🚀 go-pugleaf

In article <9106032144.AA15477@ucbvax.Berkeley.EDU> jbs@watson.ibm.com writes:
 >                                             I believe the papers to
 > which you refer basically require a way to obtain the double precis-
 > ion product of two single precision numbers.  I consider this a some-
 > what different issue.
It would be a different issue if it where true.  But it is not true, the
papers I refer to are about the accumulation of an inner product in
double (extra) precision.  See for instance: J.H.Wilkinson, Rounding Errors
in Numeric Processes, Notes on Applied Science No. 32, HMSO, London;
Prentice Hall, New Jersey, 1963.   (Yes fairly old; it was already known
in that time!)

 >           I agree that binary formats are superior to hex in that they
 > provide 2 extra bits of precision.
A nit; they provide 3 more; nearly a digit.
 >                                     I don't agree (particually for 64-bit
 > formats) that this 2 bits makes it significantly easier to avoid numer-
 > ical problems.
Oh, but they are, see the paper I mentioned above.
--
dik t. winter, cwi, amsterdam, nederland
dik@cwi.nl