"

 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'

!

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.

"

!

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).

    [author:]

        Claus Gittinger

"

! !

initialize

    FractionZero isNil ifTrue:[

	FractionZero := self numerator:0 denominator:1.

	FractionOne := self numerator:1 denominator:1

    ]

! !

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 = self;

	    __FractionInstPtr(newFraction)->f_numerator = num;

	    __FractionInstPtr(newFraction)->f_denominator = den;

	    if (! __bothSmallInteger(num, den)) {

		spc = __qSpace(newFraction);

		__STORE_SPC(newFraction, num, spc);

		__STORE_SPC(newFraction, den, spc);

	    }

	    RETURN ( newFraction );

	}

    }

%}

.

    ^ self basicNew setNumerator:num denominator:den

! !

unity

    ^ FractionOne

!

zero

    ^ FractionZero

! !

isBuiltInClass

    "return true if this class is known by the run-time-system.

     Here, true is returned for myself, false for subclasses."

    ^ self == Fraction

    "Modified: 23.4.1996 / 15:59:10 / cg"

! !

!Fraction methodsFor:'accessing'!

denominator

    "return the denominator"

    ^ denominator

!

numerator

    "return the numerator"

    ^ numerator

! !

!Fraction methodsFor:'arithmetic'!

* 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 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 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:'coercing & converting'!

asFloat

    "return a float with (approximately) my value"

    ^ (numerator asFloat) / (denominator asFloat)

!

asFraction

    "return the receiver as fraction - thats itself"

    ^ self

!

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

!

asShortFloat

    "return a shortFloat with (approximately) my value"

    ^ (numerator asShortFloat) / (denominator asShortFloat)

    "Created: 17.4.1996 / 12:21:08 / cg"

!

coerce:aNumber

    "return aNumber converted into receivers type"

    ^ aNumber asFraction

!

generality

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

    ^ 60

! !

!Fraction methodsFor:'comparing'!

< 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

!

= 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

! !

!Fraction methodsFor:'double dispatching'!

differenceFromFloat:aFloat

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

    ^ (aFloat * denominator - numerator) / denominator

!

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

!

lessFromInteger:anInteger

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

    ^ (denominator * anInteger) < numerator

!

productFromFloat:aFloat

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

    ^ aFloat * numerator / denominator

!

productFromInteger:anInteger

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

    ^ (self class numerator:(anInteger * numerator)

		denominator:denominator) reduced

!

quotientFromFloat:aFloat

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

    ^ (aFloat * denominator) / numerator

!

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

!

sumFromFloat:aFloat

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

    ^ (aFloat * denominator + numerator) / denominator

!

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

! !

!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:$)

! !

!Fraction methodsFor:'private'!

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

!

setNumerator:num denominator:den

    "set both numerator and denominator"

    numerator := num.

    denominator := den

! !

!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:'testing'!

negative

    "return true if the receiver is negative"

    (numerator < 0) ifTrue:[

	^ (denominator < 0) not

    ].

    ^ (denominator < 0)

! !

!Fraction methodsFor:'truncation and rounding'!

rounded

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

    self negative ifTrue:[

	^ (self + (1/2)) truncated - 1

    ].

    ^ (self + (1/2)) truncated

!

truncated

    "return the receiver truncated towards zero as Integer"

    ^ numerator // denominator

! !

version

! !

Fraction initialize!