History

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

Showing the changes to java/pkg/java/math (19 of 18352 files). Show all

Unified · Split

19 files
  1. java/pkg/java/math/BigDecimal$1.class +0 −0
  2. java/pkg/java/math/BigDecimal$LongOverflow.class +0 −0
  3. java/pkg/java/math/BigDecimal$StringBuilderHelper.class +0 −0
  4. java/pkg/java/math/BigDecimal.class +0 −0
  5. java/pkg/java/math/BigDecimal.java +3855 −0
  6. java/pkg/java/math/BigInteger.class +0 −0
  7. java/pkg/java/math/BigInteger.java +3186 −0
  8. java/pkg/java/math/BitSieve.class +0 −0
  9. java/pkg/java/math/BitSieve.java +212 −0
  10. java/pkg/java/math/MathContext.class +0 −0
  11. java/pkg/java/math/MathContext.java +326 −0
  12. java/pkg/java/math/MutableBigInteger.class +0 −0
  13. java/pkg/java/math/MutableBigInteger.java +1477 −0
  14. java/pkg/java/math/RoundingMode.class +0 −0
  15. java/pkg/java/math/RoundingMode.java +349 −0
  16. java/pkg/java/math/SignedMutableBigInteger.class +0 −0
  17. java/pkg/java/math/SignedMutableBigInteger.java +135 −0
  18. java/pkg/java/math/mkfile +15 −0
  19. java/pkg/java/math/package-info.java +45 −0
java/pkg/java/math/BigDecimal$1.class+0−0

Binary file not shown.

java/pkg/java/math/BigDecimal$LongOverflow.class+0−0

Binary file not shown.

java/pkg/java/math/BigDecimal$StringBuilderHelper.class+0−0

Binary file not shown.

java/pkg/java/math/BigDecimal.class+0−0

Binary file not shown.

java/pkg/java/math/BigDecimal.java+3855−0
@@ -0,0 +1,3855 @@
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+}
java/pkg/java/math/BigInteger.class+0−0

Binary file not shown.

java/pkg/java/math/BigInteger.java+3186−0
@@ -0,0 +1,3186 @@
1+/*
2+ * Copyright (c) 1996, 2007, 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 (c) 1995 Colin Plumb. All rights reserved.
28+ */
29+
30+package java.math;
31+
32+import java.util.Random;
33+import java.io.*;
34+
35+/**
36+ * Immutable arbitrary-precision integers. All operations behave as if
37+ * BigIntegers were represented in two's-complement notation (like Java's
38+ * primitive integer types). BigInteger provides analogues to all of Java's
39+ * primitive integer operators, and all relevant methods from java.lang.Math.
40+ * Additionally, BigInteger provides operations for modular arithmetic, GCD
41+ * calculation, primality testing, prime generation, bit manipulation,
42+ * and a few other miscellaneous operations.
43+ *
44+ * <p>Semantics of arithmetic operations exactly mimic those of Java's integer
45+ * arithmetic operators, as defined in <i>The Java Language Specification</i>.
46+ * For example, division by zero throws an {@code ArithmeticException}, and
47+ * division of a negative by a positive yields a negative (or zero) remainder.
48+ * All of the details in the Spec concerning overflow are ignored, as
49+ * BigIntegers are made as large as necessary to accommodate the results of an
50+ * operation.
51+ *
52+ * <p>Semantics of shift operations extend those of Java's shift operators
53+ * to allow for negative shift distances. A right-shift with a negative
54+ * shift distance results in a left shift, and vice-versa. The unsigned
55+ * right shift operator ({@code >>>}) is omitted, as this operation makes
56+ * little sense in combination with the "infinite word size" abstraction
57+ * provided by this class.
58+ *
59+ * <p>Semantics of bitwise logical operations exactly mimic those of Java's
60+ * bitwise integer operators. The binary operators ({@code and},
61+ * {@code or}, {@code xor}) implicitly perform sign extension on the shorter
62+ * of the two operands prior to performing the operation.
63+ *
64+ * <p>Comparison operations perform signed integer comparisons, analogous to
65+ * those performed by Java's relational and equality operators.
66+ *
67+ * <p>Modular arithmetic operations are provided to compute residues, perform
68+ * exponentiation, and compute multiplicative inverses. These methods always
69+ * return a non-negative result, between {@code 0} and {@code (modulus - 1)},
70+ * inclusive.
71+ *
72+ * <p>Bit operations operate on a single bit of the two's-complement
73+ * representation of their operand. If necessary, the operand is sign-
74+ * extended so that it contains the designated bit. None of the single-bit
75+ * operations can produce a BigInteger with a different sign from the
76+ * BigInteger being operated on, as they affect only a single bit, and the
77+ * "infinite word size" abstraction provided by this class ensures that there
78+ * are infinitely many "virtual sign bits" preceding each BigInteger.
79+ *
80+ * <p>For the sake of brevity and clarity, pseudo-code is used throughout the
81+ * descriptions of BigInteger methods. The pseudo-code expression
82+ * {@code (i + j)} is shorthand for "a BigInteger whose value is
83+ * that of the BigInteger {@code i} plus that of the BigInteger {@code j}."
84+ * The pseudo-code expression {@code (i == j)} is shorthand for
85+ * "{@code true} if and only if the BigInteger {@code i} represents the same
86+ * value as the BigInteger {@code j}." Other pseudo-code expressions are
87+ * interpreted similarly.
88+ *
89+ * <p>All methods and constructors in this class throw
90+ * {@code NullPointerException} when passed
91+ * a null object reference for any input parameter.
92+ *
93+ * @see BigDecimal
94+ * @author Josh Bloch
95+ * @author Michael McCloskey
96+ * @since JDK1.1
97+ */
98+
99+public class BigInteger extends Number implements Comparable<BigInteger> {
100+ /**
101+ * The signum of this BigInteger: -1 for negative, 0 for zero, or
102+ * 1 for positive. Note that the BigInteger zero <i>must</i> have
103+ * a signum of 0. This is necessary to ensures that there is exactly one
104+ * representation for each BigInteger value.
105+ *
106+ * @serial
107+ */
108+ final int signum;
109+
110+ /**
111+ * The magnitude of this BigInteger, in <i>big-endian</i> order: the
112+ * zeroth element of this array is the most-significant int of the
113+ * magnitude. The magnitude must be "minimal" in that the most-significant
114+ * int ({@code mag[0]}) must be non-zero. This is necessary to
115+ * ensure that there is exactly one representation for each BigInteger
116+ * value. Note that this implies that the BigInteger zero has a
117+ * zero-length mag array.
118+ */
119+ final int[] mag;
120+
121+ // These "redundant fields" are initialized with recognizable nonsense
122+ // values, and cached the first time they are needed (or never, if they
123+ // aren't needed).
124+
125+ /**
126+ * One plus the bitCount of this BigInteger. Zeros means unitialized.
127+ *
128+ * @serial
129+ * @see #bitCount
130+ * @deprecated Deprecated since logical value is offset from stored
131+ * value and correction factor is applied in accessor method.
132+ */
133+ @Deprecated
134+ private int bitCount;
135+
136+ /**
137+ * One plus the bitLength of this BigInteger. Zeros means unitialized.
138+ * (either value is acceptable).
139+ *
140+ * @serial
141+ * @see #bitLength()
142+ * @deprecated Deprecated since logical value is offset from stored
143+ * value and correction factor is applied in accessor method.
144+ */
145+ @Deprecated
146+ private int bitLength;
147+
148+ /**
149+ * Two plus the lowest set bit of this BigInteger, as returned by
150+ * getLowestSetBit().
151+ *
152+ * @serial
153+ * @see #getLowestSetBit
154+ * @deprecated Deprecated since logical value is offset from stored
155+ * value and correction factor is applied in accessor method.
156+ */
157+ @Deprecated
158+ private int lowestSetBit;
159+
160+ /**
161+ * Two plus the index of the lowest-order int in the magnitude of this
162+ * BigInteger that contains a nonzero int, or -2 (either value is acceptable).
163+ * The least significant int has int-number 0, the next int in order of
164+ * increasing significance has int-number 1, and so forth.
165+ * @deprecated Deprecated since logical value is offset from stored
166+ * value and correction factor is applied in accessor method.
167+ */
168+ @Deprecated
169+ private int firstNonzeroIntNum;
170+
171+ /**
172+ * This mask is used to obtain the value of an int as if it were unsigned.
173+ */
174+ final static long LONG_MASK = 0xffffffffL;
175+
176+ //Constructors
177+
178+ /**
179+ * Translates a byte array containing the two's-complement binary
180+ * representation of a BigInteger into a BigInteger. The input array is
181+ * assumed to be in <i>big-endian</i> byte-order: the most significant
182+ * byte is in the zeroth element.
183+ *
184+ * @param val big-endian two's-complement binary representation of
185+ * BigInteger.
186+ * @throws NumberFormatException {@code val} is zero bytes long.
187+ */
188+ public BigInteger(byte[] val) {
189+ if (val.length == 0)
190+ throw new NumberFormatException("Zero length BigInteger");
191+
192+ if (val[0] < 0) {
193+ mag = makePositive(val);
194+ signum = -1;
195+ } else {
196+ mag = stripLeadingZeroBytes(val);
197+ signum = (mag.length == 0 ? 0 : 1);
198+ }
199+ }
200+
201+ /**
202+ * This private constructor translates an int array containing the
203+ * two's-complement binary representation of a BigInteger into a
204+ * BigInteger. The input array is assumed to be in <i>big-endian</i>
205+ * int-order: the most significant int is in the zeroth element.
206+ */
207+ private BigInteger(int[] val) {
208+ if (val.length == 0)
209+ throw new NumberFormatException("Zero length BigInteger");
210+
211+ if (val[0] < 0) {
212+ mag = makePositive(val);
213+ signum = -1;
214+ } else {
215+ mag = trustedStripLeadingZeroInts(val);
216+ signum = (mag.length == 0 ? 0 : 1);
217+ }
218+ }
219+
220+ /**
221+ * Translates the sign-magnitude representation of a BigInteger into a
222+ * BigInteger. The sign is represented as an integer signum value: -1 for
223+ * negative, 0 for zero, or 1 for positive. The magnitude is a byte array
224+ * in <i>big-endian</i> byte-order: the most significant byte is in the
225+ * zeroth element. A zero-length magnitude array is permissible, and will
226+ * result in a BigInteger value of 0, whether signum is -1, 0 or 1.
227+ *
228+ * @param signum signum of the number (-1 for negative, 0 for zero, 1
229+ * for positive).
230+ * @param magnitude big-endian binary representation of the magnitude of
231+ * the number.
232+ * @throws NumberFormatException {@code signum} is not one of the three
233+ * legal values (-1, 0, and 1), or {@code signum} is 0 and
234+ * {@code magnitude} contains one or more non-zero bytes.
235+ */
236+ public BigInteger(int signum, byte[] magnitude) {
237+ this.mag = stripLeadingZeroBytes(magnitude);
238+
239+ if (signum < -1 || signum > 1)
240+ throw(new NumberFormatException("Invalid signum value"));
241+
242+ if (this.mag.length==0) {
243+ this.signum = 0;
244+ } else {
245+ if (signum == 0)
246+ throw(new NumberFormatException("signum-magnitude mismatch"));
247+ this.signum = signum;
248+ }
249+ }
250+
251+ /**
252+ * A constructor for internal use that translates the sign-magnitude
253+ * representation of a BigInteger into a BigInteger. It checks the
254+ * arguments and copies the magnitude so this constructor would be
255+ * safe for external use.
256+ */
257+ private BigInteger(int signum, int[] magnitude) {
258+ this.mag = stripLeadingZeroInts(magnitude);
259+
260+ if (signum < -1 || signum > 1)
261+ throw(new NumberFormatException("Invalid signum value"));
262+
263+ if (this.mag.length==0) {
264+ this.signum = 0;
265+ } else {
266+ if (signum == 0)
267+ throw(new NumberFormatException("signum-magnitude mismatch"));
268+ this.signum = signum;
269+ }
270+ }
271+
272+ /**
273+ * Translates the String representation of a BigInteger in the
274+ * specified radix into a BigInteger. The String representation
275+ * consists of an optional minus or plus sign followed by a
276+ * sequence of one or more digits in the specified radix. The
277+ * character-to-digit mapping is provided by {@code
278+ * Character.digit}. The String may not contain any extraneous
279+ * characters (whitespace, for example).
280+ *
281+ * @param val String representation of BigInteger.
282+ * @param radix radix to be used in interpreting {@code val}.
283+ * @throws NumberFormatException {@code val} is not a valid representation
284+ * of a BigInteger in the specified radix, or {@code radix} is
285+ * outside the range from {@link Character#MIN_RADIX} to
286+ * {@link Character#MAX_RADIX}, inclusive.
287+ * @see Character#digit
288+ */
289+ public BigInteger(String val, int radix) {
290+ int cursor = 0, numDigits;
291+ final int len = val.length();
292+
293+ if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
294+ throw new NumberFormatException("Radix out of range");
295+ if (len == 0)
296+ throw new NumberFormatException("Zero length BigInteger");
297+
298+ // Check for at most one leading sign
299+ int sign = 1;
300+ int index1 = val.lastIndexOf('-');
301+ int index2 = val.lastIndexOf('+');
302+ if ((index1 + index2) <= -1) {
303+ // No leading sign character or at most one leading sign character
304+ if (index1 == 0 || index2 == 0) {
305+ cursor = 1;
306+ if (len == 1)
307+ throw new NumberFormatException("Zero length BigInteger");
308+ }
309+ if (index1 == 0)
310+ sign = -1;
311+ } else
312+ throw new NumberFormatException("Illegal embedded sign character");
313+
314+ // Skip leading zeros and compute number of digits in magnitude
315+ while (cursor < len &&
316+ Character.digit(val.charAt(cursor), radix) == 0)
317+ cursor++;
318+ if (cursor == len) {
319+ signum = 0;
320+ mag = ZERO.mag;
321+ return;
322+ }
323+
324+ numDigits = len - cursor;
325+ signum = sign;
326+
327+ // Pre-allocate array of expected size. May be too large but can
328+ // never be too small. Typically exact.
329+ int numBits = (int)(((numDigits * bitsPerDigit[radix]) >>> 10) + 1);
330+ int numWords = (numBits + 31) >>> 5;
331+ int[] magnitude = new int[numWords];
332+
333+ // Process first (potentially short) digit group
334+ int firstGroupLen = numDigits % digitsPerInt[radix];
335+ if (firstGroupLen == 0)
336+ firstGroupLen = digitsPerInt[radix];
337+ String group = val.substring(cursor, cursor += firstGroupLen);
338+ magnitude[numWords - 1] = Integer.parseInt(group, radix);
339+ if (magnitude[numWords - 1] < 0)
340+ throw new NumberFormatException("Illegal digit");
341+
342+ // Process remaining digit groups
343+ int superRadix = intRadix[radix];
344+ int groupVal = 0;
345+ while (cursor < len) {
346+ group = val.substring(cursor, cursor += digitsPerInt[radix]);
347+ groupVal = Integer.parseInt(group, radix);
348+ if (groupVal < 0)
349+ throw new NumberFormatException("Illegal digit");
350+ destructiveMulAdd(magnitude, superRadix, groupVal);
351+ }
352+ // Required for cases where the array was overallocated.
353+ mag = trustedStripLeadingZeroInts(magnitude);
354+ }
355+
356+ // Constructs a new BigInteger using a char array with radix=10
357+ BigInteger(char[] val) {
358+ int cursor = 0, numDigits;
359+ int len = val.length;
360+
361+ // Check for leading minus sign
362+ int sign = 1;
363+ if (val[0] == '-') {
364+ if (len == 1)
365+ throw new NumberFormatException("Zero length BigInteger");
366+ sign = -1;
367+ cursor = 1;
368+ } else if (val[0] == '+') {
369+ if (len == 1)
370+ throw new NumberFormatException("Zero length BigInteger");
371+ cursor = 1;
372+ }
373+
374+ // Skip leading zeros and compute number of digits in magnitude
375+ while (cursor < len && Character.digit(val[cursor], 10) == 0)
376+ cursor++;
377+ if (cursor == len) {
378+ signum = 0;
379+ mag = ZERO.mag;
380+ return;
381+ }
382+
383+ numDigits = len - cursor;
384+ signum = sign;
385+
386+ // Pre-allocate array of expected size
387+ int numWords;
388+ if (len < 10) {
389+ numWords = 1;
390+ } else {
391+ int numBits = (int)(((numDigits * bitsPerDigit[10]) >>> 10) + 1);
392+ numWords = (numBits + 31) >>> 5;
393+ }
394+ int[] magnitude = new int[numWords];
395+
396+ // Process first (potentially short) digit group
397+ int firstGroupLen = numDigits % digitsPerInt[10];
398+ if (firstGroupLen == 0)
399+ firstGroupLen = digitsPerInt[10];
400+ magnitude[numWords - 1] = parseInt(val, cursor, cursor += firstGroupLen);
401+
402+ // Process remaining digit groups
403+ while (cursor < len) {
404+ int groupVal = parseInt(val, cursor, cursor += digitsPerInt[10]);
405+ destructiveMulAdd(magnitude, intRadix[10], groupVal);
406+ }
407+ mag = trustedStripLeadingZeroInts(magnitude);
408+ }
409+
410+ // Create an integer with the digits between the two indexes
411+ // Assumes start < end. The result may be negative, but it
412+ // is to be treated as an unsigned value.
413+ private int parseInt(char[] source, int start, int end) {
414+ int result = Character.digit(source[start++], 10);
415+ if (result == -1)
416+ throw new NumberFormatException(new String(source));
417+
418+ for (int index = start; index<end; index++) {
419+ int nextVal = Character.digit(source[index], 10);
420+ if (nextVal == -1)
421+ throw new NumberFormatException(new String(source));
422+ result = 10*result + nextVal;
423+ }
424+
425+ return result;
426+ }
427+
428+ // bitsPerDigit in the given radix times 1024
429+ // Rounded up to avoid underallocation.
430+ private static long bitsPerDigit[] = { 0, 0,
431+ 1024, 1624, 2048, 2378, 2648, 2875, 3072, 3247, 3402, 3543, 3672,
432+ 3790, 3899, 4001, 4096, 4186, 4271, 4350, 4426, 4498, 4567, 4633,
433+ 4696, 4756, 4814, 4870, 4923, 4975, 5025, 5074, 5120, 5166, 5210,
434+ 5253, 5295};
435+
436+ // Multiply x array times word y in place, and add word z
437+ private static void destructiveMulAdd(int[] x, int y, int z) {
438+ // Perform the multiplication word by word
439+ long ylong = y & LONG_MASK;
440+ long zlong = z & LONG_MASK;
441+ int len = x.length;
442+
443+ long product = 0;
444+ long carry = 0;
445+ for (int i = len-1; i >= 0; i--) {
446+ product = ylong * (x[i] & LONG_MASK) + carry;
447+ x[i] = (int)product;
448+ carry = product >>> 32;
449+ }
450+
451+ // Perform the addition
452+ long sum = (x[len-1] & LONG_MASK) + zlong;
453+ x[len-1] = (int)sum;
454+ carry = sum >>> 32;
455+ for (int i = len-2; i >= 0; i--) {
456+ sum = (x[i] & LONG_MASK) + carry;
457+ x[i] = (int)sum;
458+ carry = sum >>> 32;
459+ }
460+ }
461+
462+ /**
463+ * Translates the decimal String representation of a BigInteger into a
464+ * BigInteger. The String representation consists of an optional minus
465+ * sign followed by a sequence of one or more decimal digits. The
466+ * character-to-digit mapping is provided by {@code Character.digit}.
467+ * The String may not contain any extraneous characters (whitespace, for
468+ * example).
469+ *
470+ * @param val decimal String representation of BigInteger.
471+ * @throws NumberFormatException {@code val} is not a valid representation
472+ * of a BigInteger.
473+ * @see Character#digit
474+ */
475+ public BigInteger(String val) {
476+ this(val, 10);
477+ }
478+
479+ /**
480+ * Constructs a randomly generated BigInteger, uniformly distributed over
481+ * the range 0 to (2<sup>{@code numBits}</sup> - 1), inclusive.
482+ * The uniformity of the distribution assumes that a fair source of random
483+ * bits is provided in {@code rnd}. Note that this constructor always
484+ * constructs a non-negative BigInteger.
485+ *
486+ * @param numBits maximum bitLength of the new BigInteger.
487+ * @param rnd source of randomness to be used in computing the new
488+ * BigInteger.
489+ * @throws IllegalArgumentException {@code numBits} is negative.
490+ * @see #bitLength()
491+ */
492+ public BigInteger(int numBits, Random rnd) {
493+ this(1, randomBits(numBits, rnd));
494+ }
495+
496+ private static byte[] randomBits(int numBits, Random rnd) {
497+ if (numBits < 0)
498+ throw new IllegalArgumentException("numBits must be non-negative");
499+ int numBytes = (int)(((long)numBits+7)/8); // avoid overflow
500+ byte[] randomBits = new byte[numBytes];
501+
502+ // Generate random bytes and mask out any excess bits
503+ if (numBytes > 0) {
504+ rnd.nextBytes(randomBits);
505+ int excessBits = 8*numBytes - numBits;
506+ randomBits[0] &= (1 << (8-excessBits)) - 1;
507+ }
508+ return randomBits;
509+ }
510+
511+ /**
512+ * Constructs a randomly generated positive BigInteger that is probably
513+ * prime, with the specified bitLength.
514+ *
515+ * <p>It is recommended that the {@link #probablePrime probablePrime}
516+ * method be used in preference to this constructor unless there
517+ * is a compelling need to specify a certainty.
518+ *
519+ * @param bitLength bitLength of the returned BigInteger.
520+ * @param certainty a measure of the uncertainty that the caller is
521+ * willing to tolerate. The probability that the new BigInteger
522+ * represents a prime number will exceed
523+ * (1 - 1/2<sup>{@code certainty}</sup>). The execution time of
524+ * this constructor is proportional to the value of this parameter.
525+ * @param rnd source of random bits used to select candidates to be
526+ * tested for primality.
527+ * @throws ArithmeticException {@code bitLength < 2}.
528+ * @see #bitLength()
529+ */
530+ public BigInteger(int bitLength, int certainty, Random rnd) {
531+ BigInteger prime;
532+
533+ if (bitLength < 2)
534+ throw new ArithmeticException("bitLength < 2");
535+ // The cutoff of 95 was chosen empirically for best performance
536+ prime = (bitLength < 95 ? smallPrime(bitLength, certainty, rnd)
537+ : largePrime(bitLength, certainty, rnd));
538+ signum = 1;
539+ mag = prime.mag;
540+ }
541+
542+ // Minimum size in bits that the requested prime number has
543+ // before we use the large prime number generating algorithms
544+ private static final int SMALL_PRIME_THRESHOLD = 95;
545+
546+ // Certainty required to meet the spec of probablePrime
547+ private static final int DEFAULT_PRIME_CERTAINTY = 100;
548+
549+ /**
550+ * Returns a positive BigInteger that is probably prime, with the
551+ * specified bitLength. The probability that a BigInteger returned
552+ * by this method is composite does not exceed 2<sup>-100</sup>.
553+ *
554+ * @param bitLength bitLength of the returned BigInteger.
555+ * @param rnd source of random bits used to select candidates to be
556+ * tested for primality.
557+ * @return a BigInteger of {@code bitLength} bits that is probably prime
558+ * @throws ArithmeticException {@code bitLength < 2}.
559+ * @see #bitLength()
560+ * @since 1.4
561+ */
562+ public static BigInteger probablePrime(int bitLength, Random rnd) {
563+ if (bitLength < 2)
564+ throw new ArithmeticException("bitLength < 2");
565+
566+ // The cutoff of 95 was chosen empirically for best performance
567+ return (bitLength < SMALL_PRIME_THRESHOLD ?
568+ smallPrime(bitLength, DEFAULT_PRIME_CERTAINTY, rnd) :
569+ largePrime(bitLength, DEFAULT_PRIME_CERTAINTY, rnd));
570+ }
571+
572+ /**
573+ * Find a random number of the specified bitLength that is probably prime.
574+ * This method is used for smaller primes, its performance degrades on
575+ * larger bitlengths.
576+ *
577+ * This method assumes bitLength > 1.
578+ */
579+ private static BigInteger smallPrime(int bitLength, int certainty, Random rnd) {
580+ int magLen = (bitLength + 31) >>> 5;
581+ int temp[] = new int[magLen];
582+ int highBit = 1 << ((bitLength+31) & 0x1f); // High bit of high int
583+ int highMask = (highBit << 1) - 1; // Bits to keep in high int
584+
585+ while(true) {
586+ // Construct a candidate
587+ for (int i=0; i<magLen; i++)
588+ temp[i] = rnd.nextInt();
589+ temp[0] = (temp[0] & highMask) | highBit; // Ensure exact length
590+ if (bitLength > 2)
591+ temp[magLen-1] |= 1; // Make odd if bitlen > 2
592+
593+ BigInteger p = new BigInteger(temp, 1);
594+
595+ // Do cheap "pre-test" if applicable
596+ if (bitLength > 6) {
597+ long r = p.remainder(SMALL_PRIME_PRODUCT).longValue();
598+ if ((r%3==0) || (r%5==0) || (r%7==0) || (r%11==0) ||
599+ (r%13==0) || (r%17==0) || (r%19==0) || (r%23==0) ||
600+ (r%29==0) || (r%31==0) || (r%37==0) || (r%41==0))
601+ continue; // Candidate is composite; try another
602+ }
603+
604+ // All candidates of bitLength 2 and 3 are prime by this point
605+ if (bitLength < 4)
606+ return p;
607+
608+ // Do expensive test if we survive pre-test (or it's inapplicable)
609+ if (p.primeToCertainty(certainty, rnd))
610+ return p;
611+ }
612+ }
613+
614+ private static final BigInteger SMALL_PRIME_PRODUCT
615+ = valueOf(3L*5*7*11*13*17*19*23*29*31*37*41);
616+
617+ /**
618+ * Find a random number of the specified bitLength that is probably prime.
619+ * This method is more appropriate for larger bitlengths since it uses
620+ * a sieve to eliminate most composites before using a more expensive
621+ * test.
622+ */
623+ private static BigInteger largePrime(int bitLength, int certainty, Random rnd) {
624+ BigInteger p;
625+ p = new BigInteger(bitLength, rnd).setBit(bitLength-1);
626+ p.mag[p.mag.length-1] &= 0xfffffffe;
627+
628+ // Use a sieve length likely to contain the next prime number
629+ int searchLen = (bitLength / 20) * 64;
630+ BitSieve searchSieve = new BitSieve(p, searchLen);
631+ BigInteger candidate = searchSieve.retrieve(p, certainty, rnd);
632+
633+ while ((candidate == null) || (candidate.bitLength() != bitLength)) {
634+ p = p.add(BigInteger.valueOf(2*searchLen));
635+ if (p.bitLength() != bitLength)
636+ p = new BigInteger(bitLength, rnd).setBit(bitLength-1);
637+ p.mag[p.mag.length-1] &= 0xfffffffe;
638+ searchSieve = new BitSieve(p, searchLen);
639+ candidate = searchSieve.retrieve(p, certainty, rnd);
640+ }
641+ return candidate;
642+ }
643+
644+ /**
645+ * Returns the first integer greater than this {@code BigInteger} that
646+ * is probably prime. The probability that the number returned by this
647+ * method is composite does not exceed 2<sup>-100</sup>. This method will
648+ * never skip over a prime when searching: if it returns {@code p}, there
649+ * is no prime {@code q} such that {@code this < q < p}.
650+ *
651+ * @return the first integer greater than this {@code BigInteger} that
652+ * is probably prime.
653+ * @throws ArithmeticException {@code this < 0}.
654+ * @since 1.5
655+ */
656+ public BigInteger nextProbablePrime() {
657+ if (this.signum < 0)
658+ throw new ArithmeticException("start < 0: " + this);
659+
660+ // Handle trivial cases
661+ if ((this.signum == 0) || this.equals(ONE))
662+ return TWO;
663+
664+ BigInteger result = this.add(ONE);
665+
666+ // Fastpath for small numbers
667+ if (result.bitLength() < SMALL_PRIME_THRESHOLD) {
668+
669+ // Ensure an odd number
670+ if (!result.testBit(0))
671+ result = result.add(ONE);
672+
673+ while(true) {
674+ // Do cheap "pre-test" if applicable
675+ if (result.bitLength() > 6) {
676+ long r = result.remainder(SMALL_PRIME_PRODUCT).longValue();
677+ if ((r%3==0) || (r%5==0) || (r%7==0) || (r%11==0) ||
678+ (r%13==0) || (r%17==0) || (r%19==0) || (r%23==0) ||
679+ (r%29==0) || (r%31==0) || (r%37==0) || (r%41==0)) {
680+ result = result.add(TWO);
681+ continue; // Candidate is composite; try another
682+ }
683+ }
684+
685+ // All candidates of bitLength 2 and 3 are prime by this point
686+ if (result.bitLength() < 4)
687+ return result;
688+
689+ // The expensive test
690+ if (result.primeToCertainty(DEFAULT_PRIME_CERTAINTY, null))
691+ return result;
692+
693+ result = result.add(TWO);
694+ }
695+ }
696+
697+ // Start at previous even number
698+ if (result.testBit(0))
699+ result = result.subtract(ONE);
700+
701+ // Looking for the next large prime
702+ int searchLen = (result.bitLength() / 20) * 64;
703+
704+ while(true) {
705+ BitSieve searchSieve = new BitSieve(result, searchLen);
706+ BigInteger candidate = searchSieve.retrieve(result,
707+ DEFAULT_PRIME_CERTAINTY, null);
708+ if (candidate != null)
709+ return candidate;
710+ result = result.add(BigInteger.valueOf(2 * searchLen));
711+ }
712+ }
713+
714+ /**
715+ * Returns {@code true} if this BigInteger is probably prime,
716+ * {@code false} if it's definitely composite.
717+ *
718+ * This method assumes bitLength > 2.
719+ *
720+ * @param certainty a measure of the uncertainty that the caller is
721+ * willing to tolerate: if the call returns {@code true}
722+ * the probability that this BigInteger is prime exceeds
723+ * {@code (1 - 1/2<sup>certainty</sup>)}. The execution time of
724+ * this method is proportional to the value of this parameter.
725+ * @return {@code true} if this BigInteger is probably prime,
726+ * {@code false} if it's definitely composite.
727+ */
728+ boolean primeToCertainty(int certainty, Random random) {
729+ int rounds = 0;
730+ int n = (Math.min(certainty, Integer.MAX_VALUE-1)+1)/2;
731+
732+ // The relationship between the certainty and the number of rounds
733+ // we perform is given in the draft standard ANSI X9.80, "PRIME
734+ // NUMBER GENERATION, PRIMALITY TESTING, AND PRIMALITY CERTIFICATES".
735+ int sizeInBits = this.bitLength();
736+ if (sizeInBits < 100) {
737+ rounds = 50;
738+ rounds = n < rounds ? n : rounds;
739+ return passesMillerRabin(rounds, random);
740+ }
741+
742+ if (sizeInBits < 256) {
743+ rounds = 27;
744+ } else if (sizeInBits < 512) {
745+ rounds = 15;
746+ } else if (sizeInBits < 768) {
747+ rounds = 8;
748+ } else if (sizeInBits < 1024) {
749+ rounds = 4;
750+ } else {
751+ rounds = 2;
752+ }
753+ rounds = n < rounds ? n : rounds;
754+
755+ return passesMillerRabin(rounds, random) && passesLucasLehmer();
756+ }
757+
758+ /**
759+ * Returns true iff this BigInteger is a Lucas-Lehmer probable prime.
760+ *
761+ * The following assumptions are made:
762+ * This BigInteger is a positive, odd number.
763+ */
764+ private boolean passesLucasLehmer() {
765+ BigInteger thisPlusOne = this.add(ONE);
766+
767+ // Step 1
768+ int d = 5;
769+ while (jacobiSymbol(d, this) != -1) {
770+ // 5, -7, 9, -11, ...
771+ d = (d<0) ? Math.abs(d)+2 : -(d+2);
772+ }
773+
774+ // Step 2
775+ BigInteger u = lucasLehmerSequence(d, thisPlusOne, this);
776+
777+ // Step 3
778+ return u.mod(this).equals(ZERO);
779+ }
780+
781+ /**
782+ * Computes Jacobi(p,n).
783+ * Assumes n positive, odd, n>=3.
784+ */
785+ private static int jacobiSymbol(int p, BigInteger n) {
786+ if (p == 0)
787+ return 0;
788+
789+ // Algorithm and comments adapted from Colin Plumb's C library.
790+ int j = 1;
791+ int u = n.mag[n.mag.length-1];
792+
793+ // Make p positive
794+ if (p < 0) {
795+ p = -p;
796+ int n8 = u & 7;
797+ if ((n8 == 3) || (n8 == 7))
798+ j = -j; // 3 (011) or 7 (111) mod 8
799+ }
800+
801+ // Get rid of factors of 2 in p
802+ while ((p & 3) == 0)
803+ p >>= 2;
804+ if ((p & 1) == 0) {
805+ p >>= 1;
806+ if (((u ^ (u>>1)) & 2) != 0)
807+ j = -j; // 3 (011) or 5 (101) mod 8
808+ }
809+ if (p == 1)
810+ return j;
811+ // Then, apply quadratic reciprocity
812+ if ((p & u & 2) != 0) // p = u = 3 (mod 4)?
813+ j = -j;
814+ // And reduce u mod p
815+ u = n.mod(BigInteger.valueOf(p)).intValue();
816+
817+ // Now compute Jacobi(u,p), u < p
818+ while (u != 0) {
819+ while ((u & 3) == 0)
820+ u >>= 2;
821+ if ((u & 1) == 0) {
822+ u >>= 1;
823+ if (((p ^ (p>>1)) & 2) != 0)
824+ j = -j; // 3 (011) or 5 (101) mod 8
825+ }
826+ if (u == 1)
827+ return j;
828+ // Now both u and p are odd, so use quadratic reciprocity
829+ assert (u < p);
830+ int t = u; u = p; p = t;
831+ if ((u & p & 2) != 0) // u = p = 3 (mod 4)?
832+ j = -j;
833+ // Now u >= p, so it can be reduced
834+ u %= p;
835+ }
836+ return 0;
837+ }
838+
839+ private static BigInteger lucasLehmerSequence(int z, BigInteger k, BigInteger n) {
840+ BigInteger d = BigInteger.valueOf(z);
841+ BigInteger u = ONE; BigInteger u2;
842+ BigInteger v = ONE; BigInteger v2;
843+
844+ for (int i=k.bitLength()-2; i>=0; i--) {
845+ u2 = u.multiply(v).mod(n);
846+
847+ v2 = v.square().add(d.multiply(u.square())).mod(n);
848+ if (v2.testBit(0))
849+ v2 = v2.subtract(n);
850+
851+ v2 = v2.shiftRight(1);
852+
853+ u = u2; v = v2;
854+ if (k.testBit(i)) {
855+ u2 = u.add(v).mod(n);
856+ if (u2.testBit(0))
857+ u2 = u2.subtract(n);
858+
859+ u2 = u2.shiftRight(1);
860+ v2 = v.add(d.multiply(u)).mod(n);
861+ if (v2.testBit(0))
862+ v2 = v2.subtract(n);
863+ v2 = v2.shiftRight(1);
864+
865+ u = u2; v = v2;
866+ }
867+ }
868+ return u;
869+ }
870+
871+ private static volatile Random staticRandom;
872+
873+ private static Random getSecureRandom() {
874+ if (staticRandom == null) {
875+ staticRandom = new java.security.SecureRandom();
876+ }
877+ return staticRandom;
878+ }
879+
880+ /**
881+ * Returns true iff this BigInteger passes the specified number of
882+ * Miller-Rabin tests. This test is taken from the DSA spec (NIST FIPS
883+ * 186-2).
884+ *
885+ * The following assumptions are made:
886+ * This BigInteger is a positive, odd number greater than 2.
887+ * iterations<=50.
888+ */
889+ private boolean passesMillerRabin(int iterations, Random rnd) {
890+ // Find a and m such that m is odd and this == 1 + 2**a * m
891+ BigInteger thisMinusOne = this.subtract(ONE);
892+ BigInteger m = thisMinusOne;
893+ int a = m.getLowestSetBit();
894+ m = m.shiftRight(a);
895+
896+ // Do the tests
897+ if (rnd == null) {
898+ rnd = getSecureRandom();
899+ }
900+ for (int i=0; i<iterations; i++) {
901+ // Generate a uniform random on (1, this)
902+ BigInteger b;
903+ do {
904+ b = new BigInteger(this.bitLength(), rnd);
905+ } while (b.compareTo(ONE) <= 0 || b.compareTo(this) >= 0);
906+
907+ int j = 0;
908+ BigInteger z = b.modPow(m, this);
909+ while(!((j==0 && z.equals(ONE)) || z.equals(thisMinusOne))) {
910+ if (j>0 && z.equals(ONE) || ++j==a)
911+ return false;
912+ z = z.modPow(TWO, this);
913+ }
914+ }
915+ return true;
916+ }
917+
918+ /**
919+ * This internal constructor differs from its public cousin
920+ * with the arguments reversed in two ways: it assumes that its
921+ * arguments are correct, and it doesn't copy the magnitude array.
922+ */
923+ BigInteger(int[] magnitude, int signum) {
924+ this.signum = (magnitude.length==0 ? 0 : signum);
925+ this.mag = magnitude;
926+ }
927+
928+ /**
929+ * This private constructor is for internal use and assumes that its
930+ * arguments are correct.
931+ */
932+ private BigInteger(byte[] magnitude, int signum) {
933+ this.signum = (magnitude.length==0 ? 0 : signum);
934+ this.mag = stripLeadingZeroBytes(magnitude);
935+ }
936+
937+ //Static Factory Methods
938+
939+ /**
940+ * Returns a BigInteger whose value is equal to that of the
941+ * specified {@code long}. This "static factory method" is
942+ * provided in preference to a ({@code long}) constructor
943+ * because it allows for reuse of frequently used BigIntegers.
944+ *
945+ * @param val value of the BigInteger to return.
946+ * @return a BigInteger with the specified value.
947+ */
948+ public static BigInteger valueOf(long val) {
949+ // If -MAX_CONSTANT < val < MAX_CONSTANT, return stashed constant
950+ if (val == 0)
951+ return ZERO;
952+ if (val > 0 && val <= MAX_CONSTANT)
953+ return posConst[(int) val];
954+ else if (val < 0 && val >= -MAX_CONSTANT)
955+ return negConst[(int) -val];
956+
957+ return new BigInteger(val);
958+ }
959+
960+ /**
961+ * Constructs a BigInteger with the specified value, which may not be zero.
962+ */
963+ private BigInteger(long val) {
964+ if (val < 0) {
965+ val = -val;
966+ signum = -1;
967+ } else {
968+ signum = 1;
969+ }
970+
971+ int highWord = (int)(val >>> 32);
972+ if (highWord==0) {
973+ mag = new int[1];
974+ mag[0] = (int)val;
975+ } else {
976+ mag = new int[2];
977+ mag[0] = highWord;
978+ mag[1] = (int)val;
979+ }
980+ }
981+
982+ /**
983+ * Returns a BigInteger with the given two's complement representation.
984+ * Assumes that the input array will not be modified (the returned
985+ * BigInteger will reference the input array if feasible).
986+ */
987+ private static BigInteger valueOf(int val[]) {
988+ return (val[0]>0 ? new BigInteger(val, 1) : new BigInteger(val));
989+ }
990+
991+ // Constants
992+
993+ /**
994+ * Initialize static constant array when class is loaded.
995+ */
996+ private final static int MAX_CONSTANT = 16;
997+ private static BigInteger posConst[] = new BigInteger[MAX_CONSTANT+1];
998+ private static BigInteger negConst[] = new BigInteger[MAX_CONSTANT+1];
999+ static {
1000+ for (int i = 1; i <= MAX_CONSTANT; i++) {
1001+ int[] magnitude = new int[1];
1002+ magnitude[0] = i;
1003+ posConst[i] = new BigInteger(magnitude, 1);
1004+ negConst[i] = new BigInteger(magnitude, -1);
1005+ }
1006+ }
1007+
1008+ /**
1009+ * The BigInteger constant zero.
1010+ *
1011+ * @since 1.2
1012+ */
1013+ public static final BigInteger ZERO = new BigInteger(new int[0], 0);
1014+
1015+ /**
1016+ * The BigInteger constant one.
1017+ *
1018+ * @since 1.2
1019+ */
1020+ public static final BigInteger ONE = valueOf(1);
1021+
1022+ /**
1023+ * The BigInteger constant two. (Not exported.)
1024+ */
1025+ private static final BigInteger TWO = valueOf(2);
1026+
1027+ /**
1028+ * The BigInteger constant ten.
1029+ *
1030+ * @since 1.5
1031+ */
1032+ public static final BigInteger TEN = valueOf(10);
1033+
1034+ // Arithmetic Operations
1035+
1036+ /**
1037+ * Returns a BigInteger whose value is {@code (this + val)}.
1038+ *
1039+ * @param val value to be added to this BigInteger.
1040+ * @return {@code this + val}
1041+ */
1042+ public BigInteger add(BigInteger val) {
1043+ if (val.signum == 0)
1044+ return this;
1045+ if (signum == 0)
1046+ return val;
1047+ if (val.signum == signum)
1048+ return new BigInteger(add(mag, val.mag), signum);
1049+
1050+ int cmp = compareMagnitude(val);
1051+ if (cmp == 0)
1052+ return ZERO;
1053+ int[] resultMag = (cmp > 0 ? subtract(mag, val.mag)
1054+ : subtract(val.mag, mag));
1055+ resultMag = trustedStripLeadingZeroInts(resultMag);
1056+
1057+ return new BigInteger(resultMag, cmp == signum ? 1 : -1);
1058+ }
1059+
1060+ /**
1061+ * Adds the contents of the int arrays x and y. This method allocates
1062+ * a new int array to hold the answer and returns a reference to that
1063+ * array.
1064+ */
1065+ private static int[] add(int[] x, int[] y) {
1066+ // If x is shorter, swap the two arrays
1067+ if (x.length < y.length) {
1068+ int[] tmp = x;
1069+ x = y;
1070+ y = tmp;
1071+ }
1072+
1073+ int xIndex = x.length;
1074+ int yIndex = y.length;
1075+ int result[] = new int[xIndex];
1076+ long sum = 0;
1077+
1078+ // Add common parts of both numbers
1079+ while(yIndex > 0) {
1080+ sum = (x[--xIndex] & LONG_MASK) +
1081+ (y[--yIndex] & LONG_MASK) + (sum >>> 32);
1082+ result[xIndex] = (int)sum;
1083+ }
1084+
1085+ // Copy remainder of longer number while carry propagation is required
1086+ boolean carry = (sum >>> 32 != 0);
1087+ while (xIndex > 0 && carry)
1088+ carry = ((result[--xIndex] = x[xIndex] + 1) == 0);
1089+
1090+ // Copy remainder of longer number
1091+ while (xIndex > 0)
1092+ result[--xIndex] = x[xIndex];
1093+
1094+ // Grow result if necessary
1095+ if (carry) {
1096+ int bigger[] = new int[result.length + 1];
1097+ System.arraycopy(result, 0, bigger, 1, result.length);
1098+ bigger[0] = 0x01;
1099+ return bigger;
1100+ }
1101+ return result;
1102+ }
1103+
1104+ /**
1105+ * Returns a BigInteger whose value is {@code (this - val)}.
1106+ *
1107+ * @param val value to be subtracted from this BigInteger.
1108+ * @return {@code this - val}
1109+ */
1110+ public BigInteger subtract(BigInteger val) {
1111+ if (val.signum == 0)
1112+ return this;
1113+ if (signum == 0)
1114+ return val.negate();
1115+ if (val.signum != signum)
1116+ return new BigInteger(add(mag, val.mag), signum);
1117+
1118+ int cmp = compareMagnitude(val);
1119+ if (cmp == 0)
1120+ return ZERO;
1121+ int[] resultMag = (cmp > 0 ? subtract(mag, val.mag)
1122+ : subtract(val.mag, mag));
1123+ resultMag = trustedStripLeadingZeroInts(resultMag);
1124+ return new BigInteger(resultMag, cmp == signum ? 1 : -1);
1125+ }
1126+
1127+ /**
1128+ * Subtracts the contents of the second int arrays (little) from the
1129+ * first (big). The first int array (big) must represent a larger number
1130+ * than the second. This method allocates the space necessary to hold the
1131+ * answer.
1132+ */
1133+ private static int[] subtract(int[] big, int[] little) {
1134+ int bigIndex = big.length;
1135+ int result[] = new int[bigIndex];
1136+ int littleIndex = little.length;
1137+ long difference = 0;
1138+
1139+ // Subtract common parts of both numbers
1140+ while(littleIndex > 0) {
1141+ difference = (big[--bigIndex] & LONG_MASK) -
1142+ (little[--littleIndex] & LONG_MASK) +
1143+ (difference >> 32);
1144+ result[bigIndex] = (int)difference;
1145+ }
1146+
1147+ // Subtract remainder of longer number while borrow propagates
1148+ boolean borrow = (difference >> 32 != 0);
1149+ while (bigIndex > 0 && borrow)
1150+ borrow = ((result[--bigIndex] = big[bigIndex] - 1) == -1);
1151+
1152+ // Copy remainder of longer number
1153+ while (bigIndex > 0)
1154+ result[--bigIndex] = big[bigIndex];
1155+
1156+ return result;
1157+ }
1158+
1159+ /**
1160+ * Returns a BigInteger whose value is {@code (this * val)}.
1161+ *
1162+ * @param val value to be multiplied by this BigInteger.
1163+ * @return {@code this * val}
1164+ */
1165+ public BigInteger multiply(BigInteger val) {
1166+ if (val.signum == 0 || signum == 0)
1167+ return ZERO;
1168+
1169+ int[] result = multiplyToLen(mag, mag.length,
1170+ val.mag, val.mag.length, null);
1171+ result = trustedStripLeadingZeroInts(result);
1172+ return new BigInteger(result, signum == val.signum ? 1 : -1);
1173+ }
1174+
1175+ /**
1176+ * Package private methods used by BigDecimal code to multiply a BigInteger
1177+ * with a long. Assumes v is not equal to INFLATED.
1178+ */
1179+ BigInteger multiply(long v) {
1180+ if (v == 0 || signum == 0)
1181+ return ZERO;
1182+ if (v == BigDecimal.INFLATED)
1183+ return multiply(BigInteger.valueOf(v));
1184+ int rsign = (v > 0 ? signum : -signum);
1185+ if (v < 0)
1186+ v = -v;
1187+ long dh = v >>> 32; // higher order bits
1188+ long dl = v & LONG_MASK; // lower order bits
1189+
1190+ int xlen = mag.length;
1191+ int[] value = mag;
1192+ int[] rmag = (dh == 0L) ? (new int[xlen + 1]) : (new int[xlen + 2]);
1193+ long carry = 0;
1194+ int rstart = rmag.length - 1;
1195+ for (int i = xlen - 1; i >= 0; i--) {
1196+ long product = (value[i] & LONG_MASK) * dl + carry;
1197+ rmag[rstart--] = (int)product;
1198+ carry = product >>> 32;
1199+ }
1200+ rmag[rstart] = (int)carry;
1201+ if (dh != 0L) {
1202+ carry = 0;
1203+ rstart = rmag.length - 2;
1204+ for (int i = xlen - 1; i >= 0; i--) {
1205+ long product = (value[i] & LONG_MASK) * dh +
1206+ (rmag[rstart] & LONG_MASK) + carry;
1207+ rmag[rstart--] = (int)product;
1208+ carry = product >>> 32;
1209+ }
1210+ rmag[0] = (int)carry;
1211+ }
1212+ if (carry == 0L)
1213+ rmag = java.util.Arrays.copyOfRange(rmag, 1, rmag.length);
1214+ return new BigInteger(rmag, rsign);
1215+ }
1216+
1217+ /**
1218+ * Multiplies int arrays x and y to the specified lengths and places
1219+ * the result into z. There will be no leading zeros in the resultant array.
1220+ */
1221+ private int[] multiplyToLen(int[] x, int xlen, int[] y, int ylen, int[] z) {
1222+ int xstart = xlen - 1;
1223+ int ystart = ylen - 1;
1224+
1225+ if (z == null || z.length < (xlen+ ylen))
1226+ z = new int[xlen+ylen];
1227+
1228+ long carry = 0;
1229+ for (int j=ystart, k=ystart+1+xstart; j>=0; j--, k--) {
1230+ long product = (y[j] & LONG_MASK) *
1231+ (x[xstart] & LONG_MASK) + carry;
1232+ z[k] = (int)product;
1233+ carry = product >>> 32;
1234+ }
1235+ z[xstart] = (int)carry;
1236+
1237+ for (int i = xstart-1; i >= 0; i--) {
1238+ carry = 0;
1239+ for (int j=ystart, k=ystart+1+i; j>=0; j--, k--) {
1240+ long product = (y[j] & LONG_MASK) *
1241+ (x[i] & LONG_MASK) +
1242+ (z[k] & LONG_MASK) + carry;
1243+ z[k] = (int)product;
1244+ carry = product >>> 32;
1245+ }
1246+ z[i] = (int)carry;
1247+ }
1248+ return z;
1249+ }
1250+
1251+ /**
1252+ * Returns a BigInteger whose value is {@code (this<sup>2</sup>)}.
1253+ *
1254+ * @return {@code this<sup>2</sup>}
1255+ */
1256+ private BigInteger square() {
1257+ if (signum == 0)
1258+ return ZERO;
1259+ int[] z = squareToLen(mag, mag.length, null);
1260+ return new BigInteger(trustedStripLeadingZeroInts(z), 1);
1261+ }
1262+
1263+ /**
1264+ * Squares the contents of the int array x. The result is placed into the
1265+ * int array z. The contents of x are not changed.
1266+ */
1267+ private static final int[] squareToLen(int[] x, int len, int[] z) {
1268+ /*
1269+ * The algorithm used here is adapted from Colin Plumb's C library.
1270+ * Technique: Consider the partial products in the multiplication
1271+ * of "abcde" by itself:
1272+ *
1273+ * a b c d e
1274+ * * a b c d e
1275+ * ==================
1276+ * ae be ce de ee
1277+ * ad bd cd dd de
1278+ * ac bc cc cd ce
1279+ * ab bb bc bd be
1280+ * aa ab ac ad ae
1281+ *
1282+ * Note that everything above the main diagonal:
1283+ * ae be ce de = (abcd) * e
1284+ * ad bd cd = (abc) * d
1285+ * ac bc = (ab) * c
1286+ * ab = (a) * b
1287+ *
1288+ * is a copy of everything below the main diagonal:
1289+ * de
1290+ * cd ce
1291+ * bc bd be
1292+ * ab ac ad ae
1293+ *
1294+ * Thus, the sum is 2 * (off the diagonal) + diagonal.
1295+ *
1296+ * This is accumulated beginning with the diagonal (which
1297+ * consist of the squares of the digits of the input), which is then
1298+ * divided by two, the off-diagonal added, and multiplied by two
1299+ * again. The low bit is simply a copy of the low bit of the
1300+ * input, so it doesn't need special care.
1301+ */
1302+ int zlen = len << 1;
1303+ if (z == null || z.length < zlen)
1304+ z = new int[zlen];
1305+
1306+ // Store the squares, right shifted one bit (i.e., divided by 2)
1307+ int lastProductLowWord = 0;
1308+ for (int j=0, i=0; j<len; j++) {
1309+ long piece = (x[j] & LONG_MASK);
1310+ long product = piece * piece;
1311+ z[i++] = (lastProductLowWord << 31) | (int)(product >>> 33);
1312+ z[i++] = (int)(product >>> 1);
1313+ lastProductLowWord = (int)product;
1314+ }
1315+
1316+ // Add in off-diagonal sums
1317+ for (int i=len, offset=1; i>0; i--, offset+=2) {
1318+ int t = x[i-1];
1319+ t = mulAdd(z, x, offset, i-1, t);
1320+ addOne(z, offset-1, i, t);
1321+ }
1322+
1323+ // Shift back up and set low bit
1324+ primitiveLeftShift(z, zlen, 1);
1325+ z[zlen-1] |= x[len-1] & 1;
1326+
1327+ return z;
1328+ }
1329+
1330+ /**
1331+ * Returns a BigInteger whose value is {@code (this / val)}.
1332+ *
1333+ * @param val value by which this BigInteger is to be divided.
1334+ * @return {@code this / val}
1335+ * @throws ArithmeticException if {@code val} is zero.
1336+ */
1337+ public BigInteger divide(BigInteger val) {
1338+ MutableBigInteger q = new MutableBigInteger(),
1339+ a = new MutableBigInteger(this.mag),
1340+ b = new MutableBigInteger(val.mag);
1341+
1342+ a.divide(b, q);
1343+ return q.toBigInteger(this.signum == val.signum ? 1 : -1);
1344+ }
1345+
1346+ /**
1347+ * Returns an array of two BigIntegers containing {@code (this / val)}
1348+ * followed by {@code (this % val)}.
1349+ *
1350+ * @param val value by which this BigInteger is to be divided, and the
1351+ * remainder computed.
1352+ * @return an array of two BigIntegers: the quotient {@code (this / val)}
1353+ * is the initial element, and the remainder {@code (this % val)}
1354+ * is the final element.
1355+ * @throws ArithmeticException if {@code val} is zero.
1356+ */
1357+ public BigInteger[] divideAndRemainder(BigInteger val) {
1358+ BigInteger[] result = new BigInteger[2];
1359+ MutableBigInteger q = new MutableBigInteger(),
1360+ a = new MutableBigInteger(this.mag),
1361+ b = new MutableBigInteger(val.mag);
1362+ MutableBigInteger r = a.divide(b, q);
1363+ result[0] = q.toBigInteger(this.signum == val.signum ? 1 : -1);
1364+ result[1] = r.toBigInteger(this.signum);
1365+ return result;
1366+ }
1367+
1368+ /**
1369+ * Returns a BigInteger whose value is {@code (this % val)}.
1370+ *
1371+ * @param val value by which this BigInteger is to be divided, and the
1372+ * remainder computed.
1373+ * @return {@code this % val}
1374+ * @throws ArithmeticException if {@code val} is zero.
1375+ */
1376+ public BigInteger remainder(BigInteger val) {
1377+ MutableBigInteger q = new MutableBigInteger(),
1378+ a = new MutableBigInteger(this.mag),
1379+ b = new MutableBigInteger(val.mag);
1380+
1381+ return a.divide(b, q).toBigInteger(this.signum);
1382+ }
1383+
1384+ /**
1385+ * Returns a BigInteger whose value is <tt>(this<sup>exponent</sup>)</tt>.
1386+ * Note that {@code exponent} is an integer rather than a BigInteger.
1387+ *
1388+ * @param exponent exponent to which this BigInteger is to be raised.
1389+ * @return <tt>this<sup>exponent</sup></tt>
1390+ * @throws ArithmeticException {@code exponent} is negative. (This would
1391+ * cause the operation to yield a non-integer value.)
1392+ */
1393+ public BigInteger pow(int exponent) {
1394+ if (exponent < 0)
1395+ throw new ArithmeticException("Negative exponent");
1396+ if (signum==0)
1397+ return (exponent==0 ? ONE : this);
1398+
1399+ // Perform exponentiation using repeated squaring trick
1400+ int newSign = (signum<0 && (exponent&1)==1 ? -1 : 1);
1401+ int[] baseToPow2 = this.mag;
1402+ int[] result = {1};
1403+
1404+ while (exponent != 0) {
1405+ if ((exponent & 1)==1) {
1406+ result = multiplyToLen(result, result.length,
1407+ baseToPow2, baseToPow2.length, null);
1408+ result = trustedStripLeadingZeroInts(result);
1409+ }
1410+ if ((exponent >>>= 1) != 0) {
1411+ baseToPow2 = squareToLen(baseToPow2, baseToPow2.length, null);
1412+ baseToPow2 = trustedStripLeadingZeroInts(baseToPow2);
1413+ }
1414+ }
1415+ return new BigInteger(result, newSign);
1416+ }
1417+
1418+ /**
1419+ * Returns a BigInteger whose value is the greatest common divisor of
1420+ * {@code abs(this)} and {@code abs(val)}. Returns 0 if
1421+ * {@code this==0 && val==0}.
1422+ *
1423+ * @param val value with which the GCD is to be computed.
1424+ * @return {@code GCD(abs(this), abs(val))}
1425+ */
1426+ public BigInteger gcd(BigInteger val) {
1427+ if (val.signum == 0)
1428+ return this.abs();
1429+ else if (this.signum == 0)
1430+ return val.abs();
1431+
1432+ MutableBigInteger a = new MutableBigInteger(this);
1433+ MutableBigInteger b = new MutableBigInteger(val);
1434+
1435+ MutableBigInteger result = a.hybridGCD(b);
1436+
1437+ return result.toBigInteger(1);
1438+ }
1439+
1440+ /**
1441+ * Package private method to return bit length for an integer.
1442+ */
1443+ static int bitLengthForInt(int n) {
1444+ return 32 - Integer.numberOfLeadingZeros(n);
1445+ }
1446+
1447+ /**
1448+ * Left shift int array a up to len by n bits. Returns the array that
1449+ * results from the shift since space may have to be reallocated.
1450+ */
1451+ private static int[] leftShift(int[] a, int len, int n) {
1452+ int nInts = n >>> 5;
1453+ int nBits = n&0x1F;
1454+ int bitsInHighWord = bitLengthForInt(a[0]);
1455+
1456+ // If shift can be done without recopy, do so
1457+ if (n <= (32-bitsInHighWord)) {
1458+ primitiveLeftShift(a, len, nBits);
1459+ return a;
1460+ } else { // Array must be resized
1461+ if (nBits <= (32-bitsInHighWord)) {
1462+ int result[] = new int[nInts+len];
1463+ for (int i=0; i<len; i++)
1464+ result[i] = a[i];
1465+ primitiveLeftShift(result, result.length, nBits);
1466+ return result;
1467+ } else {
1468+ int result[] = new int[nInts+len+1];
1469+ for (int i=0; i<len; i++)
1470+ result[i] = a[i];
1471+ primitiveRightShift(result, result.length, 32 - nBits);
1472+ return result;
1473+ }
1474+ }
1475+ }
1476+
1477+ // shifts a up to len right n bits assumes no leading zeros, 0<n<32
1478+ static void primitiveRightShift(int[] a, int len, int n) {
1479+ int n2 = 32 - n;
1480+ for (int i=len-1, c=a[i]; i>0; i--) {
1481+ int b = c;
1482+ c = a[i-1];
1483+ a[i] = (c << n2) | (b >>> n);
1484+ }
1485+ a[0] >>>= n;
1486+ }
1487+
1488+ // shifts a up to len left n bits assumes no leading zeros, 0<=n<32
1489+ static void primitiveLeftShift(int[] a, int len, int n) {
1490+ if (len == 0 || n == 0)
1491+ return;
1492+
1493+ int n2 = 32 - n;
1494+ for (int i=0, c=a[i], m=i+len-1; i<m; i++) {
1495+ int b = c;
1496+ c = a[i+1];
1497+ a[i] = (b << n) | (c >>> n2);
1498+ }
1499+ a[len-1] <<= n;
1500+ }
1501+
1502+ /**
1503+ * Calculate bitlength of contents of the first len elements an int array,
1504+ * assuming there are no leading zero ints.
1505+ */
1506+ private static int bitLength(int[] val, int len) {
1507+ if (len == 0)
1508+ return 0;
1509+ return ((len - 1) << 5) + bitLengthForInt(val[0]);
1510+ }
1511+
1512+ /**
1513+ * Returns a BigInteger whose value is the absolute value of this
1514+ * BigInteger.
1515+ *
1516+ * @return {@code abs(this)}
1517+ */
1518+ public BigInteger abs() {
1519+ return (signum >= 0 ? this : this.negate());
1520+ }
1521+
1522+ /**
1523+ * Returns a BigInteger whose value is {@code (-this)}.
1524+ *
1525+ * @return {@code -this}
1526+ */
1527+ public BigInteger negate() {
1528+ return new BigInteger(this.mag, -this.signum);
1529+ }
1530+
1531+ /**
1532+ * Returns the signum function of this BigInteger.
1533+ *
1534+ * @return -1, 0 or 1 as the value of this BigInteger is negative, zero or
1535+ * positive.
1536+ */
1537+ public int signum() {
1538+ return this.signum;
1539+ }
1540+
1541+ // Modular Arithmetic Operations
1542+
1543+ /**
1544+ * Returns a BigInteger whose value is {@code (this mod m}). This method
1545+ * differs from {@code remainder} in that it always returns a
1546+ * <i>non-negative</i> BigInteger.
1547+ *
1548+ * @param m the modulus.
1549+ * @return {@code this mod m}
1550+ * @throws ArithmeticException {@code m} &le; 0
1551+ * @see #remainder
1552+ */
1553+ public BigInteger mod(BigInteger m) {
1554+ if (m.signum <= 0)
1555+ throw new ArithmeticException("BigInteger: modulus not positive");
1556+
1557+ BigInteger result = this.remainder(m);
1558+ return (result.signum >= 0 ? result : result.add(m));
1559+ }
1560+
1561+ /**
1562+ * Returns a BigInteger whose value is
1563+ * <tt>(this<sup>exponent</sup> mod m)</tt>. (Unlike {@code pow}, this
1564+ * method permits negative exponents.)
1565+ *
1566+ * @param exponent the exponent.
1567+ * @param m the modulus.
1568+ * @return <tt>this<sup>exponent</sup> mod m</tt>
1569+ * @throws ArithmeticException {@code m} &le; 0 or the exponent is
1570+ * negative and this BigInteger is not <i>relatively
1571+ * prime</i> to {@code m}.
1572+ * @see #modInverse
1573+ */
1574+ public BigInteger modPow(BigInteger exponent, BigInteger m) {
1575+ if (m.signum <= 0)
1576+ throw new ArithmeticException("BigInteger: modulus not positive");
1577+
1578+ // Trivial cases
1579+ if (exponent.signum == 0)
1580+ return (m.equals(ONE) ? ZERO : ONE);
1581+
1582+ if (this.equals(ONE))
1583+ return (m.equals(ONE) ? ZERO : ONE);
1584+
1585+ if (this.equals(ZERO) && exponent.signum >= 0)
1586+ return ZERO;
1587+
1588+ if (this.equals(negConst[1]) && (!exponent.testBit(0)))
1589+ return (m.equals(ONE) ? ZERO : ONE);
1590+
1591+ boolean invertResult;
1592+ if ((invertResult = (exponent.signum < 0)))
1593+ exponent = exponent.negate();
1594+
1595+ BigInteger base = (this.signum < 0 || this.compareTo(m) >= 0
1596+ ? this.mod(m) : this);
1597+ BigInteger result;
1598+ if (m.testBit(0)) { // odd modulus
1599+ result = base.oddModPow(exponent, m);
1600+ } else {
1601+ /*
1602+ * Even modulus. Tear it into an "odd part" (m1) and power of two
1603+ * (m2), exponentiate mod m1, manually exponentiate mod m2, and
1604+ * use Chinese Remainder Theorem to combine results.
1605+ */
1606+
1607+ // Tear m apart into odd part (m1) and power of 2 (m2)
1608+ int p = m.getLowestSetBit(); // Max pow of 2 that divides m
1609+
1610+ BigInteger m1 = m.shiftRight(p); // m/2**p
1611+ BigInteger m2 = ONE.shiftLeft(p); // 2**p
1612+
1613+ // Calculate new base from m1
1614+ BigInteger base2 = (this.signum < 0 || this.compareTo(m1) >= 0
1615+ ? this.mod(m1) : this);
1616+
1617+ // Caculate (base ** exponent) mod m1.
1618+ BigInteger a1 = (m1.equals(ONE) ? ZERO :
1619+ base2.oddModPow(exponent, m1));
1620+
1621+ // Calculate (this ** exponent) mod m2
1622+ BigInteger a2 = base.modPow2(exponent, p);
1623+
1624+ // Combine results using Chinese Remainder Theorem
1625+ BigInteger y1 = m2.modInverse(m1);
1626+ BigInteger y2 = m1.modInverse(m2);
1627+
1628+ result = a1.multiply(m2).multiply(y1).add
1629+ (a2.multiply(m1).multiply(y2)).mod(m);
1630+ }
1631+
1632+ return (invertResult ? result.modInverse(m) : result);
1633+ }
1634+
1635+ static int[] bnExpModThreshTable = {7, 25, 81, 241, 673, 1793,
1636+ Integer.MAX_VALUE}; // Sentinel
1637+
1638+ /**
1639+ * Returns a BigInteger whose value is x to the power of y mod z.
1640+ * Assumes: z is odd && x < z.
1641+ */
1642+ private BigInteger oddModPow(BigInteger y, BigInteger z) {
1643+ /*
1644+ * The algorithm is adapted from Colin Plumb's C library.
1645+ *
1646+ * The window algorithm:
1647+ * The idea is to keep a running product of b1 = n^(high-order bits of exp)
1648+ * and then keep appending exponent bits to it. The following patterns
1649+ * apply to a 3-bit window (k = 3):
1650+ * To append 0: square
1651+ * To append 1: square, multiply by n^1
1652+ * To append 10: square, multiply by n^1, square
1653+ * To append 11: square, square, multiply by n^3
1654+ * To append 100: square, multiply by n^1, square, square
1655+ * To append 101: square, square, square, multiply by n^5
1656+ * To append 110: square, square, multiply by n^3, square
1657+ * To append 111: square, square, square, multiply by n^7
1658+ *
1659+ * Since each pattern involves only one multiply, the longer the pattern
1660+ * the better, except that a 0 (no multiplies) can be appended directly.
1661+ * We precompute a table of odd powers of n, up to 2^k, and can then
1662+ * multiply k bits of exponent at a time. Actually, assuming random
1663+ * exponents, there is on average one zero bit between needs to
1664+ * multiply (1/2 of the time there's none, 1/4 of the time there's 1,
1665+ * 1/8 of the time, there's 2, 1/32 of the time, there's 3, etc.), so
1666+ * you have to do one multiply per k+1 bits of exponent.
1667+ *
1668+ * The loop walks down the exponent, squaring the result buffer as
1669+ * it goes. There is a wbits+1 bit lookahead buffer, buf, that is
1670+ * filled with the upcoming exponent bits. (What is read after the
1671+ * end of the exponent is unimportant, but it is filled with zero here.)
1672+ * When the most-significant bit of this buffer becomes set, i.e.
1673+ * (buf & tblmask) != 0, we have to decide what pattern to multiply
1674+ * by, and when to do it. We decide, remember to do it in future
1675+ * after a suitable number of squarings have passed (e.g. a pattern
1676+ * of "100" in the buffer requires that we multiply by n^1 immediately;
1677+ * a pattern of "110" calls for multiplying by n^3 after one more
1678+ * squaring), clear the buffer, and continue.
1679+ *
1680+ * When we start, there is one more optimization: the result buffer
1681+ * is implcitly one, so squaring it or multiplying by it can be
1682+ * optimized away. Further, if we start with a pattern like "100"
1683+ * in the lookahead window, rather than placing n into the buffer
1684+ * and then starting to square it, we have already computed n^2
1685+ * to compute the odd-powers table, so we can place that into
1686+ * the buffer and save a squaring.
1687+ *
1688+ * This means that if you have a k-bit window, to compute n^z,
1689+ * where z is the high k bits of the exponent, 1/2 of the time
1690+ * it requires no squarings. 1/4 of the time, it requires 1
1691+ * squaring, ... 1/2^(k-1) of the time, it reqires k-2 squarings.
1692+ * And the remaining 1/2^(k-1) of the time, the top k bits are a
1693+ * 1 followed by k-1 0 bits, so it again only requires k-2
1694+ * squarings, not k-1. The average of these is 1. Add that
1695+ * to the one squaring we have to do to compute the table,
1696+ * and you'll see that a k-bit window saves k-2 squarings
1697+ * as well as reducing the multiplies. (It actually doesn't
1698+ * hurt in the case k = 1, either.)
1699+ */
1700+ // Special case for exponent of one
1701+ if (y.equals(ONE))
1702+ return this;
1703+
1704+ // Special case for base of zero
1705+ if (signum==0)
1706+ return ZERO;
1707+
1708+ int[] base = mag.clone();
1709+ int[] exp = y.mag;
1710+ int[] mod = z.mag;
1711+ int modLen = mod.length;
1712+
1713+ // Select an appropriate window size
1714+ int wbits = 0;
1715+ int ebits = bitLength(exp, exp.length);
1716+ // if exponent is 65537 (0x10001), use minimum window size
1717+ if ((ebits != 17) || (exp[0] != 65537)) {
1718+ while (ebits > bnExpModThreshTable[wbits]) {
1719+ wbits++;
1720+ }
1721+ }
1722+
1723+ // Calculate appropriate table size
1724+ int tblmask = 1 << wbits;
1725+
1726+ // Allocate table for precomputed odd powers of base in Montgomery form
1727+ int[][] table = new int[tblmask][];
1728+ for (int i=0; i<tblmask; i++)
1729+ table[i] = new int[modLen];
1730+
1731+ // Compute the modular inverse
1732+ int inv = -MutableBigInteger.inverseMod32(mod[modLen-1]);
1733+
1734+ // Convert base to Montgomery form
1735+ int[] a = leftShift(base, base.length, modLen << 5);
1736+
1737+ MutableBigInteger q = new MutableBigInteger(),
1738+ a2 = new MutableBigInteger(a),
1739+ b2 = new MutableBigInteger(mod);
1740+
1741+ MutableBigInteger r= a2.divide(b2, q);
1742+ table[0] = r.toIntArray();
1743+
1744+ // Pad table[0] with leading zeros so its length is at least modLen
1745+ if (table[0].length < modLen) {
1746+ int offset = modLen - table[0].length;
1747+ int[] t2 = new int[modLen];
1748+ for (int i=0; i<table[0].length; i++)
1749+ t2[i+offset] = table[0][i];
1750+ table[0] = t2;
1751+ }
1752+
1753+ // Set b to the square of the base
1754+ int[] b = squareToLen(table[0], modLen, null);
1755+ b = montReduce(b, mod, modLen, inv);
1756+
1757+ // Set t to high half of b
1758+ int[] t = new int[modLen];
1759+ for(int i=0; i<modLen; i++)
1760+ t[i] = b[i];
1761+
1762+ // Fill in the table with odd powers of the base
1763+ for (int i=1; i<tblmask; i++) {
1764+ int[] prod = multiplyToLen(t, modLen, table[i-1], modLen, null);
1765+ table[i] = montReduce(prod, mod, modLen, inv);
1766+ }
1767+
1768+ // Pre load the window that slides over the exponent
1769+ int bitpos = 1 << ((ebits-1) & (32-1));
1770+
1771+ int buf = 0;
1772+ int elen = exp.length;
1773+ int eIndex = 0;
1774+ for (int i = 0; i <= wbits; i++) {
1775+ buf = (buf << 1) | (((exp[eIndex] & bitpos) != 0)?1:0);
1776+ bitpos >>>= 1;
1777+ if (bitpos == 0) {
1778+ eIndex++;
1779+ bitpos = 1 << (32-1);
1780+ elen--;
1781+ }
1782+ }
1783+
1784+ int multpos = ebits;
1785+
1786+ // The first iteration, which is hoisted out of the main loop
1787+ ebits--;
1788+ boolean isone = true;
1789+
1790+ multpos = ebits - wbits;
1791+ while ((buf & 1) == 0) {
1792+ buf >>>= 1;
1793+ multpos++;
1794+ }
1795+
1796+ int[] mult = table[buf >>> 1];
1797+
1798+ buf = 0;
1799+ if (multpos == ebits)
1800+ isone = false;
1801+
1802+ // The main loop
1803+ while(true) {
1804+ ebits--;
1805+ // Advance the window
1806+ buf <<= 1;
1807+
1808+ if (elen != 0) {
1809+ buf |= ((exp[eIndex] & bitpos) != 0) ? 1 : 0;
1810+ bitpos >>>= 1;
1811+ if (bitpos == 0) {
1812+ eIndex++;
1813+ bitpos = 1 << (32-1);
1814+ elen--;
1815+ }
1816+ }
1817+
1818+ // Examine the window for pending multiplies
1819+ if ((buf & tblmask) != 0) {
1820+ multpos = ebits - wbits;
1821+ while ((buf & 1) == 0) {
1822+ buf >>>= 1;
1823+ multpos++;
1824+ }
1825+ mult = table[buf >>> 1];
1826+ buf = 0;
1827+ }
1828+
1829+ // Perform multiply
1830+ if (ebits == multpos) {
1831+ if (isone) {
1832+ b = mult.clone();
1833+ isone = false;
1834+ } else {
1835+ t = b;
1836+ a = multiplyToLen(t, modLen, mult, modLen, a);
1837+ a = montReduce(a, mod, modLen, inv);
1838+ t = a; a = b; b = t;
1839+ }
1840+ }
1841+
1842+ // Check if done
1843+ if (ebits == 0)
1844+ break;
1845+
1846+ // Square the input
1847+ if (!isone) {
1848+ t = b;
1849+ a = squareToLen(t, modLen, a);
1850+ a = montReduce(a, mod, modLen, inv);
1851+ t = a; a = b; b = t;
1852+ }
1853+ }
1854+
1855+ // Convert result out of Montgomery form and return
1856+ int[] t2 = new int[2*modLen];
1857+ for(int i=0; i<modLen; i++)
1858+ t2[i+modLen] = b[i];
1859+
1860+ b = montReduce(t2, mod, modLen, inv);
1861+
1862+ t2 = new int[modLen];
1863+ for(int i=0; i<modLen; i++)
1864+ t2[i] = b[i];
1865+
1866+ return new BigInteger(1, t2);
1867+ }
1868+
1869+ /**
1870+ * Montgomery reduce n, modulo mod. This reduces modulo mod and divides
1871+ * by 2^(32*mlen). Adapted from Colin Plumb's C library.
1872+ */
1873+ private static int[] montReduce(int[] n, int[] mod, int mlen, int inv) {
1874+ int c=0;
1875+ int len = mlen;
1876+ int offset=0;
1877+
1878+ do {
1879+ int nEnd = n[n.length-1-offset];
1880+ int carry = mulAdd(n, mod, offset, mlen, inv * nEnd);
1881+ c += addOne(n, offset, mlen, carry);
1882+ offset++;
1883+ } while(--len > 0);
1884+
1885+ while(c>0)
1886+ c += subN(n, mod, mlen);
1887+
1888+ while (intArrayCmpToLen(n, mod, mlen) >= 0)
1889+ subN(n, mod, mlen);
1890+
1891+ return n;
1892+ }
1893+
1894+
1895+ /*
1896+ * Returns -1, 0 or +1 as big-endian unsigned int array arg1 is less than,
1897+ * equal to, or greater than arg2 up to length len.
1898+ */
1899+ private static int intArrayCmpToLen(int[] arg1, int[] arg2, int len) {
1900+ for (int i=0; i<len; i++) {
1901+ long b1 = arg1[i] & LONG_MASK;
1902+ long b2 = arg2[i] & LONG_MASK;
1903+ if (b1 < b2)
1904+ return -1;
1905+ if (b1 > b2)
1906+ return 1;
1907+ }
1908+ return 0;
1909+ }
1910+
1911+ /**
1912+ * Subtracts two numbers of same length, returning borrow.
1913+ */
1914+ private static int subN(int[] a, int[] b, int len) {
1915+ long sum = 0;
1916+
1917+ while(--len >= 0) {
1918+ sum = (a[len] & LONG_MASK) -
1919+ (b[len] & LONG_MASK) + (sum >> 32);
1920+ a[len] = (int)sum;
1921+ }
1922+
1923+ return (int)(sum >> 32);
1924+ }
1925+
1926+ /**
1927+ * Multiply an array by one word k and add to result, return the carry
1928+ */
1929+ static int mulAdd(int[] out, int[] in, int offset, int len, int k) {
1930+ long kLong = k & LONG_MASK;
1931+ long carry = 0;
1932+
1933+ offset = out.length-offset - 1;
1934+ for (int j=len-1; j >= 0; j--) {
1935+ long product = (in[j] & LONG_MASK) * kLong +
1936+ (out[offset] & LONG_MASK) + carry;
1937+ out[offset--] = (int)product;
1938+ carry = product >>> 32;
1939+ }
1940+ return (int)carry;
1941+ }
1942+
1943+ /**
1944+ * Add one word to the number a mlen words into a. Return the resulting
1945+ * carry.
1946+ */
1947+ static int addOne(int[] a, int offset, int mlen, int carry) {
1948+ offset = a.length-1-mlen-offset;
1949+ long t = (a[offset] & LONG_MASK) + (carry & LONG_MASK);
1950+
1951+ a[offset] = (int)t;
1952+ if ((t >>> 32) == 0)
1953+ return 0;
1954+ while (--mlen >= 0) {
1955+ if (--offset < 0) { // Carry out of number
1956+ return 1;
1957+ } else {
1958+ a[offset]++;
1959+ if (a[offset] != 0)
1960+ return 0;
1961+ }
1962+ }
1963+ return 1;
1964+ }
1965+
1966+ /**
1967+ * Returns a BigInteger whose value is (this ** exponent) mod (2**p)
1968+ */
1969+ private BigInteger modPow2(BigInteger exponent, int p) {
1970+ /*
1971+ * Perform exponentiation using repeated squaring trick, chopping off
1972+ * high order bits as indicated by modulus.
1973+ */
1974+ BigInteger result = valueOf(1);
1975+ BigInteger baseToPow2 = this.mod2(p);
1976+ int expOffset = 0;
1977+
1978+ int limit = exponent.bitLength();
1979+
1980+ if (this.testBit(0))
1981+ limit = (p-1) < limit ? (p-1) : limit;
1982+
1983+ while (expOffset < limit) {
1984+ if (exponent.testBit(expOffset))
1985+ result = result.multiply(baseToPow2).mod2(p);
1986+ expOffset++;
1987+ if (expOffset < limit)
1988+ baseToPow2 = baseToPow2.square().mod2(p);
1989+ }
1990+
1991+ return result;
1992+ }
1993+
1994+ /**
1995+ * Returns a BigInteger whose value is this mod(2**p).
1996+ * Assumes that this {@code BigInteger >= 0} and {@code p > 0}.
1997+ */
1998+ private BigInteger mod2(int p) {
1999+ if (bitLength() <= p)
2000+ return this;
2001+
2002+ // Copy remaining ints of mag
2003+ int numInts = (p + 31) >>> 5;
2004+ int[] mag = new int[numInts];
2005+ for (int i=0; i<numInts; i++)
2006+ mag[i] = this.mag[i + (this.mag.length - numInts)];
2007+
2008+ // Mask out any excess bits
2009+ int excessBits = (numInts << 5) - p;
2010+ mag[0] &= (1L << (32-excessBits)) - 1;
2011+
2012+ return (mag[0]==0 ? new BigInteger(1, mag) : new BigInteger(mag, 1));
2013+ }
2014+
2015+ /**
2016+ * Returns a BigInteger whose value is {@code (this}<sup>-1</sup> {@code mod m)}.
2017+ *
2018+ * @param m the modulus.
2019+ * @return {@code this}<sup>-1</sup> {@code mod m}.
2020+ * @throws ArithmeticException {@code m} &le; 0, or this BigInteger
2021+ * has no multiplicative inverse mod m (that is, this BigInteger
2022+ * is not <i>relatively prime</i> to m).
2023+ */
2024+ public BigInteger modInverse(BigInteger m) {
2025+ if (m.signum != 1)
2026+ throw new ArithmeticException("BigInteger: modulus not positive");
2027+
2028+ if (m.equals(ONE))
2029+ return ZERO;
2030+
2031+ // Calculate (this mod m)
2032+ BigInteger modVal = this;
2033+ if (signum < 0 || (this.compareMagnitude(m) >= 0))
2034+ modVal = this.mod(m);
2035+
2036+ if (modVal.equals(ONE))
2037+ return ONE;
2038+
2039+ MutableBigInteger a = new MutableBigInteger(modVal);
2040+ MutableBigInteger b = new MutableBigInteger(m);
2041+
2042+ MutableBigInteger result = a.mutableModInverse(b);
2043+ return result.toBigInteger(1);
2044+ }
2045+
2046+ // Shift Operations
2047+
2048+ /**
2049+ * Returns a BigInteger whose value is {@code (this << n)}.
2050+ * The shift distance, {@code n}, may be negative, in which case
2051+ * this method performs a right shift.
2052+ * (Computes <tt>floor(this * 2<sup>n</sup>)</tt>.)
2053+ *
2054+ * @param n shift distance, in bits.
2055+ * @return {@code this << n}
2056+ * @throws ArithmeticException if the shift distance is {@code
2057+ * Integer.MIN_VALUE}.
2058+ * @see #shiftRight
2059+ */
2060+ public BigInteger shiftLeft(int n) {
2061+ if (signum == 0)
2062+ return ZERO;
2063+ if (n==0)
2064+ return this;
2065+ if (n<0) {
2066+ if (n == Integer.MIN_VALUE) {
2067+ throw new ArithmeticException("Shift distance of Integer.MIN_VALUE not supported.");
2068+ } else {
2069+ return shiftRight(-n);
2070+ }
2071+ }
2072+
2073+ int nInts = n >>> 5;
2074+ int nBits = n & 0x1f;
2075+ int magLen = mag.length;
2076+ int newMag[] = null;
2077+
2078+ if (nBits == 0) {
2079+ newMag = new int[magLen + nInts];
2080+ for (int i=0; i<magLen; i++)
2081+ newMag[i] = mag[i];
2082+ } else {
2083+ int i = 0;
2084+ int nBits2 = 32 - nBits;
2085+ int highBits = mag[0] >>> nBits2;
2086+ if (highBits != 0) {
2087+ newMag = new int[magLen + nInts + 1];
2088+ newMag[i++] = highBits;
2089+ } else {
2090+ newMag = new int[magLen + nInts];
2091+ }
2092+ int j=0;
2093+ while (j < magLen-1)
2094+ newMag[i++] = mag[j++] << nBits | mag[j] >>> nBits2;
2095+ newMag[i] = mag[j] << nBits;
2096+ }
2097+
2098+ return new BigInteger(newMag, signum);
2099+ }
2100+
2101+ /**
2102+ * Returns a BigInteger whose value is {@code (this >> n)}. Sign
2103+ * extension is performed. The shift distance, {@code n}, may be
2104+ * negative, in which case this method performs a left shift.
2105+ * (Computes <tt>floor(this / 2<sup>n</sup>)</tt>.)
2106+ *
2107+ * @param n shift distance, in bits.
2108+ * @return {@code this >> n}
2109+ * @throws ArithmeticException if the shift distance is {@code
2110+ * Integer.MIN_VALUE}.
2111+ * @see #shiftLeft
2112+ */
2113+ public BigInteger shiftRight(int n) {
2114+ if (n==0)
2115+ return this;
2116+ if (n<0) {
2117+ if (n == Integer.MIN_VALUE) {
2118+ throw new ArithmeticException("Shift distance of Integer.MIN_VALUE not supported.");
2119+ } else {
2120+ return shiftLeft(-n);
2121+ }
2122+ }
2123+
2124+ int nInts = n >>> 5;
2125+ int nBits = n & 0x1f;
2126+ int magLen = mag.length;
2127+ int newMag[] = null;
2128+
2129+ // Special case: entire contents shifted off the end
2130+ if (nInts >= magLen)
2131+ return (signum >= 0 ? ZERO : negConst[1]);
2132+
2133+ if (nBits == 0) {
2134+ int newMagLen = magLen - nInts;
2135+ newMag = new int[newMagLen];
2136+ for (int i=0; i<newMagLen; i++)
2137+ newMag[i] = mag[i];
2138+ } else {
2139+ int i = 0;
2140+ int highBits = mag[0] >>> nBits;
2141+ if (highBits != 0) {
2142+ newMag = new int[magLen - nInts];
2143+ newMag[i++] = highBits;
2144+ } else {
2145+ newMag = new int[magLen - nInts -1];
2146+ }
2147+
2148+ int nBits2 = 32 - nBits;
2149+ int j=0;
2150+ while (j < magLen - nInts - 1)
2151+ newMag[i++] = (mag[j++] << nBits2) | (mag[j] >>> nBits);
2152+ }
2153+
2154+ if (signum < 0) {
2155+ // Find out whether any one-bits were shifted off the end.
2156+ boolean onesLost = false;
2157+ for (int i=magLen-1, j=magLen-nInts; i>=j && !onesLost; i--)
2158+ onesLost = (mag[i] != 0);
2159+ if (!onesLost && nBits != 0)
2160+ onesLost = (mag[magLen - nInts - 1] << (32 - nBits) != 0);
2161+
2162+ if (onesLost)
2163+ newMag = javaIncrement(newMag);
2164+ }
2165+
2166+ return new BigInteger(newMag, signum);
2167+ }
2168+
2169+ int[] javaIncrement(int[] val) {
2170+ int lastSum = 0;
2171+ for (int i=val.length-1; i >= 0 && lastSum == 0; i--)
2172+ lastSum = (val[i] += 1);
2173+ if (lastSum == 0) {
2174+ val = new int[val.length+1];
2175+ val[0] = 1;
2176+ }
2177+ return val;
2178+ }
2179+
2180+ // Bitwise Operations
2181+
2182+ /**
2183+ * Returns a BigInteger whose value is {@code (this & val)}. (This
2184+ * method returns a negative BigInteger if and only if this and val are
2185+ * both negative.)
2186+ *
2187+ * @param val value to be AND'ed with this BigInteger.
2188+ * @return {@code this & val}
2189+ */
2190+ public BigInteger and(BigInteger val) {
2191+ int[] result = new int[Math.max(intLength(), val.intLength())];
2192+ for (int i=0; i<result.length; i++)
2193+ result[i] = (getInt(result.length-i-1)
2194+ & val.getInt(result.length-i-1));
2195+
2196+ return valueOf(result);
2197+ }
2198+
2199+ /**
2200+ * Returns a BigInteger whose value is {@code (this | val)}. (This method
2201+ * returns a negative BigInteger if and only if either this or val is
2202+ * negative.)
2203+ *
2204+ * @param val value to be OR'ed with this BigInteger.
2205+ * @return {@code this | val}
2206+ */
2207+ public BigInteger or(BigInteger val) {
2208+ int[] result = new int[Math.max(intLength(), val.intLength())];
2209+ for (int i=0; i<result.length; i++)
2210+ result[i] = (getInt(result.length-i-1)
2211+ | val.getInt(result.length-i-1));
2212+
2213+ return valueOf(result);
2214+ }
2215+
2216+ /**
2217+ * Returns a BigInteger whose value is {@code (this ^ val)}. (This method
2218+ * returns a negative BigInteger if and only if exactly one of this and
2219+ * val are negative.)
2220+ *
2221+ * @param val value to be XOR'ed with this BigInteger.
2222+ * @return {@code this ^ val}
2223+ */
2224+ public BigInteger xor(BigInteger val) {
2225+ int[] result = new int[Math.max(intLength(), val.intLength())];
2226+ for (int i=0; i<result.length; i++)
2227+ result[i] = (getInt(result.length-i-1)
2228+ ^ val.getInt(result.length-i-1));
2229+
2230+ return valueOf(result);
2231+ }
2232+
2233+ /**
2234+ * Returns a BigInteger whose value is {@code (~this)}. (This method
2235+ * returns a negative value if and only if this BigInteger is
2236+ * non-negative.)
2237+ *
2238+ * @return {@code ~this}
2239+ */
2240+ public BigInteger not() {
2241+ int[] result = new int[intLength()];
2242+ for (int i=0; i<result.length; i++)
2243+ result[i] = ~getInt(result.length-i-1);
2244+
2245+ return valueOf(result);
2246+ }
2247+
2248+ /**
2249+ * Returns a BigInteger whose value is {@code (this & ~val)}. This
2250+ * method, which is equivalent to {@code and(val.not())}, is provided as
2251+ * a convenience for masking operations. (This method returns a negative
2252+ * BigInteger if and only if {@code this} is negative and {@code val} is
2253+ * positive.)
2254+ *
2255+ * @param val value to be complemented and AND'ed with this BigInteger.
2256+ * @return {@code this & ~val}
2257+ */
2258+ public BigInteger andNot(BigInteger val) {
2259+ int[] result = new int[Math.max(intLength(), val.intLength())];
2260+ for (int i=0; i<result.length; i++)
2261+ result[i] = (getInt(result.length-i-1)
2262+ & ~val.getInt(result.length-i-1));
2263+
2264+ return valueOf(result);
2265+ }
2266+
2267+
2268+ // Single Bit Operations
2269+
2270+ /**
2271+ * Returns {@code true} if and only if the designated bit is set.
2272+ * (Computes {@code ((this & (1<<n)) != 0)}.)
2273+ *
2274+ * @param n index of bit to test.
2275+ * @return {@code true} if and only if the designated bit is set.
2276+ * @throws ArithmeticException {@code n} is negative.
2277+ */
2278+ public boolean testBit(int n) {
2279+ if (n<0)
2280+ throw new ArithmeticException("Negative bit address");
2281+
2282+ return (getInt(n >>> 5) & (1 << (n & 31))) != 0;
2283+ }
2284+
2285+ /**
2286+ * Returns a BigInteger whose value is equivalent to this BigInteger
2287+ * with the designated bit set. (Computes {@code (this | (1<<n))}.)
2288+ *
2289+ * @param n index of bit to set.
2290+ * @return {@code this | (1<<n)}
2291+ * @throws ArithmeticException {@code n} is negative.
2292+ */
2293+ public BigInteger setBit(int n) {
2294+ if (n<0)
2295+ throw new ArithmeticException("Negative bit address");
2296+
2297+ int intNum = n >>> 5;
2298+ int[] result = new int[Math.max(intLength(), intNum+2)];
2299+
2300+ for (int i=0; i<result.length; i++)
2301+ result[result.length-i-1] = getInt(i);
2302+
2303+ result[result.length-intNum-1] |= (1 << (n & 31));
2304+
2305+ return valueOf(result);
2306+ }
2307+
2308+ /**
2309+ * Returns a BigInteger whose value is equivalent to this BigInteger
2310+ * with the designated bit cleared.
2311+ * (Computes {@code (this & ~(1<<n))}.)
2312+ *
2313+ * @param n index of bit to clear.
2314+ * @return {@code this & ~(1<<n)}
2315+ * @throws ArithmeticException {@code n} is negative.
2316+ */
2317+ public BigInteger clearBit(int n) {
2318+ if (n<0)
2319+ throw new ArithmeticException("Negative bit address");
2320+
2321+ int intNum = n >>> 5;
2322+ int[] result = new int[Math.max(intLength(), ((n + 1) >>> 5) + 1)];
2323+
2324+ for (int i=0; i<result.length; i++)
2325+ result[result.length-i-1] = getInt(i);
2326+
2327+ result[result.length-intNum-1] &= ~(1 << (n & 31));
2328+
2329+ return valueOf(result);
2330+ }
2331+
2332+ /**
2333+ * Returns a BigInteger whose value is equivalent to this BigInteger
2334+ * with the designated bit flipped.
2335+ * (Computes {@code (this ^ (1<<n))}.)
2336+ *
2337+ * @param n index of bit to flip.
2338+ * @return {@code this ^ (1<<n)}
2339+ * @throws ArithmeticException {@code n} is negative.
2340+ */
2341+ public BigInteger flipBit(int n) {
2342+ if (n<0)
2343+ throw new ArithmeticException("Negative bit address");
2344+
2345+ int intNum = n >>> 5;
2346+ int[] result = new int[Math.max(intLength(), intNum+2)];
2347+
2348+ for (int i=0; i<result.length; i++)
2349+ result[result.length-i-1] = getInt(i);
2350+
2351+ result[result.length-intNum-1] ^= (1 << (n & 31));
2352+
2353+ return valueOf(result);
2354+ }
2355+
2356+ /**
2357+ * Returns the index of the rightmost (lowest-order) one bit in this
2358+ * BigInteger (the number of zero bits to the right of the rightmost
2359+ * one bit). Returns -1 if this BigInteger contains no one bits.
2360+ * (Computes {@code (this==0? -1 : log2(this & -this))}.)
2361+ *
2362+ * @return index of the rightmost one bit in this BigInteger.
2363+ */
2364+ public int getLowestSetBit() {
2365+ @SuppressWarnings("deprecation") int lsb = lowestSetBit - 2;
2366+ if (lsb == -2) { // lowestSetBit not initialized yet
2367+ lsb = 0;
2368+ if (signum == 0) {
2369+ lsb -= 1;
2370+ } else {
2371+ // Search for lowest order nonzero int
2372+ int i,b;
2373+ for (i=0; (b = getInt(i))==0; i++)
2374+ ;
2375+ lsb += (i << 5) + Integer.numberOfTrailingZeros(b);
2376+ }
2377+ lowestSetBit = lsb + 2;
2378+ }
2379+ return lsb;
2380+ }
2381+
2382+
2383+ // Miscellaneous Bit Operations
2384+
2385+ /**
2386+ * Returns the number of bits in the minimal two's-complement
2387+ * representation of this BigInteger, <i>excluding</i> a sign bit.
2388+ * For positive BigIntegers, this is equivalent to the number of bits in
2389+ * the ordinary binary representation. (Computes
2390+ * {@code (ceil(log2(this < 0 ? -this : this+1)))}.)
2391+ *
2392+ * @return number of bits in the minimal two's-complement
2393+ * representation of this BigInteger, <i>excluding</i> a sign bit.
2394+ */
2395+ public int bitLength() {
2396+ @SuppressWarnings("deprecation") int n = bitLength - 1;
2397+ if (n == -1) { // bitLength not initialized yet
2398+ int[] m = mag;
2399+ int len = m.length;
2400+ if (len == 0) {
2401+ n = 0; // offset by one to initialize
2402+ } else {
2403+ // Calculate the bit length of the magnitude
2404+ int magBitLength = ((len - 1) << 5) + bitLengthForInt(mag[0]);
2405+ if (signum < 0) {
2406+ // Check if magnitude is a power of two
2407+ boolean pow2 = (Integer.bitCount(mag[0]) == 1);
2408+ for(int i=1; i< len && pow2; i++)
2409+ pow2 = (mag[i] == 0);
2410+
2411+ n = (pow2 ? magBitLength -1 : magBitLength);
2412+ } else {
2413+ n = magBitLength;
2414+ }
2415+ }
2416+ bitLength = n + 1;
2417+ }
2418+ return n;
2419+ }
2420+
2421+ /**
2422+ * Returns the number of bits in the two's complement representation
2423+ * of this BigInteger that differ from its sign bit. This method is
2424+ * useful when implementing bit-vector style sets atop BigIntegers.
2425+ *
2426+ * @return number of bits in the two's complement representation
2427+ * of this BigInteger that differ from its sign bit.
2428+ */
2429+ public int bitCount() {
2430+ @SuppressWarnings("deprecation") int bc = bitCount - 1;
2431+ if (bc == -1) { // bitCount not initialized yet
2432+ bc = 0; // offset by one to initialize
2433+ // Count the bits in the magnitude
2434+ for (int i=0; i<mag.length; i++)
2435+ bc += Integer.bitCount(mag[i]);
2436+ if (signum < 0) {
2437+ // Count the trailing zeros in the magnitude
2438+ int magTrailingZeroCount = 0, j;
2439+ for (j=mag.length-1; mag[j]==0; j--)
2440+ magTrailingZeroCount += 32;
2441+ magTrailingZeroCount += Integer.numberOfTrailingZeros(mag[j]);
2442+ bc += magTrailingZeroCount - 1;
2443+ }
2444+ bitCount = bc + 1;
2445+ }
2446+ return bc;
2447+ }
2448+
2449+ // Primality Testing
2450+
2451+ /**
2452+ * Returns {@code true} if this BigInteger is probably prime,
2453+ * {@code false} if it's definitely composite. If
2454+ * {@code certainty} is &le; 0, {@code true} is
2455+ * returned.
2456+ *
2457+ * @param certainty a measure of the uncertainty that the caller is
2458+ * willing to tolerate: if the call returns {@code true}
2459+ * the probability that this BigInteger is prime exceeds
2460+ * (1 - 1/2<sup>{@code certainty}</sup>). The execution time of
2461+ * this method is proportional to the value of this parameter.
2462+ * @return {@code true} if this BigInteger is probably prime,
2463+ * {@code false} if it's definitely composite.
2464+ */
2465+ public boolean isProbablePrime(int certainty) {
2466+ if (certainty <= 0)
2467+ return true;
2468+ BigInteger w = this.abs();
2469+ if (w.equals(TWO))
2470+ return true;
2471+ if (!w.testBit(0) || w.equals(ONE))
2472+ return false;
2473+
2474+ return w.primeToCertainty(certainty, null);
2475+ }
2476+
2477+ // Comparison Operations
2478+
2479+ /**
2480+ * Compares this BigInteger with the specified BigInteger. This
2481+ * method is provided in preference to individual methods for each
2482+ * of the six boolean comparison operators ({@literal <}, ==,
2483+ * {@literal >}, {@literal >=}, !=, {@literal <=}). The suggested
2484+ * idiom for performing these comparisons is: {@code
2485+ * (x.compareTo(y)} &lt;<i>op</i>&gt; {@code 0)}, where
2486+ * &lt;<i>op</i>&gt; is one of the six comparison operators.
2487+ *
2488+ * @param val BigInteger to which this BigInteger is to be compared.
2489+ * @return -1, 0 or 1 as this BigInteger is numerically less than, equal
2490+ * to, or greater than {@code val}.
2491+ */
2492+ public int compareTo(BigInteger val) {
2493+ if (signum == val.signum) {
2494+ switch (signum) {
2495+ case 1:
2496+ return compareMagnitude(val);
2497+ case -1:
2498+ return val.compareMagnitude(this);
2499+ default:
2500+ return 0;
2501+ }
2502+ }
2503+ return signum > val.signum ? 1 : -1;
2504+ }
2505+
2506+ /**
2507+ * Compares the magnitude array of this BigInteger with the specified
2508+ * BigInteger's. This is the version of compareTo ignoring sign.
2509+ *
2510+ * @param val BigInteger whose magnitude array to be compared.
2511+ * @return -1, 0 or 1 as this magnitude array is less than, equal to or
2512+ * greater than the magnitude aray for the specified BigInteger's.
2513+ */
2514+ final int compareMagnitude(BigInteger val) {
2515+ int[] m1 = mag;
2516+ int len1 = m1.length;
2517+ int[] m2 = val.mag;
2518+ int len2 = m2.length;
2519+ if (len1 < len2)
2520+ return -1;
2521+ if (len1 > len2)
2522+ return 1;
2523+ for (int i = 0; i < len1; i++) {
2524+ int a = m1[i];
2525+ int b = m2[i];
2526+ if (a != b)
2527+ return ((a & LONG_MASK) < (b & LONG_MASK)) ? -1 : 1;
2528+ }
2529+ return 0;
2530+ }
2531+
2532+ /**
2533+ * Compares this BigInteger with the specified Object for equality.
2534+ *
2535+ * @param x Object to which this BigInteger is to be compared.
2536+ * @return {@code true} if and only if the specified Object is a
2537+ * BigInteger whose value is numerically equal to this BigInteger.
2538+ */
2539+ public boolean equals(Object x) {
2540+ // This test is just an optimization, which may or may not help
2541+ if (x == this)
2542+ return true;
2543+
2544+ if (!(x instanceof BigInteger))
2545+ return false;
2546+
2547+ BigInteger xInt = (BigInteger) x;
2548+ if (xInt.signum != signum)
2549+ return false;
2550+
2551+ int[] m = mag;
2552+ int len = m.length;
2553+ int[] xm = xInt.mag;
2554+ if (len != xm.length)
2555+ return false;
2556+
2557+ for (int i = 0; i < len; i++)
2558+ if (xm[i] != m[i])
2559+ return false;
2560+
2561+ return true;
2562+ }
2563+
2564+ /**
2565+ * Returns the minimum of this BigInteger and {@code val}.
2566+ *
2567+ * @param val value with which the minimum is to be computed.
2568+ * @return the BigInteger whose value is the lesser of this BigInteger and
2569+ * {@code val}. If they are equal, either may be returned.
2570+ */
2571+ public BigInteger min(BigInteger val) {
2572+ return (compareTo(val)<0 ? this : val);
2573+ }
2574+
2575+ /**
2576+ * Returns the maximum of this BigInteger and {@code val}.
2577+ *
2578+ * @param val value with which the maximum is to be computed.
2579+ * @return the BigInteger whose value is the greater of this and
2580+ * {@code val}. If they are equal, either may be returned.
2581+ */
2582+ public BigInteger max(BigInteger val) {
2583+ return (compareTo(val)>0 ? this : val);
2584+ }
2585+
2586+
2587+ // Hash Function
2588+
2589+ /**
2590+ * Returns the hash code for this BigInteger.
2591+ *
2592+ * @return hash code for this BigInteger.
2593+ */
2594+ public int hashCode() {
2595+ int hashCode = 0;
2596+
2597+ for (int i=0; i<mag.length; i++)
2598+ hashCode = (int)(31*hashCode + (mag[i] & LONG_MASK));
2599+
2600+ return hashCode * signum;
2601+ }
2602+
2603+ /**
2604+ * Returns the String representation of this BigInteger in the
2605+ * given radix. If the radix is outside the range from {@link
2606+ * Character#MIN_RADIX} to {@link Character#MAX_RADIX} inclusive,
2607+ * it will default to 10 (as is the case for
2608+ * {@code Integer.toString}). The digit-to-character mapping
2609+ * provided by {@code Character.forDigit} is used, and a minus
2610+ * sign is prepended if appropriate. (This representation is
2611+ * compatible with the {@link #BigInteger(String, int) (String,
2612+ * int)} constructor.)
2613+ *
2614+ * @param radix radix of the String representation.
2615+ * @return String representation of this BigInteger in the given radix.
2616+ * @see Integer#toString
2617+ * @see Character#forDigit
2618+ * @see #BigInteger(java.lang.String, int)
2619+ */
2620+ public String toString(int radix) {
2621+ if (signum == 0)
2622+ return "0";
2623+ if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
2624+ radix = 10;
2625+
2626+ // Compute upper bound on number of digit groups and allocate space
2627+ int maxNumDigitGroups = (4*mag.length + 6)/7;
2628+ String digitGroup[] = new String[maxNumDigitGroups];
2629+
2630+ // Translate number to string, a digit group at a time
2631+ BigInteger tmp = this.abs();
2632+ int numGroups = 0;
2633+ while (tmp.signum != 0) {
2634+ BigInteger d = longRadix[radix];
2635+
2636+ MutableBigInteger q = new MutableBigInteger(),
2637+ a = new MutableBigInteger(tmp.mag),
2638+ b = new MutableBigInteger(d.mag);
2639+ MutableBigInteger r = a.divide(b, q);
2640+ BigInteger q2 = q.toBigInteger(tmp.signum * d.signum);
2641+ BigInteger r2 = r.toBigInteger(tmp.signum * d.signum);
2642+
2643+ digitGroup[numGroups++] = Long.toString(r2.longValue(), radix);
2644+ tmp = q2;
2645+ }
2646+
2647+ // Put sign (if any) and first digit group into result buffer
2648+ StringBuilder buf = new StringBuilder(numGroups*digitsPerLong[radix]+1);
2649+ if (signum<0)
2650+ buf.append('-');
2651+ buf.append(digitGroup[numGroups-1]);
2652+
2653+ // Append remaining digit groups padded with leading zeros
2654+ for (int i=numGroups-2; i>=0; i--) {
2655+ // Prepend (any) leading zeros for this digit group
2656+ int numLeadingZeros = digitsPerLong[radix]-digitGroup[i].length();
2657+ if (numLeadingZeros != 0)
2658+ buf.append(zeros[numLeadingZeros]);
2659+ buf.append(digitGroup[i]);
2660+ }
2661+ return buf.toString();
2662+ }
2663+
2664+ /* zero[i] is a string of i consecutive zeros. */
2665+ private static String zeros[] = new String[64];
2666+ static {
2667+ zeros[63] =
2668+ "000000000000000000000000000000000000000000000000000000000000000";
2669+ for (int i=0; i<63; i++)
2670+ zeros[i] = zeros[63].substring(0, i);
2671+ }
2672+
2673+ /**
2674+ * Returns the decimal String representation of this BigInteger.
2675+ * The digit-to-character mapping provided by
2676+ * {@code Character.forDigit} is used, and a minus sign is
2677+ * prepended if appropriate. (This representation is compatible
2678+ * with the {@link #BigInteger(String) (String)} constructor, and
2679+ * allows for String concatenation with Java's + operator.)
2680+ *
2681+ * @return decimal String representation of this BigInteger.
2682+ * @see Character#forDigit
2683+ * @see #BigInteger(java.lang.String)
2684+ */
2685+ public String toString() {
2686+ return toString(10);
2687+ }
2688+
2689+ /**
2690+ * Returns a byte array containing the two's-complement
2691+ * representation of this BigInteger. The byte array will be in
2692+ * <i>big-endian</i> byte-order: the most significant byte is in
2693+ * the zeroth element. The array will contain the minimum number
2694+ * of bytes required to represent this BigInteger, including at
2695+ * least one sign bit, which is {@code (ceil((this.bitLength() +
2696+ * 1)/8))}. (This representation is compatible with the
2697+ * {@link #BigInteger(byte[]) (byte[])} constructor.)
2698+ *
2699+ * @return a byte array containing the two's-complement representation of
2700+ * this BigInteger.
2701+ * @see #BigInteger(byte[])
2702+ */
2703+ public byte[] toByteArray() {
2704+ int byteLen = bitLength()/8 + 1;
2705+ byte[] byteArray = new byte[byteLen];
2706+
2707+ for (int i=byteLen-1, bytesCopied=4, nextInt=0, intIndex=0; i>=0; i--) {
2708+ if (bytesCopied == 4) {
2709+ nextInt = getInt(intIndex++);
2710+ bytesCopied = 1;
2711+ } else {
2712+ nextInt >>>= 8;
2713+ bytesCopied++;
2714+ }
2715+ byteArray[i] = (byte)nextInt;
2716+ }
2717+ return byteArray;
2718+ }
2719+
2720+ /**
2721+ * Converts this BigInteger to an {@code int}. This
2722+ * conversion is analogous to a
2723+ * <i>narrowing primitive conversion</i> from {@code long} to
2724+ * {@code int} as defined in section 5.1.3 of
2725+ * <cite>The Java&trade; Language Specification</cite>:
2726+ * if this BigInteger is too big to fit in an
2727+ * {@code int}, only the low-order 32 bits are returned.
2728+ * Note that this conversion can lose information about the
2729+ * overall magnitude of the BigInteger value as well as return a
2730+ * result with the opposite sign.
2731+ *
2732+ * @return this BigInteger converted to an {@code int}.
2733+ */
2734+ public int intValue() {
2735+ int result = 0;
2736+ result = getInt(0);
2737+ return result;
2738+ }
2739+
2740+ /**
2741+ * Converts this BigInteger to a {@code long}. This
2742+ * conversion is analogous to a
2743+ * <i>narrowing primitive conversion</i> from {@code long} to
2744+ * {@code int} as defined in section 5.1.3 of
2745+ * <cite>The Java&trade; Language Specification</cite>:
2746+ * if this BigInteger is too big to fit in a
2747+ * {@code long}, only the low-order 64 bits are returned.
2748+ * Note that this conversion can lose information about the
2749+ * overall magnitude of the BigInteger value as well as return a
2750+ * result with the opposite sign.
2751+ *
2752+ * @return this BigInteger converted to a {@code long}.
2753+ */
2754+ public long longValue() {
2755+ long result = 0;
2756+
2757+ for (int i=1; i>=0; i--)
2758+ result = (result << 32) + (getInt(i) & LONG_MASK);
2759+ return result;
2760+ }
2761+
2762+ /**
2763+ * Converts this BigInteger to a {@code float}. This
2764+ * conversion is similar to the
2765+ * <i>narrowing primitive conversion</i> from {@code double} to
2766+ * {@code float} as defined in section 5.1.3 of
2767+ * <cite>The Java&trade; Language Specification</cite>:
2768+ * if this BigInteger has too great a magnitude
2769+ * to represent as a {@code float}, it will be converted to
2770+ * {@link Float#NEGATIVE_INFINITY} or {@link
2771+ * Float#POSITIVE_INFINITY} as appropriate. Note that even when
2772+ * the return value is finite, this conversion can lose
2773+ * information about the precision of the BigInteger value.
2774+ *
2775+ * @return this BigInteger converted to a {@code float}.
2776+ */
2777+ public float floatValue() {
2778+ // Somewhat inefficient, but guaranteed to work.
2779+ return Float.parseFloat(this.toString());
2780+ }
2781+
2782+ /**
2783+ * Converts this BigInteger to a {@code double}. This
2784+ * conversion is similar to the
2785+ * <i>narrowing primitive conversion</i> from {@code double} to
2786+ * {@code float} as defined in section 5.1.3 of
2787+ * <cite>The Java&trade; Language Specification</cite>:
2788+ * if this BigInteger has too great a magnitude
2789+ * to represent as a {@code double}, it will be converted to
2790+ * {@link Double#NEGATIVE_INFINITY} or {@link
2791+ * Double#POSITIVE_INFINITY} as appropriate. Note that even when
2792+ * the return value is finite, this conversion can lose
2793+ * information about the precision of the BigInteger value.
2794+ *
2795+ * @return this BigInteger converted to a {@code double}.
2796+ */
2797+ public double doubleValue() {
2798+ // Somewhat inefficient, but guaranteed to work.
2799+ return Double.parseDouble(this.toString());
2800+ }
2801+
2802+ /**
2803+ * Returns a copy of the input array stripped of any leading zero bytes.
2804+ */
2805+ private static int[] stripLeadingZeroInts(int val[]) {
2806+ int vlen = val.length;
2807+ int keep;
2808+
2809+ // Find first nonzero byte
2810+ for (keep = 0; keep < vlen && val[keep] == 0; keep++)
2811+ ;
2812+ return java.util.Arrays.copyOfRange(val, keep, vlen);
2813+ }
2814+
2815+ /**
2816+ * Returns the input array stripped of any leading zero bytes.
2817+ * Since the source is trusted the copying may be skipped.
2818+ */
2819+ private static int[] trustedStripLeadingZeroInts(int val[]) {
2820+ int vlen = val.length;
2821+ int keep;
2822+
2823+ // Find first nonzero byte
2824+ for (keep = 0; keep < vlen && val[keep] == 0; keep++)
2825+ ;
2826+ return keep == 0 ? val : java.util.Arrays.copyOfRange(val, keep, vlen);
2827+ }
2828+
2829+ /**
2830+ * Returns a copy of the input array stripped of any leading zero bytes.
2831+ */
2832+ private static int[] stripLeadingZeroBytes(byte a[]) {
2833+ int byteLength = a.length;
2834+ int keep;
2835+
2836+ // Find first nonzero byte
2837+ for (keep = 0; keep < byteLength && a[keep]==0; keep++)
2838+ ;
2839+
2840+ // Allocate new array and copy relevant part of input array
2841+ int intLength = ((byteLength - keep) + 3) >>> 2;
2842+ int[] result = new int[intLength];
2843+ int b = byteLength - 1;
2844+ for (int i = intLength-1; i >= 0; i--) {
2845+ result[i] = a[b--] & 0xff;
2846+ int bytesRemaining = b - keep + 1;
2847+ int bytesToTransfer = Math.min(3, bytesRemaining);
2848+ for (int j=8; j <= (bytesToTransfer << 3); j += 8)
2849+ result[i] |= ((a[b--] & 0xff) << j);
2850+ }
2851+ return result;
2852+ }
2853+
2854+ /**
2855+ * Takes an array a representing a negative 2's-complement number and
2856+ * returns the minimal (no leading zero bytes) unsigned whose value is -a.
2857+ */
2858+ private static int[] makePositive(byte a[]) {
2859+ int keep, k;
2860+ int byteLength = a.length;
2861+
2862+ // Find first non-sign (0xff) byte of input
2863+ for (keep=0; keep<byteLength && a[keep]==-1; keep++)
2864+ ;
2865+
2866+
2867+ /* Allocate output array. If all non-sign bytes are 0x00, we must
2868+ * allocate space for one extra output byte. */
2869+ for (k=keep; k<byteLength && a[k]==0; k++)
2870+ ;
2871+
2872+ int extraByte = (k==byteLength) ? 1 : 0;
2873+ int intLength = ((byteLength - keep + extraByte) + 3)/4;
2874+ int result[] = new int[intLength];
2875+
2876+ /* Copy one's complement of input into output, leaving extra
2877+ * byte (if it exists) == 0x00 */
2878+ int b = byteLength - 1;
2879+ for (int i = intLength-1; i >= 0; i--) {
2880+ result[i] = a[b--] & 0xff;
2881+ int numBytesToTransfer = Math.min(3, b-keep+1);
2882+ if (numBytesToTransfer < 0)
2883+ numBytesToTransfer = 0;
2884+ for (int j=8; j <= 8*numBytesToTransfer; j += 8)
2885+ result[i] |= ((a[b--] & 0xff) << j);
2886+
2887+ // Mask indicates which bits must be complemented
2888+ int mask = -1 >>> (8*(3-numBytesToTransfer));
2889+ result[i] = ~result[i] & mask;
2890+ }
2891+
2892+ // Add one to one's complement to generate two's complement
2893+ for (int i=result.length-1; i>=0; i--) {
2894+ result[i] = (int)((result[i] & LONG_MASK) + 1);
2895+ if (result[i] != 0)
2896+ break;
2897+ }
2898+
2899+ return result;
2900+ }
2901+
2902+ /**
2903+ * Takes an array a representing a negative 2's-complement number and
2904+ * returns the minimal (no leading zero ints) unsigned whose value is -a.
2905+ */
2906+ private static int[] makePositive(int a[]) {
2907+ int keep, j;
2908+
2909+ // Find first non-sign (0xffffffff) int of input
2910+ for (keep=0; keep<a.length && a[keep]==-1; keep++)
2911+ ;
2912+
2913+ /* Allocate output array. If all non-sign ints are 0x00, we must
2914+ * allocate space for one extra output int. */
2915+ for (j=keep; j<a.length && a[j]==0; j++)
2916+ ;
2917+ int extraInt = (j==a.length ? 1 : 0);
2918+ int result[] = new int[a.length - keep + extraInt];
2919+
2920+ /* Copy one's complement of input into output, leaving extra
2921+ * int (if it exists) == 0x00 */
2922+ for (int i = keep; i<a.length; i++)
2923+ result[i - keep + extraInt] = ~a[i];
2924+
2925+ // Add one to one's complement to generate two's complement
2926+ for (int i=result.length-1; ++result[i]==0; i--)
2927+ ;
2928+
2929+ return result;
2930+ }
2931+
2932+ /*
2933+ * The following two arrays are used for fast String conversions. Both
2934+ * are indexed by radix. The first is the number of digits of the given
2935+ * radix that can fit in a Java long without "going negative", i.e., the
2936+ * highest integer n such that radix**n < 2**63. The second is the
2937+ * "long radix" that tears each number into "long digits", each of which
2938+ * consists of the number of digits in the corresponding element in
2939+ * digitsPerLong (longRadix[i] = i**digitPerLong[i]). Both arrays have
2940+ * nonsense values in their 0 and 1 elements, as radixes 0 and 1 are not
2941+ * used.
2942+ */
2943+ private static int digitsPerLong[] = {0, 0,
2944+ 62, 39, 31, 27, 24, 22, 20, 19, 18, 18, 17, 17, 16, 16, 15, 15, 15, 14,
2945+ 14, 14, 14, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12, 12, 12, 12};
2946+
2947+ private static BigInteger longRadix[] = {null, null,
2948+ valueOf(0x4000000000000000L), valueOf(0x383d9170b85ff80bL),
2949+ valueOf(0x4000000000000000L), valueOf(0x6765c793fa10079dL),
2950+ valueOf(0x41c21cb8e1000000L), valueOf(0x3642798750226111L),
2951+ valueOf(0x1000000000000000L), valueOf(0x12bf307ae81ffd59L),
2952+ valueOf( 0xde0b6b3a7640000L), valueOf(0x4d28cb56c33fa539L),
2953+ valueOf(0x1eca170c00000000L), valueOf(0x780c7372621bd74dL),
2954+ valueOf(0x1e39a5057d810000L), valueOf(0x5b27ac993df97701L),
2955+ valueOf(0x1000000000000000L), valueOf(0x27b95e997e21d9f1L),
2956+ valueOf(0x5da0e1e53c5c8000L), valueOf( 0xb16a458ef403f19L),
2957+ valueOf(0x16bcc41e90000000L), valueOf(0x2d04b7fdd9c0ef49L),
2958+ valueOf(0x5658597bcaa24000L), valueOf( 0x6feb266931a75b7L),
2959+ valueOf( 0xc29e98000000000L), valueOf(0x14adf4b7320334b9L),
2960+ valueOf(0x226ed36478bfa000L), valueOf(0x383d9170b85ff80bL),
2961+ valueOf(0x5a3c23e39c000000L), valueOf( 0x4e900abb53e6b71L),
2962+ valueOf( 0x7600ec618141000L), valueOf( 0xaee5720ee830681L),
2963+ valueOf(0x1000000000000000L), valueOf(0x172588ad4f5f0981L),
2964+ valueOf(0x211e44f7d02c1000L), valueOf(0x2ee56725f06e5c71L),
2965+ valueOf(0x41c21cb8e1000000L)};
2966+
2967+ /*
2968+ * These two arrays are the integer analogue of above.
2969+ */
2970+ private static int digitsPerInt[] = {0, 0, 30, 19, 15, 13, 11,
2971+ 11, 10, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6,
2972+ 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5};
2973+
2974+ private static int intRadix[] = {0, 0,
2975+ 0x40000000, 0x4546b3db, 0x40000000, 0x48c27395, 0x159fd800,
2976+ 0x75db9c97, 0x40000000, 0x17179149, 0x3b9aca00, 0xcc6db61,
2977+ 0x19a10000, 0x309f1021, 0x57f6c100, 0xa2f1b6f, 0x10000000,
2978+ 0x18754571, 0x247dbc80, 0x3547667b, 0x4c4b4000, 0x6b5a6e1d,
2979+ 0x6c20a40, 0x8d2d931, 0xb640000, 0xe8d4a51, 0x1269ae40,
2980+ 0x17179149, 0x1cb91000, 0x23744899, 0x2b73a840, 0x34e63b41,
2981+ 0x40000000, 0x4cfa3cc1, 0x5c13d840, 0x6d91b519, 0x39aa400
2982+ };
2983+
2984+ /**
2985+ * These routines provide access to the two's complement representation
2986+ * of BigIntegers.
2987+ */
2988+
2989+ /**
2990+ * Returns the length of the two's complement representation in ints,
2991+ * including space for at least one sign bit.
2992+ */
2993+ private int intLength() {
2994+ return (bitLength() >>> 5) + 1;
2995+ }
2996+
2997+ /* Returns sign bit */
2998+ private int signBit() {
2999+ return signum < 0 ? 1 : 0;
3000+ }
3001+
3002+ /* Returns an int of sign bits */
3003+ private int signInt() {
3004+ return signum < 0 ? -1 : 0;
3005+ }
3006+
3007+ /**
3008+ * Returns the specified int of the little-endian two's complement
3009+ * representation (int 0 is the least significant). The int number can
3010+ * be arbitrarily high (values are logically preceded by infinitely many
3011+ * sign ints).
3012+ */
3013+ private int getInt(int n) {
3014+ if (n < 0)
3015+ return 0;
3016+ if (n >= mag.length)
3017+ return signInt();
3018+
3019+ int magInt = mag[mag.length-n-1];
3020+
3021+ return (signum >= 0 ? magInt :
3022+ (n <= firstNonzeroIntNum() ? -magInt : ~magInt));
3023+ }
3024+
3025+ /**
3026+ * Returns the index of the int that contains the first nonzero int in the
3027+ * little-endian binary representation of the magnitude (int 0 is the
3028+ * least significant). If the magnitude is zero, return value is undefined.
3029+ */
3030+ private int firstNonzeroIntNum() {
3031+ int fn = firstNonzeroIntNum - 2;
3032+ if (fn == -2) { // firstNonzeroIntNum not initialized yet
3033+ fn = 0;
3034+
3035+ // Search for the first nonzero int
3036+ int i;
3037+ int mlen = mag.length;
3038+ for (i = mlen - 1; i >= 0 && mag[i] == 0; i--)
3039+ ;
3040+ fn = mlen - i - 1;
3041+ firstNonzeroIntNum = fn + 2; // offset by two to initialize
3042+ }
3043+ return fn;
3044+ }
3045+
3046+ /** use serialVersionUID from JDK 1.1. for interoperability */
3047+ private static final long serialVersionUID = -8287574255936472291L;
3048+
3049+ /**
3050+ * Serializable fields for BigInteger.
3051+ *
3052+ * @serialField signum int
3053+ * signum of this BigInteger.
3054+ * @serialField magnitude int[]
3055+ * magnitude array of this BigInteger.
3056+ * @serialField bitCount int
3057+ * number of bits in this BigInteger
3058+ * @serialField bitLength int
3059+ * the number of bits in the minimal two's-complement
3060+ * representation of this BigInteger
3061+ * @serialField lowestSetBit int
3062+ * lowest set bit in the twos complement representation
3063+ */
3064+ private static final ObjectStreamField[] serialPersistentFields = {
3065+ new ObjectStreamField("signum", Integer.TYPE),
3066+ new ObjectStreamField("magnitude", byte[].class),
3067+ new ObjectStreamField("bitCount", Integer.TYPE),
3068+ new ObjectStreamField("bitLength", Integer.TYPE),
3069+ new ObjectStreamField("firstNonzeroByteNum", Integer.TYPE),
3070+ new ObjectStreamField("lowestSetBit", Integer.TYPE)
3071+ };
3072+
3073+ /**
3074+ * Reconstitute the {@code BigInteger} instance from a stream (that is,
3075+ * deserialize it). The magnitude is read in as an array of bytes
3076+ * for historical reasons, but it is converted to an array of ints
3077+ * and the byte array is discarded.
3078+ * Note:
3079+ * The current convention is to initialize the cache fields, bitCount,
3080+ * bitLength and lowestSetBit, to 0 rather than some other marker value.
3081+ * Therefore, no explicit action to set these fields needs to be taken in
3082+ * readObject because those fields already have a 0 value be default since
3083+ * defaultReadObject is not being used.
3084+ */
3085+ private void readObject(java.io.ObjectInputStream s)
3086+ throws java.io.IOException, ClassNotFoundException {
3087+ /*
3088+ * In order to maintain compatibility with previous serialized forms,
3089+ * the magnitude of a BigInteger is serialized as an array of bytes.
3090+ * The magnitude field is used as a temporary store for the byte array
3091+ * that is deserialized. The cached computation fields should be
3092+ * transient but are serialized for compatibility reasons.
3093+ */
3094+
3095+ // prepare to read the alternate persistent fields
3096+ ObjectInputStream.GetField fields = s.readFields();
3097+
3098+ // Read the alternate persistent fields that we care about
3099+ int sign = fields.get("signum", -2);
3100+ byte[] magnitude = (byte[])fields.get("magnitude", null);
3101+
3102+ // Validate signum
3103+ if (sign < -1 || sign > 1) {
3104+ String message = "BigInteger: Invalid signum value";
3105+ if (fields.defaulted("signum"))
3106+ message = "BigInteger: Signum not present in stream";
3107+ throw new java.io.StreamCorruptedException(message);
3108+ }
3109+ if ((magnitude.length == 0) != (sign == 0)) {
3110+ String message = "BigInteger: signum-magnitude mismatch";
3111+ if (fields.defaulted("magnitude"))
3112+ message = "BigInteger: Magnitude not present in stream";
3113+ throw new java.io.StreamCorruptedException(message);
3114+ }
3115+
3116+ // Commit final fields via Unsafe
3117+ unsafe.putIntVolatile(this, signumOffset, sign);
3118+
3119+ // Calculate mag field from magnitude and discard magnitude
3120+ unsafe.putObjectVolatile(this, magOffset,
3121+ stripLeadingZeroBytes(magnitude));
3122+ }
3123+
3124+ // Support for resetting final fields while deserializing
3125+ private static final sun.misc.Unsafe unsafe = sun.misc.Unsafe.getUnsafe();
3126+ private static final long signumOffset;
3127+ private static final long magOffset;
3128+ static {
3129+ try {
3130+ signumOffset = unsafe.objectFieldOffset
3131+ (BigInteger.class.getDeclaredField("signum"));
3132+ magOffset = unsafe.objectFieldOffset
3133+ (BigInteger.class.getDeclaredField("mag"));
3134+ } catch (Exception ex) {
3135+ throw new Error(ex);
3136+ }
3137+ }
3138+
3139+ /**
3140+ * Save the {@code BigInteger} instance to a stream.
3141+ * The magnitude of a BigInteger is serialized as a byte array for
3142+ * historical reasons.
3143+ *
3144+ * @serialData two necessary fields are written as well as obsolete
3145+ * fields for compatibility with older versions.
3146+ */
3147+ private void writeObject(ObjectOutputStream s) throws IOException {
3148+ // set the values of the Serializable fields
3149+ ObjectOutputStream.PutField fields = s.putFields();
3150+ fields.put("signum", signum);
3151+ fields.put("magnitude", magSerializedForm());
3152+ // The values written for cached fields are compatible with older
3153+ // versions, but are ignored in readObject so don't otherwise matter.
3154+ fields.put("bitCount", -1);
3155+ fields.put("bitLength", -1);
3156+ fields.put("lowestSetBit", -2);
3157+ fields.put("firstNonzeroByteNum", -2);
3158+
3159+ // save them
3160+ s.writeFields();
3161+}
3162+
3163+ /**
3164+ * Returns the mag array as an array of bytes.
3165+ */
3166+ private byte[] magSerializedForm() {
3167+ int len = mag.length;
3168+
3169+ int bitLen = (len == 0 ? 0 : ((len - 1) << 5) + bitLengthForInt(mag[0]));
3170+ int byteLen = (bitLen + 7) >>> 3;
3171+ byte[] result = new byte[byteLen];
3172+
3173+ for (int i = byteLen - 1, bytesCopied = 4, intIndex = len - 1, nextInt = 0;
3174+ i>=0; i--) {
3175+ if (bytesCopied == 4) {
3176+ nextInt = mag[intIndex--];
3177+ bytesCopied = 1;
3178+ } else {
3179+ nextInt >>>= 8;
3180+ bytesCopied++;
3181+ }
3182+ result[i] = (byte)nextInt;
3183+ }
3184+ return result;
3185+ }
3186+}
java/pkg/java/math/BitSieve.class+0−0

Binary file not shown.

java/pkg/java/math/BitSieve.java+212−0
@@ -0,0 +1,212 @@
1+/*
2+ * Copyright (c) 1999, 2007, 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+package java.math;
27+
28+/**
29+ * A simple bit sieve used for finding prime number candidates. Allows setting
30+ * and clearing of bits in a storage array. The size of the sieve is assumed to
31+ * be constant to reduce overhead. All the bits of a new bitSieve are zero, and
32+ * bits are removed from it by setting them.
33+ *
34+ * To reduce storage space and increase efficiency, no even numbers are
35+ * represented in the sieve (each bit in the sieve represents an odd number).
36+ * The relationship between the index of a bit and the number it represents is
37+ * given by
38+ * N = offset + (2*index + 1);
39+ * Where N is the integer represented by a bit in the sieve, offset is some
40+ * even integer offset indicating where the sieve begins, and index is the
41+ * index of a bit in the sieve array.
42+ *
43+ * @see BigInteger
44+ * @author Michael McCloskey
45+ * @since 1.3
46+ */
47+class BitSieve {
48+ /**
49+ * Stores the bits in this bitSieve.
50+ */
51+ private long bits[];
52+
53+ /**
54+ * Length is how many bits this sieve holds.
55+ */
56+ private int length;
57+
58+ /**
59+ * A small sieve used to filter out multiples of small primes in a search
60+ * sieve.
61+ */
62+ private static BitSieve smallSieve = new BitSieve();
63+
64+ /**
65+ * Construct a "small sieve" with a base of 0. This constructor is
66+ * used internally to generate the set of "small primes" whose multiples
67+ * are excluded from sieves generated by the main (package private)
68+ * constructor, BitSieve(BigInteger base, int searchLen). The length
69+ * of the sieve generated by this constructor was chosen for performance;
70+ * it controls a tradeoff between how much time is spent constructing
71+ * other sieves, and how much time is wasted testing composite candidates
72+ * for primality. The length was chosen experimentally to yield good
73+ * performance.
74+ */
75+ private BitSieve() {
76+ length = 150 * 64;
77+ bits = new long[(unitIndex(length - 1) + 1)];
78+
79+ // Mark 1 as composite
80+ set(0);
81+ int nextIndex = 1;
82+ int nextPrime = 3;
83+
84+ // Find primes and remove their multiples from sieve
85+ do {
86+ sieveSingle(length, nextIndex + nextPrime, nextPrime);
87+ nextIndex = sieveSearch(length, nextIndex + 1);
88+ nextPrime = 2*nextIndex + 1;
89+ } while((nextIndex > 0) && (nextPrime < length));
90+ }
91+
92+ /**
93+ * Construct a bit sieve of searchLen bits used for finding prime number
94+ * candidates. The new sieve begins at the specified base, which must
95+ * be even.
96+ */
97+ BitSieve(BigInteger base, int searchLen) {
98+ /*
99+ * Candidates are indicated by clear bits in the sieve. As a candidates
100+ * nonprimality is calculated, a bit is set in the sieve to eliminate
101+ * it. To reduce storage space and increase efficiency, no even numbers
102+ * are represented in the sieve (each bit in the sieve represents an
103+ * odd number).
104+ */
105+ bits = new long[(unitIndex(searchLen-1) + 1)];
106+ length = searchLen;
107+ int start = 0;
108+
109+ int step = smallSieve.sieveSearch(smallSieve.length, start);
110+ int convertedStep = (step *2) + 1;
111+
112+ // Construct the large sieve at an even offset specified by base
113+ MutableBigInteger b = new MutableBigInteger(base);
114+ MutableBigInteger q = new MutableBigInteger();
115+ do {
116+ // Calculate base mod convertedStep
117+ start = b.divideOneWord(convertedStep, q);
118+
119+ // Take each multiple of step out of sieve
120+ start = convertedStep - start;
121+ if (start%2 == 0)
122+ start += convertedStep;
123+ sieveSingle(searchLen, (start-1)/2, convertedStep);
124+
125+ // Find next prime from small sieve
126+ step = smallSieve.sieveSearch(smallSieve.length, step+1);
127+ convertedStep = (step *2) + 1;
128+ } while (step > 0);
129+ }
130+
131+ /**
132+ * Given a bit index return unit index containing it.
133+ */
134+ private static int unitIndex(int bitIndex) {
135+ return bitIndex >>> 6;
136+ }
137+
138+ /**
139+ * Return a unit that masks the specified bit in its unit.
140+ */
141+ private static long bit(int bitIndex) {
142+ return 1L << (bitIndex & ((1<<6) - 1));
143+ }
144+
145+ /**
146+ * Get the value of the bit at the specified index.
147+ */
148+ private boolean get(int bitIndex) {
149+ int unitIndex = unitIndex(bitIndex);
150+ return ((bits[unitIndex] & bit(bitIndex)) != 0);
151+ }
152+
153+ /**
154+ * Set the bit at the specified index.
155+ */
156+ private void set(int bitIndex) {
157+ int unitIndex = unitIndex(bitIndex);
158+ bits[unitIndex] |= bit(bitIndex);
159+ }
160+
161+ /**
162+ * This method returns the index of the first clear bit in the search
163+ * array that occurs at or after start. It will not search past the
164+ * specified limit. It returns -1 if there is no such clear bit.
165+ */
166+ private int sieveSearch(int limit, int start) {
167+ if (start >= limit)
168+ return -1;
169+
170+ int index = start;
171+ do {
172+ if (!get(index))
173+ return index;
174+ index++;
175+ } while(index < limit-1);
176+ return -1;
177+ }
178+
179+ /**
180+ * Sieve a single set of multiples out of the sieve. Begin to remove
181+ * multiples of the specified step starting at the specified start index,
182+ * up to the specified limit.
183+ */
184+ private void sieveSingle(int limit, int start, int step) {
185+ while(start < limit) {
186+ set(start);
187+ start += step;
188+ }
189+ }
190+
191+ /**
192+ * Test probable primes in the sieve and return successful candidates.
193+ */
194+ BigInteger retrieve(BigInteger initValue, int certainty, java.util.Random random) {
195+ // Examine the sieve one long at a time to find possible primes
196+ int offset = 1;
197+ for (int i=0; i<bits.length; i++) {
198+ long nextLong = ~bits[i];
199+ for (int j=0; j<64; j++) {
200+ if ((nextLong & 1) == 1) {
201+ BigInteger candidate = initValue.add(
202+ BigInteger.valueOf(offset));
203+ if (candidate.primeToCertainty(certainty, random))
204+ return candidate;
205+ }
206+ nextLong >>>= 1;
207+ offset+=2;
208+ }
209+ }
210+ return null;
211+ }
212+}
java/pkg/java/math/MathContext.class+0−0

Binary file not shown.

java/pkg/java/math/MathContext.java+326−0
@@ -0,0 +1,326 @@
1+/*
2+ * Copyright (c) 2003, 2007, 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, 1997, 2001. All Rights Reserved.
28+ */
29+
30+package java.math;
31+import java.io.*;
32+
33+/**
34+ * Immutable objects which encapsulate the context settings which
35+ * describe certain rules for numerical operators, such as those
36+ * implemented by the {@link BigDecimal} class.
37+ *
38+ * <p>The base-independent settings are:
39+ * <ol>
40+ * <li>{@code precision}:
41+ * the number of digits to be used for an operation; results are
42+ * rounded to this precision
43+ *
44+ * <li>{@code roundingMode}:
45+ * a {@link RoundingMode} object which specifies the algorithm to be
46+ * used for rounding.
47+ * </ol>
48+ *
49+ * @see BigDecimal
50+ * @see RoundingMode
51+ * @author Mike Cowlishaw
52+ * @author Joseph D. Darcy
53+ * @since 1.5
54+ */
55+
56+public final class MathContext implements Serializable {
57+
58+ /* ----- Constants ----- */
59+
60+ // defaults for constructors
61+ private static final int DEFAULT_DIGITS = 9;
62+ private static final RoundingMode DEFAULT_ROUNDINGMODE = RoundingMode.HALF_UP;
63+ // Smallest values for digits (Maximum is Integer.MAX_VALUE)
64+ private static final int MIN_DIGITS = 0;
65+
66+ // Serialization version
67+ private static final long serialVersionUID = 5579720004786848255L;
68+
69+ /* ----- Public Properties ----- */
70+ /**
71+ * A {@code MathContext} object whose settings have the values
72+ * required for unlimited precision arithmetic.
73+ * The values of the settings are:
74+ * <code>
75+ * precision=0 roundingMode=HALF_UP
76+ * </code>
77+ */
78+ public static final MathContext UNLIMITED =
79+ new MathContext(0, RoundingMode.HALF_UP);
80+
81+ /**
82+ * A {@code MathContext} object with a precision setting
83+ * matching the IEEE 754R Decimal32 format, 7 digits, and a
84+ * rounding mode of {@link RoundingMode#HALF_EVEN HALF_EVEN}, the
85+ * IEEE 754R default.
86+ */
87+ public static final MathContext DECIMAL32 =
88+ new MathContext(7, RoundingMode.HALF_EVEN);
89+
90+ /**
91+ * A {@code MathContext} object with a precision setting
92+ * matching the IEEE 754R Decimal64 format, 16 digits, and a
93+ * rounding mode of {@link RoundingMode#HALF_EVEN HALF_EVEN}, the
94+ * IEEE 754R default.
95+ */
96+ public static final MathContext DECIMAL64 =
97+ new MathContext(16, RoundingMode.HALF_EVEN);
98+
99+ /**
100+ * A {@code MathContext} object with a precision setting
101+ * matching the IEEE 754R Decimal128 format, 34 digits, and a
102+ * rounding mode of {@link RoundingMode#HALF_EVEN HALF_EVEN}, the
103+ * IEEE 754R default.
104+ */
105+ public static final MathContext DECIMAL128 =
106+ new MathContext(34, RoundingMode.HALF_EVEN);
107+
108+ /* ----- Shared Properties ----- */
109+ /**
110+ * The number of digits to be used for an operation. A value of 0
111+ * indicates that unlimited precision (as many digits as are
112+ * required) will be used. Note that leading zeros (in the
113+ * coefficient of a number) are never significant.
114+ *
115+ * <p>{@code precision} will always be non-negative.
116+ *
117+ * @serial
118+ */
119+ final int precision;
120+
121+ /**
122+ * The rounding algorithm to be used for an operation.
123+ *
124+ * @see RoundingMode
125+ * @serial
126+ */
127+ final RoundingMode roundingMode;
128+
129+ /* ----- Constructors ----- */
130+
131+ /**
132+ * Constructs a new {@code MathContext} with the specified
133+ * precision and the {@link RoundingMode#HALF_UP HALF_UP} rounding
134+ * mode.
135+ *
136+ * @param setPrecision The non-negative {@code int} precision setting.
137+ * @throws IllegalArgumentException if the {@code setPrecision} parameter is less
138+ * than zero.
139+ */
140+ public MathContext(int setPrecision) {
141+ this(setPrecision, DEFAULT_ROUNDINGMODE);
142+ return;
143+ }
144+
145+ /**
146+ * Constructs a new {@code MathContext} with a specified
147+ * precision and rounding mode.
148+ *
149+ * @param setPrecision The non-negative {@code int} precision setting.
150+ * @param setRoundingMode The rounding mode to use.
151+ * @throws IllegalArgumentException if the {@code setPrecision} parameter is less
152+ * than zero.
153+ * @throws NullPointerException if the rounding mode argument is {@code null}
154+ */
155+ public MathContext(int setPrecision,
156+ RoundingMode setRoundingMode) {
157+ if (setPrecision < MIN_DIGITS)
158+ throw new IllegalArgumentException("Digits < 0");
159+ if (setRoundingMode == null)
160+ throw new NullPointerException("null RoundingMode");
161+
162+ precision = setPrecision;
163+ roundingMode = setRoundingMode;
164+ return;
165+ }
166+
167+ /**
168+ * Constructs a new {@code MathContext} from a string.
169+ *
170+ * The string must be in the same format as that produced by the
171+ * {@link #toString} method.
172+ *
173+ * <p>An {@code IllegalArgumentException} is thrown if the precision
174+ * section of the string is out of range ({@code < 0}) or the string is
175+ * not in the format created by the {@link #toString} method.
176+ *
177+ * @param val The string to be parsed
178+ * @throws IllegalArgumentException if the precision section is out of range
179+ * or of incorrect format
180+ * @throws NullPointerException if the argument is {@code null}
181+ */
182+ public MathContext(String val) {
183+ boolean bad = false;
184+ int setPrecision;
185+ if (val == null)
186+ throw new NullPointerException("null String");
187+ try { // any error here is a string format problem
188+ if (!val.startsWith("precision=")) throw new RuntimeException();
189+ int fence = val.indexOf(' '); // could be -1
190+ int off = 10; // where value starts
191+ setPrecision = Integer.parseInt(val.substring(10, fence));
192+
193+ if (!val.startsWith("roundingMode=", fence+1))
194+ throw new RuntimeException();
195+ off = fence + 1 + 13;
196+ String str = val.substring(off, val.length());
197+ roundingMode = RoundingMode.valueOf(str);
198+ } catch (RuntimeException re) {
199+ throw new IllegalArgumentException("bad string format");
200+ }
201+
202+ if (setPrecision < MIN_DIGITS)
203+ throw new IllegalArgumentException("Digits < 0");
204+ // the other parameters cannot be invalid if we got here
205+ precision = setPrecision;
206+ }
207+
208+ /**
209+ * Returns the {@code precision} setting.
210+ * This value is always non-negative.
211+ *
212+ * @return an {@code int} which is the value of the {@code precision}
213+ * setting
214+ */
215+ public int getPrecision() {
216+ return precision;
217+ }
218+
219+ /**
220+ * Returns the roundingMode setting.
221+ * This will be one of
222+ * {@link RoundingMode#CEILING},
223+ * {@link RoundingMode#DOWN},
224+ * {@link RoundingMode#FLOOR},
225+ * {@link RoundingMode#HALF_DOWN},
226+ * {@link RoundingMode#HALF_EVEN},
227+ * {@link RoundingMode#HALF_UP},
228+ * {@link RoundingMode#UNNECESSARY}, or
229+ * {@link RoundingMode#UP}.
230+ *
231+ * @return a {@code RoundingMode} object which is the value of the
232+ * {@code roundingMode} setting
233+ */
234+
235+ public RoundingMode getRoundingMode() {
236+ return roundingMode;
237+ }
238+
239+ /**
240+ * Compares this {@code MathContext} with the specified
241+ * {@code Object} for equality.
242+ *
243+ * @param x {@code Object} to which this {@code MathContext} is to
244+ * be compared.
245+ * @return {@code true} if and only if the specified {@code Object} is
246+ * a {@code MathContext} object which has exactly the same
247+ * settings as this object
248+ */
249+ public boolean equals(Object x){
250+ MathContext mc;
251+ if (!(x instanceof MathContext))
252+ return false;
253+ mc = (MathContext) x;
254+ return mc.precision == this.precision
255+ && mc.roundingMode == this.roundingMode; // no need for .equals()
256+ }
257+
258+ /**
259+ * Returns the hash code for this {@code MathContext}.
260+ *
261+ * @return hash code for this {@code MathContext}
262+ */
263+ public int hashCode() {
264+ return this.precision + roundingMode.hashCode() * 59;
265+ }
266+
267+ /**
268+ * Returns the string representation of this {@code MathContext}.
269+ * The {@code String} returned represents the settings of the
270+ * {@code MathContext} object as two space-delimited words
271+ * (separated by a single space character, <tt>'&#92;u0020'</tt>,
272+ * and with no leading or trailing white space), as follows:
273+ * <ol>
274+ * <li>
275+ * The string {@code "precision="}, immediately followed
276+ * by the value of the precision setting as a numeric string as if
277+ * generated by the {@link Integer#toString(int) Integer.toString}
278+ * method.
279+ *
280+ * <li>
281+ * The string {@code "roundingMode="}, immediately
282+ * followed by the value of the {@code roundingMode} setting as a
283+ * word. This word will be the same as the name of the
284+ * corresponding public constant in the {@link RoundingMode}
285+ * enum.
286+ * </ol>
287+ * <p>
288+ * For example:
289+ * <pre>
290+ * precision=9 roundingMode=HALF_UP
291+ * </pre>
292+ *
293+ * Additional words may be appended to the result of
294+ * {@code toString} in the future if more properties are added to
295+ * this class.
296+ *
297+ * @return a {@code String} representing the context settings
298+ */
299+ public java.lang.String toString() {
300+ return "precision=" + precision + " " +
301+ "roundingMode=" + roundingMode.toString();
302+ }
303+
304+ // Private methods
305+
306+ /**
307+ * Reconstitute the {@code MathContext} instance from a stream (that is,
308+ * deserialize it).
309+ *
310+ * @param s the stream being read.
311+ */
312+ private void readObject(java.io.ObjectInputStream s)
313+ throws java.io.IOException, ClassNotFoundException {
314+ s.defaultReadObject(); // read in all fields
315+ // validate possibly bad fields
316+ if (precision < MIN_DIGITS) {
317+ String message = "MathContext: invalid digits in stream";
318+ throw new java.io.StreamCorruptedException(message);
319+ }
320+ if (roundingMode == null) {
321+ String message = "MathContext: null roundingMode in stream";
322+ throw new java.io.StreamCorruptedException(message);
323+ }
324+ }
325+
326+}
java/pkg/java/math/MutableBigInteger.class+0−0

Binary file not shown.

java/pkg/java/math/MutableBigInteger.java+1477−0
@@ -0,0 +1,1477 @@
1+/*
2+ * Copyright (c) 1999, 2007, 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+package java.math;
27+
28+/**
29+ * A class used to represent multiprecision integers that makes efficient
30+ * use of allocated space by allowing a number to occupy only part of
31+ * an array so that the arrays do not have to be reallocated as often.
32+ * When performing an operation with many iterations the array used to
33+ * hold a number is only reallocated when necessary and does not have to
34+ * be the same size as the number it represents. A mutable number allows
35+ * calculations to occur on the same number without having to create
36+ * a new number for every step of the calculation as occurs with
37+ * BigIntegers.
38+ *
39+ * @see BigInteger
40+ * @author Michael McCloskey
41+ * @since 1.3
42+ */
43+
44+import java.util.Arrays;
45+
46+import static java.math.BigInteger.LONG_MASK;
47+import static java.math.BigDecimal.INFLATED;
48+
49+class MutableBigInteger {
50+ /**
51+ * Holds the magnitude of this MutableBigInteger in big endian order.
52+ * The magnitude may start at an offset into the value array, and it may
53+ * end before the length of the value array.
54+ */
55+ int[] value;
56+
57+ /**
58+ * The number of ints of the value array that are currently used
59+ * to hold the magnitude of this MutableBigInteger. The magnitude starts
60+ * at an offset and offset + intLen may be less than value.length.
61+ */
62+ int intLen;
63+
64+ /**
65+ * The offset into the value array where the magnitude of this
66+ * MutableBigInteger begins.
67+ */
68+ int offset = 0;
69+
70+ // Constants
71+ /**
72+ * MutableBigInteger with one element value array with the value 1. Used by
73+ * BigDecimal divideAndRound to increment the quotient. Use this constant
74+ * only when the method is not going to modify this object.
75+ */
76+ static final MutableBigInteger ONE = new MutableBigInteger(1);
77+
78+ // Constructors
79+
80+ /**
81+ * The default constructor. An empty MutableBigInteger is created with
82+ * a one word capacity.
83+ */
84+ MutableBigInteger() {
85+ value = new int[1];
86+ intLen = 0;
87+ }
88+
89+ /**
90+ * Construct a new MutableBigInteger with a magnitude specified by
91+ * the int val.
92+ */
93+ MutableBigInteger(int val) {
94+ value = new int[1];
95+ intLen = 1;
96+ value[0] = val;
97+ }
98+
99+ /**
100+ * Construct a new MutableBigInteger with the specified value array
101+ * up to the length of the array supplied.
102+ */
103+ MutableBigInteger(int[] val) {
104+ value = val;
105+ intLen = val.length;
106+ }
107+
108+ /**
109+ * Construct a new MutableBigInteger with a magnitude equal to the
110+ * specified BigInteger.
111+ */
112+ MutableBigInteger(BigInteger b) {
113+ intLen = b.mag.length;
114+ value = Arrays.copyOf(b.mag, intLen);
115+ }
116+
117+ /**
118+ * Construct a new MutableBigInteger with a magnitude equal to the
119+ * specified MutableBigInteger.
120+ */
121+ MutableBigInteger(MutableBigInteger val) {
122+ intLen = val.intLen;
123+ value = Arrays.copyOfRange(val.value, val.offset, val.offset + intLen);
124+ }
125+
126+ /**
127+ * Internal helper method to return the magnitude array. The caller is not
128+ * supposed to modify the returned array.
129+ */
130+ private int[] getMagnitudeArray() {
131+ if (offset > 0 || value.length != intLen)
132+ return Arrays.copyOfRange(value, offset, offset + intLen);
133+ return value;
134+ }
135+
136+ /**
137+ * Convert this MutableBigInteger to a long value. The caller has to make
138+ * sure this MutableBigInteger can be fit into long.
139+ */
140+ private long toLong() {
141+ assert (intLen <= 2) : "this MutableBigInteger exceeds the range of long";
142+ if (intLen == 0)
143+ return 0;
144+ long d = value[offset] & LONG_MASK;
145+ return (intLen == 2) ? d << 32 | (value[offset + 1] & LONG_MASK) : d;
146+ }
147+
148+ /**
149+ * Convert this MutableBigInteger to a BigInteger object.
150+ */
151+ BigInteger toBigInteger(int sign) {
152+ if (intLen == 0 || sign == 0)
153+ return BigInteger.ZERO;
154+ return new BigInteger(getMagnitudeArray(), sign);
155+ }
156+
157+ /**
158+ * Convert this MutableBigInteger to BigDecimal object with the specified sign
159+ * and scale.
160+ */
161+ BigDecimal toBigDecimal(int sign, int scale) {
162+ if (intLen == 0 || sign == 0)
163+ return BigDecimal.valueOf(0, scale);
164+ int[] mag = getMagnitudeArray();
165+ int len = mag.length;
166+ int d = mag[0];
167+ // If this MutableBigInteger can't be fit into long, we need to
168+ // make a BigInteger object for the resultant BigDecimal object.
169+ if (len > 2 || (d < 0 && len == 2))
170+ return new BigDecimal(new BigInteger(mag, sign), INFLATED, scale, 0);
171+ long v = (len == 2) ?
172+ ((mag[1] & LONG_MASK) | (d & LONG_MASK) << 32) :
173+ d & LONG_MASK;
174+ return new BigDecimal(null, sign == -1 ? -v : v, scale, 0);
175+ }
176+
177+ /**
178+ * Clear out a MutableBigInteger for reuse.
179+ */
180+ void clear() {
181+ offset = intLen = 0;
182+ for (int index=0, n=value.length; index < n; index++)
183+ value[index] = 0;
184+ }
185+
186+ /**
187+ * Set a MutableBigInteger to zero, removing its offset.
188+ */
189+ void reset() {
190+ offset = intLen = 0;
191+ }
192+
193+ /**
194+ * Compare the magnitude of two MutableBigIntegers. Returns -1, 0 or 1
195+ * as this MutableBigInteger is numerically less than, equal to, or
196+ * greater than <tt>b</tt>.
197+ */
198+ final int compare(MutableBigInteger b) {
199+ int blen = b.intLen;
200+ if (intLen < blen)
201+ return -1;
202+ if (intLen > blen)
203+ return 1;
204+
205+ // Add Integer.MIN_VALUE to make the comparison act as unsigned integer
206+ // comparison.
207+ int[] bval = b.value;
208+ for (int i = offset, j = b.offset; i < intLen + offset; i++, j++) {
209+ int b1 = value[i] + 0x80000000;
210+ int b2 = bval[j] + 0x80000000;
211+ if (b1 < b2)
212+ return -1;
213+ if (b1 > b2)
214+ return 1;
215+ }
216+ return 0;
217+ }
218+
219+ /**
220+ * Compare this against half of a MutableBigInteger object (Needed for
221+ * remainder tests).
222+ * Assumes no leading unnecessary zeros, which holds for results
223+ * from divide().
224+ */
225+ final int compareHalf(MutableBigInteger b) {
226+ int blen = b.intLen;
227+ int len = intLen;
228+ if (len <= 0)
229+ return blen <=0 ? 0 : -1;
230+ if (len > blen)
231+ return 1;
232+ if (len < blen - 1)
233+ return -1;
234+ int[] bval = b.value;
235+ int bstart = 0;
236+ int carry = 0;
237+ // Only 2 cases left:len == blen or len == blen - 1
238+ if (len != blen) { // len == blen - 1
239+ if (bval[bstart] == 1) {
240+ ++bstart;
241+ carry = 0x80000000;
242+ } else
243+ return -1;
244+ }
245+ // compare values with right-shifted values of b,
246+ // carrying shifted-out bits across words
247+ int[] val = value;
248+ for (int i = offset, j = bstart; i < len + offset;) {
249+ int bv = bval[j++];
250+ long hb = ((bv >>> 1) + carry) & LONG_MASK;
251+ long v = val[i++] & LONG_MASK;
252+ if (v != hb)
253+ return v < hb ? -1 : 1;
254+ carry = (bv & 1) << 31; // carray will be either 0x80000000 or 0
255+ }
256+ return carry == 0? 0 : -1;
257+ }
258+
259+ /**
260+ * Return the index of the lowest set bit in this MutableBigInteger. If the
261+ * magnitude of this MutableBigInteger is zero, -1 is returned.
262+ */
263+ private final int getLowestSetBit() {
264+ if (intLen == 0)
265+ return -1;
266+ int j, b;
267+ for (j=intLen-1; (j>0) && (value[j+offset]==0); j--)
268+ ;
269+ b = value[j+offset];
270+ if (b==0)
271+ return -1;
272+ return ((intLen-1-j)<<5) + Integer.numberOfTrailingZeros(b);
273+ }
274+
275+ /**
276+ * Return the int in use in this MutableBigInteger at the specified
277+ * index. This method is not used because it is not inlined on all
278+ * platforms.
279+ */
280+ private final int getInt(int index) {
281+ return value[offset+index];
282+ }
283+
284+ /**
285+ * Return a long which is equal to the unsigned value of the int in
286+ * use in this MutableBigInteger at the specified index. This method is
287+ * not used because it is not inlined on all platforms.
288+ */
289+ private final long getLong(int index) {
290+ return value[offset+index] & LONG_MASK;
291+ }
292+
293+ /**
294+ * Ensure that the MutableBigInteger is in normal form, specifically
295+ * making sure that there are no leading zeros, and that if the
296+ * magnitude is zero, then intLen is zero.
297+ */
298+ final void normalize() {
299+ if (intLen == 0) {
300+ offset = 0;
301+ return;
302+ }
303+
304+ int index = offset;
305+ if (value[index] != 0)
306+ return;
307+
308+ int indexBound = index+intLen;
309+ do {
310+ index++;
311+ } while(index < indexBound && value[index]==0);
312+
313+ int numZeros = index - offset;
314+ intLen -= numZeros;
315+ offset = (intLen==0 ? 0 : offset+numZeros);
316+ }
317+
318+ /**
319+ * If this MutableBigInteger cannot hold len words, increase the size
320+ * of the value array to len words.
321+ */
322+ private final void ensureCapacity(int len) {
323+ if (value.length < len) {
324+ value = new int[len];
325+ offset = 0;
326+ intLen = len;
327+ }
328+ }
329+
330+ /**
331+ * Convert this MutableBigInteger into an int array with no leading
332+ * zeros, of a length that is equal to this MutableBigInteger's intLen.
333+ */
334+ int[] toIntArray() {
335+ int[] result = new int[intLen];
336+ for(int i=0; i<intLen; i++)
337+ result[i] = value[offset+i];
338+ return result;
339+ }
340+
341+ /**
342+ * Sets the int at index+offset in this MutableBigInteger to val.
343+ * This does not get inlined on all platforms so it is not used
344+ * as often as originally intended.
345+ */
346+ void setInt(int index, int val) {
347+ value[offset + index] = val;
348+ }
349+
350+ /**
351+ * Sets this MutableBigInteger's value array to the specified array.
352+ * The intLen is set to the specified length.
353+ */
354+ void setValue(int[] val, int length) {
355+ value = val;
356+ intLen = length;
357+ offset = 0;
358+ }
359+
360+ /**
361+ * Sets this MutableBigInteger's value array to a copy of the specified
362+ * array. The intLen is set to the length of the new array.
363+ */
364+ void copyValue(MutableBigInteger src) {
365+ int len = src.intLen;
366+ if (value.length < len)
367+ value = new int[len];
368+ System.arraycopy(src.value, src.offset, value, 0, len);
369+ intLen = len;
370+ offset = 0;
371+ }
372+
373+ /**
374+ * Sets this MutableBigInteger's value array to a copy of the specified
375+ * array. The intLen is set to the length of the specified array.
376+ */
377+ void copyValue(int[] val) {
378+ int len = val.length;
379+ if (value.length < len)
380+ value = new int[len];
381+ System.arraycopy(val, 0, value, 0, len);
382+ intLen = len;
383+ offset = 0;
384+ }
385+
386+ /**
387+ * Returns true iff this MutableBigInteger has a value of one.
388+ */
389+ boolean isOne() {
390+ return (intLen == 1) && (value[offset] == 1);
391+ }
392+
393+ /**
394+ * Returns true iff this MutableBigInteger has a value of zero.
395+ */
396+ boolean isZero() {
397+ return (intLen == 0);
398+ }
399+
400+ /**
401+ * Returns true iff this MutableBigInteger is even.
402+ */
403+ boolean isEven() {
404+ return (intLen == 0) || ((value[offset + intLen - 1] & 1) == 0);
405+ }
406+
407+ /**
408+ * Returns true iff this MutableBigInteger is odd.
409+ */
410+ boolean isOdd() {
411+ return isZero() ? false : ((value[offset + intLen - 1] & 1) == 1);
412+ }
413+
414+ /**
415+ * Returns true iff this MutableBigInteger is in normal form. A
416+ * MutableBigInteger is in normal form if it has no leading zeros
417+ * after the offset, and intLen + offset <= value.length.
418+ */
419+ boolean isNormal() {
420+ if (intLen + offset > value.length)
421+ return false;
422+ if (intLen ==0)
423+ return true;
424+ return (value[offset] != 0);
425+ }
426+
427+ /**
428+ * Returns a String representation of this MutableBigInteger in radix 10.
429+ */
430+ public String toString() {
431+ BigInteger b = toBigInteger(1);
432+ return b.toString();
433+ }
434+
435+ /**
436+ * Right shift this MutableBigInteger n bits. The MutableBigInteger is left
437+ * in normal form.
438+ */
439+ void rightShift(int n) {
440+ if (intLen == 0)
441+ return;
442+ int nInts = n >>> 5;
443+ int nBits = n & 0x1F;
444+ this.intLen -= nInts;
445+ if (nBits == 0)
446+ return;
447+ int bitsInHighWord = BigInteger.bitLengthForInt(value[offset]);
448+ if (nBits >= bitsInHighWord) {
449+ this.primitiveLeftShift(32 - nBits);
450+ this.intLen--;
451+ } else {
452+ primitiveRightShift(nBits);
453+ }
454+ }
455+
456+ /**
457+ * Left shift this MutableBigInteger n bits.
458+ */
459+ void leftShift(int n) {
460+ /*
461+ * If there is enough storage space in this MutableBigInteger already
462+ * the available space will be used. Space to the right of the used
463+ * ints in the value array is faster to utilize, so the extra space
464+ * will be taken from the right if possible.
465+ */
466+ if (intLen == 0)
467+ return;
468+ int nInts = n >>> 5;
469+ int nBits = n&0x1F;
470+ int bitsInHighWord = BigInteger.bitLengthForInt(value[offset]);
471+
472+ // If shift can be done without moving words, do so
473+ if (n <= (32-bitsInHighWord)) {
474+ primitiveLeftShift(nBits);
475+ return;
476+ }
477+
478+ int newLen = intLen + nInts +1;
479+ if (nBits <= (32-bitsInHighWord))
480+ newLen--;
481+ if (value.length < newLen) {
482+ // The array must grow
483+ int[] result = new int[newLen];
484+ for (int i=0; i<intLen; i++)
485+ result[i] = value[offset+i];
486+ setValue(result, newLen);
487+ } else if (value.length - offset >= newLen) {
488+ // Use space on right
489+ for(int i=0; i<newLen - intLen; i++)
490+ value[offset+intLen+i] = 0;
491+ } else {
492+ // Must use space on left
493+ for (int i=0; i<intLen; i++)
494+ value[i] = value[offset+i];
495+ for (int i=intLen; i<newLen; i++)
496+ value[i] = 0;
497+ offset = 0;
498+ }
499+ intLen = newLen;
500+ if (nBits == 0)
501+ return;
502+ if (nBits <= (32-bitsInHighWord))
503+ primitiveLeftShift(nBits);
504+ else
505+ primitiveRightShift(32 -nBits);
506+ }
507+
508+ /**
509+ * A primitive used for division. This method adds in one multiple of the
510+ * divisor a back to the dividend result at a specified offset. It is used
511+ * when qhat was estimated too large, and must be adjusted.
512+ */
513+ private int divadd(int[] a, int[] result, int offset) {
514+ long carry = 0;
515+
516+ for (int j=a.length-1; j >= 0; j--) {
517+ long sum = (a[j] & LONG_MASK) +
518+ (result[j+offset] & LONG_MASK) + carry;
519+ result[j+offset] = (int)sum;
520+ carry = sum >>> 32;
521+ }
522+ return (int)carry;
523+ }
524+
525+ /**
526+ * This method is used for division. It multiplies an n word input a by one
527+ * word input x, and subtracts the n word product from q. This is needed
528+ * when subtracting qhat*divisor from dividend.
529+ */
530+ private int mulsub(int[] q, int[] a, int x, int len, int offset) {
531+ long xLong = x & LONG_MASK;
532+ long carry = 0;
533+ offset += len;
534+
535+ for (int j=len-1; j >= 0; j--) {
536+ long product = (a[j] & LONG_MASK) * xLong + carry;
537+ long difference = q[offset] - product;
538+ q[offset--] = (int)difference;
539+ carry = (product >>> 32)
540+ + (((difference & LONG_MASK) >
541+ (((~(int)product) & LONG_MASK))) ? 1:0);
542+ }
543+ return (int)carry;
544+ }
545+
546+ /**
547+ * Right shift this MutableBigInteger n bits, where n is
548+ * less than 32.
549+ * Assumes that intLen > 0, n > 0 for speed
550+ */
551+ private final void primitiveRightShift(int n) {
552+ int[] val = value;
553+ int n2 = 32 - n;
554+ for (int i=offset+intLen-1, c=val[i]; i>offset; i--) {
555+ int b = c;
556+ c = val[i-1];
557+ val[i] = (c << n2) | (b >>> n);
558+ }
559+ val[offset] >>>= n;
560+ }
561+
562+ /**
563+ * Left shift this MutableBigInteger n bits, where n is
564+ * less than 32.
565+ * Assumes that intLen > 0, n > 0 for speed
566+ */
567+ private final void primitiveLeftShift(int n) {
568+ int[] val = value;
569+ int n2 = 32 - n;
570+ for (int i=offset, c=val[i], m=i+intLen-1; i<m; i++) {
571+ int b = c;
572+ c = val[i+1];
573+ val[i] = (b << n) | (c >>> n2);
574+ }
575+ val[offset+intLen-1] <<= n;
576+ }
577+
578+ /**
579+ * Adds the contents of two MutableBigInteger objects.The result
580+ * is placed within this MutableBigInteger.
581+ * The contents of the addend are not changed.
582+ */
583+ void add(MutableBigInteger addend) {
584+ int x = intLen;
585+ int y = addend.intLen;
586+ int resultLen = (intLen > addend.intLen ? intLen : addend.intLen);
587+ int[] result = (value.length < resultLen ? new int[resultLen] : value);
588+
589+ int rstart = result.length-1;
590+ long sum;
591+ long carry = 0;
592+
593+ // Add common parts of both numbers
594+ while(x>0 && y>0) {
595+ x--; y--;
596+ sum = (value[x+offset] & LONG_MASK) +
597+ (addend.value[y+addend.offset] & LONG_MASK) + carry;
598+ result[rstart--] = (int)sum;
599+ carry = sum >>> 32;
600+ }
601+
602+ // Add remainder of the longer number
603+ while(x>0) {
604+ x--;
605+ if (carry == 0 && result == value && rstart == (x + offset))
606+ return;
607+ sum = (value[x+offset] & LONG_MASK) + carry;
608+ result[rstart--] = (int)sum;
609+ carry = sum >>> 32;
610+ }
611+ while(y>0) {
612+ y--;
613+ sum = (addend.value[y+addend.offset] & LONG_MASK) + carry;
614+ result[rstart--] = (int)sum;
615+ carry = sum >>> 32;
616+ }
617+
618+ if (carry > 0) { // Result must grow in length
619+ resultLen++;
620+ if (result.length < resultLen) {
621+ int temp[] = new int[resultLen];
622+ // Result one word longer from carry-out; copy low-order
623+ // bits into new result.
624+ System.arraycopy(result, 0, temp, 1, result.length);
625+ temp[0] = 1;
626+ result = temp;
627+ } else {
628+ result[rstart--] = 1;
629+ }
630+ }
631+
632+ value = result;
633+ intLen = resultLen;
634+ offset = result.length - resultLen;
635+ }
636+
637+
638+ /**
639+ * Subtracts the smaller of this and b from the larger and places the
640+ * result into this MutableBigInteger.
641+ */
642+ int subtract(MutableBigInteger b) {
643+ MutableBigInteger a = this;
644+
645+ int[] result = value;
646+ int sign = a.compare(b);
647+
648+ if (sign == 0) {
649+ reset();
650+ return 0;
651+ }
652+ if (sign < 0) {
653+ MutableBigInteger tmp = a;
654+ a = b;
655+ b = tmp;
656+ }
657+
658+ int resultLen = a.intLen;
659+ if (result.length < resultLen)
660+ result = new int[resultLen];
661+
662+ long diff = 0;
663+ int x = a.intLen;
664+ int y = b.intLen;
665+ int rstart = result.length - 1;
666+
667+ // Subtract common parts of both numbers
668+ while (y>0) {
669+ x--; y--;
670+
671+ diff = (a.value[x+a.offset] & LONG_MASK) -
672+ (b.value[y+b.offset] & LONG_MASK) - ((int)-(diff>>32));
673+ result[rstart--] = (int)diff;
674+ }
675+ // Subtract remainder of longer number
676+ while (x>0) {
677+ x--;
678+ diff = (a.value[x+a.offset] & LONG_MASK) - ((int)-(diff>>32));
679+ result[rstart--] = (int)diff;
680+ }
681+
682+ value = result;
683+ intLen = resultLen;
684+ offset = value.length - resultLen;
685+ normalize();
686+ return sign;
687+ }
688+
689+ /**
690+ * Subtracts the smaller of a and b from the larger and places the result
691+ * into the larger. Returns 1 if the answer is in a, -1 if in b, 0 if no
692+ * operation was performed.
693+ */
694+ private int difference(MutableBigInteger b) {
695+ MutableBigInteger a = this;
696+ int sign = a.compare(b);
697+ if (sign ==0)
698+ return 0;
699+ if (sign < 0) {
700+ MutableBigInteger tmp = a;
701+ a = b;
702+ b = tmp;
703+ }
704+
705+ long diff = 0;
706+ int x = a.intLen;
707+ int y = b.intLen;
708+
709+ // Subtract common parts of both numbers
710+ while (y>0) {
711+ x--; y--;
712+ diff = (a.value[a.offset+ x] & LONG_MASK) -
713+ (b.value[b.offset+ y] & LONG_MASK) - ((int)-(diff>>32));
714+ a.value[a.offset+x] = (int)diff;
715+ }
716+ // Subtract remainder of longer number
717+ while (x>0) {
718+ x--;
719+ diff = (a.value[a.offset+ x] & LONG_MASK) - ((int)-(diff>>32));
720+ a.value[a.offset+x] = (int)diff;
721+ }
722+
723+ a.normalize();
724+ return sign;
725+ }
726+
727+ /**
728+ * Multiply the contents of two MutableBigInteger objects. The result is
729+ * placed into MutableBigInteger z. The contents of y are not changed.
730+ */
731+ void multiply(MutableBigInteger y, MutableBigInteger z) {
732+ int xLen = intLen;
733+ int yLen = y.intLen;
734+ int newLen = xLen + yLen;
735+
736+ // Put z into an appropriate state to receive product
737+ if (z.value.length < newLen)
738+ z.value = new int[newLen];
739+ z.offset = 0;
740+ z.intLen = newLen;
741+
742+ // The first iteration is hoisted out of the loop to avoid extra add
743+ long carry = 0;
744+ for (int j=yLen-1, k=yLen+xLen-1; j >= 0; j--, k--) {
745+ long product = (y.value[j+y.offset] & LONG_MASK) *
746+ (value[xLen-1+offset] & LONG_MASK) + carry;
747+ z.value[k] = (int)product;
748+ carry = product >>> 32;
749+ }
750+ z.value[xLen-1] = (int)carry;
751+
752+ // Perform the multiplication word by word
753+ for (int i = xLen-2; i >= 0; i--) {
754+ carry = 0;
755+ for (int j=yLen-1, k=yLen+i; j >= 0; j--, k--) {
756+ long product = (y.value[j+y.offset] & LONG_MASK) *
757+ (value[i+offset] & LONG_MASK) +
758+ (z.value[k] & LONG_MASK) + carry;
759+ z.value[k] = (int)product;
760+ carry = product >>> 32;
761+ }
762+ z.value[i] = (int)carry;
763+ }
764+
765+ // Remove leading zeros from product
766+ z.normalize();
767+ }
768+
769+ /**
770+ * Multiply the contents of this MutableBigInteger by the word y. The
771+ * result is placed into z.
772+ */
773+ void mul(int y, MutableBigInteger z) {
774+ if (y == 1) {
775+ z.copyValue(this);
776+ return;
777+ }
778+
779+ if (y == 0) {
780+ z.clear();
781+ return;
782+ }
783+
784+ // Perform the multiplication word by word
785+ long ylong = y & LONG_MASK;
786+ int[] zval = (z.value.length<intLen+1 ? new int[intLen + 1]
787+ : z.value);
788+ long carry = 0;
789+ for (int i = intLen-1; i >= 0; i--) {
790+ long product = ylong * (value[i+offset] & LONG_MASK) + carry;
791+ zval[i+1] = (int)product;
792+ carry = product >>> 32;
793+ }
794+
795+ if (carry == 0) {
796+ z.offset = 1;
797+ z.intLen = intLen;
798+ } else {
799+ z.offset = 0;
800+ z.intLen = intLen + 1;
801+ zval[0] = (int)carry;
802+ }
803+ z.value = zval;
804+ }
805+
806+ /**
807+ * This method is used for division of an n word dividend by a one word
808+ * divisor. The quotient is placed into quotient. The one word divisor is
809+ * specified by divisor.
810+ *
811+ * @return the remainder of the division is returned.
812+ *
813+ */
814+ int divideOneWord(int divisor, MutableBigInteger quotient) {
815+ long divisorLong = divisor & LONG_MASK;
816+
817+ // Special case of one word dividend
818+ if (intLen == 1) {
819+ long dividendValue = value[offset] & LONG_MASK;
820+ int q = (int) (dividendValue / divisorLong);
821+ int r = (int) (dividendValue - q * divisorLong);
822+ quotient.value[0] = q;
823+ quotient.intLen = (q == 0) ? 0 : 1;
824+ quotient.offset = 0;
825+ return r;
826+ }
827+
828+ if (quotient.value.length < intLen)
829+ quotient.value = new int[intLen];
830+ quotient.offset = 0;
831+ quotient.intLen = intLen;
832+
833+ // Normalize the divisor
834+ int shift = Integer.numberOfLeadingZeros(divisor);
835+
836+ int rem = value[offset];
837+ long remLong = rem & LONG_MASK;
838+ if (remLong < divisorLong) {
839+ quotient.value[0] = 0;
840+ } else {
841+ quotient.value[0] = (int)(remLong / divisorLong);
842+ rem = (int) (remLong - (quotient.value[0] * divisorLong));
843+ remLong = rem & LONG_MASK;
844+ }
845+
846+ int xlen = intLen;
847+ int[] qWord = new int[2];
848+ while (--xlen > 0) {
849+ long dividendEstimate = (remLong<<32) |
850+ (value[offset + intLen - xlen] & LONG_MASK);
851+ if (dividendEstimate >= 0) {
852+ qWord[0] = (int) (dividendEstimate / divisorLong);
853+ qWord[1] = (int) (dividendEstimate - qWord[0] * divisorLong);
854+ } else {
855+ divWord(qWord, dividendEstimate, divisor);
856+ }
857+ quotient.value[intLen - xlen] = qWord[0];
858+ rem = qWord[1];
859+ remLong = rem & LONG_MASK;
860+ }
861+
862+ quotient.normalize();
863+ // Unnormalize
864+ if (shift > 0)
865+ return rem % divisor;
866+ else
867+ return rem;
868+ }
869+
870+ /**
871+ * Calculates the quotient of this div b and places the quotient in the
872+ * provided MutableBigInteger objects and the remainder object is returned.
873+ *
874+ * Uses Algorithm D in Knuth section 4.3.1.
875+ * Many optimizations to that algorithm have been adapted from the Colin
876+ * Plumb C library.
877+ * It special cases one word divisors for speed. The content of b is not
878+ * changed.
879+ *
880+ */
881+ MutableBigInteger divide(MutableBigInteger b, MutableBigInteger quotient) {
882+ if (b.intLen == 0)
883+ throw new ArithmeticException("BigInteger divide by zero");
884+
885+ // Dividend is zero
886+ if (intLen == 0) {
887+ quotient.intLen = quotient.offset;
888+ return new MutableBigInteger();
889+ }
890+
891+ int cmp = compare(b);
892+ // Dividend less than divisor
893+ if (cmp < 0) {
894+ quotient.intLen = quotient.offset = 0;
895+ return new MutableBigInteger(this);
896+ }
897+ // Dividend equal to divisor
898+ if (cmp == 0) {
899+ quotient.value[0] = quotient.intLen = 1;
900+ quotient.offset = 0;
901+ return new MutableBigInteger();
902+ }
903+
904+ quotient.clear();
905+ // Special case one word divisor
906+ if (b.intLen == 1) {
907+ int r = divideOneWord(b.value[b.offset], quotient);
908+ if (r == 0)
909+ return new MutableBigInteger();
910+ return new MutableBigInteger(r);
911+ }
912+
913+ // Copy divisor value to protect divisor
914+ int[] div = Arrays.copyOfRange(b.value, b.offset, b.offset + b.intLen);
915+ return divideMagnitude(div, quotient);
916+ }
917+
918+ /**
919+ * Internally used to calculate the quotient of this div v and places the
920+ * quotient in the provided MutableBigInteger object and the remainder is
921+ * returned.
922+ *
923+ * @return the remainder of the division will be returned.
924+ */
925+ long divide(long v, MutableBigInteger quotient) {
926+ if (v == 0)
927+ throw new ArithmeticException("BigInteger divide by zero");
928+
929+ // Dividend is zero
930+ if (intLen == 0) {
931+ quotient.intLen = quotient.offset = 0;
932+ return 0;
933+ }
934+ if (v < 0)
935+ v = -v;
936+
937+ int d = (int)(v >>> 32);
938+ quotient.clear();
939+ // Special case on word divisor
940+ if (d == 0)
941+ return divideOneWord((int)v, quotient) & LONG_MASK;
942+ else {
943+ int[] div = new int[]{ d, (int)(v & LONG_MASK) };
944+ return divideMagnitude(div, quotient).toLong();
945+ }
946+ }
947+
948+ /**
949+ * Divide this MutableBigInteger by the divisor represented by its magnitude
950+ * array. The quotient will be placed into the provided quotient object &
951+ * the remainder object is returned.
952+ */
953+ private MutableBigInteger divideMagnitude(int[] divisor,
954+ MutableBigInteger quotient) {
955+
956+ // Remainder starts as dividend with space for a leading zero
957+ MutableBigInteger rem = new MutableBigInteger(new int[intLen + 1]);
958+ System.arraycopy(value, offset, rem.value, 1, intLen);
959+ rem.intLen = intLen;
960+ rem.offset = 1;
961+
962+ int nlen = rem.intLen;
963+
964+ // Set the quotient size
965+ int dlen = divisor.length;
966+ int limit = nlen - dlen + 1;
967+ if (quotient.value.length < limit) {
968+ quotient.value = new int[limit];
969+ quotient.offset = 0;
970+ }
971+ quotient.intLen = limit;
972+ int[] q = quotient.value;
973+
974+ // D1 normalize the divisor
975+ int shift = Integer.numberOfLeadingZeros(divisor[0]);
976+ if (shift > 0) {
977+ // First shift will not grow array
978+ BigInteger.primitiveLeftShift(divisor, dlen, shift);
979+ // But this one might
980+ rem.leftShift(shift);
981+ }
982+
983+ // Must insert leading 0 in rem if its length did not change
984+ if (rem.intLen == nlen) {
985+ rem.offset = 0;
986+ rem.value[0] = 0;
987+ rem.intLen++;
988+ }
989+
990+ int dh = divisor[0];
991+ long dhLong = dh & LONG_MASK;
992+ int dl = divisor[1];
993+ int[] qWord = new int[2];
994+
995+ // D2 Initialize j
996+ for(int j=0; j<limit; j++) {
997+ // D3 Calculate qhat
998+ // estimate qhat
999+ int qhat = 0;
1000+ int qrem = 0;
1001+ boolean skipCorrection = false;
1002+ int nh = rem.value[j+rem.offset];
1003+ int nh2 = nh + 0x80000000;
1004+ int nm = rem.value[j+1+rem.offset];
1005+
1006+ if (nh == dh) {
1007+ qhat = ~0;
1008+ qrem = nh + nm;
1009+ skipCorrection = qrem + 0x80000000 < nh2;
1010+ } else {
1011+ long nChunk = (((long)nh) << 32) | (nm & LONG_MASK);
1012+ if (nChunk >= 0) {
1013+ qhat = (int) (nChunk / dhLong);
1014+ qrem = (int) (nChunk - (qhat * dhLong));
1015+ } else {
1016+ divWord(qWord, nChunk, dh);
1017+ qhat = qWord[0];
1018+ qrem = qWord[1];
1019+ }
1020+ }
1021+
1022+ if (qhat == 0)
1023+ continue;
1024+
1025+ if (!skipCorrection) { // Correct qhat
1026+ long nl = rem.value[j+2+rem.offset] & LONG_MASK;
1027+ long rs = ((qrem & LONG_MASK) << 32) | nl;
1028+ long estProduct = (dl & LONG_MASK) * (qhat & LONG_MASK);
1029+
1030+ if (unsignedLongCompare(estProduct, rs)) {
1031+ qhat--;
1032+ qrem = (int)((qrem & LONG_MASK) + dhLong);
1033+ if ((qrem & LONG_MASK) >= dhLong) {
1034+ estProduct -= (dl & LONG_MASK);
1035+ rs = ((qrem & LONG_MASK) << 32) | nl;
1036+ if (unsignedLongCompare(estProduct, rs))
1037+ qhat--;
1038+ }
1039+ }
1040+ }
1041+
1042+ // D4 Multiply and subtract
1043+ rem.value[j+rem.offset] = 0;
1044+ int borrow = mulsub(rem.value, divisor, qhat, dlen, j+rem.offset);
1045+
1046+ // D5 Test remainder
1047+ if (borrow + 0x80000000 > nh2) {
1048+ // D6 Add back
1049+ divadd(divisor, rem.value, j+1+rem.offset);
1050+ qhat--;
1051+ }
1052+
1053+ // Store the quotient digit
1054+ q[j] = qhat;
1055+ } // D7 loop on j
1056+
1057+ // D8 Unnormalize
1058+ if (shift > 0)
1059+ rem.rightShift(shift);
1060+
1061+ quotient.normalize();
1062+ rem.normalize();
1063+ return rem;
1064+ }
1065+
1066+ /**
1067+ * Compare two longs as if they were unsigned.
1068+ * Returns true iff one is bigger than two.
1069+ */
1070+ private boolean unsignedLongCompare(long one, long two) {
1071+ return (one+Long.MIN_VALUE) > (two+Long.MIN_VALUE);
1072+ }
1073+
1074+ /**
1075+ * This method divides a long quantity by an int to estimate
1076+ * qhat for two multi precision numbers. It is used when
1077+ * the signed value of n is less than zero.
1078+ */
1079+ private void divWord(int[] result, long n, int d) {
1080+ long dLong = d & LONG_MASK;
1081+
1082+ if (dLong == 1) {
1083+ result[0] = (int)n;
1084+ result[1] = 0;
1085+ return;
1086+ }
1087+
1088+ // Approximate the quotient and remainder
1089+ long q = (n >>> 1) / (dLong >>> 1);
1090+ long r = n - q*dLong;
1091+
1092+ // Correct the approximation
1093+ while (r < 0) {
1094+ r += dLong;
1095+ q--;
1096+ }
1097+ while (r >= dLong) {
1098+ r -= dLong;
1099+ q++;
1100+ }
1101+
1102+ // n - q*dlong == r && 0 <= r <dLong, hence we're done.
1103+ result[0] = (int)q;
1104+ result[1] = (int)r;
1105+ }
1106+
1107+ /**
1108+ * Calculate GCD of this and b. This and b are changed by the computation.
1109+ */
1110+ MutableBigInteger hybridGCD(MutableBigInteger b) {
1111+ // Use Euclid's algorithm until the numbers are approximately the
1112+ // same length, then use the binary GCD algorithm to find the GCD.
1113+ MutableBigInteger a = this;
1114+ MutableBigInteger q = new MutableBigInteger();
1115+
1116+ while (b.intLen != 0) {
1117+ if (Math.abs(a.intLen - b.intLen) < 2)
1118+ return a.binaryGCD(b);
1119+
1120+ MutableBigInteger r = a.divide(b, q);
1121+ a = b;
1122+ b = r;
1123+ }
1124+ return a;
1125+ }
1126+
1127+ /**
1128+ * Calculate GCD of this and v.
1129+ * Assumes that this and v are not zero.
1130+ */
1131+ private MutableBigInteger binaryGCD(MutableBigInteger v) {
1132+ // Algorithm B from Knuth section 4.5.2
1133+ MutableBigInteger u = this;
1134+ MutableBigInteger r = new MutableBigInteger();
1135+
1136+ // step B1
1137+ int s1 = u.getLowestSetBit();
1138+ int s2 = v.getLowestSetBit();
1139+ int k = (s1 < s2) ? s1 : s2;
1140+ if (k != 0) {
1141+ u.rightShift(k);
1142+ v.rightShift(k);
1143+ }
1144+
1145+ // step B2
1146+ boolean uOdd = (k==s1);
1147+ MutableBigInteger t = uOdd ? v: u;
1148+ int tsign = uOdd ? -1 : 1;
1149+
1150+ int lb;
1151+ while ((lb = t.getLowestSetBit()) >= 0) {
1152+ // steps B3 and B4
1153+ t.rightShift(lb);
1154+ // step B5
1155+ if (tsign > 0)
1156+ u = t;
1157+ else
1158+ v = t;
1159+
1160+ // Special case one word numbers
1161+ if (u.intLen < 2 && v.intLen < 2) {
1162+ int x = u.value[u.offset];
1163+ int y = v.value[v.offset];
1164+ x = binaryGcd(x, y);
1165+ r.value[0] = x;
1166+ r.intLen = 1;
1167+ r.offset = 0;
1168+ if (k > 0)
1169+ r.leftShift(k);
1170+ return r;
1171+ }
1172+
1173+ // step B6
1174+ if ((tsign = u.difference(v)) == 0)
1175+ break;
1176+ t = (tsign >= 0) ? u : v;
1177+ }
1178+
1179+ if (k > 0)
1180+ u.leftShift(k);
1181+ return u;
1182+ }
1183+
1184+ /**
1185+ * Calculate GCD of a and b interpreted as unsigned integers.
1186+ */
1187+ static int binaryGcd(int a, int b) {
1188+ if (b==0)
1189+ return a;
1190+ if (a==0)
1191+ return b;
1192+
1193+ // Right shift a & b till their last bits equal to 1.
1194+ int aZeros = Integer.numberOfTrailingZeros(a);
1195+ int bZeros = Integer.numberOfTrailingZeros(b);
1196+ a >>>= aZeros;
1197+ b >>>= bZeros;
1198+
1199+ int t = (aZeros < bZeros ? aZeros : bZeros);
1200+
1201+ while (a != b) {
1202+ if ((a+0x80000000) > (b+0x80000000)) { // a > b as unsigned
1203+ a -= b;
1204+ a >>>= Integer.numberOfTrailingZeros(a);
1205+ } else {
1206+ b -= a;
1207+ b >>>= Integer.numberOfTrailingZeros(b);
1208+ }
1209+ }
1210+ return a<<t;
1211+ }
1212+
1213+ /**
1214+ * Returns the modInverse of this mod p. This and p are not affected by
1215+ * the operation.
1216+ */
1217+ MutableBigInteger mutableModInverse(MutableBigInteger p) {
1218+ // Modulus is odd, use Schroeppel's algorithm
1219+ if (p.isOdd())
1220+ return modInverse(p);
1221+
1222+ // Base and modulus are even, throw exception
1223+ if (isEven())
1224+ throw new ArithmeticException("BigInteger not invertible.");
1225+
1226+ // Get even part of modulus expressed as a power of 2
1227+ int powersOf2 = p.getLowestSetBit();
1228+
1229+ // Construct odd part of modulus
1230+ MutableBigInteger oddMod = new MutableBigInteger(p);
1231+ oddMod.rightShift(powersOf2);
1232+
1233+ if (oddMod.isOne())
1234+ return modInverseMP2(powersOf2);
1235+
1236+ // Calculate 1/a mod oddMod
1237+ MutableBigInteger oddPart = modInverse(oddMod);
1238+
1239+ // Calculate 1/a mod evenMod
1240+ MutableBigInteger evenPart = modInverseMP2(powersOf2);
1241+
1242+ // Combine the results using Chinese Remainder Theorem
1243+ MutableBigInteger y1 = modInverseBP2(oddMod, powersOf2);
1244+ MutableBigInteger y2 = oddMod.modInverseMP2(powersOf2);
1245+
1246+ MutableBigInteger temp1 = new MutableBigInteger();
1247+ MutableBigInteger temp2 = new MutableBigInteger();
1248+ MutableBigInteger result = new MutableBigInteger();
1249+
1250+ oddPart.leftShift(powersOf2);
1251+ oddPart.multiply(y1, result);
1252+
1253+ evenPart.multiply(oddMod, temp1);
1254+ temp1.multiply(y2, temp2);
1255+
1256+ result.add(temp2);
1257+ return result.divide(p, temp1);
1258+ }
1259+
1260+ /*
1261+ * Calculate the multiplicative inverse of this mod 2^k.
1262+ */
1263+ MutableBigInteger modInverseMP2(int k) {
1264+ if (isEven())
1265+ throw new ArithmeticException("Non-invertible. (GCD != 1)");
1266+
1267+ if (k > 64)
1268+ return euclidModInverse(k);
1269+
1270+ int t = inverseMod32(value[offset+intLen-1]);
1271+
1272+ if (k < 33) {
1273+ t = (k == 32 ? t : t & ((1 << k) - 1));
1274+ return new MutableBigInteger(t);
1275+ }
1276+
1277+ long pLong = (value[offset+intLen-1] & LONG_MASK);
1278+ if (intLen > 1)
1279+ pLong |= ((long)value[offset+intLen-2] << 32);
1280+ long tLong = t & LONG_MASK;
1281+ tLong = tLong * (2 - pLong * tLong); // 1 more Newton iter step
1282+ tLong = (k == 64 ? tLong : tLong & ((1L << k) - 1));
1283+
1284+ MutableBigInteger result = new MutableBigInteger(new int[2]);
1285+ result.value[0] = (int)(tLong >>> 32);
1286+ result.value[1] = (int)tLong;
1287+ result.intLen = 2;
1288+ result.normalize();
1289+ return result;
1290+ }
1291+
1292+ /*
1293+ * Returns the multiplicative inverse of val mod 2^32. Assumes val is odd.
1294+ */
1295+ static int inverseMod32(int val) {
1296+ // Newton's iteration!
1297+ int t = val;
1298+ t *= 2 - val*t;
1299+ t *= 2 - val*t;
1300+ t *= 2 - val*t;
1301+ t *= 2 - val*t;
1302+ return t;
1303+ }
1304+
1305+ /*
1306+ * Calculate the multiplicative inverse of 2^k mod mod, where mod is odd.
1307+ */
1308+ static MutableBigInteger modInverseBP2(MutableBigInteger mod, int k) {
1309+ // Copy the mod to protect original
1310+ return fixup(new MutableBigInteger(1), new MutableBigInteger(mod), k);
1311+ }
1312+
1313+ /**
1314+ * Calculate the multiplicative inverse of this mod mod, where mod is odd.
1315+ * This and mod are not changed by the calculation.
1316+ *
1317+ * This method implements an algorithm due to Richard Schroeppel, that uses
1318+ * the same intermediate representation as Montgomery Reduction
1319+ * ("Montgomery Form"). The algorithm is described in an unpublished
1320+ * manuscript entitled "Fast Modular Reciprocals."
1321+ */
1322+ private MutableBigInteger modInverse(MutableBigInteger mod) {
1323+ MutableBigInteger p = new MutableBigInteger(mod);
1324+ MutableBigInteger f = new MutableBigInteger(this);
1325+ MutableBigInteger g = new MutableBigInteger(p);
1326+ SignedMutableBigInteger c = new SignedMutableBigInteger(1);
1327+ SignedMutableBigInteger d = new SignedMutableBigInteger();
1328+ MutableBigInteger temp = null;
1329+ SignedMutableBigInteger sTemp = null;
1330+
1331+ int k = 0;
1332+ // Right shift f k times until odd, left shift d k times
1333+ if (f.isEven()) {
1334+ int trailingZeros = f.getLowestSetBit();
1335+ f.rightShift(trailingZeros);
1336+ d.leftShift(trailingZeros);
1337+ k = trailingZeros;
1338+ }
1339+
1340+ // The Almost Inverse Algorithm
1341+ while(!f.isOne()) {
1342+ // If gcd(f, g) != 1, number is not invertible modulo mod
1343+ if (f.isZero())
1344+ throw new ArithmeticException("BigInteger not invertible.");
1345+
1346+ // If f < g exchange f, g and c, d
1347+ if (f.compare(g) < 0) {
1348+ temp = f; f = g; g = temp;
1349+ sTemp = d; d = c; c = sTemp;
1350+ }
1351+
1352+ // If f == g (mod 4)
1353+ if (((f.value[f.offset + f.intLen - 1] ^
1354+ g.value[g.offset + g.intLen - 1]) & 3) == 0) {
1355+ f.subtract(g);
1356+ c.signedSubtract(d);
1357+ } else { // If f != g (mod 4)
1358+ f.add(g);
1359+ c.signedAdd(d);
1360+ }
1361+
1362+ // Right shift f k times until odd, left shift d k times
1363+ int trailingZeros = f.getLowestSetBit();
1364+ f.rightShift(trailingZeros);
1365+ d.leftShift(trailingZeros);
1366+ k += trailingZeros;
1367+ }
1368+
1369+ while (c.sign < 0)
1370+ c.signedAdd(p);
1371+
1372+ return fixup(c, p, k);
1373+ }
1374+
1375+ /*
1376+ * The Fixup Algorithm
1377+ * Calculates X such that X = C * 2^(-k) (mod P)
1378+ * Assumes C<P and P is odd.
1379+ */
1380+ static MutableBigInteger fixup(MutableBigInteger c, MutableBigInteger p,
1381+ int k) {
1382+ MutableBigInteger temp = new MutableBigInteger();
1383+ // Set r to the multiplicative inverse of p mod 2^32
1384+ int r = -inverseMod32(p.value[p.offset+p.intLen-1]);
1385+
1386+ for(int i=0, numWords = k >> 5; i<numWords; i++) {
1387+ // V = R * c (mod 2^j)
1388+ int v = r * c.value[c.offset + c.intLen-1];
1389+ // c = c + (v * p)
1390+ p.mul(v, temp);
1391+ c.add(temp);
1392+ // c = c / 2^j
1393+ c.intLen--;
1394+ }
1395+ int numBits = k & 0x1f;
1396+ if (numBits != 0) {
1397+ // V = R * c (mod 2^j)
1398+ int v = r * c.value[c.offset + c.intLen-1];
1399+ v &= ((1<<numBits) - 1);
1400+ // c = c + (v * p)
1401+ p.mul(v, temp);
1402+ c.add(temp);
1403+ // c = c / 2^j
1404+ c.rightShift(numBits);
1405+ }
1406+
1407+ // In theory, c may be greater than p at this point (Very rare!)
1408+ while (c.compare(p) >= 0)
1409+ c.subtract(p);
1410+
1411+ return c;
1412+ }
1413+
1414+ /**
1415+ * Uses the extended Euclidean algorithm to compute the modInverse of base
1416+ * mod a modulus that is a power of 2. The modulus is 2^k.
1417+ */
1418+ MutableBigInteger euclidModInverse(int k) {
1419+ MutableBigInteger b = new MutableBigInteger(1);
1420+ b.leftShift(k);
1421+ MutableBigInteger mod = new MutableBigInteger(b);
1422+
1423+ MutableBigInteger a = new MutableBigInteger(this);
1424+ MutableBigInteger q = new MutableBigInteger();
1425+ MutableBigInteger r = b.divide(a, q);
1426+
1427+ MutableBigInteger swapper = b;
1428+ // swap b & r
1429+ b = r;
1430+ r = swapper;
1431+
1432+ MutableBigInteger t1 = new MutableBigInteger(q);
1433+ MutableBigInteger t0 = new MutableBigInteger(1);
1434+ MutableBigInteger temp = new MutableBigInteger();
1435+
1436+ while (!b.isOne()) {
1437+ r = a.divide(b, q);
1438+
1439+ if (r.intLen == 0)
1440+ throw new ArithmeticException("BigInteger not invertible.");
1441+
1442+ swapper = r;
1443+ a = swapper;
1444+
1445+ if (q.intLen == 1)
1446+ t1.mul(q.value[q.offset], temp);
1447+ else
1448+ q.multiply(t1, temp);
1449+ swapper = q;
1450+ q = temp;
1451+ temp = swapper;
1452+ t0.add(q);
1453+
1454+ if (a.isOne())
1455+ return t0;
1456+
1457+ r = b.divide(a, q);
1458+
1459+ if (r.intLen == 0)
1460+ throw new ArithmeticException("BigInteger not invertible.");
1461+
1462+ swapper = b;
1463+ b = r;
1464+
1465+ if (q.intLen == 1)
1466+ t0.mul(q.value[q.offset], temp);
1467+ else
1468+ q.multiply(t0, temp);
1469+ swapper = q; q = temp; temp = swapper;
1470+
1471+ t1.add(q);
1472+ }
1473+ mod.subtract(t1);
1474+ return mod;
1475+ }
1476+
1477+}
java/pkg/java/math/RoundingMode.class+0−0

Binary file not shown.

java/pkg/java/math/RoundingMode.java+349−0
@@ -0,0 +1,349 @@
1+/*
2+ * Copyright (c) 2003, 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+package java.math;
30+
31+/**
32+ * Specifies a <i>rounding behavior</i> for numerical operations
33+ * capable of discarding precision. Each rounding mode indicates how
34+ * the least significant returned digit of a rounded result is to be
35+ * calculated. If fewer digits are returned than the digits needed to
36+ * represent the exact numerical result, the discarded digits will be
37+ * referred to as the <i>discarded fraction</i> regardless the digits'
38+ * contribution to the value of the number. In other words,
39+ * considered as a numerical value, the discarded fraction could have
40+ * an absolute value greater than one.
41+ *
42+ * <p>Each rounding mode description includes a table listing how
43+ * different two-digit decimal values would round to a one digit
44+ * decimal value under the rounding mode in question. The result
45+ * column in the tables could be gotten by creating a
46+ * {@code BigDecimal} number with the specified value, forming a
47+ * {@link MathContext} object with the proper settings
48+ * ({@code precision} set to {@code 1}, and the
49+ * {@code roundingMode} set to the rounding mode in question), and
50+ * calling {@link BigDecimal#round round} on this number with the
51+ * proper {@code MathContext}. A summary table showing the results
52+ * of these rounding operations for all rounding modes appears below.
53+ *
54+ *<p>
55+ *<table border>
56+ * <caption><b>Summary of Rounding Operations Under Different Rounding Modes</b></caption>
57+ * <tr><th></th><th colspan=8>Result of rounding input to one digit with the given
58+ * rounding mode</th>
59+ * <tr valign=top>
60+ * <th>Input Number</th> <th>{@code UP}</th>
61+ * <th>{@code DOWN}</th>
62+ * <th>{@code CEILING}</th>
63+ * <th>{@code FLOOR}</th>
64+ * <th>{@code HALF_UP}</th>
65+ * <th>{@code HALF_DOWN}</th>
66+ * <th>{@code HALF_EVEN}</th>
67+ * <th>{@code UNNECESSARY}</th>
68+ *
69+ * <tr align=right><td>5.5</td> <td>6</td> <td>5</td> <td>6</td> <td>5</td> <td>6</td> <td>5</td> <td>6</td> <td>throw {@code ArithmeticException}</td>
70+ * <tr align=right><td>2.5</td> <td>3</td> <td>2</td> <td>3</td> <td>2</td> <td>3</td> <td>2</td> <td>2</td> <td>throw {@code ArithmeticException}</td>
71+ * <tr align=right><td>1.6</td> <td>2</td> <td>1</td> <td>2</td> <td>1</td> <td>2</td> <td>2</td> <td>2</td> <td>throw {@code ArithmeticException}</td>
72+ * <tr align=right><td>1.1</td> <td>2</td> <td>1</td> <td>2</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>throw {@code ArithmeticException}</td>
73+ * <tr align=right><td>1.0</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td>
74+ * <tr align=right><td>-1.0</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>-1</td>
75+ * <tr align=right><td>-1.1</td> <td>-2</td> <td>-1</td> <td>-1</td> <td>-2</td> <td>-1</td> <td>-1</td> <td>-1</td> <td>throw {@code ArithmeticException}</td>
76+ * <tr align=right><td>-1.6</td> <td>-2</td> <td>-1</td> <td>-1</td> <td>-2</td> <td>-2</td> <td>-2</td> <td>-2</td> <td>throw {@code ArithmeticException}</td>
77+ * <tr align=right><td>-2.5</td> <td>-3</td> <td>-2</td> <td>-2</td> <td>-3</td> <td>-3</td> <td>-2</td> <td>-2</td> <td>throw {@code ArithmeticException}</td>
78+ * <tr align=right><td>-5.5</td> <td>-6</td> <td>-5</td> <td>-5</td> <td>-6</td> <td>-6</td> <td>-5</td> <td>-6</td> <td>throw {@code ArithmeticException}</td>
79+ *</table>
80+ *
81+ *
82+ * <p>This {@code enum} is intended to replace the integer-based
83+ * enumeration of rounding mode constants in {@link BigDecimal}
84+ * ({@link BigDecimal#ROUND_UP}, {@link BigDecimal#ROUND_DOWN},
85+ * etc. ).
86+ *
87+ * @see BigDecimal
88+ * @see MathContext
89+ * @author Josh Bloch
90+ * @author Mike Cowlishaw
91+ * @author Joseph D. Darcy
92+ * @since 1.5
93+ */
94+public enum RoundingMode {
95+
96+ /**
97+ * Rounding mode to round away from zero. Always increments the
98+ * digit prior to a non-zero discarded fraction. Note that this
99+ * rounding mode never decreases the magnitude of the calculated
100+ * value.
101+ *
102+ *<p>Example:
103+ *<table border>
104+ *<tr valign=top><th>Input Number</th>
105+ * <th>Input rounded to one digit<br> with {@code UP} rounding
106+ *<tr align=right><td>5.5</td> <td>6</td>
107+ *<tr align=right><td>2.5</td> <td>3</td>
108+ *<tr align=right><td>1.6</td> <td>2</td>
109+ *<tr align=right><td>1.1</td> <td>2</td>
110+ *<tr align=right><td>1.0</td> <td>1</td>
111+ *<tr align=right><td>-1.0</td> <td>-1</td>
112+ *<tr align=right><td>-1.1</td> <td>-2</td>
113+ *<tr align=right><td>-1.6</td> <td>-2</td>
114+ *<tr align=right><td>-2.5</td> <td>-3</td>
115+ *<tr align=right><td>-5.5</td> <td>-6</td>
116+ *</table>
117+ */
118+ UP(BigDecimal.ROUND_UP),
119+
120+ /**
121+ * Rounding mode to round towards zero. Never increments the digit
122+ * prior to a discarded fraction (i.e., truncates). Note that this
123+ * rounding mode never increases the magnitude of the calculated value.
124+ *
125+ *<p>Example:
126+ *<table border>
127+ *<tr valign=top><th>Input Number</th>
128+ * <th>Input rounded to one digit<br> with {@code DOWN} rounding
129+ *<tr align=right><td>5.5</td> <td>5</td>
130+ *<tr align=right><td>2.5</td> <td>2</td>
131+ *<tr align=right><td>1.6</td> <td>1</td>
132+ *<tr align=right><td>1.1</td> <td>1</td>
133+ *<tr align=right><td>1.0</td> <td>1</td>
134+ *<tr align=right><td>-1.0</td> <td>-1</td>
135+ *<tr align=right><td>-1.1</td> <td>-1</td>
136+ *<tr align=right><td>-1.6</td> <td>-1</td>
137+ *<tr align=right><td>-2.5</td> <td>-2</td>
138+ *<tr align=right><td>-5.5</td> <td>-5</td>
139+ *</table>
140+ */
141+ DOWN(BigDecimal.ROUND_DOWN),
142+
143+ /**
144+ * Rounding mode to round towards positive infinity. If the
145+ * result is positive, behaves as for {@code RoundingMode.UP};
146+ * if negative, behaves as for {@code RoundingMode.DOWN}. Note
147+ * that this rounding mode never decreases the calculated value.
148+ *
149+ *<p>Example:
150+ *<table border>
151+ *<tr valign=top><th>Input Number</th>
152+ * <th>Input rounded to one digit<br> with {@code CEILING} rounding
153+ *<tr align=right><td>5.5</td> <td>6</td>
154+ *<tr align=right><td>2.5</td> <td>3</td>
155+ *<tr align=right><td>1.6</td> <td>2</td>
156+ *<tr align=right><td>1.1</td> <td>2</td>
157+ *<tr align=right><td>1.0</td> <td>1</td>
158+ *<tr align=right><td>-1.0</td> <td>-1</td>
159+ *<tr align=right><td>-1.1</td> <td>-1</td>
160+ *<tr align=right><td>-1.6</td> <td>-1</td>
161+ *<tr align=right><td>-2.5</td> <td>-2</td>
162+ *<tr align=right><td>-5.5</td> <td>-5</td>
163+ *</table>
164+ */
165+ CEILING(BigDecimal.ROUND_CEILING),
166+
167+ /**
168+ * Rounding mode to round towards negative infinity. If the
169+ * result is positive, behave as for {@code RoundingMode.DOWN};
170+ * if negative, behave as for {@code RoundingMode.UP}. Note that
171+ * this rounding mode never increases the calculated value.
172+ *
173+ *<p>Example:
174+ *<table border>
175+ *<tr valign=top><th>Input Number</th>
176+ * <th>Input rounded to one digit<br> with {@code FLOOR} rounding
177+ *<tr align=right><td>5.5</td> <td>5</td>
178+ *<tr align=right><td>2.5</td> <td>2</td>
179+ *<tr align=right><td>1.6</td> <td>1</td>
180+ *<tr align=right><td>1.1</td> <td>1</td>
181+ *<tr align=right><td>1.0</td> <td>1</td>
182+ *<tr align=right><td>-1.0</td> <td>-1</td>
183+ *<tr align=right><td>-1.1</td> <td>-2</td>
184+ *<tr align=right><td>-1.6</td> <td>-2</td>
185+ *<tr align=right><td>-2.5</td> <td>-3</td>
186+ *<tr align=right><td>-5.5</td> <td>-6</td>
187+ *</table>
188+ */
189+ FLOOR(BigDecimal.ROUND_FLOOR),
190+
191+ /**
192+ * Rounding mode to round towards {@literal "nearest neighbor"}
193+ * unless both neighbors are equidistant, in which case round up.
194+ * Behaves as for {@code RoundingMode.UP} if the discarded
195+ * fraction is &ge; 0.5; otherwise, behaves as for
196+ * {@code RoundingMode.DOWN}. Note that this is the rounding
197+ * mode commonly taught at school.
198+ *
199+ *<p>Example:
200+ *<table border>
201+ *<tr valign=top><th>Input Number</th>
202+ * <th>Input rounded to one digit<br> with {@code HALF_UP} rounding
203+ *<tr align=right><td>5.5</td> <td>6</td>
204+ *<tr align=right><td>2.5</td> <td>3</td>
205+ *<tr align=right><td>1.6</td> <td>2</td>
206+ *<tr align=right><td>1.1</td> <td>1</td>
207+ *<tr align=right><td>1.0</td> <td>1</td>
208+ *<tr align=right><td>-1.0</td> <td>-1</td>
209+ *<tr align=right><td>-1.1</td> <td>-1</td>
210+ *<tr align=right><td>-1.6</td> <td>-2</td>
211+ *<tr align=right><td>-2.5</td> <td>-3</td>
212+ *<tr align=right><td>-5.5</td> <td>-6</td>
213+ *</table>
214+ */
215+ HALF_UP(BigDecimal.ROUND_HALF_UP),
216+
217+ /**
218+ * Rounding mode to round towards {@literal "nearest neighbor"}
219+ * unless both neighbors are equidistant, in which case round
220+ * down. Behaves as for {@code RoundingMode.UP} if the discarded
221+ * fraction is &gt; 0.5; otherwise, behaves as for
222+ * {@code RoundingMode.DOWN}.
223+ *
224+ *<p>Example:
225+ *<table border>
226+ *<tr valign=top><th>Input Number</th>
227+ * <th>Input rounded to one digit<br> with {@code HALF_DOWN} rounding
228+ *<tr align=right><td>5.5</td> <td>5</td>
229+ *<tr align=right><td>2.5</td> <td>2</td>
230+ *<tr align=right><td>1.6</td> <td>2</td>
231+ *<tr align=right><td>1.1</td> <td>1</td>
232+ *<tr align=right><td>1.0</td> <td>1</td>
233+ *<tr align=right><td>-1.0</td> <td>-1</td>
234+ *<tr align=right><td>-1.1</td> <td>-1</td>
235+ *<tr align=right><td>-1.6</td> <td>-2</td>
236+ *<tr align=right><td>-2.5</td> <td>-2</td>
237+ *<tr align=right><td>-5.5</td> <td>-5</td>
238+ *</table>
239+ */
240+ HALF_DOWN(BigDecimal.ROUND_HALF_DOWN),
241+
242+ /**
243+ * Rounding mode to round towards the {@literal "nearest neighbor"}
244+ * unless both neighbors are equidistant, in which case, round
245+ * towards the even neighbor. Behaves as for
246+ * {@code RoundingMode.HALF_UP} if the digit to the left of the
247+ * discarded fraction is odd; behaves as for
248+ * {@code RoundingMode.HALF_DOWN} if it's even. Note that this
249+ * is the rounding mode that statistically minimizes cumulative
250+ * error when applied repeatedly over a sequence of calculations.
251+ * It is sometimes known as {@literal "Banker's rounding,"} and is
252+ * chiefly used in the USA. This rounding mode is analogous to
253+ * the rounding policy used for {@code float} and {@code double}
254+ * arithmetic in Java.
255+ *
256+ *<p>Example:
257+ *<table border>
258+ *<tr valign=top><th>Input Number</th>
259+ * <th>Input rounded to one digit<br> with {@code HALF_EVEN} rounding
260+ *<tr align=right><td>5.5</td> <td>6</td>
261+ *<tr align=right><td>2.5</td> <td>2</td>
262+ *<tr align=right><td>1.6</td> <td>2</td>
263+ *<tr align=right><td>1.1</td> <td>1</td>
264+ *<tr align=right><td>1.0</td> <td>1</td>
265+ *<tr align=right><td>-1.0</td> <td>-1</td>
266+ *<tr align=right><td>-1.1</td> <td>-1</td>
267+ *<tr align=right><td>-1.6</td> <td>-2</td>
268+ *<tr align=right><td>-2.5</td> <td>-2</td>
269+ *<tr align=right><td>-5.5</td> <td>-6</td>
270+ *</table>
271+ */
272+ HALF_EVEN(BigDecimal.ROUND_HALF_EVEN),
273+
274+ /**
275+ * Rounding mode to assert that the requested operation has an exact
276+ * result, hence no rounding is necessary. If this rounding mode is
277+ * specified on an operation that yields an inexact result, an
278+ * {@code ArithmeticException} is thrown.
279+ *<p>Example:
280+ *<table border>
281+ *<tr valign=top><th>Input Number</th>
282+ * <th>Input rounded to one digit<br> with {@code UNNECESSARY} rounding
283+ *<tr align=right><td>5.5</td> <td>throw {@code ArithmeticException}</td>
284+ *<tr align=right><td>2.5</td> <td>throw {@code ArithmeticException}</td>
285+ *<tr align=right><td>1.6</td> <td>throw {@code ArithmeticException}</td>
286+ *<tr align=right><td>1.1</td> <td>throw {@code ArithmeticException}</td>
287+ *<tr align=right><td>1.0</td> <td>1</td>
288+ *<tr align=right><td>-1.0</td> <td>-1</td>
289+ *<tr align=right><td>-1.1</td> <td>throw {@code ArithmeticException}</td>
290+ *<tr align=right><td>-1.6</td> <td>throw {@code ArithmeticException}</td>
291+ *<tr align=right><td>-2.5</td> <td>throw {@code ArithmeticException}</td>
292+ *<tr align=right><td>-5.5</td> <td>throw {@code ArithmeticException}</td>
293+ *</table>
294+ */
295+ UNNECESSARY(BigDecimal.ROUND_UNNECESSARY);
296+
297+ // Corresponding BigDecimal rounding constant
298+ final int oldMode;
299+
300+ /**
301+ * Constructor
302+ *
303+ * @param oldMode The {@code BigDecimal} constant corresponding to
304+ * this mode
305+ */
306+ private RoundingMode(int oldMode) {
307+ this.oldMode = oldMode;
308+ }
309+
310+ /**
311+ * Returns the {@code RoundingMode} object corresponding to a
312+ * legacy integer rounding mode constant in {@link BigDecimal}.
313+ *
314+ * @param rm legacy integer rounding mode to convert
315+ * @return {@code RoundingMode} corresponding to the given integer.
316+ * @throws IllegalArgumentException integer is out of range
317+ */
318+ public static RoundingMode valueOf(int rm) {
319+ switch(rm) {
320+
321+ case BigDecimal.ROUND_UP:
322+ return UP;
323+
324+ case BigDecimal.ROUND_DOWN:
325+ return DOWN;
326+
327+ case BigDecimal.ROUND_CEILING:
328+ return CEILING;
329+
330+ case BigDecimal.ROUND_FLOOR:
331+ return FLOOR;
332+
333+ case BigDecimal.ROUND_HALF_UP:
334+ return HALF_UP;
335+
336+ case BigDecimal.ROUND_HALF_DOWN:
337+ return HALF_DOWN;
338+
339+ case BigDecimal.ROUND_HALF_EVEN:
340+ return HALF_EVEN;
341+
342+ case BigDecimal.ROUND_UNNECESSARY:
343+ return UNNECESSARY;
344+
345+ default:
346+ throw new IllegalArgumentException("argument out of range");
347+ }
348+ }
349+}
java/pkg/java/math/SignedMutableBigInteger.class+0−0

Binary file not shown.

java/pkg/java/math/SignedMutableBigInteger.java+135−0
@@ -0,0 +1,135 @@
1+/*
2+ * Copyright (c) 1999, 2007, 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+package java.math;
27+
28+/**
29+ * A class used to represent multiprecision integers that makes efficient
30+ * use of allocated space by allowing a number to occupy only part of
31+ * an array so that the arrays do not have to be reallocated as often.
32+ * When performing an operation with many iterations the array used to
33+ * hold a number is only increased when necessary and does not have to
34+ * be the same size as the number it represents. A mutable number allows
35+ * calculations to occur on the same number without having to create
36+ * a new number for every step of the calculation as occurs with
37+ * BigIntegers.
38+ *
39+ * Note that SignedMutableBigIntegers only support signed addition and
40+ * subtraction. All other operations occur as with MutableBigIntegers.
41+ *
42+ * @see BigInteger
43+ * @author Michael McCloskey
44+ * @since 1.3
45+ */
46+
47+class SignedMutableBigInteger extends MutableBigInteger {
48+
49+ /**
50+ * The sign of this MutableBigInteger.
51+ */
52+ int sign = 1;
53+
54+ // Constructors
55+
56+ /**
57+ * The default constructor. An empty MutableBigInteger is created with
58+ * a one word capacity.
59+ */
60+ SignedMutableBigInteger() {
61+ super();
62+ }
63+
64+ /**
65+ * Construct a new MutableBigInteger with a magnitude specified by
66+ * the int val.
67+ */
68+ SignedMutableBigInteger(int val) {
69+ super(val);
70+ }
71+
72+ /**
73+ * Construct a new MutableBigInteger with a magnitude equal to the
74+ * specified MutableBigInteger.
75+ */
76+ SignedMutableBigInteger(MutableBigInteger val) {
77+ super(val);
78+ }
79+
80+ // Arithmetic Operations
81+
82+ /**
83+ * Signed addition built upon unsigned add and subtract.
84+ */
85+ void signedAdd(SignedMutableBigInteger addend) {
86+ if (sign == addend.sign)
87+ add(addend);
88+ else
89+ sign = sign * subtract(addend);
90+
91+ }
92+
93+ /**
94+ * Signed addition built upon unsigned add and subtract.
95+ */
96+ void signedAdd(MutableBigInteger addend) {
97+ if (sign == 1)
98+ add(addend);
99+ else
100+ sign = sign * subtract(addend);
101+
102+ }
103+
104+ /**
105+ * Signed subtraction built upon unsigned add and subtract.
106+ */
107+ void signedSubtract(SignedMutableBigInteger addend) {
108+ if (sign == addend.sign)
109+ sign = sign * subtract(addend);
110+ else
111+ add(addend);
112+
113+ }
114+
115+ /**
116+ * Signed subtraction built upon unsigned add and subtract.
117+ */
118+ void signedSubtract(MutableBigInteger addend) {
119+ if (sign == 1)
120+ sign = sign * subtract(addend);
121+ else
122+ add(addend);
123+ if (intLen == 0)
124+ sign = 1;
125+ }
126+
127+ /**
128+ * Print out the first intLen ints of this MutableBigInteger's value
129+ * array starting at offset.
130+ */
131+ public String toString() {
132+ return this.toBigInteger(sign).toString();
133+ }
134+
135+}
java/pkg/java/math/mkfile+15−0
@@ -0,0 +1,15 @@
1+<../../../../mkconfig
2+
3+TARG=\
4+ BigDecimal.dis\
5+ BigInteger.dis\
6+ BitSieve.dis\
7+ MathContext.dis\
8+ MutableBigInteger.dis\
9+ package-info.dis\
10+ RoundingMode.dis\
11+ SignedMutableBigInteger.dis\
12+
13+DISBIN=$ROOT/java/dis/java/java/java/math
14+
15+<$ROOT/mkfiles/mkjava
java/pkg/java/math/package-info.java+45−0
@@ -0,0 +1,45 @@
1+/*
2+ * Copyright (c) 1998, 2006, 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+ * Provides classes for performing arbitrary-precision integer
28+ * arithmetic ({@code BigInteger}) and arbitrary-precision decimal
29+ * arithmetic ({@code BigDecimal}). {@code BigInteger} is analogous
30+ * to the primitive integer types except that it provides arbitrary
31+ * precision, hence operations on {@code BigInteger}s do not overflow
32+ * or lose precision. In addition to standard arithmetic operations,
33+ * {@code BigInteger} provides modular arithmetic, GCD calculation,
34+ * primality testing, prime generation, bit manipulation, and a few
35+ * other miscellaneous operations.
36+ *
37+ * {@code BigDecimal} provides arbitrary-precision signed decimal
38+ * numbers suitable for currency calculations and the like. {@code
39+ * BigDecimal} gives the user complete control over rounding behavior,
40+ * allowing the user to choose from a comprehensive set of eight
41+ * rounding modes.
42+ *
43+ * @since JDK1.1
44+ */
45+package java.math;