[Bug-gsl] [bug #45746] Incorrect results of trigonometric functions gsl_sf_sin and gsl_sf_cos

[Peter Barfuss]

Follow-up Comment #1, bug #45746 (project gsl):

So gsl_sf_angle_restrict_symm_err_e is basically equivalent to e_rem_pio2.  As
you can see in that file, this technique only works until about x ~ 2^18 *
M_PI (~823549.6645, so smaller than you think). Past that, you need to
implement Payne-Hanek reduction (which is the entirety of k_rem_pio2), which
is somewhat of a royal payne.

http://stackoverflow.com/questions/30463616/payne-hanek-algorithm-implementation-in-c
is a pretty comprehensive reference. I might throw something together myself
later if I have time.

There's really no other alternative other than that or the current
implementation, which is "return very invalid results for large values of
fabs(x)", sadly.

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