Lau writes: > P Witte wrote: > > While were talking fp, can someone please explain what the purpose of the > > $81f bias (or whatever the technical term) is? Why not just represent > > exponents as +/-32k ? > > > > Per > > > > > > It's a bit "historic", I suspect. > > It allows all operations on the exponent to be done with unsigned > arithmetic, which saves some brain work when implementing the stuff. > > It gives an easy test for a "magic" value of zero exponent, which is > handy for the "special" cases. If is were not biased, you would have to > use a value like "0x8000", which would become messy. > > The specific bias varies, but to some extent is one that preserves a > balance of mantissa precision for maximum and minimum absolute values. > It is generally just one off what you'd expect. > > Note that, with the IEEE format, operations on both exponent and > mantissa are unsigned (as it uses a separate flag to indicate > positive/negative value). The QDOS implementation is somewhat of a > hybrid, as it uses signed arithmetic for the mantissa. I suspect > Sinclair adopted that format to make the code a fraction quicker. By > doing so (instead of using the "concealed leading bit"), you lose one > bit of precision (and introduce the "invalid representation" problems), > but you can write shorter, more straightforward software code. The IEEE > format is expected to be done by harware, which can happily > "re-manifest" the concealed leading bit of the fly. I'm waffling a bit > here... but if QL used a concealed leading one on a 32-bit mantissa, it > would have to do 33-bit arithmetic all the time. > > PS. Just as an aside, I cut my teeth on IBM System/360 floating point, > which used a hexadecimal exponent! Very ragged precision - not a good > idea at all!
Thanks for the explanation. (I may have to come back to this ;) Per
