"

     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' }"

"{ NameSpace: Smalltalk }"

Fraction subclass:#FixedPoint

	instanceVariableNames:'scale'

	classVariableNames:'PrintTruncated Pi Pi_1000 E'

	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

"

    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 (rounded). 

    NOTICE:

        it seems that squeak prints these truncated,

        whereas ST/X prints them rounded.

        This behavior should probably be controllable by providing      

        a subclass (RoundedFixedPoint ?) which redefines the printOn: method.

        (it is now controlled by a classVar, which is of course not a thread-safe

        solution).

    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:]

        Number Fraction Integer Float ShortFloat LongFloat Complex

"

!

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

    "redefined to block the inherited instance creation method from fraction.

     Raises an error - you must give a scale or provide a power-of-10 denominator"

    (d isPowerOf:10) ifTrue:[

        ^ self numerator:n denominator:d scale:(d log10 asInteger)

    ].    

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

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

    "

     self numerator:123 denominator:100    

    "

    "Modified: / 03-07-2017 / 12:46:11 / cg"

!

numerator:n denominator:d scale:s

    "create and return a new fixedPoint instances with the given scale

     (post decimal digits when printed). Assume its already reduced."

    ^ self basicNew

        setNumerator:n denominator:d scale:s

!

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:'.456'  

     FixedPoint readFrom:'123.456'  

     FixedPoint readFrom:'123.'  

     FixedPoint readFrom:'3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788'

     FixedPoint readFrom:(ReadStream on:'foobar')     

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

     FixedPoint readFrom:'0b1234' onError:nil  

     FixedPoint readFrom:'1'      

     FixedPoint readFrom:'2'      

     FixedPoint readFrom:'1.5'    

    "

    "Modified: / 23-11-2010 / 14:39:29 / cg"

    "Modified (comment): / 09-03-2017 / 15:44:38 / cg"

!

readFrom:aStringOrStream decimalPointCharacters:decimalPointCharacters 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 nextChar |

    aStream := aStringOrStream readStream.

    aStream peekOrNil == $- ifTrue:[

        sign := -1.

        aStream next.

    ] ifFalse:[

        sign := 1

    ].

    nextChar := aStream peekOrNil.

    (nextChar isNil or:[nextChar isLetter]) ifTrue: [^ exceptionBlock value].

    (decimalPointCharacters includes:nextChar) ifTrue:[

        "/ no integer part

        integerPart := 0.

        aStream next.

    ] ifFalse:[

        (nextChar isDigit) ifFalse: [^ exceptionBlock value].

        "/ FIX: only read the integer chars - not to the end.

        integerPart := Integer readFrom:aStream "(aStream upToAny:decimalPointCharacters)" allowRadix:false onError:[^ exceptionBlock value].

        nextChar := aStream peekOrNil.

        (decimalPointCharacters includes:nextChar) ifFalse:[

            "/ only integer part

            ^ self basicNew 

                setNumerator:integerPart * sign

                denominator:1

                scale:0

        ].    

        aStream next.

    ].

    nextChar := aStream peekOrNil.

    (nextChar isNil or:[nextChar isDigit not]) ifTrue: [

        ^ self basicNew 

            setNumerator:integerPart * sign

            denominator:1

            scale:0

    ].

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

    [

        char := aStream nextOrNil.

        char notNil and:[char isDigit]

    ] whileTrue:[

        fractionStream nextPut:char

    ].

    scale := fractionStream position.

    fractionStream reset.

    fractionPart := Integer readFrom:fractionStream onError:[^ exceptionBlock value]. 

    ^ self basicNew 

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

        scale:scale

    "

     FixedPoint readFrom:'1.00'    

     FixedPoint readFrom:'123.456'  

     FixedPoint readFrom:'123,456' decimalPointCharacters:',' 

     FixedPoint readFrom:'-123.456'     

     FixedPoint readFrom:'123'          

     FixedPoint readFrom:'-123' 

     -- notice the difference between readFromString and readFrom:

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

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

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

     FixedPoint readFromString:'0b1234' onError:['bad fixedpoint'] 

     -- readFrom only reads what can be read, leaving the stream at the end:

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

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

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

     FixedPoint readFrom:'0b1234' onError:['bad fixedpoint'] 

    "

    "Created: / 25-10-1997 / 15:28:59 / cg"

    "Modified: / 09-03-2017 / 16:27:36 / cg"

! !

!FixedPoint class methodsFor:'coercing & converting'!

coerce:aNumber

    "convert the argument aNumber into an instance of the receiver's class and return it."

    ^ aNumber asFixedPoint

! !

!FixedPoint class methodsFor:'constants'!

e

    "e with roughly 26 valid digits..."

    |e|

    E isNil ifTrue:[

        e := super e.

        E := e asFixedPoint:(e denominator log10 asInteger - 1)

    ].

    ^ E

    "

     E := nil.

     self e

        -> 2.7182818284590452353602875

     wolfram:

           2.718281828459045235360287471352662497757247093699959574966...

     self e squared    

     self e reciprocal 

     1 / self e 

     self e * 1000000000000000000000000000000000000000000    

    "

    "Created: / 03-07-2017 / 17:25:38 / cg"

!

pi

    "pi with roughly 26 valid digits..."

    |p|

    Pi isNil ifTrue:[

        p := super pi.

        Pi := p asFixedPoint:(p denominator log10 asInteger - 1)

    ].

    ^ Pi

    "

     Pi := nil.

     self pi

        -> 3.1415926535897932384626434

     wolfram:

        -> 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904...

     self pi squared    

     self pi reciprocal 

     1 / self pi 

     self pi * 1000000000000000000000000000000000000000000    

    "

    "Modified (comment): / 03-07-2017 / 13:19:40 / cg"

!

pi1000

    "pi with roughly 1000 valid digits..."

    Pi_1000 isNil ifTrue:[

        Pi_1000 := super pi1000 asFixedPoint:1000

    ].

    ^ Pi_1000.

    "

     Pi_1000 := nil.

     self pi1000

        -> 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989

     wolfram:

        -> 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904...

     self pi1000 squared    

     self pi1000 reciprocal 

     (self pi1000 - self pi) asFloat

    "

    "Modified (comment): / 03-07-2017 / 13:20:24 / cg"

! !

!FixedPoint class methodsFor:'printing control'!

printTruncated

    "return the PrintTruncated flag, which controls printing.

     See the description in the documentation for details"

    ^ PrintTruncated ? false.

!

printTruncated:aBoolean

    "set the PrintTruncated flag, which controls printing.

     See the description in the documentation for details"

    PrintTruncated := aBoolean.

! !

!FixedPoint class methodsFor:'queries'!

exponentCharacter

    "return the character used to print between mantissa an exponent.

     Also used by the scanner when reading numbers."

    ^ $s

! !

!FixedPoint methodsFor:'accessing'!

epsilon

    ^ (1 / (10 raisedTo:scale))

    "

     (2 asFixedPoint:4) epsilon   

     (2 asFixedPoint:100) epsilon   

     (2 asFixedPoint:1000) epsilon   

    "

    "Created: / 03-07-2017 / 12:35:22 / cg"

!

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.

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

     The result's scale is the maximum of the receiver's scale and the argument's scale."

    "/ notice:

    "/ the following code handles some common cases,

    "/ and exists as an optimization, to speed up those cases.

    "/ also notice, that checks for those cases must be inlinable without

    "/ a message send; otherwise double-dispatch is just as fast.

    (aNumber isMemberOf:SmallInteger) ifTrue:[

        ^ self class 

                numerator:(numerator * aNumber)

                denominator:denominator

                scale: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').