If you haven't already seen it the following essay on the Jwiki may be of interest:
https://code.jsoftware.com/wiki/Essays/Extended_Precision_Functions On Tue, Mar 26, 2019 at 8:08 PM Ian Clark <earthspo...@gmail.com> wrote: > I'm doing trigonometry with very small angles and I want to keep all my > calculations in rational precision. Is there a J-supported way of > converting from floating-point precision to rational, or reasonably speedy > verbs to do the job routinely? > > My problem is this. Let PIa be π expressed as a rational number to 50 > places of decimals (…or more!!) > > PIa > > 31415926535897932384626433832795028841971693993751r10000000000000000000000000000000000000000000000000 > datatype PIa > rational > datatype y=: 1.23 > floating > datatype PIa + y NB. loses precision... > floating > datatype sin PIa NB. likewise loses precision... > floating > > In other words, adding in (or otherwise combining) a number (y) which is > defined *exactly* as a decimal numeral (the sort of thing the SI system of > units does often) results in an avoidable loss of precision. > > (In case anyone's thinking at this point: aren't 64 bits good enough for > this guy? -- no, they aren't.) > > At present I'm using a mickey-mouse scheme of converting the decimal > numeral (":1.23) to a rational value by omitting the decimal point to get > '123', then reintroducing it as a denominator: '123r100' -- which I then > evaluate using (".) to give, in effect: > datatype ya=: 123r100 > rational > datatype PIa + ya NB. --now it behaves itself... > rational > > And of course I'm going to have to write my own sin and cosine verbs. > > The general purpose engine I'm writing not only needs a way of converting > an inputted numeral '1.23' to a rational number (a trivial task by the > above method) but also to check my results accumulator at every step to > stop it lapsing into floating-point precision, and maybe to convert it back > into rational precision. > > This last task is inefficient, the way I'm doing it. Does J have a built-in > way, or a standard way, that's faster than how I'm doing it? > > Ian Clark > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
