1 /*
2 * Copyright (c) 1996, 2011, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26 /*
27 * Portions Copyright IBM Corporation, 2001. All Rights Reserved.
28 */
29
30 package java.math;
31
32 import java.util.Arrays;
33 import static java.math.BigInteger.LONG_MASK;
34
35 /**
36 * Immutable, arbitrary-precision signed decimal numbers. A
37 * {@code BigDecimal} consists of an arbitrary precision integer
38 * <i>unscaled value</i> and a 32-bit integer <i>scale</i>. If zero
39 * or positive, the scale is the number of digits to the right of the
40 * decimal point. If negative, the unscaled value of the number is
41 * multiplied by ten to the power of the negation of the scale. The
42 * value of the number represented by the {@code BigDecimal} is
43 * therefore <tt>(unscaledValue × 10<sup>-scale</sup>)</tt>.
44 *
45 * <p>The {@code BigDecimal} class provides operations for
46 * arithmetic, scale manipulation, rounding, comparison, hashing, and
47 * format conversion. The {@link #toString} method provides a
48 * canonical representation of a {@code BigDecimal}.
49 *
50 * <p>The {@code BigDecimal} class gives its user complete control
51 * over rounding behavior. If no rounding mode is specified and the
52 * exact result cannot be represented, an exception is thrown;
53 * otherwise, calculations can be carried out to a chosen precision
54 * and rounding mode by supplying an appropriate {@link MathContext}
55 * object to the operation. In either case, eight <em>rounding
56 * modes</em> are provided for the control of rounding. Using the
57 * integer fields in this class (such as {@link #ROUND_HALF_UP}) to
58 * represent rounding mode is largely obsolete; the enumeration values
59 * of the {@code RoundingMode} {@code enum}, (such as {@link
60 * RoundingMode#HALF_UP}) should be used instead.
61 *
62 * <p>When a {@code MathContext} object is supplied with a precision
63 * setting of 0 (for example, {@link MathContext#UNLIMITED}),
64 * arithmetic operations are exact, as are the arithmetic methods
65 * which take no {@code MathContext} object. (This is the only
66 * behavior that was supported in releases prior to 5.) As a
67 * corollary of computing the exact result, the rounding mode setting
68 * of a {@code MathContext} object with a precision setting of 0 is
69 * not used and thus irrelevant. In the case of divide, the exact
70 * quotient could have an infinitely long decimal expansion; for
71 * example, 1 divided by 3. If the quotient has a nonterminating
72 * decimal expansion and the operation is specified to return an exact
73 * result, an {@code ArithmeticException} is thrown. Otherwise, the
74 * exact result of the division is returned, as done for other
75 * operations.
76 *
77 * <p>When the precision setting is not 0, the rules of
78 * {@code BigDecimal} arithmetic are broadly compatible with selected
79 * modes of operation of the arithmetic defined in ANSI X3.274-1996
80 * and ANSI X3.274-1996/AM 1-2000 (section 7.4). Unlike those
81 * standards, {@code BigDecimal} includes many rounding modes, which
82 * were mandatory for division in {@code BigDecimal} releases prior
83 * to 5. Any conflicts between these ANSI standards and the
84 * {@code BigDecimal} specification are resolved in favor of
85 * {@code BigDecimal}.
86 *
87 * <p>Since the same numerical value can have different
88 * representations (with different scales), the rules of arithmetic
89 * and rounding must specify both the numerical result and the scale
90 * used in the result's representation.
91 *
92 *
93 * <p>In general the rounding modes and precision setting determine
94 * how operations return results with a limited number of digits when
95 * the exact result has more digits (perhaps infinitely many in the
96 * case of division) than the number of digits returned.
97 *
98 * First, the
99 * total number of digits to return is specified by the
100 * {@code MathContext}'s {@code precision} setting; this determines
101 * the result's <i>precision</i>. The digit count starts from the
102 * leftmost nonzero digit of the exact result. The rounding mode
103 * determines how any discarded trailing digits affect the returned
104 * result.
105 *
106 * <p>For all arithmetic operators , the operation is carried out as
107 * though an exact intermediate result were first calculated and then
108 * rounded to the number of digits specified by the precision setting
109 * (if necessary), using the selected rounding mode. If the exact
110 * result is not returned, some digit positions of the exact result
111 * are discarded. When rounding increases the magnitude of the
112 * returned result, it is possible for a new digit position to be
113 * created by a carry propagating to a leading {@literal "9"} digit.
114 * For example, rounding the value 999.9 to three digits rounding up
115 * would be numerically equal to one thousand, represented as
116 * 100×10<sup>1</sup>. In such cases, the new {@literal "1"} is
117 * the leading digit position of the returned result.
118 *
119 * <p>Besides a logical exact result, each arithmetic operation has a
120 * preferred scale for representing a result. The preferred
121 * scale for each operation is listed in the table below.
122 *
123 * <table border>
124 * <caption><b>Preferred Scales for Results of Arithmetic Operations
125 * </b></caption>
126 * <tr><th>Operation</th><th>Preferred Scale of Result</th></tr>
127 * <tr><td>Add</td><td>max(addend.scale(), augend.scale())</td>
128 * <tr><td>Subtract</td><td>max(minuend.scale(), subtrahend.scale())</td>
129 * <tr><td>Multiply</td><td>multiplier.scale() + multiplicand.scale()</td>
130 * <tr><td>Divide</td><td>dividend.scale() - divisor.scale()</td>
131 * </table>
132 *
133 * These scales are the ones used by the methods which return exact
134 * arithmetic results; except that an exact divide may have to use a
135 * larger scale since the exact result may have more digits. For
136 * example, {@code 1/32} is {@code 0.03125}.
137 *
138 * <p>Before rounding, the scale of the logical exact intermediate
139 * result is the preferred scale for that operation. If the exact
140 * numerical result cannot be represented in {@code precision}
141 * digits, rounding selects the set of digits to return and the scale
142 * of the result is reduced from the scale of the intermediate result
143 * to the least scale which can represent the {@code precision}
144 * digits actually returned. If the exact result can be represented
145 * with at most {@code precision} digits, the representation
146 * of the result with the scale closest to the preferred scale is
147 * returned. In particular, an exactly representable quotient may be
148 * represented in fewer than {@code precision} digits by removing
149 * trailing zeros and decreasing the scale. For example, rounding to
150 * three digits using the {@linkplain RoundingMode#FLOOR floor}
151 * rounding mode, <br>
152 *
153 * {@code 19/100 = 0.19 // integer=19, scale=2} <br>
154 *
155 * but<br>
156 *
157 * {@code 21/110 = 0.190 // integer=190, scale=3} <br>
158 *
159 * <p>Note that for add, subtract, and multiply, the reduction in
160 * scale will equal the number of digit positions of the exact result
161 * which are discarded. If the rounding causes a carry propagation to
162 * create a new high-order digit position, an additional digit of the
163 * result is discarded than when no new digit position is created.
164 *
165 * <p>Other methods may have slightly different rounding semantics.
166 * For example, the result of the {@code pow} method using the
167 * {@linkplain #pow(int, MathContext) specified algorithm} can
168 * occasionally differ from the rounded mathematical result by more
169 * than one unit in the last place, one <i>{@linkplain #ulp() ulp}</i>.
170 *
171 * <p>Two types of operations are provided for manipulating the scale
172 * of a {@code BigDecimal}: scaling/rounding operations and decimal
173 * point motion operations. Scaling/rounding operations ({@link
174 * #setScale setScale} and {@link #round round}) return a
175 * {@code BigDecimal} whose value is approximately (or exactly) equal
176 * to that of the operand, but whose scale or precision is the
177 * specified value; that is, they increase or decrease the precision
178 * of the stored number with minimal effect on its value. Decimal
179 * point motion operations ({@link #movePointLeft movePointLeft} and
180 * {@link #movePointRight movePointRight}) return a
181 * {@code BigDecimal} created from the operand by moving the decimal
182 * point a specified distance in the specified direction.
183 *
184 * <p>For the sake of brevity and clarity, pseudo-code is used
185 * throughout the descriptions of {@code BigDecimal} methods. The
186 * pseudo-code expression {@code (i + j)} is shorthand for "a
187 * {@code BigDecimal} whose value is that of the {@code BigDecimal}
188 * {@code i} added to that of the {@code BigDecimal}
189 * {@code j}." The pseudo-code expression {@code (i == j)} is
190 * shorthand for "{@code true} if and only if the
191 * {@code BigDecimal} {@code i} represents the same value as the
192 * {@code BigDecimal} {@code j}." Other pseudo-code expressions
193 * are interpreted similarly. Square brackets are used to represent
194 * the particular {@code BigInteger} and scale pair defining a
195 * {@code BigDecimal} value; for example [19, 2] is the
196 * {@code BigDecimal} numerically equal to 0.19 having a scale of 2.
197 *
198 * <p>Note: care should be exercised if {@code BigDecimal} objects
199 * are used as keys in a {@link java.util.SortedMap SortedMap} or
200 * elements in a {@link java.util.SortedSet SortedSet} since
201 * {@code BigDecimal}'s <i>natural ordering</i> is <i>inconsistent
202 * with equals</i>. See {@link Comparable}, {@link
203 * java.util.SortedMap} or {@link java.util.SortedSet} for more
204 * information.
205 *
206 * <p>All methods and constructors for this class throw
207 * {@code NullPointerException} when passed a {@code null} object
208 * reference for any input parameter.
209 *
210 * @see BigInteger
211 * @see MathContext
212 * @see RoundingMode
213 * @see java.util.SortedMap
214 * @see java.util.SortedSet
215 * @author Josh Bloch
216 * @author Mike Cowlishaw
217 * @author Joseph D. Darcy
218 */
219 public class BigDecimal extends Number implements Comparable<BigDecimal> {
220 /**
221 * The unscaled value of this BigDecimal, as returned by {@link
222 * #unscaledValue}.
223 *
224 * @serial
225 * @see #unscaledValue
226 */
227 private final BigInteger intVal;
228
229 /**
230 * The scale of this BigDecimal, as returned by {@link #scale}.
231 *
232 * @serial
233 * @see #scale
234 */
235 private final int scale; // Note: this may have any value, so
236 // calculations must be done in longs
237
238 /**
239 * The number of decimal digits in this BigDecimal, or 0 if the
240 * number of digits are not known (lookaside information). If
241 * nonzero, the value is guaranteed correct. Use the precision()
242 * method to obtain and set the value if it might be 0. This
243 * field is mutable until set nonzero.
244 *
245 * @since 1.5
246 */
247 private transient int precision;
248
249 /**
250 * Used to store the canonical string representation, if computed.
251 */
252 private transient String stringCache;
253
254 /**
255 * Sentinel value for {@link #intCompact} indicating the
256 * significand information is only available from {@code intVal}.
257 */
258 static final long INFLATED = Long.MIN_VALUE;
259
260 private static final BigInteger INFLATED_BIGINT = BigInteger.valueOf(INFLATED);
261
262 /**
263 * If the absolute value of the significand of this BigDecimal is
264 * less than or equal to {@code Long.MAX_VALUE}, the value can be
265 * compactly stored in this field and used in computations.
266 */
267 private final transient long intCompact;
268
269 // All 18-digit base ten strings fit into a long; not all 19-digit
270 // strings will
271 private static final int MAX_COMPACT_DIGITS = 18;
272
273 /* Appease the serialization gods */
274 private static final long serialVersionUID = 6108874887143696463L;
275
276 private static final ThreadLocal<StringBuilderHelper>
277 threadLocalStringBuilderHelper = new ThreadLocal<StringBuilderHelper>() {
278 @Override
279 protected StringBuilderHelper initialValue() {
280 return new StringBuilderHelper();
281 }
282 };
283
284 // Cache of common small BigDecimal values.
285 private static final BigDecimal zeroThroughTen[] = {
286 new BigDecimal(BigInteger.ZERO, 0, 0, 1),
287 new BigDecimal(BigInteger.ONE, 1, 0, 1),
288 new BigDecimal(BigInteger.valueOf(2), 2, 0, 1),
289 new BigDecimal(BigInteger.valueOf(3), 3, 0, 1),
290 new BigDecimal(BigInteger.valueOf(4), 4, 0, 1),
291 new BigDecimal(BigInteger.valueOf(5), 5, 0, 1),
292 new BigDecimal(BigInteger.valueOf(6), 6, 0, 1),
293 new BigDecimal(BigInteger.valueOf(7), 7, 0, 1),
294 new BigDecimal(BigInteger.valueOf(8), 8, 0, 1),
295 new BigDecimal(BigInteger.valueOf(9), 9, 0, 1),
296 new BigDecimal(BigInteger.TEN, 10, 0, 2),
297 };
298
299 // Cache of zero scaled by 0 - 15
300 private static final BigDecimal[] ZERO_SCALED_BY = {
301 zeroThroughTen[0],
302 new BigDecimal(BigInteger.ZERO, 0, 1, 1),
303 new BigDecimal(BigInteger.ZERO, 0, 2, 1),
304 new BigDecimal(BigInteger.ZERO, 0, 3, 1),
305 new BigDecimal(BigInteger.ZERO, 0, 4, 1),
306 new BigDecimal(BigInteger.ZERO, 0, 5, 1),
307 new BigDecimal(BigInteger.ZERO, 0, 6, 1),
308 new BigDecimal(BigInteger.ZERO, 0, 7, 1),
309 new BigDecimal(BigInteger.ZERO, 0, 8, 1),
310 new BigDecimal(BigInteger.ZERO, 0, 9, 1),
311 new BigDecimal(BigInteger.ZERO, 0, 10, 1),
312 new BigDecimal(BigInteger.ZERO, 0, 11, 1),
313 new BigDecimal(BigInteger.ZERO, 0, 12, 1),
314 new BigDecimal(BigInteger.ZERO, 0, 13, 1),
315 new BigDecimal(BigInteger.ZERO, 0, 14, 1),
316 new BigDecimal(BigInteger.ZERO, 0, 15, 1),
317 };
318
319 // Half of Long.MIN_VALUE & Long.MAX_VALUE.
320 private static final long HALF_LONG_MAX_VALUE = Long.MAX_VALUE / 2;
321 private static final long HALF_LONG_MIN_VALUE = Long.MIN_VALUE / 2;
322
323 // Constants
324 /**
325 * The value 0, with a scale of 0.
326 *
327 * @since 1.5
328 */
329 public static final BigDecimal ZERO =
330 zeroThroughTen[0];
331
332 /**
333 * The value 1, with a scale of 0.
334 *
335 * @since 1.5
336 */
337 public static final BigDecimal ONE =
338 zeroThroughTen[1];
339
340 /**
341 * The value 10, with a scale of 0.
342 *
343 * @since 1.5
344 */
345 public static final BigDecimal TEN =
346 zeroThroughTen[10];
347
348 // Constructors
349
350 /**
351 * Trusted package private constructor.
352 * Trusted simply means if val is INFLATED, intVal could not be null and
353 * if intVal is null, val could not be INFLATED.
354 */
355 BigDecimal(BigInteger intVal, long val, int scale, int prec) {
356 this.scale = scale;
357 this.precision = prec;
358 this.intCompact = val;
359 this.intVal = intVal;
360 }
361
362 /**
363 * Translates a character array representation of a
364 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
365 * same sequence of characters as the {@link #BigDecimal(String)}
366 * constructor, while allowing a sub-array to be specified.
367 *
368 * <p>Note that if the sequence of characters is already available
369 * within a character array, using this constructor is faster than
370 * converting the {@code char} array to string and using the
371 * {@code BigDecimal(String)} constructor .
372 *
373 * @param in {@code char} array that is the source of characters.
374 * @param offset first character in the array to inspect.
375 * @param len number of characters to consider.
376 * @throws NumberFormatException if {@code in} is not a valid
377 * representation of a {@code BigDecimal} or the defined subarray
378 * is not wholly within {@code in}.
379 * @since 1.5
380 */
381 public BigDecimal(char[] in, int offset, int len) {
382 this(in,offset,len,MathContext.UNLIMITED);
383 }
384
385 /**
386 * Translates a character array representation of a
387 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
388 * same sequence of characters as the {@link #BigDecimal(String)}
389 * constructor, while allowing a sub-array to be specified and
390 * with rounding according to the context settings.
391 *
392 * <p>Note that if the sequence of characters is already available
393 * within a character array, using this constructor is faster than
394 * converting the {@code char} array to string and using the
395 * {@code BigDecimal(String)} constructor .
396 *
397 * @param in {@code char} array that is the source of characters.
398 * @param offset first character in the array to inspect.
399 * @param len number of characters to consider..
400 * @param mc the context to use.
401 * @throws ArithmeticException if the result is inexact but the
402 * rounding mode is {@code UNNECESSARY}.
403 * @throws NumberFormatException if {@code in} is not a valid
404 * representation of a {@code BigDecimal} or the defined subarray
405 * is not wholly within {@code in}.
406 * @since 1.5
407 */
408 public BigDecimal(char[] in, int offset, int len, MathContext mc) {
409 // protect against huge length.
410 if (offset + len > in.length || offset < 0)
411 throw new NumberFormatException();
412 // This is the primary string to BigDecimal constructor; all
413 // incoming strings end up here; it uses explicit (inline)
414 // parsing for speed and generates at most one intermediate
415 // (temporary) object (a char[] array) for non-compact case.
416
417 // Use locals for all fields values until completion
418 int prec = 0; // record precision value
419 int scl = 0; // record scale value
420 long rs = 0; // the compact value in long
421 BigInteger rb = null; // the inflated value in BigInteger
422 // use array bounds checking to handle too-long, len == 0,
423 // bad offset, etc.
424 try {
425 // handle the sign
426 boolean isneg = false; // assume positive
427 if (in[offset] == '-') {
428 isneg = true; // leading minus means negative
429 offset++;
430 len--;
431 } else if (in[offset] == '+') { // leading + allowed
432 offset++;
433 len--;
434 }
435
436 // should now be at numeric part of the significand
437 // int cfirst = offset; // record start of integer
438 long exp = 0; // exponent
439 char c; // current character
440 boolean dot = false; // true when there is a '.'
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;
506 if (mcp > 0 && (drop = prec - mcp) > 0) { // do rounding
507 while (drop > 0) {
508 scl = checkScaleNonZero((long) scl - drop);
509 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
510 prec = longDigitLength(rs);
511 drop = prec - mcp;
512 }
513 }
514 } else {
515 char coeff[] = new char[len];
516 for (; len > 0; offset++, len--) {
517 c = in[offset];
518 // have digit
519 if ((c >= '0' && c <= '9') || Character.isDigit(c)) {
520 // First compact case, we need not to preserve the character
521 // and we can just compute the value in place.
522 if (c == '0' || Character.digit(c, 10) == 0) {
523 if (prec == 0) {
524 coeff[idx] = c;
525 prec = 1;
526 } else if (idx != 0) {
527 coeff[idx++] = c;
528 ++prec;
529 } // else c must be a redundant leading zero
530 } else {
531 if (prec != 1 || idx != 0)
532 ++prec; // prec unchanged if preceded by 0s
533 coeff[idx++] = c;
534 }
535 if (dot)
536 ++scl;
537 continue;
538 }
539 // have dot
540 if (c == '.') {
541 // have dot
542 if (dot) // two dots
543 throw new NumberFormatException();
544 dot = true;
545 continue;
546 }
547 // exponent expected
548 if ((c != 'e') && (c != 'E'))
549 throw new NumberFormatException();
550 exp = parseExp(in, offset, len);
551 // Next test is required for backwards compatibility
552 if ((int) exp != exp) // overflow
553 throw new NumberFormatException();
554 break; // [saves a test]
555 }
556 // here when no characters left
557 if (prec == 0) // no digits found
558 throw new NumberFormatException();
559 // Adjust scale if exp is not zero.
560 if (exp != 0) { // had significant exponent
561 scl = adjustScale(scl, exp);
562 }
563 // Remove leading zeros from precision (digits count)
564 rb = new BigInteger(coeff, isneg ? -1 : 1, prec);
565 rs = compactValFor(rb);
566 int mcp = mc.precision;
567 if (mcp > 0 && (prec > mcp)) {
568 if (rs == INFLATED) {
569 int drop = prec - mcp;
570 while (drop > 0) {
571 scl = checkScaleNonZero((long) scl - drop);
572 rb = divideAndRoundByTenPow(rb, drop, mc.roundingMode.oldMode);
573 rs = compactValFor(rb);
574 if (rs != INFLATED) {
575 prec = longDigitLength(rs);
576 break;
577 }
578 prec = bigDigitLength(rb);
579 drop = prec - mcp;
580 }
581 }
582 if (rs != INFLATED) {
583 int drop = prec - mcp;
584 while (drop > 0) {
585 scl = checkScaleNonZero((long) scl - drop);
586 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
587 prec = longDigitLength(rs);
588 drop = prec - mcp;
589 }
590 rb = null;
591 }
592 }
593 }
594 } catch (ArrayIndexOutOfBoundsException e) {
595 throw new NumberFormatException();
596 } catch (NegativeArraySizeException e) {
597 throw new NumberFormatException();
598 }
599 this.scale = scl;
600 this.precision = prec;
601 this.intCompact = rs;
602 this.intVal = rb;
603 }
604
605 private int adjustScale(int scl, long exp) {
606 long adjustedScale = scl - exp;
607 if (adjustedScale > Integer.MAX_VALUE || adjustedScale < Integer.MIN_VALUE)
608 throw new NumberFormatException("Scale out of range.");
609 scl = (int) adjustedScale;
610 return scl;
611 }
612
613 /*
614 * parse exponent
615 */
616 private static long parseExp(char[] in, int offset, int len){
617 long exp = 0;
618 offset++;
619 char c = in[offset];
620 len--;
621 boolean negexp = (c == '-');
622 // optional sign
623 if (negexp || c == '+') {
624 offset++;
625 c = in[offset];
626 len--;
627 }
628 if (len <= 0) // no exponent digits
629 throw new NumberFormatException();
630 // skip leading zeros in the exponent
631 while (len > 10 && (c=='0' || (Character.digit(c, 10) == 0))) {
632 offset++;
633 c = in[offset];
634 len--;
635 }
636 if (len > 10) // too many nonzero exponent digits
637 throw new NumberFormatException();
638 // c now holds first digit of exponent
639 for (;; len--) {
640 int v;
641 if (c >= '0' && c <= '9') {
642 v = c - '0';
643 } else {
644 v = Character.digit(c, 10);
645 if (v < 0) // not a digit
646 throw new NumberFormatException();
647 }
648 exp = exp * 10 + v;
649 if (len == 1)
650 break; // that was final character
651 offset++;
652 c = in[offset];
653 }
654 if (negexp) // apply sign
655 exp = -exp;
656 return exp;
657 }
658
659 /**
660 * Translates a character array representation of a
661 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
662 * same sequence of characters as the {@link #BigDecimal(String)}
663 * constructor.
664 *
665 * <p>Note that if the sequence of characters is already available
666 * as a character array, using this constructor is faster than
667 * converting the {@code char} array to string and using the
668 * {@code BigDecimal(String)} constructor .
669 *
670 * @param in {@code char} array that is the source of characters.
671 * @throws NumberFormatException if {@code in} is not a valid
672 * representation of a {@code BigDecimal}.
673 * @since 1.5
674 */
675 public BigDecimal(char[] in) {
676 this(in, 0, in.length);
677 }
678
679 /**
680 * Translates a character array representation of a
681 * {@code BigDecimal} into a {@code BigDecimal}, accepting the
682 * same sequence of characters as the {@link #BigDecimal(String)}
683 * constructor and with rounding according to the context
684 * settings.
685 *
686 * <p>Note that if the sequence of characters is already available
687 * as a character array, using this constructor is faster than
688 * converting the {@code char} array to string and using the
689 * {@code BigDecimal(String)} constructor .
690 *
691 * @param in {@code char} array that is the source of characters.
692 * @param mc the context to use.
693 * @throws ArithmeticException if the result is inexact but the
694 * rounding mode is {@code UNNECESSARY}.
695 * @throws NumberFormatException if {@code in} is not a valid
696 * representation of a {@code BigDecimal}.
697 * @since 1.5
698 */
699 public BigDecimal(char[] in, MathContext mc) {
700 this(in, 0, in.length, mc);
701 }
702
703 /**
704 * Translates the string representation of a {@code BigDecimal}
705 * into a {@code BigDecimal}. The string representation consists
706 * of an optional sign, {@code '+'} (<tt> '\u002B'</tt>) or
707 * {@code '-'} (<tt>'\u002D'</tt>), followed by a sequence of
708 * zero or more decimal digits ("the integer"), optionally
709 * followed by a fraction, optionally followed by an exponent.
710 *
711 * <p>The fraction consists of a decimal point followed by zero
712 * or more decimal digits. The string must contain at least one
713 * digit in either the integer or the fraction. The number formed
714 * by the sign, the integer and the fraction is referred to as the
715 * <i>significand</i>.
716 *
717 * <p>The exponent consists of the character {@code 'e'}
718 * (<tt>'\u0065'</tt>) or {@code 'E'} (<tt>'\u0045'</tt>)
719 * followed by one or more decimal digits. The value of the
720 * exponent must lie between -{@link Integer#MAX_VALUE} ({@link
721 * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive.
722 *
723 * <p>More formally, the strings this constructor accepts are
724 * described by the following grammar:
725 * <blockquote>
726 * <dl>
727 * <dt><i>BigDecimalString:</i>
728 * <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i>
729 * <p>
730 * <dt><i>Sign:</i>
731 * <dd>{@code +}
732 * <dd>{@code -}
733 * <p>
734 * <dt><i>Significand:</i>
735 * <dd><i>IntegerPart</i> {@code .} <i>FractionPart<sub>opt</sub></i>
736 * <dd>{@code .} <i>FractionPart</i>
737 * <dd><i>IntegerPart</i>
738 * <p>
739 * <dt><i>IntegerPart:</i>
740 * <dd><i>Digits</i>
741 * <p>
742 * <dt><i>FractionPart:</i>
743 * <dd><i>Digits</i>
744 * <p>
745 * <dt><i>Exponent:</i>
746 * <dd><i>ExponentIndicator SignedInteger</i>
747 * <p>
748 * <dt><i>ExponentIndicator:</i>
749 * <dd>{@code e}
750 * <dd>{@code E}
751 * <p>
752 * <dt><i>SignedInteger:</i>
753 * <dd><i>Sign<sub>opt</sub> Digits</i>
754 * <p>
755 * <dt><i>Digits:</i>
756 * <dd><i>Digit</i>
757 * <dd><i>Digits Digit</i>
758 * <p>
759 * <dt><i>Digit:</i>
760 * <dd>any character for which {@link Character#isDigit}
761 * returns {@code true}, including 0, 1, 2 ...
762 * </dl>
763 * </blockquote>
764 *
765 * <p>The scale of the returned {@code BigDecimal} will be the
766 * number of digits in the fraction, or zero if the string
767 * contains no decimal point, subject to adjustment for any
768 * exponent; if the string contains an exponent, the exponent is
769 * subtracted from the scale. The value of the resulting scale
770 * must lie between {@code Integer.MIN_VALUE} and
771 * {@code Integer.MAX_VALUE}, inclusive.
772 *
773 * <p>The character-to-digit mapping is provided by {@link
774 * java.lang.Character#digit} set to convert to radix 10. The
775 * String may not contain any extraneous characters (whitespace,
776 * for example).
777 *
778 * <p><b>Examples:</b><br>
779 * The value of the returned {@code BigDecimal} is equal to
780 * <i>significand</i> × 10<sup> <i>exponent</i></sup>.
781 * For each string on the left, the resulting representation
782 * [{@code BigInteger}, {@code scale}] is shown on the right.
783 * <pre>
784 * "0" [0,0]
785 * "0.00" [0,2]
786 * "123" [123,0]
787 * "-123" [-123,0]
788 * "1.23E3" [123,-1]
789 * "1.23E+3" [123,-1]
790 * "12.3E+7" [123,-6]
791 * "12.0" [120,1]
792 * "12.3" [123,1]
793 * "0.00123" [123,5]
794 * "-1.23E-12" [-123,14]
795 * "1234.5E-4" [12345,5]
796 * "0E+7" [0,-7]
797 * "-0" [0,0]
798 * </pre>
799 *
800 * <p>Note: For values other than {@code float} and
801 * {@code double} NaN and ±Infinity, this constructor is
802 * compatible with the values returned by {@link Float#toString}
803 * and {@link Double#toString}. This is generally the preferred
804 * way to convert a {@code float} or {@code double} into a
805 * BigDecimal, as it doesn't suffer from the unpredictability of
806 * the {@link #BigDecimal(double)} constructor.
807 *
808 * @param val String representation of {@code BigDecimal}.
809 *
810 * @throws NumberFormatException if {@code val} is not a valid
811 * representation of a {@code BigDecimal}.
812 */
813 public BigDecimal(String val) {
814 this(val.toCharArray(), 0, val.length());
815 }
816
817 /**
818 * Translates the string representation of a {@code BigDecimal}
819 * into a {@code BigDecimal}, accepting the same strings as the
820 * {@link #BigDecimal(String)} constructor, with rounding
821 * according to the context settings.
822 *
823 * @param val string representation of a {@code BigDecimal}.
824 * @param mc the context to use.
825 * @throws ArithmeticException if the result is inexact but the
826 * rounding mode is {@code UNNECESSARY}.
827 * @throws NumberFormatException if {@code val} is not a valid
828 * representation of a BigDecimal.
829 * @since 1.5
830 */
831 public BigDecimal(String val, MathContext mc) {
832 this(val.toCharArray(), 0, val.length(), mc);
833 }
834
835 /**
836 * Translates a {@code double} into a {@code BigDecimal} which
837 * is the exact decimal representation of the {@code double}'s
838 * binary floating-point value. The scale of the returned
839 * {@code BigDecimal} is the smallest value such that
840 * <tt>(10<sup>scale</sup> × val)</tt> is an integer.
841 * <p>
842 * <b>Notes:</b>
843 * <ol>
844 * <li>
845 * The results of this constructor can be somewhat unpredictable.
846 * One might assume that writing {@code new BigDecimal(0.1)} in
847 * Java creates a {@code BigDecimal} which is exactly equal to
848 * 0.1 (an unscaled value of 1, with a scale of 1), but it is
849 * actually equal to
850 * 0.1000000000000000055511151231257827021181583404541015625.
851 * This is because 0.1 cannot be represented exactly as a
852 * {@code double} (or, for that matter, as a binary fraction of
853 * any finite length). Thus, the value that is being passed
854 * <i>in</i> to the constructor is not exactly equal to 0.1,
855 * appearances notwithstanding.
856 *
857 * <li>
858 * The {@code String} constructor, on the other hand, is
859 * perfectly predictable: writing {@code new BigDecimal("0.1")}
860 * creates a {@code BigDecimal} which is <i>exactly</i> equal to
861 * 0.1, as one would expect. Therefore, it is generally
862 * recommended that the {@linkplain #BigDecimal(String)
863 * <tt>String</tt> constructor} be used in preference to this one.
864 *
865 * <li>
866 * When a {@code double} must be used as a source for a
867 * {@code BigDecimal}, note that this constructor provides an
868 * exact conversion; it does not give the same result as
869 * converting the {@code double} to a {@code String} using the
870 * {@link Double#toString(double)} method and then using the
871 * {@link #BigDecimal(String)} constructor. To get that result,
872 * use the {@code static} {@link #valueOf(double)} method.
873 * </ol>
874 *
875 * @param val {@code double} value to be converted to
876 * {@code BigDecimal}.
877 * @throws NumberFormatException if {@code val} is infinite or NaN.
878 */
879 public BigDecimal(double val) {
880 this(val,MathContext.UNLIMITED);
881 }
882
883 /**
884 * Translates a {@code double} into a {@code BigDecimal}, with
885 * rounding according to the context settings. The scale of the
886 * {@code BigDecimal} is the smallest value such that
887 * <tt>(10<sup>scale</sup> × val)</tt> is an integer.
888 *
889 * <p>The results of this constructor can be somewhat unpredictable
890 * and its use is generally not recommended; see the notes under
891 * the {@link #BigDecimal(double)} constructor.
892 *
893 * @param val {@code double} value to be converted to
894 * {@code BigDecimal}.
895 * @param mc the context to use.
896 * @throws ArithmeticException if the result is inexact but the
897 * RoundingMode is UNNECESSARY.
898 * @throws NumberFormatException if {@code val} is infinite or NaN.
899 * @since 1.5
900 */
901 public BigDecimal(double val, MathContext mc) {
902 if (Double.isInfinite(val) || Double.isNaN(val))
903 throw new NumberFormatException("Infinite or NaN");
904 // Translate the double into sign, exponent and significand, according
905 // to the formulae in JLS, Section 20.10.22.
906 long valBits = Double.doubleToLongBits(val);
907 int sign = ((valBits >> 63) == 0 ? 1 : -1);
908 int exponent = (int) ((valBits >> 52) & 0x7ffL);
909 long significand = (exponent == 0
910 ? (valBits & ((1L << 52) - 1)) << 1
911 : (valBits & ((1L << 52) - 1)) | (1L << 52));
912 exponent -= 1075;
913 // At this point, val == sign * significand * 2**exponent.
914
915 /*
916 * Special case zero to supress nonterminating normalization and bogus
917 * scale calculation.
918 */
919 if (significand == 0) {
920 this.intVal = BigInteger.ZERO;
921 this.scale = 0;
922 this.intCompact = 0;
923 this.precision = 1;
924 return;
925 }
926 // Normalize
927 while ((significand & 1) == 0) { // i.e., significand is even
928 significand >>= 1;
929 exponent++;
930 }
931 int scale = 0;
932 // Calculate intVal and scale
933 BigInteger intVal;
934 long compactVal = sign * significand;
935 if (exponent == 0) {
936 intVal = (compactVal == INFLATED) ? INFLATED_BIGINT : null;
937 } else {
938 if (exponent < 0) {
939 intVal = BigInteger.valueOf(5).pow(-exponent).multiply(compactVal);
940 scale = -exponent;
941 } else { // (exponent > 0)
942 intVal = BigInteger.valueOf(2).pow(exponent).multiply(compactVal);
943 }
944 compactVal = compactValFor(intVal);
945 }
946 int prec = 0;
947 int mcp = mc.precision;
948 if (mcp > 0) { // do rounding
949 int mode = mc.roundingMode.oldMode;
950 int drop;
951 if (compactVal == INFLATED) {
952 prec = bigDigitLength(intVal);
953 drop = prec - mcp;
954 while (drop > 0) {
955 scale = checkScaleNonZero((long) scale - drop);
956 intVal = divideAndRoundByTenPow(intVal, drop, mode);
957 compactVal = compactValFor(intVal);
958 if (compactVal != INFLATED) {
959 break;
960 }
961 prec = bigDigitLength(intVal);
962 drop = prec - mcp;
963 }
964 }
965 if (compactVal != INFLATED) {
966 prec = longDigitLength(compactVal);
967 drop = prec - mcp;
968 while (drop > 0) {
969 scale = checkScaleNonZero((long) scale - drop);
970 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
971 prec = longDigitLength(compactVal);
972 drop = prec - mcp;
973 }
974 intVal = null;
975 }
976 }
977 this.intVal = intVal;
978 this.intCompact = compactVal;
979 this.scale = scale;
980 this.precision = prec;
981 }
982
983 /**
984 * Translates a {@code BigInteger} into a {@code BigDecimal}.
985 * The scale of the {@code BigDecimal} is zero.
986 *
987 * @param val {@code BigInteger} value to be converted to
988 * {@code BigDecimal}.
989 */
990 public BigDecimal(BigInteger val) {
991 scale = 0;
992 intVal = val;
993 intCompact = compactValFor(val);
994 }
995
996 /**
997 * Translates a {@code BigInteger} into a {@code BigDecimal}
998 * rounding according to the context settings. The scale of the
999 * {@code BigDecimal} is zero.
1000 *
1001 * @param val {@code BigInteger} value to be converted to
1002 * {@code BigDecimal}.
1003 * @param mc the context to use.
1004 * @throws ArithmeticException if the result is inexact but the
1005 * rounding mode is {@code UNNECESSARY}.
1006 * @since 1.5
1007 */
1008 public BigDecimal(BigInteger val, MathContext mc) {
1009 this(val,0,mc);
1010 }
1011
1012 /**
1013 * Translates a {@code BigInteger} unscaled value and an
1014 * {@code int} scale into a {@code BigDecimal}. The value of
1015 * the {@code BigDecimal} is
1016 * <tt>(unscaledVal × 10<sup>-scale</sup>)</tt>.
1017 *
1018 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1019 * @param scale scale of the {@code BigDecimal}.
1020 */
1021 public BigDecimal(BigInteger unscaledVal, int scale) {
1022 // Negative scales are now allowed
1023 this.intVal = unscaledVal;
1024 this.intCompact = compactValFor(unscaledVal);
1025 this.scale = scale;
1026 }
1027
1028 /**
1029 * Translates a {@code BigInteger} unscaled value and an
1030 * {@code int} scale into a {@code BigDecimal}, with rounding
1031 * according to the context settings. The value of the
1032 * {@code BigDecimal} is <tt>(unscaledVal ×
1033 * 10<sup>-scale</sup>)</tt>, rounded according to the
1034 * {@code precision} and rounding mode settings.
1035 *
1036 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1037 * @param scale scale of the {@code BigDecimal}.
1038 * @param mc the context to use.
1039 * @throws ArithmeticException if the result is inexact but the
1040 * rounding mode is {@code UNNECESSARY}.
1041 * @since 1.5
1042 */
1043 public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {
1044 long compactVal = compactValFor(unscaledVal);
1045 int mcp = mc.precision;
1046 int prec = 0;
1047 if (mcp > 0) { // do rounding
1048 int mode = mc.roundingMode.oldMode;
1049 if (compactVal == INFLATED) {
1050 prec = bigDigitLength(unscaledVal);
1051 int drop = prec - mcp;
1052 while (drop > 0) {
1053 scale = checkScaleNonZero((long) scale - drop);
1054 unscaledVal = divideAndRoundByTenPow(unscaledVal, drop, mode);
1055 compactVal = compactValFor(unscaledVal);
1056 if (compactVal != INFLATED) {
1057 break;
1058 }
1059 prec = bigDigitLength(unscaledVal);
1060 drop = prec - mcp;
1061 }
1062 }
1063 if (compactVal != INFLATED) {
1064 prec = longDigitLength(compactVal);
1065 int drop = prec - mcp; // drop can't be more than 18
1066 while (drop > 0) {
1067 scale = checkScaleNonZero((long) scale - drop);
1068 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mode);
1069 prec = longDigitLength(compactVal);
1070 drop = prec - mcp;
1071 }
1072 unscaledVal = null;
1073 }
1074 }
1075 this.intVal = unscaledVal;
1076 this.intCompact = compactVal;
1077 this.scale = scale;
1078 this.precision = prec;
1079 }
1080
1081 /**
1082 * Translates an {@code int} into a {@code BigDecimal}. The
1083 * scale of the {@code BigDecimal} is zero.
1084 *
1085 * @param val {@code int} value to be converted to
1086 * {@code BigDecimal}.
1087 * @since 1.5
1088 */
1089 public BigDecimal(int val) {
1090 this.intCompact = val;
1091 this.scale = 0;
1092 this.intVal = null;
1093 }
1094
1095 /**
1096 * Translates an {@code int} into a {@code BigDecimal}, with
1097 * rounding according to the context settings. The scale of the
1098 * {@code BigDecimal}, before any rounding, is zero.
1099 *
1100 * @param val {@code int} value to be converted to {@code BigDecimal}.
1101 * @param mc the context to use.
1102 * @throws ArithmeticException if the result is inexact but the
1103 * rounding mode is {@code UNNECESSARY}.
1104 * @since 1.5
1105 */
1106 public BigDecimal(int val, MathContext mc) {
1107 int mcp = mc.precision;
1108 long compactVal = val;
1109 int scale = 0;
1110 int prec = 0;
1111 if (mcp > 0) { // do rounding
1112 prec = longDigitLength(compactVal);
1113 int drop = prec - mcp; // drop can't be more than 18
1114 while (drop > 0) {
1115 scale = checkScaleNonZero((long) scale - drop);
1116 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1117 prec = longDigitLength(compactVal);
1118 drop = prec - mcp;
1119 }
1120 }
1121 this.intVal = null;
1122 this.intCompact = compactVal;
1123 this.scale = scale;
1124 this.precision = prec;
1125 }
1126
1127 /**
1128 * Translates a {@code long} into a {@code BigDecimal}. The
1129 * scale of the {@code BigDecimal} is zero.
1130 *
1131 * @param val {@code long} value to be converted to {@code BigDecimal}.
1132 * @since 1.5
1133 */
1134 public BigDecimal(long val) {
1135 this.intCompact = val;
1136 this.intVal = (val == INFLATED) ? INFLATED_BIGINT : null;
1137 this.scale = 0;
1138 }
1139
1140 /**
1141 * Translates a {@code long} into a {@code BigDecimal}, with
1142 * rounding according to the context settings. The scale of the
1143 * {@code BigDecimal}, before any rounding, is zero.
1144 *
1145 * @param val {@code long} value to be converted to {@code BigDecimal}.
1146 * @param mc the context to use.
1147 * @throws ArithmeticException if the result is inexact but the
1148 * rounding mode is {@code UNNECESSARY}.
1149 * @since 1.5
1150 */
1151 public BigDecimal(long val, MathContext mc) {
1152 int mcp = mc.precision;
1153 int mode = mc.roundingMode.oldMode;
1154 int prec = 0;
1155 int scale = 0;
1156 BigInteger intVal = (val == INFLATED) ? INFLATED_BIGINT : null;
1157 if (mcp > 0) { // do rounding
1158 if (val == INFLATED) {
1159 prec = 19;
1160 int drop = prec - mcp;
1161 while (drop > 0) {
1162 scale = checkScaleNonZero((long) scale - drop);
1163 intVal = divideAndRoundByTenPow(intVal, drop, mode);
1164 val = compactValFor(intVal);
1165 if (val != INFLATED) {
1166 break;
1167 }
1168 prec = bigDigitLength(intVal);
1169 drop = prec - mcp;
1170 }
1171 }
1172 if (val != INFLATED) {
1173 prec = longDigitLength(val);
1174 int drop = prec - mcp;
1175 while (drop > 0) {
1176 scale = checkScaleNonZero((long) scale - drop);
1177 val = divideAndRound(val, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
1178 prec = longDigitLength(val);
1179 drop = prec - mcp;
1180 }
1181 intVal = null;
1182 }
1183 }
1184 this.intVal = intVal;
1185 this.intCompact = val;
1186 this.scale = scale;
1187 this.precision = prec;
1188 }
1189
1190 // Static Factory Methods
1191
1192 /**
1193 * Translates a {@code long} unscaled value and an
1194 * {@code int} scale into a {@code BigDecimal}. This
1195 * {@literal "static factory method"} is provided in preference to
1196 * a ({@code long}, {@code int}) constructor because it
1197 * allows for reuse of frequently used {@code BigDecimal} values..
1198 *
1199 * @param unscaledVal unscaled value of the {@code BigDecimal}.
1200 * @param scale scale of the {@code BigDecimal}.
1201 * @return a {@code BigDecimal} whose value is
1202 * <tt>(unscaledVal × 10<sup>-scale</sup>)</tt>.
1203 */
1204 public static BigDecimal valueOf(long unscaledVal, int scale) {
1205 if (scale == 0)
1206 return valueOf(unscaledVal);
1207 else if (unscaledVal == 0) {
1208 return zeroValueOf(scale);
1209 }
1210 return new BigDecimal(unscaledVal == INFLATED ?
1211 INFLATED_BIGINT : null,
1212 unscaledVal, scale, 0);
1213 }
1214
1215 /**
1216 * Translates a {@code long} value into a {@code BigDecimal}
1217 * with a scale of zero. This {@literal "static factory method"}
1218 * is provided in preference to a ({@code long}) constructor
1219 * because it allows for reuse of frequently used
1220 * {@code BigDecimal} values.
1221 *
1222 * @param val value of the {@code BigDecimal}.
1223 * @return a {@code BigDecimal} whose value is {@code val}.
1224 */
1225 public static BigDecimal valueOf(long val) {
1226 if (val >= 0 && val < zeroThroughTen.length)
1227 return zeroThroughTen[(int)val];
1228 else if (val != INFLATED)
1229 return new BigDecimal(null, val, 0, 0);
1230 return new BigDecimal(INFLATED_BIGINT, val, 0, 0);
1231 }
1232
1233 static BigDecimal valueOf(long unscaledVal, int scale, int prec) {
1234 if (scale == 0 && unscaledVal >= 0 && unscaledVal < zeroThroughTen.length) {
1235 return zeroThroughTen[(int) unscaledVal];
1236 } else if (unscaledVal == 0) {
1237 return zeroValueOf(scale);
1238 }
1239 return new BigDecimal(unscaledVal == INFLATED ? INFLATED_BIGINT : null,
1240 unscaledVal, scale, prec);
1241 }
1242
1243 static BigDecimal valueOf(BigInteger intVal, int scale, int prec) {
1244 long val = compactValFor(intVal);
1245 if (val == 0) {
1246 return zeroValueOf(scale);
1247 } else if (scale == 0 && val >= 0 && val < zeroThroughTen.length) {
1248 return zeroThroughTen[(int) val];
1249 }
1250 return new BigDecimal(intVal, val, scale, prec);
1251 }
1252
1253 static BigDecimal zeroValueOf(int scale) {
1254 if (scale >= 0 && scale < ZERO_SCALED_BY.length)
1255 return ZERO_SCALED_BY[scale];
1256 else
1257 return new BigDecimal(BigInteger.ZERO, 0, scale, 1);
1258 }
1259
1260 /**
1261 * Translates a {@code double} into a {@code BigDecimal}, using
1262 * the {@code double}'s canonical string representation provided
1263 * by the {@link Double#toString(double)} method.
1264 *
1265 * <p><b>Note:</b> This is generally the preferred way to convert
1266 * a {@code double} (or {@code float}) into a
1267 * {@code BigDecimal}, as the value returned is equal to that
1268 * resulting from constructing a {@code BigDecimal} from the
1269 * result of using {@link Double#toString(double)}.
1270 *
1271 * @param val {@code double} to convert to a {@code BigDecimal}.
1272 * @return a {@code BigDecimal} whose value is equal to or approximately
1273 * equal to the value of {@code val}.
1274 * @throws NumberFormatException if {@code val} is infinite or NaN.
1275 * @since 1.5
1276 */
1277 public static BigDecimal valueOf(double val) {
1278 // Reminder: a zero double returns '0.0', so we cannot fastpath
1279 // to use the constant ZERO. This might be important enough to
1280 // justify a factory approach, a cache, or a few private
1281 // constants, later.
1282 return new BigDecimal(Double.toString(val));
1283 }
1284
1285 // Arithmetic Operations
1286 /**
1287 * Returns a {@code BigDecimal} whose value is {@code (this +
1288 * augend)}, and whose scale is {@code max(this.scale(),
1289 * augend.scale())}.
1290 *
1291 * @param augend value to be added to this {@code BigDecimal}.
1292 * @return {@code this + augend}
1293 */
1294 public BigDecimal add(BigDecimal augend) {
1295 if (this.intCompact != INFLATED) {
1296 if ((augend.intCompact != INFLATED)) {
1297 return add(this.intCompact, this.scale, augend.intCompact, augend.scale);
1298 } else {
1299 return add(this.intCompact, this.scale, augend.intVal, augend.scale);
1300 }
1301 } else {
1302 if ((augend.intCompact != INFLATED)) {
1303 return add(augend.intCompact, augend.scale, this.intVal, this.scale);
1304 } else {
1305 return add(this.intVal, this.scale, augend.intVal, augend.scale);
1306 }
1307 }
1308 }
1309
1310 /**
1311 * Returns a {@code BigDecimal} whose value is {@code (this + augend)},
1312 * with rounding according to the context settings.
1313 *
1314 * If either number is zero and the precision setting is nonzero then
1315 * the other number, rounded if necessary, is used as the result.
1316 *
1317 * @param augend value to be added to this {@code BigDecimal}.
1318 * @param mc the context to use.
1319 * @return {@code this + augend}, rounded as necessary.
1320 * @throws ArithmeticException if the result is inexact but the
1321 * rounding mode is {@code UNNECESSARY}.
1322 * @since 1.5
1323 */
1324 public BigDecimal add(BigDecimal augend, MathContext mc) {
1325 if (mc.precision == 0)
1326 return add(augend);
1327 BigDecimal lhs = this;
1328
1329 // If either number is zero then the other number, rounded and
1330 // scaled if necessary, is used as the result.
1331 {
1332 boolean lhsIsZero = lhs.signum() == 0;
1333 boolean augendIsZero = augend.signum() == 0;
1334
1335 if (lhsIsZero || augendIsZero) {
1336 int preferredScale = Math.max(lhs.scale(), augend.scale());
1337 BigDecimal result;
1338 // Could use a factory for zero instead of a new object
1339 if (lhsIsZero && augendIsZero)
1340 return zeroValueOf(preferredScale);
1341 result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc);
1342
1343 if (result.scale() == preferredScale)
1344 return result;
1345 else if (result.scale() > preferredScale) {
1346 return stripZerosToMatchScale(result.intVal, result.intCompact, result.scale, preferredScale);
1347 } else { // result.scale < preferredScale
1348 int precisionDiff = mc.precision - result.precision();
1349 int scaleDiff = preferredScale - result.scale();
1350
1351 if (precisionDiff >= scaleDiff)
1352 return result.setScale(preferredScale); // can achieve target scale
1353 else
1354 return result.setScale(result.scale() + precisionDiff);
1355 }
1356 }
1357 }
1358
1359 long padding = (long) lhs.scale - augend.scale;
1360 if (padding != 0) { // scales differ; alignment needed
1361 BigDecimal arg[] = preAlign(lhs, augend, padding, mc);
1362 matchScale(arg);
1363 lhs = arg[0];
1364 augend = arg[1];
1365 }
1366 return doRound(lhs.inflated().add(augend.inflated()), lhs.scale, mc);
1367 }
1368
1369 /**
1370 * Returns an array of length two, the sum of whose entries is
1371 * equal to the rounded sum of the {@code BigDecimal} arguments.
1372 *
1373 * <p>If the digit positions of the arguments have a sufficient
1374 * gap between them, the value smaller in magnitude can be
1375 * condensed into a {@literal "sticky bit"} and the end result will
1376 * round the same way <em>if</em> the precision of the final
1377 * result does not include the high order digit of the small
1378 * magnitude operand.
1379 *
1380 * <p>Note that while strictly speaking this is an optimization,
1381 * it makes a much wider range of additions practical.
1382 *
1383 * <p>This corresponds to a pre-shift operation in a fixed
1384 * precision floating-point adder; this method is complicated by
1385 * variable precision of the result as determined by the
1386 * MathContext. A more nuanced operation could implement a
1387 * {@literal "right shift"} on the smaller magnitude operand so
1388 * that the number of digits of the smaller operand could be
1389 * reduced even though the significands partially overlapped.
1390 */
1391 private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend, long padding, MathContext mc) {
1392 assert padding != 0;
1393 BigDecimal big;
1394 BigDecimal small;
1395
1396 if (padding < 0) { // lhs is big; augend is small
1397 big = lhs;
1398 small = augend;
1399 } else { // lhs is small; augend is big
1400 big = augend;
1401 small = lhs;
1402 }
1403
1404 /*
1405 * This is the estimated scale of an ulp of the result; it assumes that
1406 * the result doesn't have a carry-out on a true add (e.g. 999 + 1 =>
1407 * 1000) or any subtractive cancellation on borrowing (e.g. 100 - 1.2 =>
1408 * 98.8)
1409 */
1410 long estResultUlpScale = (long) big.scale - big.precision() + mc.precision;
1411
1412 /*
1413 * The low-order digit position of big is big.scale(). This
1414 * is true regardless of whether big has a positive or
1415 * negative scale. The high-order digit position of small is
1416 * small.scale - (small.precision() - 1). To do the full
1417 * condensation, the digit positions of big and small must be
1418 * disjoint *and* the digit positions of small should not be
1419 * directly visible in the result.
1420 */
1421 long smallHighDigitPos = (long) small.scale - small.precision() + 1;
1422 if (smallHighDigitPos > big.scale + 2 && // big and small disjoint
1423 smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible
1424 small = BigDecimal.valueOf(small.signum(), this.checkScale(Math.max(big.scale, estResultUlpScale) + 3));
1425 }
1426
1427 // Since addition is symmetric, preserving input order in
1428 // returned operands doesn't matter
1429 BigDecimal[] result = {big, small};
1430 return result;
1431 }
1432
1433 /**
1434 * Returns a {@code BigDecimal} whose value is {@code (this -
1435 * subtrahend)}, and whose scale is {@code max(this.scale(),
1436 * subtrahend.scale())}.
1437 *
1438 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1439 * @return {@code this - subtrahend}
1440 */
1441 public BigDecimal subtract(BigDecimal subtrahend) {
1442 if (this.intCompact != INFLATED) {
1443 if ((subtrahend.intCompact != INFLATED)) {
1444 return add(this.intCompact, this.scale, -subtrahend.intCompact, subtrahend.scale);
1445 } else {
1446 return add(this.intCompact, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1447 }
1448 } else {
1449 if ((subtrahend.intCompact != INFLATED)) {
1450 // Pair of subtrahend values given before pair of
1451 // values from this BigDecimal to avoid need for
1452 // method overloading on the specialized add method
1453 return add(-subtrahend.intCompact, subtrahend.scale, this.intVal, this.scale);
1454 } else {
1455 return add(this.intVal, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
1456 }
1457 }
1458 }
1459
1460 /**
1461 * Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)},
1462 * with rounding according to the context settings.
1463 *
1464 * If {@code subtrahend} is zero then this, rounded if necessary, is used as the
1465 * result. If this is zero then the result is {@code subtrahend.negate(mc)}.
1466 *
1467 * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1468 * @param mc the context to use.
1469 * @return {@code this - subtrahend}, rounded as necessary.
1470 * @throws ArithmeticException if the result is inexact but the
1471 * rounding mode is {@code UNNECESSARY}.
1472 * @since 1.5
1473 */
1474 public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) {
1475 if (mc.precision == 0)
1476 return subtract(subtrahend);
1477 // share the special rounding code in add()
1478 return add(subtrahend.negate(), mc);
1479 }
1480
1481 /**
1482 * Returns a {@code BigDecimal} whose value is <tt>(this ×
1483 * multiplicand)</tt>, and whose scale is {@code (this.scale() +
1484 * multiplicand.scale())}.
1485 *
1486 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1487 * @return {@code this * multiplicand}
1488 */
1489 public BigDecimal multiply(BigDecimal multiplicand) {
1490 int productScale = checkScale((long) scale + multiplicand.scale);
1491 if (this.intCompact != INFLATED) {
1492 if ((multiplicand.intCompact != INFLATED)) {
1493 return multiply(this.intCompact, multiplicand.intCompact, productScale);
1494 } else {
1495 return multiply(this.intCompact, multiplicand.intVal, productScale);
1496 }
1497 } else {
1498 if ((multiplicand.intCompact != INFLATED)) {
1499 return multiply(multiplicand.intCompact, this.intVal, productScale);
1500 } else {
1501 return multiply(this.intVal, multiplicand.intVal, productScale);
1502 }
1503 }
1504 }
1505
1506 /**
1507 * Returns a {@code BigDecimal} whose value is <tt>(this ×
1508 * multiplicand)</tt>, with rounding according to the context settings.
1509 *
1510 * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1511 * @param mc the context to use.
1512 * @return {@code this * multiplicand}, rounded as necessary.
1513 * @throws ArithmeticException if the result is inexact but the
1514 * rounding mode is {@code UNNECESSARY}.
1515 * @since 1.5
1516 */
1517 public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) {
1518 if (mc.precision == 0)
1519 return multiply(multiplicand);
1520 int productScale = checkScale((long) scale + multiplicand.scale);
1521 if (this.intCompact != INFLATED) {
1522 if ((multiplicand.intCompact != INFLATED)) {
1523 return multiplyAndRound(this.intCompact, multiplicand.intCompact, productScale, mc);
1524 } else {
1525 return multiplyAndRound(this.intCompact, multiplicand.intVal, productScale, mc);
1526 }
1527 } else {
1528 if ((multiplicand.intCompact != INFLATED)) {
1529 return multiplyAndRound(multiplicand.intCompact, this.intVal, productScale, mc);
1530 } else {
1531 return multiplyAndRound(this.intVal, multiplicand.intVal, productScale, mc);
1532 }
1533 }
1534 }
1535
1536 /**
1537 * Returns a {@code BigDecimal} whose value is {@code (this /
1538 * divisor)}, and whose scale is as specified. If rounding must
1539 * be performed to generate a result with the specified scale, the
1540 * specified rounding mode is applied.
1541 *
1542 * <p>The new {@link #divide(BigDecimal, int, RoundingMode)} method
1543 * should be used in preference to this legacy method.
1544 *
1545 * @param divisor value by which this {@code BigDecimal} is to be divided.
1546 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1547 * @param roundingMode rounding mode to apply.
1548 * @return {@code this / divisor}
1549 * @throws ArithmeticException if {@code divisor} is zero,
1550 * {@code roundingMode==ROUND_UNNECESSARY} and
1551 * the specified scale is insufficient to represent the result
1552 * of the division exactly.
1553 * @throws IllegalArgumentException if {@code roundingMode} does not
1554 * represent a valid rounding mode.
1555 * @see #ROUND_UP
1556 * @see #ROUND_DOWN
1557 * @see #ROUND_CEILING
1558 * @see #ROUND_FLOOR
1559 * @see #ROUND_HALF_UP
1560 * @see #ROUND_HALF_DOWN
1561 * @see #ROUND_HALF_EVEN
1562 * @see #ROUND_UNNECESSARY
1563 */
1564 public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) {
1565 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
1566 throw new IllegalArgumentException("Invalid rounding mode");
1567 if (this.intCompact != INFLATED) {
1568 if ((divisor.intCompact != INFLATED)) {
1569 return divide(this.intCompact, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1570 } else {
1571 return divide(this.intCompact, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1572 }
1573 } else {
1574 if ((divisor.intCompact != INFLATED)) {
1575 return divide(this.intVal, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
1576 } else {
1577 return divide(this.intVal, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
1578 }
1579 }
1580 }
1581
1582 /**
1583 * Returns a {@code BigDecimal} whose value is {@code (this /
1584 * divisor)}, and whose scale is as specified. If rounding must
1585 * be performed to generate a result with the specified scale, the
1586 * specified rounding mode is applied.
1587 *
1588 * @param divisor value by which this {@code BigDecimal} is to be divided.
1589 * @param scale scale of the {@code BigDecimal} quotient to be returned.
1590 * @param roundingMode rounding mode to apply.
1591 * @return {@code this / divisor}
1592 * @throws ArithmeticException if {@code divisor} is zero,
1593 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1594 * the specified scale is insufficient to represent the result
1595 * of the division exactly.
1596 * @since 1.5
1597 */
1598 public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) {
1599 return divide(divisor, scale, roundingMode.oldMode);
1600 }
1601
1602 /**
1603 * Returns a {@code BigDecimal} whose value is {@code (this /
1604 * divisor)}, and whose scale is {@code this.scale()}. If
1605 * rounding must be performed to generate a result with the given
1606 * scale, the specified rounding mode is applied.
1607 *
1608 * <p>The new {@link #divide(BigDecimal, RoundingMode)} method
1609 * should be used in preference to this legacy method.
1610 *
1611 * @param divisor value by which this {@code BigDecimal} is to be divided.
1612 * @param roundingMode rounding mode to apply.
1613 * @return {@code this / divisor}
1614 * @throws ArithmeticException if {@code divisor==0}, or
1615 * {@code roundingMode==ROUND_UNNECESSARY} and
1616 * {@code this.scale()} is insufficient to represent the result
1617 * of the division exactly.
1618 * @throws IllegalArgumentException if {@code roundingMode} does not
1619 * represent a valid rounding mode.
1620 * @see #ROUND_UP
1621 * @see #ROUND_DOWN
1622 * @see #ROUND_CEILING
1623 * @see #ROUND_FLOOR
1624 * @see #ROUND_HALF_UP
1625 * @see #ROUND_HALF_DOWN
1626 * @see #ROUND_HALF_EVEN
1627 * @see #ROUND_UNNECESSARY
1628 */
1629 public BigDecimal divide(BigDecimal divisor, int roundingMode) {
1630 return this.divide(divisor, scale, roundingMode);
1631 }
1632
1633 /**
1634 * Returns a {@code BigDecimal} whose value is {@code (this /
1635 * divisor)}, and whose scale is {@code this.scale()}. If
1636 * rounding must be performed to generate a result with the given
1637 * scale, the specified rounding mode is applied.
1638 *
1639 * @param divisor value by which this {@code BigDecimal} is to be divided.
1640 * @param roundingMode rounding mode to apply.
1641 * @return {@code this / divisor}
1642 * @throws ArithmeticException if {@code divisor==0}, or
1643 * {@code roundingMode==RoundingMode.UNNECESSARY} and
1644 * {@code this.scale()} is insufficient to represent the result
1645 * of the division exactly.
1646 * @since 1.5
1647 */
1648 public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) {
1649 return this.divide(divisor, scale, roundingMode.oldMode);
1650 }
1651
1652 /**
1653 * Returns a {@code BigDecimal} whose value is {@code (this /
1654 * divisor)}, and whose preferred scale is {@code (this.scale() -
1655 * divisor.scale())}; if the exact quotient cannot be
1656 * represented (because it has a non-terminating decimal
1657 * expansion) an {@code ArithmeticException} is thrown.
1658 *
1659 * @param divisor value by which this {@code BigDecimal} is to be divided.
1660 * @throws ArithmeticException if the exact quotient does not have a
1661 * terminating decimal expansion
1662 * @return {@code this / divisor}
1663 * @since 1.5
1664 * @author Joseph D. Darcy
1665 */
1666 public BigDecimal divide(BigDecimal divisor) {
1667 /*
1668 * Handle zero cases first.
1669 */
1670 if (divisor.signum() == 0) { // x/0
1671 if (this.signum() == 0) // 0/0
1672 throw new ArithmeticException("Division undefined"); // NaN
1673 throw new ArithmeticException("Division by zero");
1674 }
1675
1676 // Calculate preferred scale
1677 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1678
1679 if (this.signum() == 0) // 0/y
1680 return zeroValueOf(preferredScale);
1681 else {
1682 /*
1683 * If the quotient this/divisor has a terminating decimal
1684 * expansion, the expansion can have no more than
1685 * (a.precision() + ceil(10*b.precision)/3) digits.
1686 * Therefore, create a MathContext object with this
1687 * precision and do a divide with the UNNECESSARY rounding
1688 * mode.
1689 */
1690 MathContext mc = new MathContext( (int)Math.min(this.precision() +
1691 (long)Math.ceil(10.0*divisor.precision()/3.0),
1692 Integer.MAX_VALUE),
1693 RoundingMode.UNNECESSARY);
1694 BigDecimal quotient;
1695 try {
1696 quotient = this.divide(divisor, mc);
1697 } catch (ArithmeticException e) {
1698 throw new ArithmeticException("Non-terminating decimal expansion; " +
1699 "no exact representable decimal result.");
1700 }
1701
1702 int quotientScale = quotient.scale();
1703
1704 // divide(BigDecimal, mc) tries to adjust the quotient to
1705 // the desired one by removing trailing zeros; since the
1706 // exact divide method does not have an explicit digit
1707 // limit, we can add zeros too.
1708 if (preferredScale > quotientScale)
1709 return quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1710
1711 return quotient;
1712 }
1713 }
1714
1715 /**
1716 * Returns a {@code BigDecimal} whose value is {@code (this /
1717 * divisor)}, with rounding according to the context settings.
1718 *
1719 * @param divisor value by which this {@code BigDecimal} is to be divided.
1720 * @param mc the context to use.
1721 * @return {@code this / divisor}, rounded as necessary.
1722 * @throws ArithmeticException if the result is inexact but the
1723 * rounding mode is {@code UNNECESSARY} or
1724 * {@code mc.precision == 0} and the quotient has a
1725 * non-terminating decimal expansion.
1726 * @since 1.5
1727 */
1728 public BigDecimal divide(BigDecimal divisor, MathContext mc) {
1729 int mcp = mc.precision;
1730 if (mcp == 0)
1731 return divide(divisor);
1732
1733 BigDecimal dividend = this;
1734 long preferredScale = (long)dividend.scale - divisor.scale;
1735 // Now calculate the answer. We use the existing
1736 // divide-and-round method, but as this rounds to scale we have
1737 // to normalize the values here to achieve the desired result.
1738 // For x/y we first handle y=0 and x=0, and then normalize x and
1739 // y to give x' and y' with the following constraints:
1740 // (a) 0.1 <= x' < 1
1741 // (b) x' <= y' < 10*x'
1742 // Dividing x'/y' with the required scale set to mc.precision then
1743 // will give a result in the range 0.1 to 1 rounded to exactly
1744 // the right number of digits (except in the case of a result of
1745 // 1.000... which can arise when x=y, or when rounding overflows
1746 // The 1.000... case will reduce properly to 1.
1747 if (divisor.signum() == 0) { // x/0
1748 if (dividend.signum() == 0) // 0/0
1749 throw new ArithmeticException("Division undefined"); // NaN
1750 throw new ArithmeticException("Division by zero");
1751 }
1752 if (dividend.signum() == 0) // 0/y
1753 return zeroValueOf(saturateLong(preferredScale));
1754 int xscale = dividend.precision();
1755 int yscale = divisor.precision();
1756 if(dividend.intCompact!=INFLATED) {
1757 if(divisor.intCompact!=INFLATED) {
1758 return divide(dividend.intCompact, xscale, divisor.intCompact, yscale, preferredScale, mc);
1759 } else {
1760 return divide(dividend.intCompact, xscale, divisor.intVal, yscale, preferredScale, mc);
1761 }
1762 } else {
1763 if(divisor.intCompact!=INFLATED) {
1764 return divide(dividend.intVal, xscale, divisor.intCompact, yscale, preferredScale, mc);
1765 } else {
1766 return divide(dividend.intVal, xscale, divisor.intVal, yscale, preferredScale, mc);
1767 }
1768 }
1769 }
1770
1771 /**
1772 * Returns a {@code BigDecimal} whose value is the integer part
1773 * of the quotient {@code (this / divisor)} rounded down. The
1774 * preferred scale of the result is {@code (this.scale() -
1775 * divisor.scale())}.
1776 *
1777 * @param divisor value by which this {@code BigDecimal} is to be divided.
1778 * @return The integer part of {@code this / divisor}.
1779 * @throws ArithmeticException if {@code divisor==0}
1780 * @since 1.5
1781 */
1782 public BigDecimal divideToIntegralValue(BigDecimal divisor) {
1783 // Calculate preferred scale
1784 int preferredScale = saturateLong((long) this.scale - divisor.scale);
1785 if (this.compareMagnitude(divisor) < 0) {
1786 // much faster when this << divisor
1787 return zeroValueOf(preferredScale);
1788 }
1789
1790 if (this.signum() == 0 && divisor.signum() != 0)
1791 return this.setScale(preferredScale, ROUND_UNNECESSARY);
1792
1793 // Perform a divide with enough digits to round to a correct
1794 // integer value; then remove any fractional digits
1795
1796 int maxDigits = (int)Math.min(this.precision() +
1797 (long)Math.ceil(10.0*divisor.precision()/3.0) +
1798 Math.abs((long)this.scale() - divisor.scale()) + 2,
1799 Integer.MAX_VALUE);
1800 BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits,
1801 RoundingMode.DOWN));
1802 if (quotient.scale > 0) {
1803 quotient = quotient.setScale(0, RoundingMode.DOWN);
1804 quotient = stripZerosToMatchScale(quotient.intVal, quotient.intCompact, quotient.scale, preferredScale);
1805 }
1806
1807 if (quotient.scale < preferredScale) {
1808 // pad with zeros if necessary
1809 quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1810 }
1811
1812 return quotient;
1813 }
1814
1815 /**
1816 * Returns a {@code BigDecimal} whose value is the integer part
1817 * of {@code (this / divisor)}. Since the integer part of the
1818 * exact quotient does not depend on the rounding mode, the
1819 * rounding mode does not affect the values returned by this
1820 * method. The preferred scale of the result is
1821 * {@code (this.scale() - divisor.scale())}. An
1822 * {@code ArithmeticException} is thrown if the integer part of
1823 * the exact quotient needs more than {@code mc.precision}
1824 * digits.
1825 *
1826 * @param divisor value by which this {@code BigDecimal} is to be divided.
1827 * @param mc the context to use.
1828 * @return The integer part of {@code this / divisor}.
1829 * @throws ArithmeticException if {@code divisor==0}
1830 * @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result
1831 * requires a precision of more than {@code mc.precision} digits.
1832 * @since 1.5
1833 * @author Joseph D. Darcy
1834 */
1835 public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) {
1836 if (mc.precision == 0 || // exact result
1837 (this.compareMagnitude(divisor) < 0)) // zero result
1838 return divideToIntegralValue(divisor);
1839
1840 // Calculate preferred scale
1841 int preferredScale = saturateLong((long)this.scale - divisor.scale);
1842
1843 /*
1844 * Perform a normal divide to mc.precision digits. If the
1845 * remainder has absolute value less than the divisor, the
1846 * integer portion of the quotient fits into mc.precision
1847 * digits. Next, remove any fractional digits from the
1848 * quotient and adjust the scale to the preferred value.
1849 */
1850 BigDecimal result = this.divide(divisor, new MathContext(mc.precision, RoundingMode.DOWN));
1851
1852 if (result.scale() < 0) {
1853 /*
1854 * Result is an integer. See if quotient represents the
1855 * full integer portion of the exact quotient; if it does,
1856 * the computed remainder will be less than the divisor.
1857 */
1858 BigDecimal product = result.multiply(divisor);
1859 // If the quotient is the full integer value,
1860 // |dividend-product| < |divisor|.
1861 if (this.subtract(product).compareMagnitude(divisor) >= 0) {
1862 throw new ArithmeticException("Division impossible");
1863 }
1864 } else if (result.scale() > 0) {
1865 /*
1866 * Integer portion of quotient will fit into precision
1867 * digits; recompute quotient to scale 0 to avoid double
1868 * rounding and then try to adjust, if necessary.
1869 */
1870 result = result.setScale(0, RoundingMode.DOWN);
1871 }
1872 // else result.scale() == 0;
1873
1874 int precisionDiff;
1875 if ((preferredScale > result.scale()) &&
1876 (precisionDiff = mc.precision - result.precision()) > 0) {
1877 return result.setScale(result.scale() +
1878 Math.min(precisionDiff, preferredScale - result.scale) );
1879 } else {
1880 return stripZerosToMatchScale(result.intVal,result.intCompact,result.scale,preferredScale);
1881 }
1882 }
1883
1884 /**
1885 * Returns a {@code BigDecimal} whose value is {@code (this % divisor)}.
1886 *
1887 * <p>The remainder is given by
1888 * {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}.
1889 * Note that this is not the modulo operation (the result can be
1890 * negative).
1891 *
1892 * @param divisor value by which this {@code BigDecimal} is to be divided.
1893 * @return {@code this % divisor}.
1894 * @throws ArithmeticException if {@code divisor==0}
1895 * @since 1.5
1896 */
1897 public BigDecimal remainder(BigDecimal divisor) {
1898 BigDecimal divrem[] = this.divideAndRemainder(divisor);
1899 return divrem[1];
1900 }
1901
1902
1903 /**
1904 * Returns a {@code BigDecimal} whose value is {@code (this %
1905 * divisor)}, with rounding according to the context settings.
1906 * The {@code MathContext} settings affect the implicit divide
1907 * used to compute the remainder. The remainder computation
1908 * itself is by definition exact. Therefore, the remainder may
1909 * contain more than {@code mc.getPrecision()} digits.
1910 *
1911 * <p>The remainder is given by
1912 * {@code this.subtract(this.divideToIntegralValue(divisor,
1913 * mc).multiply(divisor))}. Note that this is not the modulo
1914 * operation (the result can be negative).
1915 *
1916 * @param divisor value by which this {@code BigDecimal} is to be divided.
1917 * @param mc the context to use.
1918 * @return {@code this % divisor}, rounded as necessary.
1919 * @throws ArithmeticException if {@code divisor==0}
1920 * @throws ArithmeticException if the result is inexact but the
1921 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1922 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1923 * require a precision of more than {@code mc.precision} digits.
1924 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1925 * @since 1.5
1926 */
1927 public BigDecimal remainder(BigDecimal divisor, MathContext mc) {
1928 BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
1929 return divrem[1];
1930 }
1931
1932 /**
1933 * Returns a two-element {@code BigDecimal} array containing the
1934 * result of {@code divideToIntegralValue} followed by the result of
1935 * {@code remainder} on the two operands.
1936 *
1937 * <p>Note that if both the integer quotient and remainder are
1938 * needed, this method is faster than using the
1939 * {@code divideToIntegralValue} and {@code remainder} methods
1940 * separately because the division need only be carried out once.
1941 *
1942 * @param divisor value by which this {@code BigDecimal} is to be divided,
1943 * and the remainder computed.
1944 * @return a two element {@code BigDecimal} array: the quotient
1945 * (the result of {@code divideToIntegralValue}) is the initial element
1946 * and the remainder is the final element.
1947 * @throws ArithmeticException if {@code divisor==0}
1948 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1949 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1950 * @since 1.5
1951 */
1952 public BigDecimal[] divideAndRemainder(BigDecimal divisor) {
1953 // we use the identity x = i * y + r to determine r
1954 BigDecimal[] result = new BigDecimal[2];
1955
1956 result[0] = this.divideToIntegralValue(divisor);
1957 result[1] = this.subtract(result[0].multiply(divisor));
1958 return result;
1959 }
1960
1961 /**
1962 * Returns a two-element {@code BigDecimal} array containing the
1963 * result of {@code divideToIntegralValue} followed by the result of
1964 * {@code remainder} on the two operands calculated with rounding
1965 * according to the context settings.
1966 *
1967 * <p>Note that if both the integer quotient and remainder are
1968 * needed, this method is faster than using the
1969 * {@code divideToIntegralValue} and {@code remainder} methods
1970 * separately because the division need only be carried out once.
1971 *
1972 * @param divisor value by which this {@code BigDecimal} is to be divided,
1973 * and the remainder computed.
1974 * @param mc the context to use.
1975 * @return a two element {@code BigDecimal} array: the quotient
1976 * (the result of {@code divideToIntegralValue}) is the
1977 * initial element and the remainder is the final element.
1978 * @throws ArithmeticException if {@code divisor==0}
1979 * @throws ArithmeticException if the result is inexact but the
1980 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1981 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1982 * require a precision of more than {@code mc.precision} digits.
1983 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1984 * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1985 * @since 1.5
1986 */
1987 public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) {
1988 if (mc.precision == 0)
1989 return divideAndRemainder(divisor);
1990
1991 BigDecimal[] result = new BigDecimal[2];
1992 BigDecimal lhs = this;
1993
1994 result[0] = lhs.divideToIntegralValue(divisor, mc);
1995 result[1] = lhs.subtract(result[0].multiply(divisor));
1996 return result;
1997 }
1998
1999 /**
2000 * Returns a {@code BigDecimal} whose value is
2001 * <tt>(this<sup>n</sup>)</tt>, The power is computed exactly, to
2002 * unlimited precision.
2003 *
2004 * <p>The parameter {@code n} must be in the range 0 through
2005 * 999999999, inclusive. {@code ZERO.pow(0)} returns {@link
2006 * #ONE}.
2007 *
2008 * Note that future releases may expand the allowable exponent
2009 * range of this method.
2010 *
2011 * @param n power to raise this {@code BigDecimal} to.
2012 * @return <tt>this<sup>n</sup></tt>
2013 * @throws ArithmeticException if {@code n} is out of range.
2014 * @since 1.5
2015 */
2016 public BigDecimal pow(int n) {
2017 if (n < 0 || n > 999999999)
2018 throw new ArithmeticException("Invalid operation");
2019 // No need to calculate pow(n) if result will over/underflow.
2020 // Don't attempt to support "supernormal" numbers.
2021 int newScale = checkScale((long)scale * n);
2022 return new BigDecimal(this.inflated().pow(n), newScale);
2023 }
2024
2025
2026 /**
2027 * Returns a {@code BigDecimal} whose value is
2028 * <tt>(this<sup>n</sup>)</tt>. The current implementation uses
2029 * the core algorithm defined in ANSI standard X3.274-1996 with
2030 * rounding according to the context settings. In general, the
2031 * returned numerical value is within two ulps of the exact
2032 * numerical value for the chosen precision. Note that future
2033 * releases may use a different algorithm with a decreased
2034 * allowable error bound and increased allowable exponent range.
2035 *
2036 * <p>The X3.274-1996 algorithm is:
2037 *
2038 * <ul>
2039 * <li> An {@code ArithmeticException} exception is thrown if
2040 * <ul>
2041 * <li>{@code abs(n) > 999999999}
2042 * <li>{@code mc.precision == 0} and {@code n < 0}
2043 * <li>{@code mc.precision > 0} and {@code n} has more than
2044 * {@code mc.precision} decimal digits
2045 * </ul>
2046 *
2047 * <li> if {@code n} is zero, {@link #ONE} is returned even if
2048 * {@code this} is zero, otherwise
2049 * <ul>
2050 * <li> if {@code n} is positive, the result is calculated via
2051 * the repeated squaring technique into a single accumulator.
2052 * The individual multiplications with the accumulator use the
2053 * same math context settings as in {@code mc} except for a
2054 * precision increased to {@code mc.precision + elength + 1}
2055 * where {@code elength} is the number of decimal digits in
2056 * {@code n}.
2057 *
2058 * <li> if {@code n} is negative, the result is calculated as if
2059 * {@code n} were positive; this value is then divided into one
2060 * using the working precision specified above.
2061 *
2062 * <li> The final value from either the positive or negative case
2063 * is then rounded to the destination precision.
2064 * </ul>
2065 * </ul>
2066 *
2067 * @param n power to raise this {@code BigDecimal} to.
2068 * @param mc the context to use.
2069 * @return <tt>this<sup>n</sup></tt> using the ANSI standard X3.274-1996
2070 * algorithm
2071 * @throws ArithmeticException if the result is inexact but the
2072 * rounding mode is {@code UNNECESSARY}, or {@code n} is out
2073 * of range.
2074 * @since 1.5
2075 */
2076 public BigDecimal pow(int n, MathContext mc) {
2077 if (mc.precision == 0)
2078 return pow(n);
2079 if (n < -999999999 || n > 999999999)
2080 throw new ArithmeticException("Invalid operation");
2081 if (n == 0)
2082 return ONE; // x**0 == 1 in X3.274
2083 BigDecimal lhs = this;
2084 MathContext workmc = mc; // working settings
2085 int mag = Math.abs(n); // magnitude of n
2086 if (mc.precision > 0) {
2087 int elength = longDigitLength(mag); // length of n in digits
2088 if (elength > mc.precision) // X3.274 rule
2089 throw new ArithmeticException("Invalid operation");
2090 workmc = new MathContext(mc.precision + elength + 1,
2091 mc.roundingMode);
2092 }
2093 // ready to carry out power calculation...
2094 BigDecimal acc = ONE; // accumulator
2095 boolean seenbit = false; // set once we've seen a 1-bit
2096 for (int i=1;;i++) { // for each bit [top bit ignored]
2097 mag += mag; // shift left 1 bit
2098 if (mag < 0) { // top bit is set
2099 seenbit = true; // OK, we're off
2100 acc = acc.multiply(lhs, workmc); // acc=acc*x
2101 }
2102 if (i == 31)
2103 break; // that was the last bit
2104 if (seenbit)
2105 acc=acc.multiply(acc, workmc); // acc=acc*acc [square]
2106 // else (!seenbit) no point in squaring ONE
2107 }
2108 // if negative n, calculate the reciprocal using working precision
2109 if (n < 0) // [hence mc.precision>0]
2110 acc=ONE.divide(acc, workmc);
2111 // round to final precision and strip zeros
2112 return doRound(acc, mc);
2113 }
2114
2115 /**
2116 * Returns a {@code BigDecimal} whose value is the absolute value
2117 * of this {@code BigDecimal}, and whose scale is
2118 * {@code this.scale()}.
2119 *
2120 * @return {@code abs(this)}
2121 */
2122 public BigDecimal abs() {
2123 return (signum() < 0 ? negate() : this);
2124 }
2125
2126 /**
2127 * Returns a {@code BigDecimal} whose value is the absolute value
2128 * of this {@code BigDecimal}, with rounding according to the
2129 * context settings.
2130 *
2131 * @param mc the context to use.
2132 * @return {@code abs(this)}, rounded as necessary.
2133 * @throws ArithmeticException if the result is inexact but the
2134 * rounding mode is {@code UNNECESSARY}.
2135 * @since 1.5
2136 */
2137 public BigDecimal abs(MathContext mc) {
2138 return (signum() < 0 ? negate(mc) : plus(mc));
2139 }
2140
2141 /**
2142 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2143 * and whose scale is {@code this.scale()}.
2144 *
2145 * @return {@code -this}.
2146 */
2147 public BigDecimal negate() {
2148 if (intCompact == INFLATED) {
2149 return new BigDecimal(intVal.negate(), INFLATED, scale, precision);
2150 } else {
2151 return valueOf(-intCompact, scale, precision);
2152 }
2153 }
2154
2155 /**
2156 * Returns a {@code BigDecimal} whose value is {@code (-this)},
2157 * with rounding according to the context settings.
2158 *
2159 * @param mc the context to use.
2160 * @return {@code -this}, rounded as necessary.
2161 * @throws ArithmeticException if the result is inexact but the
2162 * rounding mode is {@code UNNECESSARY}.
2163 * @since 1.5
2164 */
2165 public BigDecimal negate(MathContext mc) {
2166 return negate().plus(mc);
2167 }
2168
2169 /**
2170 * Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose
2171 * scale is {@code this.scale()}.
2172 *
2173 * <p>This method, which simply returns this {@code BigDecimal}
2174 * is included for symmetry with the unary minus method {@link
2175 * #negate()}.
2176 *
2177 * @return {@code this}.
2178 * @see #negate()
2179 * @since 1.5
2180 */
2181 public BigDecimal plus() {
2182 return this;
2183 }
2184
2185 /**
2186 * Returns a {@code BigDecimal} whose value is {@code (+this)},
2187 * with rounding according to the context settings.
2188 *
2189 * <p>The effect of this method is identical to that of the {@link
2190 * #round(MathContext)} method.
2191 *
2192 * @param mc the context to use.
2193 * @return {@code this}, rounded as necessary. A zero result will
2194 * have a scale of 0.
2195 * @throws ArithmeticException if the result is inexact but the
2196 * rounding mode is {@code UNNECESSARY}.
2197 * @see #round(MathContext)
2198 * @since 1.5
2199 */
2200 public BigDecimal plus(MathContext mc) {
2201 if (mc.precision == 0) // no rounding please
2202 return this;
2203 return doRound(this, mc);
2204 }
2205
2206 /**
2207 * Returns the signum function of this {@code BigDecimal}.
2208 *
2209 * @return -1, 0, or 1 as the value of this {@code BigDecimal}
2210 * is negative, zero, or positive.
2211 */
2212 public int signum() {
2213 return (intCompact != INFLATED)?
2214 Long.signum(intCompact):
2215 intVal.signum();
2216 }
2217
2218 /**
2219 * Returns the <i>scale</i> of this {@code BigDecimal}. If zero
2220 * or positive, the scale is the number of digits to the right of
2221 * the decimal point. If negative, the unscaled value of the
2222 * number is multiplied by ten to the power of the negation of the
2223 * scale. For example, a scale of {@code -3} means the unscaled
2224 * value is multiplied by 1000.
2225 *
2226 * @return the scale of this {@code BigDecimal}.
2227 */
2228 public int scale() {
2229 return scale;
2230 }
2231
2232 /**
2233 * Returns the <i>precision</i> of this {@code BigDecimal}. (The
2234 * precision is the number of digits in the unscaled value.)
2235 *
2236 * <p>The precision of a zero value is 1.
2237 *
2238 * @return the precision of this {@code BigDecimal}.
2239 * @since 1.5
2240 */
2241 public int precision() {
2242 int result = precision;
2243 if (result == 0) {
2244 long s = intCompact;
2245 if (s != INFLATED)
2246 result = longDigitLength(s);
2247 else
2248 result = bigDigitLength(intVal);
2249 precision = result;
2250 }
2251 return result;
2252 }
2253
2254
2255 /**
2256 * Returns a {@code BigInteger} whose value is the <i>unscaled
2257 * value</i> of this {@code BigDecimal}. (Computes <tt>(this *
2258 * 10<sup>this.scale()</sup>)</tt>.)
2259 *
2260 * @return the unscaled value of this {@code BigDecimal}.
2261 * @since 1.2
2262 */
2263 public BigInteger unscaledValue() {
2264 return this.inflated();
2265 }
2266
2267 // Rounding Modes
2268
2269 /**
2270 * Rounding mode to round away from zero. Always increments the
2271 * digit prior to a nonzero discarded fraction. Note that this rounding
2272 * mode never decreases the magnitude of the calculated value.
2273 */
2274 public final static int ROUND_UP = 0;
2275
2276 /**
2277 * Rounding mode to round towards zero. Never increments the digit
2278 * prior to a discarded fraction (i.e., truncates). Note that this
2279 * rounding mode never increases the magnitude of the calculated value.
2280 */
2281 public final static int ROUND_DOWN = 1;
2282
2283 /**
2284 * Rounding mode to round towards positive infinity. If the
2285 * {@code BigDecimal} is positive, behaves as for
2286 * {@code ROUND_UP}; if negative, behaves as for
2287 * {@code ROUND_DOWN}. Note that this rounding mode never
2288 * decreases the calculated value.
2289 */
2290 public final static int ROUND_CEILING = 2;
2291
2292 /**
2293 * Rounding mode to round towards negative infinity. If the
2294 * {@code BigDecimal} is positive, behave as for
2295 * {@code ROUND_DOWN}; if negative, behave as for
2296 * {@code ROUND_UP}. Note that this rounding mode never
2297 * increases the calculated value.
2298 */
2299 public final static int ROUND_FLOOR = 3;
2300
2301 /**
2302 * Rounding mode to round towards {@literal "nearest neighbor"}
2303 * unless both neighbors are equidistant, in which case round up.
2304 * Behaves as for {@code ROUND_UP} if the discarded fraction is
2305 * ≥ 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note
2306 * that this is the rounding mode that most of us were taught in
2307 * grade school.
2308 */
2309 public final static int ROUND_HALF_UP = 4;
2310
2311 /**
2312 * Rounding mode to round towards {@literal "nearest neighbor"}
2313 * unless both neighbors are equidistant, in which case round
2314 * down. Behaves as for {@code ROUND_UP} if the discarded
2315 * fraction is {@literal >} 0.5; otherwise, behaves as for
2316 * {@code ROUND_DOWN}.
2317 */
2318 public final static int ROUND_HALF_DOWN = 5;
2319
2320 /**
2321 * Rounding mode to round towards the {@literal "nearest neighbor"}
2322 * unless both neighbors are equidistant, in which case, round
2323 * towards the even neighbor. Behaves as for
2324 * {@code ROUND_HALF_UP} if the digit to the left of the
2325 * discarded fraction is odd; behaves as for
2326 * {@code ROUND_HALF_DOWN} if it's even. Note that this is the
2327 * rounding mode that minimizes cumulative error when applied
2328 * repeatedly over a sequence of calculations.
2329 */
2330 public final static int ROUND_HALF_EVEN = 6;
2331
2332 /**
2333 * Rounding mode to assert that the requested operation has an exact
2334 * result, hence no rounding is necessary. If this rounding mode is
2335 * specified on an operation that yields an inexact result, an
2336 * {@code ArithmeticException} is thrown.
2337 */
2338 public final static int ROUND_UNNECESSARY = 7;
2339
2340
2341 // Scaling/Rounding Operations
2342
2343 /**
2344 * Returns a {@code BigDecimal} rounded according to the
2345 * {@code MathContext} settings. If the precision setting is 0 then
2346 * no rounding takes place.
2347 *
2348 * <p>The effect of this method is identical to that of the
2349 * {@link #plus(MathContext)} method.
2350 *
2351 * @param mc the context to use.
2352 * @return a {@code BigDecimal} rounded according to the
2353 * {@code MathContext} settings.
2354 * @throws ArithmeticException if the rounding mode is
2355 * {@code UNNECESSARY} and the
2356 * {@code BigDecimal} operation would require rounding.
2357 * @see #plus(MathContext)
2358 * @since 1.5
2359 */
2360 public BigDecimal round(MathContext mc) {
2361 return plus(mc);
2362 }
2363
2364 /**
2365 * Returns a {@code BigDecimal} whose scale is the specified
2366 * value, and whose unscaled value is determined by multiplying or
2367 * dividing this {@code BigDecimal}'s unscaled value by the
2368 * appropriate power of ten to maintain its overall value. If the
2369 * scale is reduced by the operation, the unscaled value must be
2370 * divided (rather than multiplied), and the value may be changed;
2371 * in this case, the specified rounding mode is applied to the
2372 * division.
2373 *
2374 * <p>Note that since BigDecimal objects are immutable, calls of
2375 * this method do <i>not</i> result in the original object being
2376 * modified, contrary to the usual convention of having methods
2377 * named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
2378 * Instead, {@code setScale} returns an object with the proper
2379 * scale; the returned object may or may not be newly allocated.
2380 *
2381 * @param newScale scale of the {@code BigDecimal} value to be returned.
2382 * @param roundingMode The rounding mode to apply.
2383 * @return a {@code BigDecimal} whose scale is the specified value,
2384 * and whose unscaled value is determined by multiplying or
2385 * dividing this {@code BigDecimal}'s unscaled value by the
2386 * appropriate power of ten to maintain its overall value.
2387 * @throws ArithmeticException if {@code roundingMode==UNNECESSARY}
2388 * and the specified scaling operation would require
2389 * rounding.
2390 * @see RoundingMode
2391 * @since 1.5
2392 */
2393 public BigDecimal setScale(int newScale, RoundingMode roundingMode) {
2394 return setScale(newScale, roundingMode.oldMode);
2395 }
2396
2397 /**
2398 * Returns a {@code BigDecimal} whose scale is the specified
2399 * value, and whose unscaled value is determined by multiplying or
2400 * dividing this {@code BigDecimal}'s unscaled value by the
2401 * appropriate power of ten to maintain its overall value. If the
2402 * scale is reduced by the operation, the unscaled value must be
2403 * divided (rather than multiplied), and the value may be changed;
2404 * in this case, the specified rounding mode is applied to the
2405 * division.
2406 *
2407 * <p>Note that since BigDecimal objects are immutable, calls of
2408 * this method do <i>not</i> result in the original object being
2409 * modified, contrary to the usual convention of having methods
2410 * named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
2411 * Instead, {@code setScale} returns an object with the proper
2412 * scale; the returned object may or may not be newly allocated.
2413 *
2414 * <p>The new {@link #setScale(int, RoundingMode)} method should
2415 * be used in preference to this legacy method.
2416 *
2417 * @param newScale scale of the {@code BigDecimal} value to be returned.
2418 * @param roundingMode The rounding mode to apply.
2419 * @return a {@code BigDecimal} whose scale is the specified value,
2420 * and whose unscaled value is determined by multiplying or
2421 * dividing this {@code BigDecimal}'s unscaled value by the
2422 * appropriate power of ten to maintain its overall value.
2423 * @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY}
2424 * and the specified scaling operation would require
2425 * rounding.
2426 * @throws IllegalArgumentException if {@code roundingMode} does not
2427 * represent a valid rounding mode.
2428 * @see #ROUND_UP
2429 * @see #ROUND_DOWN
2430 * @see #ROUND_CEILING
2431 * @see #ROUND_FLOOR
2432 * @see #ROUND_HALF_UP
2433 * @see #ROUND_HALF_DOWN
2434 * @see #ROUND_HALF_EVEN
2435 * @see #ROUND_UNNECESSARY
2436 */
2437 public BigDecimal setScale(int newScale, int roundingMode) {
2438 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
2439 throw new IllegalArgumentException("Invalid rounding mode");
2440
2441 int oldScale = this.scale;
2442 if (newScale == oldScale) // easy case
2443 return this;
2444 if (this.signum() == 0) // zero can have any scale
2445 return zeroValueOf(newScale);
2446 if(this.intCompact!=INFLATED) {
2447 long rs = this.intCompact;
2448 if (newScale > oldScale) {
2449 int raise = checkScale((long) newScale - oldScale);
2450 if ((rs = longMultiplyPowerTen(rs, raise)) != INFLATED) {
2451 return valueOf(rs,newScale);
2452 }
2453 BigInteger rb = bigMultiplyPowerTen(raise);
2454 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2455 } else {
2456 // newScale < oldScale -- drop some digits
2457 // Can't predict the precision due to the effect of rounding.
2458 int drop = checkScale((long) oldScale - newScale);
2459 if (drop < LONG_TEN_POWERS_TABLE.length) {
2460 return divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, newScale);
2461 } else {
2462 return divideAndRound(this.inflated(), bigTenToThe(drop), newScale, roundingMode, newScale);
2463 }
2464 }
2465 } else {
2466 if (newScale > oldScale) {
2467 int raise = checkScale((long) newScale - oldScale);
2468 BigInteger rb = bigMultiplyPowerTen(this.intVal,raise);
2469 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
2470 } else {
2471 // newScale < oldScale -- drop some digits
2472 // Can't predict the precision due to the effect of rounding.
2473 int drop = checkScale((long) oldScale - newScale);
2474 if (drop < LONG_TEN_POWERS_TABLE.length)
2475 return divideAndRound(this.intVal, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode,
2476 newScale);
2477 else
2478 return divideAndRound(this.intVal, bigTenToThe(drop), newScale, roundingMode, newScale);
2479 }
2480 }
2481 }
2482
2483 /**
2484 * Returns a {@code BigDecimal} whose scale is the specified
2485 * value, and whose value is numerically equal to this
2486 * {@code BigDecimal}'s. Throws an {@code ArithmeticException}
2487 * if this is not possible.
2488 *
2489 * <p>This call is typically used to increase the scale, in which
2490 * case it is guaranteed that there exists a {@code BigDecimal}
2491 * of the specified scale and the correct value. The call can
2492 * also be used to reduce the scale if the caller knows that the
2493 * {@code BigDecimal} has sufficiently many zeros at the end of
2494 * its fractional part (i.e., factors of ten in its integer value)
2495 * to allow for the rescaling without changing its value.
2496 *
2497 * <p>This method returns the same result as the two-argument
2498 * versions of {@code setScale}, but saves the caller the trouble
2499 * of specifying a rounding mode in cases where it is irrelevant.
2500 *
2501 * <p>Note that since {@code BigDecimal} objects are immutable,
2502 * calls of this method do <i>not</i> result in the original
2503 * object being modified, contrary to the usual convention of
2504 * having methods named <tt>set<i>X</i></tt> mutate field
2505 * <i>{@code X}</i>. Instead, {@code setScale} returns an
2506 * object with the proper scale; the returned object may or may
2507 * not be newly allocated.
2508 *
2509 * @param newScale scale of the {@code BigDecimal} value to be returned.
2510 * @return a {@code BigDecimal} whose scale is the specified value, and
2511 * whose unscaled value is determined by multiplying or dividing
2512 * this {@code BigDecimal}'s unscaled value by the appropriate
2513 * power of ten to maintain its overall value.
2514 * @throws ArithmeticException if the specified scaling operation would
2515 * require rounding.
2516 * @see #setScale(int, int)
2517 * @see #setScale(int, RoundingMode)
2518 */
2519 public BigDecimal setScale(int newScale) {
2520 return setScale(newScale, ROUND_UNNECESSARY);
2521 }
2522
2523 // Decimal Point Motion Operations
2524
2525 /**
2526 * Returns a {@code BigDecimal} which is equivalent to this one
2527 * with the decimal point moved {@code n} places to the left. If
2528 * {@code n} is non-negative, the call merely adds {@code n} to
2529 * the scale. If {@code n} is negative, the call is equivalent
2530 * to {@code movePointRight(-n)}. The {@code BigDecimal}
2531 * returned by this call has value <tt>(this ×
2532 * 10<sup>-n</sup>)</tt> and scale {@code max(this.scale()+n,
2533 * 0)}.
2534 *
2535 * @param n number of places to move the decimal point to the left.
2536 * @return a {@code BigDecimal} which is equivalent to this one with the
2537 * decimal point moved {@code n} places to the left.
2538 * @throws ArithmeticException if scale overflows.
2539 */
2540 public BigDecimal movePointLeft(int n) {
2541 // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE
2542 int newScale = checkScale((long)scale + n);
2543 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2544 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2545 }
2546
2547 /**
2548 * Returns a {@code BigDecimal} which is equivalent to this one
2549 * with the decimal point moved {@code n} places to the right.
2550 * If {@code n} is non-negative, the call merely subtracts
2551 * {@code n} from the scale. If {@code n} is negative, the call
2552 * is equivalent to {@code movePointLeft(-n)}. The
2553 * {@code BigDecimal} returned by this call has value <tt>(this
2554 * × 10<sup>n</sup>)</tt> and scale {@code max(this.scale()-n,
2555 * 0)}.
2556 *
2557 * @param n number of places to move the decimal point to the right.
2558 * @return a {@code BigDecimal} which is equivalent to this one
2559 * with the decimal point moved {@code n} places to the right.
2560 * @throws ArithmeticException if scale overflows.
2561 */
2562 public BigDecimal movePointRight(int n) {
2563 // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE
2564 int newScale = checkScale((long)scale - n);
2565 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2566 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2567 }
2568
2569 /**
2570 * Returns a BigDecimal whose numerical value is equal to
2571 * ({@code this} * 10<sup>n</sup>). The scale of
2572 * the result is {@code (this.scale() - n)}.
2573 *
2574 * @throws ArithmeticException if the scale would be
2575 * outside the range of a 32-bit integer.
2576 *
2577 * @since 1.5
2578 */
2579 public BigDecimal scaleByPowerOfTen(int n) {
2580 return new BigDecimal(intVal, intCompact,
2581 checkScale((long)scale - n), precision);
2582 }
2583
2584 /**
2585 * Returns a {@code BigDecimal} which is numerically equal to
2586 * this one but with any trailing zeros removed from the
2587 * representation. For example, stripping the trailing zeros from
2588 * the {@code BigDecimal} value {@code 600.0}, which has
2589 * [{@code BigInteger}, {@code scale}] components equals to
2590 * [6000, 1], yields {@code 6E2} with [{@code BigInteger},
2591 * {@code scale}] components equals to [6, -2]
2592 *
2593 * @return a numerically equal {@code BigDecimal} with any
2594 * trailing zeros removed.
2595 * @since 1.5
2596 */
2597 public BigDecimal stripTrailingZeros() {
2598 if(intCompact!=INFLATED) {
2599 return createAndStripZerosToMatchScale(intCompact, scale, Long.MIN_VALUE);
2600 } else {
2601 return createAndStripZerosToMatchScale(intVal, scale, Long.MIN_VALUE);
2602 }
2603 }
2604
2605 // Comparison Operations
2606
2607 /**
2608 * Compares this {@code BigDecimal} with the specified
2609 * {@code BigDecimal}. Two {@code BigDecimal} objects that are
2610 * equal in value but have a different scale (like 2.0 and 2.00)
2611 * are considered equal by this method. This method is provided
2612 * in preference to individual methods for each of the six boolean
2613 * comparison operators ({@literal <}, ==,
2614 * {@literal >}, {@literal >=}, !=, {@literal <=}). The
2615 * suggested idiom for performing these comparisons is:
2616 * {@code (x.compareTo(y)} <<i>op</i>> {@code 0)}, where
2617 * <<i>op</i>> is one of the six comparison operators.
2618 *
2619 * @param val {@code BigDecimal} to which this {@code BigDecimal} is
2620 * to be compared.
2621 * @return -1, 0, or 1 as this {@code BigDecimal} is numerically
2622 * less than, equal to, or greater than {@code val}.
2623 */
2624 public int compareTo(BigDecimal val) {
2625 // Quick path for equal scale and non-inflated case.
2626 if (scale == val.scale) {
2627 long xs = intCompact;
2628 long ys = val.intCompact;
2629 if (xs != INFLATED && ys != INFLATED)
2630 return xs != ys ? ((xs > ys) ? 1 : -1) : 0;
2631 }
2632 int xsign = this.signum();
2633 int ysign = val.signum();
2634 if (xsign != ysign)
2635 return (xsign > ysign) ? 1 : -1;
2636 if (xsign == 0)
2637 return 0;
2638 int cmp = compareMagnitude(val);
2639 return (xsign > 0) ? cmp : -cmp;
2640 }
2641
2642 /**
2643 * Version of compareTo that ignores sign.
2644 */
2645 private int compareMagnitude(BigDecimal val) {
2646 // Match scales, avoid unnecessary inflation
2647 long ys = val.intCompact;
2648 long xs = this.intCompact;
2649 if (xs == 0)
2650 return (ys == 0) ? 0 : -1;
2651 if (ys == 0)
2652 return 1;
2653
2654 int sdiff = this.scale - val.scale;
2655 if (sdiff != 0) {
2656 // Avoid matching scales if the (adjusted) exponents differ
2657 int xae = this.precision() - this.scale; // [-1]
2658 int yae = val.precision() - val.scale; // [-1]
2659 if (xae < yae)
2660 return -1;
2661 if (xae > yae)
2662 return 1;
2663 BigInteger rb = null;
2664 if (sdiff < 0) {
2665 if ( (xs == INFLATED ||
2666 (xs = longMultiplyPowerTen(xs, -sdiff)) == INFLATED) &&
2667 ys == INFLATED) {
2668 rb = bigMultiplyPowerTen(-sdiff);
2669 return rb.compareMagnitude(val.intVal);
2670 }
2671 } else { // sdiff > 0
2672 if ( (ys == INFLATED ||
2673 (ys = longMultiplyPowerTen(ys, sdiff)) == INFLATED) &&
2674 xs == INFLATED) {
2675 rb = val.bigMultiplyPowerTen(sdiff);
2676 return this.intVal.compareMagnitude(rb);
2677 }
2678 }
2679 }
2680 if (xs != INFLATED)
2681 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
2682 else if (ys != INFLATED)
2683 return 1;
2684 else
2685 return this.intVal.compareMagnitude(val.intVal);
2686 }
2687
2688 /**
2689 * Compares this {@code BigDecimal} with the specified
2690 * {@code Object} for equality. Unlike {@link
2691 * #compareTo(BigDecimal) compareTo}, this method considers two
2692 * {@code BigDecimal} objects equal only if they are equal in
2693 * value and scale (thus 2.0 is not equal to 2.00 when compared by
2694 * this method).
2695 *
2696 * @param x {@code Object} to which this {@code BigDecimal} is
2697 * to be compared.
2698 * @return {@code true} if and only if the specified {@code Object} is a
2699 * {@code BigDecimal} whose value and scale are equal to this
2700 * {@code BigDecimal}'s.
2701 * @see #compareTo(java.math.BigDecimal)
2702 * @see #hashCode
2703 */
2704 @Override
2705 public boolean equals(Object x) {
2706 if (!(x instanceof BigDecimal))
2707 return false;
2708 BigDecimal xDec = (BigDecimal) x;
2709 if (x == this)
2710 return true;
2711 if (scale != xDec.scale)
2712 return false;
2713 long s = this.intCompact;
2714 long xs = xDec.intCompact;
2715 if (s != INFLATED) {
2716 if (xs == INFLATED)
2717 xs = compactValFor(xDec.intVal);
2718 return xs == s;
2719 } else if (xs != INFLATED)
2720 return xs == compactValFor(this.intVal);
2721
2722 return this.inflated().equals(xDec.inflated());
2723 }
2724
2725 /**
2726 * Returns the minimum of this {@code BigDecimal} and
2727 * {@code val}.
2728 *
2729 * @param val value with which the minimum is to be computed.
2730 * @return the {@code BigDecimal} whose value is the lesser of this
2731 * {@code BigDecimal} and {@code val}. If they are equal,
2732 * as defined by the {@link #compareTo(BigDecimal) compareTo}
2733 * method, {@code this} is returned.
2734 * @see #compareTo(java.math.BigDecimal)
2735 */
2736 public BigDecimal min(BigDecimal val) {
2737 return (compareTo(val) <= 0 ? this : val);
2738 }
2739
2740 /**
2741 * Returns the maximum of this {@code BigDecimal} and {@code val}.
2742 *
2743 * @param val value with which the maximum is to be computed.
2744 * @return the {@code BigDecimal} whose value is the greater of this
2745 * {@code BigDecimal} and {@code val}. If they are equal,
2746 * as defined by the {@link #compareTo(BigDecimal) compareTo}
2747 * method, {@code this} is returned.
2748 * @see #compareTo(java.math.BigDecimal)
2749 */
2750 public BigDecimal max(BigDecimal val) {
2751 return (compareTo(val) >= 0 ? this : val);
2752 }
2753
2754 // Hash Function
2755
2756 /**
2757 * Returns the hash code for this {@code BigDecimal}. Note that
2758 * two {@code BigDecimal} objects that are numerically equal but
2759 * differ in scale (like 2.0 and 2.00) will generally <i>not</i>
2760 * have the same hash code.
2761 *
2762 * @return hash code for this {@code BigDecimal}.
2763 * @see #equals(Object)
2764 */
2765 @Override
2766 public int hashCode() {
2767 if (intCompact != INFLATED) {
2768 long val2 = (intCompact < 0)? -intCompact : intCompact;
2769 int temp = (int)( ((int)(val2 >>> 32)) * 31 +
2770 (val2 & LONG_MASK));
2771 return 31*((intCompact < 0) ?-temp:temp) + scale;
2772 } else
2773 return 31*intVal.hashCode() + scale;
2774 }
2775
2776 // Format Converters
2777
2778 /**
2779 * Returns the string representation of this {@code BigDecimal},
2780 * using scientific notation if an exponent is needed.
2781 *
2782 * <p>A standard canonical string form of the {@code BigDecimal}
2783 * is created as though by the following steps: first, the
2784 * absolute value of the unscaled value of the {@code BigDecimal}
2785 * is converted to a string in base ten using the characters
2786 * {@code '0'} through {@code '9'} with no leading zeros (except
2787 * if its value is zero, in which case a single {@code '0'}
2788 * character is used).
2789 *
2790 * <p>Next, an <i>adjusted exponent</i> is calculated; this is the
2791 * negated scale, plus the number of characters in the converted
2792 * unscaled value, less one. That is,
2793 * {@code -scale+(ulength-1)}, where {@code ulength} is the
2794 * length of the absolute value of the unscaled value in decimal
2795 * digits (its <i>precision</i>).
2796 *
2797 * <p>If the scale is greater than or equal to zero and the
2798 * adjusted exponent is greater than or equal to {@code -6}, the
2799 * number will be converted to a character form without using
2800 * exponential notation. In this case, if the scale is zero then
2801 * no decimal point is added and if the scale is positive a
2802 * decimal point will be inserted with the scale specifying the
2803 * number of characters to the right of the decimal point.
2804 * {@code '0'} characters are added to the left of the converted
2805 * unscaled value as necessary. If no character precedes the
2806 * decimal point after this insertion then a conventional
2807 * {@code '0'} character is prefixed.
2808 *
2809 * <p>Otherwise (that is, if the scale is negative, or the
2810 * adjusted exponent is less than {@code -6}), the number will be
2811 * converted to a character form using exponential notation. In
2812 * this case, if the converted {@code BigInteger} has more than
2813 * one digit a decimal point is inserted after the first digit.
2814 * An exponent in character form is then suffixed to the converted
2815 * unscaled value (perhaps with inserted decimal point); this
2816 * comprises the letter {@code 'E'} followed immediately by the
2817 * adjusted exponent converted to a character form. The latter is
2818 * in base ten, using the characters {@code '0'} through
2819 * {@code '9'} with no leading zeros, and is always prefixed by a
2820 * sign character {@code '-'} (<tt>'\u002D'</tt>) if the
2821 * adjusted exponent is negative, {@code '+'}
2822 * (<tt>'\u002B'</tt>) otherwise).
2823 *
2824 * <p>Finally, the entire string is prefixed by a minus sign
2825 * character {@code '-'} (<tt>'\u002D'</tt>) if the unscaled
2826 * value is less than zero. No sign character is prefixed if the
2827 * unscaled value is zero or positive.
2828 *
2829 * <p><b>Examples:</b>
2830 * <p>For each representation [<i>unscaled value</i>, <i>scale</i>]
2831 * on the left, the resulting string is shown on the right.
2832 * <pre>
2833 * [123,0] "123"
2834 * [-123,0] "-123"
2835 * [123,-1] "1.23E+3"
2836 * [123,-3] "1.23E+5"
2837 * [123,1] "12.3"
2838 * [123,5] "0.00123"
2839 * [123,10] "1.23E-8"
2840 * [-123,12] "-1.23E-10"
2841 * </pre>
2842 *
2843 * <b>Notes:</b>
2844 * <ol>
2845 *
2846 * <li>There is a one-to-one mapping between the distinguishable
2847 * {@code BigDecimal} values and the result of this conversion.
2848 * That is, every distinguishable {@code BigDecimal} value
2849 * (unscaled value and scale) has a unique string representation
2850 * as a result of using {@code toString}. If that string
2851 * representation is converted back to a {@code BigDecimal} using
2852 * the {@link #BigDecimal(String)} constructor, then the original
2853 * value will be recovered.
2854 *
2855 * <li>The string produced for a given number is always the same;
2856 * it is not affected by locale. This means that it can be used
2857 * as a canonical string representation for exchanging decimal
2858 * data, or as a key for a Hashtable, etc. Locale-sensitive
2859 * number formatting and parsing is handled by the {@link
2860 * java.text.NumberFormat} class and its subclasses.
2861 *
2862 * <li>The {@link #toEngineeringString} method may be used for
2863 * presenting numbers with exponents in engineering notation, and the
2864 * {@link #setScale(int,RoundingMode) setScale} method may be used for
2865 * rounding a {@code BigDecimal} so it has a known number of digits after
2866 * the decimal point.
2867 *
2868 * <li>The digit-to-character mapping provided by
2869 * {@code Character.forDigit} is used.
2870 *
2871 * </ol>
2872 *
2873 * @return string representation of this {@code BigDecimal}.
2874 * @see Character#forDigit
2875 * @see #BigDecimal(java.lang.String)
2876 */
2877 @Override
2878 public String toString() {
2879 String sc = stringCache;
2880 if (sc == null)
2881 stringCache = sc = layoutChars(true);
2882 return sc;
2883 }
2884
2885 /**
2886 * Returns a string representation of this {@code BigDecimal},
2887 * using engineering notation if an exponent is needed.
2888 *
2889 * <p>Returns a string that represents the {@code BigDecimal} as
2890 * described in the {@link #toString()} method, except that if
2891 * exponential notation is used, the power of ten is adjusted to
2892 * be a multiple of three (engineering notation) such that the
2893 * integer part of nonzero values will be in the range 1 through
2894 * 999. If exponential notation is used for zero values, a
2895 * decimal point and one or two fractional zero digits are used so
2896 * that the scale of the zero value is preserved. Note that
2897 * unlike the output of {@link #toString()}, the output of this
2898 * method is <em>not</em> guaranteed to recover the same [integer,
2899 * scale] pair of this {@code BigDecimal} if the output string is
2900 * converting back to a {@code BigDecimal} using the {@linkplain
2901 * #BigDecimal(String) string constructor}. The result of this method meets
2902 * the weaker constraint of always producing a numerically equal
2903 * result from applying the string constructor to the method's output.
2904 *
2905 * @return string representation of this {@code BigDecimal}, using
2906 * engineering notation if an exponent is needed.
2907 * @since 1.5
2908 */
2909 public String toEngineeringString() {
2910 return layoutChars(false);
2911 }
2912
2913 /**
2914 * Returns a string representation of this {@code BigDecimal}
2915 * without an exponent field. For values with a positive scale,
2916 * the number of digits to the right of the decimal point is used
2917 * to indicate scale. For values with a zero or negative scale,
2918 * the resulting string is generated as if the value were
2919 * converted to a numerically equal value with zero scale and as
2920 * if all the trailing zeros of the zero scale value were present
2921 * in the result.
2922 *
2923 * The entire string is prefixed by a minus sign character '-'
2924 * (<tt>'\u002D'</tt>) if the unscaled value is less than
2925 * zero. No sign character is prefixed if the unscaled value is
2926 * zero or positive.
2927 *
2928 * Note that if the result of this method is passed to the
2929 * {@linkplain #BigDecimal(String) string constructor}, only the
2930 * numerical value of this {@code BigDecimal} will necessarily be
2931 * recovered; the representation of the new {@code BigDecimal}
2932 * may have a different scale. In particular, if this
2933 * {@code BigDecimal} has a negative scale, the string resulting
2934 * from this method will have a scale of zero when processed by
2935 * the string constructor.
2936 *
2937 * (This method behaves analogously to the {@code toString}
2938 * method in 1.4 and earlier releases.)
2939 *
2940 * @return a string representation of this {@code BigDecimal}
2941 * without an exponent field.
2942 * @since 1.5
2943 * @see #toString()
2944 * @see #toEngineeringString()
2945 */
2946 public String toPlainString() {
2947 if(scale==0) {
2948 if(intCompact!=INFLATED) {
2949 return Long.toString(intCompact);
2950 } else {
2951 return intVal.toString();
2952 }
2953 }
2954 if(this.scale<0) { // No decimal point
2955 if(signum()==0) {
2956 return "0";
2957 }
2958 int tailingZeros = checkScaleNonZero((-(long)scale));
2959 StringBuilder buf;
2960 if(intCompact!=INFLATED) {
2961 buf = new StringBuilder(20+tailingZeros);
2962 buf.append(intCompact);
2963 } else {
2964 String str = intVal.toString();
2965 buf = new StringBuilder(str.length()+tailingZeros);
2966 buf.append(str);
2967 }
2968 for (int i = 0; i < tailingZeros; i++)
2969 buf.append('0');
2970 return buf.toString();
2971 }
2972 String str ;
2973 if(intCompact!=INFLATED) {
2974 str = Long.toString(Math.abs(intCompact));
2975 } else {
2976 str = intVal.abs().toString();
2977 }
2978 return getValueString(signum(), str, scale);
2979 }
2980
2981 /* Returns a digit.digit string */
2982 private String getValueString(int signum, String intString, int scale) {
2983 /* Insert decimal point */
2984 StringBuilder buf;
2985 int insertionPoint = intString.length() - scale;
2986 if (insertionPoint == 0) { /* Point goes right before intVal */
2987 return (signum<0 ? "-0." : "0.") + intString;
2988 } else if (insertionPoint > 0) { /* Point goes inside intVal */
2989 buf = new StringBuilder(intString);
2990 buf.insert(insertionPoint, '.');
2991 if (signum < 0)
2992 buf.insert(0, '-');
2993 } else { /* We must insert zeros between point and intVal */
2994 buf = new StringBuilder(3-insertionPoint + intString.length());
2995 buf.append(signum<0 ? "-0." : "0.");
2996 for (int i=0; i<-insertionPoint; i++)
2997 buf.append('0');
2998 buf.append(intString);
2999 }
3000 return buf.toString();
3001 }
3002
3003 /**
3004 * Converts this {@code BigDecimal} to a {@code BigInteger}.
3005 * This conversion is analogous to the
3006 * <i>narrowing primitive conversion</i> from {@code double} to
3007 * {@code long} as defined in section 5.1.3 of
3008 * <cite>The Java™ Language Specification</cite>:
3009 * any fractional part of this
3010 * {@code BigDecimal} will be discarded. Note that this
3011 * conversion can lose information about the precision of the
3012 * {@code BigDecimal} value.
3013 * <p>
3014 * To have an exception thrown if the conversion is inexact (in
3015 * other words if a nonzero fractional part is discarded), use the
3016 * {@link #toBigIntegerExact()} method.
3017 *
3018 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3019 */
3020 public BigInteger toBigInteger() {
3021 // force to an integer, quietly
3022 return this.setScale(0, ROUND_DOWN).inflated();
3023 }
3024
3025 /**
3026 * Converts this {@code BigDecimal} to a {@code BigInteger},
3027 * checking for lost information. An exception is thrown if this
3028 * {@code BigDecimal} has a nonzero fractional part.
3029 *
3030 * @return this {@code BigDecimal} converted to a {@code BigInteger}.
3031 * @throws ArithmeticException if {@code this} has a nonzero
3032 * fractional part.
3033 * @since 1.5
3034 */
3035 public BigInteger toBigIntegerExact() {
3036 // round to an integer, with Exception if decimal part non-0
3037 return this.setScale(0, ROUND_UNNECESSARY).inflated();
3038 }
3039
3040 /**
3041 * Converts this {@code BigDecimal} to a {@code long}.
3042 * This conversion is analogous to the
3043 * <i>narrowing primitive conversion</i> from {@code double} to
3044 * {@code short} as defined in section 5.1.3 of
3045 * <cite>The Java™ Language Specification</cite>:
3046 * any fractional part of this
3047 * {@code BigDecimal} will be discarded, and if the resulting
3048 * "{@code BigInteger}" is too big to fit in a
3049 * {@code long}, only the low-order 64 bits are returned.
3050 * Note that this conversion can lose information about the
3051 * overall magnitude and precision of this {@code BigDecimal} value as well
3052 * as return a result with the opposite sign.
3053 *
3054 * @return this {@code BigDecimal} converted to a {@code long}.
3055 */
3056 public long longValue(){
3057 return (intCompact != INFLATED && scale == 0) ?
3058 intCompact:
3059 toBigInteger().longValue();
3060 }
3061
3062 /**
3063 * Converts this {@code BigDecimal} to a {@code long}, checking
3064 * for lost information. If this {@code BigDecimal} has a
3065 * nonzero fractional part or is out of the possible range for a
3066 * {@code long} result then an {@code ArithmeticException} is
3067 * thrown.
3068 *
3069 * @return this {@code BigDecimal} converted to a {@code long}.
3070 * @throws ArithmeticException if {@code this} has a nonzero
3071 * fractional part, or will not fit in a {@code long}.
3072 * @since 1.5
3073 */
3074 public long longValueExact() {
3075 if (intCompact != INFLATED && scale == 0)
3076 return intCompact;
3077 // If more than 19 digits in integer part it cannot possibly fit
3078 if ((precision() - scale) > 19) // [OK for negative scale too]
3079 throw new java.lang.ArithmeticException("Overflow");
3080 // Fastpath zero and < 1.0 numbers (the latter can be very slow
3081 // to round if very small)
3082 if (this.signum() == 0)
3083 return 0;
3084 if ((this.precision() - this.scale) <= 0)
3085 throw new ArithmeticException("Rounding necessary");
3086 // round to an integer, with Exception if decimal part non-0
3087 BigDecimal num = this.setScale(0, ROUND_UNNECESSARY);
3088 if (num.precision() >= 19) // need to check carefully
3089 LongOverflow.check(num);
3090 return num.inflated().longValue();
3091 }
3092
3093 private static class LongOverflow {
3094 /** BigInteger equal to Long.MIN_VALUE. */
3095 private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE);
3096
3097 /** BigInteger equal to Long.MAX_VALUE. */
3098 private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE);
3099
3100 public static void check(BigDecimal num) {
3101 BigInteger intVal = num.inflated();
3102 if (intVal.compareTo(LONGMIN) < 0 ||
3103 intVal.compareTo(LONGMAX) > 0)
3104 throw new java.lang.ArithmeticException("Overflow");
3105 }
3106 }
3107
3108 /**
3109 * Converts this {@code BigDecimal} to an {@code int}.
3110 * This conversion is analogous to the
3111 * <i>narrowing primitive conversion</i> from {@code double} to
3112 * {@code short} as defined in section 5.1.3 of
3113 * <cite>The Java™ Language Specification</cite>:
3114 * any fractional part of this
3115 * {@code BigDecimal} will be discarded, and if the resulting
3116 * "{@code BigInteger}" is too big to fit in an
3117 * {@code int}, only the low-order 32 bits are returned.
3118 * Note that this conversion can lose information about the
3119 * overall magnitude and precision of this {@code BigDecimal}
3120 * value as well as return a result with the opposite sign.
3121 *
3122 * @return this {@code BigDecimal} converted to an {@code int}.
3123 */
3124 public int intValue() {
3125 return (intCompact != INFLATED && scale == 0) ?
3126 (int)intCompact :
3127 toBigInteger().intValue();
3128 }
3129
3130 /**
3131 * Converts this {@code BigDecimal} to an {@code int}, checking
3132 * for lost information. If this {@code BigDecimal} has a
3133 * nonzero fractional part or is out of the possible range for an
3134 * {@code int} result then an {@code ArithmeticException} is
3135 * thrown.
3136 *
3137 * @return this {@code BigDecimal} converted to an {@code int}.
3138 * @throws ArithmeticException if {@code this} has a nonzero
3139 * fractional part, or will not fit in an {@code int}.
3140 * @since 1.5
3141 */
3142 public int intValueExact() {
3143 long num;
3144 num = this.longValueExact(); // will check decimal part
3145 if ((int)num != num)
3146 throw new java.lang.ArithmeticException("Overflow");
3147 return (int)num;
3148 }
3149
3150 /**
3151 * Converts this {@code BigDecimal} to a {@code short}, checking
3152 * for lost information. If this {@code BigDecimal} has a
3153 * nonzero fractional part or is out of the possible range for a
3154 * {@code short} result then an {@code ArithmeticException} is
3155 * thrown.
3156 *
3157 * @return this {@code BigDecimal} converted to a {@code short}.
3158 * @throws ArithmeticException if {@code this} has a nonzero
3159 * fractional part, or will not fit in a {@code short}.
3160 * @since 1.5
3161 */
3162 public short shortValueExact() {
3163 long num;
3164 num = this.longValueExact(); // will check decimal part
3165 if ((short)num != num)
3166 throw new java.lang.ArithmeticException("Overflow");
3167 return (short)num;
3168 }
3169
3170 /**
3171 * Converts this {@code BigDecimal} to a {@code byte}, checking
3172 * for lost information. If this {@code BigDecimal} has a
3173 * nonzero fractional part or is out of the possible range for a
3174 * {@code byte} result then an {@code ArithmeticException} is
3175 * thrown.
3176 *
3177 * @return this {@code BigDecimal} converted to a {@code byte}.
3178 * @throws ArithmeticException if {@code this} has a nonzero
3179 * fractional part, or will not fit in a {@code byte}.
3180 * @since 1.5
3181 */
3182 public byte byteValueExact() {
3183 long num;
3184 num = this.longValueExact(); // will check decimal part
3185 if ((byte)num != num)
3186 throw new java.lang.ArithmeticException("Overflow");
3187 return (byte)num;
3188 }
3189
3190 /**
3191 * Converts this {@code BigDecimal} to a {@code float}.
3192 * This conversion is similar to the
3193 * <i>narrowing primitive conversion</i> from {@code double} to
3194 * {@code float} as defined in section 5.1.3 of
3195 * <cite>The Java™ Language Specification</cite>:
3196 * if this {@code BigDecimal} has too great a
3197 * magnitude to represent as a {@code float}, it will be
3198 * converted to {@link Float#NEGATIVE_INFINITY} or {@link
3199 * Float#POSITIVE_INFINITY} as appropriate. Note that even when
3200 * the return value is finite, this conversion can lose
3201 * information about the precision of the {@code BigDecimal}
3202 * value.
3203 *
3204 * @return this {@code BigDecimal} converted to a {@code float}.
3205 */
3206 public float floatValue(){
3207 if(intCompact != INFLATED) {
3208 if (scale == 0) {
3209 return (float)intCompact;
3210 } else {
3211 /*
3212 * If both intCompact and the scale can be exactly
3213 * represented as float values, perform a single float
3214 * multiply or divide to compute the (properly
3215 * rounded) result.
3216 */
3217 if (scale > 0 && scale < float10pow.length
3218 && intCompact > -1L<<22 && intCompact < 1L<<22) {
3219 return (float)intCompact / float10pow[scale];
3220 } else if (scale < 0 && scale > -float10pow.length
3221 && intCompact > -1L<<22 && intCompact < 1L<<22) {
3222 return (float)intCompact * float10pow[-scale];
3223 }
3224 }
3225 }
3226 // Somewhat inefficient, but guaranteed to work.
3227 return Float.parseFloat(this.toString());
3228 }
3229
3230 /**
3231 * Converts this {@code BigDecimal} to a {@code double}.
3232 * This conversion is similar to the
3233 * <i>narrowing primitive conversion</i> from {@code double} to
3234 * {@code float} as defined in section 5.1.3 of
3235 * <cite>The Java™ Language Specification</cite>:
3236 * if this {@code BigDecimal} has too great a
3237 * magnitude represent as a {@code double}, it will be
3238 * converted to {@link Double#NEGATIVE_INFINITY} or {@link
3239 * Double#POSITIVE_INFINITY} as appropriate. Note that even when
3240 * the return value is finite, this conversion can lose
3241 * information about the precision of the {@code BigDecimal}
3242 * value.
3243 *
3244 * @return this {@code BigDecimal} converted to a {@code double}.
3245 */
3246 public double doubleValue(){
3247 if(intCompact != INFLATED) {
3248 if (scale == 0) {
3249 return (double)intCompact;
3250 } else {
3251 /*
3252 * If both intCompact and the scale can be exactly
3253 * represented as double values, perform a single
3254 * double multiply or divide to compute the (properly
3255 * rounded) result.
3256 */
3257 if (scale > 0 && scale < double10pow.length
3258 && intCompact > -1L<<52 && intCompact < 1L<<52) {
3259 return (double)intCompact / double10pow[scale];
3260 } else if (scale < 0 && scale > -double10pow.length
3261 && intCompact > -1L<<52 && intCompact < 1L<<52) {
3262 return (double)intCompact * double10pow[-scale];
3263 }
3264 }
3265 }
3266 // Somewhat inefficient, but guaranteed to work.
3267 return Double.parseDouble(this.toString());
3268 }
3269
3270 /**
3271 * Powers of 10 which can be represented exactly in {@code
3272 * double}.
3273 */
3274 private static final double double10pow[] = {
3275 1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5,
3276 1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, 1.0e11,
3277 1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17,
3278 1.0e18, 1.0e19, 1.0e20, 1.0e21, 1.0e22
3279 };
3280
3281 /**
3282 * Powers of 10 which can be represented exactly in {@code
3283 * float}.
3284 */
3285 private static final float float10pow[] = {
3286 1.0e0f, 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f,
3287 1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f
3288 };
3289
3290 /**
3291 * Returns the size of an ulp, a unit in the last place, of this
3292 * {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal}
3293 * value is the positive distance between this value and the
3294 * {@code BigDecimal} value next larger in magnitude with the
3295 * same number of digits. An ulp of a zero value is numerically
3296 * equal to 1 with the scale of {@code this}. The result is
3297 * stored with the same scale as {@code this} so the result
3298 * for zero and nonzero values is equal to {@code [1,
3299 * this.scale()]}.
3300 *
3301 * @return the size of an ulp of {@code this}
3302 * @since 1.5
3303 */
3304 public BigDecimal ulp() {
3305 return BigDecimal.valueOf(1, this.scale(), 1);
3306 }
3307
3308 // Private class to build a string representation for BigDecimal object.
3309 // "StringBuilderHelper" is constructed as a thread local variable so it is
3310 // thread safe. The StringBuilder field acts as a buffer to hold the temporary
3311 // representation of BigDecimal. The cmpCharArray holds all the characters for
3312 // the compact representation of BigDecimal (except for '-' sign' if it is
3313 // negative) if its intCompact field is not INFLATED. It is shared by all
3314 // calls to toString() and its variants in that particular thread.
3315 static class StringBuilderHelper {
3316 final StringBuilder sb; // Placeholder for BigDecimal string
3317 final char[] cmpCharArray; // character array to place the intCompact
3318
3319 StringBuilderHelper() {
3320 sb = new StringBuilder();
3321 // All non negative longs can be made to fit into 19 character array.
3322 cmpCharArray = new char[19];
3323 }
3324
3325 // Accessors.
3326 StringBuilder getStringBuilder() {
3327 sb.setLength(0);
3328 return sb;
3329 }
3330
3331 char[] getCompactCharArray() {
3332 return cmpCharArray;
3333 }
3334
3335 /**
3336 * Places characters representing the intCompact in {@code long} into
3337 * cmpCharArray and returns the offset to the array where the
3338 * representation starts.
3339 *
3340 * @param intCompact the number to put into the cmpCharArray.
3341 * @return offset to the array where the representation starts.
3342 * Note: intCompact must be greater or equal to zero.
3343 */
3344 int putIntCompact(long intCompact) {
3345 assert intCompact >= 0;
3346
3347 long q;
3348 int r;
3349 // since we start from the least significant digit, charPos points to
3350 // the last character in cmpCharArray.
3351 int charPos = cmpCharArray.length;
3352
3353 // Get 2 digits/iteration using longs until quotient fits into an int
3354 while (intCompact > Integer.MAX_VALUE) {
3355 q = intCompact / 100;
3356 r = (int)(intCompact - q * 100);
3357 intCompact = q;
3358 cmpCharArray[--charPos] = DIGIT_ONES[r];
3359 cmpCharArray[--charPos] = DIGIT_TENS[r];
3360 }
3361
3362 // Get 2 digits/iteration using ints when i2 >= 100
3363 int q2;
3364 int i2 = (int)intCompact;
3365 while (i2 >= 100) {
3366 q2 = i2 / 100;
3367 r = i2 - q2 * 100;
3368 i2 = q2;
3369 cmpCharArray[--charPos] = DIGIT_ONES[r];
3370 cmpCharArray[--charPos] = DIGIT_TENS[r];
3371 }
3372
3373 cmpCharArray[--charPos] = DIGIT_ONES[i2];
3374 if (i2 >= 10)
3375 cmpCharArray[--charPos] = DIGIT_TENS[i2];
3376
3377 return charPos;
3378 }
3379
3380 final static char[] DIGIT_TENS = {
3381 '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
3382 '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
3383 '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
3384 '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
3385 '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
3386 '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
3387 '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
3388 '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
3389 '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
3390 '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
3391 };
3392
3393 final static char[] DIGIT_ONES = {
3394 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3395 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3396 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3397 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3398 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3399 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3400 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3401 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3402 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3403 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3404 };
3405 }
3406
3407 /**
3408 * Lay out this {@code BigDecimal} into a {@code char[]} array.
3409 * The Java 1.2 equivalent to this was called {@code getValueString}.
3410 *
3411 * @param sci {@code true} for Scientific exponential notation;
3412 * {@code false} for Engineering
3413 * @return string with canonical string representation of this
3414 * {@code BigDecimal}
3415 */
3416 private String layoutChars(boolean sci) {
3417 if (scale == 0) // zero scale is trivial
3418 return (intCompact != INFLATED) ?
3419 Long.toString(intCompact):
3420 intVal.toString();
3421 if (scale == 2 &&
3422 intCompact >= 0 && intCompact < Integer.MAX_VALUE) {
3423 // currency fast path
3424 int lowInt = (int)intCompact % 100;
3425 int highInt = (int)intCompact / 100;
3426 return (Integer.toString(highInt) + '.' +
3427 StringBuilderHelper.DIGIT_TENS[lowInt] +
3428 StringBuilderHelper.DIGIT_ONES[lowInt]) ;
3429 }
3430
3431 StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get();
3432 char[] coeff;
3433 int offset; // offset is the starting index for coeff array
3434 // Get the significand as an absolute value
3435 if (intCompact != INFLATED) {
3436 offset = sbHelper.putIntCompact(Math.abs(intCompact));
3437 coeff = sbHelper.getCompactCharArray();
3438 } else {
3439 offset = 0;
3440 coeff = intVal.abs().toString().toCharArray();
3441 }
3442
3443 // Construct a buffer, with sufficient capacity for all cases.
3444 // If E-notation is needed, length will be: +1 if negative, +1
3445 // if '.' needed, +2 for "E+", + up to 10 for adjusted exponent.
3446 // Otherwise it could have +1 if negative, plus leading "0.00000"
3447 StringBuilder buf = sbHelper.getStringBuilder();
3448 if (signum() < 0) // prefix '-' if negative
3449 buf.append('-');
3450 int coeffLen = coeff.length - offset;
3451 long adjusted = -(long)scale + (coeffLen -1);
3452 if ((scale >= 0) && (adjusted >= -6)) { // plain number
3453 int pad = scale - coeffLen; // count of padding zeros
3454 if (pad >= 0) { // 0.xxx form
3455 buf.append('0');
3456 buf.append('.');
3457 for (; pad>0; pad--) {
3458 buf.append('0');
3459 }
3460 buf.append(coeff, offset, coeffLen);
3461 } else { // xx.xx form
3462 buf.append(coeff, offset, -pad);
3463 buf.append('.');
3464 buf.append(coeff, -pad + offset, scale);
3465 }
3466 } else { // E-notation is needed
3467 if (sci) { // Scientific notation
3468 buf.append(coeff[offset]); // first character
3469 if (coeffLen > 1) { // more to come
3470 buf.append('.');
3471 buf.append(coeff, offset + 1, coeffLen - 1);
3472 }
3473 } else { // Engineering notation
3474 int sig = (int)(adjusted % 3);
3475 if (sig < 0)
3476 sig += 3; // [adjusted was negative]
3477 adjusted -= sig; // now a multiple of 3
3478 sig++;
3479 if (signum() == 0) {
3480 switch (sig) {
3481 case 1:
3482 buf.append('0'); // exponent is a multiple of three
3483 break;
3484 case 2:
3485 buf.append("0.00");
3486 adjusted += 3;
3487 break;
3488 case 3:
3489 buf.append("0.0");
3490 adjusted += 3;
3491 break;
3492 default:
3493 throw new AssertionError("Unexpected sig value " + sig);
3494 }
3495 } else if (sig >= coeffLen) { // significand all in integer
3496 buf.append(coeff, offset, coeffLen);
3497 // may need some zeros, too
3498 for (int i = sig - coeffLen; i > 0; i--)
3499 buf.append('0');
3500 } else { // xx.xxE form
3501 buf.append(coeff, offset, sig);
3502 buf.append('.');
3503 buf.append(coeff, offset + sig, coeffLen - sig);
3504 }
3505 }
3506 if (adjusted != 0) { // [!sci could have made 0]
3507 buf.append('E');
3508 if (adjusted > 0) // force sign for positive
3509 buf.append('+');
3510 buf.append(adjusted);
3511 }
3512 }
3513 return buf.toString();
3514 }
3515
3516 /**
3517 * Return 10 to the power n, as a {@code BigInteger}.
3518 *
3519 * @param n the power of ten to be returned (>=0)
3520 * @return a {@code BigInteger} with the value (10<sup>n</sup>)
3521 */
3522 private static BigInteger bigTenToThe(int n) {
3523 if (n < 0)
3524 return BigInteger.ZERO;
3525
3526 if (n < BIG_TEN_POWERS_TABLE_MAX) {
3527 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3528 if (n < pows.length)
3529 return pows[n];
3530 else
3531 return expandBigIntegerTenPowers(n);
3532 }
3533 // BigInteger.pow is slow, so make 10**n by constructing a
3534 // BigInteger from a character string (still not very fast)
3535 char tenpow[] = new char[n + 1];
3536 tenpow[0] = '1';
3537 for (int i = 1; i <= n; i++)
3538 tenpow[i] = '0';
3539 return new BigInteger(tenpow,1, tenpow.length);
3540 }
3541
3542 /**
3543 * Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n.
3544 *
3545 * @param n the power of ten to be returned (>=0)
3546 * @return a {@code BigDecimal} with the value (10<sup>n</sup>) and
3547 * in the meantime, the BIG_TEN_POWERS_TABLE array gets
3548 * expanded to the size greater than n.
3549 */
3550 private static BigInteger expandBigIntegerTenPowers(int n) {
3551 synchronized(BigDecimal.class) {
3552 BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3553 int curLen = pows.length;
3554 // The following comparison and the above synchronized statement is
3555 // to prevent multiple threads from expanding the same array.
3556 if (curLen <= n) {
3557 int newLen = curLen << 1;
3558 while (newLen <= n)
3559 newLen <<= 1;
3560 pows = Arrays.copyOf(pows, newLen);
3561 for (int i = curLen; i < newLen; i++)
3562 pows[i] = pows[i - 1].multiply(BigInteger.TEN);
3563 // Based on the following facts:
3564 // 1. pows is a private local varible;
3565 // 2. the following store is a volatile store.
3566 // the newly created array elements can be safely published.
3567 BIG_TEN_POWERS_TABLE = pows;
3568 }
3569 return pows[n];
3570 }
3571 }
3572
3573 private static final long[] LONG_TEN_POWERS_TABLE = {
3574 1, // 0 / 10^0
3575 10, // 1 / 10^1
3576 100, // 2 / 10^2
3577 1000, // 3 / 10^3
3578 10000, // 4 / 10^4
3579 100000, // 5 / 10^5
3580 1000000, // 6 / 10^6
3581 10000000, // 7 / 10^7
3582 100000000, // 8 / 10^8
3583 1000000000, // 9 / 10^9
3584 10000000000L, // 10 / 10^10
3585 100000000000L, // 11 / 10^11
3586 1000000000000L, // 12 / 10^12
3587 10000000000000L, // 13 / 10^13
3588 100000000000000L, // 14 / 10^14
3589 1000000000000000L, // 15 / 10^15
3590 10000000000000000L, // 16 / 10^16
3591 100000000000000000L, // 17 / 10^17
3592 1000000000000000000L // 18 / 10^18
3593 };
3594
3595 private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = {
3596 BigInteger.ONE,
3597 BigInteger.valueOf(10),
3598 BigInteger.valueOf(100),
3599 BigInteger.valueOf(1000),
3600 BigInteger.valueOf(10000),
3601 BigInteger.valueOf(100000),
3602 BigInteger.valueOf(1000000),
3603 BigInteger.valueOf(10000000),
3604 BigInteger.valueOf(100000000),
3605 BigInteger.valueOf(1000000000),
3606 BigInteger.valueOf(10000000000L),
3607 BigInteger.valueOf(100000000000L),
3608 BigInteger.valueOf(1000000000000L),
3609 BigInteger.valueOf(10000000000000L),
3610 BigInteger.valueOf(100000000000000L),
3611 BigInteger.valueOf(1000000000000000L),
3612 BigInteger.valueOf(10000000000000000L),
3613 BigInteger.valueOf(100000000000000000L),
3614 BigInteger.valueOf(1000000000000000000L)
3615 };
3616
3617 private static final int BIG_TEN_POWERS_TABLE_INITLEN =
3618 BIG_TEN_POWERS_TABLE.length;
3619 private static final int BIG_TEN_POWERS_TABLE_MAX =
3620 16 * BIG_TEN_POWERS_TABLE_INITLEN;
3621
3622 private static final long THRESHOLDS_TABLE[] = {
3623 Long.MAX_VALUE, // 0
3624 Long.MAX_VALUE/10L, // 1
3625 Long.MAX_VALUE/100L, // 2
3626 Long.MAX_VALUE/1000L, // 3
3627 Long.MAX_VALUE/10000L, // 4
3628 Long.MAX_VALUE/100000L, // 5
3629 Long.MAX_VALUE/1000000L, // 6
3630 Long.MAX_VALUE/10000000L, // 7
3631 Long.MAX_VALUE/100000000L, // 8
3632 Long.MAX_VALUE/1000000000L, // 9
3633 Long.MAX_VALUE/10000000000L, // 10
3634 Long.MAX_VALUE/100000000000L, // 11
3635 Long.MAX_VALUE/1000000000000L, // 12
3636 Long.MAX_VALUE/10000000000000L, // 13
3637 Long.MAX_VALUE/100000000000000L, // 14
3638 Long.MAX_VALUE/1000000000000000L, // 15
3639 Long.MAX_VALUE/10000000000000000L, // 16
3640 Long.MAX_VALUE/100000000000000000L, // 17
3641 Long.MAX_VALUE/1000000000000000000L // 18
3642 };
3643
3644 /**
3645 * Compute val * 10 ^ n; return this product if it is
3646 * representable as a long, INFLATED otherwise.
3647 */
3648 private static long longMultiplyPowerTen(long val, int n) {
3649 if (val == 0 || n <= 0)
3650 return val;
3651 long[] tab = LONG_TEN_POWERS_TABLE;
3652 long[] bounds = THRESHOLDS_TABLE;
3653 if (n < tab.length && n < bounds.length) {
3654 long tenpower = tab[n];
3655 if (val == 1)
3656 return tenpower;
3657 if (Math.abs(val) <= bounds[n])
3658 return val * tenpower;
3659 }
3660 return INFLATED;
3661 }
3662
3663 /**
3664 * Compute this * 10 ^ n.
3665 * Needed mainly to allow special casing to trap zero value
3666 */
3667 private BigInteger bigMultiplyPowerTen(int n) {
3668 if (n <= 0)
3669 return this.inflated();
3670
3671 if (intCompact != INFLATED)
3672 return bigTenToThe(n).multiply(intCompact);
3673 else
3674 return intVal.multiply(bigTenToThe(n));
3675 }
3676
3677 /**
3678 * Returns appropriate BigInteger from intVal field if intVal is
3679 * null, i.e. the compact representation is in use.
3680 */
3681 private BigInteger inflated() {
3682 if (intVal == null) {
3683 return BigInteger.valueOf(intCompact);
3684 }
3685 return intVal;
3686 }
3687
3688 /**
3689 * Match the scales of two {@code BigDecimal}s to align their
3690 * least significant digits.
3691 *
3692 * <p>If the scales of val[0] and val[1] differ, rescale
3693 * (non-destructively) the lower-scaled {@code BigDecimal} so
3694 * they match. That is, the lower-scaled reference will be
3695 * replaced by a reference to a new object with the same scale as
3696 * the other {@code BigDecimal}.
3697 *
3698 * @param val array of two elements referring to the two
3699 * {@code BigDecimal}s to be aligned.
3700 */
3701 private static void matchScale(BigDecimal[] val) {
3702 if (val[0].scale == val[1].scale) {
3703 return;
3704 } else if (val[0].scale < val[1].scale) {
3705 val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY);
3706 } else if (val[1].scale < val[0].scale) {
3707 val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY);
3708 }
3709 }
3710
3711 private static final sun.misc.Unsafe unsafe = sun.misc.Unsafe.getUnsafe();
3712 private static final long intCompactOffset;
3713 private static final long intValOffset;
3714 static {
3715 try {
3716 intCompactOffset = unsafe.objectFieldOffset
3717 (BigDecimal.class.getDeclaredField("intCompact"));
3718 intValOffset = unsafe.objectFieldOffset
3719 (BigDecimal.class.getDeclaredField("intVal"));
3720 } catch (Exception ex) {
3721 throw new Error(ex);
3722 }
3723 }
3724
3725 private void setIntCompactVolatile(long val) {
3726 unsafe.putLongVolatile(this, intCompactOffset, val);
3727 }
3728
3729 private void setIntValVolatile(BigInteger val) {
3730 unsafe.putObjectVolatile(this, intValOffset, val);
3731 }
3732
3733 /**
3734 * Reconstitute the {@code BigDecimal} instance from a stream (that is,
3735 * deserialize it).
3736 *
3737 * @param s the stream being read.
3738 */
3739 private void readObject(java.io.ObjectInputStream s)
3740 throws java.io.IOException, ClassNotFoundException {
3741 // Read in all fields
3742 s.defaultReadObject();
3743 // validate possibly bad fields
3744 if (intVal == null) {
3745 String message = "BigDecimal: null intVal in stream";
3746 throw new java.io.StreamCorruptedException(message);
3747 // [all values of scale are now allowed]
3748 }
3749 setIntCompactVolatile(compactValFor(intVal));
3750 }
3751
3752 /**
3753 * Serialize this {@code BigDecimal} to the stream in question
3754 *
3755 * @param s the stream to serialize to.
3756 */
3757 private void writeObject(java.io.ObjectOutputStream s)
3758 throws java.io.IOException {
3759 // Must inflate to maintain compatible serial form.
3760 if (this.intVal == null)
3761 this.setIntValVolatile(BigInteger.valueOf(this.intCompact));
3762 s.defaultWriteObject();
3763 }
3764
3765 /**
3766 * Returns the length of the absolute value of a {@code long}, in decimal
3767 * digits.
3768 *
3769 * @param x
3770 * the {@code long}
3771 * @return the length of the unscaled value, in deciaml digits.
3772 */
3773 static int longDigitLength(long x) {
3774 /*
3775 * As described in "Bit Twiddling Hacks" by Sean Anderson,
3776 * (http://graphics.stanford.edu/~seander/bithacks.html) integer log 10
3777 * of x is within 1 of (1233/4096)* (1 + integer log 2 of x). The
3778 * fraction 1233/4096 approximates log10(2). So we first do a version of
3779 * log2 (a variant of Long class with pre-checks and opposite
3780 * directionality) and then scale and check against powers table. This
3781 * is a little simpler in present context than the version in Hacker's
3782 * Delight sec 11-4. Adding one to bit length allows comparing downward
3783 * from the LONG_TEN_POWERS_TABLE that we need anyway.
3784 */
3785 assert x != BigDecimal.INFLATED;
3786 if (x < 0)
3787 x = -x;
3788 if (x < 10) // must screen for 0, might as well 10
3789 return 1;
3790 int r = ((64 - Long.numberOfLeadingZeros(x) + 1) * 1233) >>> 12;
3791 long[] tab = LONG_TEN_POWERS_TABLE;
3792 // if r >= length, must have max possible digits for long
3793 return (r >= tab.length || x < tab[r]) ? r : r + 1;
3794 }
3795
3796 /**
3797 * Returns the length of the absolute value of a BigInteger, in
3798 * decimal digits.
3799 *
3800 * @param b the BigInteger
3801 * @return the length of the unscaled value, in decimal digits
3802 */
3803 private static int bigDigitLength(BigInteger b) {
3804 /*
3805 * Same idea as the long version, but we need a better
3806 * approximation of log10(2). Using 646456993/2^31
3807 * is accurate up to max possible reported bitLength.
3808 */
3809 if (b.signum == 0)
3810 return 1;
3811 int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31);
3812 return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1;
3813 }
3814
3815 /**
3816 * Check a scale for Underflow or Overflow. If this BigDecimal is
3817 * nonzero, throw an exception if the scale is outof range. If this
3818 * is zero, saturate the scale to the extreme value of the right
3819 * sign if the scale is out of range.
3820 *
3821 * @param val The new scale.
3822 * @throws ArithmeticException (overflow or underflow) if the new
3823 * scale is out of range.
3824 * @return validated scale as an int.
3825 */
3826 private int checkScale(long val) {
3827 int asInt = (int)val;
3828 if (asInt != val) {
3829 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3830 BigInteger b;
3831 if (intCompact != 0 &&
3832 ((b = intVal) == null || b.signum() != 0))
3833 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3834 }
3835 return asInt;
3836 }
3837
3838 /**
3839 * Returns the compact value for given {@code BigInteger}, or
3840 * INFLATED if too big. Relies on internal representation of
3841 * {@code BigInteger}.
3842 */
3843 private static long compactValFor(BigInteger b) {
3844 int[] m = b.mag;
3845 int len = m.length;
3846 if (len == 0)
3847 return 0;
3848 int d = m[0];
3849 if (len > 2 || (len == 2 && d < 0))
3850 return INFLATED;
3851
3852 long u = (len == 2)?
3853 (((long) m[1] & LONG_MASK) + (((long)d) << 32)) :
3854 (((long)d) & LONG_MASK);
3855 return (b.signum < 0)? -u : u;
3856 }
3857
3858 private static int longCompareMagnitude(long x, long y) {
3859 if (x < 0)
3860 x = -x;
3861 if (y < 0)
3862 y = -y;
3863 return (x < y) ? -1 : ((x == y) ? 0 : 1);
3864 }
3865
3866 private static int saturateLong(long s) {
3867 int i = (int)s;
3868 return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE);
3869 }
3870
3871 /*
3872 * Internal printing routine
3873 */
3874 private static void print(String name, BigDecimal bd) {
3875 System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n",
3876 name,
3877 bd.intCompact,
3878 bd.intVal,
3879 bd.scale,
3880 bd.precision);
3881 }
3882
3883 /**
3884 * Check internal invariants of this BigDecimal. These invariants
3885 * include:
3886 *
3887 * <ul>
3888 *
3889 * <li>The object must be initialized; either intCompact must not be
3890 * INFLATED or intVal is non-null. Both of these conditions may
3891 * be true.
3892 *
3893 * <li>If both intCompact and intVal and set, their values must be
3894 * consistent.
3895 *
3896 * <li>If precision is nonzero, it must have the right value.
3897 * </ul>
3898 *
3899 * Note: Since this is an audit method, we are not supposed to change the
3900 * state of this BigDecimal object.
3901 */
3902 private BigDecimal audit() {
3903 if (intCompact == INFLATED) {
3904 if (intVal == null) {
3905 print("audit", this);
3906 throw new AssertionError("null intVal");
3907 }
3908 // Check precision
3909 if (precision > 0 && precision != bigDigitLength(intVal)) {
3910 print("audit", this);
3911 throw new AssertionError("precision mismatch");
3912 }
3913 } else {
3914 if (intVal != null) {
3915 long val = intVal.longValue();
3916 if (val != intCompact) {
3917 print("audit", this);
3918 throw new AssertionError("Inconsistent state, intCompact=" +
3919 intCompact + "\t intVal=" + val);
3920 }
3921 }
3922 // Check precision
3923 if (precision > 0 && precision != longDigitLength(intCompact)) {
3924 print("audit", this);
3925 throw new AssertionError("precision mismatch");
3926 }
3927 }
3928 return this;
3929 }
3930
3931 /* the same as checkScale where value!=0 */
3932 private static int checkScaleNonZero(long val) {
3933 int asInt = (int)val;
3934 if (asInt != val) {
3935 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3936 }
3937 return asInt;
3938 }
3939
3940 private static int checkScale(long intCompact, long val) {
3941 int asInt = (int)val;
3942 if (asInt != val) {
3943 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3944 if (intCompact != 0)
3945 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3946 }
3947 return asInt;
3948 }
3949
3950 private static int checkScale(BigInteger intVal, long val) {
3951 int asInt = (int)val;
3952 if (asInt != val) {
3953 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3954 if (intVal.signum() != 0)
3955 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3956 }
3957 return asInt;
3958 }
3959
3960 /**
3961 * Returns a {@code BigDecimal} rounded according to the MathContext
3962 * settings;
3963 * If rounding is needed a new {@code BigDecimal} is created and returned.
3964 *
3965 * @param val the value to be rounded
3966 * @param mc the context to use.
3967 * @return a {@code BigDecimal} rounded according to the MathContext
3968 * settings. May return {@code value}, if no rounding needed.
3969 * @throws ArithmeticException if the rounding mode is
3970 * {@code RoundingMode.UNNECESSARY} and the
3971 * result is inexact.
3972 */
3973 private static BigDecimal doRound(BigDecimal val, MathContext mc) {
3974 int mcp = mc.precision;
3975 boolean wasDivided = false;
3976 if (mcp > 0) {
3977 BigInteger intVal = val.intVal;
3978 long compactVal = val.intCompact;
3979 int scale = val.scale;
3980 int prec = val.precision();
3981 int mode = mc.roundingMode.oldMode;
3982 int drop;
3983 if (compactVal == INFLATED) {
3984 drop = prec - mcp;
3985 while (drop > 0) {
3986 scale = checkScaleNonZero((long) scale - drop);
3987 intVal = divideAndRoundByTenPow(intVal, drop, mode);
3988 wasDivided = true;
3989 compactVal = compactValFor(intVal);
3990 if (compactVal != INFLATED) {
3991 prec = longDigitLength(compactVal);
3992 break;
3993 }
3994 prec = bigDigitLength(intVal);
3995 drop = prec - mcp;
3996 }
3997 }
3998 if (compactVal != INFLATED) {
3999 drop = prec - mcp; // drop can't be more than 18
4000 while (drop > 0) {
4001 scale = checkScaleNonZero((long) scale - drop);
4002 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4003 wasDivided = true;
4004 prec = longDigitLength(compactVal);
4005 drop = prec - mcp;
4006 intVal = null;
4007 }
4008 }
4009 return wasDivided ? new BigDecimal(intVal,compactVal,scale,prec) : val;
4010 }
4011 return val;
4012 }
4013
4014 /*
4015 * Returns a {@code BigDecimal} created from {@code long} value with
4016 * given scale rounded according to the MathContext settings
4017 */
4018 private static BigDecimal doRound(long compactVal, int scale, MathContext mc) {
4019 int mcp = mc.precision;
4020 if (mcp > 0 && mcp<19) {
4021 int prec = longDigitLength(compactVal);
4022 int drop = prec - mcp; // drop can't be more than 18
4023 while (drop > 0) {
4024 scale = checkScaleNonZero((long) scale - drop);
4025 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4026 prec = longDigitLength(compactVal);
4027 drop = prec - mcp;
4028 }
4029 return valueOf(compactVal, scale, prec);
4030 }
4031 return valueOf(compactVal, scale);
4032 }
4033
4034 /*
4035 * Returns a {@code BigDecimal} created from {@code BigInteger} value with
4036 * given scale rounded according to the MathContext settings
4037 */
4038 private static BigDecimal doRound(BigInteger intVal, int scale, MathContext mc) {
4039 int mcp = mc.precision;
4040 int prec = 0;
4041 if (mcp > 0) {
4042 long compactVal = compactValFor(intVal);
4043 int mode = mc.roundingMode.oldMode;
4044 int drop;
4045 if (compactVal == INFLATED) {
4046 prec = bigDigitLength(intVal);
4047 drop = prec - mcp;
4048 while (drop > 0) {
4049 scale = checkScaleNonZero((long) scale - drop);
4050 intVal = divideAndRoundByTenPow(intVal, drop, mode);
4051 compactVal = compactValFor(intVal);
4052 if (compactVal != INFLATED) {
4053 break;
4054 }
4055 prec = bigDigitLength(intVal);
4056 drop = prec - mcp;
4057 }
4058 }
4059 if (compactVal != INFLATED) {
4060 prec = longDigitLength(compactVal);
4061 drop = prec - mcp; // drop can't be more than 18
4062 while (drop > 0) {
4063 scale = checkScaleNonZero((long) scale - drop);
4064 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
4065 prec = longDigitLength(compactVal);
4066 drop = prec - mcp;
4067 }
4068 return valueOf(compactVal,scale,prec);
4069 }
4070 }
4071 return new BigDecimal(intVal,INFLATED,scale,prec);
4072 }
4073
4074 /*
4075 * Divides {@code BigInteger} value by ten power.
4076 */
4077 private static BigInteger divideAndRoundByTenPow(BigInteger intVal, int tenPow, int roundingMode) {
4078 if (tenPow < LONG_TEN_POWERS_TABLE.length)
4079 intVal = divideAndRound(intVal, LONG_TEN_POWERS_TABLE[tenPow], roundingMode);
4080 else
4081 intVal = divideAndRound(intVal, bigTenToThe(tenPow), roundingMode);
4082 return intVal;
4083 }
4084
4085 /**
4086 * Internally used for division operation for division {@code long} by
4087 * {@code long}.
4088 * The returned {@code BigDecimal} object is the quotient whose scale is set
4089 * to the passed in scale. If the remainder is not zero, it will be rounded
4090 * based on the passed in roundingMode. Also, if the remainder is zero and
4091 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4092 * trailing zeros of the result is stripped to match the preferredScale.
4093 */
4094 private static BigDecimal divideAndRound(long ldividend, long ldivisor, int scale, int roundingMode,
4095 int preferredScale) {
4096
4097 int qsign; // quotient sign
4098 long q = ldividend / ldivisor; // store quotient in long
4099 if (roundingMode == ROUND_DOWN && scale == preferredScale)
4100 return valueOf(q, scale);
4101 long r = ldividend % ldivisor; // store remainder in long
4102 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4103 if (r != 0) {
4104 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4105 return valueOf((increment ? q + qsign : q), scale);
4106 } else {
4107 if (preferredScale != scale)
4108 return createAndStripZerosToMatchScale(q, scale, preferredScale);
4109 else
4110 return valueOf(q, scale);
4111 }
4112 }
4113
4114 /**
4115 * Divides {@code long} by {@code long} and do rounding based on the
4116 * passed in roundingMode.
4117 */
4118 private static long divideAndRound(long ldividend, long ldivisor, int roundingMode) {
4119 int qsign; // quotient sign
4120 long q = ldividend / ldivisor; // store quotient in long
4121 if (roundingMode == ROUND_DOWN)
4122 return q;
4123 long r = ldividend % ldivisor; // store remainder in long
4124 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
4125 if (r != 0) {
4126 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
4127 return increment ? q + qsign : q;
4128 } else {
4129 return q;
4130 }
4131 }
4132
4133 /**
4134 * Tests if quotient has to be incremented according the roundingMode
4135 */
4136 private static boolean needIncrement(long ldivisor, int roundingMode,
4137 int qsign, long q, long r) {
4138 boolean increment = false;
4139 int cmpFracHalf;
4140 /* Round as appropriate */
4141 if (roundingMode == ROUND_UNNECESSARY) { // Rounding prohibited
4142 throw new ArithmeticException("Rounding necessary");
4143 } else if (roundingMode == ROUND_UP) { // Away from zero
4144 increment = true;
4145 } else if (roundingMode == ROUND_DOWN) { // Towards zero
4146 increment = false;
4147 } else if (roundingMode == ROUND_CEILING) { // Towards +infinity
4148 increment = (qsign > 0);
4149 } else if (roundingMode == ROUND_FLOOR) { // Towards -infinity
4150 increment = (qsign < 0);
4151 } else {
4152 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4153 cmpFracHalf = 1; // 2 * r can't fit into long
4154 } else {
4155 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4156 }
4157 if (cmpFracHalf < 0)
4158 increment = false; // We're closer to higher digit
4159 else if (cmpFracHalf > 0) // We're closer to lower digit
4160 increment = true;
4161 else if (roundingMode == ROUND_HALF_UP)
4162 increment = true;
4163 else if (roundingMode == ROUND_HALF_DOWN)
4164 increment = false;
4165 else
4166 // roundingMode == ROUND_HALF_EVEN, true iff quotient is odd
4167 increment = (q & 1L) != 0L ;
4168 }
4169 return increment;
4170 }
4171
4172 /**
4173 * Divides {@code BigInteger} value by {@code long} value and
4174 * do rounding based on the passed in roundingMode.
4175 */
4176 private static BigInteger divideAndRound(BigInteger bdividend, long ldivisor, int roundingMode) {
4177 boolean isRemainderZero; // record remainder is zero or not
4178 int qsign; // quotient sign
4179 long r = 0; // store quotient & remainder in long
4180 MutableBigInteger mq = null; // store quotient
4181 // Descend into mutables for faster remainder checks
4182 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4183 mq = new MutableBigInteger();
4184 r = mdividend.divide(ldivisor, mq);
4185 isRemainderZero = (r == 0);
4186 qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4187 if (!isRemainderZero) {
4188 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4189 mq.add(MutableBigInteger.ONE);
4190 }
4191 }
4192 return mq.toBigInteger(qsign);
4193 }
4194
4195 /**
4196 * Internally used for division operation for division {@code BigInteger}
4197 * by {@code long}.
4198 * The returned {@code BigDecimal} object is the quotient whose scale is set
4199 * to the passed in scale. If the remainder is not zero, it will be rounded
4200 * based on the passed in roundingMode. Also, if the remainder is zero and
4201 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4202 * trailing zeros of the result is stripped to match the preferredScale.
4203 */
4204 private static BigDecimal divideAndRound(BigInteger bdividend,
4205 long ldivisor, int scale, int roundingMode, int preferredScale) {
4206 boolean isRemainderZero; // record remainder is zero or not
4207 int qsign; // quotient sign
4208 long r = 0; // store quotient & remainder in long
4209 MutableBigInteger mq = null; // store quotient
4210 // Descend into mutables for faster remainder checks
4211 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4212 mq = new MutableBigInteger();
4213 r = mdividend.divide(ldivisor, mq);
4214 isRemainderZero = (r == 0);
4215 qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
4216 if (!isRemainderZero) {
4217 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
4218 mq.add(MutableBigInteger.ONE);
4219 }
4220 return mq.toBigDecimal(qsign, scale);
4221 } else {
4222 if (preferredScale != scale) {
4223 long compactVal = mq.toCompactValue(qsign);
4224 if(compactVal!=INFLATED) {
4225 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4226 }
4227 BigInteger intVal = mq.toBigInteger(qsign);
4228 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
4229 } else {
4230 return mq.toBigDecimal(qsign, scale);
4231 }
4232 }
4233 }
4234
4235 /**
4236 * Tests if quotient has to be incremented according the roundingMode
4237 */
4238 private static boolean needIncrement(long ldivisor, int roundingMode,
4239 int qsign, MutableBigInteger mq, long r) {
4240 boolean increment = false;
4241 /* Round as appropriate */
4242 if (roundingMode == ROUND_UNNECESSARY) { // Rounding prohibited
4243 throw new ArithmeticException("Rounding necessary");
4244 } else if (roundingMode == ROUND_UP) { // Away from zero
4245 increment = true;
4246 } else if (roundingMode == ROUND_DOWN) { // Towards zero
4247 increment = false;
4248 } else if (roundingMode == ROUND_CEILING) { // Towards +infinity
4249 increment = (qsign > 0);
4250 } else if (roundingMode == ROUND_FLOOR) { // Towards -infinity
4251 increment = (qsign < 0);
4252 } else {
4253 int cmpFracHalf;
4254 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
4255 cmpFracHalf = 1; // 2 * r can't fit into long
4256 } else {
4257 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
4258 }
4259 if (cmpFracHalf < 0)
4260 increment = false; // We're closer to higher digit
4261 else if (cmpFracHalf > 0) // We're closer to lower digit
4262 increment = true;
4263 else if (roundingMode == ROUND_HALF_UP)
4264 increment = true;
4265 else if (roundingMode == ROUND_HALF_DOWN)
4266 increment = false;
4267 else
4268 // roundingMode == ROUND_HALF_EVEN, true iff quotient is odd
4269 increment = mq.isOdd();
4270 }
4271 return increment;
4272 }
4273
4274 /**
4275 * Divides {@code BigInteger} value by {@code BigInteger} value and
4276 * do rounding based on the passed in roundingMode.
4277 */
4278 private static BigInteger divideAndRound(BigInteger bdividend, BigInteger bdivisor, int roundingMode) {
4279 boolean isRemainderZero; // record remainder is zero or not
4280 int qsign; // quotient sign
4281 // Descend into mutables for faster remainder checks
4282 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4283 MutableBigInteger mq = new MutableBigInteger();
4284 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4285 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4286 isRemainderZero = mr.isZero();
4287 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4288 if (!isRemainderZero) {
4289 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4290 mq.add(MutableBigInteger.ONE);
4291 }
4292 }
4293 return mq.toBigInteger(qsign);
4294 }
4295
4296 /**
4297 * Internally used for division operation for division {@code BigInteger}
4298 * by {@code BigInteger}.
4299 * The returned {@code BigDecimal} object is the quotient whose scale is set
4300 * to the passed in scale. If the remainder is not zero, it will be rounded
4301 * based on the passed in roundingMode. Also, if the remainder is zero and
4302 * the last parameter, i.e. preferredScale is NOT equal to scale, the
4303 * trailing zeros of the result is stripped to match the preferredScale.
4304 */
4305 private static BigDecimal divideAndRound(BigInteger bdividend, BigInteger bdivisor, int scale, int roundingMode,
4306 int preferredScale) {
4307 boolean isRemainderZero; // record remainder is zero or not
4308 int qsign; // quotient sign
4309 // Descend into mutables for faster remainder checks
4310 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
4311 MutableBigInteger mq = new MutableBigInteger();
4312 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
4313 MutableBigInteger mr = mdividend.divide(mdivisor, mq);
4314 isRemainderZero = mr.isZero();
4315 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
4316 if (!isRemainderZero) {
4317 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
4318 mq.add(MutableBigInteger.ONE);
4319 }
4320 return mq.toBigDecimal(qsign, scale);
4321 } else {
4322 if (preferredScale != scale) {
4323 long compactVal = mq.toCompactValue(qsign);
4324 if (compactVal != INFLATED) {
4325 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
4326 }
4327 BigInteger intVal = mq.toBigInteger(qsign);
4328 return createAndStripZerosToMatchScale(intVal, scale, preferredScale);
4329 } else {
4330 return mq.toBigDecimal(qsign, scale);
4331 }
4332 }
4333 }
4334
4335 /**
4336 * Tests if quotient has to be incremented according the roundingMode
4337 */
4338 private static boolean needIncrement(MutableBigInteger mdivisor, int roundingMode, int qsign, MutableBigInteger mq,
4339 MutableBigInteger mr) {
4340 boolean increment = false;
4341 /* Round as appropriate */
4342 if (roundingMode == ROUND_UNNECESSARY) { // Rounding prohibited
4343 throw new ArithmeticException("Rounding necessary");
4344 } else if (roundingMode == ROUND_UP) { // Away from zero
4345 increment = true;
4346 } else if (roundingMode == ROUND_DOWN) { // Towards zero
4347 increment = false;
4348 } else if (roundingMode == ROUND_CEILING) { // Towards +infinity
4349 increment = (qsign > 0);
4350 } else if (roundingMode == ROUND_FLOOR) { // Towards -infinity
4351 increment = (qsign < 0);
4352 } else {
4353 int cmpFracHalf = mr.compareHalf(mdivisor);
4354 if (cmpFracHalf < 0)
4355 increment = false; // We're closer to higher digit
4356 else if (cmpFracHalf > 0) // We're closer to lower digit
4357 increment = true;
4358 else if (roundingMode == ROUND_HALF_UP)
4359 increment = true;
4360 else if (roundingMode == ROUND_HALF_DOWN)
4361 increment = false;
4362 else
4363 // roundingMode == ROUND_HALF_EVEN, true iff quotient is odd
4364 increment = mq.isOdd();
4365 }
4366 return increment;
4367 }
4368
4369 /**
4370 * Remove insignificant trailing zeros from this
4371 * {@code BigInteger} value until the preferred scale is reached or no
4372 * more zeros can be removed. If the preferred scale is less than
4373 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4374 *
4375 * @return new {@code BigDecimal} with a scale possibly reduced
4376 * to be closed to the preferred scale.
4377 */
4378 private static BigDecimal createAndStripZerosToMatchScale(BigInteger intVal, int scale, long preferredScale) {
4379 BigInteger qr[]; // quotient-remainder pair
4380 while (intVal.compareMagnitude(BigInteger.TEN) >= 0
4381 && scale > preferredScale) {
4382 if (intVal.testBit(0))
4383 break; // odd number cannot end in 0
4384 qr = intVal.divideAndRemainder(BigInteger.TEN);
4385 if (qr[1].signum() != 0)
4386 break; // non-0 remainder
4387 intVal = qr[0];
4388 scale = checkScale(intVal,(long) scale - 1); // could Overflow
4389 }
4390 return valueOf(intVal, scale, 0);
4391 }
4392
4393 /**
4394 * Remove insignificant trailing zeros from this
4395 * {@code long} value until the preferred scale is reached or no
4396 * more zeros can be removed. If the preferred scale is less than
4397 * Integer.MIN_VALUE, all the trailing zeros will be removed.
4398 *
4399 * @return new {@code BigDecimal} with a scale possibly reduced
4400 * to be closed to the preferred scale.
4401 */
4402 private static BigDecimal createAndStripZerosToMatchScale(long compactVal, int scale, long preferredScale) {
4403 while (Math.abs(compactVal) >= 10L && scale > preferredScale) {
4404 if ((compactVal & 1L) != 0L)
4405 break; // odd number cannot end in 0
4406 long r = compactVal % 10L;
4407 if (r != 0L)
4408 break; // non-0 remainder
4409 compactVal /= 10;
4410 scale = checkScale(compactVal, (long) scale - 1); // could Overflow
4411 }
4412 return valueOf(compactVal, scale);
4413 }
4414
4415 private static BigDecimal stripZerosToMatchScale(BigInteger intVal, long intCompact, int scale, int preferredScale) {
4416 if(intCompact!=INFLATED) {
4417 return createAndStripZerosToMatchScale(intCompact, scale, preferredScale);
4418 } else {
4419 return createAndStripZerosToMatchScale(intVal==null ? INFLATED_BIGINT : intVal,
4420 scale, preferredScale);
4421 }
4422 }
4423
4424 /*
4425 * returns INFLATED if oveflow
4426 */
4427 private static long add(long xs, long ys){
4428 long sum = xs + ys;
4429 // See "Hacker's Delight" section 2-12 for explanation of
4430 // the overflow test.
4431 if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) { // not overflowed
4432 return sum;
4433 }
4434 return INFLATED;
4435 }
4436
4437 private static BigDecimal add(long xs, long ys, int scale){
4438 long sum = add(xs, ys);
4439 if (sum!=INFLATED)
4440 return BigDecimal.valueOf(sum, scale);
4441 return new BigDecimal(BigInteger.valueOf(xs).add(ys), scale);
4442 }
4443
4444 private static BigDecimal add(final long xs, int scale1, final long ys, int scale2) {
4445 long sdiff = (long) scale1 - scale2;
4446 if (sdiff == 0) {
4447 return add(xs, ys, scale1);
4448 } else if (sdiff < 0) {
4449 int raise = checkScale(xs,-sdiff);
4450 long scaledX = longMultiplyPowerTen(xs, raise);
4451 if (scaledX != INFLATED) {
4452 return add(scaledX, ys, scale2);
4453 } else {
4454 BigInteger bigsum = bigMultiplyPowerTen(xs,raise).add(ys);
4455 return ((xs^ys)>=0) ? // same sign test
4456 new BigDecimal(bigsum, INFLATED, scale2, 0)
4457 : valueOf(bigsum, scale2, 0);
4458 }
4459 } else {
4460 int raise = checkScale(ys,sdiff);
4461 long scaledY = longMultiplyPowerTen(ys, raise);
4462 if (scaledY != INFLATED) {
4463 return add(xs, scaledY, scale1);
4464 } else {
4465 BigInteger bigsum = bigMultiplyPowerTen(ys,raise).add(xs);
4466 return ((xs^ys)>=0) ?
4467 new BigDecimal(bigsum, INFLATED, scale1, 0)
4468 : valueOf(bigsum, scale1, 0);
4469 }
4470 }
4471 }
4472
4473 private static BigDecimal add(final long xs, int scale1, BigInteger snd, int scale2) {
4474 int rscale = scale1;
4475 long sdiff = (long)rscale - scale2;
4476 boolean sameSigns = (Long.signum(xs) == snd.signum);
4477 BigInteger sum;
4478 if (sdiff < 0) {
4479 int raise = checkScale(xs,-sdiff);
4480 rscale = scale2;
4481 long scaledX = longMultiplyPowerTen(xs, raise);
4482 if (scaledX == INFLATED) {
4483 sum = snd.add(bigMultiplyPowerTen(xs,raise));
4484 } else {
4485 sum = snd.add(scaledX);
4486 }
4487 } else { //if (sdiff > 0) {
4488 int raise = checkScale(snd,sdiff);
4489 snd = bigMultiplyPowerTen(snd,raise);
4490 sum = snd.add(xs);
4491 }
4492 return (sameSigns) ?
4493 new BigDecimal(sum, INFLATED, rscale, 0) :
4494 valueOf(sum, rscale, 0);
4495 }
4496
4497 private static BigDecimal add(BigInteger fst, int scale1, BigInteger snd, int scale2) {
4498 int rscale = scale1;
4499 long sdiff = (long)rscale - scale2;
4500 if (sdiff != 0) {
4501 if (sdiff < 0) {
4502 int raise = checkScale(fst,-sdiff);
4503 rscale = scale2;
4504 fst = bigMultiplyPowerTen(fst,raise);
4505 } else {
4506 int raise = checkScale(snd,sdiff);
4507 snd = bigMultiplyPowerTen(snd,raise);
4508 }
4509 }
4510 BigInteger sum = fst.add(snd);
4511 return (fst.signum == snd.signum) ?
4512 new BigDecimal(sum, INFLATED, rscale, 0) :
4513 valueOf(sum, rscale, 0);
4514 }
4515
4516 private static BigInteger bigMultiplyPowerTen(long value, int n) {
4517 if (n <= 0)
4518 return BigInteger.valueOf(value);
4519 return bigTenToThe(n).multiply(value);
4520 }
4521
4522 private static BigInteger bigMultiplyPowerTen(BigInteger value, int n) {
4523 if (n <= 0)
4524 return value;
4525 if(n<LONG_TEN_POWERS_TABLE.length) {
4526 return value.multiply(LONG_TEN_POWERS_TABLE[n]);
4527 }
4528 return value.multiply(bigTenToThe(n));
4529 }
4530
4531 /**
4532 * Returns a {@code BigDecimal} whose value is {@code (xs /
4533 * ys)}, with rounding according to the context settings.
4534 *
4535 * Fast path - used only when (xscale <= yscale && yscale < 18
4536 * && mc.presision<18) {
4537 */
4538 private static BigDecimal divideSmallFastPath(final long xs, int xscale, final long ys, int yscale, long preferredScale, MathContext mc) {
4539 int mcp = mc.precision;
4540 int roundingMode = mc.roundingMode.oldMode;
4541
4542 // assert xscale <= yscale && yscale<18 && mcp<18
4543 int xraise = yscale - xscale; // xraise >=0
4544 long scaledX = (xraise==0) ? xs :
4545 longMultiplyPowerTen(xs, xraise); // can't overflow here!
4546 BigDecimal quotient;
4547
4548 int cmp = longCompareMagnitude(scaledX, ys);
4549 if(cmp > 0) { // satisfy constraint (b)
4550 yscale -= 1; // [that is, divisor *= 10]
4551 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4552 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4553 // assert newScale >= xscale
4554 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4555 long scaledXs;
4556 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
4557 quotient = null;
4558 if((mcp-1) >=0 && (mcp-1)<LONG_TEN_POWERS_TABLE.length) {
4559 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp-1], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4560 }
4561 if(quotient==null) {
4562 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp-1);
4563 quotient = divideAndRound(rb, ys,
4564 scl, roundingMode, checkScaleNonZero(preferredScale));
4565 }
4566 } else {
4567 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4568 }
4569 } else {
4570 int newScale = checkScaleNonZero((long) xscale - mcp);
4571 // assert newScale >= yscale
4572 if (newScale == yscale) { // easy case
4573 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4574 } else {
4575 int raise = checkScaleNonZero((long) newScale - yscale);
4576 long scaledYs;
4577 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4578 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4579 quotient = divideAndRound(BigInteger.valueOf(xs),
4580 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4581 } else {
4582 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4583 }
4584 }
4585 }
4586 } else {
4587 // abs(scaledX) <= abs(ys)
4588 // result is "scaledX * 10^msp / ys"
4589 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4590 if(cmp==0) {
4591 // abs(scaleX)== abs(ys) => result will be scaled 10^mcp + correct sign
4592 quotient = roundedTenPower(((scaledX < 0) == (ys < 0)) ? 1 : -1, mcp, scl, checkScaleNonZero(preferredScale));
4593 } else {
4594 // abs(scaledX) < abs(ys)
4595 long scaledXs;
4596 if ((scaledXs = longMultiplyPowerTen(scaledX, mcp)) == INFLATED) {
4597 quotient = null;
4598 if(mcp<LONG_TEN_POWERS_TABLE.length) {
4599 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4600 }
4601 if(quotient==null) {
4602 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp);
4603 quotient = divideAndRound(rb, ys,
4604 scl, roundingMode, checkScaleNonZero(preferredScale));
4605 }
4606 } else {
4607 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4608 }
4609 }
4610 }
4611 // doRound, here, only affects 1000000000 case.
4612 return doRound(quotient,mc);
4613 }
4614
4615 /**
4616 * Returns a {@code BigDecimal} whose value is {@code (xs /
4617 * ys)}, with rounding according to the context settings.
4618 */
4619 private static BigDecimal divide(final long xs, int xscale, final long ys, int yscale, long preferredScale, MathContext mc) {
4620 int mcp = mc.precision;
4621 if(xscale <= yscale && yscale < 18 && mcp<18) {
4622 return divideSmallFastPath(xs, xscale, ys, yscale, preferredScale, mc);
4623 }
4624 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
4625 yscale -= 1; // [that is, divisor *= 10]
4626 }
4627 int roundingMode = mc.roundingMode.oldMode;
4628 // In order to find out whether the divide generates the exact result,
4629 // we avoid calling the above divide method. 'quotient' holds the
4630 // return BigDecimal object whose scale will be set to 'scl'.
4631 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4632 BigDecimal quotient;
4633 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4634 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4635 long scaledXs;
4636 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) {
4637 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4638 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4639 } else {
4640 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4641 }
4642 } else {
4643 int newScale = checkScaleNonZero((long) xscale - mcp);
4644 // assert newScale >= yscale
4645 if (newScale == yscale) { // easy case
4646 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4647 } else {
4648 int raise = checkScaleNonZero((long) newScale - yscale);
4649 long scaledYs;
4650 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4651 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4652 quotient = divideAndRound(BigInteger.valueOf(xs),
4653 rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4654 } else {
4655 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4656 }
4657 }
4658 }
4659 // doRound, here, only affects 1000000000 case.
4660 return doRound(quotient,mc);
4661 }
4662
4663 /**
4664 * Returns a {@code BigDecimal} whose value is {@code (xs /
4665 * ys)}, with rounding according to the context settings.
4666 */
4667 private static BigDecimal divide(BigInteger xs, int xscale, long ys, int yscale, long preferredScale, MathContext mc) {
4668 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4669 if ((-compareMagnitudeNormalized(ys, yscale, xs, xscale)) > 0) {// satisfy constraint (b)
4670 yscale -= 1; // [that is, divisor *= 10]
4671 }
4672 int mcp = mc.precision;
4673 int roundingMode = mc.roundingMode.oldMode;
4674
4675 // In order to find out whether the divide generates the exact result,
4676 // we avoid calling the above divide method. 'quotient' holds the
4677 // return BigDecimal object whose scale will be set to 'scl'.
4678 BigDecimal quotient;
4679 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4680 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4681 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4682 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4683 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4684 } else {
4685 int newScale = checkScaleNonZero((long) xscale - mcp);
4686 // assert newScale >= yscale
4687 if (newScale == yscale) { // easy case
4688 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale));
4689 } else {
4690 int raise = checkScaleNonZero((long) newScale - yscale);
4691 long scaledYs;
4692 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) {
4693 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4694 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4695 } else {
4696 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale));
4697 }
4698 }
4699 }
4700 // doRound, here, only affects 1000000000 case.
4701 return doRound(quotient, mc);
4702 }
4703
4704 /**
4705 * Returns a {@code BigDecimal} whose value is {@code (xs /
4706 * ys)}, with rounding according to the context settings.
4707 */
4708 private static BigDecimal divide(long xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
4709 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4710 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
4711 yscale -= 1; // [that is, divisor *= 10]
4712 }
4713 int mcp = mc.precision;
4714 int roundingMode = mc.roundingMode.oldMode;
4715
4716 // In order to find out whether the divide generates the exact result,
4717 // we avoid calling the above divide method. 'quotient' holds the
4718 // return BigDecimal object whose scale will be set to 'scl'.
4719 BigDecimal quotient;
4720 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4721 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4722 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4723 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4724 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4725 } else {
4726 int newScale = checkScaleNonZero((long) xscale - mcp);
4727 int raise = checkScaleNonZero((long) newScale - yscale);
4728 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4729 quotient = divideAndRound(BigInteger.valueOf(xs), rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4730 }
4731 // doRound, here, only affects 1000000000 case.
4732 return doRound(quotient, mc);
4733 }
4734
4735 /**
4736 * Returns a {@code BigDecimal} whose value is {@code (xs /
4737 * ys)}, with rounding according to the context settings.
4738 */
4739 private static BigDecimal divide(BigInteger xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) {
4740 // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4741 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b)
4742 yscale -= 1; // [that is, divisor *= 10]
4743 }
4744 int mcp = mc.precision;
4745 int roundingMode = mc.roundingMode.oldMode;
4746
4747 // In order to find out whether the divide generates the exact result,
4748 // we avoid calling the above divide method. 'quotient' holds the
4749 // return BigDecimal object whose scale will be set to 'scl'.
4750 BigDecimal quotient;
4751 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp);
4752 if (checkScaleNonZero((long) mcp + yscale) > xscale) {
4753 int raise = checkScaleNonZero((long) mcp + yscale - xscale);
4754 BigInteger rb = bigMultiplyPowerTen(xs,raise);
4755 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale));
4756 } else {
4757 int newScale = checkScaleNonZero((long) xscale - mcp);
4758 int raise = checkScaleNonZero((long) newScale - yscale);
4759 BigInteger rb = bigMultiplyPowerTen(ys,raise);
4760 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale));
4761 }
4762 // doRound, here, only affects 1000000000 case.
4763 return doRound(quotient, mc);
4764 }
4765
4766 /*
4767 * performs divideAndRound for (dividend0*dividend1, divisor)
4768 * returns null if quotient can't fit into long value;
4769 */
4770 private static BigDecimal multiplyDivideAndRound(long dividend0, long dividend1, long divisor, int scale, int roundingMode,
4771 int preferredScale) {
4772 int qsign = Long.signum(dividend0)*Long.signum(dividend1)*Long.signum(divisor);
4773 dividend0 = Math.abs(dividend0);
4774 dividend1 = Math.abs(dividend1);
4775 divisor = Math.abs(divisor);
4776 // multiply dividend0 * dividend1
4777 long d0_hi = dividend0 >>> 32;
4778 long d0_lo = dividend0 & LONG_MASK;
4779 long d1_hi = dividend1 >>> 32;
4780 long d1_lo = dividend1 & LONG_MASK;
4781 long product = d0_lo * d1_lo;
4782 long d0 = product & LONG_MASK;
4783 long d1 = product >>> 32;
4784 product = d0_hi * d1_lo + d1;
4785 d1 = product & LONG_MASK;
4786 long d2 = product >>> 32;
4787 product = d0_lo * d1_hi + d1;
4788 d1 = product & LONG_MASK;
4789 d2 += product >>> 32;
4790 long d3 = d2>>>32;
4791 d2 &= LONG_MASK;
4792 product = d0_hi*d1_hi + d2;
4793 d2 = product & LONG_MASK;
4794 d3 = ((product>>>32) + d3) & LONG_MASK;
4795 final long dividendHi = make64(d3,d2);
4796 final long dividendLo = make64(d1,d0);
4797 // divide
4798 return divideAndRound128(dividendHi, dividendLo, divisor, qsign, scale, roundingMode, preferredScale);
4799 }
4800
4801 private static final long DIV_NUM_BASE = (1L<<32); // Number base (32 bits).
4802
4803 /*
4804 * divideAndRound 128-bit value by long divisor.
4805 * returns null if quotient can't fit into long value;
4806 * Specialized version of Knuth's division
4807 */
4808 private static BigDecimal divideAndRound128(final long dividendHi, final long dividendLo, long divisor, int sign,
4809 int scale, int roundingMode, int preferredScale) {
4810 if (dividendHi >= divisor) {
4811 return null;
4812 }
4813 final int shift = Long.numberOfLeadingZeros(divisor);
4814 divisor <<= shift;
4815
4816 final long v1 = divisor >>> 32;
4817 final long v0 = divisor & LONG_MASK;
4818
4819 long q1, q0;
4820 long r_tmp;
4821
4822 long tmp = dividendLo << shift;
4823 long u1 = tmp >>> 32;
4824 long u0 = tmp & LONG_MASK;
4825
4826 tmp = (dividendHi << shift) | (dividendLo >>> 64 - shift);
4827 long u2 = tmp & LONG_MASK;
4828 tmp = divWord(tmp,v1);
4829 q1 = tmp & LONG_MASK;
4830 r_tmp = tmp >>> 32;
4831 while(q1 >= DIV_NUM_BASE || unsignedLongCompare(q1*v0, make64(r_tmp, u1))) {
4832 q1--;
4833 r_tmp += v1;
4834 if (r_tmp >= DIV_NUM_BASE)
4835 break;
4836 }
4837 tmp = mulsub(u2,u1,v1,v0,q1);
4838 u1 = tmp & LONG_MASK;
4839 tmp = divWord(tmp,v1);
4840 q0 = tmp & LONG_MASK;
4841 r_tmp = tmp >>> 32;
4842 while(q0 >= DIV_NUM_BASE || unsignedLongCompare(q0*v0,make64(r_tmp,u0))) {
4843 q0--;
4844 r_tmp += v1;
4845 if (r_tmp >= DIV_NUM_BASE)
4846 break;
4847 }
4848 if((int)q1 < 0) {
4849 // result (which is positive and unsigned here)
4850 // can't fit into long due to sign bit is used for value
4851 MutableBigInteger mq = new MutableBigInteger(new int[]{(int)q1, (int)q0});
4852 if (roundingMode == ROUND_DOWN && scale == preferredScale) {
4853 return mq.toBigDecimal(sign, scale);
4854 }
4855 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
4856 if (r != 0) {
4857 if(needIncrement(divisor >>> shift, roundingMode, sign, mq, r)){
4858 mq.add(MutableBigInteger.ONE);
4859 }
4860 return mq.toBigDecimal(sign, scale);
4861 } else {
4862 if (preferredScale != scale) {
4863 BigInteger intVal = mq.toBigInteger(sign);
4864 return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
4865 } else {
4866 return mq.toBigDecimal(sign, scale);
4867 }
4868 }
4869 }
4870 long q = make64(q1,q0);
4871 q*=sign;
4872 if (roundingMode == ROUND_DOWN && scale == preferredScale)
4873 return valueOf(q, scale);
4874 long r = mulsub(u1, u0, v1, v0, q0) >>> shift;
4875 if (r != 0) {
4876 boolean increment = needIncrement(divisor >>> shift, roundingMode, sign, q, r);
4877 return valueOf((increment ? q + sign : q), scale);
4878 } else {
4879 if (preferredScale != scale) {
4880 return createAndStripZerosToMatchScale(q, scale, preferredScale);
4881 } else {
4882 return valueOf(q, scale);
4883 }
4884 }
4885 }
4886
4887 /*
4888 * calculate divideAndRound for ldividend*10^raise / divisor
4889 * when abs(dividend)==abs(divisor);
4890 */
4891 private static BigDecimal roundedTenPower(int qsign, int raise, int scale, int preferredScale) {
4892 if (scale > preferredScale) {
4893 int diff = scale - preferredScale;
4894 if(diff < raise) {
4895 return scaledTenPow(raise - diff, qsign, preferredScale);
4896 } else {
4897 return valueOf(qsign,scale-raise);
4898 }
4899 } else {
4900 return scaledTenPow(raise, qsign, scale);
4901 }
4902 }
4903
4904 static BigDecimal scaledTenPow(int n, int sign, int scale) {
4905 if (n < LONG_TEN_POWERS_TABLE.length)
4906 return valueOf(sign*LONG_TEN_POWERS_TABLE[n],scale);
4907 else {
4908 BigInteger unscaledVal = bigTenToThe(n);
4909 if(sign==-1) {
4910 unscaledVal = unscaledVal.negate();
4911 }
4912 return new BigDecimal(unscaledVal, INFLATED, scale, n+1);
4913 }
4914 }
4915
4916 private static long divWord(long n, long dLong) {
4917 long r;
4918 long q;
4919 if (dLong == 1) {
4920 q = (int)n;
4921 return (q & LONG_MASK);
4922 }
4923 // Approximate the quotient and remainder
4924 q = (n >>> 1) / (dLong >>> 1);
4925 r = n - q*dLong;
4926
4927 // Correct the approximation
4928 while (r < 0) {
4929 r += dLong;
4930 q--;
4931 }
4932 while (r >= dLong) {
4933 r -= dLong;
4934 q++;
4935 }
4936 // n - q*dlong == r && 0 <= r <dLong, hence we're done.
4937 return (r << 32) | (q & LONG_MASK);
4938 }
4939
4940 private static long make64(long hi, long lo) {
4941 return hi<<32 | lo;
4942 }
4943
4944 private static long mulsub(long u1, long u0, final long v1, final long v0, long q0) {
4945 long tmp = u0 - q0*v0;
4946 return make64(u1 + (tmp>>>32) - q0*v1,tmp & LONG_MASK);
4947 }
4948
4949 private static boolean unsignedLongCompare(long one, long two) {
4950 return (one+Long.MIN_VALUE) > (two+Long.MIN_VALUE);
4951 }
4952
4953 private static boolean unsignedLongCompareEq(long one, long two) {
4954 return (one+Long.MIN_VALUE) >= (two+Long.MIN_VALUE);
4955 }
4956
4957
4958 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4959 private static int compareMagnitudeNormalized(long xs, int xscale, long ys, int yscale) {
4960 // assert xs!=0 && ys!=0
4961 int sdiff = xscale - yscale;
4962 if (sdiff != 0) {
4963 if (sdiff < 0) {
4964 xs = longMultiplyPowerTen(xs, -sdiff);
4965 } else { // sdiff > 0
4966 ys = longMultiplyPowerTen(ys, sdiff);
4967 }
4968 }
4969 if (xs != INFLATED)
4970 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
4971 else
4972 return 1;
4973 }
4974
4975 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4976 private static int compareMagnitudeNormalized(long xs, int xscale, BigInteger ys, int yscale) {
4977 // assert "ys can't be represented as long"
4978 if (xs == 0)
4979 return -1;
4980 int sdiff = xscale - yscale;
4981 if (sdiff < 0) {
4982 if (longMultiplyPowerTen(xs, -sdiff) == INFLATED ) {
4983 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
4984 }
4985 }
4986 return -1;
4987 }
4988
4989 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
4990 private static int compareMagnitudeNormalized(BigInteger xs, int xscale, BigInteger ys, int yscale) {
4991 int sdiff = xscale - yscale;
4992 if (sdiff < 0) {
4993 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys);
4994 } else { // sdiff >= 0
4995 return xs.compareMagnitude(bigMultiplyPowerTen(ys, sdiff));
4996 }
4997 }
4998
4999 private static long multiply(long x, long y){
5000 long product = x * y;
5001 long ax = Math.abs(x);
5002 long ay = Math.abs(y);
5003 if (((ax | ay) >>> 31 == 0) || (y == 0) || (product / y == x)){
5004 return product;
5005 }
5006 return INFLATED;
5007 }
5008
5009 private static BigDecimal multiply(long x, long y, int scale) {
5010 long product = multiply(x, y);
5011 if(product!=INFLATED) {
5012 return valueOf(product,scale);
5013 }
5014 return new BigDecimal(BigInteger.valueOf(x).multiply(y),INFLATED,scale,0);
5015 }
5016
5017 private static BigDecimal multiply(long x, BigInteger y, int scale) {
5018 if(x==0) {
5019 return zeroValueOf(scale);
5020 }
5021 return new BigDecimal(y.multiply(x),INFLATED,scale,0);
5022 }
5023
5024 private static BigDecimal multiply(BigInteger x, BigInteger y, int scale) {
5025 return new BigDecimal(x.multiply(y),INFLATED,scale,0);
5026 }
5027
5028 /**
5029 * Multiplies two long values and rounds according {@code MathContext}
5030 */
5031 private static BigDecimal multiplyAndRound(long x, long y, int scale, MathContext mc) {
5032 long product = multiply(x, y);
5033 if(product!=INFLATED) {
5034 return doRound(product, scale, mc);
5035 }
5036 // attempt to do it in 128 bits
5037 int rsign = 1;
5038 if(x < 0) {
5039 x = -x;
5040 rsign = -1;
5041 }
5042 if(y < 0) {
5043 y = -y;
5044 rsign *= -1;
5045 }
5046 // multiply dividend0 * dividend1
5047 long m0_hi = x >>> 32;
5048 long m0_lo = x & LONG_MASK;
5049 long m1_hi = y >>> 32;
5050 long m1_lo = y & LONG_MASK;
5051 product = m0_lo * m1_lo;
5052 long m0 = product & LONG_MASK;
5053 long m1 = product >>> 32;
5054 product = m0_hi * m1_lo + m1;
5055 m1 = product & LONG_MASK;
5056 long m2 = product >>> 32;
5057 product = m0_lo * m1_hi + m1;
5058 m1 = product & LONG_MASK;
5059 m2 += product >>> 32;
5060 long m3 = m2>>>32;
5061 m2 &= LONG_MASK;
5062 product = m0_hi*m1_hi + m2;
5063 m2 = product & LONG_MASK;
5064 m3 = ((product>>>32) + m3) & LONG_MASK;
5065 final long mHi = make64(m3,m2);
5066 final long mLo = make64(m1,m0);
5067 BigDecimal res = doRound128(mHi, mLo, rsign, scale, mc);
5068 if(res!=null) {
5069 return res;
5070 }
5071 res = new BigDecimal(BigInteger.valueOf(x).multiply(y*rsign), INFLATED, scale, 0);
5072 return doRound(res,mc);
5073 }
5074
5075 private static BigDecimal multiplyAndRound(long x, BigInteger y, int scale, MathContext mc) {
5076 if(x==0) {
5077 return zeroValueOf(scale);
5078 }
5079 return doRound(y.multiply(x), scale, mc);
5080 }
5081
5082 private static BigDecimal multiplyAndRound(BigInteger x, BigInteger y, int scale, MathContext mc) {
5083 return doRound(x.multiply(y), scale, mc);
5084 }
5085
5086 /**
5087 * rounds 128-bit value according {@code MathContext}
5088 * returns null if result can't be repsented as compact BigDecimal.
5089 */
5090 private static BigDecimal doRound128(long hi, long lo, int sign, int scale, MathContext mc) {
5091 int mcp = mc.precision;
5092 int drop;
5093 BigDecimal res = null;
5094 if(((drop = precision(hi, lo) - mcp) > 0)&&(drop<LONG_TEN_POWERS_TABLE.length)) {
5095 scale = checkScaleNonZero((long)scale - drop);
5096 res = divideAndRound128(hi, lo, LONG_TEN_POWERS_TABLE[drop], sign, scale, mc.roundingMode.oldMode, scale);
5097 }
5098 if(res!=null) {
5099 return doRound(res,mc);
5100 }
5101 return null;
5102 }
5103
5104 private static final long[][] LONGLONG_TEN_POWERS_TABLE = {
5105 { 0L, 0x8AC7230489E80000L }, //10^19
5106 { 0x5L, 0x6bc75e2d63100000L }, //10^20
5107 { 0x36L, 0x35c9adc5dea00000L }, //10^21
5108 { 0x21eL, 0x19e0c9bab2400000L }, //10^22
5109 { 0x152dL, 0x02c7e14af6800000L }, //10^23
5110 { 0xd3c2L, 0x1bcecceda1000000L }, //10^24
5111 { 0x84595L, 0x161401484a000000L }, //10^25
5112 { 0x52b7d2L, 0xdcc80cd2e4000000L }, //10^26
5113 { 0x33b2e3cL, 0x9fd0803ce8000000L }, //10^27
5114 { 0x204fce5eL, 0x3e25026110000000L }, //10^28
5115 { 0x1431e0faeL, 0x6d7217caa0000000L }, //10^29
5116 { 0xc9f2c9cd0L, 0x4674edea40000000L }, //10^30
5117 { 0x7e37be2022L, 0xc0914b2680000000L }, //10^31
5118 { 0x4ee2d6d415bL, 0x85acef8100000000L }, //10^32
5119 { 0x314dc6448d93L, 0x38c15b0a00000000L }, //10^33
5120 { 0x1ed09bead87c0L, 0x378d8e6400000000L }, //10^34
5121 { 0x13426172c74d82L, 0x2b878fe800000000L }, //10^35
5122 { 0xc097ce7bc90715L, 0xb34b9f1000000000L }, //10^36
5123 { 0x785ee10d5da46d9L, 0x00f436a000000000L }, //10^37
5124 { 0x4b3b4ca85a86c47aL, 0x098a224000000000L }, //10^38
5125 };
5126
5127 /*
5128 * returns precision of 128-bit value
5129 */
5130 private static int precision(long hi, long lo){
5131 if(hi==0) {
5132 if(lo>=0) {
5133 return longDigitLength(lo);
5134 }
5135 return (unsignedLongCompareEq(lo, LONGLONG_TEN_POWERS_TABLE[0][1])) ? 20 : 19;
5136 // 0x8AC7230489E80000L = unsigned 2^19
5137 }
5138 int r = ((128 - Long.numberOfLeadingZeros(hi) + 1) * 1233) >>> 12;
5139 int idx = r-19;
5140 return (idx >= LONGLONG_TEN_POWERS_TABLE.length || longLongCompareMagnitude(hi, lo,
5141 LONGLONG_TEN_POWERS_TABLE[idx][0], LONGLONG_TEN_POWERS_TABLE[idx][1])) ? r : r + 1;
5142 }
5143
5144 /*
5145 * returns true if 128 bit number <hi0,lo0> is less then <hi1,lo1>
5146 * hi0 & hi1 should be non-negative
5147 */
5148 private static boolean longLongCompareMagnitude(long hi0, long lo0, long hi1, long lo1) {
5149 if(hi0!=hi1) {
5150 return hi0<hi1;
5151 }
5152 return (lo0+Long.MIN_VALUE) <(lo1+Long.MIN_VALUE);
5153 }
5154
5155 private static BigDecimal divide(long dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5156 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5157 int newScale = scale + divisorScale;
5158 int raise = newScale - dividendScale;
5159 if(raise<LONG_TEN_POWERS_TABLE.length) {
5160 long xs = dividend;
5161 if ((xs = longMultiplyPowerTen(xs, raise)) != INFLATED) {
5162 return divideAndRound(xs, divisor, scale, roundingMode, scale);
5163 }
5164 BigDecimal q = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[raise], dividend, divisor, scale, roundingMode, scale);
5165 if(q!=null) {
5166 return q;
5167 }
5168 }
5169 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5170 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5171 } else {
5172 int newScale = checkScale(divisor,(long)dividendScale - scale);
5173 int raise = newScale - divisorScale;
5174 if(raise<LONG_TEN_POWERS_TABLE.length) {
5175 long ys = divisor;
5176 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5177 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5178 }
5179 }
5180 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5181 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5182 }
5183 }
5184
5185 private static BigDecimal divide(BigInteger dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) {
5186 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5187 int newScale = scale + divisorScale;
5188 int raise = newScale - dividendScale;
5189 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5190 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5191 } else {
5192 int newScale = checkScale(divisor,(long)dividendScale - scale);
5193 int raise = newScale - divisorScale;
5194 if(raise<LONG_TEN_POWERS_TABLE.length) {
5195 long ys = divisor;
5196 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) {
5197 return divideAndRound(dividend, ys, scale, roundingMode, scale);
5198 }
5199 }
5200 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5201 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5202 }
5203 }
5204
5205 private static BigDecimal divide(long dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5206 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5207 int newScale = scale + divisorScale;
5208 int raise = newScale - dividendScale;
5209 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5210 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5211 } else {
5212 int newScale = checkScale(divisor,(long)dividendScale - scale);
5213 int raise = newScale - divisorScale;
5214 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5215 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale);
5216 }
5217 }
5218
5219 private static BigDecimal divide(BigInteger dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) {
5220 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) {
5221 int newScale = scale + divisorScale;
5222 int raise = newScale - dividendScale;
5223 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise);
5224 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale);
5225 } else {
5226 int newScale = checkScale(divisor,(long)dividendScale - scale);
5227 int raise = newScale - divisorScale;
5228 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise);
5229 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale);
5230 }
5231 }
5232
5233 }