On Sun, Nov 11, 2012 at 03:11:50PM +0400, Dmitry Pavlov wrote: > Neil, Matthias, > > Certainly not #2, and I doubt that #4 is a problem for us > (although it may be, buried somewhere in specific calculations). > > #1 and #3 definitely are our case. We are doing numerical > integration of celestial bodies over large periods of time > (100 years is a norm). The forces that act on bodies may be of > quite different orders of magnitude: for example, for near-Earth > objects the acceleration towards the Sun is about 2.9e-4 AU/days^2, > while corrections for peculiar relativistic effects (Lense-Thirring > acceleration etc.) can be as small as 1e-17 AU/days^2 (I do not > have exact numbers now). And those effects must be taken > into account. Yet the numerical integration procedure has its > numerical inaccuracies, too. So when we integrate these > accelerations over ten or more years, it sort of pushes the > limit of double precision representation. Again, I do not > (yet) have a precise mathematical proof of it, but it is > more or less obvious that we need to try 80-bit at least.
Is it conceivable that you need multiple-precision fixed-point? -- hendrik ____________________ Racket Users list: http://lists.racket-lang.org/users
