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