001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017 package org.apache.commons.lang3.math;
018
019 import java.math.BigInteger;
020
021 /**
022 * <p><code>Fraction</code> is a <code>Number</code> implementation that
023 * stores fractions accurately.</p>
024 *
025 * <p>This class is immutable, and interoperable with most methods that accept
026 * a <code>Number</code>.</p>
027 *
028 * @author Apache Software Foundation
029 * @author Travis Reeder
030 * @author Tim O'Brien
031 * @author Pete Gieser
032 * @author C. Scott Ananian
033 * @since 2.0
034 * @version $Id: Fraction.java 889215 2009-12-10 11:56:38Z bayard $
035 */
036 public final class Fraction extends Number implements Comparable<Fraction> {
037
038 /**
039 * Required for serialization support. Lang version 2.0.
040 *
041 * @see java.io.Serializable
042 */
043 private static final long serialVersionUID = 65382027393090L;
044
045 /**
046 * <code>Fraction</code> representation of 0.
047 */
048 public static final Fraction ZERO = new Fraction(0, 1);
049 /**
050 * <code>Fraction</code> representation of 1.
051 */
052 public static final Fraction ONE = new Fraction(1, 1);
053 /**
054 * <code>Fraction</code> representation of 1/2.
055 */
056 public static final Fraction ONE_HALF = new Fraction(1, 2);
057 /**
058 * <code>Fraction</code> representation of 1/3.
059 */
060 public static final Fraction ONE_THIRD = new Fraction(1, 3);
061 /**
062 * <code>Fraction</code> representation of 2/3.
063 */
064 public static final Fraction TWO_THIRDS = new Fraction(2, 3);
065 /**
066 * <code>Fraction</code> representation of 1/4.
067 */
068 public static final Fraction ONE_QUARTER = new Fraction(1, 4);
069 /**
070 * <code>Fraction</code> representation of 2/4.
071 */
072 public static final Fraction TWO_QUARTERS = new Fraction(2, 4);
073 /**
074 * <code>Fraction</code> representation of 3/4.
075 */
076 public static final Fraction THREE_QUARTERS = new Fraction(3, 4);
077 /**
078 * <code>Fraction</code> representation of 1/5.
079 */
080 public static final Fraction ONE_FIFTH = new Fraction(1, 5);
081 /**
082 * <code>Fraction</code> representation of 2/5.
083 */
084 public static final Fraction TWO_FIFTHS = new Fraction(2, 5);
085 /**
086 * <code>Fraction</code> representation of 3/5.
087 */
088 public static final Fraction THREE_FIFTHS = new Fraction(3, 5);
089 /**
090 * <code>Fraction</code> representation of 4/5.
091 */
092 public static final Fraction FOUR_FIFTHS = new Fraction(4, 5);
093
094
095 /**
096 * The numerator number part of the fraction (the three in three sevenths).
097 */
098 private final int numerator;
099 /**
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 @Override
420 public int intValue() {
421 return numerator / denominator;
422 }
423
424 /**
425 * <p>Gets the fraction as a <code>long</code>. This returns the whole number
426 * part of the fraction.</p>
427 *
428 * @return the whole number fraction part
429 */
430 @Override
431 public long longValue() {
432 return (long) numerator / denominator;
433 }
434
435 /**
436 * <p>Gets the fraction as a <code>float</code>. This calculates the fraction
437 * as the numerator divided by denominator.</p>
438 *
439 * @return the fraction as a <code>float</code>
440 */
441 @Override
442 public float floatValue() {
443 return ((float) numerator) / ((float) denominator);
444 }
445
446 /**
447 * <p>Gets the fraction as a <code>double</code>. This calculates the fraction
448 * as the numerator divided by denominator.</p>
449 *
450 * @return the fraction as a <code>double</code>
451 */
452 @Override
453 public double doubleValue() {
454 return ((double) numerator) / ((double) denominator);
455 }
456
457 // Calculations
458 //-------------------------------------------------------------------
459
460 /**
461 * <p>Reduce the fraction to the smallest values for the numerator and
462 * denominator, returning the result.</p>
463 *
464 * <p>For example, if this fraction represents 2/4, then the result
465 * will be 1/2.</p>
466 *
467 * @return a new reduced fraction instance, or this if no simplification possible
468 */
469 public Fraction reduce() {
470 if (numerator == 0) {
471 return equals(ZERO) ? this : ZERO;
472 }
473 int gcd = greatestCommonDivisor(Math.abs(numerator), denominator);
474 if (gcd == 1) {
475 return this;
476 }
477 return Fraction.getFraction(numerator / gcd, denominator / gcd);
478 }
479
480 /**
481 * <p>Gets a fraction that is the inverse (1/fraction) of this one.</p>
482 *
483 * <p>The returned fraction is not reduced.</p>
484 *
485 * @return a new fraction instance with the numerator and denominator
486 * inverted.
487 * @throws ArithmeticException if the fraction represents zero.
488 */
489 public Fraction invert() {
490 if (numerator == 0) {
491 throw new ArithmeticException("Unable to invert zero.");
492 }
493 if (numerator==Integer.MIN_VALUE) {
494 throw new ArithmeticException("overflow: can't negate numerator");
495 }
496 if (numerator<0) {
497 return new Fraction(-denominator, -numerator);
498 } else {
499 return new Fraction(denominator, numerator);
500 }
501 }
502
503 /**
504 * <p>Gets a fraction that is the negative (-fraction) of this one.</p>
505 *
506 * <p>The returned fraction is not reduced.</p>
507 *
508 * @return a new fraction instance with the opposite signed numerator
509 */
510 public Fraction negate() {
511 // the positive range is one smaller than the negative range of an int.
512 if (numerator==Integer.MIN_VALUE) {
513 throw new ArithmeticException("overflow: too large to negate");
514 }
515 return new Fraction(-numerator, denominator);
516 }
517
518 /**
519 * <p>Gets a fraction that is the positive equivalent of this one.</p>
520 * <p>More precisely: <code>(fraction >= 0 ? this : -fraction)</code></p>
521 *
522 * <p>The returned fraction is not reduced.</p>
523 *
524 * @return <code>this</code> if it is positive, or a new positive fraction
525 * instance with the opposite signed numerator
526 */
527 public Fraction abs() {
528 if (numerator >= 0) {
529 return this;
530 }
531 return negate();
532 }
533
534 /**
535 * <p>Gets a fraction that is raised to the passed in power.</p>
536 *
537 * <p>The returned fraction is in reduced form.</p>
538 *
539 * @param power the power to raise the fraction to
540 * @return <code>this</code> if the power is one, <code>ONE</code> if the power
541 * is zero (even if the fraction equals ZERO) or a new fraction instance
542 * raised to the appropriate power
543 * @throws ArithmeticException if the resulting numerator or denominator exceeds
544 * <code>Integer.MAX_VALUE</code>
545 */
546 public Fraction pow(int power) {
547 if (power == 1) {
548 return this;
549 } else if (power == 0) {
550 return ONE;
551 } else if (power < 0) {
552 if (power==Integer.MIN_VALUE) { // MIN_VALUE can't be negated.
553 return this.invert().pow(2).pow(-(power/2));
554 }
555 return this.invert().pow(-power);
556 } else {
557 Fraction f = this.multiplyBy(this);
558 if ((power % 2) == 0) { // if even...
559 return f.pow(power/2);
560 } else { // if odd...
561 return f.pow(power/2).multiplyBy(this);
562 }
563 }
564 }
565
566 /**
567 * <p>Gets the greatest common divisor of the absolute value of
568 * two numbers, using the "binary gcd" method which avoids
569 * division and modulo operations. See Knuth 4.5.2 algorithm B.
570 * This algorithm is due to Josef Stein (1961).</p>
571 *
572 * @param u a non-zero number
573 * @param v a non-zero number
574 * @return the greatest common divisor, never zero
575 */
576 private static int greatestCommonDivisor(int u, int v) {
577 //if either op. is abs 0 or 1, return 1:
578 if (Math.abs(u) <= 1 || Math.abs(v) <= 1) {
579 return 1;
580 }
581 // keep u and v negative, as negative integers range down to
582 // -2^31, while positive numbers can only be as large as 2^31-1
583 // (i.e. we can't necessarily negate a negative number without
584 // overflow)
585 if (u>0) { u=-u; } // make u negative
586 if (v>0) { v=-v; } // make v negative
587 // B1. [Find power of 2]
588 int k=0;
589 while ((u&1)==0 && (v&1)==0 && k<31) { // while u and v are both even...
590 u/=2; v/=2; k++; // cast out twos.
591 }
592 if (k==31) {
593 throw new ArithmeticException("overflow: gcd is 2^31");
594 }
595 // B2. Initialize: u and v have been divided by 2^k and at least
596 // one is odd.
597 int t = ((u&1)==1) ? v : -(u/2)/*B3*/;
598 // t negative: u was odd, v may be even (t replaces v)
599 // t positive: u was even, v is odd (t replaces u)
600 do {
601 /* assert u<0 && v<0; */
602 // B4/B3: cast out twos from t.
603 while ((t&1)==0) { // while t is even..
604 t/=2; // cast out twos
605 }
606 // B5 [reset max(u,v)]
607 if (t>0) {
608 u = -t;
609 } else {
610 v = t;
611 }
612 // B6/B3. at this point both u and v should be odd.
613 t = (v - u)/2;
614 // |u| larger: t positive (replace u)
615 // |v| larger: t negative (replace v)
616 } while (t!=0);
617 return -u*(1<<k); // gcd is u*2^k
618 }
619
620 // Arithmetic
621 //-------------------------------------------------------------------
622
623 /**
624 * Multiply two integers, checking for overflow.
625 *
626 * @param x a factor
627 * @param y a factor
628 * @return the product <code>x*y</code>
629 * @throws ArithmeticException if the result can not be represented as
630 * an int
631 */
632 private static int mulAndCheck(int x, int y) {
633 long m = ((long)x)*((long)y);
634 if (m < Integer.MIN_VALUE ||
635 m > Integer.MAX_VALUE) {
636 throw new ArithmeticException("overflow: mul");
637 }
638 return (int)m;
639 }
640
641 /**
642 * Multiply two non-negative integers, checking for overflow.
643 *
644 * @param x a non-negative factor
645 * @param y a non-negative factor
646 * @return the product <code>x*y</code>
647 * @throws ArithmeticException if the result can not be represented as
648 * an int
649 */
650 private static int mulPosAndCheck(int x, int y) {
651 /* assert x>=0 && y>=0; */
652 long m = ((long)x)*((long)y);
653 if (m > Integer.MAX_VALUE) {
654 throw new ArithmeticException("overflow: mulPos");
655 }
656 return (int)m;
657 }
658
659 /**
660 * Add two integers, checking for overflow.
661 *
662 * @param x an addend
663 * @param y an addend
664 * @return the sum <code>x+y</code>
665 * @throws ArithmeticException if the result can not be represented as
666 * an int
667 */
668 private static int addAndCheck(int x, int y) {
669 long s = (long)x+(long)y;
670 if (s < Integer.MIN_VALUE ||
671 s > Integer.MAX_VALUE) {
672 throw new ArithmeticException("overflow: add");
673 }
674 return (int)s;
675 }
676
677 /**
678 * Subtract two integers, checking for overflow.
679 *
680 * @param x the minuend
681 * @param y the subtrahend
682 * @return the difference <code>x-y</code>
683 * @throws ArithmeticException if the result can not be represented as
684 * an int
685 */
686 private static int subAndCheck(int x, int y) {
687 long s = (long)x-(long)y;
688 if (s < Integer.MIN_VALUE ||
689 s > Integer.MAX_VALUE) {
690 throw new ArithmeticException("overflow: add");
691 }
692 return (int)s;
693 }
694
695 /**
696 * <p>Adds the value of this fraction to another, returning the result in reduced form.
697 * The algorithm follows Knuth, 4.5.1.</p>
698 *
699 * @param fraction the fraction to add, must not be <code>null</code>
700 * @return a <code>Fraction</code> instance with the resulting values
701 * @throws IllegalArgumentException if the fraction is <code>null</code>
702 * @throws ArithmeticException if the resulting numerator or denominator exceeds
703 * <code>Integer.MAX_VALUE</code>
704 */
705 public Fraction add(Fraction fraction) {
706 return addSub(fraction, true /* add */);
707 }
708
709 /**
710 * <p>Subtracts the value of another fraction from the value of this one,
711 * returning the result in reduced form.</p>
712 *
713 * @param fraction the fraction to subtract, must not be <code>null</code>
714 * @return a <code>Fraction</code> instance with the resulting values
715 * @throws IllegalArgumentException if the fraction is <code>null</code>
716 * @throws ArithmeticException if the resulting numerator or denominator
717 * cannot be represented in an <code>int</code>.
718 */
719 public Fraction subtract(Fraction fraction) {
720 return addSub(fraction, false /* subtract */);
721 }
722
723 /**
724 * Implement add and subtract using algorithm described in Knuth 4.5.1.
725 *
726 * @param fraction the fraction to subtract, must not be <code>null</code>
727 * @param isAdd true to add, false to subtract
728 * @return a <code>Fraction</code> instance with the resulting values
729 * @throws IllegalArgumentException if the fraction is <code>null</code>
730 * @throws ArithmeticException if the resulting numerator or denominator
731 * cannot be represented in an <code>int</code>.
732 */
733 private Fraction addSub(Fraction fraction, boolean isAdd) {
734 if (fraction == null) {
735 throw new IllegalArgumentException("The fraction must not be null");
736 }
737 // zero is identity for addition.
738 if (numerator == 0) {
739 return isAdd ? fraction : fraction.negate();
740 }
741 if (fraction.numerator == 0) {
742 return this;
743 }
744 // if denominators are randomly distributed, d1 will be 1 about 61%
745 // of the time.
746 int d1 = greatestCommonDivisor(denominator, fraction.denominator);
747 if (d1==1) {
748 // result is ( (u*v' +/- u'v) / u'v')
749 int uvp = mulAndCheck(numerator, fraction.denominator);
750 int upv = mulAndCheck(fraction.numerator, denominator);
751 return new Fraction
752 (isAdd ? addAndCheck(uvp, upv) : subAndCheck(uvp, upv),
753 mulPosAndCheck(denominator, fraction.denominator));
754 }
755 // the quantity 't' requires 65 bits of precision; see knuth 4.5.1
756 // exercise 7. we're going to use a BigInteger.
757 // t = u(v'/d1) +/- v(u'/d1)
758 BigInteger uvp = BigInteger.valueOf(numerator)
759 .multiply(BigInteger.valueOf(fraction.denominator/d1));
760 BigInteger upv = BigInteger.valueOf(fraction.numerator)
761 .multiply(BigInteger.valueOf(denominator/d1));
762 BigInteger t = isAdd ? uvp.add(upv) : uvp.subtract(upv);
763 // but d2 doesn't need extra precision because
764 // d2 = gcd(t,d1) = gcd(t mod d1, d1)
765 int tmodd1 = t.mod(BigInteger.valueOf(d1)).intValue();
766 int d2 = (tmodd1==0)?d1:greatestCommonDivisor(tmodd1, d1);
767
768 // result is (t/d2) / (u'/d1)(v'/d2)
769 BigInteger w = t.divide(BigInteger.valueOf(d2));
770 if (w.bitLength() > 31) {
771 throw new ArithmeticException
772 ("overflow: numerator too large after multiply");
773 }
774 return new Fraction
775 (w.intValue(),
776 mulPosAndCheck(denominator/d1, fraction.denominator/d2));
777 }
778
779 /**
780 * <p>Multiplies the value of this fraction by another, returning the
781 * result in reduced form.</p>
782 *
783 * @param fraction the fraction to multiply by, must not be <code>null</code>
784 * @return a <code>Fraction</code> instance with the resulting values
785 * @throws IllegalArgumentException if the fraction is <code>null</code>
786 * @throws ArithmeticException if the resulting numerator or denominator exceeds
787 * <code>Integer.MAX_VALUE</code>
788 */
789 public Fraction multiplyBy(Fraction fraction) {
790 if (fraction == null) {
791 throw new IllegalArgumentException("The fraction must not be null");
792 }
793 if (numerator == 0 || fraction.numerator == 0) {
794 return ZERO;
795 }
796 // knuth 4.5.1
797 // make sure we don't overflow unless the result *must* overflow.
798 int d1 = greatestCommonDivisor(numerator, fraction.denominator);
799 int d2 = greatestCommonDivisor(fraction.numerator, denominator);
800 return getReducedFraction
801 (mulAndCheck(numerator/d1, fraction.numerator/d2),
802 mulPosAndCheck(denominator/d2, fraction.denominator/d1));
803 }
804
805 /**
806 * <p>Divide the value of this fraction by another.</p>
807 *
808 * @param fraction the fraction to divide by, must not be <code>null</code>
809 * @return a <code>Fraction</code> instance with the resulting values
810 * @throws IllegalArgumentException if the fraction is <code>null</code>
811 * @throws ArithmeticException if the fraction to divide by is zero
812 * @throws ArithmeticException if the resulting numerator or denominator exceeds
813 * <code>Integer.MAX_VALUE</code>
814 */
815 public Fraction divideBy(Fraction fraction) {
816 if (fraction == null) {
817 throw new IllegalArgumentException("The fraction must not be null");
818 }
819 if (fraction.numerator == 0) {
820 throw new ArithmeticException("The fraction to divide by must not be zero");
821 }
822 return multiplyBy(fraction.invert());
823 }
824
825 // Basics
826 //-------------------------------------------------------------------
827
828 /**
829 * <p>Compares this fraction to another object to test if they are equal.</p>.
830 *
831 * <p>To be equal, both values must be equal. Thus 2/4 is not equal to 1/2.</p>
832 *
833 * @param obj the reference object with which to compare
834 * @return <code>true</code> if this object is equal
835 */
836 @Override
837 public boolean equals(Object obj) {
838 if (obj == this) {
839 return true;
840 }
841 if (obj instanceof Fraction == false) {
842 return false;
843 }
844 Fraction other = (Fraction) obj;
845 return (getNumerator() == other.getNumerator() &&
846 getDenominator() == other.getDenominator());
847 }
848
849 /**
850 * <p>Gets a hashCode for the fraction.</p>
851 *
852 * @return a hash code value for this object
853 */
854 @Override
855 public int hashCode() {
856 if (hashCode == 0) {
857 // hashcode update should be atomic.
858 hashCode = 37 * (37 * 17 + getNumerator()) + getDenominator();
859 }
860 return hashCode;
861 }
862
863 /**
864 * <p>Compares this object to another based on size.</p>
865 *
866 * <p>Note: this class has a natural ordering that is inconsistent
867 * with equals, because, for example, equals treats 1/2 and 2/4 as
868 * different, whereas compareTo treats them as equal.
869 *
870 * @param other the object to compare to
871 * @return -1 if this is less, 0 if equal, +1 if greater
872 * @throws ClassCastException if the object is not a <code>Fraction</code>
873 * @throws NullPointerException if the object is <code>null</code>
874 */
875 public int compareTo(Fraction other) {
876 if (this==other) {
877 return 0;
878 }
879 if (numerator == other.numerator && denominator == other.denominator) {
880 return 0;
881 }
882
883 // otherwise see which is less
884 long first = (long) numerator * (long) other.denominator;
885 long second = (long) other.numerator * (long) denominator;
886 if (first == second) {
887 return 0;
888 } else if (first < second) {
889 return -1;
890 } else {
891 return 1;
892 }
893 }
894
895 /**
896 * <p>Gets the fraction as a <code>String</code>.</p>
897 *
898 * <p>The format used is '<i>numerator</i>/<i>denominator</i>' always.
899 *
900 * @return a <code>String</code> form of the fraction
901 */
902 @Override
903 public String toString() {
904 if (toString == null) {
905 toString = new StringBuilder(32)
906 .append(getNumerator())
907 .append('/')
908 .append(getDenominator()).toString();
909 }
910 return toString;
911 }
912
913 /**
914 * <p>Gets the fraction as a proper <code>String</code> in the format X Y/Z.</p>
915 *
916 * <p>The format used in '<i>wholeNumber</i> <i>numerator</i>/<i>denominator</i>'.
917 * If the whole number is zero it will be ommitted. If the numerator is zero,
918 * only the whole number is returned.</p>
919 *
920 * @return a <code>String</code> form of the fraction
921 */
922 public String toProperString() {
923 if (toProperString == null) {
924 if (numerator == 0) {
925 toProperString = "0";
926 } else if (numerator == denominator) {
927 toProperString = "1";
928 } else if (numerator == -1 * denominator) {
929 toProperString = "-1";
930 } else if ((numerator>0?-numerator:numerator) < -denominator) {
931 // note that we do the magnitude comparison test above with
932 // NEGATIVE (not positive) numbers, since negative numbers
933 // have a larger range. otherwise numerator==Integer.MIN_VALUE
934 // is handled incorrectly.
935 int properNumerator = getProperNumerator();
936 if (properNumerator == 0) {
937 toProperString = Integer.toString(getProperWhole());
938 } else {
939 toProperString = new StringBuilder(32)
940 .append(getProperWhole()).append(' ')
941 .append(properNumerator).append('/')
942 .append(getDenominator()).toString();
943 }
944 } else {
945 toProperString = new StringBuilder(32)
946 .append(getNumerator()).append('/')
947 .append(getDenominator()).toString();
948 }
949 }
950 return toProperString;
951 }
952 }