"

 COPYRIGHT (c) 1994 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.

"

"{ Package: 'stx:libbasic' }"

Number subclass:#LimitedPrecisionReal

	instanceVariableNames:''

	classVariableNames:''

	poolDictionaries:''

	category:'Magnitude-Numbers'

!

!LimitedPrecisionReal class methodsFor:'documentation'!

copyright

"

 COPYRIGHT (c) 1994 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

"

    Abstract superclass for any-precision floating point numbers (i.e. Float and Double).

    Due to historic reasons, ST/X's Floats are what Doubles are in ST-80.

    This may change soon (implementing LPReal is a first step towards this).

    Range and Precision of Storage Formats:

      Format |   Class    | Significant Digits (Binary) | Smallest Pos Number | Largest Pos Number | Significant Digits (Decimal)

      -------+------------+-----------------------------+---------------------+--------------------+------------------------------    

      single | ShortFloat |         24                  |  1.175... 10-38     |  3.402... 10+38    |      6-9

      -------+------------+-----------------------------+---------------------+--------------------+------------------------------    

      double | Float      |         53                  |  2.225... 10-308    |  1.797... 10+308   |     15-17

      -------+------------+-----------------------------+---------------------+--------------------+------------------------------    

      double | LongFloat  |        113                  |  3.362... 10-4932   |  1.189... 10+4932  |     33-36

      ext    |            |                             |                     |                    |

      (SPARC)|            |                             |                     |                    |

      -------+            |-----------------------------+---------------------+--------------------+------------------------------    

      double |            |         64                  |  3.362... 10-4932   |  1.189... 10+4932  |     18-21

      ext    |            |                             |                     |                    |

      (x86)  |            |                             |                     |                    |

      -------+------------+-----------------------------+---------------------+--------------------+------------------------------    

        --   | LargeFloat |         arbitrary           |  arbitrarily small  |  arbitrarily large |     arbitrary

      -------+------------+-----------------------------+---------------------+--------------------+------------------------------    

    [author:]

        Claus Gittinger

    [see also:]

        Fraction FixedPoint

"

! !

!LimitedPrecisionReal class methodsFor:'instance creation'!

fromInteger:anInteger

    "return a float with anInteger's value.

     Since floats have a limited precision, you usually loose bits when doing this

     (see Float decimalPrecision, LongFloat decimalPrecision."

    |newFloat sign absVal completeAbsVal delta mask|

    newFloat := self zero.

    sign := anInteger sign.

    (sign ~~ 0) ifTrue:[

        "be careful to do round to nearest even floating point value -

         thanks to Nicolas Cellier for this code"

        absVal := anInteger abs.

        delta := absVal highBit - self precision.

        delta > 0 ifTrue: [

            completeAbsVal := absVal.

            "eliminate insignificant/trailing bits"

            absVal := absVal bitShift: delta negated.

            "inexact := trailingBits ~= 0.

             Round to nearest even"

            (completeAbsVal bitAt:delta) ~= 0 ifTrue:[

                mask := (1 bitShift:delta-1) - 1.

                ((completeAbsVal bitAnd:mask) ~= 0 or:[absVal odd]) ifTrue:[

                    absVal := absVal + 1

                ].

            ].

        ] ifFalse: [

            delta := 0

        ].

        absVal digitLength to:1 by:-1 do:[:i |

            newFloat := (newFloat * 256) + (absVal digitByteAt:i).

        ].

        delta ~~ 0 ifTrue: [

            newFloat := newFloat timesTwoPower:delta.

        ].

        (sign < 0) ifTrue:[

            newFloat := newFloat negated

        ]

    ].

    ^ newFloat

    "

     ShortFloat fromInteger:2

     12345678901234567890 asShortFloat            

     1234567890 asFloat                     

     1234567890 asFloat asInteger                    

     -1234567890 asFloat asInteger                    

     12345678901234567890 asFloat storeString            

     12345678901234567890 asFloat asInteger   

     -12345678901234567890 asFloat asInteger   

     12345678901234567890 asLongFloat           

     12345678901234567890 asLongFloat asInteger 

     -12345678901234567890 asLongFloat asInteger 

     123456789012345678901234567890 asLongFloat           

     123456789012345678901234567890 asLongFloat asInteger  

     -123456789012345678901234567890 asLongFloat asInteger  

     1234567890123456789012345678901234567890 asLongFloat           

     1234567890123456789012345678901234567890 asLongFloat asInteger  

     -1234567890123456789012345678901234567890 asLongFloat asInteger

     'this test is on 65 bits'.

     self assert: 16r1FFFFFFFFFFFF0801 asDouble ~= 16r1FFFFFFFFFFFF0800 asDouble.

     'this test is on 64 bits'.

     self assert: 16r1FFFFFFFFFFFF0802 asDouble ~= 16r1FFFFFFFFFFFF0800 asDouble.

     'nearest even is upper'.

     self assert: 16r1FFFFFFFFFFF1F800 asDouble = 16r1FFFFFFFFFFF20000 asDouble.

     'nearest even is lower'.

     self assert: 16r1FFFFFFFFFFFF0800 asDouble = 16r1FFFFFFFFFFFF0000 asDouble.

    "

!

fromLimitedPrecisionReal:anLPReal

    "return a float with anLPReals value.

     You might loose bits when doing this.

     Slow fallback."

    |fract|

    anLPReal isFinite ifFalse:[

        anLPReal isNaN ifTrue:[^ self NaN].

        anLPReal negative ifTrue:[^ self negativeInfinity].

        ^ self infinity

    ].

    fract := anLPReal asTrueFraction.

    ^ (self fromInteger:fract numerator) / (self fromInteger:fract denominator)

!

fromNumerator:numerator denominator:denominator

    "Create a limited precision real from a Rational.

     This version will answer the nearest flotaing point value,

     according to IEEE 754 round to nearest even default mode"

    |a b q r exponent floatExponent n ha hb hq q1 eMin zero precision nSubHq|

    a := numerator abs.

    b := denominator abs.

    ha := a highBit.

    hb := b highBit.    

    zero := self zero.

    precision := self precision.

    "If both numerator and denominator are represented exactly in floating point number,

     then fastest thing to do is to use hardwired float division"

    (ha <= precision and:[hb <= precision]) ifTrue: [

        ^ (zero coerce:numerator) / (zero coerce:denominator)

    ].

    "Try and obtain a mantissa with 1 bit excess precision.

     First guess is rough, we might get one more bit or one less"

    exponent := ha - hb - precision - 1.

    exponent > 0

        ifTrue: [b := b bitShift: exponent]

        ifFalse: [a := a bitShift: exponent negated].

    q := a quo: b.

    r := a - (q * b).

    hq := q highBit.

    "check for gradual underflow, in which case we should use less bits"

    floatExponent := exponent + hq - 1.

    eMin := 2 - (1 bitShift: (self numBitsInExponent - 1)).

    n := floatExponent >= eMin

        ifTrue: [precision + 1]

        ifFalse: [precision + 1 + floatExponent - eMin].

    nSubHq := n - hq.

    nSubHq < 0 ifTrue: [

        exponent := exponent + hq - n.

        r := (q bitAnd: (1 bitShift:nSubHq) - 1) * b + r.

        q := q bitShift:nSubHq

    ] ifFalse:[nSubHq > 0 ifTrue: [

        exponent := exponent + hq - n.

        q1 := (r bitShift:nSubHq) quo: b.

        q := (q bitShift:nSubHq) bitAnd: q1.

        r := r - (q1 * b)

    ]].

    "check if we should round upward.

     The case of exact half (q bitAnd: 1) isZero not & (r isZero)

     will be handled by self fromInteger: conversion"

    ((q bitAnd:1) ~~ 0 and:[r ~~ 0]) ifTrue:[

        q := q + 1

    ].

    (numerator negative xor:denominator negative) ifTrue: [

        q := q negated.

    ].

    ^ (zero coerce:q) timesTwoPower:exponent

    "

        Time millisecondsToRun:[

            1000000  timesRepeat:[

                Float fromNumerator:12345678901234567890 denominator:987654321

            ].

        ]

        |fraction|

        fraction := 12345678901234567890//987654321.

        Time millisecondsToRun:[

            1000000  timesRepeat:[

                fraction asFloat

            ].

        ]

    "

!

new:aNumber

    "catch this message - not allowed for floats/doubles"

    self error:'Floats/Doubles cannot be created with new:'

! !

!LimitedPrecisionReal class methodsFor:'class initialization'!

initialize

    "initialize ANSI compliant float globals"

    Smalltalk at:#FloatE put:ShortFloat.

    Smalltalk at:#FloatD put:Float.

    Smalltalk at:#FloatQ put:LongFloat.

    "

     self initialize

    "

    "Created: / 7.9.2001 / 14:02:45 / cg"

    "Modified: / 7.9.2001 / 14:02:54 / cg"

! !

!LimitedPrecisionReal class methodsFor:'constants & defaults'!

NaN

    "return the constant NaN (not a Number)."

    ^ self zero uncheckedDivide:self zero

    "

      ShortFloat NaN  

      Float NaN       

      LongFloat NaN   

      LargeFloat NaN   

    "

!

e

    "return the closest approximation of the irrational number e"

    self subclassResponsibility

    "Modified: / 7.9.2001 / 14:05:02 / cg"

!

emax

    "return the largest exponent"

    self subclassResponsibility

    "Created: / 7.9.2001 / 14:05:28 / cg"

!

emin

    "return the smallest exponent"

    self subclassResponsibility

    "Created: / 7.9.2001 / 14:05:35 / cg"

!

epsilon

    "return the maximum relative spacing"

    ^ self radix asFloat raisedToInteger:(1 - self precision)

    "

      ShortFloat epsilon  

      Float epsilon       

      LongFloat epsilon   

    "

!

fmax

    "return the largest value allowed"

    self subclassResponsibility

    "Created: / 7.9.2001 / 14:06:56 / cg"

!

fmin

    "return the minimum value allowed"

    self subclassResponsibility

    "Created: / 7.9.2001 / 14:07:06 / cg"

!

infinity

    "return a float representing infinity"

    ^ self unity uncheckedDivide:self zero

    "

      ShortFloat infinity  

      Float infinity       

      LongFloat infinity   

      LargeFloat infinity   

    "

!

negativeInfinity

    "return a float representing negative infinity"

    ^ self unity negated uncheckedDivide:self zero

    "

      ShortFloat negativeInfinity   

      Float negativeInfinity       

      LongFloat negativeInfinity   

      LargeFloat negativeInfinity   

    "

!

pi

    "return the closest approximation of the irrational number pi"

    self subclassResponsibility

    "Created: / 7.9.2001 / 14:07:35 / cg"

! !

!LimitedPrecisionReal class methodsFor:'queries'!

decimalPrecision

    "return the number of valid decimal digits"

    ^ (self precision / (10.0 log:self radix)) floor

    "

     ShortFloat decimalPrecision 

     Float decimalPrecision      

     LongFloat decimalPrecision  

    "

!

isAbstract

    ^ self == LimitedPrecisionReal

    "

     1.0 class isAbstract

    "

!

numBitsInExponent

    "return the number of bits in the exponent"

    ^ self subclassResponsibility

!

numBitsInIntegerPart

    ^ 0

!

numBitsInMantissa

    "return the number of bits in the mantissa

     (typically 1 less than the precision due to the hidden bit)"

    ^ self subclassResponsibility

!

precision

    "return the number of valid mantissa bits"

    ^ self numBitsInMantissa + 1 - self numBitsInIntegerPart 

!

radix

    "return the radix (base)"

    self subclassResponsibility

    "Created: / 7.9.2001 / 14:08:20 / cg"

! !

!LimitedPrecisionReal methodsFor:'accessing'!

at:index

    "redefined to prevent access to individual bytes in a real."

    self error:'not allowed for floats/doubles'

!

at:index put:aValue

    "redefined to prevent access to individual bytes in a real"

    self error:'not allowed for floats/doubles'

! !

!LimitedPrecisionReal methodsFor:'arithmetic'!

* aNumber

    "return the product of the receiver and the argument, aNumber"

"/ as soon as Float are float & Double are doubles,

"/ use:

"/    ^ aNumber productFromDouble:self asDouble

    ^ aNumber productFromFloat:self asFloat

    "Modified: 17.4.1996 / 12:35:36 / cg"

!

+ aNumber

    "return the sum of the receiver and the argument, aNumber"

"/ as soon as Float are float & Double are doubles,

"/ use:

"/    ^ aNumber sumFromDouble:self asDouble

    ^ aNumber sumFromFloat:self asFloat

    "Modified: 17.4.1996 / 12:35:55 / cg"

!

- aNumber

    "return the difference of the receiver and the argument, aNumber"

"/ as soon as Float are float & Double are doubles,

"/ use:

"/    ^ aNumber differenceFromDouble:self asDouble

    ^ aNumber differenceFromFloat:self asFloat

    "Modified: 17.4.1996 / 12:36:07 / cg"

!

/ aNumber

    "return the quotient of the receiver and the argument, aNumber"

    ((aNumber == 0) or:[aNumber = 0.0]) ifTrue:[

        ^ ZeroDivide raiseRequestWith:thisContext.

    ].

"/ as soon as Float are float & Double are doubles,

"/ use:

"/    ^ aNumber quotientFromDouble:self asDouble

    ^ aNumber quotientFromFloat:self asFloat

    "Modified: / 17.4.1996 / 12:36:21 / cg"

    "Modified: / 26.7.1999 / 10:46:11 / stefan"