/**
* 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 static BigDecimal Multiply(BigDecimal value, BigDecimal multiplicand, MathContext mc)
{
BigDecimal result = Multiply(value, multiplicand);
result.InplaceRound(mc);
return(result);
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this % divisor}.
* <p>
* The remainder is defined as {@code this -
* this.divideToIntegralValue(divisor) * divisor}.
* <p>
* 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 static BigDecimal Remainder(BigDecimal a, BigDecimal b, MathContext context)
{
BigDecimal remainder;
DivideAndRemainder(a, b, context, out remainder);
return(remainder);
}
/**
* 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 static BigDecimal DivideAndRemainder(BigDecimal a,
BigDecimal b,
MathContext context,
out BigDecimal remainder)
{
return(BigDecimalMath.DivideAndRemainder(a, b, context, out remainder));
}
public BigComplex Inverse(MathContext mc)
{
BigDecimal hyp = Norm();
/* 1/(x+iy)= (x-iy)/(x^2+y^2 */
return(new BigComplex(Real.Divide(hyp, mc), Imaginary.Divide(hyp, mc).Negate()));
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this}, rounded
* according to the passed context {@code mc}.
* <p>
* If {@code mc.precision = 0}, then no rounding is performed.
* <p>
* 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 static BigDecimal Round(BigDecimal number, MathContext mc)
{
var thisBD = new BigDecimal(number.UnscaledValue, number.Scale);
thisBD.InplaceRound(mc);
return(thisBD);
}
public BigComplex Sqrt(MathContext mc)
{
BigDecimal half = new BigDecimal(2);
/* compute l=sqrt(re^2+im^2), then u=sqrt((l+re)/2)
* and v= +- sqrt((l-re)/2 as the new real and imaginary parts.
*/
BigDecimal l = Abs(mc);
if (l.CompareTo(BigDecimal.Zero) == 0)
{
return(new BigComplex(BigMath.ScalePrecision(BigDecimal.Zero, mc),
BigMath.ScalePrecision(BigDecimal.Zero, mc)));
}
BigDecimal u = BigMath.Sqrt(l.Add(Real).Divide(half, mc), mc);
BigDecimal v = BigMath.Sqrt(l.Subtract(Real).Divide(half, mc), mc);
if (Imaginary.CompareTo(BigDecimal.Zero) >= 0)
{
return(new BigComplex(u, v));
}
else
{
return(new BigComplex(u, v.Negate()));
}
}
public BigComplex Multiply(BigComplex oth, MathContext mc)
{
BigDecimal a = Real.Add(Imaginary).Multiply(oth.Real);
BigDecimal b = oth.Real.Add(oth.Imaginary).Multiply(Imaginary);
BigDecimal c = oth.Imaginary.Subtract(oth.Real).Multiply(Real);
BigDecimal x = a.Subtract(b, mc);
BigDecimal y = a.Add(c, mc);
return(new BigComplex(x, y));
}
public static BigDecimal Add(BigDecimal value, 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)value.Scale - augend.Scale;
// Some operand is zero or the precision is infinity
if ((augend.IsZero) || (value.IsZero) || (mc.Precision == 0))
{
return(BigMath.Round(Add(value, augend), mc));
}
// Cases where there is room for optimizations
if (value.AproxPrecision() < diffScale - 1)
{
larger = augend;
smaller = value;
}
else if (augend.AproxPrecision() < -diffScale - 1)
{
larger = value;
smaller = augend;
}
else
{
// No optimization is done
return(BigMath.Round(Add(value, augend), mc));
}
if (mc.Precision >= larger.AproxPrecision())
{
// No optimization is done
return(BigMath.Round(Add(value, augend), mc));
}
// Cases where it's unnecessary to add two numbers with very different scales
var largerSignum = larger.Sign;
if (largerSignum == smaller.Sign)
{
tempBi = Multiplication.MultiplyByPositiveInt(larger.UnscaledValue, 10) +
BigInteger.FromInt64(largerSignum);
}
else
{
tempBi = larger.UnscaledValue - BigInteger.FromInt64(largerSignum);
tempBi = Multiplication.MultiplyByPositiveInt(tempBi, 10) +
BigInteger.FromInt64(largerSignum * 9);
}
// Rounding the improved adding
larger = new BigDecimal(tempBi, larger.Scale + 1);
return(BigMath.Round(larger, mc));
}
public BigDecimal ToBigDecimal(MathContext mc)
{
/* numerator and denominator individually rephrased
*/
var n = new BigDecimal(Numerator);
var d = new BigDecimal(Denominator);
/* the problem with n.divide(d,mc) is that the apparent precision might be
* smaller than what is set by mc if the value has a precise truncated representation.
* 1/4 will appear as 0.25, independent of mc
*/
return(BigMath.ScalePrecision(n.Divide(d, mc), mc));
}
public static BigDecimal Pow(BigDecimal number, int n, MathContext mc)
{
// The ANSI standard X3.274-1996 algorithm
int m = System.Math.Abs(n);
int mcPrecision = mc.Precision;
int elength = (int)System.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) || ((number.IsZero) && (n > 0)))
{
return(Pow(number, n));
}
if ((m > 999999999) || ((mcPrecision == 0) && (n < 0)) ||
((mcPrecision > 0) && (elength > mcPrecision)))
{
// math.07=Invalid Operation
throw new ArithmeticException(Messages.math07); //$NON-NLS-1$
}
if (mcPrecision > 0)
{
newPrecision = new MathContext(mcPrecision + elength + 1,
mc.RoundingMode);
}
// The result is calculated as if 'n' were positive
accum = BigMath.Round(number, newPrecision);
oneBitMask = Utils.HighestOneBit(m) >> 1;
while (oneBitMask > 0)
{
accum = BigMath.Multiply(accum, accum, newPrecision);
if ((m & oneBitMask) == oneBitMask)
{
accum = BigMath.Multiply(accum, number, newPrecision);
}
oneBitMask >>= 1;
}
// If 'n' is negative, the value is divided into 'ONE'
if (n < 0)
{
accum = Divide(BigDecimal.One, accum, newPrecision);
}
// The final value is rounded to the destination precision
accum.InplaceRound(mc);
return(accum);
}
public static BigDecimal Subtract(BigDecimal value, BigDecimal subtrahend, MathContext mc)
{
if (subtrahend == null)
{
throw new ArgumentNullException("subtrahend");
}
if (mc == null)
{
throw new ArgumentNullException("mc");
}
long diffScale = subtrahend.Scale - (long)value.Scale;
// Some operand is zero or the precision is infinity
if ((subtrahend.IsZero) || (value.IsZero) || (mc.Precision == 0))
{
return(BigMath.Round(Subtract(value, subtrahend), 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.Precision < value.AproxPrecision())
{
var thisSignum = value.Sign;
BigInteger tempBI;
if (thisSignum != subtrahend.Sign)
{
tempBI = Multiplication.MultiplyByPositiveInt(value.UnscaledValue, 10) +
BigInteger.FromInt64(thisSignum);
}
else
{
tempBI = value.UnscaledValue - BigInteger.FromInt64(thisSignum);
tempBI = Multiplication.MultiplyByPositiveInt(tempBI, 10) +
BigInteger.FromInt64(thisSignum * 9);
}
// Rounding the improved subtracting
var leftOperand = new BigDecimal(tempBI, value.Scale + 1); // it will be only the left operand (this)
return(BigMath.Round(leftOperand, mc));
}
}
// No optimization is done
return(BigMath.Round(Subtract(value, subtrahend), mc));
}
public void MathContextConstruction()
{
String a = "-12380945E+61";
BigDecimal aNumber = BigDecimal.Parse(a);
int precision = 6;
RoundingMode rm = RoundingMode.HalfDown;
MathContext mcIntRm = new MathContext(precision, rm);
MathContext mcStr = MathContext.Parse("precision=6 roundingMode=HALFDOWN");
MathContext mcInt = new MathContext(precision);
BigDecimal res = BigMath.Abs(aNumber, mcInt);
Assert.Equal(res, BigDecimal.Parse("1.23809E+68"));
Assert.Equal(mcIntRm, mcStr);
Assert.Equal(mcInt.Equals(mcStr), false);
Assert.Equal(mcIntRm.GetHashCode(), mcStr.GetHashCode());
Assert.Equal(mcIntRm.ToString(), "precision=6 roundingMode=HalfDown");
}
public void MathContextConstruction()
{
String a = "-12380945E+61";
BigDecimal aNumber = BigDecimal.Parse(a);
int precision = 6;
RoundingMode rm = RoundingMode.HalfDown;
MathContext mcIntRm = new MathContext(precision, rm);
MathContext mcStr = MathContext.Parse("precision=6 roundingMode=HALFDOWN");
MathContext mcInt = new MathContext(precision);
BigDecimal res = aNumber.Abs(mcInt);
Assert.AreEqual(res, BigDecimal.Parse("1.23809E+68"), "MathContext Constructor with int precision failed");
Assert.AreEqual(mcIntRm, mcStr, "Equal MathContexts are not Equal ");
Assert.AreEqual(mcInt.Equals(mcStr), false, "Different MathContext are reported as Equal ");
Assert.AreEqual(mcIntRm.GetHashCode(), mcStr.GetHashCode(), "Equal MathContexts have different hashcodes ");
Assert.AreEqual(mcIntRm.ToString(), "precision=6 roundingMode=HalfDown",
"MathContext.ToString() returning incorrect value");
}
public BigDecimal Abs(MathContext mc)
{
return(BigMath.Sqrt(Norm(), mc));
}
/**
* Returns a new {@code BigDecimal} whose value is the integral part of
* {@code this / divisor}. The quotient is rounded down towards zero to the
* next integer. 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 static BigDecimal DivideToIntegral(BigDecimal a, BigDecimal b, MathContext context)
{
return(BigDecimalMath.DivideToIntegralValue(a, b, context));
}
public BigComplex Divide(BigComplex oth, MathContext mc)
{
/* lazy implementation: (x+iy)/(a+ib)= (x+iy)* 1/(a+ib) */
return(Multiply(oth.Inverse(mc), mc));
}
/**
* Returns a new {@code BigDecimal} whose value is {@code this ^ n}. The
* result is rounded according to the passed context {@code mc}.
* <p>
* 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 static BigDecimal Pow(BigDecimal number, int exp, MathContext context)
{
return(BigDecimalMath.Pow(number, exp, context));
}
/**
* 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 static BigDecimal Abs(BigDecimal value, MathContext mc)
{
return(Abs(Round(value, mc)));
}
public static BigDecimal DivideAndRemainder(BigDecimal dividend, BigDecimal divisor, MathContext mc, out BigDecimal remainder)
{
var quotient = DivideToIntegralValue(dividend, divisor, mc);
remainder = Subtract(dividend, Multiply(quotient, divisor));
return(quotient);
}
public static BigDecimal DivideToIntegralValue(BigDecimal dividend, BigDecimal divisor, MathContext mc)
{
int mcPrecision = mc.Precision;
int diffPrecision = dividend.Precision - divisor.Precision;
int lastPow = BigDecimal.TenPow.Length - 1;
long diffScale = (long)dividend.Scale - divisor.Scale;
long newScale = diffScale;
long quotPrecision = diffPrecision - diffScale + 1;
BigInteger quotient;
BigInteger remainder;
// In special cases it call the dual method
if ((mcPrecision == 0) || (dividend.IsZero) || (divisor.IsZero))
{
return(DivideToIntegralValue(dividend, divisor));
}
// Let be: this = [u1,s1] and divisor = [u2,s2]
if (quotPrecision <= 0)
{
quotient = BigInteger.Zero;
}
else if (diffScale == 0)
{
// CASE s1 == s2: to calculate u1 / u2
quotient = dividend.UnscaledValue / divisor.UnscaledValue;
}
else if (diffScale > 0)
{
// CASE s1 >= s2: to calculate u1 / (u2 * 10^(s1-s2)
quotient = dividend.UnscaledValue / (divisor.UnscaledValue * Multiplication.PowerOf10(diffScale));
// To chose 10^newScale to get a quotient with at least 'mc.precision()' digits
newScale = System.Math.Min(diffScale, System.Math.Max(mcPrecision - quotPrecision + 1, 0));
// To calculate: (u1 / (u2 * 10^(s1-s2)) * 10^newScale
quotient = quotient * 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 = System.Math.Min(-diffScale, System.Math.Max((long)mcPrecision - diffPrecision, 0));
long compRemDiv;
// Let be: (u1 * 10^exp) / u2 = [q,r]
quotient = BigMath.DivideAndRemainder(dividend.UnscaledValue * Multiplication.PowerOf10(exp),
divisor.UnscaledValue, out remainder);
newScale += exp; // To fix the scale
exp = -newScale; // The remaining power of ten
// If after division there is a remainder...
if ((remainder.Sign != 0) && (exp > 0))
{
// Log10(r) + ((s2 - s1) - exp) > mc.precision ?
compRemDiv = (new BigDecimal(remainder)).Precision
+ exp - divisor.Precision;
if (compRemDiv == 0)
{
// To calculate: (r * 10^exp2) / u2
remainder = (remainder * Multiplication.PowerOf10(exp)) / divisor.UnscaledValue;
compRemDiv = System.Math.Abs(remainder.Sign);
}
if (compRemDiv > 0)
{
// The quotient won't fit in 'mc.precision()' digits
// math.06=Division impossible
throw new ArithmeticException(Messages.math06); //$NON-NLS-1$
}
}
}
// Fast return if the quotient is zero
if (quotient.Sign == 0)
{
return(BigDecimal.GetZeroScaledBy(diffScale));
}
BigInteger strippedBI = quotient;
BigDecimal integralValue = new BigDecimal(quotient);
long resultPrecision = integralValue.Precision;
int i = 1;
// To strip trailing zeros until the specified precision is reached
while (!BigInteger.TestBit(strippedBI, 0))
{
quotient = BigMath.DivideAndRemainder(strippedBI, BigDecimal.TenPow[i], out remainder);
if ((remainder.Sign == 0) &&
((resultPrecision - i >= mcPrecision) ||
(newScale - i >= diffScale)))
{
resultPrecision -= i;
newScale -= i;
if (i < lastPow)
{
i++;
}
strippedBI = quotient;
}
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(Messages.math06); //$NON-NLS-1$
}
integralValue.Scale = BigDecimal.ToIntScale(newScale);
integralValue.SetUnscaledValue(strippedBI);
return(integralValue);
}
/**
* 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 static BigDecimal Divide(BigDecimal a, BigDecimal b, MathContext context)
{
return(BigDecimalMath.Divide(a, b, context));
}
/// <summary>
/// Adds a value to the current instance of <see cref="BigDecimal"/>,
/// rounding the result according to the provided context.
/// </summary>
/// <param name="augend">The value to be added to this instance.</param>
/// <param name="mc">The rounding mode and precision for the result of
/// this operation.</param>
/// <returns>
/// Returns a new <see cref="BigDecimal"/> whose value is <c>this + <paramref name="augend"/></c>.
/// </returns>
/// <exception cref="ArgumentNullException">
/// If the given <paramref name="augend"/> or <paramref name="mc"/> is <c>null</c>.
/// </exception>
public static BigDecimal Add(BigDecimal value, BigDecimal augend, MathContext mc)
{
return(BigDecimalMath.Add(value, augend, mc));
}
/// <remarks>
/// Returns a new <see cref="BigDecimal"/> whose value is <c>+this</c>.
/// </remarks>
/// <param name="mc">Rounding mode and precision for the result of this operation.</param>
/// <remarks>
/// The result is rounded according to the passed context <paramref name="mc"/>.
/// </remarks>
/// <returns>
/// Returns this decimal value rounded.
/// </returns>
public static BigDecimal Plus(BigDecimal number, MathContext mc)
{
return(Round(number, mc));
}
/**
* 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 static BigDecimal Negate(BigDecimal number, MathContext mc)
{
return(Negate(Round(number, mc)));
}
public static BigDecimal Divide(BigDecimal dividend, 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.Precision + 2L
+ divisor.AproxPrecision() - dividend.AproxPrecision();
long diffScale = (long)dividend.Scale - divisor.Scale;
long newScale = diffScale; // scale of the final quotient
int compRem; // to compare the remainder
int i = 1; // index
int lastPow = BigDecimal.TenPow.Length - 1; // last power of ten
BigInteger integerQuot; // for temporal results
BigInteger quotient = dividend.UnscaledValue;
BigInteger remainder;
// In special cases it reduces the problem to call the dual method
if ((mc.Precision == 0) || (dividend.IsZero) || (divisor.IsZero))
{
return(Divide(dividend, divisor));
}
if (traillingZeros > 0)
{
// To append trailing zeros at end of dividend
quotient = dividend.UnscaledValue * Multiplication.PowerOf10(traillingZeros);
newScale += traillingZeros;
}
quotient = BigMath.DivideAndRemainder(quotient, divisor.UnscaledValue, out remainder);
integerQuot = quotient;
// Calculating the exact quotient with at least 'mc.precision()' digits
if (remainder.Sign != 0)
{
// Checking if: 2 * remainder >= divisor ?
compRem = remainder.ShiftLeftOneBit().CompareTo(divisor.UnscaledValue);
// quot := quot * 10 + r; with 'r' in {-6,-5,-4, 0,+4,+5,+6}
integerQuot = (integerQuot * BigInteger.Ten) +
BigInteger.FromInt64(quotient.Sign * (5 + compRem));
newScale++;
}
else
{
// To strip trailing zeros until the preferred scale is reached
while (!BigInteger.TestBit(integerQuot, 0))
{
quotient = BigMath.DivideAndRemainder(integerQuot, BigDecimal.TenPow[i], out remainder);
if ((remainder.Sign == 0) &&
(newScale - i >= diffScale))
{
newScale -= i;
if (i < lastPow)
{
i++;
}
integerQuot = quotient;
}
else
{
if (i == 1)
{
break;
}
i = 1;
}
}
}
// To perform rounding
return(new BigDecimal(integerQuot, BigDecimal.ToIntScale(newScale), mc));
}
/// <summary>
/// Subtracts the given value from this instance of <see cref="BigDecimal"/>.
/// </summary>
/// <remarks>
/// <para>
/// This overload rounds the result of the operation to the <paramref name="mc">context</paramref>
/// provided as argument.
/// </para>
/// </remarks>
/// <param name="subtrahend">The value to be subtracted from this <see cref="BigDecimal"/>.</param>
/// <param name="mc">The context used to round the result of this operation.</param>
/// <returns>
/// Returns an instance of <see cref="BigDecimal"/> that is the result of the
/// subtraction of the given <paramref name="subtrahend"/> from this instance.
/// </returns>
/// <exception cref="ArgumentNullException">
/// If either of the given <paramref name="subtrahend"/> or <paramref name="mc"/> are <c>null</c>.
/// </exception>
public static BigDecimal Subtract(BigDecimal value, BigDecimal subtrahend, MathContext mc)
{
return(BigDecimalMath.Subtract(value, subtrahend, mc));
}
