/*

 * Copyright (c) 1996, 2011, Oracle and/or its affiliates. All rights reserved.

 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

 *

 * This code is free software; you can redistribute it and/or modify it

 * under the terms of the GNU General Public License version 2 only, as

 * published by the Free Software Foundation.  Oracle designates this

 * particular file as subject to the "Classpath" exception as provided

 * by Oracle in the LICENSE file that accompanied this code.

 *

 * This code is distributed in the hope that it will be useful, but WITHOUT

 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

 *

 * You should have received a copy of the GNU General Public License version

 * 2 along with this work; if not, write to the Free Software Foundation,

 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

 *

 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

 * or visit www.oracle.com if you need additional information or have any

 * questions.

 */

/*

 * Portions Copyright IBM Corporation, 2001. All Rights Reserved.

 */

package java.math;

import java.util.Arrays;

import static java.math.BigInteger.LONG_MASK;

/**

 * Immutable, arbitrary-precision signed decimal numbers.  A

 * {@code BigDecimal} consists of an arbitrary precision integer

 * <i>unscaled value</i> and a 32-bit integer <i>scale</i>.  If zero

 * or positive, the scale is the number of digits to the right of the

 * decimal point.  If negative, the unscaled value of the number is

 * multiplied by ten to the power of the negation of the scale.  The

 * value of the number represented by the {@code BigDecimal} is

 * therefore <tt>(unscaledValue &times; 10<sup>-scale</sup>)</tt>.

 *

 * <p>The {@code BigDecimal} class provides operations for

 * arithmetic, scale manipulation, rounding, comparison, hashing, and

 * format conversion.  The {@link #toString} method provides a

 * canonical representation of a {@code BigDecimal}.

 *

 * <p>The {@code BigDecimal} class gives its user complete control

 * over rounding behavior.  If no rounding mode is specified and the

 * exact result cannot be represented, an exception is thrown;

 * otherwise, calculations can be carried out to a chosen precision

 * and rounding mode by supplying an appropriate {@link MathContext}

 * object to the operation.  In either case, eight <em>rounding

 * modes</em> are provided for the control of rounding.  Using the

 * integer fields in this class (such as {@link #ROUND_HALF_UP}) to

 * represent rounding mode is largely obsolete; the enumeration values

 * of the {@code RoundingMode} {@code enum}, (such as {@link

 * RoundingMode#HALF_UP}) should be used instead.

 *

 * <p>When a {@code MathContext} object is supplied with a precision

 * setting of 0 (for example, {@link MathContext#UNLIMITED}),

 * arithmetic operations are exact, as are the arithmetic methods

 * which take no {@code MathContext} object.  (This is the only

 * behavior that was supported in releases prior to 5.)  As a

 * corollary of computing the exact result, the rounding mode setting

 * of a {@code MathContext} object with a precision setting of 0 is

 * not used and thus irrelevant.  In the case of divide, the exact

 * quotient could have an infinitely long decimal expansion; for

 * example, 1 divided by 3.  If the quotient has a nonterminating

 * decimal expansion and the operation is specified to return an exact

 * result, an {@code ArithmeticException} is thrown.  Otherwise, the

 * exact result of the division is returned, as done for other

 * operations.

 *

 * <p>When the precision setting is not 0, the rules of

 * {@code BigDecimal} arithmetic are broadly compatible with selected

 * modes of operation of the arithmetic defined in ANSI X3.274-1996

 * and ANSI X3.274-1996/AM 1-2000 (section 7.4).  Unlike those

 * standards, {@code BigDecimal} includes many rounding modes, which

 * were mandatory for division in {@code BigDecimal} releases prior

 * to 5.  Any conflicts between these ANSI standards and the

 * {@code BigDecimal} specification are resolved in favor of

 * {@code BigDecimal}.

 *

 * <p>Since the same numerical value can have different

 * representations (with different scales), the rules of arithmetic

 * and rounding must specify both the numerical result and the scale

 * used in the result's representation.

 *

 *

 * <p>In general the rounding modes and precision setting determine

 * how operations return results with a limited number of digits when

 * the exact result has more digits (perhaps infinitely many in the

 * case of division) than the number of digits returned.

 *

 * First, the

 * total number of digits to return is specified by the

 * {@code MathContext}'s {@code precision} setting; this determines

 * the result's <i>precision</i>.  The digit count starts from the

 * leftmost nonzero digit of the exact result.  The rounding mode

 * determines how any discarded trailing digits affect the returned

 * result.

 *

 * <p>For all arithmetic operators , the operation is carried out as

 * though an exact intermediate result were first calculated and then

 * rounded to the number of digits specified by the precision setting

 * (if necessary), using the selected rounding mode.  If the exact

 * result is not returned, some digit positions of the exact result

 * are discarded.  When rounding increases the magnitude of the

 * returned result, it is possible for a new digit position to be

 * created by a carry propagating to a leading {@literal "9"} digit.

 * For example, rounding the value 999.9 to three digits rounding up

 * would be numerically equal to one thousand, represented as

 * 100&times;10<sup>1</sup>.  In such cases, the new {@literal "1"} is

 * the leading digit position of the returned result.

 *

 * <p>Besides a logical exact result, each arithmetic operation has a

 * preferred scale for representing a result.  The preferred

 * scale for each operation is listed in the table below.

 *

 * <table border>

 * <caption><b>Preferred Scales for Results of Arithmetic Operations

 * </b></caption>

 * <tr><th>Operation</th><th>Preferred Scale of Result</th></tr>

 * <tr><td>Add</td><td>max(addend.scale(), augend.scale())</td>

 * <tr><td>Subtract</td><td>max(minuend.scale(), subtrahend.scale())</td>

 * <tr><td>Multiply</td><td>multiplier.scale() + multiplicand.scale()</td>

 * <tr><td>Divide</td><td>dividend.scale() - divisor.scale()</td>

 * </table>

 *

 * These scales are the ones used by the methods which return exact

 * arithmetic results; except that an exact divide may have to use a

 * larger scale since the exact result may have more digits.  For

 * example, {@code 1/32} is {@code 0.03125}.

 *

 * <p>Before rounding, the scale of the logical exact intermediate

 * result is the preferred scale for that operation.  If the exact

 * numerical result cannot be represented in {@code precision}

 * digits, rounding selects the set of digits to return and the scale

 * of the result is reduced from the scale of the intermediate result

 * to the least scale which can represent the {@code precision}

 * digits actually returned.  If the exact result can be represented

 * with at most {@code precision} digits, the representation

 * of the result with the scale closest to the preferred scale is

 * returned.  In particular, an exactly representable quotient may be

 * represented in fewer than {@code precision} digits by removing

 * trailing zeros and decreasing the scale.  For example, rounding to

 * three digits using the {@linkplain RoundingMode#FLOOR floor}

 * rounding mode, <br>

 *

 * {@code 19/100 = 0.19   // integer=19,  scale=2} <br>

 *

 * but<br>

 *

 * {@code 21/110 = 0.190  // integer=190, scale=3} <br>

 *

 * <p>Note that for add, subtract, and multiply, the reduction in

 * scale will equal the number of digit positions of the exact result

 * which are discarded. If the rounding causes a carry propagation to

 * create a new high-order digit position, an additional digit of the

 * result is discarded than when no new digit position is created.

 *

 * <p>Other methods may have slightly different rounding semantics.

 * For example, the result of the {@code pow} method using the

 * {@linkplain #pow(int, MathContext) specified algorithm} can

 * occasionally differ from the rounded mathematical result by more

 * than one unit in the last place, one <i>{@linkplain #ulp() ulp}</i>.

 *

 * <p>Two types of operations are provided for manipulating the scale

 * of a {@code BigDecimal}: scaling/rounding operations and decimal

 * point motion operations.  Scaling/rounding operations ({@link

 * #setScale setScale} and {@link #round round}) return a

 * {@code BigDecimal} whose value is approximately (or exactly) equal

 * to that of the operand, but whose scale or precision is the

 * specified value; that is, they increase or decrease the precision

 * of the stored number with minimal effect on its value.  Decimal

 * point motion operations ({@link #movePointLeft movePointLeft} and

 * {@link #movePointRight movePointRight}) return a

 * {@code BigDecimal} created from the operand by moving the decimal

 * point a specified distance in the specified direction.

 *

 * <p>For the sake of brevity and clarity, pseudo-code is used

 * throughout the descriptions of {@code BigDecimal} methods.  The

 * pseudo-code expression {@code (i + j)} is shorthand for "a

 * {@code BigDecimal} whose value is that of the {@code BigDecimal}

 * {@code i} added to that of the {@code BigDecimal}

 * {@code j}." The pseudo-code expression {@code (i == j)} is

 * shorthand for "{@code true} if and only if the

 * {@code BigDecimal} {@code i} represents the same value as the

 * {@code BigDecimal} {@code j}." Other pseudo-code expressions

 * are interpreted similarly.  Square brackets are used to represent

 * the particular {@code BigInteger} and scale pair defining a

 * {@code BigDecimal} value; for example [19, 2] is the

 * {@code BigDecimal} numerically equal to 0.19 having a scale of 2.

 *

 * <p>Note: care should be exercised if {@code BigDecimal} objects

 * are used as keys in a {@link java.util.SortedMap SortedMap} or

 * elements in a {@link java.util.SortedSet SortedSet} since

 * {@code BigDecimal}'s <i>natural ordering</i> is <i>inconsistent

 * with equals</i>.  See {@link Comparable}, {@link

 * java.util.SortedMap} or {@link java.util.SortedSet} for more

 * information.

 *

 * <p>All methods and constructors for this class throw

 * {@code NullPointerException} when passed a {@code null} object

 * reference for any input parameter.

 *

 * @see     BigInteger

 * @see     MathContext

 * @see     RoundingMode

 * @see     java.util.SortedMap

 * @see     java.util.SortedSet

 * @author  Josh Bloch

 * @author  Mike Cowlishaw

 * @author  Joseph D. Darcy

 */

public class BigDecimal extends Number implements Comparable<BigDecimal> {

    /**

     * The unscaled value of this BigDecimal, as returned by {@link

     * #unscaledValue}.

     *

     * @serial

     * @see #unscaledValue

     */

    private volatile BigInteger intVal;

    /**

     * The scale of this BigDecimal, as returned by {@link #scale}.

     *

     * @serial

     * @see #scale

     */

    private int scale;  // Note: this may have any value, so

                        // calculations must be done in longs

    /**

     * The number of decimal digits in this BigDecimal, or 0 if the

     * number of digits are not known (lookaside information).  If

     * nonzero, the value is guaranteed correct.  Use the precision()

     * method to obtain and set the value if it might be 0.  This

     * field is mutable until set nonzero.

     *

     * @since  1.5

     */

    private transient int precision;

    /**

     * Used to store the canonical string representation, if computed.

     */

    private transient String stringCache;

    /**

     * Sentinel value for {@link #intCompact} indicating the

     * significand information is only available from {@code intVal}.

     */

    static final long INFLATED = Long.MIN_VALUE;

    /**

     * If the absolute value of the significand of this BigDecimal is

     * less than or equal to {@code Long.MAX_VALUE}, the value can be

     * compactly stored in this field and used in computations.

     */

    private transient long intCompact;

    // All 18-digit base ten strings fit into a long; not all 19-digit

    // strings will

    private static final int MAX_COMPACT_DIGITS = 18;

    private static final int MAX_BIGINT_BITS = 62;

    /* Appease the serialization gods */

    private static final long serialVersionUID = 6108874887143696463L;

    private static final ThreadLocal<StringBuilderHelper>

        threadLocalStringBuilderHelper = new ThreadLocal<StringBuilderHelper>() {

        @Override

        protected StringBuilderHelper initialValue() {

            return new StringBuilderHelper();

        }

    };

    // Cache of common small BigDecimal values.

    private static final BigDecimal zeroThroughTen[] = {

        new BigDecimal(BigInteger.ZERO,         0,  0, 1),

        new BigDecimal(BigInteger.ONE,          1,  0, 1),

        new BigDecimal(BigInteger.valueOf(2),   2,  0, 1),

        new BigDecimal(BigInteger.valueOf(3),   3,  0, 1),

        new BigDecimal(BigInteger.valueOf(4),   4,  0, 1),

        new BigDecimal(BigInteger.valueOf(5),   5,  0, 1),

        new BigDecimal(BigInteger.valueOf(6),   6,  0, 1),

        new BigDecimal(BigInteger.valueOf(7),   7,  0, 1),

        new BigDecimal(BigInteger.valueOf(8),   8,  0, 1),

        new BigDecimal(BigInteger.valueOf(9),   9,  0, 1),

        new BigDecimal(BigInteger.TEN,          10, 0, 2),

    };

    // Cache of zero scaled by 0 - 15

    private static final BigDecimal[] ZERO_SCALED_BY = {

        zeroThroughTen[0],

        new BigDecimal(BigInteger.ZERO, 0, 1, 1),

        new BigDecimal(BigInteger.ZERO, 0, 2, 1),

        new BigDecimal(BigInteger.ZERO, 0, 3, 1),

        new BigDecimal(BigInteger.ZERO, 0, 4, 1),

        new BigDecimal(BigInteger.ZERO, 0, 5, 1),

        new BigDecimal(BigInteger.ZERO, 0, 6, 1),

        new BigDecimal(BigInteger.ZERO, 0, 7, 1),

        new BigDecimal(BigInteger.ZERO, 0, 8, 1),

        new BigDecimal(BigInteger.ZERO, 0, 9, 1),

        new BigDecimal(BigInteger.ZERO, 0, 10, 1),

        new BigDecimal(BigInteger.ZERO, 0, 11, 1),

        new BigDecimal(BigInteger.ZERO, 0, 12, 1),

        new BigDecimal(BigInteger.ZERO, 0, 13, 1),

        new BigDecimal(BigInteger.ZERO, 0, 14, 1),

        new BigDecimal(BigInteger.ZERO, 0, 15, 1),

    };

    // Half of Long.MIN_VALUE & Long.MAX_VALUE.

    private static final long HALF_LONG_MAX_VALUE = Long.MAX_VALUE / 2;

    private static final long HALF_LONG_MIN_VALUE = Long.MIN_VALUE / 2;

    // Constants

    /**

     * The value 0, with a scale of 0.

     *

     * @since  1.5

     */

    public static final BigDecimal ZERO =

        zeroThroughTen[0];

    /**

     * The value 1, with a scale of 0.

     *

     * @since  1.5

     */

    public static final BigDecimal ONE =

        zeroThroughTen[1];

    /**

     * The value 10, with a scale of 0.

     *

     * @since  1.5

     */

    public static final BigDecimal TEN =

        zeroThroughTen[10];

    // Constructors

    /**

     * Trusted package private constructor.

     * Trusted simply means if val is INFLATED, intVal could not be null and

     * if intVal is null, val could not be INFLATED.

     */

    BigDecimal(BigInteger intVal, long val, int scale, int prec) {

        this.scale = scale;

        this.precision = prec;

        this.intCompact = val;

        this.intVal = intVal;

    }

    /**

     * Translates a character array representation of a

     * {@code BigDecimal} into a {@code BigDecimal}, accepting the

     * same sequence of characters as the {@link #BigDecimal(String)}

     * constructor, while allowing a sub-array to be specified.

     *

     * <p>Note that if the sequence of characters is already available

     * within a character array, using this constructor is faster than

     * converting the {@code char} array to string and using the

     * {@code BigDecimal(String)} constructor .

     *

     * @param  in {@code char} array that is the source of characters.

     * @param  offset first character in the array to inspect.

     * @param  len number of characters to consider.

     * @throws NumberFormatException if {@code in} is not a valid

     *         representation of a {@code BigDecimal} or the defined subarray

     *         is not wholly within {@code in}.

     * @since  1.5

     */

    public BigDecimal(char[] in, int offset, int len) {

        // protect against huge length.

        if (offset+len > in.length || offset < 0)

            throw new NumberFormatException();

        // This is the primary string to BigDecimal constructor; all

        // incoming strings end up here; it uses explicit (inline)

        // parsing for speed and generates at most one intermediate

        // (temporary) object (a char[] array) for non-compact case.

        // Use locals for all fields values until completion

        int prec = 0;                 // record precision value

        int scl = 0;                  // record scale value

        long rs = 0;                  // the compact value in long

        BigInteger rb = null;         // the inflated value in BigInteger

        // use array bounds checking to handle too-long, len == 0,

        // bad offset, etc.

        try {

            // handle the sign

            boolean isneg = false;          // assume positive

            if (in[offset] == '-') {

                isneg = true;               // leading minus means negative

                offset++;

                len--;

            } else if (in[offset] == '+') { // leading + allowed

                offset++;

                len--;

            }

            // should now be at numeric part of the significand

            boolean dot = false;             // true when there is a '.'

            int cfirst = offset;             // record start of integer

            long exp = 0;                    // exponent

            char c;                          // current character

            boolean isCompact = (len <= MAX_COMPACT_DIGITS);

            // integer significand array & idx is the index to it. The array

            // is ONLY used when we can't use a compact representation.

            char coeff[] = isCompact ? null : new char[len];

            int idx = 0;

            for (; len > 0; offset++, len--) {

                c = in[offset];

                // have digit

                if ((c >= '0' && c <= '9') || Character.isDigit(c)) {

                    // First compact case, we need not to preserve the character

                    // and we can just compute the value in place.

                    if (isCompact) {

                        int digit = Character.digit(c, 10);

                        if (digit == 0) {

                            if (prec == 0)

                                prec = 1;

                            else if (rs != 0) {

                                rs *= 10;

                                ++prec;

                            } // else digit is a redundant leading zero

                        } else {

                            if (prec != 1 || rs != 0)

                                ++prec; // prec unchanged if preceded by 0s

                            rs = rs * 10 + digit;

                        }

                    } else { // the unscaled value is likely a BigInteger object.

                        if (c == '0' || Character.digit(c, 10) == 0) {

                            if (prec == 0) {

                                coeff[idx] = c;

                                prec = 1;

                            } else if (idx != 0) {

                                coeff[idx++] = c;

                                ++prec;

                            } // else c must be a redundant leading zero

                        } else {

                            if (prec != 1 || idx != 0)

                                ++prec; // prec unchanged if preceded by 0s

                            coeff[idx++] = c;

                        }

                    }

                    if (dot)

                        ++scl;

                    continue;

                }

                // have dot

                if (c == '.') {

                    // have dot

                    if (dot)         // two dots

                        throw new NumberFormatException();

                    dot = true;

                    continue;

                }

                // exponent expected

                if ((c != 'e') && (c != 'E'))

                    throw new NumberFormatException();

                offset++;

                c = in[offset];

                len--;

                boolean negexp = (c == '-');

                // optional sign

                if (negexp || c == '+') {

                    offset++;

                    c = in[offset];

                    len--;

                }

                if (len <= 0)    // no exponent digits

                    throw new NumberFormatException();

                // skip leading zeros in the exponent

                while (len > 10 && Character.digit(c, 10) == 0) {

                    offset++;

                    c = in[offset];

                    len--;

                }

                if (len > 10)  // too many nonzero exponent digits

                    throw new NumberFormatException();

                // c now holds first digit of exponent

                for (;; len--) {

                    int v;

                    if (c >= '0' && c <= '9') {

                        v = c - '0';

                    } else {

                        v = Character.digit(c, 10);

                        if (v < 0)            // not a digit

                            throw new NumberFormatException();

                    }

                    exp = exp * 10 + v;

                    if (len == 1)

                        break;               // that was final character

                    offset++;

                    c = in[offset];

                }

                if (negexp)                  // apply sign

                    exp = -exp;

                // Next test is required for backwards compatibility

                if ((int)exp != exp)         // overflow

                    throw new NumberFormatException();

                break;                       // [saves a test]

            }

            // here when no characters left

            if (prec == 0)              // no digits found

                throw new NumberFormatException();

            // Adjust scale if exp is not zero.

            if (exp != 0) {                  // had significant exponent

                // Can't call checkScale which relies on proper fields value

                long adjustedScale = scl - exp;

                if (adjustedScale > Integer.MAX_VALUE ||

                    adjustedScale < Integer.MIN_VALUE)

                    throw new NumberFormatException("Scale out of range.");

                scl = (int)adjustedScale;

            }

            // Remove leading zeros from precision (digits count)

            if (isCompact) {

                rs = isneg ? -rs : rs;

            } else {

                char quick[];

                if (!isneg) {

                    quick = (coeff.length != prec) ?

                        Arrays.copyOf(coeff, prec) : coeff;

                } else {

                    quick = new char[prec + 1];

                    quick[0] = '-';

                    System.arraycopy(coeff, 0, quick, 1, prec);

                }

                rb = new BigInteger(quick);

                rs = compactValFor(rb);

            }

        } catch (ArrayIndexOutOfBoundsException e) {

            throw new NumberFormatException();

        } catch (NegativeArraySizeException e) {

            throw new NumberFormatException();

        }

        this.scale = scl;

        this.precision = prec;

        this.intCompact = rs;

        this.intVal = (rs != INFLATED) ? null : rb;

    }

    /**

     * Translates a character array representation of a

     * {@code BigDecimal} into a {@code BigDecimal}, accepting the

     * same sequence of characters as the {@link #BigDecimal(String)}

     * constructor, while allowing a sub-array to be specified and

     * with rounding according to the context settings.

     *

     * <p>Note that if the sequence of characters is already available

     * within a character array, using this constructor is faster than

     * converting the {@code char} array to string and using the

     * {@code BigDecimal(String)} constructor .

     *

     * @param  in {@code char} array that is the source of characters.

     * @param  offset first character in the array to inspect.

     * @param  len number of characters to consider..

     * @param  mc the context to use.

     * @throws ArithmeticException if the result is inexact but the

     *         rounding mode is {@code UNNECESSARY}.

     * @throws NumberFormatException if {@code in} is not a valid

     *         representation of a {@code BigDecimal} or the defined subarray

     *         is not wholly within {@code in}.

     * @since  1.5

     */

    public BigDecimal(char[] in, int offset, int len, MathContext mc) {

        this(in, offset, len);

        if (mc.precision > 0)

            roundThis(mc);

    }

    /**

     * Translates a character array representation of a

     * {@code BigDecimal} into a {@code BigDecimal}, accepting the

     * same sequence of characters as the {@link #BigDecimal(String)}

     * constructor.

     *

     * <p>Note that if the sequence of characters is already available

     * as a character array, using this constructor is faster than

     * converting the {@code char} array to string and using the

     * {@code BigDecimal(String)} constructor .

     *

     * @param in {@code char} array that is the source of characters.

     * @throws NumberFormatException if {@code in} is not a valid

     *         representation of a {@code BigDecimal}.

     * @since  1.5

     */

    public BigDecimal(char[] in) {

        this(in, 0, in.length);

    }

    /**

     * Translates a character array representation of a

     * {@code BigDecimal} into a {@code BigDecimal}, accepting the

     * same sequence of characters as the {@link #BigDecimal(String)}

     * constructor and with rounding according to the context

     * settings.

     *

     * <p>Note that if the sequence of characters is already available

     * as a character array, using this constructor is faster than

     * converting the {@code char} array to string and using the

     * {@code BigDecimal(String)} constructor .

     *

     * @param  in {@code char} array that is the source of characters.

     * @param  mc the context to use.

     * @throws ArithmeticException if the result is inexact but the

     *         rounding mode is {@code UNNECESSARY}.

     * @throws NumberFormatException if {@code in} is not a valid

     *         representation of a {@code BigDecimal}.

     * @since  1.5

     */

    public BigDecimal(char[] in, MathContext mc) {

        this(in, 0, in.length, mc);

    }

    /**

     * Translates the string representation of a {@code BigDecimal}

     * into a {@code BigDecimal}.  The string representation consists

     * of an optional sign, {@code '+'} (<tt> '&#92;u002B'</tt>) or

     * {@code '-'} (<tt>'&#92;u002D'</tt>), followed by a sequence of

     * zero or more decimal digits ("the integer"), optionally

     * followed by a fraction, optionally followed by an exponent.

     *

     * <p>The fraction consists of a decimal point followed by zero

     * or more decimal digits.  The string must contain at least one

     * digit in either the integer or the fraction.  The number formed

     * by the sign, the integer and the fraction is referred to as the

     * <i>significand</i>.

     *

     * <p>The exponent consists of the character {@code 'e'}

     * (<tt>'&#92;u0065'</tt>) or {@code 'E'} (<tt>'&#92;u0045'</tt>)

     * followed by one or more decimal digits.  The value of the

     * exponent must lie between -{@link Integer#MAX_VALUE} ({@link

     * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive.

     *

     * <p>More formally, the strings this constructor accepts are

     * described by the following grammar:

     * <blockquote>

     * <dl>

     * <dt><i>BigDecimalString:</i>

     * <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i>

     * <p>

     * <dt><i>Sign:</i>

     * <dd>{@code +}

     * <dd>{@code -}

     * <p>

     * <dt><i>Significand:</i>

     * <dd><i>IntegerPart</i> {@code .} <i>FractionPart<sub>opt</sub></i>

     * <dd>{@code .} <i>FractionPart</i>

     * <dd><i>IntegerPart</i>

     * <p>

     * <dt><i>IntegerPart:</i>

     * <dd><i>Digits</i>

     * <p>

     * <dt><i>FractionPart:</i>

     * <dd><i>Digits</i>

     * <p>

     * <dt><i>Exponent:</i>

     * <dd><i>ExponentIndicator SignedInteger</i>

     * <p>

     * <dt><i>ExponentIndicator:</i>

     * <dd>{@code e}

     * <dd>{@code E}

     * <p>

     * <dt><i>SignedInteger:</i>

     * <dd><i>Sign<sub>opt</sub> Digits</i>

     * <p>

     * <dt><i>Digits:</i>

     * <dd><i>Digit</i>

     * <dd><i>Digits Digit</i>

     * <p>

     * <dt><i>Digit:</i>

     * <dd>any character for which {@link Character#isDigit}

     * returns {@code true}, including 0, 1, 2 ...

     * </dl>

     * </blockquote>

     *

     * <p>The scale of the returned {@code BigDecimal} will be the

     * number of digits in the fraction, or zero if the string

     * contains no decimal point, subject to adjustment for any

     * exponent; if the string contains an exponent, the exponent is

     * subtracted from the scale.  The value of the resulting scale

     * must lie between {@code Integer.MIN_VALUE} and

     * {@code Integer.MAX_VALUE}, inclusive.

     *

     * <p>The character-to-digit mapping is provided by {@link

     * java.lang.Character#digit} set to convert to radix 10.  The

     * String may not contain any extraneous characters (whitespace,

     * for example).

     *

     * <p><b>Examples:</b><br>

     * The value of the returned {@code BigDecimal} is equal to

     * <i>significand</i> &times; 10<sup>&nbsp;<i>exponent</i></sup>.

     * For each string on the left, the resulting representation

     * [{@code BigInteger}, {@code scale}] is shown on the right.

     * <pre>

     * "0"            [0,0]

     * "0.00"         [0,2]

     * "123"          [123,0]

     * "-123"         [-123,0]

     * "1.23E3"       [123,-1]

     * "1.23E+3"      [123,-1]

     * "12.3E+7"      [123,-6]

     * "12.0"         [120,1]

     * "12.3"         [123,1]

     * "0.00123"      [123,5]

     * "-1.23E-12"    [-123,14]

     * "1234.5E-4"    [12345,5]

     * "0E+7"         [0,-7]

     * "-0"           [0,0]

     * </pre>

     *

     * <p>Note: For values other than {@code float} and

     * {@code double} NaN and ±Infinity, this constructor is

     * compatible with the values returned by {@link Float#toString}

     * and {@link Double#toString}.  This is generally the preferred

     * way to convert a {@code float} or {@code double} into a

     * BigDecimal, as it doesn't suffer from the unpredictability of

     * the {@link #BigDecimal(double)} constructor.

     *

     * @param val String representation of {@code BigDecimal}.

     *

     * @throws NumberFormatException if {@code val} is not a valid

     *         representation of a {@code BigDecimal}.

     */

    public BigDecimal(String val) {

        this(val.toCharArray(), 0, val.length());

    }

    /**

     * Translates the string representation of a {@code BigDecimal}

     * into a {@code BigDecimal}, accepting the same strings as the

     * {@link #BigDecimal(String)} constructor, with rounding

     * according to the context settings.

     *

     * @param  val string representation of a {@code BigDecimal}.

     * @param  mc the context to use.

     * @throws ArithmeticException if the result is inexact but the

     *         rounding mode is {@code UNNECESSARY}.

     * @throws NumberFormatException if {@code val} is not a valid

     *         representation of a BigDecimal.

     * @since  1.5

     */

    public BigDecimal(String val, MathContext mc) {

        this(val.toCharArray(), 0, val.length());

        if (mc.precision > 0)

            roundThis(mc);

    }

    /**

     * Translates a {@code double} into a {@code BigDecimal} which

     * is the exact decimal representation of the {@code double}'s

     * binary floating-point value.  The scale of the returned

     * {@code BigDecimal} is the smallest value such that

     * <tt>(10<sup>scale</sup> &times; val)</tt> is an integer.

     * <p>

     * <b>Notes:</b>

     * <ol>

     * <li>

     * The results of this constructor can be somewhat unpredictable.

     * One might assume that writing {@code new BigDecimal(0.1)} in

     * Java creates a {@code BigDecimal} which is exactly equal to

     * 0.1 (an unscaled value of 1, with a scale of 1), but it is

     * actually equal to

     * 0.1000000000000000055511151231257827021181583404541015625.

     * This is because 0.1 cannot be represented exactly as a

     * {@code double} (or, for that matter, as a binary fraction of

     * any finite length).  Thus, the value that is being passed

     * <i>in</i> to the constructor is not exactly equal to 0.1,

     * appearances notwithstanding.

     *

     * <li>

     * The {@code String} constructor, on the other hand, is

     * perfectly predictable: writing {@code new BigDecimal("0.1")}

     * creates a {@code BigDecimal} which is <i>exactly</i> equal to

     * 0.1, as one would expect.  Therefore, it is generally

     * recommended that the {@linkplain #BigDecimal(String)

     * <tt>String</tt> constructor} be used in preference to this one.

     *

     * <li>

     * When a {@code double} must be used as a source for a

     * {@code BigDecimal}, note that this constructor provides an

     * exact conversion; it does not give the same result as

     * converting the {@code double} to a {@code String} using the

     * {@link Double#toString(double)} method and then using the

     * {@link #BigDecimal(String)} constructor.  To get that result,

     * use the {@code static} {@link #valueOf(double)} method.

     * </ol>

     *

     * @param val {@code double} value to be converted to

     *        {@code BigDecimal}.

     * @throws NumberFormatException if {@code val} is infinite or NaN.

     */

    public BigDecimal(double val) {

        if (Double.isInfinite(val) || Double.isNaN(val))

            throw new NumberFormatException("Infinite or NaN");

        // Translate the double into sign, exponent and significand, according

        // to the formulae in JLS, Section 20.10.22.

        long valBits = Double.doubleToLongBits(val);

        int sign = ((valBits >> 63)==0 ? 1 : -1);

        int exponent = (int) ((valBits >> 52) & 0x7ffL);

        long significand = (exponent==0 ? (valBits & ((1L<<52) - 1)) << 1

                            : (valBits & ((1L<<52) - 1)) | (1L<<52));

        exponent -= 1075;

        // At this point, val == sign * significand * 2**exponent.

        /*

         * Special case zero to supress nonterminating normalization

         * and bogus scale calculation.

         */

        if (significand == 0) {

            intVal = BigInteger.ZERO;

            intCompact = 0;

            precision = 1;

            return;

        }

        // Normalize

        while((significand & 1) == 0) {    //  i.e., significand is even

            significand >>= 1;

            exponent++;

        }

        // Calculate intVal and scale

        long s = sign * significand;

        BigInteger b;

        if (exponent < 0) {

            b = BigInteger.valueOf(5).pow(-exponent).multiply(s);

            scale = -exponent;

        } else if (exponent > 0) {

            b = BigInteger.valueOf(2).pow(exponent).multiply(s);

        } else {

            b = BigInteger.valueOf(s);

        }

        intCompact = compactValFor(b);

        intVal = (intCompact != INFLATED) ? null : b;

    }

    /**

     * Translates a {@code double} into a {@code BigDecimal}, with

     * rounding according to the context settings.  The scale of the

     * {@code BigDecimal} is the smallest value such that

     * <tt>(10<sup>scale</sup> &times; val)</tt> is an integer.

     *

     * <p>The results of this constructor can be somewhat unpredictable

     * and its use is generally not recommended; see the notes under

     * the {@link #BigDecimal(double)} constructor.

     *

     * @param  val {@code double} value to be converted to

     *         {@code BigDecimal}.

     * @param  mc the context to use.

     * @throws ArithmeticException if the result is inexact but the

     *         RoundingMode is UNNECESSARY.

     * @throws NumberFormatException if {@code val} is infinite or NaN.

     * @since  1.5

     */

    public BigDecimal(double val, MathContext mc) {

        this(val);

        if (mc.precision > 0)

            roundThis(mc);

    }

    /**

     * Translates a {@code BigInteger} into a {@code BigDecimal}.

     * The scale of the {@code BigDecimal} is zero.

     *

     * @param val {@code BigInteger} value to be converted to

     *            {@code BigDecimal}.

     */

    public BigDecimal(BigInteger val) {

        intCompact = compactValFor(val);

        intVal = (intCompact != INFLATED) ? null : val;

    }

    /**

     * Translates a {@code BigInteger} into a {@code BigDecimal}

     * rounding according to the context settings.  The scale of the

     * {@code BigDecimal} is zero.

     *

     * @param val {@code BigInteger} value to be converted to

     *            {@code BigDecimal}.

     * @param  mc the context to use.

     * @throws ArithmeticException if the result is inexact but the

     *         rounding mode is {@code UNNECESSARY}.

     * @since  1.5

     */

    public BigDecimal(BigInteger val, MathContext mc) {

        this(val);

        if (mc.precision > 0)

            roundThis(mc);

    }

    /**

     * Translates a {@code BigInteger} unscaled value and an

     * {@code int} scale into a {@code BigDecimal}.  The value of

     * the {@code BigDecimal} is

     * <tt>(unscaledVal &times; 10<sup>-scale</sup>)</tt>.

     *

     * @param unscaledVal unscaled value of the {@code BigDecimal}.

     * @param scale scale of the {@code BigDecimal}.

     */

    public BigDecimal(BigInteger unscaledVal, int scale) {

        // Negative scales are now allowed

        this(unscaledVal);

        this.scale = scale;

    }

    /**

     * Translates a {@code BigInteger} unscaled value and an

     * {@code int} scale into a {@code BigDecimal}, with rounding

     * according to the context settings.  The value of the

     * {@code BigDecimal} is <tt>(unscaledVal &times;

     * 10<sup>-scale</sup>)</tt>, rounded according to the

     * {@code precision} and rounding mode settings.

     *

     * @param  unscaledVal unscaled value of the {@code BigDecimal}.

     * @param  scale scale of the {@code BigDecimal}.

     * @param  mc the context to use.

     * @throws ArithmeticException if the result is inexact but the

     *         rounding mode is {@code UNNECESSARY}.

     * @since  1.5

     */

    public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {

        this(unscaledVal);

        this.scale = scale;

        if (mc.precision > 0)

            roundThis(mc);

    }

    /**

     * Translates an {@code int} into a {@code BigDecimal}.  The

     * scale of the {@code BigDecimal} is zero.

     *

     * @param val {@code int} value to be converted to

     *            {@code BigDecimal}.

     * @since  1.5

     */

    public BigDecimal(int val) {

        intCompact = val;

    }

    /**

     * Translates an {@code int} into a {@code BigDecimal}, with

     * rounding according to the context settings.  The scale of the

     * {@code BigDecimal}, before any rounding, is zero.

     *

     * @param  val {@code int} value to be converted to {@code BigDecimal}.

     * @param  mc the context to use.

     * @throws ArithmeticException if the result is inexact but the

     *         rounding mode is {@code UNNECESSARY}.

     * @since  1.5

     */

    public BigDecimal(int val, MathContext mc) {

        intCompact = val;

        if (mc.precision > 0)

            roundThis(mc);

    }

    /**

     * Translates a {@code long} into a {@code BigDecimal}.  The

     * scale of the {@code BigDecimal} is zero.

     *

     * @param val {@code long} value to be converted to {@code BigDecimal}.

     * @since  1.5

     */

    public BigDecimal(long val) {

        this.intCompact = val;

        this.intVal = (val == INFLATED) ? BigInteger.valueOf(val) : null;

    }

    /**

     * Translates a {@code long} into a {@code BigDecimal}, with

     * rounding according to the context settings.  The scale of the

     * {@code BigDecimal}, before any rounding, is zero.

     *

     * @param  val {@code long} value to be converted to {@code BigDecimal}.

     * @param  mc the context to use.

     * @throws ArithmeticException if the result is inexact but the

     *         rounding mode is {@code UNNECESSARY}.

     * @since  1.5

     */