[Steven D'Aprano] > ...
The initial proposal is fine: a separate set of trig functions that take > their arguments in degrees would have no unexpected surprises (only the > expected ones). With a decent implementation i.e. not this one: > > # don't do this > def sind(angle): > return math.sin(math.radians(angle)) > But that's good enough for almost all real purposes. Indeed, except for argument reduction, it's essentially how scipy's sindg and cosdg _are_ implemented: https://github.com/scipy/scipy/blob/master/scipy/special/cephes/sindg.c > and equivalent for cos, we ought to be able to get correctly rounded > values for nearly all the "interesting" angles of the circle, without > those pesky rounding issues caused by π not being exactly representable > as a float. > > If people are overly ;-) worried about tiny rounding errors, just compute things with some extra bits of precision to absorb them. For example, install `mpmath` and use this: def sindg(d): import math, mpmath d = math.fmod(d, 360.0) if abs(d) == 180.0: return 0.0 with mpmath.extraprec(12): return float(mpmath.sin(mpmath.radians(d))) Then, e.g, >>> for x in (0, 30, 90, 150, 180, 210, 270, 330, 360): ... print(x, sindg(x)) 0 0.0 30 0.5 90 1.0 150 0.5 180 0.0 210 -0.5 270 -1.0 330 -0.5 360 0.0 Notes: 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 2. Using a dozen extra bits of precision make it very likely you'll get the correctly rounded 53-bit result; it will almost certainly (barring bugs in `mpmath`) always be good to less than 1 ULP. 3. Except for +-180. No matter how many bits of float precision (including the number of bits used to approximate pi) are used, converting that to radians can never yield the mathematical `pi`; and sin(pi+x) is approximately equal to -x for tiny |x|; e.g., here with a thousand bits: >>> mpmath.mp.prec = 1000 >>> float(mpmath.sin(mpmath.radians(180))) 1.2515440597544546e-301 So +-180 is special-cased. For cosdg, +-{90. 270} would need to be special-cased for the same reason.
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