"

     This is public domain code, not covered by the ST/X copyright.

     Code is provided 'as is', as a goody, without any warranty.

     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 ...

"

"{ Package: 'stx:libbasic' }"

Fraction subclass:#FixedPoint

	instanceVariableNames:'scale'

	classVariableNames:'PI_1000'

	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 is public domain code, not covered by the ST/X copyright.

     Code is provided 'as is', as a goody, without any warranty.

     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' asFixedPoint * 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

        adapted, modified & enhanced by Claus Gittinger

    [see also:]

        Integer Float Number Fraction

"

!

examples

"

                                                                [exBegin]

     |a b r|

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

     b := '1.10' asFixedPoint.

     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 := 0.0000001 asFixedPoint. 

     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'!

numerator:n denominator:d 

    self shouldNotImplement. "use #numerator:denominator:scale"

    "/ ^ self numerator:n denominator:d scale:(d log max:n log) ceiling

    "

     self numerator:123 denominator:100    

    "

!

numerator:n denominator:d scale:s

    ^ self basicNew

        setNumerator:n denominator:d scale:s

        "/ ; reduced

!

readFrom:aStringOrStream 

    "return the next FixedPoint from the (character-)stream aStream. 

     NOTICE:   

       This behaves different from the default readFrom:, in returning

       0 (instead of raising an error) in case no number can be read.

       It is unclear, if this is the correct behavior (ST-80 does this)

       - depending on the upcoming ANSI standard, this may change."

    ^ self readFrom:aStringOrStream onError:0

    "

     FixedPoint readFrom:'123.456'

     FixedPoint readFrom:'3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788'

     FixedPoint readFrom:(ReadStream on:'foobar')     

     FixedPoint readFrom:(ReadStream on:'foobar') onError:nil  

    "

    "Modified: / 25.10.1997 / 15:30:29 / cg"

!

readFrom:aStringOrStream onError:exceptionBlock

    "return an instance of me as described on the string or stream, aStringOrStream.

     If an error occurs during conversion, return the result

     from evaluating exceptionBlock"

    | aStream sign integerPart fractionStream char fractionPart scale |

    aStream := aStringOrStream readStream.

    aStream peek == $- ifTrue:[

        sign := -1.

        aStream next.

    ] ifFalse:[

        sign := 1

    ].

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

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

    (aStream atEnd or: [aStream peek isLetter]) ifTrue: [

        fractionPart := 0.

        scale := 1.

    ] ifFalse:[

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

        [

            char := aStream next.

            char ~~ nil and:[char isDigit]

        ] whileTrue:[

            fractionStream nextPut:char

        ].

        scale := fractionStream position0Based.

        fractionStream reset.

        fractionPart := Number readFrom:fractionStream.

    ].

    ^ self basicNew 

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

        scale:scale

    "

     FixedPoint readFrom:'1.00' 

     FixedPoint readFrom:'123.456' 

     FixedPoint readFrom:'-123.456' 

     FixedPoint readFrom:'123' 

     FixedPoint readFrom:'-123' 

     FixedPoint readFrom:'-123.abcd' onError:[47.5] 

     FixedPoint readFrom:'-1a.bcd' onError:[47.5] 

     FixedPoint readFrom:'foot' onError:['bad fixedpoint'] 

    "

    "Created: / 25.10.1997 / 15:28:59 / cg"

    "Modified: / 25.10.1997 / 15:31:47 / cg"

! !

!FixedPoint class methodsFor:'constants'!

pi

    "pi with 1000 valid digits..."

    PI_1000 isNil ifTrue:[

        PI_1000 := self

                     readFrom:'3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788'

    ].

    ^ PI_1000.

    "

     self pi squared    

     self pi reciprocal 

     1 / self pi 

     self pi * 1000000000000000000000000000000000000000000    

    "

! !

!FixedPoint class methodsFor:'queries'!

exponentCharacter

    ^ $s

! !

!FixedPoint methodsFor:'accessing'!

scale

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

    ^ scale

    "Modified: 12.4.1997 / 11:21:05 / cg"

! !

!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."

    aNumber isInteger ifTrue:[

        ^ self class 

                numerator:(numerator * aNumber)

                denominator:denominator

                scale:scale

    ].

    aNumber isFraction ifTrue:[

        ^ self class 

            numerator:(numerator * aNumber numerator) 

            denominator:(denominator * aNumber denominator)

            scale:(scale max:aNumber scale)

    ].

    ^ 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).

    "

    "                       

     |a r|

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

     r := a * 5.0.    

     Transcript showCR:r.    

     Transcript showCR:(r withScale:2).

    "

    "                       

     |a r|

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

     r := 5.0 * a.    

     Transcript showCR:r.    

     Transcript showCR:(r withScale:2).

    "

!

+ 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 results scale will be the maximum of the receivers and the

     arguments scale."

    |n d|

    (aNumber isInteger or:[aNumber isFraction]) ifTrue:[

        n := aNumber numerator.

        d := aNumber denominator.

        "save a multiplication if possible"

        denominator == d ifTrue:[

            ^ self class 

                numerator:(numerator + n) 

                denominator:d

                scale:scale

        ].

        ^ self class 

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

                denominator:(denominator * d)

                scale:scale

    ].

    aNumber isFixedPoint ifTrue:[  

        n := aNumber numerator.

        d := aNumber denominator.

        "save a multiplication if possible"

        denominator == d ifTrue:[

            n := numerator + n

        ] ifFalse:[

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

            d := denominator * d.

        ].

        ^ self class 

                numerator:n 

                denominator:d

                scale:(scale max:aNumber scale)

    ].

    ^ 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|

    (aNumber isInteger or:[aNumber isFraction]) ifTrue:[

        n := aNumber numerator.

        d := aNumber denominator.

        "save a multiplication if possible"

        denominator == d ifTrue:[

            ^ self class 

                numerator:(numerator - n) 

                denominator:d

                scale:scale

        ].

        ^ self class 

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

                denominator:(denominator * d)

                scale:scale

    ].

    aNumber isFixedPoint ifTrue:[

        n := aNumber numerator.

        d := aNumber denominator.

        "save a multiplication if possible"

        denominator == d ifTrue:[

            n := numerator - n

        ] ifFalse:[

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

            d := denominator * d

        ].

        ^ self class 

                numerator:n 

                denominator:d

                scale:(scale max:aNumber scale)