author | Claus Gittinger <cg@exept.de> |
Thu, 02 Mar 2000 15:14:57 +0100 | |
changeset 5287 | b3b0d0e3ce98 |
parent 3637 | 2b4d733c9a01 |
child 6500 | d2ce5b0a1a78 |
permissions | -rw-r--r-- |
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1 |
"{ Package: 'stx:goodies' }" |
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parents:
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" |
4 |
This is a Manchester Goodie. It is distributed freely on condition |
|
5 |
that you observe these conditions in respect of the whole Goodie, and on |
|
6 |
any significant part of it which is separately transmitted or stored: |
|
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* You must ensure that every copy includes this notice, and that |
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parents:
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|
8 |
source and author(s) of the material are acknowledged. |
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parents:
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|
9 |
* These conditions must be imposed on anyone who receives a copy. |
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parents:
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|
10 |
* The material shall not be used for commercial gain without the prior |
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parents:
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written consent of the author(s). |
3637 | 12 |
|
13 |
For more information about the Manchester Goodies Library (from which |
|
14 |
this file was distributed) send e-mail: |
|
5287
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To: goodies-lib@cs.man.ac.uk |
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16 |
Subject: help |
3637 | 17 |
|
18 |
This is an additional goody-class, which is NOT covered by the |
|
19 |
ST/X license. It has been packaged with the ST/X distribution to |
|
20 |
make your live easier instead. NO WARRANTY. |
|
21 |
" |
|
22 |
||
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ArithmeticValue subclass:#Complex |
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instanceVariableNames:'real imaginary' |
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classVariableNames:'' |
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poolDictionaries:'' |
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category:'Magnitude-Numbers' |
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! |
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||
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!Complex class methodsFor:'documentation'! |
31 |
||
32 |
copyright |
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" |
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This is a Manchester Goodie. It is distributed freely on condition |
|
35 |
that you observe these conditions in respect of the whole Goodie, and on |
|
36 |
any significant part of it which is separately transmitted or stored: |
|
5287
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parents:
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* You must ensure that every copy includes this notice, and that |
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Claus Gittinger <cg@exept.de>
parents:
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|
38 |
source and author(s) of the material are acknowledged. |
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parents:
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* These conditions must be imposed on anyone who receives a copy. |
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parents:
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* The material shall not be used for commercial gain without the prior |
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parents:
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written consent of the author(s). |
3637 | 42 |
|
43 |
For more information about the Manchester Goodies Library (from which |
|
44 |
this file was distributed) send e-mail: |
|
5287
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To: goodies-lib@cs.man.ac.uk |
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Subject: help |
3637 | 47 |
|
48 |
This is an additional goody-class, which is NOT covered by the |
|
49 |
ST/X license. It has been packaged with the ST/X distribution to |
|
50 |
make your live easier instead. NO WARRANTY. |
|
51 |
" |
|
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! |
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||
54 |
documentation |
|
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" |
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This is an implementation of complex numbers. A complex number has real and |
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imaginary parts which must be manipulated simultaneously in any numeric processing. |
58 |
Complex numbers can be used in many of the same places that regular numbers |
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can be used with one major exception of comparisons, since complex numbers cannot |
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be directly compared for size (except through lengths of vectors (see absolute |
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value)). |
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||
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Instance variables: |
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real <Number> the part of the number which can be expressed as a Real number |
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imaginary <Number> the part of the number which, in terms of how the number behaves, |
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has been multiplied by 'i' (-1 sqrt) |
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Author: Kurt Hebel (hebel@uinova.cerl.uiuc.edu) |
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" |
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! ! |
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!Complex class methodsFor:'instance creation'! |
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fromReal: aNumber |
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"Create a new complex number from the given real number." |
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^ self basicNew setReal: aNumber setImaginary: 0 |
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! |
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real: u imaginary: v |
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"Create a new complex number with the given real and imaginary parts. If the |
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imaginary part is zero, return the real part of the number." |
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^v = 0 ifTrue: [u] |
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ifFalse: [self basicNew setReal: u setImaginary: v] |
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! ! |
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|
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!Complex class methodsFor:'constants access'! |
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unity |
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"Answer the value which allows, for any given arithmetic value, the following to be true |
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aNumber * aNumber class unity = aNumber |
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This must be true regardless of how a given subclass chooses to define #*" |
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^self fromReal: 1 |
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! |
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zero |
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"Answer the value which allows, for any given arithmetic value, the following to be true |
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aNumber + aNumber class zero = aNumber |
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This must be true regardless of how a given subclass chooses to define #+" |
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^self fromReal: 0 |
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! ! |
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|
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!Complex class methodsFor:'exception handling'! |
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trapImaginary: aBlock |
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"Complex trapImaginary: [-27 sqrt]" |
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|
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| send | |
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^Number domainErrorSignal handle: [ :ex | |
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send := ex parameter. |
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(send selector = #sqrt or: [send selector = #sqrtTruncated]) ifTrue: [ |
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send receiver: send receiver asComplex. |
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ex proceedWith: send value |
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] ifFalse: [ |
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ex reject |
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] |
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] do: aBlock |
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! ! |
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|
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!Complex methodsFor:'accessing'! |
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imaginary |
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"Return the imaginary part of the complex number." |
130 |
^ imaginary |
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! |
132 |
||
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real |
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"Return the real part of the complex number." |
135 |
^ real |
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! ! |
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!Complex methodsFor:'arithmetic'! |
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* aNumber |
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"Return the product of the receiver and the argument." |
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| u v r i | |
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aNumber isComplex ifTrue:[ |
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u := aNumber real. |
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v := aNumber imaginary. |
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r := (real * u) - (imaginary * v). |
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i := (real * v) + (imaginary * u). |
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i = 0 ifTrue:[ ^ r ]. |
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^ Complex real:r imaginary:i |
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]. |
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^ self retry: #* coercing: aNumber |
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"Modified: / 8.7.1998 / 12:12:37 / cg" |
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! |
157 |
||
158 |
+ aNumber |
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"Return the sum of the receiver and the argument." |
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| r i | |
265 | 162 |
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aNumber isComplex ifTrue: [ |
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r := aNumber real + real. |
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i := aNumber imaginary + imaginary. |
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i = 0 ifTrue:[ ^ r ]. |
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^ Complex real:r imaginary:i |
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]. |
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^ self retry: #+ coercing: aNumber |
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171 |
"Modified: / 8.7.1998 / 12:15:42 / cg" |
265 | 172 |
! |
173 |
||
174 |
- aNumber |
|
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175 |
"Return the difference of the receiver and the argument." |
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176 |
|
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177 |
| r i | |
265 | 178 |
|
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179 |
aNumber isComplex ifTrue: [ |
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180 |
r := real - aNumber real. |
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181 |
i := imaginary - aNumber imaginary. |
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|
182 |
i = 0 ifTrue:[ ^ r ]. |
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|
183 |
^ Complex real:r imaginary:i. |
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184 |
]. |
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|
185 |
^ self retry: #- coercing: aNumber |
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186 |
|
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187 |
"Modified: / 8.7.1998 / 12:15:38 / cg" |
265 | 188 |
! |
189 |
||
190 |
/ aNumber |
|
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191 |
"Return the quotient of the receiver and the argument." |
265 | 192 |
|
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|
193 |
| denom u v r i | |
265 | 194 |
|
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195 |
aNumber isComplex ifTrue:[ |
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196 |
u := aNumber real. |
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197 |
v := aNumber imaginary. |
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|
198 |
denom := u * u + (v * v). |
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199 |
r := u * real + (v * imaginary) / denom. |
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200 |
i := u * imaginary - (v * real) / denom. |
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201 |
i = 0 ifTrue:[ ^ r ]. |
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|
202 |
^ Complex real:r imaginary:i |
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|
203 |
]. |
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|
204 |
^ self retry: #/ coercing: aNumber |
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205 |
|
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206 |
"Modified: / 8.7.1998 / 12:15:34 / cg" |
265 | 207 |
! |
208 |
||
209 |
abs |
|
1944 | 210 |
"Return the magnitude (or absolute value) of the complex number." |
265 | 211 |
|
1944 | 212 |
^ (real * real + (imaginary * imaginary)) sqrt |
265 | 213 |
! |
214 |
||
215 |
conjugated |
|
1944 | 216 |
"Return the complex conjugate of this complex number." |
265 | 217 |
|
1944 | 218 |
^ Complex real: real imaginary: imaginary negated |
265 | 219 |
! ! |
220 |
||
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221 |
!Complex methodsFor:'coercing'! |
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|
222 |
|
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223 |
coerce: aNumber |
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|
224 |
|
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225 |
^aNumber asComplex |
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|
226 |
! |
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|
227 |
|
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|
228 |
generality |
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|
229 |
|
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230 |
^150 |
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|
231 |
! ! |
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|
232 |
|
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|
233 |
!Complex methodsFor:'comparing'! |
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|
234 |
|
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|
235 |
< aNumber |
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|
236 |
^Number |
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|
237 |
raise: #unorderedSignal |
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|
238 |
receiver: self |
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|
239 |
selector: #< |
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|
240 |
arg: aNumber |
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|
241 |
errorString: 'Complex numbers are not well ordered'! |
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|
242 |
|
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|
243 |
= aNumber |
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|
244 |
^ (aNumber real = real) and:[aNumber imaginary = imaginary] |
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|
245 |
! |
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|
246 |
|
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|
247 |
hash |
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|
248 |
"Hash is implemented because equals is implemented." |
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|
249 |
|
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|
250 |
^ real hash |
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|
251 |
! ! |
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|
252 |
|
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|
253 |
!Complex methodsFor:'converting'! |
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|
254 |
|
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|
255 |
asComplex |
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|
256 |
|
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|
257 |
^self |
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|
258 |
! |
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|
259 |
|
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|
260 |
asFloat |
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|
261 |
|
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|
262 |
imaginary = 0 ifTrue: [^real asFloat]. |
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|
263 |
^Number |
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|
264 |
raise: #coercionErrorSignal |
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|
265 |
receiver: self |
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|
266 |
selector: #asFloat |
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|
267 |
errorString: 'Can''t coerce an instance of Complex to a Float' |
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|
268 |
! |
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|
269 |
|
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|
270 |
asInteger |
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|
271 |
|
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|
272 |
imaginary = 0 ifTrue: [^real asInteger]. |
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|
273 |
^Number |
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|
274 |
raise: #coercionErrorSignal |
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|
275 |
receiver: self |
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|
276 |
selector: #asInteger |
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|
277 |
errorString: 'Can''t coerce an instance of Complex to an Integer' |
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|
278 |
! |
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|
279 |
|
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|
280 |
asPoint |
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|
281 |
"Return the complex number as a point." |
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|
282 |
^ real @ imaginary |
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|
283 |
! |
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|
284 |
|
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|
285 |
reduceGeneralityIfPossible |
89f1f31527f4
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diff
changeset
|
286 |
"Answer the receiver transformed to a lower generality, if such a |
89f1f31527f4
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|
287 |
transformation is possible without losing information. If not, answer |
89f1f31527f4
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|
288 |
the receiver" |
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diff
changeset
|
289 |
|
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|
290 |
imaginary isZero |
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|
291 |
ifTrue: [^real] |
89f1f31527f4
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|
292 |
ifFalse: [^self] |
89f1f31527f4
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|
293 |
! ! |
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|
294 |
|
89f1f31527f4
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changeset
|
295 |
!Complex methodsFor:'double dispatching'! |
265 | 296 |
|
297 |
differenceFromFloat: argument |
|
1944 | 298 |
^ argument asComplex - self |
265 | 299 |
! |
300 |
||
301 |
differenceFromFraction: argument |
|
1944 | 302 |
^ argument asComplex - self |
265 | 303 |
! |
304 |
||
305 |
differenceFromInteger: argument |
|
1944 | 306 |
^ argument asComplex - self |
265 | 307 |
! |
308 |
||
309 |
productFromFloat: argument |
|
1944 | 310 |
^ argument asComplex * self |
265 | 311 |
! |
312 |
||
313 |
productFromFraction: argument |
|
1944 | 314 |
^ argument asComplex * self |
265 | 315 |
! |
316 |
||
317 |
productFromInteger: argument |
|
1944 | 318 |
^ argument asComplex * self |
265 | 319 |
! |
320 |
||
321 |
quotientFromFloat: argument |
|
1944 | 322 |
^ argument asComplex / self |
265 | 323 |
! |
324 |
||
325 |
quotientFromFraction: argument |
|
1944 | 326 |
^ argument asComplex / self |
265 | 327 |
! |
328 |
||
329 |
quotientFromInteger: argument |
|
1944 | 330 |
^ argument asComplex / self |
265 | 331 |
! |
332 |
||
333 |
sumFromFloat: argument |
|
1944 | 334 |
^ argument asComplex + self |
265 | 335 |
! |
336 |
||
337 |
sumFromFraction: argument |
|
1944 | 338 |
^ argument asComplex + self |
265 | 339 |
! |
340 |
||
341 |
sumFromInteger: argument |
|
1944 | 342 |
^ argument asComplex + self |
265 | 343 |
! ! |
344 |
||
3633
89f1f31527f4
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Claus Gittinger <cg@exept.de>
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1944
diff
changeset
|
345 |
!Complex methodsFor:'mathematical functions'! |
265 | 346 |
|
347 |
angle |
|
1944 | 348 |
"Return the radian angle for this Complex number." |
265 | 349 |
|
1944 | 350 |
real < 0 ifTrue: [ |
351 |
imaginary < 0 ifTrue: [ |
|
352 |
^ (imaginary / real) arcTan - Float pi |
|
353 |
]. |
|
354 |
^ Float pi + (imaginary / real) arcTan |
|
355 |
]. |
|
356 |
^ (imaginary / real) arcTan |
|
265 | 357 |
! |
358 |
||
359 |
exp |
|
1944 | 360 |
"Return the complex exponential of the receiver." |
265 | 361 |
|
1944 | 362 |
^ imaginary cos % imaginary sin * real exp |
265 | 363 |
! |
364 |
||
365 |
sqrt |
|
1944 | 366 |
"Return the square root of the receiver" |
265 | 367 |
|
1944 | 368 |
| u v | |
369 |
(imaginary = 0 and: [real >= 0]) ifTrue: [^real sqrt]. |
|
370 |
v := (self abs - real / 2) sqrt. |
|
371 |
u := imaginary / 2 / v. |
|
372 |
^Complex real: u imaginary: v |
|
265 | 373 |
|
1944 | 374 |
"-4 asComplex sqrt" |
375 |
"-4 asComplex sqrt squared" |
|
265 | 376 |
! ! |
377 |
||
3633
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
378 |
!Complex methodsFor:'printing'! |
265 | 379 |
|
3633
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
380 |
printOn: aStream |
89f1f31527f4
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parents:
1944
diff
changeset
|
381 |
aStream nextPut: $(. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
382 |
real storeOn: aStream. |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
383 |
aStream nextPutAll: '%'. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
384 |
imaginary storeOn: aStream. |
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
385 |
aStream nextPut: $). |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
386 |
! |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
387 |
|
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
388 |
printString |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
389 |
^ '(' , real printString, '%', imaginary printString, ')' |
265 | 390 |
! |
391 |
||
3633
89f1f31527f4
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parents:
1944
diff
changeset
|
392 |
storeOn: aStream |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
393 |
aStream nextPut: $(. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
394 |
real storeOn: aStream. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
395 |
aStream nextPutAll: '%'. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
396 |
imaginary storeOn: aStream. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
397 |
aStream nextPut: $). |
265 | 398 |
! ! |
399 |
||
3633
89f1f31527f4
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Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
400 |
!Complex methodsFor:'private'! |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
401 |
|
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
402 |
setReal: u setImaginary: v |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
403 |
real := u. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
404 |
imaginary := v. |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
405 |
! ! |
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
406 |
|
89f1f31527f4
avoid a send if the result of an arithmetic op
Claus Gittinger <cg@exept.de>
parents:
1944
diff
changeset
|
407 |
!Complex methodsFor:'testing'! |
265 | 408 |
|
409 |
isComplex |
|
410 |
||
1944 | 411 |
^true |
265 | 412 |
! |
413 |
||
414 |
isReal |
|
1944 | 415 |
"Return true if this Complex number has a zero imaginary part." |
416 |
^ imaginary = 0 |
|
265 | 417 |
! |
418 |
||
419 |
isZero |
|
1944 | 420 |
"Answer whether 'self = self class zero'. We can't use #= because |
421 |
#= is defined in terms of #isZero" |
|
265 | 422 |
|
1944 | 423 |
^real isZero and: [imaginary isZero] |
265 | 424 |
! |
425 |
||
426 |
sign |
|
427 |
||
1944 | 428 |
^Complex real: real sign imaginary: imaginary sign |
265 | 429 |
! ! |
430 |
||
3637 | 431 |
!Complex class methodsFor:'documentation'! |
432 |
||
433 |
version |
|
5287
b3b0d0e3ce98
package-definitions fixed/updated
Claus Gittinger <cg@exept.de>
parents:
3637
diff
changeset
|
434 |
^ '$Header: /cvs/stx/stx/libbasic/Complex.st,v 1.5 2000-03-02 14:14:56 cg Exp $' |
3637 | 435 |
! ! |