On 12/30/19 6:55 PM, David Mertz wrote:
> The order he generates is very close to the IEEE total order, the
difference are:
> 1) It doesn't seperate -0 for +0, which shouldn't matter for
most applications.
> 2) It doesn't provide an order between NaNs, but unless you are
taking special measures to distinguish the NaNs anyway, that
doesn't really matter.
And it also doesn’t distinguish equal but distinct-bit-pattern
subnormal values.
This is more in the category of "things that definitely do not
matter", but I had forgotten about subnomal floating-point values.
How does IEEE totalOrder mandate ordering those vs. equivalent normal
numbers?
So yes, my implementation of totalOrder probably has another
incompleteness for the IEEE spec. It was THREE LINES of code, and I
never claimed the goal was useful even if done correctly.
IEEE BINARY floating point doesn't have subnormal values the equivalent
of normal numbers. The binary format has an assumed leading one to the
mantissa for exponents greater than 0 (and less than all ones which are
the Infinities and NaNs). This assumed one makes multiple
representations for most values impossible, it one happens for 0, having
+0 and -0. The first level of the ordering is the basic value of the
number, which provides a total order for all finite numbers but 0 in the
binary format.
Other floating point bases, like decimal floating point or hex based,
don't have a consistent leading digit, so it isn't omitted, and you
could have subnormal values if the leading digit is 0. The clause on
handling different representations really just apply to those non-binary
formats.
--
Richard Damon
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