Re: [Numpy-discussion] Re: numpy.sin

[Alan G I. <ai...@am...>]

On Thu, 25 May 2006, Robert Kern apparently wrote:=20
> What continuity? This is floating-point arithmetic.=20

Sure, but a continuity argument suggests (in the absence of=20
specific floating point reasons to doubt it) that a better=20
approximation at one point will mean better approximations=20
nearby.  E.g.,

>>> epsilon =3D 0.00001
>>> sin(100*pi+epsilon)
9.999999976550551e-006
>>> sin((100*pi+epsilon)%(2*pi))
9.9999999887966145e-006

Compare to the bc result of
9.9999999998333333e-006


bc 1.05
Copyright 1991, 1992, 1993, 1994, 1997, 1998 Free Software Foundation, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'.
scale =3D 50
epsilon =3D 0.00001
s(100*pi + epsilon)
.00000999999999983333333333416666666666468253968254

Cheers,
Alan