On 10/30/2013 6:50 AM, Don wrote:
Unpredictable, sure, but it is unpredictable in that the error is less than a
guaranteed maximum error. The error falls in a range 0<=error<=epsilon. As an
analogy, all engineering parts are designed with a maximum deviation from the
ideal size, not a minimum deviation.
I don't think the analagy is strong. There's no reason for there to be any error
at all.
Besides, in the x87 case, there are exponent errors as well precision. Eg,
double.min * double.min can be zero on some systems, but non-zero on others.
This causes a total loss of precision.
If this is allowed to happen anywhere (and not even consistently) then it's back
to the pre-IEEE 754 days: underflow and overflow lead to unspecified behaviour.
The idea that extra precision is always a good thing, is simply incorrect.
Not exactly what I meant - I mean the algorithm should be designed so that extra
precision does not break it.
The problem is that, if calculations can carry extra precision, double rounding
can occur. This is a form of error that doesn't otherwise exist. If all
calculations are allowed to do it, there is absolutely nothing you can do to fix
the problem.
Thus we lose the other major improvement from IEEE 754: predictable rounding
behaviour.
Fundamentally, there is a primitive operation "discard extra precision" which is
crucial to most mathematical algorithms but which is rarely explicit.
In theory in C and C++ this is applied at each sequence point, but in practice
that's not actually done (for x87 anyway) -- for performance, you want to be
able to keep values in registers sometimes. So C didn't get this exactly right.
I think we can do better. But the current behaviour is worse.
This issue is becoming more obvious in CTFE because the extra precision is not
merely theoretical, it actually happens.
I think it's reasonable to add 3 functions (similar to peek and poke) that force
rounding to float/double/real precision. By inserting that into the code where
the algorithm requires it would make it far more clear than the C idea of
"sequence points" and having no clue whether they matter or not.
