Classical Fortran Programming for Engineering and Scientific Applications 2nd Edition Solu, Exams of Computer Engineering and Programming

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Allk 17 kChapterskCovered

SOLUTIONS

S

e is m ic i s o la ti o n

Contents

1 AboutkThiskSolutionskManual 1

1.1 TokthekStudent .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k.

1.2 TokthekInstructork k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k.

2 SolutionsktokthekExercises 3

Chapterk 1 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

.k .k .k .k .k.

Chapterk 2 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 3 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 4 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 5 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 6 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 7 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 8 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 9 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 10 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 11 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 12 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 13 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 14 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 15 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 16 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

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Chapterk 17 .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k .k

.k .k .k .k .k.

3 Extrak Exercisesk andk Theirk Solutions 221

4 Teachingk FORTRANk Programming 259

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1

AboutkThiskSolutionskManual

1.1 TokthekStudent

Thisk Solutionsk Manualk isk intendedk fork thek instructorkofk ak coursekthatk usesk Classicalk FORTRAN

askaktextbook,kandkforkthekstudentkwhokisklearningktheksubjectkindependently.

Ifkyoukarekakstudentktakingkthekcoursekforkcreditkyoukshouldkknowkthatkitkiskakviol

ationk ofkacademickethicskforkyouktokconsultkthisk SolutionskManual,k whetherkyoukcopykve

rbatimkfromkitkorkonlykusekitktokgetkideaskaboutkhowktokworkkthekexercises.k Thekexercis

eskarekakvaluablekaidktoklearningkthekmaterialkinkthektextbook,kbutkonlykifkyoukworkkthe

mk yourselfk !kLookingkupkthekanswerskinsteadkofkfiguringkthemkoutkdepriveskyoukofkankop

portunityktoklearnkthekmaterial.k Ifkankanswerkiskforkcredit,kcheatingkiskalsokpersonallykde

gradingktokyoukandkunfairk tok yourk classmates,kandk itk mightk placek youk ink jeopardykofk d

isciplinarykaction.k Ifk thiskiskankillicitkcopy,kpleasekdestroykitknow.k Ifkthiskiskakstolenkcopy,

kpleasekreturnkitktokitskrightfulkowner.k Eitherkway,kSTOPkREADING.

Ifkyoukarekakstudentklearningktheksubjectkbykyourselfkthenkyoukarekyourkownkinstruc-

tor.k Pleasekreadktheknextksection.

1.2 TokthekInstructor

Thisk Solutionsk Manualk isk intendedk fork thek instructorkofk ak coursekthatk usesk Classicalk FORTRAN

askaktextbook,kandkforkthekstudentkwhokisklearningktheksubjectkindependently.

Ifkyoukarekinkeitherkcategorykyoukshouldkknowkthatkitkgreatlykdiminisheskthekusefulnes

skofkthekexerciseskforkgradedkworkkifktheirksolutionskbecomekpublic.k Pleasekrefrainkfromk

loaningkthiskbookktokothers,kdistributingksolutionsktokothers,korkpostingksolutionskonkthek

WorldkWidekWeb.k Ifkyoukwantktokshowkakgroupkhowktoksolvekakproblem,kIksuggestkmaki

ngkaktransparencykork scanningk tok ak.pdfkfilek fork projection,k ork postingk thek solutionk i

nk ak displaykcasekunderkglass,ksokasktokrevealkthekanswerkwhilekdiscouragingkphotocopyin

gkorkelectronickscanning.

Atktheksamektime,kitkiskprudentkforkinstructorsktokexpectkthatksomekstudentskwillkhave

kaccessktoktheksolutionskandkthuskankunfairkadvantagekoverktheirkclassmateskwhokdoknot.

k Ifkyouksuspectkthiskmightkbekthekcase,kyoukshouldkconsiderkassigningktextbookkexercises

kwhoseksolutionskarek notk includedkinkthisk Manualk orkmakingkupkproblemskofkyourkown,k

perhapskmodeledkonkexerciseskinkthektextbook.

Chapterk 2 kofkthisk Manualk providesksolutionsktokaboutkhalfkofkthekexerciseskinkthektext,

kdistributedkinksuchkakwaykasktokrepresentkeachkproblemktypekinkeachkchapterkwhilekfav

oringkeasykproblemskandkearlykchapters.k Chapterk 3 kofkthisk Manualk containsksomekadditi

onalkexerciseskandk theirk solutions.k Chapterk 4 k containsk somek materialsk thatkIkhavek fou

ndk usefulkink teachingkprogrammingkfromk Classicalk FORTRAN.

S

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⌈k k ×k

k ⌉

2

Solutionsk tok thek Exercises

Eachksolutionkincludeskmykroughkestimatekofkhowkdifficultkthekexercisekis.k Easykprobl

ems,kmarkedk[E],ktestkthekstudent’skrecallkofkfactskandkconceptskdiscussedkinkthekt

ext.k Hardkproblems,kmarkedk[H],kneedksomekindependentkthoughtkandkpossiblyksome

kprogrammingkbutkusuallykdoknotkexplicitlykrequirekthekstudentktokdeliverkakprogram.

k Projects,kmarkedk[P],ktypicallykaskkforkakfinishedkprogramkaskpartkofktheksolutionktokt

hekexercise,kandkinkmostkcaseskprovidingkonekrequireskanalysis,kprogramkdesign,kandkd

ebuggingkaskwellkaskcodingkinkFORTRAN.k Thekfractionkofksolutionskpresentedkherekvarieskfr

omkonekpartkofkthektextbookktokanotherkandkbykproblemkdifficulty,kaccordingktokthektab

lekbelow.

partk(seek§0.5.3) [E]k easy [H]khard [P]k project

INSPIRATION none none none

ELEMENTARY all

1

2

1

3

INTERMEDIATE

1

2

1

3

1

4

ADVANCED

1

3

1

4

1

5

REFERENCE none none none

Thekpartskofkthekbookkthatkareklistedkinkthekleftkcolumnkarekthosekidentifiedkinkthektablekof

0.5.3kinkthektext.kThekactualknumberkofksolutionskprovidedkforkeachkchapterkandkdiffi

cultyklevelkisk nk fk ,kwherek nk isktheknumberkofkproblemskhavingkthatkdifficultykinkthe

kchapterkandk fk iskthekfractionksolvedkofkthatkdifficultykinkthekpartkofkthekbookktokwhi

chkthekchapterkbelongs.k Applyingk thek formulakyieldskthek distributionk ofksolutionskshownki

nk thek tablek onktheknextkpage.

Manykofktheksolutionskprovidekakmorekthoroughkdiscussionkofkthekproblemkthankonek

mightkexpectkfromkakstudent,kakfewkreferkincidentallyktoktextksectionskthatkthekstudentkne

edknotkhavekreadkyet,kandksomekofkthekprojectskareksufficientlykopen-

endedkthatkmanykdifferentk“answers”kcouldkbekconsideredkcorrect.kThus,ktheseksolutionsk

arekmeantktokenlightenkthekgraderkratherkthanktokservekaskstrictktemplateskagainstkwhich

kstudentkworkkiskdirectlykcompared.

Becausekeachksolutionkiskself-

contained,kliteraturekcitationskinkthisk Manualk arekgivenkwithinkeachksolutionkratherkthankb

eingkcollectedkinkakbibliography.kSectionkreferenceskappearingkinktheksolutionskarekto

ksectionskinkthektextbook,knotktoksectionskofkthisk Manual.k Outputkformattingkinkthekte

rminalksessionkexcerptskvarieskslightlykdependingkonkthekUNIX

TM ksystemk (Sun,kIBM,kSGI,kor

kLinux)kthatkIkusedktokrunkeachkprogram.

Ifk youk needk ak solutionk thatk wask notk selectedk fork inclusionk here,k pleasek contactk thek a

uthorkbyksendingkemailktokmikek@rpi.edukorkpaperkmailktokPOkBoxk215,kCropseyville,k

NYk12052.

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4 ClassicalkFORTRANk SolutionskManual

part chapter easy hard project total

given done given done given done given done

INSPIRATION 0 19 0 4 0 0 0 23 0

ELEMENTARY 1 12 12 2 1 0 0 14 13

INTERMEDIATE 7 12 6 8 3 3 1 23 10

ADVANCED 11 22 8 6 2 8 2 36 12

REFERENCE 18 11 0 9 0 3 0 23 0

totals 321 183 167 60 89 30 577 268

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Solutionsk tok thek Exercises 5

Hello,kWorld!

1.5.1 [E]k (a)k Thek syntaxk ofk ak programmingk languagek isk thek setk ofk rulesk prescribingk

howkitsksymbolskmaykbekassembledktokformkmeaningfulkstatements.k (b)kTheksemanticsk

ofkakprogrammingklanguagekarekthekruleskdescribingkwhatkmeaningkattachesktokeachksynt

actically-kcorrectkstatement.k (c)kSourcekcodekiskhuman-

readablektextkconsistingkofkcommentskandksyntactically-

correctkstatementskinksomekprogrammingklanguage.k (d)kObjectkcodekiskaksequencekofkm

achine-

readableksymbols,kusuallyknotkcorrespondingktokprintablekcharacters,krepresentingkthekm

achinekinstructionskthatkresultkfromktranslatingkaksourcekprogramkforkakparticularkprocess

or.k (e)kLinkagekeditingkiskthekprocesskofkconcatenatingkthekobjectkcodekforkthekvariousk

routineskofkakprogram,kincludingkuser-

written,klibrary,kandksystemksubprograms,kandkfillingkinktheirk(relative)kstartingkaddresses

kwhereverkthosekmightkbekrequiredktokresolvekreferencesk byk eachk routinek tok thek othe

rsk makingk upk thek program.k (f)k Ank executablek iskakconcatenationkofkobjectkmodulesk

withkallkofkthekcrossreferenceskresolved,kcompletekandkreadyktokbekloadedkintokthekmem

orykofkakcomputerkwherekitkcankbekbranchedktokinkorderktokrunkthekcompiledkprogram.

1.5.2 [E]kInkthiskbookk(accordingktok 1.1)kthekfollowingkcharacterksetkiskusedkinkFORTRAN

statements.

ABCDEFGHIJKLMNOPQRSTUVWXYZk

Theklower-

casekalphabetickcharacters,kandkoccasionallykotherkcharacters,karekalsokusedkinkFORTRAN

k commentsk inkthektextbook.k Theksemicolonk;kiskusedkaskthekcontinuationkcharacterkink t

hek textbook.k Thek underscorekcharacterk k isk mentionedk ink 13.2.2kandk appearskink 16.

kinktheknameskofkMPIkroutineskandkvariables.k Ink 13.6.1,kthekampersandkcharacterk&kisk

mentioned.

1.5.3 [E]kClassicalk FORTRANk usesk fixedk sourcek form,k ink whichk statementsk begink ink o

rk tokthekrightkofkcolumnk 7 kandkextendkonlykthroughkcolumnk72.k Therefore,kblankskareksi

gnificantkinkcolumnsk 1 -

6 kofkeachkstatementkandkmayknotkbekomitted,kandkblankskusedkforkindentationkmustk no

tk pushk thek textk ofk ak statementk pastk columnk 72 k (butk seek 13.1.3).k Ask discussedk ink10,

kblankskmaykoccurkinkcharacterkstringskandktheykarekthenksignificantkaskdata.k Otherwise,

kblankskmaykbekinsertedkorkomittedkatkthekprogrammer’skoption.k Thus,kforkexample,kthe

kfollowingkprogramskarekregardedkaskequivalentkbykthekg77kcompiler.

A=3.14 AAk =k 3 k.k 1 k 4

B=4.753 BBk =k 4 k.k 7 k 5 k 3

C=SQRT(A2+B2)

Ck =k Sk Qk Rk Tk(kAk Ak *k *k 2 k +k Bk Bk *

k k 2 k)kPRINT,C Pk RkIkNk Tk *k,kC

STOP Sk Tk Ok P

END Ek Nk D

Advicekiskgivenkink 12.4.5kaboutkhowkmuchkwhitekspacektokusekwhereksokthatkyourkprogr

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6 ClassicalkFORTRANk SolutionskManual

1.5.4 [E]kAccordingktok 1.1,k(a)kakcommentkiskanyksourceklinekthatkhaskakCkinkcolum

nk 1 kandk(b)kakstatementkmustkappearkinkcolumnsk 1 -

72.k(c)kAnyktextkextendingkbeyondkcolumnk 72 kiskignoredkbykthekcompiler.k(d)kAkcom

mentkcankbekcontinuedkonlykbykinsertingkanotherkcommentkline.k(e)kAkstatementkcan

kbeginkinkcolumnk8,korkinkanykotherkcolumnktokthekrightkofkcolumnk7,kasklongkaskitke

ndskbeforekcolumnk73.

1.5.5 [E]k Eachk commentk linek ink ak Classicalk FORTRANk programk hask ak Ck ink columnk 1,

k andkiskignoredkbykthekcompiler.k Commentskcankbekcontinuedkonlykbykinsertingkanotherk

commentkline.k Inkthiskbook,kcommentskarekwrittenkusingkmixedkcase.

EachkstatementklinekinkakClassicalkFORTRANkprogramkbeginskinkorktokthekrightkofkcolumn

7 kandkendskinkorkbeforekcolumnk72.k ItkmustkbekconstructedkaccordingktokthekruleskofkF

ORTRANksyntax,kandkisktranslatedkbykthekcompiler.k Statementskcankbekcontinuedkbykplac

ingkaknonblankkcharacterkotherkthank 0 kinkcolumnk 6 kofkeachkcontinuationklinek(seek 13.1.

8).k Ink thiskbook,kstatementskarekwrittenkusingkupperk casekletters,kandkthekcontinuationk

characterk isk;.

Ankexecutablekstatementkgenerateskmachinekinstructionskthatkarekexecutedkatkrunktime,

afterkcontrolkisktransferredkbykthekoperatingksystemktokthekexecutablekprogram.

Thek non-

executablek statementsk ofk ak programk providek thek compilerk withk informationkaboutk thek

sourcek textk (e.g.,k ENDk marksk thek endk ofk thek sourcek fork eachk routine)k ork aboutkthek da

tak structuresk thatk willk bek usedk byk thek programk (e.g.,k COMMONk statementsk describekth

eklayoutkofksharedkdatakareas,kaskexplainedkink 8).kNon-

executablekstatementsk(e.g.,ktypekdeclarations)k cank affectk thek machinek codek thatk isk gener

atedk fork executablek statements,k ork(e.g.,kcompile-

timekinitializations)kcankcausekthekgenerationkofkmachinekcodekthatkstoreskdatakwhenkthek pr

ogramkisk loadedkintok memory.

1.5.6 [E]kThekthreekstatementskintroducedkinkthiskchapterkarekPRINT,kSTOP,kandkEND.kT

hekPRINTkstatementkcankbekusedktokprintktextkork(askwekshallkseeklater)kthekvalueskofkva

riables.kThekSTOPkstatementkiskexecutable,kandkreturnskcontrolkofkthekprocessorktoktheko

peratingksystem.k ThekENDkstatementkisknon-

executable,kandkmarkskthekendkofkeachkroutine’sksourcektext.

1.5.7 [E]kTokbeginkrunningkyourkprogram,kthekoperatingksystemkcopieskyourkexecuta

blekintokmemorykandktransferskcontrolktokitskfirstkmachinekinstruction.kWhenkyourkpr

ogramkiskfinishedkitkexecuteskakSTOPkstatementktokreturnkcontrolkofkthekprocessorktok

thekoperatingksystem.k Ak programk cank containk anyk numberk ofk STOPk statementsk (thoughk

itk makesk sensek andkisk syntacticallyklegalktok havekmorek thank onek onlykifk thek programkhask

morek thank onek possiblekpathkforkthekflowkofkcontrol,kaskexplainedkink 3).k Inkcontrast,k

ENDkisktheklastkstatementkofktheksourcektextkofkakroutinekandkisknotkexecutable.kInkakf

ilekcontainingkseveralkroutines,kthekENDkstatementskshowkthekcompilerkwherekonekro

utinekendskandktheknextkbeginsk(thiskcankhappenkwhenkakprogramkconsistskofkseveralk

routines,kaskexplainedkink§6).

1.5.8 [E]kClassicalkFORTRANkiskakratherklow-

levelklanguage,kbutkitkiskeasierktokwritekthankassemblerklanguagekandk muchk easierkto

kwritekthankmachineklanguage.k Ankassembler-korkmachine-

languagekprogramkcankbekusedkonlykonkprocessorskhavingkakparticularkinstructionkset,k

butkakFORTRANkprogramkcankbekusedkonkanykcomputerkthatkhaskakFORTRANkcompiler

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SolutionsktokthekExercises 7

1.5.9 [E]kAccordingktok1.2,kthekcompiler’sktwokmainktaskskarektranslatingkFORTRANkso

urcekcodekintokmachinekinstructionskandklinkingkinkanykoperatingksystemkroutineskus

edkbykthekprogram.k Askwekshallkseeklaterkitkiskalsokpossiblekforkakprogramktokbekma

dekupkofkseveralkroutines,kandktokusekroutineskstoredkinkaksubprogramklibrary,kandkin

kthatkcasektheklinkagekeditingkstepkperformedkbykthekcompilerkcombineskallkofkthekpa

rtsktokmakekankexecutable.

1.5.10 [E]kIfkakClassicalkFORTRANksourcekprogramkiskinkthekfileksource.f,kwekcouldkco

mpilekandkrunkitkbykusingkUNIX

TM kcommandsksimilarktokthese.

unix[1]kf77ksource.fku

nix[2]k a.out

1.5.12 [E]kAnkexecutablekpreparedkforkonekcomputerkcankbekrunkonkanotherkonlykifkthe

kprocessorskofkthektwokmachineskbothkusektheksameksetkofkmachinekinstructions,kbecaus

ekthekobjectkcodekinkankexecutablekconsistskofkmachinekinstructionskforkthekprocessorkof

kthekcom-

kputerkwherekthekprogramkwaskcompiled.k Evenkifkthekprocessorskarektheksame,kthekexecu

tablekwon’tkrunkonktheksecondkcomputerkifkthekcomputerskhavekdifferentksystemkroutine

s,kwhichktheykprobablykwillkunlesskthek operatingksystemskarekidenticalkversionskofkUNIX

TM .k TokmovekakFORTRANkprogramkfromkonekmachinektokanotherkofkakdifferentkkindkitkis

kusuallyknecessaryktokrecompilekthekprogramk(thatkis,ktranslatektheksourcektokmachinekla

nguagekandklinkkinktheksystemkroutines)konktheknewkmachine.

1.5.13 [H]kAskIkwritekupkthisksolution,kmykcomputerkiskakPCkrunningkLinux.k Ikused

kthekviktextkeditorktoktypekthektextkofkthekprogramkintokakfileknamedkhello.f,kchan

gingkthekprogrammer’sknamektokmykown.k ThenkIkfollowedktheksamplekterminalksessi

onkink 1.3ktokcompilekthekprogramkandkrunkit,kaskshownkbykthekfollowingkconversatio

n.

mike[1243]k vik hello.

fkmike[1244]kmorekhell

o.fkC

CodekbykMichaelkKupferschmi

dkC

C

Thiskprogramksayskhell

o.kC

PRINTk*,’Hello,kworld!’

kSTOP

END

mike[1245]kg77khello.f

kmike[1246]ka.outkH

ello,k world!kmike[

47]

MykUNIX

TM kpromptkiskmykloginkname,kwhichkiskmike,kfollowedkbykakcommandknumb

erkinksquarekbrackets.kIkhadkbeenkusingkmykmachinekforkakwhilekonkthekdaykthatkIkdi

dkthis,kandkthekcommandknumberkhadkreachedk 1243 kwhenkIkbegan.kTokshowkwhatkIke

nteredkinkthekfilekusingkvi,kIkusedkthekUNIX

TM kmorekcommandktoklistkitskcontents.k T

heknamekofkthekLinuxkcompilerkiskg77,ksokIkusedkthatktokcompilekthekprogram.k Then

kIkenteredktheknamekofkthekexecutablekproducedkbykthekcompiler,ka.out,ktokrunkthe

kprogram.

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2

Solutionsk tok thek Exercises 9

ExpressionskandkAssignmentkStatements

2.9.1 [E]kThekonlykstatementskthatkcankbekinterchangedkinkthekhypotenusekprogramkwit

houtkaffectingkitskresultskarekthekassignmentsktokAkandkB.

2.9.2 [E]k Thek FORTRANk variablek GODk isk real,k becausek itk doesk notk begink withk I,k J,

k K,k L,kM,korkN.kWhetherkGodkiskrealkiskbeyondkthekscopekofkthisktext;kyoukwillkhavektok

decidekforkyourself.

2.9.3 [E]kItkisknotknecessarykforkthekvaluekofkakFORTRANkvariablektokchangekduringk

thekexecutionkofkakprogram;kitkcankretainktheksamekvaluekthroughoutkthekcalculation.kF

ORTRANkconsiderskvariableskbeginningkwithkthekletterskI,kJ,kK,kL,kM,kandkNktokbekinteg

erskbykdefault.kAkspacekisknotkaklegalkcharacterkinkakvariablekname,ksokvariableskcannot

khaveknamesksuchkaskITEMkAk(butkseekExercisesk1.5.3kandk3.8.13).k Itkisklegalktokusekt

heksamekvariableknamekforkmorekthankonekquantity,kbutkaskwekshallkseekink§12.4.2kt

hatkiskusuallyknotkakgoodkidea.

2.9.4 [E]k(a)k[ e

1 ]

(^3). 2 k=k e

(^1) × (^3). 2 k=k e

(^3). 2 ksokthekexpressionkcankbekrewrittenkEXP(3.2).k T

heknumericalkvaluekofkEXP(3.2)kisk24.5325317,ksokthekexpressionkcouldkinsteadksi

mplykbekreplacedkbykthatknumber.k(b)k[ e

(^3). 2 ]

(^3). 2 k=k e

(^3). (^2) × (^3). 2 k=k e

(^3). 2 k sokthekexpressionkca

nkbekrewrittenkEXP(3.2**2)korkreplacedkbyk28001.1465,kwhichkiskitsknumericalkvalue.

k (c)k 3_._ 2

2 k=k 10_._ 24,ksokEXP(3.2**2)kcank ink turnk bek rewrittenk EXP(10.24)k ork replacedk

byk 28001.1465k ask ink (b).

(d)k e

ln k

(A) k=k Ak andk e

ln k

(B) k=k B ,ksokEXP(ALOG(A)+ALOG(B))kcankbekreplacedkbykA*B.

2.9.5 [H]kItkisktokbekshownkthatkI/J/K/L=I/(JKL)kevenkthoughkintegerkdivisionktr

un-kcates.kThekfollowingkproofkiskduektokM.kS.kKrishnamoorthy.

Ink numberk theory,k truncationk isk justk thek “floor”k operation,k ⌊ a,kb ⌋,k yieldingk thek smallestk

inte-

kgerknotklesskthankthekrealkquotientk a/b .k Thuskitksufficesktokprovekthatk⌊⌊ x,ki ⌋ ,kj ⌋k=k⌊ x,k

( ik ×k j )⌋.

Letk xk =k pk ×k ik +k q,k 0 k≤k qkk 0,kwekcankmultiplykthruktheksecondkinequalitykabovektokobtaink 0 k≤k sk ×k ik

_

S

e is m ic i s o la ti o n

⌊ x,k ( ik ×k j )⌋k=k r ,kwhichkcompleteskthekproof.k ✷

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e is m ic i s o la ti o n

Solutionsk tok thek Exercises 11

2.9.6 [E]kAkmathematicalkequationkexpresseskakpermanentkrelationshipkbetweenkseveral

kquantities.k AkFORTRANkassignmentkstatementkiskankorderktokreplacekthekcontentskofkth

ekstorageklocationknamedkbykthekvariablekonkthekleftkofkthek=kwithktheknumericalkresultk

ofkperformingkthekcalculationkindicatedkonkthekrightkofkthek=.

2.9.7 [E]kSomekinterpretationkisknecessaryktokdecidekwhatkitkmeansktok“correct”keac

hkofkthesekstatements.k Thekintentkofkthekfirstkonekiskevidentlyktokgivek-

Jkthekvaluek5,kwhichkisktheksamekaskassigningkJkthekvaluek-

5.kTheksecondkstatementkassertskakrelationshipkbetweenkX,kA,kB,kandkC.kAssumingkthat

kX,kA,kandkBkarekknown,kwekcankrewritekitktoksolvekforkC.

J=- 5

C=-AX2-BX

IfkwekassumekinsteadkthatkX,kA,kandkCkarekknown,kandkthatkXkisknonzero,kwekcankturnkth

eksecondkstatementkintokankassignmentkbykrewritingkitktoksolvekforkB.

B=(-AX*2-C)/X

IfkwekassumekinsteadkthatkA,kB,kandkCkarekknown,kandkthatkAkisknonzero,kwekcankturnkt

heksecondkstatementkintokankassignmentkbykusingkthekquadratickformulaktoksolvekforkX.k

Wekalsokhavektokmakekankassumptionkaboutkwhichkrootkiskdesired.k Ifkwekwantkthekposit

ivekone,kwekgetkthekfirstkstatementkbelow;kifkwekwantktheknegativekone,kwekgetktheksec

ond.

X1=(-B+SQRT(B2-4.AC))/(2.*A)

X2=(-B-SQRT(B2-4.AC))/(2.*A)

2.9.8 [E]kTheksecondkstatementkisklonger,kbutkbothkhavekexactlyktheksamekeffect.k Anykc

ompetentkcompilerkgenerateskidenticalkmachinekcodekforkbothkstatements.

2.9.9 [E]kThekprogramkonkthekleftkbelowkevaluateskthekexpressionskasktheykarekgivenkink

thekquestion.k Thekprogramkonkthekrightkuseskparenthesesktokindicatekthekorderkofkopera

tionskresultingkfromkthekprecedencekrules.

I=7 I=

X=3. X=3.

I=I+1/I- 3 I=I+(1/I)- 3

X=X/(X-1.)2(-1)-1. X=(X/((X-1.)(2(-1))))-1.

PRINTk,I,X PRINTk,I,X

STOP STOP

END END

Ifkeitherkprogramkiskcompiledkandkrunkitkproduceskthekoutputkshownkbelow.

4 k k 2.

However,k itk shouldk bek possiblek fork thek studentk tok reasonk outk thek answersk beforek condu

ctingkthekexperiment,k askfollows.k (a)k Inkthek formulakforkI,kthek operationkwithk highestkprece

dencekiskthekdivisionkandk1/7kyieldsk0.kThenk7+0-

3 kgiveskI=4.k(b)kThekexpressionk2**(-

1)kreducesktok1/2,kwhichkyieldsk 0 kbecausekintegerkdivisionktruncates.k Thenk(X-

1.)**0kisk1.,kandk(3./1.)-1.kgiveskX=2.

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e is m ic i s o la ti o n

12 ClassicalkFORTRANk SolutionskManual

2.9.10 [E]kBlankskinkcolumnsk 7 -

72 kofkakFORTRANkstatementkareknotksignificantkexceptkinkcharacterkstrings,k sok thek state

mentk Yk =kSINk Xk iskinterpretedkaskY=SINX,kandkthek variablekSINXkiskneverkgivenkakvalue

kbykthekprogram.k Inksomekoperatingksystemkenvironmentskthekmemorykallocatedkforkakp

rogram’skdatakiskinitializedktokzeros,kandkinkthatkcasekthekgivenkprogramkwouldkprintkakz

ero.k Inkotherkoperatingksystemkenvironmentskuninitializedkvariableskcankhavekanykvalue,k

andkinkthatkcasekthekoutputkiskunpredictable.k Tokprintktheksinekofk 1 kradian,kthekstateme

ntkmustkbekrecodedkYk=kSIN(X).

2.9.11 [E]kHerekiskthekprogramkrewrittenktokpromptkforkAkandkBkbeforekreadingkthem.

PRINTk*,’A=

’kREADk *,Ak

PRINTk*,’B=

’kREADk *,B

HYP=SQRT(A2k +k B2)k

PRINTk *,’HYP=’,HYPkST

OP

END

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heksidekofklengthk a ),kthenk B ,kthenk C ,kandkthekuserkmustkknowkthisktokproperlykinterp

retkthekoutput.

2 SeekFreilich,kAaron;k Shanholt,k Henryk H.;k McCormack,kJosephk P.,k Planek Trigonometry,

k Silver,kBurdettkandkCompany,kNewkYork,kNY,k1934,korkanyksimilarkhigh-

schoolktrigonometryktextbook.

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e is m ic i s o la ti o n

14 ClassicalkFORTRANk SolutionskManual

C

Thiskprogramkfindsktrianglekangl

eskC oppositek givenk sides.

C

C

promptkforkandkreadkthekside

klengthskPRINTk *,’sides:’

READk *,SA,SB,SC

C

C

useklawkofkcosinesktokfindkthe

kangleskCA=(SB2k+kSC2k-

kSA2)/(2.SBSC)kCB=(SA2k+kSC

2 k-

kSB2)/(2.SASC)kCC=(SA2k+kSB

2 k-kSC2)/(2.SASB)kA=ACOS(CA)

B=ACOS(CB)kC=ACOS(

CC)

C

C

convertkanglesktokdegreeskfor

koutputkPI=4.*ATAN(1.)

DPR=180./PIkA

=DPR*AkB=DP

RBkC=DPRC

PRINTk*,’oppositekangles:’kP

RINTk*,A,B,C

STOP

kEND

Somektypicalkinteractionskwithkthekprogramkarekshownkbelow.

unix[1]ka.outksid

es:

1 k 1 k 1

oppositekangles:

60.00000000k 60.00000000k 60.

unix[2]ka.outksid

es:

3 k 4 k 5

oppositekangles:

36.86989594k 53.13010025k 90.

unix[3]ka.outksid

es:

3 k 8 k 10

oppositekangles:

14.36151028k 41.40962219k 124.

unix[4]ka.outksid

es:

1 k 1 k 2

oppositekangles:

0.0000000000E+00k k 0.0000000000E+00k k 180.

unix[5]ka.outksid

es:

1 k 1 k 3

oppositek angles:k

NaNQk NaNQk NaNQ