Thread Subject: How do I increase the precision of MATLAB?

Folks,

Simple question. How do I increase the precision of MATLAB, if that is possible by any means? I'm trying to calculate this:

----------------------------------------------------------------------------------------------
>> z

z =

     2.225167162095353e+003 -9.020383145678592e+002i

>> exp( i*z )

ans =

               Inf + Infi
----------------------------------------------------------------------------------------------

Yes, I know that exponentials grow fast, but I'd like to find an exact number.

Thanks

It seems to me you could define:

t = i*z

t =

     9.020383145678592e+002 +2.225167162095353e+003i

Then use

e^z = e^(a+bi) = e^a [cos(b) + i*sin(b)] = (e^(a/2)) * (e^(a/2))*[cos(b) + i*sin(b)]

Now we can get numbers for each term using Matlab and go from there manually adding exponents. Someone else probably knows a scaling trick that is much better.

Oops, obviously I meant:

e^t = e^(a+bi) = ...

"Thiago " <thiago@mathworks.com> wrote in message <gkb7mu$4r$1@fred.mathworks.com>...
> ......
> z = 2.225167162095353e+003 -9.020383145678592e+002i
> >> exp( i*z )
> ans = Inf + Infi
> .......

  What you have asked for is impossible with the IEEE 754 binary double precision floating point (double) numbers that matlab uses. However, it is possible to represent the value of 'exp' for large arguments in terms of an integer power of ten and mantissa separately. For this purpose I will just use a real example.

  Suppose we want to find exp(7.0873e002). This will be a large number indeed but still just barely within matlab's capability of direct calculation. However, we can find the separate exponent and mantissa without calling on 'exp' as follows;

 a = 7.0873e2;
 x = a/log(10);
 D = floor(x); % D will be an integer
 F = 10^(x-D); % F will lie in 1 <= F < 10

Then D will be the power of ten and F the mantissa

 F = 6.27376373225551 % The mantissa
 D = 307 % The exponent (power of ten)

Compare that with the direct answer:

 exp(a) = 6.273763732256170e+307

  The same trick works for larger numbers which can't be evaluated directly.

  Your problem with complex numbers is a little more complicated but the same principle applies. One difficulty you will have is that the sine and cosine of very large numbers like 2.225167162095353e+003 which you will encounter begins to lose accuracy because that represents over three hundreds periods. You will lose perhaps six or so decimal digits of accuracy out of sixteen in the process.

  Another possibility for you is using the Symbolic Toolbox for which you can set whatever accuracy you desire, though at the cost of computational speed.

Roger Stafford

Hello Thiago:
You are not looking for higher precision: you need more integers in the exponent!
Yours is a huge number; exp(709) is the largest that fit into the IEEE double precision format. You are requiring nearly the triple of the exponent, implying nearly the cube of the largest representable number. Maybe you want to manipulate your exponent some way to produce something interpretable...
Anyhow, try the MPTOOLBOX by Ben Barrowes, available in the FEX. I am not shure if it could provide a solution, but...
Regards
Carlos

"Thiago " <thiago@mathworks.com> wrote in message <gkb7mu$4r$1@fred.mathworks.com>...
> Folks,
>
> Simple question. How do I increase the precision of MATLAB, if that is possible by any means? I'm trying to calculate this:
>
> ----------------------------------------------------------------------------------------------
> >> z
>
> z =
>
> 2.225167162095353e+003 -9.020383145678592e+002i
>
> >> exp( i*z )
>
> ans =
>
> Inf + Infi
> ----------------------------------------------------------------------------------------------
>
> Yes, I know that exponentials grow fast, but I'd like to find an exact number.
>
> Thanks

Thiago wrote:

> Simple question. How do I increase the precision of MATLAB, if that is possible by any means?

There is an indefinite precision toolkit available in the matlab file exchange.
Or if you have the symbolic toolbox you could use that.

> z =
> 2.225167162095353e+003 -9.020383145678592e+002i
>>> exp( i*z )

> Yes, I know that exponentials grow fast, but I'd like to find an exact number.

That's impossible to do. e is a transcendental number -- one that is infinitely
long. e^x is certain to be infinitely long if x is finite and non-zero,
and conversely log(y) cannot be finitely long for any finitely long y
(other than 1).

Below is your answer to 10000 decimal places. The \ (backslash) indicate
continuation of the number. Watch out, the leading decimal place is 0
instead of the more common practice of writing the leading decimal place as
non-zero:

0.3410791142560920539159367203658095165749276531859709627022991675282608487\
    35634973256716650334192541528091913666079726209733590318276945111127381\
    05645705279925537111550909165350165053732654129289626520114501837751859\
    55833377248648143420642164277937392380708784121155987107877182505226111\
    93067860827282888701598925971779568841101916188660727847234970548619238\
    28655225524223203075715279873971506008005760164864049657263089835824563\
    84748364154618496705984031798198832254926411679488020281367145019655017\
    70825333996894621928222396757838091368411047178059929679708796978035873\
    62204135160544651189377254764775362735403248914527733262875748585797963\
    45186024143573243111491745148872808264303300507577139921049097582614284\
    37118097881365750215382558672602898782210135002334610315448401772244478\
    92106656466959806604563607119113609991030984042843096812974847917931106\
    00270661774930173394899049492529922869872356673494909689611612535097109\
    30572731025448050288687719118266586051799304891284920175701311934984383\
    91449917219398058054267885802629852641336166902603089973666915781095994\
    38168662208705192440173569143174227553645373854611608355171834580114158\
    14466958199188329709761693090729300787317331064912128425721563187054171\
    24733469105002635008938170343802420809406288794065623946189831442083491\
    77239925689634845338106847941194788093898100300328151110657172576642725\
    35460565909019084592185878051047349579608596387328593864854783304792407\
    10750779787652300683804858609632830149269373602600119102388789116221911\
    31645408489295940879369473000060357815198179026869381248971292035983330\
    53834826009153399342709197379394804298464716436407184126074252024348144\
    93046326028616352505235493713489944103634409331933619888310688835275742\
    46681203282333914025296494923195861254522724292685488610269741432846748\
    44855735096179156830948953418781001962060616206901861150119031311001994\
    55709590298878984663482094818962462828877424010003831648365251644165738\
    07216705690445429186901041983200578916184223996284380020323769929007335\
    40001694934496922914176637142821864949759568321688260222234559299802167\
    69075724060171045627483835384836337825676824031014130768833358943596751\
    74614556538681458275948316445847962848936463356117470044989354355532118\
    09234989932910341533272006483613235608093513144651877675386379783219298\
    29587902351394766784413174974069054955403025348037677391365625587836634\
    26296685222145252237485521282799099842318162650157290536146288930792830\
    09295294272570391668352931148807516716859103982899917014034281082350091\
    44523525872537911740641254865930551647817075769134257602519921076705588\
    43974567414873602759912454339027739831622266671007745027642027750714722\
    01587475145011166016915401163175356347846946075694700199781468189966522\
    68839732371289113248478888921757363181126465467245911138154363070117583\
    55606624987594172171674403933337333236357818098634452400300619358399268\
    01254991508584490946687080395972425417899217672767886509685302496430159\
    32633527353919800883887533358556859570577155236587482485219088575834729\
    61099216107148151753697837568075671839227592024058123712586477570288523\
    79080035701622228057315477542801170608923279917516802434142826049277190\
    17296858389688726531719768433863076023762768864072282317192955665535770\
    27053482458826410396139064009817549189732338705566147293502773997528149\
    70525272072105565311894886502739152231015395236482040654831101202125274\
    65692544073402145105655393375604994967936092670507989566784419200633968\
    14478781631679662981872523723085560457524972062234091820117247243731035\
    14483999129278777654503630365672376304377168355189988460901514130384094\
    62546608136491423947069931616501767671046677771383897981682599561959784\
    87284269702052738935403499233022725625726949955857678644661026522957333\
    91887085447852091440914767030285109463082996273620910099960933422600123\
    58154563113303122470168747218231869079495145512059974776212157466794006\
    93671787276784171185938628765695651531576009820901524774151200142318716\
    64034838625985576874951012763316136595340370595537464511700408639963819\
    64105157861663059537164816842069925195899960235217940600102162099853299\
    56819763614234390231760268422404228368254897312383314064535955487551598\
    36519495953935048546251741840590005645962213811384540180648685233404321\
    27026279021156463200279381732280739448369788477552621534203681385172768\
    91083769618071744952860891384952665375940496068558715723983449705096266\
    63353930613457413518167646484564746878413638018130929815472526092227851\
    44315224119458216980021683446843840325062722781551453341260359650546646\
    75621076411054317611176091733948942088466701916528045194767415911977361\
    23168956220048777532533978075797105189930925620507433486898476899531811\
    12128388569959663423190466732746164898128271509289076296619004952302805\
    36411456016840092454851974553461288650124502603741391964102272598219618\
    63668641510622720488850987569182066629363037359354238511072455507355700\
    97016784133777591637032098452702762755451904540959339766246368184653268\
    21607516355201141889887842973921274566586759442321539570252314081171407\
    17478383593989280098742601389589176240031231667893286205869342891475494\
    23547341110429326650637667638877874304774765066017615858714591279410843\
    04036316087364726420610234516595202395703449484829975688464489592847418\
    45515897485071577825606973998980280824932500084451746743473871847178239\
    30892537266585857464117062811463695629971133366708747891969633141800332\
    19600967349841618382825515201656496542011335498965888590465832452830987\
    90713634377282168535536728025620562108201778200674658143579850255222439\
    92932879873976058522253101123365392291660024648143099184070364973909453\
    23227934755998999562163685462984105542118708881876358118413207906492176\
    97914718625650227316643349591293805164297247931334833598486366194914429\
    10318547212641325308761258202039273688704676956794153599327485782858562\
    80875838518082965893288898678957039652530761872170241458064404071996470\
    83208685225908608997695367105955926027460457865111880624311306847720807\
    43220124957251542317852319980863188558565976658392077180833004294078801\
    28444147900751629969806894547561348132970059672535594220418101331991446\
    18272947080556747309261323570869128229926464856342786399476289652976819\
    33090664540228807968128448197429793188555969245128912007708983419112379\
    19548910063869441231567002948520183348776917264164683334757509630022524\
    76721731484100748793187656021479355440859523991681851731389909677270831\
    60986834397651939311034856035427936255433557399346059748736447282564313\
    39291855039471236400329936027966508667728538463420373699931234043485122\
    41399180204847744857712561217008089375689081884951228172590790429963322\
    37865303133761768879913775983869967704692998803151739358801964712778659\
    78222761830975654433889855828008233959514847281177609413731761464028198\
    80844758741757429285742420545761529305175365250116581264676527571443869\
    47468312751671083235268984871685451902746160208522062481556571721039733\
    26259422288689953282999240662471196813867739449001852434107377196453408\
    86243900504545841130389612532929550137040958394276100336945188517557502\
    17978399272737759152309546189309638785937545428591524061511155097135597\
    66476873003698881883027178425429645894874529265805264823409712069488580\
    95465348974614934020993347712734514433431982897800353731616098997196954\
    85613496074261109537448475972423766150042816740473951400848902471334909\
    08656753886126642724938357964571957105119095291253677140163263098007501\
    58634621231851972668651421304549805051790068957287590254676607258373158\
    75366437794562877151975812012228597328150078795507035383516062780687038\
    86051443439670424322066524161814719136431929769567748492829046885192680\
    01118891844923567027311102214711499711875077025239490526126003309161618\
    09449049318633194237120894243592015208482326242378618064881201439011518\
    36995051356382990144118375529259714162873986586844083078517748998973304\
    31311606583776889974906716005167972915319208869206357823236254391044578\
    96658467347352020561270564862910019737996448382524110297947994172912198\
    31941393296263441885769931894882102281607620349848169388782121488089552\
    24876344932717070239995206563742153695722336155727347585638750886275523\
    44067903394901558996899263079957880175584503308751331750291469157194119\
    56170567086622139043616877562947791414102610166506566483514710771747090\
    59046712323749051423429015080144874701806479507058487460774403976399820\
    41126624901002859295021991786745663000509196215971733268033726494846179\
    09703265638357373945527695246255017007334384364641179420297820997574786\
    23044478779488950692259903467238456761237553414514020755022110571499350\
    92586670386804755519841510267141639668788714601052811419407614654766541\
    26244352267577717274042432794063267025870697897140012539118851979815421\
    86387305119629511185441939674325375572576704491629688746900535050527254\
    09615736330481373468639512388905713562827636059190467686076309505131173\
    74112655701263826417336266009161808126735202572384898304078576132587971\
    51918745036447307428430265416894273845302980273401223619739030765208768\
    68264641671064050354823708123946130829537248281599376619589688609229386\
    89913865666550116230105499440777867075389527974286789476073471952859379\
    07632319424369857822360687778568623323081591964917035434217478174858507\
    25538598337541676562497314933618378065472950946953980030797651633638762\
    16753390822207736855983465900528076292947288778072542476369618628862581\
    75479796281719381764973766172617617991598739917423099534831538211490030\
    36839714474023370085261105612788130417833359476605882109371857809263484\
    55867285404701429252446697433646998003407999880332566458655365291077089\
    45946596709262935892587497533825076626265569811968054366220394530430253\
    29762376031866073562598999150915480474629766120290688926930078414573115\
    92528102499433394101884272526766123223331900729604634979662326743572715\
    12760746897720173880992979942904717846194744849767740738293763574101855\
    48884007803606773262789145856715883348082693916349884320204005635471542\
    92637185622990732065483858963713308359297875439819991845486925726725979\
    84696305557470095965823603581049591717287531884651399108374404836717401\
    5638826434896866642626394548681637463952828157049934969851*10^392 +

    0.44\
    75212655676737435045552766009719480471798083766177736277453836166132138\
    99518512529997961452905882467144781429885788514373549631198447607333475\
    43766375833980488697438044868964130765963807328022944103762872499671371\
    14200053270351632657211521730111673733966459538275534907746943150266030\
    81712894628359730461412030082267908903300009341529099670623167372822767\
    14286112810770766140076390662667918973459306804162233605890117680091005\
    07216131427520762586920652768744083344791049108223861490550319894456987\
    29609298152972434975532352088392683982024791875819165369112945339860083\
    17555194763462828678101103415110266588143673456942533438764230695334028\
    50569701737527840988442418402740372505234315477409145727857969840621064\
    55649098067726199912776433101575134158051874959090548581067795706111035\
    68752007697022037304352831367349450817804314029574815214280197780474393\
    21638823394285681367476434338403987433549326729680975314840421144739446\
    92068897318159177434467770665047714180865538543251387735636566967095149\
    61907252324701262797006056258334641856342350361352042807078546352703378\
    50439663954640515382320716941163821968135608526944846754303481627005651\
    60364487238313246148394445741545415303281999311251426932732846001829393\
    44383193016626984867145613819511833475057447661242126964327977764217077\
    93993588315210452489756929955285605451804306905888056648717180513862078\
    19674477305063704303010326862312518150783470015607671874099360426636587\
    16722434518938727388055347011156136264003288224242911318262582837508078\
    48033181933853750566991700210620004165062404639735307963644128419963771\
    45596920617647752296651972613788921298367013571607920531970368248520576\
    49609196264678848695057653005071600563892495872885103835750545219418408\
    75002542470746331449401978765100481057086352041718385921048209474118998\
    63116295005253410214524280983493178521386800319522631660604628909993398\
    80461103939412270912431670163720961832582390082306031471531790095793817\
    82528158303707584565425077422471802559958167315282283456078599935005709\
    52018174539862592247918577961419485689762107299414964809751525985944662\
    69977241250411701439676069003126171779881832963360424477666349101399695\
    41382500444049938372981216617936103613093436596157593906863061600627963\
    10154937217642636573164216637619207975402926180256300905411423148984254\
    09946666998714142831292313932329068987583153887978535136032911684294103\
    65968774710815013155711450554017817731097256622900141942168628000061125\
    48165441542405666216921851597592390085511124379309389272920950685782760\
    85048760979278722342244727662928118220215636663835653874233007366458533\
    44141774012415931206706963019366942404370250557270737540837194024929557\
    23853254839079957279483811777372153981276150658553701018813735496670045\
    03822109115252094831516866677041772974105401306607062222092659884360388\
    78942310706651372968138597837370651206885617528207353604557476637910797\
    84477778234899969279637333430347034507866990667890270855195333693755146\
    15417800628018455800013642155590868143533038616413360349726480598943403\
    12441533410816816255801562901935335729653418995733717660423693698118074\
    12776423050468237000049964008646000678998635445371558733362999184967151\
    42454988417487010452824336744791548067832267067339930661070969943920937\
    52441468163047689047965422831810755344773153348396147292364405182569160\
    76134900792198640201501166754364329383521909473793976286237243421099699\
    15469057024173612313903645946184871091969919029907448869515450301792387\
    25545871840417851465048110812042348838163871456601821244032569831737984\
    72287430303796449072292389341029292715744675288606779191532171913521398\
    92417168681922878297723344810976119295824995891958508805662284466395913\
    09190870289599142323890296259491893130001284698984227161526648043533761\
    50767757201259973127673196829960766411406541797919477786098592036567364\
    57457563797310713245487458420916177961400290876234131890878222548882800\
    24101654403156429551981048066760895623393513262544946869353038182112541\
    90932637152520091189421500444332490109745688973860057672702599381748621\
    26389209091403682509668065894067893663141480172101397632070950994110341\
    91138100820583208393031844898420953253125547267233405803705028011436011\
    27835095902332861900833320897532945778034164083126970095039782574203948\
    86809871337701788150311616727417455295463744174711797396317631005039259\
    07308783643666131577652797957170858932017844579865239396408289012546464\
    58089986144998152825326492578634907239727723676629987366527529661214328\
    47523129598431783248575676142734583802586217682939503302011144158713346\
    24264099158670828764700683566109164230333651931766016423408296410931507\
    37984759730747620820591318992817577545222494785246080278702156796961800\
    97136146957309945357874413588750332427544768078767653160731393029883780\
    71606047759627327859608780962230989668177672958616705712900109356549004\
    20199088704179963301328424150797824115908838144548180604160742196920348\
    73774253111282618831700001821192057060822777559326199241210435691444052\
    82881709208833212362673110749492821417102706536638246324544390919342354\
    19986967962642010906905377311610602458070267007924167985008045214760805\
    74599620805689613140010786305802432240021334169987196841411810169293974\
    21136010882198999824803921528631432843177764071404624474807646051464145\
    94269163284857227654642220654129598001377092199147463009870965256938232\
    41044965661302462634097677857818643817652113128388412782449261667027306\
    84126477255985987902482450267855509274669252988522462693016809675715022\
    61872112648298127608594092953237155265066298062053939602282299269428309\
    20564661878826738217590195282810154214778029069864511038499014939175228\
    53579288839322326753568459067322452184747640867096781712629957065003271\
    41701941844442345148148944387927932879115018129376487920229836882638601\
    57388433926416656240480089849029392033355647118820769435087743286083770\
    39504761739763461387062912641040390010723232526152097814228827501256475\
    59712528565223229069890379550546111810233075563218346882965237961697358\
    43131446226547799704342595227981590769198628947240341222964151586403116\
    70648892576245753664381725709097909979554913146578497219473619203099849\
    70245494739659335593180960024520766924259093428443173213234851862913668\
    43967259242331286687143418286648047571723704353656645899453987789448080\
    32917780972777475130699014602052891393304414165095836939433721894472905\
    25904900073322816678998664619223482029734673296995911431258752443213071\
    56247632584946745777439971579099567029372160079925495110453062241282666\
    35042112530486252059606337065539505400388350712980222726080860581744545\
    55357644472072192188755750771547543008633631503157588052476494002800690\
    80680513039722483439682727519728048716949566242902401466316669028680116\
    24783982488288345277670090980584264872868177094416737595298891476191880\
    18538337594337920972989334051913135795200205082667665058401533680127472\
    88904231254108870225999452343536699166203912896495477885127966578301128\
    47432831886978574733641013829082659752896257229876705336669223625175736\
    77134464144126068444098848183108971440468792953891301598475956027769736\
    34366625952972038205085339005671388183342400181755559493783527902103244\
    05276970686453055823211439015139600216486425464599933022471944813307411\
    63710044875034315680510306757379394294399491896503566304688307573607914\
    87594840945449267771717429698392010168258064826364930983586748916342026\
    48764846003806034609444158518938174570042455903077443194661936230134929\
    99546671123782996768196343141284770024299591571005948441746275586008704\
    04277374292615759769309876248943977404114472621835430405142837156060858\
    35088699124654479955703783379054760641598618197100031704759225364323309\
    98808428417365468674037829631011353607333726350124437948663496708803066\
    27637711902196449155394157677779692673844812725713258802177841913795914\
    31632939738119788089504342145324284764298602650877665766888936446753234\
    12025043008572727337936020215325426603826062728982406888558821169145102\
    30228835316326936241121421947712213964917198660949425163546194829862612\
    42969215366860176543815558732483368496229779794612974388008729997723337\
    03053961325003773974285836494273525462073879363943061441540138625919831\
    07980363705022242208683378787253052544477654931282407925870563718039510\
    49786618313958608151925289346850577497663541663649400266513904305809112\
    71509950216030936579570697333723072347371230752494533186800912349837632\
    66621463426429053529221183893090874055338387916530601245188031567123788\
    96139081449868826718774693437659702514296752995586948701918181621161480\
    10707824537544444631765295949688677387454508383033587137891746777815919\
    00799556478723481681911919812315441915893413965188960575440742279615041\
    67658739131895898655641000029941142398834323120576499870203231310123194\
    72552706894774100776241110828669488238798224596156033791002905886039676\
    33958369854167167227448994074342285722900893913281081389173431512672860\
    47361031791025882473674510952863837643416869465393724290916251686398394\
    96447206448890784187482697371661750722382287781104128050653379759096481\
    89600517066301991685355024853575152426397915613246158803779226760075820\
    11163576158872697389829519792252869201885673065796777576733035019451691\
    71285955098826437901512086332123016151502853247823089077412606462154554\
    12802186506209522206597559172505919498430887567416733112028736955854953\
    52261469503429849226397797163880642257173534974645822324881371011267697\
    38418557878664970971250828302888912337300679465299510273729322000304937\
    69563168915539397730017678582095299204329921004354725002059454655057981\
    00006921522607577094283560847393601398375133944361743463378259284158086\
    29448546825165437608400775616725038469580369194128081580152695829926893\
    41008338773611673627280919108235371760486660093413228646191120230298865\
    20839382140242219432135284066304394170372266497281561390763915658365319\
    52401763594247681986576005764516164821395269460618062627023027759398073\
    28525476659104022791679261928308522258801892840649662427069093987830771\
    54312363737784586024039869762700942882276763868118638928232836559237023\
    39346244347912667559146765971971830213091399652391351869036058351794456\
    3190107751228318653969013047157306679028567200548852925742*10^392 * I
 
--
.signature note: I am now avoiding replying to unclear or ambiguous postings.
Please review questions before posting them. Be specific. Use examples of what you mean,
of what you don't mean. Specify boundary conditions, and data classes and value
relationships -- what if we scrambled your data or used -Inf, NaN, or complex(rand,rand)?

Walter Roberson <roberson@hushmail.com> wrote in message
> Wowsers....

The method I proposed gives:

34.107911425609309e190 + 44.752126556765489e190i

We can really see the fp issue come into play compared to Walter's (Maple?) solution.

Matt Fig wrote:
> Walter Roberson <roberson@hushmail.com> wrote in message
>> Wowsers....
>
> The method I proposed gives:
>
> 34.107911425609309e190 + 44.752126556765489e190i
>
> We can really see the fp issue come into play compared to Walter's (Maple?) solution.

It was maple, but even with 10 digits precision I get roughly 3E391 + 4E391*I
I tried with your method and get close to the same values -- same order of magnitude
anyhow, with the first 7 digits being the same.

--
.signature note: I am now avoiding replying to unclear or ambiguous postings.
Please review questions before posting them. Be specific. Use examples of what you mean,
of what you don't mean. Specify boundary conditions, and data classes and value
relationships -- what if we scrambled your data or used -Inf, NaN, or complex(rand,rand)?

"Matt Fig" <spamanon@yahoo.com> wrote in message
> 34.107911425609309e190 + 44.752126556765489e190i


Of course those exponents should be 390... typo #2 and counting.

Thiago wrote:

> z =
> 2.225167162095353e+003 -9.020383145678592e+002i
>>> exp( i*z )
> ans =
> Inf + Infi
> ----------------------------------------------------------------------------------------------
>
> Yes, I know that exponentials grow fast, but I'd like to find an exact number.

Thaigo, you may have a perfectly valid reason for wanting to do this, and others have suggested strategies, and perhaps it's an interesting exercise. But usually this sort of question is a sign of a naively implemented "textbook" formula that was never intended for real computations, and a sign that intermediate values are getting out of hand. It's hard for me to imagine that a number whose magnitude is something like 10^300 times the number of atoms in the observable universe (source: Wikipedia) represents anything real and could really be a quantity of interest. It seems much more likely that you are now going to turn around and divide it by a similarly large (and similarly imprecisely-computed) value. I could be wrong.

Thanks for your feedback, folks.

Walter, I could not find the "indefinite precision toolkit" in the MATLAB file exchange; I think you meant the "Multiple Precision Toolbox for MATLAB," correct? Well, instead of downloading it, I first tried the Symbolic Math Toolbox, and it seems to work. Thanks again.

Here's a sample input/output:
------------------------------------------------------------------

>> z = sym(2.225167162095353e+003 -9.020383145678592e+002i,'r')
 
z =
 
(4893194336938328*2^(-41))-(7934412924534611*2^(-43))*i
 
 
>> w = vpa(exp(i*z),12)
 
w =
 
.341079112224e392+.447521267216e392*i

------------------------------------------------------------------

Walter Roberson a