Code archives/Algorithms/Infinitely Large +/- Ints
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| My first attempt at adding and subtracting arbitrarily large positive and negative integers. I am sure it could use some fine tuning. However, it can give you the exact value of 2^768 (more than 230 digits long!! At least i am pretty sure... The Windows XP calculator doesn't show me every digit, so I cannot verify the value exactly) | |||||
' Examples Calculating Very Large numbers with Type Inf
'
' CREATED: MARCH 11, 2009
' TERMS OF USE: Any person/entity can use this code. Note that it's a work in prog.
' (a little credit would be nice too!) ;)
'____________________________________________________________________________________
Global A:String
Global B:String
Global C:String
A = "-1000000000000000000000000000000000000"
B = "+ 00000 001233"
'NOTE: "+" sign is always optional.
'NOTE: spaces and leading zeros are ignored
Print Inf.Add(A,B)
Print Inf.Sub(A,B)
'---------------------------------------------------------------
' what is 2^768 ?
A = "2" ' 2^1 = 2
For x = 2 To 768
A = Inf.Add(A,A)
Print "2^"+(x+1) + " = " + A
Next
'---------------------------------------------------------------
'---------------------------------------------------------------
'can be used as an Object too
Global Atype:Inf = New INf
Atype.Value = "-1000000000000000000000"
Atype.Plus(B)
Print "FROM AType.Value=" + Atype.Value
Atype = Null
'---------------------------------------------------------------
GCCollect()
'*******************************************************************************************************
'* '*
'*******************************************************************************************************
'* TYPE: Inf '*
'* PURPOSE: Calculate the addition and subtraction of (n)-digit long positive and negative integers '*
'* Functional applications include high score counters and monetary values. '*
'* CREATED: MARCH 11, 2009 '*
'* (USA) '*
'* '*
'* TERMS OF USE: Any person/entity can use this code. (a little credit would be nice too!) ;) '*
'* NOTE: It's a work in progress. '*
'*******************************************************************************************************
Type Inf '*
'*
Field Value:String '*
'*
'----------------------------------------------------------- '*
Method Plus(ValueToAdd:String) '*
Value = Inf.Add(Value,ValueToAdd) '*
End Method '*
'----------------------------------------------------------- '*
'*
'----------------------------------------------------------- '*
Method Minus(ValueToSubtract:String) '*
Value = Inf.Sub(Value,ValueToSubtract) '*
End Method '*
'----------------------------------------------------------- '*
'*
'-------------------------------------------------------------------------------- '*
Function Add:String(Value1:String,Value2:String) '*
Return Replace(Inf.FormatValue(Inf.Calculate("+",Value1,Value2)),"+","") '*
End Function '*
'-------------------------------------------------------------------------------- '*
'*
'-------------------------------------------------------------------------------- '*
Function Sub:String(Value1:String,Value2:String) '*
Return Replace(Inf.FormatValue(Inf.Calculate("-",Value1,Value2)),"+","") '*
End Function '*
'-------------------------------------------------------------------------------- '*
'*
'*
'-------------------------------------------------------------------------------- '*
Function Calculate:String(Opperator:String, Value1:String, Value2:String) '*
'*
Local Result : String '*
Local Sign1 : String '*
Local Sign2 : String '*
Local SignCombo: String '*
'*
Value1 = FormatValue(Value1) '*
Value2 = FormatValue(Value2) '*
'*
Sign1 = Left(Value1,1) '*
Sign2 = Left(Value2,1) '*
'*
SignCombo = Sign1+Opperator+Sign2 '*
'*
Value1 = Right(Value1,Value1.Length-1) '*
Value2 = Right(Value2,Value2.Length-1) '*
'*
Select SignCombo '*
'*
Case "+++" '*
Result = Inf.InternalAdditionFunction(Value1,Value2) '*
'*
Case "-++" '*
Result = Inf.InternalSubtractionFunction(Value2,Value1) '*
Case "++-" '*
Result = Inf.InternalSubtractionFunction(Value1,Value2) '*
Case "-+-" '*
Result = "-" + Inf.InternalAdditionFunction(Value1,value2) '*
Case "+-+" '*
Result = Inf.InternalSubtractionFunction(Value1,Value2) '*
'*
Case "--+" '*
Result = "-" + Inf.InternalAdditionFunction(Value1,value2) '*
Case "+--" '*
Result = Inf.InternalAdditionFunction(Value1,value2) '*
'*
Case "---" '*
Result = Inf.InternalSubtractionFunction(Value2,Value1) '*
'*
End Select '*
'*
Return Result '*
'*
End Function '*
'-------------------------------------------------------------------------------- '*
'*
'-------------------------------------------------------------------------------- '*
Function InternalAdditionFunction:String(Value1:String, Value2:String) '*
'*
Value1 = "0" + Value1 '*
Value2 = "0" + Value2 '*
'*
While Value1.Length < Value2.Length '*
Value1 = "0" + Value1 '*
Wend '*
'*
While Value2.Length < Value1.Length '*
Value2 = "0" + Value2 '*
Wend '*
'*
Local TempDecimalPlace : Int '*
Local DecimalPlaces : Int '*
Local CarryValue : Byte '*
Local Digit : Byte '*
Local DigitToAdd : Byte '*
Local DigitSum : Byte '*
Local Result : String '*
'*
DecimalPlaces = Value1.Length '*
'*
For TempDecimalPlace = DecimalPlaces To 1 Step -1 '*
'*
Digit = Int(Mid(Value1 ,TempDecimalPlace ,1)) '*
DigitToAdd = Int(Mid(Value2,TempDecimalPlace ,1)) '*
DigitSum = Digit + DigitToAdd + CarryValue '*
'*
If DigitSum > 9 Then '*
CarryValue = 1 '*
Else '*
CarryValue = 0 '*
EndIf '*
'*
Result = Right(String(DigitSum),1) + Result '*
Next '*
'*
If Left(Result,1) = "0" Then '*
Return Right(Result,Len(Result)-1) '*
Else '*
Return Result '*
EndIf '*
'*
End Function '*
'-------------------------------------------------------------------------------- '*
'*
'-------------------------------------------------------------------------------- '*
'REF: http://en.wikipedia.org/wiki/Ten%27s_complement '*
Function GetTensComplement:String(Value:String) '*
'*
Local Complement : String '*
Local TempDigit : Byte '*
Local TempRadix : Byte '*
Local Decimals : Int '*
'*
Decimals = Value.Length '*
'*
For Local TempDecimal:Int = Decimals To 1 Step -1 '*
'*
TempDigit = Int(Mid(Value,TempDecimal,1)) '*
TempRadix = 9 - TempDigit '*
Complement = String(TempRadix) + Complement '*
'*
Next '*
'*
Return Complement '*
'*
End Function '*
'-------------------------------------------------------------------------------- '*
'*
'*
'-------------------------------------------------------------------------------- '*
Function InternalSubtractionFunction:String(Value1:String, Value2:String) '*
'*
Local TempValue : String '*
Local Value1Digit : Int '*
Local Value2Digit : Int '*
Local ValuesAreEqual : Byte = False '*
Local ResultWillBeNegative : Byte = False '*
Local Result : String '*
'*
If Value2.Length > Value1.Length Then '*
'*
TempValue = Value1 '*
Value1 = Value2 '*
Value2 = TempValue '*
ResultWillBeNegative = True '*
'*
ElseIf Value2.Length = Value1.Length Then '*
'*
ValuesAreEqual = True '*
'*
For Local CurrentDigitPos = 1 To Value2.Length Step 1 '*
'*
Value1Digit = Int(Mid(Value1,CurrentDigitPos,1)) '*
Value2Digit = Int(Mid(Value2,CurrentDigitPos,1)) '*
'*
If Value1Digit > Value2Digit Then '*
'*
ValuesAreEqual = False '*
Exit 'For Loop '*
'*
ElseIf Value2Digit > Value1Digit Then '*
'*
ValuesAreEqual = False '*
TempValue = Value1 '*
Value1 = Value2 '*
Value2 = TempValue '*
ResultWillBeNegative = True '*
Exit 'For Loop '*
'*
EndIf '*
'*
Next '*
'*
If ValuesAreEqual Then '*
'*
Return "0" '*
'*
EndIf '*
'*
EndIf '*
'*
'*
While Value1.Length < Value2.Length '*
Value1 = "0" + Value1 '*
Wend '*
'*
While Value2.Length < Value1.Length '*
Value2 = "0" + Value2 '*
Wend '*
'*
Local TensComplement:String = Inf.GetTensComplement(Value2) '*
'*
Result = Inf.Add(Value1, TensComplement) '*
Result = Inf.Add(Result,"1") '*
'*
If Int(Left(Result,1)) > 1 Then '*
'*
Result = String(Int(Left(Result,1))-1) + Right(Result,Result.Length-1) '*
Else '*
Result = Right(Result,Result.Length-1) '*
'*
EndIf '*
'*
'*
If ResultWillBeNegative Then '*
'*
Result = "-" + Result '*
'*
EndIf '*
'*
Return Result '*
'*
End Function '*
'-------------------------------------------------------------------------------- '*
'*
'-------------------------------------------------------------------------------- '*
Function FormatValue:String(Value:String) '*
'*
Local ReturnValue : String '*
Local CurrentDigit : String '*
Local ValueSign : String '*
Local TempPosition : Int '*
'*
Value = Trim(Value) '*
'*
If Left(Value,1) = "-" Then '*
'*
ValueSign = "-" '*
Value = Right(Value,Value.Length-1) '*
'*
ElseIf Left(Value,1) = "+" Then '*
'*
ValueSign = "+" '*
Value = Right(Value,Value.Length-1) '*
Else '*
'*
ValueSign = "+" '*
EndIf '*
'*
TempPosition = 1 '*
'*
While Mid(Value,TempPosition,1)="0" '*
'*
Value = Right(Value,Value.Length-(TempPosition-1)) '*
TempPosition = TempPosition + 1 '*
'*
Wend '*
'*
For Local DigitPosition = 1 To Value.Length Step 1 '*
'*
CurrentDigit = Mid(Value,DigitPosition,1) '*
'*
Select CurrentDigit '*
'*
Case "0","1","2","3","4","5","6","7","8","9" '*
ReturnValue = ReturnValue + CurrentDigit '*
Default '*
ReturnValue = ReturnValue + "0" '*
'*
End Select '*
'*
Next '*
'*
ReturnValue = ValueSign + ReturnValue '*
'*
Return ReturnValue '*
'*
End Function '*
'-------------------------------------------------------------------------------- '*
'*
End Type '*
'*******************************************************************************************************
'*End of Type Inf '*
'* '*
'* '*
'* '*
'* '*
'* '*
'******************************************************************************************************* |
Comments
| ||
| Great code. I seem to have found a bug despite how reliable it seems though. Try inf.sub("11900","11800") and you get... "00" instead of "100" like you should. Unfortunately I cannot understand a bit of this code so I have no idea what is causing the bug or I would fix it myself. Is there anyone familiar with parsers/string addition that could help? edit: sorry for the bump, didn't realize this was 2 yrs old |
| ||
| @[Nate the Great] No worries Nate! its been a while since I've been on. I re-wrote the functions and i'm pretty sure i've removed the error. I posted the update in the Code Archives under Algorithms. The new functions only handle positive values. New Version: http://www.blitzbasic.com/codearcs/codearcs.php?code=2891 |
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