1 /*
2 * Copyright (c) 1996, 2019, 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 static java.math.BigInteger.LONG_MASK;
33 import java.util.Arrays;
34 import java.util.Objects;
35
36 /**
37 * Immutable, arbitrary-precision signed decimal numbers. A
38 * {@code BigDecimal} consists of an arbitrary precision integer
39 * <i>unscaled value</i> and a 32-bit integer <i>scale</i>. If zero
40 * or positive, the scale is the number of digits to the right of the
41 * decimal point. If negative, the unscaled value of the number is
42 * multiplied by ten to the power of the negation of the scale. The
43 * value of the number represented by the {@code BigDecimal} is
44 * therefore <code>(unscaledValue × 10<sup>-scale</sup>)</code>.
45 *
46 * <p>The {@code BigDecimal} class provides operations for
47 * arithmetic, scale manipulation, rounding, comparison, hashing, and
48 * format conversion. The {@link #toString} method provides a
49 * canonical representation of a {@code BigDecimal}.
50 *
51 * <p>The {@code BigDecimal} class gives its user complete control
52 * over rounding behavior. If no rounding mode is specified and the
53 * exact result cannot be represented, an exception is thrown;
54 * otherwise, calculations can be carried out to a chosen precision
55 * and rounding mode by supplying an appropriate {@link MathContext}
56 * object to the operation. In either case, eight <em>rounding
57 * modes</em> are provided for the control of rounding. Using the
58 * integer fields in this class (such as {@link #ROUND_HALF_UP}) to
59 * represent rounding mode is deprecated; the enumeration values
60 * of the {@code RoundingMode} {@code enum}, (such as {@link
61 * RoundingMode#HALF_UP}) should be used instead.
62 *
63 * <p>When a {@code MathContext} object is supplied with a precision
64 * setting of 0 (for example, {@link MathContext#UNLIMITED}),
65 * arithmetic operations are exact, as are the arithmetic methods
66 * which take no {@code MathContext} object. (This is the only
67 * behavior that was supported in releases prior to 5.) As a
68 * corollary of computing the exact result, the rounding mode setting
69 * of a {@code MathContext} object with a precision setting of 0 is
70 * not used and thus irrelevant. In the case of divide, the exact
71 * quotient could have an infinitely long decimal expansion; for
72 * example, 1 divided by 3. If the quotient has a nonterminating
73 * decimal expansion and the operation is specified to return an exact
74 * result, an {@code ArithmeticException} is thrown. Otherwise, the
75 * exact result of the division is returned, as done for other
76 * operations.
77 *
78 * <p>When the precision setting is not 0, the rules of
79 * {@code BigDecimal} arithmetic are broadly compatible with selected
80 * modes of operation of the arithmetic defined in ANSI X3.274-1996
81 * and ANSI X3.274-1996/AM 1-2000 (section 7.4). Unlike those
82 * standards, {@code BigDecimal} includes many rounding modes, which
83 * were mandatory for division in {@code BigDecimal} releases prior
84 * to 5. Any conflicts between these ANSI standards and the
85 * {@code BigDecimal} specification are resolved in favor of
86 * {@code BigDecimal}.
87 *
88 * <p>Since the same numerical value can have different
89 * representations (with different scales), the rules of arithmetic
90 * and rounding must specify both the numerical result and the scale
91 * used in the result's representation.
92 *
93 *
94 * <p>In general the rounding modes and precision setting determine
95 * how operations return results with a limited number of digits when
96 * the exact result has more digits (perhaps infinitely many in the
97 * case of division and square root) than the number of digits returned.
98 *
99 * First, the
100 * total number of digits to return is specified by the
101 * {@code MathContext}'s {@code precision} setting; this determines
102 * the result's <i>precision</i>. The digit count starts from the
103 * leftmost nonzero digit of the exact result. The rounding mode
104 * determines how any discarded trailing digits affect the returned
105 * result.
106 *
107 * <p>For all arithmetic operators , the operation is carried out as
108 * though an exact intermediate result were first calculated and then
109 * rounded to the number of digits specified by the precision setting
110 * (if necessary), using the selected rounding mode. If the exact
111 * result is not returned, some digit positions of the exact result
112 * are discarded. When rounding increases the magnitude of the
113 * returned result, it is possible for a new digit position to be
114 * created by a carry propagating to a leading {@literal "9"} digit.
115 * For example, rounding the value 999.9 to three digits rounding up
116 * would be numerically equal to one thousand, represented as
117 * 100×10<sup>1</sup>. In such cases, the new {@literal "1"} is
118 * the leading digit position of the returned result.
119 *
120 * <p>Besides a logical exact result, each arithmetic operation has a
121 * preferred scale for representing a result. The preferred
122 * scale for each operation is listed in the table below.
123 *
124 * <table class="striped" style="text-align:left">
125 * <caption>Preferred Scales for Results of Arithmetic Operations
126 * </caption>
127 * <thead>
128 * <tr><th scope="col">Operation</th><th scope="col">Preferred Scale of Result</th></tr>
129 * </thead>
130 * <tbody>
131 * <tr><th scope="row">Add</th><td>max(addend.scale(), augend.scale())</td>
132 * <tr><th scope="row">Subtract</th><td>max(minuend.scale(), subtrahend.scale())</td>
133 * <tr><th scope="row">Multiply</th><td>multiplier.scale() + multiplicand.scale()</td>
134 * <tr><th scope="row">Divide</th><td>dividend.scale() - divisor.scale()</td>
135 * <tr><th scope="row">Square root</th><td>radicand.scale()/2</td>
136 * </tbody>
137 * </table>
138 *
139 * These scales are the ones used by the methods which return exact
140 * arithmetic results; except that an exact divide may have to use a
141 * larger scale since the exact result may have more digits. For
142 * example, {@code 1/32} is {@code 0.03125}.
143 *
144 * <p>Before rounding, the scale of the logical exact intermediate
145 * result is the preferred scale for that operation. If the exact
146 * numerical result cannot be represented in {@code precision}
147 * digits, rounding selects the set of digits to return and the scale
148 * of the result is reduced from the scale of the intermediate result
149 * to the least scale which can represent the {@code precision}
150 * digits actually returned. If the exact result can be represented
151 * with at most {@code precision} digits, the representation
152 * of the result with the scale closest to the preferred scale is
153 * returned. In particular, an exactly representable quotient may be
154 * represented in fewer than {@code precision} digits by removing
155 * trailing zeros and decreasing the scale. For example, rounding to
156 * three digits using the {@linkplain RoundingMode#FLOOR floor}
157 * rounding mode, <br>
158 *
159 * {@code 19/100 = 0.19 // integer=19, scale=2} <br>
160 *
161 * but<br>
162 *
163 * {@code 21/110 = 0.190 // integer=190, scale=3} <br>
164 *
165 * <p>Note that for add, subtract, and multiply, the reduction in
166 * scale will equal the number of digit positions of the exact result
167 * which are discarded. If the rounding causes a carry propagation to
168 * create a new high-order digit position, an additional digit of the
169 * result is discarded than when no new digit position is created.
170 *
171 * <p>Other methods may have slightly different rounding semantics.
172 * For example, the result of the {@code pow} method using the
173 * {@linkplain #pow(int, MathContext) specified algorithm} can
174 * occasionally differ from the rounded mathematical result by more
175 * than one unit in the last place, one <i>{@linkplain #ulp() ulp}</i>.
176 *
177 * <p>Two types of operations are provided for manipulating the scale
178 * of a {@code BigDecimal}: scaling/rounding operations and decimal
179 * point motion operations. Scaling/rounding operations ({@link
180 * #setScale setScale} and {@link #round round}) return a
181 * {@code BigDecimal} whose value is approximately (or exactly) equal
182 * to that of the operand, but whose scale or precision is the
183 * specified value; that is, they increase or decrease the precision
184 * of the stored number with minimal effect on its value. Decimal
185 * point motion operations ({@link #movePointLeft movePointLeft} and
186 * {@link #movePointRight movePointRight}) return a
187 * {@code BigDecimal} created from the operand by moving the decimal
188 * point a specified distance in the specified direction.
189 *
190 * <p>For the sake of brevity and clarity, pseudo-code is used
191 * throughout the descriptions of {@code BigDecimal} methods. The
192 * pseudo-code expression {@code (i + j)} is shorthand for "a
193 * {@code BigDecimal} whose value is that of the {@code BigDecimal}
194 * {@code i} added to that of the {@code BigDecimal}
195 * {@code j}." The pseudo-code expression {@code (i == j)} is
196 * shorthand for "{@code true} if and only if the
197 * {@code BigDecimal} {@code i} represents the same value as the
198 * {@code BigDecimal} {@code j}." Other pseudo-code expressions
199 * are interpreted similarly. Square brackets are used to represent
200 * the particular {@code BigInteger} and scale pair defining a
201 * {@code BigDecimal} value; for example [19, 2] is the
202 * {@code BigDecimal} numerically equal to 0.19 having a scale of 2.
203 *
204 *
205 * <p>All methods and constructors for this class throw
206 * {@code NullPointerException} when passed a {@code null} object
207 * reference for any input parameter.
208 *
209 * @apiNote Care should be exercised if {@code BigDecimal} objects
210 * are used as keys in a {@link java.util.SortedMap SortedMap} or
211 * elements in a {@link java.util.SortedSet SortedSet} since
212 * {@code BigDecimal}'s <i>natural ordering</i> is <em>inconsistent
213 * with equals</em>. See {@link Comparable}, {@link
214 * java.util.SortedMap} or {@link java.util.SortedSet} for more
215 * information.
216 *
217 * @see BigInteger
218 * @see MathContext
219 * @see RoundingMode
220 * @see java.util.SortedMap
221 * @see java.util.SortedSet
222 * @author Josh Bloch
223 * @author Mike Cowlishaw
224 * @author Joseph D. Darcy
225 * @author Sergey V. Kuksenko
226 * @since 1.1
227 */
228 public class BigDecimal extends Number implements Comparable<BigDecimal> {
229 /**
230 * The unscaled value of this BigDecimal, as returned by {@link
231 * #unscaledValue}.
232 *
233 * @serial
234 * @see #unscaledValue
235 */
236 private final BigInteger intVal;
237
238 /**
239 * The scale of this BigDecimal, as returned by {@link #scale}.
240 *
241 * @serial
242 * @see #scale
243 */
244 private final int scale; // Note: this may have any value, so
245 // calculations must be done in longs
246
247 /**
248 * The number of decimal digits in this BigDecimal, or 0 if the
249 * number of digits are not known (lookaside information). If
250 * nonzero, the value is guaranteed correct. Use the precision()
251 * method to obtain and set the value if it might be 0. This
252 * field is mutable until set nonzero.
253 *
254 * @since 1.5
255 */
256 private transient int precision;
257
258 /**
259 * Used to store the canonical string representation, if computed.
260 */
261 private transient String stringCache;
262
263 /**
264 * Sentinel value for {@link #intCompact} indicating the
265 * significand information is only available from {@code intVal}.
266 */
267 static final long INFLATED = Long.MIN_VALUE;
268
269 private static final BigInteger INFLATED_BIGINT = BigInteger.valueOf(INFLATED);
270
271 /**
272 * If the absolute value of the significand of this BigDecimal is
273 * less than or equal to {@code Long.MAX_VALUE}, the value can be
274 * compactly stored in this field and used in computations.
275 */
276 private final transient long intCompact;
277
278 // All 18-digit base ten strings fit into a long; not all 19-digit
279 // strings will
280 private static final int MAX_COMPACT_DIGITS = 18;
281
282 /* Appease the serialization gods */
283 @java.io.Serial
284 private static final long serialVersionUID = 6108874887143696463L;
285
286 private static final ThreadLocal<StringBuilderHelper>
287 threadLocalStringBuilderHelper = new ThreadLocal<StringBuilderHelper>() {
288 @Override
289 protected StringBuilderHelper initialValue() {
290 return new StringBuilderHelper();
291 }
292 };
293
294 // Cache of common small BigDecimal values.
295 private static final BigDecimal ZERO_THROUGH_TEN[] = {
296 new BigDecimal(BigInteger.ZERO, 0, 0, 1),
297 new BigDecimal(BigInteger.ONE, 1, 0, 1),
298 new BigDecimal(BigInteger.TWO, 2, 0, 1),
299 new BigDecimal(BigInteger.valueOf(3), 3, 0, 1),
300 new BigDecimal(BigInteger.valueOf(4), 4, 0, 1),
301 new BigDecimal(BigInteger.valueOf(5), 5, 0, 1),
302 new BigDecimal(BigInteger.valueOf(6), 6, 0, 1),
303 new BigDecimal(BigInteger.valueOf(7), 7, 0, 1),
304 new BigDecimal(BigInteger.valueOf(8), 8, 0, 1),
305 new BigDecimal(BigInteger.valueOf(9), 9, 0, 1),
306 new BigDecimal(BigInteger.TEN, 10, 0, 2),
307 };
308
309 // Cache of zero scaled by 0 - 15
310 private static final BigDecimal[] ZERO_SCALED_BY = {
311 ZERO_THROUGH_TEN[0],
312 new BigDecimal(BigInteger.ZERO, 0, 1, 1),
313 new BigDecimal(BigInteger.ZERO, 0, 2, 1),
314 new BigDecimal(BigInteger.ZERO, 0, 3, 1),
315 new BigDecimal(BigInteger.ZERO, 0, 4, 1),
316 new BigDecimal(BigInteger.ZERO, 0, 5, 1),
317 new BigDecimal(BigInteger.ZERO, 0, 6, 1),
318 new BigDecimal(BigInteger.ZERO, 0, 7, 1),
319 new BigDecimal(BigInteger.ZERO, 0, 8, 1),
320 new BigDecimal(BigInteger.ZERO, 0, 9, 1),
321 new BigDecimal(BigInteger.ZERO, 0, 10, 1),
322 new BigDecimal(BigInteger.ZERO, 0, 11, 1),
323 new BigDecimal(BigInteger.ZERO, 0, 12, 1),
324 new BigDecimal(BigInteger.ZERO, 0, 13, 1),
325 new BigDecimal(BigInteger.ZERO, 0, 14, 1),
326 new BigDecimal(BigInteger.ZERO, 0, 15, 1),
327 };
328
329 // Half of Long.MIN_VALUE & Long.MAX_VALUE.
330 private static final long HALF_LONG_MAX_VALUE = Long.MAX_VALUE / 2;
331 private static final long HALF_LONG_MIN_VALUE = Long.MIN_VALUE / 2;
332
333 // Constants
334 /**
335 * The value 0, with a scale of 0.
336 *
337 * @since 1.5
338 */
339 public static final BigDecimal ZERO =
340 ZERO_THROUGH_TEN[0];
341
342 /**
343 * The value 1, with a scale of 0.
344 *
345 * @since 1.5
346 */
347 public static final BigDecimal ONE =
348 ZERO_THROUGH_TEN[1];
349
350 /**
351 * The value 10, with a scale of 0.
352 *
353 * @since 1.5
354 */
355 public static final BigDecimal TEN =
356 ZERO_THROUGH_TEN[10];
357
358 /**
359 * The value 0.1, with a scale of 1.
360 */
361 private static final BigDecimal ONE_TENTH = valueOf(1L, 1);
362
363 /**
364 * The value 0.5, with a scale of 1.
365 */
366 private static final BigDecimal ONE_HALF = valueOf(5L, 1);
367
368 // Constructors
369
370 /**
371 * Trusted package private constructor.
372 * Trusted simply means if val is INFLATED, intVal could not be null and
373 * if intVal is null, val could not be INFLATED.
374 */
375 BigDecimal(BigInteger intVal, long val, int scale, int prec) {
376 this.scale = scale;
377 this.precision = prec;
378 this.intCompact = val;
379 this.intVal = intVal;
380 }
381
382 /**
383 * Translates a character array representation of a
384 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
385 * same sequence of characters as the {@link #BigDecimal(String)}
386 * constructor, while allowing a sub-array to be specified.
387 *
388 * @implNote If the sequence of characters is already available
389 * within a character array, using this constructor is faster than
390 * converting the {@code char} array to string and using the
391 * {@code BigDecimal(String)} constructor.
392 *
393 * @param in {@code char} array that is the source of characters.
394 * @param offset first character in the array to inspect.
395 * @param len number of characters to consider.
396 * @throws NumberFormatException if {@code in} is not a valid
397 * representation of a {@code BigDecimal} or the defined subarray
398 * is not wholly within {@code in}.
399 * @since 1.5
400 */
401 public BigDecimal(char[] in, int offset, int len) {
402 this(in,offset,len,MathContext.UNLIMITED);
403 }
404
405 /**
406 * Translates a character array representation of a
407 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
408 * same sequence of characters as the {@link #BigDecimal(String)}
409 * constructor, while allowing a sub-array to be specified and
410 * with rounding according to the context settings.
411 *
412 * @implNote If the sequence of characters is already available
413 * within a character array, using this constructor is faster than
414 * converting the {@code char} array to string and using the
415 * {@code BigDecimal(String)} constructor.
416 *
417 * @param in {@code char} array that is the source of characters.
418 * @param offset first character in the array to inspect.
419 * @param len number of characters to consider.
420 * @param mc the context to use.
421 * @throws ArithmeticException if the result is inexact but the
422 * rounding mode is {@code UNNECESSARY}.
423 * @throws NumberFormatException if {@code in} is not a valid
424 * representation of a {@code BigDecimal} or the defined subarray
425 * is not wholly within {@code in}.
426 * @since 1.5
427 */
428 public BigDecimal(char[] in, int offset, int len, MathContext mc) {
429 // protect against huge length, negative values, and integer overflow
430 try {
431 Objects.checkFromIndexSize(offset, len, in.length);
432 } catch (IndexOutOfBoundsException e) {
433 throw new NumberFormatException
434 ("Bad offset or len arguments for char[] input.");
435 }
436
437 // This is the primary string to BigDecimal constructor; all
438 // incoming strings end up here; it uses explicit (inline)
439 // parsing for speed and generates at most one intermediate
440 // (temporary) object (a char[] array) for non-compact case.
441
442 // Use locals for all fields values until completion
443 int prec = 0; // record precision value
444 int scl = 0; // record scale value
445 long rs = 0; // the compact value in long
446 BigInteger rb = null; // the inflated value in BigInteger
447 // use array bounds checking to handle too-long, len == 0,
448 // bad offset, etc.
449 try {
450 // handle the sign
451 boolean isneg = false; // assume positive
452 if (in[offset] == '-') {
453 isneg = true; // leading minus means negative
454 offset++;
455 len--;
456 } else if (in[offset] == '+') { // leading + allowed
457 offset++;
458 len--;
459 }
460
461 // should now be at numeric part of the significand
462 boolean dot = false; // true when there is a '.'
463 long exp = 0; // exponent
464 char c; // current character
465 boolean isCompact = (len <= MAX_COMPACT_DIGITS);
466 // integer significand array & idx is the index to it. The array
467 // is ONLY used when we can't use a compact representation.
468 int idx = 0;
469 if (isCompact) {
470 // First compact case, we need not to preserve the character
471 // and we can just compute the value in place.
472 for (; len > 0; offset++, len--) {
473 c = in[offset];
474 if ((c == '0')) { // have zero
475 if (prec == 0)
476 prec = 1;
477 else if (rs != 0) {
478 rs *= 10;
479 ++prec;
480 } // else digit is a redundant leading zero
481 if (dot)
482 ++scl;
483 } else if ((c >= '1' && c <= '9')) { // have digit
484 int digit = c - '0';
485 if (prec != 1 || rs != 0)
486 ++prec; // prec unchanged if preceded by 0s
487 rs = rs * 10 + digit;
488 if (dot)
489 ++scl;
490 } else if (c == '.') { // have dot
491 // have dot
492 if (dot) // two dots
493 throw new NumberFormatException("Character array"
494 + " contains more than one decimal point.");
495 dot = true;
496 } else if (Character.isDigit(c)) { // slow path
497 int digit = Character.digit(c, 10);
498 if (digit == 0) {
499 if (prec == 0)
500 prec = 1;
501 else if (rs != 0) {
502 rs *= 10;
503 ++prec;
504 } // else digit is a redundant leading zero
505 } else {
506 if (prec != 1 || rs != 0)
507 ++prec; // prec unchanged if preceded by 0s
508 rs = rs * 10 + digit;
509 }
510 if (dot)
511 ++scl;
512 } else if ((c == 'e') || (c == 'E')) {
513 exp = parseExp(in, offset, len);
514 // Next test is required for backwards compatibility
515 if ((int) exp != exp) // overflow
516 throw new NumberFormatException("Exponent overflow.");
517 break; // [saves a test]
518 } else {
519 throw new NumberFormatException("Character " + c
520 + " is neither a decimal digit number, decimal point, nor"
521 + " \"e\" notation exponential mark.");
522 }
523 }
524 if (prec == 0) // no digits found
525 throw new NumberFormatException("No digits found.");
526 // Adjust scale if exp is not zero.
527 if (exp != 0) { // had significant exponent
528 scl = adjustScale(scl, exp);
529 }
530 rs = isneg ? -rs : rs;
531 int mcp = mc.precision;
532 int drop = prec - mcp; // prec has range [1, MAX_INT], mcp has range [0, MAX_INT];
533 // therefore, this subtract cannot overflow
534 if (mcp > 0 && drop > 0) { // do rounding
535 while (drop > 0) {
536 scl = checkScaleNonZero((long) scl - drop);
537 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
538 prec = longDigitLength(rs);
539 drop = prec - mcp;
540 }
541 }
542 } else {
543 char coeff[] = new char[len];
544 for (; len > 0; offset++, len--) {
545 c = in[offset];
546 // have digit
547 if ((c >= '0' && c <= '9') || Character.isDigit(c)) {
548 // First compact case, we need not to preserve the character
549 // and we can just compute the value in place.
550 if (c == '0' || Character.digit(c, 10) == 0) {
551 if (prec == 0) {
552 coeff[idx] = c;
553 prec = 1;
554 } else if (idx != 0) {
555 coeff[idx++] = c;
556 ++prec;
557 } // else c must be a redundant leading zero
558 } else {
559 if (prec != 1 || idx != 0)
560 ++prec; // prec unchanged if preceded by 0s
561 coeff[idx++] = c;
562 }
563 if (dot)
564 ++scl;
565 continue;
566 }
567 // have dot
568 if (c == '.') {
569 // have dot
570 if (dot) // two dots
571 throw new NumberFormatException("Character array"
572 + " contains more than one decimal point.");
573 dot = true;
574 continue;
575 }
576 // exponent expected
577 if ((c != 'e') && (c != 'E'))
578 throw new NumberFormatException("Character array"
579 + " is missing \"e\" notation exponential mark.");
580 exp = parseExp(in, offset, len);
581 // Next test is required for backwards compatibility
582 if ((int) exp != exp) // overflow
583 throw new NumberFormatException("Exponent overflow.");
584 break; // [saves a test]
585 }
586 // here when no characters left
587 if (prec == 0) // no digits found
588 throw new NumberFormatException("No digits found.");
589 // Adjust scale if exp is not zero.
590 if (exp != 0) { // had significant exponent
591 scl = adjustScale(scl, exp);
592 }
593 // Remove leading zeros from precision (digits count)
594 rb = new BigInteger(coeff, isneg ? -1 : 1, prec);
595 rs = compactValFor(rb);
596 int mcp = mc.precision;
597 if (mcp > 0 && (prec > mcp)) {
598 if (rs == INFLATED) {
599 int drop = prec - mcp;
600 while (drop > 0) {
601 scl = checkScaleNonZero((long) scl - drop);
602 rb = divideAndRoundByTenPow(rb, drop, mc.roundingMode.oldMode);
603 rs = compactValFor(rb);
604 if (rs != INFLATED) {
605 prec = longDigitLength(rs);
606 break;
607 }
608 prec = bigDigitLength(rb);
609 drop = prec - mcp;
610 }
611 }
612 if (rs != INFLATED) {
613 int drop = prec - mcp;
614 while (drop > 0) {
615 scl = checkScaleNonZero((long) scl - drop);
616 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
617 prec = longDigitLength(rs);
618 drop = prec - mcp;
619 }
620 rb = null;
621 }
622 }
623 }
624 } catch (ArrayIndexOutOfBoundsException | NegativeArraySizeException e) {
625 NumberFormatException nfe = new NumberFormatException();
626 nfe.initCause(e);
627 throw nfe;
628 }
629 this.scale = scl;
630 this.precision = prec;
631 this.intCompact = rs;
632 this.intVal = rb;
633 }
634
635 private int adjustScale(int scl, long exp) {
636 long adjustedScale = scl - exp;
637 if (adjustedScale > Integer.MAX_VALUE || adjustedScale < Integer.MIN_VALUE)
638 throw new NumberFormatException("Scale out of range.");
639 scl = (int) adjustedScale;
640 return scl;
641 }
642
643 /*
644 * parse exponent
645 */
646 private static long parseExp(char[] in, int offset, int len){
647 long exp = 0;
648 offset++;
649 char c = in[offset];
650 len--;
651 boolean negexp = (c == '-');
652 // optional sign
653 if (negexp || c == '+') {
654 offset++;
655 c = in[offset];
656 len--;
657 }
658 if (len <= 0) // no exponent digits
659 throw new NumberFormatException("No exponent digits.");
660 // skip leading zeros in the exponent
661 while (len > 10 && (c=='0' || (Character.digit(c, 10) == 0))) {
662 offset++;
663 c = in[offset];
664 len--;
665 }
666 if (len > 10) // too many nonzero exponent digits
667 throw new NumberFormatException("Too many nonzero exponent digits.");
668 // c now holds first digit of exponent
669 for (;; len--) {
670 int v;
671 if (c >= '0' && c <= '9') {
672 v = c - '0';
673 } else {
674 v = Character.digit(c, 10);
675 if (v < 0) // not a digit
676 throw new NumberFormatException("Not a digit.");
677 }
678 exp = exp * 10 + v;
679 if (len == 1)
680 break; // that was final character
681 offset++;
682 c = in[offset];
683 }
684 if (negexp) // apply sign
685 exp = -exp;
686 return exp;
687 }
688
689 /**
690 * Translates a character array representation of a
691 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
692 * same sequence of characters as the {@link #BigDecimal(String)}
693 * constructor.
694 *
695 * @implNote If the sequence of characters is already available
696 * as a character array, using this constructor is faster than
697 * converting the {@code char} array to string and using the
698 * {@code BigDecimal(String)} constructor.
699 *
700 * @param in {@code char} array that is the source of characters.
701 * @throws NumberFormatException if {@code in} is not a valid
702 * representation of a {@code BigDecimal}.
703 * @since 1.5
704 */
705 public BigDecimal(char[] in) {
706 this(in, 0, in.length);
707 }
708
709 /**
710 * Translates a character array representation of a
711 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
712 * same sequence of characters as the {@link #BigDecimal(String)}
713 * constructor and with rounding according to the context
714 * settings.
715 *
716 * @implNote If the sequence of characters is already available
717 * as a character array, using this constructor is faster than
718 * converting the {@code char} array to string and using the
719 * {@code BigDecimal(String)} constructor.
720 *
721 * @param in {@code char} array that is the source of characters.
722 * @param mc the context to use.
723 * @throws ArithmeticException if the result is inexact but the
724 * rounding mode is {@code UNNECESSARY}.
725 * @throws NumberFormatException if {@code in} is not a valid
726 * representation of a {@code BigDecimal}.
727 * @since 1.5
728 */
729 public BigDecimal(char[] in, MathContext mc) {
730 this(in, 0, in.length, mc);
731 }
732
733 /**
734 * Translates the string representation of a {@code BigDecimal}
735 * into a {@code BigDecimal}. The string representation consists
736 * of an optional sign, {@code '+'} (<code> '\u002B'</code>) or
737 * {@code '-'} (<code>'\u002D'</code>), followed by a sequence of
738 * zero or more decimal digits ("the integer"), optionally
739 * followed by a fraction, optionally followed by an exponent.
740 *
741 * <p>The fraction consists of a decimal point followed by zero
742 * or more decimal digits. The string must contain at least one
743 * digit in either the integer or the fraction. The number formed
744 * by the sign, the integer and the fraction is referred to as the
745 * <i>significand</i>.
746 *
747 * <p>The exponent consists of the character {@code 'e'}
748 * (<code>'\u0065'</code>) or {@code 'E'} (<code>'\u0045'</code>)
749 * followed by one or more decimal digits. The value of the
750 * exponent must lie between -{@link Integer#MAX_VALUE} ({@link
751 * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive.
752 *
753 * <p>More formally, the strings this constructor accepts are
754 * described by the following grammar:
755 * <blockquote>
756 * <dl>
757 * <dt><i>BigDecimalString:</i>
758 * <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i>
759 * <dt><i>Sign:</i>
760 * <dd>{@code +}
761 * <dd>{@code -}
762 * <dt><i>Significand:</i>
763 * <dd><i>IntegerPart</i> {@code .} <i>FractionPart<sub>opt</sub></i>
764 * <dd>{@code .} <i>FractionPart</i>
765 * <dd><i>IntegerPart</i>
766 * <dt><i>IntegerPart:</i>
767 * <dd><i>Digits</i>
768 * <dt><i>FractionPart:</i>
769 * <dd><i>Digits</i>
770 * <dt><i>Exponent:</i>
771 * <dd><i>ExponentIndicator SignedInteger</i>
772 * <dt><i>ExponentIndicator:</i>
773 * <dd>{@code e}
774 * <dd>{@code E}
775 * <dt><i>SignedInteger:</i>
776 * <dd><i>Sign<sub>opt</sub> Digits</i>
777 * <dt><i>Digits:</i>
778 * <dd><i>Digit</i>
779 * <dd><i>Digits Digit</i>
780 * <dt><i>Digit:</i>
781 * <dd>any character for which {@link Character#isDigit}
782 * returns {@code true}, including 0, 1, 2 ...
783 * </dl>
784 * </blockquote>
785 *
786 * <p>The scale of the returned {@code BigDecimal} will be the
787 * number of digits in the fraction, or zero if the string
788 * contains no decimal point, subject to adjustment for any
789 * exponent; if the string contains an exponent, the exponent is
790 * subtracted from the scale. The value of the resulting scale
791 * must lie between {@code Integer.MIN_VALUE} and
792 * {@code Integer.MAX_VALUE}, inclusive.
793 *
794 * <p>The character-to-digit mapping is provided by {@link
795 * java.lang.Character#digit} set to convert to radix 10. The
796 * String may not contain any extraneous characters (whitespace,
797 * for example).
798 *
799 * <p><b>Examples:</b><br>
800 * The value of the returned {@code BigDecimal} is equal to
801 * <i>significand</i> × 10<sup> <i>exponent</i></sup>.
802 * For each string on the left, the resulting representation
803 * [{@code BigInteger}, {@code scale}] is shown on the right.
804 * <pre>
805 * "0" [0,0]
806 * "0.00" [0,2]
807 * "123" [123,0]
808 * "-123" [-123,0]
809 * "1.23E3" [123,-1]
810 * "1.23E+3" [123,-1]
811 * "12.3E+7" [123,-6]
812 * "12.0" [120,1]
813 * "12.3" [123,1]
814 * "0.00123" [123,5]
815 * "-1.23E-12" [-123,14]
816 * "1234.5E-4" [12345,5]
817 * "0E+7" [0,-7]
818 * "-0" [0,0]
819 * </pre>
820 *
821 * @apiNote For values other than {@code float} and
822 * {@code double} NaN and ±Infinity, this constructor is
823 * compatible with the values returned by {@link Float#toString}
824 * and {@link Double#toString}. This is generally the preferred
825 * way to convert a {@code float} or {@code double} into a
826 * BigDecimal, as it doesn't suffer from the unpredictability of
827 * the {@link #BigDecimal(double)} constructor.
828 *
829 * @param val String representation of {@code BigDecimal}.
830 *
831 * @throws NumberFormatException if {@code val} is not a valid
832 * representation of a {@code BigDecimal}.
833 */
834 public BigDecimal(String val) {
835 this(val.toCharArray(), 0, val.length());
836 }
837
838 /**
839 * Translates the string representation of a {@code BigDecimal}
840 * into a {@code BigDecimal}, accepting the same strings as the
841 * {@link #BigDecimal(String)} constructor, with rounding
842 * according to the context settings.
843 *
844 * @param val string representation of a {@code BigDecimal}.
845 * @param mc the context to use.
846 * @throws ArithmeticException if the result is inexact but the
847 * rounding mode is {@code UNNECESSARY}.
848 * @throws NumberFormatException if {@code val} is not a valid
849 * representation of a BigDecimal.
850 * @since 1.5
851 */
852 public BigDecimal(String val, MathContext mc) {
853 this(val.toCharArray(), 0, val.length(), mc);
854 }
855
856 /**
857 * Translates a {@code double} into a {@code BigDecimal} which
858 * is the exact decimal representation of the {@code double}'s
859 * binary floating-point value. The scale of the returned
860 * {@code BigDecimal} is the smallest value such that
861 * <code>(10<sup>scale</sup> × val)</code> is an integer.
862 * <p>
863 * <b>Notes:</b>
864 * <ol>
865 * <li>
866 * The results of this constructor can be somewhat unpredictable.
867 * One might assume that writing {@code new BigDecimal(0.1)} in
868 * Java creates a {@code BigDecimal} which is exactly equal to
869 * 0.1 (an unscaled value of 1, with a scale of 1), but it is
870 * actually equal to
871 * 0.1000000000000000055511151231257827021181583404541015625.
872 * This is because 0.1 cannot be represented exactly as a
873 * {@code double} (or, for that matter, as a binary fraction of
874 * any finite length). Thus, the value that is being passed
875 * <em>in</em> to the constructor is not exactly equal to 0.1,
876 * appearances notwithstanding.
877 *
878 * <li>
879 * The {@code String} constructor, on the other hand, is
880 * perfectly predictable: writing {@code new BigDecimal("0.1")}
881 * creates a {@code BigDecimal} which is <em>exactly</em> equal to
882 * 0.1, as one would expect. Therefore, it is generally
883 * recommended that the {@linkplain #BigDecimal(String)
884 * String constructor} be used in preference to this one.
885 *
886 * <li>
887 * When a {@code double} must be used as a source for a
888 * {@code BigDecimal}, note that this constructor provides an
889 * exact conversion; it does not give the same result as
890 * converting the {@code double} to a {@code String} using the
891 * {@link Double#toString(double)} method and then using the
892 * {@link #BigDecimal(String)} constructor. To get that result,
893 * use the {@code static} {@link #valueOf(double)} method.
894 * </ol>
895 *
896 * @param val {@code double} value to be converted to
897 * {@code BigDecimal}.
898 * @throws NumberFormatException if {@code val} is infinite or NaN.
899 */
900 public BigDecimal(double val) {
901 this(val,MathContext.UNLIMITED);
902 }
903
904 /**
905 * Translates a {@code double} into a {@code BigDecimal}, with
906 * rounding according to the context settings. The scale of the
907 * {@code BigDecimal} is the smallest value such that
908 * <code>(10<sup>scale</sup> × val)</code> is an integer.
909 *
910 * <p>The results of this constructor can be somewhat unpredictable
911 * and its use is generally not recommended; see the notes under
912 * the {@link #BigDecimal(double)} constructor.
913 *
914 * @param val {@code double} value to be converted to
915 * {@code BigDecimal}.
916 * @param mc the context to use.
917 * @throws ArithmeticException if the result is inexact but the
918 * RoundingMode is UNNECESSARY.
919 * @throws NumberFormatException if {@code val} is infinite or NaN.
920 * @since 1.5
921 */
922 public BigDecimal(double val, MathContext mc) {
923 if (Double.isInfinite(val) || Double.isNaN(val))
924 throw new NumberFormatException("Infinite or NaN");
925 // Translate the double into sign, exponent and significand, according
926 // to the formulae in JLS, Section 20.10.22.
927 long valBits = Double.doubleToLongBits(val);
928 int sign = ((valBits >> 63) == 0 ? 1 : -1);
929 int exponent = (int) ((valBits >> 52) & 0x7ffL);
930 long significand = (exponent == 0
931 ? (valBits & ((1L << 52) - 1)) << 1
932 : (valBits & ((1L << 52) - 1)) | (1L << 52));
933 exponent -= 1075;
934 // At this point, val == sign * significand * 2**exponent.
935
936 /*
937 * Special case zero to supress nonterminating normalization and bogus
938 * scale calculation.
939 */
940 if (significand == 0) {
941 this.intVal = BigInteger.ZERO;
942 this.scale = 0;
943 this.intCompact = 0;
944 this.precision = 1;
945 return;
946 }
947 // Normalize
948 while ((significand & 1) == 0) { // i.e., significand is even
949 significand >>= 1;
950 exponent++;
951 }
952 int scl = 0;
953 // Calculate intVal and scale
954 BigInteger rb;
955 long compactVal = sign * significand;
956 if (exponent == 0) {
957 rb = (compactVal == INFLATED) ? INFLATED_BIGINT : null;
958 } else {
959 if (exponent < 0) {
960 rb = BigInteger.valueOf(5).pow(-exponent).multiply(compactVal);
961 scl = -exponent;
962 } else { // (exponent > 0)
963 rb = BigInteger.TWO.pow(exponent).multiply(compactVal);
964 }
965 compactVal = compactValFor(rb);
966 }
967 int prec = 0;
968 int mcp = mc.precision;
969 if (mcp > 0) { // do rounding
970 int mode = mc.roundingMode.oldMode;
971 int drop;
972 if (compactVal == INFLATED) {
973 prec = bigDigitLength(rb);
974 drop = prec - mcp;
975 while (drop > 0) {
976 scl = checkScaleNonZero((long) scl - drop);
977 rb = divideAndRoundByTenPow(rb, drop, mode);
978 compactVal = compactValFor(rb);
979 if (compactVal != INFLATED) {
980 break;
981 }
982 prec = bigDigitLength(rb);
983 drop = prec - mcp;
984 }
985 }
986 if (compactVal != INFLATED) {
987 prec = longDigitLength(compactVal);
988 drop = prec - mcp;
989 while (drop > 0) {
990 scl = checkScaleNonZero((long) scl - drop);
991 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
992 prec = longDigitLength(compactVal);
993 drop = prec - mcp;
994 }
995 rb = null;
996 }
997 }
998 this.intVal = rb;
999 this.intCompact = compactVal;
1000 this.scale = scl;
1001 this.precision = prec;
1002 }
1003
1004 /**
1005 * Translates a {@code BigInteger} into a {@code BigDecimal}.
1006 * The scale of the {@code BigDecimal} is zero.
1007 *
1008 * @param val {@code BigInteger} value to be converted to
1009 * {@code BigDecimal}.
1010 */
1011 public BigDecimal(BigInteger val) {
1012 scale = 0;
1013 intVal = val;
1014 intCompact = compactValFor(val);
1015 }
1016
1017 /**
1018 * Translates a {@code BigInteger} into a {@code BigDecimal}
1019 * rounding according to the context settings. The scale of the
1020 * {@code BigDecimal} is zero.
1021 *
1022 * @param val {@code BigInteger} value to be converted to
1023 * {@code BigDecimal}.
1024 * @param mc the context to use.
1025 * @throws ArithmeticException if the result is inexact but the
1026 * rounding mode is {@code UNNECESSARY}.
1027 * @since 1.5
1028 */
1029 public BigDecimal(BigInteger val, MathContext mc) {
1030 this(val,0,mc);
1031 }
1032
1033 /**
1034 * Translates a {@code BigInteger} unscaled value and an
1035 * {@code int} scale into a {@code BigDecimal}. The value of
1036 * the {@code BigDecimal} is
1037 * <code>(unscaledVal × 10<sup>-scale</sup>)</code>.
1038 *
1039 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1040 * @param scale scale of the {@code BigDecimal}.
1041 */
1042 public BigDecimal(BigInteger unscaledVal, int scale) {
1043 // Negative scales are now allowed
1044 this.intVal = unscaledVal;
1045 this.intCompact = compactValFor(unscaledVal);
1046 this.scale = scale;
1047 }
1048
1049 /**
1050 * Translates a {@code BigInteger} unscaled value and an
1051 * {@code int} scale into a {@code BigDecimal}, with rounding
1052 * according to the context settings. The value of the
1053 * {@code BigDecimal} is <code>(unscaledVal ×
1054 * 10<sup>-scale</sup>)</code>, rounded according to the
1055 * {@code precision} and rounding mode settings.
1056 *
1057 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1058 * @param scale scale of the {@code BigDecimal}.
1059 * @param mc the context to use.
1060 * @throws ArithmeticException if the result is inexact but the
1061 * rounding mode is {@code UNNECESSARY}.
1062 * @since 1.5
1063 */
1064 public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {
1065 long compactVal = compactValFor(unscaledVal);
1066 int mcp = mc.precision;
1067 int prec = 0;
1068 if (mcp > 0) { // do rounding
1069 int mode = mc.roundingMode.oldMode;
1070 if (compactVal == INFLATED) {
1071 prec = bigDigitLength(unscaledVal);
1072 int drop = prec - mcp;
1073 while (drop > 0) {
1074 scale = checkScaleNonZero((long) scale - drop);
1075 unscaledVal = divideAndRoundByTenPow(unscaledVal, drop, mode);
1076 compactVal = compactValFor(unscaledVal);
1077 if (compactVal != INFLATED) {
1078 break;
1079 }
1080 prec = bigDigitLength(unscaledVal);
1081 drop = prec - mcp;
1082 }
1083 }
1084 if (compactVal != INFLATED) {
1085 prec = longDigitLength(compactVal);
1086 int drop = prec - mcp; // drop can't be more than 18
1087 while (drop > 0) {
1088 scale = checkScaleNonZero((long) scale - drop);
1089 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mode);
1090 prec = longDigitLength(compactVal);
1091 drop = prec - mcp;
1092 }
1093 unscaledVal = null;
1094 }
1095 }
1096 this.intVal = unscaledVal;
1097 this.intCompact = compactVal;
1098 this.scale = scale;
1099 this.precision = prec;
1100 }
1101
1102 /**
1103 * Translates an {@code int} into a {@code BigDecimal}. The
1104 * scale of the {@code BigDecimal} is zero.
1105 *
1106 * @param val {@code int} value to be converted to
1107 * {@code BigDecimal}.
1108 * @since 1.5
1109 */
1110 public BigDecimal(int val) {
1111 this.intCompact = val;
1112 this.scale = 0;
1113 this.intVal = null;
1114 }
1115
1116 /**
1117 * Translates an {@code int} into a {@code BigDecimal}, with
1118 * rounding according to the context settings. The scale of the
1119 * {@code BigDecimal}, before any rounding, is zero.
1120 *
1121 * @param val {@code int} value to be converted to {@code BigDecimal}.
1122 * @param mc the context to use.
1123 * @throws ArithmeticException if the result is inexact but the
1124 * rounding mode is {@code UNNECESSARY}.
1125 * @since 1.5
1126 */
1127 public BigDecimal(int val, MathContext mc) {
1128 int mcp = mc.precision;
1129 long compactVal = val;
1130 int scl = 0;
1131 int prec = 0;
1132 if (mcp > 0) { // do rounding
1133 prec = longDigitLength(compactVal);
1134 int drop = prec - mcp; // drop can't be more than 18
1135 while (drop > 0) {
1136 scl = checkScaleNonZero((long) scl - drop);
1137 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1138 prec = longDigitLength(compactVal);
1139 drop = prec - mcp;
1140 }
1141 }
1142 this.intVal = null;
1143 this.intCompact = compactVal;
1144 this.scale = scl;
1145 this.precision = prec;
1146 }
1147
1148 /**
1149 * Translates a {@code long} into a {@code BigDecimal}. The
1150 * scale of the {@code BigDecimal} is zero.
1151 *
1152 * @param val {@code long} value to be converted to {@code BigDecimal}.
1153 * @since 1.5
1154 */
1155 public BigDecimal(long val) {
1156 this.intCompact = val;
1157 this.intVal = (val == INFLATED) ? INFLATED_BIGINT : null;
1158 this.scale = 0;
1159 }
1160
1161 /**
1162 * Translates a {@code long} into a {@code BigDecimal}, with
1163 * rounding according to the context settings. The scale of the
1164 * {@code BigDecimal}, before any rounding, is zero.
1165 *
1166 * @param val {@code long} value to be converted to {@code BigDecimal}.
1167 * @param mc the context to use.
1168 * @throws ArithmeticException if the result is inexact but the
1169 * rounding mode is {@code UNNECESSARY}.
1170 * @since 1.5
1171 */
1172 public BigDecimal(long val, MathContext mc) {
1173 int mcp = mc.precision;
1174 int mode = mc.roundingMode.oldMode;
1175 int prec = 0;
1176 int scl = 0;
1177 BigInteger rb = (val == INFLATED) ? INFLATED_BIGINT : null;
1178 if (mcp > 0) { // do rounding
1179 if (val == INFLATED) {
1180 prec = 19;
1181 int drop = prec - mcp;
1182 while (drop > 0) {
1183 scl = checkScaleNonZero((long) scl - drop);
1184 rb = divideAndRoundByTenPow(rb, drop, mode);
1185 val = compactValFor(rb);
1186 if (val != INFLATED) {
1187 break;
1188 }
1189 prec = bigDigitLength(rb);
1190 drop = prec - mcp;
1191 }
1192 }
1193 if (val != INFLATED) {
1194 prec = longDigitLength(val);
1195 int drop = prec - mcp;
1196 while (drop > 0) {
1197 scl = checkScaleNonZero((long) scl - drop);
1198 val = divideAndRound(val, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1199 prec = longDigitLength(val);
1200 drop = prec - mcp;
1201 }
1202 rb = null;
1203 }
1204 }
1205 this.intVal = rb;
1206 this.intCompact = val;
1207 this.scale = scl;
1208 this.precision = prec;
1209 }
1210
1211 // Static Factory Methods
1212
1213 /**
1214 * Translates a {@code long} unscaled value and an
1215 * {@code int} scale into a {@code BigDecimal}.
1216 *
1217 * @apiNote This static factory method is provided in preference
1218 * to a ({@code long}, {@code int}) constructor because it allows
1219 * for reuse of frequently used {@code BigDecimal} values.
1220 *
1221 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1222 * @param scale scale of the {@code BigDecimal}.
1223 * @return a {@code BigDecimal} whose value is
1224 * <code>(unscaledVal × 10<sup>-scale</sup>)</code>.
1225 */
1226 public static BigDecimal valueOf(long unscaledVal, int scale) {
1227 if (scale == 0)
1228 return valueOf(unscaledVal);
1229 else if (unscaledVal == 0) {
1230 return zeroValueOf(scale);
1231 }
1232 return new BigDecimal(unscaledVal == INFLATED ?
1233 INFLATED_BIGINT : null,
1234 unscaledVal, scale, 0);
1235 }
1236
1237 /**
1238 * Translates a {@code long} value into a {@code BigDecimal}
1239 * with a scale of zero.
1240 *
1241 * @apiNote This static factory method is provided in preference
1242 * to a ({@code long}) constructor because it allows for reuse of
1243 * frequently used {@code BigDecimal} values.
1244 *
1245 * @param val value of the {@code BigDecimal}.
1246 * @return a {@code BigDecimal} whose value is {@code val}.
1247 */
1248 public static BigDecimal valueOf(long val) {
1249 if (val >= 0 && val < ZERO_THROUGH_TEN.length)
1250 return ZERO_THROUGH_TEN[(int)val];
1251 else if (val != INFLATED)
1252 return new BigDecimal(null, val, 0, 0);
1253 return new BigDecimal(INFLATED_BIGINT, val, 0, 0);
1254 }
1255
1256 static BigDecimal valueOf(long unscaledVal, int scale, int prec) {
1257 if (scale == 0 && unscaledVal >= 0 && unscaledVal < ZERO_THROUGH_TEN.length) {
1258 return ZERO_THROUGH_TEN[(int) unscaledVal];
1259 } else if (unscaledVal == 0) {
1260 return zeroValueOf(scale);
1261 }
1262 return new BigDecimal(unscaledVal == INFLATED ? INFLATED_BIGINT : null,
1263 unscaledVal, scale, prec);
1264 }
1265
1266 static BigDecimal valueOf(BigInteger intVal, int scale, int prec) {
1267 long val = compactValFor(intVal);
1268 if (val == 0) {
1269 return zeroValueOf(scale);
1270 } else if (scale == 0 && val >= 0 && val < ZERO_THROUGH_TEN.length) {
1271 return ZERO_THROUGH_TEN[(int) val];
1272 }
1273 return new BigDecimal(intVal, val, scale, prec);
1274 }
1275
1276 static BigDecimal zeroValueOf(int scale) {
1277 if (scale >= 0 && scale < ZERO_SCALED_BY.length)
1278 return ZERO_SCALED_BY[scale];
1279 else
1280 return new BigDecimal(BigInteger.ZERO, 0, scale, 1);
1281 }
1282
1283 /**
1284 * Translates a {@code double} into a {@code BigDecimal}, using
1285 * the {@code double}'s canonical string representation provided
1286 * by the {@link Double#toString(double)} method.
1287 *
1288 * @apiNote This is generally the preferred way to convert a
1289 * {@code double} (or {@code float}) into a {@code BigDecimal}, as
1290 * the value returned is equal to that resulting from constructing
1291 * a {@code BigDecimal} from the result of using {@link
1292 * Double#toString(double)}.
1293 *
1294 * @param val {@code double} to convert to a {@code BigDecimal}.
1295 * @return a {@code BigDecimal} whose value is equal to or approximately
1296 * equal to the value of {@code val}.
1297 * @throws NumberFormatException if {@code val} is infinite or NaN.
1298 * @since 1.5
1299 */
1300 public static BigDecimal valueOf(double val) {
1301 // Reminder: a zero double returns '0.0', so we cannot fastpath
1302 // to use the constant ZERO. This might be important enough to
1303 // justify a factory approach, a cache, or a few private
1304 // constants, later.
1305 return new BigDecimal(Double.toString(val));
1306 }
1307
1308 // Arithmetic Operations
1309 /**
1310 * Returns a {@code BigDecimal} whose value is {@code (this +
1311 * augend)}, and whose scale is {@code max(this.scale(),
1312 * augend.scale())}.
1313 *
1314 * @param augend value to be added to this {@code BigDecimal}.
1315 * @return {@code this + augend}
1316 */
1317 public BigDecimal add(BigDecimal augend) {
1318 if (this.intCompact != INFLATED) {
1319 if ((augend.intCompact != INFLATED)) {
1320 return add(this.intCompact, this.scale, augend.intCompact, augend.scale);
1321 } else {
1322 return add(this.intCompact, this.scale, augend.intVal, augend.scale);
1323 }
1324 } else {
1325 if ((augend.intCompact != INFLATED)) {
1326 return add(augend.intCompact, augend.scale, this.intVal, this.scale);
1327 } else {
1328 return add(this.intVal, this.scale, augend.intVal, augend.scale);
1329 }
1330 }
1331 }
1332
1333 /**
1334 * Returns a {@code BigDecimal} whose value is {@code (this + augend)},
1335 * with rounding according to the context settings.
1336 *
1337 * If either number is zero and the precision setting is nonzero then
1338 * the other number, rounded if necessary, is used as the result.
1339 *
1340 * @param augend value to be added to this {@code BigDecimal}.
1341 * @param mc the context to use.
1342 * @return {@code this + augend}, rounded as necessary.
1343 * @throws ArithmeticException if the result is inexact but the
1344 * rounding mode is {@code UNNECESSARY}.
1345 * @since 1.5
1346 */
1347 public BigDecimal add(BigDecimal augend, MathContext mc) {
1348 if (mc.precision == 0)
1349 return add(augend);
1350 BigDecimal lhs = this;
1351
1352 // If either number is zero then the other number, rounded and
1353 // scaled if necessary, is used as the result.
1354 {
1355 boolean lhsIsZero = lhs.signum() == 0;
1356 boolean augendIsZero = augend.signum() == 0;
1357
1358 if (lhsIsZero || augendIsZero) {
1359 int preferredScale = Math.max(lhs.scale(), augend.scale());
1360 BigDecimal result;
1361
1362 if (lhsIsZero && augendIsZero)
1363 return zeroValueOf(preferredScale);
1364 result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc);
1365
1366 if (result.scale() == preferredScale)
1367 return result;
1368 else if (result.scale() > preferredScale) {
1369 return stripZerosToMatchScale(result.intVal, result.intCompact, result.scale, preferredScale);
1370 } else { // result.scale < preferredScale
1371 int precisionDiff = mc.precision - result.precision();
1372 int scaleDiff = preferredScale - result.scale();
1373
1374 if (precisionDiff >= scaleDiff)
1375 return result.setScale(preferredScale); // can achieve target scale
1376 else
1377 return result.setScale(result.scale() + precisionDiff);
1378 }
1379 }
1380 }
1381
1382 long padding = (long) lhs.scale - augend.scale;
1383 if (padding != 0) { // scales differ; alignment needed
1384 BigDecimal arg[] = preAlign(lhs, augend, padding, mc);
1385 matchScale(arg);
1386 lhs = arg[0];
1387 augend = arg[1];
1388 }
1389 return doRound(lhs.inflated().add(augend.inflated()), lhs.scale, mc);
1390 }
1391
1392 /**
1393 * Returns an array of length two, the sum of whose entries is
1394 * equal to the rounded sum of the {@code BigDecimal} arguments.
1395 *
1396 * <p>If the digit positions of the arguments have a sufficient
1397 * gap between them, the value smaller in magnitude can be
1398 * condensed into a {@literal "sticky bit"} and the end result will
1399 * round the same way <em>if</em> the precision of the final
1400 * result does not include the high order digit of the small
1401 * magnitude operand.
1402 *
1403 * <p>Note that while strictly speaking this is an optimization,
1404 * it makes a much wider range of additions practical.
1405 *
1406 * <p>This corresponds to a pre-shift operation in a fixed
1407 * precision floating-point adder; this method is complicated by
1408 * variable precision of the result as determined by the
1409 * MathContext. A more nuanced operation could implement a
1410 * {@literal "right shift"} on the smaller magnitude operand so
1411 * that the number of digits of the smaller operand could be
1412 * reduced even though the significands partially overlapped.
1413 */
1414 private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend, long padding, MathContext mc) {
1415 assert padding != 0;
1416 BigDecimal big;
1417 BigDecimal small;
1418
1419 if (padding < 0) { // lhs is big; augend is small
1420 big = lhs;
1421 small = augend;
1422 } else { // lhs is small; augend is big
1423 big = augend;
1424 small = lhs;
1425 }
1426
1427 /*
1428 * This is the estimated scale of an ulp of the result; it assumes that
1429 * the result doesn't have a carry-out on a true add (e.g. 999 + 1 =>
1430 * 1000) or any subtractive cancellation on borrowing (e.g. 100 - 1.2 =>
1431 * 98.8)
1432 */
1433 long estResultUlpScale = (long) big.scale - big.precision() + mc.precision;
1434
1435 /*
1436 * The low-order digit position of big is big.scale(). This
1437 * is true regardless of whether big has a positive or
1438 * negative scale. The high-order digit position of small is
1439 * small.scale - (small.precision() - 1). To do the full
1440 * condensation, the digit positions of big and small must be
1441 * disjoint *and* the digit positions of small should not be
1442 * directly visible in the result.
1443 */
1444 long smallHighDigitPos = (long) small.scale - small.precision() + 1;
1445 if (smallHighDigitPos > big.scale + 2 && // big and small disjoint
1446 smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible
1447 small = BigDecimal.valueOf(small.signum(), this.checkScale(Math.max(big.scale, estResultUlpScale) + 3));
1448 }
1449
1450 // Since addition is symmetric, preserving input order in
1451 // returned operands doesn't matter
1452 BigDecimal[] result = {big, small};
1453 return result;
1454 }
1455
1456 /**
1457 * Returns a {@code BigDecimal} whose value is {@code (this -
1458 * subtrahend)}, and whose scale is {@code max(this.scale(),
1459 * subtrahend.scale())}.
1460 *
1461 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1462 * @return {@code this - subtrahend}
1463 */
1464 public BigDecimal subtract(BigDecimal subtrahend) {
1465 if (this.intCompact != INFLATED) {
1466 if ((subtrahend.intCompact != INFLATED)) {
1467 return add(this.intCompact, this.scale, -subtrahend.intCompact, subtrahend.scale);
1468 } else {
1469 return add(this.intCompact, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1470 }
1471 } else {
1472 if ((subtrahend.intCompact != INFLATED)) {
1473 // Pair of subtrahend values given before pair of
1474 // values from this BigDecimal to avoid need for
1475 // method overloading on the specialized add method
1476 return add(-subtrahend.intCompact, subtrahend.scale, this.intVal, this.scale);
1477 } else {
1478 return add(this.intVal, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1479 }
1480 }
1481 }
1482
1483 /**
1484 * Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)},
1485 * with rounding according to the context settings.
1486 *
1487 * If {@code subtrahend} is zero then this, rounded if necessary, is used as the
1488 * result. If this is zero then the result is {@code subtrahend.negate(mc)}.
1489 *
1490 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1491 * @param mc the context to use.
1492 * @return {@code this - subtrahend}, rounded as necessary.
1493 * @throws ArithmeticException if the result is inexact but the
1494 * rounding mode is {@code UNNECESSARY}.
1495 * @since 1.5
1496 */
1497 public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) {
1498 if (mc.precision == 0)
1499 return subtract(subtrahend);
1500 // share the special rounding code in add()
1501 return add(subtrahend.negate(), mc);
1502 }
1503
1504 /**
1505 * Returns a {@code BigDecimal} whose value is <code>(this ×
1506 * multiplicand)</code>, and whose scale is {@code (this.scale() +
1507 * multiplicand.scale())}.
1508 *
1509 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1510 * @return {@code this * multiplicand}
1511 */
1512 public BigDecimal multiply(BigDecimal multiplicand) {
1513 int productScale = checkScale((long) scale + multiplicand.scale);
1514 if (this.intCompact != INFLATED) {
1515 if ((multiplicand.intCompact != INFLATED)) {
1516 return multiply(this.intCompact, multiplicand.intCompact, productScale);
1517 } else {
1518 return multiply(this.intCompact, multiplicand.intVal, productScale);
1519 }
1520 } else {
1521 if ((multiplicand.intCompact != INFLATED)) {
1522 return multiply(multiplicand.intCompact, this.intVal, productScale);
1523 } else {
1524 return multiply(this.intVal, multiplicand.intVal, productScale);
1525 }
1526 }
1527 }
1528
1529 /**
1530 * Returns a {@code BigDecimal} whose value is <code>(this ×
1531 * multiplicand)</code>, with rounding according to the context settings.
1532 *
1533 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1534 * @param mc the context to use.
1535 * @return {@code this * multiplicand}, rounded as necessary.
1536 * @throws ArithmeticException if the result is inexact but the
1537 * rounding mode is {@code UNNECESSARY}.
1538 * @since 1.5
1539 */
1540 public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) {
1541 if (mc.precision == 0)
1542 return multiply(multiplicand);
1543 int productScale = checkScale((long) scale + multiplicand.scale);
1544 if (this.intCompact != INFLATED) {
1545 if ((multiplicand.intCompact != INFLATED)) {
1546 return multiplyAndRound(this.intCompact, multiplicand.intCompact, productScale, mc);
1547 } else {
1548 return multiplyAndRound(this.intCompact, multiplicand.intVal, productScale, mc);
1549 }
1550 } else {
1551 if ((multiplicand.intCompact != INFLATED)) {
1552 return multiplyAndRound(multiplicand.intCompact, this.intVal, productScale, mc);
1553 } else {
1554 return multiplyAndRound(this.intVal, multiplicand.intVal, productScale, mc);
1555 }
1556 }
1557 }
1558
1559 /**
1560 * Returns a {@code BigDecimal} whose value is {@code (this /
1561 * divisor)}, and whose scale is as specified. If rounding must
1562 * be performed to generate a result with the specified scale, the
1563 * specified rounding mode is applied.
1564 *
1565 * @deprecated The method {@link #divide(BigDecimal, int, RoundingMode)}
1566 * should be used in preference to this legacy method.
1567 *
1568 * @param divisor value by which this {@code BigDecimal} is to be divided.
1569 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1570 * @param roundingMode rounding mode to apply.
1571 * @return {@code this / divisor}
1572 * @throws ArithmeticException if {@code divisor} is zero,
1573 * {@code roundingMode==ROUND_UNNECESSARY} and
1574 * the specified scale is insufficient to represent the result
1575 * of the division exactly.
1576 * @throws IllegalArgumentException if {@code roundingMode} does not
1577 * represent a valid rounding mode.
1578 * @see #ROUND_UP
1579 * @see #ROUND_DOWN
1580 * @see #ROUND_CEILING
1581 * @see #ROUND_FLOOR
1582 * @see #ROUND_HALF_UP
1583 * @see #ROUND_HALF_DOWN
1584 * @see #ROUND_HALF_EVEN
1585 * @see #ROUND_UNNECESSARY
1586 */
1587 @Deprecated(since="9")
1588 public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) {
1589 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
1590 throw new IllegalArgumentException("Invalid rounding mode");
1591 if (this.intCompact != INFLATED) {
1592 if ((divisor.intCompact != INFLATED)) {
1593 return divide(this.intCompact, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1594 } else {
1595 return divide(this.intCompact, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1596 }
1597 } else {
1598 if ((divisor.intCompact != INFLATED)) {
1599 return divide(this.intVal, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1600 } else {
1601 return divide(this.intVal, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1602 }
1603 }
1604 }
1605
1606 /**
1607 * Returns a {@code BigDecimal} whose value is {@code (this /
1608 * divisor)}, and whose scale is as specified. If rounding must
1609 * be performed to generate a result with the specified scale, the
1610 * specified rounding mode is applied.
1611 *
1612 * @param divisor value by which this {@code BigDecimal} is to be divided.
1613 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1614 * @param roundingMode rounding mode to apply.
1615 * @return {@code this / divisor}
1616 * @throws ArithmeticException if {@code divisor} is zero,
1617 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1618 * the specified scale is insufficient to represent the result
1619 * of the division exactly.
1620 * @since 1.5
1621 */
1622 public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) {
1623 return divide(divisor, scale, roundingMode.oldMode);
1624 }
1625
1626 /**
1627 * Returns a {@code BigDecimal} whose value is {@code (this /
1628 * divisor)}, and whose scale is {@code this.scale()}. If
1629 * rounding must be performed to generate a result with the given
1630 * scale, the specified rounding mode is applied.
1631 *
1632 * @deprecated The method {@link #divide(BigDecimal, RoundingMode)}
1633 * should be used in preference to this legacy method.
1634 *
1635 * @param divisor value by which this {@code BigDecimal} is to be divided.
1636 * @param roundingMode rounding mode to apply.
1637 * @return {@code this / divisor}
1638 * @throws ArithmeticException if {@code divisor==0}, or
1639 * {@code roundingMode==ROUND_UNNECESSARY} and
1640 * {@code this.scale()} is insufficient to represent the result
1641 * of the division exactly.
1642 * @throws IllegalArgumentException if {@code roundingMode} does not
1643 * represent a valid rounding mode.
1644 * @see #ROUND_UP
1645 * @see #ROUND_DOWN
1646 * @see #ROUND_CEILING
1647 * @see #ROUND_FLOOR
1648 * @see #ROUND_HALF_UP
1649 * @see #ROUND_HALF_DOWN
1650 * @see #ROUND_HALF_EVEN
1651 * @see #ROUND_UNNECESSARY
1652 */
1653 @Deprecated(since="9")
1654 public BigDecimal divide(BigDecimal divisor, int roundingMode) {
1655 return this.divide(divisor, scale, roundingMode);
1656 }
1657
1658 /**
1659 * Returns a {@code BigDecimal} whose value is {@code (this /
1660 * divisor)}, and whose scale is {@code this.scale()}. If
1661 * rounding must be performed to generate a result with the given
1662 * scale, the specified rounding mode is applied.
1663 *
1664 * @param divisor value by which this {@code BigDecimal} is to be divided.
1665 * @param roundingMode rounding mode to apply.
1666 * @return {@code this / divisor}
1667 * @throws ArithmeticException if {@code divisor==0}, or
1668 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1669 * {@code this.scale()} is insufficient to represent the result
1670 * of the division exactly.
1671 * @since 1.5
1672 */
1673 public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) {
1674 return this.divide(divisor, scale, roundingMode.oldMode);
1675 }
1676
1677 /**
1678 * Returns a {@code BigDecimal} whose value is {@code (this /
1679 * divisor)}, and whose preferred scale is {@code (this.scale() -
1680 * divisor.scale())}; if the exact quotient cannot be
1681 * represented (because it has a non-terminating decimal
1682 * expansion) an {@code ArithmeticException} is thrown.
1683 *
1684 * @param divisor value by which this {@code BigDecimal} is to be divided.
1685 * @throws ArithmeticException if the exact quotient does not have a
1686 * terminating decimal expansion
1687 * @return {@code this / divisor}
1688 * @since 1.5
1689 * @author Joseph D. Darcy
1690 */
1691 public BigDecimal divide(BigDecimal divisor) {
1692 /*
1693 * Handle zero cases first.
1694 */
1695 if (divisor.signum() == 0) { // x/0
1696 if (this.signum() == 0) // 0/0
1697 throw new ArithmeticException("Division undefined"); // NaN
1698 throw new ArithmeticException("Division by zero");
1699 }
1700
1701 // Calculate preferred scale
1702 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1703
1704 if (this.signum() == 0) // 0/y
1705 return zeroValueOf(preferredScale);
1706 else {
1707 /*
1708 * If the quotient this/divisor has a terminating decimal
1709 * expansion, the expansion can have no more than
1710 * (a.precision() + ceil(10*b.precision)/3) digits.
1711 * Therefore, create a MathContext object with this
1712 * precision and do a divide with the UNNECESSARY rounding
1713 * mode.
1714 */
1715 MathContext mc = new MathContext( (int)Math.min(this.precision() +
1716 (long)Math.ceil(10.0*divisor.precision()/3.0),
1717 Integer.MAX_VALUE),
1718 RoundingMode.UNNECESSARY);
1719 BigDecimal quotient;
1720 try {
1721 quotient = this.divide(divisor, mc);
1722 } catch (ArithmeticException e) {
1723 throw new ArithmeticException("Non-terminating decimal expansion; " +
1724 "no exact representable decimal result.");
1725 }
1726
1727 int quotientScale = quotient.scale();
1728
1729 // divide(BigDecimal, mc) tries to adjust the quotient to
1730 // the desired one by removing trailing zeros; since the
1731 // exact divide method does not have an explicit digit
1732 // limit, we can add zeros too.
1733 if (preferredScale > quotientScale)
1734 return quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1735
1736 return quotient;
1737 }
1738 }
1739
1740 /**
1741 * Returns a {@code BigDecimal} whose value is {@code (this /
1742 * divisor)}, with rounding according to the context settings.
1743 *
1744 * @param divisor value by which this {@code BigDecimal} is to be divided.
1745 * @param mc the context to use.
1746 * @return {@code this / divisor}, rounded as necessary.
1747 * @throws ArithmeticException if the result is inexact but the
1748 * rounding mode is {@code UNNECESSARY} or
1749 * {@code mc.precision == 0} and the quotient has a
1750 * non-terminating decimal expansion.
1751 * @since 1.5
1752 */
1753 public BigDecimal divide(BigDecimal divisor, MathContext mc) {
1754 int mcp = mc.precision;
1755 if (mcp == 0)
1756 return divide(divisor);
1757
1758 BigDecimal dividend = this;
1759 long preferredScale = (long)dividend.scale - divisor.scale;
1760 // Now calculate the answer. We use the existing
1761 // divide-and-round method, but as this rounds to scale we have
1762 // to normalize the values here to achieve the desired result.
1763 // For x/y we first handle y=0 and x=0, and then normalize x and
1764 // y to give x' and y' with the following constraints:
1765 // (a) 0.1 <= x' < 1
1766 // (b) x' <= y' < 10*x'
1767 // Dividing x'/y' with the required scale set to mc.precision then
1768 // will give a result in the range 0.1 to 1 rounded to exactly
1769 // the right number of digits (except in the case of a result of
1770 // 1.000... which can arise when x=y, or when rounding overflows
1771 // The 1.000... case will reduce properly to 1.
1772 if (divisor.signum() == 0) { // x/0
1773 if (dividend.signum() == 0) // 0/0
1774 throw new ArithmeticException("Division undefined"); // NaN
1775 throw new ArithmeticException("Division by zero");
1776 }
1777 if (dividend.signum() == 0) // 0/y
1778 return zeroValueOf(saturateLong(preferredScale));
1779 int xscale = dividend.precision();
1780 int yscale = divisor.precision();
1781 if(dividend.intCompact!=INFLATED) {
1782 if(divisor.intCompact!=INFLATED) {
1783 return divide(dividend.intCompact, xscale, divisor.intCompact, yscale, preferredScale, mc);
1784 } else {
1785 return divide(dividend.intCompact, xscale, divisor.intVal, yscale, preferredScale, mc);
1786 }
1787 } else {
1788 if(divisor.intCompact!=INFLATED) {
1789 return divide(dividend.intVal, xscale, divisor.intCompact, yscale, preferredScale, mc);
1790 } else {
1791 return divide(dividend.intVal, xscale, divisor.intVal, yscale, preferredScale, mc);
1792 }
1793 }
1794 }
1795
1796 /**
1797 * Returns a {@code BigDecimal} whose value is the integer part
1798 * of the quotient {@code (this / divisor)} rounded down. The
1799 * preferred scale of the result is {@code (this.scale() -
1800 * divisor.scale())}.
1801 *
1802 * @param divisor value by which this {@code BigDecimal} is to be divided.
1803 * @return The integer part of {@code this / divisor}.
1804 * @throws ArithmeticException if {@code divisor==0}
1805 * @since 1.5
1806 */
1807 public BigDecimal divideToIntegralValue(BigDecimal divisor) {
1808 // Calculate preferred scale
1809 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1810 if (this.compareMagnitude(divisor) < 0) {
1811 // much faster when this << divisor
1812 return zeroValueOf(preferredScale);
1813 }
1814
1815 if (this.signum() == 0 && divisor.signum() != 0)
1816 return this.setScale(preferredScale, ROUND_UNNECESSARY);
1817
1818 // Perform a divide with enough digits to round to a correct
1819 // integer value; then remove any fractional digits
1820
1821 int maxDigits = (int)Math.min(this.precision() +
1822 (long)Math.ceil(10.0*divisor.precision()/3.0) +
1823 Math.abs((long)this.scale() - divisor.scale()) + 2,
1824 Integer.MAX_VALUE);
1825 BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits,
1826 RoundingMode.DOWN));
1827 if (quotient.scale > 0) {
1828 quotient = quotient.setScale(0, RoundingMode.DOWN);
1829 quotient = stripZerosToMatchScale(quotient.intVal, quotient.intCompact, quotient.scale, preferredScale);
1830 }
1831
1832 if (quotient.scale < preferredScale) {
1833 // pad with zeros if necessary
1834 quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1835 }
1836
1837 return quotient;
1838 }
1839
1840 /**
1841 * Returns a {@code BigDecimal} whose value is the integer part
1842 * of {@code (this / divisor)}. Since the integer part of the
1843 * exact quotient does not depend on the rounding mode, the
1844 * rounding mode does not affect the values returned by this
1845 * method. The preferred scale of the result is
1846 * {@code (this.scale() - divisor.scale())}. An
1847 * {@code ArithmeticException} is thrown if the integer part of
1848 * the exact quotient needs more than {@code mc.precision}
1849 * digits.
1850 *
1851 * @param divisor value by which this {@code BigDecimal} is to be divided.
1852 * @param mc the context to use.
1853 * @return The integer part of {@code this / divisor}.
1854 * @throws ArithmeticException if {@code divisor==0}
1855 * @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result
1856 * requires a precision of more than {@code mc.precision} digits.
1857 * @since 1.5
1858 * @author Joseph D. Darcy
1859 */
1860 public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) {
1861 if (mc.precision == 0 || // exact result
1862 (this.compareMagnitude(divisor) < 0)) // zero result
1863 return divideToIntegralValue(divisor);
1864
1865 // Calculate preferred scale
1866 int preferredScale = saturateLong((long)this.scale - divisor.scale);
1867
1868 /*
1869 * Perform a normal divide to mc.precision digits. If the
1870 * remainder has absolute value less than the divisor, the
1871 * integer portion of the quotient fits into mc.precision
1872 * digits. Next, remove any fractional digits from the
1873 * quotient and adjust the scale to the preferred value.
1874 */
1875 BigDecimal result = this.divide(divisor, new MathContext(mc.precision, RoundingMode.DOWN));
1876
1877 if (result.scale() < 0) {
1878 /*
1879 * Result is an integer. See if quotient represents the
1880 * full integer portion of the exact quotient; if it does,
1881 * the computed remainder will be less than the divisor.
1882 */
1883 BigDecimal product = result.multiply(divisor);
1884 // If the quotient is the full integer value,
1885 // |dividend-product| < |divisor|.
1886 if (this.subtract(product).compareMagnitude(divisor) >= 0) {
1887 throw new ArithmeticException("Division impossible");
1888 }
1889 } else if (result.scale() > 0) {
1890 /*
1891 * Integer portion of quotient will fit into precision
1892 * digits; recompute quotient to scale 0 to avoid double
1893 * rounding and then try to adjust, if necessary.
1894 */
1895 result = result.setScale(0, RoundingMode.DOWN);
1896 }
1897 // else result.scale() == 0;
1898
1899 int precisionDiff;
1900 if ((preferredScale > result.scale()) &&
1901 (precisionDiff = mc.precision - result.precision()) > 0) {
1902 return result.setScale(result.scale() +
1903 Math.min(precisionDiff, preferredScale - result.scale) );
1904 } else {
1905 return stripZerosToMatchScale(result.intVal,result.intCompact,result.scale,preferredScale);
1906 }
1907 }
1908
1909 /**
1910 * Returns a {@code BigDecimal} whose value is {@code (this % divisor)}.
1911 *
1912 * <p>The remainder is given by
1913 * {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}.
1914 * Note that this is <em>not</em> the modulo operation (the result can be
1915 * negative).
1916 *
1917 * @param divisor value by which this {@code BigDecimal} is to be divided.
1918 * @return {@code this % divisor}.
1919 * @throws ArithmeticException if {@code divisor==0}
1920 * @since 1.5
1921 */
1922 public BigDecimal remainder(BigDecimal divisor) {
1923 BigDecimal divrem[] = this.divideAndRemainder(divisor);
1924 return divrem[1];
1925 }
1926
1927
1928 /**
1929 * Returns a {@code BigDecimal} whose value is {@code (this %
1930 * divisor)}, with rounding according to the context settings.
1931 * The {@code MathContext} settings affect the implicit divide
1932 * used to compute the remainder. The remainder computation
1933 * itself is by definition exact. Therefore, the remainder may
1934 * contain more than {@code mc.getPrecision()} digits.
1935 *
1936 * <p>The remainder is given by
1937 * {@code this.subtract(this.divideToIntegralValue(divisor,
1938 * mc).multiply(divisor))}. Note that this is not the modulo
1939 * operation (the result can be negative).
1940 *
1941 * @param divisor value by which this {@code BigDecimal} is to be divided.
1942 * @param mc the context to use.
1943 * @return {@code this % divisor}, rounded as necessary.
1944 * @throws ArithmeticException if {@code divisor==0}
1945 * @throws ArithmeticException if the result is inexact but the
1946 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1947 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1948 * require a precision of more than {@code mc.precision} digits.
1949 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1950 * @since 1.5
1951 */
1952 public BigDecimal remainder(BigDecimal divisor, MathContext mc) {
1953 BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
1954 return divrem[1];
1955 }
1956
1957 /**
1958 * Returns a two-element {@code BigDecimal} array containing the
1959 * result of {@code divideToIntegralValue} followed by the result of
1960 * {@code remainder} on the two operands.
1961 *
1962 * <p>Note that if both the integer quotient and remainder are
1963 * needed, this method is faster than using the
1964 * {@code divideToIntegralValue} and {@code remainder} methods
1965 * separately because the division need only be carried out once.
1966 *
1967 * @param divisor value by which this {@code BigDecimal} is to be divided,
1968 * and the remainder computed.
1969 * @return a two element {@code BigDecimal} array: the quotient
1970 * (the result of {@code divideToIntegralValue}) is the initial element
1971 * and the remainder is the final element.
1972 * @throws ArithmeticException if {@code divisor==0}
1973 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1974 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1975 * @since 1.5
1976 */
1977 public BigDecimal[] divideAndRemainder(BigDecimal divisor) {
1978 // we use the identity x = i * y + r to determine r
1979 BigDecimal[] result = new BigDecimal[2];
1980
1981 result[0] = this.divideToIntegralValue(divisor);
1982 result[1] = this.subtract(result[0].multiply(divisor));
1983 return result;
1984 }
1985
1986 /**
1987 * Returns a two-element {@code BigDecimal} array containing the
1988 * result of {@code divideToIntegralValue} followed by the result of
1989 * {@code remainder} on the two operands calculated with rounding
1990 * according to the context settings.
1991 *
1992 * <p>Note that if both the integer quotient and remainder are
1993 * needed, this method is faster than using the
1994 * {@code divideToIntegralValue} and {@code remainder} methods
1995 * separately because the division need only be carried out once.
1996 *
1997 * @param divisor value by which this {@code BigDecimal} is to be divided,
1998 * and the remainder computed.
1999 * @param mc the context to use.
2000 * @return a two element {@code BigDecimal} array: the quotient
2001 * (the result of {@code divideToIntegralValue}) is the
2002 * initial element and the remainder is the final element.
2003 * @throws ArithmeticException if {@code divisor==0}
2004 * @throws ArithmeticException if the result is inexact but the
2005 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
2006 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
2007 * require a precision of more than {@code mc.precision} digits.
2008 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
2009 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
2010 * @since 1.5
2011 */
2012 public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) {
2013 if (mc.precision == 0)
2014 return divideAndRemainder(divisor);
2015
2016 BigDecimal[] result = new BigDecimal[2];
2017 BigDecimal lhs = this;
2018
2019 result[0] = lhs.divideToIntegralValue(divisor, mc);
2020 result[1] = lhs.subtract(result[0].multiply(divisor));
2021 return result;
2022 }
2023
2024 /**
2025 * Returns an approximation to the square root of {@code this}
2026 * with rounding according to the context settings.
2027 *
2028 * <p>The preferred scale of the returned result is equal to
2029 * {@code this.scale()/2}. The value of the returned result is
2030 * always within one ulp of the exact decimal value for the
2031 * precision in question. If the rounding mode is {@link
2032 * RoundingMode#HALF_UP HALF_UP}, {@link RoundingMode#HALF_DOWN
2033 * HALF_DOWN}, or {@link RoundingMode#HALF_EVEN HALF_EVEN}, the
2034 * result is within one half an ulp of the exact decimal value.
2035 *
2036 * <p>Special case:
2037 * <ul>
2038 * <li> The square root of a number numerically equal to {@code
2039 * ZERO} is numerically equal to {@code ZERO} with a preferred
2040 * scale according to the general rule above. In particular, for
2041 * {@code ZERO}, {@code ZERO.sqrt(mc).equals(ZERO)} is true with
2042 * any {@code MathContext} as an argument.
2043 * </ul>
2044 *
2045 * @param mc the context to use.
2046 * @return the square root of {@code this}.
2047 * @throws ArithmeticException if {@code this} is less than zero.
2048 * @throws ArithmeticException if an exact result is requested
2049 * ({@code mc.getPrecision()==0}) and there is no finite decimal
2050 * expansion of the exact result
2051 * @throws ArithmeticException if
2052 * {@code (mc.getRoundingMode()==RoundingMode.UNNECESSARY}) and
2053 * the exact result cannot fit in {@code mc.getPrecision()}
2054 * digits.
2055 * @see BigInteger#sqrt()
2056 * @since 9
2057 */
2058 public BigDecimal sqrt(MathContext mc) {
2059 int signum = signum();
2060 if (signum == 1) {
2061 /*
2062 * The following code draws on the algorithm presented in
2063 * "Properly Rounded Variable Precision Square Root," Hull and
2064 * Abrham, ACM Transactions on Mathematical Software, Vol 11,
2065 * No. 3, September 1985, Pages 229-237.
2066 *
2067 * The BigDecimal computational model differs from the one
2068 * presented in the paper in several ways: first BigDecimal
2069 * numbers aren't necessarily normalized, second many more
2070 * rounding modes are supported, including UNNECESSARY, and
2071 * exact results can be requested.
2072 *
2073 * The main steps of the algorithm below are as follows,
2074 * first argument reduce the value to the numerical range
2075 * [1, 10) using the following relations:
2076 *
2077 * x = y * 10 ^ exp
2078 * sqrt(x) = sqrt(y) * 10^(exp / 2) if exp is even
2079 * sqrt(x) = sqrt(y/10) * 10 ^((exp+1)/2) is exp is odd
2080 *
2081 * Then use Newton's iteration on the reduced value to compute
2082 * the numerical digits of the desired result.
2083 *
2084 * Finally, scale back to the desired exponent range and
2085 * perform any adjustment to get the preferred scale in the
2086 * representation.
2087 */
2088
2089 // The code below favors relative simplicity over checking
2090 // for special cases that could run faster.
2091
2092 int preferredScale = this.scale()/2;
2093 BigDecimal zeroWithFinalPreferredScale = valueOf(0L, preferredScale);
2094
2095 // First phase of numerical normalization, strip trailing
2096 // zeros and check for even powers of 10.
2097 BigDecimal stripped = this.stripTrailingZeros();
2098 int strippedScale = stripped.scale();
2099
2100 // Numerically sqrt(10^2N) = 10^N
2101 if (stripped.isPowerOfTen() &&
2102 strippedScale % 2 == 0) {
2103 BigDecimal result = valueOf(1L, strippedScale/2);
2104 if (result.scale() != preferredScale) {
2105 // Adjust to requested precision and preferred
2106 // scale as appropriate.
2107 result = result.add(zeroWithFinalPreferredScale, mc);
2108 }
2109 return result;
2110 }
2111
2112 // After stripTrailingZeros, the representation is normalized as
2113 //
2114 // unscaledValue * 10^(-scale)
2115 //
2116 // where unscaledValue is an integer with the mimimum
2117 // precision for the cohort of the numerical value. To
2118 // allow binary floating-point hardware to be used to get
2119 // approximately a 15 digit approximation to the square
2120 // root, it is helpful to instead normalize this so that
2121 // the significand portion is to right of the decimal
2122 // point by roughly (scale() - precision() +1).
2123
2124 // Now the precision / scale adjustment
2125 int scaleAdjust = 0;
2126 int scale = stripped.scale() - stripped.precision() + 1;
2127 if (scale % 2 == 0) {
2128 scaleAdjust = scale;
2129 } else {
2130 scaleAdjust = scale - 1;
2131 }
2132
2133 BigDecimal working = stripped.scaleByPowerOfTen(scaleAdjust);
2134
2135 assert // Verify 0.1 <= working < 10
2136 ONE_TENTH.compareTo(working) <= 0 && working.compareTo(TEN) < 0;
2137
2138 // Use good ole' Math.sqrt to get the initial guess for
2139 // the Newton iteration, good to at least 15 decimal
2140 // digits. This approach does incur the cost of a
2141 //
2142 // BigDecimal -> double -> BigDecimal
2143 //
2144 // conversion cycle, but it avoids the need for several
2145 // Newton iterations in BigDecimal arithmetic to get the
2146 // working answer to 15 digits of precision. If many fewer
2147 // than 15 digits were needed, it might be faster to do
2148 // the loop entirely in BigDecimal arithmetic.
2149 //
2150 // (A double value might have as much many as 17 decimal
2151 // digits of precision; it depends on the relative density
2152 // of binary and decimal numbers at different regions of
2153 // the number line.)
2154 //
2155 // (It would be possible to check for certain special
2156 // cases to avoid doing any Newton iterations. For
2157 // example, if the BigDecimal -> double conversion was
2158 // known to be exact and the rounding mode had a
2159 // low-enough precision, the post-Newton rounding logic
2160 // could be applied directly.)
2161
2162 BigDecimal guess = new BigDecimal(Math.sqrt(working.doubleValue()));
2163 int guessPrecision = 15;
2164 int originalPrecision = mc.getPrecision();
2165 int targetPrecision;
2166
2167 // If an exact value is requested, it must only need about
2168 // half of the input digits to represent since multiplying
2169 // an N digit number by itself yield a 2N-1 digit or 2N
2170 // digit result.
2171 if (originalPrecision == 0) {
2172 targetPrecision = stripped.precision()/2 + 1;
2173 } else {
2174 targetPrecision = originalPrecision;
2175 }
2176
2177 // When setting the precision to use inside the Newton
2178 // iteration loop, take care to avoid the case where the
2179 // precision of the input exceeds the requested precision
2180 // and rounding the input value too soon.
2181 BigDecimal approx = guess;
2182 int workingPrecision = working.precision();
2183 do {
2184 int tmpPrecision = Math.max(Math.max(guessPrecision, targetPrecision + 2),
2185 workingPrecision);
2186 MathContext mcTmp = new MathContext(tmpPrecision, RoundingMode.HALF_EVEN);
2187 // approx = 0.5 * (approx + fraction / approx)
2188 approx = ONE_HALF.multiply(approx.add(working.divide(approx, mcTmp), mcTmp));
2189 guessPrecision *= 2;
2190 } while (guessPrecision < targetPrecision + 2);
2191
2192 BigDecimal result;
2193 RoundingMode targetRm = mc.getRoundingMode();
2194 if (targetRm == RoundingMode.UNNECESSARY || originalPrecision == 0) {
2195 RoundingMode tmpRm =
2196 (targetRm == RoundingMode.UNNECESSARY) ? RoundingMode.DOWN : targetRm;
2197 MathContext mcTmp = new MathContext(targetPrecision, tmpRm);
2198 result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mcTmp);
2199
2200 // If result*result != this numerically, the square
2201 // root isn't exact
2202 if (this.subtract(result.multiply(result)).compareTo(ZERO) != 0) {
2203 throw new ArithmeticException("Computed square root not exact.");
2204 }
2205 } else {
2206 result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mc);
2207
2208 switch (targetRm) {
2209 case DOWN:
2210 case FLOOR:
2211 // Check if too big
2212 if (result.multiply(result).compareTo(this) > 0 ) {
2213 BigDecimal ulp = ulp = result.ulp();
2214 // Adjust increment down in case of 1.0 = 10^0
2215 // since the next smaller number is 1/10
2216 // closer than the next larger at exponent
2217 // boundaries.
2218 if (result.compareTo(ONE) == 0) {
2219 ulp = ulp.multiply(ONE_TENTH);
2220 }
2221 result = result.subtract(ulp);
2222 }
2223 break;
2224
2225 case UP:
2226 case CEILING:
2227 // Check if too small
2228 if (result.multiply(result).compareTo(this) < 0 ) {
2229 result = result.add(result.ulp());
2230 }
2231 break;
2232
2233 default:
2234 // Do nothing for half-way cases
2235 // HALF_DOWN, HALF_EVEN, HALF_UP
2236 // See fix-up in paper, up down by *1/2* ulp
2237 break;
2238 }
2239
2240 }
2241
2242 if (result.scale() != preferredScale) {
2243 // The preferred scale of an add is
2244 // max(addend.scale(), augend.scale()). Therefore, if
2245 // the scale of the result is first minimized using
2246 // stripTrailingZeros(), adding a zero of the
2247 // preferred scale rounding the correct precision will
2248 // perform the proper scale vs precision tradeoffs.
2249 result = result.stripTrailingZeros().
2250 add(zeroWithFinalPreferredScale,
2251 new MathContext(originalPrecision, RoundingMode.UNNECESSARY));
2252 }
2253 assert squareRootResultAssertions(result, mc);
2254 return result;
2255 } else {
2256 switch (signum) {
2257 case -1:
2258 throw new ArithmeticException("Attempted square root " +
2259 "of negative BigDecimal");
2260 case 0:
2261 return valueOf(0L, scale()/2);
2262
2263 default:
2264 throw new AssertionError("Bad value from signum");
2265 }
2266 }
2267 }
2268
2269 private boolean isPowerOfTen() {
2270 return BigInteger.ONE.equals(this.unscaledValue());
2271 }
2272
2273 /**
2274 * For nonzero values, check numerical correctness properties of
2275 * the computed result for the chosen rounding mode.
2276 *
2277 * For the directed roundings, for DOWN and FLOOR, result^2 must
2278 * be {@code <=} the input and (result+ulp)^2 must be {@code >} the
2279 * input. Conversely, for UP and CEIL, result^2 must be {@code >=} the
2280 * input and (result-ulp)^2 must be {@code <} the input.
2281 */
2282 private boolean squareRootResultAssertions(BigDecimal result, MathContext mc) {
2283 if (result.signum() == 0) {
2284 return squareRootZeroResultAssertions(result, mc);
2285 } else {
2286 RoundingMode rm = mc.getRoundingMode();
2287 BigDecimal ulp = result.ulp();
2288 BigDecimal neighborUp = result.add(ulp);
2289 // Make neighbor down accurate even for powers of ten
2290 if (this.isPowerOfTen()) {
2291 ulp = ulp.divide(TEN);
2292 }
2293 BigDecimal neighborDown = result.subtract(ulp);
2294
2295 // Both the starting value and result should be nonzero and positive.
2296 if (result.signum() != 1 ||
2297 this.signum() != 1) {
2298 return false;
2299 }
2300
2301 switch (rm) {
2302 case DOWN:
2303 case FLOOR:
2304 return
2305 result.multiply(result).compareTo(this) <= 0 &&
2306 neighborUp.multiply(neighborUp).compareTo(this) > 0;
2307
2308 case UP:
2309 case CEILING:
2310 return
2311 result.multiply(result).compareTo(this) >= 0 &&
2312 neighborDown.multiply(neighborDown).compareTo(this) < 0;
2313
2314 case HALF_DOWN:
2315 case HALF_EVEN:
2316 case HALF_UP:
2317 BigDecimal err = result.multiply(result).subtract(this).abs();
2318 BigDecimal errUp = neighborUp.multiply(neighborUp).subtract(this);
2319 BigDecimal errDown = this.subtract(neighborDown.multiply(neighborDown));
2320 // All error values should be positive so don't need to
2321 // compare absolute values.
2322
2323 int err_comp_errUp = err.compareTo(errUp);
2324 int err_comp_errDown = err.compareTo(errDown);
2325
2326 return
2327 errUp.signum() == 1 &&
2328 errDown.signum() == 1 &&
2329
2330 err_comp_errUp <= 0 &&
2331 err_comp_errDown <= 0 &&
2332
2333 ((err_comp_errUp == 0 ) ? err_comp_errDown < 0 : true) &&
2334 ((err_comp_errDown == 0 ) ? err_comp_errUp < 0 : true);
2335 // && could check for digit conditions for ties too
2336
2337 default: // Definition of UNNECESSARY already verified.
2338 return true;
2339 }
2340 }
2341 }
2342
2343 private boolean squareRootZeroResultAssertions(BigDecimal result, MathContext mc) {
2344 return this.compareTo(ZERO) == 0;
2345 }
2346
2347 /**
2348 * Returns a {@code BigDecimal} whose value is
2349 * <code>(this<sup>n</sup>)</code>, The power is computed exactly, to
2350 * unlimited precision.
2351 *
2352 * <p>The parameter {@code n} must be in the range 0 through
2353 * 999999999, inclusive. {@code ZERO.pow(0)} returns {@link
2354 * #ONE}.
2355 *
2356 * Note that future releases may expand the allowable exponent
2357 * range of this method.
2358 *
2359 * @param n power to raise this {@code BigDecimal} to.
2360 * @return <code>this<sup>n</sup></code>
2361 * @throws ArithmeticException if {@code n} is out of range.
2362 * @since 1.5
2363 */
2364 public BigDecimal pow(int n) {
2365 if (n < 0 || n > 999999999)
2366 throw new ArithmeticException("Invalid operation");
2367 // No need to calculate pow(n) if result will over/underflow.
2368 // Don't attempt to support "supernormal" numbers.
2369 int newScale = checkScale((long)scale * n);
2370 return new BigDecimal(this.inflated().pow(n), newScale);
2371 }
2372
2373
2374 /**
2375 * Returns a {@code BigDecimal} whose value is
2376 * <code>(this<sup>n</sup>)</code>. The current implementation uses
2377 * the core algorithm defined in ANSI standard X3.274-1996 with
2378 * rounding according to the context settings. In general, the
2379 * returned numerical value is within two ulps of the exact
2380 * numerical value for the chosen precision. Note that future
2381 * releases may use a different algorithm with a decreased
2382 * allowable error bound and increased allowable exponent range.
2383 *
2384 * <p>The X3.274-1996 algorithm is:
2385 *
2386 * <ul>
2387 * <li> An {@code ArithmeticException} exception is thrown if
2388 * <ul>
2389 * <li>{@code abs(n) > 999999999}
2390 * <li>{@code mc.precision == 0} and {@code n < 0}
2391 * <li>{@code mc.precision > 0} and {@code n} has more than
2392 * {@code mc.precision} decimal digits
2393 * </ul>
2394 *
2395 * <li> if {@code n} is zero, {@link #ONE} is returned even if
2396 * {@code this} is zero, otherwise
2397 * <ul>
2398 * <li> if {@code n} is positive, the result is calculated via
2399 * the repeated squaring technique into a single accumulator.
2400 * The individual multiplications with the accumulator use the
2401 * same math context settings as in {@code mc} except for a
2402 * precision increased to {@code mc.precision + elength + 1}
2403 * where {@code elength} is the number of decimal digits in
2404 * {@code n}.
2405 *
2406 * <li> if {@code n} is negative, the result is calculated as if
2407 * {@code n} were positive; this value is then divided into one
2408 * using the working precision specified above.
2409 *
2410 * <li> The final value from either the positive or negative case
2411 * is then rounded to the destination precision.
2412 * </ul>
2413 * </ul>
2414 *
2415 * @param n power to raise this {@code BigDecimal} to.
2416 * @param mc the context to use.
2417 * @return <code>this<sup>n</sup></code> using the ANSI standard X3.274-1996
2418 * algorithm
2419 * @throws ArithmeticException if the result is inexact but the
2420 * rounding mode is {@code UNNECESSARY}, or {@code n} is out
2421 * of range.
2422 * @since 1.5
2423 */
2424 public BigDecimal pow(int n, MathContext mc) {
2425 if (mc.precision == 0)
2426 return pow(n);
2427 if (n < -999999999 || n > 999999999)
2428 throw new ArithmeticException("Invalid operation");
2429 if (n == 0)
2430 return ONE; // x**0 == 1 in X3.274
2431 BigDecimal lhs = this;
2432 MathContext workmc = mc; // working settings
2433 int mag = Math.abs(n); // magnitude of n
2434 if (mc.precision > 0) {
2435 int elength = longDigitLength(mag); // length of n in digits
2436 if (elength > mc.precision) // X3.274 rule
2437 throw new ArithmeticException("Invalid operation");
2438 workmc = new MathContext(mc.precision + elength + 1,
2439 mc.roundingMode);
2440 }
2441 // ready to carry out power calculation...
2442 BigDecimal acc = ONE; // accumulator
2443 boolean seenbit = false; // set once we've seen a 1-bit
2444 for (int i=1;;i++) { // for each bit [top bit ignored]
2445 mag += mag; // shift left 1 bit
2446 if (mag < 0) { // top bit is set
2447 seenbit = true; // OK, we're off
2448 acc = acc.multiply(lhs, workmc); // acc=acc*x
2449 }
2450 if (i == 31)
2451 break; // that was the last bit
2452 if (seenbit)
2453 acc=acc.multiply(acc, workmc); // acc=acc*acc [square]
2454 // else (!seenbit) no point in squaring ONE
2455 }
2456 // if negative n, calculate the reciprocal using working precision
2457 if (n < 0) // [hence mc.precision>0]
2458 acc=ONE.divide(acc, workmc);
2459 // round to final precision and strip zeros
2460 return doRound(acc, mc);
2461 }
2462
2463 /**
2464 * Returns a {@code BigDecimal} whose value is the absolute value
2465 * of this {@code BigDecimal}, and whose scale is
2466 * {@code this.scale()}.
2467 *
2468 * @return {@code abs(this)}
2469 */
2470 public BigDecimal abs() {
2471 return (signum() < 0 ? negate() : this);
2472 }
2473
2474 /**
2475 * Returns a {@code BigDecimal} whose value is the absolute value
2476 * of this {@code BigDecimal}, with rounding according to the
2477 * context settings.
2478 *
2479 * @param mc the context to use.
2480 * @return {@code abs(this)}, rounded as necessary.
2481 * @throws ArithmeticException if the result is inexact but the
2482 * rounding mode is {@code UNNECESSARY}.
2483 * @since 1.5
2484 */
2485 public BigDecimal abs(MathContext mc) {
2486 return (signum() < 0 ? negate(mc) : plus(mc));
2487 }
2488
2489 /**
2490 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2491 * and whose scale is {@code this.scale()}.
2492 *
2493 * @return {@code -this}.
2494 */
2495 public BigDecimal negate() {
2496 if (intCompact == INFLATED) {
2497 return new BigDecimal(intVal.negate(), INFLATED, scale, precision);
2498 } else {
2499 return valueOf(-intCompact, scale, precision);
2500 }
2501 }
2502
2503 /**
2504 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2505 * with rounding according to the context settings.
2506 *
2507 * @param mc the context to use.
2508 * @return {@code -this}, rounded as necessary.
2509 * @throws ArithmeticException if the result is inexact but the
2510 * rounding mode is {@code UNNECESSARY}.
2511 * @since 1.5
2512 */
2513 public BigDecimal negate(MathContext mc) {
2514 return negate().plus(mc);
2515 }
2516
2517 /**
2518 * Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose
2519 * scale is {@code this.scale()}.
2520 *
2521 * <p>This method, which simply returns this {@code BigDecimal}
2522 * is included for symmetry with the unary minus method {@link
2523 * #negate()}.
2524 *
2525 * @return {@code this}.
2526 * @see #negate()
2527 * @since 1.5
2528 */
2529 public BigDecimal plus() {
2530 return this;
2531 }
2532
2533 /**
2534 * Returns a {@code BigDecimal} whose value is {@code (+this)},
2535 * with rounding according to the context settings.
2536 *
2537 * <p>The effect of this method is identical to that of the {@link
2538 * #round(MathContext)} method.
2539 *
2540 * @param mc the context to use.
2541 * @return {@code this}, rounded as necessary. A zero result will
2542 * have a scale of 0.
2543 * @throws ArithmeticException if the result is inexact but the
2544 * rounding mode is {@code UNNECESSARY}.
2545 * @see #round(MathContext)
2546 * @since 1.5
2547 */
2548 public BigDecimal plus(MathContext mc) {
2549 if (mc.precision == 0) // no rounding please
2550 return this;
2551 return doRound(this, mc);
2552 }
2553
2554 /**
2555 * Returns the signum function of this {@code BigDecimal}.
2556 *
2557 * @return -1, 0, or 1 as the value of this {@code BigDecimal}
2558 * is negative, zero, or positive.
2559 */
2560 public int signum() {
2561 return (intCompact != INFLATED)?
2562 Long.signum(intCompact):
2563 intVal.signum();
2564 }
2565
2566 /**
2567 * Returns the <i>scale</i> of this {@code BigDecimal}. If zero
2568 * or positive, the scale is the number of digits to the right of
2569 * the decimal point. If negative, the unscaled value of the
2570 * number is multiplied by ten to the power of the negation of the
2571 * scale. For example, a scale of {@code -3} means the unscaled
2572 * value is multiplied by 1000.
2573 *
2574 * @return the scale of this {@code BigDecimal}.
2575 */
2576 public int scale() {
2577 return scale;
2578 }
2579
2580 /**
2581 * Returns the <i>precision</i> of this {@code BigDecimal}. (The
2582 * precision is the number of digits in the unscaled value.)
2583 *
2584 * <p>The precision of a zero value is 1.
2585 *
2586 * @return the precision of this {@code BigDecimal}.
2587 * @since 1.5
2588 */
2589 public int precision() {
2590 int result = precision;
2591 if (result == 0) {
2592 long s = intCompact;
2593 if (s != INFLATED)
2594 result = longDigitLength(s);
2595 else
2596 result = bigDigitLength(intVal);
2597 precision = result;
2598 }
2599 return result;
2600 }
2601
2602
2603 /**
2604 * Returns a {@code BigInteger} whose value is the <i>unscaled
2605 * value</i> of this {@code BigDecimal}. (Computes <code>(this *
2606 * 10<sup>this.scale()</sup>)</code>.)
2607 *
2608 * @return the unscaled value of this {@code BigDecimal}.
2609 * @since 1.2
2610 */
2611 public BigInteger unscaledValue() {
2612 return this.inflated();
2613 }
2614
2615 // Rounding Modes
2616
2617 /**
2618 * Rounding mode to round away from zero. Always increments the
2619 * digit prior to a nonzero discarded fraction. Note that this rounding
2620 * mode never decreases the magnitude of the calculated value.
2621 *
2622 * @deprecated Use {@link RoundingMode#UP} instead.
2623 */
2624 @Deprecated(since="9")
2625 public static final int ROUND_UP = 0;
2626
2627 /**
2628 * Rounding mode to round towards zero. Never increments the digit
2629 * prior to a discarded fraction (i.e., truncates). Note that this
2630 * rounding mode never increases the magnitude of the calculated value.
2631 *
2632 * @deprecated Use {@link RoundingMode#DOWN} instead.
2633 */
2634 @Deprecated(since="9")
2635 public static final int ROUND_DOWN = 1;
2636
2637 /**
2638 * Rounding mode to round towards positive infinity. If the
2639 * {@code BigDecimal} is positive, behaves as for
2640 * {@code ROUND_UP}; if negative, behaves as for
2641 * {@code ROUND_DOWN}. Note that this rounding mode never
2642 * decreases the calculated value.
2643 *
2644 * @deprecated Use {@link RoundingMode#CEILING} instead.
2645 */
2646 @Deprecated(since="9")
2647 public static final int ROUND_CEILING = 2;
2648
2649 /**
2650 * Rounding mode to round towards negative infinity. If the
2651 * {@code BigDecimal} is positive, behave as for
2652 * {@code ROUND_DOWN}; if negative, behave as for
2653 * {@code ROUND_UP}. Note that this rounding mode never
2654 * increases the calculated value.
2655 *
2656 * @deprecated Use {@link RoundingMode#FLOOR} instead.
2657 */
2658 @Deprecated(since="9")
2659 public static final int ROUND_FLOOR = 3;
2660
2661 /**
2662 * Rounding mode to round towards {@literal "nearest neighbor"}
2663 * unless both neighbors are equidistant, in which case round up.
2664 * Behaves as for {@code ROUND_UP} if the discarded fraction is
2665 * ≥ 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note
2666 * that this is the rounding mode that most of us were taught in
2667 * grade school.
2668 *
2669 * @deprecated Use {@link RoundingMode#HALF_UP} instead.
2670 */
2671 @Deprecated(since="9")
2672 public static final int ROUND_HALF_UP = 4;
2673
2674 /**
2675 * Rounding mode to round towards {@literal "nearest neighbor"}
2676 * unless both neighbors are equidistant, in which case round
2677 * down. Behaves as for {@code ROUND_UP} if the discarded
2678 * fraction is {@literal >} 0.5; otherwise, behaves as for
2679 * {@code ROUND_DOWN}.
2680 *
2681 * @deprecated Use {@link RoundingMode#HALF_DOWN} instead.
2682 */
2683 @Deprecated(since="9")
2684 public static final int ROUND_HALF_DOWN = 5;
2685
2686 /**
2687 * Rounding mode to round towards the {@literal "nearest neighbor"}
2688 * unless both neighbors are equidistant, in which case, round
2689 * towards the even neighbor. Behaves as for
2690 * {@code ROUND_HALF_UP} if the digit to the left of the
2691 * discarded fraction is odd; behaves as for
2692 * {@code ROUND_HALF_DOWN} if it's even. Note that this is the
2693 * rounding mode that minimizes cumulative error when applied
2694 * repeatedly over a sequence of calculations.
2695 *
2696 * @deprecated Use {@link RoundingMode#HALF_EVEN} instead.
2697 */
2698 @Deprecated(since="9")
2699 public static final int ROUND_HALF_EVEN = 6;
2700
2701 /**
2702 * Rounding mode to assert that the requested operation has an exact
2703 * result, hence no rounding is necessary. If this rounding mode is
2704 * specified on an operation that yields an inexact result, an
2705 * {@code ArithmeticException} is thrown.
2706 *
2707 * @deprecated Use {@link RoundingMode#UNNECESSARY} instead.
2708 */
2709 @Deprecated(since="9")
2710 public static final int ROUND_UNNECESSARY = 7;
2711
2712
2713 // Scaling/Rounding Operations
2714
2715 /**
2716 * Returns a {@code BigDecimal} rounded according to the
2717 * {@code MathContext} settings. If the precision setting is 0 then
2718 * no rounding takes place.
2719 *
2720 * <p>The effect of this method is identical to that of the
2721 * {@link #plus(MathContext)} method.
2722 *
2723 * @param mc the context to use.
2724 * @return a {@code BigDecimal} rounded according to the
2725 * {@code MathContext} settings.
2726 * @throws ArithmeticException if the rounding mode is
2727 * {@code UNNECESSARY} and the
2728 * {@code BigDecimal} operation would require rounding.
2729 * @see #plus(MathContext)
2730 * @since 1.5
2731 */
2732 public BigDecimal round(MathContext mc) {
2733 return plus(mc);
2734 }
2735
2736 /**
2737 * Returns a {@code BigDecimal} whose scale is the specified
2738 * value, and whose unscaled value is determined by multiplying or
2739 * dividing this {@code BigDecimal}'s unscaled value by the
2740 * appropriate power of ten to maintain its overall value. If the
2741 * scale is reduced by the operation, the unscaled value must be
2742 * divided (rather than multiplied), and the value may be changed;
2743 * in this case, the specified rounding mode is applied to the
2744 * division.
2745 *
2746 * @apiNote Since BigDecimal objects are immutable, calls of
2747 * this method do <em>not</em> result in the original object being
2748 * modified, contrary to the usual convention of having methods
2749 * named <code>set<i>X</i></code> mutate field <i>{@code X}</i>.
2750 * Instead, {@code setScale} returns an object with the proper
2751 * scale; the returned object may or may not be newly allocated.
2752 *
2753 * @param newScale scale of the {@code BigDecimal} value to be returned.
2754 * @param roundingMode The rounding mode to apply.
2755 * @return a {@code BigDecimal} whose scale is the specified value,
2756 * and whose unscaled value is determined by multiplying or
2757 * dividing this {@code BigDecimal}'s unscaled value by the
2758 * appropriate power of ten to maintain its overall value.
2759 * @throws ArithmeticException if {@code roundingMode==UNNECESSARY}
2760 * and the specified scaling operation would require
2761 * rounding.
2762 * @see RoundingMode
2763 * @since 1.5
2764 */
2765 public BigDecimal setScale(int newScale, RoundingMode roundingMode) {
2766 return setScale(newScale, roundingMode.oldMode);
2767 }
2768
2769 /**
2770 * Returns a {@code BigDecimal} whose scale is the specified
2771 * value, and whose unscaled value is determined by multiplying or
2772 * dividing this {@code BigDecimal}'s unscaled value by the
2773 * appropriate power of ten to maintain its overall value. If the
2774 * scale is reduced by the operation, the unscaled value must be
2775 * divided (rather than multiplied), and the value may be changed;
2776 * in this case, the specified rounding mode is applied to the
2777 * division.
2778 *
2779 * @apiNote Since BigDecimal objects are immutable, calls of
2780 * this method do <em>not</em> result in the original object being
2781 * modified, contrary to the usual convention of having methods
2782 * named <code>set<i>X</i></code> mutate field <i>{@code X}</i>.
2783 * Instead, {@code setScale} returns an object with the proper
2784 * scale; the returned object may or may not be newly allocated.
2785 *
2786 * @deprecated The method {@link #setScale(int, RoundingMode)} should
2787 * be used in preference to this legacy method.
2788 *
2789 * @param newScale scale of the {@code BigDecimal} value to be returned.
2790 * @param roundingMode The rounding mode to apply.
2791 * @return a {@code BigDecimal} whose scale is the specified value,
2792 * and whose unscaled value is determined by multiplying or
2793 * dividing this {@code BigDecimal}'s unscaled value by the
2794 * appropriate power of ten to maintain its overall value.
2795 * @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY}
2796 * and the specified scaling operation would require
2797 * rounding.
2798 * @throws IllegalArgumentException if {@code roundingMode} does not
2799 * represent a valid rounding mode.
2800 * @see #ROUND_UP
2801 * @see #ROUND_DOWN
2802 * @see #ROUND_CEILING
2803 * @see #ROUND_FLOOR
2804 * @see #ROUND_HALF_UP
2805 * @see #ROUND_HALF_DOWN
2806 * @see #ROUND_HALF_EVEN
2807 * @see #ROUND_UNNECESSARY
2808 */
2809 @Deprecated(since="9")
2810 public BigDecimal setScale(int newScale, int roundingMode) {
2811 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
2812 throw new IllegalArgumentException("Invalid rounding mode");
2813
2814 int oldScale = this.scale;
2815 if (newScale == oldScale) // easy case
2816 return this;
2817 if (this.signum() == 0) // zero can have any scale
2818 return zeroValueOf(newScale);
2819 if(this.intCompact!=INFLATED) {
2820 long rs = this.intCompact;
2821 if (newScale > oldScale) {
2822 int raise = checkScale((long) newScale - oldScale);
2823 if ((rs = longMultiplyPowerTen(rs, raise)) != INFLATED) {
2824 return valueOf(rs,newScale);
2825 }
2826 BigInteger rb = bigMultiplyPowerTen(raise);
2827 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2828 } else {
2829 // newScale < oldScale -- drop some digits
2830 // Can't predict the precision due to the effect of rounding.
2831 int drop = checkScale((long) oldScale - newScale);
2832 if (drop < LONG_TEN_POWERS_TABLE.length) {
2833 return divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, newScale);
2834 } else {
2835 return divideAndRound(this.inflated(), bigTenToThe(drop), newScale, roundingMode, newScale);
2836 }
2837 }
2838 } else {
2839 if (newScale > oldScale) {
2840 int raise = checkScale((long) newScale - oldScale);
2841 BigInteger rb = bigMultiplyPowerTen(this.intVal,raise);
2842 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2843 } else {
2844 // newScale < oldScale -- drop some digits
2845 // Can't predict the precision due to the effect of rounding.
2846 int drop = checkScale((long) oldScale - newScale);
2847 if (drop < LONG_TEN_POWERS_TABLE.length)
2848 return divideAndRound(this.intVal, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode,
2849 newScale);
2850 else
2851 return divideAndRound(this.intVal, bigTenToThe(drop), newScale, roundingMode, newScale);
2852 }
2853 }
2854 }
2855
2856 /**
2857 * Returns a {@code BigDecimal} whose scale is the specified
2858 * value, and whose value is numerically equal to this
2859 * {@code BigDecimal}'s. Throws an {@code ArithmeticException}
2860 * if this is not possible.
2861 *
2862 * <p>This call is typically used to increase the scale, in which
2863 * case it is guaranteed that there exists a {@code BigDecimal}
2864 * of the specified scale and the correct value. The call can
2865 * also be used to reduce the scale if the caller knows that the
2866 * {@code BigDecimal} has sufficiently many zeros at the end of
2867 * its fractional part (i.e., factors of ten in its integer value)
2868 * to allow for the rescaling without changing its value.
2869 *
2870 * <p>This method returns the same result as the two-argument
2871 * versions of {@code setScale}, but saves the caller the trouble
2872 * of specifying a rounding mode in cases where it is irrelevant.
2873 *
2874 * @apiNote Since {@code BigDecimal} objects are immutable,
2875 * calls of this method do <em>not</em> result in the original
2876 * object being modified, contrary to the usual convention of
2877 * having methods named <code>set<i>X</i></code> mutate field
2878 * <i>{@code X}</i>. Instead, {@code setScale} returns an
2879 * object with the proper scale; the returned object may or may
2880 * not be newly allocated.
2881 *
2882 * @param newScale scale of the {@code BigDecimal} value to be returned.
2883 * @return a {@code BigDecimal} whose scale is the specified value, and
2884 * whose unscaled value is determined by multiplying or dividing
2885 * this {@code BigDecimal}'s unscaled value by the appropriate
2886 * power of ten to maintain its overall value.
2887 * @throws ArithmeticException if the specified scaling operation would
2888 * require rounding.
2889 * @see #setScale(int, int)
2890 * @see #setScale(int, RoundingMode)
2891 */
2892 public BigDecimal setScale(int newScale) {
2893 return setScale(newScale, ROUND_UNNECESSARY);
2894 }
2895
2896 // Decimal Point Motion Operations
2897
2898 /**
2899 * Returns a {@code BigDecimal} which is equivalent to this one
2900 * with the decimal point moved {@code n} places to the left. If
2901 * {@code n} is non-negative, the call merely adds {@code n} to
2902 * the scale. If {@code n} is negative, the call is equivalent
2903 * to {@code movePointRight(-n)}. The {@code BigDecimal}
2904 * returned by this call has value <code>(this ×
2905 * 10<sup>-n</sup>)</code> and scale {@code max(this.scale()+n,
2906 * 0)}.
2907 *
2908 * @param n number of places to move the decimal point to the left.
2909 * @return a {@code BigDecimal} which is equivalent to this one with the
2910 * decimal point moved {@code n} places to the left.
2911 * @throws ArithmeticException if scale overflows.
2912 */
2913 public BigDecimal movePointLeft(int n) {
2914 if (n == 0) return this;
2915
2916 // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE
2917 int newScale = checkScale((long)scale + n);
2918 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2919 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2920 }
2921
2922 /**
2923 * Returns a {@code BigDecimal} which is equivalent to this one
2924 * with the decimal point moved {@code n} places to the right.
2925 * If {@code n} is non-negative, the call merely subtracts
2926 * {@code n} from the scale. If {@code n} is negative, the call
2927 * is equivalent to {@code movePointLeft(-n)}. The
2928 * {@code BigDecimal} returned by this call has value <code>(this
2929 * × 10<sup>n</sup>)</code> and scale {@code max(this.scale()-n,
2930 * 0)}.
2931 *
2932 * @param n number of places to move the decimal point to the right.
2933 * @return a {@code BigDecimal} which is equivalent to this one
2934 * with the decimal point moved {@code n} places to the right.
2935 * @throws ArithmeticException if scale overflows.
2936 */
2937 public BigDecimal movePointRight(int n) {
2938 if (n == 0) return this;
2939
2940 // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE
2941 int newScale = checkScale((long)scale - n);
2942 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2943 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2944 }
2945
2946 /**
2947 * Returns a BigDecimal whose numerical value is equal to
2948 * ({@code this} * 10<sup>n</sup>). The scale of
2949 * the result is {@code (this.scale() - n)}.
2950 *
2951 * @param n the exponent power of ten to scale by
2952 * @return a BigDecimal whose numerical value is equal to
2953 * ({@code this} * 10<sup>n</sup>)
2954 * @throws ArithmeticException if the scale would be
2955 * outside the range of a 32-bit integer.
2956 *
2957 * @since 1.5
2958 */
2959 public BigDecimal scaleByPowerOfTen(int n) {
2960 return new BigDecimal(intVal, intCompact,
2961 checkScale((long)scale - n), precision);
2962 }
2963
2964 /**
2965 * Returns a {@code BigDecimal} which is numerically equal to
2966 * this one but with any trailing zeros removed from the
2967 * representation. For example, stripping the trailing zeros from
2968 * the {@code BigDecimal} value {@code 600.0}, which has
2969 * [{@code BigInteger}, {@code scale}] components equals to
2970 * [6000, 1], yields {@code 6E2} with [{@code BigInteger},
2971 * {@code scale}] components equals to [6, -2]. If
2972 * this BigDecimal is numerically equal to zero, then
2973 * {@code BigDecimal.ZERO} is returned.
2974 *
2975 * @return a numerically equal {@code BigDecimal} with any
2976 * trailing zeros removed.
2977 * @since 1.5
2978 */
2979 public BigDecimal stripTrailingZeros() {
2980 if (intCompact == 0 || (intVal != null && intVal.signum() == 0)) {
2981 return BigDecimal.ZERO;
2982 } else if (intCompact != INFLATED) {
2983 return createAndStripZerosToMatchScale(intCompact, scale, Long.MIN_VALUE);
2984 } else {
2985 return createAndStripZerosToMatchScale(intVal, scale, Long.MIN_VALUE);
2986 }
2987 }
2988
2989 // Comparison Operations
2990
2991 /**
2992 * Compares this {@code BigDecimal} with the specified
2993 * {@code BigDecimal}. Two {@code BigDecimal} objects that are
2994 * equal in value but have a different scale (like 2.0 and 2.00)
2995 * are considered equal by this method. This method is provided
2996 * in preference to individual methods for each of the six boolean
2997 * comparison operators ({@literal <}, ==,
2998 * {@literal >}, {@literal >=}, !=, {@literal <=}). The
2999 * suggested idiom for performing these comparisons is:
3000 * {@code (x.compareTo(y)} <<i>op</i>> {@code 0)}, where
3001 * <<i>op</i>> is one of the six comparison operators.
3002 *
3003 * @param val {@code BigDecimal} to which this {@code BigDecimal} is
3004 * to be compared.
3005 * @return -1, 0, or 1 as this {@code BigDecimal} is numerically
3006 * less than, equal to, or greater than {@code val}.
3007 */
3008 @Override
3009 public int compareTo(BigDecimal val) {
3010 // Quick path for equal scale and non-inflated case.
3011 if (scale == val.scale) {
3012 long xs = intCompact;
3013 long ys = val.intCompact;
3014 if (xs != INFLATED && ys != INFLATED)
3015 return xs != ys ? ((xs > ys) ? 1 : -1) : 0;
3016 }
3017 int xsign = this.signum();
3018 int ysign = val.signum();
3019 if (xsign != ysign)
3020 return (xsign > ysign) ? 1 : -1;
3021 if (xsign == 0)
3022 return 0;
3023 int cmp = compareMagnitude(val);
3024 return (xsign > 0) ? cmp : -cmp;
3025 }
3026
3027 /**
3028 * Version of compareTo that ignores sign.
3029 */
3030 private int compareMagnitude(BigDecimal val) {
3031 // Match scales, avoid unnecessary inflation
3032 long ys = val.intCompact;
3033 long xs = this.intCompact;
3034 if (xs == 0)
3035 return (ys == 0) ? 0 : -1;
3036 if (ys == 0)
3037 return 1;
3038
3039 long sdiff = (long)this.scale - val.scale;
3040 if (sdiff != 0) {
3041 // Avoid matching scales if the (adjusted) exponents differ
3042 long xae = (long)this.precision() - this.scale; // [-1]
3043 long yae = (long)val.precision() - val.scale; // [-1]
3044 if (xae < yae)
3045 return -1;
3046 if (xae > yae)
3047 return 1;
3048 if (sdiff < 0) {
3049 // The cases sdiff <= Integer.MIN_VALUE intentionally fall through.
3050 if ( sdiff > Integer.MIN_VALUE &&
3051 (xs == INFLATED ||
3052 (xs = longMultiplyPowerTen(xs, (int)-sdiff)) == INFLATED) &&
3053 ys == INFLATED) {
3054 BigInteger rb = bigMultiplyPowerTen((int)-sdiff);
3055 return rb.compareMagnitude(val.intVal);
3056 }
3057 } else { // sdiff > 0
3058 // The cases sdiff > Integer.MAX_VALUE intentionally fall through.
3059 if ( sdiff <= Integer.MAX_VALUE &&
3060 (ys == INFLATED ||
3061 (ys = longMultiplyPowerTen(ys, (int)sdiff)) == INFLATED) &&
3062 xs == INFLATED) {
3063 BigInteger rb = val.bigMultiplyPowerTen((int)sdiff);
3064 return this.intVal.compareMagnitude(rb);
3065 }
3066 }
3067 }
3068 if (xs != INFLATED)
3069 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
3070 else if (ys != INFLATED)
3071 return 1;
3072 else
3073 return this.intVal.compareMagnitude(val.intVal);
3074 }
3075
3076 /**
3077 * Compares this {@code BigDecimal} with the specified
3078 * {@code Object} for equality. Unlike {@link
3079 * #compareTo(BigDecimal) compareTo}, this method considers two
3080 * {@code BigDecimal} objects equal only if they are equal in
3081 * value and scale (thus 2.0 is not equal to 2.00 when compared by
3082 * this method).
3083 *
3084 * @param x {@code Object} to which this {@code BigDecimal} is
3085 * to be compared.
3086 * @return {@code true} if and only if the specified {@code Object} is a
3087 * {@code BigDecimal} whose value and scale are equal to this
3088 * {@code BigDecimal}'s.
3089 * @see #compareTo(java.math.BigDecimal)
3090 * @see #hashCode
3091 */
3092 @Override
3093 public boolean equals(Object x) {
3094 if (!(x instanceof BigDecimal))
3095 return false;
3096 BigDecimal xDec = (BigDecimal) x;
3097 if (x == this)
3098 return true;
3099 if (scale != xDec.scale)
3100 return false;
3101 long s = this.intCompact;
3102 long xs = xDec.intCompact;
3103 if (s != INFLATED) {
3104 if (xs == INFLATED)
3105 xs = compactValFor(xDec.intVal);
3106 return xs == s;
3107 } else if (xs != INFLATED)
3108 return xs == compactValFor(this.intVal);
3109
3110 return this.inflated().equals(xDec.inflated());
3111 }
3112
3113 /**
3114 * Returns the minimum of this {@code BigDecimal} and
3115 * {@code val}.
3116 *
3117 * @param val value with which the minimum is to be computed.
3118 * @return the {@code BigDecimal} whose value is the lesser of this
3119 * {@code BigDecimal} and {@code val}. If they are equal,
3120 * as defined by the {@link #compareTo(BigDecimal) compareTo}
3121 * method, {@code this} is returned.
3122 * @see #compareTo(java.math.BigDecimal)
3123 */
3124 public BigDecimal min(BigDecimal val) {
3125 return (compareTo(val) <= 0 ? this : val);
3126 }
3127
3128 /**
3129 * Returns the maximum of this {@code BigDecimal} and {@code val}.
3130 *
3131 * @param val value with which the maximum is to be computed.
3132 * @return the {@code BigDecimal} whose value is the greater of this
3133 * {@code BigDecimal} and {@code val}. If they are equal,
3134 * as defined by the {@link #compareTo(BigDecimal) compareTo}
3135 * method, {@code this} is returned.
3136 * @see #compareTo(java.math.BigDecimal)
3137 */
3138 public BigDecimal max(BigDecimal val) {
3139 return (compareTo(val) >= 0 ? this : val);
3140 }
3141
3142 // Hash Function
3143
3144 /**
3145 * Returns the hash code for this {@code BigDecimal}. Note that
3146 * two {@code BigDecimal} objects that are numerically equal but
3147 * differ in scale (like 2.0 and 2.00) will generally <em>not</em>
3148 * have the same hash code.
3149 *
3150 * @return hash code for this {@code BigDecimal}.
3151 * @see #equals(Object)
3152 */
3153 @Override
3154 public int hashCode() {
3155 if (intCompact != INFLATED) {
3156 long val2 = (intCompact < 0)? -intCompact : intCompact;
3157 int temp = (int)( ((int)(val2 >>> 32)) * 31 +
3158 (val2 & LONG_MASK));
3159 return 31*((intCompact < 0) ?-temp:temp) + scale;
3160 } else
3161 return 31*intVal.hashCode() + scale;
3162 }
3163
3164 // Format Converters
3165
3166 /**
3167 * Returns the string representation of this {@code BigDecimal},
3168 * using scientific notation if an exponent is needed.
3169 *
3170 * <p>A standard canonical string form of the {@code BigDecimal}
3171 * is created as though by the following steps: first, the
3172 * absolute value of the unscaled value of the {@code BigDecimal}
3173 * is converted to a string in base ten using the characters
3174 * {@code '0'} through {@code '9'} with no leading zeros (except
3175 * if its value is zero, in which case a single {@code '0'}
3176 * character is used).
3177 *
3178 * <p>Next, an <i>adjusted exponent</i> is calculated; this is the
3179 * negated scale, plus the number of characters in the converted
3180 * unscaled value, less one. That is,
3181 * {@code -scale+(ulength-1)}, where {@code ulength} is the
3182 * length of the absolute value of the unscaled value in decimal
3183 * digits (its <i>precision</i>).
3184 *
3185 * <p>If the scale is greater than or equal to zero and the
3186 * adjusted exponent is greater than or equal to {@code -6}, the
3187 * number will be converted to a character form without using
3188 * exponential notation. In this case, if the scale is zero then
3189 * no decimal point is added and if the scale is positive a
3190 * decimal point will be inserted with the scale specifying the
3191 * number of characters to the right of the decimal point.
3192 * {@code '0'} characters are added to the left of the converted
3193 * unscaled value as necessary. If no character precedes the
3194 * decimal point after this insertion then a conventional
3195 * {@code '0'} character is prefixed.
3196 *
3197 * <p>Otherwise (that is, if the scale is negative, or the
3198 * adjusted exponent is less than {@code -6}), the number will be
3199 * converted to a character form using exponential notation. In
3200 * this case, if the converted {@code BigInteger} has more than
3201 * one digit a decimal point is inserted after the first digit.
3202 * An exponent in character form is then suffixed to the converted
3203 * unscaled value (perhaps with inserted decimal point); this
3204 * comprises the letter {@code 'E'} followed immediately by the
3205 * adjusted exponent converted to a character form. The latter is
3206 * in base ten, using the characters {@code '0'} through
3207 * {@code '9'} with no leading zeros, and is always prefixed by a
3208 * sign character {@code '-'} (<code>'\u002D'</code>) if the
3209 * adjusted exponent is negative, {@code '+'}
3210 * (<code>'\u002B'</code>) otherwise).
3211 *
3212 * <p>Finally, the entire string is prefixed by a minus sign
3213 * character {@code '-'} (<code>'\u002D'</code>) if the unscaled
3214 * value is less than zero. No sign character is prefixed if the
3215 * unscaled value is zero or positive.
3216 *
3217 * <p><b>Examples:</b>
3218 * <p>For each representation [<i>unscaled value</i>, <i>scale</i>]
3219 * on the left, the resulting string is shown on the right.
3220 * <pre>
3221 * [123,0] "123"
3222 * [-123,0] "-123"
3223 * [123,-1] "1.23E+3"
3224 * [123,-3] "1.23E+5"
3225 * [123,1] "12.3"
3226 * [123,5] "0.00123"
3227 * [123,10] "1.23E-8"
3228 * [-123,12] "-1.23E-10"
3229 * </pre>
3230 *
3231 * <b>Notes:</b>
3232 * <ol>
3233 *
3234 * <li>There is a one-to-one mapping between the distinguishable
3235 * {@code BigDecimal} values and the result of this conversion.
3236 * That is, every distinguishable {@code BigDecimal} value
3237 * (unscaled value and scale) has a unique string representation
3238 * as a result of using {@code toString}. If that string
3239 * representation is converted back to a {@code BigDecimal} using
3240 * the {@link #BigDecimal(String)} constructor, then the original
3241 * value will be recovered.
3242 *
3243 * <li>The string produced for a given number is always the same;
3244 * it is not affected by locale. This means that it can be used
3245 * as a canonical string representation for exchanging decimal
3246 * data, or as a key for a Hashtable, etc. Locale-sensitive
3247 * number formatting and parsing is handled by the {@link
3248 * java.text.NumberFormat} class and its subclasses.
3249 *
3250 * <li>The {@link #toEngineeringString} method may be used for
3251 * presenting numbers with exponents in engineering notation, and the
3252 * {@link #setScale(int,RoundingMode) setScale} method may be used for
3253 * rounding a {@code BigDecimal} so it has a known number of digits after
3254 * the decimal point.
3255 *
3256 * <li>The digit-to-character mapping provided by
3257 * {@code Character.forDigit} is used.
3258 *
3259 * </ol>
3260 *
3261 * @return string representation of this {@code BigDecimal}.
3262 * @see Character#forDigit
3263 * @see #BigDecimal(java.lang.String)
3264 */
3265 @Override
3266 public String toString() {
3267 String sc = stringCache;
3268 if (sc == null) {
3269 stringCache = sc = layoutChars(true);
3270 }
3271 return sc;
3272 }
3273
3274 /**
3275 * Returns a string representation of this {@code BigDecimal},
3276 * using engineering notation if an exponent is needed.
3277 *
3278 * <p>Returns a string that represents the {@code BigDecimal} as
3279 * described in the {@link #toString()} method, except that if
3280 * exponential notation is used, the power of ten is adjusted to
3281 * be a multiple of three (engineering notation) such that the
3282 * integer part of nonzero values will be in the range 1 through
3283 * 999. If exponential notation is used for zero values, a
3284 * decimal point and one or two fractional zero digits are used so
3285 * that the scale of the zero value is preserved. Note that
3286 * unlike the output of {@link #toString()}, the output of this
3287 * method is <em>not</em> guaranteed to recover the same [integer,
3288 * scale] pair of this {@code BigDecimal} if the output string is
3289 * converting back to a {@code BigDecimal} using the {@linkplain
3290 * #BigDecimal(String) string constructor}. The result of this method meets
3291 * the weaker constraint of always producing a numerically equal
3292 * result from applying the string constructor to the method's output.
3293 *
3294 * @return string representation of this {@code BigDecimal}, using
3295 * engineering notation if an exponent is needed.
3296 * @since 1.5
3297 */
3298 public String toEngineeringString() {
3299 return layoutChars(false);
3300 }
3301
3302 /**
3303 * Returns a string representation of this {@code BigDecimal}
3304 * without an exponent field. For values with a positive scale,
3305 * the number of digits to the right of the decimal point is used
3306 * to indicate scale. For values with a zero or negative scale,
3307 * the resulting string is generated as if the value were
3308 * converted to a numerically equal value with zero scale and as
3309 * if all the trailing zeros of the zero scale value were present
3310 * in the result.
3311 *
3312 * The entire string is prefixed by a minus sign character '-'
3313 * (<code>'\u002D'</code>) if the unscaled value is less than
3314 * zero. No sign character is prefixed if the unscaled value is
3315 * zero or positive.
3316 *
3317 * Note that if the result of this method is passed to the
3318 * {@linkplain #BigDecimal(String) string constructor}, only the
3319 * numerical value of this {@code BigDecimal} will necessarily be
3320 * recovered; the representation of the new {@code BigDecimal}
3321 * may have a different scale. In particular, if this
3322 * {@code BigDecimal} has a negative scale, the string resulting
3323 * from this method will have a scale of zero when processed by
3324 * the string constructor.
3325 *
3326 * (This method behaves analogously to the {@code toString}
3327 * method in 1.4 and earlier releases.)
3328 *
3329 * @return a string representation of this {@code BigDecimal}
3330 * without an exponent field.
3331 * @since 1.5
3332 * @see #toString()
3333 * @see #toEngineeringString()
3334 */
3335 public String toPlainString() {
3336 if(scale==0) {
3337 if(intCompact!=INFLATED) {
3338 return Long.toString(intCompact);
3339 } else {
3340 return intVal.toString();
3341 }
3342 }
3343 if(this.scale<0) { // No decimal point
3344 if(signum()==0) {
3345 return "0";
3346 }
3347 int trailingZeros = checkScaleNonZero((-(long)scale));
3348 StringBuilder buf;
3349 if(intCompact!=INFLATED) {
3350 buf = new StringBuilder(20+trailingZeros);
3351 buf.append(intCompact);
3352 } else {
3353 String str = intVal.toString();
3354 buf = new StringBuilder(str.length()+trailingZeros);
3355 buf.append(str);
3356 }
3357 for (int i = 0; i < trailingZeros; i++) {
3358 buf.append('0');
3359 }
3360 return buf.toString();
3361 }
3362 String str ;
3363 if(intCompact!=INFLATED) {
3364 str = Long.toString(Math.abs(intCompact));
3365 } else {
3366 str = intVal.abs().toString();
3367 }
3368 return getValueString(signum(), str, scale);
3369 }
3370
3371 /* Returns a digit.digit string */
3372 private String getValueString(int signum, String intString, int scale) {
3373 /* Insert decimal point */
3374 StringBuilder buf;
3375 int insertionPoint = intString.length() - scale;
3376 if (insertionPoint == 0) { /* Point goes right before intVal */
3377 return (signum<0 ? "-0." : "0.") + intString;
3378 } else if (insertionPoint > 0) { /* Point goes inside intVal */
3379 buf = new StringBuilder(intString);
3380 buf.insert(insertionPoint, '.');
3381 if (signum < 0)
3382 buf.insert(0, '-');
3383 } else { /* We must insert zeros between point and intVal */
3384 buf = new StringBuilder(3-insertionPoint + intString.length());
3385 buf.append(signum<0 ? "-0." : "0.");
3386 for (int i=0; i<-insertionPoint; i++) {
3387 buf.append('0');
3388 }
3389 buf.append(intString);
3390 }
3391 return buf.toString();
3392 }
3393
3394 /**
3395 * Converts this {@code BigDecimal} to a {@code BigInteger}.
3396 * This conversion is analogous to the
3397 * <i>narrowing primitive conversion</i> from {@code double} to
3398 * {@code long} as defined in
3399 * <cite>The Java™ Language Specification</cite>:
3400 * any fractional part of this
3401 * {@code BigDecimal} will be discarded. Note that this
3402 * conversion can lose information about the precision of the
3403 * {@code BigDecimal} value.
3404 * <p>
3405 * To have an exception thrown if the conversion is inexact (in
3406 * other words if a nonzero fractional part is discarded), use the
3407 * {@link #toBigIntegerExact()} method.
3408 *
3409 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3410 * @jls 5.1.3 Narrowing Primitive Conversion
3411 */
3412 public BigInteger toBigInteger() {
3413 // force to an integer, quietly
3414 return this.setScale(0, ROUND_DOWN).inflated();
3415 }
3416
3417 /**
3418 * Converts this {@code BigDecimal} to a {@code BigInteger},
3419 * checking for lost information. An exception is thrown if this
3420 * {@code BigDecimal} has a nonzero fractional part.
3421 *
3422 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3423 * @throws ArithmeticException if {@code this} has a nonzero
3424 * fractional part.
3425 * @since 1.5
3426 */
3427 public BigInteger toBigIntegerExact() {
3428 // round to an integer, with Exception if decimal part non-0
3429 return this.setScale(0, ROUND_UNNECESSARY).inflated();
3430 }
3431
3432 /**
3433 * Converts this {@code BigDecimal} to a {@code long}.
3434 * This conversion is analogous to the
3435 * <i>narrowing primitive conversion</i> from {@code double} to
3436 * {@code short} as defined in
3437 * <cite>The Java™ Language Specification</cite>:
3438 * any fractional part of this
3439 * {@code BigDecimal} will be discarded, and if the resulting
3440 * "{@code BigInteger}" is too big to fit in a
3441 * {@code long}, only the low-order 64 bits are returned.
3442 * Note that this conversion can lose information about the
3443 * overall magnitude and precision of this {@code BigDecimal} value as well
3444 * as return a result with the opposite sign.
3445 *
3446 * @return this {@code BigDecimal} converted to a {@code long}.
3447 * @jls 5.1.3 Narrowing Primitive Conversion
3448 */
3449 @Override
3450 public long longValue(){
3451 if (intCompact != INFLATED && scale == 0) {
3452 return intCompact;
3453 } else {
3454 // Fastpath zero and small values
3455 if (this.signum() == 0 || fractionOnly() ||
3456 // Fastpath very large-scale values that will result
3457 // in a truncated value of zero. If the scale is -64
3458 // or less, there are at least 64 powers of 10 in the
3459 // value of the numerical result. Since 10 = 2*5, in
3460 // that case there would also be 64 powers of 2 in the
3461 // result, meaning all 64 bits of a long will be zero.
3462 scale <= -64) {
3463 return 0;
3464 } else {
3465 return toBigInteger().longValue();
3466 }
3467 }
3468 }
3469
3470 /**
3471 * Return true if a nonzero BigDecimal has an absolute value less
3472 * than one; i.e. only has fraction digits.
3473 */
3474 private boolean fractionOnly() {
3475 assert this.signum() != 0;
3476 return (this.precision() - this.scale) <= 0;
3477 }
3478
3479 /**
3480 * Converts this {@code BigDecimal} to a {@code long}, checking
3481 * for lost information. If this {@code BigDecimal} has a
3482 * nonzero fractional part or is out of the possible range for a
3483 * {@code long} result then an {@code ArithmeticException} is
3484 * thrown.
3485 *
3486 * @return this {@code BigDecimal} converted to a {@code long}.
3487 * @throws ArithmeticException if {@code this} has a nonzero
3488 * fractional part, or will not fit in a {@code long}.
3489 * @since 1.5
3490 */
3491 public long longValueExact() {
3492 if (intCompact != INFLATED && scale == 0)
3493 return intCompact;
3494
3495 // Fastpath zero
3496 if (this.signum() == 0)
3497 return 0;
3498
3499 // Fastpath numbers less than 1.0 (the latter can be very slow
3500 // to round if very small)
3501 if (fractionOnly())
3502 throw new ArithmeticException("Rounding necessary");
3503
3504 // If more than 19 digits in integer part it cannot possibly fit
3505 if ((precision() - scale) > 19) // [OK for negative scale too]
3506 throw new java.lang.ArithmeticException("Overflow");
3507
3508 // round to an integer, with Exception if decimal part non-0
3509 BigDecimal num = this.setScale(0, ROUND_UNNECESSARY);
3510 if (num.precision() >= 19) // need to check carefully
3511 LongOverflow.check(num);
3512 return num.inflated().longValue();
3513 }
3514
3515 private static class LongOverflow {
3516 /** BigInteger equal to Long.MIN_VALUE. */
3517 private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE);
3518
3519 /** BigInteger equal to Long.MAX_VALUE. */
3520 private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE);
3521
3522 public static void check(BigDecimal num) {
3523 BigInteger intVal = num.inflated();
3524 if (intVal.compareTo(LONGMIN) < 0 ||
3525 intVal.compareTo(LONGMAX) > 0)
3526 throw new java.lang.ArithmeticException("Overflow");
3527 }
3528 }
3529
3530 /**
3531 * Converts this {@code BigDecimal} to an {@code int}.
3532 * This conversion is analogous to the
3533 * <i>narrowing primitive conversion</i> from {@code double} to
3534 * {@code short} as defined in
3535 * <cite>The Java™ Language Specification</cite>:
3536 * any fractional part of this
3537 * {@code BigDecimal} will be discarded, and if the resulting
3538 * "{@code BigInteger}" is too big to fit in an
3539 * {@code int}, only the low-order 32 bits are returned.
3540 * Note that this conversion can lose information about the
3541 * overall magnitude and precision of this {@code BigDecimal}
3542 * value as well as return a result with the opposite sign.
3543 *
3544 * @return this {@code BigDecimal} converted to an {@code int}.
3545 * @jls 5.1.3 Narrowing Primitive Conversion
3546 */
3547 @Override
3548 public int intValue() {
3549 return (intCompact != INFLATED && scale == 0) ?
3550 (int)intCompact :
3551 (int)longValue();
3552 }
3553
3554 /**
3555 * Converts this {@code BigDecimal} to an {@code int}, checking
3556 * for lost information. If this {@code BigDecimal} has a
3557 * nonzero fractional part or is out of the possible range for an
3558 * {@code int} result then an {@code ArithmeticException} is
3559 * thrown.
3560 *
3561 * @return this {@code BigDecimal} converted to an {@code int}.
3562 * @throws ArithmeticException if {@code this} has a nonzero
3563 * fractional part, or will not fit in an {@code int}.
3564 * @since 1.5
3565 */
3566 public int intValueExact() {
3567 long num;
3568 num = this.longValueExact(); // will check decimal part
3569 if ((int)num != num)
3570 throw new java.lang.ArithmeticException("Overflow");
3571 return (int)num;
3572 }
3573
3574 /**
3575 * Converts this {@code BigDecimal} to a {@code short}, checking
3576 * for lost information. If this {@code BigDecimal} has a
3577 * nonzero fractional part or is out of the possible range for a
3578 * {@code short} result then an {@code ArithmeticException} is
3579 * thrown.
3580 *
3581 * @return this {@code BigDecimal} converted to a {@code short}.
3582 * @throws ArithmeticException if {@code this} has a nonzero
3583 * fractional part, or will not fit in a {@code short}.
3584 * @since 1.5
3585 */
3586 public short shortValueExact() {
3587 long num;
3588 num = this.longValueExact(); // will check decimal part
3589 if ((short)num != num)
3590 throw new java.lang.ArithmeticException("Overflow");
3591 return (short)num;
3592 }
3593
3594 /**
3595 * Converts this {@code BigDecimal} to a {@code byte}, checking
3596 * for lost information. If this {@code BigDecimal} has a
3597 * nonzero fractional part or is out of the possible range for a
3598 * {@code byte} result then an {@code ArithmeticException} is
3599 * thrown.
3600 *
3601 * @return this {@code BigDecimal} converted to a {@code byte}.
3602 * @throws ArithmeticException if {@code this} has a nonzero
3603 * fractional part, or will not fit in a {@code byte}.
3604 * @since 1.5
3605 */
3606 public byte byteValueExact() {
3607 long num;
3608 num = this.longValueExact(); // will check decimal part
3609 if ((byte)num != num)
3610 throw new java.lang.ArithmeticException("Overflow");
3611 return (byte)num;
3612 }
3613
3614 /**
3615 * Converts this {@code BigDecimal} to a {@code float}.
3616 * This conversion is similar to the
3617 * <i>narrowing primitive conversion</i> from {@code double} to
3618 * {@code float} as defined in
3619 * <cite>The Java™ Language Specification</cite>:
3620 * if this {@code BigDecimal} has too great a
3621 * magnitude to represent as a {@code float}, it will be
3622 * converted to {@link Float#NEGATIVE_INFINITY} or {@link
3623 * Float#POSITIVE_INFINITY} as appropriate. Note that even when
3624 * the return value is finite, this conversion can lose
3625 * information about the precision of the {@code BigDecimal}
3626 * value.
3627 *
3628 * @return this {@code BigDecimal} converted to a {@code float}.
3629 * @jls 5.1.3 Narrowing Primitive Conversion
3630 */
3631 @Override
3632 public float floatValue(){
3633 if(intCompact != INFLATED) {
3634 if (scale == 0) {
3635 return (float)intCompact;
3636 } else {
3637 /*
3638 * If both intCompact and the scale can be exactly
3639 * represented as float values, perform a single float
3640 * multiply or divide to compute the (properly
3641 * rounded) result.
3642 */
3643 if (Math.abs(intCompact) < 1L<<22 ) {
3644 // Don't have too guard against
3645 // Math.abs(MIN_VALUE) because of outer check
3646 // against INFLATED.
3647 if (scale > 0 && scale < FLOAT_10_POW.length) {
3648 return (float)intCompact / FLOAT_10_POW[scale];
3649 } else if (scale < 0 && scale > -FLOAT_10_POW.length) {
3650 return (float)intCompact * FLOAT_10_POW[-scale];
3651 }
3652 }
3653 }
3654 }
3655 // Somewhat inefficient, but guaranteed to work.
3656 return Float.parseFloat(this.toString());
3657 }
3658
3659 /**
3660 * Converts this {@code BigDecimal} to a {@code double}.
3661 * This conversion is similar to the
3662 * <i>narrowing primitive conversion</i> from {@code double} to
3663 * {@code float} as defined in
3664 * <cite>The Java™ Language Specification</cite>:
3665 * if this {@code BigDecimal} has too great a
3666 * magnitude represent as a {@code double}, it will be
3667 * converted to {@link Double#NEGATIVE_INFINITY} or {@link
3668 * Double#POSITIVE_INFINITY} as appropriate. Note that even when
3669 * the return value is finite, this conversion can lose
3670 * information about the precision of the {@code BigDecimal}
3671 * value.
3672 *
3673 * @return this {@code BigDecimal} converted to a {@code double}.
3674 * @jls 5.1.3 Narrowing Primitive Conversion
3675 */
3676 @Override
3677 public double doubleValue(){
3678 if(intCompact != INFLATED) {
3679 if (scale == 0) {
3680 return (double)intCompact;
3681 } else {
3682 /*
3683 * If both intCompact and the scale can be exactly
3684 * represented as double values, perform a single
3685 * double multiply or divide to compute the (properly
3686 * rounded) result.
3687 */
3688 if (Math.abs(intCompact) < 1L<<52 ) {
3689 // Don't have too guard against
3690 // Math.abs(MIN_VALUE) because of outer check
3691 // against INFLATED.
3692 if (scale > 0 && scale < DOUBLE_10_POW.length) {
3693 return (double)intCompact / DOUBLE_10_POW[scale];
3694 } else if (scale < 0 && scale > -DOUBLE_10_POW.length) {
3695 return (double)intCompact * DOUBLE_10_POW[-scale];
3696 }
3697 }
3698 }
3699 }
3700 // Somewhat inefficient, but guaranteed to work.
3701 return Double.parseDouble(this.toString());
3702 }
3703
3704 /**
3705 * Powers of 10 which can be represented exactly in {@code
3706 * double}.
3707 */
3708 private static final double DOUBLE_10_POW[] = {
3709 1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5,
3710 1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, 1.0e11,
3711 1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17,
3712 1.0e18, 1.0e19, 1.0e20, 1.0e21, 1.0e22
3713 };
3714
3715 /**
3716 * Powers of 10 which can be represented exactly in {@code
3717 * float}.
3718 */
3719 private static final float FLOAT_10_POW[] = {
3720 1.0e0f, 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f,
3721 1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f
3722 };
3723
3724 /**
3725 * Returns the size of an ulp, a unit in the last place, of this
3726 * {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal}
3727 * value is the positive distance between this value and the
3728 * {@code BigDecimal} value next larger in magnitude with the
3729 * same number of digits. An ulp of a zero value is numerically
3730 * equal to 1 with the scale of {@code this}. The result is
3731 * stored with the same scale as {@code this} so the result
3732 * for zero and nonzero values is equal to {@code [1,
3733 * this.scale()]}.
3734 *
3735 * @return the size of an ulp of {@code this}
3736 * @since 1.5
3737 */
3738 public BigDecimal ulp() {
3739 return BigDecimal.valueOf(1, this.scale(), 1);
3740 }
3741
3742 // Private class to build a string representation for BigDecimal object.
3743 // "StringBuilderHelper" is constructed as a thread local variable so it is
3744 // thread safe. The StringBuilder field acts as a buffer to hold the temporary
3745 // representation of BigDecimal. The cmpCharArray holds all the characters for
3746 // the compact representation of BigDecimal (except for '-' sign' if it is
3747 // negative) if its intCompact field is not INFLATED. It is shared by all
3748 // calls to toString() and its variants in that particular thread.
3749 static class StringBuilderHelper {
3750 final StringBuilder sb; // Placeholder for BigDecimal string
3751 final char[] cmpCharArray; // character array to place the intCompact
3752
3753 StringBuilderHelper() {
3754 sb = new StringBuilder();
3755 // All non negative longs can be made to fit into 19 character array.
3756 cmpCharArray = new char[19];
3757 }
3758
3759 // Accessors.
3760 StringBuilder getStringBuilder() {
3761 sb.setLength(0);
3762 return sb;
3763 }
3764
3765 char[] getCompactCharArray() {
3766 return cmpCharArray;
3767 }
3768
3769 /**
3770 * Places characters representing the intCompact in {@code long} into
3771 * cmpCharArray and returns the offset to the array where the
3772 * representation starts.
3773 *
3774 * @param intCompact the number to put into the cmpCharArray.
3775 * @return offset to the array where the representation starts.
3776 * Note: intCompact must be greater or equal to zero.
3777 */
3778 int putIntCompact(long intCompact) {
3779 assert intCompact >= 0;
3780
3781 long q;
3782 int r;
3783 // since we start from the least significant digit, charPos points to
3784 // the last character in cmpCharArray.
3785 int charPos = cmpCharArray.length;
3786
3787 // Get 2 digits/iteration using longs until quotient fits into an int
3788 while (intCompact > Integer.MAX_VALUE) {
3789 q = intCompact / 100;
3790 r = (int)(intCompact - q * 100);
3791 intCompact = q;
3792 cmpCharArray[--charPos] = DIGIT_ONES[r];
3793 cmpCharArray[--charPos] = DIGIT_TENS[r];
3794 }
3795
3796 // Get 2 digits/iteration using ints when i2 >= 100
3797 int q2;
3798 int i2 = (int)intCompact;
3799 while (i2 >= 100) {
3800 q2 = i2 / 100;
3801 r = i2 - q2 * 100;
3802 i2 = q2;
3803 cmpCharArray[--charPos] = DIGIT_ONES[r];
3804 cmpCharArray[--charPos] = DIGIT_TENS[r];
3805 }
3806
3807 cmpCharArray[--charPos] = DIGIT_ONES[i2];
3808 if (i2 >= 10)
3809 cmpCharArray[--charPos] = DIGIT_TENS[i2];
3810
3811 return charPos;
3812 }
3813
3814 static final char[] DIGIT_TENS = {
3815 '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
3816 '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
3817 '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
3818 '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
3819 '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
3820 '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
3821 '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
3822 '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
3823 '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
3824 '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
3825 };
3826
3827 static final char[] DIGIT_ONES = {
3828 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3829 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3830 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3831 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3832 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3833 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3834 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3835 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3836 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3837 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3838 };
3839 }
3840
3841 /**
3842 * Lay out this {@code BigDecimal} into a {@code char[]} array.
3843 * The Java 1.2 equivalent to this was called {@code getValueString}.
3844 *
3845 * @param sci {@code true} for Scientific exponential notation;
3846 * {@code false} for Engineering
3847 * @return string with canonical string representation of this
3848 * {@code BigDecimal}
3849 */
3850 private String layoutChars(boolean sci) {
3851 if (scale == 0) // zero scale is trivial
3852 return (intCompact != INFLATED) ?
3853 Long.toString(intCompact):
3854 intVal.toString();
3855 if (scale == 2 &&
3856 intCompact >= 0 && intCompact < Integer.MAX_VALUE) {
3857 // currency fast path
3858 int lowInt = (int)intCompact % 100;
3859 int highInt = (int)intCompact / 100;
3860 return (Integer.toString(highInt) + '.' +
3861 StringBuilderHelper.DIGIT_TENS[lowInt] +
3862 StringBuilderHelper.DIGIT_ONES[lowInt]) ;
3863 }
3864
3865 StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get();
3866 char[] coeff;
3867 int offset; // offset is the starting index for coeff array
3868 // Get the significand as an absolute value
3869 if (intCompact != INFLATED) {
3870 offset = sbHelper.putIntCompact(Math.abs(intCompact));
3871 coeff = sbHelper.getCompactCharArray();
3872 } else {
3873 offset = 0;
3874 coeff = intVal.abs().toString().toCharArray();
3875 }
3876
3877 // Construct a buffer, with sufficient capacity for all cases.
3878 // If E-notation is needed, length will be: +1 if negative, +1
3879 // if '.' needed, +2 for "E+", + up to 10 for adjusted exponent.
3880 // Otherwise it could have +1 if negative, plus leading "0.00000"
3881 StringBuilder buf = sbHelper.getStringBuilder();
3882 if (signum() < 0) // prefix '-' if negative
3883 buf.append('-');
3884 int coeffLen = coeff.length - offset;
3885 long adjusted = -(long)scale + (coeffLen -1);
3886 if ((scale >= 0) && (adjusted >= -6)) { // plain number
3887 int pad = scale - coeffLen; // count of padding zeros
3888 if (pad >= 0) { // 0.xxx form
3889 buf.append('0');
3890 buf.append('.');
3891 for (; pad>0; pad--) {
3892 buf.append('0');
3893 }
3894 buf.append(coeff, offset, coeffLen);
3895 } else { // xx.xx form
3896 buf.append(coeff, offset, -pad);
3897 buf.append('.');
3898 buf.append(coeff, -pad + offset, scale);
3899 }
3900 } else { // E-notation is needed
3901 if (sci) { // Scientific notation
3902 buf.append(coeff[offset]); // first character
3903 if (coeffLen > 1) { // more to come
3904 buf.append('.');
3905 buf.append(coeff, offset + 1, coeffLen - 1);
3906 }
3907 } else { // Engineering notation
3908 int sig = (int)(adjusted % 3);
3909 if (sig < 0)
3910 sig += 3; // [adjusted was negative]
3911 adjusted -= sig; // now a multiple of 3
3912 sig++;
3913 if (signum() == 0) {
3914 switch (sig) {
3915 case 1:
3916 buf.append('0'); // exponent is a multiple of three
3917 break;
3918 case 2:
3919 buf.append("0.00");
3920 adjusted += 3;
3921 break;
3922 case 3:
3923 buf.append("0.0");
3924 adjusted += 3;
3925 break;
3926 default:
3927 throw new AssertionError("Unexpected sig value " + sig);
3928 }
3929 } else if (sig >= coeffLen) { // significand all in integer
3930 buf.append(coeff, offset, coeffLen);
3931 // may need some zeros, too
3932 for (int i = sig - coeffLen; i > 0; i--) {
3933 buf.append('0');
3934 }
3935 } else { // xx.xxE form
3936 buf.append(coeff, offset, sig);
3937 buf.append('.');
3938 buf.append(coeff, offset + sig, coeffLen - sig);
3939 }
3940 }
3941 if (adjusted != 0) { // [!sci could have made 0]
3942 buf.append('E');
3943 if (adjusted > 0) // force sign for positive
3944 buf.append('+');
3945 buf.append(adjusted);
3946 }
3947 }
3948 return buf.toString();
3949 }
3950
3951 /**
3952 * Return 10 to the power n, as a {@code BigInteger}.
3953 *
3954 * @param n the power of ten to be returned (>=0)
3955 * @return a {@code BigInteger} with the value (10<sup>n</sup>)
3956 */
3957 private static BigInteger bigTenToThe(int n) {
3958 if (n < 0)
3959 return BigInteger.ZERO;
3960
3961 if (n < BIG_TEN_POWERS_TABLE_MAX) {
3962 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3963 if (n < pows.length)
3964 return pows[n];
3965 else
3966 return expandBigIntegerTenPowers(n);
3967 }
3968
3969 return BigInteger.TEN.pow(n);
3970 }
3971
3972 /**
3973 * Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n.
3974 *
3975 * @param n the power of ten to be returned (>=0)
3976 * @return a {@code BigDecimal} with the value (10<sup>n</sup>) and
3977 * in the meantime, the BIG_TEN_POWERS_TABLE array gets
3978 * expanded to the size greater than n.
3979 */
3980 private static BigInteger expandBigIntegerTenPowers(int n) {
3981 synchronized(BigDecimal.class) {
3982 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3983 int curLen = pows.length;
3984 // The following comparison and the above synchronized statement is
3985 // to prevent multiple threads from expanding the same array.
3986 if (curLen <= n) {
3987 int newLen = curLen << 1;
3988 while (newLen <= n) {
3989 newLen <<= 1;
3990 }
3991 pows = Arrays.copyOf(pows, newLen);
3992 for (int i = curLen; i < newLen; i++) {
3993 pows[i] = pows[i - 1].multiply(BigInteger.TEN);
3994 }
3995 // Based on the following facts:
3996 // 1. pows is a private local varible;
3997 // 2. the following store is a volatile store.
3998 // the newly created array elements can be safely published.
3999 BIG_TEN_POWERS_TABLE = pows;
4000 }
4001 return pows[n];
4002 }
4003 }
4004
4005 private static final long[] LONG_TEN_POWERS_TABLE = {
4006 1, // 0 / 10^0
4007 10, // 1 / 10^1
4008 100, // 2 / 10^2
4009 1000, // 3 / 10^3
4010 10000, // 4 / 10^4
4011 100000, // 5 / 10^5
4012 1000000, // 6 / 10^6
4013 10000000, // 7 / 10^7
4014 100000000, // 8 / 10^8
4015 1000000000, // 9 / 10^9
4016 10000000000L, // 10 / 10^10
4017 100000000000L, // 11 / 10^11
4018 1000000000000L, // 12 / 10^12
4019 10000000000000L, // 13 / 10^13
4020 100000000000000L, // 14 / 10^14
4021 1000000000000000L, // 15 / 10^15
4022 10000000000000000L, // 16 / 10^16
4023 100000000000000000L, // 17 / 10^17
4024 1000000000000000000L // 18 / 10^18
4025 };
4026
4027 private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = {
4028 BigInteger.ONE,
4029 BigInteger.valueOf(10),
4030 BigInteger.valueOf(100),
4031 BigInteger.valueOf(1000),
4032 BigInteger.valueOf(10000),
4033 BigInteger.valueOf(100000),
4034 BigInteger.valueOf(1000000),
4035 BigInteger.valueOf(10000000),
4036 BigInteger.valueOf(100000000),
4037 BigInteger.valueOf(1000000000),
4038 BigInteger.valueOf(10000000000L),
4039 BigInteger.valueOf(100000000000L),
4040 BigInteger.valueOf(1000000000000L),
4041 BigInteger.valueOf(10000000000000L),
4042 BigInteger.valueOf(100000000000000L),
4043 BigInteger.valueOf(1000000000000000L),
4044 BigInteger.valueOf(10000000000000000L),
4045 BigInteger.valueOf(100000000000000000L),
4046 BigInteger.valueOf(1000000000000000000L)
4047 };
4048
4049 private static final int BIG_TEN_POWERS_TABLE_INITLEN =
4050 BIG_TEN_POWERS_TABLE.length;
4051 private static final int BIG_TEN_POWERS_TABLE_MAX =
4052 16 * BIG_TEN_POWERS_TABLE_INITLEN;
4053
4054 private static final long THRESHOLDS_TABLE[] = {
4055 Long.MAX_VALUE, // 0
4056 Long.MAX_VALUE/10L, // 1
4057 Long.MAX_VALUE/100L, // 2
4058 Long.MAX_VALUE/1000L, // 3
4059 Long.MAX_VALUE/10000L, // 4
4060 Long.MAX_VALUE/100000L, // 5
4061 Long.MAX_VALUE/1000000L, // 6
4062 Long.MAX_VALUE/10000000L, // 7
4063 Long.MAX_VALUE/100000000L, // 8
4064 Long.MAX_VALUE/1000000000L, // 9
4065 Long.MAX_VALUE/10000000000L, // 10
4066 Long.MAX_VALUE/100000000000L, // 11
4067 Long.MAX_VALUE/1000000000000L, // 12
4068 Long.MAX_VALUE/10000000000000L, // 13
4069 Long.MAX_VALUE/100000000000000L, // 14
4070 Long.MAX_VALUE/1000000000000000L, // 15
4071 Long.MAX_VALUE/10000000000000000L, // 16
4072 Long.MAX_VALUE/100000000000000000L, // 17
4073 Long.MAX_VALUE/1000000000000000000L // 18
4074 };
4075
4076 /**
4077 * Compute val * 10 ^ n; return this product if it is
4078 * representable as a long, INFLATED otherwise.
4079 */
4080 private static long longMultiplyPowerTen(long val, int n) {
4081 if (val == 0 || n <= 0)
4082 return val;
4083 long[] tab = LONG_TEN_POWERS_TABLE;
4084 long[] bounds = THRESHOLDS_TABLE;
4085 if (n < tab.length && n < bounds.length) {
4086 long tenpower = tab[n];
4087 if (val == 1)
4088 return tenpower;
4089 if (Math.abs(val) <= bounds[n])
4090 return val * tenpower;
4091 }
4092 return INFLATED;
4093 }
4094
4095 /**
4096 * Compute this * 10 ^ n.
4097 * Needed mainly to allow special casing to trap zero value
4098 */
4099 private BigInteger bigMultiplyPowerTen(int n) {
4100 if (n <= 0)
4101 return this.inflated();
4102
4103 if (intCompact != INFLATED)
4104 return bigTenToThe(n).multiply(intCompact);
4105 else
4106 return intVal.multiply(bigTenToThe(n));
4107 }
4108
4109 /**
4110 * Returns appropriate BigInteger from intVal field if intVal is
4111 * null, i.e. the compact representation is in use.
4112 */
4113 private BigInteger inflated() {
4114 if (intVal == null) {
4115 return BigInteger.valueOf(intCompact);
4116 }
4117 return intVal;
4118 }
4119
4120 /**
4121 * Match the scales of two {@code BigDecimal}s to align their
4122 * least significant digits.
4123 *
4124 * <p>If the scales of val[0] and val[1] differ, rescale
4125 * (non-destructively) the lower-scaled {@code BigDecimal} so
4126 * they match. That is, the lower-scaled reference will be
4127 * replaced by a reference to a new object with the same scale as
4128 * the other {@code BigDecimal}.
4129 *
4130 * @param val array of two elements referring to the two
4131 * {@code BigDecimal}s to be aligned.
4132 */
4133 private static void matchScale(BigDecimal[] val) {
4134 if (val[0].scale < val[1].scale) {
4135 val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY);
4136 } else if (val[1].scale < val[0].scale) {
4137 val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY);
4138 }
4139 }
4140
4141 private static class UnsafeHolder {
4142 private static final jdk.internal.misc.Unsafe unsafe
4143 = jdk.internal.misc.Unsafe.getUnsafe();
4144 private static final long intCompactOffset
4145 = unsafe.objectFieldOffset(BigDecimal.class, "intCompact");
4146 private static final long intValOffset
4147 = unsafe.objectFieldOffset(BigDecimal.class, "intVal");
4148
4149 static void setIntCompact(BigDecimal bd, long val) {
4150 unsafe.putLong(bd, intCompactOffset, val);
4151 }
4152
4153 static void setIntValVolatile(BigDecimal bd, BigInteger val) {
4154 unsafe.putReferenceVolatile(bd, intValOffset, val);
4155 }
4156 }
4157
4158 /**
4159 * Reconstitute the {@code BigDecimal} instance from a stream (that is,
4160 * deserialize it).
4161 *
4162 * @param s the stream being read.
4163 */
4164 @java.io.Serial
4165 private void readObject(java.io.ObjectInputStream s)
4166 throws java.io.IOException, ClassNotFoundException {
4167 // Read in all fields
4168 s.defaultReadObject();
4169 // validate possibly bad fields
4170 if (intVal == null) {
4171 String message = "BigDecimal: null intVal in stream";
4172 throw new java.io.StreamCorruptedException(message);
4173 // [all values of scale are now allowed]
4174 }
4175 UnsafeHolder.setIntCompact(this, compactValFor(intVal));
4176 }
4177
4178 /**
4179 * Serialize this {@code BigDecimal} to the stream in question
4180 *
4181 * @param s the stream to serialize to.
4182 */
4183 @java.io.Serial
4184 private void writeObject(java.io.ObjectOutputStream s)
4185 throws java.io.IOException {
4186 // Must inflate to maintain compatible serial form.
4187 if (this.intVal == null)
4188 UnsafeHolder.setIntValVolatile(this, BigInteger.valueOf(this.intCompact));
4189 // Could reset intVal back to null if it has to be set.
4190 s.defaultWriteObject();
4191 }
4192
4193 /**
4194 * Returns the length of the absolute value of a {@code long}, in decimal
4195 * digits.
4196 *
4197 * @param x the {@code long}
4198 * @return the length of the unscaled value, in deciaml digits.
4199 */
4200 static int longDigitLength(long x) {
4201 /*
4202 * As described in "Bit Twiddling Hacks" by Sean Anderson,
4203 * (http://graphics.stanford.edu/~seander/bithacks.html)
4204 * integer log 10 of x is within 1 of (1233/4096)* (1 +
4205 * integer log 2 of x). The fraction 1233/4096 approximates
4206 * log10(2). So we first do a version of log2 (a variant of
4207 * Long class with pre-checks and opposite directionality) and
4208 * then scale and check against powers table. This is a little
4209 * simpler in present context than the version in Hacker's
4210 * Delight sec 11-4. Adding one to bit length allows comparing
4211 * downward from the LONG_TEN_POWERS_TABLE that we need
4212 * anyway.
4213 */
4214 assert x != BigDecimal.INFLATED;
4215 if (x < 0)
4216 x = -x;
4217 if (x < 10) // must screen for 0, might as well 10
4218 return 1;
4219 int r = ((64 - Long.numberOfLeadingZeros(x) + 1) * 1233) >>> 12;
4220 long[] tab = LONG_TEN_POWERS_TABLE;
4221 // if r >= length, must have max possible digits for long
4222 return (r >= tab.length || x < tab[r]) ? r : r + 1;
4223 }
4224
4225 /**
4226 * Returns the length of the absolute value of a BigInteger, in
4227 * decimal digits.
4228 *
4229 * @param b the BigInteger
4230 * @return the length of the unscaled value, in decimal digits
4231 */
4232 private static int bigDigitLength(BigInteger b) {
4233 /*
4234 * Same idea as the long version, but we need a better
4235 * approximation of log10(2). Using 646456993/2^31
4236 * is accurate up to max possible reported bitLength.
4237 */
4238 if (b.signum == 0)
4239 return 1;
4240 int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31);
4241 return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1;
4242 }
4243
4244 /**
4245 * Check a scale for Underflow or Overflow. If this BigDecimal is
4246 * nonzero, throw an exception if the scale is outof range. If this
4247 * is zero, saturate the scale to the extreme value of the right
4248 * sign if the scale is out of range.
4249 *
4250 * @param val The new scale.
4251 * @throws ArithmeticException (overflow or underflow) if the new
4252 * scale is out of range.
4253 * @return validated scale as an int.
4254 */
4255 private int checkScale(long val) {
4256 int asInt = (int)val;
4257 if (asInt != val) {
4258 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
4259 BigInteger b;
4260 if (intCompact != 0 &&
4261 ((b = intVal) == null || b.signum() != 0))
4262 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
4263 }
4264 return asInt;
4265 }
4266
4267 /**
4268 * Returns the compact value for given {@code BigInteger}, or
4269 * INFLATED if too big. Relies on internal representation of
4270 * {@code BigInteger}.
4271 */
4272 private static long compactValFor(BigInteger b) {
4273 int[] m = b.mag;
4274 int len = m.length;
4275 if (len == 0)
4276 return 0;
4277 int d = m[0];
4278 if (len > 2 || (len == 2 && d < 0))
4279 return INFLATED;
4280
4281 long u = (len == 2)?
4282 (((long) m[1] & LONG_MASK) + (((long)d) << 32)) :
4283 (((long)d) & LONG_MASK);
4284 return (b.signum < 0)? -u : u;
4285 }
4286
4287 private static int longCompareMagnitude(long x, long y) {
4288 if (x < 0)
4289 x = -x;
4290 if (y < 0)
4291 y = -y;
4292 return (x < y) ? -1 : ((x == y) ? 0 : 1);
4293 }
4294
4295 private static int saturateLong(long s) {
4296 int i = (int)s;
4297 return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE);
4298 }
4299
4300 /*
4301 * Internal printing routine
4302 */
4303 private static void print(String name, BigDecimal bd) {
4304 System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n",
4305 name,
4306 bd.intCompact,
4307 bd.intVal,
4308 bd.scale,
4309 bd.precision);
4310 }
4311
4312 /**
4313 * Check internal invariants of this BigDecimal. These invariants
4314 * include:
4315 *
4316 * <ul>
4317 *
4318 * <li>The object must be initialized; either intCompact must not be
4319 * INFLATED or intVal is non-null. Both of these conditions may
4320 * be true.
4321 *
4322 * <li>If both intCompact and intVal and set, their values must be
4323 * consistent.
4324 *
4325 * <li>If precision is nonzero, it must have the right value.
4326 * </ul>
4327 *
4328 * Note: Since this is an audit method, we are not supposed to change the
4329 * state of this BigDecimal object.
4330 */
4331 private BigDecimal audit() {
4332 if (intCompact == INFLATED) {
4333 if (intVal == null) {
4334 print("audit", this);
4335 throw new AssertionError("null intVal");
4336 }
4337 // Check precision
4338 if (precision > 0 && precision != bigDigitLength(intVal)) {
4339 print("audit", this);
4340 throw new AssertionError("precision mismatch");
4341 }
4342 } else {
4343 if (intVal != null) {
4344 long val = intVal.longValue();
4345 if (val != intCompact) {
4346 print("audit", this);
4347 throw new AssertionError("Inconsistent state, intCompact=" +
4348 intCompact + "\t intVal=" + val);
4349 }
4350 }
4351 // Check precision
4352 if (precision > 0 && precision != longDigitLength(intCompact)) {
4353 print("audit", this);
4354 throw new AssertionError("precision mismatch");
4355 }
4356 }
4357 return this;
4358 }
4359
4360 /* the same as checkScale where value!=0 */
4361 private static int checkScaleNonZero(long val) {
4362 int asInt = (int)val;
4363 if (asInt != val) {
4364 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
4365 }
4366 return asInt;
4367 }
4368
4369 private static int checkScale(long intCompact, long val) {
4370 int asInt = (int)val;
4371 if (asInt != val) {
4372 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
4373 if (intCompact != 0)
4374 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
4375 }
4376 return asInt;
4377 }
4378
4379 private static int checkScale(BigInteger intVal, long val) {
4380 int asInt = (int)val;
4381 if (asInt != val) {
4382 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
4383 if (intVal.signum() != 0)
4384 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
4385 }
4386 return asInt;
4387 }
4388
4389 /**
4390 * Returns a {@code BigDecimal} rounded according to the MathContext
4391 * settings;
4392 * If rounding is needed a new {@code BigDecimal} is created and returned.
4393 *
4394 * @param val the value to be rounded
4395 * @param mc the context to use.
4396 * @return a {@code BigDecimal} rounded according to the MathContext
4397 * settings. May return {@code value}, if no rounding needed.
4398 * @throws ArithmeticException if the rounding mode is
4399 * {@code RoundingMode.UNNECESSARY} and the
4400 * result is inexact.
4401 */
4402 private static BigDecimal doRound(BigDecimal val, MathContext mc) {
4403 int mcp = mc.precision;
4404 boolean wasDivided = false;
4405 if (mcp > 0) {
4406 BigInteger intVal = val.intVal;
4407 long compactVal = val.intCompact;
4408 int scale = val.scale;
4409 int prec = val.precision();
4410 int mode = mc.roundingMode.oldMode;
4411 int drop;
4412 if (compactVal == INFLATED) {
4413 drop = prec - mcp;
4414 while (drop > 0) {
4415 scale = checkScaleNonZero((long) scale - drop);
4416 intVal = divideAndRoundByTenPow(intVal, drop, mode);
4417 wasDivided = true;
4418 compactVal = compactValFor(intVal);
4419 if (compactVal != INFLATED) {
4420 prec = longDigitLength(compactVal);
4421 break;
4422 }
4423 prec = bigDigitLength(intVal);
4424 drop = prec - mcp;
4425 }
4426 }
4427 if (compactVal != INFLATED) {
4428 drop = prec - mcp; // drop can't be more than 18
4429 while (drop > 0) {
4430 scale = checkScaleNonZero((long) scale - drop);
4431 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4432 wasDivided = true;
4433 prec = longDigitLength(compactVal);
4434 drop = prec - mcp;
4435 intVal = null;
4436 }
4437 }
4438 return wasDivided ? new BigDecimal(intVal,compactVal,scale,prec) : val;
4439 }
4440 return val;
4441 }
4442
4443 /*
4444 * Returns a {@code BigDecimal} created from {@code long} value with
4445 * given scale rounded according to the MathContext settings
4446 */
4447 private static BigDecimal doRound(long compactVal, int scale, MathContext mc) {
4448 int mcp = mc.precision;
4449 if (mcp > 0 && mcp < 19) {
4450 int prec = longDigitLength(compactVal);
4451 int drop = prec - mcp; // drop can't be more than 18
4452 while (drop > 0) {
4453 scale = checkScaleNonZero((long) scale - drop);
4454 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4455 prec = longDigitLength(compactVal);
4456 drop = prec - mcp;
4457 }
4458 return valueOf(compactVal, scale, prec);
4459 }
4460 return valueOf(compactVal, scale);
4461 }
4462
4463 /*
4464 * Returns a {@code BigDecimal} created from {@code BigInteger} value with
4465 * given scale rounded according to the MathContext settings
4466 */
4467 private static BigDecimal doRound(BigInteger intVal, int scale, MathContext mc) {
4468 int mcp = mc.precision;
4469 int prec = 0;
4470 if (mcp > 0) {
4471 long compactVal = compactValFor(intVal);
4472 int mode = mc.roundingMode.oldMode;
4473 int drop;
4474 if (compactVal == INFLATED) {
4475 prec = bigDigitLength(intVal);
4476 drop = prec - mcp;
4477 while (drop > 0) {
4478 scale = checkScaleNonZero((long) scale - drop);
4479 intVal = divideAndRoundByTenPow(intVal, drop, mode);
4480 compactVal = compactValFor(intVal);
4481 if (compactVal != INFLATED) {
4482 break;
4483 }
4484 prec = bigDigitLength(intVal);
4485 drop = prec - mcp;
4486 }
4487 }
4488 if (compactVal != INFLATED) {
4489 prec = longDigitLength(compactVal);
4490 drop = prec - mcp; // drop can't be more than 18
4491 while (drop > 0) {
4492 scale = checkScaleNonZero((long) scale - drop);
4493 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4494 prec = longDigitLength(compactVal);
4495 drop = prec - mcp;
4496 }
4497 return valueOf(compactVal,scale,prec);
4498 }
4499 }
4500 return new BigDecimal(intVal,INFLATED,scale,prec);
4501 }
4502
4503 /*
4504 * Divides {@code BigInteger} value by ten power.
4505 */
4506 private static BigInteger divideAndRoundByTenPow(BigInteger intVal, int tenPow, int roundingMode) {
4507 if (tenPow < LONG_TEN_POWERS_TABLE.length)
4508 intVal = divideAndRound(intVal, LONG_TEN_POWERS_TABLE[tenPow], roundingMode);
4509 else
4510 intVal = divideAndRound(intVal, bigTenToThe(tenPow), roundingMode);
4511 return intVal;
4512 }
4513
4514 /**
4515 * Internally used for division operation for division {@code long} by
4516 * {@code long}.
4517 * The returned {@code BigDecimal} object is the quotient whose scale is set
4518 * to the passed in scale. If the remainder is not zero, it will be rounded
4519 * based on the passed in roundingMode. Also, if the remainder is zero and
4520 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4521 * trailing zeros of the result is stripped to match the preferredScale.
4522 */
4523 private static BigDecimal divideAndRound(long ldividend, long ldivisor, int scale, int roundingMode,
4524 int preferredScale) {
4525
4526 int qsign; // quotient sign
4527 long q = ldividend / ldivisor; // store quotient in long
4528 if (roundingMode == ROUND_DOWN && scale == preferredScale)
4529 return valueOf(q, scale);
4530 long r = ldividend % ldivisor; // store remainder in long
4531 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4532 if (r != 0) {
4533 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4534 return valueOf((increment ? q + qsign : q), scale);
4535 } else {
4536 if (preferredScale != scale)
4537 return createAndStripZerosToMatchScale(q, scale, preferredScale);
4538 else
4539 return valueOf(q, scale);
4540 }
4541 }
4542
4543 /**
4544 * Divides {@code long} by {@code long} and do rounding based on the
4545 * passed in roundingMode.
4546 */
4547 private static long divideAndRound(long ldividend, long ldivisor, int roundingMode) {
4548 int qsign; // quotient sign
4549 long q = ldividend / ldivisor; // store quotient in long
4550 if (roundingMode == ROUND_DOWN)
4551 return q;
4552 long r = ldividend % ldivisor; // store remainder in long
4553 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4554 if (r != 0) {
4555 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4556 return increment ? q + qsign : q;
4557 } else {
4558 return q;
4559 }
4560 }
4561
4562 /**
4563 * Shared logic of need increment computation.
4564 */
4565 private static boolean commonNeedIncrement(int roundingMode, int qsign,
4566 int cmpFracHalf, boolean oddQuot) {
4567 switch(roundingMode) {
4568 case ROUND_UNNECESSARY:
4569 throw new ArithmeticException("Rounding necessary");
4570
4571 case ROUND_UP: // Away from zero
4572 return true;
4573
4574 case ROUND_DOWN: // Towards zero
4575 return false;
4576
4577 case ROUND_CEILING: // Towards +infinity
4578 return qsign > 0;
4579
4580 case ROUND_FLOOR: // Towards -infinity
4581 return qsign < 0;
4582
4583 default: // Some kind of half-way rounding
4584 assert roundingMode >= ROUND_HALF_UP &&
4585 roundingMode <= ROUND_HALF_EVEN: "Unexpected rounding mode" + RoundingMode.valueOf(roundingMode);
4586
4587 if (cmpFracHalf < 0 ) // We're closer to higher digit
4588 return false;
4589 else if (cmpFracHalf > 0 ) // We're closer to lower digit
4590 return true;
4591 else { // half-way
4592 assert cmpFracHalf == 0;
4593
4594 switch(roundingMode) {
4595 case ROUND_HALF_DOWN:
4596 return false;
4597
4598 case ROUND_HALF_UP:
4599 return true;
4600
4601 case ROUND_HALF_EVEN:
4602 return oddQuot;
4603
4604 default:
4605 throw new AssertionError("Unexpected rounding mode" + roundingMode);
4606 }
4607 }
4608 }
4609 }
4610
4611 /**
4612 * Tests if quotient has to be incremented according the roundingMode
4613 */
4614 private static boolean needIncrement(long ldivisor, int roundingMode,
4615 int qsign, long q, long r) {
4616 assert r != 0L;
4617
4618 int cmpFracHalf;
4619 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4620 cmpFracHalf = 1; // 2 * r can't fit into long
4621 } else {
4622 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4623 }
4624
4625 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, (q & 1L) != 0L);
4626 }
4627
4628 /**
4629 * Divides {@code BigInteger} value by {@code long} value and
4630 * do rounding based on the passed in roundingMode.
4631 */
4632 private static BigInteger divideAndRound(BigInteger bdividend, long ldivisor, int roundingMode) {
4633 // Descend into mutables for faster remainder checks
4634 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4635 // store quotient
4636 MutableBigInteger mq = new MutableBigInteger();
4637 // store quotient & remainder in long
4638 long r = mdividend.divide(ldivisor, mq);
4639 // record remainder is zero or not
4640 boolean isRemainderZero = (r == 0);
4641 // quotient sign
4642 int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4643 if (!isRemainderZero) {
4644 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4645 mq.add(MutableBigInteger.ONE);
4646 }
4647 }
4648 return mq.toBigInteger(qsign);
4649 }
4650
4651 /**
4652 * Internally used for division operation for division {@code BigInteger}
4653 * by {@code long}.
4654 * The returned {@code BigDecimal} object is the quotient whose scale is set
4655 * to the passed in scale. If the remainder is not zero, it will be rounded
4656 * based on the passed in roundingMode. Also, if the remainder is zero and
4657 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4658 * trailing zeros of the result is stripped to match the preferredScale.
4659 */
4660 private static BigDecimal divideAndRound(BigInteger bdividend,
4661 long ldivisor, int scale, int roundingMode, int preferredScale) {
4662 // Descend into mutables for faster remainder checks
4663 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4664 // store quotient
4665 MutableBigInteger mq = new MutableBigInteger();
4666 // store quotient & remainder in long
4667 long r = mdividend.divide(ldivisor, mq);
4668 // record remainder is zero or not
4669 boolean isRemainderZero = (r == 0);
4670 // quotient sign
4671 int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4672 if (!isRemainderZero) {
4673 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4674 mq.add(MutableBigInteger.ONE);
4675 }
4676 return mq.toBigDecimal(qsign, scale);
4677 } else {
4678 if (preferredScale != scale) {
4679 long compactVal = mq.toCompactValue(qsign);
4680 if(compactVal!=INFLATED) {
4681 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4682 }
4683 BigInteger intVal = mq.toBigInteger(qsign);
4684 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
4685 } else {
4686 return mq.toBigDecimal(qsign, scale);
4687 }
4688 }
4689 }
4690
4691 /**
4692 * Tests if quotient has to be incremented according the roundingMode
4693 */
4694 private static boolean needIncrement(long ldivisor, int roundingMode,
4695 int qsign, MutableBigInteger mq, long r) {
4696 assert r != 0L;
4697
4698 int cmpFracHalf;
4699 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4700 cmpFracHalf = 1; // 2 * r can't fit into long
4701 } else {
4702 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4703 }
4704
4705 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
4706 }
4707
4708 /**
4709 * Divides {@code BigInteger} value by {@code BigInteger} value and
4710 * do rounding based on the passed in roundingMode.
4711 */
4712 private static BigInteger divideAndRound(BigInteger bdividend, BigInteger bdivisor, int roundingMode) {
4713 boolean isRemainderZero; // record remainder is zero or not
4714 int qsign; // quotient sign
4715 // Descend into mutables for faster remainder checks
4716 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4717 MutableBigInteger mq = new MutableBigInteger();
4718 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4719 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4720 isRemainderZero = mr.isZero();
4721 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4722 if (!isRemainderZero) {
4723 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4724 mq.add(MutableBigInteger.ONE);
4725 }
4726 }
4727 return mq.toBigInteger(qsign);
4728 }
4729
4730 /**
4731 * Internally used for division operation for division {@code BigInteger}
4732 * by {@code BigInteger}.
4733 * The returned {@code BigDecimal} object is the quotient whose scale is set
4734 * to the passed in scale. If the remainder is not zero, it will be rounded
4735 * based on the passed in roundingMode. Also, if the remainder is zero and
4736 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4737 * trailing zeros of the result is stripped to match the preferredScale.
4738 */
4739 private static BigDecimal divideAndRound(BigInteger bdividend, BigInteger bdivisor, int scale, int roundingMode,
4740 int preferredScale) {
4741 boolean isRemainderZero; // record remainder is zero or not
4742 int qsign; // quotient sign
4743 // Descend into mutables for faster remainder checks
4744 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4745 MutableBigInteger mq = new MutableBigInteger();
4746 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4747 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4748 isRemainderZero = mr.isZero();
4749 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4750 if (!isRemainderZero) {
4751 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4752 mq.add(MutableBigInteger.ONE);
4753 }
4754 return mq.toBigDecimal(qsign, scale);
4755 } else {
4756 if (preferredScale != scale) {
4757 long compactVal = mq.toCompactValue(qsign);
4758 if (compactVal != INFLATED) {
4759 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4760 }
4761 BigInteger intVal = mq.toBigInteger(qsign);
4762 return createAndStripZerosToMatchScale(intVal, scale, preferredScale);
4763 } else {
4764 return mq.toBigDecimal(qsign, scale);
4765 }
4766 }
4767 }
4768
4769 /**
4770 * Tests if quotient has to be incremented according the roundingMode
4771 */
4772 private static boolean needIncrement(MutableBigInteger mdivisor, int roundingMode,
4773 int qsign, MutableBigInteger mq, MutableBigInteger mr) {
4774 assert !mr.isZero();
4775 int cmpFracHalf = mr.compareHalf(mdivisor);
4776 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
4777 }
4778
4779 /**
4780 * Remove insignificant trailing zeros from this
4781 * {@code BigInteger} value until the preferred scale is reached or no
4782 * more zeros can be removed. If the preferred scale is less than
4783 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4784 *
4785 * @return new {@code BigDecimal} with a scale possibly reduced
4786 * to be closed to the preferred scale.
4787 */
4788 private static BigDecimal createAndStripZerosToMatchScale(BigInteger intVal, int scale, long preferredScale) {
4789 BigInteger qr[]; // quotient-remainder pair
4790 while (intVal.compareMagnitude(BigInteger.TEN) >= 0
4791 && scale > preferredScale) {
4792 if (intVal.testBit(0))
4793 break; // odd number cannot end in 0
4794 qr = intVal.divideAndRemainder(BigInteger.TEN);
4795 if (qr[1].signum() != 0)
4796 break; // non-0 remainder
4797 intVal = qr[0];
4798 scale = checkScale(intVal,(long) scale - 1); // could Overflow
4799 }
4800 return valueOf(intVal, scale, 0);
4801 }
4802
4803 /**
4804 * Remove insignificant trailing zeros from this
4805 * {@code long} value until the preferred scale is reached or no
4806 * more zeros can be removed. If the preferred scale is less than
4807 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4808 *
4809 * @return new {@code BigDecimal} with a scale possibly reduced
4810 * to be closed to the preferred scale.
4811 */
4812 private static BigDecimal createAndStripZerosToMatchScale(long compactVal, int scale, long preferredScale) {
4813 while (Math.abs(compactVal) >= 10L && scale > preferredScale) {
4814 if ((compactVal & 1L) != 0L)
4815 break; // odd number cannot end in 0
4816 long r = compactVal % 10L;
4817 if (r != 0L)
4818 break; // non-0 remainder
4819 compactVal /= 10;
4820 scale = checkScale(compactVal, (long) scale - 1); // could Overflow
4821 }
4822 return valueOf(compactVal, scale);
4823 }
4824
4825 private static BigDecimal stripZerosToMatchScale(BigInteger intVal, long intCompact, int scale, int preferredScale) {
4826 if(intCompact!=INFLATED) {
4827 return createAndStripZerosToMatchScale(intCompact, scale, preferredScale);
4828 } else {
4829 return createAndStripZerosToMatchScale(intVal==null ? INFLATED_BIGINT : intVal,
4830 scale, preferredScale);
4831 }
4832 }
4833
4834 /*
4835 * returns INFLATED if oveflow
4836 */
4837 private static long add(long xs, long ys){
4838 long sum = xs + ys;
4839 // See "Hacker's Delight" section 2-12 for explanation of
4840 // the overflow test.
4841 if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) { // not overflowed
4842 return sum;
4843 }
4844 return INFLATED;
4845 }
4846
4847 private static BigDecimal add(long xs, long ys, int scale){
4848 long sum = add(xs, ys);
4849 if (sum!=INFLATED)
4850 return BigDecimal.valueOf(sum, scale);
4851 return new BigDecimal(BigInteger.valueOf(xs).add(ys), scale);
4852 }
4853
4854 private static BigDecimal add(final long xs, int scale1, final long ys, int scale2) {
4855 long sdiff = (long) scale1 - scale2;
4856 if (sdiff == 0) {
4857 return add(xs, ys, scale1);
4858 } else if (sdiff < 0) {
4859 int raise = checkScale(xs,-sdiff);
4860 long scaledX = longMultiplyPowerTen(xs, raise);
4861 if (scaledX != INFLATED) {
4862 return add(scaledX, ys, scale2);
4863 } else {
4864 BigInteger bigsum = bigMultiplyPowerTen(xs,raise).add(ys);
4865 return ((xs^ys)>=0) ? // same sign test
4866 new BigDecimal(bigsum, INFLATED, scale2, 0)
4867 : valueOf(bigsum, scale2, 0);
4868 }
4869 } else {
4870 int raise = checkScale(ys,sdiff);
4871 long scaledY = longMultiplyPowerTen(ys, raise);
4872 if (scaledY != INFLATED) {
4873 return add(xs, scaledY, scale1);
4874 } else {
4875 BigInteger bigsum = bigMultiplyPowerTen(ys,raise).add(xs);
4876 return ((xs^ys)>=0) ?
4877 new BigDecimal(bigsum, INFLATED, scale1, 0)
4878 : valueOf(bigsum, scale1, 0);
4879 }
4880 }
4881 }
4882
4883 private static BigDecimal add(final long xs, int scale1, BigInteger snd, int scale2) {
4884 int rscale = scale1;
4885 long sdiff = (long)rscale - scale2;
4886 boolean sameSigns = (Long.signum(xs) == snd.signum);
4887 BigInteger sum;
4888 if (sdiff < 0) {
4889 int raise = checkScale(xs,-sdiff);
4890 rscale = scale2;
4891 long scaledX = longMultiplyPowerTen(xs, raise);
4892 if (scaledX == INFLATED) {
4893 sum = snd.add(bigMultiplyPowerTen(xs,raise));
4894 } else {
4895 sum = snd.add(scaledX);
4896 }
4897 } else { //if (sdiff > 0) {
4898 int raise = checkScale(snd,sdiff);
4899 snd = bigMultiplyPowerTen(snd,raise);
4900 sum = snd.add(xs);
4901 }
4902 return (sameSigns) ?
4903 new BigDecimal(sum, INFLATED, rscale, 0) :
4904 valueOf(sum, rscale, 0);
4905 }
4906
4907 private static BigDecimal add(BigInteger fst, int scale1, BigInteger snd, int scale2) {
4908 int rscale = scale1;
4909 long sdiff = (long)rscale - scale2;
4910 if (sdiff != 0) {
4911 if (sdiff < 0) {
4912 int raise = checkScale(fst,-sdiff);
4913 rscale = scale2;
4914 fst = bigMultiplyPowerTen(fst,raise);
4915 } else {
4916 int raise = checkScale(snd,sdiff);
4917 snd = bigMultiplyPowerTen(snd,raise);
4918 }
4919 }
4920 BigInteger sum = fst.add(snd);
4921 return (fst.signum == snd.signum) ?
4922 new BigDecimal(sum, INFLATED, rscale, 0) :
4923 valueOf(sum, rscale, 0);
4924 }
4925
4926 private static BigInteger bigMultiplyPowerTen(long value, int n) {
4927 if (n <= 0)
4928 return BigInteger.valueOf(value);
4929 return bigTenToThe(n).multiply(value);
4930 }
4931
4932 private static BigInteger bigMultiplyPowerTen(BigInteger value, int n) {
4933 if (n <= 0)
4934 return value;
4935 if(n<LONG_TEN_POWERS_TABLE.length) {
4936 return value.multiply(LONG_TEN_POWERS_TABLE[n]);
4937 }
4938 return value.multiply(bigTenToThe(n));
4939 }
4940
4941 /**
4942 * Returns a {@code BigDecimal} whose value is {@code (xs /
4943 * ys)}, with rounding according to the context settings.
4944 *
4945 * Fast path - used only when (xscale <= yscale && yscale < 18
4946 * && mc.presision<18) {
4947 */
4948 private static BigDecimal divideSmallFastPath(final long xs, int xscale,
4949 final long ys, int yscale,
4950 long preferredScale, MathContext mc) {
4951 int mcp = mc.precision;
4952 int roundingMode = mc.roundingMode.oldMode;
4953
4954 assert (xscale <= yscale) && (yscale < 18) && (mcp < 18);
4955 int xraise = yscale - xscale; // xraise >=0
4956 long scaledX = (xraise==0) ? xs :
4957 longMultiplyPowerTen(xs, xraise); // can't overflow here!
4958 BigDecimal quotient;
4959
4960 int cmp = longCompareMagnitude(scaledX, ys);
4961 if(cmp > 0) { // satisfy constraint (b)
4962 yscale -= 1; // [that is, divisor *= 10]
4963 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4964 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
4965 // assert newScale >= xscale
4966 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4967 long scaledXs;
4968 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
4969 quotient = null;
4970 if((mcp-1) >=0 && (mcp-1)<LONG_TEN_POWERS_TABLE.length) {
4971 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp-1], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4972 }
4973 if(quotient==null) {
4974 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp-1);
4975 quotient = divideAndRound(rb, ys,
4976 scl, roundingMode, checkScaleNonZero(preferredScale));
4977 }
4978 } else {
4979 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4980 }
4981 } else {
4982 int newScale = checkScaleNonZero((long) xscale - mcp);
4983 // assert newScale >= yscale
4984 if (newScale == yscale) { // easy case
4985 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4986 } else {
4987 int raise = checkScaleNonZero((long) newScale - yscale);
4988 long scaledYs;
4989 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4990 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4991 quotient = divideAndRound(BigInteger.valueOf(xs),
4992 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4993 } else {
4994 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4995 }
4996 }
4997 }
4998 } else {
4999 // abs(scaledX) <= abs(ys)
5000 // result is "scaledX * 10^msp / ys"
5001 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
5002 if(cmp==0) {
5003 // abs(scaleX)== abs(ys) => result will be scaled 10^mcp + correct sign
5004 quotient = roundedTenPower(((scaledX < 0) == (ys < 0)) ? 1 : -1, mcp, scl, checkScaleNonZero(preferredScale));
5005 } else {
5006 // abs(scaledX) < abs(ys)
5007 long scaledXs;
5008 if ((scaledXs = longMultiplyPowerTen(scaledX, mcp)) == INFLATED) {
5009 quotient = null;
5010 if(mcp<LONG_TEN_POWERS_TABLE.length) {
5011 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5012 }
5013 if(quotient==null) {
5014 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp);
5015 quotient = divideAndRound(rb, ys,
5016 scl, roundingMode, checkScaleNonZero(preferredScale));
5017 }
5018 } else {
5019 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5020 }
5021 }
5022 }
5023 // doRound, here, only affects 1000000000 case.
5024 return doRound(quotient,mc);
5025 }
5026
5027 /**
5028 * Returns a {@code BigDecimal} whose value is {@code (xs /
5029 * ys)}, with rounding according to the context settings.
5030 */
5031 private static BigDecimal divide(final long xs, int xscale, final long ys, int yscale, long preferredScale, MathContext mc) {
5032 int mcp = mc.precision;
5033 if(xscale <= yscale && yscale < 18 && mcp<18) {
5034 return divideSmallFastPath(xs, xscale, ys, yscale, preferredScale, mc);
5035 }
5036 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
5037 yscale -= 1; // [that is, divisor *= 10]
5038 }
5039 int roundingMode = mc.roundingMode.oldMode;
5040 // In order to find out whether the divide generates the exact result,
5041 // we avoid calling the above divide method. 'quotient' holds the
5042 // return BigDecimal object whose scale will be set to 'scl'.
5043 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
5044 BigDecimal quotient;
5045 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
5046 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
5047 long scaledXs;
5048 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
5049 BigInteger rb = bigMultiplyPowerTen(xs,raise);
5050 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5051 } else {
5052 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5053 }
5054 } else {
5055 int newScale = checkScaleNonZero((long) xscale - mcp);
5056 // assert newScale >= yscale
5057 if (newScale == yscale) { // easy case
5058 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
5059 } else {
5060 int raise = checkScaleNonZero((long) newScale - yscale);
5061 long scaledYs;
5062 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
5063 BigInteger rb = bigMultiplyPowerTen(ys,raise);
5064 quotient = divideAndRound(BigInteger.valueOf(xs),
5065 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
5066 } else {
5067 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
5068 }
5069 }
5070 }
5071 // doRound, here, only affects 1000000000 case.
5072 return doRound(quotient,mc);
5073 }
5074
5075 /**
5076 * Returns a {@code BigDecimal} whose value is {@code (xs /
5077 * ys)}, with rounding according to the context settings.
5078 */
5079 private static BigDecimal divide(BigInteger xs, int xscale, long ys, int yscale, long preferredScale, MathContext mc) {
5080 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5081 if ((-compareMagnitudeNormalized(ys, yscale, xs, xscale)) > 0) {// satisfy constraint (b)
5082 yscale -= 1; // [that is, divisor *= 10]
5083 }
5084 int mcp = mc.precision;
5085 int roundingMode = mc.roundingMode.oldMode;
5086
5087 // In order to find out whether the divide generates the exact result,
5088 // we avoid calling the above divide method. 'quotient' holds the
5089 // return BigDecimal object whose scale will be set to 'scl'.
5090 BigDecimal quotient;
5091 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
5092 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
5093 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
5094 BigInteger rb = bigMultiplyPowerTen(xs,raise);
5095 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5096 } else {
5097 int newScale = checkScaleNonZero((long) xscale - mcp);
5098 // assert newScale >= yscale
5099 if (newScale == yscale) { // easy case
5100 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
5101 } else {
5102 int raise = checkScaleNonZero((long) newScale - yscale);
5103 long scaledYs;
5104 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
5105 BigInteger rb = bigMultiplyPowerTen(ys,raise);
5106 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
5107 } else {
5108 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
5109 }
5110 }
5111 }
5112 // doRound, here, only affects 1000000000 case.
5113 return doRound(quotient, mc);
5114 }
5115
5116 /**
5117 * Returns a {@code BigDecimal} whose value is {@code (xs /
5118 * ys)}, with rounding according to the context settings.
5119 */
5120 private static BigDecimal divide(long xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
5121 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5122 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
5123 yscale -= 1; // [that is, divisor *= 10]
5124 }
5125 int mcp = mc.precision;
5126 int roundingMode = mc.roundingMode.oldMode;
5127
5128 // In order to find out whether the divide generates the exact result,
5129 // we avoid calling the above divide method. 'quotient' holds the
5130 // return BigDecimal object whose scale will be set to 'scl'.
5131 BigDecimal quotient;
5132 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
5133 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
5134 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
5135 BigInteger rb = bigMultiplyPowerTen(xs,raise);
5136 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5137 } else {
5138 int newScale = checkScaleNonZero((long) xscale - mcp);
5139 int raise = checkScaleNonZero((long) newScale - yscale);
5140 BigInteger rb = bigMultiplyPowerTen(ys,raise);
5141 quotient = divideAndRound(BigInteger.valueOf(xs), rb, scl, roundingMode,checkScaleNonZero(preferredScale));
5142 }
5143 // doRound, here, only affects 1000000000 case.
5144 return doRound(quotient, mc);
5145 }
5146
5147 /**
5148 * Returns a {@code BigDecimal} whose value is {@code (xs /
5149 * ys)}, with rounding according to the context settings.
5150 */
5151 private static BigDecimal divide(BigInteger xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
5152 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5153 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
5154 yscale -= 1; // [that is, divisor *= 10]
5155 }
5156 int mcp = mc.precision;
5157 int roundingMode = mc.roundingMode.oldMode;
5158
5159 // In order to find out whether the divide generates the exact result,
5160 // we avoid calling the above divide method. 'quotient' holds the
5161 // return BigDecimal object whose scale will be set to 'scl'.
5162 BigDecimal quotient;
5163 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
5164 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
5165 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
5166 BigInteger rb = bigMultiplyPowerTen(xs,raise);
5167 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5168 } else {
5169 int newScale = checkScaleNonZero((long) xscale - mcp);
5170 int raise = checkScaleNonZero((long) newScale - yscale);
5171 BigInteger rb = bigMultiplyPowerTen(ys,raise);
5172 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
5173 }
5174 // doRound, here, only affects 1000000000 case.
5175 return doRound(quotient, mc);
5176 }
5177
5178 /*
5179 * performs divideAndRound for (dividend0*dividend1, divisor)
5180 * returns null if quotient can't fit into long value;
5181 */
5182 private static BigDecimal multiplyDivideAndRound(long dividend0, long dividend1, long divisor, int scale, int roundingMode,
5183 int preferredScale) {
5184 int qsign = Long.signum(dividend0)*Long.signum(dividend1)*Long.signum(divisor);
5185 dividend0 = Math.abs(dividend0);
5186 dividend1 = Math.abs(dividend1);
5187 divisor = Math.abs(divisor);
5188 // multiply dividend0 * dividend1
5189 long d0_hi = dividend0 >>> 32;
5190 long d0_lo = dividend0 & LONG_MASK;
5191 long d1_hi = dividend1 >>> 32;
5192 long d1_lo = dividend1 & LONG_MASK;
5193 long product = d0_lo * d1_lo;
5194 long d0 = product & LONG_MASK;
5195 long d1 = product >>> 32;
5196 product = d0_hi * d1_lo + d1;
5197 d1 = product & LONG_MASK;
5198 long d2 = product >>> 32;
5199 product = d0_lo * d1_hi + d1;
5200 d1 = product & LONG_MASK;
5201 d2 += product >>> 32;
5202 long d3 = d2>>>32;
5203 d2 &= LONG_MASK;
5204 product = d0_hi*d1_hi + d2;
5205 d2 = product & LONG_MASK;
5206 d3 = ((product>>>32) + d3) & LONG_MASK;
5207 final long dividendHi = make64(d3,d2);
5208 final long dividendLo = make64(d1,d0);
5209 // divide
5210 return divideAndRound128(dividendHi, dividendLo, divisor, qsign, scale, roundingMode, preferredScale);
5211 }
5212
5213 private static final long DIV_NUM_BASE = (1L<<32); // Number base (32 bits).
5214
5215 /*
5216 * divideAndRound 128-bit value by long divisor.
5217 * returns null if quotient can't fit into long value;
5218 * Specialized version of Knuth's division
5219 */
5220 private static BigDecimal divideAndRound128(final long dividendHi, final long dividendLo, long divisor, int sign,
5221 int scale, int roundingMode, int preferredScale) {
5222 if (dividendHi >= divisor) {
5223 return null;
5224 }
5225
5226 final int shift = Long.numberOfLeadingZeros(divisor);
5227 divisor <<= shift;
5228
5229 final long v1 = divisor >>> 32;
5230 final long v0 = divisor & LONG_MASK;
5231
5232 long tmp = dividendLo << shift;
5233 long u1 = tmp >>> 32;
5234 long u0 = tmp & LONG_MASK;
5235
5236 tmp = (dividendHi << shift) | (dividendLo >>> 64 - shift);
5237 long u2 = tmp & LONG_MASK;
5238 long q1, r_tmp;
5239 if (v1 == 1) {
5240 q1 = tmp;
5241 r_tmp = 0;
5242 } else if (tmp >= 0) {
5243 q1 = tmp / v1;
5244 r_tmp = tmp - q1 * v1;
5245 } else {
5246 long[] rq = divRemNegativeLong(tmp, v1);
5247 q1 = rq[1];
5248 r_tmp = rq[0];
5249 }
5250
5251 while(q1 >= DIV_NUM_BASE || unsignedLongCompare(q1*v0, make64(r_tmp, u1))) {
5252 q1--;
5253 r_tmp += v1;
5254 if (r_tmp >= DIV_NUM_BASE)
5255 break;
5256 }
5257
5258 tmp = mulsub(u2,u1,v1,v0,q1);
5259 u1 = tmp & LONG_MASK;
5260 long q0;
5261 if (v1 == 1) {
5262 q0 = tmp;
5263 r_tmp = 0;
5264 } else if (tmp >= 0) {
5265 q0 = tmp / v1;
5266 r_tmp = tmp - q0 * v1;
5267 } else {
5268 long[] rq = divRemNegativeLong(tmp, v1);
5269 q0 = rq[1];
5270 r_tmp = rq[0];
5271 }
5272
5273 while(q0 >= DIV_NUM_BASE || unsignedLongCompare(q0*v0,make64(r_tmp,u0))) {
5274 q0--;
5275 r_tmp += v1;
5276 if (r_tmp >= DIV_NUM_BASE)
5277 break;
5278 }
5279
5280 if((int)q1 < 0) {
5281 // result (which is positive and unsigned here)
5282 // can't fit into long due to sign bit is used for value
5283 MutableBigInteger mq = new MutableBigInteger(new int[]{(int)q1, (int)q0});
5284 if (roundingMode == ROUND_DOWN && scale == preferredScale) {
5285 return mq.toBigDecimal(sign, scale);
5286 }
5287 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
5288 if (r != 0) {
5289 if(needIncrement(divisor >>> shift, roundingMode, sign, mq, r)){
5290 mq.add(MutableBigInteger.ONE);
5291 }
5292 return mq.toBigDecimal(sign, scale);
5293 } else {
5294 if (preferredScale != scale) {
5295 BigInteger intVal = mq.toBigInteger(sign);
5296 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
5297 } else {
5298 return mq.toBigDecimal(sign, scale);
5299 }
5300 }
5301 }
5302
5303 long q = make64(q1,q0);
5304 q*=sign;
5305
5306 if (roundingMode == ROUND_DOWN && scale == preferredScale)
5307 return valueOf(q, scale);
5308
5309 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
5310 if (r != 0) {
5311 boolean increment = needIncrement(divisor >>> shift, roundingMode, sign, q, r);
5312 return valueOf((increment ? q + sign : q), scale);
5313 } else {
5314 if (preferredScale != scale) {
5315 return createAndStripZerosToMatchScale(q, scale, preferredScale);
5316 } else {
5317 return valueOf(q, scale);
5318 }
5319 }
5320 }
5321
5322 /*
5323 * calculate divideAndRound for ldividend*10^raise / divisor
5324 * when abs(dividend)==abs(divisor);
5325 */
5326 private static BigDecimal roundedTenPower(int qsign, int raise, int scale, int preferredScale) {
5327 if (scale > preferredScale) {
5328 int diff = scale - preferredScale;
5329 if(diff < raise) {
5330 return scaledTenPow(raise - diff, qsign, preferredScale);
5331 } else {
5332 return valueOf(qsign,scale-raise);
5333 }
5334 } else {
5335 return scaledTenPow(raise, qsign, scale);
5336 }
5337 }
5338
5339 static BigDecimal scaledTenPow(int n, int sign, int scale) {
5340 if (n < LONG_TEN_POWERS_TABLE.length)
5341 return valueOf(sign*LONG_TEN_POWERS_TABLE[n],scale);
5342 else {
5343 BigInteger unscaledVal = bigTenToThe(n);
5344 if(sign==-1) {
5345 unscaledVal = unscaledVal.negate();
5346 }
5347 return new BigDecimal(unscaledVal, INFLATED, scale, n+1);
5348 }
5349 }
5350
5351 /**
5352 * Calculate the quotient and remainder of dividing a negative long by
5353 * another long.
5354 *
5355 * @param n the numerator; must be negative
5356 * @param d the denominator; must not be unity
5357 * @return a two-element {@long} array with the remainder and quotient in
5358 * the initial and final elements, respectively
5359 */
5360 private static long[] divRemNegativeLong(long n, long d) {
5361 assert n < 0 : "Non-negative numerator " + n;
5362 assert d != 1 : "Unity denominator";
5363
5364 // Approximate the quotient and remainder
5365 long q = (n >>> 1) / (d >>> 1);
5366 long r = n - q * d;
5367
5368 // Correct the approximation
5369 while (r < 0) {
5370 r += d;
5371 q--;
5372 }
5373 while (r >= d) {
5374 r -= d;
5375 q++;
5376 }
5377
5378 // n - q*d == r && 0 <= r < d, hence we're done.
5379 return new long[] {r, q};
5380 }
5381
5382 private static long make64(long hi, long lo) {
5383 return hi<<32 | lo;
5384 }
5385
5386 private static long mulsub(long u1, long u0, final long v1, final long v0, long q0) {
5387 long tmp = u0 - q0*v0;
5388 return make64(u1 + (tmp>>>32) - q0*v1,tmp & LONG_MASK);
5389 }
5390
5391 private static boolean unsignedLongCompare(long one, long two) {
5392 return (one+Long.MIN_VALUE) > (two+Long.MIN_VALUE);
5393 }
5394
5395 private static boolean unsignedLongCompareEq(long one, long two) {
5396 return (one+Long.MIN_VALUE) >= (two+Long.MIN_VALUE);
5397 }
5398
5399
5400 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5401 private static int compareMagnitudeNormalized(long xs, int xscale, long ys, int yscale) {
5402 // assert xs!=0 && ys!=0
5403 int sdiff = xscale - yscale;
5404 if (sdiff != 0) {
5405 if (sdiff < 0) {
5406 xs = longMultiplyPowerTen(xs, -sdiff);
5407 } else { // sdiff > 0
5408 ys = longMultiplyPowerTen(ys, sdiff);
5409 }
5410 }
5411 if (xs != INFLATED)
5412 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
5413 else
5414 return 1;
5415 }
5416
5417 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5418 private static int compareMagnitudeNormalized(long xs, int xscale, BigInteger ys, int yscale) {
5419 // assert "ys can't be represented as long"
5420 if (xs == 0)
5421 return -1;
5422 int sdiff = xscale - yscale;
5423 if (sdiff < 0) {
5424 if (longMultiplyPowerTen(xs, -sdiff) == INFLATED ) {
5425 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
5426 }
5427 }
5428 return -1;
5429 }
5430
5431 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5432 private static int compareMagnitudeNormalized(BigInteger xs, int xscale, BigInteger ys, int yscale) {
5433 int sdiff = xscale - yscale;
5434 if (sdiff < 0) {
5435 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
5436 } else { // sdiff >= 0
5437 return xs.compareMagnitude(bigMultiplyPowerTen(ys, sdiff));
5438 }
5439 }
5440
5441 private static long multiply(long x, long y){
5442 long product = x * y;
5443 long ax = Math.abs(x);
5444 long ay = Math.abs(y);
5445 if (((ax | ay) >>> 31 == 0) || (y == 0) || (product / y == x)){
5446 return product;
5447 }
5448 return INFLATED;
5449 }
5450
5451 private static BigDecimal multiply(long x, long y, int scale) {
5452 long product = multiply(x, y);
5453 if(product!=INFLATED) {
5454 return valueOf(product,scale);
5455 }
5456 return new BigDecimal(BigInteger.valueOf(x).multiply(y),INFLATED,scale,0);
5457 }
5458
5459 private static BigDecimal multiply(long x, BigInteger y, int scale) {
5460 if(x==0) {
5461 return zeroValueOf(scale);
5462 }
5463 return new BigDecimal(y.multiply(x),INFLATED,scale,0);
5464 }
5465
5466 private static BigDecimal multiply(BigInteger x, BigInteger y, int scale) {
5467 return new BigDecimal(x.multiply(y),INFLATED,scale,0);
5468 }
5469
5470 /**
5471 * Multiplies two long values and rounds according {@code MathContext}
5472 */
5473 private static BigDecimal multiplyAndRound(long x, long y, int scale, MathContext mc) {
5474 long product = multiply(x, y);
5475 if(product!=INFLATED) {
5476 return doRound(product, scale, mc);
5477 }
5478 // attempt to do it in 128 bits
5479 int rsign = 1;
5480 if(x < 0) {
5481 x = -x;
5482 rsign = -1;
5483 }
5484 if(y < 0) {
5485 y = -y;
5486 rsign *= -1;
5487 }
5488 // multiply dividend0 * dividend1
5489 long m0_hi = x >>> 32;
5490 long m0_lo = x & LONG_MASK;
5491 long m1_hi = y >>> 32;
5492 long m1_lo = y & LONG_MASK;
5493 product = m0_lo * m1_lo;
5494 long m0 = product & LONG_MASK;
5495 long m1 = product >>> 32;
5496 product = m0_hi * m1_lo + m1;
5497 m1 = product & LONG_MASK;
5498 long m2 = product >>> 32;
5499 product = m0_lo * m1_hi + m1;
5500 m1 = product & LONG_MASK;
5501 m2 += product >>> 32;
5502 long m3 = m2>>>32;
5503 m2 &= LONG_MASK;
5504 product = m0_hi*m1_hi + m2;
5505 m2 = product & LONG_MASK;
5506 m3 = ((product>>>32) + m3) & LONG_MASK;
5507 final long mHi = make64(m3,m2);
5508 final long mLo = make64(m1,m0);
5509 BigDecimal res = doRound128(mHi, mLo, rsign, scale, mc);
5510 if(res!=null) {
5511 return res;
5512 }
5513 res = new BigDecimal(BigInteger.valueOf(x).multiply(y*rsign), INFLATED, scale, 0);
5514 return doRound(res,mc);
5515 }
5516
5517 private static BigDecimal multiplyAndRound(long x, BigInteger y, int scale, MathContext mc) {
5518 if(x==0) {
5519 return zeroValueOf(scale);
5520 }
5521 return doRound(y.multiply(x), scale, mc);
5522 }
5523
5524 private static BigDecimal multiplyAndRound(BigInteger x, BigInteger y, int scale, MathContext mc) {
5525 return doRound(x.multiply(y), scale, mc);
5526 }
5527
5528 /**
5529 * rounds 128-bit value according {@code MathContext}
5530 * returns null if result can't be repsented as compact BigDecimal.
5531 */
5532 private static BigDecimal doRound128(long hi, long lo, int sign, int scale, MathContext mc) {
5533 int mcp = mc.precision;
5534 int drop;
5535 BigDecimal res = null;
5536 if(((drop = precision(hi, lo) - mcp) > 0)&&(drop<LONG_TEN_POWERS_TABLE.length)) {
5537 scale = checkScaleNonZero((long)scale - drop);
5538 res = divideAndRound128(hi, lo, LONG_TEN_POWERS_TABLE[drop], sign, scale, mc.roundingMode.oldMode, scale);
5539 }
5540 if(res!=null) {
5541 return doRound(res,mc);
5542 }
5543 return null;
5544 }
5545
5546 private static final long[][] LONGLONG_TEN_POWERS_TABLE = {
5547 { 0L, 0x8AC7230489E80000L }, //10^19
5548 { 0x5L, 0x6bc75e2d63100000L }, //10^20
5549 { 0x36L, 0x35c9adc5dea00000L }, //10^21
5550 { 0x21eL, 0x19e0c9bab2400000L }, //10^22
5551 { 0x152dL, 0x02c7e14af6800000L }, //10^23
5552 { 0xd3c2L, 0x1bcecceda1000000L }, //10^24
5553 { 0x84595L, 0x161401484a000000L }, //10^25
5554 { 0x52b7d2L, 0xdcc80cd2e4000000L }, //10^26
5555 { 0x33b2e3cL, 0x9fd0803ce8000000L }, //10^27
5556 { 0x204fce5eL, 0x3e25026110000000L }, //10^28
5557 { 0x1431e0faeL, 0x6d7217caa0000000L }, //10^29
5558 { 0xc9f2c9cd0L, 0x4674edea40000000L }, //10^30
5559 { 0x7e37be2022L, 0xc0914b2680000000L }, //10^31
5560 { 0x4ee2d6d415bL, 0x85acef8100000000L }, //10^32
5561 { 0x314dc6448d93L, 0x38c15b0a00000000L }, //10^33
5562 { 0x1ed09bead87c0L, 0x378d8e6400000000L }, //10^34
5563 { 0x13426172c74d82L, 0x2b878fe800000000L }, //10^35
5564 { 0xc097ce7bc90715L, 0xb34b9f1000000000L }, //10^36
5565 { 0x785ee10d5da46d9L, 0x00f436a000000000L }, //10^37
5566 { 0x4b3b4ca85a86c47aL, 0x098a224000000000L }, //10^38
5567 };
5568
5569 /*
5570 * returns precision of 128-bit value
5571 */
5572 private static int precision(long hi, long lo){
5573 if(hi==0) {
5574 if(lo>=0) {
5575 return longDigitLength(lo);
5576 }
5577 return (unsignedLongCompareEq(lo, LONGLONG_TEN_POWERS_TABLE[0][1])) ? 20 : 19;
5578 // 0x8AC7230489E80000L = unsigned 2^19
5579 }
5580 int r = ((128 - Long.numberOfLeadingZeros(hi) + 1) * 1233) >>> 12;
5581 int idx = r-19;
5582 return (idx >= LONGLONG_TEN_POWERS_TABLE.length || longLongCompareMagnitude(hi, lo,
5583 LONGLONG_TEN_POWERS_TABLE[idx][0], LONGLONG_TEN_POWERS_TABLE[idx][1])) ? r : r + 1;
5584 }
5585
5586 /*
5587 * returns true if 128 bit number <hi0,lo0> is less than <hi1,lo1>
5588 * hi0 & hi1 should be non-negative
5589 */
5590 private static boolean longLongCompareMagnitude(long hi0, long lo0, long hi1, long lo1) {
5591 if(hi0!=hi1) {
5592 return hi0<hi1;
5593 }
5594 return (lo0+Long.MIN_VALUE) <(lo1+Long.MIN_VALUE);
5595 }
5596
5597 private static BigDecimal divide(long dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5598 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5599 int newScale = scale + divisorScale;
5600 int raise = newScale - dividendScale;
5601 if(raise<LONG_TEN_POWERS_TABLE.length) {
5602 long xs = dividend;
5603 if ((xs = longMultiplyPowerTen(xs, raise)) != INFLATED) {
5604 return divideAndRound(xs, divisor, scale, roundingMode, scale);
5605 }
5606 BigDecimal q = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[raise], dividend, divisor, scale, roundingMode, scale);
5607 if(q!=null) {
5608 return q;
5609 }
5610 }
5611 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5612 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5613 } else {
5614 int newScale = checkScale(divisor,(long)dividendScale - scale);
5615 int raise = newScale - divisorScale;
5616 if(raise<LONG_TEN_POWERS_TABLE.length) {
5617 long ys = divisor;
5618 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5619 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5620 }
5621 }
5622 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5623 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5624 }
5625 }
5626
5627 private static BigDecimal divide(BigInteger dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5628 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5629 int newScale = scale + divisorScale;
5630 int raise = newScale - dividendScale;
5631 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5632 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5633 } else {
5634 int newScale = checkScale(divisor,(long)dividendScale - scale);
5635 int raise = newScale - divisorScale;
5636 if(raise<LONG_TEN_POWERS_TABLE.length) {
5637 long ys = divisor;
5638 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5639 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5640 }
5641 }
5642 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5643 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5644 }
5645 }
5646
5647 private static BigDecimal divide(long dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5648 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5649 int newScale = scale + divisorScale;
5650 int raise = newScale - dividendScale;
5651 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5652 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5653 } else {
5654 int newScale = checkScale(divisor,(long)dividendScale - scale);
5655 int raise = newScale - divisorScale;
5656 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5657 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5658 }
5659 }
5660
5661 private static BigDecimal divide(BigInteger dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5662 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5663 int newScale = scale + divisorScale;
5664 int raise = newScale - dividendScale;
5665 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5666 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5667 } else {
5668 int newScale = checkScale(divisor,(long)dividendScale - scale);
5669 int raise = newScale - divisorScale;
5670 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5671 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5672 }
5673 }
5674
5675 }