/// <summary>
/// Compute e^x to a given scale. <br />Break x into its whole and
/// fraction parts and compute (e^(1 + fraction/whole))^whole using
/// Taylor's formula.
/// </summary>
/// <param name="scale">
/// the desired <c>scale</c> of the result. (where the <c>scale</c> is
/// the number of digits to the right of the decimal point.
/// </param>
/// <returns>
/// the result value
/// </returns>
/// <exception cref="ArgumentException">
/// if <c>scale</c> <= 0.
/// </exception>
public static DecimalX Exp(this DecimalX x, int scale)
{
if (scale <= 0)
{
throw new ArgumentException(InvalidScale2);
}
if (x.Signum() == 0)
{
return(DecimalX.Create(1));
}
if (x.Signum() == -1)
{
var a = DecimalX.Create(1);
return(a.CDivide(x.Negate().Exp(scale), scale, RoundingMode.HalfEven));
}
// Compute the whole part of x.
var xWhole = DecimalX.Rescale(x, 0, RoundingMode.Down);
// If there isn't a whole part, compute and return e^x.
if (xWhole.Signum() == 0)
{
return(expTaylor(x, scale));
}
// Compute the fraction part of x.
var xFraction = x.Subtract(xWhole);
// z = 1 + fraction/whole
var b = DecimalX.Create(1);
var z = b.Add(xFraction.CDivide(xWhole, scale, RoundingMode.HalfEven));
// t = e^z
var t = expTaylor(z, scale);
var maxLong = DecimalX.Create(long.MaxValue);
var tempRes = DecimalX.Create(1);
// Compute and return t^whole using IntPower().
// If whole > Int64.MaxValue, then first compute products
// of e^Int64.MaxValue.
while (xWhole.CompareTo(maxLong) >= 0)
{
tempRes = tempRes.Multiply(t.IntPower(long.MaxValue, scale));
tempRes = DecimalX.Rescale(tempRes, -scale, RoundingMode.HalfEven);
xWhole = xWhole.Subtract(maxLong);
}
var result = tempRes.Multiply(t.IntPower(xWhole.ToLong(), scale));
return(DecimalX.Rescale(result, -scale, RoundingMode.HalfEven));
}