public static BigDouble Normalize(double mantissa, long exponent)
{
if (mantissa >= 1 && mantissa < 10 || !IsFinite(mantissa))
{
return(new BigDouble(mantissa, exponent));
}
if (IsZero(mantissa))
{
return(Zero);
}
var tempExponent = (long)Math.Floor(Math.Log10(Math.Abs(mantissa)));
//SAFETY: handle 5e-324, -5e-324 separately
if (tempExponent == DoubleExpMin)
{
mantissa = mantissa * 10 / 1e-323;
}
else
{
mantissa = mantissa / PowersOf10.Lookup(tempExponent);
}
return(new BigDouble(mantissa, exponent + tempExponent));
}
public static BigDouble Add(BigDouble left, BigDouble right)
{
//figure out which is bigger, shrink the mantissa of the smaller by the difference in exponents, add mantissas, normalize and return
//TODO: Optimizations and simplification may be possible, see https://github.com/Patashu/break_infinity.js/issues/8
if (IsZero(left.Mantissa))
{
return(right);
}
if (IsZero(right.Mantissa))
{
return(left);
}
if (IsNaN(left) || IsNaN(right) || IsInfinity(left) || IsInfinity(right))
{
// Let Double handle these cases.
return(left.Mantissa + right.Mantissa);
}
BigDouble bigger, smaller;
if (left.Exponent >= right.Exponent)
{
bigger = left;
smaller = right;
}
else
{
bigger = right;
smaller = left;
}
if (bigger.Exponent - smaller.Exponent > MaxSignificantDigits)
{
return(bigger);
}
//have to do this because adding numbers that were once integers but scaled down is imprecise.
//Example: 299 + 18
return(Normalize(
Math.Round(1e14 * bigger.Mantissa + 1e14 * smaller.Mantissa *
PowersOf10.Lookup(smaller.Exponent - bigger.Exponent)),
bigger.Exponent - 14));
}
public double ToDouble()
{
if (IsNaN(this))
{
return(double.NaN);
}
if (Exponent > DoubleExpMax)
{
return(Mantissa > 0 ? double.PositiveInfinity : double.NegativeInfinity);
}
if (Exponent < DoubleExpMin)
{
return(0.0);
}
//SAFETY: again, handle 5e-324, -5e-324 separately
if (Exponent == DoubleExpMin)
{
return(Mantissa > 0 ? 5e-324 : -5e-324);
}
var result = Mantissa * PowersOf10.Lookup(Exponent);
if (!IsFinite(result) || Exponent < 0)
{
return(result);
}
var resultrounded = Math.Round(result);
if (Math.Abs(resultrounded - result) < 1e-10)
{
return(resultrounded);
}
return(result);
}
