1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.lang.math;
18
19 import java.math.BigInteger;
20
21 /**
22 * <p><code>Fraction</code> is a <code>Number</code> implementation that
23 * stores fractions accurately.</p>
24 *
25 * <p>This class is immutable, and interoperable with most methods that accept
26 * a <code>Number</code>.</p>
27 *
28 * @author Travis Reeder
29 * @author Stephen Colebourne
30 * @author Tim O'Brien
31 * @author Pete Gieser
32 * @author C. Scott Ananian
33 * @since 2.0
34 * @version $Id: Fraction.java 599500 2007-11-29 16:25:54Z mbenson $
35 */
36 public final class Fraction extends Number implements Comparable {
37
38 /**
39 * Required for serialization support. Lang version 2.0.
40 *
41 * @see java.io.Serializable
42 */
43 private static final long serialVersionUID = 65382027393090L;
44
45 /**
46 * <code>Fraction</code> representation of 0.
47 */
48 public static final Fraction ZERO = new Fraction(0, 1);
49 /**
50 * <code>Fraction</code> representation of 1.
51 */
52 public static final Fraction ONE = new Fraction(1, 1);
53 /**
54 * <code>Fraction</code> representation of 1/2.
55 */
56 public static final Fraction ONE_HALF = new Fraction(1, 2);
57 /**
58 * <code>Fraction</code> representation of 1/3.
59 */
60 public static final Fraction ONE_THIRD = new Fraction(1, 3);
61 /**
62 * <code>Fraction</code> representation of 2/3.
63 */
64 public static final Fraction TWO_THIRDS = new Fraction(2, 3);
65 /**
66 * <code>Fraction</code> representation of 1/4.
67 */
68 public static final Fraction ONE_QUARTER = new Fraction(1, 4);
69 /**
70 * <code>Fraction</code> representation of 2/4.
71 */
72 public static final Fraction TWO_QUARTERS = new Fraction(2, 4);
73 /**
74 * <code>Fraction</code> representation of 3/4.
75 */
76 public static final Fraction THREE_QUARTERS = new Fraction(3, 4);
77 /**
78 * <code>Fraction</code> representation of 1/5.
79 */
80 public static final Fraction ONE_FIFTH = new Fraction(1, 5);
81 /**
82 * <code>Fraction</code> representation of 2/5.
83 */
84 public static final Fraction TWO_FIFTHS = new Fraction(2, 5);
85 /**
86 * <code>Fraction</code> representation of 3/5.
87 */
88 public static final Fraction THREE_FIFTHS = new Fraction(3, 5);
89 /**
90 * <code>Fraction</code> representation of 4/5.
91 */
92 public static final Fraction FOUR_FIFTHS = new Fraction(4, 5);
93
94
95 /**
96 * The numerator number part of the fraction (the three in three sevenths).
97 */
98 private final int numerator;
99 /**
100 * The denominator number part of the fraction (the seven in three sevenths).
101 */
102 private final int denominator;
103
104 /**
105 * Cached output hashCode (class is immutable).
106 */
107 private transient int hashCode = 0;
108 /**
109 * Cached output toString (class is immutable).
110 */
111 private transient String toString = null;
112 /**
113 * Cached output toProperString (class is immutable).
114 */
115 private transient String toProperString = null;
116
117 /**
118 * <p>Constructs a <code>Fraction</code> instance with the 2 parts
119 * of a fraction Y/Z.</p>
120 *
121 * @param numerator the numerator, for example the three in 'three sevenths'
122 * @param denominator the denominator, for example the seven in 'three sevenths'
123 */
124 private Fraction(int numerator, int denominator) {
125 super();
126 this.numerator = numerator;
127 this.denominator = denominator;
128 }
129
130 /**
131 * <p>Creates a <code>Fraction</code> instance with the 2 parts
132 * of a fraction Y/Z.</p>
133 *
134 * <p>Any negative signs are resolved to be on the numerator.</p>
135 *
136 * @param numerator the numerator, for example the three in 'three sevenths'
137 * @param denominator the denominator, for example the seven in 'three sevenths'
138 * @return a new fraction instance
139 * @throws ArithmeticException if the denomiator is <code>zero</code>
140 */
141 public static Fraction getFraction(int numerator, int denominator) {
142 if (denominator == 0) {
143 throw new ArithmeticException("The denominator must not be zero");
144 }
145 if (denominator < 0) {
146 if (numerator==Integer.MIN_VALUE ||
147 denominator==Integer.MIN_VALUE) {
148 throw new ArithmeticException("overflow: can't negate");
149 }
150 numerator = -numerator;
151 denominator = -denominator;
152 }
153 return new Fraction(numerator, denominator);
154 }
155
156 /**
157 * <p>Creates a <code>Fraction</code> instance with the 3 parts
158 * of a fraction X Y/Z.</p>
159 *
160 * <p>The negative sign must be passed in on the whole number part.</p>
161 *
162 * @param whole the whole number, for example the one in 'one and three sevenths'
163 * @param numerator the numerator, for example the three in 'one and three sevenths'
164 * @param denominator the denominator, for example the seven in 'one and three sevenths'
165 * @return a new fraction instance
166 * @throws ArithmeticException if the denomiator is <code>zero</code>
167 * @throws ArithmeticException if the denominator is negative
168 * @throws ArithmeticException if the numerator is negative
169 * @throws ArithmeticException if the resulting numerator exceeds
170 * <code>Integer.MAX_VALUE</code>
171 */
172 public static Fraction getFraction(int whole, int numerator, int denominator) {
173 if (denominator == 0) {
174 throw new ArithmeticException("The denominator must not be zero");
175 }
176 if (denominator < 0) {
177 throw new ArithmeticException("The denominator must not be negative");
178 }
179 if (numerator < 0) {
180 throw new ArithmeticException("The numerator must not be negative");
181 }
182 long numeratorValue;
183 if (whole < 0) {
184 numeratorValue = whole * (long)denominator - numerator;
185 } else {
186 numeratorValue = whole * (long)denominator + numerator;
187 }
188 if (numeratorValue < Integer.MIN_VALUE ||
189 numeratorValue > Integer.MAX_VALUE) {
190 throw new ArithmeticException("Numerator too large to represent as an Integer.");
191 }
192 return new Fraction((int) numeratorValue, denominator);
193 }
194
195 /**
196 * <p>Creates a reduced <code>Fraction</code> instance with the 2 parts
197 * of a fraction Y/Z.</p>
198 *
199 * <p>For example, if the input parameters represent 2/4, then the created
200 * fraction will be 1/2.</p>
201 *
202 * <p>Any negative signs are resolved to be on the numerator.</p>
203 *
204 * @param numerator the numerator, for example the three in 'three sevenths'
205 * @param denominator the denominator, for example the seven in 'three sevenths'
206 * @return a new fraction instance, with the numerator and denominator reduced
207 * @throws ArithmeticException if the denominator is <code>zero</code>
208 */
209 public static Fraction getReducedFraction(int numerator, int denominator) {
210 if (denominator == 0) {
211 throw new ArithmeticException("The denominator must not be zero");
212 }
213 if (numerator==0) {
214 return ZERO; // normalize zero.
215 }
216 // allow 2^k/-2^31 as a valid fraction (where k>0)
217 if (denominator==Integer.MIN_VALUE && (numerator&1)==0) {
218 numerator/=2; denominator/=2;
219 }
220 if (denominator < 0) {
221 if (numerator==Integer.MIN_VALUE ||
222 denominator==Integer.MIN_VALUE) {
223 throw new ArithmeticException("overflow: can't negate");
224 }
225 numerator = -numerator;
226 denominator = -denominator;
227 }
228 // simplify fraction.
229 int gcd = greatestCommonDivisor(numerator, denominator);
230 numerator /= gcd;
231 denominator /= gcd;
232 return new Fraction(numerator, denominator);
233 }
234
235 /**
236 * <p>Creates a <code>Fraction</code> instance from a <code>double</code> value.</p>
237 *
238 * <p>This method uses the <a href="http://archives.math.utk.edu/articles/atuyl/confrac/">
239 * continued fraction algorithm</a>, computing a maximum of
240 * 25 convergents and bounding the denominator by 10,000.</p>
241 *
242 * @param value the double value to convert
243 * @return a new fraction instance that is close to the value
244 * @throws ArithmeticException if <code>|value| > Integer.MAX_VALUE</code>
245 * or <code>value = NaN</code>
246 * @throws ArithmeticException if the calculated denominator is <code>zero</code>
247 * @throws ArithmeticException if the the algorithm does not converge
248 */
249 public static Fraction getFraction(double value) {
250 int sign = (value < 0 ? -1 : 1);
251 value = Math.abs(value);
252 if (value > Integer.MAX_VALUE || Double.isNaN(value)) {
253 throw new ArithmeticException
254 ("The value must not be greater than Integer.MAX_VALUE or NaN");
255 }
256 int wholeNumber = (int) value;
257 value -= wholeNumber;
258
259 int numer0 = 0; // the pre-previous
260 int denom0 = 1; // the pre-previous
261 int numer1 = 1; // the previous
262 int denom1 = 0; // the previous
263 int numer2 = 0; // the current, setup in calculation
264 int denom2 = 0; // the current, setup in calculation
265 int a1 = (int) value;
266 int a2 = 0;
267 double x1 = 1;
268 double x2 = 0;
269 double y1 = value - a1;
270 double y2 = 0;
271 double delta1, delta2 = Double.MAX_VALUE;
272 double fraction;
273 int i = 1;
274 // System.out.println("---");
275 do {
276 delta1 = delta2;
277 a2 = (int) (x1 / y1);
278 x2 = y1;
279 y2 = x1 - a2 * y1;
280 numer2 = a1 * numer1 + numer0;
281 denom2 = a1 * denom1 + denom0;
282 fraction = (double) numer2 / (double) denom2;
283 delta2 = Math.abs(value - fraction);
284 // System.out.println(numer2 + " " + denom2 + " " + fraction + " " + delta2 + " " + y1);
285 a1 = a2;
286 x1 = x2;
287 y1 = y2;
288 numer0 = numer1;
289 denom0 = denom1;
290 numer1 = numer2;
291 denom1 = denom2;
292 i++;
293 // System.out.println(">>" + delta1 +" "+ delta2+" "+(delta1 > delta2)+" "+i+" "+denom2);
294 } while ((delta1 > delta2) && (denom2 <= 10000) && (denom2 > 0) && (i < 25));
295 if (i == 25) {
296 throw new ArithmeticException("Unable to convert double to fraction");
297 }
298 return getReducedFraction((numer0 + wholeNumber * denom0) * sign, denom0);
299 }
300
301 /**
302 * <p>Creates a Fraction from a <code>String</code>.</p>
303 *
304 * <p>The formats accepted are:</p>
305 *
306 * <ol>
307 * <li><code>double</code> String containing a dot</li>
308 * <li>'X Y/Z'</li>
309 * <li>'Y/Z'</li>
310 * <li>'X' (a simple whole number)</li>
311 * </ol>
312 * and a .</p>
313 *
314 * @param str the string to parse, must not be <code>null</code>
315 * @return the new <code>Fraction</code> instance
316 * @throws IllegalArgumentException if the string is <code>null</code>
317 * @throws NumberFormatException if the number format is invalid
318 */
319 public static Fraction getFraction(String str) {
320 if (str == null) {
321 throw new IllegalArgumentException("The string must not be null");
322 }
323 // parse double format
324 int pos = str.indexOf('.');
325 if (pos >= 0) {
326 return getFraction(Double.parseDouble(str));
327 }
328
329 // parse X Y/Z format
330 pos = str.indexOf(' ');
331 if (pos > 0) {
332 int whole = Integer.parseInt(str.substring(0, pos));
333 str = str.substring(pos + 1);
334 pos = str.indexOf('/');
335 if (pos < 0) {
336 throw new NumberFormatException("The fraction could not be parsed as the format X Y/Z");
337 } else {
338 int numer = Integer.parseInt(str.substring(0, pos));
339 int denom = Integer.parseInt(str.substring(pos + 1));
340 return getFraction(whole, numer, denom);
341 }
342 }
343
344 // parse Y/Z format
345 pos = str.indexOf('/');
346 if (pos < 0) {
347 // simple whole number
348 return getFraction(Integer.parseInt(str), 1);
349 } else {
350 int numer = Integer.parseInt(str.substring(0, pos));
351 int denom = Integer.parseInt(str.substring(pos + 1));
352 return getFraction(numer, denom);
353 }
354 }
355
356 // Accessors
357 //-------------------------------------------------------------------
358
359 /**
360 * <p>Gets the numerator part of the fraction.</p>
361 *
362 * <p>This method may return a value greater than the denominator, an
363 * improper fraction, such as the seven in 7/4.</p>
364 *
365 * @return the numerator fraction part
366 */
367 public int getNumerator() {
368 return numerator;
369 }
370
371 /**
372 * <p>Gets the denominator part of the fraction.</p>
373 *
374 * @return the denominator fraction part
375 */
376 public int getDenominator() {
377 return denominator;
378 }
379
380 /**
381 * <p>Gets the proper numerator, always positive.</p>
382 *
383 * <p>An improper fraction 7/4 can be resolved into a proper one, 1 3/4.
384 * This method returns the 3 from the proper fraction.</p>
385 *
386 * <p>If the fraction is negative such as -7/4, it can be resolved into
387 * -1 3/4, so this method returns the positive proper numerator, 3.</p>
388 *
389 * @return the numerator fraction part of a proper fraction, always positive
390 */
391 public int getProperNumerator() {
392 return Math.abs(numerator % denominator);
393 }
394
395 /**
396 * <p>Gets the proper whole part of the fraction.</p>
397 *
398 * <p>An improper fraction 7/4 can be resolved into a proper one, 1 3/4.
399 * This method returns the 1 from the proper fraction.</p>
400 *
401 * <p>If the fraction is negative such as -7/4, it can be resolved into
402 * -1 3/4, so this method returns the positive whole part -1.</p>
403 *
404 * @return the whole fraction part of a proper fraction, that includes the sign
405 */
406 public int getProperWhole() {
407 return numerator / denominator;
408 }
409
410 // Number methods
411 //-------------------------------------------------------------------
412
413 /**
414 * <p>Gets the fraction as an <code>int</code>. This returns the whole number
415 * part of the fraction.</p>
416 *
417 * @return the whole number fraction part
418 */
419 public int intValue() {
420 return numerator / denominator;
421 }
422
423 /**
424 * <p>Gets the fraction as a <code>long</code>. This returns the whole number
425 * part of the fraction.</p>
426 *
427 * @return the whole number fraction part
428 */
429 public long longValue() {
430 return (long) numerator / denominator;
431 }
432
433 /**
434 * <p>Gets the fraction as a <code>float</code>. This calculates the fraction
435 * as the numerator divided by denominator.</p>
436 *
437 * @return the fraction as a <code>float</code>
438 */
439 public float floatValue() {
440 return ((float) numerator) / ((float) denominator);
441 }
442
443 /**
444 * <p>Gets the fraction as a <code>double</code>. This calculates the fraction
445 * as the numerator divided by denominator.</p>
446 *
447 * @return the fraction as a <code>double</code>
448 */
449 public double doubleValue() {
450 return ((double) numerator) / ((double) denominator);
451 }
452
453 // Calculations
454 //-------------------------------------------------------------------
455
456 /**
457 * <p>Reduce the fraction to the smallest values for the numerator and
458 * denominator, returning the result.</p>
459 *
460 * <p>For example, if this fraction represents 2/4, then the result
461 * will be 1/2.</p>
462 *
463 * @return a new reduced fraction instance, or this if no simplification possible
464 */
465 public Fraction reduce() {
466 if (numerator == 0) {
467 return equals(ZERO) ? this : ZERO;
468 }
469 int gcd = greatestCommonDivisor(Math.abs(numerator), denominator);
470 if (gcd == 1) {
471 return this;
472 }
473 return Fraction.getFraction(numerator / gcd, denominator / gcd);
474 }
475
476 /**
477 * <p>Gets a fraction that is the inverse (1/fraction) of this one.</p>
478 *
479 * <p>The returned fraction is not reduced.</p>
480 *
481 * @return a new fraction instance with the numerator and denominator
482 * inverted.
483 * @throws ArithmeticException if the fraction represents zero.
484 */
485 public Fraction invert() {
486 if (numerator == 0) {
487 throw new ArithmeticException("Unable to invert zero.");
488 }
489 if (numerator==Integer.MIN_VALUE) {
490 throw new ArithmeticException("overflow: can't negate numerator");
491 }
492 if (numerator<0) {
493 return new Fraction(-denominator, -numerator);
494 } else {
495 return new Fraction(denominator, numerator);
496 }
497 }
498
499 /**
500 * <p>Gets a fraction that is the negative (-fraction) of this one.</p>
501 *
502 * <p>The returned fraction is not reduced.</p>
503 *
504 * @return a new fraction instance with the opposite signed numerator
505 */
506 public Fraction negate() {
507 // the positive range is one smaller than the negative range of an int.
508 if (numerator==Integer.MIN_VALUE) {
509 throw new ArithmeticException("overflow: too large to negate");
510 }
511 return new Fraction(-numerator, denominator);
512 }
513
514 /**
515 * <p>Gets a fraction that is the positive equivalent of this one.</p>
516 * <p>More precisely: <code>(fraction >= 0 ? this : -fraction)</code></p>
517 *
518 * <p>The returned fraction is not reduced.</p>
519 *
520 * @return <code>this</code> if it is positive, or a new positive fraction
521 * instance with the opposite signed numerator
522 */
523 public Fraction abs() {
524 if (numerator >= 0) {
525 return this;
526 }
527 return negate();
528 }
529
530 /**
531 * <p>Gets a fraction that is raised to the passed in power.</p>
532 *
533 * <p>The returned fraction is in reduced form.</p>
534 *
535 * @param power the power to raise the fraction to
536 * @return <code>this</code> if the power is one, <code>ONE</code> if the power
537 * is zero (even if the fraction equals ZERO) or a new fraction instance
538 * raised to the appropriate power
539 * @throws ArithmeticException if the resulting numerator or denominator exceeds
540 * <code>Integer.MAX_VALUE</code>
541 */
542 public Fraction pow(int power) {
543 if (power == 1) {
544 return this;
545 } else if (power == 0) {
546 return ONE;
547 } else if (power < 0) {
548 if (power==Integer.MIN_VALUE) { // MIN_VALUE can't be negated.
549 return this.invert().pow(2).pow(-(power/2));
550 }
551 return this.invert().pow(-power);
552 } else {
553 Fraction f = this.multiplyBy(this);
554 if ((power % 2) == 0) { // if even...
555 return f.pow(power/2);
556 } else { // if odd...
557 return f.pow(power/2).multiplyBy(this);
558 }
559 }
560 }
561
562 /**
563 * <p>Gets the greatest common divisor of the absolute value of
564 * two numbers, using the "binary gcd" method which avoids
565 * division and modulo operations. See Knuth 4.5.2 algorithm B.
566 * This algorithm is due to Josef Stein (1961).</p>
567 *
568 * @param u a non-zero number
569 * @param v a non-zero number
570 * @return the greatest common divisor, never zero
571 */
572 private static int greatestCommonDivisor(int u, int v) {
573 //if either op. is abs 0 or 1, return 1:
574 if (Math.abs(u) <= 1 || Math.abs(v) <= 1) {
575 return 1;
576 }
577 // keep u and v negative, as negative integers range down to
578 // -2^31, while positive numbers can only be as large as 2^31-1
579 // (i.e. we can't necessarily negate a negative number without
580 // overflow)
581 if (u>0) { u=-u; } // make u negative
582 if (v>0) { v=-v; } // make v negative
583 // B1. [Find power of 2]
584 int k=0;
585 while ((u&1)==0 && (v&1)==0 && k<31) { // while u and v are both even...
586 u/=2; v/=2; k++; // cast out twos.
587 }
588 if (k==31) {
589 throw new ArithmeticException("overflow: gcd is 2^31");
590 }
591 // B2. Initialize: u and v have been divided by 2^k and at least
592 // one is odd.
593 int t = ((u&1)==1) ? v : -(u/2)/*B3*/;
594 // t negative: u was odd, v may be even (t replaces v)
595 // t positive: u was even, v is odd (t replaces u)
596 do {
597 /* assert u<0 && v<0; */
598 // B4/B3: cast out twos from t.
599 while ((t&1)==0) { // while t is even..
600 t/=2; // cast out twos
601 }
602 // B5 [reset max(u,v)]
603 if (t>0) {
604 u = -t;
605 } else {
606 v = t;
607 }
608 // B6/B3. at this point both u and v should be odd.
609 t = (v - u)/2;
610 // |u| larger: t positive (replace u)
611 // |v| larger: t negative (replace v)
612 } while (t!=0);
613 return -u*(1<<k); // gcd is u*2^k
614 }
615
616 // Arithmetic
617 //-------------------------------------------------------------------
618
619 /**
620 * Multiply two integers, checking for overflow.
621 *
622 * @param x a factor
623 * @param y a factor
624 * @return the product <code>x*y</code>
625 * @throws ArithmeticException if the result can not be represented as
626 * an int
627 */
628 private static int mulAndCheck(int x, int y) {
629 long m = ((long)x)*((long)y);
630 if (m < Integer.MIN_VALUE ||
631 m > Integer.MAX_VALUE) {
632 throw new ArithmeticException("overflow: mul");
633 }
634 return (int)m;
635 }
636
637 /**
638 * Multiply two non-negative integers, checking for overflow.
639 *
640 * @param x a non-negative factor
641 * @param y a non-negative factor
642 * @return the product <code>x*y</code>
643 * @throws ArithmeticException if the result can not be represented as
644 * an int
645 */
646 private static int mulPosAndCheck(int x, int y) {
647 /* assert x>=0 && y>=0; */
648 long m = ((long)x)*((long)y);
649 if (m > Integer.MAX_VALUE) {
650 throw new ArithmeticException("overflow: mulPos");
651 }
652 return (int)m;
653 }
654
655 /**
656 * Add two integers, checking for overflow.
657 *
658 * @param x an addend
659 * @param y an addend
660 * @return the sum <code>x+y</code>
661 * @throws ArithmeticException if the result can not be represented as
662 * an int
663 */
664 private static int addAndCheck(int x, int y) {
665 long s = (long)x+(long)y;
666 if (s < Integer.MIN_VALUE ||
667 s > Integer.MAX_VALUE) {
668 throw new ArithmeticException("overflow: add");
669 }
670 return (int)s;
671 }
672
673 /**
674 * Subtract two integers, checking for overflow.
675 *
676 * @param x the minuend
677 * @param y the subtrahend
678 * @return the difference <code>x-y</code>
679 * @throws ArithmeticException if the result can not be represented as
680 * an int
681 */
682 private static int subAndCheck(int x, int y) {
683 long s = (long)x-(long)y;
684 if (s < Integer.MIN_VALUE ||
685 s > Integer.MAX_VALUE) {
686 throw new ArithmeticException("overflow: add");
687 }
688 return (int)s;
689 }
690
691 /**
692 * <p>Adds the value of this fraction to another, returning the result in reduced form.
693 * The algorithm follows Knuth, 4.5.1.</p>
694 *
695 * @param fraction the fraction to add, must not be <code>null</code>
696 * @return a <code>Fraction</code> instance with the resulting values
697 * @throws IllegalArgumentException if the fraction is <code>null</code>
698 * @throws ArithmeticException if the resulting numerator or denominator exceeds
699 * <code>Integer.MAX_VALUE</code>
700 */
701 public Fraction add(Fraction fraction) {
702 return addSub(fraction, true /* add */);
703 }
704
705 /**
706 * <p>Subtracts the value of another fraction from the value of this one,
707 * returning the result in reduced form.</p>
708 *
709 * @param fraction the fraction to subtract, must not be <code>null</code>
710 * @return a <code>Fraction</code> instance with the resulting values
711 * @throws IllegalArgumentException if the fraction is <code>null</code>
712 * @throws ArithmeticException if the resulting numerator or denominator
713 * cannot be represented in an <code>int</code>.
714 */
715 public Fraction subtract(Fraction fraction) {
716 return addSub(fraction, false /* subtract */);
717 }
718
719 /**
720 * Implement add and subtract using algorithm described in Knuth 4.5.1.
721 *
722 * @param fraction the fraction to subtract, must not be <code>null</code>
723 * @param isAdd true to add, false to subtract
724 * @return a <code>Fraction</code> instance with the resulting values
725 * @throws IllegalArgumentException if the fraction is <code>null</code>
726 * @throws ArithmeticException if the resulting numerator or denominator
727 * cannot be represented in an <code>int</code>.
728 */
729 private Fraction addSub(Fraction fraction, boolean isAdd) {
730 if (fraction == null) {
731 throw new IllegalArgumentException("The fraction must not be null");
732 }
733 // zero is identity for addition.
734 if (numerator == 0) {
735 return isAdd ? fraction : fraction.negate();
736 }
737 if (fraction.numerator == 0) {
738 return this;
739 }
740 // if denominators are randomly distributed, d1 will be 1 about 61%
741 // of the time.
742 int d1 = greatestCommonDivisor(denominator, fraction.denominator);
743 if (d1==1) {
744 // result is ( (u*v' +/- u'v) / u'v')
745 int uvp = mulAndCheck(numerator, fraction.denominator);
746 int upv = mulAndCheck(fraction.numerator, denominator);
747 return new Fraction
748 (isAdd ? addAndCheck(uvp, upv) : subAndCheck(uvp, upv),
749 mulPosAndCheck(denominator, fraction.denominator));
750 }
751 // the quantity 't' requires 65 bits of precision; see knuth 4.5.1
752 // exercise 7. we're going to use a BigInteger.
753 // t = u(v'/d1) +/- v(u'/d1)
754 BigInteger uvp = BigInteger.valueOf(numerator)
755 .multiply(BigInteger.valueOf(fraction.denominator/d1));
756 BigInteger upv = BigInteger.valueOf(fraction.numerator)
757 .multiply(BigInteger.valueOf(denominator/d1));
758 BigInteger t = isAdd ? uvp.add(upv) : uvp.subtract(upv);
759 // but d2 doesn't need extra precision because
760 // d2 = gcd(t,d1) = gcd(t mod d1, d1)
761 int tmodd1 = t.mod(BigInteger.valueOf(d1)).intValue();
762 int d2 = (tmodd1==0)?d1:greatestCommonDivisor(tmodd1, d1);
763
764 // result is (t/d2) / (u'/d1)(v'/d2)
765 BigInteger w = t.divide(BigInteger.valueOf(d2));
766 if (w.bitLength() > 31) {
767 throw new ArithmeticException
768 ("overflow: numerator too large after multiply");
769 }
770 return new Fraction
771 (w.intValue(),
772 mulPosAndCheck(denominator/d1, fraction.denominator/d2));
773 }
774
775 /**
776 * <p>Multiplies the value of this fraction by another, returning the
777 * result in reduced form.</p>
778 *
779 * @param fraction the fraction to multiply by, must not be <code>null</code>
780 * @return a <code>Fraction</code> instance with the resulting values
781 * @throws IllegalArgumentException if the fraction is <code>null</code>
782 * @throws ArithmeticException if the resulting numerator or denominator exceeds
783 * <code>Integer.MAX_VALUE</code>
784 */
785 public Fraction multiplyBy(Fraction fraction) {
786 if (fraction == null) {
787 throw new IllegalArgumentException("The fraction must not be null");
788 }
789 if (numerator == 0 || fraction.numerator == 0) {
790 return ZERO;
791 }
792 // knuth 4.5.1
793 // make sure we don't overflow unless the result *must* overflow.
794 int d1 = greatestCommonDivisor(numerator, fraction.denominator);
795 int d2 = greatestCommonDivisor(fraction.numerator, denominator);
796 return getReducedFraction
797 (mulAndCheck(numerator/d1, fraction.numerator/d2),
798 mulPosAndCheck(denominator/d2, fraction.denominator/d1));
799 }
800
801 /**
802 * <p>Divide the value of this fraction by another.</p>
803 *
804 * @param fraction the fraction to divide by, must not be <code>null</code>
805 * @return a <code>Fraction</code> instance with the resulting values
806 * @throws IllegalArgumentException if the fraction is <code>null</code>
807 * @throws ArithmeticException if the fraction to divide by is zero
808 * @throws ArithmeticException if the resulting numerator or denominator exceeds
809 * <code>Integer.MAX_VALUE</code>
810 */
811 public Fraction divideBy(Fraction fraction) {
812 if (fraction == null) {
813 throw new IllegalArgumentException("The fraction must not be null");
814 }
815 if (fraction.numerator == 0) {
816 throw new ArithmeticException("The fraction to divide by must not be zero");
817 }
818 return multiplyBy(fraction.invert());
819 }
820
821 // Basics
822 //-------------------------------------------------------------------
823
824 /**
825 * <p>Compares this fraction to another object to test if they are equal.</p>.
826 *
827 * <p>To be equal, both values must be equal. Thus 2/4 is not equal to 1/2.</p>
828 *
829 * @param obj the reference object with which to compare
830 * @return <code>true</code> if this object is equal
831 */
832 public boolean equals(Object obj) {
833 if (obj == this) {
834 return true;
835 }
836 if (obj instanceof Fraction == false) {
837 return false;
838 }
839 Fraction other = (Fraction) obj;
840 return (getNumerator() == other.getNumerator() &&
841 getDenominator() == other.getDenominator());
842 }
843
844 /**
845 * <p>Gets a hashCode for the fraction.</p>
846 *
847 * @return a hash code value for this object
848 */
849 public int hashCode() {
850 if (hashCode == 0) {
851 // hashcode update should be atomic.
852 hashCode = 37 * (37 * 17 + getNumerator()) + getDenominator();
853 }
854 return hashCode;
855 }
856
857 /**
858 * <p>Compares this object to another based on size.</p>
859 *
860 * <p>Note: this class has a natural ordering that is inconsistent
861 * with equals, because, for example, equals treats 1/2 and 2/4 as
862 * different, whereas compareTo treats them as equal.
863 *
864 * @param object the object to compare to
865 * @return -1 if this is less, 0 if equal, +1 if greater
866 * @throws ClassCastException if the object is not a <code>Fraction</code>
867 * @throws NullPointerException if the object is <code>null</code>
868 */
869 public int compareTo(Object object) {
870 Fraction other = (Fraction) object;
871 if (this==other) {
872 return 0;
873 }
874 if (numerator == other.numerator && denominator == other.denominator) {
875 return 0;
876 }
877
878 // otherwise see which is less
879 long first = (long) numerator * (long) other.denominator;
880 long second = (long) other.numerator * (long) denominator;
881 if (first == second) {
882 return 0;
883 } else if (first < second) {
884 return -1;
885 } else {
886 return 1;
887 }
888 }
889
890 /**
891 * <p>Gets the fraction as a <code>String</code>.</p>
892 *
893 * <p>The format used is '<i>numerator</i>/<i>denominator</i>' always.
894 *
895 * @return a <code>String</code> form of the fraction
896 */
897 public String toString() {
898 if (toString == null) {
899 toString = new StringBuffer(32)
900 .append(getNumerator())
901 .append('/')
902 .append(getDenominator()).toString();
903 }
904 return toString;
905 }
906
907 /**
908 * <p>Gets the fraction as a proper <code>String</code> in the format X Y/Z.</p>
909 *
910 * <p>The format used in '<i>wholeNumber</i> <i>numerator</i>/<i>denominator</i>'.
911 * If the whole number is zero it will be ommitted. If the numerator is zero,
912 * only the whole number is returned.</p>
913 *
914 * @return a <code>String</code> form of the fraction
915 */
916 public String toProperString() {
917 if (toProperString == null) {
918 if (numerator == 0) {
919 toProperString = "0";
920 } else if (numerator == denominator) {
921 toProperString = "1";
922 } else if (numerator == -1 * denominator) {
923 toProperString = "-1";
924 } else if ((numerator>0?-numerator:numerator) < -denominator) {
925 // note that we do the magnitude comparison test above with
926 // NEGATIVE (not positive) numbers, since negative numbers
927 // have a larger range. otherwise numerator==Integer.MIN_VALUE
928 // is handled incorrectly.
929 int properNumerator = getProperNumerator();
930 if (properNumerator == 0) {
931 toProperString = Integer.toString(getProperWhole());
932 } else {
933 toProperString = new StringBuffer(32)
934 .append(getProperWhole()).append(' ')
935 .append(properNumerator).append('/')
936 .append(getDenominator()).toString();
937 }
938 } else {
939 toProperString = new StringBuffer(32)
940 .append(getNumerator()).append('/')
941 .append(getDenominator()).toString();
942 }
943 }
944 return toProperString;
945 }
946 }