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

[Alexander B. <ale...@gm...>]

This is not really a numpy issue, but general floating point problem.

Consider this:
>>> x=3Dlinspace(0,10*pi,11)
>>> all(array(map(math.sin, x))=3D=3Dsin(x))
True

If anything can be improved, that would be the C math library.


On 5/25/06, Rob Hooft <ro...@ho...> wrote:
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> Robert Kern wrote:
> | Alan G Isaac wrote:
> |
> |>I am a user, not a numerics type,
> |>so this is undoubtedly a naive question.
> |>
> |>Might the sin function be written to give greater
> |>accuracy for large real numbers?  It seems that significant
> |>digits are in some sense being discarded needlessly.
> |
> |
> | Not really. The floating point representation of pi is not exact. The
> problem
> | only gets worse when you multiply it with something. The method you
> showed of
> | using % (2*pi) is only accurate when the values are created by
> multiplying the
> | same pi by another value. Otherwise, it just introduces another source
> of error,
> | I think.
> |
> | This is one of the few places where a version of trig functions that
> directly
> | operate on degrees are preferred. 360.0*n is exactly representable by
> floating
> | point arithmetic until n~=3D12509998964918 (give or take a power of
> two). Doing %
> | 360 can be done exactly.
>
> This reminds me of a story Richard Feynman tells in his autobiography.
> He used to say: "if you can pose a mathematical question in 10 seconds,
> I can solve it with 10% accuracy in one minute just calculating in my
> head". This worked for a long time, until someone told him "please
> calculate the sine of a million".
>
> Actual mantissa bits are used by the multiple of two-pi, and those are
> lost at the back of the calculated value. Calculating the sine of a
> million with the same precision as the sine of zero requires 20 more
> bits of accuracy.
>
> Rob
> - --
> Rob W.W. Hooft  ||  ro...@ho...  ||  http://www.hooft.net/people/rob/
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