Tim Peters <[email protected]> added the comment:
Mark, how about writing a clever single-rounding dot product that merely
_detects_ when it encounters troublesome cases? If so, it can fall back to a
(presumably) much slower method. For example, like this for the latter:
def srdp(xs, ys):
"Single rounding dot product."
import decimal
from decimal import Decimal, Inexact
# XXX check that len(xs) == len(ys)
with decimal.localcontext(decimal.ExtendedContext) as ctx:
ctx.traps[Inexact] = True
total = Decimal(0)
for x, y in zip(map(Decimal, xs), map(Decimal, ys)):
while True:
try:
total += x * y
break
except Inexact:
ctx.prec += 1
return float(total)
So it just converts everything to Decimal; relies on decimal following all the
IEEE rules for special cases; retries the arithmetic boosting precision until
decimal gets an exact result (which it eventually will since we're only doing +
and *); and relies on float() to get everything about final rounding, overflow,
and denorms right. If that doesn't work, I'd say it's a bug in the decimal
module ;-)
I'd bet a dollar that, in real life, falling back to this would almost never
happen, outside of test cases.
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<https://bugs.python.org/issue33089>
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