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 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");
}
if (mcPrecision > 0) {
newPrecision = new MathContext( mcPrecision + elength + 1,
mc.getRoundingMode());
}
// The result is calculated as if 'n' were positive
accum = round(newPrecision);
oneBitMask = 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;
}
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 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);
}
private void smallRound(MathContext mc, int discardedPrecision)
{
long sizeOfFraction = LONG_TEN_POW[discardedPrecision];
long newScale = (long)_scale - discardedPrecision;
long unscaledVal = smallValue;
// Getting the integer part and the discarded fraction
long integer = unscaledVal / sizeOfFraction;
long fraction = unscaledVal % sizeOfFraction;
int compRem;
// If the discarded fraction is non-zero perform rounding
if (fraction != 0) {
// To check if the discarded fraction >= 0.5
compRem = longCompareTo(Math.Abs(fraction) << 1,sizeOfFraction);
// To look if there is a carry
integer += roundingBehavior( ((int)integer) & 1,
Math.Sign(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;
}
private void inplaceRound(MathContext mc)
{
int mcPrecision = mc.getPrecision();
if (aproxPrecision() - 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 < 64) {
smallRound(mc, discardedPrecision);
return;
}
// Getting the integer part and the discarded fraction
BigInteger sizeOfFraction = Multiplication.powerOf10(discardedPrecision);
BigInteger[] integerAndFraction = getUnscaledValue().divideAndRemainder(sizeOfFraction);
long newScale = (long)_scale - discardedPrecision;
int compRem;
BigDecimal tempBD;
// If the discarded fraction is non-zero, perform rounding
if (integerAndFraction[1].signum() != 0) {
// To check if the discarded fraction >= 0.5
compRem = (integerAndFraction[1].abs().shiftLeftOneBit().compareTo(sizeOfFraction));
// To look if there is a carry
compRem = roundingBehavior( integerAndFraction[0].testBit(0) ? 1 : 0,
integerAndFraction[1].signum() * (5 + compRem),
mc.getRoundingMode());
if (compRem != 0) {
integerAndFraction[0] = integerAndFraction[0].add(BigInteger.valueOf(compRem));
}
tempBD = new BigDecimal(integerAndFraction[0]);
// If after to add the increment the precision changed, we normalize the size
if (tempBD.precision() > mcPrecision) {
integerAndFraction[0] = integerAndFraction[0].divide(BigInteger.TEN);
newScale--;
}
}
// To update all internal fields
_scale = toIntScale(newScale);
_precision = mcPrecision;
setUnscaledValue(integerAndFraction[0]);
}
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);
}