private static void TestSin(Double a)
{
String di = System.Math.Sin(a).ToString();
String ni = BigMath.Sin(BigNum.Create(a)).ToString();
Console.WriteLine("Sin({0,6}) = {1,6} : {2,6} -> {3,6}", a, di, ni, di == ni ? "Pass" : "Fail");
}
private static BigNum EvaluateFunction(Function function, BigNum num)
{
switch (function)
{
case Function.Sin: return(BigMath.Sin(num));
case Function.Cos: return(BigMath.Cos(num));
case Function.Tan: return(BigMath.Tan(num));
case Function.Csc: return(BigMath.Csc(num));
case Function.Sec: return(BigMath.Sec(num));
case Function.Cot: return(BigMath.Cot(num));
case Function.Abs: return(BigMath.Abs(num));
case Function.Ceil: return(BigMath.Ceiling(num));
case Function.Floor: return(BigMath.Floor(num));
case Function.Fact: return(BigMath.Gamma(num));
default:
throw new ExpressionException("Unknown or invalid function");
}
}
private static void TestPow(Double a, Double b)
{
Int32 power = (Int32)System.Math.Round(100 * b);
String di = System.Math.Pow(a, power).ToString();
String ni = BigMath.Pow(a, power).ToString();
Console.WriteLine("{0,6} ^ {1,6} = {2,6} : {3,6} -> {4,6}", a, power, di, ni, di == ni ? "Pass" : "Fail");
}
public static BigNum Sin(BigNum theta)
{
BigNumFactory f = theta.Factory;
// calculate sine using the taylor series, the infinite sum of x^r/r! but to n iterations
BigNum retVal = f.Zero;
// first, reduce this to between 0 and 2Pi
if (theta > f.TwoPi || theta < f.Zero)
{
theta = theta % f.TwoPi;
}
Boolean subtract = false;
// using bignums for sine computation is too heavy. It's faster (and just as accurate) to use Doubles
#if DoubleTrig
Double thetaDbl = Double.Parse(theta.ToString(), Cult.InvariantCulture);
for (Int32 r = 0; r < 20; r++) // 20 iterations is enough, any more just yields inaccurate less-significant digits
{
Double xPowerR = Math.Pow(thetaDbl, 2 * r + 1);
Double factori = BigMath.Factorial((double)(2 * r + 1));
Double element = xPowerR / factori;
Double addThis = subtract ? -element : element;
BigNum addThisBig = f.Create(addThis);
retVal += addThisBig;
subtract = !subtract;
}
#else
for (Int32 r = 0; r < _iterations; r++)
{
BigNum xPowerR = theta.Power(2 * r + 1);
BigNum factori = Factorial(2 * r + 1);
BigNum element = xPowerR / factori;
retVal += subtract ? -element : element;
subtract = !subtract;
}
#endif
// TODO: This calculation generates useless and inaccurate trailing digits that must be truncated
// so truncate them, when I figure out how many digits can be removed
retVal.Truncate(10);
return(retVal);
}
private static void Normalise(BigInt oldNum, BigInt oldDen, out BigInt newNum, out BigInt newDen)
{
// TODO: Maybe also ensure that the denominator is positive, only the numerator can be negative
// find the GCD of oldNum and oldDen, then apply it to find and return newNum and newDen
BigInt gcd = (BigInt)BigMath.Gcd(oldNum, oldDen);
newNum = (BigInt)(oldNum / gcd);
newDen = (BigInt)(oldDen / gcd);
}
private static BigNum Modulo(BigNum x, BigNum y)
{
// a % b == a - ( b * Floor[a / b] )
if (y == 0)
{
throw new DivideByZeroException("Divisor y cannot be zero");
}
if (x.IsZero)
{
return(new BigFloat(0));
}
BigNum floored = BigMath.Floor(x / y);
BigNum multbyb = y * floored;
BigNum retval = x - multbyb;
return(retval);
}
private void Reduce()
{
BigNum one = _factory.Unity;
BigNum zer = _factory.Zero;
Operator op = _operatorStack.Peek();
switch (op)
{
case Operator.Add:
// Apply E := E + E
EnsureVal(2);
BigNum aa = _valueStack.Pop();
BigNum ab = _valueStack.Pop();
_valueStack.Push(aa + ab);
break;
case Operator.Sub:
// Apply E := E - E
EnsureVal(2);
BigNum sa = _valueStack.Pop();
BigNum sb = _valueStack.Pop();
_valueStack.Push(sb - sa);
break;
case Operator.Mul:
EnsureVal(2);
BigNum ma = _valueStack.Pop();
BigNum mb = _valueStack.Pop();
_valueStack.Push(ma * mb);
break;
case Operator.Div:
EnsureVal(2);
BigNum da = _valueStack.Pop();
BigNum db = _valueStack.Pop();
_valueStack.Push(db / da);
break;
case Operator.Neg:
EnsureVal(1);
BigNum na = _valueStack.Pop();
_valueStack.Push(-na);
break;
case Operator.Pow:
EnsureVal(2);
BigNum pa = _valueStack.Pop();
BigNum pb = _valueStack.Pop();
_valueStack.Push(BigMath.Pow(pb, pa));
//Int32 exponent = Int32.Parse( pa.ToString(), N.Integer | N.AllowExponent, Cult.InvariantCulture );
// _valueStack.Push( pb.Power( exponent ) );
break;
case Operator.PaR:
_operatorStack.Pop();
break;
case Operator.CoE:
case Operator.CoN:
case Operator.CoL:
case Operator.CLE:
case Operator.CoG:
case Operator.CGE:
EnsureVal(2);
BigNum ea = _valueStack.Pop();
BigNum eb = _valueStack.Pop();
Boolean eq = ea == eb;
Boolean lt = eb < ea;
Boolean gt = eb > ea;
if (op == Operator.CoE)
{
_valueStack.Push(eq ? one : zer);
}
else if (op == Operator.CoN)
{
_valueStack.Push(eq ? zer : one);
}
else if (op == Operator.CoL)
{
_valueStack.Push(lt ? one : zer);
}
else if (op == Operator.CLE)
{
_valueStack.Push(lt || eq ? one : zer);
}
else if (op == Operator.CoG)
{
_valueStack.Push(gt ? one : zer);
}
else if (op == Operator.CGE)
{
_valueStack.Push(gt || eq ? one : zer);
}
break;
case Operator.And:
case Operator.Or:
case Operator.Xor:
EnsureVal(2);
BigNum binA = _valueStack.Pop();
BigNum binB = _valueStack.Pop();
switch (op)
{
case Operator.And:
Boolean and = binA == one && binB == one;
_valueStack.Push(and ? one : zer);
break;
case Operator.Or:
Boolean or = binA == one || binB == one;
_valueStack.Push(or ? one : zer);
break;
case Operator.Xor:
Boolean xor = (binA == one && binB != one) || (binA != one && binB == one);
_valueStack.Push(xor ? one : zer);
break;
}
break;
case Operator.Not:
EnsureVal(1);
BigNum notA = _valueStack.Pop();
if (notA == one)
{
notA = zer;
}
else
{
notA = one;
}
_valueStack.Push(notA);
break;
// Else, ignore it. Do not throw an exception
}
_operatorStack.Pop();
}