On Tuesday 12 December 2006 11:30, david eddy wrote: > I have to confess that I tend to work with > and think in terms of fixed point arithmetic. > If the source of error in floating point is > primarily the loss of guard bits (binary places) > when an intermediate number has an integer part > say 50 bits long, then I can well understand why the > analysis of errors differs fundamentally in the two cases. > > > It sounds as if an analysis should determine the frequency with which the > number of guard bits drops to dangerous levels. > > I must concede that this is not a problem in fixed point (IFF you have > enough bits to contain the integer part at all times!). > Do you agree that my conjecture about the normal distribution of errors > makes sense in fixed point? > Actually fixed or floating makes little difference. Your analysis looks reasonable so long as the precision of the results is infinite or nearly so. The problem is that it isn't. Whenever A and B are similar in sign and magnitude, the actual precision of the difference of A and B is always a lot less than its apparent precision.
The difference between fixed and floating is that, in the case of floating but not in the case of fixed, the actual precision of the difference is dependent (in a very discrete, discontinuous way) on the absolute magnitude of the input values. There still seems to be an unexplained input of some sort or other which needs to be accounted for, as if you plot max error found during N iterations against exponent (for a fixed FFT run length) you do not get a smooth monotonic increase - some exponents seem to have higher errors than others which are a bit bigger, whilst some exponents seem to have lower errors than others which are a bit smaller. This effect seems to be consistent as N increases, and persistent with different values of offset. There doesn't seem to be anything other than actual trial which can distinguish "difficult" exponents from "easy" ones, again leading towards the "safety first" strategy i.e. if you're a bit unsure, jump to the next run length. Regards Brian Beesley _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
