1
|
1 |
"
|
5
|
2 |
COPYRIGHT (c) 1989 by Claus Gittinger
|
213
|
3 |
All Rights Reserved
|
1
|
4 |
|
|
5 |
This software is furnished under a license and may be used
|
|
6 |
only in accordance with the terms of that license and with the
|
|
7 |
inclusion of the above copyright notice. This software may not
|
|
8 |
be provided or otherwise made available to, or used by, any
|
|
9 |
other person. No title to or ownership of the software is
|
|
10 |
hereby transferred.
|
|
11 |
"
|
|
12 |
|
|
13 |
Number subclass:#Fraction
|
1200
|
14 |
instanceVariableNames:'numerator denominator'
|
|
15 |
classVariableNames:'FractionOne FractionZero'
|
|
16 |
poolDictionaries:''
|
|
17 |
category:'Magnitude-Numbers'
|
1
|
18 |
!
|
|
19 |
|
88
|
20 |
!Fraction class methodsFor:'documentation'!
|
|
21 |
|
|
22 |
copyright
|
|
23 |
"
|
|
24 |
COPYRIGHT (c) 1989 by Claus Gittinger
|
213
|
25 |
All Rights Reserved
|
88
|
26 |
|
|
27 |
This software is furnished under a license and may be used
|
|
28 |
only in accordance with the terms of that license and with the
|
|
29 |
inclusion of the above copyright notice. This software may not
|
|
30 |
be provided or otherwise made available to, or used by, any
|
|
31 |
other person. No title to or ownership of the software is
|
|
32 |
hereby transferred.
|
|
33 |
"
|
|
34 |
!
|
|
35 |
|
|
36 |
documentation
|
|
37 |
"
|
|
38 |
Instances of Fraction represent fractional numbers consisting of
|
|
39 |
a numerator and denominator. Both are themselfes arbitrary precision
|
324
|
40 |
integers. Fractions are usually created by dividing Integers using /
|
|
41 |
(for exact division)."
|
88
|
42 |
! !
|
1
|
43 |
|
|
44 |
!Fraction class methodsFor:'initialization'!
|
|
45 |
|
|
46 |
initialize
|
302
|
47 |
FractionZero isNil ifTrue:[
|
|
48 |
FractionZero := self numerator:0 denominator:1.
|
|
49 |
FractionOne := self numerator:1 denominator:1
|
|
50 |
]
|
1
|
51 |
! !
|
|
52 |
|
|
53 |
!Fraction class methodsFor:'instance creation'!
|
|
54 |
|
|
55 |
new
|
|
56 |
"create and return a new fraction with value 0"
|
|
57 |
|
54
|
58 |
^ self numerator:0 denominator:1
|
1
|
59 |
!
|
|
60 |
|
|
61 |
numerator:num denominator:den
|
|
62 |
"create and return a new fraction with numerator num and denominator den"
|
|
63 |
|
|
64 |
%{ /* NOCONTEXT */
|
369
|
65 |
|
13
|
66 |
/* this check allows subclassing .. */
|
1
|
67 |
if (self == Fraction) {
|
835
|
68 |
if (__CanDoQuickAlignedNew(sizeof(struct __fraction))) {
|
213
|
69 |
OBJ newFraction;
|
293
|
70 |
int spc;
|
1
|
71 |
|
835
|
72 |
__qCheckedAlignedNew(newFraction, sizeof(struct __fraction));
|
1133
|
73 |
__InstPtr(newFraction)->o_class = self;
|
|
74 |
__FractionInstPtr(newFraction)->f_numerator = num;
|
|
75 |
__FractionInstPtr(newFraction)->f_denominator = den;
|
369
|
76 |
if (! __bothSmallInteger(num, den)) {
|
379
|
77 |
spc = __qSpace(newFraction);
|
|
78 |
__STORE_SPC(newFraction, num, spc);
|
|
79 |
__STORE_SPC(newFraction, den, spc);
|
369
|
80 |
}
|
213
|
81 |
RETURN ( newFraction );
|
|
82 |
}
|
1
|
83 |
}
|
|
84 |
%}
|
|
85 |
.
|
|
86 |
^ self basicNew setNumerator:num denominator:den
|
|
87 |
! !
|
|
88 |
|
701
|
89 |
!Fraction class methodsFor:'constants'!
|
|
90 |
|
|
91 |
unity
|
|
92 |
"return the neutral element for multiplication"
|
|
93 |
|
|
94 |
^ FractionOne
|
|
95 |
!
|
|
96 |
|
|
97 |
zero
|
|
98 |
"return the neutral element for addition"
|
|
99 |
|
|
100 |
^ FractionZero
|
|
101 |
! !
|
|
102 |
|
3
|
103 |
!Fraction class methodsFor:'queries'!
|
|
104 |
|
|
105 |
isBuiltInClass
|
1264
|
106 |
"return true if this class is known by the run-time-system.
|
|
107 |
Here, true is returned for myself, false for subclasses."
|
3
|
108 |
|
|
109 |
^ self == Fraction
|
1264
|
110 |
|
|
111 |
"Modified: 23.4.1996 / 15:59:10 / cg"
|
3
|
112 |
! !
|
|
113 |
|
1
|
114 |
!Fraction methodsFor:'accessing'!
|
|
115 |
|
|
116 |
denominator
|
|
117 |
"return the denominator"
|
|
118 |
|
|
119 |
^ denominator
|
|
120 |
!
|
|
121 |
|
701
|
122 |
numerator
|
|
123 |
"return the numerator"
|
1
|
124 |
|
701
|
125 |
^ numerator
|
1
|
126 |
! !
|
|
127 |
|
|
128 |
!Fraction methodsFor:'arithmetic'!
|
|
129 |
|
701
|
130 |
* aNumber
|
|
131 |
"return the product of the receiver and the argument, aNumber"
|
|
132 |
|
|
133 |
|n d|
|
|
134 |
|
|
135 |
(aNumber isMemberOf:SmallInteger) ifTrue:[
|
|
136 |
^ (self class numerator:(numerator * aNumber)
|
|
137 |
denominator:denominator) reduced
|
|
138 |
].
|
|
139 |
aNumber isFraction ifTrue:[
|
|
140 |
n := numerator * aNumber numerator.
|
|
141 |
d := denominator * aNumber denominator.
|
|
142 |
^ (self class numerator:n denominator:d) reduced
|
|
143 |
].
|
|
144 |
(aNumber isMemberOf:Float) ifTrue:[
|
|
145 |
^ (numerator * aNumber) / denominator
|
|
146 |
].
|
|
147 |
^ aNumber productFromFraction:self
|
|
148 |
!
|
|
149 |
|
1
|
150 |
+ aNumber
|
|
151 |
"return the sum of the receiver and the argument, aNumber"
|
|
152 |
|
|
153 |
|n d|
|
|
154 |
|
|
155 |
(aNumber isMemberOf:SmallInteger) ifTrue:[
|
213
|
156 |
^ (self class numerator:(numerator + (denominator * aNumber))
|
|
157 |
denominator:denominator) reduced
|
1
|
158 |
].
|
259
|
159 |
aNumber isFraction ifTrue:[
|
213
|
160 |
n := aNumber numerator.
|
|
161 |
d := aNumber denominator.
|
1
|
162 |
|
213
|
163 |
"save a multiplication if possible"
|
|
164 |
denominator == d ifTrue:[
|
|
165 |
^ (self class numerator:(numerator + n) denominator:d) reduced
|
|
166 |
].
|
1
|
167 |
|
213
|
168 |
^ (self class numerator:((numerator * d) + (n * denominator))
|
|
169 |
denominator:(denominator * d)) reduced
|
1
|
170 |
].
|
16
|
171 |
(aNumber isMemberOf:Float) ifTrue:[
|
213
|
172 |
^ aNumber + (numerator asFloat / denominator asFloat)
|
16
|
173 |
].
|
1
|
174 |
^ aNumber sumFromFraction:self
|
|
175 |
!
|
|
176 |
|
|
177 |
- aNumber
|
|
178 |
"return the difference of the receiver and the argument, aNumber"
|
|
179 |
|
|
180 |
|n d|
|
|
181 |
|
|
182 |
(aNumber isMemberOf:SmallInteger) ifTrue:[
|
213
|
183 |
^ (self class numerator:(numerator - (denominator * aNumber))
|
|
184 |
denominator:denominator) reduced
|
1
|
185 |
].
|
259
|
186 |
aNumber isFraction ifTrue:[
|
213
|
187 |
n := aNumber numerator.
|
|
188 |
d := aNumber denominator.
|
1
|
189 |
|
213
|
190 |
"save a multiplication if possible"
|
|
191 |
denominator == d ifTrue:[
|
|
192 |
^ (self class numerator:(numerator - n) denominator:d) reduced
|
|
193 |
].
|
1
|
194 |
|
213
|
195 |
^ (self class numerator:((numerator * d) - (n * denominator))
|
|
196 |
denominator:(denominator * d)) reduced
|
1
|
197 |
].
|
16
|
198 |
(aNumber isMemberOf:Float) ifTrue:[
|
213
|
199 |
^ (numerator asFloat / denominator asFloat) - aNumber
|
16
|
200 |
].
|
1
|
201 |
^ aNumber differenceFromFraction:self
|
|
202 |
!
|
|
203 |
|
|
204 |
/ aNumber
|
|
205 |
"return the quotient of the receiver and the argument, aNumber"
|
|
206 |
|
|
207 |
|n d|
|
|
208 |
|
16
|
209 |
(aNumber isMemberOf:SmallInteger) ifTrue:[
|
213
|
210 |
^ (self class numerator:numerator
|
|
211 |
denominator:(denominator * aNumber)) reduced
|
16
|
212 |
].
|
259
|
213 |
aNumber isFraction ifTrue:[
|
213
|
214 |
n := numerator * aNumber denominator.
|
|
215 |
d := denominator * aNumber numerator.
|
|
216 |
^ (self class numerator:n denominator:d) reduced
|
1
|
217 |
].
|
16
|
218 |
(aNumber isMemberOf:Float) ifTrue:[
|
213
|
219 |
^ numerator / (denominator * aNumber)
|
16
|
220 |
].
|
1
|
221 |
^ aNumber quotientFromFraction:self
|
|
222 |
!
|
|
223 |
|
|
224 |
// aNumber
|
|
225 |
"return the integer quotient of the receiver and the argument, aNumber"
|
|
226 |
|
|
227 |
self negative ifTrue:[
|
213
|
228 |
^ ((numerator * aNumber denominator) // (denominator * aNumber numerator)) - 1
|
1
|
229 |
].
|
|
230 |
^ (numerator * aNumber denominator) // (denominator * aNumber numerator)
|
|
231 |
!
|
|
232 |
|
|
233 |
negated
|
|
234 |
"optional - could use inherited method ..."
|
|
235 |
|
|
236 |
^ self class numerator:(numerator negated)
|
213
|
237 |
denominator:denominator
|
1
|
238 |
!
|
|
239 |
|
|
240 |
reciprocal
|
|
241 |
"optional - could use inherited method ..."
|
|
242 |
|
|
243 |
numerator == 1 ifTrue:[^ denominator].
|
|
244 |
^ self class numerator:denominator
|
213
|
245 |
denominator:numerator
|
1
|
246 |
! !
|
|
247 |
|
701
|
248 |
!Fraction methodsFor:'coercing & converting'!
|
|
249 |
|
|
250 |
asFloat
|
|
251 |
"return a float with (approximately) my value"
|
|
252 |
|
|
253 |
^ (numerator asFloat) / (denominator asFloat)
|
|
254 |
!
|
1
|
255 |
|
701
|
256 |
asFraction
|
|
257 |
"return the receiver as fraction - thats itself"
|
|
258 |
|
|
259 |
^ self
|
|
260 |
!
|
|
261 |
|
|
262 |
asInteger
|
|
263 |
"return an integer with my value - will usually truncate"
|
1
|
264 |
|
|
265 |
^ numerator // denominator
|
|
266 |
!
|
|
267 |
|
701
|
268 |
asLargeInteger
|
|
269 |
"return an integer with my value - will usually truncate"
|
|
270 |
|
|
271 |
^ self asInteger asLargeInteger
|
|
272 |
!
|
|
273 |
|
1200
|
274 |
asShortFloat
|
|
275 |
"return a shortFloat with (approximately) my value"
|
|
276 |
|
|
277 |
^ (numerator asShortFloat) / (denominator asShortFloat)
|
|
278 |
|
|
279 |
"Created: 17.4.1996 / 12:21:08 / cg"
|
|
280 |
!
|
|
281 |
|
701
|
282 |
coerce:aNumber
|
|
283 |
"return aNumber converted into receivers type"
|
|
284 |
|
|
285 |
^ aNumber asFraction
|
|
286 |
!
|
|
287 |
|
|
288 |
generality
|
|
289 |
"return the generality value - see ArithmeticValue>>retry:coercing:"
|
|
290 |
|
|
291 |
^ 60
|
|
292 |
! !
|
|
293 |
|
|
294 |
!Fraction methodsFor:'comparing'!
|
|
295 |
|
|
296 |
< aNumber
|
|
297 |
"return true if the receiver is less
|
|
298 |
than aNumber, false otherwise."
|
1
|
299 |
|
701
|
300 |
(aNumber isMemberOf:SmallInteger) ifTrue:[
|
|
301 |
^ numerator < (denominator * aNumber)
|
|
302 |
].
|
|
303 |
aNumber isFraction ifTrue:[
|
|
304 |
^ (numerator * aNumber denominator) < (denominator * aNumber numerator)
|
|
305 |
].
|
|
306 |
^ aNumber lessFromFraction:self
|
|
307 |
!
|
|
308 |
|
|
309 |
= aNumber
|
|
310 |
"return true, if the argument represents the same numeric value
|
|
311 |
as the receiver, false otherwise"
|
|
312 |
|
|
313 |
(aNumber isMemberOf:SmallInteger) ifTrue:[
|
|
314 |
(denominator = 1) ifFalse:[^ false].
|
|
315 |
^ numerator = aNumber
|
1
|
316 |
].
|
701
|
317 |
aNumber isFraction ifTrue:[
|
|
318 |
(numerator = aNumber numerator) ifFalse:[^ false].
|
|
319 |
^ denominator = aNumber denominator
|
|
320 |
].
|
|
321 |
^ self retry:#= coercing:aNumber
|
|
322 |
!
|
|
323 |
|
|
324 |
> aNumber
|
|
325 |
"return true if the receiver is greater
|
|
326 |
than aNumber, false otherwise."
|
|
327 |
"optional - could use inherited method ..."
|
|
328 |
|
|
329 |
(aNumber isMemberOf:SmallInteger) ifTrue:[
|
|
330 |
^ numerator > (denominator * aNumber)
|
|
331 |
].
|
|
332 |
aNumber isFraction ifTrue:[
|
|
333 |
^ (numerator * aNumber denominator) > (denominator * aNumber numerator)
|
|
334 |
].
|
|
335 |
^ self retry:#> coercing:aNumber
|
1
|
336 |
! !
|
|
337 |
|
|
338 |
!Fraction methodsFor:'double dispatching'!
|
|
339 |
|
701
|
340 |
differenceFromFloat:aFloat
|
|
341 |
"sent when a float does not know how to subtract the receiver, a fraction"
|
1
|
342 |
|
701
|
343 |
^ (aFloat * denominator - numerator) / denominator
|
1
|
344 |
!
|
|
345 |
|
|
346 |
differenceFromInteger:anInteger
|
213
|
347 |
"sent when an integer does not know how to subtract the receiver, a fraction"
|
1
|
348 |
|
|
349 |
^ (self class numerator:((anInteger * denominator) - numerator)
|
213
|
350 |
denominator:denominator) reduced
|
1
|
351 |
!
|
|
352 |
|
701
|
353 |
lessFromInteger:anInteger
|
|
354 |
"sent when an integer does not know how to compare to the receiver, a fraction"
|
|
355 |
|
|
356 |
^ (denominator * anInteger) < numerator
|
|
357 |
!
|
|
358 |
|
|
359 |
productFromFloat:aFloat
|
|
360 |
"sent when a float does not know how to multiply the receiver, a fraction"
|
|
361 |
|
|
362 |
^ aFloat * numerator / denominator
|
|
363 |
!
|
|
364 |
|
1
|
365 |
productFromInteger:anInteger
|
213
|
366 |
"sent when an integer does not know how to multiply the receiver, a fraction"
|
1
|
367 |
|
|
368 |
^ (self class numerator:(anInteger * numerator)
|
213
|
369 |
denominator:denominator) reduced
|
1
|
370 |
!
|
|
371 |
|
701
|
372 |
quotientFromFloat:aFloat
|
|
373 |
"sent when a float does not know how to divide by the receiver, a fraction"
|
|
374 |
|
|
375 |
^ (aFloat * denominator) / numerator
|
|
376 |
!
|
|
377 |
|
324
|
378 |
quotientFromInteger:anInteger
|
|
379 |
"sent when an integer does not know how to divide by the receiver, a fraction"
|
|
380 |
|
328
|
381 |
^ (self class numerator:(anInteger * denominator)
|
|
382 |
denominator:numerator) reduced
|
324
|
383 |
!
|
|
384 |
|
1
|
385 |
sumFromFloat:aFloat
|
213
|
386 |
"sent when a float does not know how to add the receiver, a fraction"
|
1
|
387 |
|
|
388 |
^ (aFloat * denominator + numerator) / denominator
|
|
389 |
!
|
|
390 |
|
701
|
391 |
sumFromInteger:anInteger
|
|
392 |
"sent when an integer does not know how to add the receiver, a fraction"
|
1
|
393 |
|
701
|
394 |
^ (self class numerator:(numerator + (anInteger * denominator))
|
|
395 |
denominator:denominator) reduced
|
1
|
396 |
! !
|
|
397 |
|
92
|
398 |
!Fraction methodsFor:'printing & storing'!
|
1
|
399 |
|
54
|
400 |
printOn:aStream
|
|
401 |
"append a printed representation of the receiver to the
|
|
402 |
argument, aStream"
|
|
403 |
|
|
404 |
aStream nextPut:$(.
|
|
405 |
numerator printOn:aStream.
|
|
406 |
aStream nextPut:$/.
|
|
407 |
denominator printOn:aStream.
|
|
408 |
aStream nextPut:$)
|
1
|
409 |
! !
|
701
|
410 |
|
|
411 |
!Fraction methodsFor:'private'!
|
|
412 |
|
|
413 |
reduced
|
|
414 |
"reduce the receiver"
|
|
415 |
|
|
416 |
|gc|
|
|
417 |
|
|
418 |
denominator == 1 ifTrue:[^ numerator].
|
|
419 |
numerator == 1 ifTrue:[^ self].
|
|
420 |
numerator == 0 ifTrue:[^ 0].
|
|
421 |
|
|
422 |
gc := numerator gcd:denominator.
|
|
423 |
(gc == 1) ifFalse:[
|
|
424 |
numerator := numerator // gc.
|
|
425 |
denominator := denominator // gc
|
|
426 |
].
|
|
427 |
(numerator < 0) ifTrue:[
|
|
428 |
(denominator < 0) ifTrue:[
|
|
429 |
numerator := numerator negated.
|
|
430 |
denominator := denominator negated
|
|
431 |
]
|
|
432 |
].
|
|
433 |
(denominator == 1) ifTrue:[^ numerator].
|
|
434 |
^ self
|
|
435 |
!
|
|
436 |
|
|
437 |
setNumerator:num denominator:den
|
|
438 |
"set both numerator and denominator"
|
|
439 |
|
|
440 |
numerator := num.
|
|
441 |
denominator := den
|
|
442 |
! !
|
|
443 |
|
|
444 |
!Fraction methodsFor:'queries'!
|
|
445 |
|
|
446 |
isFraction
|
|
447 |
"return true, if the receiver is some kind of fraction;
|
|
448 |
true is returned here - the method is redefined from Object."
|
|
449 |
|
|
450 |
^ true
|
|
451 |
! !
|
|
452 |
|
|
453 |
!Fraction methodsFor:'testing'!
|
|
454 |
|
|
455 |
negative
|
|
456 |
"return true if the receiver is negative"
|
|
457 |
|
|
458 |
(numerator < 0) ifTrue:[
|
|
459 |
^ (denominator < 0) not
|
|
460 |
].
|
|
461 |
^ (denominator < 0)
|
|
462 |
! !
|
|
463 |
|
|
464 |
!Fraction methodsFor:'truncation and rounding'!
|
|
465 |
|
|
466 |
rounded
|
|
467 |
"return the receiver rounded to the nearest integer as integer"
|
|
468 |
|
|
469 |
self negative ifTrue:[
|
|
470 |
^ (self + (1/2)) truncated - 1
|
|
471 |
].
|
|
472 |
^ (self + (1/2)) truncated
|
|
473 |
!
|
|
474 |
|
|
475 |
truncated
|
|
476 |
"return the receiver truncated towards zero as Integer"
|
|
477 |
|
|
478 |
^ numerator // denominator
|
|
479 |
! !
|
|
480 |
|
|
481 |
!Fraction class methodsFor:'documentation'!
|
|
482 |
|
|
483 |
version
|
1264
|
484 |
^ '$Header: /cvs/stx/stx/libbasic/Fraction.st,v 1.29 1996-04-23 14:02:26 cg Exp $'
|
701
|
485 |
! !
|
|
486 |
Fraction initialize!
|