1 /*
2 * Copyright (c) 1996, 2019, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26 /*
27 * Portions Copyright IBM Corporation, 2001. All Rights Reserved.
28 */
29
30 package java.math;
31
32 import static java.math.BigInteger.LONG_MASK;
33 import java.util.Arrays;
34 import java.util.Objects;
35
36 /**
37 * Immutable, arbitrary-precision signed decimal numbers. A
38 * {@code BigDecimal} consists of an arbitrary precision integer
39 * <i>unscaled value</i> and a 32-bit integer <i>scale</i>. If zero
40 * or positive, the scale is the number of digits to the right of the
41 * decimal point. If negative, the unscaled value of the number is
42 * multiplied by ten to the power of the negation of the scale. The
43 * value of the number represented by the {@code BigDecimal} is
44 * therefore <code>(unscaledValue × 10<sup>-scale</sup>)</code>.
45 *
46 * <p>The {@code BigDecimal} class provides operations for
47 * arithmetic, scale manipulation, rounding, comparison, hashing, and
48 * format conversion. The {@link #toString} method provides a
49 * canonical representation of a {@code BigDecimal}.
50 *
51 * <p>The {@code BigDecimal} class gives its user complete control
52 * over rounding behavior. If no rounding mode is specified and the
53 * exact result cannot be represented, an exception is thrown;
54 * otherwise, calculations can be carried out to a chosen precision
55 * and rounding mode by supplying an appropriate {@link MathContext}
56 * object to the operation. In either case, eight <em>rounding
57 * modes</em> are provided for the control of rounding. Using the
58 * integer fields in this class (such as {@link #ROUND_HALF_UP}) to
59 * represent rounding mode is deprecated; the enumeration values
60 * of the {@code RoundingMode} {@code enum}, (such as {@link
61 * RoundingMode#HALF_UP}) should be used instead.
62 *
63 * <p>When a {@code MathContext} object is supplied with a precision
64 * setting of 0 (for example, {@link MathContext#UNLIMITED}),
65 * arithmetic operations are exact, as are the arithmetic methods
66 * which take no {@code MathContext} object. (This is the only
67 * behavior that was supported in releases prior to 5.) As a
68 * corollary of computing the exact result, the rounding mode setting
69 * of a {@code MathContext} object with a precision setting of 0 is
70 * not used and thus irrelevant. In the case of divide, the exact
71 * quotient could have an infinitely long decimal expansion; for
72 * example, 1 divided by 3. If the quotient has a nonterminating
73 * decimal expansion and the operation is specified to return an exact
74 * result, an {@code ArithmeticException} is thrown. Otherwise, the
75 * exact result of the division is returned, as done for other
76 * operations.
77 *
78 * <p>When the precision setting is not 0, the rules of
79 * {@code BigDecimal} arithmetic are broadly compatible with selected
80 * modes of operation of the arithmetic defined in ANSI X3.274-1996
81 * and ANSI X3.274-1996/AM 1-2000 (section 7.4). Unlike those
82 * standards, {@code BigDecimal} includes many rounding modes, which
83 * were mandatory for division in {@code BigDecimal} releases prior
84 * to 5. Any conflicts between these ANSI standards and the
85 * {@code BigDecimal} specification are resolved in favor of
86 * {@code BigDecimal}.
87 *
88 * <p>Since the same numerical value can have different
89 * representations (with different scales), the rules of arithmetic
90 * and rounding must specify both the numerical result and the scale
91 * used in the result's representation.
92 *
93 *
94 * <p>In general the rounding modes and precision setting determine
95 * how operations return results with a limited number of digits when
96 * the exact result has more digits (perhaps infinitely many in the
97 * case of division and square root) than the number of digits returned.
98 *
99 * First, the
100 * total number of digits to return is specified by the
101 * {@code MathContext}'s {@code precision} setting; this determines
102 * the result's <i>precision</i>. The digit count starts from the
103 * leftmost nonzero digit of the exact result. The rounding mode
104 * determines how any discarded trailing digits affect the returned
105 * result.
106 *
107 * <p>For all arithmetic operators , the operation is carried out as
108 * though an exact intermediate result were first calculated and then
109 * rounded to the number of digits specified by the precision setting
110 * (if necessary), using the selected rounding mode. If the exact
111 * result is not returned, some digit positions of the exact result
112 * are discarded. When rounding increases the magnitude of the
113 * returned result, it is possible for a new digit position to be
114 * created by a carry propagating to a leading {@literal "9"} digit.
115 * For example, rounding the value 999.9 to three digits rounding up
116 * would be numerically equal to one thousand, represented as
117 * 100×10<sup>1</sup>. In such cases, the new {@literal "1"} is
118 * the leading digit position of the returned result.
119 *
120 * <p>Besides a logical exact result, each arithmetic operation has a
121 * preferred scale for representing a result. The preferred
122 * scale for each operation is listed in the table below.
123 *
124 * <table class="striped" style="text-align:left">
125 * <caption>Preferred Scales for Results of Arithmetic Operations
126 * </caption>
127 * <thead>
128 * <tr><th scope="col">Operation</th><th scope="col">Preferred Scale of Result</th></tr>
129 * </thead>
130 * <tbody>
131 * <tr><th scope="row">Add</th><td>max(addend.scale(), augend.scale())</td>
132 * <tr><th scope="row">Subtract</th><td>max(minuend.scale(), subtrahend.scale())</td>
133 * <tr><th scope="row">Multiply</th><td>multiplier.scale() + multiplicand.scale()</td>
134 * <tr><th scope="row">Divide</th><td>dividend.scale() - divisor.scale()</td>
135 * <tr><th scope="row">Square root</th><td>radicand.scale()/2</td>
136 * </tbody>
137 * </table>
138 *
139 * These scales are the ones used by the methods which return exact
140 * arithmetic results; except that an exact divide may have to use a
141 * larger scale since the exact result may have more digits. For
142 * example, {@code 1/32} is {@code 0.03125}.
143 *
144 * <p>Before rounding, the scale of the logical exact intermediate
145 * result is the preferred scale for that operation. If the exact
146 * numerical result cannot be represented in {@code precision}
147 * digits, rounding selects the set of digits to return and the scale
148 * of the result is reduced from the scale of the intermediate result
149 * to the least scale which can represent the {@code precision}
150 * digits actually returned. If the exact result can be represented
151 * with at most {@code precision} digits, the representation
152 * of the result with the scale closest to the preferred scale is
153 * returned. In particular, an exactly representable quotient may be
154 * represented in fewer than {@code precision} digits by removing
155 * trailing zeros and decreasing the scale. For example, rounding to
156 * three digits using the {@linkplain RoundingMode#FLOOR floor}
157 * rounding mode, <br>
158 *
159 * {@code 19/100 = 0.19 // integer=19, scale=2} <br>
160 *
161 * but<br>
162 *
163 * {@code 21/110 = 0.190 // integer=190, scale=3} <br>
164 *
165 * <p>Note that for add, subtract, and multiply, the reduction in
166 * scale will equal the number of digit positions of the exact result
167 * which are discarded. If the rounding causes a carry propagation to
168 * create a new high-order digit position, an additional digit of the
169 * result is discarded than when no new digit position is created.
170 *
171 * <p>Other methods may have slightly different rounding semantics.
172 * For example, the result of the {@code pow} method using the
173 * {@linkplain #pow(int, MathContext) specified algorithm} can
174 * occasionally differ from the rounded mathematical result by more
175 * than one unit in the last place, one <i>{@linkplain #ulp() ulp}</i>.
176 *
177 * <p>Two types of operations are provided for manipulating the scale
178 * of a {@code BigDecimal}: scaling/rounding operations and decimal
179 * point motion operations. Scaling/rounding operations ({@link
180 * #setScale setScale} and {@link #round round}) return a
181 * {@code BigDecimal} whose value is approximately (or exactly) equal
182 * to that of the operand, but whose scale or precision is the
183 * specified value; that is, they increase or decrease the precision
184 * of the stored number with minimal effect on its value. Decimal
185 * point motion operations ({@link #movePointLeft movePointLeft} and
186 * {@link #movePointRight movePointRight}) return a
187 * {@code BigDecimal} created from the operand by moving the decimal
188 * point a specified distance in the specified direction.
189 *
190 * <p>For the sake of brevity and clarity, pseudo-code is used
191 * throughout the descriptions of {@code BigDecimal} methods. The
192 * pseudo-code expression {@code (i + j)} is shorthand for "a
193 * {@code BigDecimal} whose value is that of the {@code BigDecimal}
194 * {@code i} added to that of the {@code BigDecimal}
195 * {@code j}." The pseudo-code expression {@code (i == j)} is
196 * shorthand for "{@code true} if and only if the
197 * {@code BigDecimal} {@code i} represents the same value as the
198 * {@code BigDecimal} {@code j}." Other pseudo-code expressions
199 * are interpreted similarly. Square brackets are used to represent
200 * the particular {@code BigInteger} and scale pair defining a
201 * {@code BigDecimal} value; for example [19, 2] is the
202 * {@code BigDecimal} numerically equal to 0.19 having a scale of 2.
203 *
204 *
205 * <p>All methods and constructors for this class throw
206 * {@code NullPointerException} when passed a {@code null} object
207 * reference for any input parameter.
208 *
209 * @apiNote Care should be exercised if {@code BigDecimal} objects
210 * are used as keys in a {@link java.util.SortedMap SortedMap} or
211 * elements in a {@link java.util.SortedSet SortedSet} since
212 * {@code BigDecimal}'s <i>natural ordering</i> is <em>inconsistent
213 * with equals</em>. See {@link Comparable}, {@link
214 * java.util.SortedMap} or {@link java.util.SortedSet} for more
215 * information.
216 *
217 * @see BigInteger
218 * @see MathContext
219 * @see RoundingMode
220 * @see java.util.SortedMap
221 * @see java.util.SortedSet
222 * @author Josh Bloch
223 * @author Mike Cowlishaw
224 * @author Joseph D. Darcy
225 * @author Sergey V. Kuksenko
226 * @since 1.1
227 */
228 public class BigDecimal extends Number implements Comparable<BigDecimal> {
229 /**
230 * The unscaled value of this BigDecimal, as returned by {@link
231 * #unscaledValue}.
232 *
233 * @serial
234 * @see #unscaledValue
235 */
236 private final BigInteger intVal;
237
238 /**
239 * The scale of this BigDecimal, as returned by {@link #scale}.
240 *
241 * @serial
242 * @see #scale
243 */
244 private final int scale; // Note: this may have any value, so
245 // calculations must be done in longs
246
247 /**
248 * The number of decimal digits in this BigDecimal, or 0 if the
249 * number of digits are not known (lookaside information). If
250 * nonzero, the value is guaranteed correct. Use the precision()
251 * method to obtain and set the value if it might be 0. This
252 * field is mutable until set nonzero.
253 *
254 * @since 1.5
255 */
256 private transient int precision;
257
258 /**
259 * Used to store the canonical string representation, if computed.
260 */
261 private transient String stringCache;
262
263 /**
264 * Sentinel value for {@link #intCompact} indicating the
265 * significand information is only available from {@code intVal}.
266 */
267 static final long INFLATED = Long.MIN_VALUE;
268
269 private static final BigInteger INFLATED_BIGINT = BigInteger.valueOf(INFLATED);
270
271 /**
272 * If the absolute value of the significand of this BigDecimal is
273 * less than or equal to {@code Long.MAX_VALUE}, the value can be
274 * compactly stored in this field and used in computations.
275 */
276 private final transient long intCompact;
277
278 // All 18-digit base ten strings fit into a long; not all 19-digit
279 // strings will
280 private static final int MAX_COMPACT_DIGITS = 18;
281
282 /* Appease the serialization gods */
283 @java.io.Serial
284 private static final long serialVersionUID = 6108874887143696463L;
285
286 private static final ThreadLocal<StringBuilderHelper>
287 threadLocalStringBuilderHelper = new ThreadLocal<StringBuilderHelper>() {
288 @Override
289 protected StringBuilderHelper initialValue() {
290 return new StringBuilderHelper();
291 }
292 };
293
294 // Cache of common small BigDecimal values.
295 private static final BigDecimal ZERO_THROUGH_TEN[] = {
296 new BigDecimal(BigInteger.ZERO, 0, 0, 1),
297 new BigDecimal(BigInteger.ONE, 1, 0, 1),
298 new BigDecimal(BigInteger.TWO, 2, 0, 1),
299 new BigDecimal(BigInteger.valueOf(3), 3, 0, 1),
300 new BigDecimal(BigInteger.valueOf(4), 4, 0, 1),
301 new BigDecimal(BigInteger.valueOf(5), 5, 0, 1),
302 new BigDecimal(BigInteger.valueOf(6), 6, 0, 1),
303 new BigDecimal(BigInteger.valueOf(7), 7, 0, 1),
304 new BigDecimal(BigInteger.valueOf(8), 8, 0, 1),
305 new BigDecimal(BigInteger.valueOf(9), 9, 0, 1),
306 new BigDecimal(BigInteger.TEN, 10, 0, 2),
307 };
308
309 // Cache of zero scaled by 0 - 15
310 private static final BigDecimal[] ZERO_SCALED_BY = {
311 ZERO_THROUGH_TEN[0],
312 new BigDecimal(BigInteger.ZERO, 0, 1, 1),
313 new BigDecimal(BigInteger.ZERO, 0, 2, 1),
314 new BigDecimal(BigInteger.ZERO, 0, 3, 1),
315 new BigDecimal(BigInteger.ZERO, 0, 4, 1),
316 new BigDecimal(BigInteger.ZERO, 0, 5, 1),
317 new BigDecimal(BigInteger.ZERO, 0, 6, 1),
318 new BigDecimal(BigInteger.ZERO, 0, 7, 1),
319 new BigDecimal(BigInteger.ZERO, 0, 8, 1),
320 new BigDecimal(BigInteger.ZERO, 0, 9, 1),
321 new BigDecimal(BigInteger.ZERO, 0, 10, 1),
322 new BigDecimal(BigInteger.ZERO, 0, 11, 1),
323 new BigDecimal(BigInteger.ZERO, 0, 12, 1),
324 new BigDecimal(BigInteger.ZERO, 0, 13, 1),
325 new BigDecimal(BigInteger.ZERO, 0, 14, 1),
326 new BigDecimal(BigInteger.ZERO, 0, 15, 1),
327 };
328
329 // Half of Long.MIN_VALUE & Long.MAX_VALUE.
330 private static final long HALF_LONG_MAX_VALUE = Long.MAX_VALUE / 2;
331 private static final long HALF_LONG_MIN_VALUE = Long.MIN_VALUE / 2;
332
333 // Constants
334 /**
335 * The value 0, with a scale of 0.
336 *
337 * @since 1.5
338 */
339 public static final BigDecimal ZERO =
340 ZERO_THROUGH_TEN[0];
341
342 /**
343 * The value 1, with a scale of 0.
344 *
345 * @since 1.5
346 */
347 public static final BigDecimal ONE =
348 ZERO_THROUGH_TEN[1];
349
350 /**
351 * The value 10, with a scale of 0.
352 *
353 * @since 1.5
354 */
355 public static final BigDecimal TEN =
356 ZERO_THROUGH_TEN[10];
357
358 /**
359 * The value 0.1, with a scale of 1.
360 */
361 private static final BigDecimal ONE_TENTH = valueOf(1L, 1);
362
363 /**
364 * The value 0.5, with a scale of 1.
365 */
366 private static final BigDecimal ONE_HALF = valueOf(5L, 1);
367
368 // Constructors
369
370 /**
371 * Trusted package private constructor.
372 * Trusted simply means if val is INFLATED, intVal could not be null and
373 * if intVal is null, val could not be INFLATED.
374 */
375 BigDecimal(BigInteger intVal, long val, int scale, int prec) {
376 this.scale = scale;
377 this.precision = prec;
378 this.intCompact = val;
379 this.intVal = intVal;
380 }
381
382 /**
383 * Translates a character array representation of a
384 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
385 * same sequence of characters as the {@link #BigDecimal(String)}
386 * constructor, while allowing a sub-array to be specified.
387 *
388 * @implNote If the sequence of characters is already available
389 * within a character array, using this constructor is faster than
390 * converting the {@code char} array to string and using the
391 * {@code BigDecimal(String)} constructor.
392 *
393 * @param in {@code char} array that is the source of characters.
394 * @param offset first character in the array to inspect.
395 * @param len number of characters to consider.
396 * @throws NumberFormatException if {@code in} is not a valid
397 * representation of a {@code BigDecimal} or the defined subarray
398 * is not wholly within {@code in}.
399 * @since 1.5
400 */
401 public BigDecimal(char[] in, int offset, int len) {
402 this(in,offset,len,MathContext.UNLIMITED);
403 }
404
405 /**
406 * Translates a character array representation of a
407 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
408 * same sequence of characters as the {@link #BigDecimal(String)}
409 * constructor, while allowing a sub-array to be specified and
410 * with rounding according to the context settings.
411 *
412 * @implNote If the sequence of characters is already available
413 * within a character array, using this constructor is faster than
414 * converting the {@code char} array to string and using the
415 * {@code BigDecimal(String)} constructor.
416 *
417 * @param in {@code char} array that is the source of characters.
418 * @param offset first character in the array to inspect.
419 * @param len number of characters to consider.
420 * @param mc the context to use.
421 * @throws ArithmeticException if the result is inexact but the
422 * rounding mode is {@code UNNECESSARY}.
423 * @throws NumberFormatException if {@code in} is not a valid
424 * representation of a {@code BigDecimal} or the defined subarray
425 * is not wholly within {@code in}.
426 * @since 1.5
427 */
428 public BigDecimal(char[] in, int offset, int len, MathContext mc) {
429 // protect against huge length, negative values, and integer overflow
430 try {
431 Objects.checkFromIndexSize(offset, len, in.length);
432 } catch (IndexOutOfBoundsException e) {
433 throw new NumberFormatException
434 ("Bad offset or len arguments for char[] input.");
435 }
436
437 // This is the primary string to BigDecimal constructor; all
438 // incoming strings end up here; it uses explicit (inline)
439 // parsing for speed and generates at most one intermediate
440 // (temporary) object (a char[] array) for non-compact case.
441
442 // Use locals for all fields values until completion
443 int prec = 0; // record precision value
444 int scl = 0; // record scale value
445 long rs = 0; // the compact value in long
446 BigInteger rb = null; // the inflated value in BigInteger
447 // use array bounds checking to handle too-long, len == 0,
448 // bad offset, etc.
449 try {
450 // handle the sign
451 boolean isneg = false; // assume positive
452 if (in[offset] == '-') {
453 isneg = true; // leading minus means negative
454 offset++;
455 len--;
456 } else if (in[offset] == '+') { // leading + allowed
457 offset++;
458 len--;
459 }
460
461 // should now be at numeric part of the significand
462 boolean dot = false; // true when there is a '.'
463 long exp = 0; // exponent
464 char c; // current character
465 boolean isCompact = (len <= MAX_COMPACT_DIGITS);
466 // integer significand array & idx is the index to it. The array
467 // is ONLY used when we can't use a compact representation.
468 int idx = 0;
469 if (isCompact) {
470 // First compact case, we need not to preserve the character
471 // and we can just compute the value in place.
472 for (; len > 0; offset++, len--) {
473 c = in[offset];
474 if ((c == '0')) { // have zero
475 if (prec == 0)
476 prec = 1;
477 else if (rs != 0) {
478 rs *= 10;
479 ++prec;
480 } // else digit is a redundant leading zero
481 if (dot)
482 ++scl;
483 } else if ((c >= '1' && c <= '9')) { // have digit
484 int digit = c - '0';
485 if (prec != 1 || rs != 0)
486 ++prec; // prec unchanged if preceded by 0s
487 rs = rs * 10 + digit;
488 if (dot)
489 ++scl;
490 } else if (c == '.') { // have dot
491 // have dot
492 if (dot) // two dots
493 throw new NumberFormatException("Character array"
494 + " contains more than one decimal point.");
495 dot = true;
496 } else if (Character.isDigit(c)) { // slow path
497 int digit = Character.digit(c, 10);
498 if (digit == 0) {
499 if (prec == 0)
500 prec = 1;
501 else if (rs != 0) {
502 rs *= 10;
503 ++prec;
504 } // else digit is a redundant leading zero
505 } else {
506 if (prec != 1 || rs != 0)
507 ++prec; // prec unchanged if preceded by 0s
508 rs = rs * 10 + digit;
509 }
510 if (dot)
511 ++scl;
512 } else if ((c == 'e') || (c == 'E')) {
513 exp = parseExp(in, offset, len);
514 // Next test is required for backwards compatibility
515 if ((int) exp != exp) // overflow
516 throw new NumberFormatException("Exponent overflow.");
517 break; // [saves a test]
518 } else {
519 throw new NumberFormatException("Character " + c
520 + " is neither a decimal digit number, decimal point, nor"
521 + " \"e\" notation exponential mark.");
522 }
523 }
524 if (prec == 0) // no digits found
525 throw new NumberFormatException("No digits found.");
526 // Adjust scale if exp is not zero.
527 if (exp != 0) { // had significant exponent
528 scl = adjustScale(scl, exp);
529 }
530 rs = isneg ? -rs : rs;
531 int mcp = mc.precision;
532 int drop = prec - mcp; // prec has range [1, MAX_INT], mcp has range [0, MAX_INT];
533 // therefore, this subtract cannot overflow
534 if (mcp > 0 && drop > 0) { // do rounding
535 while (drop > 0) {
536 scl = checkScaleNonZero((long) scl - drop);
537 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
538 prec = longDigitLength(rs);
539 drop = prec - mcp;
540 }
541 }
542 } else {
543 char coeff[] = new char[len];
544 for (; len > 0; offset++, len--) {
545 c = in[offset];
546 // have digit
547 if ((c >= '0' && c <= '9') || Character.isDigit(c)) {
548 // First compact case, we need not to preserve the character
549 // and we can just compute the value in place.
550 if (c == '0' || Character.digit(c, 10) == 0) {
551 if (prec == 0) {
552 coeff[idx] = c;
553 prec = 1;
554 } else if (idx != 0) {
555 coeff[idx++] = c;
556 ++prec;
557 } // else c must be a redundant leading zero
558 } else {
559 if (prec != 1 || idx != 0)
560 ++prec; // prec unchanged if preceded by 0s
561 coeff[idx++] = c;
562 }
563 if (dot)
564 ++scl;
565 continue;
566 }
567 // have dot
568 if (c == '.') {
569 // have dot
570 if (dot) // two dots
571 throw new NumberFormatException("Character array"
572 + " contains more than one decimal point.");
573 dot = true;
574 continue;
575 }
576 // exponent expected
577 if ((c != 'e') && (c != 'E'))
578 throw new NumberFormatException("Character array"
579 + " is missing \"e\" notation exponential mark.");
580 exp = parseExp(in, offset, len);
581 // Next test is required for backwards compatibility
582 if ((int) exp != exp) // overflow
583 throw new NumberFormatException("Exponent overflow.");
584 break; // [saves a test]
585 }
586 // here when no characters left
587 if (prec == 0) // no digits found
588 throw new NumberFormatException("No digits found.");
589 // Adjust scale if exp is not zero.
590 if (exp != 0) { // had significant exponent
591 scl = adjustScale(scl, exp);
592 }
593 // Remove leading zeros from precision (digits count)
594 rb = new BigInteger(coeff, isneg ? -1 : 1, prec);
595 rs = compactValFor(rb);
596 int mcp = mc.precision;
597 if (mcp > 0 && (prec > mcp)) {
598 if (rs == INFLATED) {
599 int drop = prec - mcp;
600 while (drop > 0) {
601 scl = checkScaleNonZero((long) scl - drop);
602 rb = divideAndRoundByTenPow(rb, drop, mc.roundingMode.oldMode);
603 rs = compactValFor(rb);
604 if (rs != INFLATED) {
605 prec = longDigitLength(rs);
606 break;
607 }
608 prec = bigDigitLength(rb);
609 drop = prec - mcp;
610 }
611 }
612 if (rs != INFLATED) {
613 int drop = prec - mcp;
614 while (drop > 0) {
615 scl = checkScaleNonZero((long) scl - drop);
616 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
617 prec = longDigitLength(rs);
618 drop = prec - mcp;
619 }
620 rb = null;
621 }
622 }
623 }
624 } catch (ArrayIndexOutOfBoundsException | NegativeArraySizeException e) {
625 NumberFormatException nfe = new NumberFormatException();
626 nfe.initCause(e);
627 throw nfe;
628 }
629 this.scale = scl;
630 this.precision = prec;
631 this.intCompact = rs;
632 this.intVal = rb;
633 }
634
635 private int adjustScale(int scl, long exp) {
636 long adjustedScale = scl - exp;
637 if (adjustedScale > Integer.MAX_VALUE || adjustedScale < Integer.MIN_VALUE)
638 throw new NumberFormatException("Scale out of range.");
639 scl = (int) adjustedScale;
640 return scl;
641 }
642
643 /*
644 * parse exponent
645 */
646 private static long parseExp(char[] in, int offset, int len){
647 long exp = 0;
648 offset++;
649 char c = in[offset];
650 len--;
651 boolean negexp = (c == '-');
652 // optional sign
653 if (negexp || c == '+') {
654 offset++;
655 c = in[offset];
656 len--;
657 }
658 if (len <= 0) // no exponent digits
659 throw new NumberFormatException("No exponent digits.");
660 // skip leading zeros in the exponent
661 while (len > 10 && (c=='0' || (Character.digit(c, 10) == 0))) {
662 offset++;
663 c = in[offset];
664 len--;
665 }
666 if (len > 10) // too many nonzero exponent digits
667 throw new NumberFormatException("Too many nonzero exponent digits.");
668 // c now holds first digit of exponent
669 for (;; len--) {
670 int v;
671 if (c >= '0' && c <= '9') {
672 v = c - '0';
673 } else {
674 v = Character.digit(c, 10);
675 if (v < 0) // not a digit
676 throw new NumberFormatException("Not a digit.");
677 }
678 exp = exp * 10 + v;
679 if (len == 1)
680 break; // that was final character
681 offset++;
682 c = in[offset];
683 }
684 if (negexp) // apply sign
685 exp = -exp;
686 return exp;
687 }
688
689 /**
690 * Translates a character array representation of a
691 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
692 * same sequence of characters as the {@link #BigDecimal(String)}
693 * constructor.
694 *
695 * @implNote If the sequence of characters is already available
696 * as a character array, using this constructor is faster than
697 * converting the {@code char} array to string and using the
698 * {@code BigDecimal(String)} constructor.
699 *
700 * @param in {@code char} array that is the source of characters.
701 * @throws NumberFormatException if {@code in} is not a valid
702 * representation of a {@code BigDecimal}.
703 * @since 1.5
704 */
705 public BigDecimal(char[] in) {
706 this(in, 0, in.length);
707 }
708
709 /**
710 * Translates a character array representation of a
711 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
712 * same sequence of characters as the {@link #BigDecimal(String)}
713 * constructor and with rounding according to the context
714 * settings.
715 *
716 * @implNote If the sequence of characters is already available
717 * as a character array, using this constructor is faster than
718 * converting the {@code char} array to string and using the
719 * {@code BigDecimal(String)} constructor.
720 *
721 * @param in {@code char} array that is the source of characters.
722 * @param mc the context to use.
723 * @throws ArithmeticException if the result is inexact but the
724 * rounding mode is {@code UNNECESSARY}.
725 * @throws NumberFormatException if {@code in} is not a valid
726 * representation of a {@code BigDecimal}.
727 * @since 1.5
728 */
729 public BigDecimal(char[] in, MathContext mc) {
730 this(in, 0, in.length, mc);
731 }
732
733 /**
734 * Translates the string representation of a {@code BigDecimal}
735 * into a {@code BigDecimal}. The string representation consists
736 * of an optional sign, {@code '+'} (<code> '\u002B'</code>) or
737 * {@code '-'} (<code>'\u002D'</code>), followed by a sequence of
738 * zero or more decimal digits ("the integer"), optionally
739 * followed by a fraction, optionally followed by an exponent.
740 *
741 * <p>The fraction consists of a decimal point followed by zero
742 * or more decimal digits. The string must contain at least one
743 * digit in either the integer or the fraction. The number formed
744 * by the sign, the integer and the fraction is referred to as the
745 * <i>significand</i>.
746 *
747 * <p>The exponent consists of the character {@code 'e'}
748 * (<code>'\u0065'</code>) or {@code 'E'} (<code>'\u0045'</code>)
749 * followed by one or more decimal digits. The value of the
750 * exponent must lie between -{@link Integer#MAX_VALUE} ({@link
751 * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive.
752 *
753 * <p>More formally, the strings this constructor accepts are
754 * described by the following grammar:
755 * <blockquote>
756 * <dl>
757 * <dt><i>BigDecimalString:</i>
758 * <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i>
759 * <dt><i>Sign:</i>
760 * <dd>{@code +}
761 * <dd>{@code -}
762 * <dt><i>Significand:</i>
763 * <dd><i>IntegerPart</i> {@code .} <i>FractionPart<sub>opt</sub></i>
764 * <dd>{@code .} <i>FractionPart</i>
765 * <dd><i>IntegerPart</i>
766 * <dt><i>IntegerPart:</i>
767 * <dd><i>Digits</i>
768 * <dt><i>FractionPart:</i>
769 * <dd><i>Digits</i>
770 * <dt><i>Exponent:</i>
771 * <dd><i>ExponentIndicator SignedInteger</i>
772 * <dt><i>ExponentIndicator:</i>
773 * <dd>{@code e}
774 * <dd>{@code E}
775 * <dt><i>SignedInteger:</i>
776 * <dd><i>Sign<sub>opt</sub> Digits</i>
777 * <dt><i>Digits:</i>
778 * <dd><i>Digit</i>
779 * <dd><i>Digits Digit</i>
780 * <dt><i>Digit:</i>
781 * <dd>any character for which {@link Character#isDigit}
782 * returns {@code true}, including 0, 1, 2 ...
783 * </dl>
784 * </blockquote>
785 *
786 * <p>The scale of the returned {@code BigDecimal} will be the
787 * number of digits in the fraction, or zero if the string
788 * contains no decimal point, subject to adjustment for any
789 * exponent; if the string contains an exponent, the exponent is
790 * subtracted from the scale. The value of the resulting scale
791 * must lie between {@code Integer.MIN_VALUE} and
792 * {@code Integer.MAX_VALUE}, inclusive.
793 *
794 * <p>The character-to-digit mapping is provided by {@link
795 * java.lang.Character#digit} set to convert to radix 10. The
796 * String may not contain any extraneous characters (whitespace,
797 * for example).
798 *
799 * <p><b>Examples:</b><br>
800 * The value of the returned {@code BigDecimal} is equal to
801 * <i>significand</i> × 10<sup> <i>exponent</i></sup>.
802 * For each string on the left, the resulting representation
803 * [{@code BigInteger}, {@code scale}] is shown on the right.
804 * <pre>
805 * "0" [0,0]
806 * "0.00" [0,2]
807 * "123" [123,0]
808 * "-123" [-123,0]
809 * "1.23E3" [123,-1]
810 * "1.23E+3" [123,-1]
811 * "12.3E+7" [123,-6]
812 * "12.0" [120,1]
813 * "12.3" [123,1]
814 * "0.00123" [123,5]
815 * "-1.23E-12" [-123,14]
816 * "1234.5E-4" [12345,5]
817 * "0E+7" [0,-7]
818 * "-0" [0,0]
819 * </pre>
820 *
821 * @apiNote For values other than {@code float} and
822 * {@code double} NaN and ±Infinity, this constructor is
823 * compatible with the values returned by {@link Float#toString}
824 * and {@link Double#toString}. This is generally the preferred
825 * way to convert a {@code float} or {@code double} into a
826 * BigDecimal, as it doesn't suffer from the unpredictability of
827 * the {@link #BigDecimal(double)} constructor.
828 *
829 * @param val String representation of {@code BigDecimal}.
830 *
831 * @throws NumberFormatException if {@code val} is not a valid
832 * representation of a {@code BigDecimal}.
833 */
834 public BigDecimal(String val) {
835 this(val.toCharArray(), 0, val.length());
836 }
837
838 /**
839 * Translates the string representation of a {@code BigDecimal}
840 * into a {@code BigDecimal}, accepting the same strings as the
841 * {@link #BigDecimal(String)} constructor, with rounding
842 * according to the context settings.
843 *
844 * @param val string representation of a {@code BigDecimal}.
845 * @param mc the context to use.
846 * @throws ArithmeticException if the result is inexact but the
847 * rounding mode is {@code UNNECESSARY}.
848 * @throws NumberFormatException if {@code val} is not a valid
849 * representation of a BigDecimal.
850 * @since 1.5
851 */
852 public BigDecimal(String val, MathContext mc) {
853 this(val.toCharArray(), 0, val.length(), mc);
854 }
855
856 /**
857 * Translates a {@code double} into a {@code BigDecimal} which
858 * is the exact decimal representation of the {@code double}'s
859 * binary floating-point value. The scale of the returned
860 * {@code BigDecimal} is the smallest value such that
861 * <code>(10<sup>scale</sup> × val)</code> is an integer.
862 * <p>
863 * <b>Notes:</b>
864 * <ol>
865 * <li>
866 * The results of this constructor can be somewhat unpredictable.
867 * One might assume that writing {@code new BigDecimal(0.1)} in
868 * Java creates a {@code BigDecimal} which is exactly equal to
869 * 0.1 (an unscaled value of 1, with a scale of 1), but it is
870 * actually equal to
871 * 0.1000000000000000055511151231257827021181583404541015625.
872 * This is because 0.1 cannot be represented exactly as a
873 * {@code double} (or, for that matter, as a binary fraction of
874 * any finite length). Thus, the value that is being passed
875 * <em>in</em> to the constructor is not exactly equal to 0.1,
876 * appearances notwithstanding.
877 *
878 * <li>
879 * The {@code String} constructor, on the other hand, is
880 * perfectly predictable: writing {@code new BigDecimal("0.1")}
881 * creates a {@code BigDecimal} which is <em>exactly</em> equal to
882 * 0.1, as one would expect. Therefore, it is generally
883 * recommended that the {@linkplain #BigDecimal(String)
884 * String constructor} be used in preference to this one.
885 *
886 * <li>
887 * When a {@code double} must be used as a source for a
888 * {@code BigDecimal}, note that this constructor provides an
889 * exact conversion; it does not give the same result as
890 * converting the {@code double} to a {@code String} using the
891 * {@link Double#toString(double)} method and then using the
892 * {@link #BigDecimal(String)} constructor. To get that result,
893 * use the {@code static} {@link #valueOf(double)} method.
894 * </ol>
895 *
896 * @param val {@code double} value to be converted to
897 * {@code BigDecimal}.
898 * @throws NumberFormatException if {@code val} is infinite or NaN.
899 */
900 public BigDecimal(double val) {
901 this(val,MathContext.UNLIMITED);
902 }
903
904 /**
905 * Translates a {@code double} into a {@code BigDecimal}, with
906 * rounding according to the context settings. The scale of the
907 * {@code BigDecimal} is the smallest value such that
908 * <code>(10<sup>scale</sup> × val)</code> is an integer.
909 *
910 * <p>The results of this constructor can be somewhat unpredictable
911 * and its use is generally not recommended; see the notes under
912 * the {@link #BigDecimal(double)} constructor.
913 *
914 * @param val {@code double} value to be converted to
915 * {@code BigDecimal}.
916 * @param mc the context to use.
917 * @throws ArithmeticException if the result is inexact but the
918 * RoundingMode is UNNECESSARY.
919 * @throws NumberFormatException if {@code val} is infinite or NaN.
920 * @since 1.5
921 */
922 public BigDecimal(double val, MathContext mc) {
923 if (Double.isInfinite(val) || Double.isNaN(val))
924 throw new NumberFormatException("Infinite or NaN");
925 // Translate the double into sign, exponent and significand, according
926 // to the formulae in JLS, Section 20.10.22.
927 long valBits = Double.doubleToLongBits(val);
928 int sign = ((valBits >> 63) == 0 ? 1 : -1);
929 int exponent = (int) ((valBits >> 52) & 0x7ffL);
930 long significand = (exponent == 0
931 ? (valBits & ((1L << 52) - 1)) << 1
932 : (valBits & ((1L << 52) - 1)) | (1L << 52));
933 exponent -= 1075;
934 // At this point, val == sign * significand * 2**exponent.
935
936 /*
937 * Special case zero to supress nonterminating normalization and bogus
938 * scale calculation.
939 */
940 if (significand == 0) {
941 this.intVal = BigInteger.ZERO;
942 this.scale = 0;
943 this.intCompact = 0;
944 this.precision = 1;
945 return;
946 }
947 // Normalize
948 while ((significand & 1) == 0) { // i.e., significand is even
949 significand >>= 1;
950 exponent++;
951 }
952 int scl = 0;
953 // Calculate intVal and scale
954 BigInteger rb;
955 long compactVal = sign * significand;
956 if (exponent == 0) {
957 rb = (compactVal == INFLATED) ? INFLATED_BIGINT : null;
958 } else {
959 if (exponent < 0) {
960 rb = BigInteger.valueOf(5).pow(-exponent).multiply(compactVal);
961 scl = -exponent;
962 } else { // (exponent > 0)
963 rb = BigInteger.TWO.pow(exponent).multiply(compactVal);
964 }
965 compactVal = compactValFor(rb);
966 }
967 int prec = 0;
968 int mcp = mc.precision;
969 if (mcp > 0) { // do rounding
970 int mode = mc.roundingMode.oldMode;
971 int drop;
972 if (compactVal == INFLATED) {
973 prec = bigDigitLength(rb);
974 drop = prec - mcp;
975 while (drop > 0) {
976 scl = checkScaleNonZero((long) scl - drop);
977 rb = divideAndRoundByTenPow(rb, drop, mode);
978 compactVal = compactValFor(rb);
979 if (compactVal != INFLATED) {
980 break;
981 }
982 prec = bigDigitLength(rb);
983 drop = prec - mcp;
984 }
985 }
986 if (compactVal != INFLATED) {
987 prec = longDigitLength(compactVal);
988 drop = prec - mcp;
989 while (drop > 0) {
990 scl = checkScaleNonZero((long) scl - drop);
991 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
992 prec = longDigitLength(compactVal);
993 drop = prec - mcp;
994 }
995 rb = null;
996 }
997 }
998 this.intVal = rb;
999 this.intCompact = compactVal;
1000 this.scale = scl;
1001 this.precision = prec;
1002 }
1003
1004 /**
1005 * Translates a {@code BigInteger} into a {@code BigDecimal}.
1006 * The scale of the {@code BigDecimal} is zero.
1007 *
1008 * @param val {@code BigInteger} value to be converted to
1009 * {@code BigDecimal}.
1010 */
1011 public BigDecimal(BigInteger val) {
1012 scale = 0;
1013 intVal = val;
1014 intCompact = compactValFor(val);
1015 }
1016
1017 /**
1018 * Translates a {@code BigInteger} into a {@code BigDecimal}
1019 * rounding according to the context settings. The scale of the
1020 * {@code BigDecimal} is zero.
1021 *
1022 * @param val {@code BigInteger} value to be converted to
1023 * {@code BigDecimal}.
1024 * @param mc the context to use.
1025 * @throws ArithmeticException if the result is inexact but the
1026 * rounding mode is {@code UNNECESSARY}.
1027 * @since 1.5
1028 */
1029 public BigDecimal(BigInteger val, MathContext mc) {
1030 this(val,0,mc);
1031 }
1032
1033 /**
1034 * Translates a {@code BigInteger} unscaled value and an
1035 * {@code int} scale into a {@code BigDecimal}. The value of
1036 * the {@code BigDecimal} is
1037 * <code>(unscaledVal × 10<sup>-scale</sup>)</code>.
1038 *
1039 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1040 * @param scale scale of the {@code BigDecimal}.
1041 */
1042 public BigDecimal(BigInteger unscaledVal, int scale) {
1043 // Negative scales are now allowed
1044 this.intVal = unscaledVal;
1045 this.intCompact = compactValFor(unscaledVal);
1046 this.scale = scale;
1047 }
1048
1049 /**
1050 * Translates a {@code BigInteger} unscaled value and an
1051 * {@code int} scale into a {@code BigDecimal}, with rounding
1052 * according to the context settings. The value of the
1053 * {@code BigDecimal} is <code>(unscaledVal ×
1054 * 10<sup>-scale</sup>)</code>, rounded according to the
1055 * {@code precision} and rounding mode settings.
1056 *
1057 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1058 * @param scale scale of the {@code BigDecimal}.
1059 * @param mc the context to use.
1060 * @throws ArithmeticException if the result is inexact but the
1061 * rounding mode is {@code UNNECESSARY}.
1062 * @since 1.5
1063 */
1064 public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {
1065 long compactVal = compactValFor(unscaledVal);
1066 int mcp = mc.precision;
1067 int prec = 0;
1068 if (mcp > 0) { // do rounding
1069 int mode = mc.roundingMode.oldMode;
1070 if (compactVal == INFLATED) {
1071 prec = bigDigitLength(unscaledVal);
1072 int drop = prec - mcp;
1073 while (drop > 0) {
1074 scale = checkScaleNonZero((long) scale - drop);
1075 unscaledVal = divideAndRoundByTenPow(unscaledVal, drop, mode);
1076 compactVal = compactValFor(unscaledVal);
1077 if (compactVal != INFLATED) {
1078 break;
1079 }
1080 prec = bigDigitLength(unscaledVal);
1081 drop = prec - mcp;
1082 }
1083 }
1084 if (compactVal != INFLATED) {
1085 prec = longDigitLength(compactVal);
1086 int drop = prec - mcp; // drop can't be more than 18
1087 while (drop > 0) {
1088 scale = checkScaleNonZero((long) scale - drop);
1089 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mode);
1090 prec = longDigitLength(compactVal);
1091 drop = prec - mcp;
1092 }
1093 unscaledVal = null;
1094 }
1095 }
1096 this.intVal = unscaledVal;
1097 this.intCompact = compactVal;
1098 this.scale = scale;
1099 this.precision = prec;
1100 }
1101
1102 /**
1103 * Translates an {@code int} into a {@code BigDecimal}. The
1104 * scale of the {@code BigDecimal} is zero.
1105 *
1106 * @param val {@code int} value to be converted to
1107 * {@code BigDecimal}.
1108 * @since 1.5
1109 */
1110 public BigDecimal(int val) {
1111 this.intCompact = val;
1112 this.scale = 0;
1113 this.intVal = null;
1114 }
1115
1116 /**
1117 * Translates an {@code int} into a {@code BigDecimal}, with
1118 * rounding according to the context settings. The scale of the
1119 * {@code BigDecimal}, before any rounding, is zero.
1120 *
1121 * @param val {@code int} value to be converted to {@code BigDecimal}.
1122 * @param mc the context to use.
1123 * @throws ArithmeticException if the result is inexact but the
1124 * rounding mode is {@code UNNECESSARY}.
1125 * @since 1.5
1126 */
1127 public BigDecimal(int val, MathContext mc) {
1128 int mcp = mc.precision;
1129 long compactVal = val;
1130 int scl = 0;
1131 int prec = 0;
1132 if (mcp > 0) { // do rounding
1133 prec = longDigitLength(compactVal);
1134 int drop = prec - mcp; // drop can't be more than 18
1135 while (drop > 0) {
1136 scl = checkScaleNonZero((long) scl - drop);
1137 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1138 prec = longDigitLength(compactVal);
1139 drop = prec - mcp;
1140 }
1141 }
1142 this.intVal = null;
1143 this.intCompact = compactVal;
1144 this.scale = scl;
1145 this.precision = prec;
1146 }
1147
1148 /**
1149 * Translates a {@code long} into a {@code BigDecimal}. The
1150 * scale of the {@code BigDecimal} is zero.
1151 *
1152 * @param val {@code long} value to be converted to {@code BigDecimal}.
1153 * @since 1.5
1154 */
1155 public BigDecimal(long val) {
1156 this.intCompact = val;
1157 this.intVal = (val == INFLATED) ? INFLATED_BIGINT : null;
1158 this.scale = 0;
1159 }
1160
1161 /**
1162 * Translates a {@code long} into a {@code BigDecimal}, with
1163 * rounding according to the context settings. The scale of the
1164 * {@code BigDecimal}, before any rounding, is zero.
1165 *
1166 * @param val {@code long} value to be converted to {@code BigDecimal}.
1167 * @param mc the context to use.
1168 * @throws ArithmeticException if the result is inexact but the
1169 * rounding mode is {@code UNNECESSARY}.
1170 * @since 1.5
1171 */
1172 public BigDecimal(long val, MathContext mc) {
1173 int mcp = mc.precision;
1174 int mode = mc.roundingMode.oldMode;
1175 int prec = 0;
1176 int scl = 0;
1177 BigInteger rb = (val == INFLATED) ? INFLATED_BIGINT : null;
1178 if (mcp > 0) { // do rounding
1179 if (val == INFLATED) {
1180 prec = 19;
1181 int drop = prec - mcp;
1182 while (drop > 0) {
1183 scl = checkScaleNonZero((long) scl - drop);
1184 rb = divideAndRoundByTenPow(rb, drop, mode);
1185 val = compactValFor(rb);
1186 if (val != INFLATED) {
1187 break;
1188 }
1189 prec = bigDigitLength(rb);
1190 drop = prec - mcp;
1191 }
1192 }
1193 if (val != INFLATED) {
1194 prec = longDigitLength(val);
1195 int drop = prec - mcp;
1196 while (drop > 0) {
1197 scl = checkScaleNonZero((long) scl - drop);
1198 val = divideAndRound(val, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1199 prec = longDigitLength(val);
1200 drop = prec - mcp;
1201 }
1202 rb = null;
1203 }
1204 }
1205 this.intVal = rb;
1206 this.intCompact = val;
1207 this.scale = scl;
1208 this.precision = prec;
1209 }
1210
1211 // Static Factory Methods
1212
1213 /**
1214 * Translates a {@code long} unscaled value and an
1215 * {@code int} scale into a {@code BigDecimal}.
1216 *
1217 * @apiNote This static factory method is provided in preference
1218 * to a ({@code long}, {@code int}) constructor because it allows
1219 * for reuse of frequently used {@code BigDecimal} values.
1220 *
1221 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1222 * @param scale scale of the {@code BigDecimal}.
1223 * @return a {@code BigDecimal} whose value is
1224 * <code>(unscaledVal × 10<sup>-scale</sup>)</code>.
1225 */
1226 public static BigDecimal valueOf(long unscaledVal, int scale) {
1227 if (scale == 0)
1228 return valueOf(unscaledVal);
1229 else if (unscaledVal == 0) {
1230 return zeroValueOf(scale);
1231 }
1232 return new BigDecimal(unscaledVal == INFLATED ?
1233 INFLATED_BIGINT : null,
1234 unscaledVal, scale, 0);
1235 }
1236
1237 /**
1238 * Translates a {@code long} value into a {@code BigDecimal}
1239 * with a scale of zero.
1240 *
1241 * @apiNote This static factory method is provided in preference
1242 * to a ({@code long}) constructor because it allows for reuse of
1243 * frequently used {@code BigDecimal} values.
1244 *
1245 * @param val value of the {@code BigDecimal}.
1246 * @return a {@code BigDecimal} whose value is {@code val}.
1247 */
1248 public static BigDecimal valueOf(long val) {
1249 if (val >= 0 && val < ZERO_THROUGH_TEN.length)
1250 return ZERO_THROUGH_TEN[(int)val];
1251 else if (val != INFLATED)
1252 return new BigDecimal(null, val, 0, 0);
1253 return new BigDecimal(INFLATED_BIGINT, val, 0, 0);
1254 }
1255
1256 static BigDecimal valueOf(long unscaledVal, int scale, int prec) {
1257 if (scale == 0 && unscaledVal >= 0 && unscaledVal < ZERO_THROUGH_TEN.length) {
1258 return ZERO_THROUGH_TEN[(int) unscaledVal];
1259 } else if (unscaledVal == 0) {
1260 return zeroValueOf(scale);
1261 }
1262 return new BigDecimal(unscaledVal == INFLATED ? INFLATED_BIGINT : null,
1263 unscaledVal, scale, prec);
1264 }
1265
1266 static BigDecimal valueOf(BigInteger intVal, int scale, int prec) {
1267 long val = compactValFor(intVal);
1268 if (val == 0) {
1269 return zeroValueOf(scale);
1270 } else if (scale == 0 && val >= 0 && val < ZERO_THROUGH_TEN.length) {
1271 return ZERO_THROUGH_TEN[(int) val];
1272 }
1273 return new BigDecimal(intVal, val, scale, prec);
1274 }
1275
1276 static BigDecimal zeroValueOf(int scale) {
1277 if (scale >= 0 && scale < ZERO_SCALED_BY.length)
1278 return ZERO_SCALED_BY[scale];
1279 else
1280 return new BigDecimal(BigInteger.ZERO, 0, scale, 1);
1281 }
1282
1283 /**
1284 * Translates a {@code double} into a {@code BigDecimal}, using
1285 * the {@code double}'s canonical string representation provided
1286 * by the {@link Double#toString(double)} method.
1287 *
1288 * @apiNote This is generally the preferred way to convert a
1289 * {@code double} (or {@code float}) into a {@code BigDecimal}, as
1290 * the value returned is equal to that resulting from constructing
1291 * a {@code BigDecimal} from the result of using {@link
1292 * Double#toString(double)}.
1293 *
1294 * @param val {@code double} to convert to a {@code BigDecimal}.
1295 * @return a {@code BigDecimal} whose value is equal to or approximately
1296 * equal to the value of {@code val}.
1297 * @throws NumberFormatException if {@code val} is infinite or NaN.
1298 * @since 1.5
1299 */
1300 public static BigDecimal valueOf(double val) {
1301 // Reminder: a zero double returns '0.0', so we cannot fastpath
1302 // to use the constant ZERO. This might be important enough to
1303 // justify a factory approach, a cache, or a few private
1304 // constants, later.
1305 return new BigDecimal(Double.toString(val));
1306 }
1307
1308 // Arithmetic Operations
1309 /**
1310 * Returns a {@code BigDecimal} whose value is {@code (this +
1311 * augend)}, and whose scale is {@code max(this.scale(),
1312 * augend.scale())}.
1313 *
1314 * @param augend value to be added to this {@code BigDecimal}.
1315 * @return {@code this + augend}
1316 */
1317 public BigDecimal add(BigDecimal augend) {
1318 if (this.intCompact != INFLATED) {
1319 if ((augend.intCompact != INFLATED)) {
1320 return add(this.intCompact, this.scale, augend.intCompact, augend.scale);
1321 } else {
1322 return add(this.intCompact, this.scale, augend.intVal, augend.scale);
1323 }
1324 } else {
1325 if ((augend.intCompact != INFLATED)) {
1326 return add(augend.intCompact, augend.scale, this.intVal, this.scale);
1327 } else {
1328 return add(this.intVal, this.scale, augend.intVal, augend.scale);
1329 }
1330 }
1331 }
1332
1333 /**
1334 * Returns a {@code BigDecimal} whose value is {@code (this + augend)},
1335 * with rounding according to the context settings.
1336 *
1337 * If either number is zero and the precision setting is nonzero then
1338 * the other number, rounded if necessary, is used as the result.
1339 *
1340 * @param augend value to be added to this {@code BigDecimal}.
1341 * @param mc the context to use.
1342 * @return {@code this + augend}, rounded as necessary.
1343 * @throws ArithmeticException if the result is inexact but the
1344 * rounding mode is {@code UNNECESSARY}.
1345 * @since 1.5
1346 */
1347 public BigDecimal add(BigDecimal augend, MathContext mc) {
1348 if (mc.precision == 0)
1349 return add(augend);
1350 BigDecimal lhs = this;
1351
1352 // If either number is zero then the other number, rounded and
1353 // scaled if necessary, is used as the result.
1354 {
1355 boolean lhsIsZero = lhs.signum() == 0;
1356 boolean augendIsZero = augend.signum() == 0;
1357
1358 if (lhsIsZero || augendIsZero) {
1359 int preferredScale = Math.max(lhs.scale(), augend.scale());
1360 BigDecimal result;
1361
1362 if (lhsIsZero && augendIsZero)
1363 return zeroValueOf(preferredScale);
1364 result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc);
1365
1366 if (result.scale() == preferredScale)
1367 return result;
1368 else if (result.scale() > preferredScale) {
1369 return stripZerosToMatchScale(result.intVal, result.intCompact, result.scale, preferredScale);
1370 } else { // result.scale < preferredScale
1371 int precisionDiff = mc.precision - result.precision();
1372 int scaleDiff = preferredScale - result.scale();
1373
1374 if (precisionDiff >= scaleDiff)
1375 return result.setScale(preferredScale); // can achieve target scale
1376 else
1377 return result.setScale(result.scale() + precisionDiff);
1378 }
1379 }
1380 }
1381
1382 long padding = (long) lhs.scale - augend.scale;
1383 if (padding != 0) { // scales differ; alignment needed
1384 BigDecimal arg[] = preAlign(lhs, augend, padding, mc);
1385 matchScale(arg);
1386 lhs = arg[0];
1387 augend = arg[1];
1388 }
1389 return doRound(lhs.inflated().add(augend.inflated()), lhs.scale, mc);
1390 }
1391
1392 /**
1393 * Returns an array of length two, the sum of whose entries is
1394 * equal to the rounded sum of the {@code BigDecimal} arguments.
1395 *
1396 * <p>If the digit positions of the arguments have a sufficient
1397 * gap between them, the value smaller in magnitude can be
1398 * condensed into a {@literal "sticky bit"} and the end result will
1399 * round the same way <em>if</em> the precision of the final
1400 * result does not include the high order digit of the small
1401 * magnitude operand.
1402 *
1403 * <p>Note that while strictly speaking this is an optimization,
1404 * it makes a much wider range of additions practical.
1405 *
1406 * <p>This corresponds to a pre-shift operation in a fixed
1407 * precision floating-point adder; this method is complicated by
1408 * variable precision of the result as determined by the
1409 * MathContext. A more nuanced operation could implement a
1410 * {@literal "right shift"} on the smaller magnitude operand so
1411 * that the number of digits of the smaller operand could be
1412 * reduced even though the significands partially overlapped.
1413 */
1414 private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend, long padding, MathContext mc) {
1415 assert padding != 0;
1416 BigDecimal big;
1417 BigDecimal small;
1418
1419 if (padding < 0) { // lhs is big; augend is small
1420 big = lhs;
1421 small = augend;
1422 } else { // lhs is small; augend is big
1423 big = augend;
1424 small = lhs;
1425 }
1426
1427 /*
1428 * This is the estimated scale of an ulp of the result; it assumes that
1429 * the result doesn't have a carry-out on a true add (e.g. 999 + 1 =>
1430 * 1000) or any subtractive cancellation on borrowing (e.g. 100 - 1.2 =>
1431 * 98.8)
1432 */
1433 long estResultUlpScale = (long) big.scale - big.precision() + mc.precision;
1434
1435 /*
1436 * The low-order digit position of big is big.scale(). This
1437 * is true regardless of whether big has a positive or
1438 * negative scale. The high-order digit position of small is
1439 * small.scale - (small.precision() - 1). To do the full
1440 * condensation, the digit positions of big and small must be
1441 * disjoint *and* the digit positions of small should not be
1442 * directly visible in the result.
1443 */
1444 long smallHighDigitPos = (long) small.scale - small.precision() + 1;
1445 if (smallHighDigitPos > big.scale + 2 && // big and small disjoint
1446 smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible
1447 small = BigDecimal.valueOf(small.signum(), this.checkScale(Math.max(big.scale, estResultUlpScale) + 3));
1448 }
1449
1450 // Since addition is symmetric, preserving input order in
1451 // returned operands doesn't matter
1452 BigDecimal[] result = {big, small};
1453 return result;
1454 }
1455
1456 /**
1457 * Returns a {@code BigDecimal} whose value is {@code (this -
1458 * subtrahend)}, and whose scale is {@code max(this.scale(),
1459 * subtrahend.scale())}.
1460 *
1461 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1462 * @return {@code this - subtrahend}
1463 */
1464 public BigDecimal subtract(BigDecimal subtrahend) {
1465 if (this.intCompact != INFLATED) {
1466 if ((subtrahend.intCompact != INFLATED)) {
1467 return add(this.intCompact, this.scale, -subtrahend.intCompact, subtrahend.scale);
1468 } else {
1469 return add(this.intCompact, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1470 }
1471 } else {
1472 if ((subtrahend.intCompact != INFLATED)) {
1473 // Pair of subtrahend values given before pair of
1474 // values from this BigDecimal to avoid need for
1475 // method overloading on the specialized add method
1476 return add(-subtrahend.intCompact, subtrahend.scale, this.intVal, this.scale);
1477 } else {
1478 return add(this.intVal, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1479 }
1480 }
1481 }
1482
1483 /**
1484 * Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)},
1485 * with rounding according to the context settings.
1486 *
1487 * If {@code subtrahend} is zero then this, rounded if necessary, is used as the
1488 * result. If this is zero then the result is {@code subtrahend.negate(mc)}.
1489 *
1490 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1491 * @param mc the context to use.
1492 * @return {@code this - subtrahend}, rounded as necessary.
1493 * @throws ArithmeticException if the result is inexact but the
1494 * rounding mode is {@code UNNECESSARY}.
1495 * @since 1.5
1496 */
1497 public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) {
1498 if (mc.precision == 0)
1499 return subtract(subtrahend);
1500 // share the special rounding code in add()
1501 return add(subtrahend.negate(), mc);
1502 }
1503
1504 /**
1505 * Returns a {@code BigDecimal} whose value is <code>(this ×
1506 * multiplicand)</code>, and whose scale is {@code (this.scale() +
1507 * multiplicand.scale())}.
1508 *
1509 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1510 * @return {@code this * multiplicand}
1511 */
1512 public BigDecimal multiply(BigDecimal multiplicand) {
1513 int productScale = checkScale((long) scale + multiplicand.scale);
1514 if (this.intCompact != INFLATED) {
1515 if ((multiplicand.intCompact != INFLATED)) {
1516 return multiply(this.intCompact, multiplicand.intCompact, productScale);
1517 } else {
1518 return multiply(this.intCompact, multiplicand.intVal, productScale);
1519 }
1520 } else {
1521 if ((multiplicand.intCompact != INFLATED)) {
1522 return multiply(multiplicand.intCompact, this.intVal, productScale);
1523 } else {
1524 return multiply(this.intVal, multiplicand.intVal, productScale);
1525 }
1526 }
1527 }
1528
1529 /**
1530 * Returns a {@code BigDecimal} whose value is <code>(this ×
1531 * multiplicand)</code>, with rounding according to the context settings.
1532 *
1533 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1534 * @param mc the context to use.
1535 * @return {@code this * multiplicand}, rounded as necessary.
1536 * @throws ArithmeticException if the result is inexact but the
1537 * rounding mode is {@code UNNECESSARY}.
1538 * @since 1.5
1539 */
1540 public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) {
1541 if (mc.precision == 0)
1542 return multiply(multiplicand);
1543 int productScale = checkScale((long) scale + multiplicand.scale);
1544 if (this.intCompact != INFLATED) {
1545 if ((multiplicand.intCompact != INFLATED)) {
1546 return multiplyAndRound(this.intCompact, multiplicand.intCompact, productScale, mc);
1547 } else {
1548 return multiplyAndRound(this.intCompact, multiplicand.intVal, productScale, mc);
1549 }
1550 } else {
1551 if ((multiplicand.intCompact != INFLATED)) {
1552 return multiplyAndRound(multiplicand.intCompact, this.intVal, productScale, mc);
1553 } else {
1554 return multiplyAndRound(this.intVal, multiplicand.intVal, productScale, mc);
1555 }
1556 }
1557 }
1558
1559 /**
1560 * Returns a {@code BigDecimal} whose value is {@code (this /
1561 * divisor)}, and whose scale is as specified. If rounding must
1562 * be performed to generate a result with the specified scale, the
1563 * specified rounding mode is applied.
1564 *
1565 * @deprecated The method {@link #divide(BigDecimal, int, RoundingMode)}
1566 * should be used in preference to this legacy method.
1567 *
1568 * @param divisor value by which this {@code BigDecimal} is to be divided.
1569 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1570 * @param roundingMode rounding mode to apply.
1571 * @return {@code this / divisor}
1572 * @throws ArithmeticException if {@code divisor} is zero,
1573 * {@code roundingMode==ROUND_UNNECESSARY} and
1574 * the specified scale is insufficient to represent the result
1575 * of the division exactly.
1576 * @throws IllegalArgumentException if {@code roundingMode} does not
1577 * represent a valid rounding mode.
1578 * @see #ROUND_UP
1579 * @see #ROUND_DOWN
1580 * @see #ROUND_CEILING
1581 * @see #ROUND_FLOOR
1582 * @see #ROUND_HALF_UP
1583 * @see #ROUND_HALF_DOWN
1584 * @see #ROUND_HALF_EVEN
1585 * @see #ROUND_UNNECESSARY
1586 */
1587 @Deprecated(since="9")
1588 public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) {
1589 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
1590 throw new IllegalArgumentException("Invalid rounding mode");
1591 if (this.intCompact != INFLATED) {
1592 if ((divisor.intCompact != INFLATED)) {
1593 return divide(this.intCompact, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1594 } else {
1595 return divide(this.intCompact, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1596 }
1597 } else {
1598 if ((divisor.intCompact != INFLATED)) {
1599 return divide(this.intVal, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1600 } else {
1601 return divide(this.intVal, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1602 }
1603 }
1604 }
1605
1606 /**
1607 * Returns a {@code BigDecimal} whose value is {@code (this /
1608 * divisor)}, and whose scale is as specified. If rounding must
1609 * be performed to generate a result with the specified scale, the
1610 * specified rounding mode is applied.
1611 *
1612 * @param divisor value by which this {@code BigDecimal} is to be divided.
1613 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1614 * @param roundingMode rounding mode to apply.
1615 * @return {@code this / divisor}
1616 * @throws ArithmeticException if {@code divisor} is zero,
1617 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1618 * the specified scale is insufficient to represent the result
1619 * of the division exactly.
1620 * @since 1.5
1621 */
1622 public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) {
1623 return divide(divisor, scale, roundingMode.oldMode);
1624 }
1625
1626 /**
1627 * Returns a {@code BigDecimal} whose value is {@code (this /
1628 * divisor)}, and whose scale is {@code this.scale()}. If
1629 * rounding must be performed to generate a result with the given
1630 * scale, the specified rounding mode is applied.
1631 *
1632 * @deprecated The method {@link #divide(BigDecimal, RoundingMode)}
1633 * should be used in preference to this legacy method.
1634 *
1635 * @param divisor value by which this {@code BigDecimal} is to be divided.
1636 * @param roundingMode rounding mode to apply.
1637 * @return {@code this / divisor}
1638 * @throws ArithmeticException if {@code divisor==0}, or
1639 * {@code roundingMode==ROUND_UNNECESSARY} and
1640 * {@code this.scale()} is insufficient to represent the result
1641 * of the division exactly.
1642 * @throws IllegalArgumentException if {@code roundingMode} does not
1643 * represent a valid rounding mode.
1644 * @see #ROUND_UP
1645 * @see #ROUND_DOWN
1646 * @see #ROUND_CEILING
1647 * @see #ROUND_FLOOR
1648 * @see #ROUND_HALF_UP
1649 * @see #ROUND_HALF_DOWN
1650 * @see #ROUND_HALF_EVEN
1651 * @see #ROUND_UNNECESSARY
1652 */
1653 @Deprecated(since="9")
1654 public BigDecimal divide(BigDecimal divisor, int roundingMode) {
1655 return this.divide(divisor, scale, roundingMode);
1656 }
1657
1658 /**
1659 * Returns a {@code BigDecimal} whose value is {@code (this /
1660 * divisor)}, and whose scale is {@code this.scale()}. If
1661 * rounding must be performed to generate a result with the given
1662 * scale, the specified rounding mode is applied.
1663 *
1664 * @param divisor value by which this {@code BigDecimal} is to be divided.
1665 * @param roundingMode rounding mode to apply.
1666 * @return {@code this / divisor}
1667 * @throws ArithmeticException if {@code divisor==0}, or
1668 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1669 * {@code this.scale()} is insufficient to represent the result
1670 * of the division exactly.
1671 * @since 1.5
1672 */
1673 public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) {
1674 return this.divide(divisor, scale, roundingMode.oldMode);
1675 }
1676
1677 /**
1678 * Returns a {@code BigDecimal} whose value is {@code (this /
1679 * divisor)}, and whose preferred scale is {@code (this.scale() -
1680 * divisor.scale())}; if the exact quotient cannot be
1681 * represented (because it has a non-terminating decimal
1682 * expansion) an {@code ArithmeticException} is thrown.
1683 *
1684 * @param divisor value by which this {@code BigDecimal} is to be divided.
1685 * @throws ArithmeticException if the exact quotient does not have a
1686 * terminating decimal expansion
1687 * @return {@code this / divisor}
1688 * @since 1.5
1689 * @author Joseph D. Darcy
1690 */
1691 public BigDecimal divide(BigDecimal divisor) {
1692 /*
1693 * Handle zero cases first.
1694 */
1695 if (divisor.signum() == 0) { // x/0
1696 if (this.signum() == 0) // 0/0
1697 throw new ArithmeticException("Division undefined"); // NaN
1698 throw new ArithmeticException("Division by zero");
1699 }
1700
1701 // Calculate preferred scale
1702 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1703
1704 if (this.signum() == 0) // 0/y
1705 return zeroValueOf(preferredScale);
1706 else {
1707 /*
1708 * If the quotient this/divisor has a terminating decimal
1709 * expansion, the expansion can have no more than
1710 * (a.precision() + ceil(10*b.precision)/3) digits.
1711 * Therefore, create a MathContext object with this
1712 * precision and do a divide with the UNNECESSARY rounding
1713 * mode.
1714 */
1715 MathContext mc = new MathContext( (int)Math.min(this.precision() +
1716 (long)Math.ceil(10.0*divisor.precision()/3.0),
1717 Integer.MAX_VALUE),
1718 RoundingMode.UNNECESSARY);
1719 BigDecimal quotient;
1720 try {
1721 quotient = this.divide(divisor, mc);
1722 } catch (ArithmeticException e) {
1723 throw new ArithmeticException("Non-terminating decimal expansion; " +
1724 "no exact representable decimal result.");
1725 }
1726
1727 int quotientScale = quotient.scale();
1728
1729 // divide(BigDecimal, mc) tries to adjust the quotient to
1730 // the desired one by removing trailing zeros; since the
1731 // exact divide method does not have an explicit digit
1732 // limit, we can add zeros too.
1733 if (preferredScale > quotientScale)
1734 return quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1735
1736 return quotient;
1737 }
1738 }
1739
1740 /**
1741 * Returns a {@code BigDecimal} whose value is {@code (this /
1742 * divisor)}, with rounding according to the context settings.
1743 *
1744 * @param divisor value by which this {@code BigDecimal} is to be divided.
1745 * @param mc the context to use.
1746 * @return {@code this / divisor}, rounded as necessary.
1747 * @throws ArithmeticException if the result is inexact but the
1748 * rounding mode is {@code UNNECESSARY} or
1749 * {@code mc.precision == 0} and the quotient has a
1750 * non-terminating decimal expansion.
1751 * @since 1.5
1752 */
1753 public BigDecimal divide(BigDecimal divisor, MathContext mc) {
1754 int mcp = mc.precision;
1755 if (mcp == 0)
1756 return divide(divisor);
1757
1758 BigDecimal dividend = this;
1759 long preferredScale = (long)dividend.scale - divisor.scale;
1760 // Now calculate the answer. We use the existing
1761 // divide-and-round method, but as this rounds to scale we have
1762 // to normalize the values here to achieve the desired result.
1763 // For x/y we first handle y=0 and x=0, and then normalize x and
1764 // y to give x' and y' with the following constraints:
1765 // (a) 0.1 <= x' < 1
1766 // (b) x' <= y' < 10*x'
1767 // Dividing x'/y' with the required scale set to mc.precision then
1768 // will give a result in the range 0.1 to 1 rounded to exactly
1769 // the right number of digits (except in the case of a result of
1770 // 1.000... which can arise when x=y, or when rounding overflows
1771 // The 1.000... case will reduce properly to 1.
1772 if (divisor.signum() == 0) { // x/0
1773 if (dividend.signum() == 0) // 0/0
1774 throw new ArithmeticException("Division undefined"); // NaN
1775 throw new ArithmeticException("Division by zero");
1776 }
1777 if (dividend.signum() == 0) // 0/y
1778 return zeroValueOf(saturateLong(preferredScale));
1779 int xscale = dividend.precision();
1780 int yscale = divisor.precision();
1781 if(dividend.intCompact!=INFLATED) {
1782 if(divisor.intCompact!=INFLATED) {
1783 return divide(dividend.intCompact, xscale, divisor.intCompact, yscale, preferredScale, mc);
1784 } else {
1785 return divide(dividend.intCompact, xscale, divisor.intVal, yscale, preferredScale, mc);
1786 }
1787 } else {
1788 if(divisor.intCompact!=INFLATED) {
1789 return divide(dividend.intVal, xscale, divisor.intCompact, yscale, preferredScale, mc);
1790 } else {
1791 return divide(dividend.intVal, xscale, divisor.intVal, yscale, preferredScale, mc);
1792 }
1793 }
1794 }
1795
1796 /**
1797 * Returns a {@code BigDecimal} whose value is the integer part
1798 * of the quotient {@code (this / divisor)} rounded down. The
1799 * preferred scale of the result is {@code (this.scale() -
1800 * divisor.scale())}.
1801 *
1802 * @param divisor value by which this {@code BigDecimal} is to be divided.
1803 * @return The integer part of {@code this / divisor}.
1804 * @throws ArithmeticException if {@code divisor==0}
1805 * @since 1.5
1806 */
1807 public BigDecimal divideToIntegralValue(BigDecimal divisor) {
1808 // Calculate preferred scale
1809 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1810 if (this.compareMagnitude(divisor) < 0) {
1811 // much faster when this << divisor
1812 return zeroValueOf(preferredScale);
1813 }
1814
1815 if (this.signum() == 0 && divisor.signum() != 0)
1816 return this.setScale(preferredScale, ROUND_UNNECESSARY);
1817
1818 // Perform a divide with enough digits to round to a correct
1819 // integer value; then remove any fractional digits
1820
1821 int maxDigits = (int)Math.min(this.precision() +
1822 (long)Math.ceil(10.0*divisor.precision()/3.0) +
1823 Math.abs((long)this.scale() - divisor.scale()) + 2,
1824 Integer.MAX_VALUE);
1825 BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits,
1826 RoundingMode.DOWN));
1827 if (quotient.scale > 0) {
1828 quotient = quotient.setScale(0, RoundingMode.DOWN);
1829 quotient = stripZerosToMatchScale(quotient.intVal, quotient.intCompact, quotient.scale, preferredScale);
1830 }
1831
1832 if (quotient.scale < preferredScale) {
1833 // pad with zeros if necessary
1834 quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1835 }
1836
1837 return quotient;
1838 }
1839
1840 /**
1841 * Returns a {@code BigDecimal} whose value is the integer part
1842 * of {@code (this / divisor)}. Since the integer part of the
1843 * exact quotient does not depend on the rounding mode, the
1844 * rounding mode does not affect the values returned by this
1845 * method. The preferred scale of the result is
1846 * {@code (this.scale() - divisor.scale())}. An
1847 * {@code ArithmeticException} is thrown if the integer part of
1848 * the exact quotient needs more than {@code mc.precision}
1849 * digits.
1850 *
1851 * @param divisor value by which this {@code BigDecimal} is to be divided.
1852 * @param mc the context to use.
1853 * @return The integer part of {@code this / divisor}.
1854 * @throws ArithmeticException if {@code divisor==0}
1855 * @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result
1856 * requires a precision of more than {@code mc.precision} digits.
1857 * @since 1.5
1858 * @author Joseph D. Darcy
1859 */
1860 public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) {
1861 if (mc.precision == 0 || // exact result
1862 (this.compareMagnitude(divisor) < 0)) // zero result
1863 return divideToIntegralValue(divisor);
1864
1865 // Calculate preferred scale
1866 int preferredScale = saturateLong((long)this.scale - divisor.scale);
1867
1868 /*
1869 * Perform a normal divide to mc.precision digits. If the
1870 * remainder has absolute value less than the divisor, the
1871 * integer portion of the quotient fits into mc.precision
1872 * digits. Next, remove any fractional digits from the
1873 * quotient and adjust the scale to the preferred value.
1874 */
1875 BigDecimal result = this.divide(divisor, new MathContext(mc.precision, RoundingMode.DOWN));
1876
1877 if (result.scale() < 0) {
1878 /*
1879 * Result is an integer. See if quotient represents the
1880 * full integer portion of the exact quotient; if it does,
1881 * the computed remainder will be less than the divisor.
1882 */
1883 BigDecimal product = result.multiply(divisor);
1884 // If the quotient is the full integer value,
1885 // |dividend-product| < |divisor|.
1886 if (this.subtract(product).compareMagnitude(divisor) >= 0) {
1887 throw new ArithmeticException("Division impossible");
1888 }
1889 } else if (result.scale() > 0) {
1890 /*
1891 * Integer portion of quotient will fit into precision
1892 * digits; recompute quotient to scale 0 to avoid double
1893 * rounding and then try to adjust, if necessary.
1894 */
1895 result = result.setScale(0, RoundingMode.DOWN);
1896 }
1897 // else result.scale() == 0;
1898
1899 int precisionDiff;
1900 if ((preferredScale > result.scale()) &&
1901 (precisionDiff = mc.precision - result.precision()) > 0) {
1902 return result.setScale(result.scale() +
1903 Math.min(precisionDiff, preferredScale - result.scale) );
1904 } else {
1905 return stripZerosToMatchScale(result.intVal,result.intCompact,result.scale,preferredScale);
1906 }
1907 }
1908
1909 /**
1910 * Returns a {@code BigDecimal} whose value is {@code (this % divisor)}.
1911 *
1912 * <p>The remainder is given by
1913 * {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}.
1914 * Note that this is <em>not</em> the modulo operation (the result can be
1915 * negative).
1916 *
1917 * @param divisor value by which this {@code BigDecimal} is to be divided.
1918 * @return {@code this % divisor}.
1919 * @throws ArithmeticException if {@code divisor==0}
1920 * @since 1.5
1921 */
1922 public BigDecimal remainder(BigDecimal divisor) {
1923 BigDecimal divrem[] = this.divideAndRemainder(divisor);
1924 return divrem[1];
1925 }
1926
1927
1928 /**
1929 * Returns a {@code BigDecimal} whose value is {@code (this %
1930 * divisor)}, with rounding according to the context settings.
1931 * The {@code MathContext} settings affect the implicit divide
1932 * used to compute the remainder. The remainder computation
1933 * itself is by definition exact. Therefore, the remainder may
1934 * contain more than {@code mc.getPrecision()} digits.
1935 *
1936 * <p>The remainder is given by
1937 * {@code this.subtract(this.divideToIntegralValue(divisor,
1938 * mc).multiply(divisor))}. Note that this is not the modulo
1939 * operation (the result can be negative).
1940 *
1941 * @param divisor value by which this {@code BigDecimal} is to be divided.
1942 * @param mc the context to use.
1943 * @return {@code this % divisor}, rounded as necessary.
1944 * @throws ArithmeticException if {@code divisor==0}
1945 * @throws ArithmeticException if the result is inexact but the
1946 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1947 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1948 * require a precision of more than {@code mc.precision} digits.
1949 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1950 * @since 1.5
1951 */
1952 public BigDecimal remainder(BigDecimal divisor, MathContext mc) {
1953 BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
1954 return divrem[1];
1955 }
1956
1957 /**
1958 * Returns a two-element {@code BigDecimal} array containing the
1959 * result of {@code divideToIntegralValue} followed by the result of
1960 * {@code remainder} on the two operands.
1961 *
1962 * <p>Note that if both the integer quotient and remainder are
1963 * needed, this method is faster than using the
1964 * {@code divideToIntegralValue} and {@code remainder} methods
1965 * separately because the division need only be carried out once.
1966 *
1967 * @param divisor value by which this {@code BigDecimal} is to be divided,
1968 * and the remainder computed.
1969 * @return a two element {@code BigDecimal} array: the quotient
1970 * (the result of {@code divideToIntegralValue}) is the initial element
1971 * and the remainder is the final element.
1972 * @throws ArithmeticException if {@code divisor==0}
1973 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1974 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1975 * @since 1.5
1976 */
1977 public BigDecimal[] divideAndRemainder(BigDecimal divisor) {
1978 // we use the identity x = i * y + r to determine r
1979 BigDecimal[] result = new BigDecimal[2];
1980
1981 result[0] = this.divideToIntegralValue(divisor);
1982 result[1] = this.subtract(result[0].multiply(divisor));
1983 return result;
1984 }
1985
1986 /**
1987 * Returns a two-element {@code BigDecimal} array containing the
1988 * result of {@code divideToIntegralValue} followed by the result of
1989 * {@code remainder} on the two operands calculated with rounding
1990 * according to the context settings.
1991 *
1992 * <p>Note that if both the integer quotient and remainder are
1993 * needed, this method is faster than using the
1994 * {@code divideToIntegralValue} and {@code remainder} methods
1995 * separately because the division need only be carried out once.
1996 *
1997 * @param divisor value by which this {@code BigDecimal} is to be divided,
1998 * and the remainder computed.
1999 * @param mc the context to use.
2000 * @return a two element {@code BigDecimal} array: the quotient
2001 * (the result of {@code divideToIntegralValue}) is the
2002 * initial element and the remainder is the final element.
2003 * @throws ArithmeticException if {@code divisor==0}
2004 * @throws ArithmeticException if the result is inexact but the
2005 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
2006 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
2007 * require a precision of more than {@code mc.precision} digits.
2008 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
2009 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
2010 * @since 1.5
2011 */
2012 public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) {
2013 if (mc.precision == 0)
2014 return divideAndRemainder(divisor);
2015
2016 BigDecimal[] result = new BigDecimal[2];
2017 BigDecimal lhs = this;
2018
2019 result[0] = lhs.divideToIntegralValue(divisor, mc);
2020 result[1] = lhs.subtract(result[0].multiply(divisor));
2021 return result;
2022 }
2023
2024 /**
2025 * Returns an approximation to the square root of {@code this}
2026 * with rounding according to the context settings.
2027 *
2028 * <p>The preferred scale of the returned result is equal to
2029 * {@code this.scale()/2}. The value of the returned result is
2030 * always within one ulp of the exact decimal value for the
2031 * precision in question. If the rounding mode is {@link
2032 * RoundingMode#HALF_UP HALF_UP}, {@link RoundingMode#HALF_DOWN
2033 * HALF_DOWN}, or {@link RoundingMode#HALF_EVEN HALF_EVEN}, the
2034 * result is within one half an ulp of the exact decimal value.
2035 *
2036 * <p>Special case:
2037 * <ul>
2038 * <li> The square root of a number numerically equal to {@code
2039 * ZERO} is numerically equal to {@code ZERO} with a preferred
2040 * scale according to the general rule above. In particular, for
2041 * {@code ZERO}, {@code ZERO.sqrt(mc).equals(ZERO)} is true with
2042 * any {@code MathContext} as an argument.
2043 * </ul>
2044 *
2045 * @param mc the context to use.
2046 * @return the square root of {@code this}.
2047 * @throws ArithmeticException if {@code this} is less than zero.
2048 * @throws ArithmeticException if an exact result is requested
2049 * ({@code mc.getPrecision()==0}) and there is no finite decimal
2050 * expansion of the exact result
2051 * @throws ArithmeticException if
2052 * {@code (mc.getRoundingMode()==RoundingMode.UNNECESSARY}) and
2053 * the exact result cannot fit in {@code mc.getPrecision()}
2054 * digits.
2055 * @see BigInteger#sqrt()
2056 * @since 9
2057 */
2058 public BigDecimal sqrt(MathContext mc) {
2059 int signum = signum();
2060 if (signum == 1) {
2061 /*
2062 * The following code draws on the algorithm presented in
2063 * "Properly Rounded Variable Precision Square Root," Hull and
2064 * Abrham, ACM Transactions on Mathematical Software, Vol 11,
2065 * No. 3, September 1985, Pages 229-237.
2066 *
2067 * The BigDecimal computational model differs from the one
2068 * presented in the paper in several ways: first BigDecimal
2069 * numbers aren't necessarily normalized, second many more
2070 * rounding modes are supported, including UNNECESSARY, and
2071 * exact results can be requested.
2072 *
2073 * The main steps of the algorithm below are as follows,
2074 * first argument reduce the value to the numerical range
2075 * [1, 10) using the following relations:
2076 *
2077 * x = y * 10 ^ exp
2078 * sqrt(x) = sqrt(y) * 10^(exp / 2) if exp is even
2079 * sqrt(x) = sqrt(y/10) * 10 ^((exp+1)/2) is exp is odd
2080 *
2081 * Then use Newton's iteration on the reduced value to compute
2082 * the numerical digits of the desired result.
2083 *
2084 * Finally, scale back to the desired exponent range and
2085 * perform any adjustment to get the preferred scale in the
2086 * representation.
2087 */
2088
2089 // The code below favors relative simplicity over checking
2090 // for special cases that could run faster.
2091
2092 int preferredScale = this.scale()/2;
2093 BigDecimal zeroWithFinalPreferredScale = valueOf(0L, preferredScale);
2094
2095 // First phase of numerical normalization, strip trailing
2096 // zeros and check for even powers of 10.
2097 BigDecimal stripped = this.stripTrailingZeros();
2098 int strippedScale = stripped.scale();
2099
2100 // Numerically sqrt(10^2N) = 10^N
2101 if (stripped.isPowerOfTen() &&
2102 strippedScale % 2 == 0) {
2103 BigDecimal result = valueOf(1L, strippedScale/2);
2104 if (result.scale() != preferredScale) {
2105 // Adjust to requested precision and preferred
2106 // scale as appropriate.
2107 result = result.add(zeroWithFinalPreferredScale, mc);
2108 }
2109 return result;
2110 }
2111
2112 // After stripTrailingZeros, the representation is normalized as
2113 //
2114 // unscaledValue * 10^(-scale)
2115 //
2116 // where unscaledValue is an integer with the mimimum
2117 // precision for the cohort of the numerical value. To
2118 // allow binary floating-point hardware to be used to get
2119 // approximately a 15 digit approximation to the square
2120 // root, it is helpful to instead normalize this so that
2121 // the significand portion is to right of the decimal
2122 // point by roughly (scale() - precision() +1).
2123
2124 // Now the precision / scale adjustment
2125 int scaleAdjust = 0;
2126 int scale = stripped.scale() - stripped.precision() + 1;
2127 if (scale % 2 == 0) {
2128 scaleAdjust = scale;
2129 } else {
2130 scaleAdjust = scale - 1;
2131 }
2132
2133 BigDecimal working = stripped.scaleByPowerOfTen(scaleAdjust);
2134
2135 assert // Verify 0.1 <= working < 10
2136 ONE_TENTH.compareTo(working) <= 0 && working.compareTo(TEN) < 0;
2137
2138 // Use good ole' Math.sqrt to get the initial guess for
2139 // the Newton iteration, good to at least 15 decimal
2140 // digits. This approach does incur the cost of a
2141 //
2142 // BigDecimal -> double -> BigDecimal
2143 //
2144 // conversion cycle, but it avoids the need for several
2145 // Newton iterations in BigDecimal arithmetic to get the
2146 // working answer to 15 digits of precision. If many fewer
2147 // than 15 digits were needed, it might be faster to do
2148 // the loop entirely in BigDecimal arithmetic.
2149 //
2150 // (A double value might have as much many as 17 decimal
2151 // digits of precision; it depends on the relative density
2152 // of binary and decimal numbers at different regions of
2153 // the number line.)
2154 //
2155 // (It would be possible to check for certain special
2156 // cases to avoid doing any Newton iterations. For
2157 // example, if the BigDecimal -> double conversion was
2158 // known to be exact and the rounding mode had a
2159 // low-enough precision, the post-Newton rounding logic
2160 // could be applied directly.)
2161
2162 BigDecimal guess = new BigDecimal(Math.sqrt(working.doubleValue()));
2163 int guessPrecision = 15;
2164 int originalPrecision = mc.getPrecision();
2165 int targetPrecision;
2166
2167 // If an exact value is requested, it must only need about
2168 // half of the input digits to represent since multiplying
2169 // an N digit number by itself yield a 2N-1 digit or 2N
2170 // digit result.
2171 if (originalPrecision == 0) {
2172 targetPrecision = stripped.precision()/2 + 1;
2173 } else {
2174 targetPrecision = originalPrecision;
2175 }
2176
2177 // When setting the precision to use inside the Newton
2178 // iteration loop, take care to avoid the case where the
2179 // precision of the input exceeds the requested precision
2180 // and rounding the input value too soon.
2181 BigDecimal approx = guess;
2182 int workingPrecision = working.precision();
2183 do {
2184 int tmpPrecision = Math.max(Math.max(guessPrecision, targetPrecision + 2),
2185 workingPrecision);
2186 MathContext mcTmp = new MathContext(tmpPrecision, RoundingMode.HALF_EVEN);
2187 // approx = 0.5 * (approx + fraction / approx)
2188 approx = ONE_HALF.multiply(approx.add(working.divide(approx, mcTmp), mcTmp));
2189 guessPrecision *= 2;
2190 } while (guessPrecision < targetPrecision + 2);
2191
2192 BigDecimal result;
2193 RoundingMode targetRm = mc.getRoundingMode();
2194 if (targetRm == RoundingMode.UNNECESSARY || originalPrecision == 0) {
2195 RoundingMode tmpRm =
2196 (targetRm == RoundingMode.UNNECESSARY) ? RoundingMode.DOWN : targetRm;
2197 MathContext mcTmp = new MathContext(targetPrecision, tmpRm);
2198 result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mcTmp);
2199
2200 // If result*result != this numerically, the square
2201 // root isn't exact
2202 if (this.subtract(result.multiply(result)).compareTo(ZERO) != 0) {
2203 throw new ArithmeticException("Computed square root not exact.");
2204 }
2205 } else {
2206 result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mc);
2207
2208 switch (targetRm) {
2209 case DOWN:
2210 case FLOOR:
2211 // Check if too big
2212 if (result.multiply(result).compareTo(this) > 0 ) {
2213 result = result.subtract(result.ulp());
2214 }
2215 break;
2216
2217 case UP:
2218 case CEILING:
2219 // Check if too small
2220 if (result.multiply(result).compareTo(this) < 0 ) {
2221 result = result.add(result.ulp());
2222 }
2223 break;
2224
2225 default:
2226 // Do nothing for half-way cases
2227 break;
2228 }
2229
2230 }
2231
2232 if (result.scale() != preferredScale) {
2233 // The preferred scale of an add is
2234 // max(addend.scale(), augend.scale()). Therefore, if
2235 // the scale of the result is first minimized using
2236 // stripTrailingZeros(), adding a zero of the
2237 // preferred scale rounding the correct precision will
2238 // perform the proper scale vs precision tradeoffs.
2239 result = result.stripTrailingZeros().
2240 add(zeroWithFinalPreferredScale,
2241 new MathContext(originalPrecision, RoundingMode.UNNECESSARY));
2242 }
2243 assert squareRootResultAssertions(result, mc);
2244 return result;
2245 } else {
2246 switch (signum) {
2247 case -1:
2248 throw new ArithmeticException("Attempted square root " +
2249 "of negative BigDecimal");
2250 case 0:
2251 return valueOf(0L, scale()/2);
2252
2253 default:
2254 throw new AssertionError("Bad value from signum");
2255 }
2256 }
2257 }
2258
2259 private boolean isPowerOfTen() {
2260 return BigInteger.ONE.equals(this.unscaledValue());
2261 }
2262
2263 /**
2264 * For nonzero values, check numerical correctness properties of
2265 * the computed result for the chosen rounding mode.
2266 *
2267 * For the directed roundings, for DOWN and FLOOR, result^2 must
2268 * be {@code <=} the input and (result+ulp)^2 must be {@code >} the
2269 * input. Conversely, for UP and CEIL, result^2 must be {@code >=} the
2270 * input and (result-ulp)^2 must be {@code <} the input.
2271 */
2272 private boolean squareRootResultAssertions(BigDecimal result, MathContext mc) {
2273 if (result.signum() == 0) {
2274 return squareRootZeroResultAssertions(result, mc);
2275 } else {
2276 RoundingMode rm = mc.getRoundingMode();
2277 BigDecimal ulp = result.ulp();
2278 BigDecimal neighborUp = result.add(ulp);
2279 // Make neighbor down accurate even for powers of ten
2280 if (this.isPowerOfTen()) {
2281 ulp = ulp.divide(TEN);
2282 }
2283 BigDecimal neighborDown = result.subtract(ulp);
2284
2285 // Both the starting value and result should be nonzero and positive.
2286 if (result.signum() != 1 ||
2287 this.signum() != 1) {
2288 return false;
2289 }
2290
2291 switch (rm) {
2292 case DOWN:
2293 case FLOOR:
2294 return
2295 result.multiply(result).compareTo(this) <= 0 &&
2296 neighborUp.multiply(neighborUp).compareTo(this) > 0;
2297
2298 case UP:
2299 case CEILING:
2300 return
2301 result.multiply(result).compareTo(this) >= 0 &&
2302 neighborDown.multiply(neighborDown).compareTo(this) < 0;
2303
2304 case HALF_DOWN:
2305 case HALF_EVEN:
2306 case HALF_UP:
2307 BigDecimal err = result.multiply(result).subtract(this).abs();
2308 BigDecimal errUp = neighborUp.multiply(neighborUp).subtract(this);
2309 BigDecimal errDown = this.subtract(neighborDown.multiply(neighborDown));
2310 // All error values should be positive so don't need to
2311 // compare absolute values.
2312
2313 int err_comp_errUp = err.compareTo(errUp);
2314 int err_comp_errDown = err.compareTo(errDown);
2315
2316 return
2317 errUp.signum() == 1 &&
2318 errDown.signum() == 1 &&
2319
2320 err_comp_errUp <= 0 &&
2321 err_comp_errDown <= 0 &&
2322
2323 ((err_comp_errUp == 0 ) ? err_comp_errDown < 0 : true) &&
2324 ((err_comp_errDown == 0 ) ? err_comp_errUp < 0 : true);
2325 // && could check for digit conditions for ties too
2326
2327 default: // Definition of UNNECESSARY already verified.
2328 return true;
2329 }
2330 }
2331 }
2332
2333 private boolean squareRootZeroResultAssertions(BigDecimal result, MathContext mc) {
2334 return this.compareTo(ZERO) == 0;
2335 }
2336
2337 /**
2338 * Returns a {@code BigDecimal} whose value is
2339 * <code>(this<sup>n</sup>)</code>, The power is computed exactly, to
2340 * unlimited precision.
2341 *
2342 * <p>The parameter {@code n} must be in the range 0 through
2343 * 999999999, inclusive. {@code ZERO.pow(0)} returns {@link
2344 * #ONE}.
2345 *
2346 * Note that future releases may expand the allowable exponent
2347 * range of this method.
2348 *
2349 * @param n power to raise this {@code BigDecimal} to.
2350 * @return <code>this<sup>n</sup></code>
2351 * @throws ArithmeticException if {@code n} is out of range.
2352 * @since 1.5
2353 */
2354 public BigDecimal pow(int n) {
2355 if (n < 0 || n > 999999999)
2356 throw new ArithmeticException("Invalid operation");
2357 // No need to calculate pow(n) if result will over/underflow.
2358 // Don't attempt to support "supernormal" numbers.
2359 int newScale = checkScale((long)scale * n);
2360 return new BigDecimal(this.inflated().pow(n), newScale);
2361 }
2362
2363
2364 /**
2365 * Returns a {@code BigDecimal} whose value is
2366 * <code>(this<sup>n</sup>)</code>. The current implementation uses
2367 * the core algorithm defined in ANSI standard X3.274-1996 with
2368 * rounding according to the context settings. In general, the
2369 * returned numerical value is within two ulps of the exact
2370 * numerical value for the chosen precision. Note that future
2371 * releases may use a different algorithm with a decreased
2372 * allowable error bound and increased allowable exponent range.
2373 *
2374 * <p>The X3.274-1996 algorithm is:
2375 *
2376 * <ul>
2377 * <li> An {@code ArithmeticException} exception is thrown if
2378 * <ul>
2379 * <li>{@code abs(n) > 999999999}
2380 * <li>{@code mc.precision == 0} and {@code n < 0}
2381 * <li>{@code mc.precision > 0} and {@code n} has more than
2382 * {@code mc.precision} decimal digits
2383 * </ul>
2384 *
2385 * <li> if {@code n} is zero, {@link #ONE} is returned even if
2386 * {@code this} is zero, otherwise
2387 * <ul>
2388 * <li> if {@code n} is positive, the result is calculated via
2389 * the repeated squaring technique into a single accumulator.
2390 * The individual multiplications with the accumulator use the
2391 * same math context settings as in {@code mc} except for a
2392 * precision increased to {@code mc.precision + elength + 1}
2393 * where {@code elength} is the number of decimal digits in
2394 * {@code n}.
2395 *
2396 * <li> if {@code n} is negative, the result is calculated as if
2397 * {@code n} were positive; this value is then divided into one
2398 * using the working precision specified above.
2399 *
2400 * <li> The final value from either the positive or negative case
2401 * is then rounded to the destination precision.
2402 * </ul>
2403 * </ul>
2404 *
2405 * @param n power to raise this {@code BigDecimal} to.
2406 * @param mc the context to use.
2407 * @return <code>this<sup>n</sup></code> using the ANSI standard X3.274-1996
2408 * algorithm
2409 * @throws ArithmeticException if the result is inexact but the
2410 * rounding mode is {@code UNNECESSARY}, or {@code n} is out
2411 * of range.
2412 * @since 1.5
2413 */
2414 public BigDecimal pow(int n, MathContext mc) {
2415 if (mc.precision == 0)
2416 return pow(n);
2417 if (n < -999999999 || n > 999999999)
2418 throw new ArithmeticException("Invalid operation");
2419 if (n == 0)
2420 return ONE; // x**0 == 1 in X3.274
2421 BigDecimal lhs = this;
2422 MathContext workmc = mc; // working settings
2423 int mag = Math.abs(n); // magnitude of n
2424 if (mc.precision > 0) {
2425 int elength = longDigitLength(mag); // length of n in digits
2426 if (elength > mc.precision) // X3.274 rule
2427 throw new ArithmeticException("Invalid operation");
2428 workmc = new MathContext(mc.precision + elength + 1,
2429 mc.roundingMode);
2430 }
2431 // ready to carry out power calculation...
2432 BigDecimal acc = ONE; // accumulator
2433 boolean seenbit = false; // set once we've seen a 1-bit
2434 for (int i=1;;i++) { // for each bit [top bit ignored]
2435 mag += mag; // shift left 1 bit
2436 if (mag < 0) { // top bit is set
2437 seenbit = true; // OK, we're off
2438 acc = acc.multiply(lhs, workmc); // acc=acc*x
2439 }
2440 if (i == 31)
2441 break; // that was the last bit
2442 if (seenbit)
2443 acc=acc.multiply(acc, workmc); // acc=acc*acc [square]
2444 // else (!seenbit) no point in squaring ONE
2445 }
2446 // if negative n, calculate the reciprocal using working precision
2447 if (n < 0) // [hence mc.precision>0]
2448 acc=ONE.divide(acc, workmc);
2449 // round to final precision and strip zeros
2450 return doRound(acc, mc);
2451 }
2452
2453 /**
2454 * Returns a {@code BigDecimal} whose value is the absolute value
2455 * of this {@code BigDecimal}, and whose scale is
2456 * {@code this.scale()}.
2457 *
2458 * @return {@code abs(this)}
2459 */
2460 public BigDecimal abs() {
2461 return (signum() < 0 ? negate() : this);
2462 }
2463
2464 /**
2465 * Returns a {@code BigDecimal} whose value is the absolute value
2466 * of this {@code BigDecimal}, with rounding according to the
2467 * context settings.
2468 *
2469 * @param mc the context to use.
2470 * @return {@code abs(this)}, rounded as necessary.
2471 * @throws ArithmeticException if the result is inexact but the
2472 * rounding mode is {@code UNNECESSARY}.
2473 * @since 1.5
2474 */
2475 public BigDecimal abs(MathContext mc) {
2476 return (signum() < 0 ? negate(mc) : plus(mc));
2477 }
2478
2479 /**
2480 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2481 * and whose scale is {@code this.scale()}.
2482 *
2483 * @return {@code -this}.
2484 */
2485 public BigDecimal negate() {
2486 if (intCompact == INFLATED) {
2487 return new BigDecimal(intVal.negate(), INFLATED, scale, precision);
2488 } else {
2489 return valueOf(-intCompact, scale, precision);
2490 }
2491 }
2492
2493 /**
2494 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2495 * with rounding according to the context settings.
2496 *
2497 * @param mc the context to use.
2498 * @return {@code -this}, rounded as necessary.
2499 * @throws ArithmeticException if the result is inexact but the
2500 * rounding mode is {@code UNNECESSARY}.
2501 * @since 1.5
2502 */
2503 public BigDecimal negate(MathContext mc) {
2504 return negate().plus(mc);
2505 }
2506
2507 /**
2508 * Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose
2509 * scale is {@code this.scale()}.
2510 *
2511 * <p>This method, which simply returns this {@code BigDecimal}
2512 * is included for symmetry with the unary minus method {@link
2513 * #negate()}.
2514 *
2515 * @return {@code this}.
2516 * @see #negate()
2517 * @since 1.5
2518 */
2519 public BigDecimal plus() {
2520 return this;
2521 }
2522
2523 /**
2524 * Returns a {@code BigDecimal} whose value is {@code (+this)},
2525 * with rounding according to the context settings.
2526 *
2527 * <p>The effect of this method is identical to that of the {@link
2528 * #round(MathContext)} method.
2529 *
2530 * @param mc the context to use.
2531 * @return {@code this}, rounded as necessary. A zero result will
2532 * have a scale of 0.
2533 * @throws ArithmeticException if the result is inexact but the
2534 * rounding mode is {@code UNNECESSARY}.
2535 * @see #round(MathContext)
2536 * @since 1.5
2537 */
2538 public BigDecimal plus(MathContext mc) {
2539 if (mc.precision == 0) // no rounding please
2540 return this;
2541 return doRound(this, mc);
2542 }
2543
2544 /**
2545 * Returns the signum function of this {@code BigDecimal}.
2546 *
2547 * @return -1, 0, or 1 as the value of this {@code BigDecimal}
2548 * is negative, zero, or positive.
2549 */
2550 public int signum() {
2551 return (intCompact != INFLATED)?
2552 Long.signum(intCompact):
2553 intVal.signum();
2554 }
2555
2556 /**
2557 * Returns the <i>scale</i> of this {@code BigDecimal}. If zero
2558 * or positive, the scale is the number of digits to the right of
2559 * the decimal point. If negative, the unscaled value of the
2560 * number is multiplied by ten to the power of the negation of the
2561 * scale. For example, a scale of {@code -3} means the unscaled
2562 * value is multiplied by 1000.
2563 *
2564 * @return the scale of this {@code BigDecimal}.
2565 */
2566 public int scale() {
2567 return scale;
2568 }
2569
2570 /**
2571 * Returns the <i>precision</i> of this {@code BigDecimal}. (The
2572 * precision is the number of digits in the unscaled value.)
2573 *
2574 * <p>The precision of a zero value is 1.
2575 *
2576 * @return the precision of this {@code BigDecimal}.
2577 * @since 1.5
2578 */
2579 public int precision() {
2580 int result = precision;
2581 if (result == 0) {
2582 long s = intCompact;
2583 if (s != INFLATED)
2584 result = longDigitLength(s);
2585 else
2586 result = bigDigitLength(intVal);
2587 precision = result;
2588 }
2589 return result;
2590 }
2591
2592
2593 /**
2594 * Returns a {@code BigInteger} whose value is the <i>unscaled
2595 * value</i> of this {@code BigDecimal}. (Computes <code>(this *
2596 * 10<sup>this.scale()</sup>)</code>.)
2597 *
2598 * @return the unscaled value of this {@code BigDecimal}.
2599 * @since 1.2
2600 */
2601 public BigInteger unscaledValue() {
2602 return this.inflated();
2603 }
2604
2605 // Rounding Modes
2606
2607 /**
2608 * Rounding mode to round away from zero. Always increments the
2609 * digit prior to a nonzero discarded fraction. Note that this rounding
2610 * mode never decreases the magnitude of the calculated value.
2611 *
2612 * @deprecated Use {@link RoundingMode#UP} instead.
2613 */
2614 @Deprecated(since="9")
2615 public static final int ROUND_UP = 0;
2616
2617 /**
2618 * Rounding mode to round towards zero. Never increments the digit
2619 * prior to a discarded fraction (i.e., truncates). Note that this
2620 * rounding mode never increases the magnitude of the calculated value.
2621 *
2622 * @deprecated Use {@link RoundingMode#DOWN} instead.
2623 */
2624 @Deprecated(since="9")
2625 public static final int ROUND_DOWN = 1;
2626
2627 /**
2628 * Rounding mode to round towards positive infinity. If the
2629 * {@code BigDecimal} is positive, behaves as for
2630 * {@code ROUND_UP}; if negative, behaves as for
2631 * {@code ROUND_DOWN}. Note that this rounding mode never
2632 * decreases the calculated value.
2633 *
2634 * @deprecated Use {@link RoundingMode#CEILING} instead.
2635 */
2636 @Deprecated(since="9")
2637 public static final int ROUND_CEILING = 2;
2638
2639 /**
2640 * Rounding mode to round towards negative infinity. If the
2641 * {@code BigDecimal} is positive, behave as for
2642 * {@code ROUND_DOWN}; if negative, behave as for
2643 * {@code ROUND_UP}. Note that this rounding mode never
2644 * increases the calculated value.
2645 *
2646 * @deprecated Use {@link RoundingMode#FLOOR} instead.
2647 */
2648 @Deprecated(since="9")
2649 public static final int ROUND_FLOOR = 3;
2650
2651 /**
2652 * Rounding mode to round towards {@literal "nearest neighbor"}
2653 * unless both neighbors are equidistant, in which case round up.
2654 * Behaves as for {@code ROUND_UP} if the discarded fraction is
2655 * ≥ 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note
2656 * that this is the rounding mode that most of us were taught in
2657 * grade school.
2658 *
2659 * @deprecated Use {@link RoundingMode#HALF_UP} instead.
2660 */
2661 @Deprecated(since="9")
2662 public static final int ROUND_HALF_UP = 4;
2663
2664 /**
2665 * Rounding mode to round towards {@literal "nearest neighbor"}
2666 * unless both neighbors are equidistant, in which case round
2667 * down. Behaves as for {@code ROUND_UP} if the discarded
2668 * fraction is {@literal >} 0.5; otherwise, behaves as for
2669 * {@code ROUND_DOWN}.
2670 *
2671 * @deprecated Use {@link RoundingMode#HALF_DOWN} instead.
2672 */
2673 @Deprecated(since="9")
2674 public static final int ROUND_HALF_DOWN = 5;
2675
2676 /**
2677 * Rounding mode to round towards the {@literal "nearest neighbor"}
2678 * unless both neighbors are equidistant, in which case, round
2679 * towards the even neighbor. Behaves as for
2680 * {@code ROUND_HALF_UP} if the digit to the left of the
2681 * discarded fraction is odd; behaves as for
2682 * {@code ROUND_HALF_DOWN} if it's even. Note that this is the
2683 * rounding mode that minimizes cumulative error when applied
2684 * repeatedly over a sequence of calculations.
2685 *
2686 * @deprecated Use {@link RoundingMode#HALF_EVEN} instead.
2687 */
2688 @Deprecated(since="9")
2689 public static final int ROUND_HALF_EVEN = 6;
2690
2691 /**
2692 * Rounding mode to assert that the requested operation has an exact
2693 * result, hence no rounding is necessary. If this rounding mode is
2694 * specified on an operation that yields an inexact result, an
2695 * {@code ArithmeticException} is thrown.
2696 *
2697 * @deprecated Use {@link RoundingMode#UNNECESSARY} instead.
2698 */
2699 @Deprecated(since="9")
2700 public static final int ROUND_UNNECESSARY = 7;
2701
2702
2703 // Scaling/Rounding Operations
2704
2705 /**
2706 * Returns a {@code BigDecimal} rounded according to the
2707 * {@code MathContext} settings. If the precision setting is 0 then
2708 * no rounding takes place.
2709 *
2710 * <p>The effect of this method is identical to that of the
2711 * {@link #plus(MathContext)} method.
2712 *
2713 * @param mc the context to use.
2714 * @return a {@code BigDecimal} rounded according to the
2715 * {@code MathContext} settings.
2716 * @throws ArithmeticException if the rounding mode is
2717 * {@code UNNECESSARY} and the
2718 * {@code BigDecimal} operation would require rounding.
2719 * @see #plus(MathContext)
2720 * @since 1.5
2721 */
2722 public BigDecimal round(MathContext mc) {
2723 return plus(mc);
2724 }
2725
2726 /**
2727 * Returns a {@code BigDecimal} whose scale is the specified
2728 * value, and whose unscaled value is determined by multiplying or
2729 * dividing this {@code BigDecimal}'s unscaled value by the
2730 * appropriate power of ten to maintain its overall value. If the
2731 * scale is reduced by the operation, the unscaled value must be
2732 * divided (rather than multiplied), and the value may be changed;
2733 * in this case, the specified rounding mode is applied to the
2734 * division.
2735 *
2736 * @apiNote Since BigDecimal objects are immutable, calls of
2737 * this method do <em>not</em> result in the original object being
2738 * modified, contrary to the usual convention of having methods
2739 * named <code>set<i>X</i></code> mutate field <i>{@code X}</i>.
2740 * Instead, {@code setScale} returns an object with the proper
2741 * scale; the returned object may or may not be newly allocated.
2742 *
2743 * @param newScale scale of the {@code BigDecimal} value to be returned.
2744 * @param roundingMode The rounding mode to apply.
2745 * @return a {@code BigDecimal} whose scale is the specified value,
2746 * and whose unscaled value is determined by multiplying or
2747 * dividing this {@code BigDecimal}'s unscaled value by the
2748 * appropriate power of ten to maintain its overall value.
2749 * @throws ArithmeticException if {@code roundingMode==UNNECESSARY}
2750 * and the specified scaling operation would require
2751 * rounding.
2752 * @see RoundingMode
2753 * @since 1.5
2754 */
2755 public BigDecimal setScale(int newScale, RoundingMode roundingMode) {
2756 return setScale(newScale, roundingMode.oldMode);
2757 }
2758
2759 /**
2760 * Returns a {@code BigDecimal} whose scale is the specified
2761 * value, and whose unscaled value is determined by multiplying or
2762 * dividing this {@code BigDecimal}'s unscaled value by the
2763 * appropriate power of ten to maintain its overall value. If the
2764 * scale is reduced by the operation, the unscaled value must be
2765 * divided (rather than multiplied), and the value may be changed;
2766 * in this case, the specified rounding mode is applied to the
2767 * division.
2768 *
2769 * @apiNote Since BigDecimal objects are immutable, calls of
2770 * this method do <em>not</em> result in the original object being
2771 * modified, contrary to the usual convention of having methods
2772 * named <code>set<i>X</i></code> mutate field <i>{@code X}</i>.
2773 * Instead, {@code setScale} returns an object with the proper
2774 * scale; the returned object may or may not be newly allocated.
2775 *
2776 * @deprecated The method {@link #setScale(int, RoundingMode)} should
2777 * be used in preference to this legacy method.
2778 *
2779 * @param newScale scale of the {@code BigDecimal} value to be returned.
2780 * @param roundingMode The rounding mode to apply.
2781 * @return a {@code BigDecimal} whose scale is the specified value,
2782 * and whose unscaled value is determined by multiplying or
2783 * dividing this {@code BigDecimal}'s unscaled value by the
2784 * appropriate power of ten to maintain its overall value.
2785 * @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY}
2786 * and the specified scaling operation would require
2787 * rounding.
2788 * @throws IllegalArgumentException if {@code roundingMode} does not
2789 * represent a valid rounding mode.
2790 * @see #ROUND_UP
2791 * @see #ROUND_DOWN
2792 * @see #ROUND_CEILING
2793 * @see #ROUND_FLOOR
2794 * @see #ROUND_HALF_UP
2795 * @see #ROUND_HALF_DOWN
2796 * @see #ROUND_HALF_EVEN
2797 * @see #ROUND_UNNECESSARY
2798 */
2799 @Deprecated(since="9")
2800 public BigDecimal setScale(int newScale, int roundingMode) {
2801 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
2802 throw new IllegalArgumentException("Invalid rounding mode");
2803
2804 int oldScale = this.scale;
2805 if (newScale == oldScale) // easy case
2806 return this;
2807 if (this.signum() == 0) // zero can have any scale
2808 return zeroValueOf(newScale);
2809 if(this.intCompact!=INFLATED) {
2810 long rs = this.intCompact;
2811 if (newScale > oldScale) {
2812 int raise = checkScale((long) newScale - oldScale);
2813 if ((rs = longMultiplyPowerTen(rs, raise)) != INFLATED) {
2814 return valueOf(rs,newScale);
2815 }
2816 BigInteger rb = bigMultiplyPowerTen(raise);
2817 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2818 } else {
2819 // newScale < oldScale -- drop some digits
2820 // Can't predict the precision due to the effect of rounding.
2821 int drop = checkScale((long) oldScale - newScale);
2822 if (drop < LONG_TEN_POWERS_TABLE.length) {
2823 return divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, newScale);
2824 } else {
2825 return divideAndRound(this.inflated(), bigTenToThe(drop), newScale, roundingMode, newScale);
2826 }
2827 }
2828 } else {
2829 if (newScale > oldScale) {
2830 int raise = checkScale((long) newScale - oldScale);
2831 BigInteger rb = bigMultiplyPowerTen(this.intVal,raise);
2832 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2833 } else {
2834 // newScale < oldScale -- drop some digits
2835 // Can't predict the precision due to the effect of rounding.
2836 int drop = checkScale((long) oldScale - newScale);
2837 if (drop < LONG_TEN_POWERS_TABLE.length)
2838 return divideAndRound(this.intVal, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode,
2839 newScale);
2840 else
2841 return divideAndRound(this.intVal, bigTenToThe(drop), newScale, roundingMode, newScale);
2842 }
2843 }
2844 }
2845
2846 /**
2847 * Returns a {@code BigDecimal} whose scale is the specified
2848 * value, and whose value is numerically equal to this
2849 * {@code BigDecimal}'s. Throws an {@code ArithmeticException}
2850 * if this is not possible.
2851 *
2852 * <p>This call is typically used to increase the scale, in which
2853 * case it is guaranteed that there exists a {@code BigDecimal}
2854 * of the specified scale and the correct value. The call can
2855 * also be used to reduce the scale if the caller knows that the
2856 * {@code BigDecimal} has sufficiently many zeros at the end of
2857 * its fractional part (i.e., factors of ten in its integer value)
2858 * to allow for the rescaling without changing its value.
2859 *
2860 * <p>This method returns the same result as the two-argument
2861 * versions of {@code setScale}, but saves the caller the trouble
2862 * of specifying a rounding mode in cases where it is irrelevant.
2863 *
2864 * @apiNote Since {@code BigDecimal} objects are immutable,
2865 * calls of this method do <em>not</em> result in the original
2866 * object being modified, contrary to the usual convention of
2867 * having methods named <code>set<i>X</i></code> mutate field
2868 * <i>{@code X}</i>. Instead, {@code setScale} returns an
2869 * object with the proper scale; the returned object may or may
2870 * not be newly allocated.
2871 *
2872 * @param newScale scale of the {@code BigDecimal} value to be returned.
2873 * @return a {@code BigDecimal} whose scale is the specified value, and
2874 * whose unscaled value is determined by multiplying or dividing
2875 * this {@code BigDecimal}'s unscaled value by the appropriate
2876 * power of ten to maintain its overall value.
2877 * @throws ArithmeticException if the specified scaling operation would
2878 * require rounding.
2879 * @see #setScale(int, int)
2880 * @see #setScale(int, RoundingMode)
2881 */
2882 public BigDecimal setScale(int newScale) {
2883 return setScale(newScale, ROUND_UNNECESSARY);
2884 }
2885
2886 // Decimal Point Motion Operations
2887
2888 /**
2889 * Returns a {@code BigDecimal} which is equivalent to this one
2890 * with the decimal point moved {@code n} places to the left. If
2891 * {@code n} is non-negative, the call merely adds {@code n} to
2892 * the scale. If {@code n} is negative, the call is equivalent
2893 * to {@code movePointRight(-n)}. The {@code BigDecimal}
2894 * returned by this call has value <code>(this ×
2895 * 10<sup>-n</sup>)</code> and scale {@code max(this.scale()+n,
2896 * 0)}.
2897 *
2898 * @param n number of places to move the decimal point to the left.
2899 * @return a {@code BigDecimal} which is equivalent to this one with the
2900 * decimal point moved {@code n} places to the left.
2901 * @throws ArithmeticException if scale overflows.
2902 */
2903 public BigDecimal movePointLeft(int n) {
2904 if (n == 0) return this;
2905
2906 // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE
2907 int newScale = checkScale((long)scale + n);
2908 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2909 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2910 }
2911
2912 /**
2913 * Returns a {@code BigDecimal} which is equivalent to this one
2914 * with the decimal point moved {@code n} places to the right.
2915 * If {@code n} is non-negative, the call merely subtracts
2916 * {@code n} from the scale. If {@code n} is negative, the call
2917 * is equivalent to {@code movePointLeft(-n)}. The
2918 * {@code BigDecimal} returned by this call has value <code>(this
2919 * × 10<sup>n</sup>)</code> and scale {@code max(this.scale()-n,
2920 * 0)}.
2921 *
2922 * @param n number of places to move the decimal point to the right.
2923 * @return a {@code BigDecimal} which is equivalent to this one
2924 * with the decimal point moved {@code n} places to the right.
2925 * @throws ArithmeticException if scale overflows.
2926 */
2927 public BigDecimal movePointRight(int n) {
2928 if (n == 0) return this;
2929
2930 // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE
2931 int newScale = checkScale((long)scale - n);
2932 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2933 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2934 }
2935
2936 /**
2937 * Returns a BigDecimal whose numerical value is equal to
2938 * ({@code this} * 10<sup>n</sup>). The scale of
2939 * the result is {@code (this.scale() - n)}.
2940 *
2941 * @param n the exponent power of ten to scale by
2942 * @return a BigDecimal whose numerical value is equal to
2943 * ({@code this} * 10<sup>n</sup>)
2944 * @throws ArithmeticException if the scale would be
2945 * outside the range of a 32-bit integer.
2946 *
2947 * @since 1.5
2948 */
2949 public BigDecimal scaleByPowerOfTen(int n) {
2950 return new BigDecimal(intVal, intCompact,
2951 checkScale((long)scale - n), precision);
2952 }
2953
2954 /**
2955 * Returns a {@code BigDecimal} which is numerically equal to
2956 * this one but with any trailing zeros removed from the
2957 * representation. For example, stripping the trailing zeros from
2958 * the {@code BigDecimal} value {@code 600.0}, which has
2959 * [{@code BigInteger}, {@code scale}] components equals to
2960 * [6000, 1], yields {@code 6E2} with [{@code BigInteger},
2961 * {@code scale}] components equals to [6, -2]. If
2962 * this BigDecimal is numerically equal to zero, then
2963 * {@code BigDecimal.ZERO} is returned.
2964 *
2965 * @return a numerically equal {@code BigDecimal} with any
2966 * trailing zeros removed.
2967 * @since 1.5
2968 */
2969 public BigDecimal stripTrailingZeros() {
2970 if (intCompact == 0 || (intVal != null && intVal.signum() == 0)) {
2971 return BigDecimal.ZERO;
2972 } else if (intCompact != INFLATED) {
2973 return createAndStripZerosToMatchScale(intCompact, scale, Long.MIN_VALUE);
2974 } else {
2975 return createAndStripZerosToMatchScale(intVal, scale, Long.MIN_VALUE);
2976 }
2977 }
2978
2979 // Comparison Operations
2980
2981 /**
2982 * Compares this {@code BigDecimal} with the specified
2983 * {@code BigDecimal}. Two {@code BigDecimal} objects that are
2984 * equal in value but have a different scale (like 2.0 and 2.00)
2985 * are considered equal by this method. This method is provided
2986 * in preference to individual methods for each of the six boolean
2987 * comparison operators ({@literal <}, ==,
2988 * {@literal >}, {@literal >=}, !=, {@literal <=}). The
2989 * suggested idiom for performing these comparisons is:
2990 * {@code (x.compareTo(y)} <<i>op</i>> {@code 0)}, where
2991 * <<i>op</i>> is one of the six comparison operators.
2992 *
2993 * @param val {@code BigDecimal} to which this {@code BigDecimal} is
2994 * to be compared.
2995 * @return -1, 0, or 1 as this {@code BigDecimal} is numerically
2996 * less than, equal to, or greater than {@code val}.
2997 */
2998 @Override
2999 public int compareTo(BigDecimal val) {
3000 // Quick path for equal scale and non-inflated case.
3001 if (scale == val.scale) {
3002 long xs = intCompact;
3003 long ys = val.intCompact;
3004 if (xs != INFLATED && ys != INFLATED)
3005 return xs != ys ? ((xs > ys) ? 1 : -1) : 0;
3006 }
3007 int xsign = this.signum();
3008 int ysign = val.signum();
3009 if (xsign != ysign)
3010 return (xsign > ysign) ? 1 : -1;
3011 if (xsign == 0)
3012 return 0;
3013 int cmp = compareMagnitude(val);
3014 return (xsign > 0) ? cmp : -cmp;
3015 }
3016
3017 /**
3018 * Version of compareTo that ignores sign.
3019 */
3020 private int compareMagnitude(BigDecimal val) {
3021 // Match scales, avoid unnecessary inflation
3022 long ys = val.intCompact;
3023 long xs = this.intCompact;
3024 if (xs == 0)
3025 return (ys == 0) ? 0 : -1;
3026 if (ys == 0)
3027 return 1;
3028
3029 long sdiff = (long)this.scale - val.scale;
3030 if (sdiff != 0) {
3031 // Avoid matching scales if the (adjusted) exponents differ
3032 long xae = (long)this.precision() - this.scale; // [-1]
3033 long yae = (long)val.precision() - val.scale; // [-1]
3034 if (xae < yae)
3035 return -1;
3036 if (xae > yae)
3037 return 1;
3038 if (sdiff < 0) {
3039 // The cases sdiff <= Integer.MIN_VALUE intentionally fall through.
3040 if ( sdiff > Integer.MIN_VALUE &&
3041 (xs == INFLATED ||
3042 (xs = longMultiplyPowerTen(xs, (int)-sdiff)) == INFLATED) &&
3043 ys == INFLATED) {
3044 BigInteger rb = bigMultiplyPowerTen((int)-sdiff);
3045 return rb.compareMagnitude(val.intVal);
3046 }
3047 } else { // sdiff > 0
3048 // The cases sdiff > Integer.MAX_VALUE intentionally fall through.
3049 if ( sdiff <= Integer.MAX_VALUE &&
3050 (ys == INFLATED ||
3051 (ys = longMultiplyPowerTen(ys, (int)sdiff)) == INFLATED) &&
3052 xs == INFLATED) {
3053 BigInteger rb = val.bigMultiplyPowerTen((int)sdiff);
3054 return this.intVal.compareMagnitude(rb);
3055 }
3056 }
3057 }
3058 if (xs != INFLATED)
3059 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
3060 else if (ys != INFLATED)
3061 return 1;
3062 else
3063 return this.intVal.compareMagnitude(val.intVal);
3064 }
3065
3066 /**
3067 * Compares this {@code BigDecimal} with the specified
3068 * {@code Object} for equality. Unlike {@link
3069 * #compareTo(BigDecimal) compareTo}, this method considers two
3070 * {@code BigDecimal} objects equal only if they are equal in
3071 * value and scale (thus 2.0 is not equal to 2.00 when compared by
3072 * this method).
3073 *
3074 * @param x {@code Object} to which this {@code BigDecimal} is
3075 * to be compared.
3076 * @return {@code true} if and only if the specified {@code Object} is a
3077 * {@code BigDecimal} whose value and scale are equal to this
3078 * {@code BigDecimal}'s.
3079 * @see #compareTo(java.math.BigDecimal)
3080 * @see #hashCode
3081 */
3082 @Override
3083 public boolean equals(Object x) {
3084 if (!(x instanceof BigDecimal))
3085 return false;
3086 BigDecimal xDec = (BigDecimal) x;
3087 if (x == this)
3088 return true;
3089 if (scale != xDec.scale)
3090 return false;
3091 long s = this.intCompact;
3092 long xs = xDec.intCompact;
3093 if (s != INFLATED) {
3094 if (xs == INFLATED)
3095 xs = compactValFor(xDec.intVal);
3096 return xs == s;
3097 } else if (xs != INFLATED)
3098 return xs == compactValFor(this.intVal);
3099
3100 return this.inflated().equals(xDec.inflated());
3101 }
3102
3103 /**
3104 * Returns the minimum of this {@code BigDecimal} and
3105 * {@code val}.
3106 *
3107 * @param val value with which the minimum is to be computed.
3108 * @return the {@code BigDecimal} whose value is the lesser of this
3109 * {@code BigDecimal} and {@code val}. If they are equal,
3110 * as defined by the {@link #compareTo(BigDecimal) compareTo}
3111 * method, {@code this} is returned.
3112 * @see #compareTo(java.math.BigDecimal)
3113 */
3114 public BigDecimal min(BigDecimal val) {
3115 return (compareTo(val) <= 0 ? this : val);
3116 }
3117
3118 /**
3119 * Returns the maximum of this {@code BigDecimal} and {@code val}.
3120 *
3121 * @param val value with which the maximum is to be computed.
3122 * @return the {@code BigDecimal} whose value is the greater of this
3123 * {@code BigDecimal} and {@code val}. If they are equal,
3124 * as defined by the {@link #compareTo(BigDecimal) compareTo}
3125 * method, {@code this} is returned.
3126 * @see #compareTo(java.math.BigDecimal)
3127 */
3128 public BigDecimal max(BigDecimal val) {
3129 return (compareTo(val) >= 0 ? this : val);
3130 }
3131
3132 // Hash Function
3133
3134 /**
3135 * Returns the hash code for this {@code BigDecimal}. Note that
3136 * two {@code BigDecimal} objects that are numerically equal but
3137 * differ in scale (like 2.0 and 2.00) will generally <em>not</em>
3138 * have the same hash code.
3139 *
3140 * @return hash code for this {@code BigDecimal}.
3141 * @see #equals(Object)
3142 */
3143 @Override
3144 public int hashCode() {
3145 if (intCompact != INFLATED) {
3146 long val2 = (intCompact < 0)? -intCompact : intCompact;
3147 int temp = (int)( ((int)(val2 >>> 32)) * 31 +
3148 (val2 & LONG_MASK));
3149 return 31*((intCompact < 0) ?-temp:temp) + scale;
3150 } else
3151 return 31*intVal.hashCode() + scale;
3152 }
3153
3154 // Format Converters
3155
3156 /**
3157 * Returns the string representation of this {@code BigDecimal},
3158 * using scientific notation if an exponent is needed.
3159 *
3160 * <p>A standard canonical string form of the {@code BigDecimal}
3161 * is created as though by the following steps: first, the
3162 * absolute value of the unscaled value of the {@code BigDecimal}
3163 * is converted to a string in base ten using the characters
3164 * {@code '0'} through {@code '9'} with no leading zeros (except
3165 * if its value is zero, in which case a single {@code '0'}
3166 * character is used).
3167 *
3168 * <p>Next, an <i>adjusted exponent</i> is calculated; this is the
3169 * negated scale, plus the number of characters in the converted
3170 * unscaled value, less one. That is,
3171 * {@code -scale+(ulength-1)}, where {@code ulength} is the
3172 * length of the absolute value of the unscaled value in decimal
3173 * digits (its <i>precision</i>).
3174 *
3175 * <p>If the scale is greater than or equal to zero and the
3176 * adjusted exponent is greater than or equal to {@code -6}, the
3177 * number will be converted to a character form without using
3178 * exponential notation. In this case, if the scale is zero then
3179 * no decimal point is added and if the scale is positive a
3180 * decimal point will be inserted with the scale specifying the
3181 * number of characters to the right of the decimal point.
3182 * {@code '0'} characters are added to the left of the converted
3183 * unscaled value as necessary. If no character precedes the
3184 * decimal point after this insertion then a conventional
3185 * {@code '0'} character is prefixed.
3186 *
3187 * <p>Otherwise (that is, if the scale is negative, or the
3188 * adjusted exponent is less than {@code -6}), the number will be
3189 * converted to a character form using exponential notation. In
3190 * this case, if the converted {@code BigInteger} has more than
3191 * one digit a decimal point is inserted after the first digit.
3192 * An exponent in character form is then suffixed to the converted
3193 * unscaled value (perhaps with inserted decimal point); this
3194 * comprises the letter {@code 'E'} followed immediately by the
3195 * adjusted exponent converted to a character form. The latter is
3196 * in base ten, using the characters {@code '0'} through
3197 * {@code '9'} with no leading zeros, and is always prefixed by a
3198 * sign character {@code '-'} (<code>'\u002D'</code>) if the
3199 * adjusted exponent is negative, {@code '+'}
3200 * (<code>'\u002B'</code>) otherwise).
3201 *
3202 * <p>Finally, the entire string is prefixed by a minus sign
3203 * character {@code '-'} (<code>'\u002D'</code>) if the unscaled
3204 * value is less than zero. No sign character is prefixed if the
3205 * unscaled value is zero or positive.
3206 *
3207 * <p><b>Examples:</b>
3208 * <p>For each representation [<i>unscaled value</i>, <i>scale</i>]
3209 * on the left, the resulting string is shown on the right.
3210 * <pre>
3211 * [123,0] "123"
3212 * [-123,0] "-123"
3213 * [123,-1] "1.23E+3"
3214 * [123,-3] "1.23E+5"
3215 * [123,1] "12.3"
3216 * [123,5] "0.00123"
3217 * [123,10] "1.23E-8"
3218 * [-123,12] "-1.23E-10"
3219 * </pre>
3220 *
3221 * <b>Notes:</b>
3222 * <ol>
3223 *
3224 * <li>There is a one-to-one mapping between the distinguishable
3225 * {@code BigDecimal} values and the result of this conversion.
3226 * That is, every distinguishable {@code BigDecimal} value
3227 * (unscaled value and scale) has a unique string representation
3228 * as a result of using {@code toString}. If that string
3229 * representation is converted back to a {@code BigDecimal} using
3230 * the {@link #BigDecimal(String)} constructor, then the original
3231 * value will be recovered.
3232 *
3233 * <li>The string produced for a given number is always the same;
3234 * it is not affected by locale. This means that it can be used
3235 * as a canonical string representation for exchanging decimal
3236 * data, or as a key for a Hashtable, etc. Locale-sensitive
3237 * number formatting and parsing is handled by the {@link
3238 * java.text.NumberFormat} class and its subclasses.
3239 *
3240 * <li>The {@link #toEngineeringString} method may be used for
3241 * presenting numbers with exponents in engineering notation, and the
3242 * {@link #setScale(int,RoundingMode) setScale} method may be used for
3243 * rounding a {@code BigDecimal} so it has a known number of digits after
3244 * the decimal point.
3245 *
3246 * <li>The digit-to-character mapping provided by
3247 * {@code Character.forDigit} is used.
3248 *
3249 * </ol>
3250 *
3251 * @return string representation of this {@code BigDecimal}.
3252 * @see Character#forDigit
3253 * @see #BigDecimal(java.lang.String)
3254 */
3255 @Override
3256 public String toString() {
3257 String sc = stringCache;
3258 if (sc == null) {
3259 stringCache = sc = layoutChars(true);
3260 }
3261 return sc;
3262 }
3263
3264 /**
3265 * Returns a string representation of this {@code BigDecimal},
3266 * using engineering notation if an exponent is needed.
3267 *
3268 * <p>Returns a string that represents the {@code BigDecimal} as
3269 * described in the {@link #toString()} method, except that if
3270 * exponential notation is used, the power of ten is adjusted to
3271 * be a multiple of three (engineering notation) such that the
3272 * integer part of nonzero values will be in the range 1 through
3273 * 999. If exponential notation is used for zero values, a
3274 * decimal point and one or two fractional zero digits are used so
3275 * that the scale of the zero value is preserved. Note that
3276 * unlike the output of {@link #toString()}, the output of this
3277 * method is <em>not</em> guaranteed to recover the same [integer,
3278 * scale] pair of this {@code BigDecimal} if the output string is
3279 * converting back to a {@code BigDecimal} using the {@linkplain
3280 * #BigDecimal(String) string constructor}. The result of this method meets
3281 * the weaker constraint of always producing a numerically equal
3282 * result from applying the string constructor to the method's output.
3283 *
3284 * @return string representation of this {@code BigDecimal}, using
3285 * engineering notation if an exponent is needed.
3286 * @since 1.5
3287 */
3288 public String toEngineeringString() {
3289 return layoutChars(false);
3290 }
3291
3292 /**
3293 * Returns a string representation of this {@code BigDecimal}
3294 * without an exponent field. For values with a positive scale,
3295 * the number of digits to the right of the decimal point is used
3296 * to indicate scale. For values with a zero or negative scale,
3297 * the resulting string is generated as if the value were
3298 * converted to a numerically equal value with zero scale and as
3299 * if all the trailing zeros of the zero scale value were present
3300 * in the result.
3301 *
3302 * The entire string is prefixed by a minus sign character '-'
3303 * (<code>'\u002D'</code>) if the unscaled value is less than
3304 * zero. No sign character is prefixed if the unscaled value is
3305 * zero or positive.
3306 *
3307 * Note that if the result of this method is passed to the
3308 * {@linkplain #BigDecimal(String) string constructor}, only the
3309 * numerical value of this {@code BigDecimal} will necessarily be
3310 * recovered; the representation of the new {@code BigDecimal}
3311 * may have a different scale. In particular, if this
3312 * {@code BigDecimal} has a negative scale, the string resulting
3313 * from this method will have a scale of zero when processed by
3314 * the string constructor.
3315 *
3316 * (This method behaves analogously to the {@code toString}
3317 * method in 1.4 and earlier releases.)
3318 *
3319 * @return a string representation of this {@code BigDecimal}
3320 * without an exponent field.
3321 * @since 1.5
3322 * @see #toString()
3323 * @see #toEngineeringString()
3324 */
3325 public String toPlainString() {
3326 if(scale==0) {
3327 if(intCompact!=INFLATED) {
3328 return Long.toString(intCompact);
3329 } else {
3330 return intVal.toString();
3331 }
3332 }
3333 if(this.scale<0) { // No decimal point
3334 if(signum()==0) {
3335 return "0";
3336 }
3337 int trailingZeros = checkScaleNonZero((-(long)scale));
3338 StringBuilder buf;
3339 if(intCompact!=INFLATED) {
3340 buf = new StringBuilder(20+trailingZeros);
3341 buf.append(intCompact);
3342 } else {
3343 String str = intVal.toString();
3344 buf = new StringBuilder(str.length()+trailingZeros);
3345 buf.append(str);
3346 }
3347 for (int i = 0; i < trailingZeros; i++) {
3348 buf.append('0');
3349 }
3350 return buf.toString();
3351 }
3352 String str ;
3353 if(intCompact!=INFLATED) {
3354 str = Long.toString(Math.abs(intCompact));
3355 } else {
3356 str = intVal.abs().toString();
3357 }
3358 return getValueString(signum(), str, scale);
3359 }
3360
3361 /* Returns a digit.digit string */
3362 private String getValueString(int signum, String intString, int scale) {
3363 /* Insert decimal point */
3364 StringBuilder buf;
3365 int insertionPoint = intString.length() - scale;
3366 if (insertionPoint == 0) { /* Point goes right before intVal */
3367 return (signum<0 ? "-0." : "0.") + intString;
3368 } else if (insertionPoint > 0) { /* Point goes inside intVal */
3369 buf = new StringBuilder(intString);
3370 buf.insert(insertionPoint, '.');
3371 if (signum < 0)
3372 buf.insert(0, '-');
3373 } else { /* We must insert zeros between point and intVal */
3374 buf = new StringBuilder(3-insertionPoint + intString.length());
3375 buf.append(signum<0 ? "-0." : "0.");
3376 for (int i=0; i<-insertionPoint; i++) {
3377 buf.append('0');
3378 }
3379 buf.append(intString);
3380 }
3381 return buf.toString();
3382 }
3383
3384 /**
3385 * Converts this {@code BigDecimal} to a {@code BigInteger}.
3386 * This conversion is analogous to the
3387 * <i>narrowing primitive conversion</i> from {@code double} to
3388 * {@code long} as defined in
3389 * <cite>The Java™ Language Specification</cite>:
3390 * any fractional part of this
3391 * {@code BigDecimal} will be discarded. Note that this
3392 * conversion can lose information about the precision of the
3393 * {@code BigDecimal} value.
3394 * <p>
3395 * To have an exception thrown if the conversion is inexact (in
3396 * other words if a nonzero fractional part is discarded), use the
3397 * {@link #toBigIntegerExact()} method.
3398 *
3399 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3400 * @jls 5.1.3 Narrowing Primitive Conversion
3401 */
3402 public BigInteger toBigInteger() {
3403 // force to an integer, quietly
3404 return this.setScale(0, ROUND_DOWN).inflated();
3405 }
3406
3407 /**
3408 * Converts this {@code BigDecimal} to a {@code BigInteger},
3409 * checking for lost information. An exception is thrown if this
3410 * {@code BigDecimal} has a nonzero fractional part.
3411 *
3412 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3413 * @throws ArithmeticException if {@code this} has a nonzero
3414 * fractional part.
3415 * @since 1.5
3416 */
3417 public BigInteger toBigIntegerExact() {
3418 // round to an integer, with Exception if decimal part non-0
3419 return this.setScale(0, ROUND_UNNECESSARY).inflated();
3420 }
3421
3422 /**
3423 * Converts this {@code BigDecimal} to a {@code long}.
3424 * This conversion is analogous to the
3425 * <i>narrowing primitive conversion</i> from {@code double} to
3426 * {@code short} as defined in
3427 * <cite>The Java™ Language Specification</cite>:
3428 * any fractional part of this
3429 * {@code BigDecimal} will be discarded, and if the resulting
3430 * "{@code BigInteger}" is too big to fit in a
3431 * {@code long}, only the low-order 64 bits are returned.
3432 * Note that this conversion can lose information about the
3433 * overall magnitude and precision of this {@code BigDecimal} value as well
3434 * as return a result with the opposite sign.
3435 *
3436 * @return this {@code BigDecimal} converted to a {@code long}.
3437 * @jls 5.1.3 Narrowing Primitive Conversion
3438 */
3439 @Override
3440 public long longValue(){
3441 if (intCompact != INFLATED && scale == 0) {
3442 return intCompact;
3443 } else {
3444 // Fastpath zero and small values
3445 if (this.signum() == 0 || fractionOnly() ||
3446 // Fastpath very large-scale values that will result
3447 // in a truncated value of zero. If the scale is -64
3448 // or less, there are at least 64 powers of 10 in the
3449 // value of the numerical result. Since 10 = 2*5, in
3450 // that case there would also be 64 powers of 2 in the
3451 // result, meaning all 64 bits of a long will be zero.
3452 scale <= -64) {
3453 return 0;
3454 } else {
3455 return toBigInteger().longValue();
3456 }
3457 }
3458 }
3459
3460 /**
3461 * Return true if a nonzero BigDecimal has an absolute value less
3462 * than one; i.e. only has fraction digits.
3463 */
3464 private boolean fractionOnly() {
3465 assert this.signum() != 0;
3466 return (this.precision() - this.scale) <= 0;
3467 }
3468
3469 /**
3470 * Converts this {@code BigDecimal} to a {@code long}, checking
3471 * for lost information. If this {@code BigDecimal} has a
3472 * nonzero fractional part or is out of the possible range for a
3473 * {@code long} result then an {@code ArithmeticException} is
3474 * thrown.
3475 *
3476 * @return this {@code BigDecimal} converted to a {@code long}.
3477 * @throws ArithmeticException if {@code this} has a nonzero
3478 * fractional part, or will not fit in a {@code long}.
3479 * @since 1.5
3480 */
3481 public long longValueExact() {
3482 if (intCompact != INFLATED && scale == 0)
3483 return intCompact;
3484
3485 // Fastpath zero
3486 if (this.signum() == 0)
3487 return 0;
3488
3489 // Fastpath numbers less than 1.0 (the latter can be very slow
3490 // to round if very small)
3491 if (fractionOnly())
3492 throw new ArithmeticException("Rounding necessary");
3493
3494 // If more than 19 digits in integer part it cannot possibly fit
3495 if ((precision() - scale) > 19) // [OK for negative scale too]
3496 throw new java.lang.ArithmeticException("Overflow");
3497
3498 // round to an integer, with Exception if decimal part non-0
3499 BigDecimal num = this.setScale(0, ROUND_UNNECESSARY);
3500 if (num.precision() >= 19) // need to check carefully
3501 LongOverflow.check(num);
3502 return num.inflated().longValue();
3503 }
3504
3505 private static class LongOverflow {
3506 /** BigInteger equal to Long.MIN_VALUE. */
3507 private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE);
3508
3509 /** BigInteger equal to Long.MAX_VALUE. */
3510 private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE);
3511
3512 public static void check(BigDecimal num) {
3513 BigInteger intVal = num.inflated();
3514 if (intVal.compareTo(LONGMIN) < 0 ||
3515 intVal.compareTo(LONGMAX) > 0)
3516 throw new java.lang.ArithmeticException("Overflow");
3517 }
3518 }
3519
3520 /**
3521 * Converts this {@code BigDecimal} to an {@code int}.
3522 * This conversion is analogous to the
3523 * <i>narrowing primitive conversion</i> from {@code double} to
3524 * {@code short} as defined in
3525 * <cite>The Java™ Language Specification</cite>:
3526 * any fractional part of this
3527 * {@code BigDecimal} will be discarded, and if the resulting
3528 * "{@code BigInteger}" is too big to fit in an
3529 * {@code int}, only the low-order 32 bits are returned.
3530 * Note that this conversion can lose information about the
3531 * overall magnitude and precision of this {@code BigDecimal}
3532 * value as well as return a result with the opposite sign.
3533 *
3534 * @return this {@code BigDecimal} converted to an {@code int}.
3535 * @jls 5.1.3 Narrowing Primitive Conversion
3536 */
3537 @Override
3538 public int intValue() {
3539 return (intCompact != INFLATED && scale == 0) ?
3540 (int)intCompact :
3541 (int)longValue();
3542 }
3543
3544 /**
3545 * Converts this {@code BigDecimal} to an {@code int}, checking
3546 * for lost information. If this {@code BigDecimal} has a
3547 * nonzero fractional part or is out of the possible range for an
3548 * {@code int} result then an {@code ArithmeticException} is
3549 * thrown.
3550 *
3551 * @return this {@code BigDecimal} converted to an {@code int}.
3552 * @throws ArithmeticException if {@code this} has a nonzero
3553 * fractional part, or will not fit in an {@code int}.
3554 * @since 1.5
3555 */
3556 public int intValueExact() {
3557 long num;
3558 num = this.longValueExact(); // will check decimal part
3559 if ((int)num != num)
3560 throw new java.lang.ArithmeticException("Overflow");
3561 return (int)num;
3562 }
3563
3564 /**
3565 * Converts this {@code BigDecimal} to a {@code short}, checking
3566 * for lost information. If this {@code BigDecimal} has a
3567 * nonzero fractional part or is out of the possible range for a
3568 * {@code short} result then an {@code ArithmeticException} is
3569 * thrown.
3570 *
3571 * @return this {@code BigDecimal} converted to a {@code short}.
3572 * @throws ArithmeticException if {@code this} has a nonzero
3573 * fractional part, or will not fit in a {@code short}.
3574 * @since 1.5
3575 */
3576 public short shortValueExact() {
3577 long num;
3578 num = this.longValueExact(); // will check decimal part
3579 if ((short)num != num)
3580 throw new java.lang.ArithmeticException("Overflow");
3581 return (short)num;
3582 }
3583
3584 /**
3585 * Converts this {@code BigDecimal} to a {@code byte}, checking
3586 * for lost information. If this {@code BigDecimal} has a
3587 * nonzero fractional part or is out of the possible range for a
3588 * {@code byte} result then an {@code ArithmeticException} is
3589 * thrown.
3590 *
3591 * @return this {@code BigDecimal} converted to a {@code byte}.
3592 * @throws ArithmeticException if {@code this} has a nonzero
3593 * fractional part, or will not fit in a {@code byte}.
3594 * @since 1.5
3595 */
3596 public byte byteValueExact() {
3597 long num;
3598 num = this.longValueExact(); // will check decimal part
3599 if ((byte)num != num)
3600 throw new java.lang.ArithmeticException("Overflow");
3601 return (byte)num;
3602 }
3603
3604 /**
3605 * Converts this {@code BigDecimal} to a {@code float}.
3606 * This conversion is similar to the
3607 * <i>narrowing primitive conversion</i> from {@code double} to
3608 * {@code float} as defined in
3609 * <cite>The Java™ Language Specification</cite>:
3610 * if this {@code BigDecimal} has too great a
3611 * magnitude to represent as a {@code float}, it will be
3612 * converted to {@link Float#NEGATIVE_INFINITY} or {@link
3613 * Float#POSITIVE_INFINITY} as appropriate. Note that even when
3614 * the return value is finite, this conversion can lose
3615 * information about the precision of the {@code BigDecimal}
3616 * value.
3617 *
3618 * @return this {@code BigDecimal} converted to a {@code float}.
3619 * @jls 5.1.3 Narrowing Primitive Conversion
3620 */
3621 @Override
3622 public float floatValue(){
3623 if(intCompact != INFLATED) {
3624 if (scale == 0) {
3625 return (float)intCompact;
3626 } else {
3627 /*
3628 * If both intCompact and the scale can be exactly
3629 * represented as float values, perform a single float
3630 * multiply or divide to compute the (properly
3631 * rounded) result.
3632 */
3633 if (Math.abs(intCompact) < 1L<<22 ) {
3634 // Don't have too guard against
3635 // Math.abs(MIN_VALUE) because of outer check
3636 // against INFLATED.
3637 if (scale > 0 && scale < FLOAT_10_POW.length) {
3638 return (float)intCompact / FLOAT_10_POW[scale];
3639 } else if (scale < 0 && scale > -FLOAT_10_POW.length) {
3640 return (float)intCompact * FLOAT_10_POW[-scale];
3641 }
3642 }
3643 }
3644 }
3645 // Somewhat inefficient, but guaranteed to work.
3646 return Float.parseFloat(this.toString());
3647 }
3648
3649 /**
3650 * Converts this {@code BigDecimal} to a {@code double}.
3651 * This conversion is similar to the
3652 * <i>narrowing primitive conversion</i> from {@code double} to
3653 * {@code float} as defined in
3654 * <cite>The Java™ Language Specification</cite>:
3655 * if this {@code BigDecimal} has too great a
3656 * magnitude represent as a {@code double}, it will be
3657 * converted to {@link Double#NEGATIVE_INFINITY} or {@link
3658 * Double#POSITIVE_INFINITY} as appropriate. Note that even when
3659 * the return value is finite, this conversion can lose
3660 * information about the precision of the {@code BigDecimal}
3661 * value.
3662 *
3663 * @return this {@code BigDecimal} converted to a {@code double}.
3664 * @jls 5.1.3 Narrowing Primitive Conversion
3665 */
3666 @Override
3667 public double doubleValue(){
3668 if(intCompact != INFLATED) {
3669 if (scale == 0) {
3670 return (double)intCompact;
3671 } else {
3672 /*
3673 * If both intCompact and the scale can be exactly
3674 * represented as double values, perform a single
3675 * double multiply or divide to compute the (properly
3676 * rounded) result.
3677 */
3678 if (Math.abs(intCompact) < 1L<<52 ) {
3679 // Don't have too guard against
3680 // Math.abs(MIN_VALUE) because of outer check
3681 // against INFLATED.
3682 if (scale > 0 && scale < DOUBLE_10_POW.length) {
3683 return (double)intCompact / DOUBLE_10_POW[scale];
3684 } else if (scale < 0 && scale > -DOUBLE_10_POW.length) {
3685 return (double)intCompact * DOUBLE_10_POW[-scale];
3686 }
3687 }
3688 }
3689 }
3690 // Somewhat inefficient, but guaranteed to work.
3691 return Double.parseDouble(this.toString());
3692 }
3693
3694 /**
3695 * Powers of 10 which can be represented exactly in {@code
3696 * double}.
3697 */
3698 private static final double DOUBLE_10_POW[] = {
3699 1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5,
3700 1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, 1.0e11,
3701 1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17,
3702 1.0e18, 1.0e19, 1.0e20, 1.0e21, 1.0e22
3703 };
3704
3705 /**
3706 * Powers of 10 which can be represented exactly in {@code
3707 * float}.
3708 */
3709 private static final float FLOAT_10_POW[] = {
3710 1.0e0f, 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f,
3711 1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f
3712 };
3713
3714 /**
3715 * Returns the size of an ulp, a unit in the last place, of this
3716 * {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal}
3717 * value is the positive distance between this value and the
3718 * {@code BigDecimal} value next larger in magnitude with the
3719 * same number of digits. An ulp of a zero value is numerically
3720 * equal to 1 with the scale of {@code this}. The result is
3721 * stored with the same scale as {@code this} so the result
3722 * for zero and nonzero values is equal to {@code [1,
3723 * this.scale()]}.
3724 *
3725 * @return the size of an ulp of {@code this}
3726 * @since 1.5
3727 */
3728 public BigDecimal ulp() {
3729 return BigDecimal.valueOf(1, this.scale(), 1);
3730 }
3731
3732 // Private class to build a string representation for BigDecimal object.
3733 // "StringBuilderHelper" is constructed as a thread local variable so it is
3734 // thread safe. The StringBuilder field acts as a buffer to hold the temporary
3735 // representation of BigDecimal. The cmpCharArray holds all the characters for
3736 // the compact representation of BigDecimal (except for '-' sign' if it is
3737 // negative) if its intCompact field is not INFLATED. It is shared by all
3738 // calls to toString() and its variants in that particular thread.
3739 static class StringBuilderHelper {
3740 final StringBuilder sb; // Placeholder for BigDecimal string
3741 final char[] cmpCharArray; // character array to place the intCompact
3742
3743 StringBuilderHelper() {
3744 sb = new StringBuilder();
3745 // All non negative longs can be made to fit into 19 character array.
3746 cmpCharArray = new char[19];
3747 }
3748
3749 // Accessors.
3750 StringBuilder getStringBuilder() {
3751 sb.setLength(0);
3752 return sb;
3753 }
3754
3755 char[] getCompactCharArray() {
3756 return cmpCharArray;
3757 }
3758
3759 /**
3760 * Places characters representing the intCompact in {@code long} into
3761 * cmpCharArray and returns the offset to the array where the
3762 * representation starts.
3763 *
3764 * @param intCompact the number to put into the cmpCharArray.
3765 * @return offset to the array where the representation starts.
3766 * Note: intCompact must be greater or equal to zero.
3767 */
3768 int putIntCompact(long intCompact) {
3769 assert intCompact >= 0;
3770
3771 long q;
3772 int r;
3773 // since we start from the least significant digit, charPos points to
3774 // the last character in cmpCharArray.
3775 int charPos = cmpCharArray.length;
3776
3777 // Get 2 digits/iteration using longs until quotient fits into an int
3778 while (intCompact > Integer.MAX_VALUE) {
3779 q = intCompact / 100;
3780 r = (int)(intCompact - q * 100);
3781 intCompact = q;
3782 cmpCharArray[--charPos] = DIGIT_ONES[r];
3783 cmpCharArray[--charPos] = DIGIT_TENS[r];
3784 }
3785
3786 // Get 2 digits/iteration using ints when i2 >= 100
3787 int q2;
3788 int i2 = (int)intCompact;
3789 while (i2 >= 100) {
3790 q2 = i2 / 100;
3791 r = i2 - q2 * 100;
3792 i2 = q2;
3793 cmpCharArray[--charPos] = DIGIT_ONES[r];
3794 cmpCharArray[--charPos] = DIGIT_TENS[r];
3795 }
3796
3797 cmpCharArray[--charPos] = DIGIT_ONES[i2];
3798 if (i2 >= 10)
3799 cmpCharArray[--charPos] = DIGIT_TENS[i2];
3800
3801 return charPos;
3802 }
3803
3804 static final char[] DIGIT_TENS = {
3805 '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
3806 '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
3807 '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
3808 '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
3809 '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
3810 '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
3811 '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
3812 '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
3813 '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
3814 '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
3815 };
3816
3817 static final char[] DIGIT_ONES = {
3818 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3819 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3820 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3821 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3822 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3823 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3824 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3825 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3826 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3827 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3828 };
3829 }
3830
3831 /**
3832 * Lay out this {@code BigDecimal} into a {@code char[]} array.
3833 * The Java 1.2 equivalent to this was called {@code getValueString}.
3834 *
3835 * @param sci {@code true} for Scientific exponential notation;
3836 * {@code false} for Engineering
3837 * @return string with canonical string representation of this
3838 * {@code BigDecimal}
3839 */
3840 private String layoutChars(boolean sci) {
3841 if (scale == 0) // zero scale is trivial
3842 return (intCompact != INFLATED) ?
3843 Long.toString(intCompact):
3844 intVal.toString();
3845 if (scale == 2 &&
3846 intCompact >= 0 && intCompact < Integer.MAX_VALUE) {
3847 // currency fast path
3848 int lowInt = (int)intCompact % 100;
3849 int highInt = (int)intCompact / 100;
3850 return (Integer.toString(highInt) + '.' +
3851 StringBuilderHelper.DIGIT_TENS[lowInt] +
3852 StringBuilderHelper.DIGIT_ONES[lowInt]) ;
3853 }
3854
3855 StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get();
3856 char[] coeff;
3857 int offset; // offset is the starting index for coeff array
3858 // Get the significand as an absolute value
3859 if (intCompact != INFLATED) {
3860 offset = sbHelper.putIntCompact(Math.abs(intCompact));
3861 coeff = sbHelper.getCompactCharArray();
3862 } else {
3863 offset = 0;
3864 coeff = intVal.abs().toString().toCharArray();
3865 }
3866
3867 // Construct a buffer, with sufficient capacity for all cases.
3868 // If E-notation is needed, length will be: +1 if negative, +1
3869 // if '.' needed, +2 for "E+", + up to 10 for adjusted exponent.
3870 // Otherwise it could have +1 if negative, plus leading "0.00000"
3871 StringBuilder buf = sbHelper.getStringBuilder();
3872 if (signum() < 0) // prefix '-' if negative
3873 buf.append('-');
3874 int coeffLen = coeff.length - offset;
3875 long adjusted = -(long)scale + (coeffLen -1);
3876 if ((scale >= 0) && (adjusted >= -6)) { // plain number
3877 int pad = scale - coeffLen; // count of padding zeros
3878 if (pad >= 0) { // 0.xxx form
3879 buf.append('0');
3880 buf.append('.');
3881 for (; pad>0; pad--) {
3882 buf.append('0');
3883 }
3884 buf.append(coeff, offset, coeffLen);
3885 } else { // xx.xx form
3886 buf.append(coeff, offset, -pad);
3887 buf.append('.');
3888 buf.append(coeff, -pad + offset, scale);
3889 }
3890 } else { // E-notation is needed
3891 if (sci) { // Scientific notation
3892 buf.append(coeff[offset]); // first character
3893 if (coeffLen > 1) { // more to come
3894 buf.append('.');
3895 buf.append(coeff, offset + 1, coeffLen - 1);
3896 }
3897 } else { // Engineering notation
3898 int sig = (int)(adjusted % 3);
3899 if (sig < 0)
3900 sig += 3; // [adjusted was negative]
3901 adjusted -= sig; // now a multiple of 3
3902 sig++;
3903 if (signum() == 0) {
3904 switch (sig) {
3905 case 1:
3906 buf.append('0'); // exponent is a multiple of three
3907 break;
3908 case 2:
3909 buf.append("0.00");
3910 adjusted += 3;
3911 break;
3912 case 3:
3913 buf.append("0.0");
3914 adjusted += 3;
3915 break;
3916 default:
3917 throw new AssertionError("Unexpected sig value " + sig);
3918 }
3919 } else if (sig >= coeffLen) { // significand all in integer
3920 buf.append(coeff, offset, coeffLen);
3921 // may need some zeros, too
3922 for (int i = sig - coeffLen; i > 0; i--) {
3923 buf.append('0');
3924 }
3925 } else { // xx.xxE form
3926 buf.append(coeff, offset, sig);
3927 buf.append('.');
3928 buf.append(coeff, offset + sig, coeffLen - sig);
3929 }
3930 }
3931 if (adjusted != 0) { // [!sci could have made 0]
3932 buf.append('E');
3933 if (adjusted > 0) // force sign for positive
3934 buf.append('+');
3935 buf.append(adjusted);
3936 }
3937 }
3938 return buf.toString();
3939 }
3940
3941 /**
3942 * Return 10 to the power n, as a {@code BigInteger}.
3943 *
3944 * @param n the power of ten to be returned (>=0)
3945 * @return a {@code BigInteger} with the value (10<sup>n</sup>)
3946 */
3947 private static BigInteger bigTenToThe(int n) {
3948 if (n < 0)
3949 return BigInteger.ZERO;
3950
3951 if (n < BIG_TEN_POWERS_TABLE_MAX) {
3952 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3953 if (n < pows.length)
3954 return pows[n];
3955 else
3956 return expandBigIntegerTenPowers(n);
3957 }
3958
3959 return BigInteger.TEN.pow(n);
3960 }
3961
3962 /**
3963 * Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n.
3964 *
3965 * @param n the power of ten to be returned (>=0)
3966 * @return a {@code BigDecimal} with the value (10<sup>n</sup>) and
3967 * in the meantime, the BIG_TEN_POWERS_TABLE array gets
3968 * expanded to the size greater than n.
3969 */
3970 private static BigInteger expandBigIntegerTenPowers(int n) {
3971 synchronized(BigDecimal.class) {
3972 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3973 int curLen = pows.length;
3974 // The following comparison and the above synchronized statement is
3975 // to prevent multiple threads from expanding the same array.
3976 if (curLen <= n) {
3977 int newLen = curLen << 1;
3978 while (newLen <= n) {
3979 newLen <<= 1;
3980 }
3981 pows = Arrays.copyOf(pows, newLen);
3982 for (int i = curLen; i < newLen; i++) {
3983 pows[i] = pows[i - 1].multiply(BigInteger.TEN);
3984 }
3985 // Based on the following facts:
3986 // 1. pows is a private local varible;
3987 // 2. the following store is a volatile store.
3988 // the newly created array elements can be safely published.
3989 BIG_TEN_POWERS_TABLE = pows;
3990 }
3991 return pows[n];
3992 }
3993 }
3994
3995 private static final long[] LONG_TEN_POWERS_TABLE = {
3996 1, // 0 / 10^0
3997 10, // 1 / 10^1
3998 100, // 2 / 10^2
3999 1000, // 3 / 10^3
4000 10000, // 4 / 10^4
4001 100000, // 5 / 10^5
4002 1000000, // 6 / 10^6
4003 10000000, // 7 / 10^7
4004 100000000, // 8 / 10^8
4005 1000000000, // 9 / 10^9
4006 10000000000L, // 10 / 10^10
4007 100000000000L, // 11 / 10^11
4008 1000000000000L, // 12 / 10^12
4009 10000000000000L, // 13 / 10^13
4010 100000000000000L, // 14 / 10^14
4011 1000000000000000L, // 15 / 10^15
4012 10000000000000000L, // 16 / 10^16
4013 100000000000000000L, // 17 / 10^17
4014 1000000000000000000L // 18 / 10^18
4015 };
4016
4017 private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = {
4018 BigInteger.ONE,
4019 BigInteger.valueOf(10),
4020 BigInteger.valueOf(100),
4021 BigInteger.valueOf(1000),
4022 BigInteger.valueOf(10000),
4023 BigInteger.valueOf(100000),
4024 BigInteger.valueOf(1000000),
4025 BigInteger.valueOf(10000000),
4026 BigInteger.valueOf(100000000),
4027 BigInteger.valueOf(1000000000),
4028 BigInteger.valueOf(10000000000L),
4029 BigInteger.valueOf(100000000000L),
4030 BigInteger.valueOf(1000000000000L),
4031 BigInteger.valueOf(10000000000000L),
4032 BigInteger.valueOf(100000000000000L),
4033 BigInteger.valueOf(1000000000000000L),
4034 BigInteger.valueOf(10000000000000000L),
4035 BigInteger.valueOf(100000000000000000L),
4036 BigInteger.valueOf(1000000000000000000L)
4037 };
4038
4039 private static final int BIG_TEN_POWERS_TABLE_INITLEN =
4040 BIG_TEN_POWERS_TABLE.length;
4041 private static final int BIG_TEN_POWERS_TABLE_MAX =
4042 16 * BIG_TEN_POWERS_TABLE_INITLEN;
4043
4044 private static final long THRESHOLDS_TABLE[] = {
4045 Long.MAX_VALUE, // 0
4046 Long.MAX_VALUE/10L, // 1
4047 Long.MAX_VALUE/100L, // 2
4048 Long.MAX_VALUE/1000L, // 3
4049 Long.MAX_VALUE/10000L, // 4
4050 Long.MAX_VALUE/100000L, // 5
4051 Long.MAX_VALUE/1000000L, // 6
4052 Long.MAX_VALUE/10000000L, // 7
4053 Long.MAX_VALUE/100000000L, // 8
4054 Long.MAX_VALUE/1000000000L, // 9
4055 Long.MAX_VALUE/10000000000L, // 10
4056 Long.MAX_VALUE/100000000000L, // 11
4057 Long.MAX_VALUE/1000000000000L, // 12
4058 Long.MAX_VALUE/10000000000000L, // 13
4059 Long.MAX_VALUE/100000000000000L, // 14
4060 Long.MAX_VALUE/1000000000000000L, // 15
4061 Long.MAX_VALUE/10000000000000000L, // 16
4062 Long.MAX_VALUE/100000000000000000L, // 17
4063 Long.MAX_VALUE/1000000000000000000L // 18
4064 };
4065
4066 /**
4067 * Compute val * 10 ^ n; return this product if it is
4068 * representable as a long, INFLATED otherwise.
4069 */
4070 private static long longMultiplyPowerTen(long val, int n) {
4071 if (val == 0 || n <= 0)
4072 return val;
4073 long[] tab = LONG_TEN_POWERS_TABLE;
4074 long[] bounds = THRESHOLDS_TABLE;
4075 if (n < tab.length && n < bounds.length) {
4076 long tenpower = tab[n];
4077 if (val == 1)
4078 return tenpower;
4079 if (Math.abs(val) <= bounds[n])
4080 return val * tenpower;
4081 }
4082 return INFLATED;
4083 }
4084
4085 /**
4086 * Compute this * 10 ^ n.
4087 * Needed mainly to allow special casing to trap zero value
4088 */
4089 private BigInteger bigMultiplyPowerTen(int n) {
4090 if (n <= 0)
4091 return this.inflated();
4092
4093 if (intCompact != INFLATED)
4094 return bigTenToThe(n).multiply(intCompact);
4095 else
4096 return intVal.multiply(bigTenToThe(n));
4097 }
4098
4099 /**
4100 * Returns appropriate BigInteger from intVal field if intVal is
4101 * null, i.e. the compact representation is in use.
4102 */
4103 private BigInteger inflated() {
4104 if (intVal == null) {
4105 return BigInteger.valueOf(intCompact);
4106 }
4107 return intVal;
4108 }
4109
4110 /**
4111 * Match the scales of two {@code BigDecimal}s to align their
4112 * least significant digits.
4113 *
4114 * <p>If the scales of val[0] and val[1] differ, rescale
4115 * (non-destructively) the lower-scaled {@code BigDecimal} so
4116 * they match. That is, the lower-scaled reference will be
4117 * replaced by a reference to a new object with the same scale as
4118 * the other {@code BigDecimal}.
4119 *
4120 * @param val array of two elements referring to the two
4121 * {@code BigDecimal}s to be aligned.
4122 */
4123 private static void matchScale(BigDecimal[] val) {
4124 if (val[0].scale < val[1].scale) {
4125 val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY);
4126 } else if (val[1].scale < val[0].scale) {
4127 val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY);
4128 }
4129 }
4130
4131 private static class UnsafeHolder {
4132 private static final jdk.internal.misc.Unsafe unsafe
4133 = jdk.internal.misc.Unsafe.getUnsafe();
4134 private static final long intCompactOffset
4135 = unsafe.objectFieldOffset(BigDecimal.class, "intCompact");
4136 private static final long intValOffset
4137 = unsafe.objectFieldOffset(BigDecimal.class, "intVal");
4138
4139 static void setIntCompact(BigDecimal bd, long val) {
4140 unsafe.putLong(bd, intCompactOffset, val);
4141 }
4142
4143 static void setIntValVolatile(BigDecimal bd, BigInteger val) {
4144 unsafe.putReferenceVolatile(bd, intValOffset, val);
4145 }
4146 }
4147
4148 /**
4149 * Reconstitute the {@code BigDecimal} instance from a stream (that is,
4150 * deserialize it).
4151 *
4152 * @param s the stream being read.
4153 */
4154 @java.io.Serial
4155 private void readObject(java.io.ObjectInputStream s)
4156 throws java.io.IOException, ClassNotFoundException {
4157 // Read in all fields
4158 s.defaultReadObject();
4159 // validate possibly bad fields
4160 if (intVal == null) {
4161 String message = "BigDecimal: null intVal in stream";
4162 throw new java.io.StreamCorruptedException(message);
4163 // [all values of scale are now allowed]
4164 }
4165 UnsafeHolder.setIntCompact(this, compactValFor(intVal));
4166 }
4167
4168 /**
4169 * Serialize this {@code BigDecimal} to the stream in question
4170 *
4171 * @param s the stream to serialize to.
4172 */
4173 @java.io.Serial
4174 private void writeObject(java.io.ObjectOutputStream s)
4175 throws java.io.IOException {
4176 // Must inflate to maintain compatible serial form.
4177 if (this.intVal == null)
4178 UnsafeHolder.setIntValVolatile(this, BigInteger.valueOf(this.intCompact));
4179 // Could reset intVal back to null if it has to be set.
4180 s.defaultWriteObject();
4181 }
4182
4183 /**
4184 * Returns the length of the absolute value of a {@code long}, in decimal
4185 * digits.
4186 *
4187 * @param x the {@code long}
4188 * @return the length of the unscaled value, in deciaml digits.
4189 */
4190 static int longDigitLength(long x) {
4191 /*
4192 * As described in "Bit Twiddling Hacks" by Sean Anderson,
4193 * (http://graphics.stanford.edu/~seander/bithacks.html)
4194 * integer log 10 of x is within 1 of (1233/4096)* (1 +
4195 * integer log 2 of x). The fraction 1233/4096 approximates
4196 * log10(2). So we first do a version of log2 (a variant of
4197 * Long class with pre-checks and opposite directionality) and
4198 * then scale and check against powers table. This is a little
4199 * simpler in present context than the version in Hacker's
4200 * Delight sec 11-4. Adding one to bit length allows comparing
4201 * downward from the LONG_TEN_POWERS_TABLE that we need
4202 * anyway.
4203 */
4204 assert x != BigDecimal.INFLATED;
4205 if (x < 0)
4206 x = -x;
4207 if (x < 10) // must screen for 0, might as well 10
4208 return 1;
4209 int r = ((64 - Long.numberOfLeadingZeros(x) + 1) * 1233) >>> 12;
4210 long[] tab = LONG_TEN_POWERS_TABLE;
4211 // if r >= length, must have max possible digits for long
4212 return (r >= tab.length || x < tab[r]) ? r : r + 1;
4213 }
4214
4215 /**
4216 * Returns the length of the absolute value of a BigInteger, in
4217 * decimal digits.
4218 *
4219 * @param b the BigInteger
4220 * @return the length of the unscaled value, in decimal digits
4221 */
4222 private static int bigDigitLength(BigInteger b) {
4223 /*
4224 * Same idea as the long version, but we need a better
4225 * approximation of log10(2). Using 646456993/2^31
4226 * is accurate up to max possible reported bitLength.
4227 */
4228 if (b.signum == 0)
4229 return 1;
4230 int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31);
4231 return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1;
4232 }
4233
4234 /**
4235 * Check a scale for Underflow or Overflow. If this BigDecimal is
4236 * nonzero, throw an exception if the scale is outof range. If this
4237 * is zero, saturate the scale to the extreme value of the right
4238 * sign if the scale is out of range.
4239 *
4240 * @param val The new scale.
4241 * @throws ArithmeticException (overflow or underflow) if the new
4242 * scale is out of range.
4243 * @return validated scale as an int.
4244 */
4245 private int checkScale(long val) {
4246 int asInt = (int)val;
4247 if (asInt != val) {
4248 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
4249 BigInteger b;
4250 if (intCompact != 0 &&
4251 ((b = intVal) == null || b.signum() != 0))
4252 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
4253 }
4254 return asInt;
4255 }
4256
4257 /**
4258 * Returns the compact value for given {@code BigInteger}, or
4259 * INFLATED if too big. Relies on internal representation of
4260 * {@code BigInteger}.
4261 */
4262 private static long compactValFor(BigInteger b) {
4263 int[] m = b.mag;
4264 int len = m.length;
4265 if (len == 0)
4266 return 0;
4267 int d = m[0];
4268 if (len > 2 || (len == 2 && d < 0))
4269 return INFLATED;
4270
4271 long u = (len == 2)?
4272 (((long) m[1] & LONG_MASK) + (((long)d) << 32)) :
4273 (((long)d) & LONG_MASK);
4274 return (b.signum < 0)? -u : u;
4275 }
4276
4277 private static int longCompareMagnitude(long x, long y) {
4278 if (x < 0)
4279 x = -x;
4280 if (y < 0)
4281 y = -y;
4282 return (x < y) ? -1 : ((x == y) ? 0 : 1);
4283 }
4284
4285 private static int saturateLong(long s) {
4286 int i = (int)s;
4287 return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE);
4288 }
4289
4290 /*
4291 * Internal printing routine
4292 */
4293 private static void print(String name, BigDecimal bd) {
4294 System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n",
4295 name,
4296 bd.intCompact,
4297 bd.intVal,
4298 bd.scale,
4299 bd.precision);
4300 }
4301
4302 /**
4303 * Check internal invariants of this BigDecimal. These invariants
4304 * include:
4305 *
4306 * <ul>
4307 *
4308 * <li>The object must be initialized; either intCompact must not be
4309 * INFLATED or intVal is non-null. Both of these conditions may
4310 * be true.
4311 *
4312 * <li>If both intCompact and intVal and set, their values must be
4313 * consistent.
4314 *
4315 * <li>If precision is nonzero, it must have the right value.
4316 * </ul>
4317 *
4318 * Note: Since this is an audit method, we are not supposed to change the
4319 * state of this BigDecimal object.
4320 */
4321 private BigDecimal audit() {
4322 if (intCompact == INFLATED) {
4323 if (intVal == null) {
4324 print("audit", this);
4325 throw new AssertionError("null intVal");
4326 }
4327 // Check precision
4328 if (precision > 0 && precision != bigDigitLength(intVal)) {
4329 print("audit", this);
4330 throw new AssertionError("precision mismatch");
4331 }
4332 } else {
4333 if (intVal != null) {
4334 long val = intVal.longValue();
4335 if (val != intCompact) {
4336 print("audit", this);
4337 throw new AssertionError("Inconsistent state, intCompact=" +
4338 intCompact + "\t intVal=" + val);
4339 }
4340 }
4341 // Check precision
4342 if (precision > 0 && precision != longDigitLength(intCompact)) {
4343 print("audit", this);
4344 throw new AssertionError("precision mismatch");
4345 }
4346 }
4347 return this;
4348 }
4349
4350 /* the same as checkScale where value!=0 */
4351 private static int checkScaleNonZero(long val) {
4352 int asInt = (int)val;
4353 if (asInt != val) {
4354 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
4355 }
4356 return asInt;
4357 }
4358
4359 private static int checkScale(long intCompact, long val) {
4360 int asInt = (int)val;
4361 if (asInt != val) {
4362 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
4363 if (intCompact != 0)
4364 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
4365 }
4366 return asInt;
4367 }
4368
4369 private static int checkScale(BigInteger intVal, long val) {
4370 int asInt = (int)val;
4371 if (asInt != val) {
4372 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
4373 if (intVal.signum() != 0)
4374 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
4375 }
4376 return asInt;
4377 }
4378
4379 /**
4380 * Returns a {@code BigDecimal} rounded according to the MathContext
4381 * settings;
4382 * If rounding is needed a new {@code BigDecimal} is created and returned.
4383 *
4384 * @param val the value to be rounded
4385 * @param mc the context to use.
4386 * @return a {@code BigDecimal} rounded according to the MathContext
4387 * settings. May return {@code value}, if no rounding needed.
4388 * @throws ArithmeticException if the rounding mode is
4389 * {@code RoundingMode.UNNECESSARY} and the
4390 * result is inexact.
4391 */
4392 private static BigDecimal doRound(BigDecimal val, MathContext mc) {
4393 int mcp = mc.precision;
4394 boolean wasDivided = false;
4395 if (mcp > 0) {
4396 BigInteger intVal = val.intVal;
4397 long compactVal = val.intCompact;
4398 int scale = val.scale;
4399 int prec = val.precision();
4400 int mode = mc.roundingMode.oldMode;
4401 int drop;
4402 if (compactVal == INFLATED) {
4403 drop = prec - mcp;
4404 while (drop > 0) {
4405 scale = checkScaleNonZero((long) scale - drop);
4406 intVal = divideAndRoundByTenPow(intVal, drop, mode);
4407 wasDivided = true;
4408 compactVal = compactValFor(intVal);
4409 if (compactVal != INFLATED) {
4410 prec = longDigitLength(compactVal);
4411 break;
4412 }
4413 prec = bigDigitLength(intVal);
4414 drop = prec - mcp;
4415 }
4416 }
4417 if (compactVal != INFLATED) {
4418 drop = prec - mcp; // drop can't be more than 18
4419 while (drop > 0) {
4420 scale = checkScaleNonZero((long) scale - drop);
4421 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4422 wasDivided = true;
4423 prec = longDigitLength(compactVal);
4424 drop = prec - mcp;
4425 intVal = null;
4426 }
4427 }
4428 return wasDivided ? new BigDecimal(intVal,compactVal,scale,prec) : val;
4429 }
4430 return val;
4431 }
4432
4433 /*
4434 * Returns a {@code BigDecimal} created from {@code long} value with
4435 * given scale rounded according to the MathContext settings
4436 */
4437 private static BigDecimal doRound(long compactVal, int scale, MathContext mc) {
4438 int mcp = mc.precision;
4439 if (mcp > 0 && mcp < 19) {
4440 int prec = longDigitLength(compactVal);
4441 int drop = prec - mcp; // drop can't be more than 18
4442 while (drop > 0) {
4443 scale = checkScaleNonZero((long) scale - drop);
4444 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4445 prec = longDigitLength(compactVal);
4446 drop = prec - mcp;
4447 }
4448 return valueOf(compactVal, scale, prec);
4449 }
4450 return valueOf(compactVal, scale);
4451 }
4452
4453 /*
4454 * Returns a {@code BigDecimal} created from {@code BigInteger} value with
4455 * given scale rounded according to the MathContext settings
4456 */
4457 private static BigDecimal doRound(BigInteger intVal, int scale, MathContext mc) {
4458 int mcp = mc.precision;
4459 int prec = 0;
4460 if (mcp > 0) {
4461 long compactVal = compactValFor(intVal);
4462 int mode = mc.roundingMode.oldMode;
4463 int drop;
4464 if (compactVal == INFLATED) {
4465 prec = bigDigitLength(intVal);
4466 drop = prec - mcp;
4467 while (drop > 0) {
4468 scale = checkScaleNonZero((long) scale - drop);
4469 intVal = divideAndRoundByTenPow(intVal, drop, mode);
4470 compactVal = compactValFor(intVal);
4471 if (compactVal != INFLATED) {
4472 break;
4473 }
4474 prec = bigDigitLength(intVal);
4475 drop = prec - mcp;
4476 }
4477 }
4478 if (compactVal != INFLATED) {
4479 prec = longDigitLength(compactVal);
4480 drop = prec - mcp; // drop can't be more than 18
4481 while (drop > 0) {
4482 scale = checkScaleNonZero((long) scale - drop);
4483 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4484 prec = longDigitLength(compactVal);
4485 drop = prec - mcp;
4486 }
4487 return valueOf(compactVal,scale,prec);
4488 }
4489 }
4490 return new BigDecimal(intVal,INFLATED,scale,prec);
4491 }
4492
4493 /*
4494 * Divides {@code BigInteger} value by ten power.
4495 */
4496 private static BigInteger divideAndRoundByTenPow(BigInteger intVal, int tenPow, int roundingMode) {
4497 if (tenPow < LONG_TEN_POWERS_TABLE.length)
4498 intVal = divideAndRound(intVal, LONG_TEN_POWERS_TABLE[tenPow], roundingMode);
4499 else
4500 intVal = divideAndRound(intVal, bigTenToThe(tenPow), roundingMode);
4501 return intVal;
4502 }
4503
4504 /**
4505 * Internally used for division operation for division {@code long} by
4506 * {@code long}.
4507 * The returned {@code BigDecimal} object is the quotient whose scale is set
4508 * to the passed in scale. If the remainder is not zero, it will be rounded
4509 * based on the passed in roundingMode. Also, if the remainder is zero and
4510 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4511 * trailing zeros of the result is stripped to match the preferredScale.
4512 */
4513 private static BigDecimal divideAndRound(long ldividend, long ldivisor, int scale, int roundingMode,
4514 int preferredScale) {
4515
4516 int qsign; // quotient sign
4517 long q = ldividend / ldivisor; // store quotient in long
4518 if (roundingMode == ROUND_DOWN && scale == preferredScale)
4519 return valueOf(q, scale);
4520 long r = ldividend % ldivisor; // store remainder in long
4521 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4522 if (r != 0) {
4523 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4524 return valueOf((increment ? q + qsign : q), scale);
4525 } else {
4526 if (preferredScale != scale)
4527 return createAndStripZerosToMatchScale(q, scale, preferredScale);
4528 else
4529 return valueOf(q, scale);
4530 }
4531 }
4532
4533 /**
4534 * Divides {@code long} by {@code long} and do rounding based on the
4535 * passed in roundingMode.
4536 */
4537 private static long divideAndRound(long ldividend, long ldivisor, int roundingMode) {
4538 int qsign; // quotient sign
4539 long q = ldividend / ldivisor; // store quotient in long
4540 if (roundingMode == ROUND_DOWN)
4541 return q;
4542 long r = ldividend % ldivisor; // store remainder in long
4543 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4544 if (r != 0) {
4545 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4546 return increment ? q + qsign : q;
4547 } else {
4548 return q;
4549 }
4550 }
4551
4552 /**
4553 * Shared logic of need increment computation.
4554 */
4555 private static boolean commonNeedIncrement(int roundingMode, int qsign,
4556 int cmpFracHalf, boolean oddQuot) {
4557 switch(roundingMode) {
4558 case ROUND_UNNECESSARY:
4559 throw new ArithmeticException("Rounding necessary");
4560
4561 case ROUND_UP: // Away from zero
4562 return true;
4563
4564 case ROUND_DOWN: // Towards zero
4565 return false;
4566
4567 case ROUND_CEILING: // Towards +infinity
4568 return qsign > 0;
4569
4570 case ROUND_FLOOR: // Towards -infinity
4571 return qsign < 0;
4572
4573 default: // Some kind of half-way rounding
4574 assert roundingMode >= ROUND_HALF_UP &&
4575 roundingMode <= ROUND_HALF_EVEN: "Unexpected rounding mode" + RoundingMode.valueOf(roundingMode);
4576
4577 if (cmpFracHalf < 0 ) // We're closer to higher digit
4578 return false;
4579 else if (cmpFracHalf > 0 ) // We're closer to lower digit
4580 return true;
4581 else { // half-way
4582 assert cmpFracHalf == 0;
4583
4584 switch(roundingMode) {
4585 case ROUND_HALF_DOWN:
4586 return false;
4587
4588 case ROUND_HALF_UP:
4589 return true;
4590
4591 case ROUND_HALF_EVEN:
4592 return oddQuot;
4593
4594 default:
4595 throw new AssertionError("Unexpected rounding mode" + roundingMode);
4596 }
4597 }
4598 }
4599 }
4600
4601 /**
4602 * Tests if quotient has to be incremented according the roundingMode
4603 */
4604 private static boolean needIncrement(long ldivisor, int roundingMode,
4605 int qsign, long q, long r) {
4606 assert r != 0L;
4607
4608 int cmpFracHalf;
4609 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4610 cmpFracHalf = 1; // 2 * r can't fit into long
4611 } else {
4612 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4613 }
4614
4615 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, (q & 1L) != 0L);
4616 }
4617
4618 /**
4619 * Divides {@code BigInteger} value by {@code long} value and
4620 * do rounding based on the passed in roundingMode.
4621 */
4622 private static BigInteger divideAndRound(BigInteger bdividend, long ldivisor, int roundingMode) {
4623 // Descend into mutables for faster remainder checks
4624 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4625 // store quotient
4626 MutableBigInteger mq = new MutableBigInteger();
4627 // store quotient & remainder in long
4628 long r = mdividend.divide(ldivisor, mq);
4629 // record remainder is zero or not
4630 boolean isRemainderZero = (r == 0);
4631 // quotient sign
4632 int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4633 if (!isRemainderZero) {
4634 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4635 mq.add(MutableBigInteger.ONE);
4636 }
4637 }
4638 return mq.toBigInteger(qsign);
4639 }
4640
4641 /**
4642 * Internally used for division operation for division {@code BigInteger}
4643 * by {@code long}.
4644 * The returned {@code BigDecimal} object is the quotient whose scale is set
4645 * to the passed in scale. If the remainder is not zero, it will be rounded
4646 * based on the passed in roundingMode. Also, if the remainder is zero and
4647 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4648 * trailing zeros of the result is stripped to match the preferredScale.
4649 */
4650 private static BigDecimal divideAndRound(BigInteger bdividend,
4651 long ldivisor, int scale, int roundingMode, int preferredScale) {
4652 // Descend into mutables for faster remainder checks
4653 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4654 // store quotient
4655 MutableBigInteger mq = new MutableBigInteger();
4656 // store quotient & remainder in long
4657 long r = mdividend.divide(ldivisor, mq);
4658 // record remainder is zero or not
4659 boolean isRemainderZero = (r == 0);
4660 // quotient sign
4661 int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4662 if (!isRemainderZero) {
4663 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4664 mq.add(MutableBigInteger.ONE);
4665 }
4666 return mq.toBigDecimal(qsign, scale);
4667 } else {
4668 if (preferredScale != scale) {
4669 long compactVal = mq.toCompactValue(qsign);
4670 if(compactVal!=INFLATED) {
4671 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4672 }
4673 BigInteger intVal = mq.toBigInteger(qsign);
4674 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
4675 } else {
4676 return mq.toBigDecimal(qsign, scale);
4677 }
4678 }
4679 }
4680
4681 /**
4682 * Tests if quotient has to be incremented according the roundingMode
4683 */
4684 private static boolean needIncrement(long ldivisor, int roundingMode,
4685 int qsign, MutableBigInteger mq, long r) {
4686 assert r != 0L;
4687
4688 int cmpFracHalf;
4689 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4690 cmpFracHalf = 1; // 2 * r can't fit into long
4691 } else {
4692 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4693 }
4694
4695 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
4696 }
4697
4698 /**
4699 * Divides {@code BigInteger} value by {@code BigInteger} value and
4700 * do rounding based on the passed in roundingMode.
4701 */
4702 private static BigInteger divideAndRound(BigInteger bdividend, BigInteger bdivisor, int roundingMode) {
4703 boolean isRemainderZero; // record remainder is zero or not
4704 int qsign; // quotient sign
4705 // Descend into mutables for faster remainder checks
4706 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4707 MutableBigInteger mq = new MutableBigInteger();
4708 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4709 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4710 isRemainderZero = mr.isZero();
4711 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4712 if (!isRemainderZero) {
4713 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4714 mq.add(MutableBigInteger.ONE);
4715 }
4716 }
4717 return mq.toBigInteger(qsign);
4718 }
4719
4720 /**
4721 * Internally used for division operation for division {@code BigInteger}
4722 * by {@code BigInteger}.
4723 * The returned {@code BigDecimal} object is the quotient whose scale is set
4724 * to the passed in scale. If the remainder is not zero, it will be rounded
4725 * based on the passed in roundingMode. Also, if the remainder is zero and
4726 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4727 * trailing zeros of the result is stripped to match the preferredScale.
4728 */
4729 private static BigDecimal divideAndRound(BigInteger bdividend, BigInteger bdivisor, int scale, int roundingMode,
4730 int preferredScale) {
4731 boolean isRemainderZero; // record remainder is zero or not
4732 int qsign; // quotient sign
4733 // Descend into mutables for faster remainder checks
4734 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4735 MutableBigInteger mq = new MutableBigInteger();
4736 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4737 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4738 isRemainderZero = mr.isZero();
4739 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4740 if (!isRemainderZero) {
4741 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4742 mq.add(MutableBigInteger.ONE);
4743 }
4744 return mq.toBigDecimal(qsign, scale);
4745 } else {
4746 if (preferredScale != scale) {
4747 long compactVal = mq.toCompactValue(qsign);
4748 if (compactVal != INFLATED) {
4749 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4750 }
4751 BigInteger intVal = mq.toBigInteger(qsign);
4752 return createAndStripZerosToMatchScale(intVal, scale, preferredScale);
4753 } else {
4754 return mq.toBigDecimal(qsign, scale);
4755 }
4756 }
4757 }
4758
4759 /**
4760 * Tests if quotient has to be incremented according the roundingMode
4761 */
4762 private static boolean needIncrement(MutableBigInteger mdivisor, int roundingMode,
4763 int qsign, MutableBigInteger mq, MutableBigInteger mr) {
4764 assert !mr.isZero();
4765 int cmpFracHalf = mr.compareHalf(mdivisor);
4766 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
4767 }
4768
4769 /**
4770 * Remove insignificant trailing zeros from this
4771 * {@code BigInteger} value until the preferred scale is reached or no
4772 * more zeros can be removed. If the preferred scale is less than
4773 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4774 *
4775 * @return new {@code BigDecimal} with a scale possibly reduced
4776 * to be closed to the preferred scale.
4777 */
4778 private static BigDecimal createAndStripZerosToMatchScale(BigInteger intVal, int scale, long preferredScale) {
4779 BigInteger qr[]; // quotient-remainder pair
4780 while (intVal.compareMagnitude(BigInteger.TEN) >= 0
4781 && scale > preferredScale) {
4782 if (intVal.testBit(0))
4783 break; // odd number cannot end in 0
4784 qr = intVal.divideAndRemainder(BigInteger.TEN);
4785 if (qr[1].signum() != 0)
4786 break; // non-0 remainder
4787 intVal = qr[0];
4788 scale = checkScale(intVal,(long) scale - 1); // could Overflow
4789 }
4790 return valueOf(intVal, scale, 0);
4791 }
4792
4793 /**
4794 * Remove insignificant trailing zeros from this
4795 * {@code long} value until the preferred scale is reached or no
4796 * more zeros can be removed. If the preferred scale is less than
4797 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4798 *
4799 * @return new {@code BigDecimal} with a scale possibly reduced
4800 * to be closed to the preferred scale.
4801 */
4802 private static BigDecimal createAndStripZerosToMatchScale(long compactVal, int scale, long preferredScale) {
4803 while (Math.abs(compactVal) >= 10L && scale > preferredScale) {
4804 if ((compactVal & 1L) != 0L)
4805 break; // odd number cannot end in 0
4806 long r = compactVal % 10L;
4807 if (r != 0L)
4808 break; // non-0 remainder
4809 compactVal /= 10;
4810 scale = checkScale(compactVal, (long) scale - 1); // could Overflow
4811 }
4812 return valueOf(compactVal, scale);
4813 }
4814
4815 private static BigDecimal stripZerosToMatchScale(BigInteger intVal, long intCompact, int scale, int preferredScale) {
4816 if(intCompact!=INFLATED) {
4817 return createAndStripZerosToMatchScale(intCompact, scale, preferredScale);
4818 } else {
4819 return createAndStripZerosToMatchScale(intVal==null ? INFLATED_BIGINT : intVal,
4820 scale, preferredScale);
4821 }
4822 }
4823
4824 /*
4825 * returns INFLATED if oveflow
4826 */
4827 private static long add(long xs, long ys){
4828 long sum = xs + ys;
4829 // See "Hacker's Delight" section 2-12 for explanation of
4830 // the overflow test.
4831 if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) { // not overflowed
4832 return sum;
4833 }
4834 return INFLATED;
4835 }
4836
4837 private static BigDecimal add(long xs, long ys, int scale){
4838 long sum = add(xs, ys);
4839 if (sum!=INFLATED)
4840 return BigDecimal.valueOf(sum, scale);
4841 return new BigDecimal(BigInteger.valueOf(xs).add(ys), scale);
4842 }
4843
4844 private static BigDecimal add(final long xs, int scale1, final long ys, int scale2) {
4845 long sdiff = (long) scale1 - scale2;
4846 if (sdiff == 0) {
4847 return add(xs, ys, scale1);
4848 } else if (sdiff < 0) {
4849 int raise = checkScale(xs,-sdiff);
4850 long scaledX = longMultiplyPowerTen(xs, raise);
4851 if (scaledX != INFLATED) {
4852 return add(scaledX, ys, scale2);
4853 } else {
4854 BigInteger bigsum = bigMultiplyPowerTen(xs,raise).add(ys);
4855 return ((xs^ys)>=0) ? // same sign test
4856 new BigDecimal(bigsum, INFLATED, scale2, 0)
4857 : valueOf(bigsum, scale2, 0);
4858 }
4859 } else {
4860 int raise = checkScale(ys,sdiff);
4861 long scaledY = longMultiplyPowerTen(ys, raise);
4862 if (scaledY != INFLATED) {
4863 return add(xs, scaledY, scale1);
4864 } else {
4865 BigInteger bigsum = bigMultiplyPowerTen(ys,raise).add(xs);
4866 return ((xs^ys)>=0) ?
4867 new BigDecimal(bigsum, INFLATED, scale1, 0)
4868 : valueOf(bigsum, scale1, 0);
4869 }
4870 }
4871 }
4872
4873 private static BigDecimal add(final long xs, int scale1, BigInteger snd, int scale2) {
4874 int rscale = scale1;
4875 long sdiff = (long)rscale - scale2;
4876 boolean sameSigns = (Long.signum(xs) == snd.signum);
4877 BigInteger sum;
4878 if (sdiff < 0) {
4879 int raise = checkScale(xs,-sdiff);
4880 rscale = scale2;
4881 long scaledX = longMultiplyPowerTen(xs, raise);
4882 if (scaledX == INFLATED) {
4883 sum = snd.add(bigMultiplyPowerTen(xs,raise));
4884 } else {
4885 sum = snd.add(scaledX);
4886 }
4887 } else { //if (sdiff > 0) {
4888 int raise = checkScale(snd,sdiff);
4889 snd = bigMultiplyPowerTen(snd,raise);
4890 sum = snd.add(xs);
4891 }
4892 return (sameSigns) ?
4893 new BigDecimal(sum, INFLATED, rscale, 0) :
4894 valueOf(sum, rscale, 0);
4895 }
4896
4897 private static BigDecimal add(BigInteger fst, int scale1, BigInteger snd, int scale2) {
4898 int rscale = scale1;
4899 long sdiff = (long)rscale - scale2;
4900 if (sdiff != 0) {
4901 if (sdiff < 0) {
4902 int raise = checkScale(fst,-sdiff);
4903 rscale = scale2;
4904 fst = bigMultiplyPowerTen(fst,raise);
4905 } else {
4906 int raise = checkScale(snd,sdiff);
4907 snd = bigMultiplyPowerTen(snd,raise);
4908 }
4909 }
4910 BigInteger sum = fst.add(snd);
4911 return (fst.signum == snd.signum) ?
4912 new BigDecimal(sum, INFLATED, rscale, 0) :
4913 valueOf(sum, rscale, 0);
4914 }
4915
4916 private static BigInteger bigMultiplyPowerTen(long value, int n) {
4917 if (n <= 0)
4918 return BigInteger.valueOf(value);
4919 return bigTenToThe(n).multiply(value);
4920 }
4921
4922 private static BigInteger bigMultiplyPowerTen(BigInteger value, int n) {
4923 if (n <= 0)
4924 return value;
4925 if(n<LONG_TEN_POWERS_TABLE.length) {
4926 return value.multiply(LONG_TEN_POWERS_TABLE[n]);
4927 }
4928 return value.multiply(bigTenToThe(n));
4929 }
4930
4931 /**
4932 * Returns a {@code BigDecimal} whose value is {@code (xs /
4933 * ys)}, with rounding according to the context settings.
4934 *
4935 * Fast path - used only when (xscale <= yscale && yscale < 18
4936 * && mc.presision<18) {
4937 */
4938 private static BigDecimal divideSmallFastPath(final long xs, int xscale,
4939 final long ys, int yscale,
4940 long preferredScale, MathContext mc) {
4941 int mcp = mc.precision;
4942 int roundingMode = mc.roundingMode.oldMode;
4943
4944 assert (xscale <= yscale) && (yscale < 18) && (mcp < 18);
4945 int xraise = yscale - xscale; // xraise >=0
4946 long scaledX = (xraise==0) ? xs :
4947 longMultiplyPowerTen(xs, xraise); // can't overflow here!
4948 BigDecimal quotient;
4949
4950 int cmp = longCompareMagnitude(scaledX, ys);
4951 if(cmp > 0) { // satisfy constraint (b)
4952 yscale -= 1; // [that is, divisor *= 10]
4953 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4954 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
4955 // assert newScale >= xscale
4956 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4957 long scaledXs;
4958 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
4959 quotient = null;
4960 if((mcp-1) >=0 && (mcp-1)<LONG_TEN_POWERS_TABLE.length) {
4961 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp-1], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4962 }
4963 if(quotient==null) {
4964 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp-1);
4965 quotient = divideAndRound(rb, ys,
4966 scl, roundingMode, checkScaleNonZero(preferredScale));
4967 }
4968 } else {
4969 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4970 }
4971 } else {
4972 int newScale = checkScaleNonZero((long) xscale - mcp);
4973 // assert newScale >= yscale
4974 if (newScale == yscale) { // easy case
4975 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4976 } else {
4977 int raise = checkScaleNonZero((long) newScale - yscale);
4978 long scaledYs;
4979 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4980 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4981 quotient = divideAndRound(BigInteger.valueOf(xs),
4982 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4983 } else {
4984 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4985 }
4986 }
4987 }
4988 } else {
4989 // abs(scaledX) <= abs(ys)
4990 // result is "scaledX * 10^msp / ys"
4991 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4992 if(cmp==0) {
4993 // abs(scaleX)== abs(ys) => result will be scaled 10^mcp + correct sign
4994 quotient = roundedTenPower(((scaledX < 0) == (ys < 0)) ? 1 : -1, mcp, scl, checkScaleNonZero(preferredScale));
4995 } else {
4996 // abs(scaledX) < abs(ys)
4997 long scaledXs;
4998 if ((scaledXs = longMultiplyPowerTen(scaledX, mcp)) == INFLATED) {
4999 quotient = null;
5000 if(mcp<LONG_TEN_POWERS_TABLE.length) {
5001 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5002 }
5003 if(quotient==null) {
5004 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp);
5005 quotient = divideAndRound(rb, ys,
5006 scl, roundingMode, checkScaleNonZero(preferredScale));
5007 }
5008 } else {
5009 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5010 }
5011 }
5012 }
5013 // doRound, here, only affects 1000000000 case.
5014 return doRound(quotient,mc);
5015 }
5016
5017 /**
5018 * Returns a {@code BigDecimal} whose value is {@code (xs /
5019 * ys)}, with rounding according to the context settings.
5020 */
5021 private static BigDecimal divide(final long xs, int xscale, final long ys, int yscale, long preferredScale, MathContext mc) {
5022 int mcp = mc.precision;
5023 if(xscale <= yscale && yscale < 18 && mcp<18) {
5024 return divideSmallFastPath(xs, xscale, ys, yscale, preferredScale, mc);
5025 }
5026 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
5027 yscale -= 1; // [that is, divisor *= 10]
5028 }
5029 int roundingMode = mc.roundingMode.oldMode;
5030 // In order to find out whether the divide generates the exact result,
5031 // we avoid calling the above divide method. 'quotient' holds the
5032 // return BigDecimal object whose scale will be set to 'scl'.
5033 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
5034 BigDecimal quotient;
5035 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
5036 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
5037 long scaledXs;
5038 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
5039 BigInteger rb = bigMultiplyPowerTen(xs,raise);
5040 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5041 } else {
5042 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5043 }
5044 } else {
5045 int newScale = checkScaleNonZero((long) xscale - mcp);
5046 // assert newScale >= yscale
5047 if (newScale == yscale) { // easy case
5048 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
5049 } else {
5050 int raise = checkScaleNonZero((long) newScale - yscale);
5051 long scaledYs;
5052 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
5053 BigInteger rb = bigMultiplyPowerTen(ys,raise);
5054 quotient = divideAndRound(BigInteger.valueOf(xs),
5055 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
5056 } else {
5057 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
5058 }
5059 }
5060 }
5061 // doRound, here, only affects 1000000000 case.
5062 return doRound(quotient,mc);
5063 }
5064
5065 /**
5066 * Returns a {@code BigDecimal} whose value is {@code (xs /
5067 * ys)}, with rounding according to the context settings.
5068 */
5069 private static BigDecimal divide(BigInteger xs, int xscale, long ys, int yscale, long preferredScale, MathContext mc) {
5070 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5071 if ((-compareMagnitudeNormalized(ys, yscale, xs, xscale)) > 0) {// satisfy constraint (b)
5072 yscale -= 1; // [that is, divisor *= 10]
5073 }
5074 int mcp = mc.precision;
5075 int roundingMode = mc.roundingMode.oldMode;
5076
5077 // In order to find out whether the divide generates the exact result,
5078 // we avoid calling the above divide method. 'quotient' holds the
5079 // return BigDecimal object whose scale will be set to 'scl'.
5080 BigDecimal quotient;
5081 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
5082 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
5083 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
5084 BigInteger rb = bigMultiplyPowerTen(xs,raise);
5085 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5086 } else {
5087 int newScale = checkScaleNonZero((long) xscale - mcp);
5088 // assert newScale >= yscale
5089 if (newScale == yscale) { // easy case
5090 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
5091 } else {
5092 int raise = checkScaleNonZero((long) newScale - yscale);
5093 long scaledYs;
5094 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
5095 BigInteger rb = bigMultiplyPowerTen(ys,raise);
5096 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
5097 } else {
5098 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
5099 }
5100 }
5101 }
5102 // doRound, here, only affects 1000000000 case.
5103 return doRound(quotient, mc);
5104 }
5105
5106 /**
5107 * Returns a {@code BigDecimal} whose value is {@code (xs /
5108 * ys)}, with rounding according to the context settings.
5109 */
5110 private static BigDecimal divide(long xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
5111 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5112 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
5113 yscale -= 1; // [that is, divisor *= 10]
5114 }
5115 int mcp = mc.precision;
5116 int roundingMode = mc.roundingMode.oldMode;
5117
5118 // In order to find out whether the divide generates the exact result,
5119 // we avoid calling the above divide method. 'quotient' holds the
5120 // return BigDecimal object whose scale will be set to 'scl'.
5121 BigDecimal quotient;
5122 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
5123 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
5124 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
5125 BigInteger rb = bigMultiplyPowerTen(xs,raise);
5126 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5127 } else {
5128 int newScale = checkScaleNonZero((long) xscale - mcp);
5129 int raise = checkScaleNonZero((long) newScale - yscale);
5130 BigInteger rb = bigMultiplyPowerTen(ys,raise);
5131 quotient = divideAndRound(BigInteger.valueOf(xs), rb, scl, roundingMode,checkScaleNonZero(preferredScale));
5132 }
5133 // doRound, here, only affects 1000000000 case.
5134 return doRound(quotient, mc);
5135 }
5136
5137 /**
5138 * Returns a {@code BigDecimal} whose value is {@code (xs /
5139 * ys)}, with rounding according to the context settings.
5140 */
5141 private static BigDecimal divide(BigInteger xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
5142 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5143 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
5144 yscale -= 1; // [that is, divisor *= 10]
5145 }
5146 int mcp = mc.precision;
5147 int roundingMode = mc.roundingMode.oldMode;
5148
5149 // In order to find out whether the divide generates the exact result,
5150 // we avoid calling the above divide method. 'quotient' holds the
5151 // return BigDecimal object whose scale will be set to 'scl'.
5152 BigDecimal quotient;
5153 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
5154 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) {
5155 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
5156 BigInteger rb = bigMultiplyPowerTen(xs,raise);
5157 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
5158 } else {
5159 int newScale = checkScaleNonZero((long) xscale - mcp);
5160 int raise = checkScaleNonZero((long) newScale - yscale);
5161 BigInteger rb = bigMultiplyPowerTen(ys,raise);
5162 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
5163 }
5164 // doRound, here, only affects 1000000000 case.
5165 return doRound(quotient, mc);
5166 }
5167
5168 /*
5169 * performs divideAndRound for (dividend0*dividend1, divisor)
5170 * returns null if quotient can't fit into long value;
5171 */
5172 private static BigDecimal multiplyDivideAndRound(long dividend0, long dividend1, long divisor, int scale, int roundingMode,
5173 int preferredScale) {
5174 int qsign = Long.signum(dividend0)*Long.signum(dividend1)*Long.signum(divisor);
5175 dividend0 = Math.abs(dividend0);
5176 dividend1 = Math.abs(dividend1);
5177 divisor = Math.abs(divisor);
5178 // multiply dividend0 * dividend1
5179 long d0_hi = dividend0 >>> 32;
5180 long d0_lo = dividend0 & LONG_MASK;
5181 long d1_hi = dividend1 >>> 32;
5182 long d1_lo = dividend1 & LONG_MASK;
5183 long product = d0_lo * d1_lo;
5184 long d0 = product & LONG_MASK;
5185 long d1 = product >>> 32;
5186 product = d0_hi * d1_lo + d1;
5187 d1 = product & LONG_MASK;
5188 long d2 = product >>> 32;
5189 product = d0_lo * d1_hi + d1;
5190 d1 = product & LONG_MASK;
5191 d2 += product >>> 32;
5192 long d3 = d2>>>32;
5193 d2 &= LONG_MASK;
5194 product = d0_hi*d1_hi + d2;
5195 d2 = product & LONG_MASK;
5196 d3 = ((product>>>32) + d3) & LONG_MASK;
5197 final long dividendHi = make64(d3,d2);
5198 final long dividendLo = make64(d1,d0);
5199 // divide
5200 return divideAndRound128(dividendHi, dividendLo, divisor, qsign, scale, roundingMode, preferredScale);
5201 }
5202
5203 private static final long DIV_NUM_BASE = (1L<<32); // Number base (32 bits).
5204
5205 /*
5206 * divideAndRound 128-bit value by long divisor.
5207 * returns null if quotient can't fit into long value;
5208 * Specialized version of Knuth's division
5209 */
5210 private static BigDecimal divideAndRound128(final long dividendHi, final long dividendLo, long divisor, int sign,
5211 int scale, int roundingMode, int preferredScale) {
5212 if (dividendHi >= divisor) {
5213 return null;
5214 }
5215
5216 final int shift = Long.numberOfLeadingZeros(divisor);
5217 divisor <<= shift;
5218
5219 final long v1 = divisor >>> 32;
5220 final long v0 = divisor & LONG_MASK;
5221
5222 long tmp = dividendLo << shift;
5223 long u1 = tmp >>> 32;
5224 long u0 = tmp & LONG_MASK;
5225
5226 tmp = (dividendHi << shift) | (dividendLo >>> 64 - shift);
5227 long u2 = tmp & LONG_MASK;
5228 long q1, r_tmp;
5229 if (v1 == 1) {
5230 q1 = tmp;
5231 r_tmp = 0;
5232 } else if (tmp >= 0) {
5233 q1 = tmp / v1;
5234 r_tmp = tmp - q1 * v1;
5235 } else {
5236 long[] rq = divRemNegativeLong(tmp, v1);
5237 q1 = rq[1];
5238 r_tmp = rq[0];
5239 }
5240
5241 while(q1 >= DIV_NUM_BASE || unsignedLongCompare(q1*v0, make64(r_tmp, u1))) {
5242 q1--;
5243 r_tmp += v1;
5244 if (r_tmp >= DIV_NUM_BASE)
5245 break;
5246 }
5247
5248 tmp = mulsub(u2,u1,v1,v0,q1);
5249 u1 = tmp & LONG_MASK;
5250 long q0;
5251 if (v1 == 1) {
5252 q0 = tmp;
5253 r_tmp = 0;
5254 } else if (tmp >= 0) {
5255 q0 = tmp / v1;
5256 r_tmp = tmp - q0 * v1;
5257 } else {
5258 long[] rq = divRemNegativeLong(tmp, v1);
5259 q0 = rq[1];
5260 r_tmp = rq[0];
5261 }
5262
5263 while(q0 >= DIV_NUM_BASE || unsignedLongCompare(q0*v0,make64(r_tmp,u0))) {
5264 q0--;
5265 r_tmp += v1;
5266 if (r_tmp >= DIV_NUM_BASE)
5267 break;
5268 }
5269
5270 if((int)q1 < 0) {
5271 // result (which is positive and unsigned here)
5272 // can't fit into long due to sign bit is used for value
5273 MutableBigInteger mq = new MutableBigInteger(new int[]{(int)q1, (int)q0});
5274 if (roundingMode == ROUND_DOWN && scale == preferredScale) {
5275 return mq.toBigDecimal(sign, scale);
5276 }
5277 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
5278 if (r != 0) {
5279 if(needIncrement(divisor >>> shift, roundingMode, sign, mq, r)){
5280 mq.add(MutableBigInteger.ONE);
5281 }
5282 return mq.toBigDecimal(sign, scale);
5283 } else {
5284 if (preferredScale != scale) {
5285 BigInteger intVal = mq.toBigInteger(sign);
5286 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
5287 } else {
5288 return mq.toBigDecimal(sign, scale);
5289 }
5290 }
5291 }
5292
5293 long q = make64(q1,q0);
5294 q*=sign;
5295
5296 if (roundingMode == ROUND_DOWN && scale == preferredScale)
5297 return valueOf(q, scale);
5298
5299 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
5300 if (r != 0) {
5301 boolean increment = needIncrement(divisor >>> shift, roundingMode, sign, q, r);
5302 return valueOf((increment ? q + sign : q), scale);
5303 } else {
5304 if (preferredScale != scale) {
5305 return createAndStripZerosToMatchScale(q, scale, preferredScale);
5306 } else {
5307 return valueOf(q, scale);
5308 }
5309 }
5310 }
5311
5312 /*
5313 * calculate divideAndRound for ldividend*10^raise / divisor
5314 * when abs(dividend)==abs(divisor);
5315 */
5316 private static BigDecimal roundedTenPower(int qsign, int raise, int scale, int preferredScale) {
5317 if (scale > preferredScale) {
5318 int diff = scale - preferredScale;
5319 if(diff < raise) {
5320 return scaledTenPow(raise - diff, qsign, preferredScale);
5321 } else {
5322 return valueOf(qsign,scale-raise);
5323 }
5324 } else {
5325 return scaledTenPow(raise, qsign, scale);
5326 }
5327 }
5328
5329 static BigDecimal scaledTenPow(int n, int sign, int scale) {
5330 if (n < LONG_TEN_POWERS_TABLE.length)
5331 return valueOf(sign*LONG_TEN_POWERS_TABLE[n],scale);
5332 else {
5333 BigInteger unscaledVal = bigTenToThe(n);
5334 if(sign==-1) {
5335 unscaledVal = unscaledVal.negate();
5336 }
5337 return new BigDecimal(unscaledVal, INFLATED, scale, n+1);
5338 }
5339 }
5340
5341 /**
5342 * Calculate the quotient and remainder of dividing a negative long by
5343 * another long.
5344 *
5345 * @param n the numerator; must be negative
5346 * @param d the denominator; must not be unity
5347 * @return a two-element {@long} array with the remainder and quotient in
5348 * the initial and final elements, respectively
5349 */
5350 private static long[] divRemNegativeLong(long n, long d) {
5351 assert n < 0 : "Non-negative numerator " + n;
5352 assert d != 1 : "Unity denominator";
5353
5354 // Approximate the quotient and remainder
5355 long q = (n >>> 1) / (d >>> 1);
5356 long r = n - q * d;
5357
5358 // Correct the approximation
5359 while (r < 0) {
5360 r += d;
5361 q--;
5362 }
5363 while (r >= d) {
5364 r -= d;
5365 q++;
5366 }
5367
5368 // n - q*d == r && 0 <= r < d, hence we're done.
5369 return new long[] {r, q};
5370 }
5371
5372 private static long make64(long hi, long lo) {
5373 return hi<<32 | lo;
5374 }
5375
5376 private static long mulsub(long u1, long u0, final long v1, final long v0, long q0) {
5377 long tmp = u0 - q0*v0;
5378 return make64(u1 + (tmp>>>32) - q0*v1,tmp & LONG_MASK);
5379 }
5380
5381 private static boolean unsignedLongCompare(long one, long two) {
5382 return (one+Long.MIN_VALUE) > (two+Long.MIN_VALUE);
5383 }
5384
5385 private static boolean unsignedLongCompareEq(long one, long two) {
5386 return (one+Long.MIN_VALUE) >= (two+Long.MIN_VALUE);
5387 }
5388
5389
5390 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5391 private static int compareMagnitudeNormalized(long xs, int xscale, long ys, int yscale) {
5392 // assert xs!=0 && ys!=0
5393 int sdiff = xscale - yscale;
5394 if (sdiff != 0) {
5395 if (sdiff < 0) {
5396 xs = longMultiplyPowerTen(xs, -sdiff);
5397 } else { // sdiff > 0
5398 ys = longMultiplyPowerTen(ys, sdiff);
5399 }
5400 }
5401 if (xs != INFLATED)
5402 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
5403 else
5404 return 1;
5405 }
5406
5407 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5408 private static int compareMagnitudeNormalized(long xs, int xscale, BigInteger ys, int yscale) {
5409 // assert "ys can't be represented as long"
5410 if (xs == 0)
5411 return -1;
5412 int sdiff = xscale - yscale;
5413 if (sdiff < 0) {
5414 if (longMultiplyPowerTen(xs, -sdiff) == INFLATED ) {
5415 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
5416 }
5417 }
5418 return -1;
5419 }
5420
5421 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
5422 private static int compareMagnitudeNormalized(BigInteger xs, int xscale, BigInteger ys, int yscale) {
5423 int sdiff = xscale - yscale;
5424 if (sdiff < 0) {
5425 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
5426 } else { // sdiff >= 0
5427 return xs.compareMagnitude(bigMultiplyPowerTen(ys, sdiff));
5428 }
5429 }
5430
5431 private static long multiply(long x, long y){
5432 long product = x * y;
5433 long ax = Math.abs(x);
5434 long ay = Math.abs(y);
5435 if (((ax | ay) >>> 31 == 0) || (y == 0) || (product / y == x)){
5436 return product;
5437 }
5438 return INFLATED;
5439 }
5440
5441 private static BigDecimal multiply(long x, long y, int scale) {
5442 long product = multiply(x, y);
5443 if(product!=INFLATED) {
5444 return valueOf(product,scale);
5445 }
5446 return new BigDecimal(BigInteger.valueOf(x).multiply(y),INFLATED,scale,0);
5447 }
5448
5449 private static BigDecimal multiply(long x, BigInteger y, int scale) {
5450 if(x==0) {
5451 return zeroValueOf(scale);
5452 }
5453 return new BigDecimal(y.multiply(x),INFLATED,scale,0);
5454 }
5455
5456 private static BigDecimal multiply(BigInteger x, BigInteger y, int scale) {
5457 return new BigDecimal(x.multiply(y),INFLATED,scale,0);
5458 }
5459
5460 /**
5461 * Multiplies two long values and rounds according {@code MathContext}
5462 */
5463 private static BigDecimal multiplyAndRound(long x, long y, int scale, MathContext mc) {
5464 long product = multiply(x, y);
5465 if(product!=INFLATED) {
5466 return doRound(product, scale, mc);
5467 }
5468 // attempt to do it in 128 bits
5469 int rsign = 1;
5470 if(x < 0) {
5471 x = -x;
5472 rsign = -1;
5473 }
5474 if(y < 0) {
5475 y = -y;
5476 rsign *= -1;
5477 }
5478 // multiply dividend0 * dividend1
5479 long m0_hi = x >>> 32;
5480 long m0_lo = x & LONG_MASK;
5481 long m1_hi = y >>> 32;
5482 long m1_lo = y & LONG_MASK;
5483 product = m0_lo * m1_lo;
5484 long m0 = product & LONG_MASK;
5485 long m1 = product >>> 32;
5486 product = m0_hi * m1_lo + m1;
5487 m1 = product & LONG_MASK;
5488 long m2 = product >>> 32;
5489 product = m0_lo * m1_hi + m1;
5490 m1 = product & LONG_MASK;
5491 m2 += product >>> 32;
5492 long m3 = m2>>>32;
5493 m2 &= LONG_MASK;
5494 product = m0_hi*m1_hi + m2;
5495 m2 = product & LONG_MASK;
5496 m3 = ((product>>>32) + m3) & LONG_MASK;
5497 final long mHi = make64(m3,m2);
5498 final long mLo = make64(m1,m0);
5499 BigDecimal res = doRound128(mHi, mLo, rsign, scale, mc);
5500 if(res!=null) {
5501 return res;
5502 }
5503 res = new BigDecimal(BigInteger.valueOf(x).multiply(y*rsign), INFLATED, scale, 0);
5504 return doRound(res,mc);
5505 }
5506
5507 private static BigDecimal multiplyAndRound(long x, BigInteger y, int scale, MathContext mc) {
5508 if(x==0) {
5509 return zeroValueOf(scale);
5510 }
5511 return doRound(y.multiply(x), scale, mc);
5512 }
5513
5514 private static BigDecimal multiplyAndRound(BigInteger x, BigInteger y, int scale, MathContext mc) {
5515 return doRound(x.multiply(y), scale, mc);
5516 }
5517
5518 /**
5519 * rounds 128-bit value according {@code MathContext}
5520 * returns null if result can't be repsented as compact BigDecimal.
5521 */
5522 private static BigDecimal doRound128(long hi, long lo, int sign, int scale, MathContext mc) {
5523 int mcp = mc.precision;
5524 int drop;
5525 BigDecimal res = null;
5526 if(((drop = precision(hi, lo) - mcp) > 0)&&(drop<LONG_TEN_POWERS_TABLE.length)) {
5527 scale = checkScaleNonZero((long)scale - drop);
5528 res = divideAndRound128(hi, lo, LONG_TEN_POWERS_TABLE[drop], sign, scale, mc.roundingMode.oldMode, scale);
5529 }
5530 if(res!=null) {
5531 return doRound(res,mc);
5532 }
5533 return null;
5534 }
5535
5536 private static final long[][] LONGLONG_TEN_POWERS_TABLE = {
5537 { 0L, 0x8AC7230489E80000L }, //10^19
5538 { 0x5L, 0x6bc75e2d63100000L }, //10^20
5539 { 0x36L, 0x35c9adc5dea00000L }, //10^21
5540 { 0x21eL, 0x19e0c9bab2400000L }, //10^22
5541 { 0x152dL, 0x02c7e14af6800000L }, //10^23
5542 { 0xd3c2L, 0x1bcecceda1000000L }, //10^24
5543 { 0x84595L, 0x161401484a000000L }, //10^25
5544 { 0x52b7d2L, 0xdcc80cd2e4000000L }, //10^26
5545 { 0x33b2e3cL, 0x9fd0803ce8000000L }, //10^27
5546 { 0x204fce5eL, 0x3e25026110000000L }, //10^28
5547 { 0x1431e0faeL, 0x6d7217caa0000000L }, //10^29
5548 { 0xc9f2c9cd0L, 0x4674edea40000000L }, //10^30
5549 { 0x7e37be2022L, 0xc0914b2680000000L }, //10^31
5550 { 0x4ee2d6d415bL, 0x85acef8100000000L }, //10^32
5551 { 0x314dc6448d93L, 0x38c15b0a00000000L }, //10^33
5552 { 0x1ed09bead87c0L, 0x378d8e6400000000L }, //10^34
5553 { 0x13426172c74d82L, 0x2b878fe800000000L }, //10^35
5554 { 0xc097ce7bc90715L, 0xb34b9f1000000000L }, //10^36
5555 { 0x785ee10d5da46d9L, 0x00f436a000000000L }, //10^37
5556 { 0x4b3b4ca85a86c47aL, 0x098a224000000000L }, //10^38
5557 };
5558
5559 /*
5560 * returns precision of 128-bit value
5561 */
5562 private static int precision(long hi, long lo){
5563 if(hi==0) {
5564 if(lo>=0) {
5565 return longDigitLength(lo);
5566 }
5567 return (unsignedLongCompareEq(lo, LONGLONG_TEN_POWERS_TABLE[0][1])) ? 20 : 19;
5568 // 0x8AC7230489E80000L = unsigned 2^19
5569 }
5570 int r = ((128 - Long.numberOfLeadingZeros(hi) + 1) * 1233) >>> 12;
5571 int idx = r-19;
5572 return (idx >= LONGLONG_TEN_POWERS_TABLE.length || longLongCompareMagnitude(hi, lo,
5573 LONGLONG_TEN_POWERS_TABLE[idx][0], LONGLONG_TEN_POWERS_TABLE[idx][1])) ? r : r + 1;
5574 }
5575
5576 /*
5577 * returns true if 128 bit number <hi0,lo0> is less than <hi1,lo1>
5578 * hi0 & hi1 should be non-negative
5579 */
5580 private static boolean longLongCompareMagnitude(long hi0, long lo0, long hi1, long lo1) {
5581 if(hi0!=hi1) {
5582 return hi0<hi1;
5583 }
5584 return (lo0+Long.MIN_VALUE) <(lo1+Long.MIN_VALUE);
5585 }
5586
5587 private static BigDecimal divide(long dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5588 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5589 int newScale = scale + divisorScale;
5590 int raise = newScale - dividendScale;
5591 if(raise<LONG_TEN_POWERS_TABLE.length) {
5592 long xs = dividend;
5593 if ((xs = longMultiplyPowerTen(xs, raise)) != INFLATED) {
5594 return divideAndRound(xs, divisor, scale, roundingMode, scale);
5595 }
5596 BigDecimal q = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[raise], dividend, divisor, scale, roundingMode, scale);
5597 if(q!=null) {
5598 return q;
5599 }
5600 }
5601 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5602 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5603 } else {
5604 int newScale = checkScale(divisor,(long)dividendScale - scale);
5605 int raise = newScale - divisorScale;
5606 if(raise<LONG_TEN_POWERS_TABLE.length) {
5607 long ys = divisor;
5608 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5609 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5610 }
5611 }
5612 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5613 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5614 }
5615 }
5616
5617 private static BigDecimal divide(BigInteger dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5618 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5619 int newScale = scale + divisorScale;
5620 int raise = newScale - dividendScale;
5621 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5622 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5623 } else {
5624 int newScale = checkScale(divisor,(long)dividendScale - scale);
5625 int raise = newScale - divisorScale;
5626 if(raise<LONG_TEN_POWERS_TABLE.length) {
5627 long ys = divisor;
5628 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5629 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5630 }
5631 }
5632 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5633 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5634 }
5635 }
5636
5637 private static BigDecimal divide(long dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5638 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5639 int newScale = scale + divisorScale;
5640 int raise = newScale - dividendScale;
5641 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5642 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5643 } else {
5644 int newScale = checkScale(divisor,(long)dividendScale - scale);
5645 int raise = newScale - divisorScale;
5646 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5647 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5648 }
5649 }
5650
5651 private static BigDecimal divide(BigInteger dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5652 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5653 int newScale = scale + divisorScale;
5654 int raise = newScale - dividendScale;
5655 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5656 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5657 } else {
5658 int newScale = checkScale(divisor,(long)dividendScale - scale);
5659 int raise = newScale - divisorScale;
5660 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5661 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5662 }
5663 }
5664
5665 }