A value is represented by an arbitrary-precision "unscaled value" and a signed 32-bit "scale", * combined thus: {@code unscaled * 10-scale}. See {@link #unscaledValue} and {@link #scale}. * *
Most operations allow you to supply a {@link MathContext} to specify a desired rounding mode.
*/
public class BigDecimal extends Number implements Comparable
* To generate a big decimal instance which is equivalent to {@code 0.1} use
* the {@code BigDecimal(String)} constructor.
*
* @param val
* double value to be converted to a {@code BigDecimal} instance.
* @throws NumberFormatException
* if {@code val} is infinity or not a number.
*/
public BigDecimal(double val) {
if (Double.isInfinite(val) || Double.isNaN(val)) {
throw new NumberFormatException("Infinity or NaN: " + val);
}
long bits = Double.doubleToLongBits(val); // IEEE-754
long mantissa;
int trailingZeros;
// Extracting the exponent, note that the bias is 1023
scale = 1075 - (int)((bits >> 52) & 0x7FFL);
// Extracting the 52 bits of the mantissa.
mantissa = (scale == 1075) ? (bits & 0xFFFFFFFFFFFFFL) << 1
: (bits & 0xFFFFFFFFFFFFFL) | 0x10000000000000L;
if (mantissa == 0) {
scale = 0;
precision = 1;
}
// To simplify all factors '2' in the mantissa
if (scale > 0) {
trailingZeros = Math.min(scale, Long.numberOfTrailingZeros(mantissa));
mantissa >>>= trailingZeros;
scale -= trailingZeros;
}
// Calculating the new unscaled value and the new scale
if((bits >> 63) != 0) {
mantissa = -mantissa;
}
int mantissaBits = bitLength(mantissa);
if (scale < 0) {
bitLength = mantissaBits == 0 ? 0 : mantissaBits - scale;
if(bitLength < 64) {
smallValue = mantissa << (-scale);
} else {
BigInt bi = new BigInt();
bi.putLongInt(mantissa);
bi.shift(-scale);
intVal = new BigInteger(bi);
}
scale = 0;
} else if (scale > 0) {
// m * 2^e = (m * 5^(-e)) * 10^e
if(scale < LONG_FIVE_POW.length
&& mantissaBits+LONG_FIVE_POW_BIT_LENGTH[scale] < 64) {
smallValue = mantissa * LONG_FIVE_POW[scale];
bitLength = bitLength(smallValue);
} else {
setUnscaledValue(Multiplication.multiplyByFivePow(BigInteger.valueOf(mantissa), scale));
}
} else { // scale == 0
smallValue = mantissa;
bitLength = mantissaBits;
}
}
/**
* Constructs a new {@code BigDecimal} instance from the 64bit double
* {@code val}. The constructed big decimal is equivalent to the given
* double. For example, {@code new BigDecimal(0.1)} is equal to {@code
* 0.1000000000000000055511151231257827021181583404541015625}. This happens
* as {@code 0.1} cannot be represented exactly in binary.
*
* To generate a big decimal instance which is equivalent to {@code 0.1} use
* the {@code BigDecimal(String)} constructor.
*
* @param val
* double value to be converted to a {@code BigDecimal} instance.
* @param mc
* rounding mode and precision for the result of this operation.
* @throws NumberFormatException
* if {@code val} is infinity or not a number.
* @throws ArithmeticException
* if {@code mc.precision > 0} and {@code mc.roundingMode ==
* UNNECESSARY} and the new big decimal cannot be represented
* within the given precision without rounding.
*/
public BigDecimal(double val, MathContext mc) {
this(val);
inplaceRound(mc);
}
/**
* Constructs a new {@code BigDecimal} instance from the given big integer
* {@code val}. The scale of the result is {@code 0}.
*/
public BigDecimal(BigInteger val) {
this(val, 0);
}
/**
* Constructs a new {@code BigDecimal} instance from the given big integer
* {@code val}. The scale of the result is {@code 0}.
*
* @param mc
* rounding mode and precision for the result of this operation.
* @throws ArithmeticException
* if {@code mc.precision > 0} and {@code mc.roundingMode ==
* UNNECESSARY} and the new big decimal cannot be represented
* within the given precision without rounding.
*/
public BigDecimal(BigInteger val, MathContext mc) {
this(val);
inplaceRound(mc);
}
/**
* Constructs a new {@code BigDecimal} instance from a given unscaled value
* {@code unscaledVal} and a given scale. The value of this instance is
* {@code unscaledVal * 10-scale}).
*
* @throws NullPointerException
* if {@code unscaledVal == null}.
*/
public BigDecimal(BigInteger unscaledVal, int scale) {
if (unscaledVal == null) {
throw new NullPointerException("unscaledVal == null");
}
this.scale = scale;
setUnscaledValue(unscaledVal);
}
/**
* Constructs a new {@code BigDecimal} instance from a given unscaled value
* {@code unscaledVal} and a given scale. The value of this instance is
* {@code unscaledVal * 10-scale). The result is rounded according
* to the specified math context.
*
* @param mc
* rounding mode and precision for the result of this operation.
* @throws ArithmeticException
* if {@code mc.precision > 0} and {@code mc.roundingMode ==
* UNNECESSARY} and the new big decimal cannot be represented
* within the given precision without rounding.
* @throws NullPointerException
* if {@code unscaledVal == null}.
*/
public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {
this(unscaledVal, scale);
inplaceRound(mc);
}
/**
* Constructs a new {@code BigDecimal} instance from the given int
* {@code val}. The scale of the result is 0.
*
* @param val
* int value to be converted to a {@code BigDecimal} instance.
*/
public BigDecimal(int val) {
this(val,0);
}
/**
* Constructs a new {@code BigDecimal} instance from the given int {@code
* val}. The scale of the result is {@code 0}. The result is rounded
* according to the specified math context.
*
* @param val
* int value to be converted to a {@code BigDecimal} instance.
* @param mc
* rounding mode and precision for the result of this operation.
* @throws ArithmeticException
* if {@code mc.precision > 0} and {@code c.roundingMode ==
* UNNECESSARY} and the new big decimal cannot be represented
* within the given precision without rounding.
*/
public BigDecimal(int val, MathContext mc) {
this(val,0);
inplaceRound(mc);
}
/**
* Constructs a new {@code BigDecimal} instance from the given long {@code
* val}. The scale of the result is {@code 0}.
*
* @param val
* long value to be converted to a {@code BigDecimal} instance.
*/
public BigDecimal(long val) {
this(val,0);
}
/**
* Constructs a new {@code BigDecimal} instance from the given long {@code
* val}. The scale of the result is {@code 0}. The result is rounded
* according to the specified math context.
*
* @param val
* long value to be converted to a {@code BigDecimal} instance.
* @param mc
* rounding mode and precision for the result of this operation.
* @throws ArithmeticException
* if {@code mc.precision > 0} and {@code mc.roundingMode ==
* UNNECESSARY} and the new big decimal cannot be represented
* within the given precision without rounding.
*/
public BigDecimal(long val, MathContext mc) {
this(val);
inplaceRound(mc);
}
/* Public Methods */
/**
* Returns a new {@code BigDecimal} instance whose value is equal to {@code
* unscaledVal * 10-scale}). The scale of the result is {@code
* scale}, and its unscaled value is {@code unscaledVal}.
*/
public static BigDecimal valueOf(long unscaledVal, int scale) {
if (scale == 0) {
return valueOf(unscaledVal);
}
if ((unscaledVal == 0) && (scale >= 0)
&& (scale < ZERO_SCALED_BY.length)) {
return ZERO_SCALED_BY[scale];
}
return new BigDecimal(unscaledVal, scale);
}
/**
* Returns a new {@code BigDecimal} instance whose value is equal to {@code
* unscaledVal}. The scale of the result is {@code 0}, and its unscaled
* value is {@code unscaledVal}.
*
* @param unscaledVal
* value to be converted to a {@code BigDecimal}.
* @return {@code BigDecimal} instance with the value {@code unscaledVal}.
*/
public static BigDecimal valueOf(long unscaledVal) {
if ((unscaledVal >= 0) && (unscaledVal < BI_SCALED_BY_ZERO_LENGTH)) {
return BI_SCALED_BY_ZERO[(int)unscaledVal];
}
return new BigDecimal(unscaledVal,0);
}
/**
* Returns a new {@code BigDecimal} instance whose value is equal to {@code
* val}. The new decimal is constructed as if the {@code BigDecimal(String)}
* constructor is called with an argument which is equal to {@code
* Double.toString(val)}. For example, {@code valueOf("0.1")} is converted to
* (unscaled=1, scale=1), although the double {@code 0.1} cannot be
* represented exactly as a double value. In contrast to that, a new {@code
* BigDecimal(0.1)} instance has the value {@code
* 0.1000000000000000055511151231257827021181583404541015625} with an
* unscaled value {@code 1000000000000000055511151231257827021181583404541015625}
* and the scale {@code 55}.
*
* @param val
* double value to be converted to a {@code BigDecimal}.
* @return {@code BigDecimal} instance with the value {@code val}.
* @throws NumberFormatException
* if {@code val} is infinite or {@code val} is not a number
*/
public static BigDecimal valueOf(double val) {
if (Double.isInfinite(val) || Double.isNaN(val)) {
throw new NumberFormatException("Infinity or NaN: " + val);
}
return new BigDecimal(Double.toString(val));
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this + augend}.
* The scale of the result is the maximum of the scales of the two
* arguments.
*
* @param augend
* value to be added to {@code this}.
* @return {@code this + augend}.
* @throws NullPointerException
* if {@code augend == null}.
*/
public BigDecimal add(BigDecimal augend) {
int diffScale = this.scale - augend.scale;
// Fast return when some operand is zero
if (this.isZero()) {
if (diffScale <= 0) {
return augend;
}
if (augend.isZero()) {
return this;
}
} else if (augend.isZero()) {
if (diffScale >= 0) {
return this;
}
}
// Let be: this = [u1,s1] and augend = [u2,s2]
if (diffScale == 0) {
// case s1 == s2: [u1 + u2 , s1]
if (Math.max(this.bitLength, augend.bitLength) + 1 < 64) {
return valueOf(this.smallValue + augend.smallValue, this.scale);
}
return new BigDecimal(this.getUnscaledValue().add(augend.getUnscaledValue()), this.scale);
} else if (diffScale > 0) {
// case s1 > s2 : [(u1 + u2) * 10 ^ (s1 - s2) , s1]
return addAndMult10(this, augend, diffScale);
} else {// case s2 > s1 : [(u2 + u1) * 10 ^ (s2 - s1) , s2]
return addAndMult10(augend, this, -diffScale);
}
}
private static BigDecimal addAndMult10(BigDecimal thisValue,BigDecimal augend, int diffScale) {
if(diffScale < MathUtils.LONG_POWERS_OF_TEN.length &&
Math.max(thisValue.bitLength,augend.bitLength+LONG_POWERS_OF_TEN_BIT_LENGTH[diffScale])+1<64) {
return valueOf(thisValue.smallValue+augend.smallValue*MathUtils.LONG_POWERS_OF_TEN[diffScale],thisValue.scale);
} else {
BigInt bi = Multiplication.multiplyByTenPow(augend.getUnscaledValue(),diffScale).getBigInt();
bi.add(thisValue.getUnscaledValue().getBigInt());
return new BigDecimal(new BigInteger(bi), thisValue.scale);
}
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this + augend}.
* The result is rounded according to the passed context {@code mc}.
*
* @param augend
* value to be added to {@code this}.
* @param mc
* rounding mode and precision for the result of this operation.
* @return {@code this + augend}.
* @throws NullPointerException
* if {@code augend == null} or {@code mc == null}.
*/
public BigDecimal add(BigDecimal augend, MathContext mc) {
BigDecimal larger; // operand with the largest unscaled value
BigDecimal smaller; // operand with the smallest unscaled value
BigInteger tempBI;
long diffScale = (long)this.scale - augend.scale;
int largerSignum;
// Some operand is zero or the precision is infinity
if ((augend.isZero()) || (this.isZero())
|| (mc.getPrecision() == 0)) {
return add(augend).round(mc);
}
// Cases where there is room for optimizations
if (this.approxPrecision() < diffScale - 1) {
larger = augend;
smaller = this;
} else if (augend.approxPrecision() < -diffScale - 1) {
larger = this;
smaller = augend;
} else {// No optimization is done
return add(augend).round(mc);
}
if (mc.getPrecision() >= larger.approxPrecision()) {
// No optimization is done
return add(augend).round(mc);
}
// Cases where it's unnecessary to add two numbers with very different scales
largerSignum = larger.signum();
if (largerSignum == smaller.signum()) {
tempBI = Multiplication.multiplyByPositiveInt(larger.getUnscaledValue(),10)
.add(BigInteger.valueOf(largerSignum));
} else {
tempBI = larger.getUnscaledValue().subtract(
BigInteger.valueOf(largerSignum));
tempBI = Multiplication.multiplyByPositiveInt(tempBI,10)
.add(BigInteger.valueOf(largerSignum * 9));
}
// Rounding the improved adding
larger = new BigDecimal(tempBI, larger.scale + 1);
return larger.round(mc);
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this - subtrahend}.
* The scale of the result is the maximum of the scales of the two arguments.
*
* @param subtrahend
* value to be subtracted from {@code this}.
* @return {@code this - subtrahend}.
* @throws NullPointerException
* if {@code subtrahend == null}.
*/
public BigDecimal subtract(BigDecimal subtrahend) {
int diffScale = this.scale - subtrahend.scale;
// Fast return when some operand is zero
if (this.isZero()) {
if (diffScale <= 0) {
return subtrahend.negate();
}
if (subtrahend.isZero()) {
return this;
}
} else if (subtrahend.isZero()) {
if (diffScale >= 0) {
return this;
}
}
// Let be: this = [u1,s1] and subtrahend = [u2,s2] so:
if (diffScale == 0) {
// case s1 = s2 : [u1 - u2 , s1]
if (Math.max(this.bitLength, subtrahend.bitLength) + 1 < 64) {
return valueOf(this.smallValue - subtrahend.smallValue,this.scale);
}
return new BigDecimal(this.getUnscaledValue().subtract(subtrahend.getUnscaledValue()), this.scale);
} else if (diffScale > 0) {
// case s1 > s2 : [ u1 - u2 * 10 ^ (s1 - s2) , s1 ]
if(diffScale < MathUtils.LONG_POWERS_OF_TEN.length &&
Math.max(this.bitLength,subtrahend.bitLength+LONG_POWERS_OF_TEN_BIT_LENGTH[diffScale])+1<64) {
return valueOf(this.smallValue-subtrahend.smallValue*MathUtils.LONG_POWERS_OF_TEN[diffScale],this.scale);
}
return new BigDecimal(this.getUnscaledValue().subtract(
Multiplication.multiplyByTenPow(subtrahend.getUnscaledValue(),diffScale)), this.scale);
} else {// case s2 > s1 : [ u1 * 10 ^ (s2 - s1) - u2 , s2 ]
diffScale = -diffScale;
if(diffScale < MathUtils.LONG_POWERS_OF_TEN.length &&
Math.max(this.bitLength+LONG_POWERS_OF_TEN_BIT_LENGTH[diffScale],subtrahend.bitLength)+1<64) {
return valueOf(this.smallValue*MathUtils.LONG_POWERS_OF_TEN[diffScale]-subtrahend.smallValue,subtrahend.scale);
}
return new BigDecimal(Multiplication.multiplyByTenPow(this.getUnscaledValue(),diffScale)
.subtract(subtrahend.getUnscaledValue()), subtrahend.scale);
}
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this - subtrahend}.
* The result is rounded according to the passed context {@code mc}.
*
* @param subtrahend
* value to be subtracted from {@code this}.
* @param mc
* rounding mode and precision for the result of this operation.
* @return {@code this - subtrahend}.
* @throws NullPointerException
* if {@code subtrahend == null} or {@code mc == null}.
*/
public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) {
long diffScale = subtrahend.scale - (long)this.scale;
int thisSignum;
BigDecimal leftOperand; // it will be only the left operand (this)
BigInteger tempBI;
// Some operand is zero or the precision is infinity
if ((subtrahend.isZero()) || (this.isZero())
|| (mc.getPrecision() == 0)) {
return subtract(subtrahend).round(mc);
}
// Now: this != 0 and subtrahend != 0
if (subtrahend.approxPrecision() < diffScale - 1) {
// Cases where it is unnecessary to subtract two numbers with very different scales
if (mc.getPrecision() < this.approxPrecision()) {
thisSignum = this.signum();
if (thisSignum != subtrahend.signum()) {
tempBI = Multiplication.multiplyByPositiveInt(this.getUnscaledValue(), 10)
.add(BigInteger.valueOf(thisSignum));
} else {
tempBI = this.getUnscaledValue().subtract(BigInteger.valueOf(thisSignum));
tempBI = Multiplication.multiplyByPositiveInt(tempBI, 10)
.add(BigInteger.valueOf(thisSignum * 9));
}
// Rounding the improved subtracting
leftOperand = new BigDecimal(tempBI, this.scale + 1);
return leftOperand.round(mc);
}
}
// No optimization is done
return subtract(subtrahend).round(mc);
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this *
* multiplicand}. The scale of the result is the sum of the scales of the
* two arguments.
*
* @param multiplicand
* value to be multiplied with {@code this}.
* @return {@code this * multiplicand}.
* @throws NullPointerException
* if {@code multiplicand == null}.
*/
public BigDecimal multiply(BigDecimal multiplicand) {
long newScale = (long)this.scale + multiplicand.scale;
if ((this.isZero()) || (multiplicand.isZero())) {
return zeroScaledBy(newScale);
}
/* Let be: this = [u1,s1] and multiplicand = [u2,s2] so:
* this x multiplicand = [ s1 * s2 , s1 + s2 ] */
if(this.bitLength + multiplicand.bitLength < 64) {
return valueOf(this.smallValue*multiplicand.smallValue, safeLongToInt(newScale));
}
return new BigDecimal(this.getUnscaledValue().multiply(
multiplicand.getUnscaledValue()), safeLongToInt(newScale));
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this *
* multiplicand}. The result is rounded according to the passed context
* {@code mc}.
*
* @param multiplicand
* value to be multiplied with {@code this}.
* @param mc
* rounding mode and precision for the result of this operation.
* @return {@code this * multiplicand}.
* @throws NullPointerException
* if {@code multiplicand == null} or {@code mc == null}.
*/
public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) {
BigDecimal result = multiply(multiplicand);
result.inplaceRound(mc);
return result;
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this / divisor}.
* As scale of the result the parameter {@code scale} is used. If rounding
* is required to meet the specified scale, then the specified rounding mode
* {@code roundingMode} is applied.
*
* @param divisor
* value by which {@code this} is divided.
* @param scale
* the scale of the result returned.
* @param roundingMode
* rounding mode to be used to round the result.
* @return {@code this / divisor} rounded according to the given rounding
* mode.
* @throws NullPointerException
* if {@code divisor == null}.
* @throws IllegalArgumentException
* if {@code roundingMode} is not a valid rounding mode.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @throws ArithmeticException
* if {@code roundingMode == ROUND_UNNECESSARY} and rounding is
* necessary according to the given scale.
*/
public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) {
return divide(divisor, scale, RoundingMode.valueOf(roundingMode));
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this / divisor}.
* As scale of the result the parameter {@code scale} is used. If rounding
* is required to meet the specified scale, then the specified rounding mode
* {@code roundingMode} is applied.
*
* @param divisor
* value by which {@code this} is divided.
* @param scale
* the scale of the result returned.
* @param roundingMode
* rounding mode to be used to round the result.
* @return {@code this / divisor} rounded according to the given rounding
* mode.
* @throws NullPointerException
* if {@code divisor == null} or {@code roundingMode == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @throws ArithmeticException
* if {@code roundingMode == RoundingMode.UNNECESSAR}Y and
* rounding is necessary according to the given scale and given
* precision.
*/
public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) {
// Let be: this = [u1,s1] and divisor = [u2,s2]
if (roundingMode == null) {
throw new NullPointerException("roundingMode == null");
}
if (divisor.isZero()) {
throw new ArithmeticException("Division by zero");
}
long diffScale = ((long)this.scale - divisor.scale) - scale;
if(this.bitLength < 64 && divisor.bitLength < 64 ) {
if(diffScale == 0) {
return dividePrimitiveLongs(this.smallValue,
divisor.smallValue,
scale,
roundingMode );
} else if(diffScale > 0) {
if(diffScale < MathUtils.LONG_POWERS_OF_TEN.length &&
divisor.bitLength + LONG_POWERS_OF_TEN_BIT_LENGTH[(int)diffScale] < 64) {
return dividePrimitiveLongs(this.smallValue,
divisor.smallValue*MathUtils.LONG_POWERS_OF_TEN[(int)diffScale],
scale,
roundingMode);
}
} else { // diffScale < 0
if(-diffScale < MathUtils.LONG_POWERS_OF_TEN.length &&
this.bitLength + LONG_POWERS_OF_TEN_BIT_LENGTH[(int)-diffScale] < 64) {
return dividePrimitiveLongs(this.smallValue*MathUtils.LONG_POWERS_OF_TEN[(int)-diffScale],
divisor.smallValue,
scale,
roundingMode);
}
}
}
BigInteger scaledDividend = this.getUnscaledValue();
BigInteger scaledDivisor = divisor.getUnscaledValue(); // for scaling of 'u2'
if (diffScale > 0) {
// Multiply 'u2' by: 10^((s1 - s2) - scale)
scaledDivisor = Multiplication.multiplyByTenPow(scaledDivisor, (int)diffScale);
} else if (diffScale < 0) {
// Multiply 'u1' by: 10^(scale - (s1 - s2))
scaledDividend = Multiplication.multiplyByTenPow(scaledDividend, (int)-diffScale);
}
return divideBigIntegers(scaledDividend, scaledDivisor, scale, roundingMode);
}
private static BigDecimal divideBigIntegers(BigInteger scaledDividend, BigInteger scaledDivisor, int scale, RoundingMode roundingMode) {
BigInteger[] quotAndRem = scaledDividend.divideAndRemainder(scaledDivisor); // quotient and remainder
// If after division there is a remainder...
BigInteger quotient = quotAndRem[0];
BigInteger remainder = quotAndRem[1];
if (remainder.signum() == 0) {
return new BigDecimal(quotient, scale);
}
int sign = scaledDividend.signum() * scaledDivisor.signum();
int compRem; // 'compare to remainder'
if(scaledDivisor.bitLength() < 63) { // 63 in order to avoid out of long after *2
long rem = remainder.longValue();
long divisor = scaledDivisor.longValue();
compRem = longCompareTo(Math.abs(rem) * 2,Math.abs(divisor));
// To look if there is a carry
compRem = roundingBehavior(quotient.testBit(0) ? 1 : 0,
sign * (5 + compRem), roundingMode);
} else {
// Checking if: remainder * 2 >= scaledDivisor
compRem = remainder.abs().shiftLeftOneBit().compareTo(scaledDivisor.abs());
compRem = roundingBehavior(quotient.testBit(0) ? 1 : 0,
sign * (5 + compRem), roundingMode);
}
if (compRem != 0) {
if(quotient.bitLength() < 63) {
return valueOf(quotient.longValue() + compRem,scale);
}
quotient = quotient.add(BigInteger.valueOf(compRem));
return new BigDecimal(quotient, scale);
}
// Constructing the result with the appropriate unscaled value
return new BigDecimal(quotient, scale);
}
private static BigDecimal dividePrimitiveLongs(long scaledDividend, long scaledDivisor, int scale, RoundingMode roundingMode) {
long quotient = scaledDividend / scaledDivisor;
long remainder = scaledDividend % scaledDivisor;
int sign = Long.signum( scaledDividend ) * Long.signum( scaledDivisor );
if (remainder != 0) {
// Checking if: remainder * 2 >= scaledDivisor
int compRem; // 'compare to remainder'
compRem = longCompareTo(Math.abs(remainder) * 2,Math.abs(scaledDivisor));
// To look if there is a carry
quotient += roundingBehavior(((int)quotient) & 1,
sign * (5 + compRem),
roundingMode);
}
// Constructing the result with the appropriate unscaled value
return valueOf(quotient, scale);
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this / divisor}.
* The scale of the result is the scale of {@code this}. If rounding is
* required to meet the specified scale, then the specified rounding mode
* {@code roundingMode} is applied.
*
* @param divisor
* value by which {@code this} is divided.
* @param roundingMode
* rounding mode to be used to round the result.
* @return {@code this / divisor} rounded according to the given rounding
* mode.
* @throws NullPointerException
* if {@code divisor == null}.
* @throws IllegalArgumentException
* if {@code roundingMode} is not a valid rounding mode.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @throws ArithmeticException
* if {@code roundingMode == ROUND_UNNECESSARY} and rounding is
* necessary according to the scale of this.
*/
public BigDecimal divide(BigDecimal divisor, int roundingMode) {
return divide(divisor, scale, RoundingMode.valueOf(roundingMode));
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this / divisor}.
* The scale of the result is the scale of {@code this}. If rounding is
* required to meet the specified scale, then the specified rounding mode
* {@code roundingMode} is applied.
*
* @param divisor
* value by which {@code this} is divided.
* @param roundingMode
* rounding mode to be used to round the result.
* @return {@code this / divisor} rounded according to the given rounding
* mode.
* @throws NullPointerException
* if {@code divisor == null} or {@code roundingMode == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @throws ArithmeticException
* if {@code roundingMode == RoundingMode.UNNECESSARY} and
* rounding is necessary according to the scale of this.
*/
public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) {
return divide(divisor, scale, roundingMode);
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this / divisor}.
* The scale of the result is the difference of the scales of {@code this}
* and {@code divisor}. If the exact result requires more digits, then the
* scale is adjusted accordingly. For example, {@code 1/128 = 0.0078125}
* which has a scale of {@code 7} and precision {@code 5}.
*
* @param divisor
* value by which {@code this} is divided.
* @return {@code this / divisor}.
* @throws NullPointerException
* if {@code divisor == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @throws ArithmeticException
* if the result cannot be represented exactly.
*/
public BigDecimal divide(BigDecimal divisor) {
BigInteger p = this.getUnscaledValue();
BigInteger q = divisor.getUnscaledValue();
BigInteger gcd; // greatest common divisor between 'p' and 'q'
BigInteger quotAndRem[];
long diffScale = (long)scale - divisor.scale;
int newScale; // the new scale for final quotient
int k; // number of factors "2" in 'q'
int l = 0; // number of factors "5" in 'q'
int i = 1;
int lastPow = FIVE_POW.length - 1;
if (divisor.isZero()) {
throw new ArithmeticException("Division by zero");
}
if (p.signum() == 0) {
return zeroScaledBy(diffScale);
}
// To divide both by the GCD
gcd = p.gcd(q);
p = p.divide(gcd);
q = q.divide(gcd);
// To simplify all "2" factors of q, dividing by 2^k
k = q.getLowestSetBit();
q = q.shiftRight(k);
// To simplify all "5" factors of q, dividing by 5^l
do {
quotAndRem = q.divideAndRemainder(FIVE_POW[i]);
if (quotAndRem[1].signum() == 0) {
l += i;
if (i < lastPow) {
i++;
}
q = quotAndRem[0];
} else {
if (i == 1) {
break;
}
i = 1;
}
} while (true);
// If abs(q) != 1 then the quotient is periodic
if (!q.abs().equals(BigInteger.ONE)) {
throw new ArithmeticException("Non-terminating decimal expansion; no exact representable decimal result");
}
// The sign of the is fixed and the quotient will be saved in 'p'
if (q.signum() < 0) {
p = p.negate();
}
// Checking if the new scale is out of range
newScale = safeLongToInt(diffScale + Math.max(k, l));
// k >= 0 and l >= 0 implies that k - l is in the 32-bit range
i = k - l;
p = (i > 0) ? Multiplication.multiplyByFivePow(p, i)
: p.shiftLeft(-i);
return new BigDecimal(p, newScale);
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this / divisor}.
* The result is rounded according to the passed context {@code mc}. If the
* passed math context specifies precision {@code 0}, then this call is
* equivalent to {@code this.divide(divisor)}.
*
* @param divisor
* value by which {@code this} is divided.
* @param mc
* rounding mode and precision for the result of this operation.
* @return {@code this / divisor}.
* @throws NullPointerException
* if {@code divisor == null} or {@code mc == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @throws ArithmeticException
* if {@code mc.getRoundingMode() == UNNECESSARY} and rounding
* is necessary according {@code mc.getPrecision()}.
*/
public BigDecimal divide(BigDecimal divisor, MathContext mc) {
/* Calculating how many zeros must be append to 'dividend'
* to obtain a quotient with at least 'mc.precision()' digits */
long trailingZeros = mc.getPrecision() + 2L
+ divisor.approxPrecision() - approxPrecision();
long diffScale = (long)scale - divisor.scale;
long newScale = diffScale; // scale of the final quotient
int compRem; // to compare the remainder
int i = 1; // index
int lastPow = TEN_POW.length - 1; // last power of ten
BigInteger integerQuot; // for temporal results
BigInteger quotAndRem[] = {getUnscaledValue()};
// In special cases it reduces the problem to call the dual method
if ((mc.getPrecision() == 0) || (this.isZero())
|| (divisor.isZero())) {
return this.divide(divisor);
}
if (trailingZeros > 0) {
// To append trailing zeros at end of dividend
quotAndRem[0] = getUnscaledValue().multiply( Multiplication.powerOf10(trailingZeros) );
newScale += trailingZeros;
}
quotAndRem = quotAndRem[0].divideAndRemainder( divisor.getUnscaledValue() );
integerQuot = quotAndRem[0];
// Calculating the exact quotient with at least 'mc.precision()' digits
if (quotAndRem[1].signum() != 0) {
// Checking if: 2 * remainder >= divisor ?
compRem = quotAndRem[1].shiftLeftOneBit().compareTo( divisor.getUnscaledValue() );
// quot := quot * 10 + r; with 'r' in {-6,-5,-4, 0,+4,+5,+6}
integerQuot = integerQuot.multiply(BigInteger.TEN)
.add(BigInteger.valueOf(quotAndRem[0].signum() * (5 + compRem)));
newScale++;
} else {
// To strip trailing zeros until the preferred scale is reached
while (!integerQuot.testBit(0)) {
quotAndRem = integerQuot.divideAndRemainder(TEN_POW[i]);
if ((quotAndRem[1].signum() == 0)
&& (newScale - i >= diffScale)) {
newScale -= i;
if (i < lastPow) {
i++;
}
integerQuot = quotAndRem[0];
} else {
if (i == 1) {
break;
}
i = 1;
}
}
}
// To perform rounding
return new BigDecimal(integerQuot, safeLongToInt(newScale), mc);
}
/**
* Returns a new {@code BigDecimal} whose value is the integral part of
* {@code this / divisor}. The quotient is rounded down towards zero to the
* next integer. For example, {@code 0.5/0.2 = 2}.
*
* @param divisor
* value by which {@code this} is divided.
* @return integral part of {@code this / divisor}.
* @throws NullPointerException
* if {@code divisor == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
*/
public BigDecimal divideToIntegralValue(BigDecimal divisor) {
BigInteger integralValue; // the integer of result
BigInteger powerOfTen; // some power of ten
BigInteger quotAndRem[] = {getUnscaledValue()};
long newScale = (long)this.scale - divisor.scale;
long tempScale = 0;
int i = 1;
int lastPow = TEN_POW.length - 1;
if (divisor.isZero()) {
throw new ArithmeticException("Division by zero");
}
if ((divisor.approxPrecision() + newScale > this.approxPrecision() + 1L)
|| (this.isZero())) {
/* If the divisor's integer part is greater than this's integer part,
* the result must be zero with the appropriate scale */
integralValue = BigInteger.ZERO;
} else if (newScale == 0) {
integralValue = getUnscaledValue().divide( divisor.getUnscaledValue() );
} else if (newScale > 0) {
powerOfTen = Multiplication.powerOf10(newScale);
integralValue = getUnscaledValue().divide( divisor.getUnscaledValue().multiply(powerOfTen) );
integralValue = integralValue.multiply(powerOfTen);
} else {// (newScale < 0)
powerOfTen = Multiplication.powerOf10(-newScale);
integralValue = getUnscaledValue().multiply(powerOfTen).divide( divisor.getUnscaledValue() );
// To strip trailing zeros approximating to the preferred scale
while (!integralValue.testBit(0)) {
quotAndRem = integralValue.divideAndRemainder(TEN_POW[i]);
if ((quotAndRem[1].signum() == 0)
&& (tempScale - i >= newScale)) {
tempScale -= i;
if (i < lastPow) {
i++;
}
integralValue = quotAndRem[0];
} else {
if (i == 1) {
break;
}
i = 1;
}
}
newScale = tempScale;
}
return ((integralValue.signum() == 0)
? zeroScaledBy(newScale)
: new BigDecimal(integralValue, safeLongToInt(newScale)));
}
/**
* Returns a new {@code BigDecimal} whose value is the integral part of
* {@code this / divisor}. The quotient is rounded down towards zero to the
* next integer. The rounding mode passed with the parameter {@code mc} is
* not considered. But if the precision of {@code mc > 0} and the integral
* part requires more digits, then an {@code ArithmeticException} is thrown.
*
* @param divisor
* value by which {@code this} is divided.
* @param mc
* math context which determines the maximal precision of the
* result.
* @return integral part of {@code this / divisor}.
* @throws NullPointerException
* if {@code divisor == null} or {@code mc == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @throws ArithmeticException
* if {@code mc.getPrecision() > 0} and the result requires more
* digits to be represented.
*/
public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) {
int mcPrecision = mc.getPrecision();
int diffPrecision = this.precision() - divisor.precision();
int lastPow = TEN_POW.length - 1;
long diffScale = (long)this.scale - divisor.scale;
long newScale = diffScale;
long quotPrecision = diffPrecision - diffScale + 1;
BigInteger quotAndRem[] = new BigInteger[2];
// In special cases it call the dual method
if ((mcPrecision == 0) || (this.isZero()) || (divisor.isZero())) {
return this.divideToIntegralValue(divisor);
}
// Let be: this = [u1,s1] and divisor = [u2,s2]
if (quotPrecision <= 0) {
quotAndRem[0] = BigInteger.ZERO;
} else if (diffScale == 0) {
// CASE s1 == s2: to calculate u1 / u2
quotAndRem[0] = this.getUnscaledValue().divide( divisor.getUnscaledValue() );
} else if (diffScale > 0) {
// CASE s1 >= s2: to calculate u1 / (u2 * 10^(s1-s2)
quotAndRem[0] = this.getUnscaledValue().divide(
divisor.getUnscaledValue().multiply(Multiplication.powerOf10(diffScale)) );
// To chose 10^newScale to get a quotient with at least 'mc.precision()' digits
newScale = Math.min(diffScale, Math.max(mcPrecision - quotPrecision + 1, 0));
// To calculate: (u1 / (u2 * 10^(s1-s2)) * 10^newScale
quotAndRem[0] = quotAndRem[0].multiply(Multiplication.powerOf10(newScale));
} else {// CASE s2 > s1:
/* To calculate the minimum power of ten, such that the quotient
* (u1 * 10^exp) / u2 has at least 'mc.precision()' digits. */
long exp = Math.min(-diffScale, Math.max((long)mcPrecision - diffPrecision, 0));
long compRemDiv;
// Let be: (u1 * 10^exp) / u2 = [q,r]
quotAndRem = this.getUnscaledValue().multiply(Multiplication.powerOf10(exp)).
divideAndRemainder(divisor.getUnscaledValue());
newScale += exp; // To fix the scale
exp = -newScale; // The remaining power of ten
// If after division there is a remainder...
if ((quotAndRem[1].signum() != 0) && (exp > 0)) {
// Log10(r) + ((s2 - s1) - exp) > mc.precision ?
compRemDiv = (new BigDecimal(quotAndRem[1])).precision()
+ exp - divisor.precision();
if (compRemDiv == 0) {
// To calculate: (r * 10^exp2) / u2
quotAndRem[1] = quotAndRem[1].multiply(Multiplication.powerOf10(exp)).
divide(divisor.getUnscaledValue());
compRemDiv = Math.abs(quotAndRem[1].signum());
}
if (compRemDiv > 0) {
throw new ArithmeticException("Division impossible");
}
}
}
// Fast return if the quotient is zero
if (quotAndRem[0].signum() == 0) {
return zeroScaledBy(diffScale);
}
BigInteger strippedBI = quotAndRem[0];
BigDecimal integralValue = new BigDecimal(quotAndRem[0]);
long resultPrecision = integralValue.precision();
int i = 1;
// To strip trailing zeros until the specified precision is reached
while (!strippedBI.testBit(0)) {
quotAndRem = strippedBI.divideAndRemainder(TEN_POW[i]);
if ((quotAndRem[1].signum() == 0) &&
((resultPrecision - i >= mcPrecision)
|| (newScale - i >= diffScale)) ) {
resultPrecision -= i;
newScale -= i;
if (i < lastPow) {
i++;
}
strippedBI = quotAndRem[0];
} else {
if (i == 1) {
break;
}
i = 1;
}
}
// To check if the result fit in 'mc.precision()' digits
if (resultPrecision > mcPrecision) {
throw new ArithmeticException("Division impossible");
}
integralValue.scale = safeLongToInt(newScale);
integralValue.setUnscaledValue(strippedBI);
return integralValue;
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this % divisor}.
*
* The remainder is defined as {@code this -
* this.divideToIntegralValue(divisor) * divisor}.
*
* @param divisor
* value by which {@code this} is divided.
* @return {@code this % divisor}.
* @throws NullPointerException
* if {@code divisor == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
*/
public BigDecimal remainder(BigDecimal divisor) {
return divideAndRemainder(divisor)[1];
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this % divisor}.
*
* The remainder is defined as {@code this -
* this.divideToIntegralValue(divisor) * divisor}.
*
* The specified rounding mode {@code mc} is used for the division only.
*
* @param divisor
* value by which {@code this} is divided.
* @param mc
* rounding mode and precision to be used.
* @return {@code this % divisor}.
* @throws NullPointerException
* if {@code divisor == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @throws ArithmeticException
* if {@code mc.getPrecision() > 0} and the result of {@code
* this.divideToIntegralValue(divisor, mc)} requires more digits
* to be represented.
*/
public BigDecimal remainder(BigDecimal divisor, MathContext mc) {
return divideAndRemainder(divisor, mc)[1];
}
/**
* Returns a {@code BigDecimal} array which contains the integral part of
* {@code this / divisor} at index 0 and the remainder {@code this %
* divisor} at index 1. The quotient is rounded down towards zero to the
* next integer.
*
* @param divisor
* value by which {@code this} is divided.
* @return {@code [this.divideToIntegralValue(divisor),
* this.remainder(divisor)]}.
* @throws NullPointerException
* if {@code divisor == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @see #divideToIntegralValue
* @see #remainder
*/
public BigDecimal[] divideAndRemainder(BigDecimal divisor) {
BigDecimal quotAndRem[] = new BigDecimal[2];
quotAndRem[0] = this.divideToIntegralValue(divisor);
quotAndRem[1] = this.subtract( quotAndRem[0].multiply(divisor) );
return quotAndRem;
}
/**
* Returns a {@code BigDecimal} array which contains the integral part of
* {@code this / divisor} at index 0 and the remainder {@code this %
* divisor} at index 1. The quotient is rounded down towards zero to the
* next integer. The rounding mode passed with the parameter {@code mc} is
* not considered. But if the precision of {@code mc > 0} and the integral
* part requires more digits, then an {@code ArithmeticException} is thrown.
*
* @param divisor
* value by which {@code this} is divided.
* @param mc
* math context which determines the maximal precision of the
* result.
* @return {@code [this.divideToIntegralValue(divisor),
* this.remainder(divisor)]}.
* @throws NullPointerException
* if {@code divisor == null}.
* @throws ArithmeticException
* if {@code divisor == 0}.
* @see #divideToIntegralValue
* @see #remainder
*/
public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) {
BigDecimal quotAndRem[] = new BigDecimal[2];
quotAndRem[0] = this.divideToIntegralValue(divisor, mc);
quotAndRem[1] = this.subtract( quotAndRem[0].multiply(divisor) );
return quotAndRem;
}
/**
* Returns a new {@code BigDecimal} whose value is {@code thisn}. The
* scale of the result is {@code n * this.scale()}.
*
* {@code x.pow(0)} returns {@code 1}, even if {@code x == 0}.
*
* Implementation Note: The implementation is based on the ANSI standard
* X3.274-1996 algorithm.
*
* @throws ArithmeticException
* if {@code n < 0} or {@code n > 999999999}.
*/
public BigDecimal pow(int n) {
if (n == 0) {
return ONE;
}
if ((n < 0) || (n > 999999999)) {
throw new ArithmeticException("Invalid operation");
}
long newScale = scale * (long)n;
// Let be: this = [u,s] so: this^n = [u^n, s*n]
return isZero() ? zeroScaledBy(newScale)
: new BigDecimal(getUnscaledValue().pow(n), safeLongToInt(newScale));
}
/**
* Returns a new {@code BigDecimal} whose value is {@code thisn}. The
* result is rounded according to the passed context {@code mc}.
*
* Implementation Note: The implementation is based on the ANSI standard
* X3.274-1996 algorithm.
*
* @param mc
* rounding mode and precision for the result of this operation.
* @throws ArithmeticException
* if {@code n < 0} or {@code n > 999999999}.
*/
public BigDecimal pow(int n, MathContext mc) {
// The ANSI standard X3.274-1996 algorithm
int m = Math.abs(n);
int mcPrecision = mc.getPrecision();
int elength = (int)Math.log10(m) + 1; // decimal digits in 'n'
int oneBitMask; // mask of bits
BigDecimal accum; // the single accumulator
MathContext newPrecision = mc; // MathContext by default
// In particular cases, it reduces the problem to call the other 'pow()'
if ((n == 0) || ((isZero()) && (n > 0))) {
return pow(n);
}
if ((m > 999999999) || ((mcPrecision == 0) && (n < 0))
|| ((mcPrecision > 0) && (elength > mcPrecision))) {
throw new ArithmeticException("Invalid operation");
}
if (mcPrecision > 0) {
newPrecision = new MathContext( mcPrecision + elength + 1,
mc.getRoundingMode());
}
// The result is calculated as if 'n' were positive
accum = round(newPrecision);
oneBitMask = Integer.highestOneBit(m) >> 1;
while (oneBitMask > 0) {
accum = accum.multiply(accum, newPrecision);
if ((m & oneBitMask) == oneBitMask) {
accum = accum.multiply(this, newPrecision);
}
oneBitMask >>= 1;
}
// If 'n' is negative, the value is divided into 'ONE'
if (n < 0) {
accum = ONE.divide(accum, newPrecision);
}
// The final value is rounded to the destination precision
accum.inplaceRound(mc);
return accum;
}
/**
* Returns a {@code BigDecimal} whose value is the absolute value of
* {@code this}. The scale of the result is the same as the scale of this.
*/
public BigDecimal abs() {
return ((signum() < 0) ? negate() : this);
}
/**
* Returns a {@code BigDecimal} whose value is the absolute value of
* {@code this}. The result is rounded according to the passed context
* {@code mc}.
*/
public BigDecimal abs(MathContext mc) {
BigDecimal result = (signum() < 0) ? negate() : new BigDecimal(getUnscaledValue(), scale);
result.inplaceRound(mc);
return result;
}
/**
* Returns a new {@code BigDecimal} whose value is the {@code -this}. The
* scale of the result is the same as the scale of this.
*
* @return {@code -this}
*/
public BigDecimal negate() {
if(bitLength < 63 || (bitLength == 63 && smallValue!=Long.MIN_VALUE)) {
return valueOf(-smallValue,scale);
}
return new BigDecimal(getUnscaledValue().negate(), scale);
}
/**
* Returns a new {@code BigDecimal} whose value is the {@code -this}. The
* result is rounded according to the passed context {@code mc}.
*
* @param mc
* rounding mode and precision for the result of this operation.
* @return {@code -this}
*/
public BigDecimal negate(MathContext mc) {
BigDecimal result = negate();
result.inplaceRound(mc);
return result;
}
/**
* Returns a new {@code BigDecimal} whose value is {@code +this}. The scale
* of the result is the same as the scale of this.
*
* @return {@code this}
*/
public BigDecimal plus() {
return this;
}
/**
* Returns a new {@code BigDecimal} whose value is {@code +this}. The result
* is rounded according to the passed context {@code mc}.
*
* @param mc
* rounding mode and precision for the result of this operation.
* @return {@code this}, rounded
*/
public BigDecimal plus(MathContext mc) {
return round(mc);
}
/**
* Returns the sign of this {@code BigDecimal}.
*
* @return {@code -1} if {@code this < 0},
* {@code 0} if {@code this == 0},
* {@code 1} if {@code this > 0}.
*/
public int signum() {
if( bitLength < 64) {
return Long.signum( this.smallValue );
}
return getUnscaledValue().signum();
}
private boolean isZero() {
//Watch out: -1 has a bitLength=0
return bitLength == 0 && this.smallValue != -1;
}
/**
* Returns the scale of this {@code BigDecimal}. The scale is the number of
* digits behind the decimal point. The value of this {@code BigDecimal} is
* the {@code unsignedValue * 10-scale}. If the scale is negative,
* then this {@code BigDecimal} represents a big integer.
*
* @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 decimal digits used to represent this decimal. It is equivalent
* to the number of digits of the unscaled value. The precision of {@code 0}
* is {@code 1} (independent of the scale).
*
* @return the precision of this {@code BigDecimal}.
*/
public int precision() {
// Return the cached value if we have one.
if (precision != 0) {
return precision;
}
if (bitLength == 0) {
precision = 1;
} else if (bitLength < 64) {
precision = decimalDigitsInLong(smallValue);
} else {
int decimalDigits = 1 + (int) ((bitLength - 1) * LOG10_2);
// If after division the number isn't zero, there exists an additional digit
if (getUnscaledValue().divide(Multiplication.powerOf10(decimalDigits)).signum() != 0) {
decimalDigits++;
}
precision = decimalDigits;
}
return precision;
}
private int decimalDigitsInLong(long value) {
if (value == Long.MIN_VALUE) {
return 19; // special case required because abs(MIN_VALUE) == MIN_VALUE
} else {
int index = Arrays.binarySearch(MathUtils.LONG_POWERS_OF_TEN, Math.abs(value));
return (index < 0) ? (-index - 1) : (index + 1);
}
}
/**
* Returns the unscaled value (mantissa) of this {@code BigDecimal} instance
* as a {@code BigInteger}. The unscaled value can be computed as
* {@code this * 10scale}.
*/
public BigInteger unscaledValue() {
return getUnscaledValue();
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this}, rounded
* according to the passed context {@code mc}.
*
* If {@code mc.precision = 0}, then no rounding is performed.
*
* If {@code mc.precision > 0} and {@code mc.roundingMode == UNNECESSARY},
* then an {@code ArithmeticException} is thrown if the result cannot be
* represented exactly within the given precision.
*
* @param mc
* rounding mode and precision for the result of this operation.
* @return {@code this} rounded according to the passed context.
* @throws ArithmeticException
* if {@code mc.precision > 0} and {@code mc.roundingMode ==
* UNNECESSARY} and this cannot be represented within the given
* precision.
*/
public BigDecimal round(MathContext mc) {
BigDecimal thisBD = new BigDecimal(getUnscaledValue(), scale);
thisBD.inplaceRound(mc);
return thisBD;
}
/**
* Returns a new {@code BigDecimal} instance with the specified scale.
*
* If the new scale is greater than the old scale, then additional zeros are
* added to the unscaled value. In this case no rounding is necessary.
*
* If the new scale is smaller than the old scale, then trailing digits are
* removed. If these trailing digits are not zero, then the remaining
* unscaled value has to be rounded. For this rounding operation the
* specified rounding mode is used.
*
* @param newScale
* scale of the result returned.
* @param roundingMode
* rounding mode to be used to round the result.
* @return a new {@code BigDecimal} instance with the specified scale.
* @throws NullPointerException
* if {@code roundingMode == null}.
* @throws ArithmeticException
* if {@code roundingMode == ROUND_UNNECESSARY} and rounding is
* necessary according to the given scale.
*/
public BigDecimal setScale(int newScale, RoundingMode roundingMode) {
if (roundingMode == null) {
throw new NullPointerException("roundingMode == null");
}
long diffScale = newScale - (long)scale;
// Let be: 'this' = [u,s]
if(diffScale == 0) {
return this;
}
if(diffScale > 0) {
// return [u * 10^(s2 - s), newScale]
if(diffScale < MathUtils.LONG_POWERS_OF_TEN.length &&
(this.bitLength + LONG_POWERS_OF_TEN_BIT_LENGTH[(int)diffScale]) < 64 ) {
return valueOf(this.smallValue*MathUtils.LONG_POWERS_OF_TEN[(int)diffScale],newScale);
}
return new BigDecimal(Multiplication.multiplyByTenPow(getUnscaledValue(),(int)diffScale), newScale);
}
// diffScale < 0
// return [u,s] / [1,newScale] with the appropriate scale and rounding
if(this.bitLength < 64 && -diffScale < MathUtils.LONG_POWERS_OF_TEN.length) {
return dividePrimitiveLongs(this.smallValue, MathUtils.LONG_POWERS_OF_TEN[(int)-diffScale], newScale,roundingMode);
}
return divideBigIntegers(this.getUnscaledValue(),Multiplication.powerOf10(-diffScale),newScale,roundingMode);
}
/**
* Returns a new {@code BigDecimal} instance with the specified scale.
*
* If the new scale is greater than the old scale, then additional zeros are
* added to the unscaled value. In this case no rounding is necessary.
*
* If the new scale is smaller than the old scale, then trailing digits are
* removed. If these trailing digits are not zero, then the remaining
* unscaled value has to be rounded. For this rounding operation the
* specified rounding mode is used.
*
* @param newScale
* scale of the result returned.
* @param roundingMode
* rounding mode to be used to round the result.
* @return a new {@code BigDecimal} instance with the specified scale.
* @throws IllegalArgumentException
* if {@code roundingMode} is not a valid rounding mode.
* @throws ArithmeticException
* if {@code roundingMode == ROUND_UNNECESSARY} and rounding is
* necessary according to the given scale.
*/
public BigDecimal setScale(int newScale, int roundingMode) {
return setScale(newScale, RoundingMode.valueOf(roundingMode));
}
/**
* Returns a new {@code BigDecimal} instance with the specified scale. If
* the new scale is greater than the old scale, then additional zeros are
* added to the unscaled value. If the new scale is smaller than the old
* scale, then trailing zeros are removed. If the trailing digits are not
* zeros then an ArithmeticException is thrown.
*
* If no exception is thrown, then the following equation holds: {@code
* x.setScale(s).compareTo(x) == 0}.
*
* @param newScale
* scale of the result returned.
* @return a new {@code BigDecimal} instance with the specified scale.
* @throws ArithmeticException
* if rounding would be necessary.
*/
public BigDecimal setScale(int newScale) {
return setScale(newScale, RoundingMode.UNNECESSARY);
}
/**
* Returns a new {@code BigDecimal} instance where the decimal point has
* been moved {@code n} places to the left. If {@code n < 0} then the
* decimal point is moved {@code -n} places to the right.
*
* The result is obtained by changing its scale. If the scale of the result
* becomes negative, then its precision is increased such that the scale is
* zero.
*
* Note, that {@code movePointLeft(0)} returns a result which is
* mathematically equivalent, but which has {@code scale >= 0}.
*/
public BigDecimal movePointLeft(int n) {
return movePoint(scale + (long)n);
}
private BigDecimal movePoint(long newScale) {
if (isZero()) {
return zeroScaledBy(Math.max(newScale, 0));
}
/*
* When: 'n'== Integer.MIN_VALUE isn't possible to call to
* movePointRight(-n) since -Integer.MIN_VALUE == Integer.MIN_VALUE
*/
if(newScale >= 0) {
if(bitLength < 64) {
return valueOf(smallValue, safeLongToInt(newScale));
}
return new BigDecimal(getUnscaledValue(), safeLongToInt(newScale));
}
if(-newScale < MathUtils.LONG_POWERS_OF_TEN.length &&
bitLength + LONG_POWERS_OF_TEN_BIT_LENGTH[(int)-newScale] < 64 ) {
return valueOf(smallValue*MathUtils.LONG_POWERS_OF_TEN[(int)-newScale],0);
}
return new BigDecimal(Multiplication.multiplyByTenPow(
getUnscaledValue(), safeLongToInt(-newScale)), 0);
}
/**
* Returns a new {@code BigDecimal} instance where the decimal point has
* been moved {@code n} places to the right. If {@code n < 0} then the
* decimal point is moved {@code -n} places to the left.
*
* The result is obtained by changing its scale. If the scale of the result
* becomes negative, then its precision is increased such that the scale is
* zero.
*
* Note, that {@code movePointRight(0)} returns a result which is
* mathematically equivalent, but which has scale >= 0.
*/
public BigDecimal movePointRight(int n) {
return movePoint(scale - (long)n);
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this * 10n}.
* The scale of the result is {@code this.scale()} - {@code n}.
* The precision of the result is the precision of {@code this}.
*
* This method has the same effect as {@link #movePointRight}, except that
* the precision is not changed.
*/
public BigDecimal scaleByPowerOfTen(int n) {
long newScale = scale - (long)n;
if(bitLength < 64) {
//Taking care when a 0 is to be scaled
if( smallValue==0 ){
return zeroScaledBy( newScale );
}
return valueOf(smallValue, safeLongToInt(newScale));
}
return new BigDecimal(getUnscaledValue(), safeLongToInt(newScale));
}
/**
* Returns a new {@code BigDecimal} instance with the same value as {@code
* this} but with a unscaled value where the trailing zeros have been
* removed. If the unscaled value of {@code this} has n trailing zeros, then
* the scale and the precision of the result has been reduced by n.
*
* @return a new {@code BigDecimal} instance equivalent to this where the
* trailing zeros of the unscaled value have been removed.
*/
public BigDecimal stripTrailingZeros() {
int i = 1; // 1 <= i <= 18
int lastPow = TEN_POW.length - 1;
long newScale = scale;
if (isZero()) {
// Preserve RI compatibility, so BigDecimal.equals (which checks
// value *and* scale) continues to work.
return this;
}
BigInteger strippedBI = getUnscaledValue();
BigInteger[] quotAndRem;
// while the number is even...
while (!strippedBI.testBit(0)) {
// To divide by 10^i
quotAndRem = strippedBI.divideAndRemainder(TEN_POW[i]);
// To look the remainder
if (quotAndRem[1].signum() == 0) {
// To adjust the scale
newScale -= i;
if (i < lastPow) {
// To set to the next power
i++;
}
strippedBI = quotAndRem[0];
} else {
if (i == 1) {
// 'this' has no more trailing zeros
break;
}
// To set to the smallest power of ten
i = 1;
}
}
return new BigDecimal(strippedBI, safeLongToInt(newScale));
}
/**
* Compares this {@code BigDecimal} with {@code val}. Returns one of the
* three values {@code 1}, {@code 0}, or {@code -1}. The method behaves as
* if {@code this.subtract(val)} is computed. If this difference is > 0 then
* 1 is returned, if the difference is < 0 then -1 is returned, and if the
* difference is 0 then 0 is returned. This means, that if two decimal
* instances are compared which are equal in value but differ in scale, then
* these two instances are considered as equal.
*
* @param val
* value to be compared with {@code this}.
* @return {@code 1} if {@code this > val}, {@code -1} if {@code this < val},
* {@code 0} if {@code this == val}.
* @throws NullPointerException
* if {@code val == null}.
*/
public int compareTo(BigDecimal val) {
int thisSign = signum();
int valueSign = val.signum();
if( thisSign == valueSign) {
if(this.scale == val.scale && this.bitLength<64 && val.bitLength<64 ) {
return (smallValue < val.smallValue) ? -1 : (smallValue > val.smallValue) ? 1 : 0;
}
long diffScale = (long)this.scale - val.scale;
int diffPrecision = this.approxPrecision() - val.approxPrecision();
if (diffPrecision > diffScale + 1) {
return thisSign;
} else if (diffPrecision < diffScale - 1) {
return -thisSign;
} else {// thisSign == val.signum() and diffPrecision is aprox. diffScale
BigInteger thisUnscaled = this.getUnscaledValue();
BigInteger valUnscaled = val.getUnscaledValue();
// If any of both precision is bigger, append zeros to the shorter one
if (diffScale < 0) {
thisUnscaled = thisUnscaled.multiply(Multiplication.powerOf10(-diffScale));
} else if (diffScale > 0) {
valUnscaled = valUnscaled.multiply(Multiplication.powerOf10(diffScale));
}
return thisUnscaled.compareTo(valUnscaled);
}
} else if (thisSign < valueSign) {
return -1;
} else {
return 1;
}
}
/**
* Returns {@code true} if {@code x} is a {@code BigDecimal} instance and if
* this instance is equal to this big decimal. Two big decimals are equal if
* their unscaled value and their scale is equal. For example, 1.0
* (10*10-1) is not equal to 1.00 (100*10-2). Similarly, zero
* instances are not equal if their scale differs.
*/
@Override
public boolean equals(Object x) {
if (this == x) {
return true;
}
if (x instanceof BigDecimal) {
BigDecimal x1 = (BigDecimal) x;
return x1.scale == scale
&& (bitLength < 64 ? (x1.smallValue == smallValue)
: intVal.equals(x1.intVal));
}
return false;
}
/**
* Returns the minimum of this {@code BigDecimal} and {@code val}.
*
* @param val
* value to be used to compute the minimum with this.
* @return {@code min(this, val}.
* @throws NullPointerException
* if {@code val == null}.
*/
public BigDecimal min(BigDecimal val) {
return ((compareTo(val) <= 0) ? this : val);
}
/**
* Returns the maximum of this {@code BigDecimal} and {@code val}.
*
* @param val
* value to be used to compute the maximum with this.
* @return {@code max(this, val}.
* @throws NullPointerException
* if {@code val == null}.
*/
public BigDecimal max(BigDecimal val) {
return ((compareTo(val) >= 0) ? this : val);
}
/**
* Returns a hash code for this {@code BigDecimal}.
*
* @return hash code for {@code this}.
*/
@Override
public int hashCode() {
if (hashCode != 0) {
return hashCode;
}
if (bitLength < 64) {
hashCode = (int)(smallValue & 0xffffffff);
hashCode = 33 * hashCode + (int)((smallValue >> 32) & 0xffffffff);
hashCode = 17 * hashCode + scale;
return hashCode;
}
hashCode = 17 * intVal.hashCode() + scale;
return hashCode;
}
/**
* Returns a canonical string representation of this {@code BigDecimal}. If
* necessary, scientific notation is used. This representation always prints
* all significant digits of this value.
*
* If the scale is negative or if {@code scale - precision >= 6} then
* scientific notation is used.
*
* @return a string representation of {@code this} in scientific notation if
* necessary.
*/
@Override
public String toString() {
if (toStringImage != null) {
return toStringImage;
}
if(bitLength < 32) {
toStringImage = Conversion.toDecimalScaledString(smallValue,scale);
return toStringImage;
}
String intString = getUnscaledValue().toString();
if (scale == 0) {
return intString;
}
int begin = (getUnscaledValue().signum() < 0) ? 2 : 1;
int end = intString.length();
long exponent = -(long)scale + end - begin;
StringBuilder result = new StringBuilder();
result.append(intString);
if ((scale > 0) && (exponent >= -6)) {
if (exponent >= 0) {
result.insert(end - scale, '.');
} else {
result.insert(begin - 1, "0.");
result.insert(begin + 1, CH_ZEROS, 0, -(int)exponent - 1);
}
} else {
if (end - begin >= 1) {
result.insert(begin, '.');
end++;
}
result.insert(end, 'E');
if (exponent > 0) {
result.insert(++end, '+');
}
result.insert(++end, Long.toString(exponent));
}
toStringImage = result.toString();
return toStringImage;
}
/**
* Returns a string representation of this {@code BigDecimal}. This
* representation always prints all significant digits of this value.
*
* If the scale is negative or if {@code scale - precision >= 6} then
* engineering notation is used. Engineering notation is similar to the
* scientific notation except that the exponent is made to be a multiple of
* 3 such that the integer part is >= 1 and < 1000.
*
* @return a string representation of {@code this} in engineering notation
* if necessary.
*/
public String toEngineeringString() {
String intString = getUnscaledValue().toString();
if (scale == 0) {
return intString;
}
int begin = (getUnscaledValue().signum() < 0) ? 2 : 1;
int end = intString.length();
long exponent = -(long)scale + end - begin;
StringBuilder result = new StringBuilder(intString);
if ((scale > 0) && (exponent >= -6)) {
if (exponent >= 0) {
result.insert(end - scale, '.');
} else {
result.insert(begin - 1, "0.");
result.insert(begin + 1, CH_ZEROS, 0, -(int)exponent - 1);
}
} else {
int delta = end - begin;
int rem = (int)(exponent % 3);
if (rem != 0) {
// adjust exponent so it is a multiple of three
if (getUnscaledValue().signum() == 0) {
// zero value
rem = (rem < 0) ? -rem : 3 - rem;
exponent += rem;
} else {
// nonzero value
rem = (rem < 0) ? rem + 3 : rem;
exponent -= rem;
begin += rem;
}
if (delta < 3) {
for (int i = rem - delta; i > 0; i--) {
result.insert(end++, '0');
}
}
}
if (end - begin >= 1) {
result.insert(begin, '.');
end++;
}
if (exponent != 0) {
result.insert(end, 'E');
if (exponent > 0) {
result.insert(++end, '+');
}
result.insert(++end, Long.toString(exponent));
}
}
return result.toString();
}
/**
* Returns a string representation of this {@code BigDecimal}. No scientific
* notation is used. This methods adds zeros where necessary.
*
* If this string representation is used to create a new instance, this
* instance is generally not identical to {@code this} as the precision
* changes.
*
* {@code x.equals(new BigDecimal(x.toPlainString())} usually returns
* {@code false}.
*
* {@code x.compareTo(new BigDecimal(x.toPlainString())} returns {@code 0}.
*
* @return a string representation of {@code this} without exponent part.
*/
public String toPlainString() {
String intStr = getUnscaledValue().toString();
if ((scale == 0) || ((isZero()) && (scale < 0))) {
return intStr;
}
int begin = (signum() < 0) ? 1 : 0;
int delta = scale;
// We take space for all digits, plus a possible decimal point, plus 'scale'
StringBuilder result = new StringBuilder(intStr.length() + 1 + Math.abs(scale));
if (begin == 1) {
// If the number is negative, we insert a '-' character at front
result.append('-');
}
if (scale > 0) {
delta -= (intStr.length() - begin);
if (delta >= 0) {
result.append("0.");
// To append zeros after the decimal point
for (; delta > CH_ZEROS.length; delta -= CH_ZEROS.length) {
result.append(CH_ZEROS);
}
result.append(CH_ZEROS, 0, delta);
result.append(intStr.substring(begin));
} else {
delta = begin - delta;
result.append(intStr.substring(begin, delta));
result.append('.');
result.append(intStr.substring(delta));
}
} else {// (scale <= 0)
result.append(intStr.substring(begin));
// To append trailing zeros
for (; delta < -CH_ZEROS.length; delta += CH_ZEROS.length) {
result.append(CH_ZEROS);
}
result.append(CH_ZEROS, 0, -delta);
}
return result.toString();
}
/**
* Returns this {@code BigDecimal} as a big integer instance. A fractional
* part is discarded.
*
* @return this {@code BigDecimal} as a big integer instance.
*/
public BigInteger toBigInteger() {
if ((scale == 0) || (isZero())) {
return getUnscaledValue();
} else if (scale < 0) {
return getUnscaledValue().multiply(Multiplication.powerOf10(-(long)scale));
} else {// (scale > 0)
return getUnscaledValue().divide(Multiplication.powerOf10(scale));
}
}
/**
* Returns this {@code BigDecimal} as a big integer instance if it has no
* fractional part. If this {@code BigDecimal} has a fractional part, i.e.
* if rounding would be necessary, an {@code ArithmeticException} is thrown.
*
* @return this {@code BigDecimal} as a big integer value.
* @throws ArithmeticException
* if rounding is necessary.
*/
public BigInteger toBigIntegerExact() {
if ((scale == 0) || (isZero())) {
return getUnscaledValue();
} else if (scale < 0) {
return getUnscaledValue().multiply(Multiplication.powerOf10(-(long)scale));
} else {// (scale > 0)
BigInteger[] integerAndFraction;
// An optimization before do a heavy division
if ((scale > approxPrecision()) || (scale > getUnscaledValue().getLowestSetBit())) {
throw new ArithmeticException("Rounding necessary");
}
integerAndFraction = getUnscaledValue().divideAndRemainder(Multiplication.powerOf10(scale));
if (integerAndFraction[1].signum() != 0) {
// It exists a non-zero fractional part
throw new ArithmeticException("Rounding necessary");
}
return integerAndFraction[0];
}
}
/**
* Returns this {@code BigDecimal} as an long value. Any fractional part is
* discarded. If the integral part of {@code this} is too big to be
* represented as an long, then {@code this % 264} is returned.
*/
@Override
public long longValue() {
/*
* If scale <= -64 there are at least 64 trailing bits zero in
* 10^(-scale). If the scale is positive and very large the long value
* could be zero.
*/
return ((scale <= -64) || (scale > approxPrecision()) ? 0L : toBigInteger().longValue());
}
/**
* Returns this {@code BigDecimal} as a long value if it has no fractional
* part and if its value fits to the int range ([-263..263-1]). If
* these conditions are not met, an {@code ArithmeticException} is thrown.
*
* @throws ArithmeticException
* if rounding is necessary or the number doesn't fit in a long.
*/
public long longValueExact() {
return valueExact(64);
}
/**
* Returns this {@code BigDecimal} as an int value. Any fractional part is
* discarded. If the integral part of {@code this} is too big to be
* represented as an int, then {@code this % 232} is returned.
*/
@Override
public int intValue() {
/*
* If scale <= -32 there are at least 32 trailing bits zero in
* 10^(-scale). If the scale is positive and very large the long value
* could be zero.
*/
return ((scale <= -32) || (scale > approxPrecision()) ? 0 : toBigInteger().intValue());
}
/**
* Returns this {@code BigDecimal} as a int value if it has no fractional
* part and if its value fits to the int range ([-231..231-1]). If
* these conditions are not met, an {@code ArithmeticException} is thrown.
*
* @throws ArithmeticException
* if rounding is necessary or the number doesn't fit in an int.
*/
public int intValueExact() {
return (int) valueExact(32);
}
/**
* Returns this {@code BigDecimal} as a short value if it has no fractional
* part and if its value fits to the short range ([-215..215-1]). If
* these conditions are not met, an {@code ArithmeticException} is thrown.
*
* @throws ArithmeticException
* if rounding is necessary of the number doesn't fit in a short.
*/
public short shortValueExact() {
return (short) valueExact(16);
}
/**
* Returns this {@code BigDecimal} as a byte value if it has no fractional
* part and if its value fits to the byte range ([-128..127]). If these
* conditions are not met, an {@code ArithmeticException} is thrown.
*
* @throws ArithmeticException
* if rounding is necessary or the number doesn't fit in a byte.
*/
public byte byteValueExact() {
return (byte) valueExact(8);
}
/**
* Returns this {@code BigDecimal} as a float value. If {@code this} is too
* big to be represented as an float, then {@code Float.POSITIVE_INFINITY}
* or {@code Float.NEGATIVE_INFINITY} is returned.
*
* Note, that if the unscaled value has more than 24 significant digits,
* then this decimal cannot be represented exactly in a float variable. In
* this case the result is rounded.
*
* For example, if the instance {@code x1 = new BigDecimal("0.1")} cannot be
* represented exactly as a float, and thus {@code x1.equals(new
* BigDecimal(x1.floatValue())} returns {@code false} for this case.
*
* Similarly, if the instance {@code new BigDecimal(16777217)} is converted
* to a float, the result is {@code 1.6777216E}7.
*
* @return this {@code BigDecimal} as a float value.
*/
@Override
public float floatValue() {
/* A similar code like in doubleValue() could be repeated here,
* but this simple implementation is quite efficient. */
float floatResult = signum();
long powerOfTwo = this.bitLength - (long)(scale / LOG10_2);
if ((powerOfTwo < -149) || (floatResult == 0.0f)) {
// Cases which 'this' is very small
floatResult *= 0.0f;
} else if (powerOfTwo > 129) {
// Cases which 'this' is very large
floatResult *= Float.POSITIVE_INFINITY;
} else {
floatResult = (float)doubleValue();
}
return floatResult;
}
/**
* Returns this {@code BigDecimal} as a double value. If {@code this} is too
* big to be represented as an float, then {@code Double.POSITIVE_INFINITY}
* or {@code Double.NEGATIVE_INFINITY} is returned.
*
* Note, that if the unscaled value has more than 53 significant digits,
* then this decimal cannot be represented exactly in a double variable. In
* this case the result is rounded.
*
* For example, if the instance {@code x1 = new BigDecimal("0.1")} cannot be
* represented exactly as a double, and thus {@code x1.equals(new
* BigDecimal(x1.doubleValue())} returns {@code false} for this case.
*
* Similarly, if the instance {@code new BigDecimal(9007199254740993L)} is
* converted to a double, the result is {@code 9.007199254740992E15}.
*
*
* @return this {@code BigDecimal} as a double value.
*/
@Override
public double doubleValue() {
int sign = signum();
int exponent = 1076; // bias + 53
int lowestSetBit;
int discardedSize;
long powerOfTwo = this.bitLength - (long)(scale / LOG10_2);
long bits; // IEEE-754 Standard
long tempBits; // for temporal calculations
BigInteger mantissa;
if ((powerOfTwo < -1074) || (sign == 0)) {
// Cases which 'this' is very small
return (sign * 0.0d);
} else if (powerOfTwo > 1025) {
// Cases which 'this' is very large
return (sign * Double.POSITIVE_INFINITY);
}
mantissa = getUnscaledValue().abs();
// Let be: this = [u,s], with s > 0
if (scale <= 0) {
// mantissa = abs(u) * 10^s
mantissa = mantissa.multiply(Multiplication.powerOf10(-scale));
} else {// (scale > 0)
BigInteger quotAndRem[];
BigInteger powerOfTen = Multiplication.powerOf10(scale);
int k = 100 - (int)powerOfTwo;
int compRem;
if (k > 0) {
/* Computing (mantissa * 2^k) , where 'k' is a enough big
* power of '2' to can divide by 10^s */
mantissa = mantissa.shiftLeft(k);
exponent -= k;
}
// Computing (mantissa * 2^k) / 10^s
quotAndRem = mantissa.divideAndRemainder(powerOfTen);
// To check if the fractional part >= 0.5
compRem = quotAndRem[1].shiftLeftOneBit().compareTo(powerOfTen);
// To add two rounded bits at end of mantissa
mantissa = quotAndRem[0].shiftLeft(2).add(
BigInteger.valueOf((compRem * (compRem + 3)) / 2 + 1));
exponent -= 2;
}
lowestSetBit = mantissa.getLowestSetBit();
discardedSize = mantissa.bitLength() - 54;
if (discardedSize > 0) {// (n > 54)
// mantissa = (abs(u) * 10^s) >> (n - 54)
bits = mantissa.shiftRight(discardedSize).longValue();
tempBits = bits;
// #bits = 54, to check if the discarded fraction produces a carry
if ((((bits & 1) == 1) && (lowestSetBit < discardedSize))
|| ((bits & 3) == 3)) {
bits += 2;
}
} else {// (n <= 54)
// mantissa = (abs(u) * 10^s) << (54 - n)
bits = mantissa.longValue() << -discardedSize;
tempBits = bits;
// #bits = 54, to check if the discarded fraction produces a carry:
if ((bits & 3) == 3) {
bits += 2;
}
}
// Testing bit 54 to check if the carry creates a new binary digit
if ((bits & 0x40000000000000L) == 0) {
// To drop the last bit of mantissa (first discarded)
bits >>= 1;
// exponent = 2^(s-n+53+bias)
exponent += discardedSize;
} else {// #bits = 54
bits >>= 2;
exponent += discardedSize + 1;
}
// To test if the 53-bits number fits in 'double'
if (exponent > 2046) {// (exponent - bias > 1023)
return (sign * Double.POSITIVE_INFINITY);
} else if (exponent <= 0) {// (exponent - bias <= -1023)
// Denormalized numbers (having exponent == 0)
if (exponent < -53) {// exponent - bias < -1076
return (sign * 0.0d);
}
// -1076 <= exponent - bias <= -1023
// To discard '- exponent + 1' bits
bits = tempBits >> 1;
tempBits = bits & (-1L >>> (63 + exponent));
bits >>= (-exponent );
// To test if after discard bits, a new carry is generated
if (((bits & 3) == 3) || (((bits & 1) == 1) && (tempBits != 0)
&& (lowestSetBit < discardedSize))) {
bits += 1;
}
exponent = 0;
bits >>= 1;
}
// Construct the 64 double bits: [sign(1), exponent(11), mantissa(52)]
bits = (sign & 0x8000000000000000L) | ((long)exponent << 52)
| (bits & 0xFFFFFFFFFFFFFL);
return Double.longBitsToDouble(bits);
}
/**
* Returns the unit in the last place (ULP) of this {@code BigDecimal}
* instance. An ULP is the distance to the nearest big decimal with the same
* precision.
*
* The amount of a rounding error in the evaluation of a floating-point
* operation is often expressed in ULPs. An error of 1 ULP is often seen as
* a tolerable error.
*
* For class {@code BigDecimal}, the ULP of a number is simply 10-scale.
* For example, {@code new BigDecimal(0.1).ulp()} returns {@code 1E-55}.
*
* @return unit in the last place (ULP) of this {@code BigDecimal} instance.
*/
public BigDecimal ulp() {
return valueOf(1, scale);
}
/* Private Methods */
/**
* It does all rounding work of the public method
* {@code round(MathContext)}, performing an inplace rounding
* without creating a new object.
*
* @param mc
* the {@code MathContext} for perform the rounding.
* @see #round(MathContext)
*/
private void inplaceRound(MathContext mc) {
int mcPrecision = mc.getPrecision();
if (approxPrecision() < mcPrecision || mcPrecision == 0) {
return;
}
int discardedPrecision = precision() - mcPrecision;
// If no rounding is necessary it returns immediately
if ((discardedPrecision <= 0)) {
return;
}
// When the number is small perform an efficient rounding
if (this.bitLength < 64) {
smallRound(mc, discardedPrecision);
return;
}
// Getting the integer part and the discarded fraction
BigInteger sizeOfFraction = Multiplication.powerOf10(discardedPrecision);
BigInteger[] integerAndFraction = getUnscaledValue().divideAndRemainder(sizeOfFraction);
long newScale = (long)scale - discardedPrecision;
int compRem;
BigDecimal tempBD;
// If the discarded fraction is non-zero, perform rounding
if (integerAndFraction[1].signum() != 0) {
// To check if the discarded fraction >= 0.5
compRem = (integerAndFraction[1].abs().shiftLeftOneBit().compareTo(sizeOfFraction));
// To look if there is a carry
compRem = roundingBehavior( integerAndFraction[0].testBit(0) ? 1 : 0,
integerAndFraction[1].signum() * (5 + compRem),
mc.getRoundingMode());
if (compRem != 0) {
integerAndFraction[0] = integerAndFraction[0].add(BigInteger.valueOf(compRem));
}
tempBD = new BigDecimal(integerAndFraction[0]);
// If after to add the increment the precision changed, we normalize the size
if (tempBD.precision() > mcPrecision) {
integerAndFraction[0] = integerAndFraction[0].divide(BigInteger.TEN);
newScale--;
}
}
// To update all internal fields
scale = safeLongToInt(newScale);
precision = mcPrecision;
setUnscaledValue(integerAndFraction[0]);
}
private static int longCompareTo(long value1, long value2) {
return value1 > value2 ? 1 : (value1 < value2 ? -1 : 0);
}
/**
* This method implements an efficient rounding for numbers which unscaled
* value fits in the type {@code long}.
*
* @param mc
* the context to use
* @param discardedPrecision
* the number of decimal digits that are discarded
* @see #round(MathContext)
*/
private void smallRound(MathContext mc, int discardedPrecision) {
long sizeOfFraction = MathUtils.LONG_POWERS_OF_TEN[discardedPrecision];
long newScale = (long)scale - discardedPrecision;
long unscaledVal = smallValue;
// Getting the integer part and the discarded fraction
long integer = unscaledVal / sizeOfFraction;
long fraction = unscaledVal % sizeOfFraction;
int compRem;
// If the discarded fraction is non-zero perform rounding
if (fraction != 0) {
// To check if the discarded fraction >= 0.5
compRem = longCompareTo(Math.abs(fraction) * 2, sizeOfFraction);
// To look if there is a carry
integer += roundingBehavior( ((int)integer) & 1,
Long.signum(fraction) * (5 + compRem),
mc.getRoundingMode());
// If after to add the increment the precision changed, we normalize the size
if (Math.log10(Math.abs(integer)) >= mc.getPrecision()) {
integer /= 10;
newScale--;
}
}
// To update all internal fields
scale = safeLongToInt(newScale);
precision = mc.getPrecision();
smallValue = integer;
bitLength = bitLength(integer);
intVal = null;
}
/**
* Return an increment that can be -1,0 or 1, depending of
* {@code roundingMode}.
*
* @param parityBit
* can be 0 or 1, it's only used in the case
* {@code HALF_EVEN}
* @param fraction
* the mantissa to be analyzed
* @param roundingMode
* the type of rounding
* @return the carry propagated after rounding
*/
private static int roundingBehavior(int parityBit, int fraction, RoundingMode roundingMode) {
int increment = 0; // the carry after rounding
switch (roundingMode) {
case UNNECESSARY:
if (fraction != 0) {
throw new ArithmeticException("Rounding necessary");
}
break;
case UP:
increment = Integer.signum(fraction);
break;
case DOWN:
break;
case CEILING:
increment = Math.max(Integer.signum(fraction), 0);
break;
case FLOOR:
increment = Math.min(Integer.signum(fraction), 0);
break;
case HALF_UP:
if (Math.abs(fraction) >= 5) {
increment = Integer.signum(fraction);
}
break;
case HALF_DOWN:
if (Math.abs(fraction) > 5) {
increment = Integer.signum(fraction);
}
break;
case HALF_EVEN:
if (Math.abs(fraction) + parityBit > 5) {
increment = Integer.signum(fraction);
}
break;
}
return increment;
}
/**
* If {@code intVal} has a fractional part throws an exception,
* otherwise it counts the number of bits of value and checks if it's out of
* the range of the primitive type. If the number fits in the primitive type
* returns this number as {@code long}, otherwise throws an
* exception.
*
* @param bitLengthOfType
* number of bits of the type whose value will be calculated
* exactly
* @return the exact value of the integer part of {@code BigDecimal}
* when is possible
* @throws ArithmeticException when rounding is necessary or the
* number don't fit in the primitive type
*/
private long valueExact(int bitLengthOfType) {
BigInteger bigInteger = toBigIntegerExact();
if (bigInteger.bitLength() < bitLengthOfType) {
// It fits in the primitive type
return bigInteger.longValue();
}
throw new ArithmeticException("Rounding necessary");
}
/**
* If the precision already was calculated it returns that value, otherwise
* it calculates a very good approximation efficiently . Note that this
* value will be {@code precision()} or {@code precision()-1}
* in the worst case.
*
* @return an approximation of {@code precision()} value
*/
private int approxPrecision() {
return precision > 0
? precision
: (int) ((this.bitLength - 1) * LOG10_2) + 1;
}
private static int safeLongToInt(long longValue) {
if (longValue < Integer.MIN_VALUE || longValue > Integer.MAX_VALUE) {
throw new ArithmeticException("Out of int range: " + longValue);
}
return (int) longValue;
}
/**
* It returns the value 0 with the most approximated scale of type
* {@code int}. if {@code longScale > Integer.MAX_VALUE} the
* scale will be {@code Integer.MAX_VALUE}; if
* {@code longScale < Integer.MIN_VALUE} the scale will be
* {@code Integer.MIN_VALUE}; otherwise {@code longScale} is
* casted to the type {@code int}.
*
* @param longScale
* the scale to which the value 0 will be scaled.
* @return the value 0 scaled by the closer scale of type {@code int}.
* @see #scale
*/
private static BigDecimal zeroScaledBy(long longScale) {
if (longScale == (int) longScale) {
return valueOf(0,(int)longScale);
}
if (longScale >= 0) {
return new BigDecimal( 0, Integer.MAX_VALUE);
}
return new BigDecimal( 0, Integer.MIN_VALUE);
}
/**
* Assigns all transient fields upon deserialization of a
* {@code BigDecimal} instance (bitLength and smallValue). The transient
* field precision is assigned lazily.
*/
private void readObject(ObjectInputStream in) throws IOException,
ClassNotFoundException {
in.defaultReadObject();
this.bitLength = intVal.bitLength();
if (this.bitLength < 64) {
this.smallValue = intVal.longValue();
}
}
/**
* Prepares this {@code BigDecimal} for serialization, i.e. the
* non-transient field {@code intVal} is assigned.
*/
private void writeObject(ObjectOutputStream out) throws IOException {
getUnscaledValue();
out.defaultWriteObject();
}
private BigInteger getUnscaledValue() {
if(intVal == null) {
intVal = BigInteger.valueOf(smallValue);
}
return intVal;
}
private void setUnscaledValue(BigInteger unscaledValue) {
this.intVal = unscaledValue;
this.bitLength = unscaledValue.bitLength();
if(this.bitLength < 64) {
this.smallValue = unscaledValue.longValue();
}
}
private static int bitLength(long smallValue) {
if(smallValue < 0) {
smallValue = ~smallValue;
}
return 64 - Long.numberOfLeadingZeros(smallValue);
}
private static int bitLength(int smallValue) {
if(smallValue < 0) {
smallValue = ~smallValue;
}
return 32 - Integer.numberOfLeadingZeros(smallValue);
}
}
String representation is cached. */
private transient String toStringImage = null;
/** Cache for the hash code. */
private transient int hashCode = 0;
/**
* An array with powers of five that fit in the type long
* (5^0,5^1,...,5^27).
*/
private static final BigInteger[] FIVE_POW;
/**
* An array with powers of ten that fit in the type long
* (10^0,10^1,...,10^18).
*/
private static final BigInteger[] TEN_POW;
private static final long[] LONG_FIVE_POW = new long[]
{ 1L,
5L,
25L,
125L,
625L,
3125L,
15625L,
78125L,
390625L,
1953125L,
9765625L,
48828125L,
244140625L,
1220703125L,
6103515625L,
30517578125L,
152587890625L,
762939453125L,
3814697265625L,
19073486328125L,
95367431640625L,
476837158203125L,
2384185791015625L,
11920928955078125L,
59604644775390625L,
298023223876953125L,
1490116119384765625L,
7450580596923828125L, };
private static final int[] LONG_FIVE_POW_BIT_LENGTH = new int[LONG_FIVE_POW.length];
private static final int[] LONG_POWERS_OF_TEN_BIT_LENGTH = new int[MathUtils.LONG_POWERS_OF_TEN.length];
private static final int BI_SCALED_BY_ZERO_LENGTH = 11;
/**
* An array with the first BigInteger scaled by zero.
* ([0,0],[1,0],...,[10,0]).
*/
private static final BigDecimal[] BI_SCALED_BY_ZERO = new BigDecimal[BI_SCALED_BY_ZERO_LENGTH];
/**
* An array with the zero number scaled by the first positive scales.
* (0*10^0, 0*10^1, ..., 0*10^10).
*/
private static final BigDecimal[] ZERO_SCALED_BY = new BigDecimal[11];
/** An array filled with characters '0'. */
private static final char[] CH_ZEROS = new char[100];
static {
Arrays.fill(CH_ZEROS, '0');
for (int i = 0; i < ZERO_SCALED_BY.length; ++i) {
BI_SCALED_BY_ZERO[i] = new BigDecimal(i, 0);
ZERO_SCALED_BY[i] = new BigDecimal(0, i);
}
for (int i = 0; i < LONG_FIVE_POW_BIT_LENGTH.length; ++i) {
LONG_FIVE_POW_BIT_LENGTH[i] = bitLength(LONG_FIVE_POW[i]);
}
for (int i = 0; i < LONG_POWERS_OF_TEN_BIT_LENGTH.length; ++i) {
LONG_POWERS_OF_TEN_BIT_LENGTH[i] = bitLength(MathUtils.LONG_POWERS_OF_TEN[i]);
}
// Taking the references of useful powers.
TEN_POW = Multiplication.bigTenPows;
FIVE_POW = Multiplication.bigFivePows;
}
/**
* The constant zero as a {@code BigDecimal}.
*/
public static final BigDecimal ZERO = new BigDecimal(0, 0);
/**
* The constant one as a {@code BigDecimal}.
*/
public static final BigDecimal ONE = new BigDecimal(1, 0);
/**
* The constant ten as a {@code BigDecimal}.
*/
public static final BigDecimal TEN = new BigDecimal(10, 0);
/**
* The arbitrary precision integer (unscaled value) in the internal
* representation of {@code BigDecimal}.
*/
private BigInteger intVal;
private transient int bitLength;
private transient long smallValue;
/**
* The 32-bit integer scale in the internal representation of {@code BigDecimal}.
*/
private int scale;
/**
* Represent the number of decimal digits in the unscaled value. This
* precision is calculated the first time, and used in the following calls
* of method precision(). Note that some call to the private
* method inplaceRound() could update this field.
*
* @see #precision()
* @see #inplaceRound(MathContext)
*/
private transient int precision = 0;
private BigDecimal(long smallValue, int scale){
this.smallValue = smallValue;
this.scale = scale;
this.bitLength = bitLength(smallValue);
}
private BigDecimal(int smallValue, int scale){
this.smallValue = smallValue;
this.scale = scale;
this.bitLength = bitLength(smallValue);
}
/**
* Constructs a new {@code BigDecimal} instance from a string representation
* given as a character array.
*
* @param in
* array of characters containing the string representation of
* this {@code BigDecimal}.
* @param offset
* first index to be copied.
* @param len
* number of characters to be used.
* @throws NumberFormatException
* if {@code offset < 0 || len <= 0 || offset+len-1 < 0 ||
* offset+len-1 >= in.length}, or if {@code in} does not
* contain a valid string representation of a big decimal.
*/
public BigDecimal(char[] in, int offset, int len) {
int begin = offset; // first index to be copied
int last = offset + (len - 1); // last index to be copied
String scaleString; // buffer for scale
StringBuilder unscaledBuffer; // buffer for unscaled value
long newScale; // the new scale
if (in == null) {
throw new NullPointerException("in == null");
}
if ((last >= in.length) || (offset < 0) || (len <= 0) || (last < 0)) {
throw new NumberFormatException("Bad offset/length: offset=" + offset +
" len=" + len + " in.length=" + in.length);
}
unscaledBuffer = new StringBuilder(len);
int bufLength = 0;
// To skip a possible '+' symbol
if ((offset <= last) && (in[offset] == '+')) {
offset++;
begin++;
}
int counter = 0;
boolean wasNonZero = false;
// Accumulating all digits until a possible decimal point
for (; (offset <= last) && (in[offset] != '.') && (in[offset] != 'e') && (in[offset] != 'E'); offset++) {
if (!wasNonZero) {
if (in[offset] == '0') {
counter++;
} else {
wasNonZero = true;
}
}
}
unscaledBuffer.append(in, begin, offset - begin);
bufLength += offset - begin;
// A decimal point was found
if ((offset <= last) && (in[offset] == '.')) {
offset++;
// Accumulating all digits until a possible exponent
begin = offset;
for (; (offset <= last) && (in[offset] != 'e')
&& (in[offset] != 'E'); offset++) {
if (!wasNonZero) {
if (in[offset] == '0') {
counter++;
} else {
wasNonZero = true;
}
}
}
scale = offset - begin;
bufLength +=scale;
unscaledBuffer.append(in, begin, scale);
} else {
scale = 0;
}
// An exponent was found
if ((offset <= last) && ((in[offset] == 'e') || (in[offset] == 'E'))) {
offset++;
// Checking for a possible sign of scale
begin = offset;
if ((offset <= last) && (in[offset] == '+')) {
offset++;
if ((offset <= last) && (in[offset] != '-')) {
begin++;
}
}
// Accumulating all remaining digits
scaleString = String.valueOf(in, begin, last + 1 - begin);
// Checking if the scale is defined
newScale = (long)scale - Integer.parseInt(scaleString);
scale = (int)newScale;
if (newScale != scale) {
throw new NumberFormatException("Scale out of range");
}
}
// Parsing the unscaled value
if (bufLength < 19) {
smallValue = Long.parseLong(unscaledBuffer.toString());
bitLength = bitLength(smallValue);
} else {
setUnscaledValue(new BigInteger(unscaledBuffer.toString()));
}
}
/**
* Constructs a new {@code BigDecimal} instance from a string representation
* given as a character array.
*
* @param in
* array of characters containing the string representation of
* this {@code BigDecimal}.
* @param offset
* first index to be copied.
* @param len
* number of characters to be used.
* @param mc
* rounding mode and precision for the result of this operation.
* @throws NumberFormatException
* if {@code offset < 0 || len <= 0 || offset+len-1 < 0 ||
* offset+len-1 >= in.length}, or if {@code in} does not
* contain a valid string representation of a big decimal.
* @throws ArithmeticException
* if {@code mc.precision > 0} and {@code mc.roundingMode ==
* UNNECESSARY} and the new big decimal cannot be represented
* within the given precision without rounding.
*/
public BigDecimal(char[] in, int offset, int len, MathContext mc) {
this(in, offset, len);
inplaceRound(mc);
}
/**
* Constructs a new {@code BigDecimal} instance from a string representation
* given as a character array.
*
* @param in
* array of characters containing the string representation of
* this {@code BigDecimal}.
* @throws NumberFormatException
* if {@code in} does not contain a valid string representation
* of a big decimal.
*/
public BigDecimal(char[] in) {
this(in, 0, in.length);
}
/**
* Constructs a new {@code BigDecimal} instance from a string representation
* given as a character array. The result is rounded according to the
* specified math context.
*
* @param in
* array of characters containing the string representation of
* this {@code BigDecimal}.
* @param mc
* rounding mode and precision for the result of this operation.
* @throws NumberFormatException
* if {@code in} does not contain a valid string representation
* of a big decimal.
* @throws ArithmeticException
* if {@code mc.precision > 0} and {@code mc.roundingMode ==
* UNNECESSARY} and the new big decimal cannot be represented
* within the given precision without rounding.
*/
public BigDecimal(char[] in, MathContext mc) {
this(in, 0, in.length);
inplaceRound(mc);
}
/**
* Constructs a new {@code BigDecimal} instance from a string
* representation.
*
* @throws NumberFormatException
* if {@code val} does not contain a valid string representation
* of a big decimal.
*/
public BigDecimal(String val) {
this(val.toCharArray(), 0, val.length());
}
/**
* Constructs a new {@code BigDecimal} instance from a string
* representation. The result is rounded according to the specified math
* context.
*
* @param mc
* rounding mode and precision for the result of this operation.
* @throws NumberFormatException
* if {@code val} does not contain a valid string representation
* of a big decimal.
* @throws ArithmeticException
* if {@code mc.precision > 0} and {@code mc.roundingMode ==
* UNNECESSARY} and the new big decimal cannot be represented
* within the given precision without rounding.
*/
public BigDecimal(String val, MathContext mc) {
this(val.toCharArray(), 0, val.length());
inplaceRound(mc);
}
/**
* Constructs a new {@code BigDecimal} instance from the 64bit double
* {@code val}. The constructed big decimal is equivalent to the given
* double. For example, {@code new BigDecimal(0.1)} is equal to {@code
* 0.1000000000000000055511151231257827021181583404541015625}. This happens
* as {@code 0.1} cannot be represented exactly in binary.
*