public BigDecimal multiply(BigDecimal multiplicand)
{
long newScale = (long)this._scale + multiplicand._scale;
if ((this.isZero()) || (multiplicand.isZero())) {
return zeroScaledBy(newScale);
}
/* Let be: this = [u1,s1] and multiplicand = [u2,s2] so:
* this x multiplicand = [ s1 * s2 , s1 + s2 ] */
if(this._bitLength + multiplicand._bitLength < 64) {
return valueOf(this.smallValue*multiplicand.smallValue,toIntScale(newScale));
}
return new BigDecimal(this.getUnscaledValue().multiply(
multiplicand.getUnscaledValue()), toIntScale(newScale));
}
public BigDecimal divideToIntegralValue(BigDecimal divisor)
{
BigInteger integralValue; // the integer of result
BigInteger powerOfTen; // some power of ten
BigInteger[] quotAndRem = {getUnscaledValue()};
long newScale = (long)this._scale - divisor._scale;
long tempScale = 0;
int i = 1;
int lastPow = TEN_POW.Length - 1;
if (divisor.isZero()) {
throw new ArithmeticException("Division by zero");
}
if ((divisor.aproxPrecision() + newScale > this.aproxPrecision() + 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)));
}
public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc)
{
int mcPrecision = mc.getPrecision();
int diffPrecision = this.precision() - divisor.precision();
int lastPow = TEN_POW.Length - 1;
long diffScale = (long)this._scale - divisor._scale;
long newScale = diffScale;
long quotPrecision = diffPrecision - diffScale + 1;
BigInteger[] quotAndRem = new BigInteger[2];
// In special cases it call the dual method
if ((mcPrecision == 0) || (this.isZero()) || (divisor.isZero())) {
return this.divideToIntegralValue(divisor);
}
// Let be: this = [u1,s1] and divisor = [u2,s2]
if (quotPrecision <= 0) {
quotAndRem[0] = BigInteger.ZERO;
} else if (diffScale == 0) {
// CASE s1 == s2: to calculate u1 / u2
quotAndRem[0] = this.getUnscaledValue().divide( divisor.getUnscaledValue() );
} else if (diffScale > 0) {
// CASE s1 >= s2: to calculate u1 / (u2 * 10^(s1-s2)
quotAndRem[0] = this.getUnscaledValue().divide(
divisor.getUnscaledValue().multiply(Multiplication.powerOf10(diffScale)) );
// To chose 10^newScale to get a quotient with at least 'mc.precision()' digits
newScale = Math.Min(diffScale, Math.Max(mcPrecision - quotPrecision + 1, 0));
// To calculate: (u1 / (u2 * 10^(s1-s2)) * 10^newScale
quotAndRem[0] = quotAndRem[0].multiply(Multiplication.powerOf10(newScale));
} else {// CASE s2 > s1:
/* To calculate the minimum power of ten, such that the quotient
* (u1 * 10^exp) / u2 has at least 'mc.precision()' digits. */
long exp = Math.Min(-diffScale, Math.Max((long)mcPrecision - diffPrecision, 0));
long compRemDiv;
// Let be: (u1 * 10^exp) / u2 = [q,r]
quotAndRem = this.getUnscaledValue().multiply(Multiplication.powerOf10(exp)).
divideAndRemainder(divisor.getUnscaledValue());
newScale += exp; // To fix the scale
exp = -newScale; // The remaining power of ten
// If after division there is a remainder...
if ((quotAndRem[1].signum() != 0) && (exp > 0)) {
// Log10(r) + ((s2 - s1) - exp) > mc.precision ?
compRemDiv = (new BigDecimal(quotAndRem[1])).precision()
+ exp - divisor.precision();
if (compRemDiv == 0) {
// To calculate: (r * 10^exp2) / u2
quotAndRem[1] = quotAndRem[1].multiply(Multiplication.powerOf10(exp)).
divide(divisor.getUnscaledValue());
compRemDiv = Math.Abs(quotAndRem[1].signum());
}
if (compRemDiv > 0) {
// The quotient won't fit in 'mc.precision()' digits
throw new ArithmeticException("Division impossible");
}
}
}
// Fast return if the quotient is zero
if (quotAndRem[0].signum() == 0) {
return zeroScaledBy(diffScale);
}
BigInteger strippedBI = quotAndRem[0];
BigDecimal integralValue = new BigDecimal(quotAndRem[0]);
long resultPrecision = integralValue.precision();
int i = 1;
// To strip trailing zeros until the specified precision is reached
while (!strippedBI.testBit(0)) {
quotAndRem = strippedBI.divideAndRemainder(TEN_POW[i]);
if ((quotAndRem[1].signum() == 0) &&
((resultPrecision - i >= mcPrecision)
|| (newScale - i >= diffScale)) ) {
resultPrecision -= i;
newScale -= i;
if (i < lastPow) {
i++;
}
strippedBI = quotAndRem[0];
} else {
if (i == 1) {
break;
}
i = 1;
}
}
// To check if the result fit in 'mc.precision()' digits
if (resultPrecision > mcPrecision) {
throw new ArithmeticException("Division impossible");
}
integralValue._scale = toIntScale(newScale);
integralValue.setUnscaledValue(strippedBI);
return integralValue;
}
public BigDecimal divide(BigDecimal divisor)
{
BigInteger p = this.getUnscaledValue();
BigInteger q = divisor.getUnscaledValue();
BigInteger gcd; // greatest common divisor between 'p' and 'q'
BigInteger[] quotAndRem;
long diffScale = (long)_scale - divisor._scale;
int newScale; // the new scale for final quotient
int k; // number of factors "2" in 'q'
int l = 0; // number of factors "5" in 'q'
int i = 1;
int lastPow = FIVE_POW.Length - 1;
if (divisor.isZero()) {
throw new ArithmeticException("Division by zero");
}
if (p.signum() == 0) {
return zeroScaledBy(diffScale);
}
// To divide both by the GCD
gcd = p.gcd(q);
p = p.divide(gcd);
q = q.divide(gcd);
// To simplify all "2" factors of q, dividing by 2^k
k = q.getLowestSetBit();
q = q.shiftRight(k);
// To simplify all "5" factors of q, dividing by 5^l
do {
quotAndRem = q.divideAndRemainder(FIVE_POW[i]);
if (quotAndRem[1].signum() == 0) {
l += i;
if (i < lastPow) {
i++;
}
q = quotAndRem[0];
} else {
if (i == 1) {
break;
}
i = 1;
}
} while (true);
// If abs(q) != 1 then the quotient is periodic
if (!q.abs().Equals(BigInteger.ONE)) {
throw new ArithmeticException("Non-terminating decimal expansion; no exact representable decimal result.");
}
// The sign of the is fixed and the quotient will be saved in 'p'
if (q.signum() < 0) {
p = p.negate();
}
// Checking if the new scale is out of range
newScale = 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);
}
public BigDecimal divide(BigDecimal divisor, MathContext mc)
{
/* Calculating how many zeros must be append to 'dividend'
* to obtain a quotient with at least 'mc.precision()' digits */
long traillingZeros = mc.getPrecision() + 2L
+ divisor.aproxPrecision() - aproxPrecision();
long diffScale = (long)_scale - divisor._scale;
long newScale = diffScale; // scale of the final quotient
int compRem; // to compare the remainder
int i = 1; // index
int lastPow = TEN_POW.Length - 1; // last power of ten
BigInteger integerQuot; // for temporal results
BigInteger[] quotAndRem = {getUnscaledValue()};
// In special cases it reduces the problem to call the dual method
if ((mc.getPrecision() == 0) || (this.isZero())
|| (divisor.isZero())) {
return this.divide(divisor);
}
if (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);
}
public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode)
{
// Let be: this = [u1,s1] and divisor = [u2,s2]
if (divisor.isZero()) {
throw new ArithmeticException("Division by zero");
}
long diffScale = ((long)this._scale - divisor._scale) - scale;
if(this._bitLength < 64 && divisor._bitLength < 64 ) {
if(diffScale == 0) {
return dividePrimitiveLongs(this.smallValue,
divisor.smallValue,
scale,
roundingMode );
} else if(diffScale > 0) {
if(diffScale < LONG_TEN_POW.Length &&
divisor._bitLength + LONG_TEN_POW_BIT_LENGTH[(int)diffScale] < 64) {
return dividePrimitiveLongs(this.smallValue,
divisor.smallValue*LONG_TEN_POW[(int)diffScale],
_scale,
roundingMode);
}
} else { // diffScale < 0
if(-diffScale < LONG_TEN_POW.Length &&
this._bitLength + LONG_TEN_POW_BIT_LENGTH[(int)-diffScale] < 64) {
return dividePrimitiveLongs(this.smallValue*LONG_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);
}
public BigDecimal add(BigDecimal augend, MathContext mc)
{
BigDecimal larger; // operand with the largest unscaled value
BigDecimal smaller; // operand with the smallest unscaled value
BigInteger tempBI;
long diffScale = (long)this._scale - augend._scale;
int largerSignum;
// Some operand is zero or the precision is infinity
if ((augend.isZero()) || (this.isZero())
|| (mc.getPrecision() == 0)) {
return add(augend).round(mc);
}
// Cases where there is room for optimizations
if (this.aproxPrecision() < diffScale - 1) {
larger = augend;
smaller = this;
} else if (augend.aproxPrecision() < -diffScale - 1) {
larger = this;
smaller = augend;
} else {// No optimization is done
return add(augend).round(mc);
}
if (mc.getPrecision() >= larger.aproxPrecision()) {
// 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);
}
public BigDecimal add(BigDecimal augend)
{
int diffScale = this._scale - augend._scale;
// Fast return when some operand is zero
if (this.isZero()) {
if (diffScale <= 0) {
return augend;
}
if (augend.isZero()) {
return this;
}
} else if (augend.isZero()) {
if (diffScale >= 0) {
return this;
}
}
// Let be: this = [u1,s1] and augend = [u2,s2]
if (diffScale == 0) {
// case s1 == s2: [u1 + u2 , s1]
if (Math.Max(this._bitLength, augend._bitLength) + 1 < 64) {
return valueOf(this.smallValue + augend.smallValue, this._scale);
}
return new BigDecimal(this.getUnscaledValue().add(augend.getUnscaledValue()), this._scale);
} else if (diffScale > 0) {
// case s1 > s2 : [(u1 + u2) * 10 ^ (s1 - s2) , s1]
return addAndMult10(this, augend, diffScale);
} else {// case s2 > s1 : [(u2 + u1) * 10 ^ (s2 - s1) , s2]
return addAndMult10(augend, this, -diffScale);
}
}
public BigDecimal subtract(BigDecimal subtrahend, MathContext mc)
{
long diffScale = subtrahend._scale - (long)this._scale;
int thisSignum;
BigDecimal leftOperand; // it will be only the left operand (this)
BigInteger tempBI;
// Some operand is zero or the precision is infinity
if ((subtrahend.isZero()) || (this.isZero())
|| (mc.getPrecision() == 0)) {
return subtract(subtrahend).round(mc);
}
// Now: this != 0 and subtrahend != 0
if (subtrahend.aproxPrecision() < diffScale - 1) {
// Cases where it is unnecessary to subtract two numbers with very different scales
if (mc.getPrecision() < this.aproxPrecision()) {
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);
}
public BigDecimal subtract(BigDecimal subtrahend)
{
int diffScale = this._scale - subtrahend._scale;
// Fast return when some operand is zero
if (this.isZero()) {
if (diffScale <= 0) {
return subtrahend.negate();
}
if (subtrahend.isZero()) {
return this;
}
} else if (subtrahend.isZero()) {
if (diffScale >= 0) {
return this;
}
}
// Let be: this = [u1,s1] and subtrahend = [u2,s2] so:
if (diffScale == 0) {
// case s1 = s2 : [u1 - u2 , s1]
if (Math.Max(this._bitLength, subtrahend._bitLength) + 1 < 64) {
return valueOf(this.smallValue - subtrahend.smallValue,this._scale);
}
return new BigDecimal(this.getUnscaledValue().subtract(subtrahend.getUnscaledValue()), this._scale);
} else if (diffScale > 0) {
// case s1 > s2 : [ u1 - u2 * 10 ^ (s1 - s2) , s1 ]
if(diffScale < LONG_TEN_POW.Length &&
Math.Max(this._bitLength,subtrahend._bitLength+LONG_TEN_POW_BIT_LENGTH[diffScale])+1<64) {
return valueOf(this.smallValue-subtrahend.smallValue*LONG_TEN_POW[diffScale],this._scale);
}
return new BigDecimal(this.getUnscaledValue().subtract(
Multiplication.multiplyByTenPow(subtrahend.getUnscaledValue(),diffScale)), this._scale);
} else {// case s2 > s1 : [ u1 * 10 ^ (s2 - s1) - u2 , s2 ]
diffScale = -diffScale;
if(diffScale < LONG_TEN_POW.Length &&
Math.Max(this._bitLength+LONG_TEN_POW_BIT_LENGTH[diffScale],subtrahend._bitLength)+1<64) {
return valueOf(this.smallValue*LONG_TEN_POW[diffScale]-subtrahend.smallValue,subtrahend._scale);
}
return new BigDecimal(Multiplication.multiplyByTenPow(this.getUnscaledValue(),diffScale)
.subtract(subtrahend.getUnscaledValue()), subtrahend._scale);
}
}
