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