public static Object Solve()
{
var diameter = FibonacciSequence.ItemsX.Take(1000).Sum();
var x = IntX.Multiply(diameter, 314159265359, MultiplyMode.Classic);
var y = IntX.Divide(x, 100000000000, DivideMode.Classic);
return(y);
}
public static DecimalX Calculate(int numberOfDigitsRequired)
{
int max = numberOfDigitsRequired + 8; // To be safe, compute 8 extra digits, to be dropped at end. The 8 is arbitrary
var a = IntX.Multiply(InverseTan(5, max), new IntX(16), MultiplyMode.AutoFht); //16 x arctan(1/5)
var b = IntX.Multiply(InverseTan(239, max), new IntX(4), MultiplyMode.AutoFht); //4 x arctan(1/239)
IntX pi = a - b;
return(new DecimalX(
IntX.Divide(pi, IntX.Pow(10, (uint)8), DivideMode.AutoNewton)
, IntX.Pow(10, (uint)numberOfDigitsRequired, MultiplyMode.AutoFht)));
}
public static IntX InverseTan(int denominator, int numberOfDigitsRequired)
{
int demonimatorSquared = denominator * denominator;
int degreeNeeded = GetDegreeOfPrecisionNeeded(demonimatorSquared, numberOfDigitsRequired);
IntX tenToNumberPowerOfDigitsRequired = GetTenToPowerOfNumberOfDigitsRequired(numberOfDigitsRequired);
int c = 2 * degreeNeeded + 1;
IntX s = IntX.Divide(tenToNumberPowerOfDigitsRequired, new IntX(c), DivideMode.AutoNewton); // s = (10^N)/c
for (int i = 0; i < degreeNeeded; i++)
{
c = c - 2;
var temp1 = IntX.Divide(tenToNumberPowerOfDigitsRequired, new IntX(c), DivideMode.AutoNewton);
var temp2 = IntX.Divide(s, new IntX(demonimatorSquared), DivideMode.AutoNewton);
s = temp1 - temp2;
}
Console.WriteLine("Number of iterations=" + degreeNeeded);
// return s/denominator, which is integer part of 10^numberOfDigitsRequired times arctan(1/k)
return(IntX.Divide(s, new IntX(denominator), DivideMode.AutoNewton));
}
public IntX Determinant(bool preserve = true)
{
if (preserve)
{
return(Copy().Determinant(false));
}
if (Width != Height)
{
throw new ArgumentOutOfRangeException("Is not a square matrix, determinant not defined");
}
/*
* if (Width == 2 && Height == 2)
* return Elements[0, 0] * Elements[1, 1] - Elements[0, 1] * Elements[1, 0];
* if (Width == 1 && Height == 1)
* return Elements[0, 0];
*
* IntX solution = 0;
* MatrixX minorMatrixX = new MatrixX(Width - 1, Height - 1);
* for (int i = 0; i < Width; i++)
* {
* GetMinor(i, 0, ref minorMatrixX);
* if (i % 2 == 0)
* solution += minorMatrixX.Determinant() * Elements[i, 0];
* else
* solution -= minorMatrixX.Determinant() * Elements[i, 0];
* }
*/
IntX determinantDivisor = 1, deterimant = 1;
for (int i = 0; i < Width - 1; i++)//column & row
{
//find canidate row
int m = i;
for (; m < Height; m++)
{
if (Elements[i, m] != 0)
{
break;
}
}
if (m == Height)
{
return(0);
}
//swap canidate with row i
if (m != i)
{
for (int j = 0; j < Width; j++)
{
IntX a = Elements[j, i], b = Elements[j, m];
Elements[j, i] = b;
Elements[m, i] = a;
}
}
if (Elements[i, i] == 0)
{
throw new ArgumentOutOfRangeException();
}
deterimant *= Elements[i, i];
//multiply and add to all other rows after i
for (int j = i + 1; j < Height; j++)//row
{
// Finding scalar multiple
IntX canidateMult = Elements[i, j];
for (int k = i; k < Width; k++)//column
{
// Column is k
// Canidate row is i
// Current row is j
// Scalar multiplier for current row is Elements[i,i]
// Scalar multiplier for subtraction canidate row is canidateMult (initially Elements[i,j])
Elements[k, j] = Elements[k, j] * Elements[i, i]
- Elements[k, i] * canidateMult;
}
}
// Find total divisor.
determinantDivisor *= IntX.Pow(Elements[i, i], (uint)(Height - i - 1));
}
return(IntX.Divide(deterimant * Elements[Width - 1, Height - 1], determinantDivisor, DivideMode.Classic));
}
