/// <summary>
/// Compares two floating point values within a specified tolerance in ULPs.
/// </summary>
/// <param name="x">One floating point value to be compared.</param>
/// <param name="y">Other floating point value to be compared.</param>
/// <param name="tolerance">The tolerance for equality in terms of ULPs.</param>
/// <param name="difference">The difference between the values in terms of ULPs.</param>
/// <returns>0 if <paramref name="x"/> = <paramref name="y"/> ± <paramref name="tolerance"/> ULPs; +1 if x > y + tolerance ULPs; -1 if x < y - tolerance ULPs.</returns>
/// <remarks>
/// <list>
/// <item> 0 if x = y ± tolerance ULPs</item>
/// <item>+1 if x > y + tolerance ULPs</item>
/// <item>-1 if x < y - tolerance ULPs</item>
/// </list>
/// </remarks>
/// <exception cref="ArgumentOutOfRangeException">Thrown if <paramref name="tolerance"/> is negative or in excess of 2<sup>51</sup> (the limit of the significand in a double-precision floating point value).</exception>
public static int Compare(double x, double y, long tolerance, out long difference)
{
// Make sure tolerance is non-negative and small enough that the
// default NAN won't compare as equal to anything.
const long maxSignificand = 2L * 1024 * 1024 * 1024 * 1024 * 1024; // double-precision values has a 51-bit significand
if (tolerance < 0 || tolerance >= maxSignificand)
{
throw new ArgumentOutOfRangeException("tolerance", "Tolerance must be in the range [0,2\u2075\u00B9)");
}
// Reinterpret double bits as sign-magnitude long integers.
long xi = DoubleBitReinterpreter.Convert(x);
long yi = DoubleBitReinterpreter.Convert(y);
// Convert from sign-magnitude to two's complement form,
// by subtracting from 0x8000000000000000.
if (xi < 0)
{
xi = long.MinValue - xi;
}
if (yi < 0)
{
yi = long.MinValue - yi;
}
// How many epsilons apart?
difference = xi - yi;
// Is the difference outside our tolerance?
if (xi > yi + tolerance)
{
return(+1);
}
if (xi < yi - tolerance)
{
return(-1);
}
else
{
return(0);
}
}
internal static double Convert(long value)
{
return(DoubleBitReinterpreter.Convert(value));
}
internal static long Convert(double value)
{
return(DoubleBitReinterpreter.Convert(value));
}