"

     this comes from:

     Jan Steinman, Bytesmiths

     2002 Parkside Court, West Linn, OR 97068-2767 USA, +1 503 657 7703

     Friedlistrasse 19, CH-3006, Bern, Switzerland, +41 31 999 3946

     this code was published in comp.lang.smalltalk; 

     added here as an example ...

"

Fraction subclass:#FixedPoint

	instanceVariableNames:'scale'

	classVariableNames:''

	poolDictionaries:''

	category:'Magnitude-Numbers'

!

FixedPoint comment:'

Description: This class implements infinite precision fixed-point numbers. 

It doesn''t really do anything too interesting except creating instances, converting, and printing, 

since its superclass Fraction does all the work.

Test: "''123456789012345678901234567890.123456789'' asFixed * 1000000000 = 123456789012345678901234567890123456789"

Notes: 1) The current implementation does not convert arbitrarily-based String representations, 

	  which shouldn''t be too much a problem for financial types.'!

!FixedPoint class methodsFor:'documentation'!

copyright

"

     this comes from:

     Jan Steinman, Bytesmiths

     2002 Parkside Court, West Linn, OR 97068-2767 USA, +1 503 657 7703

     Friedlistrasse 19, CH-3006, Bern, Switzerland, +41 31 999 3946

     this code was published in comp.lang.smalltalk; 

     added here as an example ...

"

!

documentation

"

    Description: This class implements infinite precision fixed-point numbers,

    which internally hold exact (fractional) results, but print themself with

    a limited number of digits after the decimal point. 

    These can be used in computation, where rounding errors should not accumulate,

    but only a limited precision is required for the final result.

    (i.e. business applications)

    It doesn't really do anything too interesting except creating instances, 

    converting, and printing, since its superclass Fraction does all the work.

    Test: 

        '123456789012345678901234567890.123456789' asFixed * 1000000000

        -> 123456789012345678901234567890123456789'

    Notes: 1) The current implementation does not convert arbitrarily-based 

              String representations, which shouldn't be too much a problem 

              for financial types.

           2) the implementation is a hack - it has not been optimized for speed

              in particular.

    Mixed mode arithmetic:

        fix op fix       -> fix, scale is max. of operands

        fix op fraction  -> fix; scale is fix's scale

        fix op integer   -> fix; scale is fix's scale

        fix op float     -> float

    [author:]

        Jan Steinman, Bytesmiths

        modified & enhanced by Claus Gittinger

    [see also:]

        Integer Float Number Fraction

"

!

examples

"

                                                                [exBegin]

     |a b r|

     a := (FixedPoint fromString:'123.456').

     b := (FixedPoint fromString:'1.10').

     r := a + b.

     Transcript showCR:r.

     Transcript showCR:(r withScale:2).

     Transcript showCR:(r withScale:1).

     Transcript showCR:(r rounded).

                                                                [exEnd]

                                                                [exBegin]

     |a b r|

     a := (FixedPoint fromString:'0.9999999').

     b := (FixedPoint fromString:'0.0000001').

     r := a + b.

     Transcript showCR:r.

     Transcript showCR:(r withScale:2).

     Transcript showCR:(r withScale:1).

     Transcript showCR:(r rounded).

                                                                [exEnd]

                                                                [exBegin]

     |a b r|

     a := (FixedPoint fromString:'0.9999998').

     b := (FixedPoint fromString:'0.0000001').

     r := a + b.

     Transcript showCR:r.

     Transcript showCR:(r withScale:2).

     Transcript showCR:(r withScale:1).

     Transcript showCR:(r rounded).

                                                                [exEnd]

                                                                [exBegin]

     |a b r|

     a := (FixedPoint fromString:'1.0').

     b := (FixedPoint fromString:'0.0000001').

     r := a + b.

     Transcript showCR:r.

     Transcript showCR:(r withScale:2).

     Transcript showCR:(r withScale:1).

     Transcript showCR:(r rounded).

                                                                [exEnd]

                                                                [exBegin]

     |a b r|

     a := (FixedPoint fromString:'0.99').

     b := (FixedPoint fromString:'0.0000001').

     r := a + b.

     Transcript showCR:r.

     Transcript showCR:(r withScale:2).

     Transcript showCR:(r withScale:1).

     Transcript showCR:(r rounded).

                                                                [exEnd]

"

! !

!FixedPoint class methodsFor:'instance creation'!

fromString: fixedPointString

    "Answer a new instance of the receiver which is an interpretation of the digits found in <fixedPointString>."

    ^self readFrom: (ReadStream on: fixedPointString)

    "

     Fixed fromString:'123.456'

    "

!

numerator:n denominator:d scale:s

    ^ self basicNew

        setNumerator:n

        denominator:d

        scale:s

!

readFrom:aStream 

    "return an instance of me as described on the stream, aStream."

    | sign integerPart fractionStream char fractionPart scale |

    aStream peek == $- ifTrue:[

        sign := -1.

        aStream next.

    ] ifFalse:[

        sign := 1

    ].

    (aStream atEnd or:[aStream peek isLetter]) ifTrue: [^0].

    integerPart := (aStream upTo:$.) asNumber.

    (aStream atEnd or: [aStream peek isLetter]) ifTrue: [^integerPart].

    fractionStream := ReadWriteStream on:(String new: 10).

    [

        char := aStream next.

        char ~~ nil and:[char isDigit]

    ] whileTrue:[

        fractionStream nextPut:char

    ].

    scale := fractionStream contents size.

    fractionPart := Number readFromString:(fractionStream contents).

    ^ self basicNew 

        setNumerator:(integerPart * (10 raisedTo:scale) + fractionPart) * sign

        scale:scale

    "

     Fixed readFrom:('123.456' readStream) 

     Fixed readFrom:('-123.456' readStream) 

    "

! !

!FixedPoint methodsFor:'accessing'!

scale

    "Return the number of places of significance that is carried by the receiver."

    ^ scale

! !

!FixedPoint methodsFor:'arithmetic'!

* aNumber

    "return the product of the receiver and the argument, aNumber.

     Redefined to care for the scale if the argument is another fixPoint number.

     The results scale is the maximum of the receivers scale and the arguments

     scale."

    |n d sMax|

    (aNumber isMemberOf:SmallInteger) ifTrue:[

        ^ self class 

                numerator:(numerator * aNumber)

                denominator:denominator

                scale:scale

    ].

    (aNumber isMemberOf:self class) ifTrue:[

        n := numerator * aNumber numerator.

        d := denominator * aNumber denominator.

        sMax := scale max:aNumber scale.

        ^ self class 

            numerator:n 

            denominator:d

            scale:sMax

    ].

    ^ aNumber productFromFixedPoint:self

    "                       

     |a r|

     a := (FixedPoint fromString:'123.456').

     r := a * 5.    

     Transcript showCR:r.    

     Transcript showCR:(r withScale:2).

    "

    "                       

     |a b r|

     a := (FixedPoint fromString:'123.456').

     b := (FixedPoint fromString:'1.10').

     r := a * b.    

     Transcript showCR:r.    

     Transcript showCR:(r withScale:2).

    "

    "                       

     |a b r|

     a := (FixedPoint fromString:'123.456').

     b := (FixedPoint fromString:'-1.10').

     r := a * b.    

     Transcript showCR:r.    

     Transcript showCR:(r withScale:2).

    "

    "

     |a b r|

     a := (FixedPoint fromString:'0.9999999').

     b := (FixedPoint fromString:'0.9999999').

     r := a * b.    

     Transcript show:'fixed (exact)  : '; showCR:r.    

     Transcript show:'fixed (scale2) : '; showCR:(r withScale:2).

     Transcript show:'float (inexact): '; showCR:(0.9999999 * 0.9999999).

    "

    "

     |a b r|

     a := 1.

     b := (FixedPoint fromString:'0.9999999').

     r := a * b.    

     Transcript show:'fixed (exact)  : '; showCR:r.    

     Transcript show:'fixed (scale2) : '; showCR:(r withScale:2).

     Transcript show:'float (inexact): '; showCR:(0.9999999 * 0.9999999).

    "

!

+ aNumber

    "return the sum of the receiver and the argument, aNumber.

     Redefined to care for the scale if the argument is another fixPoint number.

     The resulting scale will be the maximum of the receivers and the

     arguments scale."

    |n d sMax|

    (aNumber isMemberOf:self class) ifTrue:[

        n := aNumber numerator.

        d := aNumber denominator.

        sMax := scale max:aNumber scale.

        "save a multiplication if possible"

        denominator == d ifTrue:[

            ^ self class 

                numerator:(numerator + n) 

                denominator:d

                scale:sMax

        ].

        ^ self class 

                numerator:((numerator * d) + (n * denominator))

                denominator:(denominator * d)

                scale:sMax

    ].

    ^ aNumber sumFromFixedPoint:self

    "

     |a b|

     a := (FixedPoint fromString:'123.456').

     b := (FixedPoint fromString:'1.10').

     a + b

    "

    "

     |a b|

     a := (FixedPoint fromString:'0.9999999').

     b := (FixedPoint fromString:'0.0000001').

     a + b                   

    "

    "

     |a b|

     a := (FixedPoint fromString:'0.99').

     b := (FixedPoint fromString:'0.0000001').

     a + b                             

    "

    "

     |a b|

     a := (FixedPoint fromString:'0.99').

     b := (FixedPoint fromString:'0.0000001').

     (a + b) withScale:2  

    "

    "

     |a b|

     a := (FixedPoint fromString:'0.99').

     b := (FixedPoint fromString:'0.0000001').

     (a + b) withScale:1  

    "

    "

     |a b|

     a := 1.

     b := (FixedPoint fromString:'0.0000001').

     Transcript showCR:((a + b) withScale:1).

     Transcript showCR:(a + b)

    "

!

- aNumber

    "return the difference of the receiver and the argument, aNumber.

     Redefined to care for the scale if the argument is another fixPoint number.

     The results scale is the maximum of the receivers scale and the arguments

     scale."

    |n d sMax|

    (aNumber isMemberOf:self class) ifTrue:[

        n := aNumber numerator.

        d := aNumber denominator.

        sMax := scale max:aNumber scale.

        "save a multiplication if possible"

        denominator == d ifTrue:[

            ^ self class 

                numerator:(numerator - n) 

                denominator:d

                scale:sMax

        ].

        ^ self class 

                numerator:((numerator * d) - (n * denominator))

                denominator:(denominator * d)

                scale:sMax

    ].

    ^ aNumber differenceFromFixedPoint:self

    "

     |a b|

     a := (FixedPoint fromString:'123.456').

     b := (FixedPoint fromString:'1.10').

     a - b    

    "

    "

     |a b|

     a := (FixedPoint fromString:'0.9999999').

     b := (FixedPoint fromString:'0.0000009').

     a - b                   

    "

    "

     |a b|

     a := (FixedPoint fromString:'0.99').

     b := (FixedPoint fromString:'0.0000001').

     a - b                          

    "

    "

     |a b|

     a := (FixedPoint fromString:'0.99').

     b := (FixedPoint fromString:'0.0000001').

     (a - b) withScale:2  

    "

    "

     |a b|

     a := (FixedPoint fromString:'0.99').

     b := (FixedPoint fromString:'0.0000001').

     (a - b) withScale:1  

    "

    "

     |a b|

     a := (FixedPoint fromString:'0.0000001').

     b := (FixedPoint fromString:'0.99').

     (a - b) withScale:2   

    "

    "

     |a b|

     a := 1.

     b := (FixedPoint fromString:'0.0000001').

     Transcript showCR:((a - b) withScale:1).

     Transcript showCR:(a - b)

    "

!

/ aNumber

    "return the quotient of the receiver and the argument, aNumber.

     Redefined to care for the scale if the argument is another fixPoint number.

     The results scale is the maximum of the receivers scale and the arguments

     scale."

    |n d sMax|

    (aNumber isMemberOf:SmallInteger) ifTrue:[

        ^ (self class 

                numerator:numerator

                denominator:(denominator * aNumber)

                scale:scale) reduced

    ].

    (aNumber isMemberOf:self class) ifTrue:[

        n := numerator * aNumber denominator.

        d := denominator * aNumber numerator.

        sMax := scale max:aNumber scale.

        ^ (self class 

            numerator:n 

            denominator:d

            scale:sMax) reduced

    ].

    ^ aNumber quotientFromFixedPoint:self

    "                       

     |a r|                     

     a := (FixedPoint fromString:'123.456').

     r := a / 5.    

     Transcript showCR:r.    

     Transcript showCR:(r withScale:2).

     Transcript showCR:(r withScale:9).

    "

    "                       

     |a b r|

     a := (FixedPoint fromString:'123.456').

     b := (FixedPoint fromString:'1.10').

     r := a / b.    

     Transcript showCR:r.    

     Transcript showCR:(r withScale:2).

    "

    "                       

     |a b r|

     a := (FixedPoint fromString:'-123.456').

     b := (FixedPoint fromString:'-1.10').

     r := a / b.    

     Transcript showCR:r.    

     Transcript showCR:(r withScale:2).

    "

    "                       

     |a b r|

     a := (FixedPoint fromString:'123.456').

     b := (FixedPoint fromString:'-1.10').

     r := a / b.    

     Transcript showCR:r.    

     Transcript showCR:(r withScale:2).