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pitfalls of verifying floating-point computations



http://hal.archives-ouvertes.fr/docs/00/15/88/63/PDF/floating-point.pdf

Interesting paper; generally very well written -- so I was surprised
to see double-rounding blamed on the ties-to-even rule.  This is wrong;
double-rounding problems can occur for any flavour of round-to-nearest:
ties-away-from-zero as well as ties-towards-zero (ties-to-even is one
or the other of those two, depending on the parity of the bit preceding
the rounding bit).

(Well, there is always probabilistic tie-breaking, which I believe is
Nick Maclaren's favourite usually-unavailable feature, but in that case,
who can tell?  It won't be reproducible anyway.  Perhaps the distribution
of rounding errors would be affected, but probably not measurably.)

So plain school-rule rounding (ties-away) suffers from double-rounding too.

Michel.


Sent: 2007-07-07 00:43:44 UTC

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