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My first initial commit with all of mine experimental changes.

Dmitry Kabak (userdima committed 13 years ago

Commit d37b88d1 parent 3f5b46618352 files · +2598093 −-8690Browse files

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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 &times; 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&times;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 volatile BigInteger intVal;
228+
229+ /**
230+ * The scale of this BigDecimal, as returned by {@link #scale}.
231+ *
232+ * @serial
233+ * @see #scale
234+ */
235+ private int scale; // Note: this may have any value, so
236+ // calculations must be done in longs
237+ /**
238+ * The number of decimal digits in this BigDecimal, or 0 if the
239+ * number of digits are not known (lookaside information). If
240+ * nonzero, the value is guaranteed correct. Use the precision()
241+ * method to obtain and set the value if it might be 0. This
242+ * field is mutable until set nonzero.
243+ *
244+ * @since 1.5
245+ */
246+ private transient int precision;
247+
248+ /**
249+ * Used to store the canonical string representation, if computed.
250+ */
251+ private transient String stringCache;
252+
253+ /**
254+ * Sentinel value for {@link #intCompact} indicating the
255+ * significand information is only available from {@code intVal}.
256+ */
257+ static final long INFLATED = Long.MIN_VALUE;
258+
259+ /**
260+ * If the absolute value of the significand of this BigDecimal is
261+ * less than or equal to {@code Long.MAX_VALUE}, the value can be
262+ * compactly stored in this field and used in computations.
263+ */
264+ private transient long intCompact;
265+
266+ // All 18-digit base ten strings fit into a long; not all 19-digit
267+ // strings will
268+ private static final int MAX_COMPACT_DIGITS = 18;
269+
270+ private static final int MAX_BIGINT_BITS = 62;
271+
272+ /* Appease the serialization gods */
273+ private static final long serialVersionUID = 6108874887143696463L;
274+
275+ private static final ThreadLocal<StringBuilderHelper>
276+ threadLocalStringBuilderHelper = new ThreadLocal<StringBuilderHelper>() {
277+ @Override
278+ protected StringBuilderHelper initialValue() {
279+ return new StringBuilderHelper();
280+ }
281+ };
282+
283+ // Cache of common small BigDecimal values.
284+ private static final BigDecimal zeroThroughTen[] = {
285+ new BigDecimal(BigInteger.ZERO, 0, 0, 1),
286+ new BigDecimal(BigInteger.ONE, 1, 0, 1),
287+ new BigDecimal(BigInteger.valueOf(2), 2, 0, 1),
288+ new BigDecimal(BigInteger.valueOf(3), 3, 0, 1),
289+ new BigDecimal(BigInteger.valueOf(4), 4, 0, 1),
290+ new BigDecimal(BigInteger.valueOf(5), 5, 0, 1),
291+ new BigDecimal(BigInteger.valueOf(6), 6, 0, 1),
292+ new BigDecimal(BigInteger.valueOf(7), 7, 0, 1),
293+ new BigDecimal(BigInteger.valueOf(8), 8, 0, 1),
294+ new BigDecimal(BigInteger.valueOf(9), 9, 0, 1),
295+ new BigDecimal(BigInteger.TEN, 10, 0, 2),
296+ };
297+
298+ // Cache of zero scaled by 0 - 15
299+ private static final BigDecimal[] ZERO_SCALED_BY = {
300+ zeroThroughTen[0],
301+ new BigDecimal(BigInteger.ZERO, 0, 1, 1),
302+ new BigDecimal(BigInteger.ZERO, 0, 2, 1),
303+ new BigDecimal(BigInteger.ZERO, 0, 3, 1),
304+ new BigDecimal(BigInteger.ZERO, 0, 4, 1),
305+ new BigDecimal(BigInteger.ZERO, 0, 5, 1),
306+ new BigDecimal(BigInteger.ZERO, 0, 6, 1),
307+ new BigDecimal(BigInteger.ZERO, 0, 7, 1),
308+ new BigDecimal(BigInteger.ZERO, 0, 8, 1),
309+ new BigDecimal(BigInteger.ZERO, 0, 9, 1),
310+ new BigDecimal(BigInteger.ZERO, 0, 10, 1),
311+ new BigDecimal(BigInteger.ZERO, 0, 11, 1),
312+ new BigDecimal(BigInteger.ZERO, 0, 12, 1),
313+ new BigDecimal(BigInteger.ZERO, 0, 13, 1),
314+ new BigDecimal(BigInteger.ZERO, 0, 14, 1),
315+ new BigDecimal(BigInteger.ZERO, 0, 15, 1),
316+ };
317+
318+ // Half of Long.MIN_VALUE & Long.MAX_VALUE.
319+ private static final long HALF_LONG_MAX_VALUE = Long.MAX_VALUE / 2;
320+ private static final long HALF_LONG_MIN_VALUE = Long.MIN_VALUE / 2;
321+
322+ // Constants
323+ /**
324+ * The value 0, with a scale of 0.
325+ *
326+ * @since 1.5
327+ */
328+ public static final BigDecimal ZERO =
329+ zeroThroughTen[0];
330+
331+ /**
332+ * The value 1, with a scale of 0.
333+ *
334+ * @since 1.5
335+ */
336+ public static final BigDecimal ONE =
337+ zeroThroughTen[1];
338+
339+ /**
340+ * The value 10, with a scale of 0.
341+ *
342+ * @since 1.5
343+ */
344+ public static final BigDecimal TEN =
345+ zeroThroughTen[10];
346+
347+ // Constructors
348+
349+ /**
350+ * Trusted package private constructor.
351+ * Trusted simply means if val is INFLATED, intVal could not be null and
352+ * if intVal is null, val could not be INFLATED.
353+ */
354+ BigDecimal(BigInteger intVal, long val, int scale, int prec) {
355+ this.scale = scale;
356+ this.precision = prec;
357+ this.intCompact = val;
358+ this.intVal = intVal;
359+ }
360+
361+ /**
362+ * Translates a character array representation of a
363+ * {@code BigDecimal} into a {@code BigDecimal}, accepting the
364+ * same sequence of characters as the {@link #BigDecimal(String)}
365+ * constructor, while allowing a sub-array to be specified.
366+ *
367+ * <p>Note that if the sequence of characters is already available
368+ * within a character array, using this constructor is faster than
369+ * converting the {@code char} array to string and using the
370+ * {@code BigDecimal(String)} constructor .
371+ *
372+ * @param in {@code char} array that is the source of characters.
373+ * @param offset first character in the array to inspect.
374+ * @param len number of characters to consider.
375+ * @throws NumberFormatException if {@code in} is not a valid
376+ * representation of a {@code BigDecimal} or the defined subarray
377+ * is not wholly within {@code in}.
378+ * @since 1.5
379+ */
380+ public BigDecimal(char[] in, int offset, int len) {
381+ // protect against huge length.
382+ if (offset+len > in.length || offset < 0)
383+ throw new NumberFormatException();
384+ // This is the primary string to BigDecimal constructor; all
385+ // incoming strings end up here; it uses explicit (inline)
386+ // parsing for speed and generates at most one intermediate
387+ // (temporary) object (a char[] array) for non-compact case.
388+
389+ // Use locals for all fields values until completion
390+ int prec = 0; // record precision value
391+ int scl = 0; // record scale value
392+ long rs = 0; // the compact value in long
393+ BigInteger rb = null; // the inflated value in BigInteger
394+
395+ // use array bounds checking to handle too-long, len == 0,
396+ // bad offset, etc.
397+ try {
398+ // handle the sign
399+ boolean isneg = false; // assume positive
400+ if (in[offset] == '-') {
401+ isneg = true; // leading minus means negative
402+ offset++;
403+ len--;
404+ } else if (in[offset] == '+') { // leading + allowed
405+ offset++;
406+ len--;
407+ }
408+
409+ // should now be at numeric part of the significand
410+ boolean dot = false; // true when there is a '.'
411+ int cfirst = offset; // record start of integer
412+ long exp = 0; // exponent
413+ char c; // current character
414+
415+ boolean isCompact = (len <= MAX_COMPACT_DIGITS);
416+ // integer significand array & idx is the index to it. The array
417+ // is ONLY used when we can't use a compact representation.
418+ char coeff[] = isCompact ? null : new char[len];
419+ int idx = 0;
420+
421+ for (; len > 0; offset++, len--) {
422+ c = in[offset];
423+ // have digit
424+ if ((c >= '0' && c <= '9') || Character.isDigit(c)) {
425+ // First compact case, we need not to preserve the character
426+ // and we can just compute the value in place.
427+ if (isCompact) {
428+ int digit = Character.digit(c, 10);
429+ if (digit == 0) {
430+ if (prec == 0)
431+ prec = 1;
432+ else if (rs != 0) {
433+ rs *= 10;
434+ ++prec;
435+ } // else digit is a redundant leading zero
436+ } else {
437+ if (prec != 1 || rs != 0)
438+ ++prec; // prec unchanged if preceded by 0s
439+ rs = rs * 10 + digit;
440+ }
441+ } else { // the unscaled value is likely a BigInteger object.
442+ if (c == '0' || Character.digit(c, 10) == 0) {
443+ if (prec == 0) {
444+ coeff[idx] = c;
445+ prec = 1;
446+ } else if (idx != 0) {
447+ coeff[idx++] = c;
448+ ++prec;
449+ } // else c must be a redundant leading zero
450+ } else {
451+ if (prec != 1 || idx != 0)
452+ ++prec; // prec unchanged if preceded by 0s
453+ coeff[idx++] = c;
454+ }
455+ }
456+ if (dot)
457+ ++scl;
458+ continue;
459+ }
460+ // have dot
461+ if (c == '.') {
462+ // have dot
463+ if (dot) // two dots
464+ throw new NumberFormatException();
465+ dot = true;
466+ continue;
467+ }
468+ // exponent expected
469+ if ((c != 'e') && (c != 'E'))
470+ throw new NumberFormatException();
471+ offset++;
472+ c = in[offset];
473+ len--;
474+ boolean negexp = (c == '-');
475+ // optional sign
476+ if (negexp || c == '+') {
477+ offset++;
478+ c = in[offset];
479+ len--;
480+ }
481+ if (len <= 0) // no exponent digits
482+ throw new NumberFormatException();
483+ // skip leading zeros in the exponent
484+ while (len > 10 && Character.digit(c, 10) == 0) {
485+ offset++;
486+ c = in[offset];
487+ len--;
488+ }
489+ if (len > 10) // too many nonzero exponent digits
490+ throw new NumberFormatException();
491+ // c now holds first digit of exponent
492+ for (;; len--) {
493+ int v;
494+ if (c >= '0' && c <= '9') {
495+ v = c - '0';
496+ } else {
497+ v = Character.digit(c, 10);
498+ if (v < 0) // not a digit
499+ throw new NumberFormatException();
500+ }
501+ exp = exp * 10 + v;
502+ if (len == 1)
503+ break; // that was final character
504+ offset++;
505+ c = in[offset];
506+ }
507+ if (negexp) // apply sign
508+ exp = -exp;
509+ // Next test is required for backwards compatibility
510+ if ((int)exp != exp) // overflow
511+ throw new NumberFormatException();
512+ break; // [saves a test]
513+ }
514+ // here when no characters left
515+ if (prec == 0) // no digits found
516+ throw new NumberFormatException();
517+
518+ // Adjust scale if exp is not zero.
519+ if (exp != 0) { // had significant exponent
520+ // Can't call checkScale which relies on proper fields value
521+ long adjustedScale = scl - exp;
522+ if (adjustedScale > Integer.MAX_VALUE ||
523+ adjustedScale < Integer.MIN_VALUE)
524+ throw new NumberFormatException("Scale out of range.");
525+ scl = (int)adjustedScale;
526+ }
527+
528+ // Remove leading zeros from precision (digits count)
529+ if (isCompact) {
530+ rs = isneg ? -rs : rs;
531+ } else {
532+ char quick[];
533+ if (!isneg) {
534+ quick = (coeff.length != prec) ?
535+ Arrays.copyOf(coeff, prec) : coeff;
536+ } else {
537+ quick = new char[prec + 1];
538+ quick[0] = '-';
539+ System.arraycopy(coeff, 0, quick, 1, prec);
540+ }
541+ rb = new BigInteger(quick);
542+ rs = compactValFor(rb);
543+ }
544+ } catch (ArrayIndexOutOfBoundsException e) {
545+ throw new NumberFormatException();
546+ } catch (NegativeArraySizeException e) {
547+ throw new NumberFormatException();
548+ }
549+ this.scale = scl;
550+ this.precision = prec;
551+ this.intCompact = rs;
552+ this.intVal = (rs != INFLATED) ? null : rb;
553+ }
554+
555+ /**
556+ * Translates a character array representation of a
557+ * {@code BigDecimal} into a {@code BigDecimal}, accepting the
558+ * same sequence of characters as the {@link #BigDecimal(String)}
559+ * constructor, while allowing a sub-array to be specified and
560+ * with rounding according to the context settings.
561+ *
562+ * <p>Note that if the sequence of characters is already available
563+ * within a character array, using this constructor is faster than
564+ * converting the {@code char} array to string and using the
565+ * {@code BigDecimal(String)} constructor .
566+ *
567+ * @param in {@code char} array that is the source of characters.
568+ * @param offset first character in the array to inspect.
569+ * @param len number of characters to consider..
570+ * @param mc the context to use.
571+ * @throws ArithmeticException if the result is inexact but the
572+ * rounding mode is {@code UNNECESSARY}.
573+ * @throws NumberFormatException if {@code in} is not a valid
574+ * representation of a {@code BigDecimal} or the defined subarray
575+ * is not wholly within {@code in}.
576+ * @since 1.5
577+ */
578+ public BigDecimal(char[] in, int offset, int len, MathContext mc) {
579+ this(in, offset, len);
580+ if (mc.precision > 0)
581+ roundThis(mc);
582+ }
583+
584+ /**
585+ * Translates a character array representation of a
586+ * {@code BigDecimal} into a {@code BigDecimal}, accepting the
587+ * same sequence of characters as the {@link #BigDecimal(String)}
588+ * constructor.
589+ *
590+ * <p>Note that if the sequence of characters is already available
591+ * as a character array, using this constructor is faster than
592+ * converting the {@code char} array to string and using the
593+ * {@code BigDecimal(String)} constructor .
594+ *
595+ * @param in {@code char} array that is the source of characters.
596+ * @throws NumberFormatException if {@code in} is not a valid
597+ * representation of a {@code BigDecimal}.
598+ * @since 1.5
599+ */
600+ public BigDecimal(char[] in) {
601+ this(in, 0, in.length);
602+ }
603+
604+ /**
605+ * Translates a character array representation of a
606+ * {@code BigDecimal} into a {@code BigDecimal}, accepting the
607+ * same sequence of characters as the {@link #BigDecimal(String)}
608+ * constructor and with rounding according to the context
609+ * settings.
610+ *
611+ * <p>Note that if the sequence of characters is already available
612+ * as a character array, using this constructor is faster than
613+ * converting the {@code char} array to string and using the
614+ * {@code BigDecimal(String)} constructor .
615+ *
616+ * @param in {@code char} array that is the source of characters.
617+ * @param mc the context to use.
618+ * @throws ArithmeticException if the result is inexact but the
619+ * rounding mode is {@code UNNECESSARY}.
620+ * @throws NumberFormatException if {@code in} is not a valid
621+ * representation of a {@code BigDecimal}.
622+ * @since 1.5
623+ */
624+ public BigDecimal(char[] in, MathContext mc) {
625+ this(in, 0, in.length, mc);
626+ }
627+
628+ /**
629+ * Translates the string representation of a {@code BigDecimal}
630+ * into a {@code BigDecimal}. The string representation consists
631+ * of an optional sign, {@code '+'} (<tt> '&#92;u002B'</tt>) or
632+ * {@code '-'} (<tt>'&#92;u002D'</tt>), followed by a sequence of
633+ * zero or more decimal digits ("the integer"), optionally
634+ * followed by a fraction, optionally followed by an exponent.
635+ *
636+ * <p>The fraction consists of a decimal point followed by zero
637+ * or more decimal digits. The string must contain at least one
638+ * digit in either the integer or the fraction. The number formed
639+ * by the sign, the integer and the fraction is referred to as the
640+ * <i>significand</i>.
641+ *
642+ * <p>The exponent consists of the character {@code 'e'}
643+ * (<tt>'&#92;u0065'</tt>) or {@code 'E'} (<tt>'&#92;u0045'</tt>)
644+ * followed by one or more decimal digits. The value of the
645+ * exponent must lie between -{@link Integer#MAX_VALUE} ({@link
646+ * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive.
647+ *
648+ * <p>More formally, the strings this constructor accepts are
649+ * described by the following grammar:
650+ * <blockquote>
651+ * <dl>
652+ * <dt><i>BigDecimalString:</i>
653+ * <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i>
654+ * <p>
655+ * <dt><i>Sign:</i>
656+ * <dd>{@code +}
657+ * <dd>{@code -}
658+ * <p>
659+ * <dt><i>Significand:</i>
660+ * <dd><i>IntegerPart</i> {@code .} <i>FractionPart<sub>opt</sub></i>
661+ * <dd>{@code .} <i>FractionPart</i>
662+ * <dd><i>IntegerPart</i>
663+ * <p>
664+ * <dt><i>IntegerPart:</i>
665+ * <dd><i>Digits</i>
666+ * <p>
667+ * <dt><i>FractionPart:</i>
668+ * <dd><i>Digits</i>
669+ * <p>
670+ * <dt><i>Exponent:</i>
671+ * <dd><i>ExponentIndicator SignedInteger</i>
672+ * <p>
673+ * <dt><i>ExponentIndicator:</i>
674+ * <dd>{@code e}
675+ * <dd>{@code E}
676+ * <p>
677+ * <dt><i>SignedInteger:</i>
678+ * <dd><i>Sign<sub>opt</sub> Digits</i>
679+ * <p>
680+ * <dt><i>Digits:</i>
681+ * <dd><i>Digit</i>
682+ * <dd><i>Digits Digit</i>
683+ * <p>
684+ * <dt><i>Digit:</i>
685+ * <dd>any character for which {@link Character#isDigit}
686+ * returns {@code true}, including 0, 1, 2 ...
687+ * </dl>
688+ * </blockquote>
689+ *
690+ * <p>The scale of the returned {@code BigDecimal} will be the
691+ * number of digits in the fraction, or zero if the string
692+ * contains no decimal point, subject to adjustment for any
693+ * exponent; if the string contains an exponent, the exponent is
694+ * subtracted from the scale. The value of the resulting scale
695+ * must lie between {@code Integer.MIN_VALUE} and
696+ * {@code Integer.MAX_VALUE}, inclusive.
697+ *
698+ * <p>The character-to-digit mapping is provided by {@link
699+ * java.lang.Character#digit} set to convert to radix 10. The
700+ * String may not contain any extraneous characters (whitespace,
701+ * for example).
702+ *
703+ * <p><b>Examples:</b><br>
704+ * The value of the returned {@code BigDecimal} is equal to
705+ * <i>significand</i> &times; 10<sup>&nbsp;<i>exponent</i></sup>.
706+ * For each string on the left, the resulting representation
707+ * [{@code BigInteger}, {@code scale}] is shown on the right.
708+ * <pre>
709+ * "0" [0,0]
710+ * "0.00" [0,2]
711+ * "123" [123,0]
712+ * "-123" [-123,0]
713+ * "1.23E3" [123,-1]
714+ * "1.23E+3" [123,-1]
715+ * "12.3E+7" [123,-6]
716+ * "12.0" [120,1]
717+ * "12.3" [123,1]
718+ * "0.00123" [123,5]
719+ * "-1.23E-12" [-123,14]
720+ * "1234.5E-4" [12345,5]
721+ * "0E+7" [0,-7]
722+ * "-0" [0,0]
723+ * </pre>
724+ *
725+ * <p>Note: For values other than {@code float} and
726+ * {@code double} NaN and &plusmn;Infinity, this constructor is
727+ * compatible with the values returned by {@link Float#toString}
728+ * and {@link Double#toString}. This is generally the preferred
729+ * way to convert a {@code float} or {@code double} into a
730+ * BigDecimal, as it doesn't suffer from the unpredictability of
731+ * the {@link #BigDecimal(double)} constructor.
732+ *
733+ * @param val String representation of {@code BigDecimal}.
734+ *
735+ * @throws NumberFormatException if {@code val} is not a valid
736+ * representation of a {@code BigDecimal}.
737+ */
738+ public BigDecimal(String val) {
739+ this(val.toCharArray(), 0, val.length());
740+ }
741+
742+ /**
743+ * Translates the string representation of a {@code BigDecimal}
744+ * into a {@code BigDecimal}, accepting the same strings as the
745+ * {@link #BigDecimal(String)} constructor, with rounding
746+ * according to the context settings.
747+ *
748+ * @param val string representation of a {@code BigDecimal}.
749+ * @param mc the context to use.
750+ * @throws ArithmeticException if the result is inexact but the
751+ * rounding mode is {@code UNNECESSARY}.
752+ * @throws NumberFormatException if {@code val} is not a valid
753+ * representation of a BigDecimal.
754+ * @since 1.5
755+ */
756+ public BigDecimal(String val, MathContext mc) {
757+ this(val.toCharArray(), 0, val.length());
758+ if (mc.precision > 0)
759+ roundThis(mc);
760+ }
761+
762+ /**
763+ * Translates a {@code double} into a {@code BigDecimal} which
764+ * is the exact decimal representation of the {@code double}'s
765+ * binary floating-point value. The scale of the returned
766+ * {@code BigDecimal} is the smallest value such that
767+ * <tt>(10<sup>scale</sup> &times; val)</tt> is an integer.
768+ * <p>
769+ * <b>Notes:</b>
770+ * <ol>
771+ * <li>
772+ * The results of this constructor can be somewhat unpredictable.
773+ * One might assume that writing {@code new BigDecimal(0.1)} in
774+ * Java creates a {@code BigDecimal} which is exactly equal to
775+ * 0.1 (an unscaled value of 1, with a scale of 1), but it is
776+ * actually equal to
777+ * 0.1000000000000000055511151231257827021181583404541015625.
778+ * This is because 0.1 cannot be represented exactly as a
779+ * {@code double} (or, for that matter, as a binary fraction of
780+ * any finite length). Thus, the value that is being passed
781+ * <i>in</i> to the constructor is not exactly equal to 0.1,
782+ * appearances notwithstanding.
783+ *
784+ * <li>
785+ * The {@code String} constructor, on the other hand, is
786+ * perfectly predictable: writing {@code new BigDecimal("0.1")}
787+ * creates a {@code BigDecimal} which is <i>exactly</i> equal to
788+ * 0.1, as one would expect. Therefore, it is generally
789+ * recommended that the {@linkplain #BigDecimal(String)
790+ * <tt>String</tt> constructor} be used in preference to this one.
791+ *
792+ * <li>
793+ * When a {@code double} must be used as a source for a
794+ * {@code BigDecimal}, note that this constructor provides an
795+ * exact conversion; it does not give the same result as
796+ * converting the {@code double} to a {@code String} using the
797+ * {@link Double#toString(double)} method and then using the
798+ * {@link #BigDecimal(String)} constructor. To get that result,
799+ * use the {@code static} {@link #valueOf(double)} method.
800+ * </ol>
801+ *
802+ * @param val {@code double} value to be converted to
803+ * {@code BigDecimal}.
804+ * @throws NumberFormatException if {@code val} is infinite or NaN.
805+ */
806+ public BigDecimal(double val) {
807+ if (Double.isInfinite(val) || Double.isNaN(val))
808+ throw new NumberFormatException("Infinite or NaN");
809+
810+ // Translate the double into sign, exponent and significand, according
811+ // to the formulae in JLS, Section 20.10.22.
812+ long valBits = Double.doubleToLongBits(val);
813+ int sign = ((valBits >> 63)==0 ? 1 : -1);
814+ int exponent = (int) ((valBits >> 52) & 0x7ffL);
815+ long significand = (exponent==0 ? (valBits & ((1L<<52) - 1)) << 1
816+ : (valBits & ((1L<<52) - 1)) | (1L<<52));
817+ exponent -= 1075;
818+ // At this point, val == sign * significand * 2**exponent.
819+
820+ /*
821+ * Special case zero to supress nonterminating normalization
822+ * and bogus scale calculation.
823+ */
824+ if (significand == 0) {
825+ intVal = BigInteger.ZERO;
826+ intCompact = 0;
827+ precision = 1;
828+ return;
829+ }
830+
831+ // Normalize
832+ while((significand & 1) == 0) { // i.e., significand is even
833+ significand >>= 1;
834+ exponent++;
835+ }
836+
837+ // Calculate intVal and scale
838+ long s = sign * significand;
839+ BigInteger b;
840+ if (exponent < 0) {
841+ b = BigInteger.valueOf(5).pow(-exponent).multiply(s);
842+ scale = -exponent;
843+ } else if (exponent > 0) {
844+ b = BigInteger.valueOf(2).pow(exponent).multiply(s);
845+ } else {
846+ b = BigInteger.valueOf(s);
847+ }
848+ intCompact = compactValFor(b);
849+ intVal = (intCompact != INFLATED) ? null : b;
850+ }
851+
852+ /**
853+ * Translates a {@code double} into a {@code BigDecimal}, with
854+ * rounding according to the context settings. The scale of the
855+ * {@code BigDecimal} is the smallest value such that
856+ * <tt>(10<sup>scale</sup> &times; val)</tt> is an integer.
857+ *
858+ * <p>The results of this constructor can be somewhat unpredictable
859+ * and its use is generally not recommended; see the notes under
860+ * the {@link #BigDecimal(double)} constructor.
861+ *
862+ * @param val {@code double} value to be converted to
863+ * {@code BigDecimal}.
864+ * @param mc the context to use.
865+ * @throws ArithmeticException if the result is inexact but the
866+ * RoundingMode is UNNECESSARY.
867+ * @throws NumberFormatException if {@code val} is infinite or NaN.
868+ * @since 1.5
869+ */
870+ public BigDecimal(double val, MathContext mc) {
871+ this(val);
872+ if (mc.precision > 0)
873+ roundThis(mc);
874+ }
875+
876+ /**
877+ * Translates a {@code BigInteger} into a {@code BigDecimal}.
878+ * The scale of the {@code BigDecimal} is zero.
879+ *
880+ * @param val {@code BigInteger} value to be converted to
881+ * {@code BigDecimal}.
882+ */
883+ public BigDecimal(BigInteger val) {
884+ intCompact = compactValFor(val);
885+ intVal = (intCompact != INFLATED) ? null : val;
886+ }
887+
888+ /**
889+ * Translates a {@code BigInteger} into a {@code BigDecimal}
890+ * rounding according to the context settings. The scale of the
891+ * {@code BigDecimal} is zero.
892+ *
893+ * @param val {@code BigInteger} 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+ * rounding mode is {@code UNNECESSARY}.
898+ * @since 1.5
899+ */
900+ public BigDecimal(BigInteger val, MathContext mc) {
901+ this(val);
902+ if (mc.precision > 0)
903+ roundThis(mc);
904+ }
905+
906+ /**
907+ * Translates a {@code BigInteger} unscaled value and an
908+ * {@code int} scale into a {@code BigDecimal}. The value of
909+ * the {@code BigDecimal} is
910+ * <tt>(unscaledVal &times; 10<sup>-scale</sup>)</tt>.
911+ *
912+ * @param unscaledVal unscaled value of the {@code BigDecimal}.
913+ * @param scale scale of the {@code BigDecimal}.
914+ */
915+ public BigDecimal(BigInteger unscaledVal, int scale) {
916+ // Negative scales are now allowed
917+ this(unscaledVal);
918+ this.scale = scale;
919+ }
920+
921+ /**
922+ * Translates a {@code BigInteger} unscaled value and an
923+ * {@code int} scale into a {@code BigDecimal}, with rounding
924+ * according to the context settings. The value of the
925+ * {@code BigDecimal} is <tt>(unscaledVal &times;
926+ * 10<sup>-scale</sup>)</tt>, rounded according to the
927+ * {@code precision} and rounding mode settings.
928+ *
929+ * @param unscaledVal unscaled value of the {@code BigDecimal}.
930+ * @param scale scale of the {@code BigDecimal}.
931+ * @param mc the context to use.
932+ * @throws ArithmeticException if the result is inexact but the
933+ * rounding mode is {@code UNNECESSARY}.
934+ * @since 1.5
935+ */
936+ public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {
937+ this(unscaledVal);
938+ this.scale = scale;
939+ if (mc.precision > 0)
940+ roundThis(mc);
941+ }
942+
943+ /**
944+ * Translates an {@code int} into a {@code BigDecimal}. The
945+ * scale of the {@code BigDecimal} is zero.
946+ *
947+ * @param val {@code int} value to be converted to
948+ * {@code BigDecimal}.
949+ * @since 1.5
950+ */
951+ public BigDecimal(int val) {
952+ intCompact = val;
953+ }
954+
955+ /**
956+ * Translates an {@code int} into a {@code BigDecimal}, with
957+ * rounding according to the context settings. The scale of the
958+ * {@code BigDecimal}, before any rounding, is zero.
959+ *
960+ * @param val {@code int} value to be converted to {@code BigDecimal}.
961+ * @param mc the context to use.
962+ * @throws ArithmeticException if the result is inexact but the
963+ * rounding mode is {@code UNNECESSARY}.
964+ * @since 1.5
965+ */
966+ public BigDecimal(int val, MathContext mc) {
967+ intCompact = val;
968+ if (mc.precision > 0)
969+ roundThis(mc);
970+ }
971+
972+ /**
973+ * Translates a {@code long} into a {@code BigDecimal}. The
974+ * scale of the {@code BigDecimal} is zero.
975+ *
976+ * @param val {@code long} value to be converted to {@code BigDecimal}.
977+ * @since 1.5
978+ */
979+ public BigDecimal(long val) {
980+ this.intCompact = val;
981+ this.intVal = (val == INFLATED) ? BigInteger.valueOf(val) : null;
982+ }
983+
984+ /**
985+ * Translates a {@code long} into a {@code BigDecimal}, with
986+ * rounding according to the context settings. The scale of the
987+ * {@code BigDecimal}, before any rounding, is zero.
988+ *
989+ * @param val {@code long} value to be converted to {@code BigDecimal}.
990+ * @param mc the context to use.
991+ * @throws ArithmeticException if the result is inexact but the
992+ * rounding mode is {@code UNNECESSARY}.
993+ * @since 1.5
994+ */
995+ public BigDecimal(long val, MathContext mc) {
996+ this(val);
997+ if (mc.precision > 0)
998+ roundThis(mc);
999+ }
1000+
1001+ // Static Factory Methods
1002+
1003+ /**
1004+ * Translates a {@code long} unscaled value and an
1005+ * {@code int} scale into a {@code BigDecimal}. This
1006+ * {@literal "static factory method"} is provided in preference to
1007+ * a ({@code long}, {@code int}) constructor because it
1008+ * allows for reuse of frequently used {@code BigDecimal} values..
1009+ *
1010+ * @param unscaledVal unscaled value of the {@code BigDecimal}.
1011+ * @param scale scale of the {@code BigDecimal}.
1012+ * @return a {@code BigDecimal} whose value is
1013+ * <tt>(unscaledVal &times; 10<sup>-scale</sup>)</tt>.
1014+ */
1015+ public static BigDecimal valueOf(long unscaledVal, int scale) {
1016+ if (scale == 0)
1017+ return valueOf(unscaledVal);
1018+ else if (unscaledVal == 0) {
1019+ if (scale > 0 && scale < ZERO_SCALED_BY.length)
1020+ return ZERO_SCALED_BY[scale];
1021+ else
1022+ return new BigDecimal(BigInteger.ZERO, 0, scale, 1);
1023+ }
1024+ return new BigDecimal(unscaledVal == INFLATED ?
1025+ BigInteger.valueOf(unscaledVal) : null,
1026+ unscaledVal, scale, 0);
1027+ }
1028+
1029+ /**
1030+ * Translates a {@code long} value into a {@code BigDecimal}
1031+ * with a scale of zero. This {@literal "static factory method"}
1032+ * is provided in preference to a ({@code long}) constructor
1033+ * because it allows for reuse of frequently used
1034+ * {@code BigDecimal} values.
1035+ *
1036+ * @param val value of the {@code BigDecimal}.
1037+ * @return a {@code BigDecimal} whose value is {@code val}.
1038+ */
1039+ public static BigDecimal valueOf(long val) {
1040+ if (val >= 0 && val < zeroThroughTen.length)
1041+ return zeroThroughTen[(int)val];
1042+ else if (val != INFLATED)
1043+ return new BigDecimal(null, val, 0, 0);
1044+ return new BigDecimal(BigInteger.valueOf(val), val, 0, 0);
1045+ }
1046+
1047+ /**
1048+ * Translates a {@code double} into a {@code BigDecimal}, using
1049+ * the {@code double}'s canonical string representation provided
1050+ * by the {@link Double#toString(double)} method.
1051+ *
1052+ * <p><b>Note:</b> This is generally the preferred way to convert
1053+ * a {@code double} (or {@code float}) into a
1054+ * {@code BigDecimal}, as the value returned is equal to that
1055+ * resulting from constructing a {@code BigDecimal} from the
1056+ * result of using {@link Double#toString(double)}.
1057+ *
1058+ * @param val {@code double} to convert to a {@code BigDecimal}.
1059+ * @return a {@code BigDecimal} whose value is equal to or approximately
1060+ * equal to the value of {@code val}.
1061+ * @throws NumberFormatException if {@code val} is infinite or NaN.
1062+ * @since 1.5
1063+ */
1064+ public static BigDecimal valueOf(double val) {
1065+ // Reminder: a zero double returns '0.0', so we cannot fastpath
1066+ // to use the constant ZERO. This might be important enough to
1067+ // justify a factory approach, a cache, or a few private
1068+ // constants, later.
1069+ return new BigDecimal(Double.toString(val));
1070+ }
1071+
1072+ // Arithmetic Operations
1073+ /**
1074+ * Returns a {@code BigDecimal} whose value is {@code (this +
1075+ * augend)}, and whose scale is {@code max(this.scale(),
1076+ * augend.scale())}.
1077+ *
1078+ * @param augend value to be added to this {@code BigDecimal}.
1079+ * @return {@code this + augend}
1080+ */
1081+ public BigDecimal add(BigDecimal augend) {
1082+ long xs = this.intCompact;
1083+ long ys = augend.intCompact;
1084+ BigInteger fst = (xs != INFLATED) ? null : this.intVal;
1085+ BigInteger snd = (ys != INFLATED) ? null : augend.intVal;
1086+ int rscale = this.scale;
1087+
1088+ long sdiff = (long)rscale - augend.scale;
1089+ if (sdiff != 0) {
1090+ if (sdiff < 0) {
1091+ int raise = checkScale(-sdiff);
1092+ rscale = augend.scale;
1093+ if (xs == INFLATED ||
1094+ (xs = longMultiplyPowerTen(xs, raise)) == INFLATED)
1095+ fst = bigMultiplyPowerTen(raise);
1096+ } else {
1097+ int raise = augend.checkScale(sdiff);
1098+ if (ys == INFLATED ||
1099+ (ys = longMultiplyPowerTen(ys, raise)) == INFLATED)
1100+ snd = augend.bigMultiplyPowerTen(raise);
1101+ }
1102+ }
1103+ if (xs != INFLATED && ys != INFLATED) {
1104+ long sum = xs + ys;
1105+ // See "Hacker's Delight" section 2-12 for explanation of
1106+ // the overflow test.
1107+ if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) // not overflowed
1108+ return BigDecimal.valueOf(sum, rscale);
1109+ }
1110+ if (fst == null)
1111+ fst = BigInteger.valueOf(xs);
1112+ if (snd == null)
1113+ snd = BigInteger.valueOf(ys);
1114+ BigInteger sum = fst.add(snd);
1115+ return (fst.signum == snd.signum) ?
1116+ new BigDecimal(sum, INFLATED, rscale, 0) :
1117+ new BigDecimal(sum, rscale);
1118+ }
1119+
1120+ /**
1121+ * Returns a {@code BigDecimal} whose value is {@code (this + augend)},
1122+ * with rounding according to the context settings.
1123+ *
1124+ * If either number is zero and the precision setting is nonzero then
1125+ * the other number, rounded if necessary, is used as the result.
1126+ *
1127+ * @param augend value to be added to this {@code BigDecimal}.
1128+ * @param mc the context to use.
1129+ * @return {@code this + augend}, rounded as necessary.
1130+ * @throws ArithmeticException if the result is inexact but the
1131+ * rounding mode is {@code UNNECESSARY}.
1132+ * @since 1.5
1133+ */
1134+ public BigDecimal add(BigDecimal augend, MathContext mc) {
1135+ if (mc.precision == 0)
1136+ return add(augend);
1137+ BigDecimal lhs = this;
1138+
1139+ // Could optimize if values are compact
1140+ this.inflate();
1141+ augend.inflate();
1142+
1143+ // If either number is zero then the other number, rounded and
1144+ // scaled if necessary, is used as the result.
1145+ {
1146+ boolean lhsIsZero = lhs.signum() == 0;
1147+ boolean augendIsZero = augend.signum() == 0;
1148+
1149+ if (lhsIsZero || augendIsZero) {
1150+ int preferredScale = Math.max(lhs.scale(), augend.scale());
1151+ BigDecimal result;
1152+
1153+ // Could use a factory for zero instead of a new object
1154+ if (lhsIsZero && augendIsZero)
1155+ return new BigDecimal(BigInteger.ZERO, 0, preferredScale, 0);
1156+
1157+ result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc);
1158+
1159+ if (result.scale() == preferredScale)
1160+ return result;
1161+ else if (result.scale() > preferredScale) {
1162+ BigDecimal scaledResult =
1163+ new BigDecimal(result.intVal, result.intCompact,
1164+ result.scale, 0);
1165+ scaledResult.stripZerosToMatchScale(preferredScale);
1166+ return scaledResult;
1167+ } else { // result.scale < preferredScale
1168+ int precisionDiff = mc.precision - result.precision();
1169+ int scaleDiff = preferredScale - result.scale();
1170+
1171+ if (precisionDiff >= scaleDiff)
1172+ return result.setScale(preferredScale); // can achieve target scale
1173+ else
1174+ return result.setScale(result.scale() + precisionDiff);
1175+ }
1176+ }
1177+ }
1178+
1179+ long padding = (long)lhs.scale - augend.scale;
1180+ if (padding != 0) { // scales differ; alignment needed
1181+ BigDecimal arg[] = preAlign(lhs, augend, padding, mc);
1182+ matchScale(arg);
1183+ lhs = arg[0];
1184+ augend = arg[1];
1185+ }
1186+
1187+ BigDecimal d = new BigDecimal(lhs.inflate().add(augend.inflate()),
1188+ lhs.scale);
1189+ return doRound(d, mc);
1190+ }
1191+
1192+ /**
1193+ * Returns an array of length two, the sum of whose entries is
1194+ * equal to the rounded sum of the {@code BigDecimal} arguments.
1195+ *
1196+ * <p>If the digit positions of the arguments have a sufficient
1197+ * gap between them, the value smaller in magnitude can be
1198+ * condensed into a {@literal "sticky bit"} and the end result will
1199+ * round the same way <em>if</em> the precision of the final
1200+ * result does not include the high order digit of the small
1201+ * magnitude operand.
1202+ *
1203+ * <p>Note that while strictly speaking this is an optimization,
1204+ * it makes a much wider range of additions practical.
1205+ *
1206+ * <p>This corresponds to a pre-shift operation in a fixed
1207+ * precision floating-point adder; this method is complicated by
1208+ * variable precision of the result as determined by the
1209+ * MathContext. A more nuanced operation could implement a
1210+ * {@literal "right shift"} on the smaller magnitude operand so
1211+ * that the number of digits of the smaller operand could be
1212+ * reduced even though the significands partially overlapped.
1213+ */
1214+ private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend,
1215+ long padding, MathContext mc) {
1216+ assert padding != 0;
1217+ BigDecimal big;
1218+ BigDecimal small;
1219+
1220+ if (padding < 0) { // lhs is big; augend is small
1221+ big = lhs;
1222+ small = augend;
1223+ } else { // lhs is small; augend is big
1224+ big = augend;
1225+ small = lhs;
1226+ }
1227+
1228+ /*
1229+ * This is the estimated scale of an ulp of the result; it
1230+ * assumes that the result doesn't have a carry-out on a true
1231+ * add (e.g. 999 + 1 => 1000) or any subtractive cancellation
1232+ * on borrowing (e.g. 100 - 1.2 => 98.8)
1233+ */
1234+ long estResultUlpScale = (long)big.scale - big.precision() + mc.precision;
1235+
1236+ /*
1237+ * The low-order digit position of big is big.scale(). This
1238+ * is true regardless of whether big has a positive or
1239+ * negative scale. The high-order digit position of small is
1240+ * small.scale - (small.precision() - 1). To do the full
1241+ * condensation, the digit positions of big and small must be
1242+ * disjoint *and* the digit positions of small should not be
1243+ * directly visible in the result.
1244+ */
1245+ long smallHighDigitPos = (long)small.scale - small.precision() + 1;
1246+ if (smallHighDigitPos > big.scale + 2 && // big and small disjoint
1247+ smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible
1248+ small = BigDecimal.valueOf(small.signum(),
1249+ this.checkScale(Math.max(big.scale, estResultUlpScale) + 3));
1250+ }
1251+
1252+ // Since addition is symmetric, preserving input order in
1253+ // returned operands doesn't matter
1254+ BigDecimal[] result = {big, small};
1255+ return result;
1256+ }
1257+
1258+ /**
1259+ * Returns a {@code BigDecimal} whose value is {@code (this -
1260+ * subtrahend)}, and whose scale is {@code max(this.scale(),
1261+ * subtrahend.scale())}.
1262+ *
1263+ * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1264+ * @return {@code this - subtrahend}
1265+ */
1266+ public BigDecimal subtract(BigDecimal subtrahend) {
1267+ return add(subtrahend.negate());
1268+ }
1269+
1270+ /**
1271+ * Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)},
1272+ * with rounding according to the context settings.
1273+ *
1274+ * If {@code subtrahend} is zero then this, rounded if necessary, is used as the
1275+ * result. If this is zero then the result is {@code subtrahend.negate(mc)}.
1276+ *
1277+ * @param subtrahend value to be subtracted from this {@code BigDecimal}.
1278+ * @param mc the context to use.
1279+ * @return {@code this - subtrahend}, rounded as necessary.
1280+ * @throws ArithmeticException if the result is inexact but the
1281+ * rounding mode is {@code UNNECESSARY}.
1282+ * @since 1.5
1283+ */
1284+ public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) {
1285+ BigDecimal nsubtrahend = subtrahend.negate();
1286+ if (mc.precision == 0)
1287+ return add(nsubtrahend);
1288+ // share the special rounding code in add()
1289+ return add(nsubtrahend, mc);
1290+ }
1291+
1292+ /**
1293+ * Returns a {@code BigDecimal} whose value is <tt>(this &times;
1294+ * multiplicand)</tt>, and whose scale is {@code (this.scale() +
1295+ * multiplicand.scale())}.
1296+ *
1297+ * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1298+ * @return {@code this * multiplicand}
1299+ */
1300+ public BigDecimal multiply(BigDecimal multiplicand) {
1301+ long x = this.intCompact;
1302+ long y = multiplicand.intCompact;
1303+ int productScale = checkScale((long)scale + multiplicand.scale);
1304+
1305+ // Might be able to do a more clever check incorporating the
1306+ // inflated check into the overflow computation.
1307+ if (x != INFLATED && y != INFLATED) {
1308+ /*
1309+ * If the product is not an overflowed value, continue
1310+ * to use the compact representation. if either of x or y
1311+ * is INFLATED, the product should also be regarded as
1312+ * an overflow. Before using the overflow test suggested in
1313+ * "Hacker's Delight" section 2-12, we perform quick checks
1314+ * using the precision information to see whether the overflow
1315+ * would occur since division is expensive on most CPUs.
1316+ */
1317+ long product = x * y;
1318+ long prec = this.precision() + multiplicand.precision();
1319+ if (prec < 19 || (prec < 21 && (y == 0 || product / y == x)))
1320+ return BigDecimal.valueOf(product, productScale);
1321+ return new BigDecimal(BigInteger.valueOf(x).multiply(y), INFLATED,
1322+ productScale, 0);
1323+ }
1324+ BigInteger rb;
1325+ if (x == INFLATED && y == INFLATED)
1326+ rb = this.intVal.multiply(multiplicand.intVal);
1327+ else if (x != INFLATED)
1328+ rb = multiplicand.intVal.multiply(x);
1329+ else
1330+ rb = this.intVal.multiply(y);
1331+ return new BigDecimal(rb, INFLATED, productScale, 0);
1332+ }
1333+
1334+ /**
1335+ * Returns a {@code BigDecimal} whose value is <tt>(this &times;
1336+ * multiplicand)</tt>, with rounding according to the context settings.
1337+ *
1338+ * @param multiplicand value to be multiplied by this {@code BigDecimal}.
1339+ * @param mc the context to use.
1340+ * @return {@code this * multiplicand}, rounded as necessary.
1341+ * @throws ArithmeticException if the result is inexact but the
1342+ * rounding mode is {@code UNNECESSARY}.
1343+ * @since 1.5
1344+ */
1345+ public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) {
1346+ if (mc.precision == 0)
1347+ return multiply(multiplicand);
1348+ return doRound(this.multiply(multiplicand), mc);
1349+ }
1350+
1351+ /**
1352+ * Returns a {@code BigDecimal} whose value is {@code (this /
1353+ * divisor)}, and whose scale is as specified. If rounding must
1354+ * be performed to generate a result with the specified scale, the
1355+ * specified rounding mode is applied.
1356+ *
1357+ * <p>The new {@link #divide(BigDecimal, int, RoundingMode)} method
1358+ * should be used in preference to this legacy method.
1359+ *
1360+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1361+ * @param scale scale of the {@code BigDecimal} quotient to be returned.
1362+ * @param roundingMode rounding mode to apply.
1363+ * @return {@code this / divisor}
1364+ * @throws ArithmeticException if {@code divisor} is zero,
1365+ * {@code roundingMode==ROUND_UNNECESSARY} and
1366+ * the specified scale is insufficient to represent the result
1367+ * of the division exactly.
1368+ * @throws IllegalArgumentException if {@code roundingMode} does not
1369+ * represent a valid rounding mode.
1370+ * @see #ROUND_UP
1371+ * @see #ROUND_DOWN
1372+ * @see #ROUND_CEILING
1373+ * @see #ROUND_FLOOR
1374+ * @see #ROUND_HALF_UP
1375+ * @see #ROUND_HALF_DOWN
1376+ * @see #ROUND_HALF_EVEN
1377+ * @see #ROUND_UNNECESSARY
1378+ */
1379+ public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) {
1380+ /*
1381+ * IMPLEMENTATION NOTE: This method *must* return a new object
1382+ * since divideAndRound uses divide to generate a value whose
1383+ * scale is then modified.
1384+ */
1385+ if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
1386+ throw new IllegalArgumentException("Invalid rounding mode");
1387+ /*
1388+ * Rescale dividend or divisor (whichever can be "upscaled" to
1389+ * produce correctly scaled quotient).
1390+ * Take care to detect out-of-range scales
1391+ */
1392+ BigDecimal dividend = this;
1393+ if (checkScale((long)scale + divisor.scale) > this.scale)
1394+ dividend = this.setScale(scale + divisor.scale, ROUND_UNNECESSARY);
1395+ else
1396+ divisor = divisor.setScale(checkScale((long)this.scale - scale),
1397+ ROUND_UNNECESSARY);
1398+ return divideAndRound(dividend.intCompact, dividend.intVal,
1399+ divisor.intCompact, divisor.intVal,
1400+ scale, roundingMode, scale);
1401+ }
1402+
1403+ /**
1404+ * Internally used for division operation. The dividend and divisor are
1405+ * passed both in {@code long} format and {@code BigInteger} format. The
1406+ * returned {@code BigDecimal} object is the quotient whose scale is set to
1407+ * the passed in scale. If the remainder is not zero, it will be rounded
1408+ * based on the passed in roundingMode. Also, if the remainder is zero and
1409+ * the last parameter, i.e. preferredScale is NOT equal to scale, the
1410+ * trailing zeros of the result is stripped to match the preferredScale.
1411+ */
1412+ private static BigDecimal divideAndRound(long ldividend, BigInteger bdividend,
1413+ long ldivisor, BigInteger bdivisor,
1414+ int scale, int roundingMode,
1415+ int preferredScale) {
1416+ boolean isRemainderZero; // record remainder is zero or not
1417+ int qsign; // quotient sign
1418+ long q = 0, r = 0; // store quotient & remainder in long
1419+ MutableBigInteger mq = null; // store quotient
1420+ MutableBigInteger mr = null; // store remainder
1421+ MutableBigInteger mdivisor = null;
1422+ boolean isLongDivision = (ldividend != INFLATED && ldivisor != INFLATED);
1423+ if (isLongDivision) {
1424+ q = ldividend / ldivisor;
1425+ if (roundingMode == ROUND_DOWN && scale == preferredScale)
1426+ return new BigDecimal(null, q, scale, 0);
1427+ r = ldividend % ldivisor;
1428+ isRemainderZero = (r == 0);
1429+ qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
1430+ } else {
1431+ if (bdividend == null)
1432+ bdividend = BigInteger.valueOf(ldividend);
1433+ // Descend into mutables for faster remainder checks
1434+ MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
1435+ mq = new MutableBigInteger();
1436+ if (ldivisor != INFLATED) {
1437+ r = mdividend.divide(ldivisor, mq);
1438+ isRemainderZero = (r == 0);
1439+ qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
1440+ } else {
1441+ mdivisor = new MutableBigInteger(bdivisor.mag);
1442+ mr = mdividend.divide(mdivisor, mq);
1443+ isRemainderZero = mr.isZero();
1444+ qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
1445+ }
1446+ }
1447+ boolean increment = false;
1448+ if (!isRemainderZero) {
1449+ int cmpFracHalf;
1450+ /* Round as appropriate */
1451+ if (roundingMode == ROUND_UNNECESSARY) { // Rounding prohibited
1452+ throw new ArithmeticException("Rounding necessary");
1453+ } else if (roundingMode == ROUND_UP) { // Away from zero
1454+ increment = true;
1455+ } else if (roundingMode == ROUND_DOWN) { // Towards zero
1456+ increment = false;
1457+ } else if (roundingMode == ROUND_CEILING) { // Towards +infinity
1458+ increment = (qsign > 0);
1459+ } else if (roundingMode == ROUND_FLOOR) { // Towards -infinity
1460+ increment = (qsign < 0);
1461+ } else {
1462+ if (isLongDivision || ldivisor != INFLATED) {
1463+ if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
1464+ cmpFracHalf = 1; // 2 * r can't fit into long
1465+ } else {
1466+ cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
1467+ }
1468+ } else {
1469+ cmpFracHalf = mr.compareHalf(mdivisor);
1470+ }
1471+ if (cmpFracHalf < 0)
1472+ increment = false; // We're closer to higher digit
1473+ else if (cmpFracHalf > 0) // We're closer to lower digit
1474+ increment = true;
1475+ else if (roundingMode == ROUND_HALF_UP)
1476+ increment = true;
1477+ else if (roundingMode == ROUND_HALF_DOWN)
1478+ increment = false;
1479+ else // roundingMode == ROUND_HALF_EVEN, true iff quotient is odd
1480+ increment = isLongDivision ? (q & 1L) != 0L : mq.isOdd();
1481+ }
1482+ }
1483+ BigDecimal res;
1484+ if (isLongDivision)
1485+ res = new BigDecimal(null, (increment ? q + qsign : q), scale, 0);
1486+ else {
1487+ if (increment)
1488+ mq.add(MutableBigInteger.ONE);
1489+ res = mq.toBigDecimal(qsign, scale);
1490+ }
1491+ if (isRemainderZero && preferredScale != scale)
1492+ res.stripZerosToMatchScale(preferredScale);
1493+ return res;
1494+ }
1495+
1496+ /**
1497+ * Returns a {@code BigDecimal} whose value is {@code (this /
1498+ * divisor)}, and whose scale is as specified. If rounding must
1499+ * be performed to generate a result with the specified scale, the
1500+ * specified rounding mode is applied.
1501+ *
1502+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1503+ * @param scale scale of the {@code BigDecimal} quotient to be returned.
1504+ * @param roundingMode rounding mode to apply.
1505+ * @return {@code this / divisor}
1506+ * @throws ArithmeticException if {@code divisor} is zero,
1507+ * {@code roundingMode==RoundingMode.UNNECESSARY} and
1508+ * the specified scale is insufficient to represent the result
1509+ * of the division exactly.
1510+ * @since 1.5
1511+ */
1512+ public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) {
1513+ return divide(divisor, scale, roundingMode.oldMode);
1514+ }
1515+
1516+ /**
1517+ * Returns a {@code BigDecimal} whose value is {@code (this /
1518+ * divisor)}, and whose scale is {@code this.scale()}. If
1519+ * rounding must be performed to generate a result with the given
1520+ * scale, the specified rounding mode is applied.
1521+ *
1522+ * <p>The new {@link #divide(BigDecimal, RoundingMode)} method
1523+ * should be used in preference to this legacy method.
1524+ *
1525+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1526+ * @param roundingMode rounding mode to apply.
1527+ * @return {@code this / divisor}
1528+ * @throws ArithmeticException if {@code divisor==0}, or
1529+ * {@code roundingMode==ROUND_UNNECESSARY} and
1530+ * {@code this.scale()} is insufficient to represent the result
1531+ * of the division exactly.
1532+ * @throws IllegalArgumentException if {@code roundingMode} does not
1533+ * represent a valid rounding mode.
1534+ * @see #ROUND_UP
1535+ * @see #ROUND_DOWN
1536+ * @see #ROUND_CEILING
1537+ * @see #ROUND_FLOOR
1538+ * @see #ROUND_HALF_UP
1539+ * @see #ROUND_HALF_DOWN
1540+ * @see #ROUND_HALF_EVEN
1541+ * @see #ROUND_UNNECESSARY
1542+ */
1543+ public BigDecimal divide(BigDecimal divisor, int roundingMode) {
1544+ return this.divide(divisor, scale, roundingMode);
1545+ }
1546+
1547+ /**
1548+ * Returns a {@code BigDecimal} whose value is {@code (this /
1549+ * divisor)}, and whose scale is {@code this.scale()}. If
1550+ * rounding must be performed to generate a result with the given
1551+ * scale, the specified rounding mode is applied.
1552+ *
1553+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1554+ * @param roundingMode rounding mode to apply.
1555+ * @return {@code this / divisor}
1556+ * @throws ArithmeticException if {@code divisor==0}, or
1557+ * {@code roundingMode==RoundingMode.UNNECESSARY} and
1558+ * {@code this.scale()} is insufficient to represent the result
1559+ * of the division exactly.
1560+ * @since 1.5
1561+ */
1562+ public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) {
1563+ return this.divide(divisor, scale, roundingMode.oldMode);
1564+ }
1565+
1566+ /**
1567+ * Returns a {@code BigDecimal} whose value is {@code (this /
1568+ * divisor)}, and whose preferred scale is {@code (this.scale() -
1569+ * divisor.scale())}; if the exact quotient cannot be
1570+ * represented (because it has a non-terminating decimal
1571+ * expansion) an {@code ArithmeticException} is thrown.
1572+ *
1573+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1574+ * @throws ArithmeticException if the exact quotient does not have a
1575+ * terminating decimal expansion
1576+ * @return {@code this / divisor}
1577+ * @since 1.5
1578+ * @author Joseph D. Darcy
1579+ */
1580+ public BigDecimal divide(BigDecimal divisor) {
1581+ /*
1582+ * Handle zero cases first.
1583+ */
1584+ if (divisor.signum() == 0) { // x/0
1585+ if (this.signum() == 0) // 0/0
1586+ throw new ArithmeticException("Division undefined"); // NaN
1587+ throw new ArithmeticException("Division by zero");
1588+ }
1589+
1590+ // Calculate preferred scale
1591+ int preferredScale = saturateLong((long)this.scale - divisor.scale);
1592+ if (this.signum() == 0) // 0/y
1593+ return (preferredScale >= 0 &&
1594+ preferredScale < ZERO_SCALED_BY.length) ?
1595+ ZERO_SCALED_BY[preferredScale] :
1596+ BigDecimal.valueOf(0, preferredScale);
1597+ else {
1598+ this.inflate();
1599+ divisor.inflate();
1600+ /*
1601+ * If the quotient this/divisor has a terminating decimal
1602+ * expansion, the expansion can have no more than
1603+ * (a.precision() + ceil(10*b.precision)/3) digits.
1604+ * Therefore, create a MathContext object with this
1605+ * precision and do a divide with the UNNECESSARY rounding
1606+ * mode.
1607+ */
1608+ MathContext mc = new MathContext( (int)Math.min(this.precision() +
1609+ (long)Math.ceil(10.0*divisor.precision()/3.0),
1610+ Integer.MAX_VALUE),
1611+ RoundingMode.UNNECESSARY);
1612+ BigDecimal quotient;
1613+ try {
1614+ quotient = this.divide(divisor, mc);
1615+ } catch (ArithmeticException e) {
1616+ throw new ArithmeticException("Non-terminating decimal expansion; " +
1617+ "no exact representable decimal result.");
1618+ }
1619+
1620+ int quotientScale = quotient.scale();
1621+
1622+ // divide(BigDecimal, mc) tries to adjust the quotient to
1623+ // the desired one by removing trailing zeros; since the
1624+ // exact divide method does not have an explicit digit
1625+ // limit, we can add zeros too.
1626+
1627+ if (preferredScale > quotientScale)
1628+ return quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1629+
1630+ return quotient;
1631+ }
1632+ }
1633+
1634+ /**
1635+ * Returns a {@code BigDecimal} whose value is {@code (this /
1636+ * divisor)}, with rounding according to the context settings.
1637+ *
1638+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1639+ * @param mc the context to use.
1640+ * @return {@code this / divisor}, rounded as necessary.
1641+ * @throws ArithmeticException if the result is inexact but the
1642+ * rounding mode is {@code UNNECESSARY} or
1643+ * {@code mc.precision == 0} and the quotient has a
1644+ * non-terminating decimal expansion.
1645+ * @since 1.5
1646+ */
1647+ public BigDecimal divide(BigDecimal divisor, MathContext mc) {
1648+ int mcp = mc.precision;
1649+ if (mcp == 0)
1650+ return divide(divisor);
1651+
1652+ BigDecimal dividend = this;
1653+ long preferredScale = (long)dividend.scale - divisor.scale;
1654+ // Now calculate the answer. We use the existing
1655+ // divide-and-round method, but as this rounds to scale we have
1656+ // to normalize the values here to achieve the desired result.
1657+ // For x/y we first handle y=0 and x=0, and then normalize x and
1658+ // y to give x' and y' with the following constraints:
1659+ // (a) 0.1 <= x' < 1
1660+ // (b) x' <= y' < 10*x'
1661+ // Dividing x'/y' with the required scale set to mc.precision then
1662+ // will give a result in the range 0.1 to 1 rounded to exactly
1663+ // the right number of digits (except in the case of a result of
1664+ // 1.000... which can arise when x=y, or when rounding overflows
1665+ // The 1.000... case will reduce properly to 1.
1666+ if (divisor.signum() == 0) { // x/0
1667+ if (dividend.signum() == 0) // 0/0
1668+ throw new ArithmeticException("Division undefined"); // NaN
1669+ throw new ArithmeticException("Division by zero");
1670+ }
1671+ if (dividend.signum() == 0) // 0/y
1672+ return new BigDecimal(BigInteger.ZERO, 0,
1673+ saturateLong(preferredScale), 1);
1674+
1675+ // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
1676+ int xscale = dividend.precision();
1677+ int yscale = divisor.precision();
1678+ dividend = new BigDecimal(dividend.intVal, dividend.intCompact,
1679+ xscale, xscale);
1680+ divisor = new BigDecimal(divisor.intVal, divisor.intCompact,
1681+ yscale, yscale);
1682+ if (dividend.compareMagnitude(divisor) > 0) // satisfy constraint (b)
1683+ yscale = divisor.scale -= 1; // [that is, divisor *= 10]
1684+
1685+ // In order to find out whether the divide generates the exact result,
1686+ // we avoid calling the above divide method. 'quotient' holds the
1687+ // return BigDecimal object whose scale will be set to 'scl'.
1688+ BigDecimal quotient;
1689+ int scl = checkScale(preferredScale + yscale - xscale + mcp);
1690+ if (checkScale((long)mcp + yscale) > xscale)
1691+ dividend = dividend.setScale(mcp + yscale, ROUND_UNNECESSARY);
1692+ else
1693+ divisor = divisor.setScale(checkScale((long)xscale - mcp),
1694+ ROUND_UNNECESSARY);
1695+ quotient = divideAndRound(dividend.intCompact, dividend.intVal,
1696+ divisor.intCompact, divisor.intVal,
1697+ scl, mc.roundingMode.oldMode,
1698+ checkScale(preferredScale));
1699+ // doRound, here, only affects 1000000000 case.
1700+ quotient = doRound(quotient, mc);
1701+
1702+ return quotient;
1703+ }
1704+
1705+ /**
1706+ * Returns a {@code BigDecimal} whose value is the integer part
1707+ * of the quotient {@code (this / divisor)} rounded down. The
1708+ * preferred scale of the result is {@code (this.scale() -
1709+ * divisor.scale())}.
1710+ *
1711+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1712+ * @return The integer part of {@code this / divisor}.
1713+ * @throws ArithmeticException if {@code divisor==0}
1714+ * @since 1.5
1715+ */
1716+ public BigDecimal divideToIntegralValue(BigDecimal divisor) {
1717+ // Calculate preferred scale
1718+ int preferredScale = saturateLong((long)this.scale - divisor.scale);
1719+ if (this.compareMagnitude(divisor) < 0) {
1720+ // much faster when this << divisor
1721+ return BigDecimal.valueOf(0, preferredScale);
1722+ }
1723+
1724+ if(this.signum() == 0 && divisor.signum() != 0)
1725+ return this.setScale(preferredScale, ROUND_UNNECESSARY);
1726+
1727+ // Perform a divide with enough digits to round to a correct
1728+ // integer value; then remove any fractional digits
1729+
1730+ int maxDigits = (int)Math.min(this.precision() +
1731+ (long)Math.ceil(10.0*divisor.precision()/3.0) +
1732+ Math.abs((long)this.scale() - divisor.scale()) + 2,
1733+ Integer.MAX_VALUE);
1734+ BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits,
1735+ RoundingMode.DOWN));
1736+ if (quotient.scale > 0) {
1737+ quotient = quotient.setScale(0, RoundingMode.DOWN);
1738+ quotient.stripZerosToMatchScale(preferredScale);
1739+ }
1740+
1741+ if (quotient.scale < preferredScale) {
1742+ // pad with zeros if necessary
1743+ quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY);
1744+ }
1745+ return quotient;
1746+ }
1747+
1748+ /**
1749+ * Returns a {@code BigDecimal} whose value is the integer part
1750+ * of {@code (this / divisor)}. Since the integer part of the
1751+ * exact quotient does not depend on the rounding mode, the
1752+ * rounding mode does not affect the values returned by this
1753+ * method. The preferred scale of the result is
1754+ * {@code (this.scale() - divisor.scale())}. An
1755+ * {@code ArithmeticException} is thrown if the integer part of
1756+ * the exact quotient needs more than {@code mc.precision}
1757+ * digits.
1758+ *
1759+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1760+ * @param mc the context to use.
1761+ * @return The integer part of {@code this / divisor}.
1762+ * @throws ArithmeticException if {@code divisor==0}
1763+ * @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result
1764+ * requires a precision of more than {@code mc.precision} digits.
1765+ * @since 1.5
1766+ * @author Joseph D. Darcy
1767+ */
1768+ public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) {
1769+ if (mc.precision == 0 || // exact result
1770+ (this.compareMagnitude(divisor) < 0) ) // zero result
1771+ return divideToIntegralValue(divisor);
1772+
1773+ // Calculate preferred scale
1774+ int preferredScale = saturateLong((long)this.scale - divisor.scale);
1775+
1776+ /*
1777+ * Perform a normal divide to mc.precision digits. If the
1778+ * remainder has absolute value less than the divisor, the
1779+ * integer portion of the quotient fits into mc.precision
1780+ * digits. Next, remove any fractional digits from the
1781+ * quotient and adjust the scale to the preferred value.
1782+ */
1783+ BigDecimal result = this.
1784+ divide(divisor, new MathContext(mc.precision, RoundingMode.DOWN));
1785+
1786+ if (result.scale() < 0) {
1787+ /*
1788+ * Result is an integer. See if quotient represents the
1789+ * full integer portion of the exact quotient; if it does,
1790+ * the computed remainder will be less than the divisor.
1791+ */
1792+ BigDecimal product = result.multiply(divisor);
1793+ // If the quotient is the full integer value,
1794+ // |dividend-product| < |divisor|.
1795+ if (this.subtract(product).compareMagnitude(divisor) >= 0) {
1796+ throw new ArithmeticException("Division impossible");
1797+ }
1798+ } else if (result.scale() > 0) {
1799+ /*
1800+ * Integer portion of quotient will fit into precision
1801+ * digits; recompute quotient to scale 0 to avoid double
1802+ * rounding and then try to adjust, if necessary.
1803+ */
1804+ result = result.setScale(0, RoundingMode.DOWN);
1805+ }
1806+ // else result.scale() == 0;
1807+
1808+ int precisionDiff;
1809+ if ((preferredScale > result.scale()) &&
1810+ (precisionDiff = mc.precision - result.precision()) > 0) {
1811+ return result.setScale(result.scale() +
1812+ Math.min(precisionDiff, preferredScale - result.scale) );
1813+ } else {
1814+ result.stripZerosToMatchScale(preferredScale);
1815+ return result;
1816+ }
1817+ }
1818+
1819+ /**
1820+ * Returns a {@code BigDecimal} whose value is {@code (this % divisor)}.
1821+ *
1822+ * <p>The remainder is given by
1823+ * {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}.
1824+ * Note that this is not the modulo operation (the result can be
1825+ * negative).
1826+ *
1827+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1828+ * @return {@code this % divisor}.
1829+ * @throws ArithmeticException if {@code divisor==0}
1830+ * @since 1.5
1831+ */
1832+ public BigDecimal remainder(BigDecimal divisor) {
1833+ BigDecimal divrem[] = this.divideAndRemainder(divisor);
1834+ return divrem[1];
1835+ }
1836+
1837+
1838+ /**
1839+ * Returns a {@code BigDecimal} whose value is {@code (this %
1840+ * divisor)}, with rounding according to the context settings.
1841+ * The {@code MathContext} settings affect the implicit divide
1842+ * used to compute the remainder. The remainder computation
1843+ * itself is by definition exact. Therefore, the remainder may
1844+ * contain more than {@code mc.getPrecision()} digits.
1845+ *
1846+ * <p>The remainder is given by
1847+ * {@code this.subtract(this.divideToIntegralValue(divisor,
1848+ * mc).multiply(divisor))}. Note that this is not the modulo
1849+ * operation (the result can be negative).
1850+ *
1851+ * @param divisor value by which this {@code BigDecimal} is to be divided.
1852+ * @param mc the context to use.
1853+ * @return {@code this % divisor}, rounded as necessary.
1854+ * @throws ArithmeticException if {@code divisor==0}
1855+ * @throws ArithmeticException if the result is inexact but the
1856+ * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1857+ * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1858+ * require a precision of more than {@code mc.precision} digits.
1859+ * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1860+ * @since 1.5
1861+ */
1862+ public BigDecimal remainder(BigDecimal divisor, MathContext mc) {
1863+ BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
1864+ return divrem[1];
1865+ }
1866+
1867+ /**
1868+ * Returns a two-element {@code BigDecimal} array containing the
1869+ * result of {@code divideToIntegralValue} followed by the result of
1870+ * {@code remainder} on the two operands.
1871+ *
1872+ * <p>Note that if both the integer quotient and remainder are
1873+ * needed, this method is faster than using the
1874+ * {@code divideToIntegralValue} and {@code remainder} methods
1875+ * separately because the division need only be carried out once.
1876+ *
1877+ * @param divisor value by which this {@code BigDecimal} is to be divided,
1878+ * and the remainder computed.
1879+ * @return a two element {@code BigDecimal} array: the quotient
1880+ * (the result of {@code divideToIntegralValue}) is the initial element
1881+ * and the remainder is the final element.
1882+ * @throws ArithmeticException if {@code divisor==0}
1883+ * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1884+ * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1885+ * @since 1.5
1886+ */
1887+ public BigDecimal[] divideAndRemainder(BigDecimal divisor) {
1888+ // we use the identity x = i * y + r to determine r
1889+ BigDecimal[] result = new BigDecimal[2];
1890+
1891+ result[0] = this.divideToIntegralValue(divisor);
1892+ result[1] = this.subtract(result[0].multiply(divisor));
1893+ return result;
1894+ }
1895+
1896+ /**
1897+ * Returns a two-element {@code BigDecimal} array containing the
1898+ * result of {@code divideToIntegralValue} followed by the result of
1899+ * {@code remainder} on the two operands calculated with rounding
1900+ * according to the context settings.
1901+ *
1902+ * <p>Note that if both the integer quotient and remainder are
1903+ * needed, this method is faster than using the
1904+ * {@code divideToIntegralValue} and {@code remainder} methods
1905+ * separately because the division need only be carried out once.
1906+ *
1907+ * @param divisor value by which this {@code BigDecimal} is to be divided,
1908+ * and the remainder computed.
1909+ * @param mc the context to use.
1910+ * @return a two element {@code BigDecimal} array: the quotient
1911+ * (the result of {@code divideToIntegralValue}) is the
1912+ * initial element and the remainder is the final element.
1913+ * @throws ArithmeticException if {@code divisor==0}
1914+ * @throws ArithmeticException if the result is inexact but the
1915+ * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
1916+ * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
1917+ * require a precision of more than {@code mc.precision} digits.
1918+ * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
1919+ * @see #remainder(java.math.BigDecimal, java.math.MathContext)
1920+ * @since 1.5
1921+ */
1922+ public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) {
1923+ if (mc.precision == 0)
1924+ return divideAndRemainder(divisor);
1925+
1926+ BigDecimal[] result = new BigDecimal[2];
1927+ BigDecimal lhs = this;
1928+
1929+ result[0] = lhs.divideToIntegralValue(divisor, mc);
1930+ result[1] = lhs.subtract(result[0].multiply(divisor));
1931+ return result;
1932+ }
1933+
1934+ /**
1935+ * Returns a {@code BigDecimal} whose value is
1936+ * <tt>(this<sup>n</sup>)</tt>, The power is computed exactly, to
1937+ * unlimited precision.
1938+ *
1939+ * <p>The parameter {@code n} must be in the range 0 through
1940+ * 999999999, inclusive. {@code ZERO.pow(0)} returns {@link
1941+ * #ONE}.
1942+ *
1943+ * Note that future releases may expand the allowable exponent
1944+ * range of this method.
1945+ *
1946+ * @param n power to raise this {@code BigDecimal} to.
1947+ * @return <tt>this<sup>n</sup></tt>
1948+ * @throws ArithmeticException if {@code n} is out of range.
1949+ * @since 1.5
1950+ */
1951+ public BigDecimal pow(int n) {
1952+ if (n < 0 || n > 999999999)
1953+ throw new ArithmeticException("Invalid operation");
1954+ // No need to calculate pow(n) if result will over/underflow.
1955+ // Don't attempt to support "supernormal" numbers.
1956+ int newScale = checkScale((long)scale * n);
1957+ this.inflate();
1958+ return new BigDecimal(intVal.pow(n), newScale);
1959+ }
1960+
1961+
1962+ /**
1963+ * Returns a {@code BigDecimal} whose value is
1964+ * <tt>(this<sup>n</sup>)</tt>. The current implementation uses
1965+ * the core algorithm defined in ANSI standard X3.274-1996 with
1966+ * rounding according to the context settings. In general, the
1967+ * returned numerical value is within two ulps of the exact
1968+ * numerical value for the chosen precision. Note that future
1969+ * releases may use a different algorithm with a decreased
1970+ * allowable error bound and increased allowable exponent range.
1971+ *
1972+ * <p>The X3.274-1996 algorithm is:
1973+ *
1974+ * <ul>
1975+ * <li> An {@code ArithmeticException} exception is thrown if
1976+ * <ul>
1977+ * <li>{@code abs(n) > 999999999}
1978+ * <li>{@code mc.precision == 0} and {@code n < 0}
1979+ * <li>{@code mc.precision > 0} and {@code n} has more than
1980+ * {@code mc.precision} decimal digits
1981+ * </ul>
1982+ *
1983+ * <li> if {@code n} is zero, {@link #ONE} is returned even if
1984+ * {@code this} is zero, otherwise
1985+ * <ul>
1986+ * <li> if {@code n} is positive, the result is calculated via
1987+ * the repeated squaring technique into a single accumulator.
1988+ * The individual multiplications with the accumulator use the
1989+ * same math context settings as in {@code mc} except for a
1990+ * precision increased to {@code mc.precision + elength + 1}
1991+ * where {@code elength} is the number of decimal digits in
1992+ * {@code n}.
1993+ *
1994+ * <li> if {@code n} is negative, the result is calculated as if
1995+ * {@code n} were positive; this value is then divided into one
1996+ * using the working precision specified above.
1997+ *
1998+ * <li> The final value from either the positive or negative case
1999+ * is then rounded to the destination precision.
2000+ * </ul>
2001+ * </ul>
2002+ *
2003+ * @param n power to raise this {@code BigDecimal} to.
2004+ * @param mc the context to use.
2005+ * @return <tt>this<sup>n</sup></tt> using the ANSI standard X3.274-1996
2006+ * algorithm
2007+ * @throws ArithmeticException if the result is inexact but the
2008+ * rounding mode is {@code UNNECESSARY}, or {@code n} is out
2009+ * of range.
2010+ * @since 1.5
2011+ */
2012+ public BigDecimal pow(int n, MathContext mc) {
2013+ if (mc.precision == 0)
2014+ return pow(n);
2015+ if (n < -999999999 || n > 999999999)
2016+ throw new ArithmeticException("Invalid operation");
2017+ if (n == 0)
2018+ return ONE; // x**0 == 1 in X3.274
2019+ this.inflate();
2020+ BigDecimal lhs = this;
2021+ MathContext workmc = mc; // working settings
2022+ int mag = Math.abs(n); // magnitude of n
2023+ if (mc.precision > 0) {
2024+
2025+ int elength = longDigitLength(mag); // length of n in digits
2026+ if (elength > mc.precision) // X3.274 rule
2027+ throw new ArithmeticException("Invalid operation");
2028+ workmc = new MathContext(mc.precision + elength + 1,
2029+ mc.roundingMode);
2030+ }
2031+ // ready to carry out power calculation...
2032+ BigDecimal acc = ONE; // accumulator
2033+ boolean seenbit = false; // set once we've seen a 1-bit
2034+ for (int i=1;;i++) { // for each bit [top bit ignored]
2035+ mag += mag; // shift left 1 bit
2036+ if (mag < 0) { // top bit is set
2037+ seenbit = true; // OK, we're off
2038+ acc = acc.multiply(lhs, workmc); // acc=acc*x
2039+ }
2040+ if (i == 31)
2041+ break; // that was the last bit
2042+ if (seenbit)
2043+ acc=acc.multiply(acc, workmc); // acc=acc*acc [square]
2044+ // else (!seenbit) no point in squaring ONE
2045+ }
2046+ // if negative n, calculate the reciprocal using working precision
2047+ if (n<0) // [hence mc.precision>0]
2048+ acc=ONE.divide(acc, workmc);
2049+ // round to final precision and strip zeros
2050+ return doRound(acc, mc);
2051+ }
2052+
2053+ /**
2054+ * Returns a {@code BigDecimal} whose value is the absolute value
2055+ * of this {@code BigDecimal}, and whose scale is
2056+ * {@code this.scale()}.
2057+ *
2058+ * @return {@code abs(this)}
2059+ */
2060+ public BigDecimal abs() {
2061+ return (signum() < 0 ? negate() : this);
2062+ }
2063+
2064+ /**
2065+ * Returns a {@code BigDecimal} whose value is the absolute value
2066+ * of this {@code BigDecimal}, with rounding according to the
2067+ * context settings.
2068+ *
2069+ * @param mc the context to use.
2070+ * @return {@code abs(this)}, rounded as necessary.
2071+ * @throws ArithmeticException if the result is inexact but the
2072+ * rounding mode is {@code UNNECESSARY}.
2073+ * @since 1.5
2074+ */
2075+ public BigDecimal abs(MathContext mc) {
2076+ return (signum() < 0 ? negate(mc) : plus(mc));
2077+ }
2078+
2079+ /**
2080+ * Returns a {@code BigDecimal} whose value is {@code (-this)},
2081+ * and whose scale is {@code this.scale()}.
2082+ *
2083+ * @return {@code -this}.
2084+ */
2085+ public BigDecimal negate() {
2086+ BigDecimal result;
2087+ if (intCompact != INFLATED)
2088+ result = BigDecimal.valueOf(-intCompact, scale);
2089+ else {
2090+ result = new BigDecimal(intVal.negate(), scale);
2091+ result.precision = precision;
2092+ }
2093+ return result;
2094+ }
2095+
2096+ /**
2097+ * Returns a {@code BigDecimal} whose value is {@code (-this)},
2098+ * with rounding according to the context settings.
2099+ *
2100+ * @param mc the context to use.
2101+ * @return {@code -this}, rounded as necessary.
2102+ * @throws ArithmeticException if the result is inexact but the
2103+ * rounding mode is {@code UNNECESSARY}.
2104+ * @since 1.5
2105+ */
2106+ public BigDecimal negate(MathContext mc) {
2107+ return negate().plus(mc);
2108+ }
2109+
2110+ /**
2111+ * Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose
2112+ * scale is {@code this.scale()}.
2113+ *
2114+ * <p>This method, which simply returns this {@code BigDecimal}
2115+ * is included for symmetry with the unary minus method {@link
2116+ * #negate()}.
2117+ *
2118+ * @return {@code this}.
2119+ * @see #negate()
2120+ * @since 1.5
2121+ */
2122+ public BigDecimal plus() {
2123+ return this;
2124+ }
2125+
2126+ /**
2127+ * Returns a {@code BigDecimal} whose value is {@code (+this)},
2128+ * with rounding according to the context settings.
2129+ *
2130+ * <p>The effect of this method is identical to that of the {@link
2131+ * #round(MathContext)} method.
2132+ *
2133+ * @param mc the context to use.
2134+ * @return {@code this}, rounded as necessary. A zero result will
2135+ * have a scale of 0.
2136+ * @throws ArithmeticException if the result is inexact but the
2137+ * rounding mode is {@code UNNECESSARY}.
2138+ * @see #round(MathContext)
2139+ * @since 1.5
2140+ */
2141+ public BigDecimal plus(MathContext mc) {
2142+ if (mc.precision == 0) // no rounding please
2143+ return this;
2144+ return doRound(this, mc);
2145+ }
2146+
2147+ /**
2148+ * Returns the signum function of this {@code BigDecimal}.
2149+ *
2150+ * @return -1, 0, or 1 as the value of this {@code BigDecimal}
2151+ * is negative, zero, or positive.
2152+ */
2153+ public int signum() {
2154+ return (intCompact != INFLATED)?
2155+ Long.signum(intCompact):
2156+ intVal.signum();
2157+ }
2158+
2159+ /**
2160+ * Returns the <i>scale</i> of this {@code BigDecimal}. If zero
2161+ * or positive, the scale is the number of digits to the right of
2162+ * the decimal point. If negative, the unscaled value of the
2163+ * number is multiplied by ten to the power of the negation of the
2164+ * scale. For example, a scale of {@code -3} means the unscaled
2165+ * value is multiplied by 1000.
2166+ *
2167+ * @return the scale of this {@code BigDecimal}.
2168+ */
2169+ public int scale() {
2170+ return scale;
2171+ }
2172+
2173+ /**
2174+ * Returns the <i>precision</i> of this {@code BigDecimal}. (The
2175+ * precision is the number of digits in the unscaled value.)
2176+ *
2177+ * <p>The precision of a zero value is 1.
2178+ *
2179+ * @return the precision of this {@code BigDecimal}.
2180+ * @since 1.5
2181+ */
2182+ public int precision() {
2183+ int result = precision;
2184+ if (result == 0) {
2185+ long s = intCompact;
2186+ if (s != INFLATED)
2187+ result = longDigitLength(s);
2188+ else
2189+ result = bigDigitLength(inflate());
2190+ precision = result;
2191+ }
2192+ return result;
2193+ }
2194+
2195+
2196+ /**
2197+ * Returns a {@code BigInteger} whose value is the <i>unscaled
2198+ * value</i> of this {@code BigDecimal}. (Computes <tt>(this *
2199+ * 10<sup>this.scale()</sup>)</tt>.)
2200+ *
2201+ * @return the unscaled value of this {@code BigDecimal}.
2202+ * @since 1.2
2203+ */
2204+ public BigInteger unscaledValue() {
2205+ return this.inflate();
2206+ }
2207+
2208+ // Rounding Modes
2209+
2210+ /**
2211+ * Rounding mode to round away from zero. Always increments the
2212+ * digit prior to a nonzero discarded fraction. Note that this rounding
2213+ * mode never decreases the magnitude of the calculated value.
2214+ */
2215+ public final static int ROUND_UP = 0;
2216+
2217+ /**
2218+ * Rounding mode to round towards zero. Never increments the digit
2219+ * prior to a discarded fraction (i.e., truncates). Note that this
2220+ * rounding mode never increases the magnitude of the calculated value.
2221+ */
2222+ public final static int ROUND_DOWN = 1;
2223+
2224+ /**
2225+ * Rounding mode to round towards positive infinity. If the
2226+ * {@code BigDecimal} is positive, behaves as for
2227+ * {@code ROUND_UP}; if negative, behaves as for
2228+ * {@code ROUND_DOWN}. Note that this rounding mode never
2229+ * decreases the calculated value.
2230+ */
2231+ public final static int ROUND_CEILING = 2;
2232+
2233+ /**
2234+ * Rounding mode to round towards negative infinity. If the
2235+ * {@code BigDecimal} is positive, behave as for
2236+ * {@code ROUND_DOWN}; if negative, behave as for
2237+ * {@code ROUND_UP}. Note that this rounding mode never
2238+ * increases the calculated value.
2239+ */
2240+ public final static int ROUND_FLOOR = 3;
2241+
2242+ /**
2243+ * Rounding mode to round towards {@literal "nearest neighbor"}
2244+ * unless both neighbors are equidistant, in which case round up.
2245+ * Behaves as for {@code ROUND_UP} if the discarded fraction is
2246+ * &ge; 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note
2247+ * that this is the rounding mode that most of us were taught in
2248+ * grade school.
2249+ */
2250+ public final static int ROUND_HALF_UP = 4;
2251+
2252+ /**
2253+ * Rounding mode to round towards {@literal "nearest neighbor"}
2254+ * unless both neighbors are equidistant, in which case round
2255+ * down. Behaves as for {@code ROUND_UP} if the discarded
2256+ * fraction is {@literal >} 0.5; otherwise, behaves as for
2257+ * {@code ROUND_DOWN}.
2258+ */
2259+ public final static int ROUND_HALF_DOWN = 5;
2260+
2261+ /**
2262+ * Rounding mode to round towards the {@literal "nearest neighbor"}
2263+ * unless both neighbors are equidistant, in which case, round
2264+ * towards the even neighbor. Behaves as for
2265+ * {@code ROUND_HALF_UP} if the digit to the left of the
2266+ * discarded fraction is odd; behaves as for
2267+ * {@code ROUND_HALF_DOWN} if it's even. Note that this is the
2268+ * rounding mode that minimizes cumulative error when applied
2269+ * repeatedly over a sequence of calculations.
2270+ */
2271+ public final static int ROUND_HALF_EVEN = 6;
2272+
2273+ /**
2274+ * Rounding mode to assert that the requested operation has an exact
2275+ * result, hence no rounding is necessary. If this rounding mode is
2276+ * specified on an operation that yields an inexact result, an
2277+ * {@code ArithmeticException} is thrown.
2278+ */
2279+ public final static int ROUND_UNNECESSARY = 7;
2280+
2281+
2282+ // Scaling/Rounding Operations
2283+
2284+ /**
2285+ * Returns a {@code BigDecimal} rounded according to the
2286+ * {@code MathContext} settings. If the precision setting is 0 then
2287+ * no rounding takes place.
2288+ *
2289+ * <p>The effect of this method is identical to that of the
2290+ * {@link #plus(MathContext)} method.
2291+ *
2292+ * @param mc the context to use.
2293+ * @return a {@code BigDecimal} rounded according to the
2294+ * {@code MathContext} settings.
2295+ * @throws ArithmeticException if the rounding mode is
2296+ * {@code UNNECESSARY} and the
2297+ * {@code BigDecimal} operation would require rounding.
2298+ * @see #plus(MathContext)
2299+ * @since 1.5
2300+ */
2301+ public BigDecimal round(MathContext mc) {
2302+ return plus(mc);
2303+ }
2304+
2305+ /**
2306+ * Returns a {@code BigDecimal} whose scale is the specified
2307+ * value, and whose unscaled value is determined by multiplying or
2308+ * dividing this {@code BigDecimal}'s unscaled value by the
2309+ * appropriate power of ten to maintain its overall value. If the
2310+ * scale is reduced by the operation, the unscaled value must be
2311+ * divided (rather than multiplied), and the value may be changed;
2312+ * in this case, the specified rounding mode is applied to the
2313+ * division.
2314+ *
2315+ * <p>Note that since BigDecimal objects are immutable, calls of
2316+ * this method do <i>not</i> result in the original object being
2317+ * modified, contrary to the usual convention of having methods
2318+ * named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
2319+ * Instead, {@code setScale} returns an object with the proper
2320+ * scale; the returned object may or may not be newly allocated.
2321+ *
2322+ * @param newScale scale of the {@code BigDecimal} value to be returned.
2323+ * @param roundingMode The rounding mode to apply.
2324+ * @return a {@code BigDecimal} whose scale is the specified value,
2325+ * and whose unscaled value is determined by multiplying or
2326+ * dividing this {@code BigDecimal}'s unscaled value by the
2327+ * appropriate power of ten to maintain its overall value.
2328+ * @throws ArithmeticException if {@code roundingMode==UNNECESSARY}
2329+ * and the specified scaling operation would require
2330+ * rounding.
2331+ * @see RoundingMode
2332+ * @since 1.5
2333+ */
2334+ public BigDecimal setScale(int newScale, RoundingMode roundingMode) {
2335+ return setScale(newScale, roundingMode.oldMode);
2336+ }
2337+
2338+ /**
2339+ * Returns a {@code BigDecimal} whose scale is the specified
2340+ * value, and whose unscaled value is determined by multiplying or
2341+ * dividing this {@code BigDecimal}'s unscaled value by the
2342+ * appropriate power of ten to maintain its overall value. If the
2343+ * scale is reduced by the operation, the unscaled value must be
2344+ * divided (rather than multiplied), and the value may be changed;
2345+ * in this case, the specified rounding mode is applied to the
2346+ * division.
2347+ *
2348+ * <p>Note that since BigDecimal objects are immutable, calls of
2349+ * this method do <i>not</i> result in the original object being
2350+ * modified, contrary to the usual convention of having methods
2351+ * named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
2352+ * Instead, {@code setScale} returns an object with the proper
2353+ * scale; the returned object may or may not be newly allocated.
2354+ *
2355+ * <p>The new {@link #setScale(int, RoundingMode)} method should
2356+ * be used in preference to this legacy method.
2357+ *
2358+ * @param newScale scale of the {@code BigDecimal} value to be returned.
2359+ * @param roundingMode The rounding mode to apply.
2360+ * @return a {@code BigDecimal} whose scale is the specified value,
2361+ * and whose unscaled value is determined by multiplying or
2362+ * dividing this {@code BigDecimal}'s unscaled value by the
2363+ * appropriate power of ten to maintain its overall value.
2364+ * @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY}
2365+ * and the specified scaling operation would require
2366+ * rounding.
2367+ * @throws IllegalArgumentException if {@code roundingMode} does not
2368+ * represent a valid rounding mode.
2369+ * @see #ROUND_UP
2370+ * @see #ROUND_DOWN
2371+ * @see #ROUND_CEILING
2372+ * @see #ROUND_FLOOR
2373+ * @see #ROUND_HALF_UP
2374+ * @see #ROUND_HALF_DOWN
2375+ * @see #ROUND_HALF_EVEN
2376+ * @see #ROUND_UNNECESSARY
2377+ */
2378+ public BigDecimal setScale(int newScale, int roundingMode) {
2379+ if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
2380+ throw new IllegalArgumentException("Invalid rounding mode");
2381+
2382+ int oldScale = this.scale;
2383+ if (newScale == oldScale) // easy case
2384+ return this;
2385+ if (this.signum() == 0) // zero can have any scale
2386+ return BigDecimal.valueOf(0, newScale);
2387+
2388+ long rs = this.intCompact;
2389+ if (newScale > oldScale) {
2390+ int raise = checkScale((long)newScale - oldScale);
2391+ BigInteger rb = null;
2392+ if (rs == INFLATED ||
2393+ (rs = longMultiplyPowerTen(rs, raise)) == INFLATED)
2394+ rb = bigMultiplyPowerTen(raise);
2395+ return new BigDecimal(rb, rs, newScale,
2396+ (precision > 0) ? precision + raise : 0);
2397+ } else {
2398+ // newScale < oldScale -- drop some digits
2399+ // Can't predict the precision due to the effect of rounding.
2400+ int drop = checkScale((long)oldScale - newScale);
2401+ if (drop < LONG_TEN_POWERS_TABLE.length)
2402+ return divideAndRound(rs, this.intVal,
2403+ LONG_TEN_POWERS_TABLE[drop], null,
2404+ newScale, roundingMode, newScale);
2405+ else
2406+ return divideAndRound(rs, this.intVal,
2407+ INFLATED, bigTenToThe(drop),
2408+ newScale, roundingMode, newScale);
2409+ }
2410+ }
2411+
2412+ /**
2413+ * Returns a {@code BigDecimal} whose scale is the specified
2414+ * value, and whose value is numerically equal to this
2415+ * {@code BigDecimal}'s. Throws an {@code ArithmeticException}
2416+ * if this is not possible.
2417+ *
2418+ * <p>This call is typically used to increase the scale, in which
2419+ * case it is guaranteed that there exists a {@code BigDecimal}
2420+ * of the specified scale and the correct value. The call can
2421+ * also be used to reduce the scale if the caller knows that the
2422+ * {@code BigDecimal} has sufficiently many zeros at the end of
2423+ * its fractional part (i.e., factors of ten in its integer value)
2424+ * to allow for the rescaling without changing its value.
2425+ *
2426+ * <p>This method returns the same result as the two-argument
2427+ * versions of {@code setScale}, but saves the caller the trouble
2428+ * of specifying a rounding mode in cases where it is irrelevant.
2429+ *
2430+ * <p>Note that since {@code BigDecimal} objects are immutable,
2431+ * calls of this method do <i>not</i> result in the original
2432+ * object being modified, contrary to the usual convention of
2433+ * having methods named <tt>set<i>X</i></tt> mutate field
2434+ * <i>{@code X}</i>. Instead, {@code setScale} returns an
2435+ * object with the proper scale; the returned object may or may
2436+ * not be newly allocated.
2437+ *
2438+ * @param newScale scale of the {@code BigDecimal} value to be returned.
2439+ * @return a {@code BigDecimal} whose scale is the specified value, and
2440+ * whose unscaled value is determined by multiplying or dividing
2441+ * this {@code BigDecimal}'s unscaled value by the appropriate
2442+ * power of ten to maintain its overall value.
2443+ * @throws ArithmeticException if the specified scaling operation would
2444+ * require rounding.
2445+ * @see #setScale(int, int)
2446+ * @see #setScale(int, RoundingMode)
2447+ */
2448+ public BigDecimal setScale(int newScale) {
2449+ return setScale(newScale, ROUND_UNNECESSARY);
2450+ }
2451+
2452+ // Decimal Point Motion Operations
2453+
2454+ /**
2455+ * Returns a {@code BigDecimal} which is equivalent to this one
2456+ * with the decimal point moved {@code n} places to the left. If
2457+ * {@code n} is non-negative, the call merely adds {@code n} to
2458+ * the scale. If {@code n} is negative, the call is equivalent
2459+ * to {@code movePointRight(-n)}. The {@code BigDecimal}
2460+ * returned by this call has value <tt>(this &times;
2461+ * 10<sup>-n</sup>)</tt> and scale {@code max(this.scale()+n,
2462+ * 0)}.
2463+ *
2464+ * @param n number of places to move the decimal point to the left.
2465+ * @return a {@code BigDecimal} which is equivalent to this one with the
2466+ * decimal point moved {@code n} places to the left.
2467+ * @throws ArithmeticException if scale overflows.
2468+ */
2469+ public BigDecimal movePointLeft(int n) {
2470+ // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE
2471+ int newScale = checkScale((long)scale + n);
2472+ BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2473+ return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2474+ }
2475+
2476+ /**
2477+ * Returns a {@code BigDecimal} which is equivalent to this one
2478+ * with the decimal point moved {@code n} places to the right.
2479+ * If {@code n} is non-negative, the call merely subtracts
2480+ * {@code n} from the scale. If {@code n} is negative, the call
2481+ * is equivalent to {@code movePointLeft(-n)}. The
2482+ * {@code BigDecimal} returned by this call has value <tt>(this
2483+ * &times; 10<sup>n</sup>)</tt> and scale {@code max(this.scale()-n,
2484+ * 0)}.
2485+ *
2486+ * @param n number of places to move the decimal point to the right.
2487+ * @return a {@code BigDecimal} which is equivalent to this one
2488+ * with the decimal point moved {@code n} places to the right.
2489+ * @throws ArithmeticException if scale overflows.
2490+ */
2491+ public BigDecimal movePointRight(int n) {
2492+ // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE
2493+ int newScale = checkScale((long)scale - n);
2494+ BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
2495+ return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
2496+ }
2497+
2498+ /**
2499+ * Returns a BigDecimal whose numerical value is equal to
2500+ * ({@code this} * 10<sup>n</sup>). The scale of
2501+ * the result is {@code (this.scale() - n)}.
2502+ *
2503+ * @throws ArithmeticException if the scale would be
2504+ * outside the range of a 32-bit integer.
2505+ *
2506+ * @since 1.5
2507+ */
2508+ public BigDecimal scaleByPowerOfTen(int n) {
2509+ return new BigDecimal(intVal, intCompact,
2510+ checkScale((long)scale - n), precision);
2511+ }
2512+
2513+ /**
2514+ * Returns a {@code BigDecimal} which is numerically equal to
2515+ * this one but with any trailing zeros removed from the
2516+ * representation. For example, stripping the trailing zeros from
2517+ * the {@code BigDecimal} value {@code 600.0}, which has
2518+ * [{@code BigInteger}, {@code scale}] components equals to
2519+ * [6000, 1], yields {@code 6E2} with [{@code BigInteger},
2520+ * {@code scale}] components equals to [6, -2]
2521+ *
2522+ * @return a numerically equal {@code BigDecimal} with any
2523+ * trailing zeros removed.
2524+ * @since 1.5
2525+ */
2526+ public BigDecimal stripTrailingZeros() {
2527+ this.inflate();
2528+ BigDecimal result = new BigDecimal(intVal, scale);
2529+ result.stripZerosToMatchScale(Long.MIN_VALUE);
2530+ return result;
2531+ }
2532+
2533+ // Comparison Operations
2534+
2535+ /**
2536+ * Compares this {@code BigDecimal} with the specified
2537+ * {@code BigDecimal}. Two {@code BigDecimal} objects that are
2538+ * equal in value but have a different scale (like 2.0 and 2.00)
2539+ * are considered equal by this method. This method is provided
2540+ * in preference to individual methods for each of the six boolean
2541+ * comparison operators ({@literal <}, ==,
2542+ * {@literal >}, {@literal >=}, !=, {@literal <=}). The
2543+ * suggested idiom for performing these comparisons is:
2544+ * {@code (x.compareTo(y)} &lt;<i>op</i>&gt; {@code 0)}, where
2545+ * &lt;<i>op</i>&gt; is one of the six comparison operators.
2546+ *
2547+ * @param val {@code BigDecimal} to which this {@code BigDecimal} is
2548+ * to be compared.
2549+ * @return -1, 0, or 1 as this {@code BigDecimal} is numerically
2550+ * less than, equal to, or greater than {@code val}.
2551+ */
2552+ public int compareTo(BigDecimal val) {
2553+ // Quick path for equal scale and non-inflated case.
2554+ if (scale == val.scale) {
2555+ long xs = intCompact;
2556+ long ys = val.intCompact;
2557+ if (xs != INFLATED && ys != INFLATED)
2558+ return xs != ys ? ((xs > ys) ? 1 : -1) : 0;
2559+ }
2560+ int xsign = this.signum();
2561+ int ysign = val.signum();
2562+ if (xsign != ysign)
2563+ return (xsign > ysign) ? 1 : -1;
2564+ if (xsign == 0)
2565+ return 0;
2566+ int cmp = compareMagnitude(val);
2567+ return (xsign > 0) ? cmp : -cmp;
2568+ }
2569+
2570+ /**
2571+ * Version of compareTo that ignores sign.
2572+ */
2573+ private int compareMagnitude(BigDecimal val) {
2574+ // Match scales, avoid unnecessary inflation
2575+ long ys = val.intCompact;
2576+ long xs = this.intCompact;
2577+ if (xs == 0)
2578+ return (ys == 0) ? 0 : -1;
2579+ if (ys == 0)
2580+ return 1;
2581+
2582+ int sdiff = this.scale - val.scale;
2583+ if (sdiff != 0) {
2584+ // Avoid matching scales if the (adjusted) exponents differ
2585+ int xae = this.precision() - this.scale; // [-1]
2586+ int yae = val.precision() - val.scale; // [-1]
2587+ if (xae < yae)
2588+ return -1;
2589+ if (xae > yae)
2590+ return 1;
2591+ BigInteger rb = null;
2592+ if (sdiff < 0) {
2593+ if ( (xs == INFLATED ||
2594+ (xs = longMultiplyPowerTen(xs, -sdiff)) == INFLATED) &&
2595+ ys == INFLATED) {
2596+ rb = bigMultiplyPowerTen(-sdiff);
2597+ return rb.compareMagnitude(val.intVal);
2598+ }
2599+ } else { // sdiff > 0
2600+ if ( (ys == INFLATED ||
2601+ (ys = longMultiplyPowerTen(ys, sdiff)) == INFLATED) &&
2602+ xs == INFLATED) {
2603+ rb = val.bigMultiplyPowerTen(sdiff);
2604+ return this.intVal.compareMagnitude(rb);
2605+ }
2606+ }
2607+ }
2608+ if (xs != INFLATED)
2609+ return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
2610+ else if (ys != INFLATED)
2611+ return 1;
2612+ else
2613+ return this.intVal.compareMagnitude(val.intVal);
2614+ }
2615+
2616+ /**
2617+ * Compares this {@code BigDecimal} with the specified
2618+ * {@code Object} for equality. Unlike {@link
2619+ * #compareTo(BigDecimal) compareTo}, this method considers two
2620+ * {@code BigDecimal} objects equal only if they are equal in
2621+ * value and scale (thus 2.0 is not equal to 2.00 when compared by
2622+ * this method).
2623+ *
2624+ * @param x {@code Object} to which this {@code BigDecimal} is
2625+ * to be compared.
2626+ * @return {@code true} if and only if the specified {@code Object} is a
2627+ * {@code BigDecimal} whose value and scale are equal to this
2628+ * {@code BigDecimal}'s.
2629+ * @see #compareTo(java.math.BigDecimal)
2630+ * @see #hashCode
2631+ */
2632+ @Override
2633+ public boolean equals(Object x) {
2634+ if (!(x instanceof BigDecimal))
2635+ return false;
2636+ BigDecimal xDec = (BigDecimal) x;
2637+ if (x == this)
2638+ return true;
2639+ if (scale != xDec.scale)
2640+ return false;
2641+ long s = this.intCompact;
2642+ long xs = xDec.intCompact;
2643+ if (s != INFLATED) {
2644+ if (xs == INFLATED)
2645+ xs = compactValFor(xDec.intVal);
2646+ return xs == s;
2647+ } else if (xs != INFLATED)
2648+ return xs == compactValFor(this.intVal);
2649+
2650+ return this.inflate().equals(xDec.inflate());
2651+ }
2652+
2653+ /**
2654+ * Returns the minimum of this {@code BigDecimal} and
2655+ * {@code val}.
2656+ *
2657+ * @param val value with which the minimum is to be computed.
2658+ * @return the {@code BigDecimal} whose value is the lesser of this
2659+ * {@code BigDecimal} and {@code val}. If they are equal,
2660+ * as defined by the {@link #compareTo(BigDecimal) compareTo}
2661+ * method, {@code this} is returned.
2662+ * @see #compareTo(java.math.BigDecimal)
2663+ */
2664+ public BigDecimal min(BigDecimal val) {
2665+ return (compareTo(val) <= 0 ? this : val);
2666+ }
2667+
2668+ /**
2669+ * Returns the maximum of this {@code BigDecimal} and {@code val}.
2670+ *
2671+ * @param val value with which the maximum is to be computed.
2672+ * @return the {@code BigDecimal} whose value is the greater of this
2673+ * {@code BigDecimal} and {@code val}. If they are equal,
2674+ * as defined by the {@link #compareTo(BigDecimal) compareTo}
2675+ * method, {@code this} is returned.
2676+ * @see #compareTo(java.math.BigDecimal)
2677+ */
2678+ public BigDecimal max(BigDecimal val) {
2679+ return (compareTo(val) >= 0 ? this : val);
2680+ }
2681+
2682+ // Hash Function
2683+
2684+ /**
2685+ * Returns the hash code for this {@code BigDecimal}. Note that
2686+ * two {@code BigDecimal} objects that are numerically equal but
2687+ * differ in scale (like 2.0 and 2.00) will generally <i>not</i>
2688+ * have the same hash code.
2689+ *
2690+ * @return hash code for this {@code BigDecimal}.
2691+ * @see #equals(Object)
2692+ */
2693+ @Override
2694+ public int hashCode() {
2695+ if (intCompact != INFLATED) {
2696+ long val2 = (intCompact < 0)? -intCompact : intCompact;
2697+ int temp = (int)( ((int)(val2 >>> 32)) * 31 +
2698+ (val2 & LONG_MASK));
2699+ return 31*((intCompact < 0) ?-temp:temp) + scale;
2700+ } else
2701+ return 31*intVal.hashCode() + scale;
2702+ }
2703+
2704+ // Format Converters
2705+
2706+ /**
2707+ * Returns the string representation of this {@code BigDecimal},
2708+ * using scientific notation if an exponent is needed.
2709+ *
2710+ * <p>A standard canonical string form of the {@code BigDecimal}
2711+ * is created as though by the following steps: first, the
2712+ * absolute value of the unscaled value of the {@code BigDecimal}
2713+ * is converted to a string in base ten using the characters
2714+ * {@code '0'} through {@code '9'} with no leading zeros (except
2715+ * if its value is zero, in which case a single {@code '0'}
2716+ * character is used).
2717+ *
2718+ * <p>Next, an <i>adjusted exponent</i> is calculated; this is the
2719+ * negated scale, plus the number of characters in the converted
2720+ * unscaled value, less one. That is,
2721+ * {@code -scale+(ulength-1)}, where {@code ulength} is the
2722+ * length of the absolute value of the unscaled value in decimal
2723+ * digits (its <i>precision</i>).
2724+ *
2725+ * <p>If the scale is greater than or equal to zero and the
2726+ * adjusted exponent is greater than or equal to {@code -6}, the
2727+ * number will be converted to a character form without using
2728+ * exponential notation. In this case, if the scale is zero then
2729+ * no decimal point is added and if the scale is positive a
2730+ * decimal point will be inserted with the scale specifying the
2731+ * number of characters to the right of the decimal point.
2732+ * {@code '0'} characters are added to the left of the converted
2733+ * unscaled value as necessary. If no character precedes the
2734+ * decimal point after this insertion then a conventional
2735+ * {@code '0'} character is prefixed.
2736+ *
2737+ * <p>Otherwise (that is, if the scale is negative, or the
2738+ * adjusted exponent is less than {@code -6}), the number will be
2739+ * converted to a character form using exponential notation. In
2740+ * this case, if the converted {@code BigInteger} has more than
2741+ * one digit a decimal point is inserted after the first digit.
2742+ * An exponent in character form is then suffixed to the converted
2743+ * unscaled value (perhaps with inserted decimal point); this
2744+ * comprises the letter {@code 'E'} followed immediately by the
2745+ * adjusted exponent converted to a character form. The latter is
2746+ * in base ten, using the characters {@code '0'} through
2747+ * {@code '9'} with no leading zeros, and is always prefixed by a
2748+ * sign character {@code '-'} (<tt>'&#92;u002D'</tt>) if the
2749+ * adjusted exponent is negative, {@code '+'}
2750+ * (<tt>'&#92;u002B'</tt>) otherwise).
2751+ *
2752+ * <p>Finally, the entire string is prefixed by a minus sign
2753+ * character {@code '-'} (<tt>'&#92;u002D'</tt>) if the unscaled
2754+ * value is less than zero. No sign character is prefixed if the
2755+ * unscaled value is zero or positive.
2756+ *
2757+ * <p><b>Examples:</b>
2758+ * <p>For each representation [<i>unscaled value</i>, <i>scale</i>]
2759+ * on the left, the resulting string is shown on the right.
2760+ * <pre>
2761+ * [123,0] "123"
2762+ * [-123,0] "-123"
2763+ * [123,-1] "1.23E+3"
2764+ * [123,-3] "1.23E+5"
2765+ * [123,1] "12.3"
2766+ * [123,5] "0.00123"
2767+ * [123,10] "1.23E-8"
2768+ * [-123,12] "-1.23E-10"
2769+ * </pre>
2770+ *
2771+ * <b>Notes:</b>
2772+ * <ol>
2773+ *
2774+ * <li>There is a one-to-one mapping between the distinguishable
2775+ * {@code BigDecimal} values and the result of this conversion.
2776+ * That is, every distinguishable {@code BigDecimal} value
2777+ * (unscaled value and scale) has a unique string representation
2778+ * as a result of using {@code toString}. If that string
2779+ * representation is converted back to a {@code BigDecimal} using
2780+ * the {@link #BigDecimal(String)} constructor, then the original
2781+ * value will be recovered.
2782+ *
2783+ * <li>The string produced for a given number is always the same;
2784+ * it is not affected by locale. This means that it can be used
2785+ * as a canonical string representation for exchanging decimal
2786+ * data, or as a key for a Hashtable, etc. Locale-sensitive
2787+ * number formatting and parsing is handled by the {@link
2788+ * java.text.NumberFormat} class and its subclasses.
2789+ *
2790+ * <li>The {@link #toEngineeringString} method may be used for
2791+ * presenting numbers with exponents in engineering notation, and the
2792+ * {@link #setScale(int,RoundingMode) setScale} method may be used for
2793+ * rounding a {@code BigDecimal} so it has a known number of digits after
2794+ * the decimal point.
2795+ *
2796+ * <li>The digit-to-character mapping provided by
2797+ * {@code Character.forDigit} is used.
2798+ *
2799+ * </ol>
2800+ *
2801+ * @return string representation of this {@code BigDecimal}.
2802+ * @see Character#forDigit
2803+ * @see #BigDecimal(java.lang.String)
2804+ */
2805+ @Override
2806+ public String toString() {
2807+ String sc = stringCache;
2808+ if (sc == null)
2809+ stringCache = sc = layoutChars(true);
2810+ return sc;
2811+ }
2812+
2813+ /**
2814+ * Returns a string representation of this {@code BigDecimal},
2815+ * using engineering notation if an exponent is needed.
2816+ *
2817+ * <p>Returns a string that represents the {@code BigDecimal} as
2818+ * described in the {@link #toString()} method, except that if
2819+ * exponential notation is used, the power of ten is adjusted to
2820+ * be a multiple of three (engineering notation) such that the
2821+ * integer part of nonzero values will be in the range 1 through
2822+ * 999. If exponential notation is used for zero values, a
2823+ * decimal point and one or two fractional zero digits are used so
2824+ * that the scale of the zero value is preserved. Note that
2825+ * unlike the output of {@link #toString()}, the output of this
2826+ * method is <em>not</em> guaranteed to recover the same [integer,
2827+ * scale] pair of this {@code BigDecimal} if the output string is
2828+ * converting back to a {@code BigDecimal} using the {@linkplain
2829+ * #BigDecimal(String) string constructor}. The result of this method meets
2830+ * the weaker constraint of always producing a numerically equal
2831+ * result from applying the string constructor to the method's output.
2832+ *
2833+ * @return string representation of this {@code BigDecimal}, using
2834+ * engineering notation if an exponent is needed.
2835+ * @since 1.5
2836+ */
2837+ public String toEngineeringString() {
2838+ return layoutChars(false);
2839+ }
2840+
2841+ /**
2842+ * Returns a string representation of this {@code BigDecimal}
2843+ * without an exponent field. For values with a positive scale,
2844+ * the number of digits to the right of the decimal point is used
2845+ * to indicate scale. For values with a zero or negative scale,
2846+ * the resulting string is generated as if the value were
2847+ * converted to a numerically equal value with zero scale and as
2848+ * if all the trailing zeros of the zero scale value were present
2849+ * in the result.
2850+ *
2851+ * The entire string is prefixed by a minus sign character '-'
2852+ * (<tt>'&#92;u002D'</tt>) if the unscaled value is less than
2853+ * zero. No sign character is prefixed if the unscaled value is
2854+ * zero or positive.
2855+ *
2856+ * Note that if the result of this method is passed to the
2857+ * {@linkplain #BigDecimal(String) string constructor}, only the
2858+ * numerical value of this {@code BigDecimal} will necessarily be
2859+ * recovered; the representation of the new {@code BigDecimal}
2860+ * may have a different scale. In particular, if this
2861+ * {@code BigDecimal} has a negative scale, the string resulting
2862+ * from this method will have a scale of zero when processed by
2863+ * the string constructor.
2864+ *
2865+ * (This method behaves analogously to the {@code toString}
2866+ * method in 1.4 and earlier releases.)
2867+ *
2868+ * @return a string representation of this {@code BigDecimal}
2869+ * without an exponent field.
2870+ * @since 1.5
2871+ * @see #toString()
2872+ * @see #toEngineeringString()
2873+ */
2874+ public String toPlainString() {
2875+ BigDecimal bd = this;
2876+ if (bd.scale < 0)
2877+ bd = bd.setScale(0);
2878+ bd.inflate();
2879+ if (bd.scale == 0) // No decimal point
2880+ return bd.intVal.toString();
2881+ return bd.getValueString(bd.signum(), bd.intVal.abs().toString(), bd.scale);
2882+ }
2883+
2884+ /* Returns a digit.digit string */
2885+ private String getValueString(int signum, String intString, int scale) {
2886+ /* Insert decimal point */
2887+ StringBuilder buf;
2888+ int insertionPoint = intString.length() - scale;
2889+ if (insertionPoint == 0) { /* Point goes right before intVal */
2890+ return (signum<0 ? "-0." : "0.") + intString;
2891+ } else if (insertionPoint > 0) { /* Point goes inside intVal */
2892+ buf = new StringBuilder(intString);
2893+ buf.insert(insertionPoint, '.');
2894+ if (signum < 0)
2895+ buf.insert(0, '-');
2896+ } else { /* We must insert zeros between point and intVal */
2897+ buf = new StringBuilder(3-insertionPoint + intString.length());
2898+ buf.append(signum<0 ? "-0." : "0.");
2899+ for (int i=0; i<-insertionPoint; i++)
2900+ buf.append('0');
2901+ buf.append(intString);
2902+ }
2903+ return buf.toString();
2904+ }
2905+
2906+ /**
2907+ * Converts this {@code BigDecimal} to a {@code BigInteger}.
2908+ * This conversion is analogous to the
2909+ * <i>narrowing primitive conversion</i> from {@code double} to
2910+ * {@code long} as defined in section 5.1.3 of
2911+ * <cite>The Java&trade; Language Specification</cite>:
2912+ * any fractional part of this
2913+ * {@code BigDecimal} will be discarded. Note that this
2914+ * conversion can lose information about the precision of the
2915+ * {@code BigDecimal} value.
2916+ * <p>
2917+ * To have an exception thrown if the conversion is inexact (in
2918+ * other words if a nonzero fractional part is discarded), use the
2919+ * {@link #toBigIntegerExact()} method.
2920+ *
2921+ * @return this {@code BigDecimal} converted to a {@code BigInteger}.
2922+ */
2923+ public BigInteger toBigInteger() {
2924+ // force to an integer, quietly
2925+ return this.setScale(0, ROUND_DOWN).inflate();
2926+ }
2927+
2928+ /**
2929+ * Converts this {@code BigDecimal} to a {@code BigInteger},
2930+ * checking for lost information. An exception is thrown if this
2931+ * {@code BigDecimal} has a nonzero fractional part.
2932+ *
2933+ * @return this {@code BigDecimal} converted to a {@code BigInteger}.
2934+ * @throws ArithmeticException if {@code this} has a nonzero
2935+ * fractional part.
2936+ * @since 1.5
2937+ */
2938+ public BigInteger toBigIntegerExact() {
2939+ // round to an integer, with Exception if decimal part non-0
2940+ return this.setScale(0, ROUND_UNNECESSARY).inflate();
2941+ }
2942+
2943+ /**
2944+ * Converts this {@code BigDecimal} to a {@code long}.
2945+ * This conversion is analogous to the
2946+ * <i>narrowing primitive conversion</i> from {@code double} to
2947+ * {@code short} as defined in section 5.1.3 of
2948+ * <cite>The Java&trade; Language Specification</cite>:
2949+ * any fractional part of this
2950+ * {@code BigDecimal} will be discarded, and if the resulting
2951+ * "{@code BigInteger}" is too big to fit in a
2952+ * {@code long}, only the low-order 64 bits are returned.
2953+ * Note that this conversion can lose information about the
2954+ * overall magnitude and precision of this {@code BigDecimal} value as well
2955+ * as return a result with the opposite sign.
2956+ *
2957+ * @return this {@code BigDecimal} converted to a {@code long}.
2958+ */
2959+ public long longValue(){
2960+ return (intCompact != INFLATED && scale == 0) ?
2961+ intCompact:
2962+ toBigInteger().longValue();
2963+ }
2964+
2965+ /**
2966+ * Converts this {@code BigDecimal} to a {@code long}, checking
2967+ * for lost information. If this {@code BigDecimal} has a
2968+ * nonzero fractional part or is out of the possible range for a
2969+ * {@code long} result then an {@code ArithmeticException} is
2970+ * thrown.
2971+ *
2972+ * @return this {@code BigDecimal} converted to a {@code long}.
2973+ * @throws ArithmeticException if {@code this} has a nonzero
2974+ * fractional part, or will not fit in a {@code long}.
2975+ * @since 1.5
2976+ */
2977+ public long longValueExact() {
2978+ if (intCompact != INFLATED && scale == 0)
2979+ return intCompact;
2980+ // If more than 19 digits in integer part it cannot possibly fit
2981+ if ((precision() - scale) > 19) // [OK for negative scale too]
2982+ throw new java.lang.ArithmeticException("Overflow");
2983+ // Fastpath zero and < 1.0 numbers (the latter can be very slow
2984+ // to round if very small)
2985+ if (this.signum() == 0)
2986+ return 0;
2987+ if ((this.precision() - this.scale) <= 0)
2988+ throw new ArithmeticException("Rounding necessary");
2989+ // round to an integer, with Exception if decimal part non-0
2990+ BigDecimal num = this.setScale(0, ROUND_UNNECESSARY);
2991+ if (num.precision() >= 19) // need to check carefully
2992+ LongOverflow.check(num);
2993+ return num.inflate().longValue();
2994+ }
2995+
2996+ private static class LongOverflow {
2997+ /** BigInteger equal to Long.MIN_VALUE. */
2998+ private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE);
2999+
3000+ /** BigInteger equal to Long.MAX_VALUE. */
3001+ private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE);
3002+
3003+ public static void check(BigDecimal num) {
3004+ num.inflate();
3005+ if ((num.intVal.compareTo(LONGMIN) < 0) ||
3006+ (num.intVal.compareTo(LONGMAX) > 0))
3007+ throw new java.lang.ArithmeticException("Overflow");
3008+ }
3009+ }
3010+
3011+ /**
3012+ * Converts this {@code BigDecimal} to an {@code int}.
3013+ * This conversion is analogous to the
3014+ * <i>narrowing primitive conversion</i> from {@code double} to
3015+ * {@code short} as defined in section 5.1.3 of
3016+ * <cite>The Java&trade; Language Specification</cite>:
3017+ * any fractional part of this
3018+ * {@code BigDecimal} will be discarded, and if the resulting
3019+ * "{@code BigInteger}" is too big to fit in an
3020+ * {@code int}, only the low-order 32 bits are returned.
3021+ * Note that this conversion can lose information about the
3022+ * overall magnitude and precision of this {@code BigDecimal}
3023+ * value as well as return a result with the opposite sign.
3024+ *
3025+ * @return this {@code BigDecimal} converted to an {@code int}.
3026+ */
3027+ public int intValue() {
3028+ return (intCompact != INFLATED && scale == 0) ?
3029+ (int)intCompact :
3030+ toBigInteger().intValue();
3031+ }
3032+
3033+ /**
3034+ * Converts this {@code BigDecimal} to an {@code int}, checking
3035+ * for lost information. If this {@code BigDecimal} has a
3036+ * nonzero fractional part or is out of the possible range for an
3037+ * {@code int} result then an {@code ArithmeticException} is
3038+ * thrown.
3039+ *
3040+ * @return this {@code BigDecimal} converted to an {@code int}.
3041+ * @throws ArithmeticException if {@code this} has a nonzero
3042+ * fractional part, or will not fit in an {@code int}.
3043+ * @since 1.5
3044+ */
3045+ public int intValueExact() {
3046+ long num;
3047+ num = this.longValueExact(); // will check decimal part
3048+ if ((int)num != num)
3049+ throw new java.lang.ArithmeticException("Overflow");
3050+ return (int)num;
3051+ }
3052+
3053+ /**
3054+ * Converts this {@code BigDecimal} to a {@code short}, checking
3055+ * for lost information. If this {@code BigDecimal} has a
3056+ * nonzero fractional part or is out of the possible range for a
3057+ * {@code short} result then an {@code ArithmeticException} is
3058+ * thrown.
3059+ *
3060+ * @return this {@code BigDecimal} converted to a {@code short}.
3061+ * @throws ArithmeticException if {@code this} has a nonzero
3062+ * fractional part, or will not fit in a {@code short}.
3063+ * @since 1.5
3064+ */
3065+ public short shortValueExact() {
3066+ long num;
3067+ num = this.longValueExact(); // will check decimal part
3068+ if ((short)num != num)
3069+ throw new java.lang.ArithmeticException("Overflow");
3070+ return (short)num;
3071+ }
3072+
3073+ /**
3074+ * Converts this {@code BigDecimal} to a {@code byte}, checking
3075+ * for lost information. If this {@code BigDecimal} has a
3076+ * nonzero fractional part or is out of the possible range for a
3077+ * {@code byte} result then an {@code ArithmeticException} is
3078+ * thrown.
3079+ *
3080+ * @return this {@code BigDecimal} converted to a {@code byte}.
3081+ * @throws ArithmeticException if {@code this} has a nonzero
3082+ * fractional part, or will not fit in a {@code byte}.
3083+ * @since 1.5
3084+ */
3085+ public byte byteValueExact() {
3086+ long num;
3087+ num = this.longValueExact(); // will check decimal part
3088+ if ((byte)num != num)
3089+ throw new java.lang.ArithmeticException("Overflow");
3090+ return (byte)num;
3091+ }
3092+
3093+ /**
3094+ * Converts this {@code BigDecimal} to a {@code float}.
3095+ * This conversion is similar to the
3096+ * <i>narrowing primitive conversion</i> from {@code double} to
3097+ * {@code float} as defined in section 5.1.3 of
3098+ * <cite>The Java&trade; Language Specification</cite>:
3099+ * if this {@code BigDecimal} has too great a
3100+ * magnitude to represent as a {@code float}, it will be
3101+ * converted to {@link Float#NEGATIVE_INFINITY} or {@link
3102+ * Float#POSITIVE_INFINITY} as appropriate. Note that even when
3103+ * the return value is finite, this conversion can lose
3104+ * information about the precision of the {@code BigDecimal}
3105+ * value.
3106+ *
3107+ * @return this {@code BigDecimal} converted to a {@code float}.
3108+ */
3109+ public float floatValue(){
3110+ if (scale == 0 && intCompact != INFLATED)
3111+ return (float)intCompact;
3112+ // Somewhat inefficient, but guaranteed to work.
3113+ return Float.parseFloat(this.toString());
3114+ }
3115+
3116+ /**
3117+ * Converts this {@code BigDecimal} to a {@code double}.
3118+ * This conversion is similar to the
3119+ * <i>narrowing primitive conversion</i> from {@code double} to
3120+ * {@code float} as defined in section 5.1.3 of
3121+ * <cite>The Java&trade; Language Specification</cite>:
3122+ * if this {@code BigDecimal} has too great a
3123+ * magnitude represent as a {@code double}, it will be
3124+ * converted to {@link Double#NEGATIVE_INFINITY} or {@link
3125+ * Double#POSITIVE_INFINITY} as appropriate. Note that even when
3126+ * the return value is finite, this conversion can lose
3127+ * information about the precision of the {@code BigDecimal}
3128+ * value.
3129+ *
3130+ * @return this {@code BigDecimal} converted to a {@code double}.
3131+ */
3132+ public double doubleValue(){
3133+ if (scale == 0 && intCompact != INFLATED)
3134+ return (double)intCompact;
3135+ // Somewhat inefficient, but guaranteed to work.
3136+ return Double.parseDouble(this.toString());
3137+ }
3138+
3139+ /**
3140+ * Returns the size of an ulp, a unit in the last place, of this
3141+ * {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal}
3142+ * value is the positive distance between this value and the
3143+ * {@code BigDecimal} value next larger in magnitude with the
3144+ * same number of digits. An ulp of a zero value is numerically
3145+ * equal to 1 with the scale of {@code this}. The result is
3146+ * stored with the same scale as {@code this} so the result
3147+ * for zero and nonzero values is equal to {@code [1,
3148+ * this.scale()]}.
3149+ *
3150+ * @return the size of an ulp of {@code this}
3151+ * @since 1.5
3152+ */
3153+ public BigDecimal ulp() {
3154+ return BigDecimal.valueOf(1, this.scale());
3155+ }
3156+
3157+
3158+ // Private class to build a string representation for BigDecimal object.
3159+ // "StringBuilderHelper" is constructed as a thread local variable so it is
3160+ // thread safe. The StringBuilder field acts as a buffer to hold the temporary
3161+ // representation of BigDecimal. The cmpCharArray holds all the characters for
3162+ // the compact representation of BigDecimal (except for '-' sign' if it is
3163+ // negative) if its intCompact field is not INFLATED. It is shared by all
3164+ // calls to toString() and its variants in that particular thread.
3165+ static class StringBuilderHelper {
3166+ final StringBuilder sb; // Placeholder for BigDecimal string
3167+ final char[] cmpCharArray; // character array to place the intCompact
3168+
3169+ StringBuilderHelper() {
3170+ sb = new StringBuilder();
3171+ // All non negative longs can be made to fit into 19 character array.
3172+ cmpCharArray = new char[19];
3173+ }
3174+
3175+ // Accessors.
3176+ StringBuilder getStringBuilder() {
3177+ sb.setLength(0);
3178+ return sb;
3179+ }
3180+
3181+ char[] getCompactCharArray() {
3182+ return cmpCharArray;
3183+ }
3184+
3185+ /**
3186+ * Places characters representing the intCompact in {@code long} into
3187+ * cmpCharArray and returns the offset to the array where the
3188+ * representation starts.
3189+ *
3190+ * @param intCompact the number to put into the cmpCharArray.
3191+ * @return offset to the array where the representation starts.
3192+ * Note: intCompact must be greater or equal to zero.
3193+ */
3194+ int putIntCompact(long intCompact) {
3195+ assert intCompact >= 0;
3196+
3197+ long q;
3198+ int r;
3199+ // since we start from the least significant digit, charPos points to
3200+ // the last character in cmpCharArray.
3201+ int charPos = cmpCharArray.length;
3202+
3203+ // Get 2 digits/iteration using longs until quotient fits into an int
3204+ while (intCompact > Integer.MAX_VALUE) {
3205+ q = intCompact / 100;
3206+ r = (int)(intCompact - q * 100);
3207+ intCompact = q;
3208+ cmpCharArray[--charPos] = DIGIT_ONES[r];
3209+ cmpCharArray[--charPos] = DIGIT_TENS[r];
3210+ }
3211+
3212+ // Get 2 digits/iteration using ints when i2 >= 100
3213+ int q2;
3214+ int i2 = (int)intCompact;
3215+ while (i2 >= 100) {
3216+ q2 = i2 / 100;
3217+ r = i2 - q2 * 100;
3218+ i2 = q2;
3219+ cmpCharArray[--charPos] = DIGIT_ONES[r];
3220+ cmpCharArray[--charPos] = DIGIT_TENS[r];
3221+ }
3222+
3223+ cmpCharArray[--charPos] = DIGIT_ONES[i2];
3224+ if (i2 >= 10)
3225+ cmpCharArray[--charPos] = DIGIT_TENS[i2];
3226+
3227+ return charPos;
3228+ }
3229+
3230+ final static char[] DIGIT_TENS = {
3231+ '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
3232+ '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
3233+ '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
3234+ '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
3235+ '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
3236+ '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
3237+ '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
3238+ '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
3239+ '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
3240+ '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
3241+ };
3242+
3243+ final static char[] DIGIT_ONES = {
3244+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3245+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3246+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3247+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3248+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3249+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3250+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3251+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3252+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3253+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
3254+ };
3255+ }
3256+
3257+ /**
3258+ * Lay out this {@code BigDecimal} into a {@code char[]} array.
3259+ * The Java 1.2 equivalent to this was called {@code getValueString}.
3260+ *
3261+ * @param sci {@code true} for Scientific exponential notation;
3262+ * {@code false} for Engineering
3263+ * @return string with canonical string representation of this
3264+ * {@code BigDecimal}
3265+ */
3266+ private String layoutChars(boolean sci) {
3267+ if (scale == 0) // zero scale is trivial
3268+ return (intCompact != INFLATED) ?
3269+ Long.toString(intCompact):
3270+ intVal.toString();
3271+
3272+ StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get();
3273+ char[] coeff;
3274+ int offset; // offset is the starting index for coeff array
3275+ // Get the significand as an absolute value
3276+ if (intCompact != INFLATED) {
3277+ offset = sbHelper.putIntCompact(Math.abs(intCompact));
3278+ coeff = sbHelper.getCompactCharArray();
3279+ } else {
3280+ offset = 0;
3281+ coeff = intVal.abs().toString().toCharArray();
3282+ }
3283+
3284+ // Construct a buffer, with sufficient capacity for all cases.
3285+ // If E-notation is needed, length will be: +1 if negative, +1
3286+ // if '.' needed, +2 for "E+", + up to 10 for adjusted exponent.
3287+ // Otherwise it could have +1 if negative, plus leading "0.00000"
3288+ StringBuilder buf = sbHelper.getStringBuilder();
3289+ if (signum() < 0) // prefix '-' if negative
3290+ buf.append('-');
3291+ int coeffLen = coeff.length - offset;
3292+ long adjusted = -(long)scale + (coeffLen -1);
3293+ if ((scale >= 0) && (adjusted >= -6)) { // plain number
3294+ int pad = scale - coeffLen; // count of padding zeros
3295+ if (pad >= 0) { // 0.xxx form
3296+ buf.append('0');
3297+ buf.append('.');
3298+ for (; pad>0; pad--) {
3299+ buf.append('0');
3300+ }
3301+ buf.append(coeff, offset, coeffLen);
3302+ } else { // xx.xx form
3303+ buf.append(coeff, offset, -pad);
3304+ buf.append('.');
3305+ buf.append(coeff, -pad + offset, scale);
3306+ }
3307+ } else { // E-notation is needed
3308+ if (sci) { // Scientific notation
3309+ buf.append(coeff[offset]); // first character
3310+ if (coeffLen > 1) { // more to come
3311+ buf.append('.');
3312+ buf.append(coeff, offset + 1, coeffLen - 1);
3313+ }
3314+ } else { // Engineering notation
3315+ int sig = (int)(adjusted % 3);
3316+ if (sig < 0)
3317+ sig += 3; // [adjusted was negative]
3318+ adjusted -= sig; // now a multiple of 3
3319+ sig++;
3320+ if (signum() == 0) {
3321+ switch (sig) {
3322+ case 1:
3323+ buf.append('0'); // exponent is a multiple of three
3324+ break;
3325+ case 2:
3326+ buf.append("0.00");
3327+ adjusted += 3;
3328+ break;
3329+ case 3:
3330+ buf.append("0.0");
3331+ adjusted += 3;
3332+ break;
3333+ default:
3334+ throw new AssertionError("Unexpected sig value " + sig);
3335+ }
3336+ } else if (sig >= coeffLen) { // significand all in integer
3337+ buf.append(coeff, offset, coeffLen);
3338+ // may need some zeros, too
3339+ for (int i = sig - coeffLen; i > 0; i--)
3340+ buf.append('0');
3341+ } else { // xx.xxE form
3342+ buf.append(coeff, offset, sig);
3343+ buf.append('.');
3344+ buf.append(coeff, offset + sig, coeffLen - sig);
3345+ }
3346+ }
3347+ if (adjusted != 0) { // [!sci could have made 0]
3348+ buf.append('E');
3349+ if (adjusted > 0) // force sign for positive
3350+ buf.append('+');
3351+ buf.append(adjusted);
3352+ }
3353+ }
3354+ return buf.toString();
3355+ }
3356+
3357+ /**
3358+ * Return 10 to the power n, as a {@code BigInteger}.
3359+ *
3360+ * @param n the power of ten to be returned (>=0)
3361+ * @return a {@code BigInteger} with the value (10<sup>n</sup>)
3362+ */
3363+ private static BigInteger bigTenToThe(int n) {
3364+ if (n < 0)
3365+ return BigInteger.ZERO;
3366+
3367+ if (n < BIG_TEN_POWERS_TABLE_MAX) {
3368+ BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3369+ if (n < pows.length)
3370+ return pows[n];
3371+ else
3372+ return expandBigIntegerTenPowers(n);
3373+ }
3374+ // BigInteger.pow is slow, so make 10**n by constructing a
3375+ // BigInteger from a character string (still not very fast)
3376+ char tenpow[] = new char[n + 1];
3377+ tenpow[0] = '1';
3378+ for (int i = 1; i <= n; i++)
3379+ tenpow[i] = '0';
3380+ return new BigInteger(tenpow);
3381+ }
3382+
3383+ /**
3384+ * Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n.
3385+ *
3386+ * @param n the power of ten to be returned (>=0)
3387+ * @return a {@code BigDecimal} with the value (10<sup>n</sup>) and
3388+ * in the meantime, the BIG_TEN_POWERS_TABLE array gets
3389+ * expanded to the size greater than n.
3390+ */
3391+ private static BigInteger expandBigIntegerTenPowers(int n) {
3392+ synchronized(BigDecimal.class) {
3393+ BigInteger[] pows = BIG_TEN_POWERS_TABLE;
3394+ int curLen = pows.length;
3395+ // The following comparison and the above synchronized statement is
3396+ // to prevent multiple threads from expanding the same array.
3397+ if (curLen <= n) {
3398+ int newLen = curLen << 1;
3399+ while (newLen <= n)
3400+ newLen <<= 1;
3401+ pows = Arrays.copyOf(pows, newLen);
3402+ for (int i = curLen; i < newLen; i++)
3403+ pows[i] = pows[i - 1].multiply(BigInteger.TEN);
3404+ // Based on the following facts:
3405+ // 1. pows is a private local varible;
3406+ // 2. the following store is a volatile store.
3407+ // the newly created array elements can be safely published.
3408+ BIG_TEN_POWERS_TABLE = pows;
3409+ }
3410+ return pows[n];
3411+ }
3412+ }
3413+
3414+ private static final long[] LONG_TEN_POWERS_TABLE = {
3415+ 1, // 0 / 10^0
3416+ 10, // 1 / 10^1
3417+ 100, // 2 / 10^2
3418+ 1000, // 3 / 10^3
3419+ 10000, // 4 / 10^4
3420+ 100000, // 5 / 10^5
3421+ 1000000, // 6 / 10^6
3422+ 10000000, // 7 / 10^7
3423+ 100000000, // 8 / 10^8
3424+ 1000000000, // 9 / 10^9
3425+ 10000000000L, // 10 / 10^10
3426+ 100000000000L, // 11 / 10^11
3427+ 1000000000000L, // 12 / 10^12
3428+ 10000000000000L, // 13 / 10^13
3429+ 100000000000000L, // 14 / 10^14
3430+ 1000000000000000L, // 15 / 10^15
3431+ 10000000000000000L, // 16 / 10^16
3432+ 100000000000000000L, // 17 / 10^17
3433+ 1000000000000000000L // 18 / 10^18
3434+ };
3435+
3436+ private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = {BigInteger.ONE,
3437+ BigInteger.valueOf(10), BigInteger.valueOf(100),
3438+ BigInteger.valueOf(1000), BigInteger.valueOf(10000),
3439+ BigInteger.valueOf(100000), BigInteger.valueOf(1000000),
3440+ BigInteger.valueOf(10000000), BigInteger.valueOf(100000000),
3441+ BigInteger.valueOf(1000000000),
3442+ BigInteger.valueOf(10000000000L),
3443+ BigInteger.valueOf(100000000000L),
3444+ BigInteger.valueOf(1000000000000L),
3445+ BigInteger.valueOf(10000000000000L),
3446+ BigInteger.valueOf(100000000000000L),
3447+ BigInteger.valueOf(1000000000000000L),
3448+ BigInteger.valueOf(10000000000000000L),
3449+ BigInteger.valueOf(100000000000000000L),
3450+ BigInteger.valueOf(1000000000000000000L)
3451+ };
3452+
3453+ private static final int BIG_TEN_POWERS_TABLE_INITLEN =
3454+ BIG_TEN_POWERS_TABLE.length;
3455+ private static final int BIG_TEN_POWERS_TABLE_MAX =
3456+ 16 * BIG_TEN_POWERS_TABLE_INITLEN;
3457+
3458+ private static final long THRESHOLDS_TABLE[] = {
3459+ Long.MAX_VALUE, // 0
3460+ Long.MAX_VALUE/10L, // 1
3461+ Long.MAX_VALUE/100L, // 2
3462+ Long.MAX_VALUE/1000L, // 3
3463+ Long.MAX_VALUE/10000L, // 4
3464+ Long.MAX_VALUE/100000L, // 5
3465+ Long.MAX_VALUE/1000000L, // 6
3466+ Long.MAX_VALUE/10000000L, // 7
3467+ Long.MAX_VALUE/100000000L, // 8
3468+ Long.MAX_VALUE/1000000000L, // 9
3469+ Long.MAX_VALUE/10000000000L, // 10
3470+ Long.MAX_VALUE/100000000000L, // 11
3471+ Long.MAX_VALUE/1000000000000L, // 12
3472+ Long.MAX_VALUE/10000000000000L, // 13
3473+ Long.MAX_VALUE/100000000000000L, // 14
3474+ Long.MAX_VALUE/1000000000000000L, // 15
3475+ Long.MAX_VALUE/10000000000000000L, // 16
3476+ Long.MAX_VALUE/100000000000000000L, // 17
3477+ Long.MAX_VALUE/1000000000000000000L // 18
3478+ };
3479+
3480+ /**
3481+ * Compute val * 10 ^ n; return this product if it is
3482+ * representable as a long, INFLATED otherwise.
3483+ */
3484+ private static long longMultiplyPowerTen(long val, int n) {
3485+ if (val == 0 || n <= 0)
3486+ return val;
3487+ long[] tab = LONG_TEN_POWERS_TABLE;
3488+ long[] bounds = THRESHOLDS_TABLE;
3489+ if (n < tab.length && n < bounds.length) {
3490+ long tenpower = tab[n];
3491+ if (val == 1)
3492+ return tenpower;
3493+ if (Math.abs(val) <= bounds[n])
3494+ return val * tenpower;
3495+ }
3496+ return INFLATED;
3497+ }
3498+
3499+ /**
3500+ * Compute this * 10 ^ n.
3501+ * Needed mainly to allow special casing to trap zero value
3502+ */
3503+ private BigInteger bigMultiplyPowerTen(int n) {
3504+ if (n <= 0)
3505+ return this.inflate();
3506+
3507+ if (intCompact != INFLATED)
3508+ return bigTenToThe(n).multiply(intCompact);
3509+ else
3510+ return intVal.multiply(bigTenToThe(n));
3511+ }
3512+
3513+ /**
3514+ * Assign appropriate BigInteger to intVal field if intVal is
3515+ * null, i.e. the compact representation is in use.
3516+ */
3517+ private BigInteger inflate() {
3518+ if (intVal == null)
3519+ intVal = BigInteger.valueOf(intCompact);
3520+ return intVal;
3521+ }
3522+
3523+ /**
3524+ * Match the scales of two {@code BigDecimal}s to align their
3525+ * least significant digits.
3526+ *
3527+ * <p>If the scales of val[0] and val[1] differ, rescale
3528+ * (non-destructively) the lower-scaled {@code BigDecimal} so
3529+ * they match. That is, the lower-scaled reference will be
3530+ * replaced by a reference to a new object with the same scale as
3531+ * the other {@code BigDecimal}.
3532+ *
3533+ * @param val array of two elements referring to the two
3534+ * {@code BigDecimal}s to be aligned.
3535+ */
3536+ private static void matchScale(BigDecimal[] val) {
3537+ if (val[0].scale == val[1].scale) {
3538+ return;
3539+ } else if (val[0].scale < val[1].scale) {
3540+ val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY);
3541+ } else if (val[1].scale < val[0].scale) {
3542+ val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY);
3543+ }
3544+ }
3545+
3546+ /**
3547+ * Reconstitute the {@code BigDecimal} instance from a stream (that is,
3548+ * deserialize it).
3549+ *
3550+ * @param s the stream being read.
3551+ */
3552+ private void readObject(java.io.ObjectInputStream s)
3553+ throws java.io.IOException, ClassNotFoundException {
3554+ // Read in all fields
3555+ s.defaultReadObject();
3556+ // validate possibly bad fields
3557+ if (intVal == null) {
3558+ String message = "BigDecimal: null intVal in stream";
3559+ throw new java.io.StreamCorruptedException(message);
3560+ // [all values of scale are now allowed]
3561+ }
3562+ intCompact = compactValFor(intVal);
3563+ }
3564+
3565+ /**
3566+ * Serialize this {@code BigDecimal} to the stream in question
3567+ *
3568+ * @param s the stream to serialize to.
3569+ */
3570+ private void writeObject(java.io.ObjectOutputStream s)
3571+ throws java.io.IOException {
3572+ // Must inflate to maintain compatible serial form.
3573+ this.inflate();
3574+
3575+ // Write proper fields
3576+ s.defaultWriteObject();
3577+ }
3578+
3579+
3580+ /**
3581+ * Returns the length of the absolute value of a {@code long}, in decimal
3582+ * digits.
3583+ *
3584+ * @param x the {@code long}
3585+ * @return the length of the unscaled value, in deciaml digits.
3586+ */
3587+ private static int longDigitLength(long x) {
3588+ /*
3589+ * As described in "Bit Twiddling Hacks" by Sean Anderson,
3590+ * (http://graphics.stanford.edu/~seander/bithacks.html)
3591+ * integer log 10 of x is within 1 of
3592+ * (1233/4096)* (1 + integer log 2 of x).
3593+ * The fraction 1233/4096 approximates log10(2). So we first
3594+ * do a version of log2 (a variant of Long class with
3595+ * pre-checks and opposite directionality) and then scale and
3596+ * check against powers table. This is a little simpler in
3597+ * present context than the version in Hacker's Delight sec
3598+ * 11-4. Adding one to bit length allows comparing downward
3599+ * from the LONG_TEN_POWERS_TABLE that we need anyway.
3600+ */
3601+ assert x != INFLATED;
3602+ if (x < 0)
3603+ x = -x;
3604+ if (x < 10) // must screen for 0, might as well 10
3605+ return 1;
3606+ int n = 64; // not 63, to avoid needing to add 1 later
3607+ int y = (int)(x >>> 32);
3608+ if (y == 0) { n -= 32; y = (int)x; }
3609+ if (y >>> 16 == 0) { n -= 16; y <<= 16; }
3610+ if (y >>> 24 == 0) { n -= 8; y <<= 8; }
3611+ if (y >>> 28 == 0) { n -= 4; y <<= 4; }
3612+ if (y >>> 30 == 0) { n -= 2; y <<= 2; }
3613+ int r = (((y >>> 31) + n) * 1233) >>> 12;
3614+ long[] tab = LONG_TEN_POWERS_TABLE;
3615+ // if r >= length, must have max possible digits for long
3616+ return (r >= tab.length || x < tab[r])? r : r+1;
3617+ }
3618+
3619+ /**
3620+ * Returns the length of the absolute value of a BigInteger, in
3621+ * decimal digits.
3622+ *
3623+ * @param b the BigInteger
3624+ * @return the length of the unscaled value, in decimal digits
3625+ */
3626+ private static int bigDigitLength(BigInteger b) {
3627+ /*
3628+ * Same idea as the long version, but we need a better
3629+ * approximation of log10(2). Using 646456993/2^31
3630+ * is accurate up to max possible reported bitLength.
3631+ */
3632+ if (b.signum == 0)
3633+ return 1;
3634+ int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31);
3635+ return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1;
3636+ }
3637+
3638+
3639+ /**
3640+ * Remove insignificant trailing zeros from this
3641+ * {@code BigDecimal} until the preferred scale is reached or no
3642+ * more zeros can be removed. If the preferred scale is less than
3643+ * Integer.MIN_VALUE, all the trailing zeros will be removed.
3644+ *
3645+ * {@code BigInteger} assistance could help, here?
3646+ *
3647+ * <p>WARNING: This method should only be called on new objects as
3648+ * it mutates the value fields.
3649+ *
3650+ * @return this {@code BigDecimal} with a scale possibly reduced
3651+ * to be closed to the preferred scale.
3652+ */
3653+ private BigDecimal stripZerosToMatchScale(long preferredScale) {
3654+ this.inflate();
3655+ BigInteger qr[]; // quotient-remainder pair
3656+ while ( intVal.compareMagnitude(BigInteger.TEN) >= 0 &&
3657+ scale > preferredScale) {
3658+ if (intVal.testBit(0))
3659+ break; // odd number cannot end in 0
3660+ qr = intVal.divideAndRemainder(BigInteger.TEN);
3661+ if (qr[1].signum() != 0)
3662+ break; // non-0 remainder
3663+ intVal=qr[0];
3664+ scale = checkScale((long)scale-1); // could Overflow
3665+ if (precision > 0) // adjust precision if known
3666+ precision--;
3667+ }
3668+ if (intVal != null)
3669+ intCompact = compactValFor(intVal);
3670+ return this;
3671+ }
3672+
3673+ /**
3674+ * Check a scale for Underflow or Overflow. If this BigDecimal is
3675+ * nonzero, throw an exception if the scale is outof range. If this
3676+ * is zero, saturate the scale to the extreme value of the right
3677+ * sign if the scale is out of range.
3678+ *
3679+ * @param val The new scale.
3680+ * @throws ArithmeticException (overflow or underflow) if the new
3681+ * scale is out of range.
3682+ * @return validated scale as an int.
3683+ */
3684+ private int checkScale(long val) {
3685+ int asInt = (int)val;
3686+ if (asInt != val) {
3687+ asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
3688+ BigInteger b;
3689+ if (intCompact != 0 &&
3690+ ((b = intVal) == null || b.signum() != 0))
3691+ throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
3692+ }
3693+ return asInt;
3694+ }
3695+
3696+ /**
3697+ * Round an operand; used only if digits &gt; 0. Does not change
3698+ * {@code this}; if rounding is needed a new {@code BigDecimal}
3699+ * is created and returned.
3700+ *
3701+ * @param mc the context to use.
3702+ * @throws ArithmeticException if the result is inexact but the
3703+ * rounding mode is {@code UNNECESSARY}.
3704+ */
3705+ private BigDecimal roundOp(MathContext mc) {
3706+ BigDecimal rounded = doRound(this, mc);
3707+ return rounded;
3708+ }
3709+
3710+ /** Round this BigDecimal according to the MathContext settings;
3711+ * used only if precision {@literal >} 0.
3712+ *
3713+ * <p>WARNING: This method should only be called on new objects as
3714+ * it mutates the value fields.
3715+ *
3716+ * @param mc the context to use.
3717+ * @throws ArithmeticException if the rounding mode is
3718+ * {@code RoundingMode.UNNECESSARY} and the
3719+ * {@code BigDecimal} operation would require rounding.
3720+ */
3721+ private void roundThis(MathContext mc) {
3722+ BigDecimal rounded = doRound(this, mc);
3723+ if (rounded == this) // wasn't rounded
3724+ return;
3725+ this.intVal = rounded.intVal;
3726+ this.intCompact = rounded.intCompact;
3727+ this.scale = rounded.scale;
3728+ this.precision = rounded.precision;
3729+ }
3730+
3731+ /**
3732+ * Returns a {@code BigDecimal} rounded according to the
3733+ * MathContext settings; used only if {@code mc.precision > 0}.
3734+ * Does not change {@code this}; if rounding is needed a new
3735+ * {@code BigDecimal} is created and returned.
3736+ *
3737+ * @param mc the context to use.
3738+ * @return a {@code BigDecimal} rounded according to the MathContext
3739+ * settings. May return this, if no rounding needed.
3740+ * @throws ArithmeticException if the rounding mode is
3741+ * {@code RoundingMode.UNNECESSARY} and the
3742+ * result is inexact.
3743+ */
3744+ private static BigDecimal doRound(BigDecimal d, MathContext mc) {
3745+ int mcp = mc.precision;
3746+ int drop;
3747+ // This might (rarely) iterate to cover the 999=>1000 case
3748+ while ((drop = d.precision() - mcp) > 0) {
3749+ int newScale = d.checkScale((long)d.scale - drop);
3750+ int mode = mc.roundingMode.oldMode;
3751+ if (drop < LONG_TEN_POWERS_TABLE.length)
3752+ d = divideAndRound(d.intCompact, d.intVal,
3753+ LONG_TEN_POWERS_TABLE[drop], null,
3754+ newScale, mode, newScale);
3755+ else
3756+ d = divideAndRound(d.intCompact, d.intVal,
3757+ INFLATED, bigTenToThe(drop),
3758+ newScale, mode, newScale);
3759+ }
3760+ return d;
3761+ }
3762+
3763+ /**
3764+ * Returns the compact value for given {@code BigInteger}, or
3765+ * INFLATED if too big. Relies on internal representation of
3766+ * {@code BigInteger}.
3767+ */
3768+ private static long compactValFor(BigInteger b) {
3769+ int[] m = b.mag;
3770+ int len = m.length;
3771+ if (len == 0)
3772+ return 0;
3773+ int d = m[0];
3774+ if (len > 2 || (len == 2 && d < 0))
3775+ return INFLATED;
3776+
3777+ long u = (len == 2)?
3778+ (((long) m[1] & LONG_MASK) + (((long)d) << 32)) :
3779+ (((long)d) & LONG_MASK);
3780+ return (b.signum < 0)? -u : u;
3781+ }
3782+
3783+ private static int longCompareMagnitude(long x, long y) {
3784+ if (x < 0)
3785+ x = -x;
3786+ if (y < 0)
3787+ y = -y;
3788+ return (x < y) ? -1 : ((x == y) ? 0 : 1);
3789+ }
3790+
3791+ private static int saturateLong(long s) {
3792+ int i = (int)s;
3793+ return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE);
3794+ }
3795+
3796+ /*
3797+ * Internal printing routine
3798+ */
3799+ private static void print(String name, BigDecimal bd) {
3800+ System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n",
3801+ name,
3802+ bd.intCompact,
3803+ bd.intVal,
3804+ bd.scale,
3805+ bd.precision);
3806+ }
3807+
3808+ /**
3809+ * Check internal invariants of this BigDecimal. These invariants
3810+ * include:
3811+ *
3812+ * <ul>
3813+ *
3814+ * <li>The object must be initialized; either intCompact must not be
3815+ * INFLATED or intVal is non-null. Both of these conditions may
3816+ * be true.
3817+ *
3818+ * <li>If both intCompact and intVal and set, their values must be
3819+ * consistent.
3820+ *
3821+ * <li>If precision is nonzero, it must have the right value.
3822+ * </ul>
3823+ *
3824+ * Note: Since this is an audit method, we are not supposed to change the
3825+ * state of this BigDecimal object.
3826+ */
3827+ private BigDecimal audit() {
3828+ if (intCompact == INFLATED) {
3829+ if (intVal == null) {
3830+ print("audit", this);
3831+ throw new AssertionError("null intVal");
3832+ }
3833+ // Check precision
3834+ if (precision > 0 && precision != bigDigitLength(intVal)) {
3835+ print("audit", this);
3836+ throw new AssertionError("precision mismatch");
3837+ }
3838+ } else {
3839+ if (intVal != null) {
3840+ long val = intVal.longValue();
3841+ if (val != intCompact) {
3842+ print("audit", this);
3843+ throw new AssertionError("Inconsistent state, intCompact=" +
3844+ intCompact + "\t intVal=" + val);
3845+ }
3846+ }
3847+ // Check precision
3848+ if (precision > 0 && precision != longDigitLength(intCompact)) {
3849+ print("audit", this);
3850+ throw new AssertionError("precision mismatch");
3851+ }
3852+ }
3853+ return this;
3854+ }
3855+}