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Re: reproducibility of tininess detection for binary formats
The conclusion I came to is that there are two possible approaches to
reproducibility of underflow and FMA:
EITHER
say that the cases that differ among implementations are not
reproducible - an observation that will affect almost nobody except
test program writers
OR
prescribe the behaviors of these cases for both reproducible and
non-reproducible mode, accepting that certain existing implementations
won't be able to conform at full speed
The compromise in draft 1.5 means that each language standardization
committee will have to decide: is reproducibility worth enough on all
implementations to warrant the extra expense, required on some implementations,
to get underflow and fma right in reproducibility mode only -
but not in the normal execution mode. I have to think that most
language committees running by consensus
will decide that reproducibility can't be worth that much.
However I do agree with draft 1.5 that there is no particular reason why
the underflow rule has to be the same on binary and decimal formats.
I don't think that both radices would go through the exact same
rounding and exception detection paths.