// this method is slow
public static decimal Ln(decimal x)
{
if (x <= 0M)
{
throw new ArgumentOutOfRangeException("x");
}
// algorithm is Newton's method
decimal expy = 1;
decimal y = 2M * (x - expy) / (x + expy);
for (int i = 0; i < 1000 * 1000; ++i)
{
expy = Exp(y);
decimal diff = 2M * (x - expy) / (x + expy);
if (WWDecimalMath.IsRelativelySmall(diff, y))
{
break;
}
y += diff;
}
return(y);
}
public static decimal Exp(decimal x)
{
decimal y = 0M;
// algorithm is simple Taylor series
decimal diff = 1M;
for (int i = 1; i < 1000 * 1000; ++i)
{
y += diff;
diff *= x / i;
if (WWDecimalMath.IsRelativelySmall(diff, y))
{
break;
}
}
return(y);
}
public static decimal Sqrt(decimal v)
{
if (v < 0M)
{
throw new ArgumentOutOfRangeException("v");
}
// Algorithm is Newton's method
// https://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number
// x^2 = v
// f(x) = x^2 - v
// f'(x) = 2x
// x0 = 10
// x1 = x0 - f(x0)/f'(x0)
// x2 = x1 - f(x1)/f'(x1)
// f(x)/f'(x) = (x^2-v)/(2x) = (1/2)*(x -v/x)
decimal x = 10M;
for (int i = 0; i < 128; ++i)
{
decimal diff = (x - v / x) / 2;
if (WWDecimalMath.IsRelativelySmall(diff, x))
{
break;
}
x -= diff;
// Console.WriteLine(" {0} {1}", i, x);
}
return(x);
}