1 /*
2 * Copyright (c) 1996, 2013, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26 /*
27 * Portions Copyright IBM Corporation, 2001. All Rights Reserved.
28 */
29
30 package java.math;
31
32 import java.util.Arrays;
33 import static java.math.BigInteger.LONG_MASK;
34
35 /**
36 * Immutable, arbitrary-precision signed decimal numbers. A
37 * {@code BigDecimal} consists of an arbitrary precision integer
38 * <i>unscaled value</i> and a 32-bit integer <i>scale</i>. If zero
39 * or positive, the scale is the number of digits to the right of the
40 * decimal point. If negative, the unscaled value of the number is
41 * multiplied by ten to the power of the negation of the scale. The
42 * value of the number represented by the {@code BigDecimal} is
43 * therefore <tt>(unscaledValue × 10<sup>-scale</sup>)</tt>.
44 *
45 * <p>The {@code BigDecimal} class provides operations for
46 * arithmetic, scale manipulation, rounding, comparison, hashing, and
47 * format conversion. The {@link #toString} method provides a
48 * canonical representation of a {@code BigDecimal}.
49 *
50 * <p>The {@code BigDecimal} class gives its user complete control
51 * over rounding behavior. If no rounding mode is specified and the
52 * exact result cannot be represented, an exception is thrown;
53 * otherwise, calculations can be carried out to a chosen precision
54 * and rounding mode by supplying an appropriate {@link MathContext}
55 * object to the operation. In either case, eight <em>rounding
56 * modes</em> are provided for the control of rounding. Using the
57 * integer fields in this class (such as {@link #ROUND_HALF_UP}) to
58 * represent rounding mode is largely obsolete; the enumeration values
59 * of the {@code RoundingMode} {@code enum}, (such as {@link
60 * RoundingMode#HALF_UP}) should be used instead.
61 *
62 * <p>When a {@code MathContext} object is supplied with a precision
63 * setting of 0 (for example, {@link MathContext#UNLIMITED}),
64 * arithmetic operations are exact, as are the arithmetic methods
65 * which take no {@code MathContext} object. (This is the only
66 * behavior that was supported in releases prior to 5.) As a
67 * corollary of computing the exact result, the rounding mode setting
68 * of a {@code MathContext} object with a precision setting of 0 is
69 * not used and thus irrelevant. In the case of divide, the exact
70 * quotient could have an infinitely long decimal expansion; for
71 * example, 1 divided by 3. If the quotient has a nonterminating
72 * decimal expansion and the operation is specified to return an exact
73 * result, an {@code ArithmeticException} is thrown. Otherwise, the
74 * exact result of the division is returned, as done for other
75 * operations.
76 *
77 * <p>When the precision setting is not 0, the rules of
78 * {@code BigDecimal} arithmetic are broadly compatible with selected
79 * modes of operation of the arithmetic defined in ANSI X3.274-1996
80 * and ANSI X3.274-1996/AM 1-2000 (section 7.4). Unlike those
81 * standards, {@code BigDecimal} includes many rounding modes, which
82 * were mandatory for division in {@code BigDecimal} releases prior
83 * to 5. Any conflicts between these ANSI standards and the
84 * {@code BigDecimal} specification are resolved in favor of
85 * {@code BigDecimal}.
86 *
87 * <p>Since the same numerical value can have different
88 * representations (with different scales), the rules of arithmetic
89 * and rounding must specify both the numerical result and the scale
90 * used in the result's representation.
91 *
92 *
93 * <p>In general the rounding modes and precision setting determine
94 * how operations return results with a limited number of digits when
95 * the exact result has more digits (perhaps infinitely many in the
96 * case of division) than the number of digits returned.
97 *
98 * First, the
99 * total number of digits to return is specified by the
100 * {@code MathContext}'s {@code precision} setting; this determines
101 * the result's <i>precision</i>. The digit count starts from the
102 * leftmost nonzero digit of the exact result. The rounding mode
103 * determines how any discarded trailing digits affect the returned
104 * result.
105 *
106 * <p>For all arithmetic operators , the operation is carried out as
107 * though an exact intermediate result were first calculated and then
108 * rounded to the number of digits specified by the precision setting
109 * (if necessary), using the selected rounding mode. If the exact
110 * result is not returned, some digit positions of the exact result
111 * are discarded. When rounding increases the magnitude of the
112 * returned result, it is possible for a new digit position to be
113 * created by a carry propagating to a leading {@literal "9"} digit.
114 * For example, rounding the value 999.9 to three digits rounding up
115 * would be numerically equal to one thousand, represented as
116 * 100×10<sup>1</sup>. In such cases, the new {@literal "1"} is
117 * the leading digit position of the returned result.
118 *
119 * <p>Besides a logical exact result, each arithmetic operation has a
120 * preferred scale for representing a result. The preferred
121 * scale for each operation is listed in the table below.
122 *
123 * <table border>
124 * <caption><b>Preferred Scales for Results of Arithmetic Operations
125 * </b></caption>
126 * <tr><th>Operation</th><th>Preferred Scale of Result</th></tr>
127 * <tr><td>Add</td><td>max(addend.scale(), augend.scale())</td>
128 * <tr><td>Subtract</td><td>max(minuend.scale(), subtrahend.scale())</td>
129 * <tr><td>Multiply</td><td>multiplier.scale() + multiplicand.scale()</td>
130 * <tr><td>Divide</td><td>dividend.scale() - divisor.scale()</td>
131 * </table>
132 *
133 * These scales are the ones used by the methods which return exact
134 * arithmetic results; except that an exact divide may have to use a
135 * larger scale since the exact result may have more digits. For
136 * example, {@code 1/32} is {@code 0.03125}.
137 *
138 * <p>Before rounding, the scale of the logical exact intermediate
139 * result is the preferred scale for that operation. If the exact
140 * numerical result cannot be represented in {@code precision}
141 * digits, rounding selects the set of digits to return and the scale
142 * of the result is reduced from the scale of the intermediate result
143 * to the least scale which can represent the {@code precision}
144 * digits actually returned. If the exact result can be represented
145 * with at most {@code precision} digits, the representation
146 * of the result with the scale closest to the preferred scale is
147 * returned. In particular, an exactly representable quotient may be
148 * represented in fewer than {@code precision} digits by removing
149 * trailing zeros and decreasing the scale. For example, rounding to
150 * three digits using the {@linkplain RoundingMode#FLOOR floor}
151 * rounding mode, <br>
152 *
153 * {@code 19/100 = 0.19 // integer=19, scale=2} <br>
154 *
155 * but<br>
156 *
157 * {@code 21/110 = 0.190 // integer=190, scale=3} <br>
158 *
159 * <p>Note that for add, subtract, and multiply, the reduction in
160 * scale will equal the number of digit positions of the exact result
161 * which are discarded. If the rounding causes a carry propagation to
162 * create a new high-order digit position, an additional digit of the
163 * result is discarded than when no new digit position is created.
164 *
165 * <p>Other methods may have slightly different rounding semantics.
166 * For example, the result of the {@code pow} method using the
167 * {@linkplain #pow(int, MathContext) specified algorithm} can
168 * occasionally differ from the rounded mathematical result by more
169 * than one unit in the last place, one <i>{@linkplain #ulp() ulp}</i>.
170 *
171 * <p>Two types of operations are provided for manipulating the scale
172 * of a {@code BigDecimal}: scaling/rounding operations and decimal
173 * point motion operations. Scaling/rounding operations ({@link
174 * #setScale setScale} and {@link #round round}) return a
175 * {@code BigDecimal} whose value is approximately (or exactly) equal
176 * to that of the operand, but whose scale or precision is the
177 * specified value; that is, they increase or decrease the precision
178 * of the stored number with minimal effect on its value. Decimal
179 * point motion operations ({@link #movePointLeft movePointLeft} and
180 * {@link #movePointRight movePointRight}) return a
181 * {@code BigDecimal} created from the operand by moving the decimal
182 * point a specified distance in the specified direction.
183 *
184 * <p>For the sake of brevity and clarity, pseudo-code is used
185 * throughout the descriptions of {@code BigDecimal} methods. The
186 * pseudo-code expression {@code (i + j)} is shorthand for "a
187 * {@code BigDecimal} whose value is that of the {@code BigDecimal}
188 * {@code i} added to that of the {@code BigDecimal}
189 * {@code j}." The pseudo-code expression {@code (i == j)} is
190 * shorthand for "{@code true} if and only if the
191 * {@code BigDecimal} {@code i} represents the same value as the
192 * {@code BigDecimal} {@code j}." Other pseudo-code expressions
193 * are interpreted similarly. Square brackets are used to represent
194 * the particular {@code BigInteger} and scale pair defining a
195 * {@code BigDecimal} value; for example [19, 2] is the
196 * {@code BigDecimal} numerically equal to 0.19 having a scale of 2.
197 *
198 * <p>Note: care should be exercised if {@code BigDecimal} objects
199 * are used as keys in a {@link java.util.SortedMap SortedMap} or
200 * elements in a {@link java.util.SortedSet SortedSet} since
201 * {@code BigDecimal}'s <i>natural ordering</i> is <i>inconsistent
202 * with equals</i>. See {@link Comparable}, {@link
203 * java.util.SortedMap} or {@link java.util.SortedSet} for more
204 * information.
205 *
206 * <p>All methods and constructors for this class throw
207 * {@code NullPointerException} when passed a {@code null} object
208 * reference for any input parameter.
209 *
210 * @see BigInteger
211 * @see MathContext
212 * @see RoundingMode
213 * @see java.util.SortedMap
214 * @see java.util.SortedSet
215 * @author Josh Bloch
216 * @author Mike Cowlishaw
217 * @author Joseph D. Darcy
218 * @author Sergey V. Kuksenko
219 */
220 public class BigDecimal extends Number implements Comparable<BigDecimal> {
221 /**
222 * The unscaled value of this BigDecimal, as returned by {@link
223 * #unscaledValue}.
224 *
225 * @serial
226 * @see #unscaledValue
227 */
228 private final BigInteger intVal;
229
230 /**
231 * The scale of this BigDecimal, as returned by {@link #scale}.
232 *
233 * @serial
234 * @see #scale
235 */
236 private final int scale; // Note: this may have any value, so
237 // calculations must be done in longs
238
239 /**
240 * The number of decimal digits in this BigDecimal, or 0 if the
241 * number of digits are not known (lookaside information). If
242 * nonzero, the value is guaranteed correct. Use the precision()
243 * method to obtain and set the value if it might be 0. This
244 * field is mutable until set nonzero.
245 *
246 * @since 1.5
247 */
248 private transient int precision;
249
250 /**
251 * Used to store the canonical string representation, if computed.
252 */
253 private transient String stringCache;
254
255 /**
256 * Sentinel value for {@link #intCompact} indicating the
257 * significand information is only available from {@code intVal}.
258 */
259 static final long INFLATED = Long.MIN_VALUE;
260
261 private static final BigInteger INFLATED_BIGINT = BigInteger.valueOf(INFLATED);
262
263 /**
264 * If the absolute value of the significand of this BigDecimal is
265 * less than or equal to {@code Long.MAX_VALUE}, the value can be
266 * compactly stored in this field and used in computations.
267 */
268 private final transient long intCompact;
269
270 // All 18-digit base ten strings fit into a long; not all 19-digit
271 // strings will
272 private static final int MAX_COMPACT_DIGITS = 18;
273
274 /* Appease the serialization gods */
275 private static final long serialVersionUID = 6108874887143696463L;
276
277 private static final ThreadLocal<StringBuilderHelper>
278 threadLocalStringBuilderHelper = new ThreadLocal<StringBuilderHelper>() {
279 @Override
280 protected StringBuilderHelper initialValue() {
281 return new StringBuilderHelper();
282 }
283 };
284
285 // Cache of common small BigDecimal values.
286 private static final BigDecimal zeroThroughTen[] = {
287 new BigDecimal(BigInteger.ZERO, 0, 0, 1),
288 new BigDecimal(BigInteger.ONE, 1, 0, 1),
289 new BigDecimal(BigInteger.valueOf(2), 2, 0, 1),
290 new BigDecimal(BigInteger.valueOf(3), 3, 0, 1),
291 new BigDecimal(BigInteger.valueOf(4), 4, 0, 1),
292 new BigDecimal(BigInteger.valueOf(5), 5, 0, 1),
293 new BigDecimal(BigInteger.valueOf(6), 6, 0, 1),
294 new BigDecimal(BigInteger.valueOf(7), 7, 0, 1),
295 new BigDecimal(BigInteger.valueOf(8), 8, 0, 1),
296 new BigDecimal(BigInteger.valueOf(9), 9, 0, 1),
297 new BigDecimal(BigInteger.TEN, 10, 0, 2),
298 };
299
300 // Cache of zero scaled by 0 - 15
301 private static final BigDecimal[] ZERO_SCALED_BY = {
302 zeroThroughTen[0],
303 new BigDecimal(BigInteger.ZERO, 0, 1, 1),
304 new BigDecimal(BigInteger.ZERO, 0, 2, 1),
305 new BigDecimal(BigInteger.ZERO, 0, 3, 1),
306 new BigDecimal(BigInteger.ZERO, 0, 4, 1),
307 new BigDecimal(BigInteger.ZERO, 0, 5, 1),
308 new BigDecimal(BigInteger.ZERO, 0, 6, 1),
309 new BigDecimal(BigInteger.ZERO, 0, 7, 1),
310 new BigDecimal(BigInteger.ZERO, 0, 8, 1),
311 new BigDecimal(BigInteger.ZERO, 0, 9, 1),
312 new BigDecimal(BigInteger.ZERO, 0, 10, 1),
313 new BigDecimal(BigInteger.ZERO, 0, 11, 1),
314 new BigDecimal(BigInteger.ZERO, 0, 12, 1),
315 new BigDecimal(BigInteger.ZERO, 0, 13, 1),
316 new BigDecimal(BigInteger.ZERO, 0, 14, 1),
317 new BigDecimal(BigInteger.ZERO, 0, 15, 1),
318 };
319
320 // Half of Long.MIN_VALUE & Long.MAX_VALUE.
321 private static final long HALF_LONG_MAX_VALUE = Long.MAX_VALUE / 2;
322 private static final long HALF_LONG_MIN_VALUE = Long.MIN_VALUE / 2;
323
324 // Constants
325 /**
326 * The value 0, with a scale of 0.
327 *
328 * @since 1.5
329 */
330 public static final BigDecimal ZERO =
331 zeroThroughTen[0];
332
333 /**
334 * The value 1, with a scale of 0.
335 *
336 * @since 1.5
337 */
338 public static final BigDecimal ONE =
339 zeroThroughTen[1];
340
341 /**
342 * The value 10, with a scale of 0.
343 *
344 * @since 1.5
345 */
346 public static final BigDecimal TEN =
347 zeroThroughTen[10];
348
349 // Constructors
350
351 /**
352 * Trusted package private constructor.
353 * Trusted simply means if val is INFLATED, intVal could not be null and
354 * if intVal is null, val could not be INFLATED.
355 */
356 BigDecimal(BigInteger intVal, long val, int scale, int prec) {
357 this.scale = scale;
358 this.precision = prec;
359 this.intCompact = val;
360 this.intVal = intVal;
361 }
362
363 /**
364 * Translates a character array representation of a
365 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
366 * same sequence of characters as the {@link #BigDecimal(String)}
367 * constructor, while allowing a sub-array to be specified.
368 *
369 * <p>Note that if the sequence of characters is already available
370 * within a character array, using this constructor is faster than
371 * converting the {@code char} array to string and using the
372 * {@code BigDecimal(String)} constructor .
373 *
374 * @param in {@code char} array that is the source of characters.
375 * @param offset first character in the array to inspect.
376 * @param len number of characters to consider.
377 * @throws NumberFormatException if {@code in} is not a valid
378 * representation of a {@code BigDecimal} or the defined subarray
379 * is not wholly within {@code in}.
380 * @since 1.5
381 */
382 public BigDecimal(char[] in, int offset, int len) {
383 this(in,offset,len,MathContext.UNLIMITED);
384 }
385
386 /**
387 * Translates a character array representation of a
388 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
389 * same sequence of characters as the {@link #BigDecimal(String)}
390 * constructor, while allowing a sub-array to be specified and
391 * with rounding according to the context settings.
392 *
393 * <p>Note that if the sequence of characters is already available
394 * within a character array, using this constructor is faster than
395 * converting the {@code char} array to string and using the
396 * {@code BigDecimal(String)} constructor .
397 *
398 * @param in {@code char} array that is the source of characters.
399 * @param offset first character in the array to inspect.
400 * @param len number of characters to consider..
401 * @param mc the context to use.
402 * @throws ArithmeticException if the result is inexact but the
403 * rounding mode is {@code UNNECESSARY}.
404 * @throws NumberFormatException if {@code in} is not a valid
405 * representation of a {@code BigDecimal} or the defined subarray
406 * is not wholly within {@code in}.
407 * @since 1.5
408 */
409 public BigDecimal(char[] in, int offset, int len, MathContext mc) {
410 // protect against huge length.
411 if (offset + len > in.length || offset < 0)
412 throw new NumberFormatException("Bad offset or len arguments for char[] input.");
413 // This is the primary string to BigDecimal constructor; all
414 // incoming strings end up here; it uses explicit (inline)
415 // parsing for speed and generates at most one intermediate
416 // (temporary) object (a char[] array) for non-compact case.
417
418 // Use locals for all fields values until completion
419 int prec = 0; // record precision value
420 int scl = 0; // record scale value
421 long rs = 0; // the compact value in long
422 BigInteger rb = null; // the inflated value in BigInteger
423 // use array bounds checking to handle too-long, len == 0,
424 // bad offset, etc.
425 try {
426 // handle the sign
427 boolean isneg = false; // assume positive
428 if (in[offset] == '-') {
429 isneg = true; // leading minus means negative
430 offset++;
431 len--;
432 } else if (in[offset] == '+') { // leading + allowed
433 offset++;
434 len--;
435 }
436
437 // should now be at numeric part of the significand
438 boolean dot = false; // true when there is a '.'
439 long exp = 0; // exponent
440 char c; // current character
441 boolean isCompact = (len <= MAX_COMPACT_DIGITS);
442 // integer significand array & idx is the index to it. The array
443 // is ONLY used when we can't use a compact representation.
444 int idx = 0;
445 if (isCompact) {
446 // First compact case, we need not to preserve the character
447 // and we can just compute the value in place.
448 for (; len > 0; offset++, len--) {
449 c = in[offset];
450 if ((c == '0')) { // have zero
451 if (prec == 0)
452 prec = 1;
453 else if (rs != 0) {
454 rs *= 10;
455 ++prec;
456 } // else digit is a redundant leading zero
457 if (dot)
458 ++scl;
459 } else if ((c >= '1' && c <= '9')) { // have digit
460 int digit = c - '0';
461 if (prec != 1 || rs != 0)
462 ++prec; // prec unchanged if preceded by 0s
463 rs = rs * 10 + digit;
464 if (dot)
465 ++scl;
466 } else if (c == '.') { // have dot
467 // have dot
468 if (dot) // two dots
469 throw new NumberFormatException();
470 dot = true;
471 } else if (Character.isDigit(c)) { // slow path
472 int digit = Character.digit(c, 10);
473 if (digit == 0) {
474 if (prec == 0)
475 prec = 1;
476 else if (rs != 0) {
477 rs *= 10;
478 ++prec;
479 } // else digit is a redundant leading zero
480 } else {
481 if (prec != 1 || rs != 0)
482 ++prec; // prec unchanged if preceded by 0s
483 rs = rs * 10 + digit;
484 }
485 if (dot)
486 ++scl;
487 } else if ((c == 'e') || (c == 'E')) {
488 exp = parseExp(in, offset, len);
489 // Next test is required for backwards compatibility
490 if ((int) exp != exp) // overflow
491 throw new NumberFormatException();
492 break; // [saves a test]
493 } else {
494 throw new NumberFormatException();
495 }
496 }
497 if (prec == 0) // no digits found
498 throw new NumberFormatException();
499 // Adjust scale if exp is not zero.
500 if (exp != 0) { // had significant exponent
501 scl = adjustScale(scl, exp);
502 }
503 rs = isneg ? -rs : rs;
504 int mcp = mc.precision;
505 int drop = prec - mcp; // prec has range [1, MAX_INT], mcp has range [0, MAX_INT];
506 // therefore, this subtract cannot overflow
507 if (mcp > 0 && drop > 0) { // do rounding
508 while (drop > 0) {
509 scl = checkScaleNonZero((long) scl - drop);
510 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
511 prec = longDigitLength(rs);
512 drop = prec - mcp;
513 }
514 }
515 } else {
516 char coeff[] = new char[len];
517 for (; len > 0; offset++, len--) {
518 c = in[offset];
519 // have digit
520 if ((c >= '0' && c <= '9') || Character.isDigit(c)) {
521 // First compact case, we need not to preserve the character
522 // and we can just compute the value in place.
523 if (c == '0' || Character.digit(c, 10) == 0) {
524 if (prec == 0) {
525 coeff[idx] = c;
526 prec = 1;
527 } else if (idx != 0) {
528 coeff[idx++] = c;
529 ++prec;
530 } // else c must be a redundant leading zero
531 } else {
532 if (prec != 1 || idx != 0)
533 ++prec; // prec unchanged if preceded by 0s
534 coeff[idx++] = c;
535 }
536 if (dot)
537 ++scl;
538 continue;
539 }
540 // have dot
541 if (c == '.') {
542 // have dot
543 if (dot) // two dots
544 throw new NumberFormatException();
545 dot = true;
546 continue;
547 }
548 // exponent expected
549 if ((c != 'e') && (c != 'E'))
550 throw new NumberFormatException();
551 exp = parseExp(in, offset, len);
552 // Next test is required for backwards compatibility
553 if ((int) exp != exp) // overflow
554 throw new NumberFormatException();
555 break; // [saves a test]
556 }
557 // here when no characters left
558 if (prec == 0) // no digits found
559 throw new NumberFormatException();
560 // Adjust scale if exp is not zero.
561 if (exp != 0) { // had significant exponent
562 scl = adjustScale(scl, exp);
563 }
564 // Remove leading zeros from precision (digits count)
565 rb = new BigInteger(coeff, isneg ? -1 : 1, prec);
566 rs = compactValFor(rb);
567 int mcp = mc.precision;
568 if (mcp > 0 && (prec > mcp)) {
569 if (rs == INFLATED) {
570 int drop = prec - mcp;
571 while (drop > 0) {
572 scl = checkScaleNonZero((long) scl - drop);
573 rb = divideAndRoundByTenPow(rb, drop, mc.roundingMode.oldMode);
574 rs = compactValFor(rb);
575 if (rs != INFLATED) {
576 prec = longDigitLength(rs);
577 break;
578 }
579 prec = bigDigitLength(rb);
580 drop = prec - mcp;
581 }
582 }
583 if (rs != INFLATED) {
584 int drop = prec - mcp;
585 while (drop > 0) {
586 scl = checkScaleNonZero((long) scl - drop);
587 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
588 prec = longDigitLength(rs);
589 drop = prec - mcp;
590 }
591 rb = null;
592 }
593 }
594 }
595 } catch (ArrayIndexOutOfBoundsException e) {
596 throw new NumberFormatException();
597 } catch (NegativeArraySizeException e) {
598 throw new NumberFormatException();
599 }
600 this.scale = scl;
601 this.precision = prec;
602 this.intCompact = rs;
603 this.intVal = rb;
604 }
605
606 private int adjustScale(int scl, long exp) {
607 long adjustedScale = scl - exp;
608 if (adjustedScale > Integer.MAX_VALUE || adjustedScale < Integer.MIN_VALUE)
609 throw new NumberFormatException("Scale out of range.");
610 scl = (int) adjustedScale;
611 return scl;
612 }
613
614 /*
615 * parse exponent
616 */
617 private static long parseExp(char[] in, int offset, int len){
618 long exp = 0;
619 offset++;
620 char c = in[offset];
621 len--;
622 boolean negexp = (c == '-');
623 // optional sign
624 if (negexp || c == '+') {
625 offset++;
626 c = in[offset];
627 len--;
628 }
629 if (len <= 0) // no exponent digits
630 throw new NumberFormatException();
631 // skip leading zeros in the exponent
632 while (len > 10 && (c=='0' || (Character.digit(c, 10) == 0))) {
633 offset++;
634 c = in[offset];
635 len--;
636 }
637 if (len > 10) // too many nonzero exponent digits
638 throw new NumberFormatException();
639 // c now holds first digit of exponent
640 for (;; len--) {
641 int v;
642 if (c >= '0' && c <= '9') {
643 v = c - '0';
644 } else {
645 v = Character.digit(c, 10);
646 if (v < 0) // not a digit
647 throw new NumberFormatException();
648 }
649 exp = exp * 10 + v;
650 if (len == 1)
651 break; // that was final character
652 offset++;
653 c = in[offset];
654 }
655 if (negexp) // apply sign
656 exp = -exp;
657 return exp;
658 }
659
660 /**
661 * Translates a character array representation of a
662 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
663 * same sequence of characters as the {@link #BigDecimal(String)}
664 * constructor.
665 *
666 * <p>Note that if the sequence of characters is already available
667 * as a character array, using this constructor is faster than
668 * converting the {@code char} array to string and using the
669 * {@code BigDecimal(String)} constructor .
670 *
671 * @param in {@code char} array that is the source of characters.
672 * @throws NumberFormatException if {@code in} is not a valid
673 * representation of a {@code BigDecimal}.
674 * @since 1.5
675 */
676 public BigDecimal(char[] in) {
677 this(in, 0, in.length);
678 }
679
680 /**
681 * Translates a character array representation of a
682 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
683 * same sequence of characters as the {@link #BigDecimal(String)}
684 * constructor and with rounding according to the context
685 * settings.
686 *
687 * <p>Note that if the sequence of characters is already available
688 * as a character array, using this constructor is faster than
689 * converting the {@code char} array to string and using the
690 * {@code BigDecimal(String)} constructor .
691 *
692 * @param in {@code char} array that is the source of characters.
693 * @param mc the context to use.
694 * @throws ArithmeticException if the result is inexact but the
695 * rounding mode is {@code UNNECESSARY}.
696 * @throws NumberFormatException if {@code in} is not a valid
697 * representation of a {@code BigDecimal}.
698 * @since 1.5
699 */
700 public BigDecimal(char[] in, MathContext mc) {
701 this(in, 0, in.length, mc);
702 }
703
704 /**
705 * Translates the string representation of a {@code BigDecimal}
706 * into a {@code BigDecimal}. The string representation consists
707 * of an optional sign, {@code '+'} (<tt> '\u002B'</tt>) or
708 * {@code '-'} (<tt>'\u002D'</tt>), followed by a sequence of
709 * zero or more decimal digits ("the integer"), optionally
710 * followed by a fraction, optionally followed by an exponent.
711 *
712 * <p>The fraction consists of a decimal point followed by zero
713 * or more decimal digits. The string must contain at least one
714 * digit in either the integer or the fraction. The number formed
715 * by the sign, the integer and the fraction is referred to as the
716 * <i>significand</i>.
717 *
718 * <p>The exponent consists of the character {@code 'e'}
719 * (<tt>'\u0065'</tt>) or {@code 'E'} (<tt>'\u0045'</tt>)
720 * followed by one or more decimal digits. The value of the
721 * exponent must lie between -{@link Integer#MAX_VALUE} ({@link
722 * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive.
723 *
724 * <p>More formally, the strings this constructor accepts are
725 * described by the following grammar:
726 * <blockquote>
727 * <dl>
728 * <dt><i>BigDecimalString:</i>
729 * <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i>
730 * <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 long valBits = Double.doubleToLongBits(val);
908 int sign = ((valBits >> 63) == 0 ? 1 : -1);
909 int exponent = (int) ((valBits >> 52) & 0x7ffL);
910 long significand = (exponent == 0
911 ? (valBits & ((1L << 52) - 1)) << 1
912 : (valBits & ((1L << 52) - 1)) | (1L << 52));
913 exponent -= 1075;
914 // At this point, val == sign * significand * 2**exponent.
915
916 /*
917 * Special case zero to supress nonterminating normalization and bogus
918 * scale calculation.
919 */
920 if (significand == 0) {
921 this.intVal = BigInteger.ZERO;
922 this.scale = 0;
923 this.intCompact = 0;
924 this.precision = 1;
925 return;
926 }
927 // Normalize
928 while ((significand & 1) == 0) { // i.e., significand is even
929 significand >>= 1;
930 exponent++;
931 }
932 int scale = 0;
933 // Calculate intVal and scale
934 BigInteger intVal;
935 long compactVal = sign * significand;
936 if (exponent == 0) {
937 intVal = (compactVal == INFLATED) ? INFLATED_BIGINT : null;
938 } else {
939 if (exponent < 0) {
940 intVal = BigInteger.valueOf(5).pow(-exponent).multiply(compactVal);
941 scale = -exponent;
942 } else { // (exponent > 0)
943 intVal = BigInteger.valueOf(2).pow(exponent).multiply(compactVal);
944 }
945 compactVal = compactValFor(intVal);
946 }
947 int prec = 0;
948 int mcp = mc.precision;
949 if (mcp > 0) { // do rounding
950 int mode = mc.roundingMode.oldMode;
951 int drop;
952 if (compactVal == INFLATED) {
953 prec = bigDigitLength(intVal);
954 drop = prec - mcp;
955 while (drop > 0) {
956 scale = checkScaleNonZero((long) scale - drop);
957 intVal = divideAndRoundByTenPow(intVal, drop, mode);
958 compactVal = compactValFor(intVal);
959 if (compactVal != INFLATED) {
960 break;
961 }
962 prec = bigDigitLength(intVal);
963 drop = prec - mcp;
964 }
965 }
966 if (compactVal != INFLATED) {
967 prec = longDigitLength(compactVal);
968 drop = prec - mcp;
969 while (drop > 0) {
970 scale = checkScaleNonZero((long) scale - drop);
971 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
972 prec = longDigitLength(compactVal);
973 drop = prec - mcp;
974 }
975 intVal = null;
976 }
977 }
978 this.intVal = intVal;
979 this.intCompact = compactVal;
980 this.scale = scale;
981 this.precision = prec;
982 }
983
984 /**
985 * Translates a {@code BigInteger} into a {@code BigDecimal}.
986 * The scale of the {@code BigDecimal} is zero.
987 *
988 * @param val {@code BigInteger} value to be converted to
989 * {@code BigDecimal}.
990 */
991 public BigDecimal(BigInteger val) {
992 scale = 0;
993 intVal = val;
994 intCompact = compactValFor(val);
995 }
996
997 /**
998 * Translates a {@code BigInteger} into a {@code BigDecimal}
999 * rounding according to the context settings. The scale of the
1000 * {@code BigDecimal} is zero.
1001 *
1002 * @param val {@code BigInteger} value to be converted to
1003 * {@code BigDecimal}.
1004 * @param mc the context to use.
1005 * @throws ArithmeticException if the result is inexact but the
1006 * rounding mode is {@code UNNECESSARY}.
1007 * @since 1.5
1008 */
1009 public BigDecimal(BigInteger val, MathContext mc) {
1010 this(val,0,mc);
1011 }
1012
1013 /**
1014 * Translates a {@code BigInteger} unscaled value and an
1015 * {@code int} scale into a {@code BigDecimal}. The value of
1016 * the {@code BigDecimal} is
1017 * <tt>(unscaledVal × 10<sup>-scale</sup>)</tt>.
1018 *
1019 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1020 * @param scale scale of the {@code BigDecimal}.
1021 */
1022 public BigDecimal(BigInteger unscaledVal, int scale) {
1023 // Negative scales are now allowed
1024 this.intVal = unscaledVal;
1025 this.intCompact = compactValFor(unscaledVal);
1026 this.scale = scale;
1027 }
1028
1029 /**
1030 * Translates a {@code BigInteger} unscaled value and an
1031 * {@code int} scale into a {@code BigDecimal}, with rounding
1032 * according to the context settings. The value of the
1033 * {@code BigDecimal} is <tt>(unscaledVal ×
1034 * 10<sup>-scale</sup>)</tt>, rounded according to the
1035 * {@code precision} and rounding mode settings.
1036 *
1037 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1038 * @param scale scale of the {@code BigDecimal}.
1039 * @param mc the context to use.
1040 * @throws ArithmeticException if the result is inexact but the
1041 * rounding mode is {@code UNNECESSARY}.
1042 * @since 1.5
1043 */
1044 public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {
1045 long compactVal = compactValFor(unscaledVal);
1046 int mcp = mc.precision;
1047 int prec = 0;
1048 if (mcp > 0) { // do rounding
1049 int mode = mc.roundingMode.oldMode;
1050 if (compactVal == INFLATED) {
1051 prec = bigDigitLength(unscaledVal);
1052 int drop = prec - mcp;
1053 while (drop > 0) {
1054 scale = checkScaleNonZero((long) scale - drop);
1055 unscaledVal = divideAndRoundByTenPow(unscaledVal, drop, mode);
1056 compactVal = compactValFor(unscaledVal);
1057 if (compactVal != INFLATED) {
1058 break;
1059 }
1060 prec = bigDigitLength(unscaledVal);
1061 drop = prec - mcp;
1062 }
1063 }
1064 if (compactVal != INFLATED) {
1065 prec = longDigitLength(compactVal);
1066 int drop = prec - mcp; // drop can't be more than 18
1067 while (drop > 0) {
1068 scale = checkScaleNonZero((long) scale - drop);
1069 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mode);
1070 prec = longDigitLength(compactVal);
1071 drop = prec - mcp;
1072 }
1073 unscaledVal = null;
1074 }
1075 }
1076 this.intVal = unscaledVal;
1077 this.intCompact = compactVal;
1078 this.scale = scale;
1079 this.precision = prec;
1080 }
1081
1082 /**
1083 * Translates an {@code int} into a {@code BigDecimal}. The
1084 * scale of the {@code BigDecimal} is zero.
1085 *
1086 * @param val {@code int} value to be converted to
1087 * {@code BigDecimal}.
1088 * @since 1.5
1089 */
1090 public BigDecimal(int val) {
1091 this.intCompact = val;
1092 this.scale = 0;
1093 this.intVal = null;
1094 }
1095
1096 /**
1097 * Translates an {@code int} into a {@code BigDecimal}, with
1098 * rounding according to the context settings. The scale of the
1099 * {@code BigDecimal}, before any rounding, is zero.
1100 *
1101 * @param val {@code int} value to be converted to {@code BigDecimal}.
1102 * @param mc the context to use.
1103 * @throws ArithmeticException if the result is inexact but the
1104 * rounding mode is {@code UNNECESSARY}.
1105 * @since 1.5
1106 */
1107 public BigDecimal(int val, MathContext mc) {
1108 int mcp = mc.precision;
1109 long compactVal = val;
1110 int scale = 0;
1111 int prec = 0;
1112 if (mcp > 0) { // do rounding
1113 prec = longDigitLength(compactVal);
1114 int drop = prec - mcp; // drop can't be more than 18
1115 while (drop > 0) {
1116 scale = checkScaleNonZero((long) scale - drop);
1117 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1118 prec = longDigitLength(compactVal);
1119 drop = prec - mcp;
1120 }
1121 }
1122 this.intVal = null;
1123 this.intCompact = compactVal;
1124 this.scale = scale;
1125 this.precision = prec;
1126 }
1127
1128 /**
1129 * Translates a {@code long} into a {@code BigDecimal}. The
1130 * scale of the {@code BigDecimal} is zero.
1131 *
1132 * @param val {@code long} value to be converted to {@code BigDecimal}.
1133 * @since 1.5
1134 */
1135 public BigDecimal(long val) {
1136 this.intCompact = val;
1137 this.intVal = (val == INFLATED) ? INFLATED_BIGINT : null;
1138 this.scale = 0;
1139 }
1140
1141 /**
1142 * Translates a {@code long} into a {@code BigDecimal}, with
1143 * rounding according to the context settings. The scale of the
1144 * {@code BigDecimal}, before any rounding, is zero.
1145 *
1146 * @param val {@code long} value to be converted to {@code BigDecimal}.
1147 * @param mc the context to use.
1148 * @throws ArithmeticException if the result is inexact but the
1149 * rounding mode is {@code UNNECESSARY}.
1150 * @since 1.5
1151 */
1152 public BigDecimal(long val, MathContext mc) {
1153 int mcp = mc.precision;
1154 int mode = mc.roundingMode.oldMode;
1155 int prec = 0;
1156 int scale = 0;
1157 BigInteger intVal = (val == INFLATED) ? INFLATED_BIGINT : null;
1158 if (mcp > 0) { // do rounding
1159 if (val == INFLATED) {
1160 prec = 19;
1161 int drop = prec - mcp;
1162 while (drop > 0) {
1163 scale = checkScaleNonZero((long) scale - drop);
1164 intVal = divideAndRoundByTenPow(intVal, drop, mode);
1165 val = compactValFor(intVal);
1166 if (val != INFLATED) {
1167 break;
1168 }
1169 prec = bigDigitLength(intVal);
1170 drop = prec - mcp;
1171 }
1172 }
1173 if (val != INFLATED) {
1174 prec = longDigitLength(val);
1175 int drop = prec - mcp;
1176 while (drop > 0) {
1177 scale = checkScaleNonZero((long) scale - drop);
1178 val = divideAndRound(val, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1179 prec = longDigitLength(val);
1180 drop = prec - mcp;
1181 }
1182 intVal = null;
1183 }
1184 }
1185 this.intVal = intVal;
1186 this.intCompact = val;
1187 this.scale = scale;
1188 this.precision = prec;
1189 }
1190
1191 // Static Factory Methods
1192
1193 /**
1194 * Translates a {@code long} unscaled value and an
1195 * {@code int} scale into a {@code BigDecimal}. This
1196 * {@literal "static factory method"} is provided in preference to
1197 * a ({@code long}, {@code int}) constructor because it
1198 * allows for reuse of frequently used {@code BigDecimal} values..
1199 *
1200 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1201 * @param scale scale of the {@code BigDecimal}.
1202 * @return a {@code BigDecimal} whose value is
1203 * <tt>(unscaledVal × 10<sup>-scale</sup>)</tt>.
1204 */
1205 public static BigDecimal valueOf(long unscaledVal, int scale) {
1206 if (scale == 0)
1207 return valueOf(unscaledVal);
1208 else if (unscaledVal == 0) {
1209 return zeroValueOf(scale);
1210 }
1211 return new BigDecimal(unscaledVal == INFLATED ?
1212 INFLATED_BIGINT : null,
1213 unscaledVal, scale, 0);
1214 }
1215
1216 /**
1217 * Translates a {@code long} value into a {@code BigDecimal}
1218 * with a scale of zero. This {@literal "static factory method"}
1219 * is provided in preference to a ({@code long}) constructor
1220 * because it allows for reuse of frequently used
1221 * {@code BigDecimal} values.
1222 *
1223 * @param val value of the {@code BigDecimal}.
1224 * @return a {@code BigDecimal} whose value is {@code val}.
1225 */
1226 public static BigDecimal valueOf(long val) {
1227 if (val >= 0 && val < zeroThroughTen.length)
1228 return zeroThroughTen[(int)val];
1229 else if (val != INFLATED)
1230 return new BigDecimal(null, val, 0, 0);
1231 return new BigDecimal(INFLATED_BIGINT, val, 0, 0);
1232 }
1233
1234 static BigDecimal valueOf(long unscaledVal, int scale, int prec) {
1235 if (scale == 0 && unscaledVal >= 0 && unscaledVal < zeroThroughTen.length) {
1236 return zeroThroughTen[(int) unscaledVal];
1237 } else if (unscaledVal == 0) {
1238 return zeroValueOf(scale);
1239 }
1240 return new BigDecimal(unscaledVal == INFLATED ? INFLATED_BIGINT : null,
1241 unscaledVal, scale, prec);
1242 }
1243
1244 static BigDecimal valueOf(BigInteger intVal, int scale, int prec) {
1245 long val = compactValFor(intVal);
1246 if (val == 0) {
1247 return zeroValueOf(scale);
1248 } else if (scale == 0 && val >= 0 && val < zeroThroughTen.length) {
1249 return zeroThroughTen[(int) val];
1250 }
1251 return new BigDecimal(intVal, val, scale, prec);
1252 }
1253
1254 static BigDecimal zeroValueOf(int scale) {
1255 if (scale >= 0 && scale < ZERO_SCALED_BY.length)
1256 return ZERO_SCALED_BY[scale];
1257 else
1258 return new BigDecimal(BigInteger.ZERO, 0, scale, 1);
1259 }
1260
1261 /**
1262 * Translates a {@code double} into a {@code BigDecimal}, using
1263 * the {@code double}'s canonical string representation provided
1264 * by the {@link Double#toString(double)} method.
1265 *
1266 * <p><b>Note:</b> This is generally the preferred way to convert
1267 * a {@code double} (or {@code float}) into a
1268 * {@code BigDecimal}, as the value returned is equal to that
1269 * resulting from constructing a {@code BigDecimal} from the
1270 * result of using {@link Double#toString(double)}.
1271 *
1272 * @param val {@code double} to convert to a {@code BigDecimal}.
1273 * @return a {@code BigDecimal} whose value is equal to or approximately
1274 * equal to the value of {@code val}.
1275 * @throws NumberFormatException if {@code val} is infinite or NaN.
1276 * @since 1.5
1277 */
1278 public static BigDecimal valueOf(double val) {
1279 // Reminder: a zero double returns '0.0', so we cannot fastpath
1280 // to use the constant ZERO. This might be important enough to
1281 // justify a factory approach, a cache, or a few private
1282 // constants, later.
1283 return new BigDecimal(Double.toString(val));
1284 }
1285
1286 // Arithmetic Operations
1287 /**
1288 * Returns a {@code BigDecimal} whose value is {@code (this +
1289 * augend)}, and whose scale is {@code max(this.scale(),
1290 * augend.scale())}.
1291 *
1292 * @param augend value to be added to this {@code BigDecimal}.
1293 * @return {@code this + augend}
1294 */
1295 public BigDecimal add(BigDecimal augend) {
1296 if (this.intCompact != INFLATED) {
1297 if ((augend.intCompact != INFLATED)) {
1298 return add(this.intCompact, this.scale, augend.intCompact, augend.scale);
1299 } else {
1300 return add(this.intCompact, this.scale, augend.intVal, augend.scale);
1301 }
1302 } else {
1303 if ((augend.intCompact != INFLATED)) {
1304 return add(augend.intCompact, augend.scale, this.intVal, this.scale);
1305 } else {
1306 return add(this.intVal, this.scale, augend.intVal, augend.scale);
1307 }
1308 }
1309 }
1310
1311 /**
1312 * Returns a {@code BigDecimal} whose value is {@code (this + augend)},
1313 * with rounding according to the context settings.
1314 *
1315 * If either number is zero and the precision setting is nonzero then
1316 * the other number, rounded if necessary, is used as the result.
1317 *
1318 * @param augend value to be added to this {@code BigDecimal}.
1319 * @param mc the context to use.
1320 * @return {@code this + augend}, rounded as necessary.
1321 * @throws ArithmeticException if the result is inexact but the
1322 * rounding mode is {@code UNNECESSARY}.
1323 * @since 1.5
1324 */
1325 public BigDecimal add(BigDecimal augend, MathContext mc) {
1326 if (mc.precision == 0)
1327 return add(augend);
1328 BigDecimal lhs = this;
1329
1330 // If either number is zero then the other number, rounded and
1331 // scaled if necessary, is used as the result.
1332 {
1333 boolean lhsIsZero = lhs.signum() == 0;
1334 boolean augendIsZero = augend.signum() == 0;
1335
1336 if (lhsIsZero || augendIsZero) {
1337 int preferredScale = Math.max(lhs.scale(), augend.scale());
1338 BigDecimal result;
1339
1340 if (lhsIsZero && augendIsZero)
1341 return zeroValueOf(preferredScale);
1342 result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc);
1343
1344 if (result.scale() == preferredScale)
1345 return result;
1346 else if (result.scale() > preferredScale) {
1347 return stripZerosToMatchScale(result.intVal, result.intCompact, result.scale, preferredScale);
1348 } else { // result.scale < preferredScale
1349 int precisionDiff = mc.precision - result.precision();
1350 int scaleDiff = preferredScale - result.scale();
1351
1352 if (precisionDiff >= scaleDiff)
1353 return result.setScale(preferredScale); // can achieve target scale
1354 else
1355 return result.setScale(result.scale() + precisionDiff);
1356 }
1357 }
1358 }
1359
1360 long padding = (long) lhs.scale - augend.scale;
1361 if (padding != 0) { // scales differ; alignment needed
1362 BigDecimal arg[] = preAlign(lhs, augend, padding, mc);
1363 matchScale(arg);
1364 lhs = arg[0];
1365 augend = arg[1];
1366 }
1367 return doRound(lhs.inflated().add(augend.inflated()), lhs.scale, mc);
1368 }
1369
1370 /**
1371 * Returns an array of length two, the sum of whose entries is
1372 * equal to the rounded sum of the {@code BigDecimal} arguments.
1373 *
1374 * <p>If the digit positions of the arguments have a sufficient
1375 * gap between them, the value smaller in magnitude can be
1376 * condensed into a {@literal "sticky bit"} and the end result will
1377 * round the same way <em>if</em> the precision of the final
1378 * result does not include the high order digit of the small
1379 * magnitude operand.
1380 *
1381 * <p>Note that while strictly speaking this is an optimization,
1382 * it makes a much wider range of additions practical.
1383 *
1384 * <p>This corresponds to a pre-shift operation in a fixed
1385 * precision floating-point adder; this method is complicated by
1386 * variable precision of the result as determined by the
1387 * MathContext. A more nuanced operation could implement a
1388 * {@literal "right shift"} on the smaller magnitude operand so
1389 * that the number of digits of the smaller operand could be
1390 * reduced even though the significands partially overlapped.
1391 */
1392 private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend, long padding, MathContext mc) {
1393 assert padding != 0;
1394 BigDecimal big;
1395 BigDecimal small;
1396
1397 if (padding < 0) { // lhs is big; augend is small
1398 big = lhs;
1399 small = augend;
1400 } else { // lhs is small; augend is big
1401 big = augend;
1402 small = lhs;
1403 }
1404
1405 /*
1406 * This is the estimated scale of an ulp of the result; it assumes that
1407 * the result doesn't have a carry-out on a true add (e.g. 999 + 1 =>
1408 * 1000) or any subtractive cancellation on borrowing (e.g. 100 - 1.2 =>
1409 * 98.8)
1410 */
1411 long estResultUlpScale = (long) big.scale - big.precision() + mc.precision;
1412
1413 /*
1414 * The low-order digit position of big is big.scale(). This
1415 * is true regardless of whether big has a positive or
1416 * negative scale. The high-order digit position of small is
1417 * small.scale - (small.precision() - 1). To do the full
1418 * condensation, the digit positions of big and small must be
1419 * disjoint *and* the digit positions of small should not be
1420 * directly visible in the result.
1421 */
1422 long smallHighDigitPos = (long) small.scale - small.precision() + 1;
1423 if (smallHighDigitPos > big.scale + 2 && // big and small disjoint
1424 smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible
1425 small = BigDecimal.valueOf(small.signum(), this.checkScale(Math.max(big.scale, estResultUlpScale) + 3));
1426 }
1427
1428 // Since addition is symmetric, preserving input order in
1429 // returned operands doesn't matter
1430 BigDecimal[] result = {big, small};
1431 return result;
1432 }
1433
1434 /**
1435 * Returns a {@code BigDecimal} whose value is {@code (this -
1436 * subtrahend)}, and whose scale is {@code max(this.scale(),
1437 * subtrahend.scale())}.
1438 *
1439 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1440 * @return {@code this - subtrahend}
1441 */
1442 public BigDecimal subtract(BigDecimal subtrahend) {
1443 if (this.intCompact != INFLATED) {
1444 if ((subtrahend.intCompact != INFLATED)) {
1445 return add(this.intCompact, this.scale, -subtrahend.intCompact, subtrahend.scale);
1446 } else {
1447 return add(this.intCompact, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1448 }
1449 } else {
1450 if ((subtrahend.intCompact != INFLATED)) {
1451 // Pair of subtrahend values given before pair of
1452 // values from this BigDecimal to avoid need for
1453 // method overloading on the specialized add method
1454 return add(-subtrahend.intCompact, subtrahend.scale, this.intVal, this.scale);
1455 } else {
1456 return add(this.intVal, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1457 }
1458 }
1459 }
1460
1461 /**
1462 * Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)},
1463 * with rounding according to the context settings.
1464 *
1465 * If {@code subtrahend} is zero then this, rounded if necessary, is used as the
1466 * result. If this is zero then the result is {@code subtrahend.negate(mc)}.
1467 *
1468 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1469 * @param mc the context to use.
1470 * @return {@code this - subtrahend}, rounded as necessary.
1471 * @throws ArithmeticException if the result is inexact but the
1472 * rounding mode is {@code UNNECESSARY}.
1473 * @since 1.5
1474 */
1475 public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) {
1476 if (mc.precision == 0)
1477 return subtract(subtrahend);
1478 // share the special rounding code in add()
1479 return add(subtrahend.negate(), mc);
1480 }
1481
1482 /**
1483 * Returns a {@code BigDecimal} whose value is <tt>(this ×
1484 * multiplicand)</tt>, and whose scale is {@code (this.scale() +
1485 * multiplicand.scale())}.
1486 *
1487 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1488 * @return {@code this * multiplicand}
1489 */
1490 public BigDecimal multiply(BigDecimal multiplicand) {
1491 int productScale = checkScale((long) scale + multiplicand.scale);
1492 if (this.intCompact != INFLATED) {
1493 if ((multiplicand.intCompact != INFLATED)) {
1494 return multiply(this.intCompact, multiplicand.intCompact, productScale);
1495 } else {
1496 return multiply(this.intCompact, multiplicand.intVal, productScale);
1497 }
1498 } else {
1499 if ((multiplicand.intCompact != INFLATED)) {
1500 return multiply(multiplicand.intCompact, this.intVal, productScale);
1501 } else {
1502 return multiply(this.intVal, multiplicand.intVal, productScale);
1503 }
1504 }
1505 }
1506
1507 /**
1508 * Returns a {@code BigDecimal} whose value is <tt>(this ×
1509 * multiplicand)</tt>, with rounding according to the context settings.
1510 *
1511 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1512 * @param mc the context to use.
1513 * @return {@code this * multiplicand}, rounded as necessary.
1514 * @throws ArithmeticException if the result is inexact but the
1515 * rounding mode is {@code UNNECESSARY}.
1516 * @since 1.5
1517 */
1518 public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) {
1519 if (mc.precision == 0)
1520 return multiply(multiplicand);
1521 int productScale = checkScale((long) scale + multiplicand.scale);
1522 if (this.intCompact != INFLATED) {
1523 if ((multiplicand.intCompact != INFLATED)) {
1524 return multiplyAndRound(this.intCompact, multiplicand.intCompact, productScale, mc);
1525 } else {
1526 return multiplyAndRound(this.intCompact, multiplicand.intVal, productScale, mc);
1527 }
1528 } else {
1529 if ((multiplicand.intCompact != INFLATED)) {
1530 return multiplyAndRound(multiplicand.intCompact, this.intVal, productScale, mc);
1531 } else {
1532 return multiplyAndRound(this.intVal, multiplicand.intVal, productScale, mc);
1533 }
1534 }
1535 }
1536
1537 /**
1538 * Returns a {@code BigDecimal} whose value is {@code (this /
1539 * divisor)}, and whose scale is as specified. If rounding must
1540 * be performed to generate a result with the specified scale, the
1541 * specified rounding mode is applied.
1542 *
1543 * <p>The new {@link #divide(BigDecimal, int, RoundingMode)} method
1544 * should be used in preference to this legacy method.
1545 *
1546 * @param divisor value by which this {@code BigDecimal} is to be divided.
1547 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1548 * @param roundingMode rounding mode to apply.
1549 * @return {@code this / divisor}
1550 * @throws ArithmeticException if {@code divisor} is zero,
1551 * {@code roundingMode==ROUND_UNNECESSARY} and
1552 * the specified scale is insufficient to represent the result
1553 * of the division exactly.
1554 * @throws IllegalArgumentException if {@code roundingMode} does not
1555 * represent a valid rounding mode.
1556 * @see #ROUND_UP
1557 * @see #ROUND_DOWN
1558 * @see #ROUND_CEILING
1559 * @see #ROUND_FLOOR
1560 * @see #ROUND_HALF_UP
1561 * @see #ROUND_HALF_DOWN
1562 * @see #ROUND_HALF_EVEN
1563 * @see #ROUND_UNNECESSARY
1564 */
1565 public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) {
1566 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
1567 throw new IllegalArgumentException("Invalid rounding mode");
1568 if (this.intCompact != INFLATED) {
1569 if ((divisor.intCompact != INFLATED)) {
1570 return divide(this.intCompact, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1571 } else {
1572 return divide(this.intCompact, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1573 }
1574 } else {
1575 if ((divisor.intCompact != INFLATED)) {
1576 return divide(this.intVal, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1577 } else {
1578 return divide(this.intVal, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1579 }
1580 }
1581 }
1582
1583 /**
1584 * Returns a {@code BigDecimal} whose value is {@code (this /
1585 * divisor)}, and whose scale is as specified. If rounding must
1586 * be performed to generate a result with the specified scale, the
1587 * specified rounding mode is applied.
1588 *
1589 * @param divisor value by which this {@code BigDecimal} is to be divided.
1590 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1591 * @param roundingMode rounding mode to apply.
1592 * @return {@code this / divisor}
1593 * @throws ArithmeticException if {@code divisor} is zero,
1594 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1595 * the specified scale is insufficient to represent the result
1596 * of the division exactly.
1597 * @since 1.5
1598 */
1599 public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) {
1600 return divide(divisor, scale, roundingMode.oldMode);
1601 }
1602
1603 /**
1604 * Returns a {@code BigDecimal} whose value is {@code (this /
1605 * divisor)}, and whose scale is {@code this.scale()}. If
1606 * rounding must be performed to generate a result with the given
1607 * scale, the specified rounding mode is applied.
1608 *
1609 * <p>The new {@link #divide(BigDecimal, RoundingMode)} method
1610 * should be used in preference to this legacy method.
1611 *
1612 * @param divisor value by which this {@code BigDecimal} is to be divided.
1613 * @param roundingMode rounding mode to apply.
1614 * @return {@code this / divisor}
1615 * @throws ArithmeticException if {@code divisor==0}, or
1616 * {@code roundingMode==ROUND_UNNECESSARY} and
1617 * {@code this.scale()} is insufficient to represent the result
1618 * of the division exactly.
1619 * @throws IllegalArgumentException if {@code roundingMode} does not
1620 * represent a valid rounding mode.
1621 * @see #ROUND_UP
1622 * @see #ROUND_DOWN
1623 * @see #ROUND_CEILING
1624 * @see #ROUND_FLOOR
1625 * @see #ROUND_HALF_UP
1626 * @see #ROUND_HALF_DOWN
1627 * @see #ROUND_HALF_EVEN
1628 * @see #ROUND_UNNECESSARY
1629 */
1630 public BigDecimal divide(BigDecimal divisor, int roundingMode) {
1631 return this.divide(divisor, scale, roundingMode);
1632 }
1633
1634 /**
1635 * Returns a {@code BigDecimal} whose value is {@code (this /
1636 * divisor)}, and whose scale is {@code this.scale()}. If
1637 * rounding must be performed to generate a result with the given
1638 * scale, the specified rounding mode is applied.
1639 *
1640 * @param divisor value by which this {@code BigDecimal} is to be divided.
1641 * @param roundingMode rounding mode to apply.
1642 * @return {@code this / divisor}
1643 * @throws ArithmeticException if {@code divisor==0}, or
1644 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1645 * {@code this.scale()} is insufficient to represent the result
1646 * of the division exactly.
1647 * @since 1.5
1648 */
1649 public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) {
1650 return this.divide(divisor, scale, roundingMode.oldMode);
1651 }
1652
1653 /**
1654 * Returns a {@code BigDecimal} whose value is {@code (this /
1655 * divisor)}, and whose preferred scale is {@code (this.scale() -
1656 * divisor.scale())}; if the exact quotient cannot be
1657 * represented (because it has a non-terminating decimal
1658 * expansion) an {@code ArithmeticException} is thrown.
1659 *
1660 * @param divisor value by which this {@code BigDecimal} is to be divided.
1661 * @throws ArithmeticException if the exact quotient does not have a
1662 * terminating decimal expansion
1663 * @return {@code this / divisor}
1664 * @since 1.5
1665 * @author Joseph D. Darcy
1666 */
1667 public BigDecimal divide(BigDecimal divisor) {
1668 /*
1669 * Handle zero cases first.
1670 */
1671 if (divisor.signum() == 0) { // x/0
1672 if (this.signum() == 0) // 0/0
1673 throw new ArithmeticException("Division undefined"); // NaN
1674 throw new ArithmeticException("Division by zero");
1675 }
1676
1677 // Calculate preferred scale
1678 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1679
1680 if (this.signum() == 0) // 0/y
1681 return zeroValueOf(preferredScale);
1682 else {
1683 /*
1684 * If the quotient this/divisor has a terminating decimal
1685 * expansion, the expansion can have no more than
1686 * (a.precision() + ceil(10*b.precision)/3) digits.
1687 * Therefore, create a MathContext object with this
1688 * precision and do a divide with the UNNECESSARY rounding
1689 * mode.
1690 */
1691 MathContext mc = new MathContext( (int)Math.min(this.precision() +
1692 (long)Math.ceil(10.0*divisor.precision()/3.0),
1693 Integer.MAX_VALUE),
1694 RoundingMode.UNNECESSARY);
1695 BigDecimal quotient;
1696 try {
1697 quotient = this.divide(divisor, mc);
1698 } catch (ArithmeticException e) {
1699 throw new ArithmeticException("Non-terminating decimal expansion; " +
1700 "no exact representable decimal result.");
1701 }
1702
1703 int quotientScale = quotient.scale();
1704
1705 // divide(BigDecimal, mc) tries to adjust the quotient to
1706 // the desired one by removing trailing zeros; since the
1707 // exact divide method does not have an explicit digit
1708 // limit, we can add zeros too.
1709 if (preferredScale > quotientScale)
1710 return quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1711
1712 return quotient;
1713 }
1714 }
1715
1716 /**
1717 * Returns a {@code BigDecimal} whose value is {@code (this /
1718 * divisor)}, with rounding according to the context settings.
1719 *
1720 * @param divisor value by which this {@code BigDecimal} is to be divided.
1721 * @param mc the context to use.
1722 * @return {@code this / divisor}, rounded as necessary.
1723 * @throws ArithmeticException if the result is inexact but the
1724 * rounding mode is {@code UNNECESSARY} or
1725 * {@code mc.precision == 0} and the quotient has a
1726 * non-terminating decimal expansion.
1727 * @since 1.5
1728 */
1729 public BigDecimal divide(BigDecimal divisor, MathContext mc) {
1730 int mcp = mc.precision;
1731 if (mcp == 0)
1732 return divide(divisor);
1733
1734 BigDecimal dividend = this;
1735 long preferredScale = (long)dividend.scale - divisor.scale;
1736 // Now calculate the answer. We use the existing
1737 // divide-and-round method, but as this rounds to scale we have
1738 // to normalize the values here to achieve the desired result.
1739 // For x/y we first handle y=0 and x=0, and then normalize x and
1740 // y to give x' and y' with the following constraints:
1741 // (a) 0.1 <= x' < 1
1742 // (b) x' <= y' < 10*x'
1743 // Dividing x'/y' with the required scale set to mc.precision then
1744 // will give a result in the range 0.1 to 1 rounded to exactly
1745 // the right number of digits (except in the case of a result of
1746 // 1.000... which can arise when x=y, or when rounding overflows
1747 // The 1.000... case will reduce properly to 1.
1748 if (divisor.signum() == 0) { // x/0
1749 if (dividend.signum() == 0) // 0/0
1750 throw new ArithmeticException("Division undefined"); // NaN
1751 throw new ArithmeticException("Division by zero");
1752 }
1753 if (dividend.signum() == 0) // 0/y
1754 return zeroValueOf(saturateLong(preferredScale));
1755 int xscale = dividend.precision();
1756 int yscale = divisor.precision();
1757 if(dividend.intCompact!=INFLATED) {
1758 if(divisor.intCompact!=INFLATED) {
1759 return divide(dividend.intCompact, xscale, divisor.intCompact, yscale, preferredScale, mc);
1760 } else {
1761 return divide(dividend.intCompact, xscale, divisor.intVal, yscale, preferredScale, mc);
1762 }
1763 } else {
1764 if(divisor.intCompact!=INFLATED) {
1765 return divide(dividend.intVal, xscale, divisor.intCompact, yscale, preferredScale, mc);
1766 } else {
1767 return divide(dividend.intVal, xscale, divisor.intVal, yscale, preferredScale, mc);
1768 }
1769 }
1770 }
1771
1772 /**
1773 * Returns a {@code BigDecimal} whose value is the integer part
1774 * of the quotient {@code (this / divisor)} rounded down. The
1775 * preferred scale of the result is {@code (this.scale() -
1776 * divisor.scale())}.
1777 *
1778 * @param divisor value by which this {@code BigDecimal} is to be divided.
1779 * @return The integer part of {@code this / divisor}.
1780 * @throws ArithmeticException if {@code divisor==0}
1781 * @since 1.5
1782 */
1783 public BigDecimal divideToIntegralValue(BigDecimal divisor) {
1784 // Calculate preferred scale
1785 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1786 if (this.compareMagnitude(divisor) < 0) {
1787 // much faster when this << divisor
1788 return zeroValueOf(preferredScale);
1789 }
1790
1791 if (this.signum() == 0 && divisor.signum() != 0)
1792 return this.setScale(preferredScale, ROUND_UNNECESSARY);
1793
1794 // Perform a divide with enough digits to round to a correct
1795 // integer value; then remove any fractional digits
1796
1797 int maxDigits = (int)Math.min(this.precision() +
1798 (long)Math.ceil(10.0*divisor.precision()/3.0) +
1799 Math.abs((long)this.scale() - divisor.scale()) + 2,
1800 Integer.MAX_VALUE);
1801 BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits,
1802 RoundingMode.DOWN));
1803 if (quotient.scale > 0) {
1804 quotient = quotient.setScale(0, RoundingMode.DOWN);
1805 quotient = stripZerosToMatchScale(quotient.intVal, quotient.intCompact, quotient.scale, preferredScale);
1806 }
1807
1808 if (quotient.scale < preferredScale) {
1809 // pad with zeros if necessary
1810 quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1811 }
1812
1813 return quotient;
1814 }
1815
1816 /**
1817 * Returns a {@code BigDecimal} whose value is the integer part
1818 * of {@code (this / divisor)}. Since the integer part of the
1819 * exact quotient does not depend on the rounding mode, the
1820 * rounding mode does not affect the values returned by this
1821 * method. The preferred scale of the result is
1822 * {@code (this.scale() - divisor.scale())}. An
1823 * {@code ArithmeticException} is thrown if the integer part of
1824 * the exact quotient needs more than {@code mc.precision}
1825 * digits.
1826 *
1827 * @param divisor value by which this {@code BigDecimal} is to be divided.
1828 * @param mc the context to use.
1829 * @return The integer part of {@code this / divisor}.
1830 * @throws ArithmeticException if {@code divisor==0}
1831 * @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result
1832 * requires a precision of more than {@code mc.precision} digits.
1833 * @since 1.5
1834 * @author Joseph D. Darcy
1835 */
1836 public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) {
1837 if (mc.precision == 0 || // exact result
1838 (this.compareMagnitude(divisor) < 0)) // zero result
1839 return divideToIntegralValue(divisor);
1840
1841 // Calculate preferred scale
1842 int preferredScale = saturateLong((long)this.scale - divisor.scale);
1843
1844 /*
1845 * Perform a normal divide to mc.precision digits. If the
1846 * remainder has absolute value less than the divisor, the
1847 * integer portion of the quotient fits into mc.precision
1848 * digits. Next, remove any fractional digits from the
1849 * quotient and adjust the scale to the preferred value.
1850 */
1851 BigDecimal result = this.divide(divisor, new MathContext(mc.precision, RoundingMode.DOWN));
1852
1853 if (result.scale() < 0) {
1854 /*
1855 * Result is an integer. See if quotient represents the
1856 * full integer portion of the exact quotient; if it does,
1857 * the computed remainder will be less than the divisor.
1858 */
1859 BigDecimal product = result.multiply(divisor);
1860 // If the quotient is the full integer value,
1861 // |dividend-product| < |divisor|.
1862 if (this.subtract(product).compareMagnitude(divisor) >= 0) {
1863 throw new ArithmeticException("Division impossible");
1864 }
1865 } else if (result.scale() > 0) {
1866 /*
1867 * Integer portion of quotient will fit into precision
1868 * digits; recompute quotient to scale 0 to avoid double
1869 * rounding and then try to adjust, if necessary.
1870 */
1871 result = result.setScale(0, RoundingMode.DOWN);
1872 }
1873 // else result.scale() == 0;
1874
1875 int precisionDiff;
1876 if ((preferredScale > result.scale()) &&
1877 (precisionDiff = mc.precision - result.precision()) > 0) {
1878 return result.setScale(result.scale() +
1879 Math.min(precisionDiff, preferredScale - result.scale) );
1880 } else {
1881 return stripZerosToMatchScale(result.intVal,result.intCompact,result.scale,preferredScale);
1882 }
1883 }
1884
1885 /**
1886 * Returns a {@code BigDecimal} whose value is {@code (this % divisor)}.
1887 *
1888 * <p>The remainder is given by
1889 * {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}.
1890 * Note that this is not the modulo operation (the result can be
1891 * negative).
1892 *
1893 * @param divisor value by which this {@code BigDecimal} is to be divided.
1894 * @return {@code this % divisor}.
1895 * @throws ArithmeticException if {@code divisor==0}
1896 * @since 1.5
1897 */
1898 public BigDecimal remainder(BigDecimal divisor) {
1899 BigDecimal divrem[] = this.divideAndRemainder(divisor);
1900 return divrem[1];
1901 }
1902
1903
1904 /**
1905 * Returns a {@code BigDecimal} whose value is {@code (this %
1906 * divisor)}, with rounding according to the context settings.
1907 * The {@code MathContext} settings affect the implicit divide
1908 * used to compute the remainder. The remainder computation
1909 * itself is by definition exact. Therefore, the remainder may
1910 * contain more than {@code mc.getPrecision()} digits.
1911 *
1912 * <p>The remainder is given by
1913 * {@code this.subtract(this.divideToIntegralValue(divisor,
1914 * mc).multiply(divisor))}. Note that this is not the modulo
1915 * operation (the result can be negative).
1916 *
1917 * @param divisor value by which this {@code BigDecimal} is to be divided.
1918 * @param mc the context to use.
1919 * @return {@code this % divisor}, rounded as necessary.
1920 * @throws ArithmeticException if {@code divisor==0}
1921 * @throws ArithmeticException if the result is inexact but the
1922 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1923 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1924 * require a precision of more than {@code mc.precision} digits.
1925 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1926 * @since 1.5
1927 */
1928 public BigDecimal remainder(BigDecimal divisor, MathContext mc) {
1929 BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
1930 return divrem[1];
1931 }
1932
1933 /**
1934 * Returns a two-element {@code BigDecimal} array containing the
1935 * result of {@code divideToIntegralValue} followed by the result of
1936 * {@code remainder} on the two operands.
1937 *
1938 * <p>Note that if both the integer quotient and remainder are
1939 * needed, this method is faster than using the
1940 * {@code divideToIntegralValue} and {@code remainder} methods
1941 * separately because the division need only be carried out once.
1942 *
1943 * @param divisor value by which this {@code BigDecimal} is to be divided,
1944 * and the remainder computed.
1945 * @return a two element {@code BigDecimal} array: the quotient
1946 * (the result of {@code divideToIntegralValue}) is the initial element
1947 * and the remainder is the final element.
1948 * @throws ArithmeticException if {@code divisor==0}
1949 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1950 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1951 * @since 1.5
1952 */
1953 public BigDecimal[] divideAndRemainder(BigDecimal divisor) {
1954 // we use the identity x = i * y + r to determine r
1955 BigDecimal[] result = new BigDecimal[2];
1956
1957 result[0] = this.divideToIntegralValue(divisor);
1958 result[1] = this.subtract(result[0].multiply(divisor));
1959 return result;
1960 }
1961
1962 /**
1963 * Returns a two-element {@code BigDecimal} array containing the
1964 * result of {@code divideToIntegralValue} followed by the result of
1965 * {@code remainder} on the two operands calculated with rounding
1966 * according to the context settings.
1967 *
1968 * <p>Note that if both the integer quotient and remainder are
1969 * needed, this method is faster than using the
1970 * {@code divideToIntegralValue} and {@code remainder} methods
1971 * separately because the division need only be carried out once.
1972 *
1973 * @param divisor value by which this {@code BigDecimal} is to be divided,
1974 * and the remainder computed.
1975 * @param mc the context to use.
1976 * @return a two element {@code BigDecimal} array: the quotient
1977 * (the result of {@code divideToIntegralValue}) is the
1978 * initial element and the remainder is the final element.
1979 * @throws ArithmeticException if {@code divisor==0}
1980 * @throws ArithmeticException if the result is inexact but the
1981 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1982 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1983 * require a precision of more than {@code mc.precision} digits.
1984 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1985 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1986 * @since 1.5
1987 */
1988 public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) {
1989 if (mc.precision == 0)
1990 return divideAndRemainder(divisor);
1991
1992 BigDecimal[] result = new BigDecimal[2];
1993 BigDecimal lhs = this;
1994
1995 result[0] = lhs.divideToIntegralValue(divisor, mc);
1996 result[1] = lhs.subtract(result[0].multiply(divisor));
1997 return result;
1998 }
1999
2000 /**
2001 * Returns a {@code BigDecimal} whose value is
2002 * <tt>(this<sup>n</sup>)</tt>, The power is computed exactly, to
2003 * unlimited precision.
2004 *
2005 * <p>The parameter {@code n} must be in the range 0 through
2006 * 999999999, inclusive. {@code ZERO.pow(0)} returns {@link
2007 * #ONE}.
2008 *
2009 * Note that future releases may expand the allowable exponent
2010 * range of this method.
2011 *
2012 * @param n power to raise this {@code BigDecimal} to.
2013 * @return <tt>this<sup>n</sup></tt>
2014 * @throws ArithmeticException if {@code n} is out of range.
2015 * @since 1.5
2016 */
2017 public BigDecimal pow(int n) {
2018 if (n < 0 || n > 999999999)
2019 throw new ArithmeticException("Invalid operation");
2020 // No need to calculate pow(n) if result will over/underflow.
2021 // Don't attempt to support "supernormal" numbers.
2022 int newScale = checkScale((long)scale * n);
2023 return new BigDecimal(this.inflated().pow(n), newScale);
2024 }
2025
2026
2027 /**
2028 * Returns a {@code BigDecimal} whose value is
2029 * <tt>(this<sup>n</sup>)</tt>. The current implementation uses
2030 * the core algorithm defined in ANSI standard X3.274-1996 with
2031 * rounding according to the context settings. In general, the
2032 * returned numerical value is within two ulps of the exact
2033 * numerical value for the chosen precision. Note that future
2034 * releases may use a different algorithm with a decreased
2035 * allowable error bound and increased allowable exponent range.
2036 *
2037 * <p>The X3.274-1996 algorithm is:
2038 *
2039 * <ul>
2040 * <li> An {@code ArithmeticException} exception is thrown if
2041 * <ul>
2042 * <li>{@code abs(n) > 999999999}
2043 * <li>{@code mc.precision == 0} and {@code n < 0}
2044 * <li>{@code mc.precision > 0} and {@code n} has more than
2045 * {@code mc.precision} decimal digits
2046 * </ul>
2047 *
2048 * <li> if {@code n} is zero, {@link #ONE} is returned even if
2049 * {@code this} is zero, otherwise
2050 * <ul>
2051 * <li> if {@code n} is positive, the result is calculated via
2052 * the repeated squaring technique into a single accumulator.
2053 * The individual multiplications with the accumulator use the
2054 * same math context settings as in {@code mc} except for a
2055 * precision increased to {@code mc.precision + elength + 1}
2056 * where {@code elength} is the number of decimal digits in
2057 * {@code n}.
2058 *
2059 * <li> if {@code n} is negative, the result is calculated as if
2060 * {@code n} were positive; this value is then divided into one
2061 * using the working precision specified above.
2062 *
2063 * <li> The final value from either the positive or negative case
2064 * is then rounded to the destination precision.
2065 * </ul>
2066 * </ul>
2067 *
2068 * @param n power to raise this {@code BigDecimal} to.
2069 * @param mc the context to use.
2070 * @return <tt>this<sup>n</sup></tt> using the ANSI standard X3.274-1996
2071 * algorithm
2072 * @throws ArithmeticException if the result is inexact but the
2073 * rounding mode is {@code UNNECESSARY}, or {@code n} is out
2074 * of range.
2075 * @since 1.5
2076 */
2077 public BigDecimal pow(int n, MathContext mc) {
2078 if (mc.precision == 0)
2079 return pow(n);
2080 if (n < -999999999 || n > 999999999)
2081 throw new ArithmeticException("Invalid operation");
2082 if (n == 0)
2083 return ONE; // x**0 == 1 in X3.274
2084 BigDecimal lhs = this;
2085 MathContext workmc = mc; // working settings
2086 int mag = Math.abs(n); // magnitude of n
2087 if (mc.precision > 0) {
2088 int elength = longDigitLength(mag); // length of n in digits
2089 if (elength > mc.precision) // X3.274 rule
2090 throw new ArithmeticException("Invalid operation");
2091 workmc = new MathContext(mc.precision + elength + 1,
2092 mc.roundingMode);
2093 }
2094 // ready to carry out power calculation...
2095 BigDecimal acc = ONE; // accumulator
2096 boolean seenbit = false; // set once we've seen a 1-bit
2097 for (int i=1;;i++) { // for each bit [top bit ignored]
2098 mag += mag; // shift left 1 bit
2099 if (mag < 0) { // top bit is set
2100 seenbit = true; // OK, we're off
2101 acc = acc.multiply(lhs, workmc); // acc=acc*x
2102 }
2103 if (i == 31)
2104 break; // that was the last bit
2105 if (seenbit)
2106 acc=acc.multiply(acc, workmc); // acc=acc*acc [square]
2107 // else (!seenbit) no point in squaring ONE
2108 }
2109 // if negative n, calculate the reciprocal using working precision
2110 if (n < 0) // [hence mc.precision>0]
2111 acc=ONE.divide(acc, workmc);
2112 // round to final precision and strip zeros
2113 return doRound(acc, mc);
2114 }
2115
2116 /**
2117 * Returns a {@code BigDecimal} whose value is the absolute value
2118 * of this {@code BigDecimal}, and whose scale is
2119 * {@code this.scale()}.
2120 *
2121 * @return {@code abs(this)}
2122 */
2123 public BigDecimal abs() {
2124 return (signum() < 0 ? negate() : this);
2125 }
2126
2127 /**
2128 * Returns a {@code BigDecimal} whose value is the absolute value
2129 * of this {@code BigDecimal}, with rounding according to the
2130 * context settings.
2131 *
2132 * @param mc the context to use.
2133 * @return {@code abs(this)}, rounded as necessary.
2134 * @throws ArithmeticException if the result is inexact but the
2135 * rounding mode is {@code UNNECESSARY}.
2136 * @since 1.5
2137 */
2138 public BigDecimal abs(MathContext mc) {
2139 return (signum() < 0 ? negate(mc) : plus(mc));
2140 }
2141
2142 /**
2143 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2144 * and whose scale is {@code this.scale()}.
2145 *
2146 * @return {@code -this}.
2147 */
2148 public BigDecimal negate() {
2149 if (intCompact == INFLATED) {
2150 return new BigDecimal(intVal.negate(), INFLATED, scale, precision);
2151 } else {
2152 return valueOf(-intCompact, scale, precision);
2153 }
2154 }
2155
2156 /**
2157 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2158 * with rounding according to the context settings.
2159 *
2160 * @param mc the context to use.
2161 * @return {@code -this}, rounded as necessary.
2162 * @throws ArithmeticException if the result is inexact but the
2163 * rounding mode is {@code UNNECESSARY}.
2164 * @since 1.5
2165 */
2166 public BigDecimal negate(MathContext mc) {
2167 return negate().plus(mc);
2168 }
2169
2170 /**
2171 * Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose
2172 * scale is {@code this.scale()}.
2173 *
2174 * <p>This method, which simply returns this {@code BigDecimal}
2175 * is included for symmetry with the unary minus method {@link
2176 * #negate()}.
2177 *
2178 * @return {@code this}.
2179 * @see #negate()
2180 * @since 1.5
2181 */
2182 public BigDecimal plus() {
2183 return this;
2184 }
2185
2186 /**
2187 * Returns a {@code BigDecimal} whose value is {@code (+this)},
2188 * with rounding according to the context settings.
2189 *
2190 * <p>The effect of this method is identical to that of the {@link
2191 * #round(MathContext)} method.
2192 *
2193 * @param mc the context to use.
2194 * @return {@code this}, rounded as necessary. A zero result will
2195 * have a scale of 0.
2196 * @throws ArithmeticException if the result is inexact but the
2197 * rounding mode is {@code UNNECESSARY}.
2198 * @see #round(MathContext)
2199 * @since 1.5
2200 */
2201 public BigDecimal plus(MathContext mc) {
2202 if (mc.precision == 0) // no rounding please
2203 return this;
2204 return doRound(this, mc);
2205 }
2206
2207 /**
2208 * Returns the signum function of this {@code BigDecimal}.
2209 *
2210 * @return -1, 0, or 1 as the value of this {@code BigDecimal}
2211 * is negative, zero, or positive.
2212 */
2213 public int signum() {
2214 return (intCompact != INFLATED)?
2215 Long.signum(intCompact):
2216 intVal.signum();
2217 }
2218
2219 /**
2220 * Returns the <i>scale</i> of this {@code BigDecimal}. If zero
2221 * or positive, the scale is the number of digits to the right of
2222 * the decimal point. If negative, the unscaled value of the
2223 * number is multiplied by ten to the power of the negation of the
2224 * scale. For example, a scale of {@code -3} means the unscaled
2225 * value is multiplied by 1000.
2226 *
2227 * @return the scale of this {@code BigDecimal}.
2228 */
2229 public int scale() {
2230 return scale;
2231 }
2232
2233 /**
2234 * Returns the <i>precision</i> of this {@code BigDecimal}. (The
2235 * precision is the number of digits in the unscaled value.)
2236 *
2237 * <p>The precision of a zero value is 1.
2238 *
2239 * @return the precision of this {@code BigDecimal}.
2240 * @since 1.5
2241 */
2242 public int precision() {
2243 int result = precision;
2244 if (result == 0) {
2245 long s = intCompact;
2246 if (s != INFLATED)
2247 result = longDigitLength(s);
2248 else
2249 result = bigDigitLength(intVal);
2250 precision = result;
2251 }
2252 return result;
2253 }
2254
2255
2256 /**
2257 * Returns a {@code BigInteger} whose value is the <i>unscaled
2258 * value</i> of this {@code BigDecimal}. (Computes <tt>(this *
2259 * 10<sup>this.scale()</sup>)</tt>.)
2260 *
2261 * @return the unscaled value of this {@code BigDecimal}.
2262 * @since 1.2
2263 */
2264 public BigInteger unscaledValue() {
2265 return this.inflated();
2266 }
2267
2268 // Rounding Modes
2269
2270 /**
2271 * Rounding mode to round away from zero. Always increments the
2272 * digit prior to a nonzero discarded fraction. Note that this rounding
2273 * mode never decreases the magnitude of the calculated value.
2274 */
2275 public final static int ROUND_UP = 0;
2276
2277 /**
2278 * Rounding mode to round towards zero. Never increments the digit
2279 * prior to a discarded fraction (i.e., truncates). Note that this
2280 * rounding mode never increases the magnitude of the calculated value.
2281 */
2282 public final static int ROUND_DOWN = 1;
2283
2284 /**
2285 * Rounding mode to round towards positive infinity. If the
2286 * {@code BigDecimal} is positive, behaves as for
2287 * {@code ROUND_UP}; if negative, behaves as for
2288 * {@code ROUND_DOWN}. Note that this rounding mode never
2289 * decreases the calculated value.
2290 */
2291 public final static int ROUND_CEILING = 2;
2292
2293 /**
2294 * Rounding mode to round towards negative infinity. If the
2295 * {@code BigDecimal} is positive, behave as for
2296 * {@code ROUND_DOWN}; if negative, behave as for
2297 * {@code ROUND_UP}. Note that this rounding mode never
2298 * increases the calculated value.
2299 */
2300 public final static int ROUND_FLOOR = 3;
2301
2302 /**
2303 * Rounding mode to round towards {@literal "nearest neighbor"}
2304 * unless both neighbors are equidistant, in which case round up.
2305 * Behaves as for {@code ROUND_UP} if the discarded fraction is
2306 * ≥ 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note
2307 * that this is the rounding mode that most of us were taught in
2308 * grade school.
2309 */
2310 public final static int ROUND_HALF_UP = 4;
2311
2312 /**
2313 * Rounding mode to round towards {@literal "nearest neighbor"}
2314 * unless both neighbors are equidistant, in which case round
2315 * down. Behaves as for {@code ROUND_UP} if the discarded
2316 * fraction is {@literal >} 0.5; otherwise, behaves as for
2317 * {@code ROUND_DOWN}.
2318 */
2319 public final static int ROUND_HALF_DOWN = 5;
2320
2321 /**
2322 * Rounding mode to round towards the {@literal "nearest neighbor"}
2323 * unless both neighbors are equidistant, in which case, round
2324 * towards the even neighbor. Behaves as for
2325 * {@code ROUND_HALF_UP} if the digit to the left of the
2326 * discarded fraction is odd; behaves as for
2327 * {@code ROUND_HALF_DOWN} if it's even. Note that this is the
2328 * rounding mode that minimizes cumulative error when applied
2329 * repeatedly over a sequence of calculations.
2330 */
2331 public final static int ROUND_HALF_EVEN = 6;
2332
2333 /**
2334 * Rounding mode to assert that the requested operation has an exact
2335 * result, hence no rounding is necessary. If this rounding mode is
2336 * specified on an operation that yields an inexact result, an
2337 * {@code ArithmeticException} is thrown.
2338 */
2339 public final static int ROUND_UNNECESSARY = 7;
2340
2341
2342 // Scaling/Rounding Operations
2343
2344 /**
2345 * Returns a {@code BigDecimal} rounded according to the
2346 * {@code MathContext} settings. If the precision setting is 0 then
2347 * no rounding takes place.
2348 *
2349 * <p>The effect of this method is identical to that of the
2350 * {@link #plus(MathContext)} method.
2351 *
2352 * @param mc the context to use.
2353 * @return a {@code BigDecimal} rounded according to the
2354 * {@code MathContext} settings.
2355 * @throws ArithmeticException if the rounding mode is
2356 * {@code UNNECESSARY} and the
2357 * {@code BigDecimal} operation would require rounding.
2358 * @see #plus(MathContext)
2359 * @since 1.5
2360 */
2361 public BigDecimal round(MathContext mc) {
2362 return plus(mc);
2363 }
2364
2365 /**
2366 * Returns a {@code BigDecimal} whose scale is the specified
2367 * value, and whose unscaled value is determined by multiplying or
2368 * dividing this {@code BigDecimal}'s unscaled value by the
2369 * appropriate power of ten to maintain its overall value. If the
2370 * scale is reduced by the operation, the unscaled value must be
2371 * divided (rather than multiplied), and the value may be changed;
2372 * in this case, the specified rounding mode is applied to the
2373 * division.
2374 *
2375 * <p>Note that since BigDecimal objects are immutable, calls of
2376 * this method do <i>not</i> result in the original object being
2377 * modified, contrary to the usual convention of having methods
2378 * named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
2379 * Instead, {@code setScale} returns an object with the proper
2380 * scale; the returned object may or may not be newly allocated.
2381 *
2382 * @param newScale scale of the {@code BigDecimal} value to be returned.
2383 * @param roundingMode The rounding mode to apply.
2384 * @return a {@code BigDecimal} whose scale is the specified value,
2385 * and whose unscaled value is determined by multiplying or
2386 * dividing this {@code BigDecimal}'s unscaled value by the
2387 * appropriate power of ten to maintain its overall value.
2388 * @throws ArithmeticException if {@code roundingMode==UNNECESSARY}
2389 * and the specified scaling operation would require
2390 * rounding.
2391 * @see RoundingMode
2392 * @since 1.5
2393 */
2394 public BigDecimal setScale(int newScale, RoundingMode roundingMode) {
2395 return setScale(newScale, roundingMode.oldMode);
2396 }
2397
2398 /**
2399 * Returns a {@code BigDecimal} whose scale is the specified
2400 * value, and whose unscaled value is determined by multiplying or
2401 * dividing this {@code BigDecimal}'s unscaled value by the
2402 * appropriate power of ten to maintain its overall value. If the
2403 * scale is reduced by the operation, the unscaled value must be
2404 * divided (rather than multiplied), and the value may be changed;
2405 * in this case, the specified rounding mode is applied to the
2406 * division.
2407 *
2408 * <p>Note that since BigDecimal objects are immutable, calls of
2409 * this method do <i>not</i> result in the original object being
2410 * modified, contrary to the usual convention of having methods
2411 * named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
2412 * Instead, {@code setScale} returns an object with the proper
2413 * scale; the returned object may or may not be newly allocated.
2414 *
2415 * <p>The new {@link #setScale(int, RoundingMode)} method should
2416 * be used in preference to this legacy method.
2417 *
2418 * @param newScale scale of the {@code BigDecimal} value to be returned.
2419 * @param roundingMode The rounding mode to apply.
2420 * @return a {@code BigDecimal} whose scale is the specified value,
2421 * and whose unscaled value is determined by multiplying or
2422 * dividing this {@code BigDecimal}'s unscaled value by the
2423 * appropriate power of ten to maintain its overall value.
2424 * @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY}
2425 * and the specified scaling operation would require
2426 * rounding.
2427 * @throws IllegalArgumentException if {@code roundingMode} does not
2428 * represent a valid rounding mode.
2429 * @see #ROUND_UP
2430 * @see #ROUND_DOWN
2431 * @see #ROUND_CEILING
2432 * @see #ROUND_FLOOR
2433 * @see #ROUND_HALF_UP
2434 * @see #ROUND_HALF_DOWN
2435 * @see #ROUND_HALF_EVEN
2436 * @see #ROUND_UNNECESSARY
2437 */
2438 public BigDecimal setScale(int newScale, int roundingMode) {
2439 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
2440 throw new IllegalArgumentException("Invalid rounding mode");
2441
2442 int oldScale = this.scale;
2443 if (newScale == oldScale) // easy case
2444 return this;
2445 if (this.signum() == 0) // zero can have any scale
2446 return zeroValueOf(newScale);
2447 if(this.intCompact!=INFLATED) {
2448 long rs = this.intCompact;
2449 if (newScale > oldScale) {
2450 int raise = checkScale((long) newScale - oldScale);
2451 if ((rs = longMultiplyPowerTen(rs, raise)) != INFLATED) {
2452 return valueOf(rs,newScale);
2453 }
2454 BigInteger rb = bigMultiplyPowerTen(raise);
2455 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2456 } else {
2457 // newScale < oldScale -- drop some digits
2458 // Can't predict the precision due to the effect of rounding.
2459 int drop = checkScale((long) oldScale - newScale);
2460 if (drop < LONG_TEN_POWERS_TABLE.length) {
2461 return divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, newScale);
2462 } else {
2463 return divideAndRound(this.inflated(), bigTenToThe(drop), newScale, roundingMode, newScale);
2464 }
2465 }
2466 } else {
2467 if (newScale > oldScale) {
2468 int raise = checkScale((long) newScale - oldScale);
2469 BigInteger rb = bigMultiplyPowerTen(this.intVal,raise);
2470 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2471 } else {
2472 // newScale < oldScale -- drop some digits
2473 // Can't predict the precision due to the effect of rounding.
2474 int drop = checkScale((long) oldScale - newScale);
2475 if (drop < LONG_TEN_POWERS_TABLE.length)
2476 return divideAndRound(this.intVal, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode,
2477 newScale);
2478 else
2479 return divideAndRound(this.intVal, bigTenToThe(drop), newScale, roundingMode, newScale);
2480 }
2481 }
2482 }
2483
2484 /**
2485 * Returns a {@code BigDecimal} whose scale is the specified
2486 * value, and whose value is numerically equal to this
2487 * {@code BigDecimal}'s. Throws an {@code ArithmeticException}
2488 * if this is not possible.
2489 *
2490 * <p>This call is typically used to increase the scale, in which
2491 * case it is guaranteed that there exists a {@code BigDecimal}
2492 * of the specified scale and the correct value. The call can
2493 * also be used to reduce the scale if the caller knows that the
2494 * {@code BigDecimal} has sufficiently many zeros at the end of
2495 * its fractional part (i.e., factors of ten in its integer value)
2496 * to allow for the rescaling without changing its value.
2497 *
2498 * <p>This method returns the same result as the two-argument
2499 * versions of {@code setScale}, but saves the caller the trouble
2500 * of specifying a rounding mode in cases where it is irrelevant.
2501 *
2502 * <p>Note that since {@code BigDecimal} objects are immutable,
2503 * calls of this method do <i>not</i> result in the original
2504 * object being modified, contrary to the usual convention of
2505 * having methods named <tt>set<i>X</i></tt> mutate field
2506 * <i>{@code X}</i>. Instead, {@code setScale} returns an
2507 * object with the proper scale; the returned object may or may
2508 * not be newly allocated.
2509 *
2510 * @param newScale scale of the {@code BigDecimal} value to be returned.
2511 * @return a {@code BigDecimal} whose scale is the specified value, and
2512 * whose unscaled value is determined by multiplying or dividing
2513 * this {@code BigDecimal}'s unscaled value by the appropriate
2514 * power of ten to maintain its overall value.
2515 * @throws ArithmeticException if the specified scaling operation would
2516 * require rounding.
2517 * @see #setScale(int, int)
2518 * @see #setScale(int, RoundingMode)
2519 */
2520 public BigDecimal setScale(int newScale) {
2521 return setScale(newScale, ROUND_UNNECESSARY);
2522 }
2523
2524 // Decimal Point Motion Operations
2525
2526 /**
2527 * Returns a {@code BigDecimal} which is equivalent to this one
2528 * with the decimal point moved {@code n} places to the left. If
2529 * {@code n} is non-negative, the call merely adds {@code n} to
2530 * the scale. If {@code n} is negative, the call is equivalent
2531 * to {@code movePointRight(-n)}. The {@code BigDecimal}
2532 * returned by this call has value <tt>(this ×
2533 * 10<sup>-n</sup>)</tt> and scale {@code max(this.scale()+n,
2534 * 0)}.
2535 *
2536 * @param n number of places to move the decimal point to the left.
2537 * @return a {@code BigDecimal} which is equivalent to this one with the
2538 * decimal point moved {@code n} places to the left.
2539 * @throws ArithmeticException if scale overflows.
2540 */
2541 public BigDecimal movePointLeft(int n) {
2542 // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE
2543 int newScale = checkScale((long)scale + n);
2544 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2545 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2546 }
2547
2548 /**
2549 * Returns a {@code BigDecimal} which is equivalent to this one
2550 * with the decimal point moved {@code n} places to the right.
2551 * If {@code n} is non-negative, the call merely subtracts
2552 * {@code n} from the scale. If {@code n} is negative, the call
2553 * is equivalent to {@code movePointLeft(-n)}. The
2554 * {@code BigDecimal} returned by this call has value <tt>(this
2555 * × 10<sup>n</sup>)</tt> and scale {@code max(this.scale()-n,
2556 * 0)}.
2557 *
2558 * @param n number of places to move the decimal point to the right.
2559 * @return a {@code BigDecimal} which is equivalent to this one
2560 * with the decimal point moved {@code n} places to the right.
2561 * @throws ArithmeticException if scale overflows.
2562 */
2563 public BigDecimal movePointRight(int n) {
2564 // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE
2565 int newScale = checkScale((long)scale - n);
2566 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2567 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2568 }
2569
2570 /**
2571 * Returns a BigDecimal whose numerical value is equal to
2572 * ({@code this} * 10<sup>n</sup>). The scale of
2573 * the result is {@code (this.scale() - n)}.
2574 *
2575 * @param n the exponent power of ten to scale by
2576 * @return a BigDecimal whose numerical value is equal to
2577 * ({@code this} * 10<sup>n</sup>)
2578 * @throws ArithmeticException if the scale would be
2579 * outside the range of a 32-bit integer.
2580 *
2581 * @since 1.5
2582 */
2583 public BigDecimal scaleByPowerOfTen(int n) {
2584 return new BigDecimal(intVal, intCompact,
2585 checkScale((long)scale - n), precision);
2586 }
2587
2588 /**
2589 * Returns a {@code BigDecimal} which is numerically equal to
2590 * this one but with any trailing zeros removed from the
2591 * representation. For example, stripping the trailing zeros from
2592 * the {@code BigDecimal} value {@code 600.0}, which has
2593 * [{@code BigInteger}, {@code scale}] components equals to
2594 * [6000, 1], yields {@code 6E2} with [{@code BigInteger},
2595 * {@code scale}] components equals to [6, -2]. If
2596 * this BigDecimal is numerically equal to zero, then
2597 * {@code BigDecimal.ZERO} is returned.
2598 *
2599 * @return a numerically equal {@code BigDecimal} with any
2600 * trailing zeros removed.
2601 * @since 1.5
2602 */
2603 public BigDecimal stripTrailingZeros() {
2604 if (intCompact == 0 || (intVal != null && intVal.signum() == 0)) {
2605 return BigDecimal.ZERO;
2606 } else if (intCompact != INFLATED) {
2607 return createAndStripZerosToMatchScale(intCompact, scale, Long.MIN_VALUE);
2608 } else {
2609 return createAndStripZerosToMatchScale(intVal, scale, Long.MIN_VALUE);
2610 }
2611 }
2612
2613 // Comparison Operations
2614
2615 /**
2616 * Compares this {@code BigDecimal} with the specified
2617 * {@code BigDecimal}. Two {@code BigDecimal} objects that are
2618 * equal in value but have a different scale (like 2.0 and 2.00)
2619 * are considered equal by this method. This method is provided
2620 * in preference to individual methods for each of the six boolean
2621 * comparison operators ({@literal <}, ==,
2622 * {@literal >}, {@literal >=}, !=, {@literal <=}). The
2623 * suggested idiom for performing these comparisons is:
2624 * {@code (x.compareTo(y)} <<i>op</i>> {@code 0)}, where
2625 * <<i>op</i>> is one of the six comparison operators.
2626 *
2627 * @param val {@code BigDecimal} to which this {@code BigDecimal} is
2628 * to be compared.
2629 * @return -1, 0, or 1 as this {@code BigDecimal} is numerically
2630 * less than, equal to, or greater than {@code val}.
2631 */
2632 public int compareTo(BigDecimal val) {
2633 // Quick path for equal scale and non-inflated case.
2634 if (scale == val.scale) {
2635 long xs = intCompact;
2636 long ys = val.intCompact;
2637 if (xs != INFLATED && ys != INFLATED)
2638 return xs != ys ? ((xs > ys) ? 1 : -1) : 0;
2639 }
2640 int xsign = this.signum();
2641 int ysign = val.signum();
2642 if (xsign != ysign)
2643 return (xsign > ysign) ? 1 : -1;
2644 if (xsign == 0)
2645 return 0;
2646 int cmp = compareMagnitude(val);
2647 return (xsign > 0) ? cmp : -cmp;
2648 }
2649
2650 /**
2651 * Version of compareTo that ignores sign.
2652 */
2653 private int compareMagnitude(BigDecimal val) {
2654 // Match scales, avoid unnecessary inflation
2655 long ys = val.intCompact;
2656 long xs = this.intCompact;
2657 if (xs == 0)
2658 return (ys == 0) ? 0 : -1;
2659 if (ys == 0)
2660 return 1;
2661
2662 int sdiff = this.scale - val.scale;
2663 if (sdiff != 0) {
2664 // Avoid matching scales if the (adjusted) exponents differ
2665 int xae = this.precision() - this.scale; // [-1]
2666 int yae = val.precision() - val.scale; // [-1]
2667 if (xae < yae)
2668 return -1;
2669 if (xae > yae)
2670 return 1;
2671 BigInteger rb = null;
2672 if (sdiff < 0) {
2673 if ( (xs == INFLATED ||
2674 (xs = longMultiplyPowerTen(xs, -sdiff)) == INFLATED) &&
2675 ys == INFLATED) {
2676 rb = bigMultiplyPowerTen(-sdiff);
2677 return rb.compareMagnitude(val.intVal);
2678 }
2679 } else { // sdiff > 0
2680 if ( (ys == INFLATED ||
2681 (ys = longMultiplyPowerTen(ys, sdiff)) == INFLATED) &&
2682 xs == INFLATED) {
2683 rb = val.bigMultiplyPowerTen(sdiff);
2684 return this.intVal.compareMagnitude(rb);
2685 }
2686 }
2687 }
2688 if (xs != INFLATED)
2689 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
2690 else if (ys != INFLATED)
2691 return 1;
2692 else
2693 return this.intVal.compareMagnitude(val.intVal);
2694 }
2695
2696 /**
2697 * Compares this {@code BigDecimal} with the specified
2698 * {@code Object} for equality. Unlike {@link
2699 * #compareTo(BigDecimal) compareTo}, this method considers two
2700 * {@code BigDecimal} objects equal only if they are equal in
2701 * value and scale (thus 2.0 is not equal to 2.00 when compared by
2702 * this method).
2703 *
2704 * @param x {@code Object} to which this {@code BigDecimal} is
2705 * to be compared.
2706 * @return {@code true} if and only if the specified {@code Object} is a
2707 * {@code BigDecimal} whose value and scale are equal to this
2708 * {@code BigDecimal}'s.
2709 * @see #compareTo(java.math.BigDecimal)
2710 * @see #hashCode
2711 */
2712 @Override
2713 public boolean equals(Object x) {
2714 if (!(x instanceof BigDecimal))
2715 return false;
2716 BigDecimal xDec = (BigDecimal) x;
2717 if (x == this)
2718 return true;
2719 if (scale != xDec.scale)
2720 return false;
2721 long s = this.intCompact;
2722 long xs = xDec.intCompact;
2723 if (s != INFLATED) {
2724 if (xs == INFLATED)
2725 xs = compactValFor(xDec.intVal);
2726 return xs == s;
2727 } else if (xs != INFLATED)
2728 return xs == compactValFor(this.intVal);
2729
2730 return this.inflated().equals(xDec.inflated());
2731 }
2732
2733 /**
2734 * Returns the minimum of this {@code BigDecimal} and
2735 * {@code val}.
2736 *
2737 * @param val value with which the minimum is to be computed.
2738 * @return the {@code BigDecimal} whose value is the lesser of this
2739 * {@code BigDecimal} and {@code val}. If they are equal,
2740 * as defined by the {@link #compareTo(BigDecimal) compareTo}
2741 * method, {@code this} is returned.
2742 * @see #compareTo(java.math.BigDecimal)
2743 */
2744 public BigDecimal min(BigDecimal val) {
2745 return (compareTo(val) <= 0 ? this : val);
2746 }
2747
2748 /**
2749 * Returns the maximum of this {@code BigDecimal} and {@code val}.
2750 *
2751 * @param val value with which the maximum is to be computed.
2752 * @return the {@code BigDecimal} whose value is the greater of this
2753 * {@code BigDecimal} and {@code val}. If they are equal,
2754 * as defined by the {@link #compareTo(BigDecimal) compareTo}
2755 * method, {@code this} is returned.
2756 * @see #compareTo(java.math.BigDecimal)
2757 */
2758 public BigDecimal max(BigDecimal val) {
2759 return (compareTo(val) >= 0 ? this : val);
2760 }
2761
2762 // Hash Function
2763
2764 /**
2765 * Returns the hash code for this {@code BigDecimal}. Note that
2766 * two {@code BigDecimal} objects that are numerically equal but
2767 * differ in scale (like 2.0 and 2.00) will generally <i>not</i>
2768 * have the same hash code.
2769 *
2770 * @return hash code for this {@code BigDecimal}.
2771 * @see #equals(Object)
2772 */
2773 @Override
2774 public int hashCode() {
2775 if (intCompact != INFLATED) {
2776 long val2 = (intCompact < 0)? -intCompact : intCompact;
2777 int temp = (int)( ((int)(val2 >>> 32)) * 31 +
2778 (val2 & LONG_MASK));
2779 return 31*((intCompact < 0) ?-temp:temp) + scale;
2780 } else
2781 return 31*intVal.hashCode() + scale;
2782 }
2783
2784 // Format Converters
2785
2786 /**
2787 * Returns the string representation of this {@code BigDecimal},
2788 * using scientific notation if an exponent is needed.
2789 *
2790 * <p>A standard canonical string form of the {@code BigDecimal}
2791 * is created as though by the following steps: first, the
2792 * absolute value of the unscaled value of the {@code BigDecimal}
2793 * is converted to a string in base ten using the characters
2794 * {@code '0'} through {@code '9'} with no leading zeros (except
2795 * if its value is zero, in which case a single {@code '0'}
2796 * character is used).
2797 *
2798 * <p>Next, an <i>adjusted exponent</i> is calculated; this is the
2799 * negated scale, plus the number of characters in the converted
2800 * unscaled value, less one. That is,
2801 * {@code -scale+(ulength-1)}, where {@code ulength} is the
2802 * length of the absolute value of the unscaled value in decimal
2803 * digits (its <i>precision</i>).
2804 *
2805 * <p>If the scale is greater than or equal to zero and the
2806 * adjusted exponent is greater than or equal to {@code -6}, the
2807 * number will be converted to a character form without using
2808 * exponential notation. In this case, if the scale is zero then
2809 * no decimal point is added and if the scale is positive a
2810 * decimal point will be inserted with the scale specifying the
2811 * number of characters to the right of the decimal point.
2812 * {@code '0'} characters are added to the left of the converted
2813 * unscaled value as necessary. If no character precedes the
2814 * decimal point after this insertion then a conventional
2815 * {@code '0'} character is prefixed.
2816 *
2817 * <p>Otherwise (that is, if the scale is negative, or the
2818 * adjusted exponent is less than {@code -6}), the number will be
2819 * converted to a character form using exponential notation. In
2820 * this case, if the converted {@code BigInteger} has more than
2821 * one digit a decimal point is inserted after the first digit.
2822 * An exponent in character form is then suffixed to the converted
2823 * unscaled value (perhaps with inserted decimal point); this
2824 * comprises the letter {@code 'E'} followed immediately by the
2825 * adjusted exponent converted to a character form. The latter is
2826 * in base ten, using the characters {@code '0'} through
2827 * {@code '9'} with no leading zeros, and is always prefixed by a
2828 * sign character {@code '-'} (<tt>'\u002D'</tt>) if the
2829 * adjusted exponent is negative, {@code '+'}
2830 * (<tt>'\u002B'</tt>) otherwise).
2831 *
2832 * <p>Finally, the entire string is prefixed by a minus sign
2833 * character {@code '-'} (<tt>'\u002D'</tt>) if the unscaled
2834 * value is less than zero. No sign character is prefixed if the
2835 * unscaled value is zero or positive.
2836 *
2837 * <p><b>Examples:</b>
2838 * <p>For each representation [<i>unscaled value</i>, <i>scale</i>]
2839 * on the left, the resulting string is shown on the right.
2840 * <pre>
2841 * [123,0] "123"
2842 * [-123,0] "-123"
2843 * [123,-1] "1.23E+3"
2844 * [123,-3] "1.23E+5"
2845 * [123,1] "12.3"
2846 * [123,5] "0.00123"
2847 * [123,10] "1.23E-8"
2848 * [-123,12] "-1.23E-10"
2849 * </pre>
2850 *
2851 * <b>Notes:</b>
2852 * <ol>
2853 *
2854 * <li>There is a one-to-one mapping between the distinguishable
2855 * {@code BigDecimal} values and the result of this conversion.
2856 * That is, every distinguishable {@code BigDecimal} value
2857 * (unscaled value and scale) has a unique string representation
2858 * as a result of using {@code toString}. If that string
2859 * representation is converted back to a {@code BigDecimal} using
2860 * the {@link #BigDecimal(String)} constructor, then the original
2861 * value will be recovered.
2862 *
2863 * <li>The string produced for a given number is always the same;
2864 * it is not affected by locale. This means that it can be used
2865 * as a canonical string representation for exchanging decimal
2866 * data, or as a key for a Hashtable, etc. Locale-sensitive
2867 * number formatting and parsing is handled by the {@link
2868 * java.text.NumberFormat} class and its subclasses.
2869 *
2870 * <li>The {@link #toEngineeringString} method may be used for
2871 * presenting numbers with exponents in engineering notation, and the
2872 * {@link #setScale(int,RoundingMode) setScale} method may be used for
2873 * rounding a {@code BigDecimal} so it has a known number of digits after
2874 * the decimal point.
2875 *
2876 * <li>The digit-to-character mapping provided by
2877 * {@code Character.forDigit} is used.
2878 *
2879 * </ol>
2880 *
2881 * @return string representation of this {@code BigDecimal}.
2882 * @see Character#forDigit
2883 * @see #BigDecimal(java.lang.String)
2884 */
2885 @Override
2886 public String toString() {
2887 String sc = stringCache;
2888 if (sc == null)
2889 stringCache = sc = layoutChars(true);
2890 return sc;
2891 }
2892
2893 /**
2894 * Returns a string representation of this {@code BigDecimal},
2895 * using engineering notation if an exponent is needed.
2896 *
2897 * <p>Returns a string that represents the {@code BigDecimal} as
2898 * described in the {@link #toString()} method, except that if
2899 * exponential notation is used, the power of ten is adjusted to
2900 * be a multiple of three (engineering notation) such that the
2901 * integer part of nonzero values will be in the range 1 through
2902 * 999. If exponential notation is used for zero values, a
2903 * decimal point and one or two fractional zero digits are used so
2904 * that the scale of the zero value is preserved. Note that
2905 * unlike the output of {@link #toString()}, the output of this
2906 * method is <em>not</em> guaranteed to recover the same [integer,
2907 * scale] pair of this {@code BigDecimal} if the output string is
2908 * converting back to a {@code BigDecimal} using the {@linkplain
2909 * #BigDecimal(String) string constructor}. The result of this method meets
2910 * the weaker constraint of always producing a numerically equal
2911 * result from applying the string constructor to the method's output.
2912 *
2913 * @return string representation of this {@code BigDecimal}, using
2914 * engineering notation if an exponent is needed.
2915 * @since 1.5
2916 */
2917 public String toEngineeringString() {
2918 return layoutChars(false);
2919 }
2920
2921 /**
2922 * Returns a string representation of this {@code BigDecimal}
2923 * without an exponent field. For values with a positive scale,
2924 * the number of digits to the right of the decimal point is used
2925 * to indicate scale. For values with a zero or negative scale,
2926 * the resulting string is generated as if the value were
2927 * converted to a numerically equal value with zero scale and as
2928 * if all the trailing zeros of the zero scale value were present
2929 * in the result.
2930 *
2931 * The entire string is prefixed by a minus sign character '-'
2932 * (<tt>'\u002D'</tt>) if the unscaled value is less than
2933 * zero. No sign character is prefixed if the unscaled value is
2934 * zero or positive.
2935 *
2936 * Note that if the result of this method is passed to the
2937 * {@linkplain #BigDecimal(String) string constructor}, only the
2938 * numerical value of this {@code BigDecimal} will necessarily be
2939 * recovered; the representation of the new {@code BigDecimal}
2940 * may have a different scale. In particular, if this
2941 * {@code BigDecimal} has a negative scale, the string resulting
2942 * from this method will have a scale of zero when processed by
2943 * the string constructor.
2944 *
2945 * (This method behaves analogously to the {@code toString}
2946 * method in 1.4 and earlier releases.)
2947 *
2948 * @return a string representation of this {@code BigDecimal}
2949 * without an exponent field.
2950 * @since 1.5
2951 * @see #toString()
2952 * @see #toEngineeringString()
2953 */
2954 public String toPlainString() {
2955 if(scale==0) {
2956 if(intCompact!=INFLATED) {
2957 return Long.toString(intCompact);
2958 } else {
2959 return intVal.toString();
2960 }
2961 }
2962 if(this.scale<0) { // No decimal point
2963 if(signum()==0) {
2964 return "0";
2965 }
2966 int tailingZeros = checkScaleNonZero((-(long)scale));
2967 StringBuilder buf;
2968 if(intCompact!=INFLATED) {
2969 buf = new StringBuilder(20+tailingZeros);
2970 buf.append(intCompact);
2971 } else {
2972 String str = intVal.toString();
2973 buf = new StringBuilder(str.length()+tailingZeros);
2974 buf.append(str);
2975 }
2976 for (int i = 0; i < tailingZeros; i++)
2977 buf.append('0');
2978 return buf.toString();
2979 }
2980 String str ;
2981 if(intCompact!=INFLATED) {
2982 str = Long.toString(Math.abs(intCompact));
2983 } else {
2984 str = intVal.abs().toString();
2985 }
2986 return getValueString(signum(), str, scale);
2987 }
2988
2989 /* Returns a digit.digit string */
2990 private String getValueString(int signum, String intString, int scale) {
2991 /* Insert decimal point */
2992 StringBuilder buf;
2993 int insertionPoint = intString.length() - scale;
2994 if (insertionPoint == 0) { /* Point goes right before intVal */
2995 return (signum<0 ? "-0." : "0.") + intString;
2996 } else if (insertionPoint > 0) { /* Point goes inside intVal */
2997 buf = new StringBuilder(intString);
2998 buf.insert(insertionPoint, '.');
2999 if (signum < 0)
3000 buf.insert(0, '-');
3001 } else { /* We must insert zeros between point and intVal */
3002 buf = new StringBuilder(3-insertionPoint + intString.length());
3003 buf.append(signum<0 ? "-0." : "0.");
3004 for (int i=0; i<-insertionPoint; i++)
3005 buf.append('0');
3006 buf.append(intString);
3007 }
3008 return buf.toString();
3009 }
3010
3011 /**
3012 * Converts this {@code BigDecimal} to a {@code BigInteger}.
3013 * This conversion is analogous to the
3014 * <i>narrowing primitive conversion</i> from {@code double} to
3015 * {@code long} as defined in section 5.1.3 of
3016 * <cite>The Java™ Language Specification</cite>:
3017 * any fractional part of this
3018 * {@code BigDecimal} will be discarded. Note that this
3019 * conversion can lose information about the precision of the
3020 * {@code BigDecimal} value.
3021 * <p>
3022 * To have an exception thrown if the conversion is inexact (in
3023 * other words if a nonzero fractional part is discarded), use the
3024 * {@link #toBigIntegerExact()} method.
3025 *
3026 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3027 */
3028 public BigInteger toBigInteger() {
3029 // force to an integer, quietly
3030 return this.setScale(0, ROUND_DOWN).inflated();
3031 }
3032
3033 /**
3034 * Converts this {@code BigDecimal} to a {@code BigInteger},
3035 * checking for lost information. An exception is thrown if this
3036 * {@code BigDecimal} has a nonzero fractional part.
3037 *
3038 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3039 * @throws ArithmeticException if {@code this} has a nonzero
3040 * fractional part.
3041 * @since 1.5
3042 */
3043 public BigInteger toBigIntegerExact() {
3044 // round to an integer, with Exception if decimal part non-0
3045 return this.setScale(0, ROUND_UNNECESSARY).inflated();
3046 }
3047
3048 /**
3049 * Converts this {@code BigDecimal} to a {@code long}.
3050 * This conversion is analogous to the
3051 * <i>narrowing primitive conversion</i> from {@code double} to
3052 * {@code short} as defined in section 5.1.3 of
3053 * <cite>The Java™ Language Specification</cite>:
3054 * any fractional part of this
3055 * {@code BigDecimal} will be discarded, and if the resulting
3056 * "{@code BigInteger}" is too big to fit in a
3057 * {@code long}, only the low-order 64 bits are returned.
3058 * Note that this conversion can lose information about the
3059 * overall magnitude and precision of this {@code BigDecimal} value as well
3060 * as return a result with the opposite sign.
3061 *
3062 * @return this {@code BigDecimal} converted to a {@code long}.
3063 */
3064 public long longValue(){
3065 return (intCompact != INFLATED && scale == 0) ?
3066 intCompact:
3067 toBigInteger().longValue();
3068 }
3069
3070 /**
3071 * Converts this {@code BigDecimal} to a {@code long}, checking
3072 * for lost information. If this {@code BigDecimal} has a
3073 * nonzero fractional part or is out of the possible range for a
3074 * {@code long} result then an {@code ArithmeticException} is
3075 * thrown.
3076 *
3077 * @return this {@code BigDecimal} converted to a {@code long}.
3078 * @throws ArithmeticException if {@code this} has a nonzero
3079 * fractional part, or will not fit in a {@code long}.
3080 * @since 1.5
3081 */
3082 public long longValueExact() {
3083 if (intCompact != INFLATED && scale == 0)
3084 return intCompact;
3085 // If more than 19 digits in integer part it cannot possibly fit
3086 if ((precision() - scale) > 19) // [OK for negative scale too]
3087 throw new java.lang.ArithmeticException("Overflow");
3088 // Fastpath zero and < 1.0 numbers (the latter can be very slow
3089 // to round if very small)
3090 if (this.signum() == 0)
3091 return 0;
3092 if ((this.precision() - this.scale) <= 0)
3093 throw new ArithmeticException("Rounding necessary");
3094 // round to an integer, with Exception if decimal part non-0
3095 BigDecimal num = this.setScale(0, ROUND_UNNECESSARY);
3096 if (num.precision() >= 19) // need to check carefully
3097 LongOverflow.check(num);
3098 return num.inflated().longValue();
3099 }
3100
3101 private static class LongOverflow {
3102 /** BigInteger equal to Long.MIN_VALUE. */
3103 private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE);
3104
3105 /** BigInteger equal to Long.MAX_VALUE. */
3106 private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE);
3107
3108 public static void check(BigDecimal num) {
3109 BigInteger intVal = num.inflated();
3110 if (intVal.compareTo(LONGMIN) < 0 ||
3111 intVal.compareTo(LONGMAX) > 0)
3112 throw new java.lang.ArithmeticException("Overflow");
3113 }
3114 }
3115
3116 /**
3117 * Converts this {@code BigDecimal} to an {@code int}.
3118 * This conversion is analogous to the
3119 * <i>narrowing primitive conversion</i> from {@code double} to
3120 * {@code short} as defined in section 5.1.3 of
3121 * <cite>The Java™ Language Specification</cite>:
3122 * any fractional part of this
3123 * {@code BigDecimal} will be discarded, and if the resulting
3124 * "{@code BigInteger}" is too big to fit in an
3125 * {@code int}, only the low-order 32 bits are returned.
3126 * Note that this conversion can lose information about the
3127 * overall magnitude and precision of this {@code BigDecimal}
3128 * value as well as return a result with the opposite sign.
3129 *
3130 * @return this {@code BigDecimal} converted to an {@code int}.
3131 */
3132 public int intValue() {
3133 return (intCompact != INFLATED && scale == 0) ?
3134 (int)intCompact :
3135 toBigInteger().intValue();
3136 }
3137
3138 /**
3139 * Converts this {@code BigDecimal} to an {@code int}, checking
3140 * for lost information. If this {@code BigDecimal} has a
3141 * nonzero fractional part or is out of the possible range for an
3142 * {@code int} result then an {@code ArithmeticException} is
3143 * thrown.
3144 *
3145 * @return this {@code BigDecimal} converted to an {@code int}.
3146 * @throws ArithmeticException if {@code this} has a nonzero
3147 * fractional part, or will not fit in an {@code int}.
3148 * @since 1.5
3149 */
3150 public int intValueExact() {
3151 long num;
3152 num = this.longValueExact(); // will check decimal part
3153 if ((int)num != num)
3154 throw new java.lang.ArithmeticException("Overflow");
3155 return (int)num;
3156 }
3157
3158 /**
3159 * Converts this {@code BigDecimal} to a {@code short}, checking
3160 * for lost information. If this {@code BigDecimal} has a
3161 * nonzero fractional part or is out of the possible range for a
3162 * {@code short} result then an {@code ArithmeticException} is
3163 * thrown.
3164 *
3165 * @return this {@code BigDecimal} converted to a {@code short}.
3166 * @throws ArithmeticException if {@code this} has a nonzero
3167 * fractional part, or will not fit in a {@code short}.
3168 * @since 1.5
3169 */
3170 public short shortValueExact() {
3171 long num;
3172 num = this.longValueExact(); // will check decimal part
3173 if ((short)num != num)
3174 throw new java.lang.ArithmeticException("Overflow");
3175 return (short)num;
3176 }
3177
3178 /**
3179 * Converts this {@code BigDecimal} to a {@code byte}, checking
3180 * for lost information. If this {@code BigDecimal} has a
3181 * nonzero fractional part or is out of the possible range for a
3182 * {@code byte} result then an {@code ArithmeticException} is
3183 * thrown.
3184 *
3185 * @return this {@code BigDecimal} converted to a {@code byte}.
3186 * @throws ArithmeticException if {@code this} has a nonzero
3187 * fractional part, or will not fit in a {@code byte}.
3188 * @since 1.5
3189 */
3190 public byte byteValueExact() {
3191 long num;
3192 num = this.longValueExact(); // will check decimal part
3193 if ((byte)num != num)
3194 throw new java.lang.ArithmeticException("Overflow");
3195 return (byte)num;
3196 }
3197
3198 /**
3199 * Converts this {@code BigDecimal} to a {@code float}.
3200 * This conversion is similar to the
3201 * <i>narrowing primitive conversion</i> from {@code double} to
3202 * {@code float} as defined in section 5.1.3 of
3203 * <cite>The Java™ Language Specification</cite>:
3204 * if this {@code BigDecimal} has too great a
3205 * magnitude to represent as a {@code float}, it will be
3206 * converted to {@link Float#NEGATIVE_INFINITY} or {@link
3207 * Float#POSITIVE_INFINITY} as appropriate. Note that even when
3208 * the return value is finite, this conversion can lose
3209 * information about the precision of the {@code BigDecimal}
3210 * value.
3211 *
3212 * @return this {@code BigDecimal} converted to a {@code float}.
3213 */
3214 public float floatValue(){
3215 if(intCompact != INFLATED) {
3216 if (scale == 0) {
3217 return (float)intCompact;
3218 } else {
3219 /*
3220 * If both intCompact and the scale can be exactly
3221 * represented as float values, perform a single float
3222 * multiply or divide to compute the (properly
3223 * rounded) result.
3224 */
3225 if (Math.abs(intCompact) < 1L<<22 ) {
3226 // Don't have too guard against
3227 // Math.abs(MIN_VALUE) because of outer check
3228 // against INFLATED.
3229 if (scale > 0 && scale < float10pow.length) {
3230 return (float)intCompact / float10pow[scale];
3231 } else if (scale < 0 && scale > -float10pow.length) {
3232 return (float)intCompact * float10pow[-scale];
3233 }
3234 }
3235 }
3236 }
3237 // Somewhat inefficient, but guaranteed to work.
3238 return Float.parseFloat(this.toString());
3239 }
3240
3241 /**
3242 * Converts this {@code BigDecimal} to a {@code double}.
3243 * This conversion is similar to the
3244 * <i>narrowing primitive conversion</i> from {@code double} to
3245 * {@code float} as defined in section 5.1.3 of
3246 * <cite>The Java™ Language Specification</cite>:
3247 * if this {@code BigDecimal} has too great a
3248 * magnitude represent as a {@code double}, it will be
3249 * converted to {@link Double#NEGATIVE_INFINITY} or {@link
3250 * Double#POSITIVE_INFINITY} as appropriate. Note that even when
3251 * the return value is finite, this conversion can lose
3252 * information about the precision of the {@code BigDecimal}
3253 * value.
3254 *
3255 * @return this {@code BigDecimal} converted to a {@code double}.
3256 */
3257 public double doubleValue(){
3258 if(intCompact != INFLATED) {
3259 if (scale == 0) {
3260 return (double)intCompact;
3261 } else {
3262 /*
3263 * If both intCompact and the scale can be exactly
3264 * represented as double values, perform a single
3265 * double multiply or divide to compute the (properly
3266 * rounded) result.
3267 */
3268 if (Math.abs(intCompact) < 1L<<52 ) {
3269 // Don't have too guard against
3270 // Math.abs(MIN_VALUE) because of outer check
3271 // against INFLATED.
3272 if (scale > 0 && scale < double10pow.length) {
3273 return (double)intCompact / double10pow[scale];
3274 } else if (scale < 0 && scale > -double10pow.length) {
3275 return (double)intCompact * double10pow[-scale];
3276 }
3277 }
3278 }
3279 }
3280 // Somewhat inefficient, but guaranteed to work.
3281 return Double.parseDouble(this.toString());
3282 }
3283
3284 /**
3285 * Powers of 10 which can be represented exactly in {@code
3286 * double}.
3287 */
3288 private static final double double10pow[] = {
3289 1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5,
3290 1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, 1.0e11,
3291 1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17,
3292 1.0e18, 1.0e19, 1.0e20, 1.0e21, 1.0e22
3293 };
3294
3295 /**
3296 * Powers of 10 which can be represented exactly in {@code
3297 * float}.
3298 */
3299 private static final float float10pow[] = {
3300 1.0e0f, 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f,
3301 1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f
3302 };
3303
3304 /**
3305 * Returns the size of an ulp, a unit in the last place, of this
3306 * {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal}
3307 * value is the positive distance between this value and the
3308 * {@code BigDecimal} value next larger in magnitude with the
3309 * same number of digits. An ulp of a zero value is numerically
3310 * equal to 1 with the scale of {@code this}. The result is
3311 * stored with the same scale as {@code this} so the result
3312 * for zero and nonzero values is equal to {@code [1,
3313 * this.scale()]}.
3314 *
3315 * @return the size of an ulp of {@code this}
3316 * @since 1.5
3317 */
3318 public BigDecimal ulp() {
3319 return BigDecimal.valueOf(1, this.scale(), 1);
3320 }
3321
3322 // Private class to build a string representation for BigDecimal object.
3323 // "StringBuilderHelper" is constructed as a thread local variable so it is
3324 // thread safe. The StringBuilder field acts as a buffer to hold the temporary
3325 // representation of BigDecimal. The cmpCharArray holds all the characters for
3326 // the compact representation of BigDecimal (except for '-' sign' if it is
3327 // negative) if its intCompact field is not INFLATED. It is shared by all
3328 // calls to toString() and its variants in that particular thread.
3329 static class StringBuilderHelper {
3330 final StringBuilder sb; // Placeholder for BigDecimal string
3331 final char[] cmpCharArray; // character array to place the intCompact
3332
3333 StringBuilderHelper() {
3334 sb = new StringBuilder();
3335 // All non negative longs can be made to fit into 19 character array.
3336 cmpCharArray = new char[19];
3337 }
3338
3339 // Accessors.
3340 StringBuilder getStringBuilder() {
3341 sb.setLength(0);
3342 return sb;
3343 }
3344
3345 char[] getCompactCharArray() {
3346 return cmpCharArray;
3347 }
3348
3349 /**
3350 * Places characters representing the intCompact in {@code long} into
3351 * cmpCharArray and returns the offset to the array where the
3352 * representation starts.
3353 *
3354 * @param intCompact the number to put into the cmpCharArray.
3355 * @return offset to the array where the representation starts.
3356 * Note: intCompact must be greater or equal to zero.
3357 */
3358 int putIntCompact(long intCompact) {
3359 assert intCompact >= 0;
3360
3361 long q;
3362 int r;
3363 // since we start from the least significant digit, charPos points to
3364 // the last character in cmpCharArray.
3365 int charPos = cmpCharArray.length;
3366
3367 // Get 2 digits/iteration using longs until quotient fits into an int
3368 while (intCompact > Integer.MAX_VALUE) {
3369 q = intCompact / 100;
3370 r = (int)(intCompact - q * 100);
3371 intCompact = q;
3372 cmpCharArray[--charPos] = DIGIT_ONES[r];
3373 cmpCharArray[--charPos] = DIGIT_TENS[r];
3374 }
3375
3376 // Get 2 digits/iteration using ints when i2 >= 100
3377 int q2;
3378 int i2 = (int)intCompact;
3379 while (i2 >= 100) {
3380 q2 = i2 / 100;
3381 r = i2 - q2 * 100;
3382 i2 = q2;
3383 cmpCharArray[--charPos] = DIGIT_ONES[r];
3384 cmpCharArray[--charPos] = DIGIT_TENS[r];
3385 }
3386
3387 cmpCharArray[--charPos] = DIGIT_ONES[i2];
3388 if (i2 >= 10)
3389 cmpCharArray[--charPos] = DIGIT_TENS[i2];
3390
3391 return charPos;
3392 }
3393
3394 final static char[] DIGIT_TENS = {
3395 '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
3396 '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
3397 '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
3398 '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
3399 '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
3400 '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
3401 '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
3402 '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
3403 '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
3404 '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
3405 };
3406
3407 final static char[] DIGIT_ONES = {
3408 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3409 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3410 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3411 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3412 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3413 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3414 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3415 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3416 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3417 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3418 };
3419 }
3420
3421 /**
3422 * Lay out this {@code BigDecimal} into a {@code char[]} array.
3423 * The Java 1.2 equivalent to this was called {@code getValueString}.
3424 *
3425 * @param sci {@code true} for Scientific exponential notation;
3426 * {@code false} for Engineering
3427 * @return string with canonical string representation of this
3428 * {@code BigDecimal}
3429 */
3430 private String layoutChars(boolean sci) {
3431 if (scale == 0) // zero scale is trivial
3432 return (intCompact != INFLATED) ?
3433 Long.toString(intCompact):
3434 intVal.toString();
3435 if (scale == 2 &&
3436 intCompact >= 0 && intCompact < Integer.MAX_VALUE) {
3437 // currency fast path
3438 int lowInt = (int)intCompact % 100;
3439 int highInt = (int)intCompact / 100;
3440 return (Integer.toString(highInt) + '.' +
3441 StringBuilderHelper.DIGIT_TENS[lowInt] +
3442 StringBuilderHelper.DIGIT_ONES[lowInt]) ;
3443 }
3444
3445 StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get();
3446 char[] coeff;
3447 int offset; // offset is the starting index for coeff array
3448 // Get the significand as an absolute value
3449 if (intCompact != INFLATED) {
3450 offset = sbHelper.putIntCompact(Math.abs(intCompact));
3451 coeff = sbHelper.getCompactCharArray();
3452 } else {
3453 offset = 0;
3454 coeff = intVal.abs().toString().toCharArray();
3455 }
3456
3457 // Construct a buffer, with sufficient capacity for all cases.
3458 // If E-notation is needed, length will be: +1 if negative, +1
3459 // if '.' needed, +2 for "E+", + up to 10 for adjusted exponent.
3460 // Otherwise it could have +1 if negative, plus leading "0.00000"
3461 StringBuilder buf = sbHelper.getStringBuilder();
3462 if (signum() < 0) // prefix '-' if negative
3463 buf.append('-');
3464 int coeffLen = coeff.length - offset;
3465 long adjusted = -(long)scale + (coeffLen -1);
3466 if ((scale >= 0) && (adjusted >= -6)) { // plain number
3467 int pad = scale - coeffLen; // count of padding zeros
3468 if (pad >= 0) { // 0.xxx form
3469 buf.append('0');
3470 buf.append('.');
3471 for (; pad>0; pad--) {
3472 buf.append('0');
3473 }
3474 buf.append(coeff, offset, coeffLen);
3475 } else { // xx.xx form
3476 buf.append(coeff, offset, -pad);
3477 buf.append('.');
3478 buf.append(coeff, -pad + offset, scale);
3479 }
3480 } else { // E-notation is needed
3481 if (sci) { // Scientific notation
3482 buf.append(coeff[offset]); // first character
3483 if (coeffLen > 1) { // more to come
3484 buf.append('.');
3485 buf.append(coeff, offset + 1, coeffLen - 1);
3486 }
3487 } else { // Engineering notation
3488 int sig = (int)(adjusted % 3);
3489 if (sig < 0)
3490 sig += 3; // [adjusted was negative]
3491 adjusted -= sig; // now a multiple of 3
3492 sig++;
3493 if (signum() == 0) {
3494 switch (sig) {
3495 case 1:
3496 buf.append('0'); // exponent is a multiple of three
3497 break;
3498 case 2:
3499 buf.append("0.00");
3500 adjusted += 3;
3501 break;
3502 case 3:
3503 buf.append("0.0");
3504 adjusted += 3;
3505 break;
3506 default:
3507 throw new AssertionError("Unexpected sig value " + sig);
3508 }
3509 } else if (sig >= coeffLen) { // significand all in integer
3510 buf.append(coeff, offset, coeffLen);
3511 // may need some zeros, too
3512 for (int i = sig - coeffLen; i > 0; i--)
3513 buf.append('0');
3514 } else { // xx.xxE form
3515 buf.append(coeff, offset, sig);
3516 buf.append('.');
3517 buf.append(coeff, offset + sig, coeffLen - sig);
3518 }
3519 }
3520 if (adjusted != 0) { // [!sci could have made 0]
3521 buf.append('E');
3522 if (adjusted > 0) // force sign for positive
3523 buf.append('+');
3524 buf.append(adjusted);
3525 }
3526 }
3527 return buf.toString();
3528 }
3529
3530 /**
3531 * Return 10 to the power n, as a {@code BigInteger}.
3532 *
3533 * @param n the power of ten to be returned (>=0)
3534 * @return a {@code BigInteger} with the value (10<sup>n</sup>)
3535 */
3536 private static BigInteger bigTenToThe(int n) {
3537 if (n < 0)
3538 return BigInteger.ZERO;
3539
3540 if (n < BIG_TEN_POWERS_TABLE_MAX) {
3541 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3542 if (n < pows.length)
3543 return pows[n];
3544 else
3545 return expandBigIntegerTenPowers(n);
3546 }
3547
3548 return BigInteger.TEN.pow(n);
3549 }
3550
3551 /**
3552 * Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n.
3553 *
3554 * @param n the power of ten to be returned (>=0)
3555 * @return a {@code BigDecimal} with the value (10<sup>n</sup>) and
3556 * in the meantime, the BIG_TEN_POWERS_TABLE array gets
3557 * expanded to the size greater than n.
3558 */
3559 private static BigInteger expandBigIntegerTenPowers(int n) {
3560 synchronized(BigDecimal.class) {
3561 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3562 int curLen = pows.length;
3563 // The following comparison and the above synchronized statement is
3564 // to prevent multiple threads from expanding the same array.
3565 if (curLen <= n) {
3566 int newLen = curLen << 1;
3567 while (newLen <= n)
3568 newLen <<= 1;
3569 pows = Arrays.copyOf(pows, newLen);
3570 for (int i = curLen; i < newLen; i++)
3571 pows[i] = pows[i - 1].multiply(BigInteger.TEN);
3572 // Based on the following facts:
3573 // 1. pows is a private local varible;
3574 // 2. the following store is a volatile store.
3575 // the newly created array elements can be safely published.
3576 BIG_TEN_POWERS_TABLE = pows;
3577 }
3578 return pows[n];
3579 }
3580 }
3581
3582 private static final long[] LONG_TEN_POWERS_TABLE = {
3583 1, // 0 / 10^0
3584 10, // 1 / 10^1
3585 100, // 2 / 10^2
3586 1000, // 3 / 10^3
3587 10000, // 4 / 10^4
3588 100000, // 5 / 10^5
3589 1000000, // 6 / 10^6
3590 10000000, // 7 / 10^7
3591 100000000, // 8 / 10^8
3592 1000000000, // 9 / 10^9
3593 10000000000L, // 10 / 10^10
3594 100000000000L, // 11 / 10^11
3595 1000000000000L, // 12 / 10^12
3596 10000000000000L, // 13 / 10^13
3597 100000000000000L, // 14 / 10^14
3598 1000000000000000L, // 15 / 10^15
3599 10000000000000000L, // 16 / 10^16
3600 100000000000000000L, // 17 / 10^17
3601 1000000000000000000L // 18 / 10^18
3602 };
3603
3604 private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = {
3605 BigInteger.ONE,
3606 BigInteger.valueOf(10),
3607 BigInteger.valueOf(100),
3608 BigInteger.valueOf(1000),
3609 BigInteger.valueOf(10000),
3610 BigInteger.valueOf(100000),
3611 BigInteger.valueOf(1000000),
3612 BigInteger.valueOf(10000000),
3613 BigInteger.valueOf(100000000),
3614 BigInteger.valueOf(1000000000),
3615 BigInteger.valueOf(10000000000L),
3616 BigInteger.valueOf(100000000000L),
3617 BigInteger.valueOf(1000000000000L),
3618 BigInteger.valueOf(10000000000000L),
3619 BigInteger.valueOf(100000000000000L),
3620 BigInteger.valueOf(1000000000000000L),
3621 BigInteger.valueOf(10000000000000000L),
3622 BigInteger.valueOf(100000000000000000L),
3623 BigInteger.valueOf(1000000000000000000L)
3624 };
3625
3626 private static final int BIG_TEN_POWERS_TABLE_INITLEN =
3627 BIG_TEN_POWERS_TABLE.length;
3628 private static final int BIG_TEN_POWERS_TABLE_MAX =
3629 16 * BIG_TEN_POWERS_TABLE_INITLEN;
3630
3631 private static final long THRESHOLDS_TABLE[] = {
3632 Long.MAX_VALUE, // 0
3633 Long.MAX_VALUE/10L, // 1
3634 Long.MAX_VALUE/100L, // 2
3635 Long.MAX_VALUE/1000L, // 3
3636 Long.MAX_VALUE/10000L, // 4
3637 Long.MAX_VALUE/100000L, // 5
3638 Long.MAX_VALUE/1000000L, // 6
3639 Long.MAX_VALUE/10000000L, // 7
3640 Long.MAX_VALUE/100000000L, // 8
3641 Long.MAX_VALUE/1000000000L, // 9
3642 Long.MAX_VALUE/10000000000L, // 10
3643 Long.MAX_VALUE/100000000000L, // 11
3644 Long.MAX_VALUE/1000000000000L, // 12
3645 Long.MAX_VALUE/10000000000000L, // 13
3646 Long.MAX_VALUE/100000000000000L, // 14
3647 Long.MAX_VALUE/1000000000000000L, // 15
3648 Long.MAX_VALUE/10000000000000000L, // 16
3649 Long.MAX_VALUE/100000000000000000L, // 17
3650 Long.MAX_VALUE/1000000000000000000L // 18
3651 };
3652
3653 /**
3654 * Compute val * 10 ^ n; return this product if it is
3655 * representable as a long, INFLATED otherwise.
3656 */
3657 private static long longMultiplyPowerTen(long val, int n) {
3658 if (val == 0 || n <= 0)
3659 return val;
3660 long[] tab = LONG_TEN_POWERS_TABLE;
3661 long[] bounds = THRESHOLDS_TABLE;
3662 if (n < tab.length && n < bounds.length) {
3663 long tenpower = tab[n];
3664 if (val == 1)
3665 return tenpower;
3666 if (Math.abs(val) <= bounds[n])
3667 return val * tenpower;
3668 }
3669 return INFLATED;
3670 }
3671
3672 /**
3673 * Compute this * 10 ^ n.
3674 * Needed mainly to allow special casing to trap zero value
3675 */
3676 private BigInteger bigMultiplyPowerTen(int n) {
3677 if (n <= 0)
3678 return this.inflated();
3679
3680 if (intCompact != INFLATED)
3681 return bigTenToThe(n).multiply(intCompact);
3682 else
3683 return intVal.multiply(bigTenToThe(n));
3684 }
3685
3686 /**
3687 * Returns appropriate BigInteger from intVal field if intVal is
3688 * null, i.e. the compact representation is in use.
3689 */
3690 private BigInteger inflated() {
3691 if (intVal == null) {
3692 return BigInteger.valueOf(intCompact);
3693 }
3694 return intVal;
3695 }
3696
3697 /**
3698 * Match the scales of two {@code BigDecimal}s to align their
3699 * least significant digits.
3700 *
3701 * <p>If the scales of val[0] and val[1] differ, rescale
3702 * (non-destructively) the lower-scaled {@code BigDecimal} so
3703 * they match. That is, the lower-scaled reference will be
3704 * replaced by a reference to a new object with the same scale as
3705 * the other {@code BigDecimal}.
3706 *
3707 * @param val array of two elements referring to the two
3708 * {@code BigDecimal}s to be aligned.
3709 */
3710 private static void matchScale(BigDecimal[] val) {
3711 if (val[0].scale == val[1].scale) {
3712 return;
3713 } else if (val[0].scale < val[1].scale) {
3714 val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY);
3715 } else if (val[1].scale < val[0].scale) {
3716 val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY);
3717 }
3718 }
3719
3720 private static class UnsafeHolder {
3721 private static final sun.misc.Unsafe unsafe;
3722 private static final long intCompactOffset;
3723 private static final long intValOffset;
3724 static {
3725 try {
3726 unsafe = sun.misc.Unsafe.getUnsafe();
3727 intCompactOffset = unsafe.objectFieldOffset
3728 (BigDecimal.class.getDeclaredField("intCompact"));
3729 intValOffset = unsafe.objectFieldOffset
3730 (BigDecimal.class.getDeclaredField("intVal"));
3731 } catch (Exception ex) {
3732 throw new ExceptionInInitializerError(ex);
3733 }
3734 }
3735 static void setIntCompactVolatile(BigDecimal bd, long val) {
3736 unsafe.putLongVolatile(bd, intCompactOffset, val);
3737 }
3738
3739 static void setIntValVolatile(BigDecimal bd, BigInteger val) {
3740 unsafe.putObjectVolatile(bd, intValOffset, val);
3741 }
3742 }
3743
3744 /**
3745 * Reconstitute the {@code BigDecimal} instance from a stream (that is,
3746 * deserialize it).
3747 *
3748 * @param s the stream being read.
3749 */
3750 private void readObject(java.io.ObjectInputStream s)
3751 throws java.io.IOException, ClassNotFoundException {
3752 // Read in all fields
3753 s.defaultReadObject();
3754 // validate possibly bad fields
3755 if (intVal == null) {
3756 String message = "BigDecimal: null intVal in stream";
3757 throw new java.io.StreamCorruptedException(message);
3758 // [all values of scale are now allowed]
3759 }
3760 UnsafeHolder.setIntCompactVolatile(this, compactValFor(intVal));
3761 }
3762
3763 /**
3764 * Serialize this {@code BigDecimal} to the stream in question
3765 *
3766 * @param s the stream to serialize to.
3767 */
3768 private void writeObject(java.io.ObjectOutputStream s)
3769 throws java.io.IOException {
3770 // Must inflate to maintain compatible serial form.
3771 if (this.intVal == null)
3772 UnsafeHolder.setIntValVolatile(this, BigInteger.valueOf(this.intCompact));
3773 // Could reset intVal back to null if it has to be set.
3774 s.defaultWriteObject();
3775 }
3776
3777 /**
3778 * Returns the length of the absolute value of a {@code long}, in decimal
3779 * digits.
3780 *
3781 * @param x the {@code long}
3782 * @return the length of the unscaled value, in deciaml digits.
3783 */
3784 static int longDigitLength(long x) {
3785 /*
3786 * As described in "Bit Twiddling Hacks" by Sean Anderson,
3787 * (http://graphics.stanford.edu/~seander/bithacks.html)
3788 * integer log 10 of x is within 1 of (1233/4096)* (1 +
3789 * integer log 2 of x). The fraction 1233/4096 approximates
3790 * log10(2). So we first do a version of log2 (a variant of
3791 * Long class with pre-checks and opposite directionality) and
3792 * then scale and check against powers table. This is a little
3793 * simpler in present context than the version in Hacker's
3794 * Delight sec 11-4. Adding one to bit length allows comparing
3795 * downward from the LONG_TEN_POWERS_TABLE that we need
3796 * anyway.
3797 */
3798 assert x != BigDecimal.INFLATED;
3799 if (x < 0)
3800 x = -x;
3801 if (x < 10) // must screen for 0, might as well 10
3802 return 1;
3803 int r = ((64 - Long.numberOfLeadingZeros(x) + 1) * 1233) >>> 12;
3804 long[] tab = LONG_TEN_POWERS_TABLE;
3805 // if r >= length, must have max possible digits for long
3806 return (r >= tab.length || x < tab[r]) ? r : r + 1;
3807 }
3808
3809 /**
3810 * Returns the length of the absolute value of a BigInteger, in
3811 * decimal digits.
3812 *
3813 * @param b the BigInteger
3814 * @return the length of the unscaled value, in decimal digits
3815 */
3816 private static int bigDigitLength(BigInteger b) {
3817 /*
3818 * Same idea as the long version, but we need a better
3819 * approximation of log10(2). Using 646456993/2^31
3820 * is accurate up to max possible reported bitLength.
3821 */
3822 if (b.signum == 0)
3823 return 1;
3824 int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31);
3825 return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1;
3826 }
3827
3828 /**
3829 * Check a scale for Underflow or Overflow. If this BigDecimal is
3830 * nonzero, throw an exception if the scale is outof range. If this
3831 * is zero, saturate the scale to the extreme value of the right
3832 * sign if the scale is out of range.
3833 *
3834 * @param val The new scale.
3835 * @throws ArithmeticException (overflow or underflow) if the new
3836 * scale is out of range.
3837 * @return validated scale as an int.
3838 */
3839 private int checkScale(long val) {
3840 int asInt = (int)val;
3841 if (asInt != val) {
3842 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3843 BigInteger b;
3844 if (intCompact != 0 &&
3845 ((b = intVal) == null || b.signum() != 0))
3846 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3847 }
3848 return asInt;
3849 }
3850
3851 /**
3852 * Returns the compact value for given {@code BigInteger}, or
3853 * INFLATED if too big. Relies on internal representation of
3854 * {@code BigInteger}.
3855 */
3856 private static long compactValFor(BigInteger b) {
3857 int[] m = b.mag;
3858 int len = m.length;
3859 if (len == 0)
3860 return 0;
3861 int d = m[0];
3862 if (len > 2 || (len == 2 && d < 0))
3863 return INFLATED;
3864
3865 long u = (len == 2)?
3866 (((long) m[1] & LONG_MASK) + (((long)d) << 32)) :
3867 (((long)d) & LONG_MASK);
3868 return (b.signum < 0)? -u : u;
3869 }
3870
3871 private static int longCompareMagnitude(long x, long y) {
3872 if (x < 0)
3873 x = -x;
3874 if (y < 0)
3875 y = -y;
3876 return (x < y) ? -1 : ((x == y) ? 0 : 1);
3877 }
3878
3879 private static int saturateLong(long s) {
3880 int i = (int)s;
3881 return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE);
3882 }
3883
3884 /*
3885 * Internal printing routine
3886 */
3887 private static void print(String name, BigDecimal bd) {
3888 System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n",
3889 name,
3890 bd.intCompact,
3891 bd.intVal,
3892 bd.scale,
3893 bd.precision);
3894 }
3895
3896 /**
3897 * Check internal invariants of this BigDecimal. These invariants
3898 * include:
3899 *
3900 * <ul>
3901 *
3902 * <li>The object must be initialized; either intCompact must not be
3903 * INFLATED or intVal is non-null. Both of these conditions may
3904 * be true.
3905 *
3906 * <li>If both intCompact and intVal and set, their values must be
3907 * consistent.
3908 *
3909 * <li>If precision is nonzero, it must have the right value.
3910 * </ul>
3911 *
3912 * Note: Since this is an audit method, we are not supposed to change the
3913 * state of this BigDecimal object.
3914 */
3915 private BigDecimal audit() {
3916 if (intCompact == INFLATED) {
3917 if (intVal == null) {
3918 print("audit", this);
3919 throw new AssertionError("null intVal");
3920 }
3921 // Check precision
3922 if (precision > 0 && precision != bigDigitLength(intVal)) {
3923 print("audit", this);
3924 throw new AssertionError("precision mismatch");
3925 }
3926 } else {
3927 if (intVal != null) {
3928 long val = intVal.longValue();
3929 if (val != intCompact) {
3930 print("audit", this);
3931 throw new AssertionError("Inconsistent state, intCompact=" +
3932 intCompact + "\t intVal=" + val);
3933 }
3934 }
3935 // Check precision
3936 if (precision > 0 && precision != longDigitLength(intCompact)) {
3937 print("audit", this);
3938 throw new AssertionError("precision mismatch");
3939 }
3940 }
3941 return this;
3942 }
3943
3944 /* the same as checkScale where value!=0 */
3945 private static int checkScaleNonZero(long val) {
3946 int asInt = (int)val;
3947 if (asInt != val) {
3948 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3949 }
3950 return asInt;
3951 }
3952
3953 private static int checkScale(long intCompact, long val) {
3954 int asInt = (int)val;
3955 if (asInt != val) {
3956 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3957 if (intCompact != 0)
3958 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3959 }
3960 return asInt;
3961 }
3962
3963 private static int checkScale(BigInteger intVal, long val) {
3964 int asInt = (int)val;
3965 if (asInt != val) {
3966 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3967 if (intVal.signum() != 0)
3968 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3969 }
3970 return asInt;
3971 }
3972
3973 /**
3974 * Returns a {@code BigDecimal} rounded according to the MathContext
3975 * settings;
3976 * If rounding is needed a new {@code BigDecimal} is created and returned.
3977 *
3978 * @param val the value to be rounded
3979 * @param mc the context to use.
3980 * @return a {@code BigDecimal} rounded according to the MathContext
3981 * settings. May return {@code value}, if no rounding needed.
3982 * @throws ArithmeticException if the rounding mode is
3983 * {@code RoundingMode.UNNECESSARY} and the
3984 * result is inexact.
3985 */
3986 private static BigDecimal doRound(BigDecimal val, MathContext mc) {
3987 int mcp = mc.precision;
3988 boolean wasDivided = false;
3989 if (mcp > 0) {
3990 BigInteger intVal = val.intVal;
3991 long compactVal = val.intCompact;
3992 int scale = val.scale;
3993 int prec = val.precision();
3994 int mode = mc.roundingMode.oldMode;
3995 int drop;
3996 if (compactVal == INFLATED) {
3997 drop = prec - mcp;
3998 while (drop > 0) {
3999 scale = checkScaleNonZero((long) scale - drop);
4000 intVal = divideAndRoundByTenPow(intVal, drop, mode);
4001 wasDivided = true;
4002 compactVal = compactValFor(intVal);
4003 if (compactVal != INFLATED) {
4004 prec = longDigitLength(compactVal);
4005 break;
4006 }
4007 prec = bigDigitLength(intVal);
4008 drop = prec - mcp;
4009 }
4010 }
4011 if (compactVal != INFLATED) {
4012 drop = prec - mcp; // drop can't be more than 18
4013 while (drop > 0) {
4014 scale = checkScaleNonZero((long) scale - drop);
4015 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4016 wasDivided = true;
4017 prec = longDigitLength(compactVal);
4018 drop = prec - mcp;
4019 intVal = null;
4020 }
4021 }
4022 return wasDivided ? new BigDecimal(intVal,compactVal,scale,prec) : val;
4023 }
4024 return val;
4025 }
4026
4027 /*
4028 * Returns a {@code BigDecimal} created from {@code long} value with
4029 * given scale rounded according to the MathContext settings
4030 */
4031 private static BigDecimal doRound(long compactVal, int scale, MathContext mc) {
4032 int mcp = mc.precision;
4033 if (mcp > 0 && mcp < 19) {
4034 int prec = longDigitLength(compactVal);
4035 int drop = prec - mcp; // drop can't be more than 18
4036 while (drop > 0) {
4037 scale = checkScaleNonZero((long) scale - drop);
4038 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4039 prec = longDigitLength(compactVal);
4040 drop = prec - mcp;
4041 }
4042 return valueOf(compactVal, scale, prec);
4043 }
4044 return valueOf(compactVal, scale);
4045 }
4046
4047 /*
4048 * Returns a {@code BigDecimal} created from {@code BigInteger} value with
4049 * given scale rounded according to the MathContext settings
4050 */
4051 private static BigDecimal doRound(BigInteger intVal, int scale, MathContext mc) {
4052 int mcp = mc.precision;
4053 int prec = 0;
4054 if (mcp > 0) {
4055 long compactVal = compactValFor(intVal);
4056 int mode = mc.roundingMode.oldMode;
4057 int drop;
4058 if (compactVal == INFLATED) {
4059 prec = bigDigitLength(intVal);
4060 drop = prec - mcp;
4061 while (drop > 0) {
4062 scale = checkScaleNonZero((long) scale - drop);
4063 intVal = divideAndRoundByTenPow(intVal, drop, mode);
4064 compactVal = compactValFor(intVal);
4065 if (compactVal != INFLATED) {
4066 break;
4067 }
4068 prec = bigDigitLength(intVal);
4069 drop = prec - mcp;
4070 }
4071 }
4072 if (compactVal != INFLATED) {
4073 prec = longDigitLength(compactVal);
4074 drop = prec - mcp; // drop can't be more than 18
4075 while (drop > 0) {
4076 scale = checkScaleNonZero((long) scale - drop);
4077 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4078 prec = longDigitLength(compactVal);
4079 drop = prec - mcp;
4080 }
4081 return valueOf(compactVal,scale,prec);
4082 }
4083 }
4084 return new BigDecimal(intVal,INFLATED,scale,prec);
4085 }
4086
4087 /*
4088 * Divides {@code BigInteger} value by ten power.
4089 */
4090 private static BigInteger divideAndRoundByTenPow(BigInteger intVal, int tenPow, int roundingMode) {
4091 if (tenPow < LONG_TEN_POWERS_TABLE.length)
4092 intVal = divideAndRound(intVal, LONG_TEN_POWERS_TABLE[tenPow], roundingMode);
4093 else
4094 intVal = divideAndRound(intVal, bigTenToThe(tenPow), roundingMode);
4095 return intVal;
4096 }
4097
4098 /**
4099 * Internally used for division operation for division {@code long} by
4100 * {@code long}.
4101 * The returned {@code BigDecimal} object is the quotient whose scale is set
4102 * to the passed in scale. If the remainder is not zero, it will be rounded
4103 * based on the passed in roundingMode. Also, if the remainder is zero and
4104 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4105 * trailing zeros of the result is stripped to match the preferredScale.
4106 */
4107 private static BigDecimal divideAndRound(long ldividend, long ldivisor, int scale, int roundingMode,
4108 int preferredScale) {
4109
4110 int qsign; // quotient sign
4111 long q = ldividend / ldivisor; // store quotient in long
4112 if (roundingMode == ROUND_DOWN && scale == preferredScale)
4113 return valueOf(q, scale);
4114 long r = ldividend % ldivisor; // store remainder in long
4115 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4116 if (r != 0) {
4117 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4118 return valueOf((increment ? q + qsign : q), scale);
4119 } else {
4120 if (preferredScale != scale)
4121 return createAndStripZerosToMatchScale(q, scale, preferredScale);
4122 else
4123 return valueOf(q, scale);
4124 }
4125 }
4126
4127 /**
4128 * Divides {@code long} by {@code long} and do rounding based on the
4129 * passed in roundingMode.
4130 */
4131 private static long divideAndRound(long ldividend, long ldivisor, int roundingMode) {
4132 int qsign; // quotient sign
4133 long q = ldividend / ldivisor; // store quotient in long
4134 if (roundingMode == ROUND_DOWN)
4135 return q;
4136 long r = ldividend % ldivisor; // store remainder in long
4137 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4138 if (r != 0) {
4139 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4140 return increment ? q + qsign : q;
4141 } else {
4142 return q;
4143 }
4144 }
4145
4146 /**
4147 * Shared logic of need increment computation.
4148 */
4149 private static boolean commonNeedIncrement(int roundingMode, int qsign,
4150 int cmpFracHalf, boolean oddQuot) {
4151 switch(roundingMode) {
4152 case ROUND_UNNECESSARY:
4153 throw new ArithmeticException("Rounding necessary");
4154
4155 case ROUND_UP: // Away from zero
4156 return true;
4157
4158 case ROUND_DOWN: // Towards zero
4159 return false;
4160
4161 case ROUND_CEILING: // Towards +infinity
4162 return qsign > 0;
4163
4164 case ROUND_FLOOR: // Towards -infinity
4165 return qsign < 0;
4166
4167 default: // Some kind of half-way rounding
4168 assert roundingMode >= ROUND_HALF_UP &&
4169 roundingMode <= ROUND_HALF_EVEN: "Unexpected rounding mode" + RoundingMode.valueOf(roundingMode);
4170
4171 if (cmpFracHalf < 0 ) // We're closer to higher digit
4172 return false;
4173 else if (cmpFracHalf > 0 ) // We're closer to lower digit
4174 return true;
4175 else { // half-way
4176 assert cmpFracHalf == 0;
4177
4178 switch(roundingMode) {
4179 case ROUND_HALF_DOWN:
4180 return false;
4181
4182 case ROUND_HALF_UP:
4183 return true;
4184
4185 case ROUND_HALF_EVEN:
4186 return oddQuot;
4187
4188 default:
4189 throw new AssertionError("Unexpected rounding mode" + roundingMode);
4190 }
4191 }
4192 }
4193 }
4194
4195 /**
4196 * Tests if quotient has to be incremented according the roundingMode
4197 */
4198 private static boolean needIncrement(long ldivisor, int roundingMode,
4199 int qsign, long q, long r) {
4200 assert r != 0L;
4201
4202 int cmpFracHalf;
4203 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4204 cmpFracHalf = 1; // 2 * r can't fit into long
4205 } else {
4206 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4207 }
4208
4209 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, (q & 1L) != 0L);
4210 }
4211
4212 /**
4213 * Divides {@code BigInteger} value by {@code long} value and
4214 * do rounding based on the passed in roundingMode.
4215 */
4216 private static BigInteger divideAndRound(BigInteger bdividend, long ldivisor, int roundingMode) {
4217 boolean isRemainderZero; // record remainder is zero or not
4218 int qsign; // quotient sign
4219 long r = 0; // store quotient & remainder in long
4220 MutableBigInteger mq = null; // store quotient
4221 // Descend into mutables for faster remainder checks
4222 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4223 mq = new MutableBigInteger();
4224 r = mdividend.divide(ldivisor, mq);
4225 isRemainderZero = (r == 0);
4226 qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4227 if (!isRemainderZero) {
4228 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4229 mq.add(MutableBigInteger.ONE);
4230 }
4231 }
4232 return mq.toBigInteger(qsign);
4233 }
4234
4235 /**
4236 * Internally used for division operation for division {@code BigInteger}
4237 * by {@code long}.
4238 * The returned {@code BigDecimal} object is the quotient whose scale is set
4239 * to the passed in scale. If the remainder is not zero, it will be rounded
4240 * based on the passed in roundingMode. Also, if the remainder is zero and
4241 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4242 * trailing zeros of the result is stripped to match the preferredScale.
4243 */
4244 private static BigDecimal divideAndRound(BigInteger bdividend,
4245 long ldivisor, int scale, int roundingMode, int preferredScale) {
4246 boolean isRemainderZero; // record remainder is zero or not
4247 int qsign; // quotient sign
4248 long r = 0; // store quotient & remainder in long
4249 MutableBigInteger mq = null; // store quotient
4250 // Descend into mutables for faster remainder checks
4251 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4252 mq = new MutableBigInteger();
4253 r = mdividend.divide(ldivisor, mq);
4254 isRemainderZero = (r == 0);
4255 qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4256 if (!isRemainderZero) {
4257 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4258 mq.add(MutableBigInteger.ONE);
4259 }
4260 return mq.toBigDecimal(qsign, scale);
4261 } else {
4262 if (preferredScale != scale) {
4263 long compactVal = mq.toCompactValue(qsign);
4264 if(compactVal!=INFLATED) {
4265 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4266 }
4267 BigInteger intVal = mq.toBigInteger(qsign);
4268 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
4269 } else {
4270 return mq.toBigDecimal(qsign, scale);
4271 }
4272 }
4273 }
4274
4275 /**
4276 * Tests if quotient has to be incremented according the roundingMode
4277 */
4278 private static boolean needIncrement(long ldivisor, int roundingMode,
4279 int qsign, MutableBigInteger mq, long r) {
4280 assert r != 0L;
4281
4282 int cmpFracHalf;
4283 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4284 cmpFracHalf = 1; // 2 * r can't fit into long
4285 } else {
4286 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4287 }
4288
4289 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
4290 }
4291
4292 /**
4293 * Divides {@code BigInteger} value by {@code BigInteger} value and
4294 * do rounding based on the passed in roundingMode.
4295 */
4296 private static BigInteger divideAndRound(BigInteger bdividend, BigInteger bdivisor, int roundingMode) {
4297 boolean isRemainderZero; // record remainder is zero or not
4298 int qsign; // quotient sign
4299 // Descend into mutables for faster remainder checks
4300 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4301 MutableBigInteger mq = new MutableBigInteger();
4302 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4303 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4304 isRemainderZero = mr.isZero();
4305 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4306 if (!isRemainderZero) {
4307 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4308 mq.add(MutableBigInteger.ONE);
4309 }
4310 }
4311 return mq.toBigInteger(qsign);
4312 }
4313
4314 /**
4315 * Internally used for division operation for division {@code BigInteger}
4316 * by {@code BigInteger}.
4317 * The returned {@code BigDecimal} object is the quotient whose scale is set
4318 * to the passed in scale. If the remainder is not zero, it will be rounded
4319 * based on the passed in roundingMode. Also, if the remainder is zero and
4320 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4321 * trailing zeros of the result is stripped to match the preferredScale.
4322 */
4323 private static BigDecimal divideAndRound(BigInteger bdividend, BigInteger bdivisor, int scale, int roundingMode,
4324 int preferredScale) {
4325 boolean isRemainderZero; // record remainder is zero or not
4326 int qsign; // quotient sign
4327 // Descend into mutables for faster remainder checks
4328 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4329 MutableBigInteger mq = new MutableBigInteger();
4330 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4331 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4332 isRemainderZero = mr.isZero();
4333 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4334 if (!isRemainderZero) {
4335 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4336 mq.add(MutableBigInteger.ONE);
4337 }
4338 return mq.toBigDecimal(qsign, scale);
4339 } else {
4340 if (preferredScale != scale) {
4341 long compactVal = mq.toCompactValue(qsign);
4342 if (compactVal != INFLATED) {
4343 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4344 }
4345 BigInteger intVal = mq.toBigInteger(qsign);
4346 return createAndStripZerosToMatchScale(intVal, scale, preferredScale);
4347 } else {
4348 return mq.toBigDecimal(qsign, scale);
4349 }
4350 }
4351 }
4352
4353 /**
4354 * Tests if quotient has to be incremented according the roundingMode
4355 */
4356 private static boolean needIncrement(MutableBigInteger mdivisor, int roundingMode,
4357 int qsign, MutableBigInteger mq, MutableBigInteger mr) {
4358 assert !mr.isZero();
4359 int cmpFracHalf = mr.compareHalf(mdivisor);
4360 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
4361 }
4362
4363 /**
4364 * Remove insignificant trailing zeros from this
4365 * {@code BigInteger} value until the preferred scale is reached or no
4366 * more zeros can be removed. If the preferred scale is less than
4367 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4368 *
4369 * @return new {@code BigDecimal} with a scale possibly reduced
4370 * to be closed to the preferred scale.
4371 */
4372 private static BigDecimal createAndStripZerosToMatchScale(BigInteger intVal, int scale, long preferredScale) {
4373 BigInteger qr[]; // quotient-remainder pair
4374 while (intVal.compareMagnitude(BigInteger.TEN) >= 0
4375 && scale > preferredScale) {
4376 if (intVal.testBit(0))
4377 break; // odd number cannot end in 0
4378 qr = intVal.divideAndRemainder(BigInteger.TEN);
4379 if (qr[1].signum() != 0)
4380 break; // non-0 remainder
4381 intVal = qr[0];
4382 scale = checkScale(intVal,(long) scale - 1); // could Overflow
4383 }
4384 return valueOf(intVal, scale, 0);
4385 }
4386
4387 /**
4388 * Remove insignificant trailing zeros from this
4389 * {@code long} value until the preferred scale is reached or no
4390 * more zeros can be removed. If the preferred scale is less than
4391 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4392 *
4393 * @return new {@code BigDecimal} with a scale possibly reduced
4394 * to be closed to the preferred scale.
4395 */
4396 private static BigDecimal createAndStripZerosToMatchScale(long compactVal, int scale, long preferredScale) {
4397 while (Math.abs(compactVal) >= 10L && scale > preferredScale) {
4398 if ((compactVal & 1L) != 0L)
4399 break; // odd number cannot end in 0
4400 long r = compactVal % 10L;
4401 if (r != 0L)
4402 break; // non-0 remainder
4403 compactVal /= 10;
4404 scale = checkScale(compactVal, (long) scale - 1); // could Overflow
4405 }
4406 return valueOf(compactVal, scale);
4407 }
4408
4409 private static BigDecimal stripZerosToMatchScale(BigInteger intVal, long intCompact, int scale, int preferredScale) {
4410 if(intCompact!=INFLATED) {
4411 return createAndStripZerosToMatchScale(intCompact, scale, preferredScale);
4412 } else {
4413 return createAndStripZerosToMatchScale(intVal==null ? INFLATED_BIGINT : intVal,
4414 scale, preferredScale);
4415 }
4416 }
4417
4418 /*
4419 * returns INFLATED if oveflow
4420 */
4421 private static long add(long xs, long ys){
4422 long sum = xs + ys;
4423 // See "Hacker's Delight" section 2-12 for explanation of
4424 // the overflow test.
4425 if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) { // not overflowed
4426 return sum;
4427 }
4428 return INFLATED;
4429 }
4430
4431 private static BigDecimal add(long xs, long ys, int scale){
4432 long sum = add(xs, ys);
4433 if (sum!=INFLATED)
4434 return BigDecimal.valueOf(sum, scale);
4435 return new BigDecimal(BigInteger.valueOf(xs).add(ys), scale);
4436 }
4437
4438 private static BigDecimal add(final long xs, int scale1, final long ys, int scale2) {
4439 long sdiff = (long) scale1 - scale2;
4440 if (sdiff == 0) {
4441 return add(xs, ys, scale1);
4442 } else if (sdiff < 0) {
4443 int raise = checkScale(xs,-sdiff);
4444 long scaledX = longMultiplyPowerTen(xs, raise);
4445 if (scaledX != INFLATED) {
4446 return add(scaledX, ys, scale2);
4447 } else {
4448 BigInteger bigsum = bigMultiplyPowerTen(xs,raise).add(ys);
4449 return ((xs^ys)>=0) ? // same sign test
4450 new BigDecimal(bigsum, INFLATED, scale2, 0)
4451 : valueOf(bigsum, scale2, 0);
4452 }
4453 } else {
4454 int raise = checkScale(ys,sdiff);
4455 long scaledY = longMultiplyPowerTen(ys, raise);
4456 if (scaledY != INFLATED) {
4457 return add(xs, scaledY, scale1);
4458 } else {
4459 BigInteger bigsum = bigMultiplyPowerTen(ys,raise).add(xs);
4460 return ((xs^ys)>=0) ?
4461 new BigDecimal(bigsum, INFLATED, scale1, 0)
4462 : valueOf(bigsum, scale1, 0);
4463 }
4464 }
4465 }
4466
4467 private static BigDecimal add(final long xs, int scale1, BigInteger snd, int scale2) {
4468 int rscale = scale1;
4469 long sdiff = (long)rscale - scale2;
4470 boolean sameSigns = (Long.signum(xs) == snd.signum);
4471 BigInteger sum;
4472 if (sdiff < 0) {
4473 int raise = checkScale(xs,-sdiff);
4474 rscale = scale2;
4475 long scaledX = longMultiplyPowerTen(xs, raise);
4476 if (scaledX == INFLATED) {
4477 sum = snd.add(bigMultiplyPowerTen(xs,raise));
4478 } else {
4479 sum = snd.add(scaledX);
4480 }
4481 } else { //if (sdiff > 0) {
4482 int raise = checkScale(snd,sdiff);
4483 snd = bigMultiplyPowerTen(snd,raise);
4484 sum = snd.add(xs);
4485 }
4486 return (sameSigns) ?
4487 new BigDecimal(sum, INFLATED, rscale, 0) :
4488 valueOf(sum, rscale, 0);
4489 }
4490
4491 private static BigDecimal add(BigInteger fst, int scale1, BigInteger snd, int scale2) {
4492 int rscale = scale1;
4493 long sdiff = (long)rscale - scale2;
4494 if (sdiff != 0) {
4495 if (sdiff < 0) {
4496 int raise = checkScale(fst,-sdiff);
4497 rscale = scale2;
4498 fst = bigMultiplyPowerTen(fst,raise);
4499 } else {
4500 int raise = checkScale(snd,sdiff);
4501 snd = bigMultiplyPowerTen(snd,raise);
4502 }
4503 }
4504 BigInteger sum = fst.add(snd);
4505 return (fst.signum == snd.signum) ?
4506 new BigDecimal(sum, INFLATED, rscale, 0) :
4507 valueOf(sum, rscale, 0);
4508 }
4509
4510 private static BigInteger bigMultiplyPowerTen(long value, int n) {
4511 if (n <= 0)
4512 return BigInteger.valueOf(value);
4513 return bigTenToThe(n).multiply(value);
4514 }
4515
4516 private static BigInteger bigMultiplyPowerTen(BigInteger value, int n) {
4517 if (n <= 0)
4518 return value;
4519 if(n<LONG_TEN_POWERS_TABLE.length) {
4520 return value.multiply(LONG_TEN_POWERS_TABLE[n]);
4521 }
4522 return value.multiply(bigTenToThe(n));
4523 }
4524
4525 /**
4526 * Returns a {@code BigDecimal} whose value is {@code (xs /
4527 * ys)}, with rounding according to the context settings.
4528 *
4529 * Fast path - used only when (xscale <= yscale && yscale < 18
4530 * && mc.presision<18) {
4531 */
4532 private static BigDecimal divideSmallFastPath(final long xs, int xscale,
4533 final long ys, int yscale,
4534 long preferredScale, MathContext mc) {
4535 int mcp = mc.precision;
4536 int roundingMode = mc.roundingMode.oldMode;
4537
4538 assert (xscale <= yscale) && (yscale < 18) && (mcp < 18);
4539 int xraise = yscale - xscale; // xraise >=0
4540 long scaledX = (xraise==0) ? xs :
4541 longMultiplyPowerTen(xs, xraise); // can't overflow here!
4542 BigDecimal quotient;
4543
4544 int cmp = longCompareMagnitude(scaledX, ys);
4545 if(cmp > 0) { // satisfy constraint (b)
4546 yscale -= 1; // [that is, divisor *= 10]
4547 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4548 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4549 // assert newScale >= xscale
4550 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4551 long scaledXs;
4552 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
4553 quotient = null;
4554 if((mcp-1) >=0 && (mcp-1)<LONG_TEN_POWERS_TABLE.length) {
4555 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp-1], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4556 }
4557 if(quotient==null) {
4558 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp-1);
4559 quotient = divideAndRound(rb, ys,
4560 scl, roundingMode, checkScaleNonZero(preferredScale));
4561 }
4562 } else {
4563 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4564 }
4565 } else {
4566 int newScale = checkScaleNonZero((long) xscale - mcp);
4567 // assert newScale >= yscale
4568 if (newScale == yscale) { // easy case
4569 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4570 } else {
4571 int raise = checkScaleNonZero((long) newScale - yscale);
4572 long scaledYs;
4573 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4574 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4575 quotient = divideAndRound(BigInteger.valueOf(xs),
4576 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4577 } else {
4578 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4579 }
4580 }
4581 }
4582 } else {
4583 // abs(scaledX) <= abs(ys)
4584 // result is "scaledX * 10^msp / ys"
4585 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4586 if(cmp==0) {
4587 // abs(scaleX)== abs(ys) => result will be scaled 10^mcp + correct sign
4588 quotient = roundedTenPower(((scaledX < 0) == (ys < 0)) ? 1 : -1, mcp, scl, checkScaleNonZero(preferredScale));
4589 } else {
4590 // abs(scaledX) < abs(ys)
4591 long scaledXs;
4592 if ((scaledXs = longMultiplyPowerTen(scaledX, mcp)) == INFLATED) {
4593 quotient = null;
4594 if(mcp<LONG_TEN_POWERS_TABLE.length) {
4595 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4596 }
4597 if(quotient==null) {
4598 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp);
4599 quotient = divideAndRound(rb, ys,
4600 scl, roundingMode, checkScaleNonZero(preferredScale));
4601 }
4602 } else {
4603 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4604 }
4605 }
4606 }
4607 // doRound, here, only affects 1000000000 case.
4608 return doRound(quotient,mc);
4609 }
4610
4611 /**
4612 * Returns a {@code BigDecimal} whose value is {@code (xs /
4613 * ys)}, with rounding according to the context settings.
4614 */
4615 private static BigDecimal divide(final long xs, int xscale, final long ys, int yscale, long preferredScale, MathContext mc) {
4616 int mcp = mc.precision;
4617 if(xscale <= yscale && yscale < 18 && mcp<18) {
4618 return divideSmallFastPath(xs, xscale, ys, yscale, preferredScale, mc);
4619 }
4620 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
4621 yscale -= 1; // [that is, divisor *= 10]
4622 }
4623 int roundingMode = mc.roundingMode.oldMode;
4624 // In order to find out whether the divide generates the exact result,
4625 // we avoid calling the above divide method. 'quotient' holds the
4626 // return BigDecimal object whose scale will be set to 'scl'.
4627 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4628 BigDecimal quotient;
4629 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4630 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4631 long scaledXs;
4632 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
4633 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4634 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4635 } else {
4636 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4637 }
4638 } else {
4639 int newScale = checkScaleNonZero((long) xscale - mcp);
4640 // assert newScale >= yscale
4641 if (newScale == yscale) { // easy case
4642 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4643 } else {
4644 int raise = checkScaleNonZero((long) newScale - yscale);
4645 long scaledYs;
4646 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4647 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4648 quotient = divideAndRound(BigInteger.valueOf(xs),
4649 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4650 } else {
4651 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4652 }
4653 }
4654 }
4655 // doRound, here, only affects 1000000000 case.
4656 return doRound(quotient,mc);
4657 }
4658
4659 /**
4660 * Returns a {@code BigDecimal} whose value is {@code (xs /
4661 * ys)}, with rounding according to the context settings.
4662 */
4663 private static BigDecimal divide(BigInteger xs, int xscale, long ys, int yscale, long preferredScale, MathContext mc) {
4664 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4665 if ((-compareMagnitudeNormalized(ys, yscale, xs, xscale)) > 0) {// satisfy constraint (b)
4666 yscale -= 1; // [that is, divisor *= 10]
4667 }
4668 int mcp = mc.precision;
4669 int roundingMode = mc.roundingMode.oldMode;
4670
4671 // In order to find out whether the divide generates the exact result,
4672 // we avoid calling the above divide method. 'quotient' holds the
4673 // return BigDecimal object whose scale will be set to 'scl'.
4674 BigDecimal quotient;
4675 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4676 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4677 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4678 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4679 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4680 } else {
4681 int newScale = checkScaleNonZero((long) xscale - mcp);
4682 // assert newScale >= yscale
4683 if (newScale == yscale) { // easy case
4684 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4685 } else {
4686 int raise = checkScaleNonZero((long) newScale - yscale);
4687 long scaledYs;
4688 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4689 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4690 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4691 } else {
4692 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4693 }
4694 }
4695 }
4696 // doRound, here, only affects 1000000000 case.
4697 return doRound(quotient, mc);
4698 }
4699
4700 /**
4701 * Returns a {@code BigDecimal} whose value is {@code (xs /
4702 * ys)}, with rounding according to the context settings.
4703 */
4704 private static BigDecimal divide(long xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
4705 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4706 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
4707 yscale -= 1; // [that is, divisor *= 10]
4708 }
4709 int mcp = mc.precision;
4710 int roundingMode = mc.roundingMode.oldMode;
4711
4712 // In order to find out whether the divide generates the exact result,
4713 // we avoid calling the above divide method. 'quotient' holds the
4714 // return BigDecimal object whose scale will be set to 'scl'.
4715 BigDecimal quotient;
4716 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4717 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4718 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4719 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4720 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4721 } else {
4722 int newScale = checkScaleNonZero((long) xscale - mcp);
4723 int raise = checkScaleNonZero((long) newScale - yscale);
4724 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4725 quotient = divideAndRound(BigInteger.valueOf(xs), rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4726 }
4727 // doRound, here, only affects 1000000000 case.
4728 return doRound(quotient, mc);
4729 }
4730
4731 /**
4732 * Returns a {@code BigDecimal} whose value is {@code (xs /
4733 * ys)}, with rounding according to the context settings.
4734 */
4735 private static BigDecimal divide(BigInteger xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
4736 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4737 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
4738 yscale -= 1; // [that is, divisor *= 10]
4739 }
4740 int mcp = mc.precision;
4741 int roundingMode = mc.roundingMode.oldMode;
4742
4743 // In order to find out whether the divide generates the exact result,
4744 // we avoid calling the above divide method. 'quotient' holds the
4745 // return BigDecimal object whose scale will be set to 'scl'.
4746 BigDecimal quotient;
4747 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4748 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4749 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4750 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4751 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4752 } else {
4753 int newScale = checkScaleNonZero((long) xscale - mcp);
4754 int raise = checkScaleNonZero((long) newScale - yscale);
4755 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4756 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4757 }
4758 // doRound, here, only affects 1000000000 case.
4759 return doRound(quotient, mc);
4760 }
4761
4762 /*
4763 * performs divideAndRound for (dividend0*dividend1, divisor)
4764 * returns null if quotient can't fit into long value;
4765 */
4766 private static BigDecimal multiplyDivideAndRound(long dividend0, long dividend1, long divisor, int scale, int roundingMode,
4767 int preferredScale) {
4768 int qsign = Long.signum(dividend0)*Long.signum(dividend1)*Long.signum(divisor);
4769 dividend0 = Math.abs(dividend0);
4770 dividend1 = Math.abs(dividend1);
4771 divisor = Math.abs(divisor);
4772 // multiply dividend0 * dividend1
4773 long d0_hi = dividend0 >>> 32;
4774 long d0_lo = dividend0 & LONG_MASK;
4775 long d1_hi = dividend1 >>> 32;
4776 long d1_lo = dividend1 & LONG_MASK;
4777 long product = d0_lo * d1_lo;
4778 long d0 = product & LONG_MASK;
4779 long d1 = product >>> 32;
4780 product = d0_hi * d1_lo + d1;
4781 d1 = product & LONG_MASK;
4782 long d2 = product >>> 32;
4783 product = d0_lo * d1_hi + d1;
4784 d1 = product & LONG_MASK;
4785 d2 += product >>> 32;
4786 long d3 = d2>>>32;
4787 d2 &= LONG_MASK;
4788 product = d0_hi*d1_hi + d2;
4789 d2 = product & LONG_MASK;
4790 d3 = ((product>>>32) + d3) & LONG_MASK;
4791 final long dividendHi = make64(d3,d2);
4792 final long dividendLo = make64(d1,d0);
4793 // divide
4794 return divideAndRound128(dividendHi, dividendLo, divisor, qsign, scale, roundingMode, preferredScale);
4795 }
4796
4797 private static final long DIV_NUM_BASE = (1L<<32); // Number base (32 bits).
4798
4799 /*
4800 * divideAndRound 128-bit value by long divisor.
4801 * returns null if quotient can't fit into long value;
4802 * Specialized version of Knuth's division
4803 */
4804 private static BigDecimal divideAndRound128(final long dividendHi, final long dividendLo, long divisor, int sign,
4805 int scale, int roundingMode, int preferredScale) {
4806 if (dividendHi >= divisor) {
4807 return null;
4808 }
4809 final int shift = Long.numberOfLeadingZeros(divisor);
4810 divisor <<= shift;
4811
4812 final long v1 = divisor >>> 32;
4813 final long v0 = divisor & LONG_MASK;
4814
4815 long q1, q0;
4816 long r_tmp;
4817
4818 long tmp = dividendLo << shift;
4819 long u1 = tmp >>> 32;
4820 long u0 = tmp & LONG_MASK;
4821
4822 tmp = (dividendHi << shift) | (dividendLo >>> 64 - shift);
4823 long u2 = tmp & LONG_MASK;
4824 tmp = divWord(tmp,v1);
4825 q1 = tmp & LONG_MASK;
4826 r_tmp = tmp >>> 32;
4827 while(q1 >= DIV_NUM_BASE || unsignedLongCompare(q1*v0, make64(r_tmp, u1))) {
4828 q1--;
4829 r_tmp += v1;
4830 if (r_tmp >= DIV_NUM_BASE)
4831 break;
4832 }
4833 tmp = mulsub(u2,u1,v1,v0,q1);
4834 u1 = tmp & LONG_MASK;
4835 tmp = divWord(tmp,v1);
4836 q0 = tmp & LONG_MASK;
4837 r_tmp = tmp >>> 32;
4838 while(q0 >= DIV_NUM_BASE || unsignedLongCompare(q0*v0,make64(r_tmp,u0))) {
4839 q0--;
4840 r_tmp += v1;
4841 if (r_tmp >= DIV_NUM_BASE)
4842 break;
4843 }
4844 if((int)q1 < 0) {
4845 // result (which is positive and unsigned here)
4846 // can't fit into long due to sign bit is used for value
4847 MutableBigInteger mq = new MutableBigInteger(new int[]{(int)q1, (int)q0});
4848 if (roundingMode == ROUND_DOWN && scale == preferredScale) {
4849 return mq.toBigDecimal(sign, scale);
4850 }
4851 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
4852 if (r != 0) {
4853 if(needIncrement(divisor >>> shift, roundingMode, sign, mq, r)){
4854 mq.add(MutableBigInteger.ONE);
4855 }
4856 return mq.toBigDecimal(sign, scale);
4857 } else {
4858 if (preferredScale != scale) {
4859 BigInteger intVal = mq.toBigInteger(sign);
4860 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
4861 } else {
4862 return mq.toBigDecimal(sign, scale);
4863 }
4864 }
4865 }
4866 long q = make64(q1,q0);
4867 q*=sign;
4868 if (roundingMode == ROUND_DOWN && scale == preferredScale)
4869 return valueOf(q, scale);
4870 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
4871 if (r != 0) {
4872 boolean increment = needIncrement(divisor >>> shift, roundingMode, sign, q, r);
4873 return valueOf((increment ? q + sign : q), scale);
4874 } else {
4875 if (preferredScale != scale) {
4876 return createAndStripZerosToMatchScale(q, scale, preferredScale);
4877 } else {
4878 return valueOf(q, scale);
4879 }
4880 }
4881 }
4882
4883 /*
4884 * calculate divideAndRound for ldividend*10^raise / divisor
4885 * when abs(dividend)==abs(divisor);
4886 */
4887 private static BigDecimal roundedTenPower(int qsign, int raise, int scale, int preferredScale) {
4888 if (scale > preferredScale) {
4889 int diff = scale - preferredScale;
4890 if(diff < raise) {
4891 return scaledTenPow(raise - diff, qsign, preferredScale);
4892 } else {
4893 return valueOf(qsign,scale-raise);
4894 }
4895 } else {
4896 return scaledTenPow(raise, qsign, scale);
4897 }
4898 }
4899
4900 static BigDecimal scaledTenPow(int n, int sign, int scale) {
4901 if (n < LONG_TEN_POWERS_TABLE.length)
4902 return valueOf(sign*LONG_TEN_POWERS_TABLE[n],scale);
4903 else {
4904 BigInteger unscaledVal = bigTenToThe(n);
4905 if(sign==-1) {
4906 unscaledVal = unscaledVal.negate();
4907 }
4908 return new BigDecimal(unscaledVal, INFLATED, scale, n+1);
4909 }
4910 }
4911
4912 private static long divWord(long n, long dLong) {
4913 long r;
4914 long q;
4915 if (dLong == 1) {
4916 q = (int)n;
4917 return (q & LONG_MASK);
4918 }
4919 // Approximate the quotient and remainder
4920 q = (n >>> 1) / (dLong >>> 1);
4921 r = n - q*dLong;
4922
4923 // Correct the approximation
4924 while (r < 0) {
4925 r += dLong;
4926 q--;
4927 }
4928 while (r >= dLong) {
4929 r -= dLong;
4930 q++;
4931 }
4932 // n - q*dlong == r && 0 <= r <dLong, hence we're done.
4933 return (r << 32) | (q & LONG_MASK);
4934 }
4935
4936 private static long make64(long hi, long lo) {
4937 return hi<<32 | lo;
4938 }
4939
4940 private static long mulsub(long u1, long u0, final long v1, final long v0, long q0) {
4941 long tmp = u0 - q0*v0;
4942 return make64(u1 + (tmp>>>32) - q0*v1,tmp & LONG_MASK);
4943 }
4944
4945 private static boolean unsignedLongCompare(long one, long two) {
4946 return (one+Long.MIN_VALUE) > (two+Long.MIN_VALUE);
4947 }
4948
4949 private static boolean unsignedLongCompareEq(long one, long two) {
4950 return (one+Long.MIN_VALUE) >= (two+Long.MIN_VALUE);
4951 }
4952
4953
4954 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4955 private static int compareMagnitudeNormalized(long xs, int xscale, long ys, int yscale) {
4956 // assert xs!=0 && ys!=0
4957 int sdiff = xscale - yscale;
4958 if (sdiff != 0) {
4959 if (sdiff < 0) {
4960 xs = longMultiplyPowerTen(xs, -sdiff);
4961 } else { // sdiff > 0
4962 ys = longMultiplyPowerTen(ys, sdiff);
4963 }
4964 }
4965 if (xs != INFLATED)
4966 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
4967 else
4968 return 1;
4969 }
4970
4971 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4972 private static int compareMagnitudeNormalized(long xs, int xscale, BigInteger ys, int yscale) {
4973 // assert "ys can't be represented as long"
4974 if (xs == 0)
4975 return -1;
4976 int sdiff = xscale - yscale;
4977 if (sdiff < 0) {
4978 if (longMultiplyPowerTen(xs, -sdiff) == INFLATED ) {
4979 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
4980 }
4981 }
4982 return -1;
4983 }
4984
4985 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4986 private static int compareMagnitudeNormalized(BigInteger xs, int xscale, BigInteger ys, int yscale) {
4987 int sdiff = xscale - yscale;
4988 if (sdiff < 0) {
4989 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
4990 } else { // sdiff >= 0
4991 return xs.compareMagnitude(bigMultiplyPowerTen(ys, sdiff));
4992 }
4993 }
4994
4995 private static long multiply(long x, long y){
4996 long product = x * y;
4997 long ax = Math.abs(x);
4998 long ay = Math.abs(y);
4999 if (((ax | ay) >>> 31 == 0) || (y == 0) || (product / y == x)){
5000 return product;
5001 }
5002 return INFLATED;
5003 }
5004
5005 private static BigDecimal multiply(long x, long y, int scale) {
5006 long product = multiply(x, y);
5007 if(product!=INFLATED) {
5008 return valueOf(product,scale);
5009 }
5010 return new BigDecimal(BigInteger.valueOf(x).multiply(y),INFLATED,scale,0);
5011 }
5012
5013 private static BigDecimal multiply(long x, BigInteger y, int scale) {
5014 if(x==0) {
5015 return zeroValueOf(scale);
5016 }
5017 return new BigDecimal(y.multiply(x),INFLATED,scale,0);
5018 }
5019
5020 private static BigDecimal multiply(BigInteger x, BigInteger y, int scale) {
5021 return new BigDecimal(x.multiply(y),INFLATED,scale,0);
5022 }
5023
5024 /**
5025 * Multiplies two long values and rounds according {@code MathContext}
5026 */
5027 private static BigDecimal multiplyAndRound(long x, long y, int scale, MathContext mc) {
5028 long product = multiply(x, y);
5029 if(product!=INFLATED) {
5030 return doRound(product, scale, mc);
5031 }
5032 // attempt to do it in 128 bits
5033 int rsign = 1;
5034 if(x < 0) {
5035 x = -x;
5036 rsign = -1;
5037 }
5038 if(y < 0) {
5039 y = -y;
5040 rsign *= -1;
5041 }
5042 // multiply dividend0 * dividend1
5043 long m0_hi = x >>> 32;
5044 long m0_lo = x & LONG_MASK;
5045 long m1_hi = y >>> 32;
5046 long m1_lo = y & LONG_MASK;
5047 product = m0_lo * m1_lo;
5048 long m0 = product & LONG_MASK;
5049 long m1 = product >>> 32;
5050 product = m0_hi * m1_lo + m1;
5051 m1 = product & LONG_MASK;
5052 long m2 = product >>> 32;
5053 product = m0_lo * m1_hi + m1;
5054 m1 = product & LONG_MASK;
5055 m2 += product >>> 32;
5056 long m3 = m2>>>32;
5057 m2 &= LONG_MASK;
5058 product = m0_hi*m1_hi + m2;
5059 m2 = product & LONG_MASK;
5060 m3 = ((product>>>32) + m3) & LONG_MASK;
5061 final long mHi = make64(m3,m2);
5062 final long mLo = make64(m1,m0);
5063 BigDecimal res = doRound128(mHi, mLo, rsign, scale, mc);
5064 if(res!=null) {
5065 return res;
5066 }
5067 res = new BigDecimal(BigInteger.valueOf(x).multiply(y*rsign), INFLATED, scale, 0);
5068 return doRound(res,mc);
5069 }
5070
5071 private static BigDecimal multiplyAndRound(long x, BigInteger y, int scale, MathContext mc) {
5072 if(x==0) {
5073 return zeroValueOf(scale);
5074 }
5075 return doRound(y.multiply(x), scale, mc);
5076 }
5077
5078 private static BigDecimal multiplyAndRound(BigInteger x, BigInteger y, int scale, MathContext mc) {
5079 return doRound(x.multiply(y), scale, mc);
5080 }
5081
5082 /**
5083 * rounds 128-bit value according {@code MathContext}
5084 * returns null if result can't be repsented as compact BigDecimal.
5085 */
5086 private static BigDecimal doRound128(long hi, long lo, int sign, int scale, MathContext mc) {
5087 int mcp = mc.precision;
5088 int drop;
5089 BigDecimal res = null;
5090 if(((drop = precision(hi, lo) - mcp) > 0)&&(drop<LONG_TEN_POWERS_TABLE.length)) {
5091 scale = checkScaleNonZero((long)scale - drop);
5092 res = divideAndRound128(hi, lo, LONG_TEN_POWERS_TABLE[drop], sign, scale, mc.roundingMode.oldMode, scale);
5093 }
5094 if(res!=null) {
5095 return doRound(res,mc);
5096 }
5097 return null;
5098 }
5099
5100 private static final long[][] LONGLONG_TEN_POWERS_TABLE = {
5101 { 0L, 0x8AC7230489E80000L }, //10^19
5102 { 0x5L, 0x6bc75e2d63100000L }, //10^20
5103 { 0x36L, 0x35c9adc5dea00000L }, //10^21
5104 { 0x21eL, 0x19e0c9bab2400000L }, //10^22
5105 { 0x152dL, 0x02c7e14af6800000L }, //10^23
5106 { 0xd3c2L, 0x1bcecceda1000000L }, //10^24
5107 { 0x84595L, 0x161401484a000000L }, //10^25
5108 { 0x52b7d2L, 0xdcc80cd2e4000000L }, //10^26
5109 { 0x33b2e3cL, 0x9fd0803ce8000000L }, //10^27
5110 { 0x204fce5eL, 0x3e25026110000000L }, //10^28
5111 { 0x1431e0faeL, 0x6d7217caa0000000L }, //10^29
5112 { 0xc9f2c9cd0L, 0x4674edea40000000L }, //10^30
5113 { 0x7e37be2022L, 0xc0914b2680000000L }, //10^31
5114 { 0x4ee2d6d415bL, 0x85acef8100000000L }, //10^32
5115 { 0x314dc6448d93L, 0x38c15b0a00000000L }, //10^33
5116 { 0x1ed09bead87c0L, 0x378d8e6400000000L }, //10^34
5117 { 0x13426172c74d82L, 0x2b878fe800000000L }, //10^35
5118 { 0xc097ce7bc90715L, 0xb34b9f1000000000L }, //10^36
5119 { 0x785ee10d5da46d9L, 0x00f436a000000000L }, //10^37
5120 { 0x4b3b4ca85a86c47aL, 0x098a224000000000L }, //10^38
5121 };
5122
5123 /*
5124 * returns precision of 128-bit value
5125 */
5126 private static int precision(long hi, long lo){
5127 if(hi==0) {
5128 if(lo>=0) {
5129 return longDigitLength(lo);
5130 }
5131 return (unsignedLongCompareEq(lo, LONGLONG_TEN_POWERS_TABLE[0][1])) ? 20 : 19;
5132 // 0x8AC7230489E80000L = unsigned 2^19
5133 }
5134 int r = ((128 - Long.numberOfLeadingZeros(hi) + 1) * 1233) >>> 12;
5135 int idx = r-19;
5136 return (idx >= LONGLONG_TEN_POWERS_TABLE.length || longLongCompareMagnitude(hi, lo,
5137 LONGLONG_TEN_POWERS_TABLE[idx][0], LONGLONG_TEN_POWERS_TABLE[idx][1])) ? r : r + 1;
5138 }
5139
5140 /*
5141 * returns true if 128 bit number <hi0,lo0> is less then <hi1,lo1>
5142 * hi0 & hi1 should be non-negative
5143 */
5144 private static boolean longLongCompareMagnitude(long hi0, long lo0, long hi1, long lo1) {
5145 if(hi0!=hi1) {
5146 return hi0<hi1;
5147 }
5148 return (lo0+Long.MIN_VALUE) <(lo1+Long.MIN_VALUE);
5149 }
5150
5151 private static BigDecimal divide(long dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5152 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5153 int newScale = scale + divisorScale;
5154 int raise = newScale - dividendScale;
5155 if(raise<LONG_TEN_POWERS_TABLE.length) {
5156 long xs = dividend;
5157 if ((xs = longMultiplyPowerTen(xs, raise)) != INFLATED) {
5158 return divideAndRound(xs, divisor, scale, roundingMode, scale);
5159 }
5160 BigDecimal q = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[raise], dividend, divisor, scale, roundingMode, scale);
5161 if(q!=null) {
5162 return q;
5163 }
5164 }
5165 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5166 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5167 } else {
5168 int newScale = checkScale(divisor,(long)dividendScale - scale);
5169 int raise = newScale - divisorScale;
5170 if(raise<LONG_TEN_POWERS_TABLE.length) {
5171 long ys = divisor;
5172 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5173 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5174 }
5175 }
5176 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5177 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5178 }
5179 }
5180
5181 private static BigDecimal divide(BigInteger dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5182 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5183 int newScale = scale + divisorScale;
5184 int raise = newScale - dividendScale;
5185 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5186 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5187 } else {
5188 int newScale = checkScale(divisor,(long)dividendScale - scale);
5189 int raise = newScale - divisorScale;
5190 if(raise<LONG_TEN_POWERS_TABLE.length) {
5191 long ys = divisor;
5192 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5193 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5194 }
5195 }
5196 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5197 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5198 }
5199 }
5200
5201 private static BigDecimal divide(long dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5202 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5203 int newScale = scale + divisorScale;
5204 int raise = newScale - dividendScale;
5205 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5206 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5207 } else {
5208 int newScale = checkScale(divisor,(long)dividendScale - scale);
5209 int raise = newScale - divisorScale;
5210 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5211 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5212 }
5213 }
5214
5215 private static BigDecimal divide(BigInteger dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5216 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5217 int newScale = scale + divisorScale;
5218 int raise = newScale - dividendScale;
5219 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5220 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5221 } else {
5222 int newScale = checkScale(divisor,(long)dividendScale - scale);
5223 int raise = newScale - divisorScale;
5224 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5225 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5226 }
5227 }
5228
5229 }