on floating-point numbers

[Peter J. Holzer]

On 2021-09-04 10:01:23 -0400, Richard Damon wrote:
> On 9/4/21 9:40 AM, Hope Rouselle wrote:
> > Hm, I think I see what you're saying.  You're saying multiplication and
> > division in IEEE 754 is perfectly safe --- so long as the numbers you
> > start with are accurately representable in IEEE 754 and assuming no
> > overflow or underflow would occur.  (Addition and subtraction are not
> > safe.)
> > 
> 
> Addition and Subtraction are just as safe, as long as you stay within
> the precision limits.

That depends a lot on what you call "safe", 

a * b / a will always be very close to b (unless there's an over- or
underflow), but a + b - a can be quite different from b.

In general when analyzing a numerical algorithm you have to pay a lot
more attention to addition and subtraction than to multiplication and
division.

        hp

-- 
   _  | Peter J. Holzer    | Story must make more sense than reality.
|_|_) |                    |
| |   | hjp at hjp.at         |    -- Charles Stross, "Creative writing
__/   | http://www.hjp.at/ |       challenge!"
-------------- next part --------------
A non-text attachment was scrubbed...
Name: signature.asc
Type: application/pgp-signature
Size: 833 bytes
Desc: not available
URL: <https://mail.python.org/pipermail/python-list/attachments/20210906/1158dd93/attachment.sig>