r), True) numerator = CustomValue(0) r = F(numerator) self.assertIs(bool(r), False) def testRound(self): self.assertTypedEquals(F(-200), round(F(-150), -2)) self.assertTypedEquals(F(-200), round(F(-250), -2)) self.assertTypedEquals(F(30), round(F(26), -1)) self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1)) self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1)) def testArithmetic(self): self.assertEqual(F(1, 2), F(1, 10) + F(2, 5)) self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5)) self.assertEqual(F(1, 25), F(1, 10) * F(2, 5)) self.assertEqual(F(1, 4), F(1, 10) / F(2, 5)) self.assertTypedEquals(2, F(9, 10) // F(2, 5)) self.assertTypedEquals(10**23, F(10**23, 1) // F(1)) self.assertEqual(F(5, 6), F(7, 3) % F(3, 2)) self.assertEqual(F(2, 3), F(-7, 3) % F(3, 2)) self.assertEqual((F(1), F(5, 6)), divmod(F(7, 3), F(3, 2))) self.assertEqual((F(-2), F(2, 3)), divmod(F(-7, 3), F(3, 2))) self.assertEqual(F(8, 27), F(2, 3) ** F(3)) self.assertEqual(F(27, 8), F(2, 3) ** F(-3)) self.assertTypedEquals(2.0, F(4) ** F(1, 2)) self.assertEqual(F(1, 1), +F(1, 1)) z = pow(F(-1), F(1, 2)) self.assertAlmostEqual(z.real, 0) self.assertEqual(z.imag, 1) # Regression test for #27539. p = F(-1, 2) ** 0 self.assertEqual(p, F(1, 1)) self.assertEqual(p.numerator, 1) self.assertEqual(p.denominator, 1) p = F(-1, 2) ** -1 self.assertEqual(p, F(-2, 1)) self.assertEqual(p.numerator, -2) self.assertEqual(p.denominator, 1) p = F(-1, 2) ** -2 self.assertEqual(p, F(4, 1)) self.assertEqual(p.numerator, 4) self.assertEqual(p.denominator, 1) def testLargeArithmetic(self): self.assertTypedEquals( F(10101010100808080808080808101010101010000000000000000, 1010101010101010101010101011111111101010101010101010101010101), F(10**35+1, 10**27+1) % F(10**27+1, 10**35-1) ) self.assertTypedEquals( F(7, 1901475900342344102245054808064), F(-2**100, 3) % F(5, 2**100) ) self.assertTypedTupleEquals( (9999999999999999, F(10101010100808080808080808101010101010000000000000000, 1010101010101010101010101011111111101010101010101010101010101)), divmod(F(10**35+1, 10**27+1), F(10**27+1, 10**35-1)) ) self.assertTypedEquals( -2 ** 200 // 15, F(-2**100, 3) // F(5, 2**100) ) self.assertTypedEquals( 1, F(5, 2**100) // F(3, 2**100) ) self.assertTypedEquals( (1, F(2, 2**100)), divmod(F(5, 2**100), F(3, 2**100)) ) self.assertTypedTupleEquals( (-2 ** 200 // 15, F(7, 1901475900342344102245054808064)), divmod(F(-2**100, 3), F(5, 2**100)) ) def testMixedArithmetic(self): self.assertTypedEquals(F(11, 10), F(1, 10) + 1) self.assertTypedEquals(1.1, F(1, 10) + 1.0) self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j)) self.assertTypedEquals(F(11, 10), 1 + F(1, 10)) self.assertTypedEquals(1.1, 1.0 + F(1, 10)) self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10)) self.assertTypedEquals(F(-9, 10), F(1, 10) - 1) self.assertTypedEquals(-0.9, F(1, 10) - 1.0) self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j)) self.assertTypedEquals(F(9, 10), 1 - F(1, 10)) self.assertTypedEquals(0.9, 1.0 - F(1, 10)) self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10)) self.assertTypedEquals(F(1, 10), F(1, 10) * 1) self.assertTypedEquals(0.1, F(1, 10) * 1.0) self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j)) self.assertTypedEquals(F(1, 10), 1 * F(1, 10)) self.assertTypedEquals(0.1, 1.0 * F(1, 10)) self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10)) self.assertTypedEquals(F(1, 10), F(1, 10) / 1) self.assertTypedEquals(0.1, F(1, 10) / 1.0) self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j)) self.assertTypedEquals(F(10, 1), 1 / F(1, 10)) self.assertTypedEquals(10.0, 1.0 / F(1, 10)) self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10)) self.assertTypedEquals(0, F(1, 10) // 1) self.assertTypedEquals(0.0, F(1, 10) // 1.0) self.assertTypedEquals(10, 1 // F(1, 10)) self.assertTypedEquals(10**23, 10**22 // F(1, 10)) self.assertTypedEquals(1.0 // 0.1, 1.0 // F(1, 10)) self.assertTypedEquals(F(1, 10), F(1, 10) % 1) self.assertTypedEquals(0.1, F(1, 10) % 1.0) self.assertTypedEquals(F(0, 1), 1 % F(1, 10)) self.assertTypedEquals(1.0 % 0.1, 1.0 % F(1, 10)) self.assertTypedEquals(0.1, F(1, 10) % float('inf')) self.assertTypedEquals(float('-inf'), F(1, 10) % float('-inf')) self.assertTypedEquals(float('inf'), F(-1, 10) % float('inf')) self.assertTypedEquals(-0.1, F(-1, 10) % float('-inf')) self.assertTypedTupleEquals((0, F(1, 10)), divmod(F(1, 10), 1)) self.assertTypedTupleEquals(divmod(0.1, 1.0), divmod(F(1, 10), 1.0)) self.assertTypedTupleEquals((10, F(0)), divmod(1, F(1, 10))) self.assertTypedTupleEquals(divmod(1.0, 0.1), divmod(1.0, F(1, 10))) self.assertTypedTupleEquals(divmod(0.1, float('inf')), divmod(F(1, 10), float('inf'))) self.assertTypedTupleEquals(divmod(0.1, float('-inf')), divmod(F(1, 10), float('-inf'))) self.assertTypedTupleEquals(divmod(-0.1, float('inf')), divmod(F(-1, 10), float('inf'))) self.assertTypedTupleEquals(divmod(-0.1, float('-inf')), divmod(F(-1, 10), float('-inf'))) # ** has more interesting conversion rules. self.assertTypedEquals(F(100, 1), F(1, 10) ** -2) self.assertTypedEquals(F(100, 1), F(10, 1) ** 2) self.assertTypedEquals(0.1, F(1, 10) ** 1.0) self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j)) self.assertTypedEquals(4 , 2 ** F(2, 1)) z = pow(-1, F(1, 2)) self.assertAlmostEqual(0, z.real) self.assertEqual(1, z.imag) self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1)) self.assertTypedEquals(2.0 , 4 ** F(1, 2)) self.assertTypedEquals(0.25, 2.0 ** F(-2, 1)) self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10)) self.assertRaises(ZeroDivisionError, operator.pow, F(0, 1), -2) def testMixingWithDecimal(self): # Decimal refuses mixed arithmetic (but not mixed comparisons) self.assertRaises(TypeError, operator.add, F(3,11), Decimal('3.1415926')) self.assertRaises(TypeError, operator.add, Decimal('3.1415926'), F(3,11)) def testComparisons(self): self.assertTrue(F(1, 2) < F(2, 3)) self.assertFalse(F(1, 2) < F(1, 2)) self.assertTrue(F(1, 2) <= F(2, 3)) self.assertTrue(F(1, 2) <= F(1, 2)) self.assertFalse(F(2, 3) <= F(1, 2)) self.assertTrue(F(1, 2) == F(1, 2)) self.assertFalse(F(1, 2) == F(1, 3)) self.assertFalse(F(1, 2) != F(1, 2)) self.assertTrue(F(1, 2) != F(1, 3)) def testComparisonsDummyRational(self): self.assertTrue(F(1, 2) == DummyRational(1, 2)) self.assertTrue(DummyRational(1, 2) == F(1, 2)) self.assertFalse(F(1, 2) == DummyRational(3, 4)) self.assertFalse(DummyRational(3, 4) == F(1, 2)) self.assertTrue(F(1, 2) < DummyRational(3, 4)) self.assertFalse(F(1, 2) < DummyRational(1, 2)) self.assertFalse(F(1, 2) < DummyRational(1, 7)) self.assertFalse(F(1, 2) > DummyRational(3, 4)) self.assertFalse(F(1, 2) > DummyRational(1, 2)) self.assertTrue(F(1, 2) > DummyRational(1, 7)) self.assertTrue(F(1, 2) <= DummyRational(3, 4)) self.assertTrue(F(1, 2) <= DummyRational(1, 2)) self.assertFalse(F(1, 2) <= DummyRational(1, 7)) self.assertFalse(F(1, 2) >= DummyRational(3, 4)) self.assertTrue(F(1, 2) >= DummyRational(1, 2)) self.assertTrue(F(1, 2) >= DummyRational(1, 7)) self.assertTrue(DummyRational(1, 2) < F(3, 4)) self.assertFalse(DummyRational(1, 2) < F(1, 2)) self.assertFalse(DummyRational(1, 2) < F(1, 7)) self.assertFalse(DummyRational(1, 2) > F(3, 4)) self.assertFalse(DummyRational(1, 2) > F(1, 2)) self.assertTrue(DummyRational(1, 2) > F(1, 7)) self.assertTrue(DummyRational(1, 2) <= F(3, 4)) self.assertTrue(DummyRational(1, 2) <= F(1, 2)) self.assertFalse(DummyRational(1, 2) <= F(1, 7)) self.assertFalse(DummyRational(1, 2) >= F(3, 4)) self.assertTrue(DummyRational(1, 2) >= F(1, 2)) self.assertTrue(DummyRational(1, 2) >= F(1, 7)) def testComparisonsDummyFloat(self): x = DummyFloat(1./3.) y = F(1, 3) self.assertTrue(x != y) self.assertTrue(x < y or x > y) self.assertFalse(x == y) self.assertFalse(x <= y and x >= y) self.assertTrue(y != x) self.assertTrue(y < x or y > x) self.assertFalse(y == x) self.assertFalse(y <= x and y >= x) def testMixedLess(self): self.assertTrue(2 < F(5, 2)) self.assertFalse(2 < F(4, 2)) self.assertTrue(F(5, 2) < 3) self.assertFalse(F(4, 2) < 2) self.assertTrue(F(1, 2) < 0.6) self.assertFalse(F(1, 2) < 0.4) self.assertTrue(0.4 < F(1, 2)) self.assertFalse(0.5 < F(1, 2)) self.assertFalse(float('inf') < F(1, 2)) self.assertTrue(float('-inf') < F(0, 10)) self.assertFalse(float('nan') < F(-3, 7)) self.assertTrue(F(1, 2) < float('inf')) self.assertFalse(F(17, 12) < float('-inf')) self.assertFalse(F(144, -89) < float('nan')) def testMixedLessEqual(self): self.assertTrue(0.5 <= F(1, 2)) self.assertFalse(0.6 <= F(1, 2)) self.assertTrue(F(1, 2) <= 0.5) self.assertFalse(F(1, 2) <= 0.4) self.assertTrue(2 <= F(4, 2)) self.assertFalse(2 <= F(3, 2)) self.assertTrue(F(4, 2) <= 2) self.assertFalse(F(5, 2) <= 2) self.assertFalse(float('inf') <= F(1, 2)) self.assertTrue(float('-inf') <= F(0, 10)) self.assertFalse(float('nan') <= F(-3, 7)) self.assertTrue(F(1, 2) <= float('inf')) self.assertFalse(F(17, 12) <= float('-inf')) self.assertFalse(F(144, -89) <= float('nan')) def testBigFloatComparisons(self): # Because 10**23 can't be represented exactly as a float: self.assertFalse(F(10**23) == float(10**23)) # The first test demonstrates why these are important. self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1))) self.assertTrue(1e23 < F(math.trunc(1e23) + 1)) self.assertFalse(1e23 <= F(math.trunc(1e23) - 1)) self.assertTrue(1e23 > F(math.trunc(1e23) - 1)) self.assertFalse(1e23 >= F(math.trunc(1e23) + 1)) def testBigComplexComparisons(self): self.assertFalse(F(10**23) == complex(10**23)) self.assertRaises(TypeError, operator.gt, F(10**23), complex(10**23)) self.assertRaises(TypeError, operator.le, F(10**23), complex(10**23)) x = F(3, 8) z = complex(0.375, 0.0) w = complex(0.375, 0.2) self.assertTrue(x == z) self.assertFalse(x != z) self.assertFalse(x == w) self.assertTrue(x != w) for op in operator.lt, operator.le, operator.gt, operator.ge: self.assertRaises(TypeError, op, x, z) self.assertRaises(TypeError, op, z, x) self.assertRaises(TypeError, op, x, w) self.assertRaises(TypeError, op, w, x) def testMixedEqual(self): self.assertTrue(0.5 == F(1, 2)) self.assertFalse(0.6 == F(1, 2)) self.assertTrue(F(1, 2) == 0.5) self.assertFalse(F(1, 2) == 0.4) self.assertTrue(2 == F(4, 2)) self.assertFalse(2 == F(3, 2)) self.assertTrue(F(4, 2) == 2) self.assertFalse(F(5, 2) == 2) self.assertFalse(F(5, 2) == float('nan')) self.assertFalse(float('nan') == F(3, 7)) self.assertFalse(F(5, 2) == float('inf')) self.assertFalse(float('-inf') == F(2, 5)) def testStringification(self): self.assertEqual("Fraction(7, 3)", repr(F(7, 3))) self.assertEqual("Fraction(6283185307, 2000000000)", repr(F('3.1415926535'))) self.assertEqual("Fraction(-1, 100000000000000000000)", repr(F(1, -10**20))) self.assertEqual("7/3", str(F(7, 3))) self.assertEqual("7", str(F(7, 1))) def testHash(self): hmod = sys.hash_info.modulus hinf = sys.hash_info.inf self.assertEqual(hash(2.5), hash(F(5, 2))) self.assertEqual(hash(10**50), hash(F(10**50))) self.assertNotEqual(hash(float(10**23)), hash(F(10**23))) self.assertEqual(hinf, hash(F(1, hmod))) # Check that __hash__ produces the same value as hash(), for # consistency with int and Decimal. (See issue #10356.) self.assertEqual(hash(F(-1)), F(-1).__hash__()) def testApproximatePi(self): # Algorithm borrowed from # http://docs.python.org/lib/decimal-recipes.html three = F(3) lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24 while abs(s - lasts) > F(1, 10**9): lasts = s n, na = n+na, na+8 d, da = d+da, da+32 t = (t * n) / d s += t self.assertAlmostEqual(math.pi, s) def testApproximateCos1(self): # Algorithm borrowed from # http://docs.python.org/lib/decimal-recipes.html x = F(1) i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1 while abs(s - lasts) > F(1, 10**9): lasts = s i += 2 fact *= i * (i-1) num *= x * x sign *= -1 s += num / fact * sign self.assertAlmostEqual(math.cos(1), s) def test_copy_deepcopy_pickle(self): r = F(13, 7) dr = DummyFraction(13, 7) self.assertEqual(r, loads(dumps(r))) self.assertEqual(id(r), id(copy(r))) self.assertEqual(id(r), id(deepcopy(r))) self.assertNotEqual(id(dr), id(copy(dr))) self.assertNotEqual(id(dr), id(deepcopy(dr))) self.assertTypedEquals(dr, copy(dr)) self.assertTypedEquals(dr, deepcopy(dr)) def test_slots(self): # Issue 4998 r = F(13, 7) self.assertRaises(AttributeError, setattr, r, 'a', 10) def test_int_subclass(self): class myint(int): def __mul__(self, other): return type(self)(int(self) * int(other)) def __floordiv__(self, other): return type(self)(int(self) // int(other)) def __mod__(self, other): x = type(self)(int(self) % int(other)) return x @property def numerator(self): return type(self)(int(self)) @property def denominator(self): return type(self)(1) f = fractions.Fraction(myint(1 * 3), myint(2 * 3)) self.assertEqual(f.numerator, 1) self.assertEqual(f.denominator, 2) self.assertEqual(type(f.numerator), myint) self.assertEqual(type(f.denominator), myint) if __name__ == '__main__': unittest.main()