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

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

On Thu, 25 May 2006, Robert Kern apparently wrote:=20
> Let me clarify. Since you created your values by=20
> multiplying the floating-point approximation pi by an=20
> integer value. When you perform the operation % (2*pi) on=20
> those values, the result happens to be exact or nearly so=20
> but only because you used the same approximation of pi.=20
> Doing that operation on an arbitrary value (like 1000000)=20
> only introduces more error to the calculation.=20
> Floating-point sin(1000000.0) should return a value within=20
> eps (~2**-52) of the true, real-valued function=20
> sin(1000000). Calculating (1000000 % (2*pi)) introduces=20
> error in two places: the approximation pi and the=20
> operation %. A floating-point implementation of sin(.)=20
> will return a value within eps of the real sin(.) of the=20
> value that is the result of the floating-point operation=20
> (1000000 % (2*pi)), which already has some error=20
> accumulated.=20

I do not think that we have any disgreement here, except=20
possibly over eps, which is not constant for different=20
argument sizes.  So I wondered if there was a tradeoff:=20
smaller eps (from smaller argument) for the cost of=20
computational error in an additional operation.

Anyway, thanks for the feedback on this.

Cheers,
Alan