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"
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This is public domain code, not covered by the ST/X copyright.
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Code is provided 'as is', as a goody, without any warranty.
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this comes from:
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Jan Steinman, Bytesmiths
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2002 Parkside Court, West Linn, OR 97068-2767 USA, +1 503 657 7703
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Friedlistrasse 19, CH-3006, Bern, Switzerland, +41 31 999 3946
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this code was published in comp.lang.smalltalk;
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added here as an example ...
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"
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'From Smalltalk/X, Version:3.2.1 on 25-oct-1997 at 9:23:36 pm' !
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1886
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Fraction subclass:#FixedPoint
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instanceVariableNames:'scale'
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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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FixedPoint comment:'
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Description: This class implements infinite precision fixed-point numbers.
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It doesn''t really do anything too interesting except creating instances, converting, and printing,
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since its superclass Fraction does all the work.
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Test: "''123456789012345678901234567890.123456789'' asFixed * 1000000000 = 123456789012345678901234567890123456789"
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Notes: 1) The current implementation does not convert arbitrarily-based String representations,
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which shouldn''t be too much a problem for financial types.'!
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!FixedPoint class methodsFor:'documentation'!
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copyright
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"
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3060
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This is public domain code, not covered by the ST/X copyright.
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Code is provided 'as is', as a goody, without any warranty.
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1886
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this comes from:
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Jan Steinman, Bytesmiths
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2002 Parkside Court, West Linn, OR 97068-2767 USA, +1 503 657 7703
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Friedlistrasse 19, CH-3006, Bern, Switzerland, +41 31 999 3946
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this code was published in comp.lang.smalltalk;
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added here as an example ...
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"
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!
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documentation
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"
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Description: This class implements infinite precision fixed-point numbers,
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which internally hold exact (fractional) results, but print themself with
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a limited number of digits after the decimal point.
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These can be used in computation, where rounding errors should not accumulate,
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but only a limited precision is required for the final result.
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1898
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(i.e. business applications)
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It doesn't really do anything too interesting except creating instances,
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converting, and printing, since its superclass Fraction does all the work.
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Test:
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'123456789012345678901234567890.123456789' asFixedPoint * 1000000000
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-> 123456789012345678901234567890123456789'
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Notes: 1) The current implementation does not convert arbitrarily-based
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String representations, which shouldn't be too much a problem
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for financial types.
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2) the implementation is a hack - it has not been optimized for speed
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in particular.
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1892
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Mixed mode arithmetic:
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fix op fix -> fix, scale is max. of operands
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fix op fraction -> fix; scale is fix's scale
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fix op integer -> fix; scale is fix's scale
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fix op float -> float
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[author:]
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Jan Steinman, Bytesmiths
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adapted, modified & enhanced by Claus Gittinger
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1886
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[see also:]
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1893
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Integer Float Number Fraction
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1886
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"
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!
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examples
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"
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[exBegin]
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|a b r|
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a := (FixedPoint fromString:'123.456').
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b := '1.10' asFixedPoint.
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r := a + b.
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Transcript showCR:r.
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Transcript showCR:(r withScale:2).
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Transcript showCR:(r withScale:1).
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Transcript showCR:(r rounded).
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[exEnd]
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[exBegin]
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|a b r|
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a := (FixedPoint fromString:'0.9999999').
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b := 0.0000001 asFixedPoint.
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r := a + b.
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Transcript showCR:r.
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Transcript showCR:(r withScale:2).
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Transcript showCR:(r withScale:1).
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Transcript showCR:(r rounded).
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[exEnd]
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[exBegin]
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|a b r|
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a := (FixedPoint fromString:'0.9999998').
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b := (FixedPoint fromString:'0.0000001').
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r := a + b.
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Transcript showCR:r.
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Transcript showCR:(r withScale:2).
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Transcript showCR:(r withScale:1).
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Transcript showCR:(r rounded).
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[exEnd]
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[exBegin]
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|a b r|
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a := (FixedPoint fromString:'1.0').
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b := (FixedPoint fromString:'0.0000001').
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r := a + b.
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Transcript showCR:r.
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Transcript showCR:(r withScale:2).
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Transcript showCR:(r withScale:1).
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Transcript showCR:(r rounded).
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[exEnd]
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[exBegin]
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|a b r|
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a := (FixedPoint fromString:'0.99').
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b := (FixedPoint fromString:'0.0000001').
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r := a + b.
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Transcript showCR:r.
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Transcript showCR:(r withScale:2).
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Transcript showCR:(r withScale:1).
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Transcript showCR:(r rounded).
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[exEnd]
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"
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! !
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!FixedPoint class methodsFor:'instance creation'!
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numerator:n denominator:d scale:s
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^ self basicNew
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setNumerator:n
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denominator:d
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scale:s
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!
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readFrom:aStringOrStream
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"return the next FixedPoint from the (character-)stream aStream.
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NOTICE:
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This behaves different from the default readFrom:, in returning
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0 (instead of raising an error) in case no number can be read.
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It is unclear, if this is the correct behavior (ST-80 does this)
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- depending on the upcoming ANSI standard, this may change."
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^ self readFrom:aStringOrStream onError:0
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"
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FixedPoint readFrom:(ReadStream on:'foobar')
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FixedPoint readFrom:(ReadStream on:'foobar') onError:nil
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"
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"Modified: / 25.10.1997 / 15:30:29 / cg"
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!
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readFrom:aStringOrStream onError:exceptionBlock
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"return an instance of me as described on the string or stream, aStringOrStream.
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If an error occurs during conversion, return the result
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from evaluating exceptionBlock"
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| aStream sign integerPart fractionStream char fractionPart scale |
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aStream := aStringOrStream readStream.
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aStream peek == $- ifTrue:[
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sign := -1.
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aStream next.
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] ifFalse:[
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sign := 1
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].
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(aStream atEnd or:[aStream peek isLetter]) ifTrue: [^ exceptionBlock value].
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integerPart := (aStream upTo:$.) asNumber.
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(aStream atEnd or: [aStream peek isLetter]) ifTrue: [
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fractionPart := 0.
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scale := 1.
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] ifFalse:[
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fractionStream := WriteStream on:(String new: 10).
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[
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char := aStream next.
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char ~~ nil and:[char isDigit]
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] whileTrue:[
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fractionStream nextPut:char
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].
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scale := fractionStream contents size.
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fractionPart := Number readFromString:(fractionStream contents) onError:exceptionBlock.
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].
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^ self basicNew
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setNumerator:(integerPart * (10 raisedTo:scale) + fractionPart) * sign
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scale:scale
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"
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FixedPoint readFrom:'123.456'
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FixedPoint readFrom:'-123.456'
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FixedPoint readFrom:'123'
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FixedPoint readFrom:'-123'
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1886
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"
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3060
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"Created: / 25.10.1997 / 15:28:59 / cg"
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"Modified: / 25.10.1997 / 15:31:47 / cg"
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! !
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!FixedPoint methodsFor:'accessing'!
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scale
|
2538
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"return the number of places of significance that is carried by the receiver."
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^ scale
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2538
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"Modified: 12.4.1997 / 11:21:05 / cg"
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! !
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!FixedPoint methodsFor:'arithmetic'!
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* aNumber
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"return the product of the receiver and the argument, aNumber.
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Redefined to care for the scale if the argument is another fixPoint number.
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The results scale is the maximum of the receivers scale and the arguments
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scale."
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|n d sMax|
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(aNumber isMemberOf:SmallInteger) ifTrue:[
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^ self class
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numerator:(numerator * aNumber)
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denominator:denominator
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scale:scale
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].
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(aNumber isMemberOf:self class) ifTrue:[
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n := numerator * aNumber numerator.
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d := denominator * aNumber denominator.
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sMax := scale max:aNumber scale.
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^ self class
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numerator:n
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denominator:d
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scale:sMax
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].
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^ aNumber productFromFixedPoint:self
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"
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|a r|
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|
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a := (FixedPoint fromString:'123.456').
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r := a * 5.
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Transcript showCR:r.
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Transcript showCR:(r withScale:2).
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"
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"
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|a b r|
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282 |
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a := (FixedPoint fromString:'123.456').
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b := (FixedPoint fromString:'1.10').
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r := a * b.
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|
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Transcript showCR:r.
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Transcript showCR:(r withScale:2).
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"
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289 |
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|
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"
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|a b r|
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|
292 |
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|
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a := (FixedPoint fromString:'123.456').
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|
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b := (FixedPoint fromString:'-1.10').
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|
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r := a * b.
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|
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Transcript showCR:r.
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|
297 |
Transcript showCR:(r withScale:2).
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"
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|
299 |
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|
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"
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|a b r|
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302 |
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a := (FixedPoint fromString:'0.9999999').
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|
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b := (FixedPoint fromString:'0.9999999').
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|
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r := a * b.
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Transcript show:'fixed (exact) : '; showCR:r.
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Transcript show:'fixed (scale2) : '; showCR:(r withScale:2).
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308 |
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|
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Transcript show:'float (inexact): '; showCR:(0.9999999 * 0.9999999).
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"
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"
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|a b r|
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314 |
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|
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a := 1.
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b := (FixedPoint fromString:'0.9999999').
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|
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r := a * b.
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Transcript show:'fixed (exact) : '; showCR:r.
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Transcript show:'fixed (scale2) : '; showCR:(r withScale:2).
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Transcript show:'float (inexact): '; showCR:(0.9999999 * 0.9999999).
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"
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!
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+ aNumber
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|
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"return the sum of the receiver and the argument, aNumber.
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329 |
Redefined to care for the scale if the argument is another fixPoint number.
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330 |
The resulting scale will be the maximum of the receivers and the
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331 |
arguments scale."
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|
332 |
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|
333 |
|n d sMax|
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|
334 |
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|
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(aNumber isMemberOf:self class) ifTrue:[
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|
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n := aNumber numerator.
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|
337 |
d := aNumber denominator.
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|
338 |
sMax := scale max:aNumber scale.
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339 |
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|
340 |
"save a multiplication if possible"
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denominator == d ifTrue:[
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|
342 |
^ self class
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|
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numerator:(numerator + n)
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|
344 |
denominator:d
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|
345 |
scale:sMax
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|
346 |
].
|
|
347 |
|
|
348 |
^ self class
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|
349 |
numerator:((numerator * d) + (n * denominator))
|
|
350 |
denominator:(denominator * d)
|
|
351 |
scale:sMax
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|
352 |
].
|
|
353 |
^ aNumber sumFromFixedPoint:self
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|
354 |
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|
355 |
"
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|
356 |
|a b|
|
|
357 |
|
|
358 |
a := (FixedPoint fromString:'123.456').
|
|
359 |
b := (FixedPoint fromString:'1.10').
|
|
360 |
a + b
|
|
361 |
"
|
|
362 |
|
|
363 |
"
|
|
364 |
|a b|
|
|
365 |
|
|
366 |
a := (FixedPoint fromString:'0.9999999').
|
|
367 |
b := (FixedPoint fromString:'0.0000001').
|
|
368 |
a + b
|
|
369 |
"
|
|
370 |
|
|
371 |
"
|
|
372 |
|a b|
|
|
373 |
|
|
374 |
a := (FixedPoint fromString:'0.99').
|
|
375 |
b := (FixedPoint fromString:'0.0000001').
|
|
376 |
a + b
|
|
377 |
"
|
|
378 |
|
|
379 |
"
|
|
380 |
|a b|
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|
381 |
|
|
382 |
a := (FixedPoint fromString:'0.99').
|
|
383 |
b := (FixedPoint fromString:'0.0000001').
|
|
384 |
(a + b) withScale:2
|
|
385 |
"
|
|
386 |
|
|
387 |
"
|
|
388 |
|a b|
|
|
389 |
|
|
390 |
a := (FixedPoint fromString:'0.99').
|
|
391 |
b := (FixedPoint fromString:'0.0000001').
|
|
392 |
(a + b) withScale:1
|
|
393 |
"
|
|
394 |
|
|
395 |
"
|
|
396 |
|a b|
|
|
397 |
|
|
398 |
a := 1.
|
|
399 |
b := (FixedPoint fromString:'0.0000001').
|
|
400 |
Transcript showCR:((a + b) withScale:1).
|
|
401 |
Transcript showCR:(a + b)
|
|
402 |
"
|
|
403 |
|
|
404 |
|
|
405 |
!
|
|
406 |
|
|
407 |
- aNumber
|
|
408 |
"return the difference of the receiver and the argument, aNumber.
|
|
409 |
Redefined to care for the scale if the argument is another fixPoint number.
|
|
410 |
The results scale is the maximum of the receivers scale and the arguments
|
|
411 |
scale."
|
|
412 |
|
|
413 |
|n d sMax|
|
|
414 |
|
|
415 |
(aNumber isMemberOf:self class) ifTrue:[
|
|
416 |
n := aNumber numerator.
|
|
417 |
d := aNumber denominator.
|
|
418 |
sMax := scale max:aNumber scale.
|
|
419 |
|
|
420 |
"save a multiplication if possible"
|
|
421 |
denominator == d ifTrue:[
|
|
422 |
^ self class
|
|
423 |
numerator:(numerator - n)
|
|
424 |
denominator:d
|
|
425 |
scale:sMax
|
|
426 |
].
|
|
427 |
|
|
428 |
^ self class
|
|
429 |
numerator:((numerator * d) - (n * denominator))
|
|
430 |
denominator:(denominator * d)
|
|
431 |
scale:sMax
|
|
432 |
].
|
|
433 |
^ aNumber differenceFromFixedPoint:self
|
|
434 |
|
|
435 |
"
|
|
436 |
|a b|
|
|
437 |
|
|
438 |
a := (FixedPoint fromString:'123.456').
|
|
439 |
b := (FixedPoint fromString:'1.10').
|
|
440 |
a - b
|
|
441 |
"
|
|
442 |
|
|
443 |
"
|
|
444 |
|a b|
|
|
445 |
|
|
446 |
a := (FixedPoint fromString:'0.9999999').
|
|
447 |
b := (FixedPoint fromString:'0.0000009').
|
|
448 |
a - b
|
|
449 |
"
|
|
450 |
|
|
451 |
"
|
|
452 |
|a b|
|
|
453 |
|
|
454 |
a := (FixedPoint fromString:'0.99').
|
|
455 |
b := (FixedPoint fromString:'0.0000001').
|
|
456 |
a - b
|
|
457 |
"
|
|
458 |
|
|
459 |
"
|
|
460 |
|a b|
|
|
461 |
|
|
462 |
a := (FixedPoint fromString:'0.99').
|
|
463 |
b := (FixedPoint fromString:'0.0000001').
|
|
464 |
(a - b) withScale:2
|
|
465 |
"
|
|
466 |
|
|
467 |
"
|
|
468 |
|a b|
|
|
469 |
|
|
470 |
a := (FixedPoint fromString:'0.99').
|
|
471 |
b := (FixedPoint fromString:'0.0000001').
|
|
472 |
(a - b) withScale:1
|
|
473 |
"
|
|
474 |
|
|
475 |
"
|
|
476 |
|a b|
|
|
477 |
|
|
478 |
a := (FixedPoint fromString:'0.0000001').
|
|
479 |
b := (FixedPoint fromString:'0.99').
|
|
480 |
(a - b) withScale:2
|
|
481 |
"
|
|
482 |
|
|
483 |
"
|
|
484 |
|a b|
|
|
485 |
|
|
486 |
a := 1.
|
|
487 |
b := (FixedPoint fromString:'0.0000001').
|
|
488 |
Transcript showCR:((a - b) withScale:1).
|
|
489 |
Transcript showCR:(a - b)
|
|
490 |
"
|
|
491 |
|
|
492 |
!
|
|
493 |
|
|
494 |
/ aNumber
|
1898
|
495 |
"return the quotient of the receiver and the argument, aNumber.
|
1886
|
496 |
Redefined to care for the scale if the argument is another fixPoint number.
|
|
497 |
The results scale is the maximum of the receivers scale and the arguments
|
|
498 |
scale."
|
|
499 |
|
|
500 |
|n d sMax|
|
|
501 |
|
|
502 |
(aNumber isMemberOf:SmallInteger) ifTrue:[
|
|
503 |
^ (self class
|
|
504 |
numerator:numerator
|
|
505 |
denominator:(denominator * aNumber)
|
|
506 |
scale:scale) reduced
|
|
507 |
].
|
|
508 |
|
|
509 |
(aNumber isMemberOf:self class) ifTrue:[
|
|
510 |
n := numerator * aNumber denominator.
|
|
511 |
d := denominator * aNumber numerator.
|
|
512 |
sMax := scale max:aNumber scale.
|
|
513 |
|
|
514 |
^ (self class
|
|
515 |
numerator:n
|
|
516 |
denominator:d
|
|
517 |
scale:sMax) reduced
|
|
518 |
].
|
|
519 |
^ aNumber quotientFromFixedPoint:self
|
|
520 |
|
|
521 |
"
|
|
522 |
|a r|
|
|
523 |
|
|
524 |
a := (FixedPoint fromString:'123.456').
|
|
525 |
r := a / 5.
|
|
526 |
Transcript showCR:r.
|
|
527 |
Transcript showCR:(r withScale:2).
|
|
528 |
Transcript showCR:(r withScale:9).
|
|
529 |
"
|
|
530 |
|
|
531 |
"
|
|
532 |
|a b r|
|
|
533 |
|
|
534 |
a := (FixedPoint fromString:'123.456').
|
|
535 |
b := (FixedPoint fromString:'1.10').
|
|
536 |
r := a / b.
|
|
537 |
Transcript showCR:r.
|
|
538 |
Transcript showCR:(r withScale:2).
|
|
539 |
"
|
|
540 |
|
|
541 |
"
|
|
542 |
|a b r|
|
|
543 |
|
|
544 |
a := (FixedPoint fromString:'-123.456').
|
|
545 |
b := (FixedPoint fromString:'-1.10').
|
|
546 |
r := a / b.
|
|
547 |
Transcript showCR:r.
|
|
548 |
Transcript showCR:(r withScale:2).
|
|
549 |
"
|
|
550 |
|
|
551 |
"
|
|
552 |
|a b r|
|
|
553 |
|
|
554 |
a := (FixedPoint fromString:'123.456').
|
|
555 |
b := (FixedPoint fromString:'-1.10').
|
|
556 |
r := a / b.
|
|
557 |
Transcript showCR:r.
|
|
558 |
Transcript showCR:(r withScale:2).
|
|
559 |
"
|
|
560 |
|
|
561 |
"
|
|
562 |
|a b r|
|
|
563 |
|
|
564 |
a := 1.
|
|
565 |
b := (FixedPoint fromString:'0.9999999').
|
|
566 |
r := a / b.
|
|
567 |
Transcript show:'fixed (exact) : '; showCR:r.
|
|
568 |
Transcript show:'fixed (scale2) : '; showCR:(r withScale:2).
|
|
569 |
|
|
570 |
Transcript show:'float (inexact): '; showCR:(1 / 0.9999999).
|
|
571 |
"
|
|
572 |
! !
|
|
573 |
|
|
574 |
!FixedPoint methodsFor:'coercing & converting'!
|
|
575 |
|
|
576 |
asFixedPoint
|
2140
|
577 |
"return the receiver as a fixedPoint number - thats the receiver itself"
|
1886
|
578 |
|
|
579 |
^ self
|
|
580 |
|
2140
|
581 |
"Modified: 10.1.1997 / 19:53:14 / cg"
|
|
582 |
!
|
|
583 |
|
|
584 |
asFixedPoint:newScale
|
2538
|
585 |
"return a copy of the receiver, with newScale number of post-decimal
|
2140
|
586 |
digits"
|
|
587 |
|
|
588 |
^ self class
|
|
589 |
numerator:numerator
|
|
590 |
denominator:denominator
|
|
591 |
scale:newScale
|
|
592 |
|
|
593 |
"
|
|
594 |
(FixedPoint fromString:'12345.12345') asFixedPoint:2
|
|
595 |
|
|
596 |
((FixedPoint fromString:'0.33333333')
|
|
597 |
+
|
|
598 |
(FixedPoint fromString:'0.33333333')
|
|
599 |
) asFixedPoint:2
|
|
600 |
"
|
|
601 |
|
2538
|
602 |
"Modified: 12.4.1997 / 11:20:37 / cg"
|
1886
|
603 |
!
|
|
604 |
|
|
605 |
asFraction
|
|
606 |
"return the receiver as a fraction"
|
|
607 |
|
|
608 |
^ (Fraction
|
|
609 |
numerator:numerator
|
|
610 |
denominator:denominator) reduced
|
|
611 |
|
|
612 |
"
|
|
613 |
(FixedPoint fromString:'0.2')
|
|
614 |
(FixedPoint fromString:'0.2') asFraction
|
|
615 |
(FixedPoint fromString:'0.2') asFloat
|
|
616 |
(FixedPoint fromString:'0.2') asShortFloat
|
|
617 |
(FixedPoint fromString:'0.2') asInteger
|
|
618 |
"
|
|
619 |
!
|
|
620 |
|
|
621 |
coerce:aNumber
|
|
622 |
"return aNumber converted into receivers type"
|
|
623 |
|
|
624 |
^ aNumber asFixedPoint
|
|
625 |
|
|
626 |
!
|
|
627 |
|
|
628 |
generality
|
|
629 |
"return the generality value - see ArithmeticValue>>retry:coercing:"
|
|
630 |
|
|
631 |
^ 65
|
|
632 |
|
|
633 |
"
|
|
634 |
(FixedPoint fromString:'1.001') + 1
|
|
635 |
(FixedPoint fromString:'1.001') + 1.0
|
|
636 |
(FixedPoint fromString:'1.001') + (1/2)
|
|
637 |
(FixedPoint fromString:'1.001') + 1.0 asShortFloat
|
|
638 |
(FixedPoint fromString:'1.001') + 1 asLargeInteger
|
|
639 |
|
|
640 |
1 + (FixedPoint fromString:'1.001')
|
1892
|
641 |
1.0 + (FixedPoint fromString:'1.001')
|
1891
|
642 |
(1/2) + (FixedPoint fromString:'1.001')
|
1886
|
643 |
1.0 asShortFloat + (FixedPoint fromString:'1.001')
|
|
644 |
1 asLargeInteger + (FixedPoint fromString:'1.001')
|
|
645 |
"
|
2140
|
646 |
!
|
|
647 |
|
|
648 |
withScale:newScale
|
2538
|
649 |
"return a copy of the receiver, with newScale number of post-decimal
|
2140
|
650 |
digits"
|
|
651 |
|
|
652 |
^ self asFixedPoint:newScale
|
|
653 |
|
|
654 |
"
|
|
655 |
(FixedPoint fromString:'12345.12345') withScale:2
|
|
656 |
|
|
657 |
((FixedPoint fromString:'0.33333333')
|
|
658 |
+
|
|
659 |
(FixedPoint fromString:'0.33333333')
|
|
660 |
) withScale:2
|
|
661 |
"
|
|
662 |
|
2538
|
663 |
"Modified: 12.4.1997 / 11:22:09 / cg"
|
1886
|
664 |
! !
|
|
665 |
|
|
666 |
!FixedPoint methodsFor:'double dispatching'!
|
|
667 |
|
|
668 |
differenceFromInteger:anInteger
|
|
669 |
"sent when an integer does not know how to subtract the receiver.
|
|
670 |
Redefined here to preserve the scale."
|
|
671 |
|
|
672 |
^ (self class
|
|
673 |
numerator:((anInteger * denominator) - numerator)
|
|
674 |
denominator:denominator
|
|
675 |
scale:scale) reduced
|
|
676 |
|
|
677 |
!
|
|
678 |
|
|
679 |
productFromInteger:anInteger
|
|
680 |
"sent when an integer does not know how to multiply the receiver.
|
|
681 |
Redefined here to preserve the scale."
|
|
682 |
|
|
683 |
^ (self class
|
|
684 |
numerator:(anInteger * numerator)
|
|
685 |
denominator:denominator
|
|
686 |
scale:scale) reduced
|
|
687 |
|
|
688 |
"Modified: 5.11.1996 / 10:32:28 / cg"
|
|
689 |
|
|
690 |
|
|
691 |
!
|
|
692 |
|
|
693 |
quotientFromInteger:anInteger
|
|
694 |
"sent when an integer does not know how to divide by the receiver.
|
|
695 |
Redefined here to preserve the scale."
|
|
696 |
|
|
697 |
^ (self class
|
|
698 |
numerator:(anInteger * denominator)
|
|
699 |
denominator:numerator
|
|
700 |
scale:scale) reduced
|
|
701 |
|
|
702 |
"Modified: 5.11.1996 / 10:32:35 / cg"
|
|
703 |
|
|
704 |
|
|
705 |
!
|
|
706 |
|
|
707 |
sumFromInteger:anInteger
|
|
708 |
"sent when an integer does not know how to add the receiver.
|
|
709 |
Redefined here to preserve the scale."
|
|
710 |
|
|
711 |
^ (self class
|
|
712 |
numerator:(numerator + (anInteger * denominator))
|
|
713 |
denominator:denominator
|
|
714 |
scale:scale) reduced
|
|
715 |
|
|
716 |
"Modified: 5.11.1996 / 10:32:43 / cg"
|
|
717 |
|
|
718 |
|
|
719 |
! !
|
|
720 |
|
|
721 |
!FixedPoint methodsFor:'printing'!
|
|
722 |
|
|
723 |
printOn: aStream
|
2538
|
724 |
"append to the argument, aStream, a printed representation of the receiver.
|
1886
|
725 |
For printout, only scale post-decimal digits are printed
|
|
726 |
(and the printout is rounded to that many digits)"
|
|
727 |
|
2563
|
728 |
|e integerPart fractionPart negative num|
|
1886
|
729 |
|
|
730 |
numerator < 0 ifTrue:[
|
|
731 |
negative := true.
|
|
732 |
num := numerator negated.
|
|
733 |
] ifFalse:[
|
|
734 |
negative := false.
|
|
735 |
num := numerator.
|
|
736 |
].
|
|
737 |
integerPart := (num // denominator).
|
|
738 |
e := 10 raisedTo:scale.
|
|
739 |
fractionPart := (num \\ denominator).
|
|
740 |
|
|
741 |
"/ the most common case is a denominator fitting the scale
|
|
742 |
"/ (fixedPoint numbers are created this way)
|
|
743 |
|
|
744 |
e == denominator ifFalse:[
|
|
745 |
fractionPart := fractionPart * (e * 10) // denominator.
|
|
746 |
fractionPart := (fractionPart roundTo:10) // 10.
|
|
747 |
|
|
748 |
fractionPart >= e ifTrue:[
|
|
749 |
integerPart := integerPart + 1.
|
|
750 |
fractionPart := 0.
|
|
751 |
]
|
|
752 |
].
|
|
753 |
|
|
754 |
"/
|
|
755 |
"/ add a 1000..., so we can (mis-)use integer-printString ...
|
|
756 |
"/ the highest-1 will be cutoff after padding.
|
|
757 |
"/
|
|
758 |
fractionPart := e + fractionPart.
|
|
759 |
|
|
760 |
negative ifTrue:[
|
|
761 |
aStream nextPut:$-
|
|
762 |
].
|
|
763 |
integerPart printOn:aStream.
|
|
764 |
aStream nextPut: $..
|
|
765 |
((fractionPart printStringPaddedTo:scale with:$0) copyFrom:2) printOn:aStream
|
|
766 |
|
|
767 |
"
|
|
768 |
(FixedPoint fromString:'0.66666666')
|
|
769 |
(FixedPoint fromString:'0.66666666') withScale:2
|
|
770 |
(FixedPoint fromString:'0.99999999')
|
|
771 |
(FixedPoint fromString:'0.99999999') withScale:2
|
|
772 |
(FixedPoint fromString:'1.00000001')
|
|
773 |
(FixedPoint fromString:'1.00000001') withScale:2
|
|
774 |
(FixedPoint fromString:'1.005')
|
|
775 |
(FixedPoint fromString:'1.005') withScale:2
|
|
776 |
(FixedPoint fromString:'1.005') withScale:1
|
|
777 |
|
|
778 |
(FixedPoint fromString:'-0.66666666')
|
|
779 |
(FixedPoint fromString:'-0.66666666') withScale:2
|
|
780 |
(FixedPoint fromString:'-0.99999999')
|
|
781 |
(FixedPoint fromString:'-0.99999999') withScale:2
|
|
782 |
(FixedPoint fromString:'-1.00000001')
|
|
783 |
(FixedPoint fromString:'-1.00000001') withScale:2
|
|
784 |
(FixedPoint fromString:'-1.005')
|
|
785 |
(FixedPoint fromString:'-1.005') withScale:2
|
|
786 |
(FixedPoint fromString:'-1.005') withScale:1
|
|
787 |
(FixedPoint fromString:'-1.05')
|
|
788 |
(FixedPoint fromString:'-1.05') withScale:2
|
|
789 |
(FixedPoint fromString:'-1.05') withScale:1
|
|
790 |
(FixedPoint fromString:'-1.04')
|
|
791 |
(FixedPoint fromString:'-1.04') withScale:2
|
|
792 |
(FixedPoint fromString:'-1.04') withScale:1
|
|
793 |
"
|
|
794 |
|
|
795 |
"
|
|
796 |
|a b r|
|
|
797 |
|
|
798 |
a := (FixedPoint fromString:'0.66666666') withScale:2.
|
|
799 |
b := (FixedPoint fromString:'0.33333333').
|
|
800 |
r := (a + b) withScale:4.
|
|
801 |
Transcript show:'printout with scale of 4 :'; showCR:r.
|
|
802 |
Transcript show:'more precise value :'; showCR:(r withScale:8)
|
|
803 |
"
|
2538
|
804 |
|
|
805 |
"Modified: 12.4.1997 / 11:20:51 / cg"
|
1886
|
806 |
! !
|
|
807 |
|
|
808 |
!FixedPoint methodsFor:'private'!
|
|
809 |
|
|
810 |
reduced
|
|
811 |
|gc|
|
|
812 |
|
|
813 |
scale isNil ifTrue:[
|
|
814 |
"/ to catch inherited Fraction reduce calls
|
|
815 |
self error:'should not happen'.
|
|
816 |
scale := 3
|
|
817 |
].
|
|
818 |
|
|
819 |
denominator == 1 ifTrue:[^ numerator].
|
|
820 |
numerator == 1 ifTrue:[^ self].
|
|
821 |
numerator == 0 ifTrue:[^ 0].
|
|
822 |
|
|
823 |
gc := numerator gcd:denominator.
|
|
824 |
gc := gc gcd:(10 raisedTo:scale).
|
|
825 |
|
|
826 |
(gc == 1) ifFalse:[
|
|
827 |
numerator := numerator // gc.
|
|
828 |
denominator := denominator // gc
|
|
829 |
].
|
|
830 |
|
|
831 |
(numerator < 0) ifTrue:[
|
|
832 |
(denominator < 0) ifTrue:[
|
|
833 |
numerator := numerator negated.
|
|
834 |
denominator := denominator negated
|
|
835 |
]
|
|
836 |
].
|
|
837 |
(denominator == 1) ifTrue:[^ numerator].
|
|
838 |
^ self
|
|
839 |
|
|
840 |
!
|
|
841 |
|
|
842 |
setNumerator:nInteger denominator:d scale:s
|
2538
|
843 |
"initialize the instance variables.
|
|
844 |
Assumes that the fraction as specified by numerator and denominator
|
|
845 |
is already reduced."
|
1886
|
846 |
|
|
847 |
scale := s.
|
|
848 |
super
|
|
849 |
setNumerator:nInteger
|
|
850 |
denominator:d
|
2538
|
851 |
|
|
852 |
"Modified: 12.4.1997 / 11:21:47 / cg"
|
1886
|
853 |
!
|
|
854 |
|
|
855 |
setNumerator:nInteger scale:s
|
2538
|
856 |
"initialize the instance variables.
|
|
857 |
Assumes that the fraction as specified by numerator and denominator
|
|
858 |
is already reduced."
|
1886
|
859 |
|
|
860 |
scale := s.
|
|
861 |
super
|
|
862 |
setNumerator:nInteger
|
|
863 |
denominator:(10 raisedTo:s)
|
2538
|
864 |
|
|
865 |
"Modified: 12.4.1997 / 11:21:55 / cg"
|
1886
|
866 |
!
|
|
867 |
|
|
868 |
setScale:newScale
|
2538
|
869 |
"initialize the scale instance variables."
|
1886
|
870 |
|
|
871 |
scale := newScale.
|
2538
|
872 |
|
|
873 |
"Modified: 12.4.1997 / 11:22:02 / cg"
|
1886
|
874 |
! !
|
|
875 |
|
1891
|
876 |
!FixedPoint methodsFor:'queries'!
|
|
877 |
|
|
878 |
isFixedPoint
|
|
879 |
"return true, if the receiver is some kind of fixedPoint number;
|
|
880 |
true is returned here - the method is redefined from Object."
|
|
881 |
|
|
882 |
^ true
|
|
883 |
|
|
884 |
|
|
885 |
! !
|
|
886 |
|
1886
|
887 |
!FixedPoint class methodsFor:'documentation'!
|
|
888 |
|
|
889 |
version
|
3060
|
890 |
^ '$Header: /cvs/stx/stx/libbasic/FixedPoint.st,v 1.9 1997-10-28 19:11:58 cg Exp $'
|
1886
|
891 |
! !
|