/*

* Copyright (c) 1996, 2018, Oracle and/or its affiliates. All rights reserved.

* ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.

*

*

*

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*

*

*

*

*

*

*

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*

*

*

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*

*

*

*/

/*

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

*/

package java.math;

import static java.math.BigInteger.LONG_MASK;

import java.util.Arrays;

/**

* 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^-scale)</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;10¹. 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

* @author Sergey V. Kuksenko

*/

public class BigDecimal extends Number implements Comparable<BigDecimal> {

/**

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

* #unscaledValue}.

*

* @serial

* @see #unscaledValue

*/

private final BigInteger intVal;

/**

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

*

* @serial

* @see #scale

*/

private final 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;

private static final BigInteger INFLATED_BIGINT = BigInteger.valueOf(INFLATED);

/**

* 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 final 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;

/* 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) {

this(in,offset,len,MathContext.UNLIMITED);

}

/**

* 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) {

// protect against huge length, negative values, and integer overflow

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

throw new NumberFormatException

("Bad offset or len arguments for char[] input.");

}

// 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 '.'

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.

int idx = 0;

if (isCompact) {

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

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

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

c = in[offset];

if ((c == '0')) { // have zero

if (prec == 0)

prec = 1;

else if (rs != 0) {

rs *= 10;

++prec;

} // else digit is a redundant leading zero

if (dot)

++scl;

} else if ((c >= '1' && c <= '9')) { // have digit

int digit = c - '0';

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

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

rs = rs * 10 + digit;

if (dot)

++scl;

} else if (c == '.') { // have dot

// have dot

if (dot) // two dots

throw new NumberFormatException();

dot = true;

} else if (Character.isDigit(c)) { // slow path

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;

}

if (dot)

++scl;

} else if ((c == 'e') || (c == 'E')) {

exp = parseExp(in, offset, len);

// Next test is required for backwards compatibility

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

throw new NumberFormatException();

break; // [saves a test]

} else {

throw new NumberFormatException();

}

}

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

throw new NumberFormatException();

// Adjust scale if exp is not zero.

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

scl = adjustScale(scl, exp);

}

rs = isneg ? -rs : rs;

int mcp = mc.precision;

int drop = prec - mcp; // prec has range [1, MAX_INT], mcp has range [0, MAX_INT];

// therefore, this subtract cannot overflow

if (mcp > 0 && drop > 0) { // do rounding

while (drop > 0) {

scl = checkScaleNonZero((long) scl - drop);

rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);

prec = longDigitLength(rs);

drop = prec - mcp;

}

}

} else {

char coeff[] = new char[len];

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 (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();

exp = parseExp(in, offset, len);

// 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

scl = adjustScale(scl, exp);

}

// Remove leading zeros from precision (digits count)

rb = new BigInteger(coeff, isneg ? -1 : 1, prec);

rs = compactValFor(rb);

int mcp = mc.precision;

if (mcp > 0 && (prec > mcp)) {

if (rs == INFLATED) {

int drop = prec - mcp;

while (drop > 0) {

scl = checkScaleNonZero((long) scl - drop);

rb = divideAndRoundByTenPow(rb, drop, mc.roundingMode.oldMode);

rs = compactValFor(rb);

if (rs != INFLATED) {

prec = longDigitLength(rs);

break;

}

prec = bigDigitLength(rb);

drop = prec - mcp;

}

}

if (rs != INFLATED) {

int drop = prec - mcp;

while (drop > 0) {

scl = checkScaleNonZero((long) scl - drop);

rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);

prec = longDigitLength(rs);

drop = prec - mcp;

}

rb = null;

}

}

}

} catch (ArrayIndexOutOfBoundsException e) {

throw new NumberFormatException();

} catch (NegativeArraySizeException e) {

throw new NumberFormatException();

}

this.scale = scl;

this.precision = prec;

this.intCompact = rs;

this.intVal = rb;

}

private int adjustScale(int scl, long exp) {

long adjustedScale = scl - exp;

if (adjustedScale > Integer.MAX_VALUE || adjustedScale < Integer.MIN_VALUE)

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

scl = (int) adjustedScale;

return scl;

}

/*

* parse exponent

*/

private static long parseExp(char[] in, int offset, int len){

long exp = 0;

offset++;

char 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 && (c=='0' || (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;

return exp;

}

/**

* 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_opt Significand Exponent_opt</i>

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

* <dd>{@code +}

* <dd>{@code -}

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

* <dd><i>IntegerPart</i> {@code .} <i>FractionPart_opt</i>

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

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

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

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

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

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

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

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

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

* <dd>{@code e}

* <dd>{@code E}

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

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

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

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

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

* <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^{&nbsp;<i>exponent</i>}.

* 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 &plusmn;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(), 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^scale &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) {

this(val,MathContext.UNLIMITED);

}

/**

* 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^scale &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) {

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) {

this.intVal = BigInteger.ZERO;

this.scale = 0;

this.intCompact = 0;

this.precision = 1;

return;

}

// Normalize

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

significand >>= 1;

exponent++;

}

int scale = 0;

// Calculate intVal and scale

BigInteger intVal;

long compactVal = sign * significand;

if (exponent == 0) {

intVal = (compactVal == INFLATED) ? INFLATED_BIGINT : null;

} else {

if (exponent < 0) {

intVal = BigInteger.valueOf(5).pow(-exponent).multiply(compactVal);

scale = -exponent;

} else { // (exponent > 0)

intVal = BigInteger.valueOf(2).pow(exponent).multiply(compactVal);

}

compactVal = compactValFor(intVal);

}

int prec = 0;

int mcp = mc.precision;

if (mcp > 0) { // do rounding

int mode = mc.roundingMode.oldMode;

int drop;

if (compactVal == INFLATED) {

prec = bigDigitLength(intVal);

drop = prec - mcp;

while (drop > 0) {

scale = checkScaleNonZero((long) scale - drop);

intVal = divideAndRoundByTenPow(intVal, drop, mode);

compactVal = compactValFor(intVal);

if (compactVal != INFLATED) {

break;

}

prec = bigDigitLength(intVal);

drop = prec - mcp;

}

}

if (compactVal != INFLATED) {

prec = longDigitLength(compactVal);

drop = prec - mcp;

while (drop > 0) {

scale = checkScaleNonZero((long) scale - drop);

compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);

prec = longDigitLength(compactVal);

drop = prec - mcp;

}

intVal = null;

}

}

this.intVal = intVal;

this.intCompact = compactVal;

this.scale = scale;

this.precision = prec;

}

/**

* 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) {

scale = 0;

intVal = val;

intCompact = compactValFor(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}.