ÿØÿà JFIF    ÿÛ „  ( %"1!%)+...383,7(-.+  -+++--++++---+-+-----+---------------+---+-++7-----ÿÀ  ß â" ÿÄ     ÿÄ H    !1AQaq"‘¡2B±ÁÑð#R“Ò Tbr‚²á3csƒ’ÂñDS¢³$CÿÄ   ÿÄ %  !1AQa"23‘ÿÚ   ? ôÿ ¨pŸªáÿ —åYõõ\?àÒü©ŠÄï¨pŸªáÿ —åYõõ\?àÓü©ŠÄá 0Ÿªáÿ Ÿå[úƒ ú®ði~TÁbqÐ8OÕpÿ ƒOò¤Oè`–RÂáœá™êi€ßÉ< FtŸI“öÌ8úDf´°å}“¾œ6  öFá°y¥jñÇh†ˆ¢ã/ÃÐ:ªcÈ "Y¡ðÑl>ÿ ”ÏËte:qž\oäŠe÷󲍷˜HT4&ÿ ÓÐü6ö®¿øþßèô Ÿ•7Ñi’•j|“ñì>b…þS?*Óôÿ ÓÐü*h¥£ír¶ü UãS炟[AÐaè[ûª•õ&õj?†Éö+EzP—WeÒírJFt ‘BŒ†Ï‡%#tE Øz ¥OÛ«!1›üä±Í™%ºÍãö]°î(–:@<‹ŒÊö×òÆt¦ãº+‡¦%ÌÁ²h´OƒJŒtMÜ>ÀÜÊw3Y´•牋4ǍýʏTì>œú=Íwhyë,¾Ôò×õ¿ßÊa»«þˆѪQ|%6ž™A õ%:øj<>É—ÿ Å_ˆCbõ¥š±ý¯Ýƒï…¶|RëócÍf溪“t.СøTÿ *Ä¿-{†çàczůŽ_–^XþŒ±miB[X±d 1,é”zEù»& î9gœf™9Ð'.;—™i}!ôšåîqêÛ٤ёý£½ÆA–àôe"A$˝Úsäÿ ÷Û #°xŸëí(l »ý3—¥5m! rt`†0~'j2(]S¦¦kv,ÚÇ l¦øJA£Šƒ J3E8ÙiŽ:cÉžúeZ°€¯\®kÖ(79«Ž:¯X”¾³Š&¡* ….‰Ž(ÜíŸ2¥ª‡×Hi²TF¤ò[¨íÈRëÉ䢍mgÑ.Ÿ<öäS0í„ǹÁU´f#Vß;Õ–…P@3ío<ä-±»Ž.L|kªÀê›fÂ6@»eu‚|ÓaÞÆŸ…¨ááå>åŠ?cKü6ùTÍÆ”†sĤÚ;H2RÚ†õ\Ö·Ÿn'¾ ñ#ºI¤Å´%çÁ­‚â7›‹qT3Iï¨ÖÚ5I7Ë!ÅOóŸ¶øÝñØôת¦$Tcö‘[«Ö³šÒ';Aþ ¸èíg A2Z"i¸vdÄ÷.iõ®§)¿]¤À†–‡É&ä{V¶iŽ”.Ó×Õÿ û?h¬Mt–íª[ÿ Ñÿ ÌV(í}=ibÔ¡›¥¢±b Lô¥‡piη_Z<‡z§èŒ)iÖwiÇ 2hÙ3·=’d÷8éŽ1¦¸c¤µ€7›7Ø ð\á)} ¹fËí›pAÃL%âc2 í§æQz¿;T8sæ°qø)QFMð‰XŒÂ±N¢aF¨…8¯!U  Z©RÊ ÖPVÄÀÍin™Ì-GˆªÅËŠ›•zË}º±ŽÍFò¹}Uw×#ä5B¤{î}Ð<ÙD é©¤&‡ïDbàÁôMÁ." ¤‡ú*õ'VŽ|¼´Úgllº¼klz[Æüï÷Aób‡Eÿ dÑ»Xx9ÃÜ£ÁT/`¼¸vI±Ýµ·Ë‚“G³þ*Ÿû´r|*}<¨îºœ @¦mÄ’M¹”.œ«Y–|6ÏU¤jç¥ÕÞqO ˜kDÆÁ¨5ÿ š;ÐЦ¦€GÙk \ –Þ=â¼=SͧµªS°ÚÍpÜãQűÀõ¬?ÃÁ1Ñ•õZà?hóœ€ L¦l{Y*K˜Ù›zc˜–ˆâ ø+¾ ­-Ök¥%ùEÜA'}ˆ><ÊIè“bpÍ/qÞâvoX€w,\úªò6Z[XdÒæ­@Ö—€$òJí#é>'°Ú ôª˜<)4ryÙ£|óAÅn5žêŸyÒäMÝ2{"}‰–¤l÷ûWX\l¾Á¸góÉOÔ /óñB¤f¸çñ[.P˜ZsÊË*ßT܈§QN¢’¡¨§V¼(Üù*eÕ“”5T¨‹Âê¥FŒã½Dü[8'Ò¥a…Ú¶k7a *•›¼'Ò·\8¨ª\@\õ¢¦íq+DÙrmÎ…_ªæ»ŠÓœ¡¯’Ré9MÅ×D™lælffc+ŒÑ,ý™ÿ ¯þǤ=Å’Á7µ÷ÚÛ/“Ü€ñýã¼àí¾ÕÑ+ƒ,uµMâÀÄbm:ÒÎPæ{˜Gz[ƒ¯«® KHà`ߨŠéí¯P8Aq.C‰ à€kòpj´kN¶qô€…Õ,ÜNŠª-­{Zö’æû44‰sŽè‰îVíRœÕm" 6?³D9¡ÇTíÅꋇ`4«¸ÝÁô ï’ýorqКÇZ«x4Žâéþuïf¹µö[P ,Q£éaX±`PÉÍZ ¸äYúg üAx ’6Lê‚xÝÓ*äQ  Ï’¨hÍ =²,6ï#rÃ<¯–£»ƒ‹,–ê•€ aÛsñ'%Æ"®ÛüìBᝠHÚ3ß°©$“XnœÖ’î2ËTeûìxîß ¦å¿çÉ ðK§þ{‘t‚Ϋ¬jéîZ[ ”š7L¥4VÚCE×]m¤Øy”ä4-dz£œ§¸x.*ãÊÊ b÷•h:©‡¦s`BTÁRû¾g⻩‹jø sF¢àJøFl‘È•Xᓁà~*j¯ +(ÚÕ6-£¯÷GŠØy‚<Ç’.F‹Hœw(+)ÜÜâÈzÄäT§FߘãÏ;DmVœ3Àu@mÚüXÝü•3B¨òÌÁÛ<·ÃÜ z,Ì@õÅ·d2]ü8s÷IôÞ¯^Ç9¢u„~ëAŸï4«M? K]­ÅàPl@s_ p:°¬ZR”´›JC[CS.h‹ƒïËœ«Æ]–÷ó‚wR×k7X‰k›‘´ù¦=¡«‰¨¨Â')—71ó’c‡Ðúµ `é.{§p¹ój\Ž{1h{o±Ý=áUÊïGÖŒõ–-BÄm+AZX¶¡ ïHðæ¥JmÙ;…䡟ˆ¦ ° äšiÉg«$üMk5¤L“’çÊvïâï ,=f“"íἊ5ô¬x6{ɏžID0e¸vçmi'︧ºð9$ò¹÷*£’9ÿ ²TÔ…×>JV¥}Œ}$p[bÔ®*[jzS*8 ”·T›Í–ñUîƒwo$áè=LT™ç—~ô·¤ÈÚ$榍q‰„+´kFm)ž‹©i–ËqÞŠ‰à¶ü( ‚•§ •°ò·‡#5ª•µÊ﯅¡X¨šÁ*F#TXJÊ ušJVÍ&=iÄs1‚3•'fý§5Ñ<=[íÞ­ PÚ;ѱÌ_~Ä££8rÞ ²w;’hDT°>ÈG¬8Á²ÚzŽ®ò®qZcqJêäÞ-ö[ܘbň±çb“ж31²n×iƒðÕ;1¶þÉ ªX‰,ßqÏ$>•î íZ¥Z 1{ç൵+ƒÕµ¥°T$§K]á»Ûï*·¤tMI’ÂZbŽÕiÒ˜}bÓ0£ª5›¨ [5Ž^ÝœWøÂÝh° ¢OWun£¤5 a2Z.G2³YL]jåtì”ä ÁÓ‘%"©<Ôúʰsº UZvä‡ÄiÆÒM .÷V·™ø#kèýiíÌ–ª)µT[)BˆõÑ xB¾B€ÖT¨.¥~ð@VĶr#¸ü*åZNDŽH;âi ],©£öØpù(šºãö¼T.uCê•4@ÿ GÕÛ)Cx›®0ø#:ÏðFÒbR\(€€Ä®fã4Þ‰Fä¯HXƒÅ,†öEÑÔÜ]Öv²?tLÃvBY£ú6Êu5ÅAQ³1‘’¬x–HŒÐ‡ ^ ¸KwJôÖŽ5×CÚ¨vÜ«/B0$×k°=ðbÇ(Ï)w±A†Á† 11Í=èQšµ626ŒÜ/`G«µ<}—-Ö7KEHÈÉðóȤmݱû±·ø«Snmá=“䫚mݱŸ¡¶~ó·“äUóJæúòB|E LêŽy´jDÔ$G¢þÐñ7óR8ýÒ…Ç› WVe#·Ÿ p·Fx~•ݤF÷0Èÿ K¯æS<6’¡WШ; ´ÿ ¥Êø\Òuî†åÝ–VNœkÒ7oòX¨Á­Ø÷FÎÑä±g÷ÿ M~Çî=p,X´ ÝÌÚÅ‹’ÃjÖ.ØöÏñ qïQ¤ÓZE†° =6·]܈ s¸>v•Ž^Ý\wq9r‰Î\¸¡kURÒ$­*‹Nq?Þª*!sŠÆ:TU_u±T+øX¡ ®¹¡,ÄâÃBTsÜ$Ø›4m椴zÜK]’’›Pƒ @€#â˜`é¹=I‡fiV•Ôî“nRm+µFPOhÍ0B£ €+¬5c v•:P'ÒyÎ ‰V~‚Ó†ÖuókDoh$å\*ö%Ю=£«…aȼ½÷Û.-½VŒŠ¼'lyî±1¬3ó#ÞE¿ÔS¤gV£m›=§\û"—WU¤ÚǼÿ ÂnÁGŒÃ ‚õN D³õNÚíŒÕ;HôyÄÈ©P¹Ä{:?R‘Ô¨âF÷ø£bÅó® JS|‚R÷ivýáâ€Æé¡è³´IئÑT!§˜•ت‚¬â@q€wnïCWÄ@JU€ê¯m6]Ï:£âx'+ÒðXvÓ¦Úm=–´7œ $ì“B£~p%ÕŸUþ« N@¼üï~w˜ñø5®—'Ôe»¤5ã//€ž~‰Tþ›Å7•#¤× Íö pÄ$ùeåì*«ÓŠEØWEÈsßg ¦ûvžSsLpºÊW–âµEWöˬH; ™!CYõZ ÃÄf æ#1W. \uWâ\,\Çf j’<qTbên›Î[vxx£ë 'ö¨1›˜ÀM¼Pÿ H)ƒêêŒA7s,|F“ 꺸k³9Ìö*ç®;Ö!Ö$Eiž•¹ÒÚ†ýóéÝû¾ÕS®ó$’NÝäŸz¤5r¦ãÄÃD÷Üø!°ø‡Ô&@m™Ì^Ãä­d q5Lnÿ N;.6½·N|#ä"1Nƒx“ã<3('&ñßt  ~ªu”1Tb㫨9ê–›–bìd$ߣ=#ÕãÒmU¯eí$EFù5ýYô櫨æì™Ç—±ssM]·á¿0ÕåJRÓªîiƒ+O58ÖñªŠÒx" \µâá¨i’¤i —Ö ” M+M¤ë9‚‰A¦°Qõ¾ßøK~¼Ã‘g…Ö´~÷Ï[3GUœÒ½#…kàÔ®Ò”‰³·dWV‰IP‰Ú8u¹”E ÖqLj¾êÕCBš{A^Âß;–¨`¯¬ìö ˼ ×tìø.tƐm*n¨y4o&Àx¥n¦×î‡aupáÛj8¿m›è¶ã!o½;ß0y^ý×^EÑ¿ÒjzŒ­)vÚÑnÄL …^ªô× ‡—‚3k Îý­hï]içå–îÏ*÷ñþ»Ô CÒjøjÍznˆ´ ¹#b'Fô‹ ‰v¥'’à'T´ƒHýÍ%M‰ ƒ&ÆÇŒï1 ‘ –Þ ‰i¬s žR-Ÿ kЬá¬7:þ 0ŒÅÒÕ/aÙ¬ÃÝ#Úøœ ©aiVc‰. ¹¦ãµ” ›Yg¦›ÆÎýº°f³7ƒhá·¸­}&D9¡ÂsÉÙÞèŠõØàC™¨ñbFC|´Ü(ŸƒÚÒ-%»'a Ì¿)ËÇn¿úÿ ÞŽX…4ÊÅH^ôΑí@ù¹Eh¶“L8Çjù ¼ÎåVªóR©Ï5uà V4lZß®=€xÖŸ–ÑÈ ÷”¨°¾__yM1tÉ?uÆþIkÄgæ@þ[¢†°XÃJ£j·:nkÅ¢u ‘}âGzö­/IµèЬ¼48q¦F°ŽR¼=ûì{´¯RýicS ÕÛ íNtÍÙï£,w4rêì®»~x(©Uñ§#Ñ&œÕ¤>ÎåÍÓ9’Ö{9eV­[Öjâ²ãu]˜å2›qÑšÕJç0€sÄ|Êëè0튔bÁ>“{×_F`Ø©ºê:µä,v¤ðfc1±"«ÔÍän1#=· Âøv~H½ÐßA¾¿Ü€Óš]Õ; I¾÷ç‚Qi†î¹9ywÔKG˜áñ zQY—§ÃÕZ07§X‚ Áh;ÁM)iÌCH-¯T‘ë|A0{Ò½LÚ–TâÖkÜ’dÀ“rmm»”جPF³ÖcbE§T€ÒxKºû’Ó®7±²(\4ŽÃ¸Uu@j™yĵ;³µ!Á¢b.W¤=mõ´êµK k ¸K^ÜÛ#p*Ü14qkZç5ïë †°5Ï%ÍÛ<Õ¤×Ô¥ê†C Õ´¼ú$ƒÖ“”]Ù¬qÞÚ[4©ý!ûÏ—Áb쳐XµA¬â~`›Çr¸8ìùÝ䫦<>ä÷«?xs´ÇÑ /á;¹øüÊÈÙà{"@Žïzâ¬[âß‚ U_<ÇŸ½4èN˜ú61®qŠu ¦þF£»äJ_ˆÙÎ~ ÞAã–݄ϗrŠD;xTž‘ô`É«…suãO`?³à™ô Lý#Íc5öoæØ‚y´´÷«ZR§<&JÇ+éâô´€i!Àˆ0æAoàðLèÖ-2ŸõW.’t^–(KÁmHµV@xÜÇy®Ñø­â^:Ú3w· 7½¹°ñ¸â¹®:',«Mœ—n­Á+Ãbš LÈ‘ÄnRÓÅœ%¦²‰¨ùQ:¤f‚ "PÕtô¸…cæl…&˜Ú˜Ôkv‹ž+vŠ,=¢v­6—Xy*¥t£«<™:“aîϲ=¦6rO]XI¿Œ÷¤zÚ­›¶ 6÷”w\d ü~v®ˆÌk«^m<ÿ ¢‰Õ\)ùºŽ;… lîÙÅEŠ®cѾ@vnMÏ,¼“ñ•ŽBxðÃzãÇç%3ˆ"}Ù•Åî> BÉú;Ò]V+P˜F_´ßé> Øše|ï‡ÄOmFæÇ ãqÞ$/xÐx­z`ï9"œÜij‚!7.\Td…9M‡•iŽ‹¾‘50ÞŽn¥ß4ÉôO ¹*í^QêËÜÇÌ8=ާs‰'ÂëÙ«á%Pú[O †ÅP¯Vsް.‰,kc¶ ¬A9n˜XÎ-ÞšN["¹QÕ‰ƒMýÁߺXJæÍaLj¾×Ãmã¾ãÚ uñÒþåQô¦¥ /ÄUx:‚ÍÜ’ Đ©ØÝ3V¨‰ÕnÐ6ó*óúK­«…c ¯U òhsý­jóÔj#,ímŒRµ«lbïUTŒÑ8†Ä0œÏr`ð¡¬É Ї ë"À² ™ 6¥ f¶ ¢ÚoܱԷ-<Àî)†a¶ž'Ú»¨TXqØæ¶÷YÄHy˜9ÈIW­YÀuMFë ºÏ’AqÌ4·/Ú †ô'i$øä­=Ä Ý|öK×40è|È6p‘0§)o¥ctî§H+CA-“ xØ|ÐXАç l8íºð3Ø:³¤¬KX¯UÿÙ # big.js **A small, fast JavaScript library for arbitrary-precision decimal arithmetic.** The little sister to [bignumber.js](https://github.com/MikeMcl/bignumber.js/) and [decimal.js](https://github.com/MikeMcl/decimal.js/). See [here](https://github.com/MikeMcl/big.js/wiki) for some notes on the difference between them. ## Features - Faster, smaller and easier-to-use than JavaScript versions of Java's BigDecimal - Only 5.9 KB minified and 2.7 KB gzipped - Simple API - Replicates the `toExponential`, `toFixed` and `toPrecision` methods of JavaScript's Number type - Includes a `sqrt` method - Stores values in an accessible decimal floating point format - No dependencies - Comprehensive [documentation](http://mikemcl.github.io/big.js/) and test set ## Set up The library is the single JavaScript file *big.js* (or *big.min.js*, which is *big.js* minified). Browser: ```html ``` [Node.js](http://nodejs.org): ```bash $ npm install big.js ``` ```javascript const Big = require('big.js'); ``` ES6 module: ```javascript import Big from 'big.mjs'; ``` ## Use *In all examples below, `var`, semicolons and `toString` calls are not shown. If a commented-out value is in quotes it means `toString` has been called on the preceding expression.* The library exports a single function, `Big`, the constructor of Big number instances. It accepts a value of type number, string or Big number object. x = new Big(123.4567) y = Big('123456.7e-3') // 'new' is optional z = new Big(x) x.eq(y) && x.eq(z) && y.eq(z) // true A Big number is immutable in the sense that it is not changed by its methods. 0.3 - 0.1 // 0.19999999999999998 x = new Big(0.3) x.minus(0.1) // "0.2" x // "0.3" The methods that return a Big number can be chained. x.div(y).plus(z).times(9).minus('1.234567801234567e+8').plus(976.54321).div('2598.11772') x.sqrt().div(y).pow(3).gt(y.mod(z)) // true Like JavaScript's Number type, there are `toExponential`, `toFixed` and `toPrecision` methods. x = new Big(255.5) x.toExponential(5) // "2.55500e+2" x.toFixed(5) // "255.50000" x.toPrecision(5) // "255.50" The arithmetic methods always return the exact result except `div`, `sqrt` and `pow` (with negative exponent), as these methods involve division. The maximum number of decimal places and the rounding mode used to round the results of these methods is determined by the value of the `DP` and `RM` properties of the `Big` number constructor. Big.DP = 10 Big.RM = 1 x = new Big(2); y = new Big(3); z = x.div(y) // "0.6666666667" z.sqrt() // "0.8164965809" z.pow(-3) // "3.3749999995" z.times(z) // "0.44444444448888888889" z.times(z).round(10) // "0.4444444445" Multiple Big number constructors can be created, each with an independent configuration. The value of a Big number is stored in a decimal floating point format in terms of a coefficient, exponent and sign. x = new Big(-123.456); x.c // [1,2,3,4,5,6] coefficient (i.e. significand) x.e // 2 exponent x.s // -1 sign For further information see the [API](http://mikemcl.github.io/big.js/) reference from the *doc* folder. ## Test The *test* directory contains the test scripts for each Big number method. The tests can be run with Node.js or a browser. To run all the tests $ npm test To test a single method $ node test/toFixed For the browser, see *single-test.html* and *every-test.html* in the *test/browser* directory. *big-vs-number.html* is a simple application that enables some of the methods of big.js to be compared with those of JavaScript's Number type. ## Performance The *perf* directory contains two legacy applications and a *lib* directory containing the BigDecimal libraries used by both. *big-vs-bigdecimal.html* tests the performance of big.js against the JavaScript translations of two versions of BigDecimal, its use should be more or less self-explanatory. * [GWT: java.math.BigDecimal](https://github.com/iriscouch/bigdecimal.js) * [ICU4J: com.ibm.icu.math.BigDecimal](https://github.com/dtrebbien/BigDecimal.js) The BigDecimal in the npm registry is the GWT version. It has some bugs, see the Node.js script *perf/lib/bigdecimal_GWT/bugs.js* for examples of flaws in its *remainder*, *divide* and *compareTo* methods. *bigtime.js* is a Node.js command-line application which tests the performance of big.js against the GWT version of BigDecimal from the npm registry. For example, to compare the time taken by the big.js `plus` method and the BigDecimal `add` method $ node bigtime plus 10000 40 This will time 10000 calls to each, using operands of up to 40 random digits and will check that the results match. For help $ node bigtime -h ## Build If [uglify-js](https://github.com/mishoo/UglifyJS2) is installed globally $ npm install uglify-js -g then $ npm run build will create *big.min.js*. ## TypeScript The [DefinitelyTyped](https://github.com/borisyankov/DefinitelyTyped) project has a Typescript type definitions file for big.js. $ npm install @types/big.js Any questions about the TypeScript type definitions file should be addressed to the DefinitelyTyped project. ## Feedback Bugs/comments/questions? Open an issue, or email Michael ## Licence [MIT](LICENCE) ## Contributors This project exists thanks to all the people who contribute. [[Contribute](CONTRIBUTING.md)]. ## Backers Thank you to all our backers! 🙏 [[Become a backer](https://opencollective.com/bigjs#backer)] ## Sponsors Support this project by becoming a sponsor. Your logo will show up here with a link to your website. [[Become a sponsor](https://opencollective.com/bigjs#sponsor)]