(unscaledValue × 10-scale).
*
* The {@code BigDecimal} class provides operations for * arithmetic, scale manipulation, rounding, comparison, hashing, and * format conversion. The {@link #toString} method provides a * canonical representation of a {@code BigDecimal}. * *
The {@code BigDecimal} class gives its user complete control * over rounding behavior. If no rounding mode is specified and the * exact result cannot be represented, an {@code ArithmeticException} * 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 deprecated; the * enumeration values of the {@code RoundingMode} {@code enum}, (such * as {@link RoundingMode#HALF_UP}) should be used instead. * *
When a {@code MathContext} object is supplied with a precision * setting of 0 (for example, {@link MathContext#UNLIMITED}), * arithmetic operations are exact, as are the arithmetic methods * which take no {@code MathContext} object. As a corollary of * computing the exact result, the rounding mode setting of a {@code * MathContext} object with a precision setting of 0 is not used and * thus irrelevant. In the case of divide, the exact quotient could * have an infinitely long decimal expansion; for example, 1 divided * by 3. If the quotient has a nonterminating decimal expansion and * the operation is specified to return an exact result, an {@code * ArithmeticException} is thrown. Otherwise, the exact result of the * division is returned, as done for other operations. * *
When the precision setting is not 0, the rules of {@code * BigDecimal} arithmetic are broadly compatible with selected modes * of operation of the arithmetic defined in ANSI X3.274-1996 and ANSI * X3.274-1996/AM 1-2000 (section 7.4). Unlike those standards, * {@code BigDecimal} includes many rounding modes. Any conflicts * between these ANSI standards and the {@code BigDecimal} * specification are resolved in favor of {@code 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. * * The different representations of the same numerical value are * called members of the same cohort. The {@linkplain * #compareTo(BigDecimal) natural order} of {@code BigDecimal} * considers members of the same cohort to be equal to each other. In * contrast, the {@link #equals(Object) equals} method requires both the * numerical value and representation to be the same for equality to * hold. The results of methods like {@link #scale()} and {@link * #unscaledValue()} will differ for numerically equal values with * different representations. * *
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 and square root) than the number of digits returned. * * First, the total number of digits to return is specified by the * {@code MathContext}'s {@code precision} setting; this determines * the result's 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 {@literal "9"} digit. * For example, rounding the value 999.9 to three digits rounding up * would be numerically equal to one thousand, represented as * 100×101. In such cases, the new {@literal "1"} is * the leading digit position of the returned result. * *
For methods and constructors with a {@code MathContext} * parameter, if the result is inexact but the rounding mode is {@link * RoundingMode#UNNECESSARY UNNECESSARY}, an {@code * ArithmeticException} will be thrown. * *
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. * *
| 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() | *
| Square root | radicand.scale()/2 | *
Before rounding, the scale of the logical exact intermediate
* result is the preferred scale for that operation. If the exact
* numerical result cannot be represented in {@code precision}
* digits, rounding selects the set of digits to return and the scale
* of the result is reduced from the scale of the intermediate result
* to the least scale which can represent the {@code precision}
* digits actually returned. If the exact result can be represented
* with at most {@code precision} digits, the representation
* of the result with the scale closest to the preferred scale is
* returned. In particular, an exactly representable quotient may be
* represented in fewer than {@code precision} digits by removing
* trailing zeros and decreasing the scale. For example, rounding to
* three digits using the {@linkplain RoundingMode#FLOOR floor}
* rounding mode,
*
* {@code 19/100 = 0.19 // integer=19, scale=2}
*
* but
*
* {@code 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 {@code pow} method using the * {@linkplain #pow(int, MathContext) specified algorithm} can * occasionally differ from the rounded mathematical result by more * than one unit in the last place, one {@linkplain #ulp() ulp}. * *
Two types of operations are provided for manipulating the scale * of a {@code BigDecimal}: scaling/rounding operations and decimal * point motion operations. Scaling/rounding operations ({@link * #setScale setScale} and {@link #round round}) return a * {@code BigDecimal} whose value is approximately (or exactly) equal * to that of the operand, but whose scale or precision is the * specified value; that is, they increase or decrease the precision * of the stored number with minimal effect on its value. Decimal * point motion operations ({@link #movePointLeft movePointLeft} and * {@link #movePointRight movePointRight}) return a * {@code BigDecimal} created from the operand by moving the decimal * point a specified distance in the specified direction. * *
As a 32-bit integer, the set of values for the scale is large, * but bounded. If the scale of a result would exceed the range of a * 32-bit integer, either by overflow or underflow, the operation may * throw an {@code ArithmeticException}. * *
For the sake of brevity and clarity, pseudo-code is used * throughout the descriptions of {@code BigDecimal} methods. The * pseudo-code expression {@code (i + j)} is shorthand for "a * {@code BigDecimal} whose value is that of the {@code BigDecimal} * {@code i} added to that of the {@code BigDecimal} * {@code j}." The pseudo-code expression {@code (i == j)} is * shorthand for "{@code true} if and only if the * {@code BigDecimal} {@code i} represents the same value as the * {@code BigDecimal} {@code j}." Other pseudo-code expressions * are interpreted similarly. Square brackets are used to represent * the particular {@code BigInteger} and scale pair defining a * {@code BigDecimal} value; for example [19, 2] is the * {@code BigDecimal} numerically equal to 0.19 having a scale of 2. * *
All methods and constructors for this class throw * {@code NullPointerException} when passed a {@code null} object * reference for any input parameter. * * @apiNote Care should be exercised if {@code BigDecimal} objects are * used as keys in a {@link java.util.SortedMap SortedMap} or elements * in a {@link java.util.SortedSet SortedSet} since {@code * BigDecimal}'s {@linkplain #compareTo(BigDecimal) natural * ordering} is inconsistent with equals. See {@link * Comparable}, {@link java.util.SortedMap} or {@link * java.util.SortedSet} for more information. * *
For differences, IEEE 754 includes several kinds of values not * modeled by {@code BigDecimal} including negative zero, signed * infinities, and NaN (not-a-number). IEEE 754 defines formats, which * are parameterized by base (binary or decimal), number of digits of * precision, and exponent range. A format determines the set of * representable values. Most operations accept as input one or more * values of a given format and produce a result in the same format. * A {@code BigDecimal}'s {@linkplain #scale() scale} is equivalent to * negating an IEEE 754 value's exponent. {@code BigDecimal} values do * not have a format in the same sense; all values have the same * possible range of scale/exponent and the {@linkplain * #unscaledValue() unscaled value} has arbitrary precision. Instead, * for the {@code BigDecimal} operations taking a {@code MathContext} * parameter, if the {@code MathContext} has a nonzero precision, the * set of possible representable values for the result is determined * by the precision of the {@code MathContext} argument. For example * in {@code BigDecimal}, if a nonzero three-digit number and a * nonzero four-digit number are multiplied together in the context of * a {@code MathContext} object having a precision of three, the * result will have three digits (assuming no overflow or underflow, * etc.). * *
The rounding policies implemented by {@code BigDecimal} * operations indicated by {@linkplain RoundingMode rounding modes} * are a proper superset of the IEEE 754 rounding-direction * attributes. *
{@code BigDecimal} arithmetic will most resemble IEEE 754
* decimal arithmetic if a {@code MathContext} corresponding to an
* IEEE 754 decimal format, such as {@linkplain MathContext#DECIMAL64
* decimal64} or {@linkplain MathContext#DECIMAL128 decimal128} is
* used to round all starting values and intermediate operations. The
* numerical values computed can differ if the exponent range of the
* IEEE 754 format being approximated is exceeded since a {@code
* MathContext} does not constrain the scale of {@code BigDecimal}
* results. Operations that would generate a NaN or exact infinity,
* such as dividing by zero, throw an {@code ArithmeticException} in
* {@code BigDecimal} arithmetic.
*
* @see BigInteger
* @see MathContext
* @see RoundingMode
* @see java.util.SortedMap
* @see java.util.SortedSet
* @author Josh Bloch
* @author Mike Cowlishaw
* @author Joseph D. Darcy
* @author Sergey V. Kuksenko
* @since 1.1
*/
public class BigDecimal extends Number implements Comparable 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 {@code 'e'}
* ( More formally, the strings this constructor accepts are
* described by the following grammar:
* The scale of the returned {@code BigDecimal} will be the
* number of digits in the fraction, or zero if the string
* contains no decimal point, subject to adjustment for any
* exponent; if the string contains an exponent, the exponent is
* subtracted from the scale. The value of the resulting scale
* must lie between {@code Integer.MIN_VALUE} and
* {@code Integer.MAX_VALUE}, inclusive.
*
* 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:
* Notes:
* The results of this constructor can be somewhat unpredictable
* and its use is generally not recommended; see the notes under
* the {@link #BigDecimal(double)} constructor.
*
* @param val {@code double} value to be converted to
* {@code BigDecimal}.
* @param mc the context to use.
* @throws NumberFormatException if {@code val} is infinite or NaN.
* @since 1.5
*/
public BigDecimal(double val, MathContext mc) {
if (Double.isInfinite(val) || Double.isNaN(val))
throw new NumberFormatException("Infinite or NaN");
// Translate the double into sign, exponent and significand, according
// to the formulae in JLS, Section 20.10.22.
long valBits = Double.doubleToLongBits(val);
int sign = ((valBits >> 63) == 0 ? 1 : -1);
int exponent = (int) ((valBits >> 52) & 0x7ffL);
long significand = (exponent == 0
? (valBits & ((1L << 52) - 1)) << 1
: (valBits & ((1L << 52) - 1)) | (1L << 52));
exponent -= 1075;
// At this point, val == sign * significand * 2**exponent.
/*
* Special case zero to suppress nonterminating normalization and bogus
* scale calculation.
*/
if (significand == 0) {
this.intVal = BigInteger.ZERO;
this.scale = 0;
this.intCompact = 0;
this.precision = 1;
return;
}
// Normalize
while ((significand & 1) == 0) { // i.e., significand is even
significand >>= 1;
exponent++;
}
int scl = 0;
// Calculate intVal and scale
BigInteger rb;
long compactVal = sign * significand;
if (exponent == 0) {
rb = (compactVal == INFLATED) ? INFLATED_BIGINT : null;
} else {
if (exponent < 0) {
rb = BigInteger.valueOf(5).pow(-exponent).multiply(compactVal);
scl = -exponent;
} else { // (exponent > 0)
rb = BigInteger.TWO.pow(exponent).multiply(compactVal);
}
compactVal = compactValFor(rb);
}
int prec = 0;
int mcp = mc.precision;
if (mcp > 0) { // do rounding
int mode = mc.roundingMode.oldMode;
int drop;
if (compactVal == INFLATED) {
prec = bigDigitLength(rb);
drop = prec - mcp;
while (drop > 0) {
scl = checkScaleNonZero((long) scl - drop);
rb = divideAndRoundByTenPow(rb, drop, mode);
compactVal = compactValFor(rb);
if (compactVal != INFLATED) {
break;
}
prec = bigDigitLength(rb);
drop = prec - mcp;
}
}
if (compactVal != INFLATED) {
prec = longDigitLength(compactVal);
drop = prec - mcp;
while (drop > 0) {
scl = checkScaleNonZero((long) scl - drop);
compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
prec = longDigitLength(compactVal);
drop = prec - mcp;
}
rb = null;
}
}
this.intVal = rb;
this.intCompact = compactVal;
this.scale = scl;
this.precision = prec;
}
/**
* Accept no subclasses.
*/
private static BigInteger toStrictBigInteger(BigInteger val) {
return (val.getClass() == BigInteger.class) ?
val :
new BigInteger(val.toByteArray().clone());
}
/**
* Translates a {@code BigInteger} into a {@code BigDecimal}.
* The scale of the {@code BigDecimal} is zero.
*
* @param val {@code BigInteger} value to be converted to
* {@code BigDecimal}.
*/
public BigDecimal(BigInteger val) {
scale = 0;
intVal = toStrictBigInteger(val);
intCompact = compactValFor(intVal);
}
/**
* Translates a {@code BigInteger} into a {@code BigDecimal}
* rounding according to the context settings. The scale of the
* {@code BigDecimal} is zero.
*
* @param val {@code BigInteger} value to be converted to
* {@code BigDecimal}.
* @param mc the context to use.
* @since 1.5
*/
public BigDecimal(BigInteger val, MathContext mc) {
this(toStrictBigInteger(val), 0, mc);
}
/**
* Translates a {@code BigInteger} unscaled value and an
* {@code int} scale into a {@code BigDecimal}. The value of
* the {@code BigDecimal} is
* If the digit positions of the arguments have a sufficient
* gap between them, the value smaller in magnitude can be
* condensed into a {@literal "sticky bit"} and the end result will
* round the same way if the precision of the final
* result does not include the high order digit of the small
* magnitude operand.
*
* Note that while strictly speaking this is an optimization,
* it makes a much wider range of additions practical.
*
* This corresponds to a pre-shift operation in a fixed
* precision floating-point adder; this method is complicated by
* variable precision of the result as determined by the
* MathContext. A more nuanced operation could implement a
* {@literal "right shift"} on the smaller magnitude operand so
* that the number of digits of the smaller operand could be
* reduced even though the significands partially overlapped.
*/
private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend, long padding, MathContext mc) {
assert padding != 0;
BigDecimal big;
BigDecimal small;
if (padding < 0) { // lhs is big; augend is small
big = lhs;
small = augend;
} else { // lhs is small; augend is big
big = augend;
small = lhs;
}
/*
* This is the estimated scale of an ulp of the result; it assumes that
* the result doesn't have a carry-out on a true add (e.g. 999 + 1 =>
* 1000) or any subtractive cancellation on borrowing (e.g. 100 - 1.2 =>
* 98.8)
*/
long estResultUlpScale = (long) big.scale - big.precision() + mc.precision;
/*
* The low-order digit position of big is big.scale(). This
* is true regardless of whether big has a positive or
* negative scale. The high-order digit position of small is
* small.scale - (small.precision() - 1). To do the full
* condensation, the digit positions of big and small must be
* disjoint *and* the digit positions of small should not be
* directly visible in the result.
*/
long smallHighDigitPos = (long) small.scale - small.precision() + 1;
if (smallHighDigitPos > big.scale + 2 && // big and small disjoint
smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible
small = BigDecimal.valueOf(small.signum(), this.checkScale(Math.max(big.scale, estResultUlpScale) + 3));
}
// Since addition is symmetric, preserving input order in
// returned operands doesn't matter
BigDecimal[] result = {big, small};
return result;
}
/**
* Returns a {@code BigDecimal} whose value is {@code (this -
* subtrahend)}, and whose scale is {@code max(this.scale(),
* subtrahend.scale())}.
*
* @param subtrahend value to be subtracted from this {@code BigDecimal}.
* @return {@code this - subtrahend}
*/
public BigDecimal subtract(BigDecimal subtrahend) {
if (this.intCompact != INFLATED) {
if ((subtrahend.intCompact != INFLATED)) {
return add(this.intCompact, this.scale, -subtrahend.intCompact, subtrahend.scale);
} else {
return add(this.intCompact, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
}
} else {
if ((subtrahend.intCompact != INFLATED)) {
// Pair of subtrahend values given before pair of
// values from this BigDecimal to avoid need for
// method overloading on the specialized add method
return add(-subtrahend.intCompact, subtrahend.scale, this.intVal, this.scale);
} else {
return add(this.intVal, this.scale, subtrahend.intVal.negate(), subtrahend.scale);
}
}
}
/**
* Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)},
* with rounding according to the context settings.
*
* If {@code subtrahend} is zero then this, rounded if necessary, is used as the
* result. If this is zero then the result is {@code subtrahend.negate(mc)}.
*
* @param subtrahend value to be subtracted from this {@code BigDecimal}.
* @param mc the context to use.
* @return {@code this - subtrahend}, rounded as necessary.
* @since 1.5
*/
public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) {
if (mc.precision == 0)
return subtract(subtrahend);
// share the special rounding code in add()
return add(subtrahend.negate(), mc);
}
/**
* Returns a {@code BigDecimal} whose value is The remainder is given by
* {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}.
* Note that this is not the modulo operation (the result can be
* negative).
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @return {@code this % divisor}.
* @throws ArithmeticException if {@code divisor==0}
* @since 1.5
*/
public BigDecimal remainder(BigDecimal divisor) {
BigDecimal divrem[] = this.divideAndRemainder(divisor);
return divrem[1];
}
/**
* Returns a {@code BigDecimal} whose value is {@code (this %
* divisor)}, with rounding according to the context settings.
* The {@code 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 {@code mc.getPrecision()} digits.
*
* The remainder is given by
* {@code this.subtract(this.divideToIntegralValue(divisor,
* mc).multiply(divisor))}. Note that this is not the modulo
* operation (the result can be negative).
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @param mc the context to use.
* @return {@code this % divisor}, rounded as necessary.
* @throws ArithmeticException if {@code divisor==0}
* @throws ArithmeticException if the result is inexact but the
* rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
* {@literal >} 0 and the result of {@code this.divideToIntegralValue(divisor)} would
* require a precision of more than {@code mc.precision} digits.
* @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
* @since 1.5
*/
public BigDecimal remainder(BigDecimal divisor, MathContext mc) {
BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
return divrem[1];
}
/**
* Returns a two-element {@code BigDecimal} array containing the
* result of {@code divideToIntegralValue} followed by the result of
* {@code remainder} on the two operands.
*
* Note that if both the integer quotient and remainder are
* needed, this method is faster than using the
* {@code divideToIntegralValue} and {@code remainder} methods
* separately because the division need only be carried out once.
*
* @param divisor value by which this {@code BigDecimal} is to be divided,
* and the remainder computed.
* @return a two element {@code BigDecimal} array: the quotient
* (the result of {@code divideToIntegralValue}) is the initial element
* and the remainder is the final element.
* @throws ArithmeticException if {@code divisor==0}
* @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
* @see #remainder(java.math.BigDecimal, java.math.MathContext)
* @since 1.5
*/
public BigDecimal[] divideAndRemainder(BigDecimal divisor) {
// 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;
}
/**
* Returns a two-element {@code BigDecimal} array containing the
* result of {@code divideToIntegralValue} followed by the result of
* {@code 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
* {@code divideToIntegralValue} and {@code remainder} methods
* separately because the division need only be carried out once.
*
* @param divisor value by which this {@code BigDecimal} is to be divided,
* and the remainder computed.
* @param mc the context to use.
* @return a two element {@code BigDecimal} array: the quotient
* (the result of {@code divideToIntegralValue}) is the
* initial element and the remainder is the final element.
* @throws ArithmeticException if {@code divisor==0}
* @throws ArithmeticException if the result is inexact but the
* rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
* {@literal >} 0 and the result of {@code this.divideToIntegralValue(divisor)} would
* require a precision of more than {@code mc.precision} digits.
* @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
* @see #remainder(java.math.BigDecimal, java.math.MathContext)
* @since 1.5
*/
public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) {
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;
}
/**
* Returns an approximation to the square root of {@code this}
* with rounding according to the context settings.
*
* The preferred scale of the returned result is equal to
* {@code this.scale()/2}. The value of the returned result is
* always within one ulp of the exact decimal value for the
* precision in question. If the rounding mode is {@link
* RoundingMode#HALF_UP HALF_UP}, {@link RoundingMode#HALF_DOWN
* HALF_DOWN}, or {@link RoundingMode#HALF_EVEN HALF_EVEN}, the
* result is within one half an ulp of the exact decimal value.
*
* Special case:
* The parameter {@code n} must be in the range 0 through
* 999999999, inclusive. {@code ZERO.pow(0)} returns {@link
* #ONE}.
*
* Note that future releases may expand the allowable exponent
* range of this method.
*
* @param n power to raise this {@code BigDecimal} to.
* @return The X3.274-1996 algorithm is:
*
* This method, which simply returns this {@code BigDecimal}
* is included for symmetry with the unary minus method {@link
* #negate()}.
*
* @return {@code this}.
* @see #negate()
* @since 1.5
*/
public BigDecimal plus() {
return this;
}
/**
* Returns a {@code BigDecimal} whose value is {@code (+this)},
* with rounding according to the context settings.
*
* The effect of this method is identical to that of the {@link
* #round(MathContext)} method.
*
* @param mc the context to use.
* @return {@code this}, rounded as necessary. A zero result will
* have a scale of 0.
* @see #round(MathContext)
* @since 1.5
*/
public BigDecimal plus(MathContext mc) {
if (mc.precision == 0) // no rounding please
return this;
return doRound(this, mc);
}
/**
* Returns the signum function of this {@code BigDecimal}.
*
* @return -1, 0, or 1 as the value of this {@code BigDecimal}
* is negative, zero, or positive.
*/
public int signum() {
return (intCompact != INFLATED)?
Long.signum(intCompact):
intVal.signum();
}
/**
* Returns the scale of this {@code 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 {@code -3} means the unscaled
* value is multiplied by 1000.
*
* @return the scale of this {@code BigDecimal}.
*/
public int scale() {
return scale;
}
/**
* Returns the precision of this {@code BigDecimal}. (The
* precision is the number of digits in the unscaled value.)
*
* The precision of a zero value is 1.
*
* @return the precision of this {@code BigDecimal}.
* @since 1.5
*/
public int precision() {
int result = precision;
if (result == 0) {
long s = intCompact;
if (s != INFLATED)
result = longDigitLength(s);
else
result = bigDigitLength(intVal);
precision = result;
}
return result;
}
/**
* Returns a {@code BigInteger} whose value is the unscaled
* value of this {@code BigDecimal}. (Computes The effect of this method is identical to that of the
* {@link #plus(MathContext)} method.
*
* @param mc the context to use.
* @return a {@code BigDecimal} rounded according to the
* {@code MathContext} settings.
* @see #plus(MathContext)
* @since 1.5
*/
public BigDecimal round(MathContext mc) {
return plus(mc);
}
/**
* Returns a {@code BigDecimal} whose scale is the specified
* value, and whose unscaled value is determined by multiplying or
* dividing this {@code 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.
*
* @apiNote 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 This call is typically used to increase the scale, in which
* case it is guaranteed that there exists a {@code 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
* {@code 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 {@code setScale}, but saves the caller the trouble
* of specifying a rounding mode in cases where it is irrelevant.
*
* @apiNote Since {@code 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 A standard canonical string form of the {@code BigDecimal}
* is created as though by the following steps: first, the
* absolute value of the unscaled value of the {@code BigDecimal}
* is converted to a string in base ten using the characters
* {@code '0'} through {@code '9'} with no leading zeros (except
* if its value is zero, in which case a single {@code '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,
* {@code -scale+(ulength-1)}, where {@code 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 {@code -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.
* {@code '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
* {@code '0'} character is prefixed.
*
* Otherwise (that is, if the scale is negative, or the
* adjusted exponent is less than {@code -6}), the number will be
* converted to a character form using exponential notation. In
* this case, if the converted {@code 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 {@code 'E'} followed immediately by the
* adjusted exponent converted to a character form. The latter is
* in base ten, using the characters {@code '0'} through
* {@code '9'} with no leading zeros, and is always prefixed by a
* sign character {@code '-'} ( Finally, the entire string is prefixed by a minus sign
* character {@code '-'} ( Examples:
* For each representation [unscaled value, scale]
* on the left, the resulting string is shown on the right.
* Returns a string that represents the {@code 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 {@code BigDecimal} if the output string is
* converting back to a {@code 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 string representation of this {@code BigDecimal}, using
* engineering notation if an exponent is needed.
* @since 1.5
*/
public String toEngineeringString() {
return layoutChars(false);
}
/**
* Returns a string representation of this {@code 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 '-'
* (
* 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.
*
* @return this {@code BigDecimal} converted to a {@code BigInteger}.
* @jls 5.1.3 Narrowing Primitive Conversion
*/
public BigInteger toBigInteger() {
// force to an integer, quietly
return this.setScale(0, ROUND_DOWN).inflated();
}
/**
* Converts this {@code BigDecimal} to a {@code BigInteger},
* checking for lost information. An exception is thrown if this
* {@code BigDecimal} has a nonzero fractional part.
*
* @return this {@code BigDecimal} converted to a {@code BigInteger}.
* @throws ArithmeticException if {@code this} has a nonzero
* fractional part.
* @since 1.5
*/
public BigInteger toBigIntegerExact() {
// round to an integer, with Exception if decimal part non-0
return this.setScale(0, ROUND_UNNECESSARY).inflated();
}
/**
* Converts this {@code BigDecimal} to a {@code long}.
* This conversion is analogous to the
* narrowing primitive conversion from {@code double} to
* {@code short} as defined in
* The Java Language Specification:
* any fractional part of this
* {@code BigDecimal} will be discarded, and if the resulting
* "{@code BigInteger}" is too big to fit in a
* {@code long}, only the low-order 64 bits are returned.
* Note that this conversion can lose information about the
* overall magnitude and precision of this {@code BigDecimal} value as well
* as return a result with the opposite sign.
*
* @return this {@code BigDecimal} converted to a {@code long}.
* @jls 5.1.3 Narrowing Primitive Conversion
*/
@Override
public long longValue(){
if (intCompact != INFLATED && scale == 0) {
return intCompact;
} else {
// Fastpath zero and small values
if (this.signum() == 0 || fractionOnly() ||
// Fastpath very large-scale values that will result
// in a truncated value of zero. If the scale is -64
// or less, there are at least 64 powers of 10 in the
// value of the numerical result. Since 10 = 2*5, in
// that case there would also be 64 powers of 2 in the
// result, meaning all 64 bits of a long will be zero.
scale <= -64) {
return 0;
} else {
return toBigInteger().longValue();
}
}
}
/**
* Return true if a nonzero BigDecimal has an absolute value less
* than one; i.e. only has fraction digits.
*/
private boolean fractionOnly() {
assert this.signum() != 0;
return (this.precision() - this.scale) <= 0;
}
/**
* Converts this {@code BigDecimal} to a {@code long}, checking
* for lost information. If this {@code BigDecimal} has a
* nonzero fractional part or is out of the possible range for a
* {@code long} result then an {@code ArithmeticException} is
* thrown.
*
* @return this {@code BigDecimal} converted to a {@code long}.
* @throws ArithmeticException if {@code this} has a nonzero
* fractional part, or will not fit in a {@code long}.
* @since 1.5
*/
public long longValueExact() {
if (intCompact != INFLATED && scale == 0)
return intCompact;
// Fastpath zero
if (this.signum() == 0)
return 0;
// Fastpath numbers less than 1.0 (the latter can be very slow
// to round if very small)
if (fractionOnly())
throw new ArithmeticException("Rounding necessary");
// 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");
// round to an integer, with Exception if decimal part non-0
BigDecimal num = this.setScale(0, ROUND_UNNECESSARY);
if (num.precision() >= 19) // need to check carefully
LongOverflow.check(num);
return num.inflated().longValue();
}
private static class LongOverflow {
/** BigInteger equal to Long.MIN_VALUE. */
private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE);
/** BigInteger equal to Long.MAX_VALUE. */
private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE);
public static void check(BigDecimal num) {
BigInteger intVal = num.inflated();
if (intVal.compareTo(LONGMIN) < 0 ||
intVal.compareTo(LONGMAX) > 0)
throw new java.lang.ArithmeticException("Overflow");
}
}
/**
* Converts this {@code BigDecimal} to an {@code int}.
* This conversion is analogous to the
* narrowing primitive conversion from {@code double} to
* {@code short} as defined in
* The Java Language Specification:
* any fractional part of this
* {@code BigDecimal} will be discarded, and if the resulting
* "{@code BigInteger}" is too big to fit in an
* {@code int}, only the low-order 32 bits are returned.
* Note that this conversion can lose information about the
* overall magnitude and precision of this {@code BigDecimal}
* value as well as return a result with the opposite sign.
*
* @return this {@code BigDecimal} converted to an {@code int}.
* @jls 5.1.3 Narrowing Primitive Conversion
*/
@Override
public int intValue() {
return (intCompact != INFLATED && scale == 0) ?
(int)intCompact :
(int)longValue();
}
/**
* Converts this {@code BigDecimal} to an {@code int}, checking
* for lost information. If this {@code BigDecimal} has a
* nonzero fractional part or is out of the possible range for an
* {@code int} result then an {@code ArithmeticException} is
* thrown.
*
* @return this {@code BigDecimal} converted to an {@code int}.
* @throws ArithmeticException if {@code this} has a nonzero
* fractional part, or will not fit in an {@code int}.
* @since 1.5
*/
public int intValueExact() {
long num;
num = this.longValueExact(); // will check decimal part
if ((int)num != num)
throw new java.lang.ArithmeticException("Overflow");
return (int)num;
}
/**
* Converts this {@code BigDecimal} to a {@code short}, checking
* for lost information. If this {@code BigDecimal} has a
* nonzero fractional part or is out of the possible range for a
* {@code short} result then an {@code ArithmeticException} is
* thrown.
*
* @return this {@code BigDecimal} converted to a {@code short}.
* @throws ArithmeticException if {@code this} has a nonzero
* fractional part, or will not fit in a {@code short}.
* @since 1.5
*/
public short shortValueExact() {
long num;
num = this.longValueExact(); // will check decimal part
if ((short)num != num)
throw new java.lang.ArithmeticException("Overflow");
return (short)num;
}
/**
* Converts this {@code BigDecimal} to a {@code byte}, checking
* for lost information. If this {@code BigDecimal} has a
* nonzero fractional part or is out of the possible range for a
* {@code byte} result then an {@code ArithmeticException} is
* thrown.
*
* @return this {@code BigDecimal} converted to a {@code byte}.
* @throws ArithmeticException if {@code this} has a nonzero
* fractional part, or will not fit in a {@code byte}.
* @since 1.5
*/
public byte byteValueExact() {
long num;
num = this.longValueExact(); // will check decimal part
if ((byte)num != num)
throw new java.lang.ArithmeticException("Overflow");
return (byte)num;
}
/**
* Converts this {@code BigDecimal} to a {@code float}.
* This conversion is similar to the
* narrowing primitive conversion from {@code double} to
* {@code float} as defined in
* The Java Language Specification:
* if this {@code BigDecimal} has too great a
* magnitude to represent as a {@code 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 {@code BigDecimal}
* value.
*
* @return this {@code BigDecimal} converted to a {@code float}.
* @jls 5.1.3 Narrowing Primitive Conversion
*/
@Override
public float floatValue(){
if(intCompact != INFLATED) {
if (scale == 0) {
return (float)intCompact;
} else {
/*
* If both intCompact and the scale can be exactly
* represented as float values, perform a single float
* multiply or divide to compute the (properly
* rounded) result.
*/
if (Math.abs(intCompact) < 1L<<22 ) {
// Don't have too guard against
// Math.abs(MIN_VALUE) because of outer check
// against INFLATED.
if (scale > 0 && scale < FLOAT_10_POW.length) {
return (float)intCompact / FLOAT_10_POW[scale];
} else if (scale < 0 && scale > -FLOAT_10_POW.length) {
return (float)intCompact * FLOAT_10_POW[-scale];
}
}
}
}
// Somewhat inefficient, but guaranteed to work.
return Float.parseFloat(this.toString());
}
/**
* Converts this {@code BigDecimal} to a {@code double}.
* This conversion is similar to the
* narrowing primitive conversion from {@code double} to
* {@code float} as defined in
* The Java Language Specification:
* if this {@code BigDecimal} has too great a
* magnitude represent as a {@code 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 {@code BigDecimal}
* value.
*
* @return this {@code BigDecimal} converted to a {@code double}.
* @jls 5.1.3 Narrowing Primitive Conversion
*/
@Override
public double doubleValue(){
if(intCompact != INFLATED) {
if (scale == 0) {
return (double)intCompact;
} else {
/*
* If both intCompact and the scale can be exactly
* represented as double values, perform a single
* double multiply or divide to compute the (properly
* rounded) result.
*/
if (Math.abs(intCompact) < 1L<<52 ) {
// Don't have too guard against
// Math.abs(MIN_VALUE) because of outer check
// against INFLATED.
if (scale > 0 && scale < DOUBLE_10_POW.length) {
return (double)intCompact / DOUBLE_10_POW[scale];
} else if (scale < 0 && scale > -DOUBLE_10_POW.length) {
return (double)intCompact * DOUBLE_10_POW[-scale];
}
}
}
}
// Somewhat inefficient, but guaranteed to work.
return Double.parseDouble(this.toString());
}
/**
* Powers of 10 which can be represented exactly in {@code
* double}.
*/
private static final double DOUBLE_10_POW[] = {
1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5,
1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, 1.0e11,
1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17,
1.0e18, 1.0e19, 1.0e20, 1.0e21, 1.0e22
};
/**
* Powers of 10 which can be represented exactly in {@code
* float}.
*/
private static final float FLOAT_10_POW[] = {
1.0e0f, 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f,
1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f
};
/**
* Returns the size of an ulp, a unit in the last place, of this
* {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal}
* value is the positive distance between this value and the
* {@code 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 {@code this}. The result is
* stored with the same scale as {@code this} so the result
* for zero and nonzero values is equal to {@code [1,
* this.scale()]}.
*
* @return the size of an ulp of {@code this}
* @since 1.5
*/
public BigDecimal ulp() {
return BigDecimal.valueOf(1, this.scale(), 1);
}
// Private class to build a string representation for BigDecimal object.
// "StringBuilderHelper" is constructed as a thread local variable so it is
// thread safe. The StringBuilder field acts as a buffer to hold the temporary
// representation of BigDecimal. The cmpCharArray holds all the characters for
// the compact representation of BigDecimal (except for '-' sign' if it is
// negative) if its intCompact field is not INFLATED. It is shared by all
// calls to toString() and its variants in that particular thread.
static class StringBuilderHelper {
final StringBuilder sb; // Placeholder for BigDecimal string
final char[] cmpCharArray; // character array to place the intCompact
StringBuilderHelper() {
sb = new StringBuilder();
// All non negative longs can be made to fit into 19 character array.
cmpCharArray = new char[19];
}
// Accessors.
StringBuilder getStringBuilder() {
sb.setLength(0);
return sb;
}
char[] getCompactCharArray() {
return cmpCharArray;
}
/**
* Places characters representing the intCompact in {@code long} into
* cmpCharArray and returns the offset to the array where the
* representation starts.
*
* @param intCompact the number to put into the cmpCharArray.
* @return offset to the array where the representation starts.
* Note: intCompact must be greater or equal to zero.
*/
int putIntCompact(long intCompact) {
assert intCompact >= 0;
long q;
int r;
// since we start from the least significant digit, charPos points to
// the last character in cmpCharArray.
int charPos = cmpCharArray.length;
// Get 2 digits/iteration using longs until quotient fits into an int
while (intCompact > Integer.MAX_VALUE) {
q = intCompact / 100;
r = (int)(intCompact - q * 100);
intCompact = q;
cmpCharArray[--charPos] = DIGIT_ONES[r];
cmpCharArray[--charPos] = DIGIT_TENS[r];
}
// Get 2 digits/iteration using ints when i2 >= 100
int q2;
int i2 = (int)intCompact;
while (i2 >= 100) {
q2 = i2 / 100;
r = i2 - q2 * 100;
i2 = q2;
cmpCharArray[--charPos] = DIGIT_ONES[r];
cmpCharArray[--charPos] = DIGIT_TENS[r];
}
cmpCharArray[--charPos] = DIGIT_ONES[i2];
if (i2 >= 10)
cmpCharArray[--charPos] = DIGIT_TENS[i2];
return charPos;
}
static final char[] DIGIT_TENS = {
'0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
'1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
'2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
'3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
'4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
'5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
'6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
'7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
'8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
'9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
};
static final char[] DIGIT_ONES = {
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
};
}
/**
* Lay out this {@code BigDecimal} into a {@code char[]} array.
* The Java 1.2 equivalent to this was called {@code getValueString}.
*
* @param sci {@code true} for Scientific exponential notation;
* {@code false} for Engineering
* @return string with canonical string representation of this
* {@code BigDecimal}
*/
private String layoutChars(boolean sci) {
if (scale == 0) // zero scale is trivial
return (intCompact != INFLATED) ?
Long.toString(intCompact):
intVal.toString();
if (scale == 2 &&
intCompact >= 0 && intCompact < Integer.MAX_VALUE) {
// currency fast path
int lowInt = (int)intCompact % 100;
int highInt = (int)intCompact / 100;
return (Integer.toString(highInt) + '.' +
StringBuilderHelper.DIGIT_TENS[lowInt] +
StringBuilderHelper.DIGIT_ONES[lowInt]) ;
}
StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get();
char[] coeff;
int offset; // offset is the starting index for coeff array
// Get the significand as an absolute value
if (intCompact != INFLATED) {
offset = sbHelper.putIntCompact(Math.abs(intCompact));
coeff = sbHelper.getCompactCharArray();
} else {
offset = 0;
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 = sbHelper.getStringBuilder();
if (signum() < 0) // prefix '-' if negative
buf.append('-');
int coeffLen = coeff.length - offset;
long adjusted = -(long)scale + (coeffLen -1);
if ((scale >= 0) && (adjusted >= -6)) { // plain number
int pad = scale - coeffLen; // 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, offset, coeffLen);
} else { // xx.xx form
buf.append(coeff, offset, -pad);
buf.append('.');
buf.append(coeff, -pad + offset, scale);
}
} else { // E-notation is needed
if (sci) { // Scientific notation
buf.append(coeff[offset]); // first character
if (coeffLen > 1) { // more to come
buf.append('.');
buf.append(coeff, offset + 1, coeffLen - 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 >= coeffLen) { // significand all in integer
buf.append(coeff, offset, coeffLen);
// may need some zeros, too
for (int i = sig - coeffLen; i > 0; i--) {
buf.append('0');
}
} else { // xx.xxE form
buf.append(coeff, offset, sig);
buf.append('.');
buf.append(coeff, offset + sig, coeffLen - 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();
}
/**
* Return 10 to the power n, as a {@code BigInteger}.
*
* @param n the power of ten to be returned (>=0)
* @return a {@code BigInteger} with the value (10n)
*/
private static BigInteger bigTenToThe(int n) {
if (n < 0)
return BigInteger.ZERO;
if (n < BIG_TEN_POWERS_TABLE_MAX) {
BigInteger[] pows = BIG_TEN_POWERS_TABLE;
if (n < pows.length)
return pows[n];
else
return expandBigIntegerTenPowers(n);
}
return BigInteger.TEN.pow(n);
}
/**
* Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n.
*
* @param n the power of ten to be returned (>=0)
* @return a {@code BigDecimal} with the value (10n) and
* in the meantime, the BIG_TEN_POWERS_TABLE array gets
* expanded to the size greater than n.
*/
private static BigInteger expandBigIntegerTenPowers(int n) {
synchronized(BigDecimal.class) {
BigInteger[] pows = BIG_TEN_POWERS_TABLE;
int curLen = pows.length;
// The following comparison and the above synchronized statement is
// to prevent multiple threads from expanding the same array.
if (curLen <= n) {
int newLen = curLen << 1;
while (newLen <= n) {
newLen <<= 1;
}
pows = Arrays.copyOf(pows, newLen);
for (int i = curLen; i < newLen; i++) {
pows[i] = pows[i - 1].multiply(BigInteger.TEN);
}
// Based on the following facts:
// 1. pows is a private local variable;
// 2. the following store is a volatile store.
// the newly created array elements can be safely published.
BIG_TEN_POWERS_TABLE = pows;
}
return pows[n];
}
}
private static final long[] LONG_TEN_POWERS_TABLE = {
1, // 0 / 10^0
10, // 1 / 10^1
100, // 2 / 10^2
1000, // 3 / 10^3
10000, // 4 / 10^4
100000, // 5 / 10^5
1000000, // 6 / 10^6
10000000, // 7 / 10^7
100000000, // 8 / 10^8
1000000000, // 9 / 10^9
10000000000L, // 10 / 10^10
100000000000L, // 11 / 10^11
1000000000000L, // 12 / 10^12
10000000000000L, // 13 / 10^13
100000000000000L, // 14 / 10^14
1000000000000000L, // 15 / 10^15
10000000000000000L, // 16 / 10^16
100000000000000000L, // 17 / 10^17
1000000000000000000L // 18 / 10^18
};
private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = {
BigInteger.ONE,
BigInteger.valueOf(10),
BigInteger.valueOf(100),
BigInteger.valueOf(1000),
BigInteger.valueOf(10000),
BigInteger.valueOf(100000),
BigInteger.valueOf(1000000),
BigInteger.valueOf(10000000),
BigInteger.valueOf(100000000),
BigInteger.valueOf(1000000000),
BigInteger.valueOf(10000000000L),
BigInteger.valueOf(100000000000L),
BigInteger.valueOf(1000000000000L),
BigInteger.valueOf(10000000000000L),
BigInteger.valueOf(100000000000000L),
BigInteger.valueOf(1000000000000000L),
BigInteger.valueOf(10000000000000000L),
BigInteger.valueOf(100000000000000000L),
BigInteger.valueOf(1000000000000000000L)
};
private static final int BIG_TEN_POWERS_TABLE_INITLEN =
BIG_TEN_POWERS_TABLE.length;
private static final int BIG_TEN_POWERS_TABLE_MAX =
16 * BIG_TEN_POWERS_TABLE_INITLEN;
private static final long THRESHOLDS_TABLE[] = {
Long.MAX_VALUE, // 0
Long.MAX_VALUE/10L, // 1
Long.MAX_VALUE/100L, // 2
Long.MAX_VALUE/1000L, // 3
Long.MAX_VALUE/10000L, // 4
Long.MAX_VALUE/100000L, // 5
Long.MAX_VALUE/1000000L, // 6
Long.MAX_VALUE/10000000L, // 7
Long.MAX_VALUE/100000000L, // 8
Long.MAX_VALUE/1000000000L, // 9
Long.MAX_VALUE/10000000000L, // 10
Long.MAX_VALUE/100000000000L, // 11
Long.MAX_VALUE/1000000000000L, // 12
Long.MAX_VALUE/10000000000000L, // 13
Long.MAX_VALUE/100000000000000L, // 14
Long.MAX_VALUE/1000000000000000L, // 15
Long.MAX_VALUE/10000000000000000L, // 16
Long.MAX_VALUE/100000000000000000L, // 17
Long.MAX_VALUE/1000000000000000000L // 18
};
/**
* Compute val * 10 ^ n; return this product if it is
* representable as a long, INFLATED otherwise.
*/
private static long longMultiplyPowerTen(long val, int n) {
if (val == 0 || n <= 0)
return val;
long[] tab = LONG_TEN_POWERS_TABLE;
long[] bounds = THRESHOLDS_TABLE;
if (n < tab.length && n < bounds.length) {
long tenpower = tab[n];
if (val == 1)
return tenpower;
if (Math.abs(val) <= bounds[n])
return val * tenpower;
}
return INFLATED;
}
/**
* Compute this * 10 ^ n.
* Needed mainly to allow special casing to trap zero value
*/
private BigInteger bigMultiplyPowerTen(int n) {
if (n <= 0)
return this.inflated();
if (intCompact != INFLATED)
return bigTenToThe(n).multiply(intCompact);
else
return intVal.multiply(bigTenToThe(n));
}
/**
* Returns appropriate BigInteger from intVal field if intVal is
* null, i.e. the compact representation is in use.
*/
private BigInteger inflated() {
if (intVal == null) {
return BigInteger.valueOf(intCompact);
}
return intVal;
}
/**
* Match the scales of two {@code BigDecimal}s to align their
* least significant digits.
*
* If the scales of val[0] and val[1] differ, rescale
* (non-destructively) the lower-scaled {@code 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 {@code BigDecimal}.
*
* @param val array of two elements referring to the two
* {@code BigDecimal}s to be aligned.
*/
private static void matchScale(BigDecimal[] val) {
if (val[0].scale < val[1].scale) {
val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY);
} else if (val[1].scale < val[0].scale) {
val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY);
}
}
private static class UnsafeHolder {
private static final sun.misc.Unsafe unsafe;
private static final long intCompactOffset;
private static final long intValOffset;
private static final long scaleOffset;
static {
try {
unsafe = sun.misc.Unsafe.getUnsafe();
intCompactOffset = unsafe.objectFieldOffset
(BigDecimal.class.getDeclaredField("intCompact"));
intValOffset = unsafe.objectFieldOffset
(BigDecimal.class.getDeclaredField("intVal"));
scaleOffset = unsafe.objectFieldOffset
(BigDecimal.class.getDeclaredField("scale"));
} catch (Exception ex) {
throw new ExceptionInInitializerError(ex);
}
}
static void setIntValAndScale(BigDecimal bd, BigInteger intVal, int scale) {
unsafe.putObjectVolatile(bd, intValOffset, intVal);
unsafe.putIntVolatile(bd, scaleOffset, scale);
unsafe.putLongVolatile(bd, intCompactOffset, compactValFor(intVal));
}
static void setIntValVolatile(BigDecimal bd, BigInteger val) {
unsafe.putObjectVolatile(bd, intValOffset, val);
}
}
/**
* Reconstitute the {@code BigDecimal} instance from a stream (that is,
* deserialize it).
*
* @param s the stream being read.
* @throws IOException if an I/O error occurs
* @throws ClassNotFoundException if a serialized class cannot be loaded
*/
@java.io.Serial
private void readObject(java.io.ObjectInputStream s)
throws IOException, ClassNotFoundException {
// prepare to read the fields
ObjectInputStream.GetField fields = s.readFields();
BigInteger serialIntVal = (BigInteger) fields.get("intVal", null);
// Validate field data
if (serialIntVal == null) {
throw new StreamCorruptedException("Null or missing intVal in BigDecimal stream");
}
// Validate provenance of serialIntVal object
serialIntVal = toStrictBigInteger(serialIntVal);
// Any integer value is valid for scale
int serialScale = fields.get("scale", 0);
UnsafeHolder.setIntValAndScale(this, serialIntVal, serialScale);
}
/**
* Serialization without data not supported for this class.
*/
@java.io.Serial
private void readObjectNoData()
throws ObjectStreamException {
throw new InvalidObjectException("Deserialized BigDecimal objects need data");
}
/**
* Serialize this {@code BigDecimal} to the stream in question
*
* @param s the stream to serialize to.
* @throws IOException if an I/O error occurs
*/
@java.io.Serial
private void writeObject(java.io.ObjectOutputStream s)
throws IOException {
// Must inflate to maintain compatible serial form.
if (this.intVal == null)
UnsafeHolder.setIntValVolatile(this, BigInteger.valueOf(this.intCompact));
// Could reset intVal back to null if it has to be set.
s.defaultWriteObject();
}
/**
* Returns the length of the absolute value of a {@code long}, in decimal
* digits.
*
* @param x the {@code long}
* @return the length of the unscaled value, in deciaml digits.
*/
static int longDigitLength(long x) {
/*
* As described in "Bit Twiddling Hacks" by Sean Anderson,
* (http://graphics.stanford.edu/~seander/bithacks.html)
* integer log 10 of x is within 1 of (1233/4096)* (1 +
* integer log 2 of x). The fraction 1233/4096 approximates
* log10(2). So we first do a version of log2 (a variant of
* Long class with pre-checks and opposite directionality) and
* then scale and check against powers table. This is a little
* simpler in present context than the version in Hacker's
* Delight sec 11-4. Adding one to bit length allows comparing
* downward from the LONG_TEN_POWERS_TABLE that we need
* anyway.
*/
assert x != BigDecimal.INFLATED;
if (x < 0)
x = -x;
if (x < 10) // must screen for 0, might as well 10
return 1;
int r = ((64 - Long.numberOfLeadingZeros(x) + 1) * 1233) >>> 12;
long[] tab = LONG_TEN_POWERS_TABLE;
// if r >= length, must have max possible digits for long
return (r >= tab.length || x < tab[r]) ? r : r + 1;
}
/**
* Returns the length of the absolute value of a BigInteger, in
* decimal digits.
*
* @param b the BigInteger
* @return the length of the unscaled value, in decimal digits
*/
private static int bigDigitLength(BigInteger b) {
/*
* Same idea as the long version, but we need a better
* approximation of log10(2). Using 646456993/2^31
* is accurate up to max possible reported bitLength.
*/
if (b.signum == 0)
return 1;
int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31);
return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1;
}
/**
* Check a scale for Underflow or Overflow. If this BigDecimal is
* nonzero, throw an exception if the scale is outof range. If this
* is zero, saturate the scale to the extreme value of the right
* sign if the scale is out of range.
*
* @param val The new scale.
* @throws ArithmeticException (overflow or underflow) if the new
* scale is out of range.
* @return validated scale as an int.
*/
private int checkScale(long val) {
int asInt = (int)val;
if (asInt != val) {
asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
BigInteger b;
if (intCompact != 0 &&
((b = intVal) == null || b.signum() != 0))
throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
}
return asInt;
}
/**
* Returns the compact value for given {@code BigInteger}, or
* INFLATED if too big. Relies on internal representation of
* {@code BigInteger}.
*/
private static long compactValFor(BigInteger b) {
int[] m = b.mag;
int len = m.length;
if (len == 0)
return 0;
int d = m[0];
if (len > 2 || (len == 2 && d < 0))
return INFLATED;
long u = (len == 2)?
(((long) m[1] & LONG_MASK) + (((long)d) << 32)) :
(((long)d) & LONG_MASK);
return (b.signum < 0)? -u : u;
}
private static int longCompareMagnitude(long x, long y) {
if (x < 0)
x = -x;
if (y < 0)
y = -y;
return (x < y) ? -1 : ((x == y) ? 0 : 1);
}
private static int saturateLong(long s) {
int i = (int)s;
return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE);
}
/*
* Internal printing routine
*/
private static void print(String name, BigDecimal bd) {
System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n",
name,
bd.intCompact,
bd.intVal,
bd.scale,
bd.precision);
}
/**
* Check internal invariants of this BigDecimal. These invariants
* include:
*
* '\u002B') or
* {@code '-'} ('\u002D'), followed by a sequence of
* zero or more decimal digits ("the integer"), optionally
* followed by a fraction, optionally followed by an exponent.
*
* '\u0065') or {@code '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.
*
*
*
*
*
*
*
* The value of the returned {@code BigDecimal} is equal to
* significand × 10 exponent.
* For each string on the left, the resulting representation
* [{@code BigInteger}, {@code 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]
*
*
* @apiNote For values other than {@code float} and
* {@code double} NaN and ±Infinity, this constructor is
* compatible with the values returned by {@link Float#toString}
* and {@link Double#toString}. This is generally the preferred
* way to convert a {@code float} or {@code double} into a
* BigDecimal, as it doesn't suffer from the unpredictability of
* the {@link #BigDecimal(double)} constructor.
*
* @param val String representation of {@code BigDecimal}.
*
* @throws NumberFormatException if {@code val} is not a valid
* representation of a {@code BigDecimal}.
*/
public BigDecimal(String val) {
this(val.toCharArray(), 0, val.length());
}
/**
* Translates the string representation of a {@code BigDecimal}
* into a {@code BigDecimal}, accepting the same strings as the
* {@link #BigDecimal(String)} constructor, with rounding
* according to the context settings.
*
* @param val string representation of a {@code BigDecimal}.
* @param mc the context to use.
* @throws NumberFormatException if {@code val} is not a valid
* representation of a BigDecimal.
* @since 1.5
*/
public BigDecimal(String val, MathContext mc) {
this(val.toCharArray(), 0, val.length(), mc);
}
/**
* Translates a {@code double} into a {@code BigDecimal} which
* is the exact decimal representation of the {@code double}'s
* binary floating-point value. The scale of the returned
* {@code BigDecimal} is the smallest value such that
* (10scale × val) is an integer.
*
*
*
* @param val {@code double} value to be converted to
* {@code BigDecimal}.
* @throws NumberFormatException if {@code val} is infinite or NaN.
*/
public BigDecimal(double val) {
this(val,MathContext.UNLIMITED);
}
/**
* Translates a {@code double} into a {@code BigDecimal}, with
* rounding according to the context settings. The scale of the
* {@code BigDecimal} is the smallest value such that
* (10scale × val) is an integer.
*
* (unscaledVal × 10-scale).
*
* @param unscaledVal unscaled value of the {@code BigDecimal}.
* @param scale scale of the {@code BigDecimal}.
*/
public BigDecimal(BigInteger unscaledVal, int scale) {
// Negative scales are now allowed
this.intVal = toStrictBigInteger(unscaledVal);
this.intCompact = compactValFor(this.intVal);
this.scale = scale;
}
/**
* Translates a {@code BigInteger} unscaled value and an
* {@code int} scale into a {@code BigDecimal}, with rounding
* according to the context settings. The value of the
* {@code BigDecimal} is (unscaledVal ×
* 10-scale), rounded according to the
* {@code precision} and rounding mode settings.
*
* @param unscaledVal unscaled value of the {@code BigDecimal}.
* @param scale scale of the {@code BigDecimal}.
* @param mc the context to use.
* @since 1.5
*/
public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {
unscaledVal = toStrictBigInteger(unscaledVal);
long compactVal = compactValFor(unscaledVal);
int mcp = mc.precision;
int prec = 0;
if (mcp > 0) { // do rounding
int mode = mc.roundingMode.oldMode;
if (compactVal == INFLATED) {
prec = bigDigitLength(unscaledVal);
int drop = prec - mcp;
while (drop > 0) {
scale = checkScaleNonZero((long) scale - drop);
unscaledVal = divideAndRoundByTenPow(unscaledVal, drop, mode);
compactVal = compactValFor(unscaledVal);
if (compactVal != INFLATED) {
break;
}
prec = bigDigitLength(unscaledVal);
drop = prec - mcp;
}
}
if (compactVal != INFLATED) {
prec = longDigitLength(compactVal);
int drop = prec - mcp; // drop can't be more than 18
while (drop > 0) {
scale = checkScaleNonZero((long) scale - drop);
compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mode);
prec = longDigitLength(compactVal);
drop = prec - mcp;
}
unscaledVal = null;
}
}
this.intVal = unscaledVal;
this.intCompact = compactVal;
this.scale = scale;
this.precision = prec;
}
/**
* Translates an {@code int} into a {@code BigDecimal}. The
* scale of the {@code BigDecimal} is zero.
*
* @param val {@code int} value to be converted to
* {@code BigDecimal}.
* @since 1.5
*/
public BigDecimal(int val) {
this.intCompact = val;
this.scale = 0;
this.intVal = null;
}
/**
* Translates an {@code int} into a {@code BigDecimal}, with
* rounding according to the context settings. The scale of the
* {@code BigDecimal}, before any rounding, is zero.
*
* @param val {@code int} value to be converted to {@code BigDecimal}.
* @param mc the context to use.
* @since 1.5
*/
public BigDecimal(int val, MathContext mc) {
int mcp = mc.precision;
long compactVal = val;
int scl = 0;
int prec = 0;
if (mcp > 0) { // do rounding
prec = longDigitLength(compactVal);
int drop = prec - mcp; // drop can't be more than 18
while (drop > 0) {
scl = checkScaleNonZero((long) scl - drop);
compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
prec = longDigitLength(compactVal);
drop = prec - mcp;
}
}
this.intVal = null;
this.intCompact = compactVal;
this.scale = scl;
this.precision = prec;
}
/**
* Translates a {@code long} into a {@code BigDecimal}. The
* scale of the {@code BigDecimal} is zero.
*
* @param val {@code long} value to be converted to {@code BigDecimal}.
* @since 1.5
*/
public BigDecimal(long val) {
this.intCompact = val;
this.intVal = (val == INFLATED) ? INFLATED_BIGINT : null;
this.scale = 0;
}
/**
* Translates a {@code long} into a {@code BigDecimal}, with
* rounding according to the context settings. The scale of the
* {@code BigDecimal}, before any rounding, is zero.
*
* @param val {@code long} value to be converted to {@code BigDecimal}.
* @param mc the context to use.
* @since 1.5
*/
public BigDecimal(long val, MathContext mc) {
int mcp = mc.precision;
int mode = mc.roundingMode.oldMode;
int prec = 0;
int scl = 0;
BigInteger rb = (val == INFLATED) ? INFLATED_BIGINT : null;
if (mcp > 0) { // do rounding
if (val == INFLATED) {
prec = 19;
int drop = prec - mcp;
while (drop > 0) {
scl = checkScaleNonZero((long) scl - drop);
rb = divideAndRoundByTenPow(rb, drop, mode);
val = compactValFor(rb);
if (val != INFLATED) {
break;
}
prec = bigDigitLength(rb);
drop = prec - mcp;
}
}
if (val != INFLATED) {
prec = longDigitLength(val);
int drop = prec - mcp;
while (drop > 0) {
scl = checkScaleNonZero((long) scl - drop);
val = divideAndRound(val, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
prec = longDigitLength(val);
drop = prec - mcp;
}
rb = null;
}
}
this.intVal = rb;
this.intCompact = val;
this.scale = scl;
this.precision = prec;
}
// Static Factory Methods
/**
* Translates a {@code long} unscaled value and an
* {@code int} scale into a {@code BigDecimal}.
*
* @apiNote This static factory method is provided in preference
* to a ({@code long}, {@code int}) constructor because it allows
* for reuse of frequently used {@code BigDecimal} values.
*
* @param unscaledVal unscaled value of the {@code BigDecimal}.
* @param scale scale of the {@code BigDecimal}.
* @return a {@code BigDecimal} whose value is
* (unscaledVal × 10-scale).
*/
public static BigDecimal valueOf(long unscaledVal, int scale) {
if (scale == 0)
return valueOf(unscaledVal);
else if (unscaledVal == 0) {
return zeroValueOf(scale);
}
return new BigDecimal(unscaledVal == INFLATED ?
INFLATED_BIGINT : null,
unscaledVal, scale, 0);
}
/**
* Translates a {@code long} value into a {@code BigDecimal}
* with a scale of zero.
*
* @apiNote This static factory method is provided in preference
* to a ({@code long}) constructor because it allows for reuse of
* frequently used {@code BigDecimal} values.
*
* @param val value of the {@code BigDecimal}.
* @return a {@code BigDecimal} whose value is {@code val}.
*/
public static BigDecimal valueOf(long val) {
if (val >= 0 && val < ZERO_THROUGH_TEN.length)
return ZERO_THROUGH_TEN[(int)val];
else if (val != INFLATED)
return new BigDecimal(null, val, 0, 0);
return new BigDecimal(INFLATED_BIGINT, val, 0, 0);
}
static BigDecimal valueOf(long unscaledVal, int scale, int prec) {
if (scale == 0 && unscaledVal >= 0 && unscaledVal < ZERO_THROUGH_TEN.length) {
return ZERO_THROUGH_TEN[(int) unscaledVal];
} else if (unscaledVal == 0) {
return zeroValueOf(scale);
}
return new BigDecimal(unscaledVal == INFLATED ? INFLATED_BIGINT : null,
unscaledVal, scale, prec);
}
static BigDecimal valueOf(BigInteger intVal, int scale, int prec) {
long val = compactValFor(intVal);
if (val == 0) {
return zeroValueOf(scale);
} else if (scale == 0 && val >= 0 && val < ZERO_THROUGH_TEN.length) {
return ZERO_THROUGH_TEN[(int) val];
}
return new BigDecimal(intVal, val, scale, prec);
}
static BigDecimal zeroValueOf(int scale) {
if (scale >= 0 && scale < ZERO_SCALED_BY.length)
return ZERO_SCALED_BY[scale];
else
return new BigDecimal(BigInteger.ZERO, 0, scale, 1);
}
/**
* Translates a {@code double} into a {@code BigDecimal}, using
* the {@code double}'s canonical string representation provided
* by the {@link Double#toString(double)} method.
*
* @apiNote This is generally the preferred way to convert a
* {@code double} (or {@code float}) into a {@code BigDecimal}, as
* the value returned is equal to that resulting from constructing
* a {@code BigDecimal} from the result of using {@link
* Double#toString(double)}.
*
* @param val {@code double} to convert to a {@code BigDecimal}.
* @return a {@code BigDecimal} whose value is equal to or approximately
* equal to the value of {@code val}.
* @throws NumberFormatException if {@code val} is infinite or NaN.
* @since 1.5
*/
public static BigDecimal valueOf(double val) {
// 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));
}
// Arithmetic Operations
/**
* Returns a {@code BigDecimal} whose value is {@code (this +
* augend)}, and whose scale is {@code max(this.scale(),
* augend.scale())}.
*
* @param augend value to be added to this {@code BigDecimal}.
* @return {@code this + augend}
*/
public BigDecimal add(BigDecimal augend) {
if (this.intCompact != INFLATED) {
if ((augend.intCompact != INFLATED)) {
return add(this.intCompact, this.scale, augend.intCompact, augend.scale);
} else {
return add(this.intCompact, this.scale, augend.intVal, augend.scale);
}
} else {
if ((augend.intCompact != INFLATED)) {
return add(augend.intCompact, augend.scale, this.intVal, this.scale);
} else {
return add(this.intVal, this.scale, augend.intVal, augend.scale);
}
}
}
/**
* Returns a {@code BigDecimal} whose value is {@code (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.
*
* @param augend value to be added to this {@code BigDecimal}.
* @param mc the context to use.
* @return {@code this + augend}, rounded as necessary.
* @since 1.5
*/
public BigDecimal add(BigDecimal augend, MathContext mc) {
if (mc.precision == 0)
return add(augend);
BigDecimal lhs = this;
// 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;
if (lhsIsZero && augendIsZero)
return zeroValueOf(preferredScale);
result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc);
if (result.scale() == preferredScale)
return result;
else if (result.scale() > preferredScale) {
return stripZerosToMatchScale(result.intVal, result.intCompact, result.scale, 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);
}
}
}
long padding = (long) lhs.scale - augend.scale;
if (padding != 0) { // scales differ; alignment needed
BigDecimal arg[] = preAlign(lhs, augend, padding, mc);
matchScale(arg);
lhs = arg[0];
augend = arg[1];
}
return doRound(lhs.inflated().add(augend.inflated()), lhs.scale, mc);
}
/**
* Returns an array of length two, the sum of whose entries is
* equal to the rounded sum of the {@code BigDecimal} arguments.
*
* (this ×
* multiplicand), and whose scale is {@code (this.scale() +
* multiplicand.scale())}.
*
* @param multiplicand value to be multiplied by this {@code BigDecimal}.
* @return {@code this * multiplicand}
*/
public BigDecimal multiply(BigDecimal multiplicand) {
int productScale = checkScale((long) scale + multiplicand.scale);
if (this.intCompact != INFLATED) {
if ((multiplicand.intCompact != INFLATED)) {
return multiply(this.intCompact, multiplicand.intCompact, productScale);
} else {
return multiply(this.intCompact, multiplicand.intVal, productScale);
}
} else {
if ((multiplicand.intCompact != INFLATED)) {
return multiply(multiplicand.intCompact, this.intVal, productScale);
} else {
return multiply(this.intVal, multiplicand.intVal, productScale);
}
}
}
/**
* Returns a {@code BigDecimal} whose value is (this ×
* multiplicand), with rounding according to the context settings.
*
* @param multiplicand value to be multiplied by this {@code BigDecimal}.
* @param mc the context to use.
* @return {@code this * multiplicand}, rounded as necessary.
* @since 1.5
*/
public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) {
if (mc.precision == 0)
return multiply(multiplicand);
int productScale = checkScale((long) scale + multiplicand.scale);
if (this.intCompact != INFLATED) {
if ((multiplicand.intCompact != INFLATED)) {
return multiplyAndRound(this.intCompact, multiplicand.intCompact, productScale, mc);
} else {
return multiplyAndRound(this.intCompact, multiplicand.intVal, productScale, mc);
}
} else {
if ((multiplicand.intCompact != INFLATED)) {
return multiplyAndRound(multiplicand.intCompact, this.intVal, productScale, mc);
} else {
return multiplyAndRound(this.intVal, multiplicand.intVal, productScale, mc);
}
}
}
/**
* Returns a {@code BigDecimal} whose value is {@code (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.
*
* @deprecated The method {@link #divide(BigDecimal, int, RoundingMode)}
* should be used in preference to this legacy method.
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @param scale scale of the {@code BigDecimal} quotient to be returned.
* @param roundingMode rounding mode to apply.
* @return {@code this / divisor}
* @throws ArithmeticException if {@code divisor} is zero,
* {@code roundingMode==ROUND_UNNECESSARY} and
* the specified scale is insufficient to represent the result
* of the division exactly.
* @throws IllegalArgumentException if {@code roundingMode} does not
* represent a valid rounding mode.
* @see #ROUND_UP
* @see #ROUND_DOWN
* @see #ROUND_CEILING
* @see #ROUND_FLOOR
* @see #ROUND_HALF_UP
* @see #ROUND_HALF_DOWN
* @see #ROUND_HALF_EVEN
* @see #ROUND_UNNECESSARY
*/
@Deprecated(since="9")
public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) {
if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
throw new IllegalArgumentException("Invalid rounding mode");
if (this.intCompact != INFLATED) {
if ((divisor.intCompact != INFLATED)) {
return divide(this.intCompact, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
} else {
return divide(this.intCompact, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
}
} else {
if ((divisor.intCompact != INFLATED)) {
return divide(this.intVal, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode);
} else {
return divide(this.intVal, this.scale, divisor.intVal, divisor.scale, scale, roundingMode);
}
}
}
/**
* Returns a {@code BigDecimal} whose value is {@code (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.
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @param scale scale of the {@code BigDecimal} quotient to be returned.
* @param roundingMode rounding mode to apply.
* @return {@code this / divisor}
* @throws ArithmeticException if {@code divisor} is zero,
* {@code roundingMode==RoundingMode.UNNECESSARY} and
* the specified scale is insufficient to represent the result
* of the division exactly.
* @since 1.5
*/
public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) {
return divide(divisor, scale, roundingMode.oldMode);
}
/**
* Returns a {@code BigDecimal} whose value is {@code (this /
* divisor)}, and whose scale is {@code this.scale()}. If
* rounding must be performed to generate a result with the given
* scale, the specified rounding mode is applied.
*
* @deprecated The method {@link #divide(BigDecimal, RoundingMode)}
* should be used in preference to this legacy method.
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @param roundingMode rounding mode to apply.
* @return {@code this / divisor}
* @throws ArithmeticException if {@code divisor==0}, or
* {@code roundingMode==ROUND_UNNECESSARY} and
* {@code this.scale()} is insufficient to represent the result
* of the division exactly.
* @throws IllegalArgumentException if {@code roundingMode} does not
* represent a valid rounding mode.
* @see #ROUND_UP
* @see #ROUND_DOWN
* @see #ROUND_CEILING
* @see #ROUND_FLOOR
* @see #ROUND_HALF_UP
* @see #ROUND_HALF_DOWN
* @see #ROUND_HALF_EVEN
* @see #ROUND_UNNECESSARY
*/
@Deprecated(since="9")
public BigDecimal divide(BigDecimal divisor, int roundingMode) {
return this.divide(divisor, scale, roundingMode);
}
/**
* Returns a {@code BigDecimal} whose value is {@code (this /
* divisor)}, and whose scale is {@code this.scale()}. If
* rounding must be performed to generate a result with the given
* scale, the specified rounding mode is applied.
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @param roundingMode rounding mode to apply.
* @return {@code this / divisor}
* @throws ArithmeticException if {@code divisor==0}, or
* {@code roundingMode==RoundingMode.UNNECESSARY} and
* {@code this.scale()} is insufficient to represent the result
* of the division exactly.
* @since 1.5
*/
public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) {
return this.divide(divisor, scale, roundingMode.oldMode);
}
/**
* Returns a {@code BigDecimal} whose value is {@code (this /
* divisor)}, and whose preferred scale is {@code (this.scale() -
* divisor.scale())}; if the exact quotient cannot be
* represented (because it has a non-terminating decimal
* expansion) an {@code ArithmeticException} is thrown.
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @throws ArithmeticException if the exact quotient does not have a
* terminating decimal expansion, including dividing by zero
* @return {@code this / divisor}
* @since 1.5
* @author Joseph D. Darcy
*/
public BigDecimal divide(BigDecimal divisor) {
/*
* 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 = saturateLong((long) this.scale - divisor.scale);
if (this.signum() == 0) // 0/y
return zeroValueOf(preferredScale);
else {
/*
* 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, ROUND_UNNECESSARY);
return quotient;
}
}
/**
* Returns a {@code BigDecimal} whose value is {@code (this /
* divisor)}, with rounding according to the context settings.
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @param mc the context to use.
* @return {@code this / divisor}, rounded as necessary.
* @throws ArithmeticException if the result is inexact but the
* rounding mode is {@code UNNECESSARY} or
* {@code mc.precision == 0} and the quotient has a
* non-terminating decimal expansion,including dividing by zero
* @since 1.5
*/
public BigDecimal divide(BigDecimal divisor, MathContext mc) {
int mcp = mc.precision;
if (mcp == 0)
return divide(divisor);
BigDecimal dividend = this;
long preferredScale = (long)dividend.scale - divisor.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 (divisor.signum() == 0) { // x/0
if (dividend.signum() == 0) // 0/0
throw new ArithmeticException("Division undefined"); // NaN
throw new ArithmeticException("Division by zero");
}
if (dividend.signum() == 0) // 0/y
return zeroValueOf(saturateLong(preferredScale));
int xscale = dividend.precision();
int yscale = divisor.precision();
if(dividend.intCompact!=INFLATED) {
if(divisor.intCompact!=INFLATED) {
return divide(dividend.intCompact, xscale, divisor.intCompact, yscale, preferredScale, mc);
} else {
return divide(dividend.intCompact, xscale, divisor.intVal, yscale, preferredScale, mc);
}
} else {
if(divisor.intCompact!=INFLATED) {
return divide(dividend.intVal, xscale, divisor.intCompact, yscale, preferredScale, mc);
} else {
return divide(dividend.intVal, xscale, divisor.intVal, yscale, preferredScale, mc);
}
}
}
/**
* Returns a {@code BigDecimal} whose value is the integer part
* of the quotient {@code (this / divisor)} rounded down. The
* preferred scale of the result is {@code (this.scale() -
* divisor.scale())}.
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @return The integer part of {@code this / divisor}.
* @throws ArithmeticException if {@code divisor==0}
* @since 1.5
*/
public BigDecimal divideToIntegralValue(BigDecimal divisor) {
// Calculate preferred scale
int preferredScale = saturateLong((long) this.scale - divisor.scale);
if (this.compareMagnitude(divisor) < 0) {
// much faster when this << divisor
return zeroValueOf(preferredScale);
}
if (this.signum() == 0 && divisor.signum() != 0)
return this.setScale(preferredScale, ROUND_UNNECESSARY);
// 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);
quotient = stripZerosToMatchScale(quotient.intVal, quotient.intCompact, quotient.scale, preferredScale);
}
if (quotient.scale < preferredScale) {
// pad with zeros if necessary
quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY);
}
return quotient;
}
/**
* Returns a {@code BigDecimal} whose value is the integer part
* of {@code (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
* {@code (this.scale() - divisor.scale())}. An
* {@code ArithmeticException} is thrown if the integer part of
* the exact quotient needs more than {@code mc.precision}
* digits.
*
* @param divisor value by which this {@code BigDecimal} is to be divided.
* @param mc the context to use.
* @return The integer part of {@code this / divisor}.
* @throws ArithmeticException if {@code divisor==0}
* @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result
* requires a precision of more than {@code mc.precision} digits.
* @since 1.5
* @author Joseph D. Darcy
*/
public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) {
if (mc.precision == 0 || // exact result
(this.compareMagnitude(divisor) < 0)) // zero result
return divideToIntegralValue(divisor);
// Calculate preferred scale
int preferredScale = saturateLong((long)this.scale - divisor.scale);
/*
* 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));
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 the quotient is the full integer value,
// |dividend-product| < |divisor|.
if (this.subtract(product).compareMagnitude(divisor) >= 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 stripZerosToMatchScale(result.intVal,result.intCompact,result.scale,preferredScale);
}
}
/**
* Returns a {@code BigDecimal} whose value is {@code (this % divisor)}.
*
*
*
*
* @param mc the context to use.
* @return the square root of {@code this}.
* @throws ArithmeticException if {@code this} is less than zero.
* @throws ArithmeticException if an exact result is requested
* ({@code mc.getPrecision()==0}) and there is no finite decimal
* expansion of the exact result
* @throws ArithmeticException if
* {@code (mc.getRoundingMode()==RoundingMode.UNNECESSARY}) and
* the exact result cannot fit in {@code mc.getPrecision()}
* digits.
* @see BigInteger#sqrt()
* @since 9
*/
public BigDecimal sqrt(MathContext mc) {
int signum = signum();
if (signum == 1) {
/*
* The following code draws on the algorithm presented in
* "Properly Rounded Variable Precision Square Root," Hull and
* Abrham, ACM Transactions on Mathematical Software, Vol 11,
* No. 3, September 1985, Pages 229-237.
*
* The BigDecimal computational model differs from the one
* presented in the paper in several ways: first BigDecimal
* numbers aren't necessarily normalized, second many more
* rounding modes are supported, including UNNECESSARY, and
* exact results can be requested.
*
* The main steps of the algorithm below are as follows,
* first argument reduce the value to the numerical range
* [1, 10) using the following relations:
*
* x = y * 10 ^ exp
* sqrt(x) = sqrt(y) * 10^(exp / 2) if exp is even
* sqrt(x) = sqrt(y/10) * 10 ^((exp+1)/2) is exp is odd
*
* Then use Newton's iteration on the reduced value to compute
* the numerical digits of the desired result.
*
* Finally, scale back to the desired exponent range and
* perform any adjustment to get the preferred scale in the
* representation.
*/
// The code below favors relative simplicity over checking
// for special cases that could run faster.
int preferredScale = this.scale()/2;
BigDecimal zeroWithFinalPreferredScale = valueOf(0L, preferredScale);
// First phase of numerical normalization, strip trailing
// zeros and check for even powers of 10.
BigDecimal stripped = this.stripTrailingZeros();
int strippedScale = stripped.scale();
// Numerically sqrt(10^2N) = 10^N
if (stripped.isPowerOfTen() &&
strippedScale % 2 == 0) {
BigDecimal result = valueOf(1L, strippedScale/2);
if (result.scale() != preferredScale) {
// Adjust to requested precision and preferred
// scale as appropriate.
result = result.add(zeroWithFinalPreferredScale, mc);
}
return result;
}
// After stripTrailingZeros, the representation is normalized as
//
// unscaledValue * 10^(-scale)
//
// where unscaledValue is an integer with the mimimum
// precision for the cohort of the numerical value. To
// allow binary floating-point hardware to be used to get
// approximately a 15 digit approximation to the square
// root, it is helpful to instead normalize this so that
// the significand portion is to right of the decimal
// point by roughly (scale() - precision() + 1).
// Now the precision / scale adjustment
int scaleAdjust = 0;
int scale = stripped.scale() - stripped.precision() + 1;
if (scale % 2 == 0) {
scaleAdjust = scale;
} else {
scaleAdjust = scale - 1;
}
BigDecimal working = stripped.scaleByPowerOfTen(scaleAdjust);
assert // Verify 0.1 <= working < 10
ONE_TENTH.compareTo(working) <= 0 && working.compareTo(TEN) < 0;
// Use good ole' Math.sqrt to get the initial guess for
// the Newton iteration, good to at least 15 decimal
// digits. This approach does incur the cost of a
//
// BigDecimal -> double -> BigDecimal
//
// conversion cycle, but it avoids the need for several
// Newton iterations in BigDecimal arithmetic to get the
// working answer to 15 digits of precision. If many fewer
// than 15 digits were needed, it might be faster to do
// the loop entirely in BigDecimal arithmetic.
//
// (A double value might have as many as 17 decimal
// digits of precision; it depends on the relative density
// of binary and decimal numbers at different regions of
// the number line.)
//
// (It would be possible to check for certain special
// cases to avoid doing any Newton iterations. For
// example, if the BigDecimal -> double conversion was
// known to be exact and the rounding mode had a
// low-enough precision, the post-Newton rounding logic
// could be applied directly.)
BigDecimal guess = new BigDecimal(Math.sqrt(working.doubleValue()));
int guessPrecision = 15;
int originalPrecision = mc.getPrecision();
int targetPrecision;
// If an exact value is requested, it must only need about
// half of the input digits to represent since multiplying
// an N digit number by itself yield a 2N-1 digit or 2N
// digit result.
if (originalPrecision == 0) {
targetPrecision = stripped.precision()/2 + 1;
} else {
/*
* To avoid the need for post-Newton fix-up logic, in
* the case of half-way rounding modes, double the
* target precision so that the "2p + 2" property can
* be relied on to accomplish the final rounding.
*/
switch (mc.getRoundingMode()) {
case HALF_UP:
case HALF_DOWN:
case HALF_EVEN:
targetPrecision = 2 * originalPrecision;
if (targetPrecision < 0) // Overflow
targetPrecision = Integer.MAX_VALUE - 2;
break;
default:
targetPrecision = originalPrecision;
break;
}
}
// When setting the precision to use inside the Newton
// iteration loop, take care to avoid the case where the
// precision of the input exceeds the requested precision
// and rounding the input value too soon.
BigDecimal approx = guess;
int workingPrecision = working.precision();
do {
int tmpPrecision = Math.max(Math.max(guessPrecision, targetPrecision + 2),
workingPrecision);
MathContext mcTmp = new MathContext(tmpPrecision, RoundingMode.HALF_EVEN);
// approx = 0.5 * (approx + fraction / approx)
approx = ONE_HALF.multiply(approx.add(working.divide(approx, mcTmp), mcTmp));
guessPrecision *= 2;
} while (guessPrecision < targetPrecision + 2);
BigDecimal result;
RoundingMode targetRm = mc.getRoundingMode();
if (targetRm == RoundingMode.UNNECESSARY || originalPrecision == 0) {
RoundingMode tmpRm =
(targetRm == RoundingMode.UNNECESSARY) ? RoundingMode.DOWN : targetRm;
MathContext mcTmp = new MathContext(targetPrecision, tmpRm);
result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mcTmp);
// If result*result != this numerically, the square
// root isn't exact
if (this.subtract(result.square()).compareTo(ZERO) != 0) {
throw new ArithmeticException("Computed square root not exact.");
}
} else {
result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mc);
switch (targetRm) {
case DOWN:
case FLOOR:
// Check if too big
if (result.square().compareTo(this) > 0) {
BigDecimal ulp = result.ulp();
// Adjust increment down in case of 1.0 = 10^0
// since the next smaller number is only 1/10
// as far way as the next larger at exponent
// boundaries. Test approx and *not* result to
// avoid having to detect an arbitrary power
// of ten.
if (approx.compareTo(ONE) == 0) {
ulp = ulp.multiply(ONE_TENTH);
}
result = result.subtract(ulp);
}
break;
case UP:
case CEILING:
// Check if too small
if (result.square().compareTo(this) < 0) {
result = result.add(result.ulp());
}
break;
default:
// No additional work, rely on "2p + 2" property
// for correct rounding. Alternatively, could
// instead run the Newton iteration to around p
// digits and then do tests and fix-ups on the
// rounded value. One possible set of tests and
// fix-ups is given in the Hull and Abrham paper;
// however, additional half-way cases can occur
// for BigDecimal given the more varied
// combinations of input and output precisions
// supported.
break;
}
}
// Test numerical properties at full precision before any
// scale adjustments.
assert squareRootResultAssertions(result, mc);
if (result.scale() != preferredScale) {
// The preferred scale of an add is
// max(addend.scale(), augend.scale()). Therefore, if
// the scale of the result is first minimized using
// stripTrailingZeros(), adding a zero of the
// preferred scale rounding to the correct precision
// will perform the proper scale vs precision
// tradeoffs.
result = result.stripTrailingZeros().
add(zeroWithFinalPreferredScale,
new MathContext(originalPrecision, RoundingMode.UNNECESSARY));
}
return result;
} else {
BigDecimal result = null;
switch (signum) {
case -1:
throw new ArithmeticException("Attempted square root " +
"of negative BigDecimal");
case 0:
result = valueOf(0L, scale()/2);
assert squareRootResultAssertions(result, mc);
return result;
default:
throw new AssertionError("Bad value from signum");
}
}
}
private BigDecimal square() {
return this.multiply(this);
}
private boolean isPowerOfTen() {
return BigInteger.ONE.equals(this.unscaledValue());
}
/**
* For nonzero values, check numerical correctness properties of
* the computed result for the chosen rounding mode.
*
* For the directed rounding modes:
*
*
*
*
*/
private boolean squareRootResultAssertions(BigDecimal result, MathContext mc) {
if (result.signum() == 0) {
return squareRootZeroResultAssertions(result, mc);
} else {
RoundingMode rm = mc.getRoundingMode();
BigDecimal ulp = result.ulp();
BigDecimal neighborUp = result.add(ulp);
// Make neighbor down accurate even for powers of ten
if (result.isPowerOfTen()) {
ulp = ulp.divide(TEN);
}
BigDecimal neighborDown = result.subtract(ulp);
// Both the starting value and result should be nonzero and positive.
assert (result.signum() == 1 &&
this.signum() == 1) :
"Bad signum of this and/or its sqrt.";
switch (rm) {
case DOWN:
case FLOOR:
assert
result.square().compareTo(this) <= 0 &&
neighborUp.square().compareTo(this) > 0:
"Square of result out for bounds rounding " + rm;
return true;
case UP:
case CEILING:
assert
result.square().compareTo(this) >= 0 &&
neighborDown.square().compareTo(this) < 0:
"Square of result out for bounds rounding " + rm;
return true;
case HALF_DOWN:
case HALF_EVEN:
case HALF_UP:
BigDecimal err = result.square().subtract(this).abs();
BigDecimal errUp = neighborUp.square().subtract(this);
BigDecimal errDown = this.subtract(neighborDown.square());
// All error values should be positive so don't need to
// compare absolute values.
int err_comp_errUp = err.compareTo(errUp);
int err_comp_errDown = err.compareTo(errDown);
assert
errUp.signum() == 1 &&
errDown.signum() == 1 :
"Errors of neighbors squared don't have correct signs";
// For breaking a half-way tie, the return value may
// have a larger error than one of the neighbors. For
// example, the square root of 2.25 to a precision of
// 1 digit is either 1 or 2 depending on how the exact
// value of 1.5 is rounded. If 2 is returned, it will
// have a larger rounding error than its neighbor 1.
assert
err_comp_errUp <= 0 ||
err_comp_errDown <= 0 :
"Computed square root has larger error than neighbors for " + rm;
assert
((err_comp_errUp == 0 ) ? err_comp_errDown < 0 : true) &&
((err_comp_errDown == 0 ) ? err_comp_errUp < 0 : true) :
"Incorrect error relationships";
// && could check for digit conditions for ties too
return true;
default: // Definition of UNNECESSARY already verified.
return true;
}
}
}
private boolean squareRootZeroResultAssertions(BigDecimal result, MathContext mc) {
return this.compareTo(ZERO) == 0;
}
/**
* Returns a {@code BigDecimal} whose value is
* (thisn), The power is computed exactly, to
* unlimited precision.
*
* thisn
* @throws ArithmeticException if {@code n} is out of range.
* @since 1.5
*/
public BigDecimal pow(int n) {
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);
return new BigDecimal(this.inflated().pow(n), newScale);
}
/**
* Returns a {@code 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.
*
*
*
*
* @param n power to raise this {@code BigDecimal} to.
* @param mc the context to use.
* @return
*
*
*
*
* thisn using the ANSI standard X3.274-1996
* algorithm
* @throws ArithmeticException if the result is inexact but the
* rounding mode is {@code UNNECESSARY}, or {@code n} is out
* of range.
* @since 1.5
*/
public BigDecimal pow(int n, MathContext mc) {
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
BigDecimal lhs = this;
MathContext workmc = mc; // working settings
int mag = Math.abs(n); // magnitude of n
if (mc.precision > 0) {
int elength = longDigitLength(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 doRound(acc, mc);
}
/**
* Returns a {@code BigDecimal} whose value is the absolute value
* of this {@code BigDecimal}, and whose scale is
* {@code this.scale()}.
*
* @return {@code abs(this)}
*/
public BigDecimal abs() {
return (signum() < 0 ? negate() : this);
}
/**
* Returns a {@code BigDecimal} whose value is the absolute value
* of this {@code BigDecimal}, with rounding according to the
* context settings.
*
* @param mc the context to use.
* @return {@code abs(this)}, rounded as necessary.
* @since 1.5
*/
public BigDecimal abs(MathContext mc) {
return (signum() < 0 ? negate(mc) : plus(mc));
}
/**
* Returns a {@code BigDecimal} whose value is {@code (-this)},
* and whose scale is {@code this.scale()}.
*
* @return {@code -this}.
*/
public BigDecimal negate() {
if (intCompact == INFLATED) {
return new BigDecimal(intVal.negate(), INFLATED, scale, precision);
} else {
return valueOf(-intCompact, scale, precision);
}
}
/**
* Returns a {@code BigDecimal} whose value is {@code (-this)},
* with rounding according to the context settings.
*
* @param mc the context to use.
* @return {@code -this}, rounded as necessary.
* @since 1.5
*/
public BigDecimal negate(MathContext mc) {
return negate().plus(mc);
}
/**
* Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose
* scale is {@code this.scale()}.
*
* (this *
* 10this.scale()).)
*
* @return the unscaled value of this {@code BigDecimal}.
* @since 1.2
*/
public BigInteger unscaledValue() {
return this.inflated();
}
// Rounding Modes
/**
* 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.
*
* @deprecated Use {@link RoundingMode#UP} instead.
*/
@Deprecated(since="9")
public static final int ROUND_UP = 0;
/**
* 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.
*
* @deprecated Use {@link RoundingMode#DOWN} instead.
*/
@Deprecated(since="9")
public static final int ROUND_DOWN = 1;
/**
* Rounding mode to round towards positive infinity. If the
* {@code BigDecimal} is positive, behaves as for
* {@code ROUND_UP}; if negative, behaves as for
* {@code ROUND_DOWN}. Note that this rounding mode never
* decreases the calculated value.
*
* @deprecated Use {@link RoundingMode#CEILING} instead.
*/
@Deprecated(since="9")
public static final int ROUND_CEILING = 2;
/**
* Rounding mode to round towards negative infinity. If the
* {@code BigDecimal} is positive, behave as for
* {@code ROUND_DOWN}; if negative, behave as for
* {@code ROUND_UP}. Note that this rounding mode never
* increases the calculated value.
*
* @deprecated Use {@link RoundingMode#FLOOR} instead.
*/
@Deprecated(since="9")
public static final int ROUND_FLOOR = 3;
/**
* Rounding mode to round towards {@literal "nearest neighbor"}
* unless both neighbors are equidistant, in which case round up.
* Behaves as for {@code ROUND_UP} if the discarded fraction is
* ≥ 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note
* that this is the rounding mode that most of us were taught in
* grade school.
*
* @deprecated Use {@link RoundingMode#HALF_UP} instead.
*/
@Deprecated(since="9")
public static final int ROUND_HALF_UP = 4;
/**
* Rounding mode to round towards {@literal "nearest neighbor"}
* unless both neighbors are equidistant, in which case round
* down. Behaves as for {@code ROUND_UP} if the discarded
* fraction is {@literal >} 0.5; otherwise, behaves as for
* {@code ROUND_DOWN}.
*
* @deprecated Use {@link RoundingMode#HALF_DOWN} instead.
*/
@Deprecated(since="9")
public static final int ROUND_HALF_DOWN = 5;
/**
* Rounding mode to round towards the {@literal "nearest neighbor"}
* unless both neighbors are equidistant, in which case, round
* towards the even neighbor. Behaves as for
* {@code ROUND_HALF_UP} if the digit to the left of the
* discarded fraction is odd; behaves as for
* {@code 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.
*
* @deprecated Use {@link RoundingMode#HALF_EVEN} instead.
*/
@Deprecated(since="9")
public static final int ROUND_HALF_EVEN = 6;
/**
* 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
* {@code ArithmeticException} is thrown.
*
* @deprecated Use {@link RoundingMode#UNNECESSARY} instead.
*/
@Deprecated(since="9")
public static final int ROUND_UNNECESSARY = 7;
// Scaling/Rounding Operations
/**
* Returns a {@code BigDecimal} rounded according to the
* {@code MathContext} settings. If the precision setting is 0 then
* no rounding takes place.
*
* setX mutate field {@code X}.
* Instead, {@code setScale} returns an object with the proper
* scale; the returned object may or may not be newly allocated.
*
* @param newScale scale of the {@code BigDecimal} value to be returned.
* @param roundingMode The rounding mode to apply.
* @return a {@code BigDecimal} whose scale is the specified value,
* and whose unscaled value is determined by multiplying or
* dividing this {@code BigDecimal}'s unscaled value by the
* appropriate power of ten to maintain its overall value.
* @throws ArithmeticException if {@code roundingMode==UNNECESSARY}
* and the specified scaling operation would require
* rounding.
* @see RoundingMode
* @since 1.5
*/
public BigDecimal setScale(int newScale, RoundingMode roundingMode) {
return setScale(newScale, roundingMode.oldMode);
}
/**
* Returns a {@code BigDecimal} whose scale is the specified
* value, and whose unscaled value is determined by multiplying or
* dividing this {@code 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.
*
* @apiNote 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 {@code X}.
* Instead, {@code setScale} returns an object with the proper
* scale; the returned object may or may not be newly allocated.
*
* @deprecated The method {@link #setScale(int, RoundingMode)} should
* be used in preference to this legacy method.
*
* @param newScale scale of the {@code BigDecimal} value to be returned.
* @param roundingMode The rounding mode to apply.
* @return a {@code BigDecimal} whose scale is the specified value,
* and whose unscaled value is determined by multiplying or
* dividing this {@code BigDecimal}'s unscaled value by the
* appropriate power of ten to maintain its overall value.
* @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY}
* and the specified scaling operation would require
* rounding.
* @throws IllegalArgumentException if {@code roundingMode} does not
* represent a valid rounding mode.
* @see #ROUND_UP
* @see #ROUND_DOWN
* @see #ROUND_CEILING
* @see #ROUND_FLOOR
* @see #ROUND_HALF_UP
* @see #ROUND_HALF_DOWN
* @see #ROUND_HALF_EVEN
* @see #ROUND_UNNECESSARY
*/
@Deprecated(since="9")
public BigDecimal setScale(int newScale, int roundingMode) {
if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
throw new IllegalArgumentException("Invalid rounding mode");
int oldScale = this.scale;
if (newScale == oldScale) // easy case
return this;
if (this.signum() == 0) // zero can have any scale
return zeroValueOf(newScale);
if(this.intCompact!=INFLATED) {
long rs = this.intCompact;
if (newScale > oldScale) {
int raise = checkScale((long) newScale - oldScale);
if ((rs = longMultiplyPowerTen(rs, raise)) != INFLATED) {
return valueOf(rs,newScale);
}
BigInteger rb = bigMultiplyPowerTen(raise);
return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
} else {
// newScale < oldScale -- drop some digits
// Can't predict the precision due to the effect of rounding.
int drop = checkScale((long) oldScale - newScale);
if (drop < LONG_TEN_POWERS_TABLE.length) {
return divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, newScale);
} else {
return divideAndRound(this.inflated(), bigTenToThe(drop), newScale, roundingMode, newScale);
}
}
} else {
if (newScale > oldScale) {
int raise = checkScale((long) newScale - oldScale);
BigInteger rb = bigMultiplyPowerTen(this.intVal,raise);
return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0);
} else {
// newScale < oldScale -- drop some digits
// Can't predict the precision due to the effect of rounding.
int drop = checkScale((long) oldScale - newScale);
if (drop < LONG_TEN_POWERS_TABLE.length)
return divideAndRound(this.intVal, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode,
newScale);
else
return divideAndRound(this.intVal, bigTenToThe(drop), newScale, roundingMode, newScale);
}
}
}
/**
* Returns a {@code BigDecimal} whose scale is the specified
* value, and whose value is numerically equal to this
* {@code BigDecimal}'s. Throws an {@code ArithmeticException}
* if this is not possible.
*
* setX mutate field
* {@code X}. Instead, {@code setScale} returns an
* object with the proper scale; the returned object may or may
* not be newly allocated.
*
* @param newScale scale of the {@code BigDecimal} value to be returned.
* @return a {@code BigDecimal} whose scale is the specified value, and
* whose unscaled value is determined by multiplying or dividing
* this {@code BigDecimal}'s unscaled value by the appropriate
* power of ten to maintain its overall value.
* @throws ArithmeticException if the specified scaling operation would
* require rounding.
* @see #setScale(int, int)
* @see #setScale(int, RoundingMode)
*/
public BigDecimal setScale(int newScale) {
return setScale(newScale, ROUND_UNNECESSARY);
}
// Decimal Point Motion Operations
/**
* Returns a {@code BigDecimal} which is equivalent to this one
* with the decimal point moved {@code n} places to the left. If
* {@code n} is non-negative, the call merely adds {@code n} to
* the scale. If {@code n} is negative, the call is equivalent
* to {@code movePointRight(-n)}. The {@code BigDecimal}
* returned by this call has value (this ×
* 10-n) and scale {@code max(this.scale()+n,
* 0)}.
*
* @param n number of places to move the decimal point to the left.
* @return a {@code BigDecimal} which is equivalent to this one with the
* decimal point moved {@code n} places to the left.
* @throws ArithmeticException if scale overflows.
*/
public BigDecimal movePointLeft(int n) {
if (n == 0) return this;
// Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE
int newScale = checkScale((long)scale + n);
BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
}
/**
* Returns a {@code BigDecimal} which is equivalent to this one
* with the decimal point moved {@code n} places to the right.
* If {@code n} is non-negative, the call merely subtracts
* {@code n} from the scale. If {@code n} is negative, the call
* is equivalent to {@code movePointLeft(-n)}. The
* {@code BigDecimal} returned by this call has value (this
* × 10n) and scale {@code max(this.scale()-n,
* 0)}.
*
* @param n number of places to move the decimal point to the right.
* @return a {@code BigDecimal} which is equivalent to this one
* with the decimal point moved {@code n} places to the right.
* @throws ArithmeticException if scale overflows.
*/
public BigDecimal movePointRight(int n) {
if (n == 0) return this;
// Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE
int newScale = checkScale((long)scale - n);
BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
}
/**
* Returns a BigDecimal whose numerical value is equal to
* ({@code this} * 10n). The scale of
* the result is {@code (this.scale() - n)}.
*
* @param n the exponent power of ten to scale by
* @return a BigDecimal whose numerical value is equal to
* ({@code this} * 10n)
* @throws ArithmeticException if the scale would be
* outside the range of a 32-bit integer.
*
* @since 1.5
*/
public BigDecimal scaleByPowerOfTen(int n) {
return new BigDecimal(intVal, intCompact,
checkScale((long)scale - n), precision);
}
/**
* Returns a {@code 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 {@code BigDecimal} value {@code 600.0}, which has
* [{@code BigInteger}, {@code scale}] components equal to
* [6000, 1], yields {@code 6E2} with [{@code BigInteger},
* {@code scale}] components equal to [6, -2]. If
* this BigDecimal is numerically equal to zero, then
* {@code BigDecimal.ZERO} is returned.
*
* @return a numerically equal {@code BigDecimal} with any
* trailing zeros removed.
* @throws ArithmeticException if scale overflows.
* @since 1.5
*/
public BigDecimal stripTrailingZeros() {
if (intCompact == 0 || (intVal != null && intVal.signum() == 0)) {
return BigDecimal.ZERO;
} else if (intCompact != INFLATED) {
return createAndStripZerosToMatchScale(intCompact, scale, Long.MIN_VALUE);
} else {
return createAndStripZerosToMatchScale(intVal, scale, Long.MIN_VALUE);
}
}
// Comparison Operations
/**
* Compares this {@code BigDecimal} numerically with the specified
* {@code BigDecimal}. Two {@code BigDecimal} objects that are
* equal in value but have a different scale (like 2.0 and 2.00)
* are considered equal by this method. Such values are in the
* same cohort.
*
* This method is provided in preference to individual methods for
* each of the six boolean comparison operators ({@literal <}, ==,
* {@literal >}, {@literal >=}, !=, {@literal <=}). The suggested
* idiom for performing these comparisons is: {@code
* (x.compareTo(y)} <op> {@code 0)}, where
* <op> is one of the six comparison operators.
* @apiNote
* Note: this class has a natural ordering that is inconsistent with equals.
*
* @param val {@code BigDecimal} to which this {@code BigDecimal} is
* to be compared.
* @return -1, 0, or 1 as this {@code BigDecimal} is numerically
* less than, equal to, or greater than {@code val}.
*/
@Override
public int compareTo(BigDecimal val) {
// Quick path for equal scale and non-inflated case.
if (scale == val.scale) {
long xs = intCompact;
long ys = val.intCompact;
if (xs != INFLATED && ys != INFLATED)
return xs != ys ? ((xs > ys) ? 1 : -1) : 0;
}
int xsign = this.signum();
int ysign = val.signum();
if (xsign != ysign)
return (xsign > ysign) ? 1 : -1;
if (xsign == 0)
return 0;
int cmp = compareMagnitude(val);
return (xsign > 0) ? cmp : -cmp;
}
/**
* Version of compareTo that ignores sign.
*/
private int compareMagnitude(BigDecimal val) {
// Match scales, avoid unnecessary inflation
long ys = val.intCompact;
long xs = this.intCompact;
if (xs == 0)
return (ys == 0) ? 0 : -1;
if (ys == 0)
return 1;
long sdiff = (long)this.scale - val.scale;
if (sdiff != 0) {
// Avoid matching scales if the (adjusted) exponents differ
long xae = (long)this.precision() - this.scale; // [-1]
long yae = (long)val.precision() - val.scale; // [-1]
if (xae < yae)
return -1;
if (xae > yae)
return 1;
if (sdiff < 0) {
// The cases sdiff <= Integer.MIN_VALUE intentionally fall through.
if ( sdiff > Integer.MIN_VALUE &&
(xs == INFLATED ||
(xs = longMultiplyPowerTen(xs, (int)-sdiff)) == INFLATED) &&
ys == INFLATED) {
BigInteger rb = bigMultiplyPowerTen((int)-sdiff);
return rb.compareMagnitude(val.intVal);
}
} else { // sdiff > 0
// The cases sdiff > Integer.MAX_VALUE intentionally fall through.
if ( sdiff <= Integer.MAX_VALUE &&
(ys == INFLATED ||
(ys = longMultiplyPowerTen(ys, (int)sdiff)) == INFLATED) &&
xs == INFLATED) {
BigInteger rb = val.bigMultiplyPowerTen((int)sdiff);
return this.intVal.compareMagnitude(rb);
}
}
}
if (xs != INFLATED)
return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
else if (ys != INFLATED)
return 1;
else
return this.intVal.compareMagnitude(val.intVal);
}
/**
* Compares this {@code BigDecimal} with the specified {@code
* Object} for equality. Unlike {@link #compareTo(BigDecimal)
* compareTo}, this method considers two {@code BigDecimal}
* objects equal only if they are equal in value and
* scale. Therefore 2.0 is not equal to 2.00 when compared by this
* method since the former has [{@code BigInteger}, {@code scale}]
* components equal to [20, 1] while the latter has components
* equal to [200, 2].
*
* @apiNote
* One example that shows how 2.0 and 2.00 are not
* substitutable for each other under some arithmetic operations
* are the two expressions:
* {@code new BigDecimal("2.0" ).divide(BigDecimal.valueOf(3),
* HALF_UP)} which evaluates to 0.7 and
* {@code new BigDecimal("2.00").divide(BigDecimal.valueOf(3),
* HALF_UP)} which evaluates to 0.67.
*
* @param x {@code Object} to which this {@code BigDecimal} is
* to be compared.
* @return {@code true} if and only if the specified {@code Object} is a
* {@code BigDecimal} whose value and scale are equal to this
* {@code BigDecimal}'s.
* @see #compareTo(java.math.BigDecimal)
* @see #hashCode
*/
@Override
public boolean equals(Object x) {
if (!(x instanceof BigDecimal xDec))
return false;
if (x == this)
return true;
if (scale != xDec.scale)
return false;
long s = this.intCompact;
long xs = xDec.intCompact;
if (s != INFLATED) {
if (xs == INFLATED)
xs = compactValFor(xDec.intVal);
return xs == s;
} else if (xs != INFLATED)
return xs == compactValFor(this.intVal);
return this.inflated().equals(xDec.inflated());
}
/**
* Returns the minimum of this {@code BigDecimal} and
* {@code val}.
*
* @param val value with which the minimum is to be computed.
* @return the {@code BigDecimal} whose value is the lesser of this
* {@code BigDecimal} and {@code val}. If they are equal,
* as defined by the {@link #compareTo(BigDecimal) compareTo}
* method, {@code this} is returned.
* @see #compareTo(java.math.BigDecimal)
*/
public BigDecimal min(BigDecimal val) {
return (compareTo(val) <= 0 ? this : val);
}
/**
* Returns the maximum of this {@code BigDecimal} and {@code val}.
*
* @param val value with which the maximum is to be computed.
* @return the {@code BigDecimal} whose value is the greater of this
* {@code BigDecimal} and {@code val}. If they are equal,
* as defined by the {@link #compareTo(BigDecimal) compareTo}
* method, {@code this} is returned.
* @see #compareTo(java.math.BigDecimal)
*/
public BigDecimal max(BigDecimal val) {
return (compareTo(val) >= 0 ? this : val);
}
// Hash Function
/**
* Returns the hash code for this {@code BigDecimal}.
* The hash code is computed as a function of the {@linkplain
* #unscaledValue() unscaled value} and the {@linkplain #scale()
* scale} of this {@code BigDecimal}.
*
* @apiNote
* Two {@code BigDecimal} objects that are numerically equal but
* differ in scale (like 2.0 and 2.00) will generally not
* have the same hash code.
*
* @return hash code for this {@code BigDecimal}.
* @see #equals(Object)
*/
@Override
public int hashCode() {
if (intCompact != INFLATED) {
long val2 = (intCompact < 0)? -intCompact : intCompact;
int temp = (int)( ((int)(val2 >>> 32)) * 31 +
(val2 & LONG_MASK));
return 31*((intCompact < 0) ?-temp:temp) + scale;
} else
return 31*intVal.hashCode() + scale;
}
// Format Converters
/**
* Returns the string representation of this {@code BigDecimal},
* using scientific notation if an exponent is needed.
*
* '\u002D') if the
* adjusted exponent is negative, {@code '+'}
* ('\u002B') otherwise).
*
* '\u002D') if the unscaled
* value is less than zero. No sign character is prefixed if the
* unscaled value is zero or positive.
*
*
* [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:
*
*
*
*
* @return string representation of this {@code BigDecimal}.
* @see Character#forDigit
* @see #BigDecimal(java.lang.String)
*/
@Override
public String toString() {
String sc = stringCache;
if (sc == null) {
stringCache = sc = layoutChars(true);
}
return sc;
}
/**
* Returns a string representation of this {@code BigDecimal},
* using engineering notation if an exponent is needed.
*
* '\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 {@code BigDecimal} will necessarily be
* recovered; the representation of the new {@code BigDecimal}
* may have a different scale. In particular, if this
* {@code BigDecimal} has a negative 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 {@code toString}
* method in 1.4 and earlier releases.)
*
* @return a string representation of this {@code BigDecimal}
* without an exponent field.
* @since 1.5
* @see #toString()
* @see #toEngineeringString()
*/
public String toPlainString() {
if(scale==0) {
if(intCompact!=INFLATED) {
return Long.toString(intCompact);
} else {
return intVal.toString();
}
}
if(this.scale<0) { // No decimal point
if(signum()==0) {
return "0";
}
int trailingZeros = checkScaleNonZero((-(long)scale));
StringBuilder buf;
if(intCompact!=INFLATED) {
buf = new StringBuilder(20+trailingZeros);
buf.append(intCompact);
} else {
String str = intVal.toString();
buf = new StringBuilder(str.length()+trailingZeros);
buf.append(str);
}
for (int i = 0; i < trailingZeros; i++) {
buf.append('0');
}
return buf.toString();
}
String str ;
if(intCompact!=INFLATED) {
str = Long.toString(Math.abs(intCompact));
} else {
str = intVal.abs().toString();
}
return getValueString(signum(), str, scale);
}
/* Returns a digit.digit string */
private String getValueString(int signum, 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();
}
/**
* Converts this {@code BigDecimal} to a {@code BigInteger}.
* This conversion is analogous to the
* narrowing primitive conversion from {@code double} to
* {@code long} as defined in
* The Java Language Specification:
* any fractional part of this
* {@code BigDecimal} will be discarded. Note that this
* conversion can lose information about the precision of the
* {@code BigDecimal} value.
*
*
*
*
* Note: Since this is an audit method, we are not supposed to change the
* state of this BigDecimal object.
*/
private BigDecimal audit() {
if (intCompact == INFLATED) {
if (intVal == null) {
print("audit", this);
throw new AssertionError("null intVal");
}
// Check precision
if (precision > 0 && precision != bigDigitLength(intVal)) {
print("audit", this);
throw new AssertionError("precision mismatch");
}
} else {
if (intVal != null) {
long val = intVal.longValue();
if (val != intCompact) {
print("audit", this);
throw new AssertionError("Inconsistent state, intCompact=" +
intCompact + "\t intVal=" + val);
}
}
// Check precision
if (precision > 0 && precision != longDigitLength(intCompact)) {
print("audit", this);
throw new AssertionError("precision mismatch");
}
}
return this;
}
/* the same as checkScale where value!=0 */
private static int checkScaleNonZero(long val) {
int asInt = (int)val;
if (asInt != val) {
throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
}
return asInt;
}
private static int checkScale(long intCompact, long val) {
int asInt = (int)val;
if (asInt != val) {
asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
if (intCompact != 0)
throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
}
return asInt;
}
private static int checkScale(BigInteger intVal, long val) {
int asInt = (int)val;
if (asInt != val) {
asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
if (intVal.signum() != 0)
throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
}
return asInt;
}
/**
* Returns a {@code BigDecimal} rounded according to the MathContext
* settings;
* If rounding is needed a new {@code BigDecimal} is created and returned.
*
* @param val the value to be rounded
* @param mc the context to use.
* @return a {@code BigDecimal} rounded according to the MathContext
* settings. May return {@code value}, if no rounding needed.
* @throws ArithmeticException if the rounding mode is
* {@code RoundingMode.UNNECESSARY} and the
* result is inexact.
*/
private static BigDecimal doRound(BigDecimal val, MathContext mc) {
int mcp = mc.precision;
boolean wasDivided = false;
if (mcp > 0) {
BigInteger intVal = val.intVal;
long compactVal = val.intCompact;
int scale = val.scale;
int prec = val.precision();
int mode = mc.roundingMode.oldMode;
int drop;
if (compactVal == INFLATED) {
drop = prec - mcp;
while (drop > 0) {
scale = checkScaleNonZero((long) scale - drop);
intVal = divideAndRoundByTenPow(intVal, drop, mode);
wasDivided = true;
compactVal = compactValFor(intVal);
if (compactVal != INFLATED) {
prec = longDigitLength(compactVal);
break;
}
prec = bigDigitLength(intVal);
drop = prec - mcp;
}
}
if (compactVal != INFLATED) {
drop = prec - mcp; // drop can't be more than 18
while (drop > 0) {
scale = checkScaleNonZero((long) scale - drop);
compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
wasDivided = true;
prec = longDigitLength(compactVal);
drop = prec - mcp;
intVal = null;
}
}
return wasDivided ? new BigDecimal(intVal,compactVal,scale,prec) : val;
}
return val;
}
/*
* Returns a {@code BigDecimal} created from {@code long} value with
* given scale rounded according to the MathContext settings
*/
private static BigDecimal doRound(long compactVal, int scale, MathContext mc) {
int mcp = mc.precision;
if (mcp > 0 && mcp < 19) {
int prec = longDigitLength(compactVal);
int drop = prec - mcp; // drop can't be more than 18
while (drop > 0) {
scale = checkScaleNonZero((long) scale - drop);
compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
prec = longDigitLength(compactVal);
drop = prec - mcp;
}
return valueOf(compactVal, scale, prec);
}
return valueOf(compactVal, scale);
}
/*
* Returns a {@code BigDecimal} created from {@code BigInteger} value with
* given scale rounded according to the MathContext settings
*/
private static BigDecimal doRound(BigInteger intVal, int scale, MathContext mc) {
int mcp = mc.precision;
int prec = 0;
if (mcp > 0) {
long compactVal = compactValFor(intVal);
int mode = mc.roundingMode.oldMode;
int drop;
if (compactVal == INFLATED) {
prec = bigDigitLength(intVal);
drop = prec - mcp;
while (drop > 0) {
scale = checkScaleNonZero((long) scale - drop);
intVal = divideAndRoundByTenPow(intVal, drop, mode);
compactVal = compactValFor(intVal);
if (compactVal != INFLATED) {
break;
}
prec = bigDigitLength(intVal);
drop = prec - mcp;
}
}
if (compactVal != INFLATED) {
prec = longDigitLength(compactVal);
drop = prec - mcp; // drop can't be more than 18
while (drop > 0) {
scale = checkScaleNonZero((long) scale - drop);
compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode);
prec = longDigitLength(compactVal);
drop = prec - mcp;
}
return valueOf(compactVal,scale,prec);
}
}
return new BigDecimal(intVal,INFLATED,scale,prec);
}
/*
* Divides {@code BigInteger} value by ten power.
*/
private static BigInteger divideAndRoundByTenPow(BigInteger intVal, int tenPow, int roundingMode) {
if (tenPow < LONG_TEN_POWERS_TABLE.length)
intVal = divideAndRound(intVal, LONG_TEN_POWERS_TABLE[tenPow], roundingMode);
else
intVal = divideAndRound(intVal, bigTenToThe(tenPow), roundingMode);
return intVal;
}
/**
* Internally used for division operation for division {@code long} by
* {@code long}.
* The returned {@code BigDecimal} object is the quotient whose scale is set
* to the passed in scale. If the remainder is not zero, it will be rounded
* based on the passed in roundingMode. Also, if the remainder is zero and
* the last parameter, i.e. preferredScale is NOT equal to scale, the
* trailing zeros of the result is stripped to match the preferredScale.
*/
private static BigDecimal divideAndRound(long ldividend, long ldivisor, int scale, int roundingMode,
int preferredScale) {
int qsign; // quotient sign
long q = ldividend / ldivisor; // store quotient in long
if (roundingMode == ROUND_DOWN && scale == preferredScale)
return valueOf(q, scale);
long r = ldividend % ldivisor; // store remainder in long
qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
if (r != 0) {
boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
return valueOf((increment ? q + qsign : q), scale);
} else {
if (preferredScale != scale)
return createAndStripZerosToMatchScale(q, scale, preferredScale);
else
return valueOf(q, scale);
}
}
/**
* Divides {@code long} by {@code long} and do rounding based on the
* passed in roundingMode.
*/
private static long divideAndRound(long ldividend, long ldivisor, int roundingMode) {
int qsign; // quotient sign
long q = ldividend / ldivisor; // store quotient in long
if (roundingMode == ROUND_DOWN)
return q;
long r = ldividend % ldivisor; // store remainder in long
qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
if (r != 0) {
boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r);
return increment ? q + qsign : q;
} else {
return q;
}
}
/**
* Shared logic of need increment computation.
*/
private static boolean commonNeedIncrement(int roundingMode, int qsign,
int cmpFracHalf, boolean oddQuot) {
switch(roundingMode) {
case ROUND_UNNECESSARY:
throw new ArithmeticException("Rounding necessary");
case ROUND_UP: // Away from zero
return true;
case ROUND_DOWN: // Towards zero
return false;
case ROUND_CEILING: // Towards +infinity
return qsign > 0;
case ROUND_FLOOR: // Towards -infinity
return qsign < 0;
default: // Some kind of half-way rounding
assert roundingMode >= ROUND_HALF_UP &&
roundingMode <= ROUND_HALF_EVEN: "Unexpected rounding mode" + RoundingMode.valueOf(roundingMode);
if (cmpFracHalf < 0 ) // We're closer to higher digit
return false;
else if (cmpFracHalf > 0 ) // We're closer to lower digit
return true;
else { // half-way
assert cmpFracHalf == 0;
return switch (roundingMode) {
case ROUND_HALF_DOWN -> false;
case ROUND_HALF_UP -> true;
case ROUND_HALF_EVEN -> oddQuot;
default -> throw new AssertionError("Unexpected rounding mode" + roundingMode);
};
}
}
}
/**
* Tests if quotient has to be incremented according the roundingMode
*/
private static boolean needIncrement(long ldivisor, int roundingMode,
int qsign, long q, long r) {
assert r != 0L;
int cmpFracHalf;
if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
cmpFracHalf = 1; // 2 * r can't fit into long
} else {
cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
}
return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, (q & 1L) != 0L);
}
/**
* Divides {@code BigInteger} value by {@code long} value and
* do rounding based on the passed in roundingMode.
*/
private static BigInteger divideAndRound(BigInteger bdividend, long ldivisor, int roundingMode) {
// Descend into mutables for faster remainder checks
MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
// store quotient
MutableBigInteger mq = new MutableBigInteger();
// store quotient & remainder in long
long r = mdividend.divide(ldivisor, mq);
// record remainder is zero or not
boolean isRemainderZero = (r == 0);
// quotient sign
int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
if (!isRemainderZero) {
if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
mq.add(MutableBigInteger.ONE);
}
}
return mq.toBigInteger(qsign);
}
/**
* Internally used for division operation for division {@code BigInteger}
* by {@code long}.
* The returned {@code BigDecimal} object is the quotient whose scale is set
* to the passed in scale. If the remainder is not zero, it will be rounded
* based on the passed in roundingMode. Also, if the remainder is zero and
* the last parameter, i.e. preferredScale is NOT equal to scale, the
* trailing zeros of the result is stripped to match the preferredScale.
*/
private static BigDecimal divideAndRound(BigInteger bdividend,
long ldivisor, int scale, int roundingMode, int preferredScale) {
// Descend into mutables for faster remainder checks
MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
// store quotient
MutableBigInteger mq = new MutableBigInteger();
// store quotient & remainder in long
long r = mdividend.divide(ldivisor, mq);
// record remainder is zero or not
boolean isRemainderZero = (r == 0);
// quotient sign
int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
if (!isRemainderZero) {
if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) {
mq.add(MutableBigInteger.ONE);
}
return mq.toBigDecimal(qsign, scale);
} else {
if (preferredScale != scale) {
long compactVal = mq.toCompactValue(qsign);
if(compactVal!=INFLATED) {
return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
}
BigInteger intVal = mq.toBigInteger(qsign);
return createAndStripZerosToMatchScale(intVal,scale, preferredScale);
} else {
return mq.toBigDecimal(qsign, scale);
}
}
}
/**
* Tests if quotient has to be incremented according the roundingMode
*/
private static boolean needIncrement(long ldivisor, int roundingMode,
int qsign, MutableBigInteger mq, long r) {
assert r != 0L;
int cmpFracHalf;
if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
cmpFracHalf = 1; // 2 * r can't fit into long
} else {
cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
}
return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
}
/**
* Divides {@code BigInteger} value by {@code BigInteger} value and
* do rounding based on the passed in roundingMode.
*/
private static BigInteger divideAndRound(BigInteger bdividend, BigInteger bdivisor, int roundingMode) {
boolean isRemainderZero; // record remainder is zero or not
int qsign; // quotient sign
// Descend into mutables for faster remainder checks
MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
MutableBigInteger mq = new MutableBigInteger();
MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
MutableBigInteger mr = mdividend.divide(mdivisor, mq);
isRemainderZero = mr.isZero();
qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
if (!isRemainderZero) {
if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
mq.add(MutableBigInteger.ONE);
}
}
return mq.toBigInteger(qsign);
}
/**
* Internally used for division operation for division {@code BigInteger}
* by {@code BigInteger}.
* The returned {@code BigDecimal} object is the quotient whose scale is set
* to the passed in scale. If the remainder is not zero, it will be rounded
* based on the passed in roundingMode. Also, if the remainder is zero and
* the last parameter, i.e. preferredScale is NOT equal to scale, the
* trailing zeros of the result is stripped to match the preferredScale.
*/
private static BigDecimal divideAndRound(BigInteger bdividend, BigInteger bdivisor, int scale, int roundingMode,
int preferredScale) {
boolean isRemainderZero; // record remainder is zero or not
int qsign; // quotient sign
// Descend into mutables for faster remainder checks
MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
MutableBigInteger mq = new MutableBigInteger();
MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag);
MutableBigInteger mr = mdividend.divide(mdivisor, mq);
isRemainderZero = mr.isZero();
qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
if (!isRemainderZero) {
if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) {
mq.add(MutableBigInteger.ONE);
}
return mq.toBigDecimal(qsign, scale);
} else {
if (preferredScale != scale) {
long compactVal = mq.toCompactValue(qsign);
if (compactVal != INFLATED) {
return createAndStripZerosToMatchScale(compactVal, scale, preferredScale);
}
BigInteger intVal = mq.toBigInteger(qsign);
return createAndStripZerosToMatchScale(intVal, scale, preferredScale);
} else {
return mq.toBigDecimal(qsign, scale);
}
}
}
/**
* Tests if quotient has to be incremented according the roundingMode
*/
private static boolean needIncrement(MutableBigInteger mdivisor, int roundingMode,
int qsign, MutableBigInteger mq, MutableBigInteger mr) {
assert !mr.isZero();
int cmpFracHalf = mr.compareHalf(mdivisor);
return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd());
}
/**
* Remove insignificant trailing zeros from this
* {@code BigInteger} value 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.
*
* @return new {@code BigDecimal} with a scale possibly reduced
* to be closed to the preferred scale.
* @throws ArithmeticException if scale overflows.
*/
private static BigDecimal createAndStripZerosToMatchScale(BigInteger intVal, int scale, long preferredScale) {
BigInteger qr[]; // quotient-remainder pair
while (intVal.compareMagnitude(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; // non-0 remainder
intVal = qr[0];
scale = checkScale(intVal,(long) scale - 1); // could Overflow
}
return valueOf(intVal, scale, 0);
}
/**
* Remove insignificant trailing zeros from this
* {@code long} value 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.
*
* @return new {@code BigDecimal} with a scale possibly reduced
* to be closed to the preferred scale.
* @throws ArithmeticException if scale overflows.
*/
private static BigDecimal createAndStripZerosToMatchScale(long compactVal, int scale, long preferredScale) {
while (Math.abs(compactVal) >= 10L && scale > preferredScale) {
if ((compactVal & 1L) != 0L)
break; // odd number cannot end in 0
long r = compactVal % 10L;
if (r != 0L)
break; // non-0 remainder
compactVal /= 10;
scale = checkScale(compactVal, (long) scale - 1); // could Overflow
}
return valueOf(compactVal, scale);
}
private static BigDecimal stripZerosToMatchScale(BigInteger intVal, long intCompact, int scale, int preferredScale) {
if(intCompact!=INFLATED) {
return createAndStripZerosToMatchScale(intCompact, scale, preferredScale);
} else {
return createAndStripZerosToMatchScale(intVal==null ? INFLATED_BIGINT : intVal,
scale, preferredScale);
}
}
/*
* returns INFLATED if oveflow
*/
private static long add(long xs, long ys){
long sum = xs + ys;
// See "Hacker's Delight" section 2-12 for explanation of
// the overflow test.
if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) { // not overflowed
return sum;
}
return INFLATED;
}
private static BigDecimal add(long xs, long ys, int scale){
long sum = add(xs, ys);
if (sum!=INFLATED)
return BigDecimal.valueOf(sum, scale);
return new BigDecimal(BigInteger.valueOf(xs).add(ys), scale);
}
private static BigDecimal add(final long xs, int scale1, final long ys, int scale2) {
long sdiff = (long) scale1 - scale2;
if (sdiff == 0) {
return add(xs, ys, scale1);
} else if (sdiff < 0) {
int raise = checkScale(xs,-sdiff);
long scaledX = longMultiplyPowerTen(xs, raise);
if (scaledX != INFLATED) {
return add(scaledX, ys, scale2);
} else {
BigInteger bigsum = bigMultiplyPowerTen(xs,raise).add(ys);
return ((xs^ys)>=0) ? // same sign test
new BigDecimal(bigsum, INFLATED, scale2, 0)
: valueOf(bigsum, scale2, 0);
}
} else {
int raise = checkScale(ys,sdiff);
long scaledY = longMultiplyPowerTen(ys, raise);
if (scaledY != INFLATED) {
return add(xs, scaledY, scale1);
} else {
BigInteger bigsum = bigMultiplyPowerTen(ys,raise).add(xs);
return ((xs^ys)>=0) ?
new BigDecimal(bigsum, INFLATED, scale1, 0)
: valueOf(bigsum, scale1, 0);
}
}
}
private static BigDecimal add(final long xs, int scale1, BigInteger snd, int scale2) {
int rscale = scale1;
long sdiff = (long)rscale - scale2;
boolean sameSigns = (Long.signum(xs) == snd.signum);
BigInteger sum;
if (sdiff < 0) {
int raise = checkScale(xs,-sdiff);
rscale = scale2;
long scaledX = longMultiplyPowerTen(xs, raise);
if (scaledX == INFLATED) {
sum = snd.add(bigMultiplyPowerTen(xs,raise));
} else {
sum = snd.add(scaledX);
}
} else { //if (sdiff > 0) {
int raise = checkScale(snd,sdiff);
snd = bigMultiplyPowerTen(snd,raise);
sum = snd.add(xs);
}
return (sameSigns) ?
new BigDecimal(sum, INFLATED, rscale, 0) :
valueOf(sum, rscale, 0);
}
private static BigDecimal add(BigInteger fst, int scale1, BigInteger snd, int scale2) {
int rscale = scale1;
long sdiff = (long)rscale - scale2;
if (sdiff != 0) {
if (sdiff < 0) {
int raise = checkScale(fst,-sdiff);
rscale = scale2;
fst = bigMultiplyPowerTen(fst,raise);
} else {
int raise = checkScale(snd,sdiff);
snd = bigMultiplyPowerTen(snd,raise);
}
}
BigInteger sum = fst.add(snd);
return (fst.signum == snd.signum) ?
new BigDecimal(sum, INFLATED, rscale, 0) :
valueOf(sum, rscale, 0);
}
private static BigInteger bigMultiplyPowerTen(long value, int n) {
if (n <= 0)
return BigInteger.valueOf(value);
return bigTenToThe(n).multiply(value);
}
private static BigInteger bigMultiplyPowerTen(BigInteger value, int n) {
if (n <= 0)
return value;
if(n