"

 COPYRIGHT (c) 2003 by eXept Software AG

              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.

"

LimitedPrecisionReal subclass:#LargeFloat

	instanceVariableNames:'exponent mantissa precision'

	classVariableNames:'Zero One NaN PositiveInfinity NegativeInfinity Pi_1000 E_1000'

	poolDictionaries:''

	category:'Magnitude-Numbers'

!

!LargeFloat class methodsFor:'documentation'!

copyright

"

 COPYRIGHT (c) 2003 by eXept Software AG

              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

"

    Experimental Code.

    The implementation is neither complete nor tuned for performance - still being developed.

    This class provides arbitrary precision floats. These are represented as:

      exponent,

      mantissa

    [author:]

        Claus Gittinger

    [see also:]

        Number

        Float LongFloat ShortFloat Fraction FixedPoint 

        SmallInteger LargeInteger

"

!

examples

"

     (1 to:1000) inject:1 asLargeFloat into:[:p :m | p * m]          

     (1 to:1000) inject:1 into:[:p :m | p * m]                 

     Time millisecondsToRun:[ 

        (1 to:20000) inject:1 asLargeFloat into:[:p :m | p * m]

     ]  

     Time millisecondsToRun:[ 

        (1 to:20000) inject:1 into:[:p :m | p * m]

     ]   

"

! !

!LargeFloat class methodsFor:'instance creation'!

fromInteger:anInteger

    ^ self basicNew 

        mantissa:anInteger 

        exponent:0

    "

     LargeFloat fromInteger:123456

     1 asLargeFloat       

     2 asLargeFloat       

     1000 factorial asLargeFloat             

    "

!

fromLimitedPrecisionReal:aLimitedPrecisionReal

    |shifty numBytes numBitsInMantissa maskMantissa numBitsInExponent maskExponent

     numIntegerBits numBits biasExponent lpRealClass sign expPart fractionPart fraction exp|

    aLimitedPrecisionReal isFinite ifFalse:[

        aLimitedPrecisionReal isNaN ifTrue:[^ self NaN].

        aLimitedPrecisionReal > 0 ifTrue:[^ self infinity].

        ^ self negativeInfinity

    ].

    lpRealClass := aLimitedPrecisionReal class.

    numBytes := aLimitedPrecisionReal basicSize.

    numBitsInMantissa := lpRealClass numBitsInMantissa. maskMantissa := (1 bitShift:numBitsInMantissa) - 1.

    numBitsInExponent := lpRealClass numBitsInExponent. maskExponent := (1 bitShift:numBitsInExponent) - 1.

    numIntegerBits := lpRealClass numBitsInIntegerPart.

    numBits := numBitsInMantissa + numBitsInExponent. 

    biasExponent := maskExponent bitShift:-1.

    shifty := LargeInteger basicNew numberOfDigits:numBytes.

    UninterpretedBytes isBigEndian ifTrue:[

        1 to:numBytes do:[:i | shifty digitAt:(numBytes+1-i) put:(aLimitedPrecisionReal basicAt:i)].

    ] ifFalse:[

        1 to:numBytes do:[:i | shifty digitAt:i put:(aLimitedPrecisionReal basicAt:i)].

    ].

    sign := (shifty bitAt:numBits+1) == 0 ifTrue: [1] ifFalse: [-1].

    expPart := (shifty bitShift:numBitsInMantissa negated) bitAnd: maskExponent.

    fractionPart := shifty bitAnd:maskMantissa.

    ( expPart=0 and: [ fractionPart=0 ] ) ifTrue: [ ^ self zero  ].

    numIntegerBits == 0 ifTrue:[

        " Replace omitted leading 1 in fraction (Notice: quadIEEE format does not do this)"

        fraction := fractionPart bitOr: (maskMantissa + 1).

    ] ifFalse:[

        fraction := fractionPart.

    ].

    "Unbias exponent"

    exp := biasExponent - expPart + (numBitsInMantissa - numIntegerBits).

    ^ self basicNew 

        mantissa:(fraction * sign) 

        exponent:(exp negated)

    "

     1.0 asLargeFloat       

     2.0 asLargeFloat       

     20000.0 asLargeFloat   

     2e6 asLargeFloat                                  

     1e300 asLargeFloat             

     2e300 asLargeFloat             

     0.5 asLargeFloat      

     0.25 asLargeFloat     

     (1.0/20000.0) asLargeFloat 

     2e-6 asLargeFloat        

     2e-300 asLargeFloat      

     -1.0 asLargeFloat       

     -0.5 asLargeFloat      

     Float NaN asLargeFloat              

     Float infinity asLargeFloat         

     Float negativeInfinity asLargeFloat 

    "

!

mantissa:m exponent:e

    ^ self basicNew mantissa:m exponent:e

    "

     LargeFloat mantissa:1 exponent:0 

     LargeFloat mantissa:2 exponent:0 

     LargeFloat mantissa:4 exponent:0   

     LargeFloat mantissa:8 exponent:0 

     LargeFloat mantissa:1 exponent:-1

     LargeFloat mantissa:1 exponent:-2

     LargeFloat mantissa:1 exponent:-3

    "

!

mantissa:m exponent:e precision:p

    ^ self basicNew mantissa:m exponent:e precision:p

! !

!LargeFloat class methodsFor:'class initialization'!

initialize

    NaN := self mantissa:0 exponent:999.

    PositiveInfinity := self mantissa:0 exponent:1.

    NegativeInfinity := self mantissa:0 exponent:-1.

    One := self mantissa:1 exponent:0.

    Zero := self mantissa:0 exponent:0.

    "

     LargeFloat initialize

    "

! !

!LargeFloat class methodsFor:'constants'!

NaN

    ^ NaN

    "

     LargeFloat NaN

     (0.0 uncheckedDivide:0.0)

    "

!

infinity

    ^ PositiveInfinity 

    "

     LargeFloat infinity

     (1.0 uncheckedDivide:0.0)

    "

!

negativeInfinity

    ^ NegativeInfinity

    "

     LargeFloat negativeInfinity

     (-1.0 uncheckedDivide:0.0)

    "

!

pi

    Pi_1000 isNil ifTrue:[

        Pi_1000 := FixedPoint pi asLargeFloat

    ].

    ^ Pi_1000.

    "

     LargeFloat pi

    "

!

unity

    ^ One

    "

     LargeFloat unity

    "

!

zero

    ^ Zero

    "

     LargeFloat zero

    "

! !

!LargeFloat class methodsFor:'queries'!

radix

   "answer the radix of a LargeFloats exponent"

    ^ 2 

! !

!LargeFloat methodsFor:'accessing'!

exponent

    ^ exponent

!

mantissa

    ^ mantissa

!

precision

    ^ precision ? 200

! !

!LargeFloat methodsFor:'arithmetic'!

* aNumber

    ^ aNumber productFromLargeFloat:self

!

+ aNumber

    ^ aNumber sumFromLargeFloat:self

    "

     1.0 asLargeFloat

    "

!

- aNumber

    ^ aNumber differenceFromLargeFloat:self

!

/ aNumber

    ^ aNumber quotientFromLargeFloat:self

!

negated

    mantissa = 0 ifTrue:[

        exponent = 0 ifTrue:[ ^ self ].

        self == NaN ifTrue:[^ self].

        self == NegativeInfinity ifTrue:[^ PositiveInfinity].

        ^ NegativeInfinity

    ].

    ^ self class 

        mantissa:(mantissa negated)

        exponent:exponent 

        precision:self precision.

    "

     LargeFloat unity negated

    "

! !

!LargeFloat methodsFor:'coercing & converting'!

asInteger

    "return an integer with same value - might truncate"

    exponent = 0 ifTrue:[^ mantissa].

    mantissa == 0 ifTrue:[

        "/ INF or NAN

        ^ self class

            raise:#domainErrorSignal

            receiver:self

            selector:#asInteger

            arguments:#()

            errorString:'Cannot represent non-finite as integer'.

"/        ^ self asMetaNumber.

    ].

    exponent > 0 ifTrue:[

        ^ mantissa * (2 raisedTo:exponent)

    ].

    ^ mantissa // (2 raisedTo:exponent negated)

    "

     (self new exponent:0 mantissa:100) asInteger 

     (self new exponent:1 mantissa:100) asInteger 

     (self new exponent:-1 mantissa:100) asInteger 

    "

!

asLargeFloat

    ^ self

!

asTrueFraction

    "Answer a fraction or integer that EXACTLY represents self."

    exponent = 0 ifTrue: [ ^ mantissa].

    mantissa == 0 ifTrue:[

        "/ INF or NAN

        ^ self class

            raise:#conversionErrorSignal

            receiver:self

            selector:#asTrueFraction

            arguments:#()

            errorString:'Cannot represent non-finite float as fraction'.

"/        ^ self asMetaNumber.

    ].

    exponent > 0 ifTrue: [

        ^ mantissa bitShift:exponent 

    ].

    ^ Fraction

        numerator: mantissa

        denominator: (1 bitShift:exponent negated) 

    "

     0.3 asFloat asTrueFraction   

     0.3 asShortFloat asTrueFraction  

     0.3 asLongFloat asTrueFraction   

     0.3 asLargeFloat asTrueFraction   

     1 asLargeFloat asTrueFraction     

     2 asLargeFloat asTrueFraction     

     0.5 asLargeFloat asTrueFraction     

     0.25 asLargeFloat asTrueFraction     

     -0.25 asLargeFloat asTrueFraction    

     0.125 asLargeFloat asTrueFraction    

     -0.125 asLargeFloat asTrueFraction    

     1.25 asLargeFloat asTrueFraction       

     3e37 asLargeFloat asTrueFraction     

     LargeFloat NaN asTrueFraction               -> error

     LargeFloat infinity asTrueFraction          -> error

     LargeFloat negativeInfinity asTrueFraction  -> error

    "

!

coerce:aNumber

    "return the argument as a LargeFloat"

    ^ aNumber asLargeFloat

!

generality

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

    ^ 100

! !

!LargeFloat methodsFor:'comparing'!

< aNumber

    "return true, if the argument is greater"

    ^ aNumber lessFromLargeFloat:self

!

= aNumber

    "return true, if the argument is equal in value"

    ^ aNumber equalFromLargeFloat:self

    "

     LargeFloat unity = LargeFloat zero  

     LargeFloat unity = LargeFloat unity 

     LargeFloat unity = nil            

     LargeFloat unity ~= nil            

    "

!

hash

    "return a number for hashing; redefined, since floats compare

     by numeric value (i.e. 3.0 = 3), therefore 3.0 hash must be the same

     as 3 hash."

    exponent == 0 ifTrue:[^ mantissa hash].

    exponent < 64 ifTrue:[^ (mantissa bitShift:exponent) hash ].

    ^ mantissa hash bitXor:exponent hash

    "

     LargeFloat unity hash

     LargeFloat zero hash

     3 hash       

     3.0 hash

     3.1 hash  

     3.14159 hash  

     31.4159 hash 

     3.141591 hash 

     1.234567890123456 hash  

     1.234567890123457 hash   

     Set withAll:#(3 3.0 99 99.0 3.1415)

    "

! !

!LargeFloat methodsFor:'double dispatching'!

differenceFromLargeFloat:aLargeFloat

    |otherExponent otherMantissa e m|

    otherExponent := aLargeFloat exponent.

    otherMantissa := aLargeFloat mantissa.

    otherMantissa == 0 ifTrue:[

        otherExponent = 0 ifTrue:[^ self negated].

        "/ INF or NaN

        aLargeFloat isNaN ifTrue:[^ NaN].

        self isFinite ifTrue:[^ aLargeFloat].

        aLargeFloat sign ~~ self sign ifTrue:[^ self negated].

        ^ NaN

    ].

    mantissa == 0 ifTrue:[

        exponent = 0 ifTrue:[^ aLargeFloat].

        "/ INF or NaN

        self isNaN ifTrue:[^ NaN].

        ^ self negated

    ].

    otherExponent = exponent ifTrue:[

        m := otherMantissa - mantissa. 

        e := exponent

    ] ifFalse:[

        otherExponent> exponent ifTrue:[

            m := (otherMantissa bitShift:(otherExponent-exponent)) - mantissa.

            e := exponent

        ] ifFalse:[

            m := otherMantissa - (mantissa bitShift:(exponent-otherExponent)).

            e := otherExponent

        ]

    ].

    ^ self class

        mantissa:m 

        exponent:e

        precision:(self precision min:aLargeFloat precision)

!

equalFromLargeFloat:aLargeFloat

    aLargeFloat exponent = exponent ifTrue:[

        ^ aLargeFloat mantissa = mantissa

    ].

    "assuming normalized numbers, they cannot be equal then"

    ^ false

!

lessFromLargeFloat:aLargeFloat

    |otherExponent otherMantissa|

    otherExponent := aLargeFloat exponent.

    otherMantissa := aLargeFloat mantissa.

    otherExponent > exponent ifTrue:[

        ^ otherMantissa < (mantissa bitShift:(otherExponent-exponent))

    ].

    otherExponent < exponent ifTrue:[

        ^ (otherMantissa bitShift:(exponent-otherExponent)) < mantissa

    ].

    ^ otherMantissa < mantissa

!

productFromLargeFloat:aLargeFloat

    |otherMantissa otherExponent|

    otherMantissa := aLargeFloat mantissa.

    otherExponent := aLargeFloat exponent.

    otherMantissa == 0 ifTrue:[

        otherExponent ~= 0 ifTrue:[

            "/ INF or NaN

            aLargeFloat isNaN ifTrue:[^ NaN].

            self negative ifTrue:[^ aLargeFloat negated].

            ^ aLargeFloat