Loren Wilton wrote: >> Erm.. Loren.. While that may be true of binary fractions, nobody uses >> binary fractions. >> >> In IEEE floating point format (single precision or otherwise), 0.001 has >> an exact binary representation. >> >> Very few things in this world use binary fractions. Standard floating >> point numbers on computers is one of them. >> > > Er, sorry, no. The value of .001 in IEEE double precision (64 bit > representation) is > 0x3F50624DD2F1A9FC. That most certainly has more than one bit set in the > mantissa.
Yeah, sorry about that.. I've been doing too many esoteric formats lately.. I was thinking of IEEE 854 with base-10 exponents, and that over-wrote the part of my brain that knows that the exponents normally used are base-2. That said, even in single-precision format (32 bit representation, 23 bit mantissa) with base-2 exponents the number of additions required to introduce an error noticeable to the rounding would be quite large.. I suspect, but have not proven, this would require at least one, orders of magnitude more additions than SA+SARE has rules, and probably more like 3 or 4 orders of magnitude more.
