Number.st
author Claus Gittinger <cg@exept.de>
Fri, 17 Feb 2006 14:11:48 +0100
changeset 9130 07e7a292aa76
parent 9127 04cd80c64a30
child 9138 a43f3145527f
permissions -rw-r--r--
fixedPoint reading fixed (explicit scale)
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"
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 COPYRIGHT (c) 1988 by Claus Gittinger
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	      All Rights Reserved
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 This software is furnished under a license and may be used
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 only in accordance with the terms of that license and with the
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 inclusion of the above copyright notice.   This software may not
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 be provided or otherwise made available to, or used by, any
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 other person.  No title to or ownership of the software is
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 hereby transferred.
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"
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"{ Package: 'stx:libbasic' }"
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ArithmeticValue subclass:#Number
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	instanceVariableNames:''
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	classVariableNames:'DecimalPointCharacter DecimalPointCharacterForPrinting
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		DecimalPointCharacters DecimalPointCharactersForReading'
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	poolDictionaries:''
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	category:'Magnitude-Numbers'
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!
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!Number class methodsFor:'documentation'!
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copyright
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"
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 COPYRIGHT (c) 1988 by Claus Gittinger
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	      All Rights Reserved
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 This software is furnished under a license and may be used
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 only in accordance with the terms of that license and with the
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 inclusion of the above copyright notice.   This software may not
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 be provided or otherwise made available to, or used by, any
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 other person.  No title to or ownership of the software is
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 hereby transferred.
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"
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!
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documentation
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    abstract superclass for all kinds of numbers
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    [class variables:]
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        DecimalPointCharacterForPrinting          <Character>                     used when printing
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        DecimalPointCharactersForReading          <Collection of Character>       accepted as decimalPointChars when reading
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    [author:]
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        Claus Gittinger
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    [see also:]
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        Integer LargeInteger SmallInteger
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        LimitedPrecisionReal Float ShortFloat
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        Fraction FixedPoint
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"
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! !
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!Number class methodsFor:'instance creation'!
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fromString:aString
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    "for compatibility with other smalltalks - same as #readFrom:"
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    |s num|
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    s := aString readStream.
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    num := self readFrom:s onError:[^ self error:'invalid number'].
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    s atEnd ifFalse:[^ self error:'garbage at end of number'].
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    ^ num.
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    "
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     Number fromString:'12345'
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     Number fromString:'abc'
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     Number fromString:'1abc'
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     '12345' asNumber
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    "
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    "Modified: / 3.8.1998 / 20:05:11 / cg"
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!
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fromString:aString onError:exceptionBlock
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    "for compatibility with other smalltalks - same as #readFrom:"
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    ^ self readFrom:aString onError:exceptionBlock
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    "
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     Number fromString:'12345' onError:0
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     Number fromString:'fooBarBaz' onError:0
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    "
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    "Modified: / 3.8.1998 / 20:05:34 / cg"
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!
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readFrom:aStringOrStream onError:exceptionBlock
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    "return the next Number from the (character-)stream aStream;
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     skipping all whitespace first; return the value of exceptionBlock,
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     if no number can be read.
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     This method is less strict than the smalltalk number reader; it
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     allows for prefixed + and also allows missing fractional part after eE"
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    ^ [
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        |value intValue mantissaAndScale scale decimalPointCharacters decimalMantissa str 
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         nextChar radix negative signExp exp denom|
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        decimalPointCharacters := self decimalPointCharactersForReading.
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        str := aStringOrStream readStream.
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        nextChar := str skipSeparators.
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        nextChar isNil ifTrue:[^ exceptionBlock value].
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        (nextChar == $-) ifTrue:[
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            negative := true.
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            str next.
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            nextChar := str peekOrNil
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        ] ifFalse:[
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            negative := false.
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            (nextChar == $+) ifTrue:[
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                str next.
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                nextChar := str peekOrNil
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            ]
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        ].
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        (nextChar isDigit or:[(decimalPointCharacters includes:nextChar)]) ifFalse:[
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            ^ exceptionBlock value.
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"/          value := super readFrom:str.
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"/          negative ifTrue:[value := value negated].
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"/          ^ value
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        ].
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        (decimalPointCharacters includes:nextChar) ifTrue:[
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            radix := 10.
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            value := 0.0.
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            intValue := 0.
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        ] ifFalse:[
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            value := Integer readFrom:str radix:10.
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            nextChar := str peekOrNil.
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            ((nextChar == $r) or:[ nextChar == $R]) ifTrue:[
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                str next.
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                radix := value.
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                value := Integer readFrom:str radix:radix.
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            ] ifFalse:[
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                radix := 10
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            ].
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            intValue := value.
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        ].
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        (decimalPointCharacters includes:nextChar) ifTrue:[
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            str next.
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            nextChar := str peekOrNil.
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            decimalMantissa := 0.
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            (nextChar notNil and:[nextChar isDigitRadix:radix]) ifTrue:[
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                mantissaAndScale := Number readMantissaAndScaleFrom:str radix:radix.
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                value := value asFloat + (mantissaAndScale first).
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                nextChar := str peekOrNil
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            ]
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        ].
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        ('eEdDqQ' includes:nextChar) ifTrue:[
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            str next.
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            nextChar := str peekOrNil.
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            signExp := 1.
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            (nextChar == $+) ifTrue:[
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                str next.
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                nextChar := str peekOrNil.
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            ] ifFalse:[
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                (nextChar == $-) ifTrue:[
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                    str next.
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                    nextChar := str peekOrNil.
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                    signExp := -1
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                ]
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            ].
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            ('qQ' includes:nextChar) ifTrue:[
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                value := value asLongFloat.
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            ] ifFalse:[
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                value := value asFloat.
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"/ future: (for now, always create Doubles for Dolphin,Squeak etc. compatibility
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"/                ('eE' includes:nextChar) ifTrue:[
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"/                    value := value asShortFloat
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"/                ]
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            ].
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            (nextChar notNil and:[(nextChar isDigitRadix:radix)]) ifTrue:[
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                exp := (Integer readFrom:str radix:radix) * signExp.
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                value := value * ((value class unity * 10.0) raisedToInteger:exp)
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            ]
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        ] ifFalse:[
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            ('s' includes:nextChar) ifTrue:[
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                str next.
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                nextChar := str peekOrNil.
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                (nextChar notNil and:[(nextChar isDigitRadix:radix)]) ifTrue:[
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                    scale := (Integer readFrom:str radix:10).
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                ].
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                mantissaAndScale isNil ifTrue:[
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                    value := intValue asFixedPoint:(scale ? 0).
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                ] ifFalse:[
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                    denom := 10 raisedTo:mantissaAndScale last.
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                    value := FixedPoint 
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                                numerator:(intValue * denom) + (mantissaAndScale second)
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                                denominator:denom
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                                scale:(scale ? mantissaAndScale last).
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                ].
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            ] ifFalse:[
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                value isLimitedPrecisionReal ifTrue:[
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                    value := value asFloat.
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                ]
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            ].
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        ].
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        negative ifTrue:[
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            value := value negated
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        ].
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        value.
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    ] on:Error do:exceptionBlock
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329
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   211
    "
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   212
     Number readFrom:(ReadStream on:'54.32e-01')      
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     Number readFrom:(ReadStream on:'12345678901234567890') 
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     Number readFrom:(ReadStream on:'12345678901234567890.0') 
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     Number readFrom:(ReadStream on:'12345678901234567890.012345678901234567890') 
329
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     Number readFrom:(ReadStream on:'16rAAAAFFFFAAAAFFFF') 
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     Number readFrom:'16rAAAAFFFFAAAAFFFF' 
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     Number readFrom:'0.000001'  
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     '+00000123.45' asNumber  
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     Number readFrom:'99s'      
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     Number readFrom:'99.00s'      
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     Number readFrom:'99.0000000s'      
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     Number readFrom:'.0000000s'      
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     Number readFrom:'.0000000q'      
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     Number readFrom:'.0000000f'      
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     Number readFrom:'.0000000e'      
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     Number readFrom:'.0000000s1'      
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     Number readFrom:'.0000000q1'      
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     Number readFrom:'.0000000f1'      
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     Number readFrom:'.0000000e1'      
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     DecimalPointCharactersForReading := #( $. $, ).   
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     Number readFrom:'99,00'      
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     DecimalPointCharactersForReading := #( $. ).   
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     Number readFrom:'99,00'      
329
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diff changeset
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    "
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   238
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7c64da3964e4 faster conversion from string (due to slow #pastEnd)
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    "Modified: / 14.4.1998 / 19:22:50 / cg"
296
754358c5508a *** empty log message ***
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   240
!
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   241
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   242
readSmalltalkSyntaxFrom:aStream
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   243
    "ST-80 compatibility (thanks to a note from alpha testers)
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   244
     read and return the next Number in smalltalk syntax from the 
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   245
     (character-) aStream.
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   246
     Returns nil if aStream contains no valid number."
329
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   247
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   248
    ^ Scanner scanNumberFrom:aStream
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   249
"/    ^ Compiler evaluate:aStream compile:false "/ self readFrom:aStream.
296
754358c5508a *** empty log message ***
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   250
329
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diff changeset
   251
    "
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   252
     Number readSmalltalkSyntaxFrom:'99d'    
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   253
     Number readSmalltalkSyntaxFrom:'99.00d'    
329
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   254
     Number readSmalltalkSyntaxFrom:(ReadStream on:'54.32e-01')    
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   255
     Number readSmalltalkSyntaxFrom:(ReadStream on:'12345678901234567890')
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   256
     Number readSmalltalkSyntaxFrom:(ReadStream on:'16rAAAAFFFFAAAAFFFF')
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   257
     Number readSmalltalkSyntaxFrom:(ReadStream on:'(1/10)') 
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   258
     Number readFrom:(ReadStream on:'(1/10)') 
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   259
     Number readSmalltalkSyntaxFrom:(ReadStream on:'+00000123.45')  
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   260
     Number readFrom:(ReadStream on:'+00000123.45')  
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   261
e2aff65e6eba comment
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   262
     |s|
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   263
     s := ReadStream on:'2.'.
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   264
     Number readSmalltalkSyntaxFrom:s.
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   265
     s next    
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   266
e2aff65e6eba comment
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   267
     |s|
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   268
     s := ReadStream on:'2.0.'.
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   269
     Number readSmalltalkSyntaxFrom:s.
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   270
     s next    
329
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diff changeset
   271
    "
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   272
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   273
    "Modified: / 19.11.1999 / 18:26:47 / cg"
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   274
! !
701
a309e3ef7faf checkin from browser
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   275
7729
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
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   276
!Number class methodsFor:'constants'!
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   277
8301
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   278
decimalPointCharacter 
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   279
    "printed"
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   280
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   281
    <resource: #obsolete>
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   282
04cd80c64a30 decimapPointCharacter stuff;
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   283
    ^ self decimalPointCharacterForPrinting
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   284
!
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   285
8303
837daadaab78 decimalPointCharacter definition
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   286
decimalPointCharacter:aCharacter 
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   287
    "printed"
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    <resource: #obsolete>
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   291
    self decimalPointCharacterForPrinting:aCharacter
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   292
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   293
    "
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   294
     1.5 printString
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   296
     Number decimalPointCharacter:$,.
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   297
     1.5 printString       
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   298
     Number decimalPointCharacter:$..
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   299
    "
04cd80c64a30 decimapPointCharacter stuff;
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   300
!
04cd80c64a30 decimapPointCharacter stuff;
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   301
04cd80c64a30 decimapPointCharacter stuff;
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   302
decimalPointCharacterForPrinting 
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   303
    "printed"
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   304
04cd80c64a30 decimapPointCharacter stuff;
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   305
    DecimalPointCharacterForPrinting isNil ifTrue:[
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   306
        ^ $.
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parents: 8979
diff changeset
   307
    ].
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parents: 8979
diff changeset
   308
    ^ DecimalPointCharacterForPrinting
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   309
!
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   310
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   311
decimalPointCharacterForPrinting:aCharacter 
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   312
    "printed"
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   313
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   314
    DecimalPointCharacterForPrinting := aCharacter
8303
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   315
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   316
    "
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   317
     1.5 printString
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   318
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   319
     Number decimalPointCharacter:$,.
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   320
     1.5 printString       
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   321
     Number decimalPointCharacter:$..
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   322
    "
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   323
!
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   324
8301
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   325
decimalPointCharacters 
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   326
    "accepted when converting from a string"
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   327
9127
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   328
    <resource: #obsolete>
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   329
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   330
    ^ self decimalPointCharactersForReading
8303
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   331
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   332
    "
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   333
     1.5 printString
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   334
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   335
     Number decimalPointCharacters:#( $. $,) .
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   336
     Number fromString:'1.5'.     
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   337
     Number fromString:'1,5'.     
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   338
     Number decimalPointCharacters:#( $. ).
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   339
    "
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   340
!
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   341
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   342
decimalPointCharacters:aCollectionOfCharacters 
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   343
    "accepted when converting from a string"
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   344
9127
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   345
    <resource: #obsolete>
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   346
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   347
    self decimalPointCharactersForReading:aCollectionOfCharacters 
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   348
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   349
    "
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   350
     Number decimalPointCharacters:#( $. $,) .
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   351
     Number fromString:'1.5'.     
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   352
     Number fromString:'1,5'.     
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   353
     Number decimalPointCharacters:#( $. ).
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   354
    "
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   355
!
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   356
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   357
decimalPointCharactersForReading 
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   358
    "accepted when converting from a string"
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   359
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   360
    DecimalPointCharactersForReading isNil ifTrue:[
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   361
        ^ #( $. $,)
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   362
    ].
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   363
    ^ DecimalPointCharactersForReading
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   364
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   365
    "
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   366
     1.5 printString
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   367
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   368
     Number decimalPointCharacters:#( $. $,) .
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   369
     Number fromString:'1.5'.     
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   370
     Number fromString:'1,5'.     
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   371
     Number decimalPointCharacters:#( $. ).
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   372
    "
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   373
!
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   374
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   375
decimalPointCharactersForReading:aCollectionOfCharacters 
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   376
    "accepted when converting from a string"
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   377
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   378
    DecimalPointCharactersForReading := aCollectionOfCharacters
8303
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   379
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   380
    "
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   381
     Number decimalPointCharacters:#( $. $,) .
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   382
     Number fromString:'1.5'.     
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   383
     Number fromString:'1,5'.     
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   384
     Number decimalPointCharacters:#( $. ).
837daadaab78 decimalPointCharacter definition
werner
parents: 8301
diff changeset
   385
    "
8301
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   386
!
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   387
7729
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
   388
epsilon
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
   389
    "return the maximum relative spacing of instances of mySelf 
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
   390
     (i.e. the value-delta of the least significant bit)"
7729
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
   391
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
   392
     ^ self subclassResponsibility
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
   393
!
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
   394
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
   395
pi
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
   396
    "return Pi in my representation (and accuracy)."
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
   397
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
   398
     ^ self subclassResponsibility
7729
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
   399
! !
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
   400
1892
d3564145c15c *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 1701
diff changeset
   401
!Number class methodsFor:'error reporting'!
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   402
6195
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   403
raise:aSignalSymbolOrErrorClass receiver:someNumber selector:sel arg:arg errorString:text 
3394
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   404
    "ST-80 compatible signal raising. Provided for PD numeric classes"
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   405
4558
94044dccefab checkin from browser
Claus Gittinger <cg@exept.de>
parents: 3995
diff changeset
   406
    <context: #return>
94044dccefab checkin from browser
Claus Gittinger <cg@exept.de>
parents: 3995
diff changeset
   407
6195
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   408
    ^ self
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   409
        raise:aSignalSymbolOrErrorClass 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   410
        receiver:someNumber 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   411
        selector:sel 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   412
        arguments:(Array with:arg)
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   413
        errorString:text 
3394
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   414
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   415
    "
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   416
     Number 
6195
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   417
        raise:#domainErrorSignal
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   418
        receiver:1.0
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   419
        selector:#sin
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   420
        arg:nil
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   421
        errorString:'foo bar test'
3394
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   422
    "
6195
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   423
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   424
    "Modified: / 16.11.2001 / 14:12:50 / cg"
3394
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   425
!
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   426
6195
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   427
raise:aSignalSymbolOrErrorClass receiver:someNumber selector:sel arguments:argArray errorString:text 
6194
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   428
    "ST-80 compatible signal raising. Provided for PD numeric classes.
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   429
     aSignalSymbolOrErrorClass is either an Error-subclass, or
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   430
     the selector which is sent to myself, to retrieve the Exception class / Signal."
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   431
4558
94044dccefab checkin from browser
Claus Gittinger <cg@exept.de>
parents: 3995
diff changeset
   432
    <context: #return>
94044dccefab checkin from browser
Claus Gittinger <cg@exept.de>
parents: 3995
diff changeset
   433
6194
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   434
    |msg signalOrException|
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   435
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   436
    msg := MessageSend
6194
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   437
                receiver:someNumber
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   438
                selector:sel
6195
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   439
                arguments:argArray.
3394
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   440
6194
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   441
    aSignalSymbolOrErrorClass isSymbol ifTrue:[
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   442
        signalOrException := self perform:aSignalSymbolOrErrorClass.
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   443
    ] ifFalse:[
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   444
        signalOrException := aSignalSymbolOrErrorClass.    "/ assume its an Error-Subclass
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   445
    ].
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   446
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   447
    ^ signalOrException
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   448
         raiseRequestWith:msg 
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   449
         errorString:text 
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   450
         in:thisContext sender
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   451
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   452
    "
3394
33e8273b95f3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 3375
diff changeset
   453
     Number 
6194
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   454
        raise:#domainErrorSignal
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   455
        receiver:1.0
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   456
        selector:#foo 
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   457
        errorString:'foo bar test'
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   458
    "
6194
e060dbb4f75c allow Exception-arg in #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6155
diff changeset
   459
6195
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   460
    "Modified: / 16.11.2001 / 14:12:09 / cg"
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   461
!
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   462
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   463
raise:aSignalSymbolOrErrorClass receiver:someNumber selector:sel errorString:text 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   464
    "ST-80 compatible signal raising. Provided for PD numeric classes.
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   465
     aSignalSymbolOrErrorClass is either an Error-subclass, or
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   466
     the selector which is sent to myself, to retrieve the Exception class / Signal."
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   467
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   468
    <context: #return>
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   469
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   470
    ^ self
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   471
        raise:aSignalSymbolOrErrorClass 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   472
        receiver:someNumber 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   473
        selector:sel 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   474
        arguments:#()
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   475
        errorString:text 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   476
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   477
    "
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   478
     Number 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   479
        raise:#domainErrorSignal
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   480
        receiver:1.0
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   481
        selector:#foo 
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   482
        errorString:'foo bar test'
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   483
    "
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   484
9e60c38d1d61 #raise:receiver:selector...
Claus Gittinger <cg@exept.de>
parents: 6194
diff changeset
   485
    "Modified: / 16.11.2001 / 14:13:16 / cg"
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   486
! !
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   487
1892
d3564145c15c *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 1701
diff changeset
   488
!Number class methodsFor:'private'!
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   489
6899
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   490
readMantissaAndScaleFrom:aStream radix:radix
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   491
    "helper for readFrom: -
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   492
     return the mantissa (post-decimal-point digits) from the (character-)stream aStream;
7356
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
   493
     In addition, the scale (number of postDecimalPoint digits) is returned 
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
   494
     (to support reading fixedPoint numbers).
6899
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   495
     No whitespace is skipped.
7356
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
   496
     Errs if no number is available on aStream."
6899
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   497
7388
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   498
    |nextChar value factor intMantissa scale highPrecision|
6899
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   499
7388
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   500
    highPrecision := false.
6899
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   501
    value := 0.0.
7388
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   502
    factor := 1.0 asLongFloat / radix.
6899
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   503
    scale := 0.
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   504
    intMantissa := 0.
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   505
    nextChar := aStream peekOrNil.
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   506
    [nextChar notNil and:[nextChar isDigitRadix:radix]] whileTrue:[
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   507
        value := value + (nextChar digitValue * factor).
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   508
        intMantissa := (intMantissa * radix) + nextChar digitValue.
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   509
        factor := factor / radix.
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   510
        scale := scale + 1.
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   511
        aStream next.
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   512
        nextChar := aStream peekOrNil
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   513
    ].
7388
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   514
6899
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   515
    ^ (Array with:value with:intMantissa with:scale).
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   516
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   517
    "
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   518
     Number readMantissaAndScaleFrom:'234'    readStream radix:10. 
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   519
     Number readMantissaAndScaleFrom:'2'      readStream radix:10. 
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   520
     Number readMantissaAndScaleFrom:'234567' readStream radix:10. 
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   521
     Number readMantissaAndScaleFrom:'234000' readStream radix:10. 
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   522
     Number readMantissaAndScaleFrom:'234'    readStream radix:10. 
7356
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
   523
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
   524
     Number readMantissaAndScaleFrom:'12345678901234567890' readStream radix:10. 
6899
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   525
    "
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   526
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   527
    "Modified: / 14.4.1998 / 18:47:47 / cg"
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   528
!
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   529
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   530
readMantissaFrom:aStream radix:radix
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   531
    "helper for readFrom: -
6692
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   532
     return the mantissa (post-decimal-point digits)
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   533
     from the (character-)stream aStream;
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   534
     No whitespace is skipped.
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   535
     Errs if no number available."
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   536
6899
9ed8494c9f10 support for fixedPoint numbers (s-exponentCharacter)
Claus Gittinger <cg@exept.de>
parents: 6702
diff changeset
   537
    ^ (self readMantissaAndScaleFrom:aStream radix:radix) first
3375
7c64da3964e4 faster conversion from string (due to slow #pastEnd)
Claus Gittinger <cg@exept.de>
parents: 3060
diff changeset
   538
6692
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   539
    "
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   540
     Number readMantissaFrom:'234'    readStream radix:10.
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   541
     Number readMantissaFrom:'2'      readStream radix:10.
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   542
     Number readMantissaFrom:'234567' readStream radix:10.
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   543
    "
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   544
3375
7c64da3964e4 faster conversion from string (due to slow #pastEnd)
Claus Gittinger <cg@exept.de>
parents: 3060
diff changeset
   545
    "Modified: / 14.4.1998 / 18:47:47 / cg"
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   546
! !
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   547
8892
5d05a7f150a5 +isAbstract
Claus Gittinger <cg@exept.de>
parents: 8844
diff changeset
   548
!Number class methodsFor:'queries'!
5d05a7f150a5 +isAbstract
Claus Gittinger <cg@exept.de>
parents: 8844
diff changeset
   549
5d05a7f150a5 +isAbstract
Claus Gittinger <cg@exept.de>
parents: 8844
diff changeset
   550
isAbstract
5d05a7f150a5 +isAbstract
Claus Gittinger <cg@exept.de>
parents: 8844
diff changeset
   551
    ^ self == Number
5d05a7f150a5 +isAbstract
Claus Gittinger <cg@exept.de>
parents: 8844
diff changeset
   552
! !
5d05a7f150a5 +isAbstract
Claus Gittinger <cg@exept.de>
parents: 8844
diff changeset
   553
7261
f35fc9cee675 method category rename
Claus Gittinger <cg@exept.de>
parents: 7214
diff changeset
   554
!Number methodsFor:'Compatibility-Squeak'!
4988
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   555
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   556
asSmallAngleDegrees
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   557
    "Return the receiver normalized to lie within the range (-180, 180)"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   558
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   559
    | pos |
4988
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   560
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   561
    pos := self \\ 360.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   562
    pos > 180 ifTrue: [pos := pos - 360].
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   563
    ^ pos
4988
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   564
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   565
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   566
     #(-500 -300 -150 -5 0 5 150 300 500 1200) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   567
        collect: [:n | n asSmallAngleDegrees]
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   568
    "
6072
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   569
!
4988
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   570
6335
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   571
closeFrom:aNumber
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   572
    "are these two numbers close?"
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   573
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   574
    | fuzz |
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   575
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   576
    self isNaN == aNumber isNaN ifFalse: [^ false]. 
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   577
    self isInfinite == aNumber isInfinite ifFalse: [^ false].
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   578
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   579
    fuzz := (self abs max:aNumber abs) * 0.0001. 
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   580
    ^ (self - aNumber) abs <= fuzz
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   581
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   582
    "
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   583
     9.0 closeTo: 8.9999     
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   584
     9.9 closeTo: 9          
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   585
     (9/3) closeTo: 2.9999      
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   586
     1 closeTo: 0.9999      
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   587
     1 closeTo: 1.0001      
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   588
     1 closeTo: 1.001       
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   589
     1 closeTo: 0.999       
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   590
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   591
     0.9999 closeTo: 1      
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   592
     1.0001 closeTo: 1      
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   593
     1.001 closeTo: 1     
6345
cfe5db4fe391 Only comments
Stefan Vogel <sv@exept.de>
parents: 6335
diff changeset
   594
     0.999 closeTo: 1
cfe5db4fe391 Only comments
Stefan Vogel <sv@exept.de>
parents: 6335
diff changeset
   595
     Float NaN closeTo:Float NaN
cfe5db4fe391 Only comments
Stefan Vogel <sv@exept.de>
parents: 6335
diff changeset
   596
     Float infinity closeTo:Float infinity
6335
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   597
    "
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   598
!
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   599
6143
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
   600
closeTo:num
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   601
    "are these two numbers close to each other?"
6143
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
   602
6374
fad888313ce3 closeTo: fix
Claus Gittinger <cg@exept.de>
parents: 6345
diff changeset
   603
    num isNumber ifFalse:[^false].
6335
8286bc57d05e closeTo: generalized for all numbers
Claus Gittinger <cg@exept.de>
parents: 6258
diff changeset
   604
    ^ num closeFrom:self
6143
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
   605
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
   606
    "
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
   607
     1 closeTo:1.0000000001
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
   608
     1 closeTo:1.001
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
   609
    "
6155
00eaf2fa55bc isReal comment
Claus Gittinger <cg@exept.de>
parents: 6154
diff changeset
   610
00eaf2fa55bc isReal comment
Claus Gittinger <cg@exept.de>
parents: 6154
diff changeset
   611
    "Created: / 5.11.2001 / 18:07:26 / cg"
6143
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
   612
!
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
   613
4988
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   614
newTileMorphRepresentative
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   615
	^ TileMorph new addArrows; setLiteral: self; addSuffixIfCan
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   616
!
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   617
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   618
stringForReadout
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   619
    ^ self rounded printString
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   620
! !
ac426684e852 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4895
diff changeset
   621
6692
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   622
!Number methodsFor:'coercing'!
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   623
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   624
retry: aSymbol coercing: aNumber
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   625
    "Arithmetic represented by the symbol, aSymbol,
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   626
    could not be performed with the receiver and the argument,
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   627
    aNumber, because of the differences in representation.  Coerce either
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   628
    the receiver or the argument, depending on which has higher generality, and
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   629
    try again.  If the symbol is the equals sign, answer false if the argument
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   630
    is not a Number.  If the generalities are the same, create an error message."
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   631
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   632
    |myGenerality otherGenerality|
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   633
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   634
    (aSymbol == #=) ifTrue:[
6702
545b50725894 infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents: 6692
diff changeset
   635
        (aNumber respondsTo:#generality) ifFalse:[^ false]
6692
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   636
    ] ifFalse:[
6702
545b50725894 infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents: 6692
diff changeset
   637
        (aNumber respondsTo:#generality) ifFalse:[
545b50725894 infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents: 6692
diff changeset
   638
            self error:'retry:coercing: argument is not a number'.
545b50725894 infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents: 6692
diff changeset
   639
            ^ self
545b50725894 infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents: 6692
diff changeset
   640
        ]
6692
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   641
    ].
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   642
    myGenerality := self generality.
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   643
    otherGenerality := aNumber generality.
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   644
    (myGenerality > otherGenerality) ifTrue:[
6702
545b50725894 infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents: 6692
diff changeset
   645
        ^ self perform:aSymbol with:(self coerce:aNumber)
6692
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   646
    ].
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   647
    (myGenerality < otherGenerality) ifTrue:[
6702
545b50725894 infinitz query fix (int * point)
Claus Gittinger <cg@exept.de>
parents: 6692
diff changeset
   648
        ^ (aNumber coerce:self) perform:aSymbol with:aNumber
6692
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   649
    ].
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   650
    self error:'retry:coercing: oops - same generality'
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   651
! !
314f88dcbbd1 comment
Claus Gittinger <cg@exept.de>
parents: 6637
diff changeset
   652
9127
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   653
!Number methodsFor:'coercing & converting'!
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   654
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   655
i
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   656
    "return a complex number, with the receiver as imaginary part, 0 as real part"
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   657
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   658
    ^ Complex
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   659
        real:0
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   660
        imaginary:self
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   661
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   662
    "
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   663
     3i          
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   664
     (1+1i)      
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   665
    "
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   666
! !
04cd80c64a30 decimapPointCharacter stuff;
Claus Gittinger <cg@exept.de>
parents: 8979
diff changeset
   667
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   668
!Number methodsFor:'converting'!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   669
3634
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   670
% aNumber 
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   671
    "Return a complex number with the receiver as the real part and 
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   672
     aNumber as the imaginary part"
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   673
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   674
    ^ Complex real:self imaginary:aNumber
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   675
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   676
    "Modified: / 9.7.1998 / 10:18:12 / cg"
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   677
!
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   678
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   679
@ aNumber
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   680
    "return a Point with the receiver as x-coordinate and the argument
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   681
     as y-coordinate"
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   682
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   683
%{  /* NOCONTEXT */
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   684
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   685
    /*
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   686
     * I cannot tell if this special code is worth anything
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   687
     */
5322
411b6c0f7250 renamed sone structures;
Claus Gittinger <cg@exept.de>
parents: 5299
diff changeset
   688
    if (__CanDoQuickNew(sizeof(struct __Point))) {      /* OBJECT ALLOCATION */
7857
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   689
        OBJ newPoint;
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   690
        int spc;
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   691
7857
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   692
        __qCheckedAlignedNew(newPoint, sizeof(struct __Point));
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   693
        __InstPtr(newPoint)->o_class = @global(Point);
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   694
        __qSTORE(newPoint, @global(Point));
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   695
        __PointInstPtr(newPoint)->p_x = self;
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   696
        __PointInstPtr(newPoint)->p_y = aNumber;
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   697
        if (! __bothSmallInteger(self, aNumber)) {
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   698
            spc = __qSpace(newPoint);
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   699
            __STORE_SPC(newPoint, aNumber, spc);
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   700
            __STORE_SPC(newPoint, self, spc);
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   701
        }
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   702
        RETURN ( newPoint );
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   703
    }
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   704
%}
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   705
.
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   706
    ^ Point x:self y:aNumber
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   707
!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   708
3634
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   709
asComplex
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   710
    "Return a complex number with the receiver as the real part and 
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   711
     zero as the imaginary part"
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   712
7356
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
   713
    ^ Complex real:self
3634
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   714
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   715
    "Modified: / 9.7.1998 / 10:18:16 / cg"
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   716
!
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   717
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   718
asMetaNumber
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   719
    ^ SomeNumber new realNumber:self
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   720
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   721
7214
2315f1d48b84 *** empty log message ***
martin
parents: 6899
diff changeset
   722
asNumber
2315f1d48b84 *** empty log message ***
martin
parents: 6899
diff changeset
   723
2315f1d48b84 *** empty log message ***
martin
parents: 6899
diff changeset
   724
    ^ self.
2315f1d48b84 *** empty log message ***
martin
parents: 6899
diff changeset
   725
!
2315f1d48b84 *** empty log message ***
martin
parents: 6899
diff changeset
   726
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   727
asPoint
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   728
    "return a new Point with the receiver as all coordinates;  
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   729
     often used to supply the same value in two dimensions, as with 
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   730
     symmetrical gridding or scaling."
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   731
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   732
%{  /* NOCONTEXT */
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   733
5322
411b6c0f7250 renamed sone structures;
Claus Gittinger <cg@exept.de>
parents: 5299
diff changeset
   734
    if (__CanDoQuickNew(sizeof(struct __Point))) {      /* OBJECT ALLOCATION */
7857
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   735
        OBJ newPoint;
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   736
7857
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   737
        __qCheckedAlignedNew(newPoint, sizeof(struct __Point));
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   738
        __InstPtr(newPoint)->o_class = @global(Point);
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   739
        __qSTORE(newPoint, @global(Point));
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   740
        __PointInstPtr(newPoint)->p_x = self;
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   741
        __PointInstPtr(newPoint)->p_y = self;
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   742
        __STORE(newPoint, self);
51971c337c26 Have to call __STORE(), when assigning class.
Stefan Vogel <sv@exept.de>
parents: 7729
diff changeset
   743
        RETURN ( newPoint );
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   744
    }
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   745
%}.
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   746
    ^ Point x:self y:self
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   747
!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   748
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   749
degreesToRadians
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   750
    "interpreting the receiver as radians, return the degrees"
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   751
8203
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
   752
    ^ self * (Float pi / 180.0)
7388
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   753
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   754
    "
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   755
     180 degreesToRadians
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   756
     Float pi radiansToDegrees
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   757
    "
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   758
!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   759
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   760
literalArrayEncoding
1245
c8afea3d5af0 commentary
Claus Gittinger <cg@exept.de>
parents: 1210
diff changeset
   761
    "encode myself as an array literal, from which a copy of the receiver
c8afea3d5af0 commentary
Claus Gittinger <cg@exept.de>
parents: 1210
diff changeset
   762
     can be reconstructed with #decodeAsLiteralArray."
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   763
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   764
    ^ self
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   765
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   766
    "Modified: 1.9.1995 / 02:25:26 / claus"
1245
c8afea3d5af0 commentary
Claus Gittinger <cg@exept.de>
parents: 1210
diff changeset
   767
    "Modified: 22.4.1996 / 13:00:27 / cg"
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   768
!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   769
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   770
radiansToDegrees
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   771
    "interpreting the receiver as degrees, return the radians"
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   772
8203
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
   773
    ^ self * (180.0 / Float pi)
7388
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   774
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   775
    "
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   776
     180 degreesToRadians     
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   777
     Float pi radiansToDegrees
bb89a53e2682 fixed conversion from string to not loose precision which is later
Claus Gittinger <cg@exept.de>
parents: 7356
diff changeset
   778
    "
6637
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   779
!
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   780
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   781
withScale:newScale
8203
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
   782
    "return a fixedPoint number representing the same value as the receiver, 
6637
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   783
     with newScale number of post-decimal digits"
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   784
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   785
    ^ self asFixedPoint:newScale
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   786
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   787
    "
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   788
     1234 withScale:2 
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   789
     1234.1 withScale:2 
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   790
     1234.12 withScale:2 
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   791
     1234.123 withScale:2 
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   792
     (1/7) withScale:2
b6ee031f3096 withScale moved up.
Claus Gittinger <cg@exept.de>
parents: 6632
diff changeset
   793
    "
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   794
! !
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   795
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   796
!Number methodsFor:'intervals'!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   797
6072
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   798
downTo:stop
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   799
    "return an interval from receiver down to the argument, incrementing by -1"
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   800
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   801
    ^ self to:stop by:-1
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   802
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   803
    "
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   804
     (10 downTo:1) do:[:i | Transcript showCR:i].
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   805
    "
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   806
!
55858717097a added #downTo:
Claus Gittinger <cg@exept.de>
parents: 5565
diff changeset
   807
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   808
to:stop
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   809
    "return an interval from receiver up to the argument, incrementing by 1"
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   810
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   811
    ^ Interval from:self to:stop
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   812
!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   813
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   814
to:stop by:step
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   815
    "return an interval from receiver up to the argument, incrementing by step"
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   816
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   817
    ^ Interval from:self to:stop by:step
6154
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   818
!
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   819
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   820
to:stop byFactor:factor
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   821
    "return a geometric series from receiver up to the argument;
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   822
     elements have a constant factor in between"
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   823
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   824
    ^ GeometricSeries from:self to:stop byFactor:factor
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   825
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   826
    "
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   827
     (1 to:256 byFactor:2)
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   828
     (256 to:1 byFactor:1/2)     
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
   829
    "
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   830
! !
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   831
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   832
!Number methodsFor:'iteration'!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   833
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   834
timesRepeat:aBlock
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   835
    "evaluate the argument, aBlock self times"
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   836
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   837
    |count|
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   838
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   839
    count := self.
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   840
    [count > 0] whileTrue:[
5322
411b6c0f7250 renamed sone structures;
Claus Gittinger <cg@exept.de>
parents: 5299
diff changeset
   841
	aBlock value.
411b6c0f7250 renamed sone structures;
Claus Gittinger <cg@exept.de>
parents: 5299
diff changeset
   842
	count := count - 1
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   843
    ]
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   844
! !
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   845
3634
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   846
!Number methodsFor:'mathematical functions'!
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   847
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   848
conjugated
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   849
    "Return the complex conjugate of this Number."
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   850
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   851
    ^ self
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   852
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   853
    "Modified: / 9.7.1998 / 10:17:31 / cg"
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   854
!
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   855
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   856
exp
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   857
    "compute e**x of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   858
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   859
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   860
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   861
        ^ self asFloat exp.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   862
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
   863
    ^ self exp_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   864
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   865
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   866
floorLog:radix
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   867
    "return the logarithm truncated as an integer"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   868
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   869
    ^ (self log:radix) floor
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   870
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   871
3634
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   872
imaginary
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   873
    "Return the imaginary part of this Number."
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   874
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   875
    ^ 0
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   876
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   877
    "Modified: / 9.7.1998 / 10:17:24 / cg"
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   878
!
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   879
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   880
ln
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   881
    "compute ln of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   882
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   883
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   884
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   885
        ^ self asFloat ln.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   886
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
   887
    ^ self ln_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   888
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   889
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   890
log
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   891
    "return log base 10 of the receiver.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   892
     Alias for log10."
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   893
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   894
    ^ self log10
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   895
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   896
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   897
log10
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   898
    "return log base 10 of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   899
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   900
    ^ self log:10
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   901
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   902
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   903
log:aNumber
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   904
    "return log base aNumber of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   905
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   906
    ^ self ln / aNumber ln
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   907
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   908
7468
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   909
raisedTo:aNumber
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   910
    "return the receiver raised to aNumber"
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   911
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   912
    aNumber = 0 ifTrue:[^ 1].
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   913
    aNumber = 1 ifTrue:[^ self].
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   914
    aNumber isInteger ifTrue:[
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   915
        ^ self raisedToInteger:aNumber
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   916
    ].
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   917
    ^ self asFloat raisedTo:aNumber
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   918
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   919
    "
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   920
     2 raisedTo: 4    
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   921
     10 raisedTo: 4    
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   922
    "
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   923
!
61c8a3053bf4 moved math functions to number
Claus Gittinger <cg@exept.de>
parents: 7456
diff changeset
   924
3634
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   925
real
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   926
    "Return the real part of this Number."
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   927
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   928
    ^ self
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   929
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   930
    "Modified: / 9.7.1998 / 10:17:17 / cg"
6258
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   931
!
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   932
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   933
sqrt
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   934
    "return the square root of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   935
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   936
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   937
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   938
        ^ self asFloat sqrt.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   939
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
   940
    ^ self sqrt_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   941
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   942
6258
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   943
timesTwoPower:anInteger
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   944
    "Return the receiver multiplied by 2.0 raised to the power of the argument.
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   945
     For protocol completeness wrt. Squeak and ST80."
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   946
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   947
    ^ self * (2.0 raisedToInteger:anInteger)
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   948
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   949
    "
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   950
     123 timesTwoPower:0  
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   951
     123 timesTwoPower:1  
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   952
     123 timesTwoPower:2  
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   953
     123 timesTwoPower:3  
435600a44e73 added timesTwoPower.
Claus Gittinger <cg@exept.de>
parents: 6195
diff changeset
   954
    "
3634
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   955
! !
bbf443dce0cf complex conversion stuff
Claus Gittinger <cg@exept.de>
parents: 3613
diff changeset
   956
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   957
!Number methodsFor:'printing & storing'!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   958
5299
92b363dbd833 added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents: 5238
diff changeset
   959
printOn:aStream paddedWith:padCharacter to:size base:radix
92b363dbd833 added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents: 5238
diff changeset
   960
    |s|
92b363dbd833 added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents: 5238
diff changeset
   961
8301
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   962
    radix == 10 ifTrue:[
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   963
        s := self printString.
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   964
    ] ifFalse:[
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   965
        s := self printStringRadix:radix.
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   966
    ].
5299
92b363dbd833 added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents: 5238
diff changeset
   967
    s printOn: aStream leftPaddedTo:size with: padCharacter
8301
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   968
!
5299
92b363dbd833 added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents: 5238
diff changeset
   969
8301
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   970
printStringRadix:radix
74d9ee379019 decimalPointCharacter definition
werner
parents: 8203
diff changeset
   971
    self subclassResponsibility
5299
92b363dbd833 added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents: 5238
diff changeset
   972
!
92b363dbd833 added #printOn:paddedWith:to:base:
Claus Gittinger <cg@exept.de>
parents: 5238
diff changeset
   973
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   974
storeOn:aStream
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   975
    "append a string for storing the receiver onto the argument,
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   976
     aStream - since numbers are literals,they store as they print."
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   977
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   978
    ^ self printOn:aStream
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   979
!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   980
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   981
storeString
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   982
    "return a string for storing 
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   983
     - since numbers are literals, they store as they print."
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   984
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   985
    ^ self printString
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   986
! !
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
   987
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   988
!Number methodsFor:'taylor series'!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   989
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   990
arcSin_withAccuracy:epsilon
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   991
    "compute the arcSine of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   992
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   993
    "/ uses taylor series:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   994
    "/                 1*x^3   1*3 * x^5   
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   995
    "/    arcSin = x + ----- + ---------- + ...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   996
    "/                 2* 3    2*4 *  5    
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   997
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   998
    |x2 num numf den denf approx lastApprox d|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
   999
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1000
    ((self >= -1) and:[self <= 1]) ifFalse:[ 
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1001
        ^ self class
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1002
            raise:#domainErrorSignal
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1003
            receiver:self
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1004
            selector:#arcTanh
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1005
            arguments:#()
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1006
            errorString:'bad receiver in arcTanh'
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1007
    ].
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1008
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1009
    x2 := self * self.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1010
    num := (x2 * self).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1011
    approx := self + (num / 6).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1012
    lastApprox := self.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1013
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1014
    numf := 3.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1015
    denf  := 4.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1016
    den := 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1017
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1018
    [ (lastApprox - approx) abs > epsilon ] whileTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1019
        num := (num * x2) * numf.   numf := numf + 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1020
        den := den * denf.          denf := denf + 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1021
        d := den * numf.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1022
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1023
        lastApprox := approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1024
        approx := approx + (num / d).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1025
    ].
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1026
    ^ approx
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1027
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1028
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1029
     0.5 arcSin                                    0.523599
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1030
     0.5 asLongFloat arcSin                        0.523598776
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1031
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1032
     0.5 asLongFloat arcSin_withAccuracy:1         0.520833333
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1033
     0.5 asLongFloat arcSin_withAccuracy:0.1       0.520833333
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1034
     0.5 asLongFloat arcSin_withAccuracy:0.01      0.523177083
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1035
     0.5 asLongFloat arcSin_withAccuracy:0.001     0.523525856
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1036
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1037
     0.5 asLongFloat arcSin_withAccuracy:1e-20     0.523598776
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1038
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1039
     0.5 asLargeFloat arcSin_withAccuracy:1e-30    -- not yet 
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1040
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1041
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1042
     0.1 arcSin                                    0.100167
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1043
     0.1 asLongFloat arcSin                        0.100167421
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1044
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1045
     0.1 asLongFloat arcSin_withAccuracy:1         0.100166667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1046
     0.1 asLongFloat arcSin_withAccuracy:0.1       0.100166667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1047
     0.1 asLongFloat arcSin_withAccuracy:0.01      0.100166667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1048
     0.1 asLongFloat arcSin_withAccuracy:0.001     0.100166667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1049
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1050
     0.1 asLongFloat arcSin_withAccuracy:1e-20     0.100167421
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1051
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1052
     0.1 asLargeFloat arcSin_withAccuracy:1e-30    -- not yet 
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1053
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1054
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1055
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1056
arcTan_withAccuracy:epsilon
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1057
    "compute the arcTangent of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1058
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1059
    "/ uses taylor series:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1060
    "/                 x^3   x^5   x^7
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1061
    "/    arcTan = x - --- + --- - --- ...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1062
    "/                  3     5    7
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1063
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1064
    |x2 num den approx lastApprox|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1065
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1066
    x2 := self * self.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1067
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1068
    num := (x2 * self) negated.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1069
    den := 3.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1070
    approx := self + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1071
    lastApprox := self.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1072
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1073
    [ (lastApprox - approx) abs > epsilon ] whileTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1074
        den := den + 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1075
        num := (num * x2) negated.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1076
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1077
        lastApprox := approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1078
        approx := approx + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1079
"/Transcript show:num; show:' '.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1080
"/Transcript show:den; show:' '.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1081
"/Transcript showCR:(num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1082
"/Transcript showCR:approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1083
"/Transcript cr.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1084
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1085
Transcript showCR:(lastApprox - approx) abs.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1086
    ].
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1087
    ^ approx
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1088
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1089
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1090
     1.0 arcTan                                    0.785398
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1091
     1.0 asLongFloat arcTan                        0.785398163
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1092
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1093
     1.0 asLongFloat arcTan_withAccuracy:1         0.666666667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1094
     1.0 asLongFloat arcTan_withAccuracy:0.1       0.744011544
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1095
     1.0 asLongFloat arcTan_withAccuracy:0.01      0.790299653
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1096
     1.0 asLongFloat arcTan_withAccuracy:0.001     0.785897165
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1097
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1098
     1.0 asLongFloat arcTan_withAccuracy:1e-20     -- not yet 
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1099
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1100
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1101
     0.5 arcTan                                    0.463648
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1102
     0.5 asLongFloat arcTan                        0.463647609
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1103
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1104
     0.5 asLongFloat arcTan_withAccuracy:1         0.458333333
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1105
     0.5 asLongFloat arcTan_withAccuracy:0.1       0.458333333
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1106
     0.5 asLongFloat arcTan_withAccuracy:0.01      0.464583333
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1107
     0.5 asLongFloat arcTan_withAccuracy:0.001     0.463684276
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1108
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1109
     0.5 asLongFloat arcTan_withAccuracy:1e-20     0.463647609
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1110
     0.5 asLargeFloat arcTan_withAccuracy:1e-30    -- not yet  
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1111
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1112
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1113
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1114
cos_withAccuracy:epsilon
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1115
    "compute the cosine of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1116
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1117
    "/ uses taylor series:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1118
    "/               x^2   x^4   x^6
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1119
    "/    cos = 1 - --- + --- - --- ...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1120
    "/                2!!    4!!    6!!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1121
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1122
    |x2 facN num den approx lastApprox|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1123
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1124
    x2 := self * self.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1125
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1126
    num := x2 negated.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1127
    den := 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1128
    facN := 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1129
    approx := 1 + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1130
    lastApprox := 1.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1131
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1132
    [ (lastApprox - approx) abs > epsilon ] whileTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1133
        facN := facN + 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1134
        den := den * (facN - 1) * facN.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1135
        num := (num * x2) negated.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1136
        lastApprox := approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1137
        approx := approx + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1138
    ].
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1139
    ^ approx
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1140
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1141
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1142
     1.0 cos                                    0.540302
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1143
     1.0 asLongFloat cos_withAccuracy:1         0.5
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1144
     1.0 asLongFloat cos_withAccuracy:0.1       0.541666667 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1145
     1.0 asLongFloat cos_withAccuracy:0.01      0.540277778
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1146
     1.0 asLongFloat cos_withAccuracy:0.001     0.540302579
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1147
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1148
     1.0 asLongFloat cos_withAccuracy:1e-40     0.540302306    
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1149
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1150
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1151
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1152
cosh_withAccuracy:epsilon
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1153
    "compute the hyperbolic cosine of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1154
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1155
    "/ uses taylor series:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1156
    "/               x^2   x^4   x^6
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1157
    "/    cosh = x + --- + --- + --- ...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1158
    "/                2!!    4!!    6!!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1159
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1160
    |x2 facN num den approx lastApprox|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1161
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1162
    x2 := self * self.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1163
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1164
    num := x2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1165
    den := 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1166
    facN := 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1167
    approx := self + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1168
    lastApprox := self.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1169
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1170
    [ (lastApprox - approx) abs > epsilon ] whileTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1171
        facN := facN + 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1172
        den := den * (facN - 1) * facN.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1173
        num := num * x2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1174
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1175
        lastApprox := approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1176
        approx := approx + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1177
    ].
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1178
    ^ approx
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1179
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1180
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1181
     1.0 cosh                                    1.54308
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1182
     1.0 asLongFloat cosh_withAccuracy:1         1.5 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1183
     1.0 asLongFloat cosh_withAccuracy:0.1       1.54308 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1184
     1.0 asLongFloat cosh_withAccuracy:0.01      1.54308 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1185
     1.0 asLongFloat cosh_withAccuracy:0.001     1.54308 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1186
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1187
     1.0 asLongFloat cosh_withAccuracy:1e-40   -> 1.543080    
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1188
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1189
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1190
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1191
epsilon
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1192
    "return the maximum relative spacing of instances of mySelf 
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1193
     (i.e. the value-delta of the least significant bit)"
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1194
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1195
    ^ self class epsilon
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1196
!
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1197
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1198
exp_withAccuracy:epsilon
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1199
    "compute e**x of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1200
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1201
    "/ uses taylor series:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1202
    "/             x    x^2   x^3
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1203
    "/    e = 1 + --- + --- + --- ...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1204
    "/             1!!    2!!    3!!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1205
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1206
    |x2 facN num den approx lastApprox|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1207
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1208
    x2 := self * self.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1209
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1210
    num := x2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1211
    den := 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1212
    facN := 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1213
    approx := self + self + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1214
    lastApprox := self.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1215
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1216
    [ (lastApprox - approx) abs > epsilon ] whileTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1217
        facN := facN + 1.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1218
        den := den * facN.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1219
        num := num * self.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1220
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1221
        lastApprox := approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1222
        approx := approx + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1223
    ].
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1224
    ^ approx
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1225
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1226
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1227
     1.0 exp                                    2.71828
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1228
     1.0 asLongFloat exp                        2.71828183
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1229
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1230
     1.0 asLongFloat exp_withAccuracy:1         2.66666667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1231
     1.0 asLongFloat exp_withAccuracy:0.1       2.70833333
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1232
     1.0 asLongFloat exp_withAccuracy:0.01      2.71666667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1233
     1.0 asLongFloat exp_withAccuracy:0.001     2.71825397
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1234
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1235
     1.0 asLongFloat exp_withAccuracy:1e-40     2.71828183 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1236
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1237
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1238
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1239
ln_withAccuracy:epsilon
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1240
    "compute ln of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1241
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1242
    "/ uses taylor series:
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1243
    "/             u^2   u^3
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1244
    "/    ln = u - --- + --- ...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1245
    "/              2    3
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1246
    "/ where:
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1247
    "/         u = x - 1
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1248
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1249
    |u u2 num den approx lastApprox|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1250
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1251
    u := self - 1.
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1252
    u2 := u * u.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1253
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1254
    num := u2 negated.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1255
    den := 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1256
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1257
    approx := u + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1258
    lastApprox := self.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1259
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1260
    [ (lastApprox - approx) abs > epsilon ] whileTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1261
        den := den + 1.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1262
        num := (num * u) negated.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1263
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1264
        lastApprox := approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1265
        approx := approx + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1266
    ].
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1267
    ^ approx
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1268
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1269
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1270
     2.0 ln                                    0.693147
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1271
     2.0 asLongFloat ln                        0.693147181
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1272
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1273
     2.0 asLongFloat ln_withAccuracy:1         0.833333333
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1274
     2.0 asLongFloat ln_withAccuracy:0.1       0.645634921
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1275
     2.0 asLongFloat ln_withAccuracy:0.01      0.688172179
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1276
     2.0 asLongFloat ln_withAccuracy:0.001     0.692647431
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1277
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1278
     2.0 asLongFloat ln_withAccuracy:1e-10     
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1279
     2.0 asLongFloat ln_withAccuracy:1e-20     
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1280
     2.0 asLongFloat ln_withAccuracy:1e-40     2.71828183 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1281
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1282
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1283
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1284
sin_withAccuracy:epsilon
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1285
    "compute the sine of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1286
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1287
    "/ uses taylor series:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1288
    "/               x^3   x^5   x^7
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1289
    "/    sin = x - --- + --- - --- ...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1290
    "/                3!!    5!!    7!!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1291
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1292
    |x2 facN num den approx lastApprox|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1293
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1294
    x2 := self * self.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1295
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1296
    num := (x2 * self) negated.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1297
    den := 2*3.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1298
    facN := 3.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1299
    approx := self + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1300
    lastApprox := self.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1301
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1302
    [ (lastApprox - approx) abs > epsilon ] whileTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1303
        facN := facN + 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1304
        den := den * (facN - 1) * facN.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1305
        num := (num * x2) negated.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1306
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1307
        lastApprox := approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1308
        approx := approx + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1309
    ].
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1310
    ^ approx
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1311
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1312
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1313
     1.0 sin                                    0.841471
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1314
     1.0 asLongFloat sin                        0.841470985
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1315
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1316
     1.0 asLongFloat sin_withAccuracy:1         0.833333333
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1317
     1.0 asLongFloat sin_withAccuracy:0.1       0.841666667 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1318
     1.0 asLongFloat sin_withAccuracy:0.01      0.841666667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1319
     1.0 asLongFloat sin_withAccuracy:0.001     0.841468254
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1320
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1321
     1.0 asLongFloat sin_withAccuracy:1e-40     0.841470985
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1322
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1323
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1324
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1325
sinh_withAccuracy:epsilon
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1326
    "compute the hyperbolic sine of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1327
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1328
    "/ uses taylor series:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1329
    "/               x^3   x^5   x^7
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1330
    "/    sinh = x + --- + --- + --- ...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1331
    "/                3!!    5!!    7!!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1332
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1333
    |x2 facN num den approx lastApprox|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1334
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1335
    x2 := self * self.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1336
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1337
    num := x2 * self.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1338
    den := 2*3.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1339
    facN := 3.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1340
    approx := self + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1341
    lastApprox := self.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1342
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1343
    [ (lastApprox - approx) abs > epsilon ] whileTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1344
        facN := facN + 2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1345
        den := den * (facN - 1) * facN.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1346
        num := num * x2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1347
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1348
        lastApprox := approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1349
        approx := approx + (num / den).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1350
    ].
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1351
    ^ approx
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1352
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1353
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1354
     1.0 sinh                                    1.1752
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1355
     1.0 asLongFloat sinh                        1.17520119
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1356
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1357
     1.0 asLongFloat sinh_withAccuracy:1         1.16666667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1358
     1.0 asLongFloat sinh_withAccuracy:0.1       1.175 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1359
     1.0 asLongFloat sinh_withAccuracy:0.01      1.175
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1360
     1.0 asLongFloat sinh_withAccuracy:0.001     1.17519841
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1361
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1362
     1.0 asLongFloat sinh_withAccuracy:1e-40     1.17520119 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1363
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1364
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1365
7729
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1366
sqrt_withAccuracy:epsilon 
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1367
    "compute square root of the receiver"
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1368
    "
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1369
      Use the Heron Algorithm:
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1370
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1371
                 x_n + (a / x_n)
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1372
        x_n+1 =  ---------------
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1373
                      2
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1374
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1375
        sqrt(a) = x_n
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1376
    "
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1377
    
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1378
    |approx|
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1379
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1380
    self <= 0 ifTrue:[
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1381
        self = 0 ifTrue:[
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1382
            ^ self
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1383
        ].
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1384
        self error:'negative number in sqrt'.
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1385
    ].
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1386
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1387
    approx := 1.
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1388
    [
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1389
        |lastApprox|
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1390
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1391
        lastApprox := approx.
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1392
        approx := ((self / approx) + approx) / 2.
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1393
        (approx - lastApprox) abs > epsilon
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1394
    ] whileTrue.
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1395
    ^ approx
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1396
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1397
    "
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1398
     2 sqrt                                             1.41421
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1399
     2 asLongFloat sqrt_withAccuracy:0.01               1.41666667
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1400
     2 asLongFloat sqrt_withAccuracy:0.0001             1.41421569
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1401
     2 asLongFloat sqrt_withAccuracy:0.0000001          1.41421356
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1402
     2 asLongFloat sqrt_withAccuracy:0.0000000001       1.41421356
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1403
     2 asLongFloat sqrt_withAccuracy:0.000000000001     1.41421356
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1404
     2 asLongFloat sqrt_withAccuracy:LongFloat epsilon  1.41421356
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1405
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1406
     (4 sqrt_withAccuracy:Integer epsilon) asFloat
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1407
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1408
     MessageTally spyOn:[ |arg|
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1409
        arg := 2 asLongFloat.
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1410
        1000000 timesRepeat:[
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1411
             arg sqrt_withAccuracy:0.000000000001
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1412
        ]
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1413
     ]
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1414
     Time millisecondsToRun:[ |arg|
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1415
        arg := 2 asLongFloat.
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1416
        1000000 timesRepeat:[
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1417
             arg sqrt_withAccuracy:0.000000000001
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1418
        ]
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1419
     ]
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1420
    "
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1421
!
bbd20db09d1b Fix senders of #xxxx_withAccuracy: to use #epsilon instead of #precision.
Stefan Vogel <sv@exept.de>
parents: 7468
diff changeset
  1422
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1423
tan_withAccuracy:epsilon
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1424
    "compute the tangens of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1425
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1426
    "/ uses taylor series:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1427
    "/                x^3     x^5      x^7      x^9     2^2n * ( 2^2n - 1) * B2n * x^(2n-1)
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1428
    "/    tan = x + 1*--- + 2*--- + 17*--- + 62*----... ----------------------------------...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1429
    "/                 3       15      315      2835                 (2n)!!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1430
    "/ where Bi is the ith bernoulli number.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1431
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1432
    |factors idx x2 num t approx lastApprox|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1433
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1434
    "/    (1 to:20) collect:[:n| |num den|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1435
    "/        num := (2 raisedTo:(2*n)) * ((2 raisedTo:(2*n))-1) * ((n*2) bernoulli).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1436
    "/        den := (2*n) factorial.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1437
    "/        num / den
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1438
    "/    ]   
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1439
   factors := #(
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1440
        (1 3) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1441
        (2 15) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1442
        (17 315) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1443
        (62 2835)
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1444
        (1382 155925) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1445
        (21844 6081075) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1446
        (929569 638512875)
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1447
        (6404582 10854718875) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1448
        (443861162 1856156927625) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1449
        (18888466084 194896477400625) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1450
        (113927491862 2900518163668125) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1451
        (58870668456604 3698160658676859375) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1452
        (8374643517010684 1298054391195577640625) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1453
        (689005380505609448 263505041412702261046875) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1454
        (129848163681107301953 122529844256906551386796875) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1455
        (1736640792209901647222 4043484860477916195764296875) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1456
        (418781231495293038913922 2405873491984360136479756640625) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1457
        (56518638202982204522669764 801155872830791925447758961328125) 
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1458
        (32207686319158956594455462 1126482925555250126673224649609375)).
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1459
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1460
    x2 := self * self.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1461
8203
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
  1462
    num := x2 * self.               "/ =  x^3
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
  1463
    approx := self + (num / 3).     "/ do the first iteration
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1464
    lastApprox := self.
8203
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
  1465
    idx := 2.
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
  1466
    [
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
  1467
        t := factors at:idx.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1468
        idx := idx + 1.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1469
        num := num * x2.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1470
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1471
        lastApprox := approx.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1472
        approx := approx + (num * t first / t second).
8203
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
  1473
        epsilon < (lastApprox - approx) abs    
666bfa7bcb97 Fix C cmpiler warnings.
Stefan Vogel <sv@exept.de>
parents: 7857
diff changeset
  1474
    ] whileTrue.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1475
    ^ approx
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1476
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1477
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1478
     0.5 tan                                    0.546302
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1479
     0.5 asLongFloat tan                        0.54630249
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1480
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1481
     0.5 asLongFloat tan_withAccuracy:1         0.541666667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1482
     0.5 asLongFloat tan_withAccuracy:0.1       0.541666667
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1483
     0.5 asLongFloat tan_withAccuracy:0.01      0.545833333
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1484
     0.5 asLongFloat tan_withAccuracy:0.001     0.54625496
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1485
     0.5 asLongFloat tan_withAccuracy:1e-15     0.54630249
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1486
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1487
     0.5 asLongFloat tan_withAccuracy:1e-40     
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1488
    "
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1489
! !
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1490
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1491
!Number methodsFor:'testing'!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1492
5360
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1493
isDivisibleBy:aNumber
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1494
    "return true, if the receiver can be divided by the argument, aNumber without a remainder.
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1495
     Notice, that the result is only worth trusting, if the receiver is an integer."
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1496
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1497
    aNumber = 0 ifTrue: [^ false].
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1498
    aNumber isInteger ifFalse: [^ false].
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1499
    ^ (self \\ aNumber) = 0
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1500
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1501
    "
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1502
     3 isDivisibleBy:2     
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1503
     4 isDivisibleBy:2
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1504
     4.0 isDivisibleBy:2   
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1505
     4.5 isDivisibleBy:4.5 
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1506
     4.5 isDivisibleBy:1.0 
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1507
    "
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1508
!
1aef297d3cbe added #isDivisibleBy:
Claus Gittinger <cg@exept.de>
parents: 5322
diff changeset
  1509
6143
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
  1510
isNaN
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
  1511
    "return true, if the receiver is an invalid float (NaN - not a number)."
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
  1512
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
  1513
    ^ false
6155
00eaf2fa55bc isReal comment
Claus Gittinger <cg@exept.de>
parents: 6154
diff changeset
  1514
00eaf2fa55bc isReal comment
Claus Gittinger <cg@exept.de>
parents: 6154
diff changeset
  1515
    "Created: / 5.11.2001 / 18:07:26 / cg"
6143
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
  1516
!
695cc93a96b4 isNan, isInfinite and closeTo:
james
parents: 6087
diff changeset
  1517
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1518
isNumber
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1519
    "return true, if the receiver is a kind of number"
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1520
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1521
    ^ true
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1522
!
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1523
6087
826b87eab740 moved isReal
Claus Gittinger <cg@exept.de>
parents: 6072
diff changeset
  1524
isReal
826b87eab740 moved isReal
Claus Gittinger <cg@exept.de>
parents: 6072
diff changeset
  1525
    "return true, if the receiver is some kind of real number (as opposed to a complex);
826b87eab740 moved isReal
Claus Gittinger <cg@exept.de>
parents: 6072
diff changeset
  1526
     true is returned here - the method is redefined from Object."
826b87eab740 moved isReal
Claus Gittinger <cg@exept.de>
parents: 6072
diff changeset
  1527
826b87eab740 moved isReal
Claus Gittinger <cg@exept.de>
parents: 6072
diff changeset
  1528
    ^ true
826b87eab740 moved isReal
Claus Gittinger <cg@exept.de>
parents: 6072
diff changeset
  1529
!
826b87eab740 moved isReal
Claus Gittinger <cg@exept.de>
parents: 6072
diff changeset
  1530
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1531
isZero
1557
2c3c301cf48f checkin from browser
Claus Gittinger <cg@exept.de>
parents: 1422
diff changeset
  1532
    "return true, if the receiver is zero"
2c3c301cf48f checkin from browser
Claus Gittinger <cg@exept.de>
parents: 1422
diff changeset
  1533
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1534
    ^ self = 0
1557
2c3c301cf48f checkin from browser
Claus Gittinger <cg@exept.de>
parents: 1422
diff changeset
  1535
2c3c301cf48f checkin from browser
Claus Gittinger <cg@exept.de>
parents: 1422
diff changeset
  1536
    "Modified: 18.7.1996 / 12:40:49 / cg"
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1537
! !
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1538
4659
cdf37afc0e26 moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents: 4637
diff changeset
  1539
!Number methodsFor:'tracing'!
cdf37afc0e26 moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents: 4637
diff changeset
  1540
4682
4158042a9c8c *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 4659
diff changeset
  1541
traceInto:aRequestor level:level from:referrer
4659
cdf37afc0e26 moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents: 4637
diff changeset
  1542
    "double dispatch into tracer, passing my type implicitely in the selector"
cdf37afc0e26 moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents: 4637
diff changeset
  1543
4682
4158042a9c8c *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 4659
diff changeset
  1544
    ^ aRequestor traceNumber:self level:level from:referrer
4659
cdf37afc0e26 moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents: 4637
diff changeset
  1545
cdf37afc0e26 moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents: 4637
diff changeset
  1546
cdf37afc0e26 moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents: 4637
diff changeset
  1547
! !
cdf37afc0e26 moved isLiteral - some numbers are not.
Claus Gittinger <cg@exept.de>
parents: 4637
diff changeset
  1548
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1549
!Number methodsFor:'trigonometric'!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1550
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1551
arcCos
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1552
    "return the arccosine of the receiver (in radians)"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1553
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1554
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1555
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1556
        ^ self asFloat arcCos.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1557
    ].
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1558
    ^ (self class pi / 2) - self arcSin
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1559
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1560
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1561
arcCosh
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1562
    "return the hyperbolic arccosine of the receiver."
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1563
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1564
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1565
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1566
        ^ self asFloat arcCosh.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1567
    ].
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1568
    ^ (self + (self*self-1) sqrt) ln.
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1569
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1570
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1571
arcSin
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1572
    "return the arcsine of the receiver (in radians)"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1573
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1574
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1575
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1576
        ^ self asFloat arcSin.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1577
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1578
    ^ self arcSin_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1579
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1580
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1581
arcSinh
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1582
    "return the hyperbolic arcsine of the receiver."
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1583
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1584
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1585
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1586
        ^ self asFloat arcSinh.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1587
    ].
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1588
    ^ ( self + (self*self+1) sqrt ) ln
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1589
"/    ^ self arcSinh_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1590
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1591
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1592
arcTan
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1593
    "return the arctangent of the receiver (as radians)"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1594
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1595
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1596
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1597
        ^ self asFloat arcTan.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1598
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1599
    ^ self arcTan_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1600
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1601
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1602
arcTanh
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1603
    "return the hyperbolic arctangent of the receiver."
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1604
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1605
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1606
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1607
        ^ self asFloat arcTanh.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1608
    ].
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1609
    ^ ((self + 1) ln / 2) - ((1 - self) ln / 2)
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1610
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1611
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1612
cos
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1613
    "return the cosine of the receiver (interpreted as radians)"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1614
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1615
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1616
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1617
        ^ self asFloat cos.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1618
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1619
    ^ self cos_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1620
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1621
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1622
cosh
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1623
    "return the hyperbolic cosine of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1624
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1625
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1626
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1627
        ^ self asFloat cosh.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1628
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1629
    ^ self cosh_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1630
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1631
8844
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1632
cot
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1633
    "return the cotangent of the receiver"
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1634
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1635
    ^ 1 / self tan
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1636
!
21e7c41e277e hyperbolic functions fixed
Claus Gittinger <cg@exept.de>
parents: 8830
diff changeset
  1637
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1638
sin
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1639
    "return the sine of the receiver (interpreted as radians)"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1640
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1641
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1642
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1643
        ^ self asFloat sin.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1644
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1645
    ^ self sin_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1646
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1647
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1648
sinh
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1649
    "return the hyperbolic sine of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1650
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1651
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1652
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1653
        ^ self asFloat sinh.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1654
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1655
    ^ self sinh_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1656
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1657
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1658
tan
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1659
    "return the tangens of the receiver (interpreted as radians)"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1660
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1661
    ^ self sin / self cos
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1662
!
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1663
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1664
tanh
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1665
    "return the hyperbolic tangens of the receiver"
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1666
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1667
    (self isLimitedPrecisionReal not
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1668
    or:[self generality < 1.0 generality]) ifTrue:[
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1669
        ^ self asFloat tanh.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1670
    ].
8634
2c838074e754 epsilon
Claus Gittinger <cg@exept.de>
parents: 8303
diff changeset
  1671
    ^ self tanh_withAccuracy:self epsilon
7449
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1672
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1673
"/ If a fast exp is available, the following might be better...
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1674
"/
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1675
"/    |exp nexp|
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1676
"/
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1677
"/    "/ tanh is:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1678
"/    "/      sinh(x)
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1679
"/    "/      -------
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1680
"/    "/      cosh(x)
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1681
"/    "/
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1682
"/    "/ which is:
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1683
"/    "/      (exp(x) - exp(-x)) / 2
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1684
"/    "/      ----------------------
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1685
"/    "/      (exp(x) + exp(-x)) / 2
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1686
"/    
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1687
"/    exp := self exp.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1688
"/    nexp := self negated exp.
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1689
"/
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1690
"/    ^ (exp - nexp) / (exp + nexp)
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1691
! !
192789c6e1c2 fallback code for trigonometric;
Claus Gittinger <cg@exept.de>
parents: 7388
diff changeset
  1692
5552
31b5cc144476 category changes
Claus Gittinger <cg@exept.de>
parents: 5360
diff changeset
  1693
!Number methodsFor:'truncation & rounding'!
3900
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1694
4895
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1695
detentBy: detent atMultiplesOf: grid snap: snap
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1696
    "Map all values that are within detent/2 of any multiple of grid 
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1697
     to that multiple.  
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1698
     Otherwise, if snap is true, return self, meaning that the values 
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1699
     in the dead zone will never be returned.  
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1700
     If snap is false, then expand the range between dead zones
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1701
     so that it covers the range between multiples of the grid, 
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1702
     and scale the value by that factor."
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1703
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1704
    | r1 r2 |
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1705
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1706
    r1 := self roundTo: grid.                    "Nearest multiple of grid"
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1707
    (self roundTo: detent) = r1 ifTrue: [^ r1].  "Snap to that multiple..."
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1708
    snap ifTrue: [^ self].                       "...or return self"
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1709
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1710
    r2 := self < r1                               "Nearest end of dead zone"
5322
411b6c0f7250 renamed sone structures;
Claus Gittinger <cg@exept.de>
parents: 5299
diff changeset
  1711
	    ifTrue: [r1 - (detent asFloat/2)]
411b6c0f7250 renamed sone structures;
Claus Gittinger <cg@exept.de>
parents: 5299
diff changeset
  1712
	    ifFalse: [r1 + (detent asFloat/2)].
4895
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1713
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1714
    "Scale values between dead zones to fill range between multiples"
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1715
    ^ r1 + ((self - r2) * grid asFloat / (grid - detent))
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1716
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1717
    "
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1718
     (170 to: 190 by: 2) collect: [:a | a detentBy: 10 atMultiplesOf: 90 snap: true]         
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1719
     (170 to: 190 by: 2) collect: [:a | a detentBy: 10 atMultiplesOf: 90 snap: false]
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1720
     (3.9 to: 4.1 by: 0.02) collect: [:a | a detentBy: 0.1 atMultiplesOf: 1.0 snap: true]    
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1721
     (-3.9 to: -4.1 by: -0.02) collect: [:a | a detentBy: 0.1 atMultiplesOf: 1.0 snap: false]
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1722
    "
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1723
!
cc546b082506 checkin from browser
Claus Gittinger <cg@exept.de>
parents: 4682
diff changeset
  1724
3900
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1725
fractionPart
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1726
    "return a float with value from digits after the decimal point.
7356
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
  1727
     i.e. the receiver minus its truncated value,
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
  1728
     such that (self truncated + self fractionPart) = self"
3900
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1729
7356
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
  1730
    ^ self - self truncated
3900
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1731
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1732
    "
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1733
     1234.56789 fractionPart
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1734
     1.2345e6 fractionPart  
7356
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
  1735
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
  1736
     1.6 asLongFloat fractionPart + 1.6 asLongFloat truncated    
fe8fb0a571f2 double dispatching fixed;
Claus Gittinger <cg@exept.de>
parents: 7261
diff changeset
  1737
     -1.6 asLongFloat fractionPart + -1.6 asLongFloat truncated    
3900
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1738
    "
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1739
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1740
    "Modified: / 4.11.1996 / 20:26:54 / cg"
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1741
    "Created: / 28.10.1998 / 17:14:40 / cg"
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1742
!
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1743
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1744
integerPart
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1745
    "return a float with value from digits before the decimal point
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1746
     (i.e. the truncated value)"
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1747
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1748
    ^ self truncated asFloat
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1749
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1750
    "
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1751
     1234.56789 integerPart 
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1752
     1.2345e6 integerPart   
6154
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
  1753
     12.5 integerPart 
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
  1754
     -12.5 integerPart 
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
  1755
     (5/3) integerPart  
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
  1756
     (-5/3) integerPart 
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
  1757
     (5/3) truncated  
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
  1758
     (-5/3) truncated  
3900
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1759
    "
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1760
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1761
    "Created: / 28.10.1998 / 17:14:56 / cg"
6154
6cb999c5ace3 *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 6143
diff changeset
  1762
    "Modified: / 5.11.2001 / 17:54:22 / cg"
3900
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1763
! !
c3bc76767cfc added generic implementations of #fractionPart and #integerPart
Claus Gittinger <cg@exept.de>
parents: 3770
diff changeset
  1764
1892
d3564145c15c *** empty log message ***
Claus Gittinger <cg@exept.de>
parents: 1701
diff changeset
  1765
!Number class methodsFor:'documentation'!
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1766
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1767
version
9130
07e7a292aa76 fixedPoint reading fixed (explicit scale)
Claus Gittinger <cg@exept.de>
parents: 9127
diff changeset
  1768
    ^ '$Header: /cvs/stx/stx/libbasic/Number.st,v 1.99 2006-02-17 13:11:48 cg Exp $'
701
a309e3ef7faf checkin from browser
Claus Gittinger <cg@exept.de>
parents: 569
diff changeset
  1769
! !