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/*
* Copyright 2009 Google Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License"); you may not
* use this file except in compliance with the License. You may obtain a copy of
* the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations under
* the License.
*/
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with this
* work for additional information regarding copyright ownership. The ASF
* licenses this file to You under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations under
* the License.
*
* INCLUDES MODIFICATIONS BY RICHARD ZSCHECH AS WELL AS GOOGLE.
*/
package java.math;
import static com.google.gwt.core.shared.impl.InternalPreconditions.checkNotNull;
import com.google.gwt.core.client.JavaScriptObject;
import java.io.Serializable;
/**
* This class represents immutable arbitrary precision decimal numbers. Each
* {@code BigDecimal} instance is represented with a unscaled arbitrary
* precision mantissa (the unscaled value) and a scale. The value of the {@code
* BigDecimal} is {@code unscaledValue} 10^(-{@code scale}).
*/
public class BigDecimal extends Number implements Comparable,
Serializable {
/**
* One more than the number of bits which can be stored in {@link #smallValue}.
*/
private static final int SMALL_VALUE_BITS = 54;
/**
* The constant one as a {@code BigDecimal}.
*/
public static final BigDecimal ONE = new BigDecimal(1, 0);
/**
* Rounding mode to round towards positive infinity. For positive values this
* rounding mode behaves as {@link #ROUND_UP}, for negative values as
* {@link #ROUND_DOWN}.
*
* @see RoundingMode#CEILING
*/
public static final int ROUND_CEILING = 2;
/**
* Rounding mode where the values are rounded towards zero.
*
* @see RoundingMode#DOWN
*/
public static final int ROUND_DOWN = 1;
/**
* Rounding mode to round towards negative infinity. For positive values this
* rounding mode behaves as {@link #ROUND_DOWN}, for negative values as
* {@link #ROUND_UP}.
*
* @see RoundingMode#FLOOR
*/
public static final int ROUND_FLOOR = 3;
/**
* Rounding mode where values are rounded towards the nearest neighbor. Ties
* are broken by rounding down.
*
* @see RoundingMode#HALF_DOWN
*/
public static final int ROUND_HALF_DOWN = 5;
/**
* Rounding mode where values are rounded towards the nearest neighbor. Ties
* are broken by rounding to the even neighbor.
*
* @see RoundingMode#HALF_EVEN
*/
public static final int ROUND_HALF_EVEN = 6;
/**
* Rounding mode where values are rounded towards the nearest neighbor. Ties
* are broken by rounding up.
*
* @see RoundingMode#HALF_UP
*/
public static final int ROUND_HALF_UP = 4;
/**
* Rounding mode where the rounding operations throws an {@code
* ArithmeticException} for the case that rounding is necessary, i.e. for the
* case that the value cannot be represented exactly.
*
* @see RoundingMode#UNNECESSARY
*/
public static final int ROUND_UNNECESSARY = 7;
/**
* Rounding mode where positive values are rounded towards positive infinity
* and negative values towards negative infinity.
*
* @see RoundingMode#UP
*/
public static final int ROUND_UP = 0;
/**
* The constant ten as a {@code BigDecimal}.
*/
public static final BigDecimal TEN = new BigDecimal(10, 0);
/**
* The constant zero as a {@code BigDecimal}.
*/
public static final BigDecimal ZERO = new BigDecimal(0, 0);
protected static JavaScriptObject unscaledRegex;
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 filled with characters '0'.
*/
private static final char[] CH_ZEROS = new char[100];
private static final double[] DOUBLE_FIVE_POW = new double[] {
1D, 5D, 25D, 125D, 625D, 3125D, 15625D, 78125D, 390625D, 1953125D,
9765625D, 48828125D, 244140625D, 1220703125D, 6103515625D, 30517578125D,
152587890625D, 762939453125D, 3814697265625D, 19073486328125D,
95367431640625D, 476837158203125D, 2384185791015625D,};
private static final int[] DOUBLE_FIVE_POW_BIT_LENGTH = new int[DOUBLE_FIVE_POW.length];
/**
* An array with powers of ten that fit in the type double (
* 10^0,10^1,...,10^18).
*/
private static final double[] DOUBLE_TEN_POW = new double[] {
1D, 10D, 100D, 1000D, 10000D, 100000D, 1000000D, 10000000D, 100000000D,
1000000000D, 10000000000D, 100000000000D, 1000000000000D,
10000000000000D, 100000000000000D, 1000000000000000D,
10000000000000000D,};
private static final int[] DOUBLE_TEN_POW_BIT_LENGTH = new int[DOUBLE_TEN_POW.length];
/**
* An array with powers of five that fit in the type double (
* 5^0,5^1,...,5^27).
*/
private static final BigInteger FIVE_POW[];
/**
* The double closest to Math.log(2.0d).
*/
private static final double LOG2 = 0.6931471805599453d;
/**
* The double closest to Log10(2).
*/
private static final double LOG10_2 = 0.3010299956639812;
/**
* The double closer to Math.pow(2, 47).
*/
private static final double POW47 = 140737488355328d;
/**
* This is the serialVersionUID used by the sun implementation.
*/
private static final long serialVersionUID = 6108874887143696463L;
/**
* An array with powers of ten that fit in the type double (
* 10^0,10^1,...,10^18).
*/
private static final BigInteger TEN_POW[];
/**
* 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];
static {
// To fill all static arrays.
int i = 0;
for (; i < ZERO_SCALED_BY.length; i++) {
BI_SCALED_BY_ZERO[i] = new BigDecimal(i, 0);
ZERO_SCALED_BY[i] = new BigDecimal(0, i);
CH_ZEROS[i] = '0';
}
for (; i < CH_ZEROS.length; i++) {
CH_ZEROS[i] = '0';
}
for (int j = 0; j < DOUBLE_FIVE_POW_BIT_LENGTH.length; j++) {
DOUBLE_FIVE_POW_BIT_LENGTH[j] = bitLength(DOUBLE_FIVE_POW[j]);
}
for (int j = 0; j < DOUBLE_TEN_POW_BIT_LENGTH.length; j++) {
DOUBLE_TEN_POW_BIT_LENGTH[j] = bitLength(DOUBLE_TEN_POW[j]);
}
// Taking the references of useful powers.
TEN_POW = Multiplication.bigTenPows;
FIVE_POW = Multiplication.bigFivePows;
}
/**
* 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)) {
// math.03=Infinity or NaN
throw new NumberFormatException("Infinite or NaN"); //$NON-NLS-1$
}
return new BigDecimal(Double.toString(val));
}
/**
* 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
* unscaledVal} 10^(-{@code scale}). The scale of the result is {@code scale},
* and its unscaled value is {@code unscaledVal}.
*
* @param unscaledVal unscaled value to be used to construct the new {@code
* BigDecimal}.
* @param scale scale to be used to construct the new {@code BigDecimal}.
* @return {@code BigDecimal} instance with the value {@code unscaledVal}*
* 10^(-{@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);
}
private static BigDecimal addAndMult10(BigDecimal thisValue,
BigDecimal augend, double diffScale) {
if (diffScale < DOUBLE_TEN_POW.length
&& Math.max(thisValue.bitLength, augend.bitLength
+ DOUBLE_TEN_POW_BIT_LENGTH[(int) diffScale]) + 1
< SMALL_VALUE_BITS) {
return valueOf(thisValue.smallValue + augend.smallValue
* DOUBLE_TEN_POW[(int) diffScale], thisValue.scale);
}
return new BigDecimal(thisValue.getUnscaledValue().add(
Multiplication.multiplyByTenPow(augend.getUnscaledValue(),
(int) diffScale)), thisValue.scale);
}
private static int bitLength(double value) {
// if |value| is less than 2^47, use log
if (value > -POW47 && value < POW47) {
if (value == 0.0) {
// special-case zero, otherwise we get -INFINITY below
return 0;
}
boolean negative = (value < 0.0);
if (negative) {
value = -value;
}
int result = (int) Math.floor(Math.log(value) / LOG2);
if (!negative || value != Math.pow(2, result)) {
result++;
}
return result;
}
return bitLength((long) value);
}
private static int bitLength(long value) {
if (value < 0) {
value = ~value;
}
return 64 - Long.numberOfLeadingZeros(value);
}
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() < SMALL_VALUE_BITS) {
long rem = remainder.longValue();
long divisor = scaledDivisor.longValue();
compRem = Long.compare(Math.abs(rem) << 1, 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() < SMALL_VALUE_BITS) {
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 dividePrimitiveDoubles(double scaledDividend,
double scaledDivisor, int scale, RoundingMode roundingMode) {
double quotient = intDivide(scaledDividend, scaledDivisor);
double remainder = scaledDividend % scaledDivisor;
int sign = Double.compare(scaledDividend * scaledDivisor, 0.0);
if (remainder != 0) {
// Checking if: remainder * 2 >= scaledDivisor
int compRem; // 'compare to remainder'
compRem = Double.compare(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);
}
private static double intDivide(double dividend, double divisor) {
double quotient = dividend / divisor;
return quotient > 0 ? Math.floor(quotient) : Math.ceil(quotient);
}
private static native double parseUnscaled(String str) /*-{
var unscaledRegex = @java.math.BigDecimal::unscaledRegex;
if (!unscaledRegex) {
unscaledRegex = @java.math.BigDecimal::unscaledRegex = /^[+-]?\d*$/i;
}
if (unscaledRegex.test(str)) {
return parseInt(str, 10);
} else {
return Number.NaN;
}
}-*/;
/**
* Return an increment that can be -1,0 or 1, depending of {@code
* roundingMode}.
*
* @param parityBit can be 0 or 1, it's only used in the case {@code
* HALF_EVEN}
* @param fraction the mantisa to be analyzed
* @param roundingMode the type of rounding
* @return the carry propagated after rounding
*/
private static int roundingBehavior(int parityBit, int fraction,
RoundingMode roundingMode) {
int increment = 0; // the carry after rounding
switch (roundingMode) {
case UNNECESSARY:
if (fraction != 0) {
// math.08=Rounding necessary
throw new ArithmeticException("Rounding necessary"); //$NON-NLS-1$
}
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;
}
/**
* It tests if a scale of type {@code long} fits in 32 bits. It returns the
* same scale being casted to {@code int} type when is possible, otherwise
* throws an exception.
*
* @param doubleScale a double bit scale
* @return a 32 bit scale when is possible
* @throws ArithmeticException when {@code scale} doesn't fit in {@code int}
* type
* @see #scale
*/
private static int toIntScale(double doubleScale) {
if (doubleScale < Integer.MIN_VALUE) {
// math.09=Overflow
throw new ArithmeticException("Overflow"); //$NON-NLS-1$
} else if (doubleScale > Integer.MAX_VALUE) {
// math.0A=Underflow
throw new ArithmeticException("Underflow"); //$NON-NLS-1$
} else {
return (int) doubleScale;
}
}
/**
* Convert a double to a string with {@code digits} precision. The resulting
* string may still be in exponential notation.
*
* @param d double value
* @param digits number of digits of precision to include
* @return non-localized string representation of {@code d}
*/
private static native String toPrecision(double d, int digits) /*-{
return d.toPrecision(digits);
}-*/;
private static BigDecimal valueOf(double smallValue, double scale) {
return new BigDecimal(smallValue, scale);
}
/**
* 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 doubleScale 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(double doubleScale) {
if (doubleScale == (int) doubleScale) {
return valueOf(0, (int) doubleScale);
}
if (doubleScale >= 0) {
return new BigDecimal(0, Integer.MAX_VALUE);
}
return new BigDecimal(0, Integer.MIN_VALUE);
}
private transient int bitLength;
/**
* Cache for the hash code.
*/
private transient int hashCode;
/**
* The arbitrary precision integer (unscaled value) in the internal
* representation of {@code BigDecimal}.
*/
private BigInteger intVal;
/**
* 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;
private double scale;
/**
* The unscaled integer value (stored in a double) if the number of bits is
* less than {@link #SMALL_VALUE_BITS}.
*/
private transient double smallValue;
/**
* The String representation is cached.
*/
private transient String toStringImage;
/**
* Constructs a new {@code BigDecimal} instance from the given big integer
* {@code val}. The scale of the result is {@code 0}.
*
* @param val {@code BigInteger} value to be converted to a {@code BigDecimal}
* instance.
*/
public BigDecimal(BigInteger val) {
this(val, 0);
}
/**
* 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^(-{@code scale}).
*
* @param unscaledVal {@code BigInteger} representing the unscaled value of
* this {@code BigDecimal} instance.
* @param scale scale of this {@code BigDecimal} instance.
* @throws NullPointerException if {@code unscaledVal == null}.
*/
public BigDecimal(BigInteger unscaledVal, int scale) {
this(unscaledVal, (double) scale);
}
/**
* 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^(-{@code scale}). The result is rounded according to
* the specified math context.
*
* @param unscaledVal {@code BigInteger} representing the unscaled value of
* this {@code BigDecimal} instance.
* @param scale scale of this {@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.
* @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 big integer
* {@code val}. The scale of the result is {@code 0}.
*
* @param val {@code BigInteger} 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(BigInteger val, MathContext mc) {
this(val);
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 NullPointerException if {@code in == null}.
* @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.
*
* @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 NullPointerException if {@code in == null}.
* @throws NumberFormatException if {@code offset < 0} or {@code len <= 0} or
* {@code offset+len-1 < 0} or {@code offset+len-1 >= in.length}.
* @throws NumberFormatException if in does not contain a valid string
* representation of a big decimal.
*/
public BigDecimal(char[] in, int offset, int len) {
try {
initFrom(new String(in, offset, len));
} catch (StringIndexOutOfBoundsException e) {
throw new NumberFormatException(e.getMessage());
}
}
/**
* 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 NullPointerException if {@code in == null}.
* @throws NumberFormatException if {@code offset < 0} or {@code len <= 0} or
* {@code offset+len-1 < 0} or {@code offset+len-1 >= in.length}.
* @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, 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. 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 NullPointerException if {@code in == null}.
* @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 the given double {@code
* val}. The scale of the result is 0.
*
* @param val double value to be converted to a {@code BigDecimal} instance.
* @throws NumberFormatException if {@code val} is infinite or a NaN
*/
public BigDecimal(double val) {
if (Double.isInfinite(val) || Double.isNaN(val)) {
// math.03=Infinity or NaN
throw new NumberFormatException("Infinite or NaN"); //$NON-NLS-1$
}
initFrom(toPrecision(val, 20));
}
/**
* Constructs a new {@code BigDecimal} instance from the given double {@code
* val}. The scale of the result is 0. The result is rounded according to the
* specified math context.
*
* @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 infinite or a NaN
* @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) {
if (Double.isInfinite(val) || Double.isNaN(val)) {
// math.03=Infinity or NaN
throw new NumberFormatException("Infinite or NaN"); //$NON-NLS-1$
}
initFrom(toPrecision(val, 20));
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);
}
/**
* Constructs a new {@code BigDecimal} instance from a string representation.
*
* @param val string containing the string representation of this {@code
* BigDecimal}.
* @throws NumberFormatException if {@code val} does not contain a valid
* string representation of a big decimal.
*/
public BigDecimal(String val) {
initFrom(val);
}
/**
* Constructs a new {@code BigDecimal} instance from a string representation.
* The result is rounded according to the specified math context.
*
* @param val string containing the string representation of this {@code
* BigDecimal}.
* @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);
}
private BigDecimal(BigInteger unscaledVal, double scale) {
this.scale = scale;
setUnscaledValue(checkNotNull(unscaledVal));
}
private BigDecimal(double smallValue, double scale) {
this.smallValue = smallValue;
this.scale = scale;
this.bitLength = bitLength(smallValue);
}
private BigDecimal(long smallValue, int scale) {
this.scale = scale;
this.bitLength = bitLength(smallValue);
if (bitLength < SMALL_VALUE_BITS) {
this.smallValue = smallValue;
} else {
this.intVal = BigInteger.valueOf(smallValue);
}
}
/**
* Returns a new {@code BigDecimal} whose value is the absolute value of
* {@code this}. The scale of the result is the same as the scale of this.
*
* @return {@code abs(this)}
*/
public BigDecimal abs() {
return ((signum() < 0) ? negate() : this);
}
/**
* Returns a new {@code BigDecimal} whose value is the absolute value of
* {@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 abs(this)}
*/
public BigDecimal abs(MathContext mc) {
return round(mc).abs();
}
/**
* 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) {
double 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 < SMALL_VALUE_BITS) {
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);
}
}
/**
* 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;
double diffScale = 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 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.
*
* @return this {@code BigDecimal} as a byte value.
* @throws ArithmeticException if rounding is necessary or the number doesn't
* fit in a byte.
*/
public byte byteValueExact() {
return (byte) valueExact(8);
}
/**
* 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 < SMALL_VALUE_BITS
&& val.bitLength < SMALL_VALUE_BITS) {
return (smallValue < val.smallValue) ? -1
: (smallValue > val.smallValue) ? 1 : 0;
}
double diffScale = this.scale - val.scale;
double 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 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[];
double diffScale = 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()) {
// math.04=Division by zero
throw new ArithmeticException("Division by zero"); //$NON-NLS-1$
}
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)) {
// math.05=Non-terminating decimal expansion; no exact representable
// decimal result.
throw new ArithmeticException(
"Non-terminating decimal expansion; no exact representable decimal result"); //$NON-NLS-1$
}
// 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 = toIntScale(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
* 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, (int) 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}.
* @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) {
checkNotNull(roundingMode);
// Let be: this = [u1,s1] and divisor = [u2,s2]
if (divisor.isZero()) {
// math.04=Division by zero
throw new ArithmeticException("Division by zero"); //$NON-NLS-1$
}
double diffScale = this.scale - divisor.scale - scale;
if (this.bitLength < SMALL_VALUE_BITS
&& divisor.bitLength < SMALL_VALUE_BITS) {
if (diffScale == 0) {
return dividePrimitiveDoubles(this.smallValue, divisor.smallValue,
scale, roundingMode);
} else if (diffScale > 0) {
if (diffScale < DOUBLE_TEN_POW.length
&& divisor.bitLength + DOUBLE_TEN_POW_BIT_LENGTH[
(int) diffScale] < SMALL_VALUE_BITS) {
return dividePrimitiveDoubles(this.smallValue, divisor.smallValue
* DOUBLE_TEN_POW[(int) diffScale], scale, roundingMode);
}
} else { // diffScale < 0
if (-diffScale < DOUBLE_TEN_POW.length
&& this.bitLength + DOUBLE_TEN_POW_BIT_LENGTH[(int) -diffScale]
< SMALL_VALUE_BITS) {
return dividePrimitiveDoubles(this.smallValue
* DOUBLE_TEN_POW[(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);
}
/**
* 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
*/
double traillingZeros = mc.getPrecision() + 2L + divisor.approxPrecision()
- approxPrecision();
double diffScale = scale - divisor.scale;
double 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 (traillingZeros > 0) {
// To append trailing zeros at end of dividend
quotAndRem[0] = getUnscaledValue().multiply(
Multiplication.powerOf10(traillingZeros));
newScale += traillingZeros;
}
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, toIntScale(newScale), mc);
}
/**
* 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, (int) scale, roundingMode);
}
/**
* 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 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()};
double newScale = this.scale - divisor.scale;
double tempScale = 0;
int i = 1;
int lastPow = TEN_POW.length - 1;
if (divisor.isZero()) {
// math.04=Division by zero
throw new ArithmeticException("Division by zero"); //$NON-NLS-1$
}
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, toIntScale(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;
double diffScale = this.scale - divisor.scale;
double newScale = diffScale;
double 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.
*/
double exp = Math.min(-diffScale, Math.max((double) mcPrecision
- diffPrecision, 0));
double 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) {
// The quotient won't fit in 'mc.precision()' digits
// math.06=Division impossible
throw new ArithmeticException("Division impossible"); //$NON-NLS-1$
}
}
}
// 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]);
int 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) {
// math.06=Division impossible
throw new ArithmeticException("Division impossible"); //$NON-NLS-1$
}
integralValue.scale = toIntScale(newScale);
integralValue.setUnscaledValue(strippedBI);
return integralValue;
}
/**
* 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() {
return Double.parseDouble(this.toString());
}
/**
* 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.
*
* @param x object to be compared with {@code this}.
* @return true if {@code x} is a {@code BigDecimal} and {@code this == x}.
*/
@Override
public boolean equals(Object x) {
if (this == x) {
return true;
}
if (x instanceof BigDecimal) {
BigDecimal x1 = (BigDecimal) x;
return x1.scale == scale
&& (bitLength < SMALL_VALUE_BITS ? (x1.smallValue == smallValue)
: intVal.equals(x1.intVal));
}
return false;
}
/**
* 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.folatValue())} 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();
double powerOfTwo = this.bitLength - (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 a hash code for this {@code BigDecimal}.
*
* @return hash code for {@code this}.
*/
@Override
public int hashCode() {
if (hashCode != 0) {
return hashCode;
}
if (bitLength < SMALL_VALUE_BITS) {
long longValue = (long) smallValue;
hashCode = (int) (longValue & 0xffffffff);
hashCode = 33 * hashCode + (int) ((longValue >> 32) & 0xffffffff);
hashCode = 17 * hashCode + (int) scale;
return hashCode;
}
hashCode = 17 * intVal.hashCode() + (int) scale;
return hashCode;
}
/**
* 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} % 2^32 is returned.
*
* @return this {@code BigDecimal} as a int value.
*/
@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 ([-2^{31}..2^{31}-1]). If these
* conditions are not met, an {@code ArithmeticException} is thrown.
*
* @return this {@code BigDecimal} as a int value.
* @throws ArithmeticException if rounding is necessary or the number doesn't
* fit in a int.
*/
public int intValueExact() {
return (int) valueExact(32);
}
/**
* 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} % 2^64 is returned.
*
* @return this {@code BigDecimal} as a long value.
*/
@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 ([-2^{63}..2^{63}-1]). If these
* conditions are not met, an {@code ArithmeticException} is thrown.
*
* @return this {@code BigDecimal} as a long value.
* @throws ArithmeticException if rounding is necessary or the number doesn't
* fit in a long.
*/
public long longValueExact() {
return valueExact(64);
}
/**
* 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 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 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}.
*
* @param n number of placed the decimal point has to be moved.
* @return {@code this * 10^(-n}).
*/
public BigDecimal movePointLeft(int n) {
return movePoint(scale + n);
}
/**
* 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.
*
* @param n number of placed the decimal point has to be moved.
* @return {@code this * 10^n}.
*/
public BigDecimal movePointRight(int n) {
return movePoint(scale - n);
}
/**
* 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) {
double newScale = 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 < SMALL_VALUE_BITS) {
return valueOf(this.smallValue * multiplicand.smallValue,
toIntScale(newScale));
}
return new BigDecimal(this.getUnscaledValue().multiply(
multiplicand.getUnscaledValue()), toIntScale(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 the {@code -this}. The
* scale of the result is the same as the scale of this.
*
* @return {@code -this}
*/
public BigDecimal negate() {
if (bitLength < SMALL_VALUE_BITS) {
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) {
return round(mc).negate();
}
/**
* 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 a new {@code BigDecimal} whose value is {@code this ^ n}. The scale
* of the result is {@code n} times the scales of {@code this}.
*
* {@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.
*
* @param n exponent to which {@code this} is raised.
* @return {@code this ^ n}.
* @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)) {
// math.07=Invalid Operation
throw new ArithmeticException("Invalid Operation"); //$NON-NLS-1$
}
double newScale = scale * n;
// Let be: this = [u,s] so: this^n = [u^n, s*n]
return ((isZero()) ? zeroScaledBy(newScale) : new BigDecimal(
getUnscaledValue().pow(n), toIntScale(newScale)));
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this ^ n}. 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 n exponent to which {@code this} is raised.
* @param mc rounding mode and precision for the result of this operation.
* @return {@code this ^ n}.
* @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))) {
// math.07=Invalid Operation
throw new ArithmeticException("Invalid Operation"); //$NON-NLS-1$
}
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 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() {
// Checking if the precision already was calculated
if (precision > 0) {
return precision;
}
double decimalDigits = 1; // the precision to be calculated
double doubleUnsc = 1; // intVal in 'double'
if (bitLength < SMALL_VALUE_BITS) {
// To calculate the precision for small numbers
if (bitLength >= 1) {
doubleUnsc = smallValue;
}
decimalDigits += Math.log10(Math.abs(doubleUnsc));
} else {
// (bitLength >= 1024)
/*
* To calculate the precision for large numbers Note that: 2 ^(bitlength()
* - 1) <= intVal < 10 ^(precision())
*/
decimalDigits += (bitLength - 1) * LOG10_2;
// If after division the number isn't zero, exists an aditional digit
if (getUnscaledValue().divide(Multiplication.powerOf10(decimalDigits)).signum() != 0) {
decimalDigits++;
}
}
precision = (int) decimalDigits;
return precision;
}
/**
* 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 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 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 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 (int) scale;
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this} 10^{@code n}.
* 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.
*
* @param n number of places the decimal point has to be moved.
* @return {@code this * 10^n}
*/
public BigDecimal scaleByPowerOfTen(int n) {
double newScale = scale - n;
if (bitLength < SMALL_VALUE_BITS) {
// Taking care when a 0 is to be scaled
if (smallValue == 0) {
return zeroScaledBy(newScale);
}
return valueOf(smallValue, toIntScale(newScale));
}
return new BigDecimal(getUnscaledValue(), toIntScale(newScale));
}
/**
* 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 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. 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) {
checkNotNull(roundingMode);
double diffScale = newScale - scale;
// Let be: 'this' = [u,s]
if (diffScale == 0) {
return this;
}
if (diffScale > 0) {
// return [u * 10^(s2 - s), newScale]
if (diffScale < DOUBLE_TEN_POW.length
&& (this.bitLength + DOUBLE_TEN_POW_BIT_LENGTH[
(int) diffScale]) < SMALL_VALUE_BITS) {
return valueOf(this.smallValue * DOUBLE_TEN_POW[(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 < SMALL_VALUE_BITS
&& -diffScale < DOUBLE_TEN_POW.length) {
return dividePrimitiveDoubles(this.smallValue,
DOUBLE_TEN_POW[(int) -diffScale], newScale, roundingMode);
}
return divideBigIntegers(this.getUnscaledValue(),
Multiplication.powerOf10(-diffScale), newScale, roundingMode);
}
/**
* Returns this {@code BigDecimal} as a short value if it has no fractional
* part and if its value fits to the short range ([-2^{15}..2^{15}-1]). If
* these conditions are not met, an {@code ArithmeticException} is thrown.
*
* @return this {@code BigDecimal} as a short value.
* @throws ArithmeticException if rounding is necessary of the number doesn't
* fit in a short.
*/
public short shortValueExact() {
return (short) valueExact(16);
}
/**
* 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 < SMALL_VALUE_BITS) {
return this.smallValue < 0 ? -1 : this.smallValue > 0 ? 1 : 0;
}
return getUnscaledValue().signum();
}
/**
* 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;
double newScale = scale;
if (isZero()) {
return new BigDecimal("0");
}
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, toIntScale(newScale));
}
/**
* 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) {
double 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
< SMALL_VALUE_BITS) {
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 < DOUBLE_TEN_POW.length
&& Math.max(this.bitLength, subtrahend.bitLength
+ DOUBLE_TEN_POW_BIT_LENGTH[(int) diffScale]) + 1
< SMALL_VALUE_BITS) {
return valueOf(this.smallValue - subtrahend.smallValue
* DOUBLE_TEN_POW[(int) diffScale], this.scale);
}
return new BigDecimal(this.getUnscaledValue().subtract(
Multiplication.multiplyByTenPow(subtrahend.getUnscaledValue(),
(int) diffScale)), this.scale);
} else {
// case s2 > s1 : [ u1 * 10 ^ (s2 - s1) - u2 , s2 ]
diffScale = -diffScale;
if (diffScale < DOUBLE_TEN_POW.length
&& Math.max(this.bitLength
+ DOUBLE_TEN_POW_BIT_LENGTH[(int) diffScale],
subtrahend.bitLength) + 1 < SMALL_VALUE_BITS) {
return valueOf(this.smallValue * DOUBLE_TEN_POW[(int) diffScale]
- subtrahend.smallValue, subtrahend.scale);
}
return new BigDecimal(Multiplication.multiplyByTenPow(
this.getUnscaledValue(), (int) 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) {
double diffScale = subtrahend.scale - 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 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(-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(-scale));
} else {
// (scale > 0)
BigInteger[] integerAndFraction;
// An optimization before do a heavy division
if ((scale > approxPrecision())
|| (scale > getUnscaledValue().getLowestSetBit())) {
// math.08=Rounding necessary
throw new ArithmeticException("Rounding necessary"); //$NON-NLS-1$
}
integerAndFraction = getUnscaledValue().divideAndRemainder(
Multiplication.powerOf10(scale));
if (integerAndFraction[1].signum() != 0) {
// It exists a non-zero fractional part
// math.08=Rounding necessary
throw new ArithmeticException("Rounding necessary"); //$NON-NLS-1$
}
return integerAndFraction[0];
}
}
/**
* 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();
double exponent = -scale + end - begin;
StringBuilder result = new StringBuilder(intString);
if ((scale > 0) && (exponent >= -6)) {
if (exponent >= 0) {
result.insert(end - (int) scale, '.');
} else {
result.insert(begin - 1, "0."); //$NON-NLS-1$
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((long) 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;
double delta = scale;
// We take space for all digits, plus a possible decimal point, plus 'scale'
StringBuilder result = new StringBuilder(intStr.length() + 1
+ Math.abs((int) 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."); //$NON-NLS-1$
// 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, (int) delta);
result.append(intStr.substring(begin));
} else {
delta = begin - delta;
result.append(intStr.substring(begin, (int) delta));
result.append('.');
result.append(intStr.substring((int) 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, (int) -delta);
}
return result.toString();
}
/**
* 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) {
// TODO convert to double math dont cast to long :-(
toStringImage = Conversion.toDecimalScaledString((long) smallValue,
(int) scale);
return toStringImage;
}
String intString = getUnscaledValue().toString();
if (scale == 0) {
return intString;
}
int begin = (getUnscaledValue().signum() < 0) ? 2 : 1;
int end = intString.length();
double exponent = -scale + end - begin;
StringBuilder result = new StringBuilder();
result.append(intString);
if ((scale > 0) && (exponent >= -6)) {
if (exponent >= 0) {
result.insert(end - (int) scale, '.');
} else {
result.insert(begin - 1, "0."); //$NON-NLS-1$
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((long) exponent));
}
toStringImage = result.toString();
return toStringImage;
}
/**
* 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);
}
/**
* Returns the unscaled value (mantissa) of this {@code BigDecimal} instance
* as a {@code BigInteger}. The unscaled value can be computed as {@code this}
* 10^(scale).
*
* @return unscaled value (this * 10^(scale)).
*/
public BigInteger unscaledValue() {
return getUnscaledValue();
}
/**
* 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 double approxPrecision() {
return (precision > 0) ? precision
: Math.floor((this.bitLength - 1) * LOG10_2) + 1;
}
private BigInteger getUnscaledValue() {
if (intVal == null) {
intVal = BigInteger.valueOf(smallValue);
}
return intVal;
}
private void initFrom(String val) {
int begin = 0; // first index to be copied
int offset = 0;
int last = val.length(); // one past the last index to be copied
String scaleString = null; // buffer for scale
StringBuilder unscaledBuffer; // buffer for unscaled value
unscaledBuffer = new StringBuilder(val.length());
// To skip a possible '+' symbol
if ((offset < last) && (val.charAt(offset) == '+')) {
offset++;
begin++;
// Fail if the next character is another sign.
if ((offset < last)
&& (val.charAt(offset) == '+' || val.charAt(offset) == '-')) {
throw new NumberFormatException("For input string: \"" + val + "\"");
}
}
// Accumulating all digits until a possible decimal point
while ((offset < last) && (val.charAt(offset) != '.')
&& (val.charAt(offset) != 'e') && (val.charAt(offset) != 'E')) {
offset++;
}
unscaledBuffer.append(val, begin, offset);
// A decimal point was found
if ((offset < last) && (val.charAt(offset) == '.')) {
offset++;
// Accumulating all digits until a possible exponent
begin = offset;
while ((offset < last) && (val.charAt(offset) != 'e')
&& (val.charAt(offset) != 'E')) {
offset++;
}
scale = offset - begin;
unscaledBuffer.append(val, begin, offset);
} else {
scale = 0;
}
// An exponent was found
if ((offset < last)
&& ((val.charAt(offset) == 'e') || (val.charAt(offset) == 'E'))) {
offset++;
// Checking for a possible sign of scale
begin = offset;
if ((offset < last) && (val.charAt(offset) == '+')) {
offset++;
if ((offset < last) && (val.charAt(offset) != '-')) {
begin++;
}
}
// Accumulating all remaining digits
scaleString = val.substring(begin, last);
// Checking if the scale is defined
scale = scale - Integer.parseInt(scaleString);
if (scale != (int) scale) {
// math.02=Scale out of range.
throw new NumberFormatException("Scale out of range."); //$NON-NLS-1$
}
}
// Parsing the unscaled value
String unscaled = unscaledBuffer.toString();
if (unscaled.length() < 16) {
smallValue = parseUnscaled(unscaled);
if (Double.isNaN(smallValue)) {
throw new NumberFormatException("For input string: \"" + val + "\"");
}
bitLength = bitLength(smallValue);
} else {
setUnscaledValue(new BigInteger(unscaled));
}
precision = unscaledBuffer.length();
// Don't count leading zeros in the precision
for (int i = 0; i < unscaledBuffer.length(); ++i) {
char ch = unscaledBuffer.charAt(i);
if (ch != '-' && ch != '0') {
break;
}
--precision;
}
// The precision of a zero value is 1
if (precision == 0) {
precision = 1;
}
}
/**
* 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 < 0 || 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 < SMALL_VALUE_BITS) {
smallRound(mc, discardedPrecision);
return;
}
// Getting the integer part and the discarded fraction
BigInteger sizeOfFraction = Multiplication.powerOf10(discardedPrecision);
BigInteger[] integerAndFraction = getUnscaledValue().divideAndRemainder(
sizeOfFraction);
double newScale = 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 = toIntScale(newScale);
precision = mcPrecision;
setUnscaledValue(integerAndFraction[0]);
}
private boolean isZero() {
return bitLength == 0 && this.smallValue != -1;
}
private BigDecimal movePoint(double 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 < SMALL_VALUE_BITS) {
return valueOf(smallValue, toIntScale(newScale));
}
return new BigDecimal(getUnscaledValue(), toIntScale(newScale));
}
if (-newScale < DOUBLE_TEN_POW.length
&& bitLength + DOUBLE_TEN_POW_BIT_LENGTH[(int) -newScale]
< SMALL_VALUE_BITS) {
return valueOf(smallValue * DOUBLE_TEN_POW[(int) -newScale], 0);
}
return new BigDecimal(Multiplication.multiplyByTenPow(getUnscaledValue(),
(int) -newScale), 0);
}
private void setUnscaledValue(BigInteger unscaledValue) {
this.intVal = unscaledValue;
this.bitLength = unscaledValue.bitLength();
if (this.bitLength < SMALL_VALUE_BITS) {
this.smallValue = unscaledValue.longValue();
}
}
/**
* 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 = (long) DOUBLE_TEN_POW[discardedPrecision];
long newScale = (long) scale - discardedPrecision;
long unscaledVal = (long) smallValue; // TODO convert to double math dont
// use longs
// 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 = Long.compare(Math.abs(fraction) << 1, 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 = toIntScale(newScale);
precision = mc.getPrecision();
smallValue = integer;
bitLength = bitLength(integer);
intVal = null;
}
/**
* 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();
}
// math.08=Rounding necessary
throw new ArithmeticException("Rounding necessary"); //$NON-NLS-1$
}
}