1
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"
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COPYRIGHT (c) 1988-93 by Claus Gittinger
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All Rights Reserved
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This software is furnished under a license and may be used
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only in accordance with the terms of that license and with the
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inclusion of the above copyright notice. This software may not
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be provided or otherwise made available to, or used by, any
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other person. No title to or ownership of the software is
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hereby transferred.
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"
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Integer subclass:#LargeInteger
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instanceVariableNames:'sign digitArray'
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classVariableNames:''
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poolDictionaries:''
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category:'Magnitude-Numbers'
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!
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LargeInteger comment:'
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COPYRIGHT (c) 1988-93 by Claus Gittinger
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All Rights Reserved
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This class provides arbitrary precision integers. These are represented as:
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sign (-1/0/+1) and, if sign ~~ 0
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an Array of digits with 4 digits per element;
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least significant 4 digits at index 1 ...
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This is definitely not a good (fast) implementation -
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but ok for now, since LargeIntegers are not used very often.
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It will be reimplemented when everything else runs fine and a need arises
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(or someone rewrites it and sends me the code :-).
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%W% %E%
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'!
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!LargeInteger class methodsFor:'instance creation'!
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new:numberOfDigits
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"catch creation message"
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self error:'LargeIntegers cannot be created with new'
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!
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new
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"catch creation message"
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self error:'LargeIntegers cannot be created with new'
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!
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value:aSmallInteger
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"create and return a new LargeInteger with value taken from
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the argument, aSmallInteger"
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^ self basicNew value:aSmallInteger
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"LargeInteger value:3689"
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!
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valueLow:lowBits hi:hiBits
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"create and return a new LargeInteger with value taken from
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the two 16-bit args"
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hiBits < 0 ifTrue:[
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^ ((self value:hiBits negated) * 16r10000 + lowBits) negated
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].
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^ (self value:hiBits) * 16r10000 + lowBits
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! !
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!LargeInteger methodsFor:'coercing & converting'!
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coerce:aNumber
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"return the argument as a LargeInteger"
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^ aNumber asLargeInteger
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!
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asLargeInteger
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"return a LargeInteger with same value as myself - thats me"
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^ self
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!
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asSmallInteger
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"return a SmallInteger with same value as myself - the result
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is invalid if the receivers value cannot be represented
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as a SmallInteger"
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|value|
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value := 0.
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(sign == 0) ifFalse:[
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digitArray reverseDo:[:aDigit |
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value := (value times:10000) + aDigit
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].
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(sign < 0) ifTrue:[
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value := value negated
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]
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].
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^ value
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!
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asFloat
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"return a Float with same value as myself"
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|newFloat|
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newFloat := 0.0.
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(sign == 0) ifFalse:[
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digitArray reverseDo:[:aDigit |
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newFloat := (newFloat * 10000.0) + aDigit asFloat
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].
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(sign < 0) ifTrue:[
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newFloat := newFloat negated
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]
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].
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^ newFloat
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!
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value:aSmallInteger
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"return a new LargeInteger with value taken from a SmallInteger"
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|absValue
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index "{ Class: SmallInteger }"|
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(aSmallInteger == 0) ifTrue: [
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digitArray := nil.
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sign := 0.
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^ self
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].
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(aSmallInteger < 0) ifTrue: [
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sign := -1.
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absValue := aSmallInteger negated
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] ifFalse: [
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sign := 1.
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absValue := aSmallInteger
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].
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digitArray := Array new:3.
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index := 1.
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[absValue == 0] whileFalse: [
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digitArray at:index put:(absValue \\ 10000).
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absValue := absValue // 10000.
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index := index + 1
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].
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[index <= 3] whileTrue:[
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digitArray at:index put:0.
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index := index + 1
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]
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! !
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!LargeInteger methodsFor:'comparing'!
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= aNumber
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"return true, if the argument, aNumber has the same value as
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the receiver"
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(aNumber class == LargeInteger) ifFalse:[
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aNumber respondsToArithmetic ifFalse:[ ^ false ].
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^ self retry:#= coercing:aNumber
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].
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(aNumber sign == sign) ifFalse:[^ false].
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^ self absEq:aNumber
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!
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< aNumber
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"return true, if the argument, aNumber is greater than the receiver"
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|otherSign|
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(aNumber class == LargeInteger) ifFalse:[
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^ self retry:#< coercing:aNumber
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].
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otherSign := aNumber sign.
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(sign > 0) ifTrue:[
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"I am positive"
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(otherSign > 0) ifTrue:[^ self absLess:aNumber].
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^ false "aNumber is <= 0"
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].
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(sign == 0) ifTrue:[
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(otherSign > 0) ifTrue:[^ true].
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^ false
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].
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"I am negative"
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(otherSign > 0) ifTrue:[^ true].
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(otherSign == 0) ifTrue:[^ true].
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^ (self absLess:aNumber) not
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! !
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!LargeInteger methodsFor:'arithmetic'!
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+ aNumber
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"return the sum of the receiver and the argument, aNumber"
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|otherSign|
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(aNumber class == LargeInteger) ifFalse:[
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^ self retry:#+ coercing:aNumber
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].
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otherSign := aNumber sign.
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(sign > 0) ifTrue:[
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"I am positive"
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(otherSign > 0) ifTrue:[^ self absPlus:aNumber].
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(otherSign < 0) ifTrue:[^ self absMinus:aNumber].
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^ self
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].
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(sign == 0) ifTrue:[^ aNumber].
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"I am negative"
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(otherSign > 0) ifTrue:[^ aNumber absMinus:self].
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(otherSign < 0) ifTrue:[^ (self absPlus:aNumber) negated].
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^ self
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!
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- aNumber
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"return the difference of the receiver and the argument, aNumber"
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|otherSign|
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(aNumber class == LargeInteger) ifFalse:[
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^ self retry:#- coercing:aNumber
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].
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otherSign := aNumber sign.
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(sign > 0) ifTrue:[
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"I am positive"
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(otherSign > 0) ifTrue:[^ self absMinus:aNumber].
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(otherSign < 0) ifTrue:[^ self absPlus:aNumber].
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^ self
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].
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(sign == 0) ifTrue:[^ aNumber negated].
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"I am negative"
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(otherSign > 0) ifTrue:[^ (self absPlus:aNumber) negated].
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(otherSign < 0) ifTrue:[^ (self absMinus:aNumber) negated].
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^ self
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!
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* aNumber
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"return the product of the receiver and the argument, aNumber"
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|otherSign|
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(aNumber = 10) ifTrue:[
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^ self deepCopy mul10
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].
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(aNumber class == LargeInteger) ifFalse:[
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^ self retry:#* coercing:aNumber
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].
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otherSign := aNumber sign.
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(sign == 0) ifTrue:[^ 0].
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(sign == otherSign) ifTrue:[^ self absMul:aNumber].
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(otherSign == 0) ifTrue:[^ 0].
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^ (self absMul:aNumber) negated
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!
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/ aNumber
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"this is a q&d hack - we loose lots of precision here ..."
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^ (self asFloat / aNumber asFloat)
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!
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// aNumber
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"return the quotient of the receiver and the argument, aNumber"
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|otherSign|
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(aNumber = 10) ifTrue:[
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^ self deepCopy div10
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].
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(aNumber class == LargeInteger) ifFalse:[
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^ self retry:#// coercing:aNumber
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].
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otherSign := aNumber sign.
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sign < 0 ifTrue:[
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(sign == otherSign) ifTrue:[^ (self negated absDiv:aNumber negated) at:1].
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^ ((self negated absDiv:aNumber) at:1) negated
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].
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(sign == otherSign) ifTrue:[^ (self absDiv:aNumber) at:1].
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^ ((self absDiv:aNumber negated) at:1) negated
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!
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\\ aNumber
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"return the remainder of division of the receiver by the argument, aNumber"
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|otherSign|
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(aNumber class == LargeInteger) ifFalse:[
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^ self retry:#\\ coercing:aNumber
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].
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otherSign := aNumber sign.
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sign < 0 ifTrue:[
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(sign == otherSign) ifTrue:[^ (self negated absDiv:aNumber negated) at:2].
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^ ((self negated absDiv:aNumber) at:2) negated
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].
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(sign == otherSign) ifTrue:[^ (self absDiv:aNumber) at:2].
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^ ((self absDiv:aNumber negated) at:2) negated
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!
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negated
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"return a LargeInteger with value negated from receivers value"
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|newNumber|
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(sign == 0) ifTrue:[^ 0].
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newNumber := self shallowCopy.
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newNumber sign:(sign negated).
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^ newNumber
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! !
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!LargeInteger methodsFor:'bit operations'!
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bitAnd:anInteger
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"q & d hack to make Random work;
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this works only correctly, if my value can be represented
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as a SmallInteger"
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^ self asSmallInteger bitAnd:anInteger
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! !
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!LargeInteger methodsFor:'testing'!
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sign
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"return the sign of the receiver"
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^ sign
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!
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odd
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"return true if the receiver is odd"
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^ (digitArray at:1) even
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!
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even
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"return true if the receiver is even"
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^ (digitArray at:1) even
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!
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negative
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"return true, if the receiver is < 0"
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^ (sign < 0)
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!
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positive
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"return true, if the receiver is >= 0"
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^ (sign >= 0)
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!
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strictlyPositive
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"return true, if the receiver is > 0"
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^ (sign > 0)
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! !
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!LargeInteger methodsFor:'private'!
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absEq:aLargeInteger
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"return true, if abs(self) = abs(theArgument)"
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|len1 "{ Class: SmallInteger }"
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len2 "{ Class: SmallInteger }"
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d1 "{ Class: SmallInteger }"
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d2 "{ Class: SmallInteger }"
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otherDigits |
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len1 := digitArray size.
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otherDigits := aLargeInteger digits.
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len2 := otherDigits size.
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[(digitArray basicAt:len1) == 0] whileTrue:[
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len1 := len1 - 1
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].
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[(otherDigits basicAt:len2) == 0] whileTrue:[
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len2 := len2 - 1
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].
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(len1 ~~ len2) ifTrue:[^ false].
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[len1 > 0] whileTrue:[
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d1 := digitArray basicAt:len1.
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d2 := otherDigits basicAt:len1.
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(d1 ~~ d2) ifTrue:[^ false].
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len1 := len1 - 1
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].
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^ true
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!
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absLess:aLargeInteger
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"return true, if abs(self) < abs(theArgument)"
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|len1 "{ Class: SmallInteger }"
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len2 "{ Class: SmallInteger }"
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d1 "{ Class: SmallInteger }"
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d2 "{ Class: SmallInteger }"
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otherDigits |
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len1 := digitArray size.
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otherDigits := aLargeInteger digits.
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len2 := otherDigits size.
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405 |
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[(digitArray basicAt:len1) == 0] whileTrue:[
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len1 := len1 - 1
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].
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[(otherDigits basicAt:len2) == 0] whileTrue:[
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len2 := len2 - 1
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].
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412 |
(len1 < len2) ifTrue:[^ true].
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(len1 > len2) ifTrue:[^ false].
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414 |
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[len1 > 0] whileTrue:[
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416 |
d1 := digitArray basicAt:len1.
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d2 := otherDigits basicAt:len1.
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(d1 < d2) ifTrue:[^ true].
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(d1 > d2) ifTrue:[^ false].
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len1 := len1 - 1
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].
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^ false
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423 |
!
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424 |
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425 |
absPlus:aLargeInteger
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426 |
"return a LargeInteger representing abs(self) + abs(theArgument)"
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427 |
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428 |
|result done otherDigits resultDigits
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429 |
len1 "{ Class: SmallInteger }"
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430 |
len2 "{ Class: SmallInteger }"
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431 |
index "{ Class: SmallInteger }"
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432 |
carry "{ Class: SmallInteger }"
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433 |
sum "{ Class: SmallInteger }" |
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434 |
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435 |
len1 := digitArray size.
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436 |
otherDigits := aLargeInteger digits.
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437 |
len2 := otherDigits size.
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438 |
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439 |
result := LargeInteger basicNew
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440 |
numberOfDigits:((len1 max: len2) + 1).
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result sign:1.
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442 |
resultDigits := result digits.
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443 |
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444 |
index := 1.
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445 |
carry := 0.
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446 |
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447 |
done := false.
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448 |
[done] whileFalse:[
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449 |
sum := carry.
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450 |
(index <= len1) ifTrue:[
|
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451 |
sum := sum + (digitArray basicAt:index).
|
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452 |
(index <= len2) ifTrue:[
|
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453 |
sum := sum + (otherDigits basicAt:index)
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]
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455 |
] ifFalse:[
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456 |
(index <= len2) ifTrue:[
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457 |
sum := sum + (otherDigits basicAt:index)
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458 |
] ifFalse:[
|
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459 |
"end reached"
|
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460 |
done := true
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461 |
]
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].
|
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463 |
(sum > 9999) ifTrue:[
|
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464 |
carry := 1.
|
|
465 |
sum := sum - 10000
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466 |
] ifFalse:[
|
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467 |
carry := 0
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468 |
].
|
|
469 |
resultDigits basicAt:index put:sum.
|
|
470 |
index := index + 1
|
|
471 |
].
|
|
472 |
^ result normalize
|
|
473 |
!
|
|
474 |
|
|
475 |
absMinus:aLargeInteger
|
|
476 |
"return a LargeInteger representing abs(self) - abs(theArgument)"
|
|
477 |
|
|
478 |
|result done
|
|
479 |
otherDigits resultDigits
|
|
480 |
len1 "{ Class: SmallInteger }"
|
|
481 |
len2 "{ Class: SmallInteger }"
|
|
482 |
index "{ Class: SmallInteger }"
|
|
483 |
borrow "{ Class: SmallInteger }"
|
|
484 |
diff "{ Class: SmallInteger }"
|
|
485 |
sum "{ Class: SmallInteger }"
|
|
486 |
carry "{ Class: SmallInteger }" |
|
|
487 |
|
|
488 |
len1 := digitArray size.
|
|
489 |
otherDigits := aLargeInteger digits.
|
|
490 |
len2 := otherDigits size.
|
|
491 |
|
|
492 |
result := LargeInteger basicNew
|
|
493 |
numberOfDigits:((len1 max: len2) + 1).
|
|
494 |
result sign:1.
|
|
495 |
resultDigits := result digits.
|
|
496 |
|
|
497 |
index := 1.
|
|
498 |
borrow := 0.
|
|
499 |
|
|
500 |
done := false.
|
|
501 |
[done] whileFalse:[
|
|
502 |
diff := borrow.
|
|
503 |
(index <= len1) ifTrue:[
|
|
504 |
diff := diff + (digitArray basicAt:index).
|
|
505 |
(index <= len2) ifTrue:[
|
|
506 |
diff := diff - (otherDigits basicAt:index)
|
|
507 |
]
|
|
508 |
] ifFalse:[
|
|
509 |
(index <= len2) ifTrue:[
|
|
510 |
diff := diff - (otherDigits basicAt:index)
|
|
511 |
] ifFalse:[
|
|
512 |
"end reached"
|
|
513 |
done := true
|
|
514 |
]
|
|
515 |
].
|
|
516 |
(diff < 0) ifTrue:[
|
|
517 |
borrow := -1.
|
|
518 |
diff := diff + 10000
|
|
519 |
] ifFalse:[
|
|
520 |
borrow := 0
|
|
521 |
].
|
|
522 |
resultDigits basicAt:index put:diff.
|
|
523 |
index := index + 1
|
|
524 |
].
|
|
525 |
(borrow ~~ 0) ifTrue:[
|
|
526 |
result sign: -1.
|
|
527 |
carry := 0.
|
|
528 |
1 to:(index - 1) do:[:i |
|
|
529 |
sum := ((resultDigits at:i) + carry - 10000) negated.
|
|
530 |
resultDigits at:i put:sum.
|
|
531 |
carry := 1
|
|
532 |
]
|
|
533 |
].
|
|
534 |
^ result normalize
|
|
535 |
!
|
|
536 |
|
|
537 |
absMul:aLargeInteger
|
|
538 |
"return a LargeInteger representing abs(self) * abs(theArgument)"
|
|
539 |
|
|
540 |
|result otherDigits resultDigits
|
|
541 |
len1 "{ Class: SmallInteger }"
|
|
542 |
len2 "{ Class: SmallInteger }"
|
|
543 |
dstIndex "{ Class: SmallInteger }"
|
|
544 |
carry "{ Class: SmallInteger }"
|
|
545 |
prod "{ Class: SmallInteger }" |
|
|
546 |
|
|
547 |
len1 := digitArray size.
|
|
548 |
otherDigits := aLargeInteger digits.
|
|
549 |
len2 := otherDigits size.
|
|
550 |
|
|
551 |
result := LargeInteger basicNew numberOfDigits:(len1 + len2 + 1).
|
|
552 |
result sign:1.
|
|
553 |
resultDigits := result digits.
|
|
554 |
|
|
555 |
"clear result"
|
|
556 |
resultDigits atAllPut:0.
|
|
557 |
|
|
558 |
1 to:len1 do:[:index1 |
|
|
559 |
1 to:len2 do:[:index2 |
|
|
560 |
dstIndex := index1 + index2 - 1.
|
|
561 |
prod := (digitArray basicAt:index1) * (otherDigits basicAt:index2).
|
|
562 |
prod := prod + (resultDigits basicAt:dstIndex).
|
|
563 |
resultDigits basicAt:dstIndex put:(prod \\ 10000).
|
|
564 |
carry := prod // 10000.
|
|
565 |
(carry ~~ 0) ifTrue:[
|
|
566 |
resultDigits basicAt:(dstIndex + 1)
|
|
567 |
put:(resultDigits basicAt:(dstIndex + 1)) + carry
|
|
568 |
]
|
|
569 |
]
|
|
570 |
].
|
|
571 |
^ result normalize
|
|
572 |
!
|
|
573 |
|
|
574 |
absDiv:anInteger
|
|
575 |
"return an array with two LargeIntegers representing
|
|
576 |
abs(self) // abs(theArgument) and abs(self) \\ abs(theArgument)"
|
|
577 |
|
|
578 |
|tmp1 tmp2
|
|
579 |
rem
|
|
580 |
count "{ Class: SmallInteger }"
|
|
581 |
digit "{ Class: SmallInteger }" |
|
|
582 |
|
|
583 |
self == 0 ifTrue:[^ 0].
|
|
584 |
anInteger == 0 ifTrue:[^ self divideByZeroError].
|
|
585 |
|
|
586 |
self < anInteger ifTrue:[
|
|
587 |
^ Array with:0 with:self
|
|
588 |
].
|
|
589 |
|
|
590 |
tmp1 := self deepCopy.
|
|
591 |
tmp2 := anInteger deepCopy.
|
|
592 |
count := 0.
|
|
593 |
[tmp2 < tmp1] whileTrue:[
|
|
594 |
tmp2 mul10.
|
|
595 |
count := count + 1
|
|
596 |
].
|
|
597 |
|
|
598 |
tmp2 div10.
|
|
599 |
|
|
600 |
rem := 0 asLargeInteger.
|
|
601 |
[count == 0] whileFalse:[
|
|
602 |
digit := 0.
|
|
603 |
[tmp1 >= tmp2] whileTrue:[
|
|
604 |
digit := digit + 1.
|
|
605 |
tmp1 := tmp1 - tmp2
|
|
606 |
].
|
|
607 |
rem := rem * 10 + digit.
|
|
608 |
tmp2 div10.
|
|
609 |
count := count - 1
|
|
610 |
].
|
|
611 |
^ Array with:rem with:tmp1
|
|
612 |
!
|
|
613 |
|
|
614 |
mul10
|
|
615 |
"destructively multiply the receiver by 10.
|
|
616 |
private - used for division only"
|
|
617 |
|
|
618 |
|carry "{ Class: SmallInteger }"
|
|
619 |
prod "{ Class: SmallInteger }"|
|
|
620 |
|
|
621 |
carry := 0.
|
|
622 |
1 to:(digitArray size) do:[:index |
|
|
623 |
prod := (digitArray at:index) * 10 + carry.
|
|
624 |
digitArray at:index put:prod \\ 10000.
|
|
625 |
carry := prod // 10000
|
|
626 |
].
|
|
627 |
carry ~~ 0 ifTrue:[
|
|
628 |
digitArray := digitArray copyWith:carry
|
|
629 |
]
|
|
630 |
!
|
|
631 |
|
|
632 |
div10
|
|
633 |
"destructively divide the receiver by 10.
|
|
634 |
private - used for division only"
|
|
635 |
|
|
636 |
|nDigits|
|
|
637 |
|
|
638 |
nDigits := digitArray size.
|
|
639 |
1 to:(nDigits - 1) do:[:index |
|
|
640 |
digitArray at:index put:((digitArray at:index) // 10
|
|
641 |
+ ((digitArray at:index + 1) \\ 10 * 1000))
|
|
642 |
].
|
|
643 |
digitArray at:nDigits put:(digitArray at:nDigits) // 10
|
|
644 |
!
|
|
645 |
|
|
646 |
normalize
|
|
647 |
"if the receiver can be represented as a SmallInteger, return
|
|
648 |
a SmallInteger with my value; otherwise return self with leading
|
|
649 |
zeros removed"
|
|
650 |
|
|
651 |
|index "{ Class: SmallInteger }" |
|
|
652 |
|
|
653 |
index := digitArray size.
|
|
654 |
[(index > 0) and:[(digitArray at:index) == 0]] whileTrue:[
|
|
655 |
index := index - 1
|
|
656 |
].
|
|
657 |
(index == 1) ifTrue:[
|
|
658 |
^ (digitArray at:1) * sign
|
|
659 |
].
|
|
660 |
(index == 2) ifTrue:[
|
|
661 |
^ ((digitArray at:2) * 10000 + (digitArray at:1)) * sign
|
|
662 |
].
|
|
663 |
(index == 0) ifTrue:[
|
|
664 |
^ 0
|
|
665 |
].
|
|
666 |
(index ~~ digitArray size) ifTrue:[
|
|
667 |
digitArray := digitArray copyFrom:1 to:index
|
|
668 |
].
|
|
669 |
^ self
|
|
670 |
!
|
|
671 |
|
|
672 |
digits
|
|
673 |
^ digitArray
|
|
674 |
!
|
|
675 |
|
|
676 |
numberOfDigits
|
|
677 |
^ digitArray size
|
|
678 |
!
|
|
679 |
|
|
680 |
numberOfDigits:nDigits
|
|
681 |
digitArray := Array new:nDigits
|
|
682 |
!
|
|
683 |
|
|
684 |
sign:aNumber
|
|
685 |
sign := aNumber
|
|
686 |
! !
|
|
687 |
|
|
688 |
!LargeInteger methodsFor:'printing & storing'!
|
|
689 |
|
|
690 |
storeString
|
|
691 |
"return a string representation of the receiver, which can be
|
|
692 |
used to reconstruct the receiver"
|
|
693 |
|
|
694 |
^ self printString , ' asLargeInteger'
|
|
695 |
!
|
|
696 |
|
|
697 |
printString
|
|
698 |
|aString index fourDigits n|
|
|
699 |
|
|
700 |
index := digitArray size.
|
|
701 |
[(index > 1) and:[(digitArray at:index) == 0]] whileTrue:[
|
|
702 |
index := index - 1
|
|
703 |
].
|
|
704 |
(sign == 0) ifTrue: [^ '0'].
|
|
705 |
(sign == -1) ifTrue: [
|
|
706 |
aString := '-'
|
|
707 |
] ifFalse: [
|
|
708 |
aString := ''
|
|
709 |
].
|
|
710 |
|
|
711 |
aString := aString , (digitArray basicAt:index) printString.
|
|
712 |
index := index - 1.
|
|
713 |
[index > 0] whileTrue:[
|
|
714 |
fourDigits := (digitArray basicAt:index) printString.
|
|
715 |
n := fourDigits size.
|
|
716 |
(n < 4) ifTrue:[
|
|
717 |
aString := aString , ('000' copyFrom:n to:3)
|
|
718 |
].
|
|
719 |
aString := aString , fourDigits.
|
|
720 |
index := index - 1
|
|
721 |
].
|
|
722 |
^ aString
|
|
723 |
! !
|