"

 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

'!

!Fraction class methodsFor:'documentation'!

copyright

"

 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.

"

!

version

"

"

!

documentation

"

    Instances of Fraction represent fractional numbers consisting of

    a numerator and denominator. Both are themselfes arbitrary precision

    integers. Fractions are usually created by dividing Integers using /

    (for exact division)."

! !

!Fraction class methodsFor:'initialization'!

initialize

    FractionZero isNil ifTrue:[

	FractionZero := self numerator:0 denominator:1.

	FractionOne := self numerator:1 denominator:1

    ]

! !

!Fraction class methodsFor:'constants'!

zero

    "return the neutral element for addition"

    ^ FractionZero

!

unity

    "return the neutral element for multiplication"

    ^ FractionOne

! !

!Fraction class methodsFor:'instance creation'!

new

    "create and return a new fraction with value 0"

    ^ self numerator:0 denominator:1

!

numerator:num denominator:den

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

%{  /* NOCONTEXT */

    /* this check allows subclassing .. */

    if (self == Fraction) {

	if (_CanDoQuickAlignedNew(sizeof(struct __fraction))) {

	    OBJ newFraction;

	    int spc;

	    _qCheckedAlignedNew(newFraction, sizeof(struct __fraction));

	    _InstPtr(newFraction)->o_class = Fraction;

	    _FractionInstPtr(newFraction)->f_numerator = num;

	    _FractionInstPtr(newFraction)->f_denominator = 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:'queries'!

isFraction

    "return true, if the receiver is some kind of fraction;

     true is returned here - the method is redefined from Object."

    ^ true

! !

!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].

    numerator == 0 ifTrue:[^ 0].

    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 & converting'!

coerce:aNumber

    "return aNumber converted into receivers type"

    ^ aNumber asFraction

!

generality

    "return the generality value - see ArithmeticValue>>retry:coercing:"

    ^ 60

!

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 isFraction 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 isFraction 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 isFraction 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 isFraction 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 isFraction 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 isFraction 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 isFraction 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 receiver, a fraction"

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

		denominator:denominator) reduced

!

differenceFromInteger:anInteger

    "sent when an integer does not know how to subtract the receiver, a fraction"

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

		denominator:denominator) reduced

!

productFromInteger:anInteger

    "sent when an integer does not know how to multiply the receiver, a fraction"

    ^ (self class numerator:(anInteger * numerator)

		denominator:denominator) reduced

!

quotientFromInteger:anInteger

    "sent when an integer does not know how to divide by the receiver, a fraction"

    ^ (self class numerator:(anInteger * denominator)

		denominator:numerator) reduced

!

lessFromInteger:anInteger

    "sent when an integer does not know how to compare to the receiver, a fraction"

    ^ (denominator * anInteger) < numerator

!

sumFromFloat:aFloat

    "sent when a float does not know how to add the receiver, a fraction"

    ^ (aFloat * denominator + numerator) / denominator

!

differenceFromFloat:aFloat

    "sent when a float does not know how to subtract the receiver, a fraction"

    ^ (aFloat * denominator - numerator) / denominator

!

productFromFloat:aFloat

    "sent when a float does not know how to multiply the receiver, a fraction"

    ^ aFloat * numerator / denominator

!

quotientFromFloat:aFloat

    "sent when a float does not know how to divide by the receiver, a fraction"

    ^ (aFloat * denominator) / numerator

! !

!Fraction methodsFor:'printing & storing'!

printOn:aStream

    "append a printed representation of the receiver to the

     argument, aStream"

    aStream nextPut:$(.

    numerator printOn:aStream.

    aStream nextPut:$/.

    denominator printOn:aStream.

    aStream nextPut:$)

! !