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------------------------------------------------------------------------ -- ddRemainder.decTest -- decDouble remainder -- -- Copyright (c) IBM Corporation, 1981, 2008. All rights reserved. -- ------------------------------------------------------------------------ -- Please see the document "General Decimal Arithmetic Testcases" -- -- at http://www2.hursley.ibm.com/decimal for the description of -- -- these testcases. -- -- -- -- These testcases are experimental ('beta' versions), and they -- -- may contain errors. They are offered on an as-is basis. In -- -- particular, achieving the same results as the tests here is not -- -- a guarantee that an implementation complies with any Standard -- -- or specification. The tests are not exhaustive. -- -- -- -- Please send comments, suggestions, and corrections to the author: -- -- Mike Cowlishaw, IBM Fellow -- -- IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK -- -- mfc@uk.ibm.com -- ------------------------------------------------------------------------ version: 2.59 precision: 16 maxExponent: 384 minExponent: -383 extended: 1 clamp: 1 rounding: half_even -- sanity checks (as base, above) ddrem001 remainder 1 1 -> 0 ddrem002 remainder 2 1 -> 0 ddrem003 remainder 1 2 -> 1 ddrem004 remainder 2 2 -> 0 ddrem005 remainder 0 1 -> 0 ddrem006 remainder 0 2 -> 0 ddrem007 remainder 1 3 -> 1 ddrem008 remainder 2 3 -> 2 ddrem009 remainder 3 3 -> 0 ddrem010 remainder 2.4 1 -> 0.4 ddrem011 remainder 2.4 -1 -> 0.4 ddrem012 remainder -2.4 1 -> -0.4 ddrem013 remainder -2.4 -1 -> -0.4 ddrem014 remainder 2.40 1 -> 0.40 ddrem015 remainder 2.400 1 -> 0.400 ddrem016 remainder 2.4 2 -> 0.4 ddrem017 remainder 2.400 2 -> 0.400 ddrem018 remainder 2. 2 -> 0 ddrem019 remainder 20 20 -> 0 ddrem020 remainder 187 187 -> 0 ddrem021 remainder 5 2 -> 1 ddrem022 remainder 5 2.0 -> 1.0 ddrem023 remainder 5 2.000 -> 1.000 ddrem024 remainder 5 0.200 -> 0.000 ddrem025 remainder 5 0.200 -> 0.000 ddrem030 remainder 1 2 -> 1 ddrem031 remainder 1 4 -> 1 ddrem032 remainder 1 8 -> 1 ddrem033 remainder 1 16 -> 1 ddrem034 remainder 1 32 -> 1 ddrem035 remainder 1 64 -> 1 ddrem040 remainder 1 -2 -> 1 ddrem041 remainder 1 -4 -> 1 ddrem042 remainder 1 -8 -> 1 ddrem043 remainder 1 -16 -> 1 ddrem044 remainder 1 -32 -> 1 ddrem045 remainder 1 -64 -> 1 ddrem050 remainder -1 2 -> -1 ddrem051 remainder -1 4 -> -1 ddrem052 remainder -1 8 -> -1 ddrem053 remainder -1 16 -> -1 ddrem054 remainder -1 32 -> -1 ddrem055 remainder -1 64 -> -1 ddrem060 remainder -1 -2 -> -1 ddrem061 remainder -1 -4 -> -1 ddrem062 remainder -1 -8 -> -1 ddrem063 remainder -1 -16 -> -1 ddrem064 remainder -1 -32 -> -1 ddrem065 remainder -1 -64 -> -1 ddrem066 remainder 999999999 1 -> 0 ddrem067 remainder 999999999.4 1 -> 0.4 ddrem068 remainder 999999999.5 1 -> 0.5 ddrem069 remainder 999999999.9 1 -> 0.9 ddrem070 remainder 999999999.999 1 -> 0.999 ddrem071 remainder 999999.999999 1 -> 0.999999 ddrem072 remainder 9 1 -> 0 ddrem073 remainder 9999999999999999 1 -> 0 ddrem074 remainder 9999999999999999 2 -> 1 ddrem075 remainder 9999999999999999 3 -> 0 ddrem076 remainder 9999999999999999 4 -> 3 ddrem080 remainder 0. 1 -> 0 ddrem081 remainder .0 1 -> 0.0 ddrem082 remainder 0.00 1 -> 0.00 ddrem083 remainder 0.00E+9 1 -> 0 ddrem084 remainder 0.00E+3 1 -> 0 ddrem085 remainder 0.00E+2 1 -> 0 ddrem086 remainder 0.00E+1 1 -> 0.0 ddrem087 remainder 0.00E+0 1 -> 0.00 ddrem088 remainder 0.00E-0 1 -> 0.00 ddrem089 remainder 0.00E-1 1 -> 0.000 ddrem090 remainder 0.00E-2 1 -> 0.0000 ddrem091 remainder 0.00E-3 1 -> 0.00000 ddrem092 remainder 0.00E-4 1 -> 0.000000 ddrem093 remainder 0.00E-5 1 -> 0E-7 ddrem094 remainder 0.00E-6 1 -> 0E-8 ddrem095 remainder 0.0000E-50 1 -> 0E-54 -- Various flavours of remainder by 0 ddrem101 remainder 0 0 -> NaN Division_undefined ddrem102 remainder 0 -0 -> NaN Division_undefined ddrem103 remainder -0 0 -> NaN Division_undefined ddrem104 remainder -0 -0 -> NaN Division_undefined ddrem105 remainder 0.0E5 0 -> NaN Division_undefined ddrem106 remainder 0.000 0 -> NaN Division_undefined -- [Some think this next group should be Division_by_zero exception, but -- IEEE 854 is explicit that it is Invalid operation .. for -- remainder-near, anyway] ddrem107 remainder 0.0001 0 -> NaN Invalid_operation ddrem108 remainder 0.01 0 -> NaN Invalid_operation ddrem109 remainder 0.1 0 -> NaN Invalid_operation ddrem110 remainder 1 0 -> NaN Invalid_operation ddrem111 remainder 1 0.0 -> NaN Invalid_operation ddrem112 remainder 10 0.0 -> NaN Invalid_operation ddrem113 remainder 1E+100 0.0 -> NaN Invalid_operation ddrem114 remainder 1E+380 0 -> NaN Invalid_operation ddrem115 remainder 0.0001 -0 -> NaN Invalid_operation ddrem116 remainder 0.01 -0 -> NaN Invalid_operation ddrem119 remainder 0.1 -0 -> NaN Invalid_operation ddrem120 remainder 1 -0 -> NaN Invalid_operation ddrem121 remainder 1 -0.0 -> NaN Invalid_operation ddrem122 remainder 10 -0.0 -> NaN Invalid_operation ddrem123 remainder 1E+100 -0.0 -> NaN Invalid_operation ddrem124 remainder 1E+384 -0 -> NaN Invalid_operation -- and zeros on left ddrem130 remainder 0 1 -> 0 ddrem131 remainder 0 -1 -> 0 ddrem132 remainder 0.0 1 -> 0.0 ddrem133 remainder 0.0 -1 -> 0.0 ddrem134 remainder -0 1 -> -0 ddrem135 remainder -0 -1 -> -0 ddrem136 remainder -0.0 1 -> -0.0 ddrem137 remainder -0.0 -1 -> -0.0 -- 0.5ers ddrem143 remainder 0.5 2 -> 0.5 ddrem144 remainder 0.5 2.1 -> 0.5 ddrem145 remainder 0.5 2.01 -> 0.50 ddrem146 remainder 0.5 2.001 -> 0.500 ddrem147 remainder 0.50 2 -> 0.50 ddrem148 remainder 0.50 2.01 -> 0.50 ddrem149 remainder 0.50 2.001 -> 0.500 -- steadies ddrem150 remainder 1 1 -> 0 ddrem151 remainder 1 2 -> 1 ddrem152 remainder 1 3 -> 1 ddrem153 remainder 1 4 -> 1 ddrem154 remainder 1 5 -> 1 ddrem155 remainder 1 6 -> 1 ddrem156 remainder 1 7 -> 1 ddrem157 remainder 1 8 -> 1 ddrem158 remainder 1 9 -> 1 ddrem159 remainder 1 10 -> 1 ddrem160 remainder 1 1 -> 0 ddrem161 remainder 2 1 -> 0 ddrem162 remainder 3 1 -> 0 ddrem163 remainder 4 1 -> 0 ddrem164 remainder 5 1 -> 0 ddrem165 remainder 6 1 -> 0 ddrem166 remainder 7 1 -> 0 ddrem167 remainder 8 1 -> 0 ddrem168 remainder 9 1 -> 0 ddrem169 remainder 10 1 -> 0 -- some differences from remainderNear ddrem171 remainder 0.4 1.020 -> 0.400 ddrem172 remainder 0.50 1.020 -> 0.500 ddrem173 remainder 0.51 1.020 -> 0.510 ddrem174 remainder 0.52 1.020 -> 0.520 ddrem175 remainder 0.6 1.020 -> 0.600 -- More flavours of remainder by 0 ddrem201 remainder 0 0 -> NaN Division_undefined ddrem202 remainder 0.0E5 0 -> NaN Division_undefined ddrem203 remainder 0.000 0 -> NaN Division_undefined ddrem204 remainder 0.0001 0 -> NaN Invalid_operation ddrem205 remainder 0.01 0 -> NaN Invalid_operation ddrem206 remainder 0.1 0 -> NaN Invalid_operation ddrem207 remainder 1 0 -> NaN Invalid_operation ddrem208 remainder 1 0.0 -> NaN Invalid_operation ddrem209 remainder 10 0.0 -> NaN Invalid_operation ddrem210 remainder 1E+100 0.0 -> NaN Invalid_operation ddrem211 remainder 1E+380 0 -> NaN Invalid_operation -- some differences from remainderNear ddrem231 remainder -0.4 1.020 -> -0.400 ddrem232 remainder -0.50 1.020 -> -0.500 ddrem233 remainder -0.51 1.020 -> -0.510 ddrem234 remainder -0.52 1.020 -> -0.520 ddrem235 remainder -0.6 1.020 -> -0.600 -- high Xs ddrem240 remainder 1E+2 1.00 -> 0.00 -- ddrem3xx are from DiagBigDecimal ddrem301 remainder 1 3 -> 1 ddrem302 remainder 5 5 -> 0 ddrem303 remainder 13 10 -> 3 ddrem304 remainder 13 50 -> 13 ddrem305 remainder 13 100 -> 13 ddrem306 remainder 13 1000 -> 13 ddrem307 remainder .13 1 -> 0.13 ddrem308 remainder 0.133 1 -> 0.133 ddrem309 remainder 0.1033 1 -> 0.1033 ddrem310 remainder 1.033 1 -> 0.033 ddrem311 remainder 10.33 1 -> 0.33 ddrem312 remainder 10.33 10 -> 0.33 ddrem313 remainder 103.3 1 -> 0.3 ddrem314 remainder 133 10 -> 3 ddrem315 remainder 1033 10 -> 3 ddrem316 remainder 1033 50 -> 33 ddrem317 remainder 101.0 3 -> 2.0 ddrem318 remainder 102.0 3 -> 0.0 ddrem319 remainder 103.0 3 -> 1.0 ddrem320 remainder 2.40 1 -> 0.40 ddrem321 remainder 2.400 1 -> 0.400 ddrem322 remainder 2.4 1 -> 0.4 ddrem323 remainder 2.4 2 -> 0.4 ddrem324 remainder 2.400 2 -> 0.400 ddrem325 remainder 1 0.3 -> 0.1 ddrem326 remainder 1 0.30 -> 0.10 ddrem327 remainder 1 0.300 -> 0.100 ddrem328 remainder 1 0.3000 -> 0.1000 ddrem329 remainder 1.0 0.3 -> 0.1 ddrem330 remainder 1.00 0.3 -> 0.10 ddrem331 remainder 1.000 0.3 -> 0.100 ddrem332 remainder 1.0000 0.3 -> 0.1000 ddrem333 remainder 0.5 2 -> 0.5 ddrem334 remainder 0.5 2.1 -> 0.5 ddrem335 remainder 0.5 2.01 -> 0.50 ddrem336 remainder 0.5 2.001 -> 0.500 ddrem337 remainder 0.50 2 -> 0.50 ddrem338 remainder 0.50 2.01 -> 0.50 ddrem339 remainder 0.50 2.001 -> 0.500 ddrem340 remainder 0.5 0.5000001 -> 0.5000000 ddrem341 remainder 0.5 0.50000001 -> 0.50000000 ddrem342 remainder 0.5 0.500000001 -> 0.500000000 ddrem343 remainder 0.5 0.5000000001 -> 0.5000000000 ddrem344 remainder 0.5 0.50000000001 -> 0.50000000000 ddrem345 remainder 0.5 0.4999999 -> 1E-7 ddrem346 remainder 0.5 0.49999999 -> 1E-8 ddrem347 remainder 0.5 0.499999999 -> 1E-9 ddrem348 remainder 0.5 0.4999999999 -> 1E-10 ddrem349 remainder 0.5 0.49999999999 -> 1E-11 ddrem350 remainder 0.5 0.499999999999 -> 1E-12 ddrem351 remainder 0.03 7 -> 0.03 ddrem352 remainder 5 2 -> 1 ddrem353 remainder 4.1 2 -> 0.1 ddrem354 remainder 4.01 2 -> 0.01 ddrem355 remainder 4.001 2 -> 0.001 ddrem356 remainder 4.0001 2 -> 0.0001 ddrem357 remainder 4.00001 2 -> 0.00001 ddrem358 remainder 4.000001 2 -> 0.000001 ddrem359 remainder 4.0000001 2 -> 1E-7 ddrem360 remainder 1.2 0.7345 -> 0.4655 ddrem361 remainder 0.8 12 -> 0.8 ddrem362 remainder 0.8 0.2 -> 0.0 ddrem363 remainder 0.8 0.3 -> 0.2 ddrem364 remainder 0.800 12 -> 0.800 ddrem365 remainder 0.800 1.7 -> 0.800 ddrem366 remainder 2.400 2 -> 0.400 ddrem371 remainder 2.400 2 -> 0.400 ddrem381 remainder 12345 1 -> 0 ddrem382 remainder 12345 1.0001 -> 0.7657 ddrem383 remainder 12345 1.001 -> 0.668 ddrem384 remainder 12345 1.01 -> 0.78 ddrem385 remainder 12345 1.1 -> 0.8 ddrem386 remainder 12355 4 -> 3 ddrem387 remainder 12345 4 -> 1 ddrem388 remainder 12355 4.0001 -> 2.6912 ddrem389 remainder 12345 4.0001 -> 0.6914 ddrem390 remainder 12345 4.9 -> 1.9 ddrem391 remainder 12345 4.99 -> 4.73 ddrem392 remainder 12345 4.999 -> 2.469 ddrem393 remainder 12345 4.9999 -> 0.2469 ddrem394 remainder 12345 5 -> 0 ddrem395 remainder 12345 5.0001 -> 4.7532 ddrem396 remainder 12345 5.001 -> 2.532 ddrem397 remainder 12345 5.01 -> 0.36 ddrem398 remainder 12345 5.1 -> 3.0 -- the nasty division-by-1 cases ddrem401 remainder 0.5 1 -> 0.5 ddrem402 remainder 0.55 1 -> 0.55 ddrem403 remainder 0.555 1 -> 0.555 ddrem404 remainder 0.5555 1 -> 0.5555 ddrem405 remainder 0.55555 1 -> 0.55555 ddrem406 remainder 0.555555 1 -> 0.555555 ddrem407 remainder 0.5555555 1 -> 0.5555555 ddrem408 remainder 0.55555555 1 -> 0.55555555 ddrem409 remainder 0.555555555 1 -> 0.555555555 -- folddowns ddrem421 remainder 1E+384 1 -> NaN Division_impossible ddrem422 remainder 1E+384 1E+383 -> 0E+369 Clamped ddrem423 remainder 1E+384 2E+383 -> 0E+369 Clamped ddrem424 remainder 1E+384 3E+383 -> 1.00000000000000E+383 Clamped ddrem425 remainder 1E+384 4E+383 -> 2.00000000000000E+383 Clamped ddrem426 remainder 1E+384 5E+383 -> 0E+369 Clamped ddrem427 remainder 1E+384 6E+383 -> 4.00000000000000E+383 Clamped ddrem428 remainder 1E+384 7E+383 -> 3.00000000000000E+383 Clamped ddrem429 remainder 1E+384 8E+383 -> 2.00000000000000E+383 Clamped ddrem430 remainder 1E+384 9E+383 -> 1.00000000000000E+383 Clamped -- tinies ddrem431 remainder 1E-397 1E-398 -> 0E-398 ddrem432 remainder 1E-397 2E-398 -> 0E-398 ddrem433 remainder 1E-397 3E-398 -> 1E-398 Subnormal ddrem434 remainder 1E-397 4E-398 -> 2E-398 Subnormal ddrem435 remainder 1E-397 5E-398 -> 0E-398 ddrem436 remainder 1E-397 6E-398 -> 4E-398 Subnormal ddrem437 remainder 1E-397 7E-398 -> 3E-398 Subnormal ddrem438 remainder 1E-397 8E-398 -> 2E-398 Subnormal ddrem439 remainder 1E-397 9E-398 -> 1E-398 Subnormal ddrem440 remainder 1E-397 10E-398 -> 0E-398 ddrem441 remainder 1E-397 11E-398 -> 1.0E-397 Subnormal ddrem442 remainder 100E-397 11E-398 -> 1.0E-397 Subnormal ddrem443 remainder 100E-397 20E-398 -> 0E-398 ddrem444 remainder 100E-397 21E-398 -> 1.3E-397 Subnormal ddrem445 remainder 100E-397 30E-398 -> 1.0E-397 Subnormal -- zero signs ddrem650 remainder 1 1 -> 0 ddrem651 remainder -1 1 -> -0 ddrem652 remainder 1 -1 -> 0 ddrem653 remainder -1 -1 -> -0 ddrem654 remainder 0 1 -> 0 ddrem655 remainder -0 1 -> -0 ddrem656 remainder 0 -1 -> 0 ddrem657 remainder -0 -1 -> -0 ddrem658 remainder 0.00 1 -> 0.00 ddrem659 remainder -0.00 1 -> -0.00 -- Specials ddrem680 remainder Inf -Inf -> NaN Invalid_operation ddrem681 remainder Inf -1000 -> NaN Invalid_operation ddrem682 remainder Inf -1 -> NaN Invalid_operation ddrem683 remainder Inf 0 -> NaN Invalid_operation ddrem684 remainder Inf -0 -> NaN Invalid_operation ddrem685 remainder Inf 1 -> NaN Invalid_operation ddrem686 remainder Inf 1000 -> NaN Invalid_operation ddrem687 remainder Inf Inf -> NaN Invalid_operation ddrem688 remainder -1000 Inf -> -1000 ddrem689 remainder -Inf Inf -> NaN Invalid_operation ddrem691 remainder -1 Inf -> -1 ddrem692 remainder 0 Inf -> 0 ddrem693 remainder -0 Inf -> -0 ddrem694 remainder 1 Inf -> 1 ddrem695 remainder 1000 Inf -> 1000 ddrem696 remainder Inf Inf -> NaN Invalid_operation ddrem700 remainder -Inf -Inf -> NaN Invalid_operation ddrem701 remainder -Inf -1000 -> NaN Invalid_operation ddrem702 remainder -Inf -1 -> NaN Invalid_operation ddrem703 remainder -Inf -0 -> NaN Invalid_operation ddrem704 remainder -Inf 0 -> NaN Invalid_operation ddrem705 remainder -Inf 1 -> NaN Invalid_operation ddrem706 remainder -Inf 1000 -> NaN Invalid_operation ddrem707 remainder -Inf Inf -> NaN Invalid_operation ddrem708 remainder -Inf -Inf -> NaN Invalid_operation ddrem709 remainder -1000 Inf -> -1000 ddrem710 remainder -1 -Inf -> -1 ddrem711 remainder -0 -Inf -> -0 ddrem712 remainder 0 -Inf -> 0 ddrem713 remainder 1 -Inf -> 1 ddrem714 remainder 1000 -Inf -> 1000 ddrem715 remainder Inf -Inf -> NaN Invalid_operation ddrem721 remainder NaN -Inf -> NaN ddrem722 remainder NaN -1000 -> NaN ddrem723 remainder NaN -1 -> NaN ddrem724 remainder NaN -0 -> NaN ddrem725 remainder -NaN 0 -> -NaN ddrem726 remainder NaN 1 -> NaN ddrem727 remainder NaN 1000 -> NaN ddrem728 remainder NaN Inf -> NaN ddrem729 remainder NaN -NaN -> NaN ddrem730 remainder -Inf NaN -> NaN ddrem731 remainder -1000 NaN -> NaN ddrem732 remainder -1 NaN -> NaN ddrem733 remainder -0 -NaN -> -NaN ddrem734 remainder 0 NaN -> NaN ddrem735 remainder 1 -NaN -> -NaN ddrem736 remainder 1000 NaN -> NaN ddrem737 remainder Inf NaN -> NaN ddrem741 remainder sNaN -Inf -> NaN Invalid_operation ddrem742 remainder sNaN -1000 -> NaN Invalid_operation ddrem743 remainder -sNaN -1 -> -NaN Invalid_operation ddrem744 remainder sNaN -0 -> NaN Invalid_operation ddrem745 remainder sNaN 0 -> NaN Invalid_operation ddrem746 remainder sNaN 1 -> NaN Invalid_operation ddrem747 remainder sNaN 1000 -> NaN Invalid_operation ddrem749 remainder sNaN NaN -> NaN Invalid_operation ddrem750 remainder sNaN sNaN -> NaN Invalid_operation ddrem751 remainder NaN sNaN -> NaN Invalid_operation ddrem752 remainder -Inf sNaN -> NaN Invalid_operation ddrem753 remainder -1000 sNaN -> NaN Invalid_operation ddrem754 remainder -1 sNaN -> NaN Invalid_operation ddrem755 remainder -0 sNaN -> NaN Invalid_operation ddrem756 remainder 0 sNaN -> NaN Invalid_operation ddrem757 remainder 1 sNaN -> NaN Invalid_operation ddrem758 remainder 1000 sNaN -> NaN Invalid_operation ddrem759 remainder Inf -sNaN -> -NaN Invalid_operation -- propaging NaNs ddrem760 remainder NaN1 NaN7 -> NaN1 ddrem761 remainder sNaN2 NaN8 -> NaN2 Invalid_operation ddrem762 remainder NaN3 sNaN9 -> NaN9 Invalid_operation ddrem763 remainder sNaN4 sNaN10 -> NaN4 Invalid_operation ddrem764 remainder 15 NaN11 -> NaN11 ddrem765 remainder NaN6 NaN12 -> NaN6 ddrem766 remainder Inf NaN13 -> NaN13 ddrem767 remainder NaN14 -Inf -> NaN14 ddrem768 remainder 0 NaN15 -> NaN15 ddrem769 remainder NaN16 -0 -> NaN16 -- edge cases of impossible ddrem770 remainder 1234567890123456 10 -> 6 ddrem771 remainder 1234567890123456 1 -> 0 ddrem772 remainder 1234567890123456 0.1 -> NaN Division_impossible ddrem773 remainder 1234567890123456 0.01 -> NaN Division_impossible -- long operand checks ddrem801 remainder 12345678000 100 -> 0 ddrem802 remainder 1 12345678000 -> 1 ddrem803 remainder 1234567800 10 -> 0 ddrem804 remainder 1 1234567800 -> 1 ddrem805 remainder 1234567890 10 -> 0 ddrem806 remainder 1 1234567890 -> 1 ddrem807 remainder 1234567891 10 -> 1 ddrem808 remainder 1 1234567891 -> 1 ddrem809 remainder 12345678901 100 -> 1 ddrem810 remainder 1 12345678901 -> 1 ddrem811 remainder 1234567896 10 -> 6 ddrem812 remainder 1 1234567896 -> 1 ddrem821 remainder 12345678000 100 -> 0 ddrem822 remainder 1 12345678000 -> 1 ddrem823 remainder 1234567800 10 -> 0 ddrem824 remainder 1 1234567800 -> 1 ddrem825 remainder 1234567890 10 -> 0 ddrem826 remainder 1 1234567890 -> 1 ddrem827 remainder 1234567891 10 -> 1 ddrem828 remainder 1 1234567891 -> 1 ddrem829 remainder 12345678901 100 -> 1 ddrem830 remainder 1 12345678901 -> 1 ddrem831 remainder 1234567896 10 -> 6 ddrem832 remainder 1 1234567896 -> 1 -- from divideint ddrem840 remainder 100000000.0 1 -> 0.0 ddrem841 remainder 100000000.4 1 -> 0.4 ddrem842 remainder 100000000.5 1 -> 0.5 ddrem843 remainder 100000000.9 1 -> 0.9 ddrem844 remainder 100000000.999 1 -> 0.999 ddrem850 remainder 100000003 5 -> 3 ddrem851 remainder 10000003 5 -> 3 ddrem852 remainder 1000003 5 -> 3 ddrem853 remainder 100003 5 -> 3 ddrem854 remainder 10003 5 -> 3 ddrem855 remainder 1003 5 -> 3 ddrem856 remainder 103 5 -> 3 ddrem857 remainder 13 5 -> 3 ddrem858 remainder 1 5 -> 1 -- Vladimir's cases 1234567890123456 ddrem860 remainder 123.0e1 1000000000000000 -> 1230 ddrem861 remainder 1230 1000000000000000 -> 1230 ddrem862 remainder 12.3e2 1000000000000000 -> 1230 ddrem863 remainder 1.23e3 1000000000000000 -> 1230 ddrem864 remainder 123e1 1000000000000000 -> 1230 ddrem870 remainder 123e1 1000000000000000 -> 1230 ddrem871 remainder 123e1 100000000000000 -> 1230 ddrem872 remainder 123e1 10000000000000 -> 1230 ddrem873 remainder 123e1 1000000000000 -> 1230 ddrem874 remainder 123e1 100000000000 -> 1230 ddrem875 remainder 123e1 10000000000 -> 1230 ddrem876 remainder 123e1 1000000000 -> 1230 ddrem877 remainder 123e1 100000000 -> 1230 ddrem878 remainder 1230 100000000 -> 1230 ddrem879 remainder 123e1 10000000 -> 1230 ddrem880 remainder 123e1 1000000 -> 1230 ddrem881 remainder 123e1 100000 -> 1230 ddrem882 remainder 123e1 10000 -> 1230 ddrem883 remainder 123e1 1000 -> 230 ddrem884 remainder 123e1 100 -> 30 ddrem885 remainder 123e1 10 -> 0 ddrem886 remainder 123e1 1 -> 0 ddrem890 remainder 123e1 2000000000000000 -> 1230 ddrem891 remainder 123e1 200000000000000 -> 1230 ddrem892 remainder 123e1 20000000000000 -> 1230 ddrem893 remainder 123e1 2000000000000 -> 1230 ddrem894 remainder 123e1 200000000000 -> 1230 ddrem895 remainder 123e1 20000000000 -> 1230 ddrem896 remainder 123e1 2000000000 -> 1230 ddrem897 remainder 123e1 200000000 -> 1230 ddrem899 remainder 123e1 20000000 -> 1230 ddrem900 remainder 123e1 2000000 -> 1230 ddrem901 remainder 123e1 200000 -> 1230 ddrem902 remainder 123e1 20000 -> 1230 ddrem903 remainder 123e1 2000 -> 1230 ddrem904 remainder 123e1 200 -> 30 ddrem905 remainder 123e1 20 -> 10 ddrem906 remainder 123e1 2 -> 0 ddrem910 remainder 123e1 5000000000000000 -> 1230 ddrem911 remainder 123e1 500000000000000 -> 1230 ddrem912 remainder 123e1 50000000000000 -> 1230 ddrem913 remainder 123e1 5000000000000 -> 1230 ddrem914 remainder 123e1 500000000000 -> 1230 ddrem915 remainder 123e1 50000000000 -> 1230 ddrem916 remainder 123e1 5000000000 -> 1230 ddrem917 remainder 123e1 500000000 -> 1230 ddrem919 remainder 123e1 50000000 -> 1230 ddrem920 remainder 123e1 5000000 -> 1230 ddrem921 remainder 123e1 500000 -> 1230 ddrem922 remainder 123e1 50000 -> 1230 ddrem923 remainder 123e1 5000 -> 1230 ddrem924 remainder 123e1 500 -> 230 ddrem925 remainder 123e1 50 -> 30 ddrem926 remainder 123e1 5 -> 0 ddrem930 remainder 123e1 9000000000000000 -> 1230 ddrem931 remainder 123e1 900000000000000 -> 1230 ddrem932 remainder 123e1 90000000000000 -> 1230 ddrem933 remainder 123e1 9000000000000 -> 1230 ddrem934 remainder 123e1 900000000000 -> 1230 ddrem935 remainder 123e1 90000000000 -> 1230 ddrem936 remainder 123e1 9000000000 -> 1230 ddrem937 remainder 123e1 900000000 -> 1230 ddrem939 remainder 123e1 90000000 -> 1230 ddrem940 remainder 123e1 9000000 -> 1230 ddrem941 remainder 123e1 900000 -> 1230 ddrem942 remainder 123e1 90000 -> 1230 ddrem943 remainder 123e1 9000 -> 1230 ddrem944 remainder 123e1 900 -> 330 ddrem945 remainder 123e1 90 -> 60 ddrem946 remainder 123e1 9 -> 6 ddrem950 remainder 123e1 1000000000000000 -> 1230 ddrem961 remainder 123e1 2999999999999999 -> 1230 ddrem962 remainder 123e1 3999999999999999 -> 1230 ddrem963 remainder 123e1 4999999999999999 -> 1230 ddrem964 remainder 123e1 5999999999999999 -> 1230 ddrem965 remainder 123e1 6999999999999999 -> 1230 ddrem966 remainder 123e1 7999999999999999 -> 1230 ddrem967 remainder 123e1 8999999999999999 -> 1230 ddrem968 remainder 123e1 9999999999999999 -> 1230 ddrem969 remainder 123e1 9876543210987654 -> 1230 ddrem980 remainder 123e1 1000E299 -> 1.23E+3 -- 123E+1 internally -- overflow and underflow tests [from divide] ddrem1051 remainder 1e+277 1e-311 -> NaN Division_impossible ddrem1052 remainder 1e+277 -1e-311 -> NaN Division_impossible ddrem1053 remainder -1e+277 1e-311 -> NaN Division_impossible ddrem1054 remainder -1e+277 -1e-311 -> NaN Division_impossible ddrem1055 remainder 1e-277 1e+311 -> 1E-277 ddrem1056 remainder 1e-277 -1e+311 -> 1E-277 ddrem1057 remainder -1e-277 1e+311 -> -1E-277 ddrem1058 remainder -1e-277 -1e+311 -> -1E-277 -- destructive subtract ddrem1101 remainder 1234567890123456 1.000000000000001 -> 0.765432109876546 ddrem1102 remainder 1234567890123456 1.00000000000001 -> 0.65432109876557 ddrem1103 remainder 1234567890123456 1.0000000000001 -> 0.5432109876668 ddrem1104 remainder 1234567890123455 4.000000000000001 -> 2.691358027469137 ddrem1105 remainder 1234567890123456 4.000000000000001 -> 3.691358027469137 ddrem1106 remainder 1234567890123456 4.9999999999999 -> 0.6913578024696 ddrem1107 remainder 1234567890123456 4.99999999999999 -> 3.46913578024691 ddrem1108 remainder 1234567890123456 4.999999999999999 -> 1.246913578024691 ddrem1109 remainder 1234567890123456 5.000000000000001 -> 0.753086421975309 ddrem1110 remainder 1234567890123456 5.00000000000001 -> 3.53086421975310 ddrem1111 remainder 1234567890123456 5.0000000000001 -> 1.3086421975314 -- Null tests ddrem1000 remainder 10 # -> NaN Invalid_operation ddrem1001 remainder # 10 -> NaN Invalid_operation