"

 COPYRIGHT (c) 1993 by Claus Gittinger

	      All Rights Reserved

 This software is furnished under a license and may be used

 only in accordance with the terms of that license and with the

 inclusion of the above copyright notice.   This software may not

 be provided or otherwise made available to, or used by, any

 other person.  No title to or ownership of the software is

 hereby transferred.

"

"{ Package: 'stx:libbasic' }"

Magnitude subclass:#ArithmeticValue

	instanceVariableNames:''

	classVariableNames:'DivisionByZeroSignal DomainErrorSignal OverflowSignal

		UnderflowSignal ArithmeticSignal UnorderedSignal

		ConversionErrorSignal'

	poolDictionaries:''

	category:'Magnitude-Numbers'

!

!ArithmeticValue class methodsFor:'documentation'!

copyright

"

 COPYRIGHT (c) 1993 by Claus Gittinger

	      All Rights Reserved

 This software is furnished under a license and may be used

 only in accordance with the terms of that license and with the

 inclusion of the above copyright notice.   This software may not

 be provided or otherwise made available to, or used by, any

 other person.  No title to or ownership of the software is

 hereby transferred.

"

!

documentation

"

    ArithmeticValue is an abstract superclass for all things responding to

    arithmetic messages. It was inserted into the hierarchy, to allow objects

    like matrices, functions etc. to share the arithmetic methods defined here.

    Notice, that what used to be signals are now exception classes - the class

    variables and signal accessors remain here for backward compatibility.

    [class variables:]

        ArithmeticSignal        <Error>         parent of all arithmetic signals

                                                (never raised itself)

                                                New: now a reference to ArithmeticError

        DomainErrorSignal       <Error>         raised upon float errors

                                                (for example range in trigonometric)

                                                New: now a reference to DomainError

        DivisionByZeroSignal    <Error>         raised when division by 0 is attempted

                                                New: now a reference to ZeroDivide

        OverflowSignal          <Error>         raised on overflow/underflow conditions

        UnderflowSignal                         in float arithmetic. 

                                                Notice: some OperatingSystems do not 

                                                provide enough information for ST/X to 

                                                extract the real reason for the floatException

                                                thus raising DomainErrorSignal in these cases.

    [author:]

        Claus Gittinger

    [See also:]

        Number

"

! !

!ArithmeticValue class methodsFor:'Signal constants'!

arithmeticSignal

    "return the parent of all arithmetic signals"

    ^ ArithmeticError

!

conversionErrorSignal

    "return the signal which is raised when a conversion fails

     (such as when a NaN is to be converted)"

    ^ ConversionError

    "

     ConversionError handle:[:ex |

        Transcript flash

     ]

     do:[

        (0.0 uncheckedDivide:0.0) asFraction

     ]

    "

!

divisionByZeroSignal

    "return the signal which is raised on division by zero"

    ^ ZeroDivide

!

domainErrorSignal

    "return the signal which is raised on math errors

     (such as log of 0 etc.)"

    ^ DomainError

!

imaginaryResultSignal

    "return the signal which is raised when an imaginary result would be created

     (such as when taking the sqrt of a negative number)"

    ^ ImaginaryResultError

!

operationNotPossibleSignal

    ^ Error

!

overflowSignal

    "return the signal which is raised on overflow conditions (in floats)"

    ^ OverflowError

!

rangeErrorSignal

    "return the parent of the overflow/underflow signals"

    ^ RangeError

!

undefinedResultSignal

    ^ Error

!

underflowSignal

    "return the signal which is raised on underflow conditions (in floats)"

    ^ UnderflowError

!

unorderedSignal

    "return the signal which is raised when numbers are compared, 

     for which no ordering is defined (for example: complex numbers)"

    ^ UnorderedNumbersError

! !

!ArithmeticValue class methodsFor:'class initialization'!

initialize

    "setup the signals"

    "/ notice that we now use class based exceptions;

    "/ however, for backward compatibility, the class variables

    "/ referring to those are kept for a while, for subclass compatibility.

    "/ Please convert your code to access those via the Signal-constants class

    "/ messages (accesors) instead of referring to the class variables.

    ArithmeticSignal := ArithmeticError.

    DomainErrorSignal := DomainError.

    DivisionByZeroSignal := ZeroDivide.

    UnorderedSignal := UnorderedNumbersError.

    ConversionErrorSignal := ConversionError.

    OverflowSignal := OverflowError.

    UnderflowSignal := UnderflowError.

! !

!ArithmeticValue class methodsFor:'constants'!

NaN

    ^ NotANumber new

!

infinity

    ^ Infinity positive

!

nan

    "VW compatibility"

    ^ self NaN

!

negativeInfinity

    ^ Infinity negative

!

unity

    self subclassResponsibility

!

zero

    self subclassResponsibility

! !

!ArithmeticValue methodsFor:'arithmetic'!

* something

    "return the product of the receiver and the argument"

    ^ self subclassResponsibility

!

+ something

    "return the sum of the receiver and the argument"

    ^ self subclassResponsibility

!

- something

    "return the difference of the receiver and the argument"

    ^ self subclassResponsibility

!

/ something

    "return the quotient of the receiver and the argument"

    ^ self subclassResponsibility

!

// something

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

     truncation towards negative infinity."

    "/ Note: '^ (self / something) floor' may lead to infinite recursion

    ^ self subclassResponsibility

    "Modified: / 5.11.1996 / 11:46:27 / cg"

    "Modified: / 12.2.1998 / 16:31:36 / stefan"

!

\\ something

    "return the receiver modulo something.

     The remainder has the same sign as something.

     The following is always true:

        (receiver // something) * something + (receiver \\ something) = receiver

    "

    ^ self - ((self // something) * something)

   "

     0.9 \\ 0.4

     0.9 \\ -0.4

    -0.9 \\ 0.4

    -0.9 \\ -0.4

   "

    "Modified: / 12.2.1998 / 19:14:37 / stefan"

!

abs

    "return the absolute value of the receiver"

    (self negative) ifTrue:[^ self negated].

    ^ self

!

negated

    "return the receiver negated"

    ^ self class zero - self

!

quo:something

    "Return the integer quotient of dividing the receiver by the argument

     with truncation towards zero.

     The following is always true:

        (receiver quo: aNumber) * aNumber + (receiver rem: aNumber) = receiver

    "

    ^ (self / something) truncated

!

reciprocal

    "return the receivers reciprocal"

    ^ self class unity / self

!

rem:something

    "Return the integer remainder of dividing the receiver by the argument

     with truncation towards zero.

     The remainder has the same sign as the receiver.

     The following is always true:

        (receiver quo: something) * something + (receiver rem: something) = receiver

    "

    ^ self - ((self quo:something) * something)

!

uncheckedDivide:aNumber

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

     Do not check for divide by zero (return NaN or Infinity).

     This operation is provided for emulators of other languages/semantics,

     where no exception is raised for these results (i.e. Java).

     Its only defined if the arguments type is the same as the receivers."

    aNumber isZero ifTrue:[

        self isZero ifTrue:[^ self class NaN].

        self negative ifTrue:[^ self class negativeInfinity].

        ^ self class infinity.

    ].

    ^ self / aNumber

! !

!ArithmeticValue methodsFor:'coercing & converting'!

coerce:aNumber

    "convert aNumber into an instance of the receivers class and return it."

    ^ self subclassResponsibility

!

generality

    "return a number giving the receivers generality, that number is

     used to convert one of the arguments in a mixed expression. 

     The generality has to be defined in subclasses,

     such that gen(a) > gen(b) iff, conversion of b into a's class 

     does not cut precision. For example, Integer has 40, Float has 80,

     meaning that if we convert a Float to an Integer, some precision may

     be lost. The generality is used by ArithmeticValue>>retry:coercing:,

     which converts the lower-precision number to the higher precision

     numbers class, when mixed-type arithmetic is performed."

    ^ self subclassResponsibility

    "Modified: / 5.11.1996 / 15:05:30 / cg"

    "Modified: / 13.2.1998 / 15:36:01 / stefan"

!

retry:aSymbol coercing:aNumber

    "arithmetic represented by the binary operator, aSymbol,

     could not be performed with the receiver and the argument, aNumber, 

     because of the differences in representation.  

     Coerce either the receiver or the argument, depending on which has higher 

     generality, and try again.  

     If the operation is compare for same value (=), return false if

     the argument is not a Number. 

     If the generalities are the same, create an error message, since this

     means that a subclass has not been fully implemented."

    |hasGenerality myGenerality otherGenerality|

    hasGenerality := aNumber respondsTo:#generality.

    hasGenerality ifFalse:[

        (aSymbol == #=) ifTrue:[

            ^ false

        ].

        (aSymbol == #~=) ifTrue:[

            ^ true

        ].

        ^ self error:'retry:coercing: argument is not a number'.

    ].

    myGenerality := self generality.

    otherGenerality := aNumber generality.

    (myGenerality > otherGenerality) ifTrue:[

        ^ self perform:aSymbol with:(self coerce:aNumber)

    ].

    (myGenerality < otherGenerality) ifTrue:[

        ^ (aNumber coerce:self) perform:aSymbol with:aNumber

    ].

    self error:'retry:coercing: oops - same generality'

    "Modified: 5.11.1996 / 15:03:38 / cg"

! !

!ArithmeticValue methodsFor:'comparing'!

< something

    "return true, if the argument is greater than the receiver"

    ^ self subclassResponsibility

!

<= something

    "return true, if the argument is greater or equal than the receiver"

    ^ (something < self) not

!

> something

    "return true, if the argument is less than the receiver"

    ^ something < self

!

>= something

    "return true, if the argument is less or equal than the receiver"

    ^ (self < something) not

!

compare:arg ifLess:lessBlock ifEqual:equalBlock ifGreater:greaterBlock

    "three-way compare - thanks to Self for this idea.

     Can be redefined in subclasses to do it with a single comparison if

     comparison is expensive."

    self < arg ifTrue:[

	^ lessBlock value

    ].

    self = arg ifTrue:[

	^ equalBlock value

    ].

    ^ greaterBlock value

! !

!ArithmeticValue methodsFor:'converting'!

asDouble

    "ST80 compatibility: return a double with receivers value.

     our floats are the identical to ST80 doubles"

   ^ self asFloat

    "Created: / 13.2.1998 / 15:40:14 / stefan"

!

asFloat

    "return a float with same value"

   ^ self subclassResponsibility

!

asFloatD

    "return a double precision float with same value.

     Added for ANSI compatibility"

   ^ self asFloat

    "Created: / 7.9.2001 / 13:36:48 / cg"

    "Modified: / 7.9.2001 / 13:38:10 / cg"

!

asFloatE

    "return a single precision float with same value.

     Added for ANSI compatibility"

   ^ self asShortFloat

    "Created: / 7.9.2001 / 13:37:06 / cg"

    "Modified: / 7.9.2001 / 13:38:15 / cg"

!

asFloatQ

    "return a quad precision float with same value.

     Added for ANSI compatibility"

   ^ self asLongFloat

    "Created: / 7.9.2001 / 13:38:44 / cg"

!

asFraction

    "return a fraction with same value"

   ^ self subclassResponsibility

!

asInteger

    "return an integer with same value - might truncate"

    ^ self truncated

!

asLimitedPrecisionReal

    "return a float of any precision with same value"

   ^ self asFloat

!

asLongFloat

    "return a longFloat with same value"

   "WARNING: could loose precision here, if not redefined in concrete classes which

    have more than float precision (i.e. LargeIntegers and Fractions)"

   ^ self asFloat asLongFloat "/ subclassResponsibility

    "Modified: / 17.4.1996 / 12:21:35 / cg"

    "Created: / 7.9.2001 / 13:39:31 / cg"

!

asScaledDecimal:scale