What's the best way to represent System.Double as a sortable string?

Question

In data formats where all underlying types are strings, numeric types must be converted to a standardized string format which can be compared alphabetically. For example, a short for the value 27 could be represented as 00027 if there are no negatives.

What's the best way to represent a double as a string? In my case I can ignore negatives, but I'd be curious how you'd represent the double in either case.

UPDATE

Based on Jon Skeet's suggestion, I'm now using this, though I'm not 100% sure it'll work correctly:

static readonly string UlongFormatString = new string('0', ulong.MaxValue.ToString().Length);

public static string ToSortableString(this double n)
{
    return BitConverter.ToUInt64(BitConverter.GetBytes(BitConverter.DoubleToInt64Bits(n)), 0).ToString(UlongFormatString);
}

public static double DoubleFromSortableString(this string n)
{
    return BitConverter.Int64BitsToDouble(BitConverter.ToInt64(BitConverter.GetBytes(ulong.Parse(n)), 0));
}

UPDATE 2

I have confirmed what Jon suspected - negatives don't work using this method. Here is some sample code:

void Main()
{
    var a = double.MaxValue;
    var b = double.MaxValue/2;
    var c = 0d;
    var d = double.MinValue/2;
    var e = double.MinValue;
    Console.WriteLine(a.ToSortableString());
    Console.WriteLine(b.ToSortableString());
    Console.WriteLine(c.ToSortableString());
    Console.WriteLine(d.ToSortableString());
    Console.WriteLine(e.ToSortableString());
}

static class Test
{
    static readonly string UlongFormatString = new string('0', ulong.MaxValue.ToString().Length);
    public static string ToSortableString(this double n)
    {
        return BitConverter.ToUInt64(BitConverter.GetBytes(BitConverter.DoubleToInt64Bits(n)), 0).ToString(UlongFormatString);
    }
}

Which produces the following output:

09218868437227405311
09214364837600034815
00000000000000000000
18437736874454810623
18442240474082181119

Clearly not sorted as expected.

UPDATE 3

The accepted answer below is the correct one. Thanks guys!

Answer 1

Padding is potentially rather awkward for doubles, given the enormous range (double.MaxValue is 1.7976931348623157E+308).

Does the string representation still have to be human-readable, or just reversible?

That gives a reversible conversion leading to a reasonably short string representation preserving lexicographic ordering - but it wouldn't be at all obvious what the double value was just from the string.

EDIT: Don't use BitConverter.DoubleToInt64Bits alone. That reverses the ordering for negative values.

I'm sure you can perform this conversion using DoubleToInt64Bits and then some bit-twiddling, but unfortunately I can't get it to work right now, and I have three kids who are desperate to go to the park...

---

In order to make everything sort correctly, negative numbers need to be stored in ones-complement format instead of sign magnitude (otherwise negatives and positives sort in opposite orders), and the sign bit needs to be flipped (to make negative sort less-than positives). This code should do the trick:

static ulong EncodeDouble(double d)
{
    long ieee = System.BitConverter.DoubleToInt64Bits(d);
    ulong widezero = 0;
    return ((ieee < 0)? widezero: ((~widezero) >> 1)) ^ (ulong)~ieee;
}

static double DecodeDouble(ulong lex)
{
    ulong widezero = 0;
    long ieee = (long)(((0 <= (long)lex)? widezero: ((~widezero) >> 1)) ^ ~lex);
    return System.BitConverter.Int64BitsToDouble(ieee);
}

Demonstration here: http://ideone.com/JPNPY

Here's the complete solution, to and from strings:

static string EncodeDouble(double d)
{
    long ieee = System.BitConverter.DoubleToInt64Bits(d);
    ulong widezero = 0;
    ulong lex = ((ieee < 0)? widezero: ((~widezero) >> 1)) ^ (ulong)~ieee;
    return lex.ToString("X16");
}

static double DecodeDouble(string s)
{
    ulong lex = ulong.Parse(s, System.Globalization.NumberStyles.AllowHexSpecifier);
    ulong widezero = 0;
    long ieee = (long)(((0 <= (long)lex)? widezero: ((~widezero) >> 1)) ^ ~lex);
    return System.BitConverter.Int64BitsToDouble(ieee);
}

Demonstration: http://ideone.com/pFciY