hg/stx-libbasic: comparison Complex.st

equal deleted inserted replaced

-:b22823ab2232
+:96f466eeddf5
 "{ Package: 'stx:goodies' }"
 ArithmeticValue subclass:#Complex
 	instanceVariableNames:'real imaginary'
-	classVariableNames:''
+	classVariableNames:'ComplexOne ComplexZero'
 	poolDictionaries:''
 	category:'Magnitude-Numbers'
 !
 !Complex class methodsFor:'documentation'!
 "
 !
 documentation
 "
-This is an implementation of complex numbers.  A complex number has real and
+This class implements complex numbers.
-imaginary parts which must be manipulated simultaneously in any numeric processing.
+A complex number has real and imaginary parts which must be manipulated simultaneously
-Complex numbers can be used in many of the same places that regular numbers
+in any numeric processing.
-can be used with one major exception of comparisons, since complex numbers cannot
+Complex numbers can be used in many of the same places that regular numbers
-be directly compared for size (except through lengths of vectors (see absolute
+can be used with one major exception of comparisons, since complex numbers cannot
-value)).
+be directly compared for size
+(except through lengths of vectors (see absolute value)).
-Instance variables:
-real        <Number> the part of the number which can be expressed as a Real number
+[Instance variables:]
-imaginary   <Number> the part of the number which, in terms of how the number behaves,
+real        <Number> the part of the number which can be expressed as a Real number
-			 has been multiplied by 'i' (-1 sqrt)
+imaginary   <Number> the part of the number which, in terms of how the number behaves,
+has been multiplied by 'i' (-1 sqrt)
-Author: Kurt Hebel (hebel@uinova.cerl.uiuc.edu)
+[Author:]
+Kurt Hebel (hebel@uinova.cerl.uiuc.edu)
+minor changes and double dispatching code by cg.
 "
 !
-example
+examples
 "
 (5 % 7) real
 (5 % 7) imaginary
 (5 % 7) = 5
 (5 % 0) = 5
 (1 % 0) + (2 % 3)
 (1 % 0) * (2 % 0)
 (1 % 0) * (0 % 2)
 (1 % 0) * (2 % 3)
+(1 % 2) + 2
+(1 % 2) * 2
+2 + (1 % 2)
+2 * (1 % 2)
 "
 ! !
 !Complex class methodsFor:'instance creation'!
 fromReal: aNumber
-	"Create a new complex number from the given real number."
+"Create a new complex number from the given real number."
-	^ self basicNew setReal: aNumber setImaginary: 0
+^ self basicNew setReal: aNumber setImaginary: 0
+!
+imaginary: v
+"Create a new complex number with 0 as real and given imaginary parts.
+If the imaginary part is zero, return the real part of the number."
+v = 0 ifTrue: [^ 0].
+^ self basicNew setReal: 0 setImaginary: v
+!
+real: aNumber
+"Create a new complex number from the given real number."
+^ self basicNew setReal: aNumber setImaginary: 0
 !
 real: u imaginary: v
-	"Create a new complex number with the given real and imaginary parts.  If the
+"Create a new complex number with the given real and imaginary parts.  If the
-	 imaginary part is zero, return the real part of the number."
+imaginary part is zero, return the real part of the number."
-	^v = 0 ifTrue: [u]
-	       ifFalse: [self basicNew setReal: u setImaginary: v]
+v = 0 ifTrue: [^ u].
+^ self basicNew setReal: u setImaginary: v
 ! !
 !Complex class methodsFor:'constants access'!
 unity
-	"Answer the value which allows, for any given arithmetic value, the following to be true
+"Answer the value which allows, for any given arithmetic value, the following to be true:
+aNumber * aNumber class unity = aNumber
-	 aNumber * aNumber class unity = aNumber
+This must be true regardless of how a given subclass chooses to define #*"
-	This must be true regardless of how a given subclass chooses to define #*"
+ComplexOne isNil ifTrue:[
+ComplexOne := self fromReal: 1
-	^self fromReal: 1
+].
+^ ComplexOne
 !
 zero
-	"Answer the value which allows, for any given arithmetic value, the following to be true
+"Answer the value which allows, for any given arithmetic value, the following to be true:
+aNumber + aNumber class zero = aNumber
-		aNumber + aNumber class zero = aNumber
+This must be true regardless of how a given subclass chooses to define #+"
-	This must be true regardless of how a given subclass chooses to define #+"
+ComplexZero isNil ifTrue:[
+ComplexZero := self fromReal: 0
-	^self fromReal: 0
+].
+^ ComplexZero
 ! !
 !Complex class methodsFor:'exception handling'!
 trapImaginary: aBlock
 ! !
 !Complex methodsFor:'accessing'!
 imaginary
-	"Return the imaginary part of the complex number."
+"Return the imaginary part of the complex number."
-	^ imaginary
+^ imaginary
+!
+imaginaryPart
+"Return the imaginary part of the complex number.
+An alias for imaginary (for compatibility with other complex implementations)"
+^ imaginary
 !
 real
-	"Return the real part of the complex number."
+"Return the real part of the complex number."
-	^ real
+^ real
+!
+realPart
+"Return the real part of the complex number.
+An alias for real (for compatibility with other complex implementations)"
+^ real
 ! !
 !Complex methodsFor:'arithmetic'!
 * aNumber
-	"Return the product of the receiver and the argument."
+"Return the product of the receiver and the argument."
-	| u v r i |
+"/    | u v r i |
+"/
-	aNumber isComplex ifTrue:[
+"/    aNumber isComplex ifTrue:[
-	    u := aNumber real.
+"/        u := aNumber real.
-	    v := aNumber imaginary.
+"/        v := aNumber imaginary.
-	    r := (real * u) - (imaginary * v).
+"/        r := (real * u) - (imaginary * v).
-	    i  := (real * v) + (imaginary * u).
+"/        i  := (real * v) + (imaginary * u).
-	    i = 0 ifTrue:[ ^ r ].
+"/        i = 0 ifTrue:[ ^ r ].
-	    ^ Complex real:r imaginary:i
+"/        ^ Complex real:r imaginary:i
-	].
+"/    ].
-	^ self retry: #* coercing: aNumber
+^ aNumber productFromComplex:self.
 "Modified: / 8.7.1998 / 12:12:37 / cg"
 !
 + aNumber
-	"Return the sum of the receiver and the argument."
+"Return the sum of the receiver and the argument."
-	| r i |
+"/    | r i |
+"/
-	aNumber isComplex ifTrue: [
+"/    aNumber isComplex ifTrue: [
-	    r := aNumber real + real.
+"/        r := aNumber real + real.
-	    i := aNumber imaginary + imaginary.
+"/        i := aNumber imaginary + imaginary.
-	    i = 0 ifTrue:[ ^ r ].
+"/        i = 0 ifTrue:[ ^ r ].
-	    ^ Complex real:r imaginary:i
+"/        ^ Complex real:r imaginary:i
-	].
+"/    ].
-	^ self retry: #+ coercing: aNumber
+^ aNumber sumFromComplex:self.
 "Modified: / 8.7.1998 / 12:15:42 / cg"
 !
 - aNumber
-	"Return the difference of the receiver and the argument."
+"Return the difference of the receiver and the argument."
-	| r i |
+"/    | r i |
+"/
-	aNumber isComplex ifTrue: [
+"/    aNumber isComplex ifTrue: [
-	    r := real - aNumber real.
+"/        r := real - aNumber real.
-	    i := imaginary - aNumber imaginary.
+"/        i := imaginary - aNumber imaginary.
-	    i = 0 ifTrue:[ ^ r ].
+"/        i = 0 ifTrue:[ ^ r ].
-	    ^ Complex real:r imaginary:i.
+"/        ^ Complex real:r imaginary:i.
-	].
+"/    ].
-	^ self retry: #- coercing: aNumber
+^ aNumber differenceFromComplex:self.
 "Modified: / 8.7.1998 / 12:15:38 / cg"
 !
 / aNumber
-	"Return the quotient of the receiver and the argument."
+"Return the quotient of the receiver and the argument."
-	| denom u v r i |
+"/    | denom u v r i |
+"/
-	aNumber isComplex ifTrue:[
+"/    aNumber isComplex ifTrue:[
-	    u := aNumber real.
+"/        u := aNumber real.
-	    v := aNumber imaginary.
+"/        v := aNumber imaginary.
-	    denom := u * u + (v * v).
+"/        denom := u * u + (v * v).
-	    r := u * real + (v * imaginary) / denom.
+"/        r := u * real + (v * imaginary) / denom.
-	    i := u * imaginary - (v * real) / denom.
+"/        i := u * imaginary - (v * real) / denom.
-	    i = 0 ifTrue:[ ^ r ].
+"/        i = 0 ifTrue:[ ^ r ].
-	    ^ Complex real:r imaginary:i
+"/        ^ Complex real:r imaginary:i
-	].
+"/    ].
-	^ self retry: #/ coercing: aNumber
+^ aNumber quotientFromComplex:self.
 "Modified: / 8.7.1998 / 12:15:34 / cg"
 !
 abs
-	"Return the magnitude (or absolute value) of the complex number."
+"Return the magnitude (or absolute value) of the complex number
+(thats the distance from the origin in the complex plane)."
-	^ (real * real + (imaginary * imaginary)) sqrt
+^ (real * real + (imaginary * imaginary)) sqrt
+"
+(1 % 1) abs
+"
 !
 conjugated
-	"Return the complex conjugate of this complex number."
+"Return the complex conjugate of this complex number
+(i.e. with imaginary part negated)."
-	^ Complex real: real imaginary: imaginary negated
+^ Complex
+real: real
+imaginary: imaginary negated
+!
+differenceFromComplex:aComplex
+"Return the difference of the argument, aComplex and the receiver."
+| r i |
+r := aComplex real - real.
+i := aComplex imaginary - imaginary.
+i = 0 ifTrue:[ ^ r ].
+^ Complex real:r imaginary:i.
+!
+modulus
+| absReal absImag multiplicand quotient |
+absReal := real abs.
+absImag := imaginary abs.
+absReal >= absImag ifTrue: [
+multiplicand := absReal.
+quotient := imaginary / real
+] ifFalse: [
+multiplicand := absImag.
+quotient := real / imaginary
+].
+^ multiplicand * ((1 + (quotient * quotient)) sqrt)
+!
+negated
+"return a new complex with both real and imaginary parts negated"
+^ Complex
+real: real negated
+imaginary: imaginary negated
+!
+productFromComplex:aComplex
+"Return the product of the receiver and the argument, aComplex."
+| u v r i |
+u := aComplex real.
+v := aComplex imaginary.
+r := (real * u) - (imaginary * v).
+i  := (real * v) + (imaginary * u).
+i = 0 ifTrue:[ ^ r ].
+^ Complex real:r imaginary:i
+!
+quotientFromComplex:aComplex
+"Return the quotient of the argument, aComplex and the receiver."
+| denom nr ni r i |
+nr := aComplex real.
+ni := aComplex imaginary.
+denom := real * real + (imaginary * imaginary).
+r := real * nr + (imaginary * ni) / denom.
+i := real * ni - (imaginary * nr) / denom.
+i = 0 ifTrue:[ ^ r ].
+^ Complex real:r imaginary:i
+"/ is the stuff below better ?
+"/    "Implement complex division (a + ib) / (c + id).
+"/     Due to double dispatch, in this routine
+"/        self = (c + id) and aComplex = (a + ib)."
+"/
+"/    | quotient denominator |
+"/
+"/    self realPart abs >= (self imaginaryPart abs)
+"/        ifTrue: [
+"/            quotient := self imaginaryPart / self realPart.
+"/            denominator := self realPart + (self imaginaryPart * quotient).
+"/            ^ Complex
+"/                real: (aComplex realPart + (aComplex imaginaryPart * quotient)) / denominator
+"/                imaginary: (aComplex imaginaryPart - (aComplex realPart * quotient)) / denominator ]
+"/        ifFalse: [
+"/            quotient := self realPart / self imaginaryPart.
+"/            denominator := (self realPart * quotient) + self imaginaryPart.
+"/            ^ Complex
+"/                real: ((aComplex realPart * quotient) + aComplex imaginaryPart) / denominator
+"/                imaginary: ((aComplex imaginaryPart * quotient) - aComplex realPart) / denominator ]
+!
+sumFromComplex:aComplex
+"Return the sum of the receiver and the argument, aComplex."
+| r i |
+r := aComplex real + real.
+i := aComplex imaginary + imaginary.
+i = 0 ifTrue:[ ^ r ].
+^ Complex real:r imaginary:i
 ! !
 !Complex methodsFor:'coercing'!
 coerce: aNumber
+^ aNumber asComplex
-	^aNumber asComplex
 !
 generality
+^ 150
-	^150
 ! !
 !Complex methodsFor:'comparing'!
 < aNumber
-	^Number
+"raises an error - complex numbers are not well ordered"
-		raise: #unorderedSignal
-		receiver: self
+^ Number
-		selector: #<
+raise: #unorderedSignal
-		arg: aNumber
+receiver: self
-		errorString: 'Complex numbers are not well ordered'
+selector: #<
+arg: aNumber
+errorString: 'Complex numbers are not well ordered'
+"
+1 < (2 % 2)
+(2 % 2) < 1
+"
 !
 = aNumber
-	^ (aNumber real = real) and:[aNumber imaginary = imaginary]
+"return true, if the argument represents the same numeric value
+as the receiver, false otherwise"
+^ aNumber equalFromComplex:self
 !
 hash
-	"Hash is implemented because equals is implemented."
+"Hash is implemented because equals is implemented."
-	^ real hash
+^ real hash
 ! !
 !Complex methodsFor:'converting'!
 asComplex
+"I am a complex - so return the receiver"
-	^self
+^ self
 !
 asFloat
+imaginary = 0 ifTrue: [^ real asFloat].
-	imaginary = 0 ifTrue: [^real asFloat].
+^ Number
-	^Number
+raise: #coercionErrorSignal
-		raise: #coercionErrorSignal
+receiver: self
-		receiver: self
+selector: #asFloat
-		selector: #asFloat
+errorString: 'Can''t coerce an instance of Complex to a Float'
-		errorString: 'Can''t coerce an instance of Complex to a Float'
 !
 asInteger
+imaginary = 0 ifTrue: [^real asInteger].
-	imaginary = 0 ifTrue: [^real asInteger].
+^ Number
-	^Number
+raise: #coercionErrorSignal
-		raise: #coercionErrorSignal
+receiver: self
-		receiver: self
+selector: #asInteger
-		selector: #asInteger
+errorString: 'Can''t coerce an instance of Complex to an Integer'
-		errorString: 'Can''t coerce an instance of Complex to an Integer'
 !
 asPoint
-	"Return the complex number as a point."
+"Return the complex number as a point."
-	^ real @ imaginary
+^ real @ imaginary
 !
 reduceGeneralityIfPossible
-	"Answer the receiver transformed to a lower generality, if such a
+"Answer the receiver transformed to a lower generality, if such a
-	transformation is possible without losing information. If not, answer
+transformation is possible without losing information.
-	the receiver"
+If not, answer the receiver"
-	imaginary isZero
+imaginary isZero
-		ifTrue: [^real]
+ifTrue: [^ real]
-		ifFalse: [^self]
+ifFalse: [^ self]
 ! !
 !Complex methodsFor:'double dispatching'!
-differenceFromFloat: argument
+differenceFromFloat:aFloat
-	^ argument asComplex - self
+"Return the difference of the argument, aFloat and the receiver."
-!
+"/ ^ aFloat asComplex - self
-differenceFromFraction: argument
-	^ argument asComplex - self
+| r |
-!
+r := aFloat - real.
-differenceFromInteger: argument
+imaginary = 0 ifTrue:[ ^ r ].
-	^ argument asComplex - self
+^ Complex real:r imaginary:imaginary
-!
+"
-productFromFloat: argument
+(1 % 1) - 1.0
-	^ argument asComplex * self
+1.0 - (1 % 1)
-!
+"
+!
-productFromFraction: argument
-	^ argument asComplex * self
+differenceFromFraction: aFraction
-!
+^ aFraction asComplex - self
+!
-productFromInteger: argument
-	^ argument asComplex * self
+differenceFromInteger: anInteger
-!
+^ anInteger asComplex - self
+!
-quotientFromFloat: argument
-	^ argument asComplex / self
+equalFromComplex:aComplex
-!
+^ (aComplex real = real) and:[aComplex imaginary = imaginary]
+!
-quotientFromFraction: argument
-	^ argument asComplex / self
+equalFromFloat:aFloat
-!
+imaginary = 0 ifFalse:[^ false].
+^ real = aFloat
-quotientFromInteger: argument
+!
-	^ argument asComplex / self
-!
+productFromFloat: aFloat
+"Return the product of the receiver and the argument, aFloat."
-sumFromFloat: argument
-	^ argument asComplex + self
+"/  ^ aFloat asComplex * self
-!
+| u r i |
-sumFromFraction: argument
-	^ argument asComplex + self
+u := aFloat.
-!
+r := (real * aFloat).
+i  := (imaginary * aFloat).
-sumFromInteger: argument
+i = 0 ifTrue:[ ^ r ].
-	^ argument asComplex + self
+^ Complex real:r imaginary:i
+"
+(1 % 1) * 2.0
+(1 % 1) * 0.0
+2.0 * (1 % 1)
+"
+!
+productFromFraction: aFraction
+^ aFraction asComplex * self
+!
+productFromInteger: anInteger
+^ anInteger asComplex * self
+!
+quotientFromFloat: aFloat
+^ aFloat asComplex / self
+!
+quotientFromFraction: aFraction
+^ aFraction asComplex / self
+!
+quotientFromInteger: anInteger
+^ anInteger asComplex / self
+!
+sumFromFloat: aFloat
+"Return the sum of the receiver and the argument, aFloat."
+"/ ^ aFloat asComplex + self
+| r |
+r := aFloat + real.
+imaginary = 0 ifTrue:[ ^ r ].
+^ Complex real:r imaginary:imaginary
+"
+(1 % 1) + 1.0
+1.0 + (1 % 1)
+"
+!
+sumFromFraction: aFraction
+^ aFraction asComplex + self
+!
+sumFromInteger: anInteger
+^ anInteger asComplex + self
 ! !
 !Complex methodsFor:'mathematical functions'!
 angle
-	"Return the radian angle for this Complex number."
+"Return the radian angle for this Complex number."
-	real < 0 ifTrue: [
+real < 0 ifTrue: [
-	    imaginary < 0 ifTrue: [
+imaginary < 0 ifTrue: [
-		^ (imaginary / real) arcTan - Float pi
+^ (imaginary / real) arcTan - Float pi
-	    ].
+].
-	    ^ Float pi + (imaginary / real) arcTan
+^ Float pi + (imaginary / real) arcTan
-	].
+].
-	^ (imaginary / real) arcTan
+^ (imaginary / real) arcTan
+"
+(1 % 1) angle radiansToDegrees
+"
 !
 exp
-	"Return the complex exponential of the receiver."
+"Return the complex exponential of the receiver."
-	^ imaginary cos % imaginary sin * real exp
+^ (imaginary cos % imaginary sin) * real exp
 !
 sqrt
-	"Return the square root of the receiver"
+"Return the square root of the receiver"
-	| u v |
+| w quotient absReal absImag |
-	(imaginary = 0 and: [real >= 0]) ifTrue: [^real sqrt].
-	v := (self abs - real / 2) sqrt.
+((real = 0) and: [ imaginary = 0 ]) ifTrue: [
-	u := imaginary / 2 / v.
+^ Complex zero
-	^Complex real: u imaginary: v
+].
+absReal := real abs.
-	"-4 asComplex sqrt"
+absImag := imaginary abs.
-	"-4 asComplex sqrt squared"
+absReal >= absImag ifTrue:[
+quotient := imaginary / real.
+w := (absReal sqrt) * (((1 + (1 + (quotient * quotient)) sqrt) / 2) sqrt)
+] ifFalse: [
+quotient := real / imaginary.
+w := (absImag sqrt) * (((quotient abs + (1 + (quotient * quotient)) sqrt) / 2) sqrt)
+].
+real >= 0 ifTrue:[
+^ Complex real: w imaginary: (imaginary / (2 * w))
+].
+imaginary >= 0 ifTrue: [
+^ Complex real: absImag / (2 * w) imaginary: w
+].
+^ Complex real: absImag / (2 * w) imaginary: -1 * w
+!
+sqrt_bad
+"Return the square root of the receiver"
+| u v |
+(imaginary = 0 and: [real >= 0]) ifTrue: [^ real sqrt].
+v := (self abs - real / 2) sqrt.
+u := imaginary / 2 / v.
+^ Complex real: u imaginary: v
+"
+-4 asComplex sqrt
+4 asComplex sqrt
+"
+"
+-4 asComplex sqrt squared
+"
 ! !
 !Complex methodsFor:'printing'!
+displayOn: aStream
+aStream nextPut: $(.
+self realPart printOn: aStream.
+self imaginaryPart >= 0
+ifTrue: [ aStream nextPut: $+ ]
+ifFalse: [ aStream nextPut: $- ].
+self imaginaryPart abs printOn: aStream.
+aStream nextPutAll: 'i)'
+"
+Complex real:1 imaginary:1
+"
+!
 printOn: aStream
-	aStream nextPut: $(.
+aStream nextPut: $(.
-	real storeOn: aStream.
+real storeOn: aStream.
-	aStream nextPutAll: '%'.
+aStream nextPutAll: '%'.
-	imaginary storeOn: aStream.
+imaginary storeOn: aStream.
-	aStream nextPut: $).
+aStream nextPut: $).
 !
 printString
-	^ '(' , real printString, '%', imaginary printString, ')'
+^ '(' , real printString, '%', imaginary printString, ')'
 !
 storeOn: aStream
-	aStream nextPut: $(.
+self printOn:aStream
-	real storeOn: aStream.
-	aStream nextPutAll: '%'.
-	imaginary storeOn: aStream.
-	aStream nextPut: $).
 ! !
 !Complex methodsFor:'private'!
 setReal: u setImaginary: v
-	real := u.
+real := u.
-	imaginary := v.
+imaginary := v.
 ! !
 !Complex methodsFor:'testing'!
 isComplex
+"Answer whether the receiver has an imaginary part
-	^true
+(i.e. if it is a complex number). Always true here."
+^ true
 !
 isReal
-	"Return true if this Complex number has a zero imaginary part."
+"Return true if this Complex number has a zero imaginary part."
-	^ imaginary = 0
+^ imaginary = 0
 !
 isZero
-	"Answer whether 'self = self class zero'.  We can't use #= because
+"Answer whether 'self = self class zero'.
-	#= is defined in terms of #isZero"
+We can't use #= because #= is defined in terms of #isZero"
-	^real isZero and: [imaginary isZero]
+^real isZero and: [imaginary isZero]
 !
 sign
+"return a new complex, consisting of the signs of the real and imaginary parts"
-	^Complex real: real sign imaginary: imaginary sign
+^ Complex real: real sign imaginary: imaginary sign
+! !
+!Complex methodsFor:'truncation & rounding'!
+ceiling
+"blocked: complex numbers have no ceiling"
+^ self shouldNotImplement
+!
+floor
+"blocked: complex numbers have no floor"
+^ self shouldNotImplement
 ! !
 !Complex class methodsFor:'documentation'!
 version
-^ '$Header: /cvs/stx/stx/libbasic/Complex.st,v 1.7 2003-04-22 09:44:13 cg Exp $'
+^ '$Header: /cvs/stx/stx/libbasic/Complex.st,v 1.8 2003-06-16 09:13:42 cg Exp $'
 ! !

changeset 7355	96f466eeddf5
parent 7221	b38093d749b3
child 7377	b2f13d3b9f58