1 /*
2 * Copyright (c) 1996, 2013, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26 /*
27 * Portions Copyright IBM Corporation, 2001. All Rights Reserved.
28 */
29
30 package java.math;
31
32 import java.util.Arrays;
33 import static java.math.BigInteger.LONG_MASK;
34
35 /**
36 * Immutable, arbitrary-precision signed decimal numbers. A
37 * {@code BigDecimal} consists of an arbitrary precision integer
38 * <i>unscaled value</i> and a 32-bit integer <i>scale</i>. If zero
39 * or positive, the scale is the number of digits to the right of the
40 * decimal point. If negative, the unscaled value of the number is
41 * multiplied by ten to the power of the negation of the scale. The
42 * value of the number represented by the {@code BigDecimal} is
43 * therefore <tt>(unscaledValue × 10<sup>-scale</sup>)</tt>.
44 *
45 * <p>The {@code BigDecimal} class provides operations for
46 * arithmetic, scale manipulation, rounding, comparison, hashing, and
47 * format conversion. The {@link #toString} method provides a
48 * canonical representation of a {@code BigDecimal}.
49 *
50 * <p>The {@code BigDecimal} class gives its user complete control
51 * over rounding behavior. If no rounding mode is specified and the
52 * exact result cannot be represented, an exception is thrown;
53 * otherwise, calculations can be carried out to a chosen precision
54 * and rounding mode by supplying an appropriate {@link MathContext}
55 * object to the operation. In either case, eight <em>rounding
56 * modes</em> are provided for the control of rounding. Using the
57 * integer fields in this class (such as {@link #ROUND_HALF_UP}) to
58 * represent rounding mode is largely obsolete; the enumeration values
59 * of the {@code RoundingMode} {@code enum}, (such as {@link
60 * RoundingMode#HALF_UP}) should be used instead.
61 *
62 * <p>When a {@code MathContext} object is supplied with a precision
63 * setting of 0 (for example, {@link MathContext#UNLIMITED}),
64 * arithmetic operations are exact, as are the arithmetic methods
65 * which take no {@code MathContext} object. (This is the only
66 * behavior that was supported in releases prior to 5.) As a
67 * corollary of computing the exact result, the rounding mode setting
68 * of a {@code MathContext} object with a precision setting of 0 is
69 * not used and thus irrelevant. In the case of divide, the exact
70 * quotient could have an infinitely long decimal expansion; for
71 * example, 1 divided by 3. If the quotient has a nonterminating
72 * decimal expansion and the operation is specified to return an exact
73 * result, an {@code ArithmeticException} is thrown. Otherwise, the
74 * exact result of the division is returned, as done for other
75 * operations.
76 *
77 * <p>When the precision setting is not 0, the rules of
78 * {@code BigDecimal} arithmetic are broadly compatible with selected
79 * modes of operation of the arithmetic defined in ANSI X3.274-1996
80 * and ANSI X3.274-1996/AM 1-2000 (section 7.4). Unlike those
81 * standards, {@code BigDecimal} includes many rounding modes, which
82 * were mandatory for division in {@code BigDecimal} releases prior
83 * to 5. Any conflicts between these ANSI standards and the
84 * {@code BigDecimal} specification are resolved in favor of
85 * {@code BigDecimal}.
86 *
87 * <p>Since the same numerical value can have different
88 * representations (with different scales), the rules of arithmetic
89 * and rounding must specify both the numerical result and the scale
90 * used in the result's representation.
91 *
92 *
93 * <p>In general the rounding modes and precision setting determine
94 * how operations return results with a limited number of digits when
95 * the exact result has more digits (perhaps infinitely many in the
96 * case of division) than the number of digits returned.
97 *
98 * First, the
99 * total number of digits to return is specified by the
100 * {@code MathContext}'s {@code precision} setting; this determines
101 * the result's <i>precision</i>. The digit count starts from the
102 * leftmost nonzero digit of the exact result. The rounding mode
103 * determines how any discarded trailing digits affect the returned
104 * result.
105 *
106 * <p>For all arithmetic operators , the operation is carried out as
107 * though an exact intermediate result were first calculated and then
108 * rounded to the number of digits specified by the precision setting
109 * (if necessary), using the selected rounding mode. If the exact
110 * result is not returned, some digit positions of the exact result
111 * are discarded. When rounding increases the magnitude of the
112 * returned result, it is possible for a new digit position to be
113 * created by a carry propagating to a leading {@literal "9"} digit.
114 * For example, rounding the value 999.9 to three digits rounding up
115 * would be numerically equal to one thousand, represented as
116 * 100×10<sup>1</sup>. In such cases, the new {@literal "1"} is
117 * the leading digit position of the returned result.
118 *
119 * <p>Besides a logical exact result, each arithmetic operation has a
120 * preferred scale for representing a result. The preferred
121 * scale for each operation is listed in the table below.
122 *
123 * <table border>
124 * <caption><b>Preferred Scales for Results of Arithmetic Operations
125 * </b></caption>
126 * <tr><th>Operation</th><th>Preferred Scale of Result</th></tr>
127 * <tr><td>Add</td><td>max(addend.scale(), augend.scale())</td>
128 * <tr><td>Subtract</td><td>max(minuend.scale(), subtrahend.scale())</td>
129 * <tr><td>Multiply</td><td>multiplier.scale() + multiplicand.scale()</td>
130 * <tr><td>Divide</td><td>dividend.scale() - divisor.scale()</td>
131 * </table>
132 *
133 * These scales are the ones used by the methods which return exact
134 * arithmetic results; except that an exact divide may have to use a
135 * larger scale since the exact result may have more digits. For
136 * example, {@code 1/32} is {@code 0.03125}.
137 *
138 * <p>Before rounding, the scale of the logical exact intermediate
139 * result is the preferred scale for that operation. If the exact
140 * numerical result cannot be represented in {@code precision}
141 * digits, rounding selects the set of digits to return and the scale
142 * of the result is reduced from the scale of the intermediate result
143 * to the least scale which can represent the {@code precision}
144 * digits actually returned. If the exact result can be represented
145 * with at most {@code precision} digits, the representation
146 * of the result with the scale closest to the preferred scale is
147 * returned. In particular, an exactly representable quotient may be
148 * represented in fewer than {@code precision} digits by removing
149 * trailing zeros and decreasing the scale. For example, rounding to
150 * three digits using the {@linkplain RoundingMode#FLOOR floor}
151 * rounding mode, <br>
152 *
153 * {@code 19/100 = 0.19 // integer=19, scale=2} <br>
154 *
155 * but<br>
156 *
157 * {@code 21/110 = 0.190 // integer=190, scale=3} <br>
158 *
159 * <p>Note that for add, subtract, and multiply, the reduction in
160 * scale will equal the number of digit positions of the exact result
161 * which are discarded. If the rounding causes a carry propagation to
162 * create a new high-order digit position, an additional digit of the
163 * result is discarded than when no new digit position is created.
164 *
165 * <p>Other methods may have slightly different rounding semantics.
166 * For example, the result of the {@code pow} method using the
167 * {@linkplain #pow(int, MathContext) specified algorithm} can
168 * occasionally differ from the rounded mathematical result by more
169 * than one unit in the last place, one <i>{@linkplain #ulp() ulp}</i>.
170 *
171 * <p>Two types of operations are provided for manipulating the scale
172 * of a {@code BigDecimal}: scaling/rounding operations and decimal
173 * point motion operations. Scaling/rounding operations ({@link
174 * #setScale setScale} and {@link #round round}) return a
175 * {@code BigDecimal} whose value is approximately (or exactly) equal
176 * to that of the operand, but whose scale or precision is the
177 * specified value; that is, they increase or decrease the precision
178 * of the stored number with minimal effect on its value. Decimal
179 * point motion operations ({@link #movePointLeft movePointLeft} and
180 * {@link #movePointRight movePointRight}) return a
181 * {@code BigDecimal} created from the operand by moving the decimal
182 * point a specified distance in the specified direction.
183 *
184 * <p>For the sake of brevity and clarity, pseudo-code is used
185 * throughout the descriptions of {@code BigDecimal} methods. The
186 * pseudo-code expression {@code (i + j)} is shorthand for "a
187 * {@code BigDecimal} whose value is that of the {@code BigDecimal}
188 * {@code i} added to that of the {@code BigDecimal}
189 * {@code j}." The pseudo-code expression {@code (i == j)} is
190 * shorthand for "{@code true} if and only if the
191 * {@code BigDecimal} {@code i} represents the same value as the
192 * {@code BigDecimal} {@code j}." Other pseudo-code expressions
193 * are interpreted similarly. Square brackets are used to represent
194 * the particular {@code BigInteger} and scale pair defining a
195 * {@code BigDecimal} value; for example [19, 2] is the
196 * {@code BigDecimal} numerically equal to 0.19 having a scale of 2.
197 *
198 * <p>Note: care should be exercised if {@code BigDecimal} objects
199 * are used as keys in a {@link java.util.SortedMap SortedMap} or
200 * elements in a {@link java.util.SortedSet SortedSet} since
201 * {@code BigDecimal}'s <i>natural ordering</i> is <i>inconsistent
202 * with equals</i>. See {@link Comparable}, {@link
203 * java.util.SortedMap} or {@link java.util.SortedSet} for more
204 * information.
205 *
206 * <p>All methods and constructors for this class throw
207 * {@code NullPointerException} when passed a {@code null} object
208 * reference for any input parameter.
209 *
210 * @see BigInteger
211 * @see MathContext
212 * @see RoundingMode
213 * @see java.util.SortedMap
214 * @see java.util.SortedSet
215 * @author Josh Bloch
216 * @author Mike Cowlishaw
217 * @author Joseph D. Darcy
218 * @author Sergey V. Kuksenko
219 */
220 public class BigDecimal extends Number implements Comparable<BigDecimal> {
221 /**
222 * The unscaled value of this BigDecimal, as returned by {@link
223 * #unscaledValue}.
224 *
225 * @serial
226 * @see #unscaledValue
227 */
228 private final BigInteger intVal;
229
230 /**
231 * The scale of this BigDecimal, as returned by {@link #scale}.
232 *
233 * @serial
234 * @see #scale
235 */
236 private final int scale; // Note: this may have any value, so
237 // calculations must be done in longs
238
239 /**
240 * The number of decimal digits in this BigDecimal, or 0 if the
241 * number of digits are not known (lookaside information). If
242 * nonzero, the value is guaranteed correct. Use the precision()
243 * method to obtain and set the value if it might be 0. This
244 * field is mutable until set nonzero.
245 *
246 * @since 1.5
247 */
248 private transient int precision;
249
250 /**
251 * Used to store the canonical string representation, if computed.
252 */
253 private transient String stringCache;
254
255 /**
256 * Sentinel value for {@link #intCompact} indicating the
257 * significand information is only available from {@code intVal}.
258 */
259 static final long INFLATED = Long.MIN_VALUE;
260
261 private static final BigInteger INFLATED_BIGINT = BigInteger.valueOf(INFLATED);
262
263 /**
264 * If the absolute value of the significand of this BigDecimal is
265 * less than or equal to {@code Long.MAX_VALUE}, the value can be
266 * compactly stored in this field and used in computations.
267 */
268 private final transient long intCompact;
269
270 // All 18-digit base ten strings fit into a long; not all 19-digit
271 // strings will
272 private static final int MAX_COMPACT_DIGITS = 18;
273
274 /* Appease the serialization gods */
275 private static final long serialVersionUID = 6108874887143696463L;
276
277 private static final ThreadLocal<StringBuilderHelper>
278 threadLocalStringBuilderHelper = new ThreadLocal<StringBuilderHelper>() {
279 @Override
280 protected StringBuilderHelper initialValue() {
281 return new StringBuilderHelper();
282 }
283 };
284
285 // Cache of common small BigDecimal values.
286 private static final BigDecimal zeroThroughTen[] = {
287 new BigDecimal(BigInteger.ZERO, 0, 0, 1),
288 new BigDecimal(BigInteger.ONE, 1, 0, 1),
289 new BigDecimal(BigInteger.valueOf(2), 2, 0, 1),
290 new BigDecimal(BigInteger.valueOf(3), 3, 0, 1),
291 new BigDecimal(BigInteger.valueOf(4), 4, 0, 1),
292 new BigDecimal(BigInteger.valueOf(5), 5, 0, 1),
293 new BigDecimal(BigInteger.valueOf(6), 6, 0, 1),
294 new BigDecimal(BigInteger.valueOf(7), 7, 0, 1),
295 new BigDecimal(BigInteger.valueOf(8), 8, 0, 1),
296 new BigDecimal(BigInteger.valueOf(9), 9, 0, 1),
297 new BigDecimal(BigInteger.TEN, 10, 0, 2),
298 };
299
300 // Cache of zero scaled by 0 - 15
301 private static final BigDecimal[] ZERO_SCALED_BY = {
302 zeroThroughTen[0],
303 new BigDecimal(BigInteger.ZERO, 0, 1, 1),
304 new BigDecimal(BigInteger.ZERO, 0, 2, 1),
305 new BigDecimal(BigInteger.ZERO, 0, 3, 1),
306 new BigDecimal(BigInteger.ZERO, 0, 4, 1),
307 new BigDecimal(BigInteger.ZERO, 0, 5, 1),
308 new BigDecimal(BigInteger.ZERO, 0, 6, 1),
309 new BigDecimal(BigInteger.ZERO, 0, 7, 1),
310 new BigDecimal(BigInteger.ZERO, 0, 8, 1),
311 new BigDecimal(BigInteger.ZERO, 0, 9, 1),
312 new BigDecimal(BigInteger.ZERO, 0, 10, 1),
313 new BigDecimal(BigInteger.ZERO, 0, 11, 1),
314 new BigDecimal(BigInteger.ZERO, 0, 12, 1),
315 new BigDecimal(BigInteger.ZERO, 0, 13, 1),
316 new BigDecimal(BigInteger.ZERO, 0, 14, 1),
317 new BigDecimal(BigInteger.ZERO, 0, 15, 1),
318 };
319
320 // Half of Long.MIN_VALUE & Long.MAX_VALUE.
321 private static final long HALF_LONG_MAX_VALUE = Long.MAX_VALUE / 2;
322 private static final long HALF_LONG_MIN_VALUE = Long.MIN_VALUE / 2;
323
324 // Constants
325 /**
326 * The value 0, with a scale of 0.
327 *
328 * @since 1.5
329 */
330 public static final BigDecimal ZERO =
331 zeroThroughTen[0];
332
333 /**
334 * The value 1, with a scale of 0.
335 *
336 * @since 1.5
337 */
338 public static final BigDecimal ONE =
339 zeroThroughTen[1];
340
341 /**
342 * The value 10, with a scale of 0.
343 *
344 * @since 1.5
345 */
346 public static final BigDecimal TEN =
347 zeroThroughTen[10];
348
349 // Constructors
350
351 /**
352 * Trusted package private constructor.
353 * Trusted simply means if val is INFLATED, intVal could not be null and
354 * if intVal is null, val could not be INFLATED.
355 */
356 BigDecimal(BigInteger intVal, long val, int scale, int prec) {
357 this.scale = scale;
358 this.precision = prec;
359 this.intCompact = val;
360 this.intVal = intVal;
361 }
362
363 /**
364 * Translates a character array representation of a
365 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
366 * same sequence of characters as the {@link #BigDecimal(String)}
367 * constructor, while allowing a sub-array to be specified.
368 *
369 * <p>Note that if the sequence of characters is already available
370 * within a character array, using this constructor is faster than
371 * converting the {@code char} array to string and using the
372 * {@code BigDecimal(String)} constructor .
373 *
374 * @param in {@code char} array that is the source of characters.
375 * @param offset first character in the array to inspect.
376 * @param len number of characters to consider.
377 * @throws NumberFormatException if {@code in} is not a valid
378 * representation of a {@code BigDecimal} or the defined subarray
379 * is not wholly within {@code in}.
380 * @since 1.5
381 */
382 public BigDecimal(char[] in, int offset, int len) {
383 this(in,offset,len,MathContext.UNLIMITED);
384 }
385
386 /**
387 * Translates a character array representation of a
388 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
389 * same sequence of characters as the {@link #BigDecimal(String)}
390 * constructor, while allowing a sub-array to be specified and
391 * with rounding according to the context settings.
392 *
393 * <p>Note that if the sequence of characters is already available
394 * within a character array, using this constructor is faster than
395 * converting the {@code char} array to string and using the
396 * {@code BigDecimal(String)} constructor .
397 *
398 * @param in {@code char} array that is the source of characters.
399 * @param offset first character in the array to inspect.
400 * @param len number of characters to consider..
401 * @param mc the context to use.
402 * @throws ArithmeticException if the result is inexact but the
403 * rounding mode is {@code UNNECESSARY}.
404 * @throws NumberFormatException if {@code in} is not a valid
405 * representation of a {@code BigDecimal} or the defined subarray
406 * is not wholly within {@code in}.
407 * @since 1.5
408 */
409 public BigDecimal(char[] in, int offset, int len, MathContext mc) {
410 // protect against huge length.
411 if (offset + len > in.length || offset < 0)
412 throw new NumberFormatException("Bad offset or len arguments for char[] input.");
413 // This is the primary string to BigDecimal constructor; all
414 // incoming strings end up here; it uses explicit (inline)
415 // parsing for speed and generates at most one intermediate
416 // (temporary) object (a char[] array) for non-compact case.
417
418 // Use locals for all fields values until completion
419 int prec = 0; // record precision value
420 int scl = 0; // record scale value
421 long rs = 0; // the compact value in long
422 BigInteger rb = null; // the inflated value in BigInteger
423 // use array bounds checking to handle too-long, len == 0,
424 // bad offset, etc.
425 try {
426 // handle the sign
427 boolean isneg = false; // assume positive
428 if (in[offset] == '-') {
429 isneg = true; // leading minus means negative
430 offset++;
431 len--;
432 } else if (in[offset] == '+') { // leading + allowed
433 offset++;
434 len--;
435 }
436
437 // should now be at numeric part of the significand
438 boolean dot = false; // true when there is a '.'
439 long exp = 0; // exponent
440 char c; // current character
441 boolean isCompact = (len <= MAX_COMPACT_DIGITS);
442 // integer significand array & idx is the index to it. The array
443 // is ONLY used when we can't use a compact representation.
444 int idx = 0;
445 if (isCompact) {
446 // First compact case, we need not to preserve the character
447 // and we can just compute the value in place.
448 for (; len > 0; offset++, len--) {
449 c = in[offset];
450 if ((c == '0')) { // have zero
451 if (prec == 0)
452 prec = 1;
453 else if (rs != 0) {
454 rs *= 10;
455 ++prec;
456 } // else digit is a redundant leading zero
457 if (dot)
458 ++scl;
459 } else if ((c >= '1' && c <= '9')) { // have digit
460 int digit = c - '0';
461 if (prec != 1 || rs != 0)
462 ++prec; // prec unchanged if preceded by 0s
463 rs = rs * 10 + digit;
464 if (dot)
465 ++scl;
466 } else if (c == '.') { // have dot
467 // have dot
468 if (dot) // two dots
469 throw new NumberFormatException();
470 dot = true;
471 } else if (Character.isDigit(c)) { // slow path
472 int digit = Character.digit(c, 10);
473 if (digit == 0) {
474 if (prec == 0)
475 prec = 1;
476 else if (rs != 0) {
477 rs *= 10;
478 ++prec;
479 } // else digit is a redundant leading zero
480 } else {
481 if (prec != 1 || rs != 0)
482 ++prec; // prec unchanged if preceded by 0s
483 rs = rs * 10 + digit;
484 }
485 if (dot)
486 ++scl;
487 } else if ((c == 'e') || (c == 'E')) {
488 exp = parseExp(in, offset, len);
489 // Next test is required for backwards compatibility
490 if ((int) exp != exp) // overflow
491 throw new NumberFormatException();
492 break; // [saves a test]
493 } else {
494 throw new NumberFormatException();
495 }
496 }
497 if (prec == 0) // no digits found
498 throw new NumberFormatException();
499 // Adjust scale if exp is not zero.
500 if (exp != 0) { // had significant exponent
501 scl = adjustScale(scl, exp);
502 }
503 rs = isneg ? -rs : rs;
504 int mcp = mc.precision;
505 int drop = prec - mcp; // prec has range [1, MAX_INT], mcp has range [0, MAX_INT];
506 // therefore, this subtract cannot overflow
507 if (mcp > 0 && drop > 0) { // do rounding
508 while (drop > 0) {
509 scl = checkScaleNonZero((long) scl - drop);
510 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
511 prec = longDigitLength(rs);
512 drop = prec - mcp;
513 }
514 }
515 } else {
516 char coeff[] = new char[len];
517 for (; len > 0; offset++, len--) {
518 c = in[offset];
519 // have digit
520 if ((c >= '0' && c <= '9') || Character.isDigit(c)) {
521 // First compact case, we need not to preserve the character
522 // and we can just compute the value in place.
523 if (c == '0' || Character.digit(c, 10) == 0) {
524 if (prec == 0) {
525 coeff[idx] = c;
526 prec = 1;
527 } else if (idx != 0) {
528 coeff[idx++] = c;
529 ++prec;
530 } // else c must be a redundant leading zero
531 } else {
532 if (prec != 1 || idx != 0)
533 ++prec; // prec unchanged if preceded by 0s
534 coeff[idx++] = c;
535 }
536 if (dot)
537 ++scl;
538 continue;
539 }
540 // have dot
541 if (c == '.') {
542 // have dot
543 if (dot) // two dots
544 throw new NumberFormatException();
545 dot = true;
546 continue;
547 }
548 // exponent expected
549 if ((c != 'e') && (c != 'E'))
550 throw new NumberFormatException();
551 exp = parseExp(in, offset, len);
552 // Next test is required for backwards compatibility
553 if ((int) exp != exp) // overflow
554 throw new NumberFormatException();
555 break; // [saves a test]
556 }
557 // here when no characters left
558 if (prec == 0) // no digits found
559 throw new NumberFormatException();
560 // Adjust scale if exp is not zero.
561 if (exp != 0) { // had significant exponent
562 scl = adjustScale(scl, exp);
563 }
564 // Remove leading zeros from precision (digits count)
565 rb = new BigInteger(coeff, isneg ? -1 : 1, prec);
566 rs = compactValFor(rb);
567 int mcp = mc.precision;
568 if (mcp > 0 && (prec > mcp)) {
569 if (rs == INFLATED) {
570 int drop = prec - mcp;
571 while (drop > 0) {
572 scl = checkScaleNonZero((long) scl - drop);
573 rb = divideAndRoundByTenPow(rb, drop, mc.roundingMode.oldMode);
574 rs = compactValFor(rb);
575 if (rs != INFLATED) {
576 prec = longDigitLength(rs);
577 break;
578 }
579 prec = bigDigitLength(rb);
580 drop = prec - mcp;
581 }
582 }
583 if (rs != INFLATED) {
584 int drop = prec - mcp;
585 while (drop > 0) {
586 scl = checkScaleNonZero((long) scl - drop);
587 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
588 prec = longDigitLength(rs);
589 drop = prec - mcp;
590 }
591 rb = null;
592 }
593 }
594 }
595 } catch (ArrayIndexOutOfBoundsException e) {
596 throw new NumberFormatException();
597 } catch (NegativeArraySizeException e) {
598 throw new NumberFormatException();
599 }
600 this.scale = scl;
601 this.precision = prec;
602 this.intCompact = rs;
603 this.intVal = rb;
604 }
605
606 private int adjustScale(int scl, long exp) {
607 long adjustedScale = scl - exp;
608 if (adjustedScale > Integer.MAX_VALUE || adjustedScale < Integer.MIN_VALUE)
609 throw new NumberFormatException("Scale out of range.");
610 scl = (int) adjustedScale;
611 return scl;
612 }
613
614 /*
615 * parse exponent
616 */
617 private static long parseExp(char[] in, int offset, int len){
618 long exp = 0;
619 offset++;
620 char c = in[offset];
621 len--;
622 boolean negexp = (c == '-');
623 // optional sign
624 if (negexp || c == '+') {
625 offset++;
626 c = in[offset];
627 len--;
628 }
629 if (len <= 0) // no exponent digits
630 throw new NumberFormatException();
631 // skip leading zeros in the exponent
632 while (len > 10 && (c=='0' || (Character.digit(c, 10) == 0))) {
633 offset++;
634 c = in[offset];
635 len--;
636 }
637 if (len > 10) // too many nonzero exponent digits
638 throw new NumberFormatException();
639 // c now holds first digit of exponent
640 for (;; len--) {
641 int v;
642 if (c >= '0' && c <= '9') {
643 v = c - '0';
644 } else {
645 v = Character.digit(c, 10);
646 if (v < 0) // not a digit
647 throw new NumberFormatException();
648 }
649 exp = exp * 10 + v;
650 if (len == 1)
651 break; // that was final character
652 offset++;
653 c = in[offset];
654 }
655 if (negexp) // apply sign
656 exp = -exp;
657 return exp;
658 }
659
660 /**
661 * Translates a character array representation of a
662 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
663 * same sequence of characters as the {@link #BigDecimal(String)}
664 * constructor.
665 *
666 * <p>Note that if the sequence of characters is already available
667 * as a character array, using this constructor is faster than
668 * converting the {@code char} array to string and using the
669 * {@code BigDecimal(String)} constructor .
670 *
671 * @param in {@code char} array that is the source of characters.
672 * @throws NumberFormatException if {@code in} is not a valid
673 * representation of a {@code BigDecimal}.
674 * @since 1.5
675 */
676 public BigDecimal(char[] in) {
677 this(in, 0, in.length);
678 }
679
680 /**
681 * Translates a character array representation of a
682 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
683 * same sequence of characters as the {@link #BigDecimal(String)}
684 * constructor and with rounding according to the context
685 * settings.
686 *
687 * <p>Note that if the sequence of characters is already available
688 * as a character array, using this constructor is faster than
689 * converting the {@code char} array to string and using the
690 * {@code BigDecimal(String)} constructor .
691 *
692 * @param in {@code char} array that is the source of characters.
693 * @param mc the context to use.
694 * @throws ArithmeticException if the result is inexact but the
695 * rounding mode is {@code UNNECESSARY}.
696 * @throws NumberFormatException if {@code in} is not a valid
697 * representation of a {@code BigDecimal}.
698 * @since 1.5
699 */
700 public BigDecimal(char[] in, MathContext mc) {
701 this(in, 0, in.length, mc);
702 }
703
704 /**
705 * Translates the string representation of a {@code BigDecimal}
706 * into a {@code BigDecimal}. The string representation consists
707 * of an optional sign, {@code '+'} (<tt> '\u002B'</tt>) or
708 * {@code '-'} (<tt>'\u002D'</tt>), followed by a sequence of
709 * zero or more decimal digits ("the integer"), optionally
710 * followed by a fraction, optionally followed by an exponent.
711 *
712 * <p>The fraction consists of a decimal point followed by zero
713 * or more decimal digits. The string must contain at least one
714 * digit in either the integer or the fraction. The number formed
715 * by the sign, the integer and the fraction is referred to as the
716 * <i>significand</i>.
717 *
718 * <p>The exponent consists of the character {@code 'e'}
719 * (<tt>'\u0065'</tt>) or {@code 'E'} (<tt>'\u0045'</tt>)
720 * followed by one or more decimal digits. The value of the
721 * exponent must lie between -{@link Integer#MAX_VALUE} ({@link
722 * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive.
723 *
724 * <p>More formally, the strings this constructor accepts are
725 * described by the following grammar:
726 * <blockquote>
727 * <dl>
728 * <dt><i>BigDecimalString:</i>
729 * <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i>
730 * <dt><i>Sign:</i>
731 * <dd>{@code +}
732 * <dd>{@code -}
733 * <dt><i>Significand:</i>
734 * <dd><i>IntegerPart</i> {@code .} <i>FractionPart<sub>opt</sub></i>
735 * <dd>{@code .} <i>FractionPart</i>
736 * <dd><i>IntegerPart</i>
737 * <dt><i>IntegerPart:</i>
738 * <dd><i>Digits</i>
739 * <dt><i>FractionPart:</i>
740 * <dd><i>Digits</i>
741 * <dt><i>Exponent:</i>
742 * <dd><i>ExponentIndicator SignedInteger</i>
743 * <dt><i>ExponentIndicator:</i>
744 * <dd>{@code e}
745 * <dd>{@code E}
746 * <dt><i>SignedInteger:</i>
747 * <dd><i>Sign<sub>opt</sub> Digits</i>
748 * <dt><i>Digits:</i>
749 * <dd><i>Digit</i>
750 * <dd><i>Digits Digit</i>
751 * <dt><i>Digit:</i>
752 * <dd>any character for which {@link Character#isDigit}
753 * returns {@code true}, including 0, 1, 2 ...
754 * </dl>
755 * </blockquote>
756 *
757 * <p>The scale of the returned {@code BigDecimal} will be the
758 * number of digits in the fraction, or zero if the string
759 * contains no decimal point, subject to adjustment for any
760 * exponent; if the string contains an exponent, the exponent is
761 * subtracted from the scale. The value of the resulting scale
762 * must lie between {@code Integer.MIN_VALUE} and
763 * {@code Integer.MAX_VALUE}, inclusive.
764 *
765 * <p>The character-to-digit mapping is provided by {@link
766 * java.lang.Character#digit} set to convert to radix 10. The
767 * String may not contain any extraneous characters (whitespace,
768 * for example).
769 *
770 * <p><b>Examples:</b><br>
771 * The value of the returned {@code BigDecimal} is equal to
772 * <i>significand</i> × 10<sup> <i>exponent</i></sup>.
773 * For each string on the left, the resulting representation
774 * [{@code BigInteger}, {@code scale}] is shown on the right.
775 * <pre>
776 * "0" [0,0]
777 * "0.00" [0,2]
778 * "123" [123,0]
779 * "-123" [-123,0]
780 * "1.23E3" [123,-1]
781 * "1.23E+3" [123,-1]
782 * "12.3E+7" [123,-6]
783 * "12.0" [120,1]
784 * "12.3" [123,1]
785 * "0.00123" [123,5]
786 * "-1.23E-12" [-123,14]
787 * "1234.5E-4" [12345,5]
788 * "0E+7" [0,-7]
789 * "-0" [0,0]
790 * </pre>
791 *
792 * <p>Note: For values other than {@code float} and
793 * {@code double} NaN and ±Infinity, this constructor is
794 * compatible with the values returned by {@link Float#toString}
795 * and {@link Double#toString}. This is generally the preferred
796 * way to convert a {@code float} or {@code double} into a
797 * BigDecimal, as it doesn't suffer from the unpredictability of
798 * the {@link #BigDecimal(double)} constructor.
799 *
800 * @param val String representation of {@code BigDecimal}.
801 *
802 * @throws NumberFormatException if {@code val} is not a valid
803 * representation of a {@code BigDecimal}.
804 */
805 public BigDecimal(String val) {
806 this(val.toCharArray(), 0, val.length());
807 }
808
809 /**
810 * Translates the string representation of a {@code BigDecimal}
811 * into a {@code BigDecimal}, accepting the same strings as the
812 * {@link #BigDecimal(String)} constructor, with rounding
813 * according to the context settings.
814 *
815 * @param val string representation of a {@code BigDecimal}.
816 * @param mc the context to use.
817 * @throws ArithmeticException if the result is inexact but the
818 * rounding mode is {@code UNNECESSARY}.
819 * @throws NumberFormatException if {@code val} is not a valid
820 * representation of a BigDecimal.
821 * @since 1.5
822 */
823 public BigDecimal(String val, MathContext mc) {
824 this(val.toCharArray(), 0, val.length(), mc);
825 }
826
827 /**
828 * Translates a {@code double} into a {@code BigDecimal} which
829 * is the exact decimal representation of the {@code double}'s
830 * binary floating-point value. The scale of the returned
831 * {@code BigDecimal} is the smallest value such that
832 * <tt>(10<sup>scale</sup> × val)</tt> is an integer.
833 * <p>
834 * <b>Notes:</b>
835 * <ol>
836 * <li>
837 * The results of this constructor can be somewhat unpredictable.
838 * One might assume that writing {@code new BigDecimal(0.1)} in
839 * Java creates a {@code BigDecimal} which is exactly equal to
840 * 0.1 (an unscaled value of 1, with a scale of 1), but it is
841 * actually equal to
842 * 0.1000000000000000055511151231257827021181583404541015625.
843 * This is because 0.1 cannot be represented exactly as a
844 * {@code double} (or, for that matter, as a binary fraction of
845 * any finite length). Thus, the value that is being passed
846 * <i>in</i> to the constructor is not exactly equal to 0.1,
847 * appearances notwithstanding.
848 *
849 * <li>
850 * The {@code String} constructor, on the other hand, is
851 * perfectly predictable: writing {@code new BigDecimal("0.1")}
852 * creates a {@code BigDecimal} which is <i>exactly</i> equal to
853 * 0.1, as one would expect. Therefore, it is generally
854 * recommended that the {@linkplain #BigDecimal(String)
855 * <tt>String</tt> constructor} be used in preference to this one.
856 *
857 * <li>
858 * When a {@code double} must be used as a source for a
859 * {@code BigDecimal}, note that this constructor provides an
860 * exact conversion; it does not give the same result as
861 * converting the {@code double} to a {@code String} using the
862 * {@link Double#toString(double)} method and then using the
863 * {@link #BigDecimal(String)} constructor. To get that result,
864 * use the {@code static} {@link #valueOf(double)} method.
865 * </ol>
866 *
867 * @param val {@code double} value to be converted to
868 * {@code BigDecimal}.
869 * @throws NumberFormatException if {@code val} is infinite or NaN.
870 */
871 public BigDecimal(double val) {
872 this(val,MathContext.UNLIMITED);
873 }
874
875 /**
876 * Translates a {@code double} into a {@code BigDecimal}, with
877 * rounding according to the context settings. The scale of the
878 * {@code BigDecimal} is the smallest value such that
879 * <tt>(10<sup>scale</sup> × val)</tt> is an integer.
880 *
881 * <p>The results of this constructor can be somewhat unpredictable
882 * and its use is generally not recommended; see the notes under
883 * the {@link #BigDecimal(double)} constructor.
884 *
885 * @param val {@code double} value to be converted to
886 * {@code BigDecimal}.
887 * @param mc the context to use.
888 * @throws ArithmeticException if the result is inexact but the
889 * RoundingMode is UNNECESSARY.
890 * @throws NumberFormatException if {@code val} is infinite or NaN.
891 * @since 1.5
892 */
893 public BigDecimal(double val, MathContext mc) {
894 if (Double.isInfinite(val) || Double.isNaN(val))
895 throw new NumberFormatException("Infinite or NaN");
896 // Translate the double into sign, exponent and significand, according
897 // to the formulae in JLS, Section 20.10.22.
898 long valBits = Double.doubleToLongBits(val);
899 int sign = ((valBits >> 63) == 0 ? 1 : -1);
900 int exponent = (int) ((valBits >> 52) & 0x7ffL);
901 long significand = (exponent == 0
902 ? (valBits & ((1L << 52) - 1)) << 1
903 : (valBits & ((1L << 52) - 1)) | (1L << 52));
904 exponent -= 1075;
905 // At this point, val == sign * significand * 2**exponent.
906
907 /*
908 * Special case zero to supress nonterminating normalization and bogus
909 * scale calculation.
910 */
911 if (significand == 0) {
912 this.intVal = BigInteger.ZERO;
913 this.scale = 0;
914 this.intCompact = 0;
915 this.precision = 1;
916 return;
917 }
918 // Normalize
919 while ((significand & 1) == 0) { // i.e., significand is even
920 significand >>= 1;
921 exponent++;
922 }
923 int scale = 0;
924 // Calculate intVal and scale
925 BigInteger intVal;
926 long compactVal = sign * significand;
927 if (exponent == 0) {
928 intVal = (compactVal == INFLATED) ? INFLATED_BIGINT : null;
929 } else {
930 if (exponent < 0) {
931 intVal = BigInteger.valueOf(5).pow(-exponent).multiply(compactVal);
932 scale = -exponent;
933 } else { // (exponent > 0)
934 intVal = BigInteger.valueOf(2).pow(exponent).multiply(compactVal);
935 }
936 compactVal = compactValFor(intVal);
937 }
938 int prec = 0;
939 int mcp = mc.precision;
940 if (mcp > 0) { // do rounding
941 int mode = mc.roundingMode.oldMode;
942 int drop;
943 if (compactVal == INFLATED) {
944 prec = bigDigitLength(intVal);
945 drop = prec - mcp;
946 while (drop > 0) {
947 scale = checkScaleNonZero((long) scale - drop);
948 intVal = divideAndRoundByTenPow(intVal, drop, mode);
949 compactVal = compactValFor(intVal);
950 if (compactVal != INFLATED) {
951 break;
952 }
953 prec = bigDigitLength(intVal);
954 drop = prec - mcp;
955 }
956 }
957 if (compactVal != INFLATED) {
958 prec = longDigitLength(compactVal);
959 drop = prec - mcp;
960 while (drop > 0) {
961 scale = checkScaleNonZero((long) scale - drop);
962 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
963 prec = longDigitLength(compactVal);
964 drop = prec - mcp;
965 }
966 intVal = null;
967 }
968 }
969 this.intVal = intVal;
970 this.intCompact = compactVal;
971 this.scale = scale;
972 this.precision = prec;
973 }
974
975 /**
976 * Translates a {@code BigInteger} into a {@code BigDecimal}.
977 * The scale of the {@code BigDecimal} is zero.
978 *
979 * @param val {@code BigInteger} value to be converted to
980 * {@code BigDecimal}.
981 */
982 public BigDecimal(BigInteger val) {
983 scale = 0;
984 intVal = val;
985 intCompact = compactValFor(val);
986 }
987
988 /**
989 * Translates a {@code BigInteger} into a {@code BigDecimal}
990 * rounding according to the context settings. The scale of the
991 * {@code BigDecimal} is zero.
992 *
993 * @param val {@code BigInteger} value to be converted to
994 * {@code BigDecimal}.
995 * @param mc the context to use.
996 * @throws ArithmeticException if the result is inexact but the
997 * rounding mode is {@code UNNECESSARY}.
998 * @since 1.5
999 */
1000 public BigDecimal(BigInteger val, MathContext mc) {
1001 this(val,0,mc);
1002 }
1003
1004 /**
1005 * Translates a {@code BigInteger} unscaled value and an
1006 * {@code int} scale into a {@code BigDecimal}. The value of
1007 * the {@code BigDecimal} is
1008 * <tt>(unscaledVal × 10<sup>-scale</sup>)</tt>.
1009 *
1010 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1011 * @param scale scale of the {@code BigDecimal}.
1012 */
1013 public BigDecimal(BigInteger unscaledVal, int scale) {
1014 // Negative scales are now allowed
1015 this.intVal = unscaledVal;
1016 this.intCompact = compactValFor(unscaledVal);
1017 this.scale = scale;
1018 }
1019
1020 /**
1021 * Translates a {@code BigInteger} unscaled value and an
1022 * {@code int} scale into a {@code BigDecimal}, with rounding
1023 * according to the context settings. The value of the
1024 * {@code BigDecimal} is <tt>(unscaledVal ×
1025 * 10<sup>-scale</sup>)</tt>, rounded according to the
1026 * {@code precision} and rounding mode settings.
1027 *
1028 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1029 * @param scale scale of the {@code BigDecimal}.
1030 * @param mc the context to use.
1031 * @throws ArithmeticException if the result is inexact but the
1032 * rounding mode is {@code UNNECESSARY}.
1033 * @since 1.5
1034 */
1035 public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {
1036 long compactVal = compactValFor(unscaledVal);
1037 int mcp = mc.precision;
1038 int prec = 0;
1039 if (mcp > 0) { // do rounding
1040 int mode = mc.roundingMode.oldMode;
1041 if (compactVal == INFLATED) {
1042 prec = bigDigitLength(unscaledVal);
1043 int drop = prec - mcp;
1044 while (drop > 0) {
1045 scale = checkScaleNonZero((long) scale - drop);
1046 unscaledVal = divideAndRoundByTenPow(unscaledVal, drop, mode);
1047 compactVal = compactValFor(unscaledVal);
1048 if (compactVal != INFLATED) {
1049 break;
1050 }
1051 prec = bigDigitLength(unscaledVal);
1052 drop = prec - mcp;
1053 }
1054 }
1055 if (compactVal != INFLATED) {
1056 prec = longDigitLength(compactVal);
1057 int drop = prec - mcp; // drop can't be more than 18
1058 while (drop > 0) {
1059 scale = checkScaleNonZero((long) scale - drop);
1060 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mode);
1061 prec = longDigitLength(compactVal);
1062 drop = prec - mcp;
1063 }
1064 unscaledVal = null;
1065 }
1066 }
1067 this.intVal = unscaledVal;
1068 this.intCompact = compactVal;
1069 this.scale = scale;
1070 this.precision = prec;
1071 }
1072
1073 /**
1074 * Translates an {@code int} into a {@code BigDecimal}. The
1075 * scale of the {@code BigDecimal} is zero.
1076 *
1077 * @param val {@code int} value to be converted to
1078 * {@code BigDecimal}.
1079 * @since 1.5
1080 */
1081 public BigDecimal(int val) {
1082 this.intCompact = val;
1083 this.scale = 0;
1084 this.intVal = null;
1085 }
1086
1087 /**
1088 * Translates an {@code int} into a {@code BigDecimal}, with
1089 * rounding according to the context settings. The scale of the
1090 * {@code BigDecimal}, before any rounding, is zero.
1091 *
1092 * @param val {@code int} value to be converted to {@code BigDecimal}.
1093 * @param mc the context to use.
1094 * @throws ArithmeticException if the result is inexact but the
1095 * rounding mode is {@code UNNECESSARY}.
1096 * @since 1.5
1097 */
1098 public BigDecimal(int val, MathContext mc) {
1099 int mcp = mc.precision;
1100 long compactVal = val;
1101 int scale = 0;
1102 int prec = 0;
1103 if (mcp > 0) { // do rounding
1104 prec = longDigitLength(compactVal);
1105 int drop = prec - mcp; // drop can't be more than 18
1106 while (drop > 0) {
1107 scale = checkScaleNonZero((long) scale - drop);
1108 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1109 prec = longDigitLength(compactVal);
1110 drop = prec - mcp;
1111 }
1112 }
1113 this.intVal = null;
1114 this.intCompact = compactVal;
1115 this.scale = scale;
1116 this.precision = prec;
1117 }
1118
1119 /**
1120 * Translates a {@code long} into a {@code BigDecimal}. The
1121 * scale of the {@code BigDecimal} is zero.
1122 *
1123 * @param val {@code long} value to be converted to {@code BigDecimal}.
1124 * @since 1.5
1125 */
1126 public BigDecimal(long val) {
1127 this.intCompact = val;
1128 this.intVal = (val == INFLATED) ? INFLATED_BIGINT : null;
1129 this.scale = 0;
1130 }
1131
1132 /**
1133 * Translates a {@code long} into a {@code BigDecimal}, with
1134 * rounding according to the context settings. The scale of the
1135 * {@code BigDecimal}, before any rounding, is zero.
1136 *
1137 * @param val {@code long} value to be converted to {@code BigDecimal}.
1138 * @param mc the context to use.
1139 * @throws ArithmeticException if the result is inexact but the
1140 * rounding mode is {@code UNNECESSARY}.
1141 * @since 1.5
1142 */
1143 public BigDecimal(long val, MathContext mc) {
1144 int mcp = mc.precision;
1145 int mode = mc.roundingMode.oldMode;
1146 int prec = 0;
1147 int scale = 0;
1148 BigInteger intVal = (val == INFLATED) ? INFLATED_BIGINT : null;
1149 if (mcp > 0) { // do rounding
1150 if (val == INFLATED) {
1151 prec = 19;
1152 int drop = prec - mcp;
1153 while (drop > 0) {
1154 scale = checkScaleNonZero((long) scale - drop);
1155 intVal = divideAndRoundByTenPow(intVal, drop, mode);
1156 val = compactValFor(intVal);
1157 if (val != INFLATED) {
1158 break;
1159 }
1160 prec = bigDigitLength(intVal);
1161 drop = prec - mcp;
1162 }
1163 }
1164 if (val != INFLATED) {
1165 prec = longDigitLength(val);
1166 int drop = prec - mcp;
1167 while (drop > 0) {
1168 scale = checkScaleNonZero((long) scale - drop);
1169 val = divideAndRound(val, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1170 prec = longDigitLength(val);
1171 drop = prec - mcp;
1172 }
1173 intVal = null;
1174 }
1175 }
1176 this.intVal = intVal;
1177 this.intCompact = val;
1178 this.scale = scale;
1179 this.precision = prec;
1180 }
1181
1182 // Static Factory Methods
1183
1184 /**
1185 * Translates a {@code long} unscaled value and an
1186 * {@code int} scale into a {@code BigDecimal}. This
1187 * {@literal "static factory method"} is provided in preference to
1188 * a ({@code long}, {@code int}) constructor because it
1189 * allows for reuse of frequently used {@code BigDecimal} values..
1190 *
1191 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1192 * @param scale scale of the {@code BigDecimal}.
1193 * @return a {@code BigDecimal} whose value is
1194 * <tt>(unscaledVal × 10<sup>-scale</sup>)</tt>.
1195 */
1196 public static BigDecimal valueOf(long unscaledVal, int scale) {
1197 if (scale == 0)
1198 return valueOf(unscaledVal);
1199 else if (unscaledVal == 0) {
1200 return zeroValueOf(scale);
1201 }
1202 return new BigDecimal(unscaledVal == INFLATED ?
1203 INFLATED_BIGINT : null,
1204 unscaledVal, scale, 0);
1205 }
1206
1207 /**
1208 * Translates a {@code long} value into a {@code BigDecimal}
1209 * with a scale of zero. This {@literal "static factory method"}
1210 * is provided in preference to a ({@code long}) constructor
1211 * because it allows for reuse of frequently used
1212 * {@code BigDecimal} values.
1213 *
1214 * @param val value of the {@code BigDecimal}.
1215 * @return a {@code BigDecimal} whose value is {@code val}.
1216 */
1217 public static BigDecimal valueOf(long val) {
1218 if (val >= 0 && val < zeroThroughTen.length)
1219 return zeroThroughTen[(int)val];
1220 else if (val != INFLATED)
1221 return new BigDecimal(null, val, 0, 0);
1222 return new BigDecimal(INFLATED_BIGINT, val, 0, 0);
1223 }
1224
1225 static BigDecimal valueOf(long unscaledVal, int scale, int prec) {
1226 if (scale == 0 && unscaledVal >= 0 && unscaledVal < zeroThroughTen.length) {
1227 return zeroThroughTen[(int) unscaledVal];
1228 } else if (unscaledVal == 0) {
1229 return zeroValueOf(scale);
1230 }
1231 return new BigDecimal(unscaledVal == INFLATED ? INFLATED_BIGINT : null,
1232 unscaledVal, scale, prec);
1233 }
1234
1235 static BigDecimal valueOf(BigInteger intVal, int scale, int prec) {
1236 long val = compactValFor(intVal);
1237 if (val == 0) {
1238 return zeroValueOf(scale);
1239 } else if (scale == 0 && val >= 0 && val < zeroThroughTen.length) {
1240 return zeroThroughTen[(int) val];
1241 }
1242 return new BigDecimal(intVal, val, scale, prec);
1243 }
1244
1245 static BigDecimal zeroValueOf(int scale) {
1246 if (scale >= 0 && scale < ZERO_SCALED_BY.length)
1247 return ZERO_SCALED_BY[scale];
1248 else
1249 return new BigDecimal(BigInteger.ZERO, 0, scale, 1);
1250 }
1251
1252 /**
1253 * Translates a {@code double} into a {@code BigDecimal}, using
1254 * the {@code double}'s canonical string representation provided
1255 * by the {@link Double#toString(double)} method.
1256 *
1257 * <p><b>Note:</b> This is generally the preferred way to convert
1258 * a {@code double} (or {@code float}) into a
1259 * {@code BigDecimal}, as the value returned is equal to that
1260 * resulting from constructing a {@code BigDecimal} from the
1261 * result of using {@link Double#toString(double)}.
1262 *
1263 * @param val {@code double} to convert to a {@code BigDecimal}.
1264 * @return a {@code BigDecimal} whose value is equal to or approximately
1265 * equal to the value of {@code val}.
1266 * @throws NumberFormatException if {@code val} is infinite or NaN.
1267 * @since 1.5
1268 */
1269 public static BigDecimal valueOf(double val) {
1270 // Reminder: a zero double returns '0.0', so we cannot fastpath
1271 // to use the constant ZERO. This might be important enough to
1272 // justify a factory approach, a cache, or a few private
1273 // constants, later.
1274 return new BigDecimal(Double.toString(val));
1275 }
1276
1277 // Arithmetic Operations
1278 /**
1279 * Returns a {@code BigDecimal} whose value is {@code (this +
1280 * augend)}, and whose scale is {@code max(this.scale(),
1281 * augend.scale())}.
1282 *
1283 * @param augend value to be added to this {@code BigDecimal}.
1284 * @return {@code this + augend}
1285 */
1286 public BigDecimal add(BigDecimal augend) {
1287 if (this.intCompact != INFLATED) {
1288 if ((augend.intCompact != INFLATED)) {
1289 return add(this.intCompact, this.scale, augend.intCompact, augend.scale);
1290 } else {
1291 return add(this.intCompact, this.scale, augend.intVal, augend.scale);
1292 }
1293 } else {
1294 if ((augend.intCompact != INFLATED)) {
1295 return add(augend.intCompact, augend.scale, this.intVal, this.scale);
1296 } else {
1297 return add(this.intVal, this.scale, augend.intVal, augend.scale);
1298 }
1299 }
1300 }
1301
1302 /**
1303 * Returns a {@code BigDecimal} whose value is {@code (this + augend)},
1304 * with rounding according to the context settings.
1305 *
1306 * If either number is zero and the precision setting is nonzero then
1307 * the other number, rounded if necessary, is used as the result.
1308 *
1309 * @param augend value to be added to this {@code BigDecimal}.
1310 * @param mc the context to use.
1311 * @return {@code this + augend}, rounded as necessary.
1312 * @throws ArithmeticException if the result is inexact but the
1313 * rounding mode is {@code UNNECESSARY}.
1314 * @since 1.5
1315 */
1316 public BigDecimal add(BigDecimal augend, MathContext mc) {
1317 if (mc.precision == 0)
1318 return add(augend);
1319 BigDecimal lhs = this;
1320
1321 // If either number is zero then the other number, rounded and
1322 // scaled if necessary, is used as the result.
1323 {
1324 boolean lhsIsZero = lhs.signum() == 0;
1325 boolean augendIsZero = augend.signum() == 0;
1326
1327 if (lhsIsZero || augendIsZero) {
1328 int preferredScale = Math.max(lhs.scale(), augend.scale());
1329 BigDecimal result;
1330
1331 if (lhsIsZero && augendIsZero)
1332 return zeroValueOf(preferredScale);
1333 result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc);
1334
1335 if (result.scale() == preferredScale)
1336 return result;
1337 else if (result.scale() > preferredScale) {
1338 return stripZerosToMatchScale(result.intVal, result.intCompact, result.scale, preferredScale);
1339 } else { // result.scale < preferredScale
1340 int precisionDiff = mc.precision - result.precision();
1341 int scaleDiff = preferredScale - result.scale();
1342
1343 if (precisionDiff >= scaleDiff)
1344 return result.setScale(preferredScale); // can achieve target scale
1345 else
1346 return result.setScale(result.scale() + precisionDiff);
1347 }
1348 }
1349 }
1350
1351 long padding = (long) lhs.scale - augend.scale;
1352 if (padding != 0) { // scales differ; alignment needed
1353 BigDecimal arg[] = preAlign(lhs, augend, padding, mc);
1354 matchScale(arg);
1355 lhs = arg[0];
1356 augend = arg[1];
1357 }
1358 return doRound(lhs.inflated().add(augend.inflated()), lhs.scale, mc);
1359 }
1360
1361 /**
1362 * Returns an array of length two, the sum of whose entries is
1363 * equal to the rounded sum of the {@code BigDecimal} arguments.
1364 *
1365 * <p>If the digit positions of the arguments have a sufficient
1366 * gap between them, the value smaller in magnitude can be
1367 * condensed into a {@literal "sticky bit"} and the end result will
1368 * round the same way <em>if</em> the precision of the final
1369 * result does not include the high order digit of the small
1370 * magnitude operand.
1371 *
1372 * <p>Note that while strictly speaking this is an optimization,
1373 * it makes a much wider range of additions practical.
1374 *
1375 * <p>This corresponds to a pre-shift operation in a fixed
1376 * precision floating-point adder; this method is complicated by
1377 * variable precision of the result as determined by the
1378 * MathContext. A more nuanced operation could implement a
1379 * {@literal "right shift"} on the smaller magnitude operand so
1380 * that the number of digits of the smaller operand could be
1381 * reduced even though the significands partially overlapped.
1382 */
1383 private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend, long padding, MathContext mc) {
1384 assert padding != 0;
1385 BigDecimal big;
1386 BigDecimal small;
1387
1388 if (padding < 0) { // lhs is big; augend is small
1389 big = lhs;
1390 small = augend;
1391 } else { // lhs is small; augend is big
1392 big = augend;
1393 small = lhs;
1394 }
1395
1396 /*
1397 * This is the estimated scale of an ulp of the result; it assumes that
1398 * the result doesn't have a carry-out on a true add (e.g. 999 + 1 =>
1399 * 1000) or any subtractive cancellation on borrowing (e.g. 100 - 1.2 =>
1400 * 98.8)
1401 */
1402 long estResultUlpScale = (long) big.scale - big.precision() + mc.precision;
1403
1404 /*
1405 * The low-order digit position of big is big.scale(). This
1406 * is true regardless of whether big has a positive or
1407 * negative scale. The high-order digit position of small is
1408 * small.scale - (small.precision() - 1). To do the full
1409 * condensation, the digit positions of big and small must be
1410 * disjoint *and* the digit positions of small should not be
1411 * directly visible in the result.
1412 */
1413 long smallHighDigitPos = (long) small.scale - small.precision() + 1;
1414 if (smallHighDigitPos > big.scale + 2 && // big and small disjoint
1415 smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible
1416 small = BigDecimal.valueOf(small.signum(), this.checkScale(Math.max(big.scale, estResultUlpScale) + 3));
1417 }
1418
1419 // Since addition is symmetric, preserving input order in
1420 // returned operands doesn't matter
1421 BigDecimal[] result = {big, small};
1422 return result;
1423 }
1424
1425 /**
1426 * Returns a {@code BigDecimal} whose value is {@code (this -
1427 * subtrahend)}, and whose scale is {@code max(this.scale(),
1428 * subtrahend.scale())}.
1429 *
1430 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1431 * @return {@code this - subtrahend}
1432 */
1433 public BigDecimal subtract(BigDecimal subtrahend) {
1434 if (this.intCompact != INFLATED) {
1435 if ((subtrahend.intCompact != INFLATED)) {
1436 return add(this.intCompact, this.scale, -subtrahend.intCompact, subtrahend.scale);
1437 } else {
1438 return add(this.intCompact, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1439 }
1440 } else {
1441 if ((subtrahend.intCompact != INFLATED)) {
1442 // Pair of subtrahend values given before pair of
1443 // values from this BigDecimal to avoid need for
1444 // method overloading on the specialized add method
1445 return add(-subtrahend.intCompact, subtrahend.scale, this.intVal, this.scale);
1446 } else {
1447 return add(this.intVal, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1448 }
1449 }
1450 }
1451
1452 /**
1453 * Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)},
1454 * with rounding according to the context settings.
1455 *
1456 * If {@code subtrahend} is zero then this, rounded if necessary, is used as the
1457 * result. If this is zero then the result is {@code subtrahend.negate(mc)}.
1458 *
1459 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1460 * @param mc the context to use.
1461 * @return {@code this - subtrahend}, rounded as necessary.
1462 * @throws ArithmeticException if the result is inexact but the
1463 * rounding mode is {@code UNNECESSARY}.
1464 * @since 1.5
1465 */
1466 public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) {
1467 if (mc.precision == 0)
1468 return subtract(subtrahend);
1469 // share the special rounding code in add()
1470 return add(subtrahend.negate(), mc);
1471 }
1472
1473 /**
1474 * Returns a {@code BigDecimal} whose value is <tt>(this ×
1475 * multiplicand)</tt>, and whose scale is {@code (this.scale() +
1476 * multiplicand.scale())}.
1477 *
1478 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1479 * @return {@code this * multiplicand}
1480 */
1481 public BigDecimal multiply(BigDecimal multiplicand) {
1482 int productScale = checkScale((long) scale + multiplicand.scale);
1483 if (this.intCompact != INFLATED) {
1484 if ((multiplicand.intCompact != INFLATED)) {
1485 return multiply(this.intCompact, multiplicand.intCompact, productScale);
1486 } else {
1487 return multiply(this.intCompact, multiplicand.intVal, productScale);
1488 }
1489 } else {
1490 if ((multiplicand.intCompact != INFLATED)) {
1491 return multiply(multiplicand.intCompact, this.intVal, productScale);
1492 } else {
1493 return multiply(this.intVal, multiplicand.intVal, productScale);
1494 }
1495 }
1496 }
1497
1498 /**
1499 * Returns a {@code BigDecimal} whose value is <tt>(this ×
1500 * multiplicand)</tt>, with rounding according to the context settings.
1501 *
1502 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1503 * @param mc the context to use.
1504 * @return {@code this * multiplicand}, rounded as necessary.
1505 * @throws ArithmeticException if the result is inexact but the
1506 * rounding mode is {@code UNNECESSARY}.
1507 * @since 1.5
1508 */
1509 public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) {
1510 if (mc.precision == 0)
1511 return multiply(multiplicand);
1512 int productScale = checkScale((long) scale + multiplicand.scale);
1513 if (this.intCompact != INFLATED) {
1514 if ((multiplicand.intCompact != INFLATED)) {
1515 return multiplyAndRound(this.intCompact, multiplicand.intCompact, productScale, mc);
1516 } else {
1517 return multiplyAndRound(this.intCompact, multiplicand.intVal, productScale, mc);
1518 }
1519 } else {
1520 if ((multiplicand.intCompact != INFLATED)) {
1521 return multiplyAndRound(multiplicand.intCompact, this.intVal, productScale, mc);
1522 } else {
1523 return multiplyAndRound(this.intVal, multiplicand.intVal, productScale, mc);
1524 }
1525 }
1526 }
1527
1528 /**
1529 * Returns a {@code BigDecimal} whose value is {@code (this /
1530 * divisor)}, and whose scale is as specified. If rounding must
1531 * be performed to generate a result with the specified scale, the
1532 * specified rounding mode is applied.
1533 *
1534 * <p>The new {@link #divide(BigDecimal, int, RoundingMode)} method
1535 * should be used in preference to this legacy method.
1536 *
1537 * @param divisor value by which this {@code BigDecimal} is to be divided.
1538 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1539 * @param roundingMode rounding mode to apply.
1540 * @return {@code this / divisor}
1541 * @throws ArithmeticException if {@code divisor} is zero,
1542 * {@code roundingMode==ROUND_UNNECESSARY} and
1543 * the specified scale is insufficient to represent the result
1544 * of the division exactly.
1545 * @throws IllegalArgumentException if {@code roundingMode} does not
1546 * represent a valid rounding mode.
1547 * @see #ROUND_UP
1548 * @see #ROUND_DOWN
1549 * @see #ROUND_CEILING
1550 * @see #ROUND_FLOOR
1551 * @see #ROUND_HALF_UP
1552 * @see #ROUND_HALF_DOWN
1553 * @see #ROUND_HALF_EVEN
1554 * @see #ROUND_UNNECESSARY
1555 */
1556 public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) {
1557 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
1558 throw new IllegalArgumentException("Invalid rounding mode");
1559 if (this.intCompact != INFLATED) {
1560 if ((divisor.intCompact != INFLATED)) {
1561 return divide(this.intCompact, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1562 } else {
1563 return divide(this.intCompact, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1564 }
1565 } else {
1566 if ((divisor.intCompact != INFLATED)) {
1567 return divide(this.intVal, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1568 } else {
1569 return divide(this.intVal, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1570 }
1571 }
1572 }
1573
1574 /**
1575 * Returns a {@code BigDecimal} whose value is {@code (this /
1576 * divisor)}, and whose scale is as specified. If rounding must
1577 * be performed to generate a result with the specified scale, the
1578 * specified rounding mode is applied.
1579 *
1580 * @param divisor value by which this {@code BigDecimal} is to be divided.
1581 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1582 * @param roundingMode rounding mode to apply.
1583 * @return {@code this / divisor}
1584 * @throws ArithmeticException if {@code divisor} is zero,
1585 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1586 * the specified scale is insufficient to represent the result
1587 * of the division exactly.
1588 * @since 1.5
1589 */
1590 public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) {
1591 return divide(divisor, scale, roundingMode.oldMode);
1592 }
1593
1594 /**
1595 * Returns a {@code BigDecimal} whose value is {@code (this /
1596 * divisor)}, and whose scale is {@code this.scale()}. If
1597 * rounding must be performed to generate a result with the given
1598 * scale, the specified rounding mode is applied.
1599 *
1600 * <p>The new {@link #divide(BigDecimal, RoundingMode)} method
1601 * should be used in preference to this legacy method.
1602 *
1603 * @param divisor value by which this {@code BigDecimal} is to be divided.
1604 * @param roundingMode rounding mode to apply.
1605 * @return {@code this / divisor}
1606 * @throws ArithmeticException if {@code divisor==0}, or
1607 * {@code roundingMode==ROUND_UNNECESSARY} and
1608 * {@code this.scale()} is insufficient to represent the result
1609 * of the division exactly.
1610 * @throws IllegalArgumentException if {@code roundingMode} does not
1611 * represent a valid rounding mode.
1612 * @see #ROUND_UP
1613 * @see #ROUND_DOWN
1614 * @see #ROUND_CEILING
1615 * @see #ROUND_FLOOR
1616 * @see #ROUND_HALF_UP
1617 * @see #ROUND_HALF_DOWN
1618 * @see #ROUND_HALF_EVEN
1619 * @see #ROUND_UNNECESSARY
1620 */
1621 public BigDecimal divide(BigDecimal divisor, int roundingMode) {
1622 return this.divide(divisor, scale, roundingMode);
1623 }
1624
1625 /**
1626 * Returns a {@code BigDecimal} whose value is {@code (this /
1627 * divisor)}, and whose scale is {@code this.scale()}. If
1628 * rounding must be performed to generate a result with the given
1629 * scale, the specified rounding mode is applied.
1630 *
1631 * @param divisor value by which this {@code BigDecimal} is to be divided.
1632 * @param roundingMode rounding mode to apply.
1633 * @return {@code this / divisor}
1634 * @throws ArithmeticException if {@code divisor==0}, or
1635 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1636 * {@code this.scale()} is insufficient to represent the result
1637 * of the division exactly.
1638 * @since 1.5
1639 */
1640 public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) {
1641 return this.divide(divisor, scale, roundingMode.oldMode);
1642 }
1643
1644 /**
1645 * Returns a {@code BigDecimal} whose value is {@code (this /
1646 * divisor)}, and whose preferred scale is {@code (this.scale() -
1647 * divisor.scale())}; if the exact quotient cannot be
1648 * represented (because it has a non-terminating decimal
1649 * expansion) an {@code ArithmeticException} is thrown.
1650 *
1651 * @param divisor value by which this {@code BigDecimal} is to be divided.
1652 * @throws ArithmeticException if the exact quotient does not have a
1653 * terminating decimal expansion
1654 * @return {@code this / divisor}
1655 * @since 1.5
1656 * @author Joseph D. Darcy
1657 */
1658 public BigDecimal divide(BigDecimal divisor) {
1659 /*
1660 * Handle zero cases first.
1661 */
1662 if (divisor.signum() == 0) { // x/0
1663 if (this.signum() == 0) // 0/0
1664 throw new ArithmeticException("Division undefined"); // NaN
1665 throw new ArithmeticException("Division by zero");
1666 }
1667
1668 // Calculate preferred scale
1669 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1670
1671 if (this.signum() == 0) // 0/y
1672 return zeroValueOf(preferredScale);
1673 else {
1674 /*
1675 * If the quotient this/divisor has a terminating decimal
1676 * expansion, the expansion can have no more than
1677 * (a.precision() + ceil(10*b.precision)/3) digits.
1678 * Therefore, create a MathContext object with this
1679 * precision and do a divide with the UNNECESSARY rounding
1680 * mode.
1681 */
1682 MathContext mc = new MathContext( (int)Math.min(this.precision() +
1683 (long)Math.ceil(10.0*divisor.precision()/3.0),
1684 Integer.MAX_VALUE),
1685 RoundingMode.UNNECESSARY);
1686 BigDecimal quotient;
1687 try {
1688 quotient = this.divide(divisor, mc);
1689 } catch (ArithmeticException e) {
1690 throw new ArithmeticException("Non-terminating decimal expansion; " +
1691 "no exact representable decimal result.");
1692 }
1693
1694 int quotientScale = quotient.scale();
1695
1696 // divide(BigDecimal, mc) tries to adjust the quotient to
1697 // the desired one by removing trailing zeros; since the
1698 // exact divide method does not have an explicit digit
1699 // limit, we can add zeros too.
1700 if (preferredScale > quotientScale)
1701 return quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1702
1703 return quotient;
1704 }
1705 }
1706
1707 /**
1708 * Returns a {@code BigDecimal} whose value is {@code (this /
1709 * divisor)}, with rounding according to the context settings.
1710 *
1711 * @param divisor value by which this {@code BigDecimal} is to be divided.
1712 * @param mc the context to use.
1713 * @return {@code this / divisor}, rounded as necessary.
1714 * @throws ArithmeticException if the result is inexact but the
1715 * rounding mode is {@code UNNECESSARY} or
1716 * {@code mc.precision == 0} and the quotient has a
1717 * non-terminating decimal expansion.
1718 * @since 1.5
1719 */
1720 public BigDecimal divide(BigDecimal divisor, MathContext mc) {
1721 int mcp = mc.precision;
1722 if (mcp == 0)
1723 return divide(divisor);
1724
1725 BigDecimal dividend = this;
1726 long preferredScale = (long)dividend.scale - divisor.scale;
1727 // Now calculate the answer. We use the existing
1728 // divide-and-round method, but as this rounds to scale we have
1729 // to normalize the values here to achieve the desired result.
1730 // For x/y we first handle y=0 and x=0, and then normalize x and
1731 // y to give x' and y' with the following constraints:
1732 // (a) 0.1 <= x' < 1
1733 // (b) x' <= y' < 10*x'
1734 // Dividing x'/y' with the required scale set to mc.precision then
1735 // will give a result in the range 0.1 to 1 rounded to exactly
1736 // the right number of digits (except in the case of a result of
1737 // 1.000... which can arise when x=y, or when rounding overflows
1738 // The 1.000... case will reduce properly to 1.
1739 if (divisor.signum() == 0) { // x/0
1740 if (dividend.signum() == 0) // 0/0
1741 throw new ArithmeticException("Division undefined"); // NaN
1742 throw new ArithmeticException("Division by zero");
1743 }
1744 if (dividend.signum() == 0) // 0/y
1745 return zeroValueOf(saturateLong(preferredScale));
1746 int xscale = dividend.precision();
1747 int yscale = divisor.precision();
1748 if(dividend.intCompact!=INFLATED) {
1749 if(divisor.intCompact!=INFLATED) {
1750 return divide(dividend.intCompact, xscale, divisor.intCompact, yscale, preferredScale, mc);
1751 } else {
1752 return divide(dividend.intCompact, xscale, divisor.intVal, yscale, preferredScale, mc);
1753 }
1754 } else {
1755 if(divisor.intCompact!=INFLATED) {
1756 return divide(dividend.intVal, xscale, divisor.intCompact, yscale, preferredScale, mc);
1757 } else {
1758 return divide(dividend.intVal, xscale, divisor.intVal, yscale, preferredScale, mc);
1759 }
1760 }
1761 }
1762
1763 /**
1764 * Returns a {@code BigDecimal} whose value is the integer part
1765 * of the quotient {@code (this / divisor)} rounded down. The
1766 * preferred scale of the result is {@code (this.scale() -
1767 * divisor.scale())}.
1768 *
1769 * @param divisor value by which this {@code BigDecimal} is to be divided.
1770 * @return The integer part of {@code this / divisor}.
1771 * @throws ArithmeticException if {@code divisor==0}
1772 * @since 1.5
1773 */
1774 public BigDecimal divideToIntegralValue(BigDecimal divisor) {
1775 // Calculate preferred scale
1776 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1777 if (this.compareMagnitude(divisor) < 0) {
1778 // much faster when this << divisor
1779 return zeroValueOf(preferredScale);
1780 }
1781
1782 if (this.signum() == 0 && divisor.signum() != 0)
1783 return this.setScale(preferredScale, ROUND_UNNECESSARY);
1784
1785 // Perform a divide with enough digits to round to a correct
1786 // integer value; then remove any fractional digits
1787
1788 int maxDigits = (int)Math.min(this.precision() +
1789 (long)Math.ceil(10.0*divisor.precision()/3.0) +
1790 Math.abs((long)this.scale() - divisor.scale()) + 2,
1791 Integer.MAX_VALUE);
1792 BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits,
1793 RoundingMode.DOWN));
1794 if (quotient.scale > 0) {
1795 quotient = quotient.setScale(0, RoundingMode.DOWN);
1796 quotient = stripZerosToMatchScale(quotient.intVal, quotient.intCompact, quotient.scale, preferredScale);
1797 }
1798
1799 if (quotient.scale < preferredScale) {
1800 // pad with zeros if necessary
1801 quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1802 }
1803
1804 return quotient;
1805 }
1806
1807 /**
1808 * Returns a {@code BigDecimal} whose value is the integer part
1809 * of {@code (this / divisor)}. Since the integer part of the
1810 * exact quotient does not depend on the rounding mode, the
1811 * rounding mode does not affect the values returned by this
1812 * method. The preferred scale of the result is
1813 * {@code (this.scale() - divisor.scale())}. An
1814 * {@code ArithmeticException} is thrown if the integer part of
1815 * the exact quotient needs more than {@code mc.precision}
1816 * digits.
1817 *
1818 * @param divisor value by which this {@code BigDecimal} is to be divided.
1819 * @param mc the context to use.
1820 * @return The integer part of {@code this / divisor}.
1821 * @throws ArithmeticException if {@code divisor==0}
1822 * @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result
1823 * requires a precision of more than {@code mc.precision} digits.
1824 * @since 1.5
1825 * @author Joseph D. Darcy
1826 */
1827 public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) {
1828 if (mc.precision == 0 || // exact result
1829 (this.compareMagnitude(divisor) < 0)) // zero result
1830 return divideToIntegralValue(divisor);
1831
1832 // Calculate preferred scale
1833 int preferredScale = saturateLong((long)this.scale - divisor.scale);
1834
1835 /*
1836 * Perform a normal divide to mc.precision digits. If the
1837 * remainder has absolute value less than the divisor, the
1838 * integer portion of the quotient fits into mc.precision
1839 * digits. Next, remove any fractional digits from the
1840 * quotient and adjust the scale to the preferred value.
1841 */
1842 BigDecimal result = this.divide(divisor, new MathContext(mc.precision, RoundingMode.DOWN));
1843
1844 if (result.scale() < 0) {
1845 /*
1846 * Result is an integer. See if quotient represents the
1847 * full integer portion of the exact quotient; if it does,
1848 * the computed remainder will be less than the divisor.
1849 */
1850 BigDecimal product = result.multiply(divisor);
1851 // If the quotient is the full integer value,
1852 // |dividend-product| < |divisor|.
1853 if (this.subtract(product).compareMagnitude(divisor) >= 0) {
1854 throw new ArithmeticException("Division impossible");
1855 }
1856 } else if (result.scale() > 0) {
1857 /*
1858 * Integer portion of quotient will fit into precision
1859 * digits; recompute quotient to scale 0 to avoid double
1860 * rounding and then try to adjust, if necessary.
1861 */
1862 result = result.setScale(0, RoundingMode.DOWN);
1863 }
1864 // else result.scale() == 0;
1865
1866 int precisionDiff;
1867 if ((preferredScale > result.scale()) &&
1868 (precisionDiff = mc.precision - result.precision()) > 0) {
1869 return result.setScale(result.scale() +
1870 Math.min(precisionDiff, preferredScale - result.scale) );
1871 } else {
1872 return stripZerosToMatchScale(result.intVal,result.intCompact,result.scale,preferredScale);
1873 }
1874 }
1875
1876 /**
1877 * Returns a {@code BigDecimal} whose value is {@code (this % divisor)}.
1878 *
1879 * <p>The remainder is given by
1880 * {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}.
1881 * Note that this is not the modulo operation (the result can be
1882 * negative).
1883 *
1884 * @param divisor value by which this {@code BigDecimal} is to be divided.
1885 * @return {@code this % divisor}.
1886 * @throws ArithmeticException if {@code divisor==0}
1887 * @since 1.5
1888 */
1889 public BigDecimal remainder(BigDecimal divisor) {
1890 BigDecimal divrem[] = this.divideAndRemainder(divisor);
1891 return divrem[1];
1892 }
1893
1894
1895 /**
1896 * Returns a {@code BigDecimal} whose value is {@code (this %
1897 * divisor)}, with rounding according to the context settings.
1898 * The {@code MathContext} settings affect the implicit divide
1899 * used to compute the remainder. The remainder computation
1900 * itself is by definition exact. Therefore, the remainder may
1901 * contain more than {@code mc.getPrecision()} digits.
1902 *
1903 * <p>The remainder is given by
1904 * {@code this.subtract(this.divideToIntegralValue(divisor,
1905 * mc).multiply(divisor))}. Note that this is not the modulo
1906 * operation (the result can be negative).
1907 *
1908 * @param divisor value by which this {@code BigDecimal} is to be divided.
1909 * @param mc the context to use.
1910 * @return {@code this % divisor}, rounded as necessary.
1911 * @throws ArithmeticException if {@code divisor==0}
1912 * @throws ArithmeticException if the result is inexact but the
1913 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1914 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1915 * require a precision of more than {@code mc.precision} digits.
1916 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1917 * @since 1.5
1918 */
1919 public BigDecimal remainder(BigDecimal divisor, MathContext mc) {
1920 BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
1921 return divrem[1];
1922 }
1923
1924 /**
1925 * Returns a two-element {@code BigDecimal} array containing the
1926 * result of {@code divideToIntegralValue} followed by the result of
1927 * {@code remainder} on the two operands.
1928 *
1929 * <p>Note that if both the integer quotient and remainder are
1930 * needed, this method is faster than using the
1931 * {@code divideToIntegralValue} and {@code remainder} methods
1932 * separately because the division need only be carried out once.
1933 *
1934 * @param divisor value by which this {@code BigDecimal} is to be divided,
1935 * and the remainder computed.
1936 * @return a two element {@code BigDecimal} array: the quotient
1937 * (the result of {@code divideToIntegralValue}) is the initial element
1938 * and the remainder is the final element.
1939 * @throws ArithmeticException if {@code divisor==0}
1940 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1941 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1942 * @since 1.5
1943 */
1944 public BigDecimal[] divideAndRemainder(BigDecimal divisor) {
1945 // we use the identity x = i * y + r to determine r
1946 BigDecimal[] result = new BigDecimal[2];
1947
1948 result[0] = this.divideToIntegralValue(divisor);
1949 result[1] = this.subtract(result[0].multiply(divisor));
1950 return result;
1951 }
1952
1953 /**
1954 * Returns a two-element {@code BigDecimal} array containing the
1955 * result of {@code divideToIntegralValue} followed by the result of
1956 * {@code remainder} on the two operands calculated with rounding
1957 * according to the context settings.
1958 *
1959 * <p>Note that if both the integer quotient and remainder are
1960 * needed, this method is faster than using the
1961 * {@code divideToIntegralValue} and {@code remainder} methods
1962 * separately because the division need only be carried out once.
1963 *
1964 * @param divisor value by which this {@code BigDecimal} is to be divided,
1965 * and the remainder computed.
1966 * @param mc the context to use.
1967 * @return a two element {@code BigDecimal} array: the quotient
1968 * (the result of {@code divideToIntegralValue}) is the
1969 * initial element and the remainder is the final element.
1970 * @throws ArithmeticException if {@code divisor==0}
1971 * @throws ArithmeticException if the result is inexact but the
1972 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1973 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1974 * require a precision of more than {@code mc.precision} digits.
1975 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1976 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1977 * @since 1.5
1978 */
1979 public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) {
1980 if (mc.precision == 0)
1981 return divideAndRemainder(divisor);
1982
1983 BigDecimal[] result = new BigDecimal[2];
1984 BigDecimal lhs = this;
1985
1986 result[0] = lhs.divideToIntegralValue(divisor, mc);
1987 result[1] = lhs.subtract(result[0].multiply(divisor));
1988 return result;
1989 }
1990
1991 /**
1992 * Returns a {@code BigDecimal} whose value is
1993 * <tt>(this<sup>n</sup>)</tt>, The power is computed exactly, to
1994 * unlimited precision.
1995 *
1996 * <p>The parameter {@code n} must be in the range 0 through
1997 * 999999999, inclusive. {@code ZERO.pow(0)} returns {@link
1998 * #ONE}.
1999 *
2000 * Note that future releases may expand the allowable exponent
2001 * range of this method.
2002 *
2003 * @param n power to raise this {@code BigDecimal} to.
2004 * @return <tt>this<sup>n</sup></tt>
2005 * @throws ArithmeticException if {@code n} is out of range.
2006 * @since 1.5
2007 */
2008 public BigDecimal pow(int n) {
2009 if (n < 0 || n > 999999999)
2010 throw new ArithmeticException("Invalid operation");
2011 // No need to calculate pow(n) if result will over/underflow.
2012 // Don't attempt to support "supernormal" numbers.
2013 int newScale = checkScale((long)scale * n);
2014 return new BigDecimal(this.inflated().pow(n), newScale);
2015 }
2016
2017
2018 /**
2019 * Returns a {@code BigDecimal} whose value is
2020 * <tt>(this<sup>n</sup>)</tt>. The current implementation uses
2021 * the core algorithm defined in ANSI standard X3.274-1996 with
2022 * rounding according to the context settings. In general, the
2023 * returned numerical value is within two ulps of the exact
2024 * numerical value for the chosen precision. Note that future
2025 * releases may use a different algorithm with a decreased
2026 * allowable error bound and increased allowable exponent range.
2027 *
2028 * <p>The X3.274-1996 algorithm is:
2029 *
2030 * <ul>
2031 * <li> An {@code ArithmeticException} exception is thrown if
2032 * <ul>
2033 * <li>{@code abs(n) > 999999999}
2034 * <li>{@code mc.precision == 0} and {@code n < 0}
2035 * <li>{@code mc.precision > 0} and {@code n} has more than
2036 * {@code mc.precision} decimal digits
2037 * </ul>
2038 *
2039 * <li> if {@code n} is zero, {@link #ONE} is returned even if
2040 * {@code this} is zero, otherwise
2041 * <ul>
2042 * <li> if {@code n} is positive, the result is calculated via
2043 * the repeated squaring technique into a single accumulator.
2044 * The individual multiplications with the accumulator use the
2045 * same math context settings as in {@code mc} except for a
2046 * precision increased to {@code mc.precision + elength + 1}
2047 * where {@code elength} is the number of decimal digits in
2048 * {@code n}.
2049 *
2050 * <li> if {@code n} is negative, the result is calculated as if
2051 * {@code n} were positive; this value is then divided into one
2052 * using the working precision specified above.
2053 *
2054 * <li> The final value from either the positive or negative case
2055 * is then rounded to the destination precision.
2056 * </ul>
2057 * </ul>
2058 *
2059 * @param n power to raise this {@code BigDecimal} to.
2060 * @param mc the context to use.
2061 * @return <tt>this<sup>n</sup></tt> using the ANSI standard X3.274-1996
2062 * algorithm
2063 * @throws ArithmeticException if the result is inexact but the
2064 * rounding mode is {@code UNNECESSARY}, or {@code n} is out
2065 * of range.
2066 * @since 1.5
2067 */
2068 public BigDecimal pow(int n, MathContext mc) {
2069 if (mc.precision == 0)
2070 return pow(n);
2071 if (n < -999999999 || n > 999999999)
2072 throw new ArithmeticException("Invalid operation");
2073 if (n == 0)
2074 return ONE; // x**0 == 1 in X3.274
2075 BigDecimal lhs = this;
2076 MathContext workmc = mc; // working settings
2077 int mag = Math.abs(n); // magnitude of n
2078 if (mc.precision > 0) {
2079 int elength = longDigitLength(mag); // length of n in digits
2080 if (elength > mc.precision) // X3.274 rule
2081 throw new ArithmeticException("Invalid operation");
2082 workmc = new MathContext(mc.precision + elength + 1,
2083 mc.roundingMode);
2084 }
2085 // ready to carry out power calculation...
2086 BigDecimal acc = ONE; // accumulator
2087 boolean seenbit = false; // set once we've seen a 1-bit
2088 for (int i=1;;i++) { // for each bit [top bit ignored]
2089 mag += mag; // shift left 1 bit
2090 if (mag < 0) { // top bit is set
2091 seenbit = true; // OK, we're off
2092 acc = acc.multiply(lhs, workmc); // acc=acc*x
2093 }
2094 if (i == 31)
2095 break; // that was the last bit
2096 if (seenbit)
2097 acc=acc.multiply(acc, workmc); // acc=acc*acc [square]
2098 // else (!seenbit) no point in squaring ONE
2099 }
2100 // if negative n, calculate the reciprocal using working precision
2101 if (n < 0) // [hence mc.precision>0]
2102 acc=ONE.divide(acc, workmc);
2103 // round to final precision and strip zeros
2104 return doRound(acc, mc);
2105 }
2106
2107 /**
2108 * Returns a {@code BigDecimal} whose value is the absolute value
2109 * of this {@code BigDecimal}, and whose scale is
2110 * {@code this.scale()}.
2111 *
2112 * @return {@code abs(this)}
2113 */
2114 public BigDecimal abs() {
2115 return (signum() < 0 ? negate() : this);
2116 }
2117
2118 /**
2119 * Returns a {@code BigDecimal} whose value is the absolute value
2120 * of this {@code BigDecimal}, with rounding according to the
2121 * context settings.
2122 *
2123 * @param mc the context to use.
2124 * @return {@code abs(this)}, rounded as necessary.
2125 * @throws ArithmeticException if the result is inexact but the
2126 * rounding mode is {@code UNNECESSARY}.
2127 * @since 1.5
2128 */
2129 public BigDecimal abs(MathContext mc) {
2130 return (signum() < 0 ? negate(mc) : plus(mc));
2131 }
2132
2133 /**
2134 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2135 * and whose scale is {@code this.scale()}.
2136 *
2137 * @return {@code -this}.
2138 */
2139 public BigDecimal negate() {
2140 if (intCompact == INFLATED) {
2141 return new BigDecimal(intVal.negate(), INFLATED, scale, precision);
2142 } else {
2143 return valueOf(-intCompact, scale, precision);
2144 }
2145 }
2146
2147 /**
2148 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2149 * with rounding according to the context settings.
2150 *
2151 * @param mc the context to use.
2152 * @return {@code -this}, rounded as necessary.
2153 * @throws ArithmeticException if the result is inexact but the
2154 * rounding mode is {@code UNNECESSARY}.
2155 * @since 1.5
2156 */
2157 public BigDecimal negate(MathContext mc) {
2158 return negate().plus(mc);
2159 }
2160
2161 /**
2162 * Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose
2163 * scale is {@code this.scale()}.
2164 *
2165 * <p>This method, which simply returns this {@code BigDecimal}
2166 * is included for symmetry with the unary minus method {@link
2167 * #negate()}.
2168 *
2169 * @return {@code this}.
2170 * @see #negate()
2171 * @since 1.5
2172 */
2173 public BigDecimal plus() {
2174 return this;
2175 }
2176
2177 /**
2178 * Returns a {@code BigDecimal} whose value is {@code (+this)},
2179 * with rounding according to the context settings.
2180 *
2181 * <p>The effect of this method is identical to that of the {@link
2182 * #round(MathContext)} method.
2183 *
2184 * @param mc the context to use.
2185 * @return {@code this}, rounded as necessary. A zero result will
2186 * have a scale of 0.
2187 * @throws ArithmeticException if the result is inexact but the
2188 * rounding mode is {@code UNNECESSARY}.
2189 * @see #round(MathContext)
2190 * @since 1.5
2191 */
2192 public BigDecimal plus(MathContext mc) {
2193 if (mc.precision == 0) // no rounding please
2194 return this;
2195 return doRound(this, mc);
2196 }
2197
2198 /**
2199 * Returns the signum function of this {@code BigDecimal}.
2200 *
2201 * @return -1, 0, or 1 as the value of this {@code BigDecimal}
2202 * is negative, zero, or positive.
2203 */
2204 public int signum() {
2205 return (intCompact != INFLATED)?
2206 Long.signum(intCompact):
2207 intVal.signum();
2208 }
2209
2210 /**
2211 * Returns the <i>scale</i> of this {@code BigDecimal}. If zero
2212 * or positive, the scale is the number of digits to the right of
2213 * the decimal point. If negative, the unscaled value of the
2214 * number is multiplied by ten to the power of the negation of the
2215 * scale. For example, a scale of {@code -3} means the unscaled
2216 * value is multiplied by 1000.
2217 *
2218 * @return the scale of this {@code BigDecimal}.
2219 */
2220 public int scale() {
2221 return scale;
2222 }
2223
2224 /**
2225 * Returns the <i>precision</i> of this {@code BigDecimal}. (The
2226 * precision is the number of digits in the unscaled value.)
2227 *
2228 * <p>The precision of a zero value is 1.
2229 *
2230 * @return the precision of this {@code BigDecimal}.
2231 * @since 1.5
2232 */
2233 public int precision() {
2234 int result = precision;
2235 if (result == 0) {
2236 long s = intCompact;
2237 if (s != INFLATED)
2238 result = longDigitLength(s);
2239 else
2240 result = bigDigitLength(intVal);
2241 precision = result;
2242 }
2243 return result;
2244 }
2245
2246
2247 /**
2248 * Returns a {@code BigInteger} whose value is the <i>unscaled
2249 * value</i> of this {@code BigDecimal}. (Computes <tt>(this *
2250 * 10<sup>this.scale()</sup>)</tt>.)
2251 *
2252 * @return the unscaled value of this {@code BigDecimal}.
2253 * @since 1.2
2254 */
2255 public BigInteger unscaledValue() {
2256 return this.inflated();
2257 }
2258
2259 // Rounding Modes
2260
2261 /**
2262 * Rounding mode to round away from zero. Always increments the
2263 * digit prior to a nonzero discarded fraction. Note that this rounding
2264 * mode never decreases the magnitude of the calculated value.
2265 */
2266 public final static int ROUND_UP = 0;
2267
2268 /**
2269 * Rounding mode to round towards zero. Never increments the digit
2270 * prior to a discarded fraction (i.e., truncates). Note that this
2271 * rounding mode never increases the magnitude of the calculated value.
2272 */
2273 public final static int ROUND_DOWN = 1;
2274
2275 /**
2276 * Rounding mode to round towards positive infinity. If the
2277 * {@code BigDecimal} is positive, behaves as for
2278 * {@code ROUND_UP}; if negative, behaves as for
2279 * {@code ROUND_DOWN}. Note that this rounding mode never
2280 * decreases the calculated value.
2281 */
2282 public final static int ROUND_CEILING = 2;
2283
2284 /**
2285 * Rounding mode to round towards negative infinity. If the
2286 * {@code BigDecimal} is positive, behave as for
2287 * {@code ROUND_DOWN}; if negative, behave as for
2288 * {@code ROUND_UP}. Note that this rounding mode never
2289 * increases the calculated value.
2290 */
2291 public final static int ROUND_FLOOR = 3;
2292
2293 /**
2294 * Rounding mode to round towards {@literal "nearest neighbor"}
2295 * unless both neighbors are equidistant, in which case round up.
2296 * Behaves as for {@code ROUND_UP} if the discarded fraction is
2297 * ≥ 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note
2298 * that this is the rounding mode that most of us were taught in
2299 * grade school.
2300 */
2301 public final static int ROUND_HALF_UP = 4;
2302
2303 /**
2304 * Rounding mode to round towards {@literal "nearest neighbor"}
2305 * unless both neighbors are equidistant, in which case round
2306 * down. Behaves as for {@code ROUND_UP} if the discarded
2307 * fraction is {@literal >} 0.5; otherwise, behaves as for
2308 * {@code ROUND_DOWN}.
2309 */
2310 public final static int ROUND_HALF_DOWN = 5;
2311
2312 /**
2313 * Rounding mode to round towards the {@literal "nearest neighbor"}
2314 * unless both neighbors are equidistant, in which case, round
2315 * towards the even neighbor. Behaves as for
2316 * {@code ROUND_HALF_UP} if the digit to the left of the
2317 * discarded fraction is odd; behaves as for
2318 * {@code ROUND_HALF_DOWN} if it's even. Note that this is the
2319 * rounding mode that minimizes cumulative error when applied
2320 * repeatedly over a sequence of calculations.
2321 */
2322 public final static int ROUND_HALF_EVEN = 6;
2323
2324 /**
2325 * Rounding mode to assert that the requested operation has an exact
2326 * result, hence no rounding is necessary. If this rounding mode is
2327 * specified on an operation that yields an inexact result, an
2328 * {@code ArithmeticException} is thrown.
2329 */
2330 public final static int ROUND_UNNECESSARY = 7;
2331
2332
2333 // Scaling/Rounding Operations
2334
2335 /**
2336 * Returns a {@code BigDecimal} rounded according to the
2337 * {@code MathContext} settings. If the precision setting is 0 then
2338 * no rounding takes place.
2339 *
2340 * <p>The effect of this method is identical to that of the
2341 * {@link #plus(MathContext)} method.
2342 *
2343 * @param mc the context to use.
2344 * @return a {@code BigDecimal} rounded according to the
2345 * {@code MathContext} settings.
2346 * @throws ArithmeticException if the rounding mode is
2347 * {@code UNNECESSARY} and the
2348 * {@code BigDecimal} operation would require rounding.
2349 * @see #plus(MathContext)
2350 * @since 1.5
2351 */
2352 public BigDecimal round(MathContext mc) {
2353 return plus(mc);
2354 }
2355
2356 /**
2357 * Returns a {@code BigDecimal} whose scale is the specified
2358 * value, and whose unscaled value is determined by multiplying or
2359 * dividing this {@code BigDecimal}'s unscaled value by the
2360 * appropriate power of ten to maintain its overall value. If the
2361 * scale is reduced by the operation, the unscaled value must be
2362 * divided (rather than multiplied), and the value may be changed;
2363 * in this case, the specified rounding mode is applied to the
2364 * division.
2365 *
2366 * <p>Note that since BigDecimal objects are immutable, calls of
2367 * this method do <i>not</i> result in the original object being
2368 * modified, contrary to the usual convention of having methods
2369 * named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
2370 * Instead, {@code setScale} returns an object with the proper
2371 * scale; the returned object may or may not be newly allocated.
2372 *
2373 * @param newScale scale of the {@code BigDecimal} value to be returned.
2374 * @param roundingMode The rounding mode to apply.
2375 * @return a {@code BigDecimal} whose scale is the specified value,
2376 * and whose unscaled value is determined by multiplying or
2377 * dividing this {@code BigDecimal}'s unscaled value by the
2378 * appropriate power of ten to maintain its overall value.
2379 * @throws ArithmeticException if {@code roundingMode==UNNECESSARY}
2380 * and the specified scaling operation would require
2381 * rounding.
2382 * @see RoundingMode
2383 * @since 1.5
2384 */
2385 public BigDecimal setScale(int newScale, RoundingMode roundingMode) {
2386 return setScale(newScale, roundingMode.oldMode);
2387 }
2388
2389 /**
2390 * Returns a {@code BigDecimal} whose scale is the specified
2391 * value, and whose unscaled value is determined by multiplying or
2392 * dividing this {@code BigDecimal}'s unscaled value by the
2393 * appropriate power of ten to maintain its overall value. If the
2394 * scale is reduced by the operation, the unscaled value must be
2395 * divided (rather than multiplied), and the value may be changed;
2396 * in this case, the specified rounding mode is applied to the
2397 * division.
2398 *
2399 * <p>Note that since BigDecimal objects are immutable, calls of
2400 * this method do <i>not</i> result in the original object being
2401 * modified, contrary to the usual convention of having methods
2402 * named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
2403 * Instead, {@code setScale} returns an object with the proper
2404 * scale; the returned object may or may not be newly allocated.
2405 *
2406 * <p>The new {@link #setScale(int, RoundingMode)} method should
2407 * be used in preference to this legacy method.
2408 *
2409 * @param newScale scale of the {@code BigDecimal} value to be returned.
2410 * @param roundingMode The rounding mode to apply.
2411 * @return a {@code BigDecimal} whose scale is the specified value,
2412 * and whose unscaled value is determined by multiplying or
2413 * dividing this {@code BigDecimal}'s unscaled value by the
2414 * appropriate power of ten to maintain its overall value.
2415 * @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY}
2416 * and the specified scaling operation would require
2417 * rounding.
2418 * @throws IllegalArgumentException if {@code roundingMode} does not
2419 * represent a valid rounding mode.
2420 * @see #ROUND_UP
2421 * @see #ROUND_DOWN
2422 * @see #ROUND_CEILING
2423 * @see #ROUND_FLOOR
2424 * @see #ROUND_HALF_UP
2425 * @see #ROUND_HALF_DOWN
2426 * @see #ROUND_HALF_EVEN
2427 * @see #ROUND_UNNECESSARY
2428 */
2429 public BigDecimal setScale(int newScale, int roundingMode) {
2430 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
2431 throw new IllegalArgumentException("Invalid rounding mode");
2432
2433 int oldScale = this.scale;
2434 if (newScale == oldScale) // easy case
2435 return this;
2436 if (this.signum() == 0) // zero can have any scale
2437 return zeroValueOf(newScale);
2438 if(this.intCompact!=INFLATED) {
2439 long rs = this.intCompact;
2440 if (newScale > oldScale) {
2441 int raise = checkScale((long) newScale - oldScale);
2442 if ((rs = longMultiplyPowerTen(rs, raise)) != INFLATED) {
2443 return valueOf(rs,newScale);
2444 }
2445 BigInteger rb = bigMultiplyPowerTen(raise);
2446 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2447 } else {
2448 // newScale < oldScale -- drop some digits
2449 // Can't predict the precision due to the effect of rounding.
2450 int drop = checkScale((long) oldScale - newScale);
2451 if (drop < LONG_TEN_POWERS_TABLE.length) {
2452 return divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, newScale);
2453 } else {
2454 return divideAndRound(this.inflated(), bigTenToThe(drop), newScale, roundingMode, newScale);
2455 }
2456 }
2457 } else {
2458 if (newScale > oldScale) {
2459 int raise = checkScale((long) newScale - oldScale);
2460 BigInteger rb = bigMultiplyPowerTen(this.intVal,raise);
2461 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2462 } else {
2463 // newScale < oldScale -- drop some digits
2464 // Can't predict the precision due to the effect of rounding.
2465 int drop = checkScale((long) oldScale - newScale);
2466 if (drop < LONG_TEN_POWERS_TABLE.length)
2467 return divideAndRound(this.intVal, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode,
2468 newScale);
2469 else
2470 return divideAndRound(this.intVal, bigTenToThe(drop), newScale, roundingMode, newScale);
2471 }
2472 }
2473 }
2474
2475 /**
2476 * Returns a {@code BigDecimal} whose scale is the specified
2477 * value, and whose value is numerically equal to this
2478 * {@code BigDecimal}'s. Throws an {@code ArithmeticException}
2479 * if this is not possible.
2480 *
2481 * <p>This call is typically used to increase the scale, in which
2482 * case it is guaranteed that there exists a {@code BigDecimal}
2483 * of the specified scale and the correct value. The call can
2484 * also be used to reduce the scale if the caller knows that the
2485 * {@code BigDecimal} has sufficiently many zeros at the end of
2486 * its fractional part (i.e., factors of ten in its integer value)
2487 * to allow for the rescaling without changing its value.
2488 *
2489 * <p>This method returns the same result as the two-argument
2490 * versions of {@code setScale}, but saves the caller the trouble
2491 * of specifying a rounding mode in cases where it is irrelevant.
2492 *
2493 * <p>Note that since {@code BigDecimal} objects are immutable,
2494 * calls of this method do <i>not</i> result in the original
2495 * object being modified, contrary to the usual convention of
2496 * having methods named <tt>set<i>X</i></tt> mutate field
2497 * <i>{@code X}</i>. Instead, {@code setScale} returns an
2498 * object with the proper scale; the returned object may or may
2499 * not be newly allocated.
2500 *
2501 * @param newScale scale of the {@code BigDecimal} value to be returned.
2502 * @return a {@code BigDecimal} whose scale is the specified value, and
2503 * whose unscaled value is determined by multiplying or dividing
2504 * this {@code BigDecimal}'s unscaled value by the appropriate
2505 * power of ten to maintain its overall value.
2506 * @throws ArithmeticException if the specified scaling operation would
2507 * require rounding.
2508 * @see #setScale(int, int)
2509 * @see #setScale(int, RoundingMode)
2510 */
2511 public BigDecimal setScale(int newScale) {
2512 return setScale(newScale, ROUND_UNNECESSARY);
2513 }
2514
2515 // Decimal Point Motion Operations
2516
2517 /**
2518 * Returns a {@code BigDecimal} which is equivalent to this one
2519 * with the decimal point moved {@code n} places to the left. If
2520 * {@code n} is non-negative, the call merely adds {@code n} to
2521 * the scale. If {@code n} is negative, the call is equivalent
2522 * to {@code movePointRight(-n)}. The {@code BigDecimal}
2523 * returned by this call has value <tt>(this ×
2524 * 10<sup>-n</sup>)</tt> and scale {@code max(this.scale()+n,
2525 * 0)}.
2526 *
2527 * @param n number of places to move the decimal point to the left.
2528 * @return a {@code BigDecimal} which is equivalent to this one with the
2529 * decimal point moved {@code n} places to the left.
2530 * @throws ArithmeticException if scale overflows.
2531 */
2532 public BigDecimal movePointLeft(int n) {
2533 // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE
2534 int newScale = checkScale((long)scale + n);
2535 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2536 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2537 }
2538
2539 /**
2540 * Returns a {@code BigDecimal} which is equivalent to this one
2541 * with the decimal point moved {@code n} places to the right.
2542 * If {@code n} is non-negative, the call merely subtracts
2543 * {@code n} from the scale. If {@code n} is negative, the call
2544 * is equivalent to {@code movePointLeft(-n)}. The
2545 * {@code BigDecimal} returned by this call has value <tt>(this
2546 * × 10<sup>n</sup>)</tt> and scale {@code max(this.scale()-n,
2547 * 0)}.
2548 *
2549 * @param n number of places to move the decimal point to the right.
2550 * @return a {@code BigDecimal} which is equivalent to this one
2551 * with the decimal point moved {@code n} places to the right.
2552 * @throws ArithmeticException if scale overflows.
2553 */
2554 public BigDecimal movePointRight(int n) {
2555 // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE
2556 int newScale = checkScale((long)scale - n);
2557 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2558 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2559 }
2560
2561 /**
2562 * Returns a BigDecimal whose numerical value is equal to
2563 * ({@code this} * 10<sup>n</sup>). The scale of
2564 * the result is {@code (this.scale() - n)}.
2565 *
2566 * @param n the exponent power of ten to scale by
2567 * @return a BigDecimal whose numerical value is equal to
2568 * ({@code this} * 10<sup>n</sup>)
2569 * @throws ArithmeticException if the scale would be
2570 * outside the range of a 32-bit integer.
2571 *
2572 * @since 1.5
2573 */
2574 public BigDecimal scaleByPowerOfTen(int n) {
2575 return new BigDecimal(intVal, intCompact,
2576 checkScale((long)scale - n), precision);
2577 }
2578
2579 /**
2580 * Returns a {@code BigDecimal} which is numerically equal to
2581 * this one but with any trailing zeros removed from the
2582 * representation. For example, stripping the trailing zeros from
2583 * the {@code BigDecimal} value {@code 600.0}, which has
2584 * [{@code BigInteger}, {@code scale}] components equals to
2585 * [6000, 1], yields {@code 6E2} with [{@code BigInteger},
2586 * {@code scale}] components equals to [6, -2]. If
2587 * this BigDecimal is numerically equal to zero, then
2588 * {@code BigDecimal.ZERO} is returned.
2589 *
2590 * @return a numerically equal {@code BigDecimal} with any
2591 * trailing zeros removed.
2592 * @since 1.5
2593 */
2594 public BigDecimal stripTrailingZeros() {
2595 if (intCompact == 0 || (intVal != null && intVal.signum() == 0)) {
2596 return BigDecimal.ZERO;
2597 } else if (intCompact != INFLATED) {
2598 return createAndStripZerosToMatchScale(intCompact, scale, Long.MIN_VALUE);
2599 } else {
2600 return createAndStripZerosToMatchScale(intVal, scale, Long.MIN_VALUE);
2601 }
2602 }
2603
2604 // Comparison Operations
2605
2606 /**
2607 * Compares this {@code BigDecimal} with the specified
2608 * {@code BigDecimal}. Two {@code BigDecimal} objects that are
2609 * equal in value but have a different scale (like 2.0 and 2.00)
2610 * are considered equal by this method. This method is provided
2611 * in preference to individual methods for each of the six boolean
2612 * comparison operators ({@literal <}, ==,
2613 * {@literal >}, {@literal >=}, !=, {@literal <=}). The
2614 * suggested idiom for performing these comparisons is:
2615 * {@code (x.compareTo(y)} <<i>op</i>> {@code 0)}, where
2616 * <<i>op</i>> is one of the six comparison operators.
2617 *
2618 * @param val {@code BigDecimal} to which this {@code BigDecimal} is
2619 * to be compared.
2620 * @return -1, 0, or 1 as this {@code BigDecimal} is numerically
2621 * less than, equal to, or greater than {@code val}.
2622 */
2623 public int compareTo(BigDecimal val) {
2624 // Quick path for equal scale and non-inflated case.
2625 if (scale == val.scale) {
2626 long xs = intCompact;
2627 long ys = val.intCompact;
2628 if (xs != INFLATED && ys != INFLATED)
2629 return xs != ys ? ((xs > ys) ? 1 : -1) : 0;
2630 }
2631 int xsign = this.signum();
2632 int ysign = val.signum();
2633 if (xsign != ysign)
2634 return (xsign > ysign) ? 1 : -1;
2635 if (xsign == 0)
2636 return 0;
2637 int cmp = compareMagnitude(val);
2638 return (xsign > 0) ? cmp : -cmp;
2639 }
2640
2641 /**
2642 * Version of compareTo that ignores sign.
2643 */
2644 private int compareMagnitude(BigDecimal val) {
2645 // Match scales, avoid unnecessary inflation
2646 long ys = val.intCompact;
2647 long xs = this.intCompact;
2648 if (xs == 0)
2649 return (ys == 0) ? 0 : -1;
2650 if (ys == 0)
2651 return 1;
2652
2653 long sdiff = (long)this.scale - val.scale;
2654 if (sdiff != 0) {
2655 // Avoid matching scales if the (adjusted) exponents differ
2656 long xae = (long)this.precision() - this.scale; // [-1]
2657 long yae = (long)val.precision() - val.scale; // [-1]
2658 if (xae < yae)
2659 return -1;
2660 if (xae > yae)
2661 return 1;
2662 BigInteger rb = null;
2663 if (sdiff < 0) {
2664 // The cases sdiff <= Integer.MIN_VALUE intentionally fall through.
2665 if ( sdiff > Integer.MIN_VALUE &&
2666 (xs == INFLATED ||
2667 (xs = longMultiplyPowerTen(xs, (int)-sdiff)) == INFLATED) &&
2668 ys == INFLATED) {
2669 rb = bigMultiplyPowerTen((int)-sdiff);
2670 return rb.compareMagnitude(val.intVal);
2671 }
2672 } else { // sdiff > 0
2673 // The cases sdiff > Integer.MAX_VALUE intentionally fall through.
2674 if ( sdiff <= Integer.MAX_VALUE &&
2675 (ys == INFLATED ||
2676 (ys = longMultiplyPowerTen(ys, (int)sdiff)) == INFLATED) &&
2677 xs == INFLATED) {
2678 rb = val.bigMultiplyPowerTen((int)sdiff);
2679 return this.intVal.compareMagnitude(rb);
2680 }
2681 }
2682 }
2683 if (xs != INFLATED)
2684 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
2685 else if (ys != INFLATED)
2686 return 1;
2687 else
2688 return this.intVal.compareMagnitude(val.intVal);
2689 }
2690
2691 /**
2692 * Compares this {@code BigDecimal} with the specified
2693 * {@code Object} for equality. Unlike {@link
2694 * #compareTo(BigDecimal) compareTo}, this method considers two
2695 * {@code BigDecimal} objects equal only if they are equal in
2696 * value and scale (thus 2.0 is not equal to 2.00 when compared by
2697 * this method).
2698 *
2699 * @param x {@code Object} to which this {@code BigDecimal} is
2700 * to be compared.
2701 * @return {@code true} if and only if the specified {@code Object} is a
2702 * {@code BigDecimal} whose value and scale are equal to this
2703 * {@code BigDecimal}'s.
2704 * @see #compareTo(java.math.BigDecimal)
2705 * @see #hashCode
2706 */
2707 @Override
2708 public boolean equals(Object x) {
2709 if (!(x instanceof BigDecimal))
2710 return false;
2711 BigDecimal xDec = (BigDecimal) x;
2712 if (x == this)
2713 return true;
2714 if (scale != xDec.scale)
2715 return false;
2716 long s = this.intCompact;
2717 long xs = xDec.intCompact;
2718 if (s != INFLATED) {
2719 if (xs == INFLATED)
2720 xs = compactValFor(xDec.intVal);
2721 return xs == s;
2722 } else if (xs != INFLATED)
2723 return xs == compactValFor(this.intVal);
2724
2725 return this.inflated().equals(xDec.inflated());
2726 }
2727
2728 /**
2729 * Returns the minimum of this {@code BigDecimal} and
2730 * {@code val}.
2731 *
2732 * @param val value with which the minimum is to be computed.
2733 * @return the {@code BigDecimal} whose value is the lesser of this
2734 * {@code BigDecimal} and {@code val}. If they are equal,
2735 * as defined by the {@link #compareTo(BigDecimal) compareTo}
2736 * method, {@code this} is returned.
2737 * @see #compareTo(java.math.BigDecimal)
2738 */
2739 public BigDecimal min(BigDecimal val) {
2740 return (compareTo(val) <= 0 ? this : val);
2741 }
2742
2743 /**
2744 * Returns the maximum of this {@code BigDecimal} and {@code val}.
2745 *
2746 * @param val value with which the maximum is to be computed.
2747 * @return the {@code BigDecimal} whose value is the greater of this
2748 * {@code BigDecimal} and {@code val}. If they are equal,
2749 * as defined by the {@link #compareTo(BigDecimal) compareTo}
2750 * method, {@code this} is returned.
2751 * @see #compareTo(java.math.BigDecimal)
2752 */
2753 public BigDecimal max(BigDecimal val) {
2754 return (compareTo(val) >= 0 ? this : val);
2755 }
2756
2757 // Hash Function
2758
2759 /**
2760 * Returns the hash code for this {@code BigDecimal}. Note that
2761 * two {@code BigDecimal} objects that are numerically equal but
2762 * differ in scale (like 2.0 and 2.00) will generally <i>not</i>
2763 * have the same hash code.
2764 *
2765 * @return hash code for this {@code BigDecimal}.
2766 * @see #equals(Object)
2767 */
2768 @Override
2769 public int hashCode() {
2770 if (intCompact != INFLATED) {
2771 long val2 = (intCompact < 0)? -intCompact : intCompact;
2772 int temp = (int)( ((int)(val2 >>> 32)) * 31 +
2773 (val2 & LONG_MASK));
2774 return 31*((intCompact < 0) ?-temp:temp) + scale;
2775 } else
2776 return 31*intVal.hashCode() + scale;
2777 }
2778
2779 // Format Converters
2780
2781 /**
2782 * Returns the string representation of this {@code BigDecimal},
2783 * using scientific notation if an exponent is needed.
2784 *
2785 * <p>A standard canonical string form of the {@code BigDecimal}
2786 * is created as though by the following steps: first, the
2787 * absolute value of the unscaled value of the {@code BigDecimal}
2788 * is converted to a string in base ten using the characters
2789 * {@code '0'} through {@code '9'} with no leading zeros (except
2790 * if its value is zero, in which case a single {@code '0'}
2791 * character is used).
2792 *
2793 * <p>Next, an <i>adjusted exponent</i> is calculated; this is the
2794 * negated scale, plus the number of characters in the converted
2795 * unscaled value, less one. That is,
2796 * {@code -scale+(ulength-1)}, where {@code ulength} is the
2797 * length of the absolute value of the unscaled value in decimal
2798 * digits (its <i>precision</i>).
2799 *
2800 * <p>If the scale is greater than or equal to zero and the
2801 * adjusted exponent is greater than or equal to {@code -6}, the
2802 * number will be converted to a character form without using
2803 * exponential notation. In this case, if the scale is zero then
2804 * no decimal point is added and if the scale is positive a
2805 * decimal point will be inserted with the scale specifying the
2806 * number of characters to the right of the decimal point.
2807 * {@code '0'} characters are added to the left of the converted
2808 * unscaled value as necessary. If no character precedes the
2809 * decimal point after this insertion then a conventional
2810 * {@code '0'} character is prefixed.
2811 *
2812 * <p>Otherwise (that is, if the scale is negative, or the
2813 * adjusted exponent is less than {@code -6}), the number will be
2814 * converted to a character form using exponential notation. In
2815 * this case, if the converted {@code BigInteger} has more than
2816 * one digit a decimal point is inserted after the first digit.
2817 * An exponent in character form is then suffixed to the converted
2818 * unscaled value (perhaps with inserted decimal point); this
2819 * comprises the letter {@code 'E'} followed immediately by the
2820 * adjusted exponent converted to a character form. The latter is
2821 * in base ten, using the characters {@code '0'} through
2822 * {@code '9'} with no leading zeros, and is always prefixed by a
2823 * sign character {@code '-'} (<tt>'\u002D'</tt>) if the
2824 * adjusted exponent is negative, {@code '+'}
2825 * (<tt>'\u002B'</tt>) otherwise).
2826 *
2827 * <p>Finally, the entire string is prefixed by a minus sign
2828 * character {@code '-'} (<tt>'\u002D'</tt>) if the unscaled
2829 * value is less than zero. No sign character is prefixed if the
2830 * unscaled value is zero or positive.
2831 *
2832 * <p><b>Examples:</b>
2833 * <p>For each representation [<i>unscaled value</i>, <i>scale</i>]
2834 * on the left, the resulting string is shown on the right.
2835 * <pre>
2836 * [123,0] "123"
2837 * [-123,0] "-123"
2838 * [123,-1] "1.23E+3"
2839 * [123,-3] "1.23E+5"
2840 * [123,1] "12.3"
2841 * [123,5] "0.00123"
2842 * [123,10] "1.23E-8"
2843 * [-123,12] "-1.23E-10"
2844 * </pre>
2845 *
2846 * <b>Notes:</b>
2847 * <ol>
2848 *
2849 * <li>There is a one-to-one mapping between the distinguishable
2850 * {@code BigDecimal} values and the result of this conversion.
2851 * That is, every distinguishable {@code BigDecimal} value
2852 * (unscaled value and scale) has a unique string representation
2853 * as a result of using {@code toString}. If that string
2854 * representation is converted back to a {@code BigDecimal} using
2855 * the {@link #BigDecimal(String)} constructor, then the original
2856 * value will be recovered.
2857 *
2858 * <li>The string produced for a given number is always the same;
2859 * it is not affected by locale. This means that it can be used
2860 * as a canonical string representation for exchanging decimal
2861 * data, or as a key for a Hashtable, etc. Locale-sensitive
2862 * number formatting and parsing is handled by the {@link
2863 * java.text.NumberFormat} class and its subclasses.
2864 *
2865 * <li>The {@link #toEngineeringString} method may be used for
2866 * presenting numbers with exponents in engineering notation, and the
2867 * {@link #setScale(int,RoundingMode) setScale} method may be used for
2868 * rounding a {@code BigDecimal} so it has a known number of digits after
2869 * the decimal point.
2870 *
2871 * <li>The digit-to-character mapping provided by
2872 * {@code Character.forDigit} is used.
2873 *
2874 * </ol>
2875 *
2876 * @return string representation of this {@code BigDecimal}.
2877 * @see Character#forDigit
2878 * @see #BigDecimal(java.lang.String)
2879 */
2880 @Override
2881 public String toString() {
2882 String sc = stringCache;
2883 if (sc == null)
2884 stringCache = sc = layoutChars(true);
2885 return sc;
2886 }
2887
2888 /**
2889 * Returns a string representation of this {@code BigDecimal},
2890 * using engineering notation if an exponent is needed.
2891 *
2892 * <p>Returns a string that represents the {@code BigDecimal} as
2893 * described in the {@link #toString()} method, except that if
2894 * exponential notation is used, the power of ten is adjusted to
2895 * be a multiple of three (engineering notation) such that the
2896 * integer part of nonzero values will be in the range 1 through
2897 * 999. If exponential notation is used for zero values, a
2898 * decimal point and one or two fractional zero digits are used so
2899 * that the scale of the zero value is preserved. Note that
2900 * unlike the output of {@link #toString()}, the output of this
2901 * method is <em>not</em> guaranteed to recover the same [integer,
2902 * scale] pair of this {@code BigDecimal} if the output string is
2903 * converting back to a {@code BigDecimal} using the {@linkplain
2904 * #BigDecimal(String) string constructor}. The result of this method meets
2905 * the weaker constraint of always producing a numerically equal
2906 * result from applying the string constructor to the method's output.
2907 *
2908 * @return string representation of this {@code BigDecimal}, using
2909 * engineering notation if an exponent is needed.
2910 * @since 1.5
2911 */
2912 public String toEngineeringString() {
2913 return layoutChars(false);
2914 }
2915
2916 /**
2917 * Returns a string representation of this {@code BigDecimal}
2918 * without an exponent field. For values with a positive scale,
2919 * the number of digits to the right of the decimal point is used
2920 * to indicate scale. For values with a zero or negative scale,
2921 * the resulting string is generated as if the value were
2922 * converted to a numerically equal value with zero scale and as
2923 * if all the trailing zeros of the zero scale value were present
2924 * in the result.
2925 *
2926 * The entire string is prefixed by a minus sign character '-'
2927 * (<tt>'\u002D'</tt>) if the unscaled value is less than
2928 * zero. No sign character is prefixed if the unscaled value is
2929 * zero or positive.
2930 *
2931 * Note that if the result of this method is passed to the
2932 * {@linkplain #BigDecimal(String) string constructor}, only the
2933 * numerical value of this {@code BigDecimal} will necessarily be
2934 * recovered; the representation of the new {@code BigDecimal}
2935 * may have a different scale. In particular, if this
2936 * {@code BigDecimal} has a negative scale, the string resulting
2937 * from this method will have a scale of zero when processed by
2938 * the string constructor.
2939 *
2940 * (This method behaves analogously to the {@code toString}
2941 * method in 1.4 and earlier releases.)
2942 *
2943 * @return a string representation of this {@code BigDecimal}
2944 * without an exponent field.
2945 * @since 1.5
2946 * @see #toString()
2947 * @see #toEngineeringString()
2948 */
2949 public String toPlainString() {
2950 if(scale==0) {
2951 if(intCompact!=INFLATED) {
2952 return Long.toString(intCompact);
2953 } else {
2954 return intVal.toString();
2955 }
2956 }
2957 if(this.scale<0) { // No decimal point
2958 if(signum()==0) {
2959 return "0";
2960 }
2961 int tailingZeros = checkScaleNonZero((-(long)scale));
2962 StringBuilder buf;
2963 if(intCompact!=INFLATED) {
2964 buf = new StringBuilder(20+tailingZeros);
2965 buf.append(intCompact);
2966 } else {
2967 String str = intVal.toString();
2968 buf = new StringBuilder(str.length()+tailingZeros);
2969 buf.append(str);
2970 }
2971 for (int i = 0; i < tailingZeros; i++)
2972 buf.append('0');
2973 return buf.toString();
2974 }
2975 String str ;
2976 if(intCompact!=INFLATED) {
2977 str = Long.toString(Math.abs(intCompact));
2978 } else {
2979 str = intVal.abs().toString();
2980 }
2981 return getValueString(signum(), str, scale);
2982 }
2983
2984 /* Returns a digit.digit string */
2985 private String getValueString(int signum, String intString, int scale) {
2986 /* Insert decimal point */
2987 StringBuilder buf;
2988 int insertionPoint = intString.length() - scale;
2989 if (insertionPoint == 0) { /* Point goes right before intVal */
2990 return (signum<0 ? "-0." : "0.") + intString;
2991 } else if (insertionPoint > 0) { /* Point goes inside intVal */
2992 buf = new StringBuilder(intString);
2993 buf.insert(insertionPoint, '.');
2994 if (signum < 0)
2995 buf.insert(0, '-');
2996 } else { /* We must insert zeros between point and intVal */
2997 buf = new StringBuilder(3-insertionPoint + intString.length());
2998 buf.append(signum<0 ? "-0." : "0.");
2999 for (int i=0; i<-insertionPoint; i++)
3000 buf.append('0');
3001 buf.append(intString);
3002 }
3003 return buf.toString();
3004 }
3005
3006 /**
3007 * Converts this {@code BigDecimal} to a {@code BigInteger}.
3008 * This conversion is analogous to the
3009 * <i>narrowing primitive conversion</i> from {@code double} to
3010 * {@code long} as defined in section 5.1.3 of
3011 * <cite>The Java™ Language Specification</cite>:
3012 * any fractional part of this
3013 * {@code BigDecimal} will be discarded. Note that this
3014 * conversion can lose information about the precision of the
3015 * {@code BigDecimal} value.
3016 * <p>
3017 * To have an exception thrown if the conversion is inexact (in
3018 * other words if a nonzero fractional part is discarded), use the
3019 * {@link #toBigIntegerExact()} method.
3020 *
3021 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3022 */
3023 public BigInteger toBigInteger() {
3024 // force to an integer, quietly
3025 return this.setScale(0, ROUND_DOWN).inflated();
3026 }
3027
3028 /**
3029 * Converts this {@code BigDecimal} to a {@code BigInteger},
3030 * checking for lost information. An exception is thrown if this
3031 * {@code BigDecimal} has a nonzero fractional part.
3032 *
3033 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3034 * @throws ArithmeticException if {@code this} has a nonzero
3035 * fractional part.
3036 * @since 1.5
3037 */
3038 public BigInteger toBigIntegerExact() {
3039 // round to an integer, with Exception if decimal part non-0
3040 return this.setScale(0, ROUND_UNNECESSARY).inflated();
3041 }
3042
3043 /**
3044 * Converts this {@code BigDecimal} to a {@code long}.
3045 * This conversion is analogous to the
3046 * <i>narrowing primitive conversion</i> from {@code double} to
3047 * {@code short} as defined in section 5.1.3 of
3048 * <cite>The Java™ Language Specification</cite>:
3049 * any fractional part of this
3050 * {@code BigDecimal} will be discarded, and if the resulting
3051 * "{@code BigInteger}" is too big to fit in a
3052 * {@code long}, only the low-order 64 bits are returned.
3053 * Note that this conversion can lose information about the
3054 * overall magnitude and precision of this {@code BigDecimal} value as well
3055 * as return a result with the opposite sign.
3056 *
3057 * @return this {@code BigDecimal} converted to a {@code long}.
3058 */
3059 public long longValue(){
3060 return (intCompact != INFLATED && scale == 0) ?
3061 intCompact:
3062 toBigInteger().longValue();
3063 }
3064
3065 /**
3066 * Converts this {@code BigDecimal} to a {@code long}, checking
3067 * for lost information. If this {@code BigDecimal} has a
3068 * nonzero fractional part or is out of the possible range for a
3069 * {@code long} result then an {@code ArithmeticException} is
3070 * thrown.
3071 *
3072 * @return this {@code BigDecimal} converted to a {@code long}.
3073 * @throws ArithmeticException if {@code this} has a nonzero
3074 * fractional part, or will not fit in a {@code long}.
3075 * @since 1.5
3076 */
3077 public long longValueExact() {
3078 if (intCompact != INFLATED && scale == 0)
3079 return intCompact;
3080 // If more than 19 digits in integer part it cannot possibly fit
3081 if ((precision() - scale) > 19) // [OK for negative scale too]
3082 throw new java.lang.ArithmeticException("Overflow");
3083 // Fastpath zero and < 1.0 numbers (the latter can be very slow
3084 // to round if very small)
3085 if (this.signum() == 0)
3086 return 0;
3087 if ((this.precision() - this.scale) <= 0)
3088 throw new ArithmeticException("Rounding necessary");
3089 // round to an integer, with Exception if decimal part non-0
3090 BigDecimal num = this.setScale(0, ROUND_UNNECESSARY);
3091 if (num.precision() >= 19) // need to check carefully
3092 LongOverflow.check(num);
3093 return num.inflated().longValue();
3094 }
3095
3096 private static class LongOverflow {
3097 /** BigInteger equal to Long.MIN_VALUE. */
3098 private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE);
3099
3100 /** BigInteger equal to Long.MAX_VALUE. */
3101 private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE);
3102
3103 public static void check(BigDecimal num) {
3104 BigInteger intVal = num.inflated();
3105 if (intVal.compareTo(LONGMIN) < 0 ||
3106 intVal.compareTo(LONGMAX) > 0)
3107 throw new java.lang.ArithmeticException("Overflow");
3108 }
3109 }
3110
3111 /**
3112 * Converts this {@code BigDecimal} to an {@code int}.
3113 * This conversion is analogous to the
3114 * <i>narrowing primitive conversion</i> from {@code double} to
3115 * {@code short} as defined in section 5.1.3 of
3116 * <cite>The Java™ Language Specification</cite>:
3117 * any fractional part of this
3118 * {@code BigDecimal} will be discarded, and if the resulting
3119 * "{@code BigInteger}" is too big to fit in an
3120 * {@code int}, only the low-order 32 bits are returned.
3121 * Note that this conversion can lose information about the
3122 * overall magnitude and precision of this {@code BigDecimal}
3123 * value as well as return a result with the opposite sign.
3124 *
3125 * @return this {@code BigDecimal} converted to an {@code int}.
3126 */
3127 public int intValue() {
3128 return (intCompact != INFLATED && scale == 0) ?
3129 (int)intCompact :
3130 toBigInteger().intValue();
3131 }
3132
3133 /**
3134 * Converts this {@code BigDecimal} to an {@code int}, checking
3135 * for lost information. If this {@code BigDecimal} has a
3136 * nonzero fractional part or is out of the possible range for an
3137 * {@code int} result then an {@code ArithmeticException} is
3138 * thrown.
3139 *
3140 * @return this {@code BigDecimal} converted to an {@code int}.
3141 * @throws ArithmeticException if {@code this} has a nonzero
3142 * fractional part, or will not fit in an {@code int}.
3143 * @since 1.5
3144 */
3145 public int intValueExact() {
3146 long num;
3147 num = this.longValueExact(); // will check decimal part
3148 if ((int)num != num)
3149 throw new java.lang.ArithmeticException("Overflow");
3150 return (int)num;
3151 }
3152
3153 /**
3154 * Converts this {@code BigDecimal} to a {@code short}, checking
3155 * for lost information. If this {@code BigDecimal} has a
3156 * nonzero fractional part or is out of the possible range for a
3157 * {@code short} result then an {@code ArithmeticException} is
3158 * thrown.
3159 *
3160 * @return this {@code BigDecimal} converted to a {@code short}.
3161 * @throws ArithmeticException if {@code this} has a nonzero
3162 * fractional part, or will not fit in a {@code short}.
3163 * @since 1.5
3164 */
3165 public short shortValueExact() {
3166 long num;
3167 num = this.longValueExact(); // will check decimal part
3168 if ((short)num != num)
3169 throw new java.lang.ArithmeticException("Overflow");
3170 return (short)num;
3171 }
3172
3173 /**
3174 * Converts this {@code BigDecimal} to a {@code byte}, checking
3175 * for lost information. If this {@code BigDecimal} has a
3176 * nonzero fractional part or is out of the possible range for a
3177 * {@code byte} result then an {@code ArithmeticException} is
3178 * thrown.
3179 *
3180 * @return this {@code BigDecimal} converted to a {@code byte}.
3181 * @throws ArithmeticException if {@code this} has a nonzero
3182 * fractional part, or will not fit in a {@code byte}.
3183 * @since 1.5
3184 */
3185 public byte byteValueExact() {
3186 long num;
3187 num = this.longValueExact(); // will check decimal part
3188 if ((byte)num != num)
3189 throw new java.lang.ArithmeticException("Overflow");
3190 return (byte)num;
3191 }
3192
3193 /**
3194 * Converts this {@code BigDecimal} to a {@code float}.
3195 * This conversion is similar to the
3196 * <i>narrowing primitive conversion</i> from {@code double} to
3197 * {@code float} as defined in section 5.1.3 of
3198 * <cite>The Java™ Language Specification</cite>:
3199 * if this {@code BigDecimal} has too great a
3200 * magnitude to represent as a {@code float}, it will be
3201 * converted to {@link Float#NEGATIVE_INFINITY} or {@link
3202 * Float#POSITIVE_INFINITY} as appropriate. Note that even when
3203 * the return value is finite, this conversion can lose
3204 * information about the precision of the {@code BigDecimal}
3205 * value.
3206 *
3207 * @return this {@code BigDecimal} converted to a {@code float}.
3208 */
3209 public float floatValue(){
3210 if(intCompact != INFLATED) {
3211 if (scale == 0) {
3212 return (float)intCompact;
3213 } else {
3214 /*
3215 * If both intCompact and the scale can be exactly
3216 * represented as float values, perform a single float
3217 * multiply or divide to compute the (properly
3218 * rounded) result.
3219 */
3220 if (Math.abs(intCompact) < 1L<<22 ) {
3221 // Don't have too guard against
3222 // Math.abs(MIN_VALUE) because of outer check
3223 // against INFLATED.
3224 if (scale > 0 && scale < float10pow.length) {
3225 return (float)intCompact / float10pow[scale];
3226 } else if (scale < 0 && scale > -float10pow.length) {
3227 return (float)intCompact * float10pow[-scale];
3228 }
3229 }
3230 }
3231 }
3232 // Somewhat inefficient, but guaranteed to work.
3233 return Float.parseFloat(this.toString());
3234 }
3235
3236 /**
3237 * Converts this {@code BigDecimal} to a {@code double}.
3238 * This conversion is similar to the
3239 * <i>narrowing primitive conversion</i> from {@code double} to
3240 * {@code float} as defined in section 5.1.3 of
3241 * <cite>The Java™ Language Specification</cite>:
3242 * if this {@code BigDecimal} has too great a
3243 * magnitude represent as a {@code double}, it will be
3244 * converted to {@link Double#NEGATIVE_INFINITY} or {@link
3245 * Double#POSITIVE_INFINITY} as appropriate. Note that even when
3246 * the return value is finite, this conversion can lose
3247 * information about the precision of the {@code BigDecimal}
3248 * value.
3249 *
3250 * @return this {@code BigDecimal} converted to a {@code double}.
3251 */
3252 public double doubleValue(){
3253 if(intCompact != INFLATED) {
3254 if (scale == 0) {
3255 return (double)intCompact;
3256 } else {
3257 /*
3258 * If both intCompact and the scale can be exactly
3259 * represented as double values, perform a single
3260 * double multiply or divide to compute the (properly
3261 * rounded) result.
3262 */
3263 if (Math.abs(intCompact) < 1L<<52 ) {
3264 // Don't have too guard against
3265 // Math.abs(MIN_VALUE) because of outer check
3266 // against INFLATED.
3267 if (scale > 0 && scale < double10pow.length) {
3268 return (double)intCompact / double10pow[scale];
3269 } else if (scale < 0 && scale > -double10pow.length) {
3270 return (double)intCompact * double10pow[-scale];
3271 }
3272 }
3273 }
3274 }
3275 // Somewhat inefficient, but guaranteed to work.
3276 return Double.parseDouble(this.toString());
3277 }
3278
3279 /**
3280 * Powers of 10 which can be represented exactly in {@code
3281 * double}.
3282 */
3283 private static final double double10pow[] = {
3284 1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5,
3285 1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, 1.0e11,
3286 1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17,
3287 1.0e18, 1.0e19, 1.0e20, 1.0e21, 1.0e22
3288 };
3289
3290 /**
3291 * Powers of 10 which can be represented exactly in {@code
3292 * float}.
3293 */
3294 private static final float float10pow[] = {
3295 1.0e0f, 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f,
3296 1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f
3297 };
3298
3299 /**
3300 * Returns the size of an ulp, a unit in the last place, of this
3301 * {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal}
3302 * value is the positive distance between this value and the
3303 * {@code BigDecimal} value next larger in magnitude with the
3304 * same number of digits. An ulp of a zero value is numerically
3305 * equal to 1 with the scale of {@code this}. The result is
3306 * stored with the same scale as {@code this} so the result
3307 * for zero and nonzero values is equal to {@code [1,
3308 * this.scale()]}.
3309 *
3310 * @return the size of an ulp of {@code this}
3311 * @since 1.5
3312 */
3313 public BigDecimal ulp() {
3314 return BigDecimal.valueOf(1, this.scale(), 1);
3315 }
3316
3317 // Private class to build a string representation for BigDecimal object.
3318 // "StringBuilderHelper" is constructed as a thread local variable so it is
3319 // thread safe. The StringBuilder field acts as a buffer to hold the temporary
3320 // representation of BigDecimal. The cmpCharArray holds all the characters for
3321 // the compact representation of BigDecimal (except for '-' sign' if it is
3322 // negative) if its intCompact field is not INFLATED. It is shared by all
3323 // calls to toString() and its variants in that particular thread.
3324 static class StringBuilderHelper {
3325 final StringBuilder sb; // Placeholder for BigDecimal string
3326 final char[] cmpCharArray; // character array to place the intCompact
3327
3328 StringBuilderHelper() {
3329 sb = new StringBuilder();
3330 // All non negative longs can be made to fit into 19 character array.
3331 cmpCharArray = new char[19];
3332 }
3333
3334 // Accessors.
3335 StringBuilder getStringBuilder() {
3336 sb.setLength(0);
3337 return sb;
3338 }
3339
3340 char[] getCompactCharArray() {
3341 return cmpCharArray;
3342 }
3343
3344 /**
3345 * Places characters representing the intCompact in {@code long} into
3346 * cmpCharArray and returns the offset to the array where the
3347 * representation starts.
3348 *
3349 * @param intCompact the number to put into the cmpCharArray.
3350 * @return offset to the array where the representation starts.
3351 * Note: intCompact must be greater or equal to zero.
3352 */
3353 int putIntCompact(long intCompact) {
3354 assert intCompact >= 0;
3355
3356 long q;
3357 int r;
3358 // since we start from the least significant digit, charPos points to
3359 // the last character in cmpCharArray.
3360 int charPos = cmpCharArray.length;
3361
3362 // Get 2 digits/iteration using longs until quotient fits into an int
3363 while (intCompact > Integer.MAX_VALUE) {
3364 q = intCompact / 100;
3365 r = (int)(intCompact - q * 100);
3366 intCompact = q;
3367 cmpCharArray[--charPos] = DIGIT_ONES[r];
3368 cmpCharArray[--charPos] = DIGIT_TENS[r];
3369 }
3370
3371 // Get 2 digits/iteration using ints when i2 >= 100
3372 int q2;
3373 int i2 = (int)intCompact;
3374 while (i2 >= 100) {
3375 q2 = i2 / 100;
3376 r = i2 - q2 * 100;
3377 i2 = q2;
3378 cmpCharArray[--charPos] = DIGIT_ONES[r];
3379 cmpCharArray[--charPos] = DIGIT_TENS[r];
3380 }
3381
3382 cmpCharArray[--charPos] = DIGIT_ONES[i2];
3383 if (i2 >= 10)
3384 cmpCharArray[--charPos] = DIGIT_TENS[i2];
3385
3386 return charPos;
3387 }
3388
3389 final static char[] DIGIT_TENS = {
3390 '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
3391 '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
3392 '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
3393 '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
3394 '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
3395 '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
3396 '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
3397 '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
3398 '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
3399 '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
3400 };
3401
3402 final static char[] DIGIT_ONES = {
3403 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3404 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3405 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3406 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3407 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3408 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3409 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3410 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3411 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3412 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3413 };
3414 }
3415
3416 /**
3417 * Lay out this {@code BigDecimal} into a {@code char[]} array.
3418 * The Java 1.2 equivalent to this was called {@code getValueString}.
3419 *
3420 * @param sci {@code true} for Scientific exponential notation;
3421 * {@code false} for Engineering
3422 * @return string with canonical string representation of this
3423 * {@code BigDecimal}
3424 */
3425 private String layoutChars(boolean sci) {
3426 if (scale == 0) // zero scale is trivial
3427 return (intCompact != INFLATED) ?
3428 Long.toString(intCompact):
3429 intVal.toString();
3430 if (scale == 2 &&
3431 intCompact >= 0 && intCompact < Integer.MAX_VALUE) {
3432 // currency fast path
3433 int lowInt = (int)intCompact % 100;
3434 int highInt = (int)intCompact / 100;
3435 return (Integer.toString(highInt) + '.' +
3436 StringBuilderHelper.DIGIT_TENS[lowInt] +
3437 StringBuilderHelper.DIGIT_ONES[lowInt]) ;
3438 }
3439
3440 StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get();
3441 char[] coeff;
3442 int offset; // offset is the starting index for coeff array
3443 // Get the significand as an absolute value
3444 if (intCompact != INFLATED) {
3445 offset = sbHelper.putIntCompact(Math.abs(intCompact));
3446 coeff = sbHelper.getCompactCharArray();
3447 } else {
3448 offset = 0;
3449 coeff = intVal.abs().toString().toCharArray();
3450 }
3451
3452 // Construct a buffer, with sufficient capacity for all cases.
3453 // If E-notation is needed, length will be: +1 if negative, +1
3454 // if '.' needed, +2 for "E+", + up to 10 for adjusted exponent.
3455 // Otherwise it could have +1 if negative, plus leading "0.00000"
3456 StringBuilder buf = sbHelper.getStringBuilder();
3457 if (signum() < 0) // prefix '-' if negative
3458 buf.append('-');
3459 int coeffLen = coeff.length - offset;
3460 long adjusted = -(long)scale + (coeffLen -1);
3461 if ((scale >= 0) && (adjusted >= -6)) { // plain number
3462 int pad = scale - coeffLen; // count of padding zeros
3463 if (pad >= 0) { // 0.xxx form
3464 buf.append('0');
3465 buf.append('.');
3466 for (; pad>0; pad--) {
3467 buf.append('0');
3468 }
3469 buf.append(coeff, offset, coeffLen);
3470 } else { // xx.xx form
3471 buf.append(coeff, offset, -pad);
3472 buf.append('.');
3473 buf.append(coeff, -pad + offset, scale);
3474 }
3475 } else { // E-notation is needed
3476 if (sci) { // Scientific notation
3477 buf.append(coeff[offset]); // first character
3478 if (coeffLen > 1) { // more to come
3479 buf.append('.');
3480 buf.append(coeff, offset + 1, coeffLen - 1);
3481 }
3482 } else { // Engineering notation
3483 int sig = (int)(adjusted % 3);
3484 if (sig < 0)
3485 sig += 3; // [adjusted was negative]
3486 adjusted -= sig; // now a multiple of 3
3487 sig++;
3488 if (signum() == 0) {
3489 switch (sig) {
3490 case 1:
3491 buf.append('0'); // exponent is a multiple of three
3492 break;
3493 case 2:
3494 buf.append("0.00");
3495 adjusted += 3;
3496 break;
3497 case 3:
3498 buf.append("0.0");
3499 adjusted += 3;
3500 break;
3501 default:
3502 throw new AssertionError("Unexpected sig value " + sig);
3503 }
3504 } else if (sig >= coeffLen) { // significand all in integer
3505 buf.append(coeff, offset, coeffLen);
3506 // may need some zeros, too
3507 for (int i = sig - coeffLen; i > 0; i--)
3508 buf.append('0');
3509 } else { // xx.xxE form
3510 buf.append(coeff, offset, sig);
3511 buf.append('.');
3512 buf.append(coeff, offset + sig, coeffLen - sig);
3513 }
3514 }
3515 if (adjusted != 0) { // [!sci could have made 0]
3516 buf.append('E');
3517 if (adjusted > 0) // force sign for positive
3518 buf.append('+');
3519 buf.append(adjusted);
3520 }
3521 }
3522 return buf.toString();
3523 }
3524
3525 /**
3526 * Return 10 to the power n, as a {@code BigInteger}.
3527 *
3528 * @param n the power of ten to be returned (>=0)
3529 * @return a {@code BigInteger} with the value (10<sup>n</sup>)
3530 */
3531 private static BigInteger bigTenToThe(int n) {
3532 if (n < 0)
3533 return BigInteger.ZERO;
3534
3535 if (n < BIG_TEN_POWERS_TABLE_MAX) {
3536 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3537 if (n < pows.length)
3538 return pows[n];
3539 else
3540 return expandBigIntegerTenPowers(n);
3541 }
3542
3543 return BigInteger.TEN.pow(n);
3544 }
3545
3546 /**
3547 * Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n.
3548 *
3549 * @param n the power of ten to be returned (>=0)
3550 * @return a {@code BigDecimal} with the value (10<sup>n</sup>) and
3551 * in the meantime, the BIG_TEN_POWERS_TABLE array gets
3552 * expanded to the size greater than n.
3553 */
3554 private static BigInteger expandBigIntegerTenPowers(int n) {
3555 synchronized(BigDecimal.class) {
3556 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3557 int curLen = pows.length;
3558 // The following comparison and the above synchronized statement is
3559 // to prevent multiple threads from expanding the same array.
3560 if (curLen <= n) {
3561 int newLen = curLen << 1;
3562 while (newLen <= n)
3563 newLen <<= 1;
3564 pows = Arrays.copyOf(pows, newLen);
3565 for (int i = curLen; i < newLen; i++)
3566 pows[i] = pows[i - 1].multiply(BigInteger.TEN);
3567 // Based on the following facts:
3568 // 1. pows is a private local varible;
3569 // 2. the following store is a volatile store.
3570 // the newly created array elements can be safely published.
3571 BIG_TEN_POWERS_TABLE = pows;
3572 }
3573 return pows[n];
3574 }
3575 }
3576
3577 private static final long[] LONG_TEN_POWERS_TABLE = {
3578 1, // 0 / 10^0
3579 10, // 1 / 10^1
3580 100, // 2 / 10^2
3581 1000, // 3 / 10^3
3582 10000, // 4 / 10^4
3583 100000, // 5 / 10^5
3584 1000000, // 6 / 10^6
3585 10000000, // 7 / 10^7
3586 100000000, // 8 / 10^8
3587 1000000000, // 9 / 10^9
3588 10000000000L, // 10 / 10^10
3589 100000000000L, // 11 / 10^11
3590 1000000000000L, // 12 / 10^12
3591 10000000000000L, // 13 / 10^13
3592 100000000000000L, // 14 / 10^14
3593 1000000000000000L, // 15 / 10^15
3594 10000000000000000L, // 16 / 10^16
3595 100000000000000000L, // 17 / 10^17
3596 1000000000000000000L // 18 / 10^18
3597 };
3598
3599 private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = {
3600 BigInteger.ONE,
3601 BigInteger.valueOf(10),
3602 BigInteger.valueOf(100),
3603 BigInteger.valueOf(1000),
3604 BigInteger.valueOf(10000),
3605 BigInteger.valueOf(100000),
3606 BigInteger.valueOf(1000000),
3607 BigInteger.valueOf(10000000),
3608 BigInteger.valueOf(100000000),
3609 BigInteger.valueOf(1000000000),
3610 BigInteger.valueOf(10000000000L),
3611 BigInteger.valueOf(100000000000L),
3612 BigInteger.valueOf(1000000000000L),
3613 BigInteger.valueOf(10000000000000L),
3614 BigInteger.valueOf(100000000000000L),
3615 BigInteger.valueOf(1000000000000000L),
3616 BigInteger.valueOf(10000000000000000L),
3617 BigInteger.valueOf(100000000000000000L),
3618 BigInteger.valueOf(1000000000000000000L)
3619 };
3620
3621 private static final int BIG_TEN_POWERS_TABLE_INITLEN =
3622 BIG_TEN_POWERS_TABLE.length;
3623 private static final int BIG_TEN_POWERS_TABLE_MAX =
3624 16 * BIG_TEN_POWERS_TABLE_INITLEN;
3625
3626 private static final long THRESHOLDS_TABLE[] = {
3627 Long.MAX_VALUE, // 0
3628 Long.MAX_VALUE/10L, // 1
3629 Long.MAX_VALUE/100L, // 2
3630 Long.MAX_VALUE/1000L, // 3
3631 Long.MAX_VALUE/10000L, // 4
3632 Long.MAX_VALUE/100000L, // 5
3633 Long.MAX_VALUE/1000000L, // 6
3634 Long.MAX_VALUE/10000000L, // 7
3635 Long.MAX_VALUE/100000000L, // 8
3636 Long.MAX_VALUE/1000000000L, // 9
3637 Long.MAX_VALUE/10000000000L, // 10
3638 Long.MAX_VALUE/100000000000L, // 11
3639 Long.MAX_VALUE/1000000000000L, // 12
3640 Long.MAX_VALUE/10000000000000L, // 13
3641 Long.MAX_VALUE/100000000000000L, // 14
3642 Long.MAX_VALUE/1000000000000000L, // 15
3643 Long.MAX_VALUE/10000000000000000L, // 16
3644 Long.MAX_VALUE/100000000000000000L, // 17
3645 Long.MAX_VALUE/1000000000000000000L // 18
3646 };
3647
3648 /**
3649 * Compute val * 10 ^ n; return this product if it is
3650 * representable as a long, INFLATED otherwise.
3651 */
3652 private static long longMultiplyPowerTen(long val, int n) {
3653 if (val == 0 || n <= 0)
3654 return val;
3655 long[] tab = LONG_TEN_POWERS_TABLE;
3656 long[] bounds = THRESHOLDS_TABLE;
3657 if (n < tab.length && n < bounds.length) {
3658 long tenpower = tab[n];
3659 if (val == 1)
3660 return tenpower;
3661 if (Math.abs(val) <= bounds[n])
3662 return val * tenpower;
3663 }
3664 return INFLATED;
3665 }
3666
3667 /**
3668 * Compute this * 10 ^ n.
3669 * Needed mainly to allow special casing to trap zero value
3670 */
3671 private BigInteger bigMultiplyPowerTen(int n) {
3672 if (n <= 0)
3673 return this.inflated();
3674
3675 if (intCompact != INFLATED)
3676 return bigTenToThe(n).multiply(intCompact);
3677 else
3678 return intVal.multiply(bigTenToThe(n));
3679 }
3680
3681 /**
3682 * Returns appropriate BigInteger from intVal field if intVal is
3683 * null, i.e. the compact representation is in use.
3684 */
3685 private BigInteger inflated() {
3686 if (intVal == null) {
3687 return BigInteger.valueOf(intCompact);
3688 }
3689 return intVal;
3690 }
3691
3692 /**
3693 * Match the scales of two {@code BigDecimal}s to align their
3694 * least significant digits.
3695 *
3696 * <p>If the scales of val[0] and val[1] differ, rescale
3697 * (non-destructively) the lower-scaled {@code BigDecimal} so
3698 * they match. That is, the lower-scaled reference will be
3699 * replaced by a reference to a new object with the same scale as
3700 * the other {@code BigDecimal}.
3701 *
3702 * @param val array of two elements referring to the two
3703 * {@code BigDecimal}s to be aligned.
3704 */
3705 private static void matchScale(BigDecimal[] val) {
3706 if (val[0].scale == val[1].scale) {
3707 return;
3708 } else if (val[0].scale < val[1].scale) {
3709 val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY);
3710 } else if (val[1].scale < val[0].scale) {
3711 val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY);
3712 }
3713 }
3714
3715 private static class UnsafeHolder {
3716 private static final sun.misc.Unsafe unsafe;
3717 private static final long intCompactOffset;
3718 private static final long intValOffset;
3719 static {
3720 try {
3721 unsafe = sun.misc.Unsafe.getUnsafe();
3722 intCompactOffset = unsafe.objectFieldOffset
3723 (BigDecimal.class.getDeclaredField("intCompact"));
3724 intValOffset = unsafe.objectFieldOffset
3725 (BigDecimal.class.getDeclaredField("intVal"));
3726 } catch (Exception ex) {
3727 throw new ExceptionInInitializerError(ex);
3728 }
3729 }
3730 static void setIntCompactVolatile(BigDecimal bd, long val) {
3731 unsafe.putLongVolatile(bd, intCompactOffset, val);
3732 }
3733
3734 static void setIntValVolatile(BigDecimal bd, BigInteger val) {
3735 unsafe.putObjectVolatile(bd, intValOffset, val);
3736 }
3737 }
3738
3739 /**
3740 * Reconstitute the {@code BigDecimal} instance from a stream (that is,
3741 * deserialize it).
3742 *
3743 * @param s the stream being read.
3744 */
3745 private void readObject(java.io.ObjectInputStream s)
3746 throws java.io.IOException, ClassNotFoundException {
3747 // Read in all fields
3748 s.defaultReadObject();
3749 // validate possibly bad fields
3750 if (intVal == null) {
3751 String message = "BigDecimal: null intVal in stream";
3752 throw new java.io.StreamCorruptedException(message);
3753 // [all values of scale are now allowed]
3754 }
3755 UnsafeHolder.setIntCompactVolatile(this, compactValFor(intVal));
3756 }
3757
3758 /**
3759 * Serialize this {@code BigDecimal} to the stream in question
3760 *
3761 * @param s the stream to serialize to.
3762 */
3763 private void writeObject(java.io.ObjectOutputStream s)
3764 throws java.io.IOException {
3765 // Must inflate to maintain compatible serial form.
3766 if (this.intVal == null)
3767 UnsafeHolder.setIntValVolatile(this, BigInteger.valueOf(this.intCompact));
3768 // Could reset intVal back to null if it has to be set.
3769 s.defaultWriteObject();
3770 }
3771
3772 /**
3773 * Returns the length of the absolute value of a {@code long}, in decimal
3774 * digits.
3775 *
3776 * @param x the {@code long}
3777 * @return the length of the unscaled value, in deciaml digits.
3778 */
3779 static int longDigitLength(long x) {
3780 /*
3781 * As described in "Bit Twiddling Hacks" by Sean Anderson,
3782 * (http://graphics.stanford.edu/~seander/bithacks.html)
3783 * integer log 10 of x is within 1 of (1233/4096)* (1 +
3784 * integer log 2 of x). The fraction 1233/4096 approximates
3785 * log10(2). So we first do a version of log2 (a variant of
3786 * Long class with pre-checks and opposite directionality) and
3787 * then scale and check against powers table. This is a little
3788 * simpler in present context than the version in Hacker's
3789 * Delight sec 11-4. Adding one to bit length allows comparing
3790 * downward from the LONG_TEN_POWERS_TABLE that we need
3791 * anyway.
3792 */
3793 assert x != BigDecimal.INFLATED;
3794 if (x < 0)
3795 x = -x;
3796 if (x < 10) // must screen for 0, might as well 10
3797 return 1;
3798 int r = ((64 - Long.numberOfLeadingZeros(x) + 1) * 1233) >>> 12;
3799 long[] tab = LONG_TEN_POWERS_TABLE;
3800 // if r >= length, must have max possible digits for long
3801 return (r >= tab.length || x < tab[r]) ? r : r + 1;
3802 }
3803
3804 /**
3805 * Returns the length of the absolute value of a BigInteger, in
3806 * decimal digits.
3807 *
3808 * @param b the BigInteger
3809 * @return the length of the unscaled value, in decimal digits
3810 */
3811 private static int bigDigitLength(BigInteger b) {
3812 /*
3813 * Same idea as the long version, but we need a better
3814 * approximation of log10(2). Using 646456993/2^31
3815 * is accurate up to max possible reported bitLength.
3816 */
3817 if (b.signum == 0)
3818 return 1;
3819 int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31);
3820 return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1;
3821 }
3822
3823 /**
3824 * Check a scale for Underflow or Overflow. If this BigDecimal is
3825 * nonzero, throw an exception if the scale is outof range. If this
3826 * is zero, saturate the scale to the extreme value of the right
3827 * sign if the scale is out of range.
3828 *
3829 * @param val The new scale.
3830 * @throws ArithmeticException (overflow or underflow) if the new
3831 * scale is out of range.
3832 * @return validated scale as an int.
3833 */
3834 private int checkScale(long val) {
3835 int asInt = (int)val;
3836 if (asInt != val) {
3837 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3838 BigInteger b;
3839 if (intCompact != 0 &&
3840 ((b = intVal) == null || b.signum() != 0))
3841 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3842 }
3843 return asInt;
3844 }
3845
3846 /**
3847 * Returns the compact value for given {@code BigInteger}, or
3848 * INFLATED if too big. Relies on internal representation of
3849 * {@code BigInteger}.
3850 */
3851 private static long compactValFor(BigInteger b) {
3852 int[] m = b.mag;
3853 int len = m.length;
3854 if (len == 0)
3855 return 0;
3856 int d = m[0];
3857 if (len > 2 || (len == 2 && d < 0))
3858 return INFLATED;
3859
3860 long u = (len == 2)?
3861 (((long) m[1] & LONG_MASK) + (((long)d) << 32)) :
3862 (((long)d) & LONG_MASK);
3863 return (b.signum < 0)? -u : u;
3864 }
3865
3866 private static int longCompareMagnitude(long x, long y) {
3867 if (x < 0)
3868 x = -x;
3869 if (y < 0)
3870 y = -y;
3871 return (x < y) ? -1 : ((x == y) ? 0 : 1);
3872 }
3873
3874 private static int saturateLong(long s) {
3875 int i = (int)s;
3876 return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE);
3877 }
3878
3879 /*
3880 * Internal printing routine
3881 */
3882 private static void print(String name, BigDecimal bd) {
3883 System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n",
3884 name,
3885 bd.intCompact,
3886 bd.intVal,
3887 bd.scale,
3888 bd.precision);
3889 }
3890
3891 /**
3892 * Check internal invariants of this BigDecimal. These invariants
3893 * include:
3894 *
3895 * <ul>
3896 *
3897 * <li>The object must be initialized; either intCompact must not be
3898 * INFLATED or intVal is non-null. Both of these conditions may
3899 * be true.
3900 *
3901 * <li>If both intCompact and intVal and set, their values must be
3902 * consistent.
3903 *
3904 * <li>If precision is nonzero, it must have the right value.
3905 * </ul>
3906 *
3907 * Note: Since this is an audit method, we are not supposed to change the
3908 * state of this BigDecimal object.
3909 */
3910 private BigDecimal audit() {
3911 if (intCompact == INFLATED) {
3912 if (intVal == null) {
3913 print("audit", this);
3914 throw new AssertionError("null intVal");
3915 }
3916 // Check precision
3917 if (precision > 0 && precision != bigDigitLength(intVal)) {
3918 print("audit", this);
3919 throw new AssertionError("precision mismatch");
3920 }
3921 } else {
3922 if (intVal != null) {
3923 long val = intVal.longValue();
3924 if (val != intCompact) {
3925 print("audit", this);
3926 throw new AssertionError("Inconsistent state, intCompact=" +
3927 intCompact + "\t intVal=" + val);
3928 }
3929 }
3930 // Check precision
3931 if (precision > 0 && precision != longDigitLength(intCompact)) {
3932 print("audit", this);
3933 throw new AssertionError("precision mismatch");
3934 }
3935 }
3936 return this;
3937 }
3938
3939 /* the same as checkScale where value!=0 */
3940 private static int checkScaleNonZero(long val) {
3941 int asInt = (int)val;
3942 if (asInt != val) {
3943 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3944 }
3945 return asInt;
3946 }
3947
3948 private static int checkScale(long intCompact, long val) {
3949 int asInt = (int)val;
3950 if (asInt != val) {
3951 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3952 if (intCompact != 0)
3953 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3954 }
3955 return asInt;
3956 }
3957
3958 private static int checkScale(BigInteger intVal, long val) {
3959 int asInt = (int)val;
3960 if (asInt != val) {
3961 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3962 if (intVal.signum() != 0)
3963 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3964 }
3965 return asInt;
3966 }
3967
3968 /**
3969 * Returns a {@code BigDecimal} rounded according to the MathContext
3970 * settings;
3971 * If rounding is needed a new {@code BigDecimal} is created and returned.
3972 *
3973 * @param val the value to be rounded
3974 * @param mc the context to use.
3975 * @return a {@code BigDecimal} rounded according to the MathContext
3976 * settings. May return {@code value}, if no rounding needed.
3977 * @throws ArithmeticException if the rounding mode is
3978 * {@code RoundingMode.UNNECESSARY} and the
3979 * result is inexact.
3980 */
3981 private static BigDecimal doRound(BigDecimal val, MathContext mc) {
3982 int mcp = mc.precision;
3983 boolean wasDivided = false;
3984 if (mcp > 0) {
3985 BigInteger intVal = val.intVal;
3986 long compactVal = val.intCompact;
3987 int scale = val.scale;
3988 int prec = val.precision();
3989 int mode = mc.roundingMode.oldMode;
3990 int drop;
3991 if (compactVal == INFLATED) {
3992 drop = prec - mcp;
3993 while (drop > 0) {
3994 scale = checkScaleNonZero((long) scale - drop);
3995 intVal = divideAndRoundByTenPow(intVal, drop, mode);
3996 wasDivided = true;
3997 compactVal = compactValFor(intVal);
3998 if (compactVal != INFLATED) {
3999 prec = longDigitLength(compactVal);
4000 break;
4001 }
4002 prec = bigDigitLength(intVal);
4003 drop = prec - mcp;
4004 }
4005 }
4006 if (compactVal != INFLATED) {
4007 drop = prec - mcp; // drop can't be more than 18
4008 while (drop > 0) {
4009 scale = checkScaleNonZero((long) scale - drop);
4010 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4011 wasDivided = true;
4012 prec = longDigitLength(compactVal);
4013 drop = prec - mcp;
4014 intVal = null;
4015 }
4016 }
4017 return wasDivided ? new BigDecimal(intVal,compactVal,scale,prec) : val;
4018 }
4019 return val;
4020 }
4021
4022 /*
4023 * Returns a {@code BigDecimal} created from {@code long} value with
4024 * given scale rounded according to the MathContext settings
4025 */
4026 private static BigDecimal doRound(long compactVal, int scale, MathContext mc) {
4027 int mcp = mc.precision;
4028 if (mcp > 0 && mcp < 19) {
4029 int prec = longDigitLength(compactVal);
4030 int drop = prec - mcp; // drop can't be more than 18
4031 while (drop > 0) {
4032 scale = checkScaleNonZero((long) scale - drop);
4033 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4034 prec = longDigitLength(compactVal);
4035 drop = prec - mcp;
4036 }
4037 return valueOf(compactVal, scale, prec);
4038 }
4039 return valueOf(compactVal, scale);
4040 }
4041
4042 /*
4043 * Returns a {@code BigDecimal} created from {@code BigInteger} value with
4044 * given scale rounded according to the MathContext settings
4045 */
4046 private static BigDecimal doRound(BigInteger intVal, int scale, MathContext mc) {
4047 int mcp = mc.precision;
4048 int prec = 0;
4049 if (mcp > 0) {
4050 long compactVal = compactValFor(intVal);
4051 int mode = mc.roundingMode.oldMode;
4052 int drop;
4053 if (compactVal == INFLATED) {
4054 prec = bigDigitLength(intVal);
4055 drop = prec - mcp;
4056 while (drop > 0) {
4057 scale = checkScaleNonZero((long) scale - drop);
4058 intVal = divideAndRoundByTenPow(intVal, drop, mode);
4059 compactVal = compactValFor(intVal);
4060 if (compactVal != INFLATED) {
4061 break;
4062 }
4063 prec = bigDigitLength(intVal);
4064 drop = prec - mcp;
4065 }
4066 }
4067 if (compactVal != INFLATED) {
4068 prec = longDigitLength(compactVal);
4069 drop = prec - mcp; // drop can't be more than 18
4070 while (drop > 0) {
4071 scale = checkScaleNonZero((long) scale - drop);
4072 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4073 prec = longDigitLength(compactVal);
4074 drop = prec - mcp;
4075 }
4076 return valueOf(compactVal,scale,prec);
4077 }
4078 }
4079 return new BigDecimal(intVal,INFLATED,scale,prec);
4080 }
4081
4082 /*
4083 * Divides {@code BigInteger} value by ten power.
4084 */
4085 private static BigInteger divideAndRoundByTenPow(BigInteger intVal, int tenPow, int roundingMode) {
4086 if (tenPow < LONG_TEN_POWERS_TABLE.length)
4087 intVal = divideAndRound(intVal, LONG_TEN_POWERS_TABLE[tenPow], roundingMode);
4088 else
4089 intVal = divideAndRound(intVal, bigTenToThe(tenPow), roundingMode);
4090 return intVal;
4091 }
4092
4093 /**
4094 * Internally used for division operation for division {@code long} by
4095 * {@code long}.
4096 * The returned {@code BigDecimal} object is the quotient whose scale is set
4097 * to the passed in scale. If the remainder is not zero, it will be rounded
4098 * based on the passed in roundingMode. Also, if the remainder is zero and
4099 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4100 * trailing zeros of the result is stripped to match the preferredScale.
4101 */
4102 private static BigDecimal divideAndRound(long ldividend, long ldivisor, int scale, int roundingMode,
4103 int preferredScale) {
4104
4105 int qsign; // quotient sign
4106 long q = ldividend / ldivisor; // store quotient in long
4107 if (roundingMode == ROUND_DOWN && scale == preferredScale)
4108 return valueOf(q, scale);
4109 long r = ldividend % ldivisor; // store remainder in long
4110 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4111 if (r != 0) {
4112 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4113 return valueOf((increment ? q + qsign : q), scale);
4114 } else {
4115 if (preferredScale != scale)
4116 return createAndStripZerosToMatchScale(q, scale, preferredScale);
4117 else
4118 return valueOf(q, scale);
4119 }
4120 }
4121
4122 /**
4123 * Divides {@code long} by {@code long} and do rounding based on the
4124 * passed in roundingMode.
4125 */
4126 private static long divideAndRound(long ldividend, long ldivisor, int roundingMode) {
4127 int qsign; // quotient sign
4128 long q = ldividend / ldivisor; // store quotient in long
4129 if (roundingMode == ROUND_DOWN)
4130 return q;
4131 long r = ldividend % ldivisor; // store remainder in long
4132 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4133 if (r != 0) {
4134 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4135 return increment ? q + qsign : q;
4136 } else {
4137 return q;
4138 }
4139 }
4140
4141 /**
4142 * Shared logic of need increment computation.
4143 */
4144 private static boolean commonNeedIncrement(int roundingMode, int qsign,
4145 int cmpFracHalf, boolean oddQuot) {
4146 switch(roundingMode) {
4147 case ROUND_UNNECESSARY:
4148 throw new ArithmeticException("Rounding necessary");
4149
4150 case ROUND_UP: // Away from zero
4151 return true;
4152
4153 case ROUND_DOWN: // Towards zero
4154 return false;
4155
4156 case ROUND_CEILING: // Towards +infinity
4157 return qsign > 0;
4158
4159 case ROUND_FLOOR: // Towards -infinity
4160 return qsign < 0;
4161
4162 default: // Some kind of half-way rounding
4163 assert roundingMode >= ROUND_HALF_UP &&
4164 roundingMode <= ROUND_HALF_EVEN: "Unexpected rounding mode" + RoundingMode.valueOf(roundingMode);
4165
4166 if (cmpFracHalf < 0 ) // We're closer to higher digit
4167 return false;
4168 else if (cmpFracHalf > 0 ) // We're closer to lower digit
4169 return true;
4170 else { // half-way
4171 assert cmpFracHalf == 0;
4172
4173 switch(roundingMode) {
4174 case ROUND_HALF_DOWN:
4175 return false;
4176
4177 case ROUND_HALF_UP:
4178 return true;
4179
4180 case ROUND_HALF_EVEN:
4181 return oddQuot;
4182
4183 default:
4184 throw new AssertionError("Unexpected rounding mode" + roundingMode);
4185 }
4186 }
4187 }
4188 }
4189
4190 /**
4191 * Tests if quotient has to be incremented according the roundingMode
4192 */
4193 private static boolean needIncrement(long ldivisor, int roundingMode,
4194 int qsign, long q, long r) {
4195 assert r != 0L;
4196
4197 int cmpFracHalf;
4198 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4199 cmpFracHalf = 1; // 2 * r can't fit into long
4200 } else {
4201 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4202 }
4203
4204 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, (q & 1L) != 0L);
4205 }
4206
4207 /**
4208 * Divides {@code BigInteger} value by {@code long} value and
4209 * do rounding based on the passed in roundingMode.
4210 */
4211 private static BigInteger divideAndRound(BigInteger bdividend, long ldivisor, int roundingMode) {
4212 boolean isRemainderZero; // record remainder is zero or not
4213 int qsign; // quotient sign
4214 long r = 0; // store quotient & remainder in long
4215 MutableBigInteger mq = null; // store quotient
4216 // Descend into mutables for faster remainder checks
4217 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4218 mq = new MutableBigInteger();
4219 r = mdividend.divide(ldivisor, mq);
4220 isRemainderZero = (r == 0);
4221 qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4222 if (!isRemainderZero) {
4223 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4224 mq.add(MutableBigInteger.ONE);
4225 }
4226 }
4227 return mq.toBigInteger(qsign);
4228 }
4229
4230 /**
4231 * Internally used for division operation for division {@code BigInteger}
4232 * by {@code long}.
4233 * The returned {@code BigDecimal} object is the quotient whose scale is set
4234 * to the passed in scale. If the remainder is not zero, it will be rounded
4235 * based on the passed in roundingMode. Also, if the remainder is zero and
4236 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4237 * trailing zeros of the result is stripped to match the preferredScale.
4238 */
4239 private static BigDecimal divideAndRound(BigInteger bdividend,
4240 long ldivisor, int scale, int roundingMode, int preferredScale) {
4241 boolean isRemainderZero; // record remainder is zero or not
4242 int qsign; // quotient sign
4243 long r = 0; // store quotient & remainder in long
4244 MutableBigInteger mq = null; // store quotient
4245 // Descend into mutables for faster remainder checks
4246 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4247 mq = new MutableBigInteger();
4248 r = mdividend.divide(ldivisor, mq);
4249 isRemainderZero = (r == 0);
4250 qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4251 if (!isRemainderZero) {
4252 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4253 mq.add(MutableBigInteger.ONE);
4254 }
4255 return mq.toBigDecimal(qsign, scale);
4256 } else {
4257 if (preferredScale != scale) {
4258 long compactVal = mq.toCompactValue(qsign);
4259 if(compactVal!=INFLATED) {
4260 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4261 }
4262 BigInteger intVal = mq.toBigInteger(qsign);
4263 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
4264 } else {
4265 return mq.toBigDecimal(qsign, scale);
4266 }
4267 }
4268 }
4269
4270 /**
4271 * Tests if quotient has to be incremented according the roundingMode
4272 */
4273 private static boolean needIncrement(long ldivisor, int roundingMode,
4274 int qsign, MutableBigInteger mq, long r) {
4275 assert r != 0L;
4276
4277 int cmpFracHalf;
4278 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4279 cmpFracHalf = 1; // 2 * r can't fit into long
4280 } else {
4281 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4282 }
4283
4284 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
4285 }
4286
4287 /**
4288 * Divides {@code BigInteger} value by {@code BigInteger} value and
4289 * do rounding based on the passed in roundingMode.
4290 */
4291 private static BigInteger divideAndRound(BigInteger bdividend, BigInteger bdivisor, int roundingMode) {
4292 boolean isRemainderZero; // record remainder is zero or not
4293 int qsign; // quotient sign
4294 // Descend into mutables for faster remainder checks
4295 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4296 MutableBigInteger mq = new MutableBigInteger();
4297 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4298 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4299 isRemainderZero = mr.isZero();
4300 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4301 if (!isRemainderZero) {
4302 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4303 mq.add(MutableBigInteger.ONE);
4304 }
4305 }
4306 return mq.toBigInteger(qsign);
4307 }
4308
4309 /**
4310 * Internally used for division operation for division {@code BigInteger}
4311 * by {@code BigInteger}.
4312 * The returned {@code BigDecimal} object is the quotient whose scale is set
4313 * to the passed in scale. If the remainder is not zero, it will be rounded
4314 * based on the passed in roundingMode. Also, if the remainder is zero and
4315 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4316 * trailing zeros of the result is stripped to match the preferredScale.
4317 */
4318 private static BigDecimal divideAndRound(BigInteger bdividend, BigInteger bdivisor, int scale, int roundingMode,
4319 int preferredScale) {
4320 boolean isRemainderZero; // record remainder is zero or not
4321 int qsign; // quotient sign
4322 // Descend into mutables for faster remainder checks
4323 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4324 MutableBigInteger mq = new MutableBigInteger();
4325 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4326 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4327 isRemainderZero = mr.isZero();
4328 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4329 if (!isRemainderZero) {
4330 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4331 mq.add(MutableBigInteger.ONE);
4332 }
4333 return mq.toBigDecimal(qsign, scale);
4334 } else {
4335 if (preferredScale != scale) {
4336 long compactVal = mq.toCompactValue(qsign);
4337 if (compactVal != INFLATED) {
4338 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4339 }
4340 BigInteger intVal = mq.toBigInteger(qsign);
4341 return createAndStripZerosToMatchScale(intVal, scale, preferredScale);
4342 } else {
4343 return mq.toBigDecimal(qsign, scale);
4344 }
4345 }
4346 }
4347
4348 /**
4349 * Tests if quotient has to be incremented according the roundingMode
4350 */
4351 private static boolean needIncrement(MutableBigInteger mdivisor, int roundingMode,
4352 int qsign, MutableBigInteger mq, MutableBigInteger mr) {
4353 assert !mr.isZero();
4354 int cmpFracHalf = mr.compareHalf(mdivisor);
4355 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
4356 }
4357
4358 /**
4359 * Remove insignificant trailing zeros from this
4360 * {@code BigInteger} value until the preferred scale is reached or no
4361 * more zeros can be removed. If the preferred scale is less than
4362 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4363 *
4364 * @return new {@code BigDecimal} with a scale possibly reduced
4365 * to be closed to the preferred scale.
4366 */
4367 private static BigDecimal createAndStripZerosToMatchScale(BigInteger intVal, int scale, long preferredScale) {
4368 BigInteger qr[]; // quotient-remainder pair
4369 while (intVal.compareMagnitude(BigInteger.TEN) >= 0
4370 && scale > preferredScale) {
4371 if (intVal.testBit(0))
4372 break; // odd number cannot end in 0
4373 qr = intVal.divideAndRemainder(BigInteger.TEN);
4374 if (qr[1].signum() != 0)
4375 break; // non-0 remainder
4376 intVal = qr[0];
4377 scale = checkScale(intVal,(long) scale - 1); // could Overflow
4378 }
4379 return valueOf(intVal, scale, 0);
4380 }
4381
4382 /**
4383 * Remove insignificant trailing zeros from this
4384 * {@code long} value until the preferred scale is reached or no
4385 * more zeros can be removed. If the preferred scale is less than
4386 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4387 *
4388 * @return new {@code BigDecimal} with a scale possibly reduced
4389 * to be closed to the preferred scale.
4390 */
4391 private static BigDecimal createAndStripZerosToMatchScale(long compactVal, int scale, long preferredScale) {
4392 while (Math.abs(compactVal) >= 10L && scale > preferredScale) {
4393 if ((compactVal & 1L) != 0L)
4394 break; // odd number cannot end in 0
4395 long r = compactVal % 10L;
4396 if (r != 0L)
4397 break; // non-0 remainder
4398 compactVal /= 10;
4399 scale = checkScale(compactVal, (long) scale - 1); // could Overflow
4400 }
4401 return valueOf(compactVal, scale);
4402 }
4403
4404 private static BigDecimal stripZerosToMatchScale(BigInteger intVal, long intCompact, int scale, int preferredScale) {
4405 if(intCompact!=INFLATED) {
4406 return createAndStripZerosToMatchScale(intCompact, scale, preferredScale);
4407 } else {
4408 return createAndStripZerosToMatchScale(intVal==null ? INFLATED_BIGINT : intVal,
4409 scale, preferredScale);
4410 }
4411 }
4412
4413 /*
4414 * returns INFLATED if oveflow
4415 */
4416 private static long add(long xs, long ys){
4417 long sum = xs + ys;
4418 // See "Hacker's Delight" section 2-12 for explanation of
4419 // the overflow test.
4420 if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) { // not overflowed
4421 return sum;
4422 }
4423 return INFLATED;
4424 }
4425
4426 private static BigDecimal add(long xs, long ys, int scale){
4427 long sum = add(xs, ys);
4428 if (sum!=INFLATED)
4429 return BigDecimal.valueOf(sum, scale);
4430 return new BigDecimal(BigInteger.valueOf(xs).add(ys), scale);
4431 }
4432
4433 private static BigDecimal add(final long xs, int scale1, final long ys, int scale2) {
4434 long sdiff = (long) scale1 - scale2;
4435 if (sdiff == 0) {
4436 return add(xs, ys, scale1);
4437 } else if (sdiff < 0) {
4438 int raise = checkScale(xs,-sdiff);
4439 long scaledX = longMultiplyPowerTen(xs, raise);
4440 if (scaledX != INFLATED) {
4441 return add(scaledX, ys, scale2);
4442 } else {
4443 BigInteger bigsum = bigMultiplyPowerTen(xs,raise).add(ys);
4444 return ((xs^ys)>=0) ? // same sign test
4445 new BigDecimal(bigsum, INFLATED, scale2, 0)
4446 : valueOf(bigsum, scale2, 0);
4447 }
4448 } else {
4449 int raise = checkScale(ys,sdiff);
4450 long scaledY = longMultiplyPowerTen(ys, raise);
4451 if (scaledY != INFLATED) {
4452 return add(xs, scaledY, scale1);
4453 } else {
4454 BigInteger bigsum = bigMultiplyPowerTen(ys,raise).add(xs);
4455 return ((xs^ys)>=0) ?
4456 new BigDecimal(bigsum, INFLATED, scale1, 0)
4457 : valueOf(bigsum, scale1, 0);
4458 }
4459 }
4460 }
4461
4462 private static BigDecimal add(final long xs, int scale1, BigInteger snd, int scale2) {
4463 int rscale = scale1;
4464 long sdiff = (long)rscale - scale2;
4465 boolean sameSigns = (Long.signum(xs) == snd.signum);
4466 BigInteger sum;
4467 if (sdiff < 0) {
4468 int raise = checkScale(xs,-sdiff);
4469 rscale = scale2;
4470 long scaledX = longMultiplyPowerTen(xs, raise);
4471 if (scaledX == INFLATED) {
4472 sum = snd.add(bigMultiplyPowerTen(xs,raise));
4473 } else {
4474 sum = snd.add(scaledX);
4475 }
4476 } else { //if (sdiff > 0) {
4477 int raise = checkScale(snd,sdiff);
4478 snd = bigMultiplyPowerTen(snd,raise);
4479 sum = snd.add(xs);
4480 }
4481 return (sameSigns) ?
4482 new BigDecimal(sum, INFLATED, rscale, 0) :
4483 valueOf(sum, rscale, 0);
4484 }
4485
4486 private static BigDecimal add(BigInteger fst, int scale1, BigInteger snd, int scale2) {
4487 int rscale = scale1;
4488 long sdiff = (long)rscale - scale2;
4489 if (sdiff != 0) {
4490 if (sdiff < 0) {
4491 int raise = checkScale(fst,-sdiff);
4492 rscale = scale2;
4493 fst = bigMultiplyPowerTen(fst,raise);
4494 } else {
4495 int raise = checkScale(snd,sdiff);
4496 snd = bigMultiplyPowerTen(snd,raise);
4497 }
4498 }
4499 BigInteger sum = fst.add(snd);
4500 return (fst.signum == snd.signum) ?
4501 new BigDecimal(sum, INFLATED, rscale, 0) :
4502 valueOf(sum, rscale, 0);
4503 }
4504
4505 private static BigInteger bigMultiplyPowerTen(long value, int n) {
4506 if (n <= 0)
4507 return BigInteger.valueOf(value);
4508 return bigTenToThe(n).multiply(value);
4509 }
4510
4511 private static BigInteger bigMultiplyPowerTen(BigInteger value, int n) {
4512 if (n <= 0)
4513 return value;
4514 if(n<LONG_TEN_POWERS_TABLE.length) {
4515 return value.multiply(LONG_TEN_POWERS_TABLE[n]);
4516 }
4517 return value.multiply(bigTenToThe(n));
4518 }
4519
4520 /**
4521 * Returns a {@code BigDecimal} whose value is {@code (xs /
4522 * ys)}, with rounding according to the context settings.
4523 *
4524 * Fast path - used only when (xscale <= yscale && yscale < 18
4525 * && mc.presision<18) {
4526 */
4527 private static BigDecimal divideSmallFastPath(final long xs, int xscale,
4528 final long ys, int yscale,
4529 long preferredScale, MathContext mc) {
4530 int mcp = mc.precision;
4531 int roundingMode = mc.roundingMode.oldMode;
4532
4533 assert (xscale <= yscale) && (yscale < 18) && (mcp < 18);
4534 int xraise = yscale - xscale; // xraise >=0
4535 long scaledX = (xraise==0) ? xs :
4536 longMultiplyPowerTen(xs, xraise); // can't overflow here!
4537 BigDecimal quotient;
4538
4539 int cmp = longCompareMagnitude(scaledX, ys);
4540 if(cmp > 0) { // satisfy constraint (b)
4541 yscale -= 1; // [that is, divisor *= 10]
4542 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4543 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
4544 // assert newScale >= xscale
4545 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4546 long scaledXs;
4547 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
4548 quotient = null;
4549 if((mcp-1) >=0 && (mcp-1)<LONG_TEN_POWERS_TABLE.length) {
4550 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp-1], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4551 }
4552 if(quotient==null) {
4553 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp-1);
4554 quotient = divideAndRound(rb, ys,
4555 scl, roundingMode, checkScaleNonZero(preferredScale));
4556 }
4557 } else {
4558 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4559 }
4560 } else {
4561 int newScale = checkScaleNonZero((long) xscale - mcp);
4562 // assert newScale >= yscale
4563 if (newScale == yscale) { // easy case
4564 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4565 } else {
4566 int raise = checkScaleNonZero((long) newScale - yscale);
4567 long scaledYs;
4568 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4569 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4570 quotient = divideAndRound(BigInteger.valueOf(xs),
4571 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4572 } else {
4573 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4574 }
4575 }
4576 }
4577 } else {
4578 // abs(scaledX) <= abs(ys)
4579 // result is "scaledX * 10^msp / ys"
4580 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4581 if(cmp==0) {
4582 // abs(scaleX)== abs(ys) => result will be scaled 10^mcp + correct sign
4583 quotient = roundedTenPower(((scaledX < 0) == (ys < 0)) ? 1 : -1, mcp, scl, checkScaleNonZero(preferredScale));
4584 } else {
4585 // abs(scaledX) < abs(ys)
4586 long scaledXs;
4587 if ((scaledXs = longMultiplyPowerTen(scaledX, mcp)) == INFLATED) {
4588 quotient = null;
4589 if(mcp<LONG_TEN_POWERS_TABLE.length) {
4590 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4591 }
4592 if(quotient==null) {
4593 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp);
4594 quotient = divideAndRound(rb, ys,
4595 scl, roundingMode, checkScaleNonZero(preferredScale));
4596 }
4597 } else {
4598 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4599 }
4600 }
4601 }
4602 // doRound, here, only affects 1000000000 case.
4603 return doRound(quotient,mc);
4604 }
4605
4606 /**
4607 * Returns a {@code BigDecimal} whose value is {@code (xs /
4608 * ys)}, with rounding according to the context settings.
4609 */
4610 private static BigDecimal divide(final long xs, int xscale, final long ys, int yscale, long preferredScale, MathContext mc) {
4611 int mcp = mc.precision;
4612 if(xscale <= yscale && yscale < 18 && mcp<18) {
4613 return divideSmallFastPath(xs, xscale, ys, yscale, preferredScale, mc);
4614 }
4615 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
4616 yscale -= 1; // [that is, divisor *= 10]
4617 }
4618 int roundingMode = mc.roundingMode.oldMode;
4619 // In order to find out whether the divide generates the exact result,
4620 // we avoid calling the above divide method. 'quotient' holds the
4621 // return BigDecimal object whose scale will be set to 'scl'.
4622 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4623 BigDecimal quotient;
4624 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
4625 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4626 long scaledXs;
4627 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
4628 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4629 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4630 } else {
4631 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4632 }
4633 } else {
4634 int newScale = checkScaleNonZero((long) xscale - mcp);
4635 // assert newScale >= yscale
4636 if (newScale == yscale) { // easy case
4637 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4638 } else {
4639 int raise = checkScaleNonZero((long) newScale - yscale);
4640 long scaledYs;
4641 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4642 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4643 quotient = divideAndRound(BigInteger.valueOf(xs),
4644 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4645 } else {
4646 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4647 }
4648 }
4649 }
4650 // doRound, here, only affects 1000000000 case.
4651 return doRound(quotient,mc);
4652 }
4653
4654 /**
4655 * Returns a {@code BigDecimal} whose value is {@code (xs /
4656 * ys)}, with rounding according to the context settings.
4657 */
4658 private static BigDecimal divide(BigInteger xs, int xscale, long ys, int yscale, long preferredScale, MathContext mc) {
4659 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4660 if ((-compareMagnitudeNormalized(ys, yscale, xs, xscale)) > 0) {// satisfy constraint (b)
4661 yscale -= 1; // [that is, divisor *= 10]
4662 }
4663 int mcp = mc.precision;
4664 int roundingMode = mc.roundingMode.oldMode;
4665
4666 // In order to find out whether the divide generates the exact result,
4667 // we avoid calling the above divide method. 'quotient' holds the
4668 // return BigDecimal object whose scale will be set to 'scl'.
4669 BigDecimal quotient;
4670 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4671 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
4672 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4673 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4674 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4675 } else {
4676 int newScale = checkScaleNonZero((long) xscale - mcp);
4677 // assert newScale >= yscale
4678 if (newScale == yscale) { // easy case
4679 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4680 } else {
4681 int raise = checkScaleNonZero((long) newScale - yscale);
4682 long scaledYs;
4683 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4684 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4685 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4686 } else {
4687 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4688 }
4689 }
4690 }
4691 // doRound, here, only affects 1000000000 case.
4692 return doRound(quotient, mc);
4693 }
4694
4695 /**
4696 * Returns a {@code BigDecimal} whose value is {@code (xs /
4697 * ys)}, with rounding according to the context settings.
4698 */
4699 private static BigDecimal divide(long xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
4700 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4701 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
4702 yscale -= 1; // [that is, divisor *= 10]
4703 }
4704 int mcp = mc.precision;
4705 int roundingMode = mc.roundingMode.oldMode;
4706
4707 // In order to find out whether the divide generates the exact result,
4708 // we avoid calling the above divide method. 'quotient' holds the
4709 // return BigDecimal object whose scale will be set to 'scl'.
4710 BigDecimal quotient;
4711 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4712 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
4713 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4714 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4715 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4716 } else {
4717 int newScale = checkScaleNonZero((long) xscale - mcp);
4718 int raise = checkScaleNonZero((long) newScale - yscale);
4719 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4720 quotient = divideAndRound(BigInteger.valueOf(xs), rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4721 }
4722 // doRound, here, only affects 1000000000 case.
4723 return doRound(quotient, mc);
4724 }
4725
4726 /**
4727 * Returns a {@code BigDecimal} whose value is {@code (xs /
4728 * ys)}, with rounding according to the context settings.
4729 */
4730 private static BigDecimal divide(BigInteger xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
4731 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4732 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
4733 yscale -= 1; // [that is, divisor *= 10]
4734 }
4735 int mcp = mc.precision;
4736 int roundingMode = mc.roundingMode.oldMode;
4737
4738 // In order to find out whether the divide generates the exact result,
4739 // we avoid calling the above divide method. 'quotient' holds the
4740 // return BigDecimal object whose scale will be set to 'scl'.
4741 BigDecimal quotient;
4742 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4743 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
4744 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4745 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4746 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4747 } else {
4748 int newScale = checkScaleNonZero((long) xscale - mcp);
4749 int raise = checkScaleNonZero((long) newScale - yscale);
4750 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4751 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4752 }
4753 // doRound, here, only affects 1000000000 case.
4754 return doRound(quotient, mc);
4755 }
4756
4757 /*
4758 * performs divideAndRound for (dividend0*dividend1, divisor)
4759 * returns null if quotient can't fit into long value;
4760 */
4761 private static BigDecimal multiplyDivideAndRound(long dividend0, long dividend1, long divisor, int scale, int roundingMode,
4762 int preferredScale) {
4763 int qsign = Long.signum(dividend0)*Long.signum(dividend1)*Long.signum(divisor);
4764 dividend0 = Math.abs(dividend0);
4765 dividend1 = Math.abs(dividend1);
4766 divisor = Math.abs(divisor);
4767 // multiply dividend0 * dividend1
4768 long d0_hi = dividend0 >>> 32;
4769 long d0_lo = dividend0 & LONG_MASK;
4770 long d1_hi = dividend1 >>> 32;
4771 long d1_lo = dividend1 & LONG_MASK;
4772 long product = d0_lo * d1_lo;
4773 long d0 = product & LONG_MASK;
4774 long d1 = product >>> 32;
4775 product = d0_hi * d1_lo + d1;
4776 d1 = product & LONG_MASK;
4777 long d2 = product >>> 32;
4778 product = d0_lo * d1_hi + d1;
4779 d1 = product & LONG_MASK;
4780 d2 += product >>> 32;
4781 long d3 = d2>>>32;
4782 d2 &= LONG_MASK;
4783 product = d0_hi*d1_hi + d2;
4784 d2 = product & LONG_MASK;
4785 d3 = ((product>>>32) + d3) & LONG_MASK;
4786 final long dividendHi = make64(d3,d2);
4787 final long dividendLo = make64(d1,d0);
4788 // divide
4789 return divideAndRound128(dividendHi, dividendLo, divisor, qsign, scale, roundingMode, preferredScale);
4790 }
4791
4792 private static final long DIV_NUM_BASE = (1L<<32); // Number base (32 bits).
4793
4794 /*
4795 * divideAndRound 128-bit value by long divisor.
4796 * returns null if quotient can't fit into long value;
4797 * Specialized version of Knuth's division
4798 */
4799 private static BigDecimal divideAndRound128(final long dividendHi, final long dividendLo, long divisor, int sign,
4800 int scale, int roundingMode, int preferredScale) {
4801 if (dividendHi >= divisor) {
4802 return null;
4803 }
4804 final int shift = Long.numberOfLeadingZeros(divisor);
4805 divisor <<= shift;
4806
4807 final long v1 = divisor >>> 32;
4808 final long v0 = divisor & LONG_MASK;
4809
4810 long q1, q0;
4811 long r_tmp;
4812
4813 long tmp = dividendLo << shift;
4814 long u1 = tmp >>> 32;
4815 long u0 = tmp & LONG_MASK;
4816
4817 tmp = (dividendHi << shift) | (dividendLo >>> 64 - shift);
4818 long u2 = tmp & LONG_MASK;
4819 tmp = divWord(tmp,v1);
4820 q1 = tmp & LONG_MASK;
4821 r_tmp = tmp >>> 32;
4822 while(q1 >= DIV_NUM_BASE || unsignedLongCompare(q1*v0, make64(r_tmp, u1))) {
4823 q1--;
4824 r_tmp += v1;
4825 if (r_tmp >= DIV_NUM_BASE)
4826 break;
4827 }
4828 tmp = mulsub(u2,u1,v1,v0,q1);
4829 u1 = tmp & LONG_MASK;
4830 tmp = divWord(tmp,v1);
4831 q0 = tmp & LONG_MASK;
4832 r_tmp = tmp >>> 32;
4833 while(q0 >= DIV_NUM_BASE || unsignedLongCompare(q0*v0,make64(r_tmp,u0))) {
4834 q0--;
4835 r_tmp += v1;
4836 if (r_tmp >= DIV_NUM_BASE)
4837 break;
4838 }
4839 if((int)q1 < 0) {
4840 // result (which is positive and unsigned here)
4841 // can't fit into long due to sign bit is used for value
4842 MutableBigInteger mq = new MutableBigInteger(new int[]{(int)q1, (int)q0});
4843 if (roundingMode == ROUND_DOWN && scale == preferredScale) {
4844 return mq.toBigDecimal(sign, scale);
4845 }
4846 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
4847 if (r != 0) {
4848 if(needIncrement(divisor >>> shift, roundingMode, sign, mq, r)){
4849 mq.add(MutableBigInteger.ONE);
4850 }
4851 return mq.toBigDecimal(sign, scale);
4852 } else {
4853 if (preferredScale != scale) {
4854 BigInteger intVal = mq.toBigInteger(sign);
4855 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
4856 } else {
4857 return mq.toBigDecimal(sign, scale);
4858 }
4859 }
4860 }
4861 long q = make64(q1,q0);
4862 q*=sign;
4863 if (roundingMode == ROUND_DOWN && scale == preferredScale)
4864 return valueOf(q, scale);
4865 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
4866 if (r != 0) {
4867 boolean increment = needIncrement(divisor >>> shift, roundingMode, sign, q, r);
4868 return valueOf((increment ? q + sign : q), scale);
4869 } else {
4870 if (preferredScale != scale) {
4871 return createAndStripZerosToMatchScale(q, scale, preferredScale);
4872 } else {
4873 return valueOf(q, scale);
4874 }
4875 }
4876 }
4877
4878 /*
4879 * calculate divideAndRound for ldividend*10^raise / divisor
4880 * when abs(dividend)==abs(divisor);
4881 */
4882 private static BigDecimal roundedTenPower(int qsign, int raise, int scale, int preferredScale) {
4883 if (scale > preferredScale) {
4884 int diff = scale - preferredScale;
4885 if(diff < raise) {
4886 return scaledTenPow(raise - diff, qsign, preferredScale);
4887 } else {
4888 return valueOf(qsign,scale-raise);
4889 }
4890 } else {
4891 return scaledTenPow(raise, qsign, scale);
4892 }
4893 }
4894
4895 static BigDecimal scaledTenPow(int n, int sign, int scale) {
4896 if (n < LONG_TEN_POWERS_TABLE.length)
4897 return valueOf(sign*LONG_TEN_POWERS_TABLE[n],scale);
4898 else {
4899 BigInteger unscaledVal = bigTenToThe(n);
4900 if(sign==-1) {
4901 unscaledVal = unscaledVal.negate();
4902 }
4903 return new BigDecimal(unscaledVal, INFLATED, scale, n+1);
4904 }
4905 }
4906
4907 private static long divWord(long n, long dLong) {
4908 long r;
4909 long q;
4910 if (dLong == 1) {
4911 q = (int)n;
4912 return (q & LONG_MASK);
4913 }
4914 // Approximate the quotient and remainder
4915 q = (n >>> 1) / (dLong >>> 1);
4916 r = n - q*dLong;
4917
4918 // Correct the approximation
4919 while (r < 0) {
4920 r += dLong;
4921 q--;
4922 }
4923 while (r >= dLong) {
4924 r -= dLong;
4925 q++;
4926 }
4927 // n - q*dlong == r && 0 <= r <dLong, hence we're done.
4928 return (r << 32) | (q & LONG_MASK);
4929 }
4930
4931 private static long make64(long hi, long lo) {
4932 return hi<<32 | lo;
4933 }
4934
4935 private static long mulsub(long u1, long u0, final long v1, final long v0, long q0) {
4936 long tmp = u0 - q0*v0;
4937 return make64(u1 + (tmp>>>32) - q0*v1,tmp & LONG_MASK);
4938 }
4939
4940 private static boolean unsignedLongCompare(long one, long two) {
4941 return (one+Long.MIN_VALUE) > (two+Long.MIN_VALUE);
4942 }
4943
4944 private static boolean unsignedLongCompareEq(long one, long two) {
4945 return (one+Long.MIN_VALUE) >= (two+Long.MIN_VALUE);
4946 }
4947
4948
4949 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4950 private static int compareMagnitudeNormalized(long xs, int xscale, long ys, int yscale) {
4951 // assert xs!=0 && ys!=0
4952 int sdiff = xscale - yscale;
4953 if (sdiff != 0) {
4954 if (sdiff < 0) {
4955 xs = longMultiplyPowerTen(xs, -sdiff);
4956 } else { // sdiff > 0
4957 ys = longMultiplyPowerTen(ys, sdiff);
4958 }
4959 }
4960 if (xs != INFLATED)
4961 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
4962 else
4963 return 1;
4964 }
4965
4966 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4967 private static int compareMagnitudeNormalized(long xs, int xscale, BigInteger ys, int yscale) {
4968 // assert "ys can't be represented as long"
4969 if (xs == 0)
4970 return -1;
4971 int sdiff = xscale - yscale;
4972 if (sdiff < 0) {
4973 if (longMultiplyPowerTen(xs, -sdiff) == INFLATED ) {
4974 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
4975 }
4976 }
4977 return -1;
4978 }
4979
4980 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4981 private static int compareMagnitudeNormalized(BigInteger xs, int xscale, BigInteger ys, int yscale) {
4982 int sdiff = xscale - yscale;
4983 if (sdiff < 0) {
4984 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
4985 } else { // sdiff >= 0
4986 return xs.compareMagnitude(bigMultiplyPowerTen(ys, sdiff));
4987 }
4988 }
4989
4990 private static long multiply(long x, long y){
4991 long product = x * y;
4992 long ax = Math.abs(x);
4993 long ay = Math.abs(y);
4994 if (((ax | ay) >>> 31 == 0) || (y == 0) || (product / y == x)){
4995 return product;
4996 }
4997 return INFLATED;
4998 }
4999
5000 private static BigDecimal multiply(long x, long y, int scale) {
5001 long product = multiply(x, y);
5002 if(product!=INFLATED) {
5003 return valueOf(product,scale);
5004 }
5005 return new BigDecimal(BigInteger.valueOf(x).multiply(y),INFLATED,scale,0);
5006 }
5007
5008 private static BigDecimal multiply(long x, BigInteger y, int scale) {
5009 if(x==0) {
5010 return zeroValueOf(scale);
5011 }
5012 return new BigDecimal(y.multiply(x),INFLATED,scale,0);
5013 }
5014
5015 private static BigDecimal multiply(BigInteger x, BigInteger y, int scale) {
5016 return new BigDecimal(x.multiply(y),INFLATED,scale,0);
5017 }
5018
5019 /**
5020 * Multiplies two long values and rounds according {@code MathContext}
5021 */
5022 private static BigDecimal multiplyAndRound(long x, long y, int scale, MathContext mc) {
5023 long product = multiply(x, y);
5024 if(product!=INFLATED) {
5025 return doRound(product, scale, mc);
5026 }
5027 // attempt to do it in 128 bits
5028 int rsign = 1;
5029 if(x < 0) {
5030 x = -x;
5031 rsign = -1;
5032 }
5033 if(y < 0) {
5034 y = -y;
5035 rsign *= -1;
5036 }
5037 // multiply dividend0 * dividend1
5038 long m0_hi = x >>> 32;
5039 long m0_lo = x & LONG_MASK;
5040 long m1_hi = y >>> 32;
5041 long m1_lo = y & LONG_MASK;
5042 product = m0_lo * m1_lo;
5043 long m0 = product & LONG_MASK;
5044 long m1 = product >>> 32;
5045 product = m0_hi * m1_lo + m1;
5046 m1 = product & LONG_MASK;
5047 long m2 = product >>> 32;
5048 product = m0_lo * m1_hi + m1;
5049 m1 = product & LONG_MASK;
5050 m2 += product >>> 32;
5051 long m3 = m2>>>32;
5052 m2 &= LONG_MASK;
5053 product = m0_hi*m1_hi + m2;
5054 m2 = product & LONG_MASK;
5055 m3 = ((product>>>32) + m3) & LONG_MASK;
5056 final long mHi = make64(m3,m2);
5057 final long mLo = make64(m1,m0);
5058 BigDecimal res = doRound128(mHi, mLo, rsign, scale, mc);
5059 if(res!=null) {
5060 return res;
5061 }
5062 res = new BigDecimal(BigInteger.valueOf(x).multiply(y*rsign), INFLATED, scale, 0);
5063 return doRound(res,mc);
5064 }
5065
5066 private static BigDecimal multiplyAndRound(long x, BigInteger y, int scale, MathContext mc) {
5067 if(x==0) {
5068 return zeroValueOf(scale);
5069 }
5070 return doRound(y.multiply(x), scale, mc);
5071 }
5072
5073 private static BigDecimal multiplyAndRound(BigInteger x, BigInteger y, int scale, MathContext mc) {
5074 return doRound(x.multiply(y), scale, mc);
5075 }
5076
5077 /**
5078 * rounds 128-bit value according {@code MathContext}
5079 * returns null if result can't be repsented as compact BigDecimal.
5080 */
5081 private static BigDecimal doRound128(long hi, long lo, int sign, int scale, MathContext mc) {
5082 int mcp = mc.precision;
5083 int drop;
5084 BigDecimal res = null;
5085 if(((drop = precision(hi, lo) - mcp) > 0)&&(drop<LONG_TEN_POWERS_TABLE.length)) {
5086 scale = checkScaleNonZero((long)scale - drop);
5087 res = divideAndRound128(hi, lo, LONG_TEN_POWERS_TABLE[drop], sign, scale, mc.roundingMode.oldMode, scale);
5088 }
5089 if(res!=null) {
5090 return doRound(res,mc);
5091 }
5092 return null;
5093 }
5094
5095 private static final long[][] LONGLONG_TEN_POWERS_TABLE = {
5096 { 0L, 0x8AC7230489E80000L }, //10^19
5097 { 0x5L, 0x6bc75e2d63100000L }, //10^20
5098 { 0x36L, 0x35c9adc5dea00000L }, //10^21
5099 { 0x21eL, 0x19e0c9bab2400000L }, //10^22
5100 { 0x152dL, 0x02c7e14af6800000L }, //10^23
5101 { 0xd3c2L, 0x1bcecceda1000000L }, //10^24
5102 { 0x84595L, 0x161401484a000000L }, //10^25
5103 { 0x52b7d2L, 0xdcc80cd2e4000000L }, //10^26
5104 { 0x33b2e3cL, 0x9fd0803ce8000000L }, //10^27
5105 { 0x204fce5eL, 0x3e25026110000000L }, //10^28
5106 { 0x1431e0faeL, 0x6d7217caa0000000L }, //10^29
5107 { 0xc9f2c9cd0L, 0x4674edea40000000L }, //10^30
5108 { 0x7e37be2022L, 0xc0914b2680000000L }, //10^31
5109 { 0x4ee2d6d415bL, 0x85acef8100000000L }, //10^32
5110 { 0x314dc6448d93L, 0x38c15b0a00000000L }, //10^33
5111 { 0x1ed09bead87c0L, 0x378d8e6400000000L }, //10^34
5112 { 0x13426172c74d82L, 0x2b878fe800000000L }, //10^35
5113 { 0xc097ce7bc90715L, 0xb34b9f1000000000L }, //10^36
5114 { 0x785ee10d5da46d9L, 0x00f436a000000000L }, //10^37
5115 { 0x4b3b4ca85a86c47aL, 0x098a224000000000L }, //10^38
5116 };
5117
5118 /*
5119 * returns precision of 128-bit value
5120 */
5121 private static int precision(long hi, long lo){
5122 if(hi==0) {
5123 if(lo>=0) {
5124 return longDigitLength(lo);
5125 }
5126 return (unsignedLongCompareEq(lo, LONGLONG_TEN_POWERS_TABLE[0][1])) ? 20 : 19;
5127 // 0x8AC7230489E80000L = unsigned 2^19
5128 }
5129 int r = ((128 - Long.numberOfLeadingZeros(hi) + 1) * 1233) >>> 12;
5130 int idx = r-19;
5131 return (idx >= LONGLONG_TEN_POWERS_TABLE.length || longLongCompareMagnitude(hi, lo,
5132 LONGLONG_TEN_POWERS_TABLE[idx][0], LONGLONG_TEN_POWERS_TABLE[idx][1])) ? r : r + 1;
5133 }
5134
5135 /*
5136 * returns true if 128 bit number <hi0,lo0> is less then <hi1,lo1>
5137 * hi0 & hi1 should be non-negative
5138 */
5139 private static boolean longLongCompareMagnitude(long hi0, long lo0, long hi1, long lo1) {
5140 if(hi0!=hi1) {
5141 return hi0<hi1;
5142 }
5143 return (lo0+Long.MIN_VALUE) <(lo1+Long.MIN_VALUE);
5144 }
5145
5146 private static BigDecimal divide(long dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5147 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5148 int newScale = scale + divisorScale;
5149 int raise = newScale - dividendScale;
5150 if(raise<LONG_TEN_POWERS_TABLE.length) {
5151 long xs = dividend;
5152 if ((xs = longMultiplyPowerTen(xs, raise)) != INFLATED) {
5153 return divideAndRound(xs, divisor, scale, roundingMode, scale);
5154 }
5155 BigDecimal q = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[raise], dividend, divisor, scale, roundingMode, scale);
5156 if(q!=null) {
5157 return q;
5158 }
5159 }
5160 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5161 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5162 } else {
5163 int newScale = checkScale(divisor,(long)dividendScale - scale);
5164 int raise = newScale - divisorScale;
5165 if(raise<LONG_TEN_POWERS_TABLE.length) {
5166 long ys = divisor;
5167 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5168 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5169 }
5170 }
5171 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5172 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5173 }
5174 }
5175
5176 private static BigDecimal divide(BigInteger dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5177 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5178 int newScale = scale + divisorScale;
5179 int raise = newScale - dividendScale;
5180 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5181 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5182 } else {
5183 int newScale = checkScale(divisor,(long)dividendScale - scale);
5184 int raise = newScale - divisorScale;
5185 if(raise<LONG_TEN_POWERS_TABLE.length) {
5186 long ys = divisor;
5187 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5188 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5189 }
5190 }
5191 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5192 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5193 }
5194 }
5195
5196 private static BigDecimal divide(long dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5197 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5198 int newScale = scale + divisorScale;
5199 int raise = newScale - dividendScale;
5200 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5201 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5202 } else {
5203 int newScale = checkScale(divisor,(long)dividendScale - scale);
5204 int raise = newScale - divisorScale;
5205 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5206 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5207 }
5208 }
5209
5210 private static BigDecimal divide(BigInteger dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5211 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5212 int newScale = scale + divisorScale;
5213 int raise = newScale - dividendScale;
5214 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5215 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5216 } else {
5217 int newScale = checkScale(divisor,(long)dividendScale - scale);
5218 int raise = newScale - divisorScale;
5219 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5220 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5221 }
5222 }
5223
5224 }