"
 COPYRIGHT (c) 1989 by Claus Gittinger
              All Rights Reserved

 This software is furnished under a license and may be used
 only in accordance with the terms of that license and with the
 inclusion of the above copyright notice.   This software may not
 be provided or otherwise made available to, or used by, any
 other person.  No title to or ownership of the software is
 hereby transferred.
"

Number subclass:#Fraction
       instanceVariableNames:'numerator denominator'
       classVariableNames:'FractionOne FractionZero'
       poolDictionaries:''
       category:'Magnitude-Numbers'
!

Fraction comment:'

COPYRIGHT (c) 1989 by Claus Gittinger
              All Rights Reserved

$Header: /cvs/stx/stx/libbasic/Fraction.st,v 1.6 1993-12-12 20:53:06 claus Exp $
'!

!Fraction class methodsFor:'initialization'!

initialize
    FractionZero := self numerator:0 denominator:1.
    FractionOne := self numerator:1 denominator:1
! !

!Fraction class methodsFor:'constants'!

zero
    ^ FractionZero
!

unity
    ^ FractionOne
! !

!Fraction class methodsFor:'instance creation'!

new
    "create and return a new fraction with value 0"

    ^ self basicNew setNumerator:0 denominator:1
!

numerator:num denominator:den
    "create and return a new fraction with numerator num and denominator den"

%{  /* NOCONTEXT */
    extern char *newNextPtr, *newEndPtr;

    /* this check allows subclassing .. */
    if (self == Fraction) {
        if (_CanDoQuickNew(sizeof(struct fractionstruct))) {
            OBJ newFraction;

            _qCheckedAlignedNew(newFraction, sizeof(struct fractionstruct));
            _InstPtr(newFraction)->o_class = Fraction;
            _FractionInstPtr(newFraction)->f_numerator = num;
            _FractionInstPtr(newFraction)->f_denominator = den;
            __STORE(newFraction, num);
            __STORE(newFraction, den);
            RETURN ( newFraction );
        }
    }
%}
.
    ^ self basicNew setNumerator:num denominator:den
! !

!Fraction class methodsFor:'queries'!

isBuiltInClass
    "this class is known by the run-time-system"

    ^ self == Fraction
! !

!Fraction methodsFor:'accessing'!

numerator
    "return the numerator"

    ^ numerator
!

denominator
    "return the denominator"

    ^ denominator
! !

!Fraction methodsFor:'private'!

setNumerator:num denominator:den
    "set both numerator and denominator"

    numerator := num.
    denominator := den
!

reduced
    "reduce the receiver"

    |gc|

    denominator == 1 ifTrue:[^ numerator].
    numerator == 1 ifTrue:[^ self].

    gc := numerator gcd:denominator.
    (gc == 1) ifFalse:[
        numerator := numerator // gc.
        denominator := denominator // gc
    ].
    (numerator < 0) ifTrue:[
        (denominator < 0) ifTrue:[
            numerator := numerator negated.
            denominator := denominator negated
        ]
    ].
    (denominator == 1) ifTrue:[^ numerator].
    ^ self
! !

!Fraction methodsFor:'coercing'!

coerce:aNumber
    ^ aNumber asFraction
!

generality
    ^ 60
! !

!Fraction methodsFor:'converting'!

asInteger
    "return an integer with my value - will usually truncate"

    ^ numerator // denominator
!

asLargeInteger
    "return an integer with my value - will usually truncate"

    ^ self asInteger asLargeInteger
!

asFloat
    "return a float with (approximately) my value"

    ^ (numerator asFloat) / (denominator asFloat)
!

asFraction
    "return the receiver as fraction - thats itself"

    ^ self
! !

!Fraction methodsFor:'comparing'!

= aNumber
    "return true, if the argument represents the same numeric value
     as the receiver, false otherwise"

    (aNumber isMemberOf:SmallInteger) ifTrue:[
        (denominator = 1) ifFalse:[^ false].
        ^ numerator = aNumber
    ].
    (aNumber isKindOf:Fraction) ifTrue:[
        (numerator = aNumber numerator) ifFalse:[^ false].
        ^ denominator = aNumber denominator
    ].
    ^ self retry:#= coercing:aNumber
!

> aNumber
    "return true if the receiver is greater
     than aNumber, false otherwise."
    "optional - could use inherited method ..."

    (aNumber isMemberOf:SmallInteger) ifTrue:[
        ^ numerator > (denominator * aNumber)
    ].
    (aNumber isKindOf:Fraction) ifTrue:[
        ^ (numerator * aNumber denominator) > (denominator * aNumber numerator)
    ].
    ^ self retry:#> coercing:aNumber
!

< aNumber
    "return true if the receiver is less
     than aNumber, false otherwise."

    (aNumber isMemberOf:SmallInteger) ifTrue:[
        ^ numerator < (denominator * aNumber)
    ].
    (aNumber isKindOf:Fraction) ifTrue:[
        ^ (numerator * aNumber denominator) < (denominator * aNumber numerator)
    ].
    ^ aNumber lessFromFraction:self
! !

!Fraction methodsFor:'testing'!

negative
    "return true if the receiver is negative"

    (numerator < 0) ifTrue:[
        ^ (denominator < 0) not
    ].
    ^ (denominator < 0)
! !

!Fraction methodsFor:'arithmetic'!

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

    |n d|

    (aNumber isMemberOf:SmallInteger) ifTrue:[
        ^ (self class numerator:(numerator + (denominator * aNumber))
                    denominator:denominator) reduced
    ].
    (aNumber isKindOf:Fraction) ifTrue:[
        n := aNumber numerator.
        d := aNumber denominator.

        "save a multiplication if possible"
        denominator == d ifTrue:[
            ^ (self class numerator:(numerator + n) denominator:d) reduced
        ].

        ^ (self class numerator:((numerator * d) + (n * denominator))
                    denominator:(denominator * d)) reduced
    ].
    (aNumber isMemberOf:Float) ifTrue:[
        ^ aNumber + (numerator asFloat / denominator asFloat)
    ].
    ^ aNumber sumFromFraction:self
!

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

    |n d|

    (aNumber isMemberOf:SmallInteger) ifTrue:[
        ^ (self class numerator:(numerator - (denominator * aNumber))
                    denominator:denominator) reduced
    ].
    (aNumber isKindOf:Fraction) ifTrue:[
        n := aNumber numerator.
        d := aNumber denominator.

        "save a multiplication if possible"
        denominator == d ifTrue:[
            ^ (self class numerator:(numerator - n) denominator:d) reduced
        ].

        ^ (self class numerator:((numerator * d) - (n * denominator)) 
                    denominator:(denominator * d)) reduced
    ].
    (aNumber isMemberOf:Float) ifTrue:[
        ^ (numerator asFloat / denominator asFloat) - aNumber
    ].
    ^ aNumber differenceFromFraction:self
!

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

    |n d|

    (aNumber isMemberOf:SmallInteger) ifTrue:[
        ^ (self class numerator:(numerator * aNumber)
                    denominator:denominator) reduced
    ].
    (aNumber isKindOf:Fraction) ifTrue:[
        n := numerator * aNumber numerator.
        d := denominator * aNumber denominator.
        ^ (self class numerator:n denominator:d) reduced
    ].
    (aNumber isMemberOf:Float) ifTrue:[
        ^ (numerator * aNumber) / denominator
    ].
    ^ aNumber productFromFraction:self
!

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

    |n d|

    (aNumber isMemberOf:SmallInteger) ifTrue:[
        ^ (self class numerator:numerator
                    denominator:(denominator * aNumber)) reduced
    ].
    (aNumber isKindOf:Fraction) ifTrue:[
        n := numerator * aNumber denominator.
        d := denominator * aNumber numerator.
        ^ (self class numerator:n denominator:d) reduced
    ].
    (aNumber isMemberOf:Float) ifTrue:[
        ^ numerator / (denominator * aNumber)
    ].
    ^ aNumber quotientFromFraction:self
!

// aNumber
    "return the integer quotient of the receiver and the argument, aNumber"

    self negative ifTrue:[
         ^ ((numerator * aNumber denominator) // (denominator * aNumber numerator)) - 1
    ].
    ^ (numerator * aNumber denominator) // (denominator * aNumber numerator)
!

negated
    "optional - could use inherited method ..."

    ^ self class numerator:(numerator negated)
               denominator:denominator
!

reciprocal
    "optional - could use inherited method ..."

    numerator == 1 ifTrue:[^ denominator].
    ^ self class numerator:denominator
               denominator:numerator
! !

!Fraction methodsFor:'truncation and rounding'!

truncated
    "return the receiver truncated towards zero as Integer"

    ^ numerator // denominator
!

rounded
    "return the receiver rounded to the nearest integer as integer"

    self negative ifTrue:[
        ^ (self + (1/2)) truncated - 1
    ].
    ^ (self + (1/2)) truncated
! !

!Fraction methodsFor:'double dispatching'!

sumFromInteger:anInteger
    "sent when an integer does not know how to add the recevier, a fraction"

    ^ (self class numerator:(numerator + (anInteger * denominator))
                denominator:denominator) reduced
!

differenceFromInteger:anInteger
    "sent when an integer does not know how to subtract the recevier, a fraction"

    ^ (self class numerator:((anInteger * denominator) - numerator)
                denominator:denominator) reduced
!

productFromInteger:anInteger
    "sent when an integer does not know how to multiply the recevier, a fraction"

    ^ (self class numerator:(anInteger * numerator)
                denominator:denominator) reduced
!

lessFromInteger:anInteger
    "sent when an integer does not know how to compare to the recevier, a fraction"

    ^ (denominator * anInteger) < numerator
!

sumFromFloat:aFloat
    "sent when a float does not know how to add the recevier, a fraction"

    ^ (aFloat * denominator + numerator) / denominator
!

differenceFromFloat:aFloat
    "sent when a float does not know how to subtract the recevier, a fraction"

    ^ (aFloat * denominator - numerator) / denominator
!

productFromFloat:aFloat
    "sent when a float does not know how to multiply the recevier, a fraction"

    ^ aFloat * numerator / denominator
!

quotientFromFloat:aFloat
    "sent when a float does not know how to divide by the recevier, a fraction"

    ^ (aFloat * denominator) / numerator
! !

!Fraction methodsFor:'printing'!

printString
    ^ '(' , numerator printString, '/' , denominator printString, ')'
! !