https://gcc.gnu.org/bugzilla/show_bug.cgi?id=93871
--- Comment #32 from Steve Kargl <sgk at troutmask dot apl.washington.edu> --- On Thu, Feb 27, 2020 at 05:53:38PM +0000, thenlich at gcc dot gnu.org wrote: > https://gcc.gnu.org/bugzilla/show_bug.cgi?id=93871 > > --- Comment #31 from Thomas Henlich <thenlich at gcc dot gnu.org> --- > I wonder, if some "correct" rounding could further increase > accuracy: We know the sign and "real" magnitude of the > difference deg2rad-π/180 and can round the result of sin() > accordingly. I think we can exploit a table-driven method. Once x is folded into [0,90], x is split by x = n + dx where n = 0, 1, ..., 90 and dx is in [0.,1.). sin(x) = sin(n+d) = sin(n) * cos(d) + cos(n) * sin(d) The table contains a high,low decomposition of {sin(1),cos(1)}, {sin(3),cos(3)}, ..., {sin(90),cos(90)}. Denote the decomposition with shi(n), slo(n), chi(n), clo(n), and both C(d) = cos(d) and S(d) * sin(d) are minimax polynomials. So, we have if (x == n) /* Integral value of x. */ sin(x) = shi(n) + slo(n) ! Is addition needed. else sin(x) = shi(n)*C(d) + slo(n)*C(d) + chi(n)*S(d) + clo(n)*S(d) The else-branch summation can be done with Kahan summation.
