Op wo 13 jun. 2018 13:12 schreef Richard Damon <rich...@damon-family.org>:
> My first comment is that special casing values like this can lead to > some very undesirable properties when you use the function for numerical > analysis. Suddenly your sind is no longer continuous (sind(x) is no > longer the limit of sind(x+d) as d goes to 0). > The deviations introduced by the special casing are on the order of one ulp. At that level of detail the sin wasn't continuous to begin with. > > As I stated in my initial comment on this, if you are going to create a > sind function with the idea that you want 'nice' angles to return > 'exact' results, then what you need to do is have the degree based trig > routines do the angle reduction in degrees, and only when you have a > small enough angle, either use the radians version on the small angle or > directly include an expansion in degrees. > Yes that is what my code does. It reduces degrees to [0,90]. > > Angle reduction would be based on the identity that sin(x+y) = sin(x) * > cos(y) + cos(x) * sin(y) and cos(x+y) = cos(x)*cos(y) - sin(x) * sin(y). > > If you want to find sin(z) for an arbitrary value z, you can reduce it > to and x+y where x is some multiple of say 15 degrees, and y is in the > range -7.5 to 7.5 degrees. You can have stored exact values of sin/cos > of the 15 degree increments (and only really need them between 0 and 90) > and then compute the sin and cos of the y value. This is not how sine functions are calculated. They are calculated by reducing angle to some interval, then evaluating a polynomial which approximates the true sine within that interval. Stephan > On 6/13/18 6:07 AM, Stephan Houben wrote: > > 2018-06-13 12:00 GMT+02:00 Robert Vanden Eynde <robertv...@gmail.com > > <mailto:robertv...@gmail.com>>: > > > > What was wrong with my initial implementation with a lookup table > > ? :D > > > > def sind(x): > > if x % 90 == 0: > > return (0, 1, 0, -1)[int(x // 90) % 4] > > else: > > return sin(radians(x)) > > > > > > I kinda missed it, but now you ask: > > > > 1. It's better to reduce the angle while still in degrees since one of > > the advantages > > of degrees is that the reduction can be done exactly. Converting > > very large angles > > first to radians and then taking the sine can introduce a large error, > > > > 2. I used fmod instead of % on advice in this thread. > > > > 3. I also wanted to special case, 30, 45, and 60. > > > > > > > > If you want to support multiples of 30, you can do % 30 and // 30. > > > > > > Sure, but I also wanted to special-case 45. > > > > Stephan > > > > > > > > Le mer. 13 juin 2018 à 09:51, Stephan Houben <stephan...@gmail.com > > <mailto:stephan...@gmail.com>> a écrit : > > > > Op di 12 jun. 2018 12:41 schreef Nathaniel Smith > > <n...@pobox.com <mailto:n...@pobox.com>>: > > > > On Tue, Jun 12, 2018, 00:03 Stephan Houben > > <stephan...@gmail.com <mailto:stephan...@gmail.com>> wrote: > > > > Hi all, > > > > I wrote a possible implementation of sindg: > > > > > https://gist.github.com/stephanh42/336d54a53b31104b97e46156c7deacdd > > < > https://gist.github.com/stephanh42/336d54a53b31104b97e46156c7deacdd> > > > > This code first reduces the angle to the [0,90] interval. > > After doing so, it can be observed that the simple > > implementation > > math.sin(math.radians(angle)) > > produces exact results for 0 and 90, and a result > > already rounded to nearest for > > 60. > > > > > > You observed this on your system, but math.sin uses the > > platform libm, which might do different things on other > > people's systems. > > > > > > > > Ok, I updated the code to treat all the values 0, 30, 45, 60 > > and 90 specially. > > > > Stephan > > > > > > > > For 30 and 45, this simple implementation is one ulp > > too low. > > So I special-case those to return the > > correct/correctly-rounded value instead. > > Note that this does not affect monotonicity around > > those values. > > > > > > Again, monotonicity is preserved on your system, but it > > might not be on others. It's not clear that this matters, > > but then it's not clear that any of this matters... > > > > -n > > > > _______________________________________________ > > Python-ideas mailing list > > Python-ideas@python.org <mailto:Python-ideas@python.org> > > https://mail.python.org/mailman/listinfo/python-ideas > > <https://mail.python.org/mailman/listinfo/python-ideas> > > Code of Conduct: http://python.org/psf/codeofconduct/ > > <http://python.org/psf/codeofconduct/> > > > > > > _______________________________________________ > > Python-ideas mailing list > > Python-ideas@python.org <mailto:Python-ideas@python.org> > > https://mail.python.org/mailman/listinfo/python-ideas > > <https://mail.python.org/mailman/listinfo/python-ideas> > > Code of Conduct: http://python.org/psf/codeofconduct/ > > <http://python.org/psf/codeofconduct/> > > > > > > > > > > _______________________________________________ > > Python-ideas mailing list > > Python-ideas@python.org > > https://mail.python.org/mailman/listinfo/python-ideas > > Code of Conduct: http://python.org/psf/codeofconduct/ > > > -- > Richard Damon > > _______________________________________________ > Python-ideas mailing list > Python-ideas@python.org > https://mail.python.org/mailman/listinfo/python-ideas > Code of Conduct: http://python.org/psf/codeofconduct/ >
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