public bool Equals(SqlNumber other)
{
if (State == NumericState.NegativeInfinity &&
other.State == NumericState.NegativeInfinity)
{
return(true);
}
if (State == NumericState.PositiveInfinity &&
other.State == NumericState.PositiveInfinity)
{
return(true);
}
if (State == NumericState.NotANumber &&
other.State == NumericState.NotANumber)
{
return(true);
}
if (IsNull && other.IsNull)
{
return(true);
}
if (IsNull && !other.IsNull)
{
return(false);
}
if (!IsNull && other.IsNull)
{
return(false);
}
return(innerValue.CompareTo(other.innerValue) == 0);
}
public bool Equals(SqlNumber other)
{
if (state != other.state)
{
return(false);
}
if (state != NumericState.None)
{
return(true);
}
return(innerValue.CompareTo(other.innerValue) == 0);
}
public BigDecimal Get(BigDecimal n)
{
if (n.CompareTo(ZERO) <= 0)
{
throw new System.ArgumentException();
}
BigDecimal initialGuess = GetInitialApproximation(n);
BigDecimal lastGuess = ZERO;
BigDecimal guess = new BigDecimal(initialGuess.ToString());
int iterations = 0;
bool more = true;
while (more)
{
lastGuess = guess;
guess = n.divide(guess, scale, BigDecimal.ROUND_HALF_UP);
guess = guess.add(lastGuess);
guess = guess.divide(TWO, scale, BigDecimal.ROUND_HALF_UP);
error = n.subtract(guess.multiply(guess));
if (++iterations >= maxIterations)
{
more = false;
}
else if (lastGuess.Equals(guess))
{
more = error.abs().CompareTo(ONE) >= 0;
}
}
return(guess);
}
public static void CheckUpperBound(BigDecimal val)
{
if (val.CompareTo(MaxNativeValue) == 1)
{
throw GetOutOfBoundsException(val, "bigger", MaxNativeValue);
}
}
/// <summary>Returns a list of BigDecimals one element longer than the list of input splits.
/// </summary>
/// <remarks>
/// Returns a list of BigDecimals one element longer than the list of input splits.
/// This represents the boundaries between input splits.
/// All splits are open on the top end, except the last one.
/// So the list [0, 5, 8, 12, 18] would represent splits capturing the intervals:
/// [0, 5)
/// [5, 8)
/// [8, 12)
/// [12, 18] note the closed interval for the last split.
/// </remarks>
/// <exception cref="Java.Sql.SQLException"/>
internal virtual IList <BigDecimal> Split(BigDecimal numSplits, BigDecimal minVal,
BigDecimal maxVal)
{
IList <BigDecimal> splits = new AList <BigDecimal>();
// Use numSplits as a hint. May need an extra task if the size doesn't
// divide cleanly.
BigDecimal splitSize = TryDivide(maxVal.Subtract(minVal), (numSplits));
if (splitSize.CompareTo(MinIncrement) < 0)
{
splitSize = MinIncrement;
Log.Warn("Set BigDecimal splitSize to MIN_INCREMENT");
}
BigDecimal curVal = minVal;
while (curVal.CompareTo(maxVal) <= 0)
{
splits.AddItem(curVal);
curVal = curVal.Add(splitSize);
}
if (splits[splits.Count - 1].CompareTo(maxVal) != 0 || splits.Count == 1)
{
// We didn't end on the maxVal. Add that to the end of the list.
splits.AddItem(maxVal);
}
return(splits);
}
public void CompareToTest()
{
var v1 = new BigDecimal(100.001m);
var v2 = new BigDecimal(100.001m);
Assert.IsTrue(v1.CompareTo(v2) == 0);
}
public void Compare_MultipleValues_Pass()
{
var num1 = new BigDecimal(20);
var num2 = new BigDecimal(30);
var actual = num1.CompareTo(num2);
var expected = -1;
Assert.AreEqual(expected, actual);
actual = num1.CompareTo(num1);
expected = 0;
Assert.AreEqual(expected, actual);
actual = num2.CompareTo(num1);
expected = 1;
Assert.AreEqual(expected, actual);
}
public void CompareToBigDecimal()
{
BigDecimal comp1 = BigDecimal.Parse("1.00");
BigDecimal comp2 = new BigDecimal(1.000000D);
Assert.IsTrue(comp1.CompareTo(comp2) == 0, "1.00 and 1.000000 should be equal");
BigDecimal comp3 = BigDecimal.Parse("1.02");
Assert.IsTrue(comp3.CompareTo(comp1) == 1, "1.02 should be bigger than 1.00");
BigDecimal comp4 = new BigDecimal(0.98D);
Assert.IsTrue(comp4.CompareTo(comp1) == -1, "0.98 should be less than 1.00");
}
public String Format(BigDecimal b, int maxLength, int maxNumberOfIntegers, int maxNumberOfDecimals, bool padFractions)
{
String basePattern = "0." + StringUtils.Repeat(padFractions ? "0" : "#", maxNumberOfDecimals);
String text = String.Format("{0:" + basePattern + "}", (decimal)b);
// the above takes care of the decimals having too many digits; now to handle digits to left of decimal.
// this code preserves a negative sign to match what the java code does (this is possibly not ideal)
int decimalLocation = text.IndexOf(".");
if (decimalLocation > maxNumberOfIntegers)
{
return((b.CompareTo(BigDecimal.ZERO) < 0 ? "-" : "") + text.Substring(decimalLocation - maxNumberOfIntegers));
}
else if (decimalLocation == -1 && text.Length > maxNumberOfIntegers)
{
return((b.CompareTo(BigDecimal.ZERO) < 0 ? "-" : "") + text.Substring(text.Length - maxNumberOfIntegers));
}
else
{
return(text);
}
}
public BigDecimal calDens(BigDecimal radius)
{
BigDecimal vol = BigDecimal.Parse("0.0");
BigDecimal num = BigDecimal.Parse("1.33333333333");
BigDecimal pi = BigDecimal.Parse(Math.PI.ToString());
BigDecimal mass = BigInteger.Parse("1990000000000000000000000000000");
BigDecimal dens = BigDecimal.Parse("0.0");
num = num.Multiply(pi);
vol = radius.Pow(3);
vol = num.Multiply(vol);
dens = mass / (vol);
//while (mass.compareTo(vol.toBigInteger()) < 0)
while (mass.CompareTo(((BigInteger)vol)) < 0)
{
if (type == ("Average_Star"))
{
mass = range(Average_Starmax, Average_Starmin);
}
if (type == ("Massive_Star"))
{
mass = range(Massive_Starmax, Massive_Starmin);
}
if (type == ("White_Dwarf"))
{
mass = range(White_Dwarfmax, White_Dwarfmin);
}
if (type == ("Neutron_Star"))
{
mass = range(Neutron_Starmax, Neutron_Starmin);
}
if (type == ("Black_hole"))
{
mass = range(Black_holemax, Black_holemin);
}
else
{
break;
}
}
dens = mass / (vol);
density = dens;
//if(density.compareTo(BigDecimal.Parse("1")) < 0 ){
// Console.WriteLine("its 0");
// System.exit(0);
//}
return(dens);
}
public Number Divide(Number number)
{
if (numberState == 0)
{
if (number.numberState == 0)
{
BigDecimal divBy = number.bigDecimal;
if (divBy.CompareTo(BdZero) != 0)
{
return(new Number(NumberState.None, bigDecimal.Divide(divBy, 10, RoundingMode.HalfUp)));
}
}
}
// Return NaN if we can't divide
return(new Number(NumberState.NotANumber, null));
}
public static SqlNumber Remainder(SqlNumber a, SqlNumber b)
{
if (SqlNumber.IsNumber(a))
{
if (SqlNumber.IsNumber(b))
{
BigDecimal divBy = b.innerValue;
if (divBy.CompareTo(BigDecimal.Zero) != 0)
{
var remainder = BigMath.Remainder(a.innerValue, divBy);
return(new SqlNumber(SqlNumber.NumericState.None, remainder));
}
}
}
return(SqlNumber.NaN);
}
public Number Modulus(Number number)
{
if (numberState == 0)
{
if (number.numberState == 0)
{
BigDecimal divBy = number.bigDecimal;
if (divBy.CompareTo(BdZero) != 0)
{
BigDecimal remainder = bigDecimal.Remainder(divBy);
return(new Number(NumberState.None, remainder));
}
}
}
return(new Number(NumberState.NotANumber, null));
}
private static BigDecimal SqrtNewtonRaphson(BigDecimal c, BigDecimal xn, BigDecimal precision)
{
BigDecimal fx = xn.Pow(2).Add(c.Negate());
BigDecimal fpx = xn.Multiply(new BigDecimal(2));
BigDecimal xn1 = fx.Divide(fpx, 2 * SqrtDig.ToInt32(), RoundingMode.HalfDown);
xn1 = xn.Add(xn1.Negate());
//----
BigDecimal currentSquare = xn1.Pow(2);
BigDecimal currentPrecision = currentSquare.Subtract(c);
currentPrecision = currentPrecision.Abs();
if (currentPrecision.CompareTo(precision) <= -1)
{
return(xn1);
}
return(SqrtNewtonRaphson(c, xn1, precision));
}
public static SqlNumber Divide(SqlNumber a, SqlNumber b, int precision)
{
if (SqlNumber.IsNumber(a))
{
if (SqlNumber.IsNumber(b))
{
BigDecimal divBy = b.innerValue;
if (divBy.CompareTo(BigDecimal.Zero) != 0)
{
var context = new MathContext(precision);
var result = BigMath.Divide(a.innerValue, divBy, context);
return(new SqlNumber(SqlNumber.NumericState.None, result));
}
throw new DivideByZeroException();
}
}
// Return NaN if we can't divide
return(SqlNumber.NaN);
}
public SqlNumber Modulo(SqlNumber value)
{
if (State == NumericState.None)
{
if (value.State == NumericState.None)
{
if (IsNull || value.IsNull)
{
return(Null);
}
BigDecimal divBy = value.innerValue;
if (divBy.CompareTo(BigDecimal.Zero) != 0)
{
BigDecimal remainder = innerValue.Remainder(divBy);
return(new SqlNumber(NumericState.None, remainder));
}
}
}
return(new SqlNumber(NumericState.NotANumber, null));
}
public SqlNumber Divide(SqlNumber value)
{
if (State == NumericState.None)
{
if (value.State == NumericState.None)
{
if (IsNull || value.IsNull)
{
return(Null);
}
BigDecimal divBy = value.innerValue;
if (divBy.CompareTo(BigDecimal.Zero) != 0)
{
return(new SqlNumber(NumericState.None, innerValue.Divide(divBy, 10, RoundingMode.HalfUp)));
}
}
}
// Return NaN if we can't divide
return(new SqlNumber(NumericState.NotANumber, null));
}
public static BigDecimal Exp(BigDecimal x)
{
/* To calculate the value if x is negative, use exp(-x) = 1/exp(x)
*/
if (x.CompareTo(BigDecimal.Zero) < 0) {
BigDecimal invx = Exp(x.Negate());
/* Relative error in inverse of invx is the same as the relative errror in invx.
* This is used to define the precision of the result.
*/
var mc = new MathContext(invx.Precision);
return BigDecimal.One.Divide(invx, mc);
}
if (x.CompareTo(BigDecimal.Zero) == 0) {
/* recover the valid number of digits from x.ulp(), if x hits the
* zero. The x.precision() is 1 then, and does not provide this information.
*/
return ScalePrecision(BigDecimal.One, -(int) (System.Math.Log10(x.Ulp().ToDouble())));
}
/* Push the number in the Taylor expansion down to a small
* value where TAYLOR_NTERM terms will do. If x<1, the n-th term is of the order
* x^n/n!, and equal to both the absolute and relative error of the result
* since the result is close to 1. The x.ulp() sets the relative and absolute error
* of the result, as estimated from the first Taylor term.
* We want x^TAYLOR_NTERM/TAYLOR_NTERM! < x.ulp, which is guaranteed if
* x^TAYLOR_NTERM < TAYLOR_NTERM*(TAYLOR_NTERM-1)*...*x.ulp.
*/
double xDbl = x.ToDouble();
double xUlpDbl = x.Ulp().ToDouble();
if (System.Math.Pow(xDbl, TaylorNterm) < TaylorNterm*(TaylorNterm - 1.0)*(TaylorNterm - 2.0)*xUlpDbl) {
/* Add TAYLOR_NTERM terms of the Taylor expansion (Euler's sum formula)
*/
BigDecimal resul = BigDecimal.One;
/* x^i */
BigDecimal xpowi = BigDecimal.One;
/* i factorial */
BigInteger ifac = BigInteger.One;
/* TAYLOR_NTERM terms to be added means we move x.ulp() to the right
* for each power of 10 in TAYLOR_NTERM, so the addition won't add noise beyond
* what's already in x.
*/
var mcTay = new MathContext(ErrorToPrecision(1d, xUlpDbl/TaylorNterm));
for (int i = 1; i <= TaylorNterm; i++) {
ifac = ifac.Multiply(BigInteger.ValueOf(i));
xpowi = xpowi.Multiply(x);
BigDecimal c = xpowi.Divide(new BigDecimal(ifac), mcTay);
resul = resul.Add(c);
if (System.Math.Abs(xpowi.ToDouble()) < i &&
System.Math.Abs(c.ToDouble()) < 0.5*xUlpDbl)
break;
}
/* exp(x+deltax) = exp(x)(1+deltax) if deltax is <<1. So the relative error
* in the result equals the absolute error in the argument.
*/
var mc = new MathContext(ErrorToPrecision(xUlpDbl/2d));
return resul.Round(mc);
} else {
/* Compute exp(x) = (exp(0.1*x))^10. Division by 10 does not lead
* to loss of accuracy.
*/
var exSc = (int) (1.0 - System.Math.Log10(TaylorNterm*(TaylorNterm - 1.0)*(TaylorNterm - 2.0)*xUlpDbl
/System.Math.Pow(xDbl, TaylorNterm))/(TaylorNterm - 1.0));
BigDecimal xby10 = x.ScaleByPowerOfTen(-exSc);
BigDecimal expxby10 = Exp(xby10);
/* Final powering by 10 means that the relative error of the result
* is 10 times the relative error of the base (First order binomial expansion).
* This looses one digit.
*/
var mc = new MathContext(expxby10.Precision - exSc);
/* Rescaling the powers of 10 is done in chunks of a maximum of 8 to avoid an invalid operation
* response by the BigDecimal.pow library or integer overflow.
*/
while (exSc > 0) {
int exsub = System.Math.Min(8, exSc);
exSc -= exsub;
var mctmp = new MathContext(expxby10.Precision - exsub + 2);
int pex = 1;
while (exsub-- > 0)
pex *= 10;
expxby10 = expxby10.Pow(pex, mctmp);
}
return expxby10.Round(mc);
}
}
public static BigDecimal Cot(BigDecimal x)
{
if (x.CompareTo(BigDecimal.Zero) == 0) {
throw new ArithmeticException("Cannot take cot of zero " + x);
}
if (x.CompareTo(BigDecimal.Zero) < 0) {
return Cot(x.Negate()).Negate();
}
/* reduce modulo pi
*/
BigDecimal res = ModPi(x);
/* absolute error in the result is err(x)/sin^2(x) to lowest order
*/
double xDbl = res.ToDouble();
double xUlpDbl = x.Ulp().ToDouble()/2d;
double eps = xUlpDbl/2d/System.Math.Pow(System.Math.Sin(xDbl), 2d);
BigDecimal xhighpr = ScalePrecision(res, 2);
BigDecimal xhighprSq = MultiplyRound(xhighpr, xhighpr);
var mc = new MathContext(ErrorToPrecision(xhighpr.ToDouble(), eps));
BigDecimal resul = BigDecimal.One.Divide(xhighpr, mc);
/* x^(2i-1) */
BigDecimal xpowi = xhighpr;
var b = new Bernoulli();
/* 2^(2i) */
var fourn = BigInteger.Parse("4");
/* (2i)! */
BigInteger fac = BigInteger.One;
for (int i = 1;; i++) {
Rational f = b[2*i];
fac = fac.Multiply(BigInteger.ValueOf((2*i))).Multiply(BigInteger.ValueOf((2*i - 1)));
f = f.Multiply(fourn).Divide(fac);
BigDecimal c = MultiplyRound(xpowi, f);
if (i%2 == 0)
resul = resul.Add(c);
else
resul = resul.Subtract(c);
if (System.Math.Abs(c.ToDouble()) < 0.1*eps)
break;
fourn = fourn.ShiftLeft(2);
xpowi = MultiplyRound(xpowi, xhighprSq);
}
mc = new MathContext(ErrorToPrecision(resul.ToDouble(), eps));
return resul.Round(mc);
}
public static BigDecimal Cos(BigDecimal x)
{
if (x.CompareTo(BigDecimal.Zero) < 0)
return Cos(x.Negate());
if (x.CompareTo(BigDecimal.Zero) == 0)
return BigDecimal.One;
/* reduce modulo 2pi
*/
BigDecimal res = Mod2Pi(x);
double errpi = 0.5*System.Math.Abs(x.Ulp().ToDouble());
var mc = new MathContext(2 + ErrorToPrecision(3.14159, errpi));
BigDecimal p = PiRound(mc);
mc = new MathContext(x.Precision);
if (res.CompareTo(p) > 0) {
/* pi<x<=2pi: cos(x)= - cos(x-pi)
*/
return Cos(SubtractRound(res, p)).Negate();
}
if (res.Multiply(BigDecimal.ValueOf(2)).CompareTo(p) > 0) {
/* pi/2<x<=pi: cos(x)= -cos(pi-x)
*/
return Cos(SubtractRound(p, res)).Negate();
}
/* for the range 0<=x<Pi/2 one could use cos(2x)= 1-2*sin^2(x)
* to split this further, or use the cos up to pi/4 and the sine higher up.
throw new ProviderException("Not implemented: cosine ") ;
*/
if (res.Multiply(BigDecimal.ValueOf(4)).CompareTo(p) > 0) {
/* x>pi/4: cos(x) = sin(pi/2-x)
*/
return Sin(SubtractRound(p.Divide(BigDecimal.ValueOf(2)), res));
}
/* Simple Taylor expansion, sum_{i=0..infinity} (-1)^(..)res^(2i)/(2i)! */
BigDecimal resul = BigDecimal.One;
/* x^i */
BigDecimal xpowi = BigDecimal.One;
/* 2i factorial */
BigInteger ifac = BigInteger.One;
/* The absolute error in the result is the error in x^2/2 which is x times the error in x.
*/
double xUlpDbl = 0.5*res.Ulp().ToDouble()*res.ToDouble();
/* The error in the result is set by the error in x^2/2 itself, xUlpDbl.
* We need at most k terms to push x^(2k+1)/(2k+1)! below this value.
* x^(2k) < xUlpDbl; (2k)*log(x) < log(xUlpDbl);
*/
int k = (int) (System.Math.Log(xUlpDbl)/System.Math.Log(res.ToDouble()))/2;
var mcTay = new MathContext(ErrorToPrecision(1d, xUlpDbl/k));
for (int i = 1;; i++) {
/* TBD: at which precision will 2*i-1 or 2*i overflow?
*/
ifac = ifac.Multiply(BigInteger.ValueOf((2*i - 1)));
ifac = ifac.Multiply(BigInteger.ValueOf((2*i)));
xpowi = xpowi.Multiply(res).Multiply(res).Negate();
BigDecimal corr = xpowi.Divide(new BigDecimal(ifac), mcTay);
resul = resul.Add(corr);
if (corr.Abs().ToDouble() < 0.5*xUlpDbl)
break;
}
/* The error in the result is governed by the error in x itself.
*/
mc = new MathContext(ErrorToPrecision(resul.ToDouble(), xUlpDbl));
return resul.Round(mc);
}
public static BigDecimal Cbrt(BigDecimal x)
{
if (x.CompareTo(BigDecimal.Zero) < 0)
return Root(3, x.Negate()).Negate();
return Root(3, x);
}
public static BigDecimal Asin(BigDecimal x)
{
if (x.CompareTo(BigDecimal.One) > 0 ||
x.CompareTo(BigDecimal.One.Negate()) < 0) {
throw new ArithmeticException("Out of range argument " + x + " of asin");
}
if (x.CompareTo(BigDecimal.Zero) == 0)
return BigDecimal.Zero;
if (x.CompareTo(BigDecimal.One) == 0) {
/* arcsin(1) = pi/2
*/
double errpi = System.Math.Sqrt(x.Ulp().ToDouble());
var mc = new MathContext(ErrorToPrecision(3.14159, errpi));
return PiRound(mc).Divide(new BigDecimal(2));
}
if (x.CompareTo(BigDecimal.Zero) < 0) {
return Asin(x.Negate()).Negate();
}
if (x.ToDouble() > 0.7) {
BigDecimal xCompl = BigDecimal.One.Subtract(x);
double xDbl = x.ToDouble();
double xUlpDbl = x.Ulp().ToDouble()/2d;
double eps = xUlpDbl/2d/System.Math.Sqrt(1d - System.Math.Pow(xDbl, 2d));
BigDecimal xhighpr = ScalePrecision(xCompl, 3);
BigDecimal xhighprV = DivideRound(xhighpr, 4);
BigDecimal resul = BigDecimal.One;
/* x^(2i+1) */
BigDecimal xpowi = BigDecimal.One;
/* i factorial */
BigInteger ifacN = BigInteger.One;
BigInteger ifacD = BigInteger.One;
for (int i = 1;; i++) {
ifacN = ifacN.Multiply(BigInteger.ValueOf((2*i - 1)));
ifacD = ifacD.Multiply(BigInteger.ValueOf(i));
if (i == 1)
xpowi = xhighprV;
else
xpowi = MultiplyRound(xpowi, xhighprV);
BigDecimal c = DivideRound(MultiplyRound(xpowi, ifacN),
ifacD.Multiply(BigInteger.ValueOf((2*i + 1))));
resul = resul.Add(c);
/* series started 1+x/12+... which yields an estimate of the sum's error
*/
if (System.Math.Abs(c.ToDouble()) < xUlpDbl/120d)
break;
}
/* sqrt(2*z)*(1+...)
*/
xpowi = Sqrt(xhighpr.Multiply(new BigDecimal(2)));
resul = MultiplyRound(xpowi, resul);
var mc = new MathContext(resul.Precision);
BigDecimal pihalf = PiRound(mc).Divide(new BigDecimal(2));
mc = new MathContext(ErrorToPrecision(resul.ToDouble(), eps));
return pihalf.Subtract(resul, mc);
} else {
/* absolute error in the result is err(x)/sqrt(1-x^2) to lowest order
*/
double xDbl = x.ToDouble();
double xUlpDbl = x.Ulp().ToDouble()/2d;
double eps = xUlpDbl/2d/System.Math.Sqrt(1d - System.Math.Pow(xDbl, 2d));
BigDecimal xhighpr = ScalePrecision(x, 2);
BigDecimal xhighprSq = MultiplyRound(xhighpr, xhighpr);
BigDecimal resul = xhighpr.Plus();
/* x^(2i+1) */
BigDecimal xpowi = xhighpr;
/* i factorial */
BigInteger ifacN = BigInteger.One;
BigInteger ifacD = BigInteger.One;
for (int i = 1;; i++) {
ifacN = ifacN.Multiply(BigInteger.ValueOf((2*i - 1)));
ifacD = ifacD.Multiply(BigInteger.ValueOf((2*i)));
xpowi = MultiplyRound(xpowi, xhighprSq);
BigDecimal c = DivideRound(MultiplyRound(xpowi, ifacN),
ifacD.Multiply(BigInteger.ValueOf((2*i + 1))));
resul = resul.Add(c);
if (System.Math.Abs(c.ToDouble()) < 0.1*eps)
break;
}
var mc = new MathContext(ErrorToPrecision(resul.ToDouble(), eps));
return resul.Round(mc);
}
}
public static BigDecimal Tan(BigDecimal x)
{
if (x.CompareTo(BigDecimal.Zero) == 0)
return BigDecimal.Zero;
if (x.CompareTo(BigDecimal.Zero) < 0) {
return Tan(x.Negate()).Negate();
}
/* reduce modulo pi
*/
BigDecimal res = ModPi(x);
/* absolute error in the result is err(x)/cos^2(x) to lowest order
*/
double xDbl = res.ToDouble();
double xUlpDbl = x.Ulp().ToDouble()/2d;
double eps = xUlpDbl/2d/System.Math.Pow(System.Math.Cos(xDbl), 2d);
if (xDbl > 0.8) {
/* tan(x) = 1/cot(x) */
BigDecimal co = Cot(x);
var mc = new MathContext(ErrorToPrecision(1d/co.ToDouble(), eps));
return BigDecimal.One.Divide(co, mc);
} else {
BigDecimal xhighpr = ScalePrecision(res, 2);
BigDecimal xhighprSq = MultiplyRound(xhighpr, xhighpr);
BigDecimal resul = xhighpr.Plus();
/* x^(2i+1) */
BigDecimal xpowi = xhighpr;
var b = new Bernoulli();
/* 2^(2i) */
BigInteger fourn = BigInteger.ValueOf(4);
/* (2i)! */
BigInteger fac = BigInteger.ValueOf(2);
for (int i = 2;; i++) {
Rational f = b[2*i].Abs();
fourn = fourn.ShiftLeft(2);
fac = fac.Multiply(BigInteger.ValueOf((2*i))).Multiply(BigInteger.ValueOf((2*i - 1)));
f = f.Multiply(fourn).Multiply(fourn.Subtract(BigInteger.One)).Divide(fac);
xpowi = MultiplyRound(xpowi, xhighprSq);
BigDecimal c = MultiplyRound(xpowi, f);
resul = resul.Add(c);
if (System.Math.Abs(c.ToDouble()) < 0.1*eps)
break;
}
var mc = new MathContext(ErrorToPrecision(resul.ToDouble(), eps));
return resul.Round(mc);
}
}
public static BigDecimal Sqrt(BigDecimal x, MathContext mc)
{
if (x.CompareTo(BigDecimal.Zero) < 0)
throw new ArithmeticException("negative argument " + x + " of square root");
if (x.Abs().Subtract(new BigDecimal(System.Math.Pow(10d, -mc.Precision))).CompareTo(BigDecimal.Zero) < 0)
return ScalePrecision(BigDecimal.Zero, mc);
/* start the computation from a double precision estimate */
var s = new BigDecimal(System.Math.Sqrt(x.ToDouble()), mc);
BigDecimal half = BigDecimal.ValueOf(2);
/* increase the local accuracy by 2 digits */
var locmc = new MathContext(mc.Precision + 2, mc.RoundingMode);
/* relative accuracy requested is 10^(-precision)
*/
double eps = System.Math.Pow(10.0, -mc.Precision);
while (true) {
/* s = s -(s/2-x/2s); test correction s-x/s for being
* smaller than the precision requested. The relative correction is 1-x/s^2,
* (actually half of this, which we use for a little bit of additional protection).
*/
if (System.Math.Abs(BigDecimal.One.Subtract(x.Divide(s.Pow(2, locmc), locmc)).ToDouble()) < eps)
break;
s = s.Add(x.Divide(s, locmc)).Divide(half, locmc);
}
return s;
}
public override void Init(IokeObject obj)
{
Runtime runtime = obj.runtime;
obj.Kind = "Number Decimal";
runtime.Decimal = obj;
obj.RegisterMethod(runtime.NewNativeMethod("returns true if the left hand side decimal is equal to the right hand side decimal.",
new TypeCheckingNativeMethod("==", TypeCheckingArgumentsDefinition.builder()
.ReceiverMustMimic(runtime.Decimal)
.WithRequiredPositional("other")
.Arguments,
(method, on, args, keywords, context, message) => {
Decimal d = (Decimal)IokeObject.dataOf(on);
object other = args[0];
return(((other is IokeObject) &&
(IokeObject.dataOf(other) is Decimal) &&
((on == context.runtime.Decimal && other == on) ||
d.value.Equals(((Decimal)IokeObject.dataOf(other)).value))) ? context.runtime.True : context.runtime.False);
})));
obj.RegisterMethod(runtime.NewNativeMethod("Returns a text representation of the object",
new TypeCheckingNativeMethod.WithNoArguments("asText", obj,
(method, on, args, keywords, context, message) => {
return(runtime.NewText(on.ToString()));
})));
obj.RegisterMethod(runtime.NewNativeMethod("returns the square root of the receiver. this should return the same result as calling ** with 0.5",
new TypeCheckingNativeMethod.WithNoArguments("sqrt", obj,
(method, on, args, keywords, context, message) => {
BigDecimal value = ((Decimal)IokeObject.dataOf(on)).value;
if (value.CompareTo(BigDecimal.ZERO) < 1)
{
IokeObject condition = IokeObject.As(IokeObject.GetCellChain(context.runtime.Condition,
message,
context,
"Error",
"Arithmetic"), context).Mimic(message, context);
condition.SetCell("message", message);
condition.SetCell("context", context);
condition.SetCell("receiver", on);
context.runtime.ErrorCondition(condition);
}
return(runtime.NewDecimal(new BigSquareRoot().Get(value)));
})));
obj.RegisterMethod(obj.runtime.NewNativeMethod("Returns a text inspection of the object",
new TypeCheckingNativeMethod.WithNoArguments("inspect", obj,
(method, on, args, keywords, context, message) => {
return(method.runtime.NewText(Decimal.GetInspect(on)));
})));
obj.RegisterMethod(obj.runtime.NewNativeMethod("Returns a brief text inspection of the object",
new TypeCheckingNativeMethod.WithNoArguments("notice", obj,
(method, on, args, keywords, context, message) => {
return(method.runtime.NewText(Decimal.GetInspect(on)));
})));
obj.RegisterMethod(obj.runtime.NewNativeMethod("returns a hash for the decimal number",
new NativeMethod.WithNoArguments("hash", (method, context, message, on, outer) => {
outer.ArgumentsDefinition.CheckArgumentCount(context, message, on);
return(context.runtime.NewNumber(Decimal.GetValue(on).GetHashCode()));
})));
obj.RegisterMethod(runtime.NewNativeMethod("compares this number against the argument, true if this number is the same, otherwise false",
new TypeCheckingNativeMethod("==", TypeCheckingArgumentsDefinition.builder()
.ReceiverMustMimic(obj)
.WithRequiredPositional("other")
.Arguments,
(method, on, args, keywords, context, message) => {
object arg = args[0];
if (IokeObject.dataOf(arg) is Number)
{
return((Decimal.GetValue(on).CompareTo(Number.GetValue(arg).AsBigDecimal()) == 0) ? context.runtime.True : context.runtime.False);
}
else if (IokeObject.dataOf(arg) is Decimal)
{
return((Decimal.GetValue(on).CompareTo(Decimal.GetValue(arg)) == 0) ? context.runtime.True : context.runtime.False);
}
else
{
return(context.runtime.False);
}
})));
obj.RegisterMethod(runtime.NewNativeMethod("compares this number against the argument, returning -1, 0 or 1 based on which one is larger. if the argument is a rational, it will be converted into a form suitable for comparing against a decimal, and then compared. if the argument is neither a Rational nor a Decimal, it tries to call asDecimal, and if that doesn't work it returns nil.",
new TypeCheckingNativeMethod("<=>", TypeCheckingArgumentsDefinition.builder()
.ReceiverMustMimic(obj)
.WithRequiredPositional("other")
.Arguments,
(method, on, args, keywords, context, message) => {
object arg = args[0];
IokeData data = IokeObject.dataOf(arg);
if (data is Number)
{
return(context.runtime.NewNumber(Decimal.GetValue(on).CompareTo(Number.GetValue(arg).AsBigDecimal())));
}
else
{
if (!(data is Decimal))
{
arg = IokeObject.ConvertToDecimal(arg, message, context, false);
if (!(IokeObject.dataOf(arg) is Decimal))
{
// Can't compare, so bail out
return(context.runtime.nil);
}
}
if (on == context.runtime.Decimal || arg == context.runtime.Decimal)
{
if (arg == on)
{
return(context.runtime.NewNumber(0));
}
return(context.runtime.nil);
}
return(context.runtime.NewNumber(Decimal.GetValue(on).CompareTo(Decimal.GetValue(arg))));
}
})));
obj.RegisterMethod(runtime.NewNativeMethod("returns the difference between this number and the argument. if the argument is a rational, it will be converted into a form suitable for subtracting against a decimal, and then subtracted. if the argument is neither a Rational nor a Decimal, it tries to call asDecimal, and if that fails it signals a condition.",
new TypeCheckingNativeMethod("-", TypeCheckingArgumentsDefinition.builder()
.ReceiverMustMimic(obj)
.WithRequiredPositional("subtrahend")
.Arguments,
(method, on, args, keywords, context, message) => {
object arg = args[0];
IokeData data = IokeObject.dataOf(arg);
if (data is Number)
{
return(context.runtime.NewDecimal(Decimal.GetValue(on).subtract(Number.GetValue(arg).AsBigDecimal())));
}
else
{
if (!(data is Decimal))
{
arg = IokeObject.ConvertToDecimal(arg, message, context, true);
}
return(context.runtime.NewDecimal(Decimal.GetValue(on).subtract(Decimal.GetValue(arg))));
}
})));
obj.RegisterMethod(runtime.NewNativeMethod("returns the sum of this number and the argument. if the argument is a rational, it will be converted into a form suitable for addition against a decimal, and then added. if the argument is neither a Rational nor a Decimal, it tries to call asDecimal, and if that fails it signals a condition.",
new TypeCheckingNativeMethod("+", TypeCheckingArgumentsDefinition.builder()
.ReceiverMustMimic(obj)
.WithRequiredPositional("addend")
.Arguments,
(method, on, args, keywords, context, message) => {
object arg = args[0];
IokeData data = IokeObject.dataOf(arg);
if (data is Number)
{
return(context.runtime.NewDecimal(Decimal.GetValue(on).add(Number.GetValue(arg).AsBigDecimal())));
}
else
{
if (!(data is Decimal))
{
arg = IokeObject.ConvertToDecimal(arg, message, context, true);
}
return(context.runtime.NewDecimal(Decimal.GetValue(on).add(Decimal.GetValue(arg))));
}
})));
obj.RegisterMethod(runtime.NewNativeMethod("returns the product of this number and the argument. if the argument is a rational, the receiver will be converted into a form suitable for multiplying against a decimal, and then multiplied. if the argument is neither a Rational nor a Decimal, it tries to call asDecimal, and if that fails it signals a condition.",
new TypeCheckingNativeMethod("*", TypeCheckingArgumentsDefinition.builder()
.ReceiverMustMimic(obj)
.WithRequiredPositional("multiplier")
.Arguments,
(method, on, args, keywords, context, message) => {
object arg = args[0];
IokeData data = IokeObject.dataOf(arg);
if (data is Number)
{
return(context.runtime.NewDecimal(Decimal.GetValue(on).multiply(Number.GetValue(arg).AsBigDecimal())));
}
else
{
if (!(data is Decimal))
{
arg = IokeObject.ConvertToDecimal(arg, message, context, true);
}
return(context.runtime.NewDecimal(Decimal.GetValue(on).multiply(Decimal.GetValue(arg))));
}
})));
obj.RegisterMethod(runtime.NewNativeMethod("returns this number to the power of the argument (which has to be an integer)",
new TypeCheckingNativeMethod("**", TypeCheckingArgumentsDefinition.builder()
.ReceiverMustMimic(obj)
.WithRequiredPositional("exponent")
.Arguments,
(method, on, args, keywords, context, message) => {
object arg = args[0];
IokeData data = IokeObject.dataOf(arg);
if (!(data is Number))
{
arg = IokeObject.ConvertToRational(arg, message, context, true);
}
return(context.runtime.NewDecimal(Decimal.GetValue(on).pow(Number.IntValue(arg).intValue())));
})));
obj.RegisterMethod(runtime.NewNativeMethod("returns the quotient of this number and the argument.",
new TypeCheckingNativeMethod("/", TypeCheckingArgumentsDefinition.builder()
.ReceiverMustMimic(obj)
.WithRequiredPositional("divisor")
.Arguments,
(method, on, args, keywords, context, message) => {
object arg = args[0];
IokeData data = IokeObject.dataOf(arg);
if (data is Number)
{
return(context.runtime.NewDecimal(Decimal.GetValue(on).divide(Number.GetValue(arg).AsBigDecimal())));
}
else
{
if (!(data is Decimal))
{
arg = IokeObject.ConvertToDecimal(arg, message, context, true);
}
while (Decimal.GetValue(arg).CompareTo(BigDecimal.ZERO) == 0)
{
IokeObject condition = IokeObject.As(IokeObject.GetCellChain(context.runtime.Condition,
message,
context,
"Error",
"Arithmetic",
"DivisionByZero"), context).Mimic(message, context);
condition.SetCell("message", message);
condition.SetCell("context", context);
condition.SetCell("receiver", on);
object[] newCell = new object[] { arg };
context.runtime.WithRestartReturningArguments(() => { context.runtime.ErrorCondition(condition); },
context,
new IokeObject.UseValue("newValue", newCell));
arg = newCell[0];
}
BigDecimal result = null;
try {
result = Decimal.GetValue(on).divide(Decimal.GetValue(arg), BigDecimal.ROUND_UNNECESSARY);
} catch (System.ArithmeticException) {
result = Decimal.GetValue(on).divide(Decimal.GetValue(arg), MathContext.DECIMAL128);
}
return(context.runtime.NewDecimal(result));
}
})));
}
public int CompareTo(Number number)
{
if (Equals(this, number))
{
return(0);
}
// If this is a non-infinity number
if (numberState == 0)
{
// If both values can be represented by a long value
if (CanBeLong && number.CanBeLong)
{
// Perform a long comparison check,
if (longRepresentation > number.longRepresentation)
{
return(1);
}
if (longRepresentation < number.longRepresentation)
{
return(-1);
}
return(0);
}
// And the compared number is non-infinity then use the BigDecimal
// compareTo method.
if (number.numberState == 0)
{
return(bigDecimal.CompareTo(number.bigDecimal));
}
// Comparing a regular number with a NaN number.
// If positive infinity or if NaN
if (number.numberState == NumberState.PositiveInfinity ||
number.numberState == NumberState.NotANumber)
{
return(-1);
}
// If negative infinity
if (number.numberState == NumberState.NegativeInfinity)
{
return(1);
}
throw new ApplicationException("Unknown number state.");
}
// This number is a NaN number.
// Are we comparing with a regular number?
if (number.numberState == 0)
{
// Yes, negative infinity
if (numberState == NumberState.NegativeInfinity)
{
return(-1);
}
// positive infinity or NaN
if (numberState == NumberState.PositiveInfinity ||
numberState == NumberState.NotANumber)
{
return(1);
}
throw new ApplicationException("Unknown number state.");
}
// Comparing NaN number with a NaN number.
// This compares -Inf less than Inf and NaN and NaN greater than
// Inf and -Inf. -Inf < Inf < NaN
return(numberState - number.numberState);
}
///***
// * Creates {@code H} of size {@code m x m} as described in [1] (see above).
// *
// * @param d statistic
// * @return H matrix
// * @throws NumberIsTooLargeException if fractional part is greater than 1
// * @throws FractionConversionException if algorithm fails to convert
// * {@code h} to a {@link org.apache.commons.math3.fraction.BigFraction} in
// * expressing {@code d} as {@code (k - h) / m} for integer {@code k, m} and
// * {@code 0 <= h < 1}.
// */
private BigDecimal[,] createH(double d)
{
int k = (int)Math.Ceiling(n * d);
int m = 2 * k - 1;
double hDouble = k - n * d;
if (hDouble >= 1)
{
throw new Exception("Value to large: " + hDouble);
}
BigDecimal h = hDouble;
BigDecimal[,] Hdata = new BigDecimal[m, m];
///*
// * Start by filling everything with either 0 or 1.
// */
for (int i = 0; i < m; ++i)
{
for (int j = 0; j < m; ++j)
{
if (i - j + 1 < 0)
{
Hdata[i, j] = 0.0;
}
else
{
Hdata[i, j] = 1.0;
}
}
}
///*
// * Setting up power-array to avoid calculating the same value twice:
// * hPowers[0] = h^1 ... hPowers[m-1] = h^m
// */
BigDecimal[] hPowers = new BigDecimal[m];
hPowers[0] = h;
for (int i = 1; i < m; ++i)
{
hPowers[i] = h * (hPowers[i - 1]);
}
///*
// * First column and last row has special values (each other reversed).
// */
for (int i = 0; i < m; ++i)
{
Hdata[i, 0] = Hdata[i, 0] - (hPowers[i]);
Hdata[m - 1, i] = Hdata[m - 1, i] - (hPowers[m - i - 1]);
}
///*
// * [1] states: "For 1/2 < h < 1 the bottom left element of the matrix
// * should be (1 - 2*h^m + (2h - 1)^m )/m!" Since 0 <= h < 1, then if h >
// * 1/2 is sufficient to check:
// */
if (h.CompareTo(0.5) == 1)
{
Hdata[m - 1, 0] = Hdata[m - 1, 0] + ToolsMathBigDecimal.Pow((h * 2) - 1, m);
}
///*
// * Aside from the first column and last row, the (i, j)-th element is
// * 1/(i - j + 1)! if i - j + 1 >= 0, else 0. 1's and 0's are already
// * put, so only division with (i - j + 1)! is needed in the elements
// * that have 1's. There is no need to calculate (i - j + 1)! and then
// * divide - small steps avoid overflows.
// *
// * Note that i - j + 1 > 0 <=> i + 1 > j instead of j'ing all the way to
// * m. Also note that it is started at g = 2 because dividing by 1 isn't
// * really necessary.
// */
for (int i = 0; i < m; ++i)
{
for (int j = 0; j < i + 1; ++j)
{
if (i - j + 1 > 0)
{
for (int g = 2; g <= i - j + 1; ++g)
{
Hdata[i, j] = Hdata[i, j] / g;
}
}
}
}
return(Hdata);
}
public static BigDecimal Log(BigDecimal x)
{
/* the value is undefined if x is negative.
*/
if (x.CompareTo(BigDecimal.Zero) < 0)
throw new ArithmeticException("Cannot take log of negative " + x);
if (x.CompareTo(BigDecimal.One) == 0) {
/* log 1. = 0. */
return ScalePrecision(BigDecimal.Zero, x.Precision - 1);
}
if (System.Math.Abs(x.ToDouble() - 1.0) <= 0.3) {
/* The standard Taylor series around x=1, z=0, z=x-1. Abramowitz-Stegun 4.124.
* The absolute error is err(z)/(1+z) = err(x)/x.
*/
BigDecimal z = ScalePrecision(x.Subtract(BigDecimal.One), 2);
BigDecimal zpown = z;
double eps = 0.5*x.Ulp().ToDouble()/System.Math.Abs(x.ToDouble());
BigDecimal resul = z;
for (int k = 2;; k++) {
zpown = MultiplyRound(zpown, z);
BigDecimal c = DivideRound(zpown, k);
if (k%2 == 0)
resul = resul.Subtract(c);
else
resul = resul.Add(c);
if (System.Math.Abs(c.ToDouble()) < eps)
break;
}
var mc = new MathContext(ErrorToPrecision(resul.ToDouble(), eps));
return resul.Round(mc);
} else {
double xDbl = x.ToDouble();
double xUlpDbl = x.Ulp().ToDouble();
/* Map log(x) = log root[r](x)^r = r*log( root[r](x)) with the aim
* to move roor[r](x) near to 1.2 (that is, below the 0.3 appearing above), where log(1.2) is roughly 0.2.
*/
var r = (int) (System.Math.Log(xDbl)/0.2);
/* Since the actual requirement is a function of the value 0.3 appearing above,
* we avoid the hypothetical case of endless recurrence by ensuring that r >= 2.
*/
r = System.Math.Max(2, r);
/* Compute r-th root with 2 additional digits of precision
*/
BigDecimal xhighpr = ScalePrecision(x, 2);
BigDecimal resul = Root(r, xhighpr);
resul = Log(resul).Multiply(new BigDecimal(r));
/* error propagation: log(x+errx) = log(x)+errx/x, so the absolute error
* in the result equals the relative error in the input, xUlpDbl/xDbl .
*/
var mc = new MathContext(ErrorToPrecision(resul.ToDouble(), xUlpDbl/xDbl));
return resul.Round(mc);
}
}
public static BigDecimal Sin(BigDecimal x)
{
if (x.CompareTo(BigDecimal.Zero) < 0)
return Sin(x.Negate()).Negate();
if (x.CompareTo(BigDecimal.Zero) == 0)
return BigDecimal.Zero;
/* reduce modulo 2pi
*/
BigDecimal res = Mod2Pi(x);
double errpi = 0.5*System.Math.Abs(x.Ulp().ToDouble());
var mc = new MathContext(2 + ErrorToPrecision(3.14159, errpi));
BigDecimal p = PiRound(mc);
mc = new MathContext(x.Precision);
if (res.CompareTo(p) > 0) {
/* pi<x<=2pi: sin(x)= - sin(x-pi)
*/
return Sin(SubtractRound(res, p)).Negate();
}
if (res.Multiply(BigDecimal.ValueOf(2)).CompareTo(p) > 0) {
/* pi/2<x<=pi: sin(x)= sin(pi-x)
*/
return Sin(SubtractRound(p, res));
}
/* for the range 0<=x<Pi/2 one could use sin(2x)=2sin(x)cos(x)
* to split this further. Here, use the sine up to pi/4 and the cosine higher up.
*/
if (res.Multiply(BigDecimal.ValueOf(4)).CompareTo(p) > 0) {
/* x>pi/4: sin(x) = cos(pi/2-x)
*/
return Cos(SubtractRound(p.Divide(BigDecimal.ValueOf(2)), res));
}
/* Simple Taylor expansion, sum_{i=1..infinity} (-1)^(..)res^(2i+1)/(2i+1)! */
BigDecimal resul = res;
/* x^i */
BigDecimal xpowi = res;
/* 2i+1 factorial */
BigInteger ifac = BigInteger.One;
/* The error in the result is set by the error in x itself.
*/
double xUlpDbl = res.Ulp().ToDouble();
/* The error in the result is set by the error in x itself.
* We need at most k terms to squeeze x^(2k+1)/(2k+1)! below this value.
* x^(2k+1) < x.ulp; (2k+1)*log10(x) < -x.precision; 2k*log10(x)< -x.precision;
* 2k*(-log10(x)) > x.precision; 2k*log10(1/x) > x.precision
*/
int k = (int) (res.Precision/System.Math.Log10(1.0/res.ToDouble()))/2;
var mcTay = new MathContext(ErrorToPrecision(res.ToDouble(), xUlpDbl/k));
for (int i = 1;; i++) {
/* TBD: at which precision will 2*i or 2*i+1 overflow?
*/
ifac = ifac.Multiply(BigInteger.ValueOf(2*i));
ifac = ifac.Multiply(BigInteger.ValueOf((2*i + 1)));
xpowi = xpowi.Multiply(res).Multiply(res).Negate();
BigDecimal corr = xpowi.Divide(new BigDecimal(ifac), mcTay);
resul = resul.Add(corr);
if (corr.Abs().ToDouble() < 0.5*xUlpDbl)
break;
}
/* The error in the result is set by the error in x itself.
*/
mc = new MathContext(res.Precision);
return resul.Round(mc);
}
public static BigDecimal Sqrt(BigDecimal x)
{
if (x.CompareTo(BigDecimal.Zero) < 0)
throw new ArithmeticException("negative argument " + x + " of square root");
return Root(2, x);
}
public int CompareTo(RealNumber other)
{
return(Value.CompareTo(other.Value));
}
public static BigDecimal Pow(BigDecimal x, BigDecimal y)
{
if (x.CompareTo(BigDecimal.Zero) < 0)
throw new ArithmeticException("Cannot power negative " + x);
if (x.CompareTo(BigDecimal.Zero) == 0)
return BigDecimal.Zero;
/* return x^y = exp(y*log(x)) ;
*/
BigDecimal logx = Log(x);
BigDecimal ylogx = y.Multiply(logx);
BigDecimal resul = Exp(ylogx);
/* The estimation of the relative error in the result is |log(x)*err(y)|+|y*err(x)/x|
*/
double errR = System.Math.Abs(logx.ToDouble())*y.Ulp().ToDouble()/2d
+ System.Math.Abs(y.ToDouble()*x.Ulp().ToDouble()/2d/x.ToDouble());
var mcR = new MathContext(ErrorToPrecision(1.0, errR));
return resul.Round(mcR);
}
protected override int UnsafeCompareTo(Dynamic other)
{
return(value.CompareTo(other.AsBigDecimal));
}
public static BigDecimal PowRound(BigDecimal x, Rational q)
{
/** Special cases: x^1=x and x^0 = 1
*/
if (q.CompareTo(BigInteger.One) == 0)
return x;
if (q.Sign == 0)
return BigDecimal.One;
if (q.IsInteger) {
/* We are sure that the denominator is positive here, because normalize() has been
* called during constrution etc.
*/
return PowRound(x, q.Numerator);
}
/* Refuse to operate on the general negative basis. The integer q have already been handled above.
*/
if (x.CompareTo(BigDecimal.Zero) < 0)
throw new ArithmeticException("Cannot power negative " + x);
if (q.IsIntegerFraction) {
/* Newton method with first estimate in double precision.
* The disadvantage of this first line here is that the result must fit in the
* standard range of double precision numbers exponents.
*/
double estim = System.Math.Pow(x.ToDouble(), q.ToDouble());
var res = new BigDecimal(estim);
/* The error in x^q is q*x^(q-1)*Delta(x).
* The relative error is q*Delta(x)/x, q times the relative error of x.
*/
var reserr = new BigDecimal(0.5*q.Abs().ToDouble()
*x.Ulp().Divide(x.Abs(), MathContext.Decimal64).ToDouble());
/* The main point in branching the cases above is that this conversion
* will succeed for numerator and denominator of q.
*/
int qa = q.Numerator.ToInt32();
int qb = q.Denominator.ToInt32();
/* Newton iterations. */
BigDecimal xpowa = PowRound(x, qa);
for (;;) {
/* numerator and denominator of the Newton term. The major
* disadvantage of this implementation is that the updates of the powers
* of the new estimate are done in full precision calling BigDecimal.pow(),
* which becomes slow if the denominator of q is large.
*/
BigDecimal nu = res.Pow(qb).Subtract(xpowa);
BigDecimal de = MultiplyRound(res.Pow(qb - 1), q.Denominator);
/* estimated correction */
BigDecimal eps = nu.Divide(de, MathContext.Decimal64);
BigDecimal err = res.Multiply(reserr, MathContext.Decimal64);
int precDiv = 2 + ErrorToPrecision(eps, err);
if (precDiv <= 0) {
/* The case when the precision is already reached and any precision
* will do. */
eps = nu.Divide(de, MathContext.Decimal32);
} else {
eps = nu.Divide(de, new MathContext(precDiv));
}
res = SubtractRound(res, eps);
/* reached final precision if the relative error fell below reserr,
* |eps/res| < reserr
*/
if (eps.Divide(res, MathContext.Decimal64).Abs().CompareTo(reserr) < 0) {
/* delete the bits of extra precision kept in this
* working copy.
*/
return res.Round(new MathContext(ErrorToPrecision(reserr.ToDouble())));
}
}
}
/* The error in x^q is q*x^(q-1)*Delta(x) + Delta(q)*x^q*log(x).
* The relative error is q/x*Delta(x) + Delta(q)*log(x). Convert q to a floating point
* number such that its relative error becomes negligible: Delta(q)/q << Delta(x)/x/log(x) .
*/
int precq = 3 + ErrorToPrecision((x.Ulp().Divide(x, MathContext.Decimal64)).ToDouble()
/System.Math.Log(x.ToDouble()));
/* Perform the actual calculation as exponentiation of two floating point numbers.
*/
return Pow(x, q.ToBigDecimal(new MathContext(precq)));
}
/// <summary>
/// Compares the value of this AseDecimal with the AseDecimal value.
/// </summary>
public int CompareTo(AseDecimal value)
{
return(Backing.CompareTo(value.Backing));
}
public static BigDecimal Root(int n, BigDecimal x)
{
if (x.CompareTo(BigDecimal.Zero) < 0)
throw new ArithmeticException("negative argument " + x + " of root");
if (n <= 0)
throw new ArithmeticException("negative power " + n + " of root");
if (n == 1)
return x;
/* start the computation from a double precision estimate */
var s = new BigDecimal(System.Math.Pow(x.ToDouble(), 1.0/n));
/* this creates nth with nominal precision of 1 digit
*/
var nth = new BigDecimal(n);
/* Specify an internal accuracy within the loop which is
* slightly larger than what is demanded by 'eps' below.
*/
BigDecimal xhighpr = ScalePrecision(x, 2);
var mc = new MathContext(2 + x.Precision);
/* Relative accuracy of the result is eps.
*/
double eps = x.Ulp().ToDouble()/(2*n*x.ToDouble());
for (;;) {
/* s = s -(s/n-x/n/s^(n-1)) = s-(s-x/s^(n-1))/n; test correction s/n-x/s for being
* smaller than the precision requested. The relative correction is (1-x/s^n)/n,
*/
BigDecimal c = xhighpr.Divide(s.Pow(n - 1), mc);
c = s.Subtract(c);
var locmc = new MathContext(c.Precision);
c = c.Divide(nth, locmc);
s = s.Subtract(c);
if (System.Math.Abs(c.ToDouble()/s.ToDouble()) < eps)
break;
}
return s.Round(new MathContext(ErrorToPrecision(eps)));
}