Hi all, I wrote a possible implementation of sindg:
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. 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. So I am still unsure if this belong in the stdlib, but if so, this is how it could be done. Stephan 2018-06-12 8:50 GMT+02:00 Chris Angelico <ros...@gmail.com>: > On Tue, Jun 12, 2018 at 4:40 PM, Greg Ewing <greg.ew...@canterbury.ac.nz> > wrote: > > Tim Peters wrote: > > > >> 1. Python's float "%" is unsuitable for argument reduction; e.g., > >> > >> >>> -1e-14 % 360.0 > >> 360.0 > >> > >> `math.fmod` is suitable, because it's exact: > >> > >> >>> math.fmod(-1e-14, 360.0) > >> -1e-14 > > > > > > So why doesn't float % use math.fmod? > > https://docs.python.org/3/reference/expressions.html# > binary-arithmetic-operations > https://docs.python.org/3/reference/expressions.html#id17 > https://docs.python.org/3/reference/expressions.html#id18 > > (the latter two being footnotes from the section in the first link) > > With real numbers, divmod (and thus the // and % operators) would > always return values such that: > > div, mod = divmod(x, y): > 1) div*y + mod == x > 2) sign(mod) == sign(y) > 3) 0 <= abs(mod) < abs(y) > > But with floats, you can't guarantee all three of these. The divmod > function focuses on the first, guaranteeing the fundamental arithmetic > equality, but to do so, it sometimes has to bend the third one and > return mod==y. > > There are times when it's better to sacrifice one than the other, and > there are other times when it's the other way around. We get the two > options. > > ChrisA > _______________________________________________ > 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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