[PATCH 2/6] Remove slow paths from sin/cos

[Zack Weinberg]

On Mon, Mar 12, 2018 at 11:36 AM, Wilco Dijkstra <Wilco.Dijkstra@arm.com> wrote:
> Joseph Myers wrote:
>
>> Yes.  A floating-point number represents a particular real number, not an
>> interval, so all the usual accuracy goals (of results within a few ulps of
>> the correct answer) apply for large inputs (but performance is not a
>> concern for those inputs).  Only for IBM long double is this relaxed, to
>> treat values not representable in 106 mantissa bits as if they do
>> represent intervals.
>
> Though these patches keep the ULP accuracy across the full range as is,
> we could agree on higher ULP errors for large/huge range reduction cases
> in the future. The main complexity is for certain rare inputs which happen to
> be extremely close to an integer multiple of PI/2, and those few cases mean
> you need significant extra work to guarantee 0.5 ULP error bound on range
> reduction.

I think 0.5 ULP error bound for values close to _small_ integer
multiples of pi/2 is worth preserving.  I'm not sure what the right
cutoff is, but if we need to do that "significant extra work" for,
like, values close to 10*pi and the most natural way to implement that
also gives us the same error bound for values close to 1e6*pi, then I
don't see why we shouldn't keep it for both.

zw