public static double Sqrt(double x)
{
if (x < 0)
{
throw new ArgumentException("");
}
int count = 0;
int a = 2;
for (int i = 308; i > -15; i -= 2)
{
double b = x / PowI(10, i);
if (b >= 1 && b < 10)
{
count = i / 2;
break;
}
else if (b >= 1 && b >= 10)
{
count = i / 2;
a = 6;
break;
}
}
double y = a * PowI(10, count);
double x_n = (y + x / y) / 2.0;
double tol = PowI(10, -12);
while (1000 * Simple.Abs(y - x_n) >= tol)
{
y = x_n;
x_n = (y + x / y) / 2.0;
}
return(y);
}
public static double Pow(double x, double y)
{
if (y - (int)(y) == 0)
{
return(PowI(x, (int)(y)));
}
else if (x < 0 && (1 / y) % 2 == 0)
{
throw new ArgumentException("Imaginary number!");
}
double answer = PowI(Simple.Abs(x), (int)(y));
double value = (Abs(y) - (int)(Abs(y))) * 10;
int count = 1;
while (value > 0)
{
answer *= Exp((int)(value) * Ln(Simple.Abs(x)) / PowI(10, count));
value -= (int)(value);
value *= 10;
count += 1;
}
if (x < 0)
{
return(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 Arccos(double x)
{
if (x < -1 || x > 1)
{
throw new ArgumentException("Can't compute!");
}
else if (x == -1)
{
return(0 - pi / 2.0);
}
else if (x == 1)
{
return(pi / 2.0);
}
else if (x == 0)
{
return(0.0);
}
double y = Simple.Abs(x);
double x1 = pi / 2.0;
double x2 = 0;
double xm = pi / 4.0;
double y2 = 0.0;
while (y2 > Simple.Abs(x) + 0.000000000000001 || y2 < Simple.Abs(x) - 0.000000000000001)
{
double y1 = Cos(x1);
y2 = Cos(x2);
double ym = Cos(xm);
double m1 = (xm - x1) / (ym - y1);
double m2 = (x2 - xm) / (y2 - ym);
if (y > y1 && y < ym)
{
x2 = m1 * (y - y1) + x1;
}
else if (y > ym && y < y2)
{
x2 = m2 * (y - ym) + xm;
}
xm = (x1 - x2) / 2.0 + x2;
}
if (x < 0)
{
return(pi - x2);
}
return(x2);
}
