public static double Arctan(double x)
{
if (x == 0)
{
return(0.0);
}
double answer = 0.0;
double y = x;
if (x > 1)
{
y = 1.0 / x;
}
double t = y;
for (int i = 0; i < 30; i++)
{
answer += Simple.Pow(-1, (int)(i)) * t / (2 * i + 1);
t *= y * y;
}
if (x > 1)
{
return(pi / 2.0 - answer);
}
return(answer);
}
public static double Sin(double x)
{
if (x == 0)
{
return(0);
}
else if (Simple.Abs(2 * x / pi - 3) % 4 == 0)
{
return(-1);
}
else if (Simple.Abs(2 * x / pi - 3) % 4 == 2)
{
return(1);
}
else if (Simple.Abs(x) % pi == 0)
{
return(0);
}
double y = x;
if (x < 0)
{
y = Math.Round(0 - x / (2.0 * pi)) * 2.0 * pi + x;
}
double mod = y % (2.0 * pi);
if (mod > pi / 2.0 && mod < pi)
{
y = pi - y;
}
else if (mod > pi && mod < 3.0 * pi / 2.0)
{
y -= pi;
}
else if (mod > 3.0 * pi / 2.0)
{
y = 2.0 * pi - y;
}
double x_n = y;
UInt64 fact = 1;
double answer = y / (1.0 * fact);
for (int i = 1; i < 19; i += 2)
{
x_n *= y * y;
fact = fact * (UInt64)((i + 1) * (i + 2));
answer += Simple.Pow(-1, (int)((i + 1) / 2)) * x_n / (1.0 * fact);
}
if (mod > pi)
{
return(0 - answer);
}
return(answer);
}
public static double Tan(double x)
{
if ((2.0 * x / pi) % 2 == 1)
{
throw new ArgumentException("Can't compute!");
}
else if (x % pi == 0)
{
return(0.0);
}
else if (x > 0)
{
return(Simple.Sqrt(Simple.Pow(1.0 / Cos(x), 2) - 1));
}
return(0 - Simple.Sqrt(Simple.Pow(1.0 / Cos(x), 2) - 1));
}
public double[] Quadratic()
{
double[] pieces = new double[9];
pieces = GetCoefficients(left, pieces, 1);
pieces = GetCoefficients(right, pieces, -1);
double[] answer = { 0.0, 0.0 };
double d = Simple.Pow(pieces[pieces.Length - 2], 2) - 4.0 * pieces[pieces.Length - 3] * pieces[pieces.Length - 1];
if (d < 0)
{
throw new ArgumentException("Imaginary number!");
}
else if (d == 0)
{
d = 0.0;
}
else
{
d = Simple.Sqrt(d);
}
answer[0] = (0 - pieces[pieces.Length - 2] + d) / (2.0 * pieces[pieces.Length - 3]);
answer[1] = (0 - pieces[pieces.Length - 2] - d) / (2.0 * pieces[pieces.Length - 3]);
return(answer);
}
private double[] GetCoefficients(string[] parts, double[] coefficients, int side)
{
for (int i = 0; i < parts.Length; i++)
{
string result = parts[i];
if (result.IndexOf("arcsin") != -1 && result.IndexOf(")^") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 3, "arcsin", result);
}
else if (result.IndexOf("arccos") != -1 && result.IndexOf(")^") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 4, "arccos", result);
}
else if (result.IndexOf("arctan") != -1 && result.IndexOf(")^") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 5, "arctan", result);
}
else if (result.IndexOf("sin") != -1 && result.IndexOf(")^") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 0, "sin", result);
}
else if (result.IndexOf("cos") != -1 && result.IndexOf(")^") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 1, "cos", result);
}
else if (result.IndexOf("tan") != -1 && result.IndexOf(")^") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 2, "tan", result);
}
else if (result.IndexOf("arcsin") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 9, "arcsin", result);
}
else if (result.IndexOf("arccos") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 10, "arccos", result);
}
else if (result.IndexOf("arctan") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 11, "arctan", result);
}
else if (result.IndexOf("sin") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 6, "sin", result);
}
else if (result.IndexOf("cos") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 7, "cos", result);
}
else if (result.IndexOf("tan") != -1 && coefficients[12] == 0 && coefficients[13] == 0)
{
coefficients = Inside(coefficients, side, 8, "tan", result);
}
else if (result.IndexOf("(x") != -1 && result.IndexOf(")^2") != -1)
{
double c = 1.0;
if (result.IndexOf("(") > 0 && result.ElementAt(0) == '-')
{
c = -1.0;
}
else if (result.IndexOf("(") > 0)
{
c = Double.Parse(result.Substring(0, result.IndexOf("(")));
}
double b = Coefficient(side, "x", result.Substring(result.IndexOf("("), result.IndexOf("x") - result.IndexOf("(")));
coefficients[12] += side * c * Simple.Pow(b, 2);
double a = Double.Parse(result.Substring(result.IndexOf("x") + 2, result.IndexOf(")^2") - result.IndexOf("x") - 2));;
if (result.IndexOf("−") != -1)
{
a = 0 - a;
}
coefficients[13] += 2.0 * c * b * a;
coefficients[14] += side * c * Simple.Pow(a, 2);
}
else if (result.IndexOf("x^2") != -1)
{
coefficients[12] += Coefficient(side, "x^2", result);
}
else if (result.IndexOf("x") != -1)
{
coefficients[13] += Coefficient(side, "x", result);
}
else
{
coefficients[14] += side * Double.Parse(result);
}
}
return(coefficients);
}
public double[] PolySolve()
{
double[] pieces = new double[15];
if (left.Length == 1 && right[0].Equals("0"))
{
int count = 0;
for (int i = 0; i < left[0].Length; i++)
{
if (left[0].ElementAt(i) == '(')
{
count++;
}
}
double[] aResults = new double[count];
string full = left[0];
int j = 0;
while (j <= count)
{
string next = full.Substring(1, full.IndexOf(")") - 1);
int max = 0;
if (next.IndexOf("x") != -1)
{
max = 1;
}
for (int i = 0; i < next.Length; i++)
{
int min = next.Substring(i).IndexOf("+");
if (next.Substring(i).IndexOf("−") > -1 && next.Substring(i).IndexOf("−") < min)
{
min = next.Substring(i).IndexOf("−");
}
else if (min == -1)
{
min = next.Substring(i).IndexOf("−");
}
if (next[i] == '^' && max < Int32.Parse("" + next.Substring(i + 1, min - i)))
{
max = Int32.Parse("" + next.Substring(i + 1, min - i));
}
}
if (j == 0)
{
aResults = new double[max];
}
else
{
double[] pResults = new double[aResults.Length + max];
for (int i = 0; i < aResults.Length; i++)
{
pResults[i] = aResults[i];
}
aResults = pResults;
}
if (max == 1)
{
pieces = new double[15];
pieces = GetCoefficients(GetParts(next), pieces, 1);
if (pieces[pieces.Length - 2] == 0.0)
{
double[] newResults = new double[count - 1];
for (int i = 0; i < aResults.Length - 1; i++)
{
if (i < j)
{
newResults[i] = aResults[i];
}
else if (i >= j)
{
newResults[i] = aResults[i + 1];
}
}
aResults = newResults;
}
else
{
aResults[j] = (0 - pieces[pieces.Length - 1]) / pieces[pieces.Length - 2];
}
}
else if (max == 2)
{
pieces = new double[15];
pieces = GetCoefficients(GetParts(next), pieces, 1);
double d = Simple.Sqrt(Simple.Pow(pieces[pieces.Length - 2], 2) - 4.0 * pieces[pieces.Length - 1] * pieces[pieces.Length - 3]);
aResults[j++] = (0 - pieces[pieces.Length - 2] + d) / (2.0 * pieces[pieces.Length - 3]);
aResults[j] = (0 - pieces[pieces.Length - 2] - d) / (2.0 * pieces[pieces.Length - 3]);
}
full = full.Substring(full.IndexOf(")^") + 3);
j++;
}
return(aResults);
}
double[] results = { 0.0 };
return(results);
}
private double[] TrigAnswers(MyFunction f, double[] pieces, int index, int count)
{
if (pieces[pieces.Length - 4] != 0 && count == 1 && pieces[pieces.Length - 5] % 2 == 0)
{
double a = Simple.Pow((0 - pieces[pieces.Length - 1]) / pieces[index], 1.0 / pieces[pieces.Length - 5]);
double c1 = pieces[pieces.Length - 2] - f(a);
double c2 = pieces[pieces.Length - 2] - f(-a);
double d1 = -1.0;
if (Simple.Pow(pieces[pieces.Length - 3], 2) - 4.0 * pieces[pieces.Length - 4] * c1 >= 0)
{
d1 = Simple.Sqrt(Simple.Pow(pieces[pieces.Length - 3], 2) - 4.0 * pieces[pieces.Length - 4] * c1);
}
double d2 = -1.0;
if (Simple.Pow(pieces[pieces.Length - 3], 2) - 4.0 * pieces[pieces.Length - 4] * c2 >= 0)
{
d2 = Simple.Sqrt(Simple.Pow(pieces[pieces.Length - 3], 2) - 4.0 * pieces[pieces.Length - 4] * c2);
}
if (d1 >= 0 && d2 >= 0)
{
double[] results = { (0 - pieces[pieces.Length - 3] + d1) / (2.0 * pieces[pieces.Length - 4]),
(0 - pieces[pieces.Length - 3] - d1) / (2.0 * pieces[pieces.Length - 4]),
(0 - pieces[pieces.Length - 3] + d2) / (2.0 * pieces[pieces.Length - 4]),
(0 - pieces[pieces.Length - 3] - d2) / (2.0 * pieces[pieces.Length - 4]) };
return(results);
}
else if (d1 >= 0)
{
double[] results = { (0 - pieces[pieces.Length - 3] + d1) / (2.0 * pieces[pieces.Length - 4]),
(0 - pieces[pieces.Length - 3] - d1) / (2.0 * pieces[pieces.Length - 4]) };
return(results);
}
else if (d2 >= 0)
{
double[] results = { (0 - pieces[pieces.Length - 3] + d2) / (2.0 * pieces[pieces.Length - 4]),
(0 - pieces[pieces.Length - 3] - d2) / (2.0 * pieces[pieces.Length - 4]) };
return(results);
}
throw new ArgumentException("Imaginary number!");
}
else if (pieces[pieces.Length - 4] != 0)
{
if (pieces[pieces.Length - 5] == 0)
{
pieces[pieces.Length - 5] = 1.0;
}
double c = pieces[pieces.Length - 2] - f(Simple.Pow((0 - pieces[pieces.Length - 1]) / pieces[index], 1.0 / pieces[pieces.Length - 5]));
double d = Simple.Sqrt(Simple.Pow(pieces[pieces.Length - 3], 2) - 4.0 * pieces[pieces.Length - 4] * c);
double[] results = { (0 - pieces[pieces.Length - 3] + d) / (2.0 * pieces[pieces.Length - 4]),
(0 - pieces[pieces.Length - 3] - d) / (2.0 * pieces[pieces.Length - 4]) };
return(results);
}
else if (pieces[pieces.Length - 4] == 0 && count == 1 && (1.0 / pieces[pieces.Length - 5]) % 2 == 0)
{
double a = Simple.Pow(((0 - pieces[pieces.Length - 1]) / pieces[index]), 1.0 / pieces[pieces.Length - 5]);
double[] results = { (f(a) - pieces[pieces.Length - 2]) / pieces[pieces.Length - 3],
(f(-a) - pieces[pieces.Length - 2]) / pieces[pieces.Length - 3] };
return(results);
}
else
{
if (pieces[pieces.Length - 5] == 0)
{
pieces[pieces.Length - 5] = 1.0;
}
double[] results = { (f(Simple.Pow((0 - pieces[pieces.Length - 1]) / pieces[index], 1.0 / pieces[pieces.Length - 5])) -
pieces[pieces.Length - 2]) / pieces[pieces.Length - 3] };
return(results);
}
}