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
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