No worse than chaining definition?

[reginalio]

In some cases of 2D and 3D dot product, the definition is very vague, resulting in cases where the acceptable answer are all +inf, -inf and NaN.

One case of 2D dot product is illustrated below. We have (+inf)(+inf) + (+large norm)(-norm), if we obtain the two products separately, we have (+inf) + (-inf), which would result in a NaN. However, since the second product is finite in infinite precision, our test entity gives +inf. In my opinion both result should be passed in this cases, but there are other cases esp. in 3D dot product where the situation is a lot more awkward as shown below.

Warning: 2D dot product of 0:11111111:00000000000000000000000, 0:11111111:00000000000000000000000, 0:11100001:10010010101111000100001 and 1:10011110:00110010000011101111001gives 0:11111111:00000000000000000000000 which is incorrect. Correct answer is NAN

---

Our 3D dot product at the moment is constructed from a 2D dot product sub-entity and a multacc sub-entity. i.e. with input a,b,c,d,e,f, we perform (ef + (ab+cd)).

In a case where ab,cd,ef = ( -1e50, 1, 1e100) = (-inf from overflow, norm, inf from overflow)

At infinite precision, ab + cd + ef gives +inf

With our chained operation using dot2 and multacc, ef + (ab+cd) gives -inf since (ab+cd) is rounded to (-inf) and e*f is finitely large.

If we perform the operation as three mult and two adds, (ab)+(cd)+(ef) = NaN since we are adding (-inf) to (+inf)

Therefore, which result should the testbench pass? all three? or just the top two?

[EightAndAHalfTails]

I think the "correct answer" should be the one obtained by doing the computations at infinite precision, only rounding at the end of the operation (that is, +inf for the first and +inf for the second). Whether it's feasible to have our entities return these values every time is another question, however. :P

[reginalio]

but the specification states "no worse than chaining", which means the testbench should pass the less "correct" results as well...? and if reducing precision gives lower latency I think we should go for the reduced precision method