BigDecimalpublic class BigDecimal extends Number implements ComparableImmutable, arbitraryprecision signed decimal numbers. A
BigDecimal consists of an arbitrary precision integer
unscaled value and a 32bit 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 X3.2741996
and ANSI X3.2741996/AM 12000 (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
100×10^{1}. 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
Operation  Preferred Scale of Result 
Add  max(addend.scale(), augend.scale()) 
Subtract  max(minuend.scale(), subtrahend.scale()) 
Multiply  multiplier.scale() + multiplicand.scale() 
Divide  dividend.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 highorder 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, pseudocode is used
throughout the descriptions of BigDecimal methods. The
pseudocode expression (i + j) is shorthand for "a
BigDecimal whose value is that of the BigDecimal
i added to that of the BigDecimal
j." The pseudocode expression (i == j) is
shorthand for "true if and only if the
BigDecimal i represents the same value as the
BigDecimal j." Other pseudocode 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. 
Fields Summary 

private volatile BigInteger  intValThe unscaled value of this BigDecimal, as returned by {@link
#unscaledValue}.  private int  scaleThe scale of this BigDecimal, as returned by {@link #scale}.  private volatile transient int  precisionThe 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  stringCacheUsed to store the canonical string representation, if computed.  private static final long  INFLATEDSentinel value for {@link #intCompact} indicating the
significand information is only available from {@code intVal}.  private transient long  intCompactIf 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  ZEROThe value 0, with a scale of 0.  public static final BigDecimal  ONEThe value 1, with a scale of 0.  public static final BigDecimal  TENThe value 10, with a scale of 0.  public static final int  ROUND_UPRounding 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_DOWNRounding 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_CEILINGRounding 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_FLOORRounding 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_UPRounding 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_DOWNRounding 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_EVENRounding 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_UNNECESSARYRounding 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  LONGMINBigInteger equal to Long.MIN_VALUE.  private static BigInteger  LONGMAXBigInteger 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 subarray 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 .
// 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 toolong, 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 exactsized 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[0] = '";
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.
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}).
// 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.
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.
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.
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.
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.
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 subarray 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 .
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 .
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 .
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:
 Sign_{opt} Significand Exponent_{opt}
 Sign:
 +
 
 Significand:
 IntegerPart . FractionPart_{opt}
 . FractionPart
 IntegerPart
 IntegerPart:
 Digits
 FractionPart:
 Digits
 Exponent:
 ExponentIndicator SignedInteger
 ExponentIndicator:
 e
 E
 SignedInteger:
 Sign_{opt} 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 charactertodigit 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]
"1.23E12" [123,14]
"1234.5E4" [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.
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.
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 floatingpoint value. The scale of the returned
BigDecimal is the smallest value such that
(10^{scale} × val) is an integer.
Notes:

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.

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.

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.
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
(10^{scale} × 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.
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.
intVal = val;
if (val.bitLength() <= MAX_BIGINT_BITS) {
intCompact = val.longValue();
}

Methods Summary 

public java.math.BigDecimal  abs()Returns a BigDecimal whose value is the absolute value
of this BigDecimal, and whose scale is
this.scale().
return (signum() < 0 ? negate() : this);
 public java.math.BigDecimal  abs(java.math.MathContext mc)Returns a BigDecimal whose value is the absolute value
of this BigDecimal, with rounding according to the
context settings.
return (signum() < 0 ? negate(mc) : plus(mc));
 public java.math.BigDecimal  add(java.math.BigDecimal augend)Returns a BigDecimal whose value is (this +
augend), and whose scale is max(this.scale(),
augend.scale()).
BigDecimal arg[] = {this, augend};
matchScale(arg);
long x = arg[0].intCompact;
long y = arg[1].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 212 for
* explanation of the overflow test.
*/
if ( (((sum ^ x) & (sum ^ y)) >> 63) == 0L ) // not overflowed
return BigDecimal.valueOf(sum, arg[0].scale);
}
return new BigDecimal(arg[0].inflate().intVal.add(arg[1].inflate().intVal), arg[0].scale);
 public java.math.BigDecimal  add(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.
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[2];
arg[0] = lhs; arg[1] = augend;
matchScale(arg);
lhs = arg[0];
augend = arg[1];
}
return new BigDecimal(lhs.inflate().intVal.add(augend.inflate().intVal),
lhs.scale).doRound(mc);
 private java.math.BigDecimal  audit()Check internal invariants of this BigDecimal. These invariants
include:
 The object must be initialized; either intCompact must not be
INFLATED or intVal is nonnull. 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 byte  byteValueExact()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.
long num;
num = this.longValueExact(); // will check decimal part
if ((byte)num != num)
throw new java.lang.ArithmeticException("Overflow");
return (byte)num;
 private int  checkScale(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.
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 boolean  compactLong(long val)
return (val != Long.MIN_VALUE);
 public int  compareTo(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.
// 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[0].intCompact != INFLATED && arg[1].intCompact != INFLATED)
return longCompareTo(arg[0].intCompact, arg[1].intCompact);
return arg[0].inflate().intVal.compareTo(arg[1].inflate().intVal);
 private int  digitLength()Returns the length of this BigDecimal, in decimal digits.
Notes:
 public java.math.BigDecimal  divide(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.
/*
* 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 outofrange 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[0];
r = i[1];
}
// 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 nearestneighbor 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 deadcenter
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.BigDecimal  divide(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.
return divide(divisor, scale, roundingMode.oldMode);
 public java.math.BigDecimal  divide(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.
return this.divide(divisor, scale, roundingMode);
 public java.math.BigDecimal  divide(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.
return this.divide(divisor, scale, roundingMode.oldMode);
 public java.math.BigDecimal  divide(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 nonterminating decimal
expansion) an ArithmeticException is thrown.
/*
* 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("Nonterminating 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.BigDecimal  divide(java.math.BigDecimal divisor, java.math.MathContext mc)Returns a BigDecimal whose value is (this /
divisor), with rounding according to the context settings.
if (mc.precision == 0)
return divide(divisor);
BigDecimal lhs = this.inflate(); // lefthandside
BigDecimal rhs = divisor.inflate(); // righthandside
BigDecimal result; // work
long preferredScale = (long)lhs.scale()  rhs.scale();
// Now calculate the answer. We use the existing
// divideandround 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 twoelement 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.
// we use the identity x = i * y + r to determine r
BigDecimal[] result = new BigDecimal[2];
result[0] = this.divideToIntegralValue(divisor);
result[1] = this.subtract(result[0].multiply(divisor));
return result;
 public java.math.BigDecimal[]  divideAndRemainder(java.math.BigDecimal divisor, java.math.MathContext mc)Returns a twoelement 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.
if (mc.precision == 0)
return divideAndRemainder(divisor);
BigDecimal[] result = new BigDecimal[2];
BigDecimal lhs = this;
result[0] = lhs.divideToIntegralValue(divisor, mc);
result[1] = lhs.subtract(result[0].multiply(divisor));
return result;
 public java.math.BigDecimal  divideToIntegralValue(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()) .
// 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.BigDecimal  divideToIntegralValue(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.
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.BigDecimal  doRound(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.
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 doublecheck, in case of the 999=>1000 case
return rounded.doRound(mc);
 public double  doubleValue()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.
if (scale == 0 && intCompact != INFLATED)
return (double)intCompact;
// Somewhat inefficient, but guaranteed to work.
return Double.parseDouble(this.toString());
 private java.math.BigDecimal  dropDigits(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 roundtolength rather than roundtoscale.
// 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 boolean  equals(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).
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 float  floatValue()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.
if (scale == 0 && intCompact != INFLATED)
return (float)intCompact;
// Somewhat inefficient, but guaranteed to work.
return Float.parseFloat(this.toString());
 private java.lang.String  getValueString(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(3insertionPoint + 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 int  hashCode()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.
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.BigDecimal  inflate()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 int  intLength(int x)Returns the length of an unsigned int, 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 114
for(int i = 1; ; i++) {
if (x <= ilogTable[i+1])
return i +1;
}
}
 public int  intValue()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 loworder 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.
return (intCompact != INFLATED && scale == 0) ?
(int)intCompact :
toBigInteger().intValue();
 public int  intValueExact()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.
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.String  layoutChars(boolean sci)Lay out this BigDecimal into a char[] array.
The Java 1.2 equivalent to this was called getValueString.
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 Enotation 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.length1);
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 { // Enotation is needed
if (sci) { // Scientific notation
buf.append(coeff[0]); // first character
if (coeff.length > 1) { // more to come
buf.append('.");
buf.append(coeff, 1, coeff.length1);
}
} 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.lengthsig);
}
}
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 int  longCompareTo(long x, long y)
return (x < y) ? 1 : (x == y) ? 0 : 1;
 private static long  longTenToThe(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][0] ) {
// System.err.println(val * thresholds[n][1]);
return val * thresholds[n][1];
}
}
// System.err.println(INFLATED);
return INFLATED;
 public long  longValue()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 loworder 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.
return (intCompact != INFLATED && scale == 0) ?
intCompact:
toBigInteger().longValue();
 public long  longValueExact()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.
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 non0
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 void  matchScale(java.math.BigDecimal[] val)Match the scales of two BigDecimals to align their
least significant digits.
If the scales of val[0] and val[1] differ, rescale
(nondestructively) the lowerscaled BigDecimal so
they match. That is, the lowerscaled reference will be
replaced by a reference to a new object with the same scale as
the other BigDecimal.
if (val[0].scale < val[1].scale)
val[0] = val[0].setScale(val[1].scale);
else if (val[1].scale < val[0].scale)
val[1] = val[1].setScale(val[0].scale);
 public java.math.BigDecimal  max(java.math.BigDecimal val)Returns the maximum of this BigDecimal and val.
return (compareTo(val) >= 0 ? this : val);
 public java.math.BigDecimal  min(java.math.BigDecimal val)Returns the minimum of this BigDecimal and
val.
return (compareTo(val) <= 0 ? this : val);
 public java.math.BigDecimal  movePointLeft(int n)Returns a BigDecimal which is equivalent to this one
with the decimal point moved n places to the left. If
n is nonnegative, 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).
// 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.BigDecimal  movePointRight(int n)Returns a BigDecimal which is equivalent to this one
with the decimal point moved n places to the right.
If n is nonnegative, 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
× 10^{n}) and scale max(this.scale()n,
0).
// 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.BigDecimal  multiply(java.math.BigDecimal multiplicand)Returns a BigDecimal whose value is (this ×
multiplicand), and whose scale is (this.scale() +
multiplicand.scale()).
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 212 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.BigDecimal  multiply(java.math.BigDecimal multiplicand, java.math.MathContext mc)Returns a BigDecimal whose value is (this ×
multiplicand), with rounding according to the context settings.
if (mc.precision == 0)
return multiply(multiplicand);
BigDecimal lhs = this;
return lhs.inflate().multiply(multiplicand.inflate()).doRound(mc);
 public java.math.BigDecimal  negate()Returns a BigDecimal whose value is (this),
and whose scale is this.scale().
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.BigDecimal  negate(java.math.MathContext mc)Returns a BigDecimal whose value is (this),
with rounding according to the context settings.
return plus(mc).negate();
 public java.math.BigDecimal  plus()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()}.
return this;
 public java.math.BigDecimal  plus(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.
if (mc.precision == 0) // no rounding please
return this;
return this.doRound(mc);
 public java.math.BigDecimal  pow(int n)Returns a BigDecimal whose value is
(this^{n}), 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.
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.BigDecimal  pow(int n, java.math.MathContext mc)Returns a BigDecimal whose value is
(this^{n}). The current implementation uses
the core algorithm defined in ANSI standard X3.2741996 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 X3.2741996 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.
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 1bit
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 int  precision()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.
int result = precision;
if (result == 0) {
result = digitLength();
precision = result;
}
return result;
 private static void  print(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 void  readObject(java.io.ObjectInputStream s)Reconstitute the BigDecimal instance from a stream (that is,
deserialize it).
// 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.BigDecimal  remainder(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).
BigDecimal divrem[] = this.divideAndRemainder(divisor);
return divrem[1];
 public java.math.BigDecimal  remainder(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).
BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
return divrem[1];
 public java.math.BigDecimal  round(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.
// Scaling/Rounding Operations
return plus(mc);
 private java.math.BigDecimal  roundOp(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.
BigDecimal rounded = doRound(mc);
return rounded;
 private void  roundThis(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.
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 int  scale()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.
return scale;
 public java.math.BigDecimal  scaleByPowerOfTen(int n)Returns a BigDecimal whose numerical value is equal to
(this * 10^{n}). The scale of
the result is (this.scale()  n).
this.inflate();
BigDecimal num = new BigDecimal(intVal, checkScale((long)scale  n));
num.precision = precision;
return num;
 public java.math.BigDecimal  setScale(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.
return setScale(newScale, roundingMode.oldMode);
 public java.math.BigDecimal  setScale(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.
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.BigDecimal  setScale(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 twoargument
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.
return setScale(newScale, ROUND_UNNECESSARY);
 public short  shortValueExact()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.
long num;
num = this.longValueExact(); // will check decimal part
if ((short)num != num)
throw new java.lang.ArithmeticException("Overflow");
return (short)num;
 public int  signum()Returns the signum function of this BigDecimal.
return (intCompact != INFLATED)?
Long.signum(intCompact):
intVal.signum();
 public java.math.BigDecimal  stripTrailingZeros()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]
this.inflate();
return (new BigDecimal(intVal, scale)).stripZerosToMatchScale(Long.MIN_VALUE);
 private java.math.BigDecimal  stripZerosToMatchScale(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.
boolean compact = (intCompact != INFLATED);
this.inflate();
BigInteger qr[]; // quotientremainder 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[1].signum() != 0)
break; // non0 remainder
intVal=qr[0];
scale = checkScale((long)scale1); // could Overflow
if (precision > 0) // adjust precision if known
precision;
}
if (compact)
intCompact = intVal.longValue();
return this;
 public java.math.BigDecimal  subtract(java.math.BigDecimal subtrahend)Returns a BigDecimal whose value is (this 
subtrahend), and whose scale is max(this.scale(),
subtrahend.scale()).
BigDecimal arg[] = {this, subtrahend};
matchScale(arg);
long x = arg[0].intCompact;
long y = arg[1].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 212 for
* explanation of the overflow test.
*/
if ( ((x ^ y) & (difference ^ x) ) >> 63 == 0L ) // not overflowed
return BigDecimal.valueOf(difference, arg[0].scale);
}
return new BigDecimal(arg[0].inflate().intVal.subtract(arg[1].inflate().intVal),
arg[0].scale);
 public java.math.BigDecimal  subtract(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).
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.BigInteger  tenToThe(int n)Return 10 to the power n, as a BigInteger.
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[0] = '1";
for (int i = 1; i <= n; i++)
tenpow[i] = '0";
return new BigInteger(tenpow);
 public java.math.BigInteger  toBigInteger()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.
// force to an integer, quietly
return this.setScale(0, ROUND_DOWN).inflate().intVal;
 public java.math.BigInteger  toBigIntegerExact()Converts this BigDecimal to a BigInteger,
checking for lost information. An exception is thrown if this
BigDecimal has a nonzero fractional part.
// round to an integer, with Exception if decimal part non0
return this.setScale(0, ROUND_UNNECESSARY).inflate().intVal;
 public java.lang.String  toEngineeringString()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.
return layoutChars(false);
 public java.lang.String  toPlainString()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.)
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.String  toString()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+(ulength1), 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] "1.23E8"
[123,12] "1.23E10"
Notes:
 There is a onetoone 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.
 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. Localesensitive
number formatting and parsing is handled by the {@link
java.text.NumberFormat} class and its subclasses.
 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.
 The digittocharacter mapping provided by
Character.forDigit is used.
if (stringCache == null)
stringCache = layoutChars(true);
return stringCache;
 public java.math.BigDecimal  ulp()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()] .
return BigDecimal.valueOf(1, this.scale());
 public java.math.BigInteger  unscaledValue()Returns a BigInteger whose value is the unscaled
value of this BigDecimal. (Computes (this *
10^{this.scale()}).)
return this.inflate().intVal;
 public static java.math.BigDecimal  valueOf(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..
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.BigDecimal  valueOf(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.
return valueOf(val, 0);
 public static java.math.BigDecimal  valueOf(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)}.
// 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 void  writeObject(java.io.ObjectOutputStream s)Serialize this BigDecimal to the stream in question
// Must inflate to maintain compatible serial form.
this.inflate();
// Write proper fields
s.defaultWriteObject();

