LargeFloat.st
author Claus Gittinger <cg@exept.de>
Wed, 13 Feb 2019 22:10:53 +0100
changeset 23735 77363fc65861
parent 22299 0ae55bd04f33
child 23739 3a4a83bb825b
permissions -rw-r--r--
#FEATURE by cg class: OrderedDictionary changed: #copyValuesFrom:to: class: OrderedDictionary class changed: #version_CVS

"
 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.
"
"{ Package: 'stx:libbasic' }"

"{ NameSpace: Smalltalk }"

LimitedPrecisionReal subclass:#LargeFloat
	instanceVariableNames:'exponent mantissa precision'
	classVariableNames:'Zero One NaN PositiveInfinity NegativeInfinity Pi_1000 E_1000
		Ln10 DefaultPrecision'
	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
"
    Attention:
        Experimental & Unfinished 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
      precision
      
    [author:]
        Claus Gittinger

    [see also:]
        Number
        Float LongFloat ShortFloat Fraction FixedPoint 
        SmallInteger LargeInteger
"
!

examples
"
  1000 factorial as a LargeFloat:
     (1 to:1000) inject:1 asLargeFloat into:[:p :m | p * m]          

  1000 factorial as an Integer:
     (1 to:1000) inject:1 into:[:p :m | p * m]                 

  compute 20000.0 factorial:
     Time millisecondsToRun:[ 
        (1 to:20000) inject:1 asLargeFloat into:[:p :m | p * m]
     ] -> 210

  compute 20000 factorial:
     Time millisecondsToRun:[ 
        (1 to:20000) inject:1 into:[:p :m | p * m]
     ] -> 160 
"
! !

!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)
        precision:(aLimitedPrecisionReal precision)

    "
     1.0 asLargeFloat

     take a look at the precision...
     
     1.0 asShortFloat asLargeFloat       
     1.0 asLongFloat asLargeFloat       
     1.0 asQDouble asLargeFloat       
     1 asLargeFloat       
     (5/3) asLargeFloat       
     (3/5) asLargeFloat       
     (1/2) 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 
    "

    "Modified (comment): / 17-07-2017 / 15:09:30 / cg"
!

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.

    DefaultPrecision := 200.
    
    
    "
     LargeFloat initialize
    "

    "Modified: / 10-10-2017 / 15:56:36 / cg"
! !

!LargeFloat class methodsFor:'coercing & converting'!

coerce:aNumber
    "return the argument as a LargeFloat"

    ^ aNumber asLargeFloat
! !

!LargeFloat class methodsFor:'constants'!

NaN
    ^ NaN

    "
     LargeFloat NaN
     (0.0 uncheckedDivide:0.0)
    "
!

infinity
    ^ PositiveInfinity 

    "
     LargeFloat infinity
     (1.0 uncheckedDivide:0.0)
    "
!

ln10
    "return the ln(10) as largeFloat with approx. 500 bits of precision"

    Ln10 isNil ifTrue:[
        Ln10 := (10.0 asLargeFloat ln_withAccuracy:(LongFloat readFrom:'1e-100')) precision:100
    ].
    ^ Ln10

    "
     LargeFloat ln10
    "

    "Created: / 17-07-2017 / 15:15:25 / cg"
    "Modified: / 17-07-2017 / 16:42:27 / cg"
!

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'!

defaultPrecision
    ^ DefaultPrecision

    "Created: / 10-10-2017 / 15:58:03 / cg"
!

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 + 20 asLargeFloat
     1.0 asLargeFloat + 20
     1.0 asLargeFloat + 20.0 
     1.0 asLargeFloat + ( 2 / 5 ) 
     1.0 asLargeFloat + 0.4 asLargeFloat 

     20 asLargeFloat + 1.0 asLargeFloat
     20 + 1.0 asLargeFloat 
     20.0 + 1.0 asLargeFloat 
     ( 2 / 5 ) + 1.0 asLargeFloat 
    "

    "Modified (comment): / 17-07-2017 / 15:06:20 / cg"
!

- aNumber
    ^ aNumber differenceFromLargeFloat:self
!

/ aNumber
    ^ aNumber quotientFromLargeFloat:self
!

// aNumber
    "return the integer quotient of dividing the receiver by aNumber with
     truncation towards negative infinity."

    ^ (self / aNumber) asInteger

    "
     8 asFloat // 2
     -8 asFloat // 2   
     9 asFloat // 2
     -9 asFloat // 2   

     8 asLargeFloat // 2 
     -8 asLargeFloat // 2   
     9 asLargeFloat // 2 
     -9 asLargeFloat // 2   
    "

    "Created: / 10-10-2017 / 15:50:01 / cg"
!

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
    "return a large float with same value - that's me"

    ^ self

    "Modified (comment): / 12-06-2017 / 20:56:44 / cg"
!

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
    "return true if aLargeFloat < self"
    
    |otherExponent otherMantissa|

    otherExponent := aLargeFloat exponent.
    otherMantissa := aLargeFloat mantissa.

    exponent < otherExponent ifTrue:[
        "/ my exponent is < than the other number's exponent.
        "/ left-shift the other mantissa
        ^ (otherMantissa bitShift:(otherExponent-exponent)) < mantissa
    ].
    otherExponent < exponent ifTrue:[
        "/ my exponent is > than the other number's exponent.
        "/ left-shift my mantissa
        ^ otherMantissa < (mantissa bitShift:(exponent-otherExponent))
    ].
    
    "/ same exponents
    ^ otherMantissa < mantissa

    "
     (LargeFloat 
         mantissa: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
         exponent:-352674
     ) < (LongFloat readFrom:'1q-500') 
     
     4.0 asLargeFloat < 4.5 asLargeFloat
     4.1 asLargeFloat < 4.2 asLargeFloat
     4.1 asLargeFloat < 4.0 asLargeFloat

     4.0 asLargeFloat < 8.0 asLargeFloat

     1.0 asLargeFloat < 2.0 asLargeFloat
     2.0 asLargeFloat < 1.0 asLargeFloat
     3.0 asLargeFloat < 1.0 asLargeFloat
     3.0 asLargeFloat < 2.0 asLargeFloat
     
     5.0 asLargeFloat < 500.0 asLargeFloat
     499.0 asLargeFloat < 500.0 asLargeFloat

     5.0 asLargeFloat < 7.0 asLargeFloat
     5.0 asLargeFloat < 17.0 asLargeFloat

    "

    "Modified (comment): / 17-07-2017 / 16:38:59 / cg"
!

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
        ].
    ].
    mantissa == 0 ifTrue:[
        exponent = 0 ifTrue:[^ self].
        "/ INF or NaN
        self isNaN ifTrue:[^ NaN].
        aLargeFloat negative ifTrue:[^ self negated].
        ^ self
    ].

    ^ self class
        mantissa:(mantissa * otherMantissa) 
        exponent:(exponent + otherExponent)
        precision:(self precision min:aLargeFloat precision)

    "
     5.0 asLargeFloat * 4
     (5.0 asLargeFloat precision:20) * 4
    "

    "Modified (comment): / 17-07-2017 / 14:50:42 / cg"
!

quotientFromLargeFloat:aLargeFloat
    "Return the quotient of the argument, aLargeFloat and the receiver.
     (i.e. divide aLargeFloat by self)
     Sent when aLargeFloat does not know how to divide by the receiver."

    |otherMantissa otherExponent otherPrecision q e pMin limit prec n|

    otherMantissa := aLargeFloat mantissa.
    otherExponent := aLargeFloat exponent.
    otherPrecision := aLargeFloat precision.
    
    otherMantissa == 0 ifTrue:[
        otherExponent = 0 ifTrue:[^ aLargeFloat].
        "/ INF or NaN
        aLargeFloat isNaN ifTrue:[^ NaN].
        self negative ifTrue:[^ aLargeFloat negated].
        ^ aLargeFloat
    ].
    mantissa == 0 ifTrue:[
        exponent = 0 ifTrue:[^ self].
        "/ INF or NaN
        self isNaN ifTrue:[^ NaN].
        aLargeFloat negative ifTrue:[^ self negated].
        ^ self
    ].

    pMin := (otherPrecision min:precision).
    pMin isFinite ifFalse:[
        pMin := DefaultPrecision.
    ].    

    "/ (m1 * (2^e1))
    "/ -------------
    "/ (m2 * (2^e2))

    "/ (m1/m2) * (2^(e1-e2))

    e := (otherExponent - exponent).
    q := (otherMantissa / mantissa).

    q isInteger ifFalse:[
        "/ now q must be made an integer with at least pMin bits
        q := (otherMantissa bitShift:pMin) / mantissa.
        e := e - pMin.

        q := q asInteger.
        (n := q lowBit - 1) > 0 ifTrue:[
            e > 0 ifTrue:[
                q := q rightShift:n.
                e := e - n.
            ] ifFalse:[
                q := q rightShift:n.
                e := e + n.
            ].    
        ].

"/        limit := pMin.
"/        prec := 0.
"/        [ q isInteger or:[ limit >= 0 ]] whileTrue:[
"/            q := q * 2. e := e - 1.
"/            prec := prec + 1.
"/            limit := limit - 1.
"/        ].
"/        q isInteger ifFalse:[
"/            pMin := prec.
"/            q := q asInteger.
"/        ].
    ].
    ^ self class
        mantissa:q 
        exponent:e
        precision:pMin

    "Modified: / 10-10-2017 / 15:57:06 / cg"
!

sumFromLargeFloat:aLargeFloat
    |otherExponent otherMantissa e m|

    otherExponent := aLargeFloat exponent.
    otherMantissa := aLargeFloat mantissa.

    otherMantissa == 0 ifTrue:[
        otherExponent = 0 ifTrue:[^ self].
        "/ INF or NaN
        aLargeFloat isNaN ifTrue:[^ NaN].
        self isFinite ifTrue:[^ aLargeFloat].
        aLargeFloat sign == self sign ifTrue:[^ aLargeFloat].
        ^ NaN
    ].
    mantissa == 0 ifTrue:[
        exponent = 0 ifTrue:[^ aLargeFloat].
        "/ INF or NaN
        self isNaN ifTrue:[^ NaN].
        ^ self
    ].

    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)
! !

!LargeFloat methodsFor:'printing'!

printOn:aStream
    exponent == 0 ifTrue:[
        mantissa printOn:aStream.
        aStream nextPutAll:'.0'.
        ^ self
    ].
    mantissa == 0 ifTrue:[
        "/ a zero mantissa is impossible - except for zero and a few others
        exponent == 0 ifTrue:[ aStream nextPutAll:'0.0'. ^ self].
        self == NaN ifTrue:[ aStream nextPutAll:'NAN'. ^ self ].
        self == NegativeInfinity ifTrue:[ aStream nextPutAll:'-INF'. ^ self].
        self == PositiveInfinity ifTrue:[ aStream nextPutAll:'INF'. ^ self].

        self error:'invalid largeFloat' mayProceed:true.
        aStream nextPutAll:'Invalid'. ^ self.
    ].

    exponent >= 0 ifTrue:[
        (mantissa bitShift:exponent) printOn:aStream.
        aStream nextPutAll:'.0'.
        ^ self
    ].
    ((mantissa / (1 bitShift:exponent negated)) asFixedPoint:6) printOn:aStream.

    "Modified: / 10-10-2017 / 14:16:04 / cg"
! !

!LargeFloat methodsFor:'private'!

mantissa:mantissaArg exponent:exponentArg  
    "set instance variables.
     Notice, that the float's value is m * 2^e"

    exponent := exponentArg.
    mantissa := mantissaArg.
    precision := Infinity positive.
    self normalize.

    "Modified (comment): / 17-07-2017 / 14:50:14 / cg"
!

mantissa:mantissaArg exponent:exponentArg precision:precisionArg  
    "set instance variables.
     Notice, that the float's value is m * 2^e"

    exponent := exponentArg.
    mantissa := mantissaArg.
    precision := precisionArg.
    self normalize

    "Modified (comment): / 17-07-2017 / 14:50:10 / cg"
!

normalize
    "adjust m & e such that m is the smallest possible 
     (i.e. has no least significant zero bit).
     Notice, that the floats value is m * 2^e"

    |shift|

    shift := mantissa lowBit - 1.
    shift > 0 ifTrue:[
        mantissa := mantissa bitShift:shift negated.
        exponent := exponent + shift
    ].

    "
     self mantissa:1 exponent:0
     self mantissa:2 exponent:0
     self mantissa:4 exponent:0  
     self mantissa:8 exponent:0  
     self mantissa:10 exponent:-1
     self mantissa:10 exponent:0 
     self mantissa:10 exponent:1 
    "
!

precision:precisionArg  
    "set instance variables.
     Notice, that the float's value is m * 2^e"

    precision := precisionArg.
    self normalize

    "Created: / 17-07-2017 / 14:50:04 / cg"
! !

!LargeFloat methodsFor:'queries'!

decimalPrecision
    "return the number of valid decimal digits"

    ^ ((self precision + 1) / (10.0 log:2)) ceiling   "use ceiling, since the last decimal digit contains some precision"

    "
     1 asShortFloat decimalPrecision 
     1 asFloat decimalPrecision      
     1 asLongFloat decimalPrecision  
     1 asLargeFloat decimalPrecision  
    "

    "Created: / 10-10-2017 / 15:48:30 / cg"
!

epsilon
    "return the maximum relative spacing of instances of mySelf
     (i.e. the value-delta of the least significant bit)"

    |p|

    p := precision.
    p isFinite ifTrue:[
        ^ self class radix asFloat raisedTo:(1 - p)
    ].
    
    "/ mhmh - what should we use here for an infinite precision ???
    ^ 1e-300
    "/ ^ LongFloat epsilon

    "Modified: / 10-10-2017 / 15:55:12 / cg"
! !

!LargeFloat methodsFor:'testing'!

isFinite
    ^ mantissa ~= 0 or:[exponent = 0]
!

isInfinite
    ^ mantissa = 0 and:[exponent ~= 0]
!

isNaN
    ^ self == NaN
!

isZero
    ^ self == Zero
!

negative
    "return true if the receiver is negative"

    mantissa == 0 ifTrue:[ ^ exponent negative].
    ^ mantissa negative
!

sign
    "return the sign of the receiver"

    mantissa == 0 ifTrue:[ 
        "special value for infinites"
        ^ exponent sign
    ].
    ^ mantissa sign
! !

!LargeFloat class methodsFor:'documentation'!

version
    ^ '$Header$'
!

version_CVS
    ^ '$Header$'
! !


LargeFloat initialize!