Fonction puissance en string

Version imprimable

20/05/2019, 12h03
Gorzyne

Fonction puissance en string

Bonjour à tous et à toutes,

Est-il possible d'écrire la fonction puissance de vba à base de string pour contourner la limite de capacité des formats numériques, je sais que ça se fait avec la fonction modulo par exemple

mon idée est de faire le calcul avec un string en sortie, afin de ne pas avoir de problème de dépassement de capacité, qui arrive malheureusement très vite avec la fonction puissance ...

merci bcp,
Gorz
20/05/2019, 12h50
Menhir

Avec le type LongLong, on peut aller jusqu'à 9 223 372 036 854 775 807 (et autant en négatif).
Pour donner un équivalent, c'est la distance jusqu'à Alpha du Centaure aller-retour mesuré en millimètres.
https://docs.microsoft.com/fr-fr/off...long-data-type

As-tu besoin de plus de capacité ?
Cela dit, personnellement, si j'avais besoin d'une capacité supérieure, je ne passerait pas par les String mais par les logarithmes.

Je suppose que tu as besoin de nombre de grande taille pour faire des stat ou des proba.
Si c'est le cas, généralement on a besoin de grands nombres pour les calculs intermédiaires mais pas pour le résultat final.

Dans ce cas, tu convertis tes nombres en logarithmes (par exemple des logarithmes décimaux). Du coup, ça te fait des nombres incroyablement plus petits (1 milliard de milliard devient... 18, autant dire que tu peux mesurer l'univers en microns sans problème) et tu peux faire tes opérations en transformant les multiplications en additions (et donc les division en soustractions et les puissances en multiplications).

C'est le principe que j'utilisais dans les années 80, à l'époque où on ne pouvait pas dépasser le mur de la factorielle 69 sur les calculatrices.
20/05/2019, 14h09
Gorzyne

j'ai codé l'algorithme tachtenberg en vba pour faire ça en string
"longlong" ne semble pas être un type reconnu en vba, peut être s'agit il d'un autre langage ?
je vais avoir besoin de coder un équivalent de modulo en string également

Gorz
20/05/2019, 14h46
Igloobel

Bonjour,

longlong est connu en VBA sur du 64 bit

Trachtenberg + puissance + modulo version string en vba

ok bon bah niveau portabilité ça va être un peu précoce alors

j'ai implémenté une version string de modulo, par contre le diviseur est un long

Code:

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Function mod3(S As String, div As Long)
    res = 0
    For i = 1 To Len(S)
 
        res = (res * 10 + Mid(S, i, 1)) Mod div
 
    Next i
    mod3 = res
End Function

pour la fonction puissance au format string je vais contribuer un peu en ressources:

Code:

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Function puissance(S1 As String, S2 As Long)
    puiss = "1"
    For i = 1 To S2
        puiss = multiplication(puiss & "", S1 & "")
    Next i
    puissance = puiss
End Function
Function multiplication(S1 As String, S2 As String) As String
 
If Len(S1) > Len(S2) Then 'S1 le plus petit
    temp = S2
    S2 = S1
    S1 = temp
End If
S3 = ""
S0 = ""
For i = Len(S1) To 1 Step -1
    S3 = add_string(multi(S2, Mid(S1, i, 1)) & S0, S3 & "")
    S0 = S0 & "0"
Next i
multiplication = S3
 
End Function
Function add_string(S1 As String, S2 As String) As String
    L1 = Len(S1)
    L2 = Len(S2)
    If L1 > L2 Then 'S1 le plus petit
        For i = L2 To L1 - 1
            S2 = "0" & S2
        Next i
    Else
        For i = L1 To L2 - 1
            S1 = "0" & S1
        Next i
    End If
    L1 = Len(S1)
    report = 0
    S = ""
    For i = L1 To 1 Step -1
        k = Mid(S1, i, 1) + report + Mid(S2, i, 1)
        S = k Mod 10 & S
        report = Int(k / 10)
    Next i
    S = report & S
    While Left(S, 1) = "0"
        S = Right(S, Len(S) - 1)
    Wend
    add_string = S
End Function
 
 
Function sub_string(S1 As String, S2 As String)
    L1 = Len(S1)
    L2 = Len(S2)
 
    If L1 > L2 Then 'S1 le plus petit
        For i = L2 To L1 - 1
            S2 = "0" & S2
        Next i
    ElseIf L2 > L1 Then '
        For i = L1 To L2 - 1
            S1 = "0" & S1
        Next i
    End If
 
    L1 = Len(S1)
    report = 0
    S = ""
 
    For i = L1 To 1 Step -1
        k = Mid(S1, i, 1) + report - Mid(S2, i, 1)
        report = 0
        While k < 0
            k = k + 10
            report = report + 1
        Wend
        S = k & S
    Next i
    S = report & S
 
    While Left(S, 1) = "0"
        S = Right(S, Len(S) - 1)
    Wend
    sub_string = S
End Function
Function mul2(S As String)
    S2 = ""
    report = 0
    For i = Len(S) To 1 Step -1
        k = Mid(S, i, 1) * 2
        S2 = (report + k) Mod 10 & S2
        report = Int(k / 10)
    Next i
    S2 = report & S2
    While Left(S2, 1) = "0"
        S2 = Right(S2, Len(S2) - 1)
    Wend
    mul2 = S2
End Function
Function mul3(S As String)
    S2 = ""
    j = Mid(S, Len(S), 1)
    k = 2 * (10 - j)
    If j Mod 2 = 1 Then k = k + 5
    report = Int(k / 10)
    k = k Mod 10
    S2 = k & S2
    For i = Len(S) - 1 To 1 Step -1
        j = Mid(S, i, 1)
        j2 = Mid(S, i + 1, 1)
        k = (9 - j) * 2 + Int(j2 / 2) + report
        If j Mod 2 = 1 Then k = k + 5
 
        report = Int(k / 10)
        k = k Mod 10
        S2 = k & S2
    Next i
    j = Mid(S, 1, 1)
    k = Int(j / 2) - 2 + report
    S2 = k & S2
    While Left(S2, 1) = "0"
        S2 = Right(S2, Len(S2) - 1)
    Wend
    mul3 = S2
End Function
Function mul4(S As String)
    S2 = ""
    j = Mid(S, Len(S), 1)
    k = (10 - j)
    If j Mod 2 = 1 Then k = k + 5
    report = Int(k / 10)
    k = k Mod 10
    S2 = k & S2
    For i = Len(S) - 1 To 1 Step -1
        j = Mid(S, i, 1)
        j2 = Mid(S, i + 1, 1)
        k = 9 - j + Int(j2 / 2) + report
        If j Mod 2 = 1 Then k = k + 5
        report = Int(k / 10)
        k = k Mod 10
        S2 = k & S2
    Next i
    j = Mid(S, 1, 1)
    k = Int(j / 2) - 1 + report
    S2 = k & S2
    While Left(S2, 1) = "0"
        S2 = Right(S2, Len(S2) - 1)
    Wend
    mul4 = S2
End Function
Function mul5(S As String)
    S2 = ""
    S = "0" & S
    j = Mid(S, Len(S), 1)
    If j Mod 2 = 1 Then
        S2 = "5"
    Else
        S2 = "0"
    End If
    report = 0
    For i = Len(S) - 1 To 1 Step -1
        j = Mid(S, i, 1)
        j2 = Mid(S, i + 1, 1)
        k = Int(j2 / 2) + report
        If j Mod 2 = 1 Then k = k + 5
        report = Int(k / 10)
        k = k Mod 10
        S2 = k & S2
    Next i
    While Left(S2, 1) = "0"
        S2 = Right(S2, Len(S2) - 1)
    Wend
    mul5 = S2
End Function
Function mul6(S As String)
    S2 = ""
    S = "0" & S
    j = Mid(S, Len(S), 1)
    If j Mod 2 = 1 Then
        k = j + 5
    Else
        k = j
    End If
    report = Int(k / 10)
    k = k Mod 10
    S2 = k & S2
 
    For i = Len(S) - 1 To 1 Step -1
        j = Mid(S, i, 1)
        j2 = Mid(S, i + 1, 1)
        k = j + Int(j2 / 2) + report
        If j Mod 2 = 1 Then k = k + 5
        report = Int(k / 10)
        k = k Mod 10
        S2 = k & S2
    Next i
    While Left(S2, 1) = "0"
        S2 = Right(S2, Len(S2) - 1)
    Wend
    mul6 = S2
End Function
Function mul7(S As String)
    S2 = ""
    S = "0" & S
    j = Mid(S, Len(S), 1)
    If j Mod 2 = 1 Then
        k = 2 * j + 5
    Else
        k = 2 * j
    End If
    report = Int(k / 10)
    k = k Mod 10
    S2 = k & S2
    For i = Len(S) - 1 To 1 Step -1
        j = Mid(S, i, 1)
        j2 = Mid(S, i + 1, 1)
        k = 2 * j + Int(j2 / 2) + report
        If j Mod 2 = 1 Then k = k + 5
        report = Int(k / 10)
        k = k Mod 10
        S2 = k & S2
    Next i
    While Left(S2, 1) = "0"
        S2 = Right(S2, Len(S2) - 1)
    Wend
    mul7 = S2
End Function
Function mul8(S As String)
    S2 = ""
    k = 20 - 2 * Mid(S, Len(S), 1)
    report = Int(k / 10)
    k = k Mod 10
    S2 = k & S2
    For i = Len(S) - 1 To 1 Step -1
        j = Mid(S, i, 1)
        j2 = Mid(S, i + 1, 1)
        k = (9 - j) * 2 + j2 + report
        report = Int(k / 10)
        k = k Mod 10
        S2 = k & S2
    Next i
    j = Mid(S, 1, 1)
    k = j - 2 + report
    S2 = k & S2
    While Left(S2, 1) = "0"
        S2 = Right(S2, Len(S2) - 1)
    Wend
    mul8 = S2
End Function
Function mul9(S As String)
    S2 = ""
    k = 10 - Mid(S, Len(S), 1)
    report = Int(k / 10)
    k = k Mod 10
    S2 = k & S2
    For i = Len(S) - 1 To 1 Step -1
        j = Mid(S, i, 1)
        j2 = Mid(S, i + 1, 1)
        k = (9 - j) + j2 + report
        report = Int(k / 10)
        k = k Mod 10
        S2 = k & S2
    Next i
    j = Mid(S, 1, 1)
    k = j - 1 + report
    S2 = k & S2
    While Left(S2, 1) = "0"
        S2 = Right(S2, Len(S2) - 1)
    Wend
    mul9 = S2
End Function
 
Function mul10(S As String)
    mul10 = S & "0"
End Function
Function multi(S As String, C As String)
    Select Case C
    Case "0"
        multi = "0"
    Case "1"
     multi = S
    Case "2"
        multi = mul2(S)
    Case "3"
        multi = mul3(S)
    Case "4"
        multi = mul4(S)
    Case "5"
        multi = mul5(S)
    Case "6"
        multi = mul6(S)
    Case "7"
        multi = mul7(S)
    Case "8"
        multi = mul8(S)
    Case "9"
        multi = mul9(S)
    End Select
End Function
'codé par Gorzyne pour Developpez.net

pour info c'est pour faire du chiffrement assymétrique

bonjour

"CDEC" faire une recherche dans l'aide

Code:

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Sub test()
MsgBox result_puissance(CDec(35), CDec(20))
End Sub
'
Function result_puissance(N#, K#) As Variant
   'FORMULE PATRICKTOULON DVP
    'Dim nb# 'en double on obbtient le nombre en abrégé
    Dim nb As Variant ' en variant on obtient le nombre en numerique
    Dim i#
    nb = CDec(N)
    For i = 1 To K - 1: nb = nb * (N - i): Next: result_puissance = nb
End Function

voir cette discussion
;)

20/05/2019, 17h27
Gorzyne

exemples et temps d'execution

merci pour cette ressource
malheureusement on atteint rapidement le dépassement de capacité, que ma version permet de contourner, la seule limitation étant la longueur max du string et la puissance de calcul.

un exemple

?puissance("79",43)
3962460313228512959999178162321193840226011986176362928682080669354289847669616239

temps de calcul immédiat

?puissance("126",73)
2123487914341640748721363763898849434212102775632653001833314535451684428025884160564630174412406003395971580607230447530234280769413999637353375912165376

temps de calcul immédiat

?puissance("189",92)
271948071840725876780856570168986791548965361904599312205860448226938155528552628856003536074151321946596951862195370567221395201109110874375723303640241669118361927858460366287705235486680731364798612984227121

?puissance("189",137)
750355675420415841279032980335639923684353833249627998802878353076447547825820945137004149429559546594399744844494685100665038484937817064247844438100415645408652280972298131351119427588835385547921588899724509597396655257193019200204674510764461373809096678321962992957706919335374270484383642924702279732798429

?puissance("287",169)
24101304407900263226031777358578740027571127741949396002497373311429323460222208898137310421747806699668608662041967638570715667133619874517467897826291522693592098198906684686340696438897328221345992731815343721505855959139521295460856112511922360361824360382210998950486756019519383002778001812229764742552501790122803221360487883423880815189865293585573493521288981312238526656870990662146330935082865076139716127

temps de calcul <1s

?puissance("299",199)
4555819158140630495006026912040404796443921929314619851759658156890980165054974634989098908837093113186962315524475959313139333120175923384002926734781226466482861661198644658295480007111593245041759017471349901944904002897373871833263870717135192189533787136567934488108060437946509122653905819550112576164964664178970611305712402510378103082238996252969743780314529635061309939416414806912804956463194051624759532570421031460918771113774764039783837602735127248732880811842564204064999969699

temps de calcul ~=1s
(selon configuration)

?puissance("299",2991)
540162310620048412419483315624030345815823761235099115133839656195943426848620671461662947939263615706800836017747243150453545480237522684059811464241975360129109578103200425086744256949055194881821508874470830304991129471789073841588096436397401211587668229655661559530425369945865532102064062159891275025312234753566963970511981652192060652319009739073779154692371722528882484116242650959711592292647012751196162847092306233572478340735632318602923171116410856644601258314567889490800095741551316458724697924692273049001478261153326376865248777670728097872174582067529297764336613717326520954795539752372566551287302792813802706494813414867000434168084420521632422864347787175770573186627531309582278418172719518057897527139542039496707010134464714967772446028581016913742694768103967564959584567005099428682221997965227549465330312556791663228411105965932333240559640187182600370510151618397556629953910514040686893055981854634051224863191529435492670933349046748487666767744945512684065098707922120732552585529213658247
699404079893648270370066111699570630184638564637287846859708257170094904562801690813410668374755437348983997801959287111020787434760539844482204067006516542459669085869579011991060934242129024493804504044795742984277499689340865827468692387626573750491895636129126035265045372982793051189096663302359816103201029042699813653676310482853717022999279670230224803145969691514466269118668806676167178552579982849932314864561333510862065822980617689502525738919563729912798048766041719225139058799872986560795091106525986505274675875059505315295765952572137220596440411614929286668312019113060572296703761584846402468846439006059974841786934138930081343584778735548067010725832605513751759173259818850206719506115308352284319016367814709258569735380632641053344217202410806281390267087459845143054833180926861422566932043208581016586686021516327826407536665067196590135297071387634660555205952074386103753547110873751149241176099062892579174916071635964770437674284509861120926076266871169985259669621425752187848529569767590660
070806705675549651757620790440182958285271572837897466465545220488027688865769707860070559898520694694697608891888057007377811815028408506219696066528297025479687617994104585391700511553555574360522989927222516947623831465735576521104757323610525083326586832962898908395812720331307311710769900577013294219347459288709256560884528360265134052090081028740795553426141347660584061806661265025933597456589307671869391765405733891731381745023060847862059859584178164433335591157095280420748780991246653763661430966489943694401253476499124627658623063777057116835666436398856478916460298328677120354105601571242676430099934583326925806695628087780680081509305866092184508422202163388247079940229773496943033298048807256343159959500855468660773073699233962321810296525598381330458067340945980851217319328697693602577585505296314910387408954763927341811244725691440971198242187421748271657739822850842297239833272728078584247927685650187056842170832012161896224868536219335326748823365862908582472460364988860307382239240489925045
257727270178078524892236503582255753821881101182981952447508655185723959146518364818040641233544548329166693434131773385996860690190794403979563619251183240685861985307736700979330158332652159076470911930589536311214668641871130186954343704807371461898470641516502615901914663071126254455352791574955738451026268639550282721171425427710644349884129105606842733385060379036460871783049581544308684860819643128406558399671241351008015900241420928100309307375112918724867121437813785192125958304602458923807309039416557999678875861351513041265340509443751293176589796889067792021469781846507563800291728465633101750296924497677532818229370882875857672659314175189557925596263599859203435215411208830406065292918782653999170926713240864968745212241078727197197339650268505371387429965041573777940900453982672393049995411694644082728914038439980233903589036886649820413623225454954404653313544500252089601674592682246138651354115214026097780578407613656461073137051519508271127897200736205162420311214916022257550819568925538740
860559997544712831275898858610216764644250735690967441817534465724214432695035052352309807090703554974742898418818790490670534231089091220725642159644075761852673212471179264963945502904821275557895832866972862961233710916899486986883855340783105052891025849335274651127728550733583160199988741718827764911353233230744080394239198016411032902931289946545094141343035364710479565740859239335764524563731848724369391581939354272810753883878079548278415246779866233541938286227334804759920111049092856030012403410511274762316782791855408808403671651911503782311435372482659559836722558923606368921385192811064345956289228901381713596692253866191502147010888592656439928864963977044593331338918892262494828236327609930845102375140172628205929355446724647607382012281018072977728750320157300717195501441837429785645200808281811005637478926036924400801364165096123762109979405073088978584960489204265537902846808372816555395735301500319293978184442671467237575049987352597837036483002413101155091846807836053679014615890733654287
209505715660526408734063775943366353793437376312162735034724733209514471446349082621879598527680784976149317914782153231451301939359935460197565333018868101786763687747743647680139318752509914875990816708867059043461377867059434985158563760935544747712427541895151777358658394707234509996586797319819243977381221819573132518517700205721634517631232978930373745885609334223472005462394304893161138112630338335345662713096861425158444695097038442663589096879741396228546887340248294427680319592742958565750543750020599783633741133188544855994420545854103828272389426592162290148976924171415152509686183819748481107410225418951554837542502247858830979365685766548262726816187180195175032631929768430576389051077818039207423108968995177773489770550550636436228193939362427650997606915440495462155479450700269809438369720807108936810733137818457939978123807201394235018318617278565530600231498865268833701730735580046709383962726500198833149452305518068799771351176479999861919792177841209934552474420904340408333557077290081327
279783318271491177686914239013335157376710955920514286193982942713911391898267198481122595691713966800768387458328333192531920396723166641024758591262683669002578058072802513397583150336756998137722308518522069331920108445357148529589637619854235463324374878835708711068330264482315931250919750832797605365760609897712665631967216076821236536942710383214880078189934649156691829523272910190682941162050046046031322686881521780684788840414471581512228761269363887551879922982970534402266482284621236641318914844171309748782201104735730203688193445345152122837954706290741851140625087289968890859760036012761345686703945771716188262439776697457726222063634917376346090696681375621581255282791727336647481534881250329526754242147849028764816444926322218634994343822001742768883372399035214976569612938902996960809719791056917359641049932269756637624628959054077561720777807410205054896984085448938356908775784701608612565978273328096850209866215033285048051309936854085736676878305570453317083607767450699542867013567658488978
8665813675046693624610284861882441214544287486688428799766062115210151898557287905995073678799298915632206940691871094285410646157639078849847015805832052063465345192516015390690504015810385237605338165849476156372941110937836348678435106847299

temps de calcul quelques dizaines de secondes < 1 min :bravo:

Gorz