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

[Joseph Myers]

On Mon, 12 Mar 2018, Wilco Dijkstra wrote:

> 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 don't think the work for having an error bound not much more than 0.5ulp 
on the final result of sin/cos for large arguments is significantly 
different from the work for having an error bound of say 3ulp (the 
testsuite has a global maximum of 9ulp (16ulp for IBM long double) beyond 
which it will not accept errors even if those large errors are listed in 
libm-test-ulps files - that bound is simply based on the errors 
empirically observed at present, for functions other than Bessel functions 
and cpow which are known to have cases with much larger errors).

-- 
Joseph S. Myers
joseph@codesourcery.com