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 Re: l3fp and sin(pi), cos(pi/2) aparsloe <[log in to unmask]> Thu, 29 May 2014 09:41:25 +1200 text/plain (45 lines) On 28/05/2014 1:42 a.m., Bruno Le Floch wrote: > Hello Will, > >> about the typesetting; should/can we provide an easy way to typeset negative >> zero just as zero? > I suppose there are two cases where one needs to display numbers: for > typesetting, and when writing to a file (terminal, log,...). For the > first case, I'd advocate using siunitx, which has all the settings you > may want, and more. For the second case, I feel that in all contexts > where 0 is better than -0 (e.g. pdf specials) there is also a need to > limit the number of significant digits to less than 16. This requires > rounding. We should provide formatting functions which produce a > string of characters from floating points. Doing this correctly is a > bit subtle, and it is not clear what should be implemented and what > can be left out (see e.g. > http://www.cplusplus.com/reference/cstdio/printf/ for a long list of > things C++ does). > >> When I was trying it out, I thought perhaps that \fp_eval:n would return >> negative zero but \fp_to_decimal:n would “normalise” it; is that a crazy >> idea? > I'm not keen on that, but I don't have a very strong argument against > it. Mainly, -0 is the correct result, so I don't see what's wrong > with it. Actually... thinking about it, there is an easy way to get 0 > for -0: add +0 to it. It turns out that 0+(-0) = +0, so for all x, > 0+x is exactly x, except when x is -0, then 0+x is +0. If I remember > correctly, the signs of (±0)±(±0) are not mandated by the standard, so > we could presumably document that 0+x does the right thing, and make > sure that this is mentioned in the code and tested. > > Bruno > I had the experience recently of checking a complicated trigonometric expression derived, after an embarrassingly long labour, from another complicated trigonometric expression. Had I made a mistake in the working? I evaluated the expressions using l3fp. One, for a number of different parameter values gave 0, the other for the same parameter values gave -0. I concluded, ruefully, that the derivation was correct. To someone, like me, not versed in numerical analysis, the occurrence of signed zero was a surprise. The 0+x trick is good to know and perhaps worth mentioning in the documentation. Andrew