equality definition is not symmetric

[I-Sokolov]

x == v ⇒ (v - abs(v) × ϵ - ϵ) < x < (v + abs(v) × ϵ + ϵ) with a tolerance value being: ϵ = 1.0e⁻⁶

So
-1000001.0000011 != -1000000
but
-1000000 == -1000001.0000011

(fail-comparison_tolerance_for_floating_point_negative_high_number_lower_bound)

[I-Sokolov]

As I recall from my study in ancient century mathematically correct comparison (symmetric and transitive) can be based on number of significant digits and round-off.

[aothms]

Not disagreeing. I think the intent for the current approach was to come up with something 'automatic' that works off the single value specified in IDS. I like the approach of trimming to a number of significant digits, but you need to know the number of significant digits then, basically you need to know the intent. When a user requires 0.00001 is that ~ 0.000 or 0.00001000? So that makes things more complicated in the spec, editors and end-users. But I agree it's mathematically more pure. Something to consider.

[I-Sokolov]

0.00001, 10000 and 0.000000001 all have one significant digit, it does not depend on intention.
Any value can be represented as d.dd..dddEmmm - this is floating point number.
Natively for computer representation as well natural for physic is a number of digits 'd'

[aothms]

I get that, but you'd have to convince your XML parser and serializer then to add additional trailing zeros (based on the intended precision... that's what I meant with intention) and when parsed as a native double 0.1 is the same binary encoding as 0.1000, so again that "intention" is not retained automatically.