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------------------------------------------------------------------------ -- remainderNear.decTest -- decimal remainder-near (IEEE 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 extended: 1 precision: 9 rounding: half_up maxExponent: 384 minexponent: -383 rmnx001 remaindernear 1 1 -> 0 rmnx002 remaindernear 2 1 -> 0 rmnx003 remaindernear 1 2 -> 1 rmnx004 remaindernear 2 2 -> 0 rmnx005 remaindernear 0 1 -> 0 rmnx006 remaindernear 0 2 -> 0 rmnx007 remaindernear 1 3 -> 1 rmnx008 remaindernear 2 3 -> -1 rmnx009 remaindernear 3 3 -> 0 rmnx010 remaindernear 2.4 1 -> 0.4 rmnx011 remaindernear 2.4 -1 -> 0.4 rmnx012 remaindernear -2.4 1 -> -0.4 rmnx013 remaindernear -2.4 -1 -> -0.4 rmnx014 remaindernear 2.40 1 -> 0.40 rmnx015 remaindernear 2.400 1 -> 0.400 rmnx016 remaindernear 2.4 2 -> 0.4 rmnx017 remaindernear 2.400 2 -> 0.400 rmnx018 remaindernear 2. 2 -> 0 rmnx019 remaindernear 20 20 -> 0 rmnx020 remaindernear 187 187 -> 0 rmnx021 remaindernear 5 2 -> 1 rmnx022 remaindernear 5 2.0 -> 1.0 rmnx023 remaindernear 5 2.000 -> 1.000 rmnx024 remaindernear 5 0.200 -> 0.000 rmnx025 remaindernear 5 0.200 -> 0.000 rmnx030 remaindernear 1 2 -> 1 rmnx031 remaindernear 1 4 -> 1 rmnx032 remaindernear 1 8 -> 1 rmnx033 remaindernear 1 16 -> 1 rmnx034 remaindernear 1 32 -> 1 rmnx035 remaindernear 1 64 -> 1 rmnx040 remaindernear 1 -2 -> 1 rmnx041 remaindernear 1 -4 -> 1 rmnx042 remaindernear 1 -8 -> 1 rmnx043 remaindernear 1 -16 -> 1 rmnx044 remaindernear 1 -32 -> 1 rmnx045 remaindernear 1 -64 -> 1 rmnx050 remaindernear -1 2 -> -1 rmnx051 remaindernear -1 4 -> -1 rmnx052 remaindernear -1 8 -> -1 rmnx053 remaindernear -1 16 -> -1 rmnx054 remaindernear -1 32 -> -1 rmnx055 remaindernear -1 64 -> -1 rmnx060 remaindernear -1 -2 -> -1 rmnx061 remaindernear -1 -4 -> -1 rmnx062 remaindernear -1 -8 -> -1 rmnx063 remaindernear -1 -16 -> -1 rmnx064 remaindernear -1 -32 -> -1 rmnx065 remaindernear -1 -64 -> -1 rmnx066 remaindernear 999999997 1 -> 0 rmnx067 remaindernear 999999997.4 1 -> 0.4 rmnx068 remaindernear 999999997.5 1 -> -0.5 rmnx069 remaindernear 999999997.9 1 -> -0.1 rmnx070 remaindernear 999999997.999 1 -> -0.001 rmnx071 remaindernear 999999998 1 -> 0 rmnx072 remaindernear 999999998.4 1 -> 0.4 rmnx073 remaindernear 999999998.5 1 -> 0.5 rmnx074 remaindernear 999999998.9 1 -> -0.1 rmnx075 remaindernear 999999998.999 1 -> -0.001 rmnx076 remaindernear 999999999 1 -> 0 rmnx077 remaindernear 999999999.4 1 -> 0.4 rmnx078 remaindernear 999999999.5 1 -> NaN Division_impossible rmnx079 remaindernear 999999999.9 1 -> NaN Division_impossible rmnx080 remaindernear 999999999.999 1 -> NaN Division_impossible precision: 6 rmnx081 remaindernear 999999999 1 -> NaN Division_impossible rmnx082 remaindernear 99999999 1 -> NaN Division_impossible rmnx083 remaindernear 9999999 1 -> NaN Division_impossible rmnx084 remaindernear 999999 1 -> 0 rmnx085 remaindernear 99999 1 -> 0 rmnx086 remaindernear 9999 1 -> 0 rmnx087 remaindernear 999 1 -> 0 rmnx088 remaindernear 99 1 -> 0 rmnx089 remaindernear 9 1 -> 0 precision: 9 rmnx090 remaindernear 0. 1 -> 0 rmnx091 remaindernear .0 1 -> 0.0 rmnx092 remaindernear 0.00 1 -> 0.00 rmnx093 remaindernear 0.00E+9 1 -> 0 rmnx094 remaindernear 0.0000E-50 1 -> 0E-54 -- Various flavours of remaindernear by 0 precision: 9 maxexponent: 999999999 minexponent: -999999999 rmnx101 remaindernear 0 0 -> NaN Division_undefined rmnx102 remaindernear 0 -0 -> NaN Division_undefined rmnx103 remaindernear -0 0 -> NaN Division_undefined rmnx104 remaindernear -0 -0 -> NaN Division_undefined rmnx105 remaindernear 0.0E5 0 -> NaN Division_undefined rmnx106 remaindernear 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 -- remaindernear-near, anyway] rmnx107 remaindernear 0.0001 0 -> NaN Invalid_operation rmnx108 remaindernear 0.01 0 -> NaN Invalid_operation rmnx109 remaindernear 0.1 0 -> NaN Invalid_operation rmnx110 remaindernear 1 0 -> NaN Invalid_operation rmnx111 remaindernear 1 0.0 -> NaN Invalid_operation rmnx112 remaindernear 10 0.0 -> NaN Invalid_operation rmnx113 remaindernear 1E+100 0.0 -> NaN Invalid_operation rmnx114 remaindernear 1E+1000 0 -> NaN Invalid_operation rmnx115 remaindernear 0.0001 -0 -> NaN Invalid_operation rmnx116 remaindernear 0.01 -0 -> NaN Invalid_operation rmnx119 remaindernear 0.1 -0 -> NaN Invalid_operation rmnx120 remaindernear 1 -0 -> NaN Invalid_operation rmnx121 remaindernear 1 -0.0 -> NaN Invalid_operation rmnx122 remaindernear 10 -0.0 -> NaN Invalid_operation rmnx123 remaindernear 1E+100 -0.0 -> NaN Invalid_operation rmnx124 remaindernear 1E+1000 -0 -> NaN Invalid_operation -- and zeros on left rmnx130 remaindernear 0 1 -> 0 rmnx131 remaindernear 0 -1 -> 0 rmnx132 remaindernear 0.0 1 -> 0.0 rmnx133 remaindernear 0.0 -1 -> 0.0 rmnx134 remaindernear -0 1 -> -0 rmnx135 remaindernear -0 -1 -> -0 rmnx136 remaindernear -0.0 1 -> -0.0 rmnx137 remaindernear -0.0 -1 -> -0.0 -- 0.5ers rmmx143 remaindernear 0.5 2 -> 0.5 rmmx144 remaindernear 0.5 2.1 -> 0.5 rmmx145 remaindernear 0.5 2.01 -> 0.50 rmmx146 remaindernear 0.5 2.001 -> 0.500 rmmx147 remaindernear 0.50 2 -> 0.50 rmmx148 remaindernear 0.50 2.01 -> 0.50 rmmx149 remaindernear 0.50 2.001 -> 0.500 -- some differences from remainder rmnx150 remaindernear 0.4 1.020 -> 0.400 rmnx151 remaindernear 0.50 1.020 -> 0.500 rmnx152 remaindernear 0.51 1.020 -> 0.510 rmnx153 remaindernear 0.52 1.020 -> -0.500 rmnx154 remaindernear 0.6 1.020 -> -0.420 rmnx155 remaindernear 0.49 1 -> 0.49 rmnx156 remaindernear 0.50 1 -> 0.50 rmnx157 remaindernear 1.50 1 -> -0.50 rmnx158 remaindernear 2.50 1 -> 0.50 rmnx159 remaindernear 9.50 1 -> -0.50 rmnx160 remaindernear 0.51 1 -> -0.49 -- the nasty division-by-1 cases rmnx161 remaindernear 0.4 1 -> 0.4 rmnx162 remaindernear 0.45 1 -> 0.45 rmnx163 remaindernear 0.455 1 -> 0.455 rmnx164 remaindernear 0.4555 1 -> 0.4555 rmnx165 remaindernear 0.45555 1 -> 0.45555 rmnx166 remaindernear 0.455555 1 -> 0.455555 rmnx167 remaindernear 0.4555555 1 -> 0.4555555 rmnx168 remaindernear 0.45555555 1 -> 0.45555555 rmnx169 remaindernear 0.455555555 1 -> 0.455555555 -- with spill... rmnx171 remaindernear 0.5 1 -> 0.5 rmnx172 remaindernear 0.55 1 -> -0.45 rmnx173 remaindernear 0.555 1 -> -0.445 rmnx174 remaindernear 0.5555 1 -> -0.4445 rmnx175 remaindernear 0.55555 1 -> -0.44445 rmnx176 remaindernear 0.555555 1 -> -0.444445 rmnx177 remaindernear 0.5555555 1 -> -0.4444445 rmnx178 remaindernear 0.55555555 1 -> -0.44444445 rmnx179 remaindernear 0.555555555 1 -> -0.444444445 -- progression rmnx180 remaindernear 1 1 -> 0 rmnx181 remaindernear 1 2 -> 1 rmnx182 remaindernear 1 3 -> 1 rmnx183 remaindernear 1 4 -> 1 rmnx184 remaindernear 1 5 -> 1 rmnx185 remaindernear 1 6 -> 1 rmnx186 remaindernear 1 7 -> 1 rmnx187 remaindernear 1 8 -> 1 rmnx188 remaindernear 1 9 -> 1 rmnx189 remaindernear 1 10 -> 1 rmnx190 remaindernear 1 1 -> 0 rmnx191 remaindernear 2 1 -> 0 rmnx192 remaindernear 3 1 -> 0 rmnx193 remaindernear 4 1 -> 0 rmnx194 remaindernear 5 1 -> 0 rmnx195 remaindernear 6 1 -> 0 rmnx196 remaindernear 7 1 -> 0 rmnx197 remaindernear 8 1 -> 0 rmnx198 remaindernear 9 1 -> 0 rmnx199 remaindernear 10 1 -> 0 -- Various flavours of remaindernear by 0 maxexponent: 999999999 minexponent: -999999999 rmnx201 remaindernear 0 0 -> NaN Division_undefined rmnx202 remaindernear 0.0E5 0 -> NaN Division_undefined rmnx203 remaindernear 0.000 0 -> NaN Division_undefined rmnx204 remaindernear 0.0001 0 -> NaN Invalid_operation rmnx205 remaindernear 0.01 0 -> NaN Invalid_operation rmnx206 remaindernear 0.1 0 -> NaN Invalid_operation rmnx207 remaindernear 1 0 -> NaN Invalid_operation rmnx208 remaindernear 1 0.0 -> NaN Invalid_operation rmnx209 remaindernear 10 0.0 -> NaN Invalid_operation rmnx210 remaindernear 1E+100 0.0 -> NaN Invalid_operation rmnx211 remaindernear 1E+1000 0 -> NaN Invalid_operation -- tests from the extended specification rmnx221 remaindernear 2.1 3 -> -0.9 rmnx222 remaindernear 10 6 -> -2 rmnx223 remaindernear 10 3 -> 1 rmnx224 remaindernear -10 3 -> -1 rmnx225 remaindernear 10.2 1 -> 0.2 rmnx226 remaindernear 10 0.3 -> 0.1 rmnx227 remaindernear 3.6 1.3 -> -0.3 -- some differences from remainder rmnx231 remaindernear 0.4 1.020 -> 0.400 rmnx232 remaindernear 0.50 1.020 -> 0.500 rmnx233 remaindernear 0.51 1.020 -> 0.510 rmnx234 remaindernear 0.52 1.020 -> -0.500 rmnx235 remaindernear 0.6 1.020 -> -0.420 -- test some cases that are close to exponent overflow maxexponent: 999999999 minexponent: -999999999 rmnx270 remaindernear 1 1e999999999 -> 1 rmnx271 remaindernear 1 0.9e999999999 -> 1 rmnx272 remaindernear 1 0.99e999999999 -> 1 rmnx273 remaindernear 1 0.999999999e999999999 -> 1 rmnx274 remaindernear 9e999999999 1 -> NaN Division_impossible rmnx275 remaindernear 9.9e999999999 1 -> NaN Division_impossible rmnx276 remaindernear 9.99e999999999 1 -> NaN Division_impossible rmnx277 remaindernear 9.99999999e999999999 1 -> NaN Division_impossible rmnx280 remaindernear 0.1 9e-999999999 -> NaN Division_impossible rmnx281 remaindernear 0.1 99e-999999999 -> NaN Division_impossible rmnx282 remaindernear 0.1 999e-999999999 -> NaN Division_impossible rmnx283 remaindernear 0.1 9e-999999998 -> NaN Division_impossible rmnx284 remaindernear 0.1 99e-999999998 -> NaN Division_impossible rmnx285 remaindernear 0.1 999e-999999998 -> NaN Division_impossible rmnx286 remaindernear 0.1 999e-999999997 -> NaN Division_impossible rmnx287 remaindernear 0.1 9999e-999999997 -> NaN Division_impossible rmnx288 remaindernear 0.1 99999e-999999997 -> NaN Division_impossible -- rmnx3xx are from DiagBigDecimal rmnx301 remaindernear 1 3 -> 1 rmnx302 remaindernear 5 5 -> 0 rmnx303 remaindernear 13 10 -> 3 rmnx304 remaindernear 13 50 -> 13 rmnx305 remaindernear 13 100 -> 13 rmnx306 remaindernear 13 1000 -> 13 rmnx307 remaindernear .13 1 -> 0.13 rmnx308 remaindernear 0.133 1 -> 0.133 rmnx309 remaindernear 0.1033 1 -> 0.1033 rmnx310 remaindernear 1.033 1 -> 0.033 rmnx311 remaindernear 10.33 1 -> 0.33 rmnx312 remaindernear 10.33 10 -> 0.33 rmnx313 remaindernear 103.3 1 -> 0.3 rmnx314 remaindernear 133 10 -> 3 rmnx315 remaindernear 1033 10 -> 3 rmnx316 remaindernear 1033 50 -> -17 rmnx317 remaindernear 101.0 3 -> -1.0 rmnx318 remaindernear 102.0 3 -> 0.0 rmnx319 remaindernear 103.0 3 -> 1.0 rmnx320 remaindernear 2.40 1 -> 0.40 rmnx321 remaindernear 2.400 1 -> 0.400 rmnx322 remaindernear 2.4 1 -> 0.4 rmnx323 remaindernear 2.4 2 -> 0.4 rmnx324 remaindernear 2.400 2 -> 0.400 rmnx325 remaindernear 1 0.3 -> 0.1 rmnx326 remaindernear 1 0.30 -> 0.10 rmnx327 remaindernear 1 0.300 -> 0.100 rmnx328 remaindernear 1 0.3000 -> 0.1000 rmnx329 remaindernear 1.0 0.3 -> 0.1 rmnx330 remaindernear 1.00 0.3 -> 0.10 rmnx331 remaindernear 1.000 0.3 -> 0.100 rmnx332 remaindernear 1.0000 0.3 -> 0.1000 rmnx333 remaindernear 0.5 2 -> 0.5 rmnx334 remaindernear 0.5 2.1 -> 0.5 rmnx335 remaindernear 0.5 2.01 -> 0.50 rmnx336 remaindernear 0.5 2.001 -> 0.500 rmnx337 remaindernear 0.50 2 -> 0.50 rmnx338 remaindernear 0.50 2.01 -> 0.50 rmnx339 remaindernear 0.50 2.001 -> 0.500 rmnx340 remaindernear 0.5 0.5000001 -> -1E-7 rmnx341 remaindernear 0.5 0.50000001 -> -1E-8 rmnx342 remaindernear 0.5 0.500000001 -> -1E-9 rmnx343 remaindernear 0.5 0.5000000001 -> -1E-10 rmnx344 remaindernear 0.5 0.50000000001 -> -1E-11 rmnx345 remaindernear 0.5 0.4999999 -> 1E-7 rmnx346 remaindernear 0.5 0.49999999 -> 1E-8 rmnx347 remaindernear 0.5 0.499999999 -> 1E-9 rmnx348 remaindernear 0.5 0.4999999999 -> 1E-10 rmnx349 remaindernear 0.5 0.49999999999 -> 1E-11 rmnx350 remaindernear 0.03 7 -> 0.03 rmnx351 remaindernear 5 2 -> 1 rmnx352 remaindernear 4.1 2 -> 0.1 rmnx353 remaindernear 4.01 2 -> 0.01 rmnx354 remaindernear 4.001 2 -> 0.001 rmnx355 remaindernear 4.0001 2 -> 0.0001 rmnx356 remaindernear 4.00001 2 -> 0.00001 rmnx357 remaindernear 4.000001 2 -> 0.000001 rmnx358 remaindernear 4.0000001 2 -> 1E-7 rmnx360 remaindernear 1.2 0.7345 -> -0.2690 rmnx361 remaindernear 0.8 12 -> 0.8 rmnx362 remaindernear 0.8 0.2 -> 0.0 rmnx363 remaindernear 0.8 0.3 -> -0.1 rmnx364 remaindernear 0.800 12 -> 0.800 rmnx365 remaindernear 0.800 1.7 -> 0.800 rmnx366 remaindernear 2.400 2 -> 0.400 precision: 6 rmnx371 remaindernear 2.400 2 -> 0.400 precision: 3 rmnx372 remaindernear 12345678900000 12e+12 -> 3.46E+11 Inexact Rounded precision: 5 rmnx381 remaindernear 12345 1 -> 0 rmnx382 remaindernear 12345 1.0001 -> -0.2344 rmnx383 remaindernear 12345 1.001 -> -0.333 rmnx384 remaindernear 12345 1.01 -> -0.23 rmnx385 remaindernear 12345 1.1 -> -0.3 rmnx386 remaindernear 12355 4 -> -1 rmnx387 remaindernear 12345 4 -> 1 rmnx388 remaindernear 12355 4.0001 -> -1.3089 rmnx389 remaindernear 12345 4.0001 -> 0.6914 rmnx390 remaindernear 12345 4.9 -> 1.9 rmnx391 remaindernear 12345 4.99 -> -0.26 rmnx392 remaindernear 12345 4.999 -> 2.469 rmnx393 remaindernear 12345 4.9999 -> 0.2469 rmnx394 remaindernear 12345 5 -> 0 rmnx395 remaindernear 12345 5.0001 -> -0.2469 rmnx396 remaindernear 12345 5.001 -> -2.469 rmnx397 remaindernear 12345 5.01 -> 0.36 rmnx398 remaindernear 12345 5.1 -> -2.1 precision: 9 -- some nasty division-by-1 cases [some similar above] rmnx401 remaindernear 0.4 1 -> 0.4 rmnx402 remaindernear 0.45 1 -> 0.45 rmnx403 remaindernear 0.455 1 -> 0.455 rmnx404 remaindernear 0.4555 1 -> 0.4555 rmnx405 remaindernear 0.45555 1 -> 0.45555 rmnx406 remaindernear 0.455555 1 -> 0.455555 rmnx407 remaindernear 0.4555555 1 -> 0.4555555 rmnx408 remaindernear 0.45555555 1 -> 0.45555555 rmnx409 remaindernear 0.455555555 1 -> 0.455555555 -- some tricky LHSs rmnx420 remaindernear 99999999.999999999 1E+8 -> -1E-9 rmnx421 remaindernear 999999999.999999999 1E+9 -> -1E-9 precision: 9 rmnx430 remaindernear 0.455555555 1 -> 0.455555555 precision: 8 rmnx431 remaindernear 0.455555555 1 -> 0.45555556 Inexact Rounded precision: 7 rmnx432 remaindernear 0.455555555 1 -> 0.4555556 Inexact Rounded precision: 6 rmnx433 remaindernear 0.455555555 1 -> 0.455556 Inexact Rounded precision: 5 rmnx434 remaindernear 0.455555555 1 -> 0.45556 Inexact Rounded precision: 4 rmnx435 remaindernear 0.455555555 1 -> 0.4556 Inexact Rounded precision: 3 rmnx436 remaindernear 0.455555555 1 -> 0.456 Inexact Rounded precision: 2 rmnx437 remaindernear 0.455555555 1 -> 0.46 Inexact Rounded precision: 1 rmnx438 remaindernear 0.455555555 1 -> 0.5 Inexact Rounded -- early tests; from text descriptions precision: 9 rmnx601 remaindernear 10 6 -> -2 rmnx602 remaindernear -10 6 -> 2 rmnx603 remaindernear 11 3 -> -1 rmnx604 remaindernear 11 5 -> 1 rmnx605 remaindernear 7.7 8 -> -0.3 rmnx606 remaindernear 31.5 3 -> 1.5 -- i=10 rmnx607 remaindernear 34.5 3 -> -1.5 -- i=11 -- zero signs rmnx650 remaindernear 1 1 -> 0 rmnx651 remaindernear -1 1 -> -0 rmnx652 remaindernear 1 -1 -> 0 rmnx653 remaindernear -1 -1 -> -0 rmnx654 remaindernear 0 1 -> 0 rmnx655 remaindernear -0 1 -> -0 rmnx656 remaindernear 0 -1 -> 0 rmnx657 remaindernear -0 -1 -> -0 rmnx658 remaindernear 0.00 1 -> 0.00 rmnx659 remaindernear -0.00 1 -> -0.00 -- Specials rmnx680 remaindernear Inf -Inf -> NaN Invalid_operation rmnx681 remaindernear Inf -1000 -> NaN Invalid_operation rmnx682 remaindernear Inf -1 -> NaN Invalid_operation rmnx683 remaindernear Inf 0 -> NaN Invalid_operation rmnx684 remaindernear Inf -0 -> NaN Invalid_operation rmnx685 remaindernear Inf 1 -> NaN Invalid_operation rmnx686 remaindernear Inf 1000 -> NaN Invalid_operation rmnx687 remaindernear Inf Inf -> NaN Invalid_operation rmnx688 remaindernear -1000 Inf -> -1000 rmnx689 remaindernear -Inf Inf -> NaN Invalid_operation rmnx691 remaindernear -1 Inf -> -1 rmnx692 remaindernear 0 Inf -> 0 rmnx693 remaindernear -0 Inf -> -0 rmnx694 remaindernear 1 Inf -> 1 rmnx695 remaindernear 1000 Inf -> 1000 rmnx696 remaindernear Inf Inf -> NaN Invalid_operation rmnx700 remaindernear -Inf -Inf -> NaN Invalid_operation rmnx701 remaindernear -Inf -1000 -> NaN Invalid_operation rmnx702 remaindernear -Inf -1 -> NaN Invalid_operation rmnx703 remaindernear -Inf -0 -> NaN Invalid_operation rmnx704 remaindernear -Inf 0 -> NaN Invalid_operation rmnx705 remaindernear -Inf 1 -> NaN Invalid_operation rmnx706 remaindernear -Inf 1000 -> NaN Invalid_operation rmnx707 remaindernear -Inf Inf -> NaN Invalid_operation rmnx708 remaindernear -Inf -Inf -> NaN Invalid_operation rmnx709 remaindernear -1000 Inf -> -1000 rmnx710 remaindernear -1 -Inf -> -1 rmnx711 remaindernear -0 -Inf -> -0 rmnx712 remaindernear 0 -Inf -> 0 rmnx713 remaindernear 1 -Inf -> 1 rmnx714 remaindernear 1000 -Inf -> 1000 rmnx715 remaindernear Inf -Inf -> NaN Invalid_operation rmnx721 remaindernear NaN -Inf -> NaN rmnx722 remaindernear NaN -1000 -> NaN rmnx723 remaindernear NaN -1 -> NaN rmnx724 remaindernear NaN -0 -> NaN rmnx725 remaindernear NaN 0 -> NaN rmnx726 remaindernear NaN 1 -> NaN rmnx727 remaindernear NaN 1000 -> NaN rmnx728 remaindernear NaN Inf -> NaN rmnx729 remaindernear NaN NaN -> NaN rmnx730 remaindernear -Inf NaN -> NaN rmnx731 remaindernear -1000 NaN -> NaN rmnx732 remaindernear -1 -NaN -> -NaN rmnx733 remaindernear -0 NaN -> NaN rmnx734 remaindernear 0 NaN -> NaN rmnx735 remaindernear 1 NaN -> NaN rmnx736 remaindernear 1000 NaN -> NaN rmnx737 remaindernear Inf NaN -> NaN rmnx741 remaindernear sNaN -Inf -> NaN Invalid_operation rmnx742 remaindernear sNaN -1000 -> NaN Invalid_operation rmnx743 remaindernear -sNaN -1 -> -NaN Invalid_operation rmnx744 remaindernear sNaN -0 -> NaN Invalid_operation rmnx745 remaindernear sNaN 0 -> NaN Invalid_operation rmnx746 remaindernear sNaN 1 -> NaN Invalid_operation rmnx747 remaindernear sNaN 1000 -> NaN Invalid_operation rmnx749 remaindernear sNaN NaN -> NaN Invalid_operation rmnx750 remaindernear sNaN sNaN -> NaN Invalid_operation rmnx751 remaindernear NaN sNaN -> NaN Invalid_operation rmnx752 remaindernear -Inf sNaN -> NaN Invalid_operation rmnx753 remaindernear -1000 sNaN -> NaN Invalid_operation rmnx754 remaindernear -1 sNaN -> NaN Invalid_operation rmnx755 remaindernear -0 -sNaN -> -NaN Invalid_operation rmnx756 remaindernear 0 sNaN -> NaN Invalid_operation rmnx757 remaindernear 1 sNaN -> NaN Invalid_operation rmnx758 remaindernear 1000 sNaN -> NaN Invalid_operation rmnx759 remaindernear Inf sNaN -> NaN Invalid_operation rmnx760 remaindernear NaN sNaN -> NaN Invalid_operation -- propaging NaNs rmnx761 remaindernear NaN1 NaN7 -> NaN1 rmnx762 remaindernear sNaN2 NaN8 -> NaN2 Invalid_operation rmnx763 remaindernear NaN3 -sNaN9 -> -NaN9 Invalid_operation rmnx764 remaindernear sNaN4 sNaN10 -> NaN4 Invalid_operation rmnx765 remaindernear 15 NaN11 -> NaN11 rmnx766 remaindernear NaN6 NaN12 -> NaN6 rmnx767 remaindernear Inf -NaN13 -> -NaN13 rmnx768 remaindernear NaN14 -Inf -> NaN14 rmnx769 remaindernear 0 NaN15 -> NaN15 rmnx770 remaindernear -NaN16 -0 -> -NaN16 -- test some cases that are close to exponent overflow maxexponent: 999999999 minexponent: -999999999 rmnx780 remaindernear 1 1e999999999 -> 1 rmnx781 remaindernear 1 0.9e999999999 -> 1 rmnx782 remaindernear 1 0.99e999999999 -> 1 rmnx783 remaindernear 1 0.999999999e999999999 -> 1 rmnx784 remaindernear 9e999999999 1 -> NaN Division_impossible rmnx785 remaindernear 9.9e999999999 1 -> NaN Division_impossible rmnx786 remaindernear 9.99e999999999 1 -> NaN Division_impossible rmnx787 remaindernear 9.99999999e999999999 1 -> NaN Division_impossible -- overflow and underflow tests [from divide] precision: 9 maxexponent: 999999999 minexponent: -999999999 rmnx790 remaindernear +1.23456789012345E-0 9E+999999999 -> 1.23456789 Inexact Rounded rmnx791 remaindernear 9E+999999999 +0.23456789012345E-0 -> NaN Division_impossible rmnx792 remaindernear +0.100 9E+999999999 -> 0.100 rmnx793 remaindernear 9E-999999999 +9.100 -> 9E-999999999 rmnx795 remaindernear -1.23456789012345E-0 9E+999999999 -> -1.23456789 Inexact Rounded rmnx796 remaindernear 9E+999999999 -0.83456789012345E-0 -> NaN Division_impossible rmnx797 remaindernear -0.100 9E+999999999 -> -0.100 rmnx798 remaindernear 9E-999999999 -9.100 -> 9E-999999999 -- long operands checks maxexponent: 999 minexponent: -999 precision: 9 rmnx801 remaindernear 12345678000 100 -> 0 rmnx802 remaindernear 1 12345678000 -> 1 rmnx803 remaindernear 1234567800 10 -> 0 rmnx804 remaindernear 1 1234567800 -> 1 rmnx805 remaindernear 1234567890 10 -> 0 rmnx806 remaindernear 1 1234567890 -> 1 rmnx807 remaindernear 1234567891 10 -> 1 rmnx808 remaindernear 1 1234567891 -> 1 rmnx809 remaindernear 12345678901 100 -> 1 rmnx810 remaindernear 1 12345678901 -> 1 rmnx811 remaindernear 1234567896 10 -> -4 rmnx812 remaindernear 1 1234567896 -> 1 precision: 15 rmnx841 remaindernear 12345678000 100 -> 0 rmnx842 remaindernear 1 12345678000 -> 1 rmnx843 remaindernear 1234567800 10 -> 0 rmnx844 remaindernear 1 1234567800 -> 1 rmnx845 remaindernear 1234567890 10 -> 0 rmnx846 remaindernear 1 1234567890 -> 1 rmnx847 remaindernear 1234567891 10 -> 1 rmnx848 remaindernear 1 1234567891 -> 1 rmnx849 remaindernear 12345678901 100 -> 1 rmnx850 remaindernear 1 12345678901 -> 1 rmnx851 remaindernear 1234567896 10 -> -4 rmnx852 remaindernear 1 1234567896 -> 1 -- Null tests rmnx900 remaindernear 10 # -> NaN Invalid_operation rmnx901 remaindernear # 10 -> NaN Invalid_operation