"

 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 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.

"

!

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).

    Mixed mode arithmetic:

        fraction op fraction    -> fraction

        fraction op fix         -> fix; scale is fix's scale

        fraction op integer     -> fraction

        fraction op float       -> float

    [author:]

        Claus Gittinger

    [see also:]

        Number

        Float Integer FixedPoint 

"

! !

!Fraction class methodsFor:'initialization'!

initialize

    FractionZero isNil ifTrue:[

	FractionZero := self numerator:0 denominator:1.

	FractionOne := self numerator:1 denominator:1

    ]

! !

!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) {

	    }

	}

    }

! !

!Fraction class methodsFor:'constants'!

pi

    "return the constant pi as Fraction"

    ^ self 

        numerator:  31415926535897932384626434

        denominator:10000000000000000000000000

    "

     Fraction pi         

     Fraction pi asFloat

     Float pi            

    "

    "Modified: 5.11.1996 / 11:11:44 / cg"

!

unity

    "return the neutral element for multiplication (1 / 1)"

    ^ FractionOne

    "Modified: 18.7.1996 / 12:26:06 / cg"

!

zero

    "return the neutral element for addition (0 / 1)"

    ^ FractionZero

    "Modified: 18.7.1996 / 12:26:12 / cg"

! !

!Fraction class methodsFor:'queries'!

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:[

        aNumber isFixedPoint ifFalse:[  "/ the value was corrent, but the scale is lost

            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

    "Modified: 5.11.1996 / 19:31:50 / cg"

!

+ 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:[

        aNumber isFixedPoint ifFalse:[  "/ the value was corrent, but the scale is lost

            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) reduced

        ]

    ].

    (aNumber isMemberOf:Float) ifTrue:[

        ^ aNumber + (numerator asFloat / denominator asFloat)

    ].

    ^ aNumber sumFromFraction:self

    "Modified: 5.11.1996 / 19:31:41 / cg"

!

- 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:[

        aNumber isFixedPoint ifFalse:[  "/ the value was corrent, but the scale is lost

            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) reduced

        ]

    ].

    (aNumber isMemberOf:Float) ifTrue:[

        ^ (numerator asFloat / denominator asFloat) - aNumber

    ].

    ^ aNumber differenceFromFraction:self

    "

     (1/3) - (1/9)      

     (1/9) - (1/3)      

     (999/1000) - (1/1000)      

     (999/1000) - (1/1000000)      

     (999000/1000000) - (1/1000000)      

    "

    "Modified: 5.11.1996 / 19:31:32 / cg"

!

/ 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:[

        aNumber isFixedPoint ifFalse:[  "/ the value was corrent, but the scale is lost

            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

    "Modified: 5.11.1996 / 19:31:23 / cg"

!

// aNumber

    "return the integer quotient of dividing the receiver by aNumber with

     truncation towards negative infinity."

    self negative ifTrue:[

         ^ ((numerator * aNumber denominator) // (denominator * aNumber numerator)) - 1

    ].

    ^ (numerator * aNumber denominator) // (denominator * aNumber numerator)

    "

     0.5 // 1

     -0.5 // 1

     (1/2) // 1

     (1/2) negated // 1

    "

    "Modified: 5.11.1996 / 11:47:14 / cg"

!

negated

    "optional - could use inherited method ..."

    ^ self class 

        numerator:(numerator negated)

        denominator:denominator

    "Modified: 5.11.1996 / 10:29:11 / cg"

!

reciprocal

    "optional - could use inherited method ..."

    numerator == 1 ifTrue:[^ denominator].

    ^ self class 

        numerator:denominator

        denominator:numerator

    "Modified: 5.11.1996 / 10:29:22 / cg"

! !

!Fraction methodsFor:'coercing & converting'!

asFixedPoint

    "return the receiver as fixedPoint number.

     Q: what should the scale be here ?"

    ^ FixedPoint numerator:numerator denominator:denominator scale:2

    "

     (1/2) asFixedPoint

    "

    "Created: 5.11.1996 / 15:15:54 / cg"

!

asFixedPoint:scale

    "return the receiver as fixedPoint number, with the given number

     of post-decimal-point digits."

    ^ FixedPoint numerator:numerator denominator:denominator scale:scale

    "

     (1/2) asFixedPoint:2 

     (1/3) asFixedPoint:2 

     (1/3) asFixedPoint:5 

     (2/3) asFixedPoint:2 

     (2/3) asFixedPoint:5 

    "

    "Created: 5.11.1996 / 15:15:54 / cg"

    "Modified: 10.1.1997 / 19:54:50 / cg"

!

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."

    |d n|

    (aNumber isMemberOf:SmallInteger) ifTrue:[

        ^ numerator < (denominator * aNumber)

    ].

    aNumber isFraction ifTrue:[

        d := aNumber denominator.

        n := aNumber numerator.

        "/ save a multiplication if possible

        d == denominator ifTrue:[

            ^ numerator < n

        ].

        ^ (numerator * d) < (denominator * n)

    ].

    ^ aNumber lessFromFraction:self

    "Modified: 5.11.1996 / 10:30:52 / cg"

!

= 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 ..."

    |d n|

    (aNumber isMemberOf:SmallInteger) ifTrue:[

        ^ numerator > (denominator * aNumber)

    ].

    aNumber isFraction ifTrue:[

        d := aNumber denominator.

        n := aNumber numerator.

        "/ save a multiplication if possible

        d == denominator ifTrue:[

            ^ numerator > n

        ].

        ^ (numerator * d) > (denominator * n)

    ].

    ^ self retry:#> coercing:aNumber

    "Modified: 5.11.1996 / 10:31:28 / cg"

! !

!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

    "Modified: 5.11.1996 / 10:32:14 / cg"

!

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"