"

 This is a Manchester Goodie.  It is distributed freely on condition

 that you observe these conditions in respect of the whole Goodie, and on

 any significant part of it which is separately transmitted or stored:

	* You must ensure that every copy includes this notice, and that

	  source and author(s) of the material are acknowledged.

	* These conditions must be imposed on anyone who receives a copy.

	* The material shall not be used for commercial gain without the prior

	  written consent of the author(s).

 For more information about the Manchester Goodies Library (from which

 this file was distributed) send e-mail:

	To: goodies-lib@cs.man.ac.uk

	Subject: help

 This is an additional goody-class, which is NOT covered by the

 ST/X license. It has been packaged with the ST/X distribution to

 make your live easier instead. NO WARRANTY.

"

"{ Package: 'stx:libbasic' }"

ArithmeticValue subclass:#Complex

	instanceVariableNames:'real imaginary'

	classVariableNames:'ComplexOne ComplexZero'

	poolDictionaries:''

	category:'Magnitude-Numbers'

!

!Complex class methodsFor:'documentation'!

copyright

"

 This is a Manchester Goodie.  It is distributed freely on condition

 that you observe these conditions in respect of the whole Goodie, and on

 any significant part of it which is separately transmitted or stored:

	* You must ensure that every copy includes this notice, and that

	  source and author(s) of the material are acknowledged.

	* These conditions must be imposed on anyone who receives a copy.

	* The material shall not be used for commercial gain without the prior

	  written consent of the author(s).

 For more information about the Manchester Goodies Library (from which

 this file was distributed) send e-mail:

	To: goodies-lib@cs.man.ac.uk

	Subject: help

 This is an additional goody-class, which is NOT covered by the

 ST/X license. It has been packaged with the ST/X distribution to

 make your live easier instead. NO WARRANTY.

"

!

documentation

"

    This class implements complex numbers.

    A complex number has real and imaginary parts which must be manipulated simultaneously

    in any numeric processing.

    Complex numbers can be used in many of the same places that regular numbers

    can be used with one major exception of comparisons, since complex numbers cannot

    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

       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)

	minor changes and double dispatching code by cg.

"

!

examples

"

    (5 % 7) real

    (5 % 7) imaginary

    (5 % 7) = 5

    (5 % 0) = 5

    (5.0 % 0) = 5

    (1 % 0) + (2 % 0)

    (1 % 0) + (0 % 2)

    (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'!

abs:aNumber1 arg:aNumber2

    |real imaginary|

    real := aNumber1 * aNumber2 cos.

    imaginary := aNumber1 * aNumber2 sin.

    ^ real + imaginary i

!

fromReal: aNumber

    "Create a new complex number from the given real number."

    ^ 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

     imaginary part is zero, return the real part of the number."

    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:

	aNumber * aNumber class unity = aNumber

     This must be true regardless of how a given subclass chooses to define #*"

    ComplexOne isNil ifTrue:[

	ComplexOne := self fromReal: 1

    ].

    ^ ComplexOne

!

zero

    "Answer the value which allows, for any given arithmetic value, the following to be true:

	aNumber + aNumber class zero = aNumber

     This must be true regardless of how a given subclass chooses to define #+"

    ComplexZero isNil ifTrue:[

	ComplexZero := self fromReal: 0

    ].

    ^ ComplexZero

! !

!Complex class methodsFor:'exception handling'!

trapImaginary:aBlock

    "evaluate aBlock; if any DomainError occurs inside, with respect to square roots,

     convert the root to a complex root and proceed.

     This allows for regular (failing) code to transparently convert to complex."

    |send|

    ^ ImaginaryResultError handle: [:ex |

	|selector|

	send := ex parameter.

	selector := send selector.

	(selector = #sqrt or: [selector = #sqrtTruncated]) ifTrue: [

	    send receiver: send receiver asComplex.

	    ex proceedWith: send value

	] ifFalse: [

	    ex reject

	]

    ] do: aBlock

    "

     Complex trapImaginary: [-2 sqrt]

    "

    "failing code:

	 |a|

	 a := -2.

	 (a sqrt + 5) * 17.

    "

    "complex code:

	 |a|

	 Complex trapImaginary:[

	     a := -2.

	     (a sqrt + 5) * 2.

	 ]

    "

! !

!Complex methodsFor:'accessing'!

imaginary

    "Return the imaginary part of the complex number."

    ^ 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."

    ^ 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."

"/    | u v r i |

"/

"/    aNumber isComplex ifTrue:[

"/        u := aNumber real.

"/        v := aNumber imaginary.

"/        r := (real * u) - (imaginary * v).

"/        i  := (real * v) + (imaginary * u).

"/        i = 0 ifTrue:[ ^ r ].

"/        ^ Complex real:r imaginary:i

"/    ].

    ^ aNumber productFromComplex:self.

    "Modified: / 8.7.1998 / 12:12:37 / cg"

!

+ aNumber

    "Return the sum of the receiver and the argument."

"/    | r i |

"/

"/    aNumber isComplex ifTrue: [

"/        r := aNumber real + real.

"/        i := aNumber imaginary + imaginary.

"/        i = 0 ifTrue:[ ^ r ].

"/        ^ Complex real:r imaginary:i

"/    ].

    ^ aNumber sumFromComplex:self.

    "Modified: / 8.7.1998 / 12:15:42 / cg"

!

- aNumber

    "Return the difference of the receiver and the argument."

"/    | r i |

"/

"/    aNumber isComplex ifTrue: [

"/        r := real - aNumber real.

"/        i := imaginary - aNumber imaginary.

"/        i = 0 ifTrue:[ ^ r ].

"/        ^ Complex real:r imaginary:i.

"/    ].

    ^ aNumber differenceFromComplex:self.

    "Modified: / 8.7.1998 / 12:15:38 / cg"

!

/ aNumber

    "Return the quotient of the receiver and the argument."

"/    | denom u v r i |

"/

"/    aNumber isComplex ifTrue:[

"/        u := aNumber real.

"/        v := aNumber imaginary.

"/        denom := u * u + (v * v).

"/        r := u * real + (v * imaginary) / denom.

"/        i := u * imaginary - (v * real) / denom.

"/        i = 0 ifTrue:[ ^ r ].

"/        ^ Complex real:r imaginary:i

"/    ].

    ^ aNumber quotientFromComplex:self.

    "Modified: / 8.7.1998 / 12:15:34 / cg"

!

abs

    "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

    "

     (1 % 1) abs

    "

!

conjugated

    "Return the complex conjugate of this complex number

     (i.e. with imaginary part negated)."

    ^ self class

        real: real

        imaginary: imaginary negated

!

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"

    ^ self class

        real: real negated

        imaginary: imaginary negated

! !

!Complex methodsFor:'coercing'!

coerce: aNumber

    ^ aNumber asComplex

!

generality

    ^ 150

! !

!Complex methodsFor:'comparing'!

< aNumber

    "raises an error - complex numbers are not well ordered"

    ^ Number

	raise: #unorderedSignal

	receiver: self

	selector: #<

	arg: aNumber

	errorString: 'Complex numbers are not well ordered'

    "

     1 < (2 % 2)

     (2 % 2) < 1

    "

!

= aNumber

    "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."

    ^ (real hash) bitXor:(imaginary hash bitShift:16)

    "

     (1+0i) hash

     (1+1i) hash

    "

! !

!Complex methodsFor:'converting'!

asComplex

    "I am a complex - so return the receiver"

    ^ self

!

asFloat

    imaginary = 0 ifTrue: [^ real asFloat].

    ^ Number

	    raise: #coercionErrorSignal

	    receiver: self

	    selector: #asFloat

	    errorString: 'Can''t coerce an instance of Complex to a Float'

!

asInteger

    imaginary = 0 ifTrue: [^real asInteger].

    ^ Number

	raise: #coercionErrorSignal

	receiver: self

	selector: #asInteger

	errorString: 'Can''t coerce an instance of Complex to an Integer'

!

asPoint

    "Return the complex number as a point."

    ^ real @ imaginary

!

reduceGeneralityIfPossible

    "Answer the receiver transformed to a lower generality, if such a

     transformation is possible without losing information.

     If not, answer the receiver"

    imaginary isZero

	ifTrue: [^ real]

	ifFalse: [^ self]

! !

!Complex methodsFor:'double dispatching'!

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 ].

    ^ self class real:r imaginary:i.

!

differenceFromFloat:aFloat

    "Return the difference of the argument, aFloat and the receiver."

    "/ ^ aFloat asComplex - self

    | r |

    r := aFloat - real.

    imaginary = 0 ifTrue:[ ^ r ].

    ^ self class real:r imaginary:imaginary negated

    "

     (1 % 1) - 1.0

     1.0 - (1 % 1)

    "

!

differenceFromFraction: aFraction

    ^ aFraction asComplex - self

!

differenceFromInteger: anInteger

    ^ anInteger asComplex - self

!

equalFromComplex:aComplex

    ^ (aComplex real = real) and:[aComplex imaginary = imaginary]

!

equalFromFloat:aFloat

    imaginary = 0 ifFalse:[^ false].

    ^ real = aFloat

!

productFromComplex:aComplex

    "Return the product of the receiver and the argument, aComplex."

    | u v r i |

    u := aComplex real.

    v := aComplex imaginary.