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BigDecimal.javaAPI DocJava SE 5 API140003Fri Aug 26 14:57:06 BST 2005java.math

# BigDecimal

public class BigDecimal extends Number implements Comparable
Immutable, arbitrary-precision signed decimal numbers. A BigDecimal consists of an arbitrary precision integer unscaled value and a 32-bit integer scale. 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 BigDecimal is therefore (unscaledValue × 10-scale).

The BigDecimal class provides operations for arithmetic, scale manipulation, rounding, comparison, hashing, and format conversion. The {@link #toString} method provides a canonical representation of a BigDecimal.

The 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 rounding modes 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 RoundingMode enum, (such as {@link RoundingMode#HALF_UP}) should be used instead.

When a 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 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 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 ArithmeticException is thrown. Otherwise, the exact result of the division is returned, as done for other operations.

When the precision setting is not 0, the rules of 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, BigDecimal includes many rounding modes, which were mandatory for division in BigDecimal releases prior to 5. Any conflicts between these ANSI standards and the BigDecimal specification are resolved in favor of BigDecimal.

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.

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 MathContext's precision setting; this determines the result's precision. 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.

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 "9" digit. For example, rounding the value 999.9 to three digits rounding up would be numerically equal to one thousand, represented as 100×101. In such cases, the new "1" is the leading digit position of the returned result.

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.

### Preferred Scales for Results of Arithmetic Operations

OperationPreferred Scale of Result
Addmax(addend.scale(), augend.scale())
Subtractmax(minuend.scale(), subtrahend.scale())
Multiplymultiplier.scale() + multiplicand.scale()
Dividedividend.scale() - divisor.scale()
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, 1/32 is 0.03125.

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 `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 `precision` digits actually returned. If the exact result can be represented with at most `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 `precision` digits by removing trailing zeros and decreasing the scale. For example, rounding to three digits using the {@linkplain RoundingMode#FLOOR floor} rounding mode,
`19/100 = 0.19 // integer=19, scale=2`
but
`21/110 = 0.190 // integer=190, scale=3`

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.

Other methods may have slightly different rounding semantics. For example, the result of the 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 {@linkplain #ulp() ulp}.

Two types of operations are provided for manipulating the scale of a BigDecimal: scaling/rounding operations and decimal point motion operations. Scaling/rounding operations ({@link #setScale setScale} and {@link #round round}) return a 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 BigDecimal created from the operand by moving the decimal point a specified distance in the specified direction.

For the sake of brevity and clarity, pseudo-code is used throughout the descriptions of BigDecimal methods. The pseudo-code expression (i + j) is shorthand for "a BigDecimal whose value is that of the BigDecimal i added to that of the BigDecimal j." The pseudo-code expression (i == j) is shorthand for "true if and only if the BigDecimal i represents the same value as the BigDecimal j." Other pseudo-code expressions are interpreted similarly. Square brackets are used to represent the particular BigInteger and scale pair defining a BigDecimal value; for example [19, 2] is the BigDecimal numerically equal to 0.19 having a scale of 2.

Note: care should be exercised if BigDecimal objects are used as keys in a {@link java.util.SortedMap SortedMap} or elements in a {@link java.util.SortedSet SortedSet} since BigDecimal's natural ordering is inconsistent with equals. See {@link Comparable}, {@link java.util.SortedMap} or {@link java.util.SortedSet} for more information.

All methods and constructors for this class throw NullPointerException when passed a null object reference for any input parameter.

 seeBigIntegerseeMathContextseeRoundingModeseejava.util.SortedMapseejava.util.SortedSetauthorJosh BlochauthorMike CowlishawauthorJoseph D. Darcy

Fields Summary
private volatile BigInteger
intVal
The unscaled value of this BigDecimal, as returned by {@link #unscaledValue}.
private int
scale
The scale of this BigDecimal, as returned by {@link #scale}.
private volatile transient int
precision
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.
private volatile transient String
stringCache
Used to store the canonical string representation, if computed.
private static final long
INFLATED
Sentinel value for {@link #intCompact} indicating the significand information is only available from {@code intVal}.
private transient long
intCompact
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 static final int
MAX_COMPACT_DIGITS
private static final int
MAX_BIGINT_BITS
private static final long
serialVersionUID
private static final BigDecimal[]
zeroThroughTen
public static final BigDecimal
ZERO
The value 0, with a scale of 0.
public static final BigDecimal
ONE
The value 1, with a scale of 0.
public static final BigDecimal
TEN
The value 10, with a scale of 0.
public static final int
ROUND_UP
Rounding mode to round away from zero. Always increments the digit prior to a nonzero discarded fraction. Note that this rounding mode never decreases the magnitude of the calculated value.
public static final int
ROUND_DOWN
Rounding mode to round towards zero. Never increments the digit prior to a discarded fraction (i.e., truncates). Note that this rounding mode never increases the magnitude of the calculated value.
public static final int
ROUND_CEILING
Rounding mode to round towards positive infinity. If the BigDecimal is positive, behaves as for ROUND_UP; if negative, behaves as for ROUND_DOWN. Note that this rounding mode never decreases the calculated value.
public static final int
ROUND_FLOOR
Rounding mode to round towards negative infinity. If the BigDecimal is positive, behave as for ROUND_DOWN; if negative, behave as for ROUND_UP. Note that this rounding mode never increases the calculated value.
public static final int
ROUND_HALF_UP
Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round up. Behaves as for ROUND_UP if the discarded fraction is >= 0.5; otherwise, behaves as for ROUND_DOWN. Note that this is the rounding mode that most of us were taught in grade school.
public static final int
ROUND_HALF_DOWN
Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round down. Behaves as for ROUND_UP if the discarded fraction is > 0.5; otherwise, behaves as for ROUND_DOWN.
public static final int
ROUND_HALF_EVEN
Rounding mode to round towards the "nearest neighbor" unless both neighbors are equidistant, in which case, round towards the even neighbor. Behaves as for ROUND_HALF_UP if the digit to the left of the discarded fraction is odd; behaves as for ROUND_HALF_DOWN if it's even. Note that this is the rounding mode that minimizes cumulative error when applied repeatedly over a sequence of calculations.
public static final int
ROUND_UNNECESSARY
Rounding mode to assert that the requested operation has an exact result, hence no rounding is necessary. If this rounding mode is specified on an operation that yields an inexact result, an ArithmeticException is thrown.
private static BigInteger
LONGMIN
BigInteger equal to Long.MIN_VALUE.
private static BigInteger
LONGMAX
BigInteger equal to Long.MAX_VALUE.
private static BigInteger[]
TENPOWERS
private static long[]
thresholds
private static int[]
ilogTable
Constructors Summary
public BigDecimal(char[] in, int offset, int len)
Translates a character array representation of a BigDecimal into a BigDecimal, accepting the same sequence of characters as the {@link #BigDecimal(String)} constructor, while allowing a sub-array to be specified.

Note that if the sequence of characters is already available within a character array, using this constructor is faster than converting the char array to string and using the BigDecimal(String) constructor .

 paramin char array that is the source of characters.paramoffset first character in the array to inspect.paramlen number of characters to consider.throwsNumberFormatException if in is not a valid representation of a BigDecimal or the defined subarray is not wholly within in.since1.5

``````
// Constructors

// 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).

// 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
int dotoff = -1;                 // '.' offset, -1 if none
int cfirst = offset;             // record start of integer
long exp = 0;                    // exponent
if (len > in.length)             // protect against huge length
throw new NumberFormatException();
char coeff[] = new char[len];    // integer significand array
char c;                          // work

for (; len > 0; offset++, len--) {
c = in[offset];
if ((c >= '0" && c <= '9") || Character.isDigit(c)) {
// have digit
coeff[precision] = c;
precision++;             // count of digits
continue;
}
if (c == '.") {
// have dot
if (dotoff >= 0)         // two dots
throw new NumberFormatException();
dotoff = offset;
continue;
}
// exponent expected
if ((c != 'e") && (c != 'E"))
throw new NumberFormatException();
offset++;
c = in[offset];
len--;
boolean negexp = false;
// optional sign
if (c == '-" || c == '+") {
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 (precision == 0)              // no digits found
throw new NumberFormatException();

if (dotoff >= 0) {               // had dot; set scale
scale = precision - (dotoff - cfirst);
// [cannot overflow]
}
if (exp != 0) {                  // had significant exponent
try {
scale = checkScale(-exp + scale); // adjust
} catch (ArithmeticException e) {
throw new NumberFormatException("Scale out of range.");
}
}

// Remove leading zeros from precision (digits count)
int first = 0;
for (; (coeff[first] == '0" || Character.digit(coeff[first], 10) == 0) &&
precision > 1;
first++)
precision--;

// Set the significand ..
// Copy significand to exact-sized array, with sign if
// negative
// Later use: BigInteger(coeff, first, precision) for
//   both cases, by allowing an extra char at the front of
//   coeff.
char quick[];
if (!isneg) {
quick = new char[precision];
System.arraycopy(coeff, first, quick, 0, precision);
} else {
quick = new char[precision+1];
quick = '-";
System.arraycopy(coeff, first, quick, 1, precision);
}
if (precision <= MAX_COMPACT_DIGITS)
intCompact = Long.parseLong(new String(quick));
else
intVal = new BigInteger(quick);
// System.out.println(" new: " +intVal+" ["+scale+"] "+precision);
} catch (ArrayIndexOutOfBoundsException e) {
throw new NumberFormatException();
} catch (NegativeArraySizeException e) {
throw new NumberFormatException();
}
``````
public BigDecimal(BigInteger val, MathContext mc)
Translates a BigInteger into a BigDecimal rounding according to the context settings. The scale of the BigDecimal is zero.

 paramval BigInteger value to be converted to BigDecimal.parammc the context to use.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.since1.5

``````        intVal = val;
if (mc.precision > 0)
roundThis(mc);
``````
public BigDecimal(BigInteger unscaledVal, int scale)
Translates a BigInteger unscaled value and an int scale into a BigDecimal. The value of the BigDecimal is (unscaledVal × 10-scale).

 paramunscaledVal unscaled value of the BigDecimal.paramscale scale of the BigDecimal.

``````        // Negative scales are now allowed
intVal = unscaledVal;
this.scale = scale;
if (unscaledVal.bitLength() <= MAX_BIGINT_BITS) {
intCompact = unscaledVal.longValue();
}
``````
public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc)
Translates a BigInteger unscaled value and an int scale into a BigDecimal, with rounding according to the context settings. The value of the BigDecimal is (unscaledVal × 10-scale), rounded according to the precision and rounding mode settings.

 paramunscaledVal unscaled value of the BigDecimal.paramscale scale of the BigDecimal.parammc the context to use.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.since1.5

``````        intVal = unscaledVal;
this.scale = scale;
if (mc.precision > 0)
roundThis(mc);
``````
public BigDecimal(int val)
Translates an int into a BigDecimal. The scale of the BigDecimal is zero.

 paramval int value to be converted to BigDecimal.since1.5

``````	intCompact = val;
``````
public BigDecimal(int val, MathContext mc)
Translates an int into a BigDecimal, with rounding according to the context settings. The scale of the BigDecimal, before any rounding, is zero.

 paramval int value to be converted to BigDecimal.parammc the context to use.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.since1.5

``````	intCompact = val;
if (mc.precision > 0)
roundThis(mc);
``````
public BigDecimal(long val)
Translates a long into a BigDecimal. The scale of the BigDecimal is zero.

 paramval long value to be converted to BigDecimal.since1.5

``````	if (compactLong(val))
intCompact = val;
else
intVal = BigInteger.valueOf(val);
``````
public BigDecimal(long val, MathContext mc)
Translates a long into a BigDecimal, with rounding according to the context settings. The scale of the BigDecimal, before any rounding, is zero.

 paramval long value to be converted to BigDecimal.parammc the context to use.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.since1.5

``````	if (compactLong(val))
intCompact = val;
else
intVal = BigInteger.valueOf(val);
if (mc.precision > 0)
roundThis(mc);
``````
private BigDecimal(long val, int scale)
Trusted internal constructor

``````	this.intCompact = val;
this.scale = scale;
``````
private BigDecimal(BigInteger intVal, long val, int scale)
Trusted internal constructor

``````	this.intVal = intVal;
this.intCompact = val;
this.scale = scale;
``````
public BigDecimal(char[] in, int offset, int len, MathContext mc)
Translates a character array representation of a BigDecimal into a 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.

Note that if the sequence of characters is already available within a character array, using this constructor is faster than converting the char array to string and using the BigDecimal(String) constructor .

 paramin char array that is the source of characters.paramoffset first character in the array to inspect.paramlen number of characters to consider..parammc the context to use.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.throwsNumberFormatException if in is not a valid representation of a BigDecimal or the defined subarray is not wholly within in.since1.5

``````        this(in, offset, len);
if (mc.precision > 0)
roundThis(mc);
``````
public BigDecimal(char[] in)
Translates a character array representation of a BigDecimal into a BigDecimal, accepting the same sequence of characters as the {@link #BigDecimal(String)} constructor.

Note that if the sequence of characters is already available as a character array, using this constructor is faster than converting the char array to string and using the BigDecimal(String) constructor .

 paramin char array that is the source of characters.throwsNumberFormatException if in is not a valid representation of a BigDecimal.since1.5

``````        this(in, 0, in.length);
``````
public BigDecimal(char[] in, MathContext mc)
Translates a character array representation of a BigDecimal into a BigDecimal, accepting the same sequence of characters as the {@link #BigDecimal(String)} constructor and with rounding according to the context settings.

Note that if the sequence of characters is already available as a character array, using this constructor is faster than converting the char array to string and using the BigDecimal(String) constructor .

 paramin char array that is the source of characters.parammc the context to use.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.throwsNumberFormatException if in is not a valid representation of a BigDecimal.since1.5

``````        this(in, 0, in.length, mc);
``````
public BigDecimal(String val)
Translates the string representation of a BigDecimal into a BigDecimal. The string representation consists of an optional sign, '+' ('\u002B') or '-' ('\u002D'), followed by a sequence of zero or more decimal digits ("the integer"), optionally followed by a fraction, optionally followed by an exponent.

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 significand.

The exponent consists of the character 'e' ('\u0075') or 'E' ('\u0045') 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.

More formally, the strings this constructor accepts are described by the following grammar:

BigDecimalString:
Signopt Significand Exponentopt

Sign:
+
-

Significand:
IntegerPart . FractionPartopt
. FractionPart
IntegerPart

IntegerPart:
Digits

FractionPart:
Digits

Exponent:
ExponentIndicator SignedInteger

ExponentIndicator:
e
E

SignedInteger:
Signopt Digits

Digits:
Digit
Digits Digit

Digit:
any character for which {@link Character#isDigit} returns true, including 0, 1, 2 ...

The scale of the returned 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 Integer.MIN_VALUE and Integer.MAX_VALUE, inclusive.

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).

Examples:
The value of the returned BigDecimal is equal to significand × 10 exponent. For each string on the left, the resulting representation [BigInteger, scale] is shown on the right.

```"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]
```

Note: For values other than float and 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 float or double into a BigDecimal, as it doesn't suffer from the unpredictability of the {@link #BigDecimal(double)} constructor.

 paramval String representation of BigDecimal.throwsNumberFormatException if val is not a valid representation of a BigDecimal.

``````        this(val.toCharArray(), 0, val.length());
``````
public BigDecimal(String val, MathContext mc)
Translates the string representation of a BigDecimal into a BigDecimal, accepting the same strings as the {@link #BigDecimal(String)} constructor, with rounding according to the context settings.

 paramval string representation of a BigDecimal.parammc the context to use.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.throwsNumberFormatException if val is not a valid representation of a BigDecimal.since1.5

``````        this(val.toCharArray(), 0, val.length());
if (mc.precision > 0)
roundThis(mc);
``````
public BigDecimal(double val)
Translates a double into a BigDecimal which is the exact decimal representation of the double's binary floating-point value. The scale of the returned BigDecimal is the smallest value such that (10scale × val) is an integer.

Notes:

1. The results of this constructor can be somewhat unpredictable. One might assume that writing new BigDecimal(0.1) in Java creates a 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 double (or, for that matter, as a binary fraction of any finite length). Thus, the value that is being passed in to the constructor is not exactly equal to 0.1, appearances notwithstanding.
2. The String constructor, on the other hand, is perfectly predictable: writing new BigDecimal("0.1") creates a BigDecimal which is exactly equal to 0.1, as one would expect. Therefore, it is generally recommended that the {@linkplain #BigDecimal(String) String constructor} be used in preference to this one.
3. When a double must be used as a source for a BigDecimal, note that this constructor provides an exact conversion; it does not give the same result as converting the double to a String using the {@link Double#toString(double)} method and then using the {@link #BigDecimal(String)} constructor. To get that result, use the static {@link #valueOf(double)} method.

 paramval double value to be converted to BigDecimal.throwsNumberFormatException if val is infinite or NaN.

`````` 	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
intVal = BigInteger.valueOf(sign*significand);
if (exponent < 0) {
intVal = intVal.multiply(BigInteger.valueOf(5).pow(-exponent));
scale = -exponent;
} else if (exponent > 0) {
intVal = intVal.multiply(BigInteger.valueOf(2).pow(exponent));
}
if (intVal.bitLength() <= MAX_BIGINT_BITS) {
intCompact = intVal.longValue();
}
``````
public BigDecimal(double val, MathContext mc)
Translates a double into a BigDecimal, with rounding according to the context settings. The scale of the BigDecimal is the smallest value such that (10scale × val) is an integer.

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.

 paramval double value to be converted to BigDecimal.parammc the context to use.throwsArithmeticException if the result is inexact but the RoundingMode is UNNECESSARY.throwsNumberFormatException if val is infinite or NaN.since1.5

``````        this(val);
if (mc.precision > 0)
roundThis(mc);
``````
public BigDecimal(BigInteger val)
Translates a BigInteger into a BigDecimal. The scale of the BigDecimal is zero.

 paramval BigInteger value to be converted to BigDecimal.

``````        intVal = val;
if (val.bitLength() <= MAX_BIGINT_BITS) {
intCompact = val.longValue();
}
``````
Methods Summary
public java.math.BigDecimalabs()
Returns a BigDecimal whose value is the absolute value of this BigDecimal, and whose scale is this.scale().

 returnabs(this)

``````        return (signum() < 0 ? negate() : this);
``````
public java.math.BigDecimalabs(java.math.MathContext mc)
Returns a BigDecimal whose value is the absolute value of this BigDecimal, with rounding according to the context settings.

 parammc the context to use.returnabs(this), rounded as necessary.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.

``````        return (signum() < 0 ? negate(mc) : plus(mc));
``````
public java.math.BigDecimaladd(java.math.BigDecimal augend)
Returns a BigDecimal whose value is (this + augend), and whose scale is max(this.scale(), augend.scale()).

 paramaugend value to be added to this BigDecimal.returnthis + augend

``````        BigDecimal arg[] = {this, augend};
matchScale(arg);

long x = arg.intCompact;
long y = arg.intCompact;

// Might be able to do a more clever check incorporating the
// inflated check into the overflow computation.
if (x != INFLATED && y != INFLATED) {
long sum = x + y;
/*
* If the sum is not an overflowed value, continue to use
* the compact representation.  if either of x or y is
* INFLATED, the sum should also be regarded as an
* overflow.  See "Hacker's Delight" section 2-12 for
* explanation of the overflow test.
*/
if ( (((sum ^ x) & (sum ^ y)) >> 63) == 0L )	// not overflowed
return BigDecimal.valueOf(sum, arg.scale);
}
return new BigDecimal(arg.inflate().intVal.add(arg.inflate().intVal), arg.scale);
``````
public java.math.BigDecimaladd(java.math.BigDecimal augend, java.math.MathContext mc)
Returns a BigDecimal whose value is (this + augend), with rounding according to the context settings. If either number is zero and the precision setting is nonzero then the other number, rounded if necessary, is used as the result.

 paramaugend value to be added to this BigDecimal.parammc the context to use.returnthis + augend, rounded as necessary.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.since1.5

``````        if (mc.precision == 0)
return add(augend);
BigDecimal lhs = this;

// Could optimize if values are compact
this.inflate();
augend.inflate();

// If either number is zero then the other number, rounded and
// scaled if necessary, is used as the result.
{
boolean lhsIsZero = lhs.signum() == 0;
boolean augendIsZero = augend.signum() == 0;

if (lhsIsZero || augendIsZero) {
int preferredScale = Math.max(lhs.scale(), augend.scale());
BigDecimal result;

// Could use a factory for zero instead of a new object
if (lhsIsZero && augendIsZero)
return new BigDecimal(BigInteger.ZERO, 0, preferredScale);

result = lhsIsZero ? augend.doRound(mc) : lhs.doRound(mc);

if (result.scale() == preferredScale)
return result;
else if (result.scale() > preferredScale)
return new BigDecimal(result.intVal, result.intCompact, result.scale).
stripZerosToMatchScale(preferredScale);
else { // result.scale < preferredScale
int precisionDiff = mc.precision - result.precision();
int scaleDiff     = preferredScale - result.scale();

if (precisionDiff >= scaleDiff)
return result.setScale(preferredScale); // can achieve target scale
else
return result.setScale(result.scale() + precisionDiff);
}
}
}

int padding = checkScale((long)lhs.scale - augend.scale);
if (padding != 0) {        // scales differ; alignment needed
// if one operand is < 0.01 ulp of the other at full
// precision, replace it by a 'sticky bit' of +0.001/-0.001 ulp.
// [In a sense this is an 'optimization', but it also makes
// a much wider range of additions practical.]
if (padding < 0) {     // lhs will be padded
int ulpscale = lhs.scale - lhs.precision + mc.precision;
if (augend.scale - augend.precision() > ulpscale + 1) {
augend = BigDecimal.valueOf(augend.signum(), ulpscale + 3);
}
} else {               // rhs (augend) will be padded
int ulpscale = augend.scale - augend.precision + mc.precision;
if (lhs.scale - lhs.precision() > ulpscale + 1)
lhs = BigDecimal.valueOf(lhs.signum(), ulpscale + 3);
}
BigDecimal arg[] = new BigDecimal;
arg = lhs;  arg = augend;
matchScale(arg);
lhs = arg;
augend = arg;
}

return new BigDecimal(lhs.inflate().intVal.add(augend.inflate().intVal),
lhs.scale).doRound(mc);
``````
private java.math.BigDecimalaudit()
Check internal invariants of this BigDecimal. These invariants include:
• The object must be initialized; either intCompact must not be INFLATED or intVal is non-null. Both of these conditions may be true.
• If both intCompact and intVal and set, their values must be consistent.
• If precision is nonzero, it must have the right value.

``````	// Check precision
if (precision > 0) {
if (precision != digitLength()) {
print("audit", this);
throw new AssertionError("precision mismatch");
}
}

if (intCompact == INFLATED) {
if (intVal == null) {
print("audit", this);
throw new AssertionError("null intVal");
}
} else {
if (intVal != null) {
long val = intVal.longValue();
if (val != intCompact) {
print("audit", this);
throw new AssertionError("Inconsistent state, intCompact=" +
intCompact + "\t intVal=" + val);
}
}
}
return this;
``````
public bytebyteValueExact()
Converts this BigDecimal to a byte, checking for lost information. If this BigDecimal has a nonzero fractional part or is out of the possible range for a byte result then an ArithmeticException is thrown.

 returnthis BigDecimal converted to a byte.throwsArithmeticException if this has a nonzero fractional part, or will not fit in a byte.since1.5

``````       long num;
num = this.longValueExact();     // will check decimal part
if ((byte)num != num)
throw new java.lang.ArithmeticException("Overflow");
return (byte)num;
``````
private intcheckScale(long val)
Check a scale for Underflow or Overflow. If this BigDecimal. is uninitialized or initialized and nonzero, throw an exception if the scale is out of range. If this is zero, saturate the scale to the extreme value of the right sign if the scale is out of range.

 paramval The new scale.throwsArithmeticException (overflow or underflow) if the new scale is out of range.returnvalidated scale as an int.

``````        if ((int)val != val) {
if ((this.intCompact != INFLATED && this.intCompact != 0) ||
(this.intVal   != null     && this.signum() != 0) ||
(this.intVal == null && this.intCompact == INFLATED) ) {
if (val > Integer.MAX_VALUE)
throw new ArithmeticException("Underflow");
if (val < Integer.MIN_VALUE)
throw new ArithmeticException("Overflow");
} else {
return (val > Integer.MAX_VALUE)?Integer.MAX_VALUE:Integer.MIN_VALUE;
}
}
return (int)val;
``````
private static booleancompactLong(long val)

``````

return (val != Long.MIN_VALUE);
``````
public intcompareTo(java.math.BigDecimal val)
Compares this BigDecimal with the specified BigDecimal. Two BigDecimal objects that are equal in value but have a different scale (like 2.0 and 2.00) are considered equal by this method. This method is provided in preference to individual methods for each of the six boolean comparison operators (<, ==, >, >=, !=, <=). The suggested idiom for performing these comparisons is: (x.compareTo(y) <op> 0), where <op> is one of the six comparison operators.

 paramval BigDecimal to which this BigDecimal is to be compared.return-1, 0, or 1 as this BigDecimal is numerically less than, equal to, or greater than val.

``````	// Optimization: would run fine without the next three lines
int sigDiff = signum() - val.signum();
if (sigDiff != 0)
return (sigDiff > 0 ? 1 : -1);

// If the (adjusted) exponents are different we do not need to
// expensively match scales and compare the significands
int aethis = this.precision() - this.scale;    // [-1]
int aeval  =  val.precision() - val.scale;     // [-1]
if (aethis < aeval)
return -this.signum();
else if (aethis > aeval)
return this.signum();

// Scale and compare intVals
BigDecimal arg[] = {this, val};
matchScale(arg);
if (arg.intCompact != INFLATED && arg.intCompact != INFLATED)
return longCompareTo(arg.intCompact, arg.intCompact);
return arg.inflate().intVal.compareTo(arg.inflate().intVal);
``````
private intdigitLength()
Returns the length of this BigDecimal, in decimal digits. Notes:
• This is performance-critical; most operations where a context is supplied will need at least one call to this method.
• This should be a method on BigInteger; the call to this method in precision() can then be replaced with the term: intVal.digitLength(). It could also be called precision() in BigInteger. Better still -- the precision lookaside could be moved to BigInteger, too.
• This could/should use MutableBigIntegers directly for the reduction loop.

 returnthe length of the unscaled value, in decimal digits

``````	if (intCompact != INFLATED && Math.abs(intCompact) <= Integer.MAX_VALUE)
return intLength(Math.abs((int)intCompact));
if (signum() == 0)       // 0 is one decimal digit
return 1;
this.inflate();
// we have a nonzero magnitude
BigInteger work = intVal;
int digits = 0;                 // counter
for (;work.mag.length>1;) {
// here when more than one integer in the magnitude; divide
// by a billion (reduce by 9 digits) and try again
work = work.divide(TENPOWERS);
digits += 9;
if (work.signum() == 0)     // the division was exact
return digits;          // (a power of a billion)
}
// down to a simple nonzero integer
digits += intLength(work.mag);
// System.out.println("digitLength... "+this+"  ->  "+digits);
return digits;
``````
public java.math.BigDecimaldivide(java.math.BigDecimal divisor, int scale, int roundingMode)
Returns a BigDecimal whose value is (this / divisor), and whose scale is as specified. If rounding must be performed to generate a result with the specified scale, the specified rounding mode is applied.

The new {@link #divide(BigDecimal, int, RoundingMode)} method should be used in preference to this legacy method.

 paramdivisor value by which this BigDecimal is to be divided.paramscale scale of the BigDecimal quotient to be returned.paramroundingMode rounding mode to apply.returnthis / divisorthrowsArithmeticException if divisor is zero, roundingMode==ROUND_UNNECESSARY and the specified scale is insufficient to represent the result of the division exactly.throwsIllegalArgumentException if roundingMode does not represent a valid rounding mode.see#ROUND_UPsee#ROUND_DOWNsee#ROUND_CEILINGsee#ROUND_FLOORsee#ROUND_HALF_UPsee#ROUND_HALF_DOWNsee#ROUND_HALF_EVENsee#ROUND_UNNECESSARY

``````	/*
* IMPLEMENTATION NOTE: This method *must* return a new object
* since dropDigits uses divide to generate a value whose
* scale is then modified.
*/
if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
throw new IllegalArgumentException("Invalid rounding mode");
/*
* Rescale dividend or divisor (whichever can be "upscaled" to
* produce correctly scaled quotient).
* Take care to detect out-of-range scales
*/
BigDecimal dividend;
if (checkScale((long)scale + divisor.scale) >= this.scale) {
dividend = this.setScale(scale + divisor.scale);
} else {
dividend = this;
divisor = divisor.setScale(checkScale((long)this.scale - scale));
}

boolean compact = dividend.intCompact != INFLATED && divisor.intCompact != INFLATED;
long div = INFLATED;
long rem = INFLATED;;
BigInteger q=null, r=null;

if (compact) {
div = dividend.intCompact / divisor.intCompact;
rem = dividend.intCompact % divisor.intCompact;
} else {
// Do the division and return result if it's exact.
BigInteger i[] = dividend.inflate().intVal.divideAndRemainder(divisor.inflate().intVal);
q = i;
r = i;
}

// Check for exact result
if (compact) {
if (rem == 0)
return new BigDecimal(div, scale);
} else {
if (r.signum() == 0)
return new BigDecimal(q, scale);
}

if (roundingMode == ROUND_UNNECESSARY)      // Rounding prohibited
throw new ArithmeticException("Rounding necessary");

/* Round as appropriate */
int signum = dividend.signum() * divisor.signum(); // Sign of result
boolean increment;
if (roundingMode == ROUND_UP) {             // Away from zero
increment = true;
} else if (roundingMode == ROUND_DOWN) {    // Towards zero
increment = false;
} else if (roundingMode == ROUND_CEILING) { // Towards +infinity
increment = (signum > 0);
} else if (roundingMode == ROUND_FLOOR) {   // Towards -infinity
increment = (signum < 0);
} else { // Remaining modes based on nearest-neighbor determination
int cmpFracHalf;
if (compact) {
cmpFracHalf = longCompareTo(Math.abs(2*rem), Math.abs(divisor.intCompact));
} else {
// add(r) here is faster than multiply(2) or shiftLeft(1)
cmpFracHalf= r.add(r).abs().compareTo(divisor.intVal.abs());
}
if (cmpFracHalf < 0) {         // We're closer to higher digit
increment = false;
} else if (cmpFracHalf > 0) {  // We're closer to lower digit
increment = true;
} else {                       // We're dead-center
if (roundingMode == ROUND_HALF_UP)
increment = true;
else if (roundingMode == ROUND_HALF_DOWN)
increment = false;
else { // roundingMode == ROUND_HALF_EVEN
if (compact)
increment = (div & 1L) != 0L;
else
increment = q.testBit(0);   // true iff q is odd
}
}
}

if (compact) {
if (increment)
div += signum; // guaranteed not to overflow
return new BigDecimal(div, scale);
} else {
return (increment
? new BigDecimal(q.add(BigInteger.valueOf(signum)), scale)
: new BigDecimal(q, scale));
}
``````
public java.math.BigDecimaldivide(java.math.BigDecimal divisor, int scale, java.math.RoundingMode roundingMode)
Returns a BigDecimal whose value is (this / divisor), and whose scale is as specified. If rounding must be performed to generate a result with the specified scale, the specified rounding mode is applied.

 paramdivisor value by which this BigDecimal is to be divided.paramscale scale of the BigDecimal quotient to be returned.paramroundingMode rounding mode to apply.returnthis / divisorthrowsArithmeticException if divisor is zero, roundingMode==RoundingMode.UNNECESSARY and the specified scale is insufficient to represent the result of the division exactly.since1.5

``````	return divide(divisor, scale, roundingMode.oldMode);
``````
public java.math.BigDecimaldivide(java.math.BigDecimal divisor, int roundingMode)
Returns a BigDecimal whose value is (this / divisor), and whose scale is this.scale(). If rounding must be performed to generate a result with the given scale, the specified rounding mode is applied.

The new {@link #divide(BigDecimal, RoundingMode)} method should be used in preference to this legacy method.

 paramdivisor value by which this BigDecimal is to be divided.paramroundingMode rounding mode to apply.returnthis / divisorthrowsArithmeticException if divisor==0, or roundingMode==ROUND_UNNECESSARY and this.scale() is insufficient to represent the result of the division exactly.throwsIllegalArgumentException if roundingMode does not represent a valid rounding mode.see#ROUND_UPsee#ROUND_DOWNsee#ROUND_CEILINGsee#ROUND_FLOORsee#ROUND_HALF_UPsee#ROUND_HALF_DOWNsee#ROUND_HALF_EVENsee#ROUND_UNNECESSARY

``````            return this.divide(divisor, scale, roundingMode);
``````
public java.math.BigDecimaldivide(java.math.BigDecimal divisor, java.math.RoundingMode roundingMode)
Returns a BigDecimal whose value is (this / divisor), and whose scale is this.scale(). If rounding must be performed to generate a result with the given scale, the specified rounding mode is applied.

 paramdivisor value by which this BigDecimal is to be divided.paramroundingMode rounding mode to apply.returnthis / divisorthrowsArithmeticException if divisor==0, or roundingMode==RoundingMode.UNNECESSARY and this.scale() is insufficient to represent the result of the division exactly.

``````	return this.divide(divisor, scale, roundingMode.oldMode);
``````
public java.math.BigDecimaldivide(java.math.BigDecimal divisor)
Returns a BigDecimal whose value is (this / divisor), and whose preferred scale is (this.scale() - divisor.scale()); if the exact quotient cannot be represented (because it has a non-terminating decimal expansion) an ArithmeticException is thrown.

 paramdivisor value by which this BigDecimal is to be divided.throwsArithmeticException if the exact quotient does not have a terminating decimal expansionreturnthis / divisorsince1.5authorJoseph D. Darcy

``````	/*
* Handle zero cases first.
*/
if (divisor.signum() == 0) {   // x/0
if (this.signum() == 0)    // 0/0
throw new ArithmeticException("Division undefined");  // NaN
throw new ArithmeticException("Division by zero");
}

// Calculate preferred scale
int preferredScale = (int)Math.max(Math.min((long)this.scale() - divisor.scale(),
Integer.MAX_VALUE), Integer.MIN_VALUE);
if (this.signum() == 0)        // 0/y
return new BigDecimal(0, preferredScale);
else {
this.inflate();
divisor.inflate();
/*
* If the quotient this/divisor has a terminating decimal
* expansion, the expansion can have no more than
* (a.precision() + ceil(10*b.precision)/3) digits.
* Therefore, create a MathContext object with this
* precision and do a divide with the UNNECESSARY rounding
* mode.
*/
MathContext mc = new MathContext( (int)Math.min(this.precision() +
(long)Math.ceil(10.0*divisor.precision()/3.0),
Integer.MAX_VALUE),
RoundingMode.UNNECESSARY);
BigDecimal quotient;
try {
quotient = this.divide(divisor, mc);
} catch (ArithmeticException e) {
throw new ArithmeticException("Non-terminating decimal expansion; " +
"no exact representable decimal result.");
}

int quotientScale = quotient.scale();

// divide(BigDecimal, mc) tries to adjust the quotient to
// the desired one by removing trailing zeros; since the
// exact divide method does not have an explicit digit
// limit, we can add zeros too.

if (preferredScale > quotientScale)
return quotient.setScale(preferredScale);

return quotient;
}
``````
public java.math.BigDecimaldivide(java.math.BigDecimal divisor, java.math.MathContext mc)
Returns a BigDecimal whose value is (this / divisor), with rounding according to the context settings.

 paramdivisor value by which this BigDecimal is to be divided.parammc the context to use.returnthis / divisor, rounded as necessary.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY or mc.precision == 0 and the quotient has a non-terminating decimal expansion.since1.5

``````        if (mc.precision == 0)
return divide(divisor);
BigDecimal lhs = this.inflate();     // left-hand-side
BigDecimal rhs = divisor.inflate();  // right-hand-side
BigDecimal result;                   // work

long preferredScale = (long)lhs.scale() - rhs.scale();

// Now calculate the answer.  We use the existing
// divide-and-round method, but as this rounds to scale we have
// to normalize the values here to achieve the desired result.
// For x/y we first handle y=0 and x=0, and then normalize x and
// y to give x' and y' with the following constraints:
//   (a) 0.1 <= x' < 1
//   (b)  x' <= y' < 10*x'
// Dividing x'/y' with the required scale set to mc.precision then
// will give a result in the range 0.1 to 1 rounded to exactly
// the right number of digits (except in the case of a result of
// 1.000... which can arise when x=y, or when rounding overflows
// The 1.000... case will reduce properly to 1.
if (rhs.signum() == 0) {      // x/0
if (lhs.signum() == 0)    // 0/0
throw new ArithmeticException("Division undefined");  // NaN
throw new ArithmeticException("Division by zero");
}
if (lhs.signum() == 0)        // 0/y
return new BigDecimal(BigInteger.ZERO,
(int)Math.max(Math.min(preferredScale,
Integer.MAX_VALUE),
Integer.MIN_VALUE));

BigDecimal xprime = new BigDecimal(lhs.intVal.abs(), lhs.precision());
BigDecimal yprime = new BigDecimal(rhs.intVal.abs(), rhs.precision());
// xprime and yprime are now both in range 0.1 through 0.999...
if (mc.roundingMode == RoundingMode.CEILING ||
mc.roundingMode == RoundingMode.FLOOR) {
// The floor (round toward negative infinity) and ceil
// (round toward positive infinity) rounding modes are not
// invariant under a sign flip.  If xprime/yprime has a
// different sign than lhs/rhs, the rounding mode must be
// changed.
if ((xprime.signum() != lhs.signum()) ^
(yprime.signum() != rhs.signum())) {
mc = new MathContext(mc.precision,
(mc.roundingMode==RoundingMode.CEILING)?
RoundingMode.FLOOR:RoundingMode.CEILING);
}
}

if (xprime.compareTo(yprime) > 0)    // satisfy constraint (b)
yprime.scale -= 1;                 // [that is, yprime *= 10]
result = xprime.divide(yprime, mc.precision, mc.roundingMode.oldMode);
// correct the scale of the result...
result.scale = checkScale((long)yprime.scale - xprime.scale
- (rhs.scale - lhs.scale) + mc.precision);
// apply the sign
if (lhs.signum() != rhs.signum())
result = result.negate();
// doRound, here, only affects 1000000000 case.
result = result.doRound(mc);

if (result.multiply(divisor).compareTo(this) == 0) {
// Apply preferred scale rules for exact quotients
return result.stripZerosToMatchScale(preferredScale);
}
else {
return result;
}
``````
public java.math.BigDecimal[]divideAndRemainder(java.math.BigDecimal divisor)
Returns a two-element BigDecimal array containing the result of divideToIntegralValue followed by the result of remainder on the two operands.

Note that if both the integer quotient and remainder are needed, this method is faster than using the divideToIntegralValue and remainder methods separately because the division need only be carried out once.

 paramdivisor value by which this BigDecimal is to be divided, and the remainder computed.returna two element BigDecimal array: the quotient (the result of divideToIntegralValue) is the initial element and the remainder is the final element.throwsArithmeticException if divisor==0see#divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)see#remainder(java.math.BigDecimal, java.math.MathContext)since1.5

``````        // we use the identity  x = i * y + r to determine r
BigDecimal[] result = new BigDecimal;

result = this.divideToIntegralValue(divisor);
result = this.subtract(result.multiply(divisor));
return result;
``````
public java.math.BigDecimal[]divideAndRemainder(java.math.BigDecimal divisor, java.math.MathContext mc)
Returns a two-element BigDecimal array containing the result of divideToIntegralValue followed by the result of remainder on the two operands calculated with rounding according to the context settings.

Note that if both the integer quotient and remainder are needed, this method is faster than using the divideToIntegralValue and remainder methods separately because the division need only be carried out once.

 paramdivisor value by which this BigDecimal is to be divided, and the remainder computed.parammc the context to use.returna two element BigDecimal array: the quotient (the result of divideToIntegralValue) is the initial element and the remainder is the final element.throwsArithmeticException if divisor==0throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY, or mc.precision > 0 and the result of this.divideToIntgralValue(divisor) would require a precision of more than mc.precision digits.see#divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)see#remainder(java.math.BigDecimal, java.math.MathContext)since1.5

``````        if (mc.precision == 0)
return divideAndRemainder(divisor);

BigDecimal[] result = new BigDecimal;
BigDecimal lhs = this;

result = lhs.divideToIntegralValue(divisor, mc);
result = lhs.subtract(result.multiply(divisor));
return result;
``````
public java.math.BigDecimaldivideToIntegralValue(java.math.BigDecimal divisor)
Returns a BigDecimal whose value is the integer part of the quotient (this / divisor) rounded down. The preferred scale of the result is ```(this.scale() - divisor.scale())```.

 paramdivisor value by which this BigDecimal is to be divided.returnThe integer part of this / divisor.throwsArithmeticException if divisor==0since1.5

``````	// Calculate preferred scale
int preferredScale = (int)Math.max(Math.min((long)this.scale() - divisor.scale(),
Integer.MAX_VALUE), Integer.MIN_VALUE);
this.inflate();
divisor.inflate();
if (this.abs().compareTo(divisor.abs()) < 0) {
// much faster when this << divisor
return BigDecimal.valueOf(0, preferredScale);
}

if(this.signum() == 0 && divisor.signum() != 0)
return this.setScale(preferredScale);

// Perform a divide with enough digits to round to a correct
// integer value; then remove any fractional digits

int maxDigits = (int)Math.min(this.precision() +
(long)Math.ceil(10.0*divisor.precision()/3.0) +
Math.abs((long)this.scale() - divisor.scale()) + 2,
Integer.MAX_VALUE);

BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits,
RoundingMode.DOWN));
if (quotient.scale > 0) {
quotient = quotient.setScale(0, RoundingMode.DOWN).
stripZerosToMatchScale(preferredScale);
}

if (quotient.scale < preferredScale) {
// pad with zeros if necessary
quotient = quotient.setScale(preferredScale);
}

return quotient;
``````
public java.math.BigDecimaldivideToIntegralValue(java.math.BigDecimal divisor, java.math.MathContext mc)
Returns a BigDecimal whose value is the integer part of (this / divisor). Since the integer part of the exact quotient does not depend on the rounding mode, the rounding mode does not affect the values returned by this method. The preferred scale of the result is `(this.scale() - divisor.scale())`. An ArithmeticException is thrown if the integer part of the exact quotient needs more than mc.precision digits.

 paramdivisor value by which this BigDecimal is to be divided.parammc the context to use.returnThe integer part of this / divisor.throwsArithmeticException if divisor==0throwsArithmeticException if mc.precision > 0 and the result requires a precision of more than mc.precision digits.since1.5authorJoseph D. Darcy

``````        if (mc.precision == 0 || 			// exact result
(this.abs().compareTo(divisor.abs()) < 0) )	// zero result
return divideToIntegralValue(divisor);

// Calculate preferred scale
int preferredScale = (int)Math.max(Math.min((long)this.scale() - divisor.scale(),
Integer.MAX_VALUE), Integer.MIN_VALUE);

/*
* Perform a normal divide to mc.precision digits.  If the
* remainder has absolute value less than the divisor, the
* integer portion of the quotient fits into mc.precision
* digits.  Next, remove any fractional digits from the
* quotient and adjust the scale to the preferred value.
*/
BigDecimal result = this.divide(divisor, new MathContext(mc.precision,
RoundingMode.DOWN));
int resultScale = result.scale();

if (result.scale() < 0) {
/*
* Result is an integer. See if quotient represents the
* full integer portion of the exact quotient; if it does,
* the computed remainder will be less than the divisor.
*/
BigDecimal product = result.multiply(divisor);
if (this.subtract(product).abs().compareTo(divisor.abs()) > 0) {
throw new ArithmeticException("Division impossible");
}
} else if (result.scale() > 0) {
/*
* Integer portion of quotient will fit into precision
* digits; recompute quotient to scale 0 to avoid double
* rounding and then try to adjust, if necessary.
*/
result = result.setScale(0, RoundingMode.DOWN);
}
// else result.scale() == 0;

int precisionDiff;
if ((preferredScale > result.scale()) &&
(precisionDiff = mc.precision - result.precision()) > 0  ) {
return result.setScale(result.scale() +
Math.min(precisionDiff, preferredScale - result.scale) );
} else
return result.stripZerosToMatchScale(preferredScale);
``````
private java.math.BigDecimaldoRound(java.math.MathContext mc)
Returns a BigDecimal rounded according to the MathContext settings; used only if mc.precision>0. Does not change this; if rounding is needed a new BigDecimal is created and returned.

 parammc the context to use.returna BigDecimal rounded according to the MathContext settings. May return this, if no rounding needed.throwsArithmeticException if the rounding mode is RoundingMode.UNNECESSARY and the result is inexact.

``````	this.inflate();
if (precision == 0) {
if (mc.roundingMax != null
&& intVal.compareTo(mc.roundingMax) < 0
&& intVal.compareTo(mc.roundingMin) > 0)
return this; // no rounding needed
precision();                     // find it
}
int drop = precision - mc.precision;   // digits to discard
if (drop <= 0)                       // we fit
return this;
BigDecimal rounded = dropDigits(mc, drop);
// we need to double-check, in case of the 999=>1000 case
return rounded.doRound(mc);
``````
public doubledoubleValue()
Converts this BigDecimal to a double. This conversion is similar to the narrowing primitive conversion from double to float as defined in the Java Language Specification: if this BigDecimal has too great a magnitude represent as a double, it will be converted to {@link Double#NEGATIVE_INFINITY} or {@link Double#POSITIVE_INFINITY} as appropriate. Note that even when the return value is finite, this conversion can lose information about the precision of the BigDecimal value.

 returnthis BigDecimal converted to a double.

``````	if (scale == 0 && intCompact != INFLATED)
return (double)intCompact;
// Somewhat inefficient, but guaranteed to work.
return Double.parseDouble(this.toString());
``````
private java.math.BigDecimaldropDigits(java.math.MathContext mc, int drop)
Removes digits from the significand of a BigDecimal, rounding according to the MathContext settings. Does not change this; a new BigDecimal is always created and returned.

Actual rounding is carried out, as before, by the divide method, as this minimized code changes. It might be more efficient in most cases to move rounding to here, so we can do a round-to-length rather than round-to-scale.

 parammc the context to use.paramdrop the number of digits to drop, must be > 0returna BigDecimal rounded according to the MathContext settings. May return this, if no rounding needed.throwsArithmeticException if the rounding mode is RoundingMode.UNNECESSARY and the result is inexact.

``````        // here if we need to round; make the divisor = 10**drop)
// [calculating the BigInteger here saves setScale later]
BigDecimal divisor = new BigDecimal(tenToThe(drop), 0);

// divide to same scale to force round to length
BigDecimal rounded = this.divide(divisor, scale,
mc.roundingMode.oldMode);
rounded.scale -= drop;               // adjust the scale
return rounded;
``````
public booleanequals(java.lang.Object x)
Compares this BigDecimal with the specified Object for equality. Unlike {@link #compareTo(BigDecimal) compareTo}, this method considers two BigDecimal objects equal only if they are equal in value and scale (thus 2.0 is not equal to 2.00 when compared by this method).

 paramx Object to which this BigDecimal is to be compared.returntrue if and only if the specified Object is a BigDecimal whose value and scale are equal to this BigDecimal's.see#compareTo(java.math.BigDecimal)see#hashCode

``````        if (!(x instanceof BigDecimal))
return false;
BigDecimal xDec = (BigDecimal) x;
if (scale != xDec.scale)
return false;
if (this.intCompact != INFLATED && xDec.intCompact != INFLATED)
return this.intCompact == xDec.intCompact;
return this.inflate().intVal.equals(xDec.inflate().intVal);
``````
public floatfloatValue()
Converts this BigDecimal to a float. This conversion is similar to the narrowing primitive conversion from double to float defined in the Java Language Specification: if this BigDecimal has too great a magnitude to represent as a float, it will be converted to {@link Float#NEGATIVE_INFINITY} or {@link Float#POSITIVE_INFINITY} as appropriate. Note that even when the return value is finite, this conversion can lose information about the precision of the BigDecimal value.

 returnthis BigDecimal converted to a float.

``````	if (scale == 0 && intCompact != INFLATED)
return (float)intCompact;
// Somewhat inefficient, but guaranteed to work.
return Float.parseFloat(this.toString());
``````
private java.lang.StringgetValueString(int signum, java.lang.String intString, int scale)

`````` 	/* Insert decimal point */
StringBuilder buf;
int insertionPoint = intString.length() - scale;
if (insertionPoint == 0) {  /* Point goes right before intVal */
return (signum<0 ? "-0." : "0.") + intString;
} else if (insertionPoint > 0) { /* Point goes inside intVal */
buf = new StringBuilder(intString);
buf.insert(insertionPoint, '.");
if (signum < 0)
buf.insert(0, '-");
} else { /* We must insert zeros between point and intVal */
buf = new StringBuilder(3-insertionPoint + intString.length());
buf.append(signum<0 ? "-0." : "0.");
for (int i=0; i<-insertionPoint; i++)
buf.append('0");
buf.append(intString);
}
return buf.toString();
``````
public inthashCode()
Returns the hash code for this BigDecimal. Note that two BigDecimal objects that are numerically equal but differ in scale (like 2.0 and 2.00) will generally not have the same hash code.

 returnhash code for this BigDecimal.see#equals(Object)

`````` 	if (intCompact != INFLATED) {
long val2 = (intCompact < 0)?-intCompact:intCompact;
int temp = (int)( ((int)(val2 >>> 32)) * 31  +
(val2 & 0xffffffffL));
return 31*((intCompact < 0) ?-temp:temp) + scale;
} else
return 31*intVal.hashCode() + scale;
``````
private java.math.BigDecimalinflate()
Assign appropriate BigInteger to intVal field if intVal is null, i.e. the compact representation is in use.

``````	if (intVal == null)
intVal = BigInteger.valueOf(intCompact);
return this;
``````
private intintLength(int x)
Returns the length of an unsigned int, in decimal digits.

 parami the int (treated as unsigned)returnthe length of the unscaled value, in decimal digits

``````

int digits;
if (x < 0) {            // 'negative' is 10 digits unsigned
return  10;
} else {                // positive integer
if (x <= 9)
return 1;
// "Hacker's Delight"  section 11-4
for(int i = -1; ; i++) {
if (x <= ilogTable[i+1])
return i +1;
}
}
``````
public intintValue()
Converts this BigDecimal to an int. This conversion is analogous to a narrowing primitive conversion from double to short as defined in the Java Language Specification: any fractional part of this BigDecimal will be discarded, and if the resulting "BigInteger" is too big to fit in an int, only the low-order 32 bits are returned. Note that this conversion can lose information about the overall magnitude and precision of this BigDecimal value as well as return a result with the opposite sign.

 returnthis BigDecimal converted to an int.

``````

return  (intCompact != INFLATED && scale == 0) ?
(int)intCompact :
toBigInteger().intValue();
``````
public intintValueExact()
Converts this BigDecimal to an int, checking for lost information. If this BigDecimal has a nonzero fractional part or is out of the possible range for an int result then an ArithmeticException is thrown.

 returnthis BigDecimal converted to an int.throwsArithmeticException if this has a nonzero fractional part, or will not fit in an int.since1.5

``````       long num;
num = this.longValueExact();     // will check decimal part
if ((int)num != num)
throw new java.lang.ArithmeticException("Overflow");
return (int)num;
``````
private java.lang.StringlayoutChars(boolean sci)
Lay out this BigDecimal into a char[] array. The Java 1.2 equivalent to this was called getValueString.

 paramsci true for Scientific exponential notation; false for Engineeringreturnstring with canonical string representation of this BigDecimal

``````        if (scale == 0)                      // zero scale is trivial
return (intCompact != INFLATED) ?
Long.toString(intCompact):
intVal.toString();

// Get the significand as an absolute value
char coeff[];
if (intCompact != INFLATED)
coeff = Long.toString(Math.abs(intCompact)).toCharArray();
else
coeff = intVal.abs().toString().toCharArray();

// Construct a buffer, with sufficient capacity for all cases.
// If E-notation is needed, length will be: +1 if negative, +1
// if '.' needed, +2 for "E+", + up to 10 for adjusted exponent.
// Otherwise it could have +1 if negative, plus leading "0.00000"
StringBuilder buf=new StringBuilder(coeff.length+14);
if (signum() < 0)             // prefix '-' if negative
buf.append('-");
long adjusted = -(long)scale + (coeff.length-1);
if ((scale >= 0) && (adjusted >= -6)) { // plain number
int pad = scale - coeff.length;  // count of padding zeros
if (pad >= 0) {                  // 0.xxx form
buf.append('0");
buf.append('.");
for (; pad>0; pad--) {
buf.append('0");
}
buf.append(coeff);
} else {                         // xx.xx form
buf.append(coeff, 0, -pad);
buf.append('.");
buf.append(coeff, -pad, scale);
}
} else { // E-notation is needed
if (sci) {                       // Scientific notation
buf.append(coeff);        // first character
if (coeff.length > 1) {      // more to come
buf.append('.");
buf.append(coeff, 1, coeff.length-1);
}
} else {                         // Engineering notation
int sig = (int)(adjusted % 3);
if (sig < 0)
sig += 3;                // [adjusted was negative]
adjusted -= sig;             // now a multiple of 3
sig++;
if (signum() == 0) {
switch (sig) {
case 1:
buf.append('0"); // exponent is a multiple of three
break;
case 2:
buf.append("0.00");
adjusted += 3;
break;
case 3:
buf.append("0.0");
adjusted += 3;
break;
default:
throw new AssertionError("Unexpected sig value " + sig);
}
} else if (sig >= coeff.length) {   // significand all in integer
buf.append(coeff, 0, coeff.length);
// may need some zeros, too
for (int i = sig - coeff.length; i > 0; i--)
buf.append('0");
} else {                     // xx.xxE form
buf.append(coeff, 0, sig);
buf.append('.");
buf.append(coeff, sig, coeff.length-sig);
}
}
if (adjusted != 0) {             // [!sci could have made 0]
buf.append('E");
if (adjusted > 0)            // force sign for positive
buf.append('+");
buf.append(adjusted);
}
}
return buf.toString();
``````
private static intlongCompareTo(long x, long y)

``````	return (x < y) ? -1 : (x == y) ? 0 : 1;
``````
private static longlongTenToThe(long val, int n)
Compute val * 10 ^ n; return this product if it is representable as a long, INFLATED otherwise.

``````

// System.err.print("\tval " + val + "\t power " + n + "\tresult ");
if (n >= 0 && n < thresholds.length) {
if (Math.abs(val) <= thresholds[n] ) {
// System.err.println(val * thresholds[n]);
return val * thresholds[n];
}
}
// System.err.println(INFLATED);
return INFLATED;
``````
public longlongValue()
Converts this BigDecimal to a long. This conversion is analogous to a narrowing primitive conversion from double to short as defined in the Java Language Specification: any fractional part of this BigDecimal will be discarded, and if the resulting "BigInteger" is too big to fit in a long, only the low-order 64 bits are returned. Note that this conversion can lose information about the overall magnitude and precision of this BigDecimal value as well as return a result with the opposite sign.

 returnthis BigDecimal converted to a long.

``````	return (intCompact != INFLATED && scale == 0) ?
intCompact:
toBigInteger().longValue();
``````
public longlongValueExact()
Converts this BigDecimal to a long, checking for lost information. If this BigDecimal has a nonzero fractional part or is out of the possible range for a long result then an ArithmeticException is thrown.

 returnthis BigDecimal converted to a long.throwsArithmeticException if this has a nonzero fractional part, or will not fit in a long.since1.5

``````	if (intCompact != INFLATED && scale == 0)
return intCompact;
// If more than 19 digits in integer part it cannot possibly fit
if ((precision() - scale) > 19) // [OK for negative scale too]
throw new java.lang.ArithmeticException("Overflow");
// Fastpath zero and < 1.0 numbers (the latter can be very slow
// to round if very small)
if (this.signum() == 0)
return 0;
if ((this.precision() - this.scale) <= 0)
throw new ArithmeticException("Rounding necessary");
// round to an integer, with Exception if decimal part non-0
BigDecimal num = this.setScale(0, ROUND_UNNECESSARY).inflate();
if (num.precision() >= 19) {    // need to check carefully
if (LONGMIN == null) {      // initialize constants
LONGMIN = BigInteger.valueOf(Long.MIN_VALUE);
LONGMAX = BigInteger.valueOf(Long.MAX_VALUE);
}
if ((num.intVal.compareTo(LONGMIN) < 0) ||
(num.intVal.compareTo(LONGMAX) > 0))
throw new java.lang.ArithmeticException("Overflow");
}
return num.intVal.longValue();
``````
private static voidmatchScale(java.math.BigDecimal[] val)
Match the scales of two BigDecimals to align their least significant digits.

If the scales of val and val differ, rescale (non-destructively) the lower-scaled BigDecimal so they match. That is, the lower-scaled reference will be replaced by a reference to a new object with the same scale as the other BigDecimal.

 paramval array of two elements referring to the two BigDecimals to be aligned.

``````        if (val.scale < val.scale)
val = val.setScale(val.scale);
else if (val.scale < val.scale)
val = val.setScale(val.scale);
``````
public java.math.BigDecimalmax(java.math.BigDecimal val)
Returns the maximum of this BigDecimal and val.

 paramval value with which the maximum is to be computed.returnthe BigDecimal whose value is the greater of this BigDecimal and val. If they are equal, as defined by the {@link #compareTo(BigDecimal) compareTo} method, this is returned.see#compareTo(java.math.BigDecimal)

``````        return (compareTo(val) >= 0 ? this : val);
``````
public java.math.BigDecimalmin(java.math.BigDecimal val)
Returns the minimum of this BigDecimal and val.

 paramval value with which the minimum is to be computed.returnthe BigDecimal whose value is the lesser of this BigDecimal and val. If they are equal, as defined by the {@link #compareTo(BigDecimal) compareTo} method, this is returned.see#compareTo(java.math.BigDecimal)

``````        return (compareTo(val) <= 0 ? this : val);
``````
public java.math.BigDecimalmovePointLeft(int n)
Returns a BigDecimal which is equivalent to this one with the decimal point moved n places to the left. If n is non-negative, the call merely adds n to the scale. If n is negative, the call is equivalent to movePointRight(-n). The BigDecimal returned by this call has value (this × 10-n) and scale max(this.scale()+n, 0).

 paramn number of places to move the decimal point to the left.returna BigDecimal which is equivalent to this one with the decimal point moved n places to the left.throwsArithmeticException if scale overflows.

``````        // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE
int newScale = checkScale((long)scale + n);
BigDecimal num;
if (intCompact != INFLATED)
num = BigDecimal.valueOf(intCompact, newScale);
else
num = new BigDecimal(intVal, newScale);
return (num.scale<0 ? num.setScale(0) : num);
``````
public java.math.BigDecimalmovePointRight(int n)
Returns a BigDecimal which is equivalent to this one with the decimal point moved n places to the right. If n is non-negative, the call merely subtracts n from the scale. If n is negative, the call is equivalent to movePointLeft(-n). The BigDecimal returned by this call has value (this × 10n) and scale max(this.scale()-n, 0).

 paramn number of places to move the decimal point to the right.returna BigDecimal which is equivalent to this one with the decimal point moved n places to the right.throwsArithmeticException if scale overflows.

``````        // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE
int newScale = checkScale((long)scale - n);
BigDecimal num;
if (intCompact != INFLATED)
num = BigDecimal.valueOf(intCompact, newScale);
else
num = new BigDecimal(intVal, newScale);
return (num.scale<0 ? num.setScale(0) : num);
``````
public java.math.BigDecimalmultiply(java.math.BigDecimal multiplicand)
Returns a BigDecimal whose value is (this × multiplicand), and whose scale is (this.scale() + multiplicand.scale()).

 parammultiplicand value to be multiplied by this BigDecimal.returnthis * multiplicand

``````	long x = this.intCompact;
long y = multiplicand.intCompact;
int productScale = checkScale((long)scale+multiplicand.scale);

// Might be able to do a more clever check incorporating the
// inflated check into the overflow computation.
if (x != INFLATED && y != INFLATED) {
/*
* If the product is not an overflowed value, continue
* to use the compact representation.  if either of x or y
* is INFLATED, the product should also be regarded as
* an overflow.  See "Hacker's Delight" section 2-12 for
* explanation of the overflow test.
*/
long product = x * y;
if ( !(y != 0L && product/y != x)  )	// not overflowed
return BigDecimal.valueOf(product, productScale);
}

BigDecimal result = new BigDecimal(this.inflate().intVal.multiply(multiplicand.inflate().intVal), productScale);
return result;
``````
public java.math.BigDecimalmultiply(java.math.BigDecimal multiplicand, java.math.MathContext mc)
Returns a BigDecimal whose value is (this × multiplicand), with rounding according to the context settings.

 parammultiplicand value to be multiplied by this BigDecimal.parammc the context to use.returnthis * multiplicand, rounded as necessary.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.since1.5

``````        if (mc.precision == 0)
return multiply(multiplicand);
BigDecimal lhs = this;
return lhs.inflate().multiply(multiplicand.inflate()).doRound(mc);
``````
public java.math.BigDecimalnegate()
Returns a BigDecimal whose value is (-this), and whose scale is this.scale().

 return-this.

``````	BigDecimal result;
if (intCompact != INFLATED)
result = BigDecimal.valueOf(-intCompact, scale);
else {
result = new BigDecimal(intVal.negate(), scale);
result.precision = precision;
}
return result;
``````
public java.math.BigDecimalnegate(java.math.MathContext mc)
Returns a BigDecimal whose value is (-this), with rounding according to the context settings.

 parammc the context to use.return-this, rounded as necessary.throwsArithmeticException if or the result is inexact but the rounding mode is UNNECESSARY.since1.5

``````        return plus(mc).negate();
``````
public java.math.BigDecimalplus()
Returns a BigDecimal whose value is (+this), and whose scale is this.scale().

This method, which simply returns this BigDecimal is included for symmetry with the unary minus method {@link #negate()}.

 returnthis.see#negate()since1.5

``````        return this;
``````
public java.math.BigDecimalplus(java.math.MathContext mc)
Returns a BigDecimal whose value is (+this), with rounding according to the context settings.

The effect of this method is identical to that of the {@link #round(MathContext)} method.

 parammc the context to use.returnthis, rounded as necessary. A zero result will have a scale of 0.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.see#round(MathContext)since1.5

``````        if (mc.precision == 0)                 // no rounding please
return this;
return this.doRound(mc);
``````
public java.math.BigDecimalpow(int n)
Returns a BigDecimal whose value is (thisn), The power is computed exactly, to unlimited precision.

The parameter n must be in the range 0 through 999999999, inclusive. ZERO.pow(0) returns {@link #ONE}. Note that future releases may expand the allowable exponent range of this method.

 paramn power to raise this BigDecimal to.returnthisnthrowsArithmeticException if n is out of range.since1.5

``````        if (n < 0 || n > 999999999)
throw new ArithmeticException("Invalid operation");
// No need to calculate pow(n) if result will over/underflow.
// Don't attempt to support "supernormal" numbers.
int newScale = checkScale((long)scale * n);
this.inflate();
return new BigDecimal(intVal.pow(n), newScale);
``````
public java.math.BigDecimalpow(int n, java.math.MathContext mc)
Returns a BigDecimal whose value is (thisn). The current implementation uses the core algorithm defined in ANSI standard X3.274-1996 with rounding according to the context settings. In general, the returned numerical value is within two ulps of the exact numerical value for the chosen precision. Note that future releases may use a different algorithm with a decreased allowable error bound and increased allowable exponent range.

The X3.274-1996 algorithm is:

• An ArithmeticException exception is thrown if
• abs(n) > 999999999
• mc.precision == 0 and n < 0
• mc.precision > 0 and n has more than mc.precision decimal digits
• if n is zero, {@link #ONE} is returned even if this is zero, otherwise
• if n is positive, the result is calculated via the repeated squaring technique into a single accumulator. The individual multiplications with the accumulator use the same math context settings as in mc except for a precision increased to mc.precision + elength + 1 where elength is the number of decimal digits in n.
• if n is negative, the result is calculated as if n were positive; this value is then divided into one using the working precision specified above.
• The final value from either the positive or negative case is then rounded to the destination precision.

 paramn power to raise this BigDecimal to.parammc the context to use.returnthisn using the ANSI standard X3.274-1996 algorithmthrowsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY, or n is out of range.since1.5

``````        if (mc.precision == 0)
return pow(n);
if (n < -999999999 || n > 999999999)
throw new ArithmeticException("Invalid operation");
if (n == 0)
return ONE;                      // x**0 == 1 in X3.274
this.inflate();
BigDecimal lhs = this;
MathContext workmc = mc;           // working settings
int mag = Math.abs(n);               // magnitude of n
if (mc.precision > 0) {

int elength = intLength(mag);    // length of n in digits
if (elength > mc.precision)        // X3.274 rule
throw new ArithmeticException("Invalid operation");
workmc = new MathContext(mc.precision + elength + 1,
mc.roundingMode);
}
// ready to carry out power calculation...
BigDecimal acc = ONE;           // accumulator
boolean seenbit = false;        // set once we've seen a 1-bit
for (int i=1;;i++) {            // for each bit [top bit ignored]
mag += mag;                 // shift left 1 bit
if (mag < 0) {              // top bit is set
seenbit = true;         // OK, we're off
acc = acc.multiply(lhs, workmc); // acc=acc*x
}
if (i == 31)
break;                  // that was the last bit
if (seenbit)
acc=acc.multiply(acc, workmc);   // acc=acc*acc [square]
// else (!seenbit) no point in squaring ONE
}
// if negative n, calculate the reciprocal using working precision
if (n<0)                          // [hence mc.precision>0]
acc=ONE.divide(acc, workmc);
// round to final precision and strip zeros
return acc.doRound(mc);
``````
public intprecision()
Returns the precision of this BigDecimal. (The precision is the number of digits in the unscaled value.)

The precision of a zero value is 1.

 returnthe precision of this BigDecimal.since1.5

``````        int result = precision;
if (result == 0) {
result = digitLength();
precision = result;
}
return result;
``````
private static voidprint(java.lang.String name, java.math.BigDecimal bd)

``````	System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n",
name,
bd.intCompact,
bd.intVal,
bd.scale,
bd.precision);
``````
private synchronized voidreadObject(java.io.ObjectInputStream s)
Reconstitute the BigDecimal instance from a stream (that is, deserialize it).

 params the stream being read.

``````        // Read in all fields
s.defaultReadObject();
// validate possibly bad fields
if (intVal == null) {
String message = "BigDecimal: null intVal in stream";
throw new java.io.StreamCorruptedException(message);
// [all values of scale are now allowed]
}
// Set intCompact to uninitialized value; could also see if the
// intVal was small enough to fit as a compact value.
intCompact = INFLATED;
``````
public java.math.BigDecimalremainder(java.math.BigDecimal divisor)
Returns a BigDecimal whose value is (this % divisor).

The remainder is given by this.subtract(this.divideToIntegralValue(divisor).multiply(divisor)). Note that this is not the modulo operation (the result can be negative).

 paramdivisor value by which this BigDecimal is to be divided.returnthis % divisor.throwsArithmeticException if divisor==0since1.5

``````        BigDecimal divrem[] = this.divideAndRemainder(divisor);
return divrem;
``````
public java.math.BigDecimalremainder(java.math.BigDecimal divisor, java.math.MathContext mc)
Returns a BigDecimal whose value is (this % divisor), with rounding according to the context settings. The MathContext settings affect the implicit divide used to compute the remainder. The remainder computation itself is by definition exact. Therefore, the remainder may contain more than mc.getPrecision() digits.

The remainder is given by this.subtract(this.divideToIntegralValue(divisor, mc).multiply(divisor)). Note that this is not the modulo operation (the result can be negative).

 paramdivisor value by which this BigDecimal is to be divided.parammc the context to use.returnthis % divisor, rounded as necessary.throwsArithmeticException if divisor==0throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY, or mc.precision > 0 and the result of this.divideToIntgralValue(divisor) would require a precision of more than mc.precision digits.see#divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)since1.5

``````        BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
return divrem;
``````
public java.math.BigDecimalround(java.math.MathContext mc)
Returns a BigDecimal rounded according to the MathContext settings. If the precision setting is 0 then no rounding takes place.

The effect of this method is identical to that of the {@link #plus(MathContext)} method.

 parammc the context to use.returna BigDecimal rounded according to the MathContext settings.throwsArithmeticException if the rounding mode is UNNECESSARY and the BigDecimal operation would require rounding.see#plus(MathContext)since1.5

``````

// Scaling/Rounding Operations

return plus(mc);
``````
private java.math.BigDecimalroundOp(java.math.MathContext mc)
Round an operand; used only if digits > 0. Does not change this; if rounding is needed a new BigDecimal is created and returned.

 parammc the context to use.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.

``````        BigDecimal rounded = doRound(mc);
return rounded;
``````
private voidroundThis(java.math.MathContext mc)
Round this BigDecimal according to the MathContext settings; used only if precision > 0.

WARNING: This method should only be called on new objects as it mutates the value fields.

 parammc the context to use.throwsArithmeticException if the rounding mode is RoundingMode.UNNECESSARY and the BigDecimal operation would require rounding.

``````        BigDecimal rounded = doRound(mc);
if (rounded == this)                 // wasn't rounded
return;
this.intVal	= rounded.intVal;
this.intCompact	= rounded.intCompact;
this.scale	= rounded.scale;
this.precision	= rounded.precision;
``````
public intscale()
Returns the scale of this BigDecimal. 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. For example, a scale of -3 means the unscaled value is multiplied by 1000.

 returnthe scale of this BigDecimal.

``````        return scale;
``````
public java.math.BigDecimalscaleByPowerOfTen(int n)
Returns a BigDecimal whose numerical value is equal to (this * 10n). The scale of the result is (this.scale() - n).

 throwsArithmeticException if the scale would be outside the range of a 32-bit integer.since1.5

``````	this.inflate();
BigDecimal num = new BigDecimal(intVal, checkScale((long)scale - n));
num.precision = precision;
return num;
``````
public java.math.BigDecimalsetScale(int newScale, java.math.RoundingMode roundingMode)
Returns a BigDecimal whose scale is the specified value, and whose unscaled value is determined by multiplying or dividing this BigDecimal's unscaled value by the appropriate power of ten to maintain its overall value. If the scale is reduced by the operation, the unscaled value must be divided (rather than multiplied), and the value may be changed; in this case, the specified rounding mode is applied to the division.

 paramnewScale scale of the BigDecimal value to be returned.paramroundingMode The rounding mode to apply.returna BigDecimal whose scale is the specified value, and whose unscaled value is determined by multiplying or dividing this BigDecimal's unscaled value by the appropriate power of ten to maintain its overall value.throwsArithmeticException if roundingMode==UNNECESSARY and the specified scaling operation would require rounding.seeRoundingModesince1.5

``````        return setScale(newScale, roundingMode.oldMode);
``````
public java.math.BigDecimalsetScale(int newScale, int roundingMode)
Returns a BigDecimal whose scale is the specified value, and whose unscaled value is determined by multiplying or dividing this BigDecimal's unscaled value by the appropriate power of ten to maintain its overall value. If the scale is reduced by the operation, the unscaled value must be divided (rather than multiplied), and the value may be changed; in this case, the specified rounding mode is applied to the division.

Note that since BigDecimal objects are immutable, calls of this method do not result in the original object being modified, contrary to the usual convention of having methods named setX mutate field X. Instead, setScale returns an object with the proper scale; the returned object may or may not be newly allocated.

The new {@link #setScale(int, RoundingMode)} method should be used in preference to this legacy method.

 paramnewScale scale of the BigDecimal value to be returned.paramroundingMode The rounding mode to apply.returna BigDecimal whose scale is the specified value, and whose unscaled value is determined by multiplying or dividing this BigDecimal's unscaled value by the appropriate power of ten to maintain its overall value.throwsArithmeticException if roundingMode==ROUND_UNNECESSARY and the specified scaling operation would require rounding.throwsIllegalArgumentException if roundingMode does not represent a valid rounding mode.see#ROUND_UPsee#ROUND_DOWNsee#ROUND_CEILINGsee#ROUND_FLOORsee#ROUND_HALF_UPsee#ROUND_HALF_DOWNsee#ROUND_HALF_EVENsee#ROUND_UNNECESSARY

``````        if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
throw new IllegalArgumentException("Invalid rounding mode");

if (newScale == this.scale)        // easy case
return this;
if (this.signum() == 0) 	   // zero can have any scale
return BigDecimal.valueOf(0, newScale);
if (newScale > this.scale) {
// [we can use checkScale to assure multiplier is valid]
int raise = checkScale((long)newScale - this.scale);

if (intCompact != INFLATED) {
long scaledResult = longTenToThe(intCompact, raise);
if (scaledResult != INFLATED)
return BigDecimal.valueOf(scaledResult, newScale);
this.inflate();
}

BigDecimal result = new BigDecimal(intVal.multiply(tenToThe(raise)),
newScale);
if (this.precision > 0)
result.precision = this.precision + newScale - this.scale;
return result;
}
// scale < this.scale
// we cannot perfectly predict the precision after rounding
return divide(ONE, newScale, roundingMode);
``````
public java.math.BigDecimalsetScale(int newScale)
Returns a BigDecimal whose scale is the specified value, and whose value is numerically equal to this BigDecimal's. Throws an ArithmeticException if this is not possible.

This call is typically used to increase the scale, in which case it is guaranteed that there exists a BigDecimal of the specified scale and the correct value. The call can also be used to reduce the scale if the caller knows that the BigDecimal has sufficiently many zeros at the end of its fractional part (i.e., factors of ten in its integer value) to allow for the rescaling without changing its value.

This method returns the same result as the two-argument versions of setScale, but saves the caller the trouble of specifying a rounding mode in cases where it is irrelevant.

Note that since BigDecimal objects are immutable, calls of this method do not result in the original object being modified, contrary to the usual convention of having methods named setX mutate field X. Instead, setScale returns an object with the proper scale; the returned object may or may not be newly allocated.

 paramnewScale scale of the BigDecimal value to be returned.returna BigDecimal whose scale is the specified value, and whose unscaled value is determined by multiplying or dividing this BigDecimal's unscaled value by the appropriate power of ten to maintain its overall value.throwsArithmeticException if the specified scaling operation would require rounding.see#setScale(int, int)see#setScale(int, RoundingMode)

``````        return setScale(newScale, ROUND_UNNECESSARY);
``````
public shortshortValueExact()
Converts this BigDecimal to a short, checking for lost information. If this BigDecimal has a nonzero fractional part or is out of the possible range for a short result then an ArithmeticException is thrown.

 returnthis BigDecimal converted to a short.throwsArithmeticException if this has a nonzero fractional part, or will not fit in a short.since1.5

``````       long num;
num = this.longValueExact();     // will check decimal part
if ((short)num != num)
throw new java.lang.ArithmeticException("Overflow");
return (short)num;
``````
public intsignum()
Returns the signum function of this BigDecimal.

 return-1, 0, or 1 as the value of this BigDecimal is negative, zero, or positive.

``````	return (intCompact != INFLATED)?
Long.signum(intCompact):
intVal.signum();
``````
public java.math.BigDecimalstripTrailingZeros()
Returns a BigDecimal which is numerically equal to this one but with any trailing zeros removed from the representation. For example, stripping the trailing zeros from the BigDecimal value 600.0, which has [BigInteger, scale] components equals to [6000, 1], yields 6E2 with [BigInteger, scale] components equals to [6, -2]

 returna numerically equal BigDecimal with any trailing zeros removed.

``````	this.inflate();
return (new BigDecimal(intVal, scale)).stripZerosToMatchScale(Long.MIN_VALUE);
``````
private java.math.BigDecimalstripZerosToMatchScale(long preferredScale)
Remove insignificant trailing zeros from this BigDecimal until the preferred scale is reached or no more zeros can be removed. If the preferred scale is less than Integer.MIN_VALUE, all the trailing zeros will be removed. BigInteger assistance could help, here?

WARNING: This method should only be called on new objects as it mutates the value fields.

 returnthis BigDecimal with a scale possibly reduced to be closed to the preferred scale.

``````	boolean compact = (intCompact != INFLATED);
this.inflate();
BigInteger qr[];                // quotient-remainder pair
while ( intVal.abs().compareTo(BigInteger.TEN) >= 0 &&
scale > preferredScale) {
if (intVal.testBit(0))
break;                  // odd number cannot end in 0
qr = intVal.divideAndRemainder(BigInteger.TEN);
if (qr.signum() != 0)
break;                  // non-0 remainder
intVal=qr;
scale = checkScale((long)scale-1);  // could Overflow
if (precision > 0)          // adjust precision if known
precision--;
}
if (compact)
intCompact = intVal.longValue();
return this;
``````
public java.math.BigDecimalsubtract(java.math.BigDecimal subtrahend)
Returns a BigDecimal whose value is (this - subtrahend), and whose scale is max(this.scale(), subtrahend.scale()).

 paramsubtrahend value to be subtracted from this BigDecimal.returnthis - subtrahend

``````        BigDecimal arg[] = {this, subtrahend};
matchScale(arg);

long x = arg.intCompact;
long y = arg.intCompact;

// Might be able to do a more clever check incorporating the
// inflated check into the overflow computation.
if (x != INFLATED && y != INFLATED) {
long difference = x - y;
/*
* If the difference is not an overflowed value, continue
* to use the compact representation.  if either of x or y
* is INFLATED, the difference should also be regarded as
* an overflow.  See "Hacker's Delight" section 2-12 for
* explanation of the overflow test.
*/
if ( ((x ^ y) & (difference ^ x) ) >> 63 == 0L )	// not overflowed
return BigDecimal.valueOf(difference, arg.scale);
}
return new BigDecimal(arg.inflate().intVal.subtract(arg.inflate().intVal),
arg.scale);
``````
public java.math.BigDecimalsubtract(java.math.BigDecimal subtrahend, java.math.MathContext mc)
Returns a BigDecimal whose value is (this - subtrahend), with rounding according to the context settings. If subtrahend is zero then this, rounded if necessary, is used as the result. If this is zero then the result is subtrahend.negate(mc).

 paramsubtrahend value to be subtracted from this BigDecimal.parammc the context to use.returnthis - subtrahend, rounded as necessary.throwsArithmeticException if the result is inexact but the rounding mode is UNNECESSARY.since1.5

``````        if (mc.precision == 0)
return subtract(subtrahend);
// share the special rounding code in add()
this.inflate();
subtrahend.inflate();
BigDecimal rhs = new BigDecimal(subtrahend.intVal.negate(), subtrahend.scale);
rhs.precision = subtrahend.precision;
return add(rhs, mc);
``````
private static java.math.BigIntegertenToThe(int n)
Return 10 to the power n, as a BigInteger.

 paramn the power of ten to be returned (>=0)returna BigInteger with the value (10n)

``````        if (n < TENPOWERS.length)     // use value from constant array
return TENPOWERS[n];
// BigInteger.pow is slow, so make 10**n by constructing a
// BigInteger from a character string (still not very fast)
char tenpow[] = new char[n + 1];
tenpow = '1";
for (int i = 1; i <= n; i++)
tenpow[i] = '0";
return new BigInteger(tenpow);
``````
public java.math.BigIntegertoBigInteger()
Converts this BigDecimal to a BigInteger. This conversion is analogous to a narrowing primitive conversion from double to long as defined in the Java Language Specification: any fractional part of this BigDecimal will be discarded. Note that this conversion can lose information about the precision of the BigDecimal value.

To have an exception thrown if the conversion is inexact (in other words if a nonzero fractional part is discarded), use the {@link #toBigIntegerExact()} method.

 returnthis BigDecimal converted to a BigInteger.

``````        // force to an integer, quietly
return this.setScale(0, ROUND_DOWN).inflate().intVal;
``````
public java.math.BigIntegertoBigIntegerExact()
Converts this BigDecimal to a BigInteger, checking for lost information. An exception is thrown if this BigDecimal has a nonzero fractional part.

 returnthis BigDecimal converted to a BigInteger.throwsArithmeticException if this has a nonzero fractional part.since1.5

``````        // round to an integer, with Exception if decimal part non-0
return this.setScale(0, ROUND_UNNECESSARY).inflate().intVal;
``````
public java.lang.StringtoEngineeringString()
Returns a string representation of this BigDecimal, using engineering notation if an exponent is needed.

Returns a string that represents the BigDecimal as described in the {@link #toString()} method, except that if exponential notation is used, the power of ten is adjusted to be a multiple of three (engineering notation) such that the integer part of nonzero values will be in the range 1 through 999. If exponential notation is used for zero values, a decimal point and one or two fractional zero digits are used so that the scale of the zero value is preserved. Note that unlike the output of {@link #toString()}, the output of this method is not guaranteed to recover the same [integer, scale] pair of this BigDecimal if the output string is converting back to a BigDecimal using the {@linkplain #BigDecimal(String) string constructor}. The result of this method meets the weaker constraint of always producing a numerically equal result from applying the string constructor to the method's output.

 returnstring representation of this BigDecimal, using engineering notation if an exponent is needed.since1.5

``````        return layoutChars(false);
``````
public java.lang.StringtoPlainString()
Returns a string representation of this BigDecimal without an exponent field. For values with a positive scale, the number of digits to the right of the decimal point is used to indicate scale. For values with a zero or negative scale, the resulting string is generated as if the value were converted to a numerically equal value with zero scale and as if all the trailing zeros of the zero scale value were present in the result. The entire string is prefixed by a minus sign character '-' ('\u002D') if the unscaled value is less than zero. No sign character is prefixed if the unscaled value is zero or positive. Note that if the result of this method is passed to the {@linkplain #BigDecimal(String) string constructor}, only the numerical value of this BigDecimal will necessarily be recovered; the representation of the new BigDecimal may have a different scale. In particular, if this BigDecimal has a positive scale, the string resulting from this method will have a scale of zero when processed by the string constructor. (This method behaves analogously to the toString method in 1.4 and earlier releases.)

 returna string representation of this BigDecimal without an exponent field.since1.5see#toString()see#toEngineeringString()

``````	BigDecimal bd = this;
if (bd.scale < 0)
bd = bd.setScale(0);
bd.inflate();
if (bd.scale == 0)	// No decimal point
return bd.intVal.toString();
return bd.getValueString(bd.signum(), bd.intVal.abs().toString(), bd.scale);
``````
public java.lang.StringtoString()
Returns the string representation of this BigDecimal, using scientific notation if an exponent is needed.

A standard canonical string form of the BigDecimal is created as though by the following steps: first, the absolute value of the unscaled value of the BigDecimal is converted to a string in base ten using the characters '0' through '9' with no leading zeros (except if its value is zero, in which case a single '0' character is used).

Next, an adjusted exponent is calculated; this is the negated scale, plus the number of characters in the converted unscaled value, less one. That is, -scale+(ulength-1), where ulength is the length of the absolute value of the unscaled value in decimal digits (its precision).

If the scale is greater than or equal to zero and the adjusted exponent is greater than or equal to -6, the number will be converted to a character form without using exponential notation. In this case, if the scale is zero then no decimal point is added and if the scale is positive a decimal point will be inserted with the scale specifying the number of characters to the right of the decimal point. '0' characters are added to the left of the converted unscaled value as necessary. If no character precedes the decimal point after this insertion then a conventional '0' character is prefixed.

Otherwise (that is, if the scale is negative, or the adjusted exponent is less than -6), the number will be converted to a character form using exponential notation. In this case, if the converted BigInteger has more than one digit a decimal point is inserted after the first digit. An exponent in character form is then suffixed to the converted unscaled value (perhaps with inserted decimal point); this comprises the letter 'E' followed immediately by the adjusted exponent converted to a character form. The latter is in base ten, using the characters '0' through '9' with no leading zeros, and is always prefixed by a sign character '-' ('\u002D') if the adjusted exponent is negative, '+' ('\u002B') otherwise).

Finally, the entire string is prefixed by a minus sign character '-' ('\u002D') if the unscaled value is less than zero. No sign character is prefixed if the unscaled value is zero or positive.

Examples:

For each representation [unscaled value, scale] on the left, the resulting string is shown on the right.

```[123,0] "123"
[-123,0] "-123"
[123,-1] "1.23E+3"
[123,-3] "1.23E+5"
[123,1] "12.3"
[123,5] "0.00123"
[123,10] "1.23E-8"
[-123,12] "-1.23E-10"
```
Notes:
1. There is a one-to-one mapping between the distinguishable BigDecimal values and the result of this conversion. That is, every distinguishable BigDecimal value (unscaled value and scale) has a unique string representation as a result of using toString. If that string representation is converted back to a BigDecimal using the {@link #BigDecimal(String)} constructor, then the original value will be recovered.
2. The string produced for a given number is always the same; it is not affected by locale. This means that it can be used as a canonical string representation for exchanging decimal data, or as a key for a Hashtable, etc. Locale-sensitive number formatting and parsing is handled by the {@link java.text.NumberFormat} class and its subclasses.
3. The {@link #toEngineeringString} method may be used for presenting numbers with exponents in engineering notation, and the {@link #setScale(int,RoundingMode) setScale} method may be used for rounding a BigDecimal so it has a known number of digits after the decimal point.
4. The digit-to-character mapping provided by Character.forDigit is used.

 returnstring representation of this BigDecimal.seeCharacter#forDigitsee#BigDecimal(java.lang.String)

``````	if (stringCache == null)
stringCache = layoutChars(true);
return stringCache;
``````
public java.math.BigDecimalulp()
Returns the size of an ulp, a unit in the last place, of this BigDecimal. An ulp of a nonzero BigDecimal value is the positive distance between this value and the BigDecimal value next larger in magnitude with the same number of digits. An ulp of a zero value is numerically equal to 1 with the scale of this. The result is stored with the same scale as `this` so the result for zero and nonzero values is equal to ```[1, this.scale()]```.

 returnthe size of an ulp of thissince1.5

``````	return BigDecimal.valueOf(1, this.scale());
``````
public java.math.BigIntegerunscaledValue()
Returns a BigInteger whose value is the unscaled value of this BigDecimal. (Computes (this * 10this.scale()).)

 returnthe unscaled value of this BigDecimal.since1.2

``````        return this.inflate().intVal;
``````
public static java.math.BigDecimalvalueOf(long unscaledVal, int scale)
Translates a long unscaled value and an int scale into a BigDecimal. This "static factory method" is provided in preference to a (long, int) constructor because it allows for reuse of frequently used BigDecimal values..

 paramunscaledVal unscaled value of the BigDecimal.paramscale scale of the BigDecimal.returna BigDecimal whose value is (unscaledVal × 10-scale).

``````        if (scale == 0 && unscaledVal >= 0 && unscaledVal <= 10) {
return zeroThroughTen[(int)unscaledVal];
}
if (compactLong(unscaledVal))
return new BigDecimal(unscaledVal, scale);
return new BigDecimal(BigInteger.valueOf(unscaledVal), scale);
``````
public static java.math.BigDecimalvalueOf(long val)
Translates a long value into a BigDecimal with a scale of zero. This "static factory method" is provided in preference to a (long) constructor because it allows for reuse of frequently used BigDecimal values.

 paramval value of the BigDecimal.returna BigDecimal whose value is val.

``````	return valueOf(val, 0);
``````
public static java.math.BigDecimalvalueOf(double val)
Translates a double into a BigDecimal, using the double's canonical string representation provided by the {@link Double#toString(double)} method.

Note: This is generally the preferred way to convert a double (or float) into a BigDecimal, as the value returned is equal to that resulting from constructing a BigDecimal from the result of using {@link Double#toString(double)}.

 paramval double to convert to a BigDecimal.returna BigDecimal whose value is equal to or approximately equal to the value of val.throwsNumberFormatException if val is infinite or NaN.since1.5

``````        // Reminder: a zero double returns '0.0', so we cannot fastpath
// to use the constant ZERO.  This might be important enough to
// justify a factory approach, a cache, or a few private
// constants, later.
return new BigDecimal(Double.toString(val));
``````
private voidwriteObject(java.io.ObjectOutputStream s)
Serialize this BigDecimal to the stream in question

 params the stream to serialize to.

``````       // Must inflate to maintain compatible serial form.
this.inflate();

// Write proper fields
s.defaultWriteObject();
``````
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