public static MultiPrecision <N> Atan(MultiPrecision <N> x)
{
if (x.IsNaN)
{
return(NaN);
}
if (!x.IsFinite)
{
return(x.Sign == Sign.Plus ? PI / 2 : -PI / 2);
}
MultiPrecision <Plus1 <N> > x_ex = x.Convert <Plus1 <N> >();
if (x <= One && x >= MinusOne)
{
MultiPrecision <Plus1 <N> > z = MultiPrecision <Plus1 <N> > .Abs(x_ex) / MultiPrecision <Plus1 <N> > .Sqrt(x_ex *x_ex + 1);
MultiPrecision <N> w = MultiPrecision <Plus1 <N> > .Sqrt(MultiPrecision <Plus1 <N> > .SquareAsin(z)).Convert <N>();
if (w.IsZero)
{
return(x);
}
return(new MultiPrecision <N>(x.Sign, w.exponent, w.mantissa));
}
else
{
MultiPrecision <Plus1 <N> > invx = 1 / x_ex;
MultiPrecision <Plus1 <N> > z = MultiPrecision <Plus1 <N> > .Abs(invx) / MultiPrecision <Plus1 <N> > .Sqrt(invx *invx + 1);
MultiPrecision <N> w = MultiPrecision <Plus1 <N> > .Sqrt(MultiPrecision <Plus1 <N> > .SquareAsin(z)).Convert <N>();
if (x.Sign == Sign.Plus)
{
return(PI / 2 - w);
}
else
{
return(w - PI / 2);
}
}
}
public static MultiPrecision <N> Asin(MultiPrecision <N> x)
{
if (!(x >= MinusOne && x <= One))
{
return(NaN);
}
if (x == MinusOne)
{
return(-PI / 2);
}
if (x == One)
{
return(PI / 2);
}
if (Abs(x) <= Sqrt2 / 2)
{
MultiPrecision <Plus1 <N> > x_ex = x.Convert <Plus1 <N> >();
MultiPrecision <N> w =
MultiPrecision <Plus1 <N> > .Sqrt(
MultiPrecision <Plus1 <N> > .SquareAsin(
MultiPrecision <Plus1 <N> > .Abs(x_ex))).Convert <N>();
if (w.IsZero)
{
return(x);
}
return(new MultiPrecision <N>(x.Sign, w.exponent, w.mantissa));
}
else
{
MultiPrecision <N> z = x / (Sqrt(1 - x * x) + 1);
return(Atan(z) * 2);
}
}
