test_velocity_in_ITRF_to_GCRS2 too tight for 32-bit Intel

In relation to #404: 32-bit intel is not precise enough for this test

[   93s] =================================== FAILURES ===================================
[   93s] ________________________ test_velocity_in_ITRF_to_GCRS2 ________________________
[   93s] 
[   93s]     def test_velocity_in_ITRF_to_GCRS2():
[   93s]         # TODO: Get test working with these vectors too, showing it works
[   93s]         # with a non-zero velocity vector, but in that case the test will
[   93s]         # have to be fancier in how it corrects.
[   93s]         # r = np.array([(1, 0, 0), (1, 1 / DAY_S, 0)]).T
[   93s]         # v = np.array([(0, 1, 0), (0, 1, 0)]).T
[   93s]     
[   93s]         ts = api.load.timescale(builtin=True)
[   93s]         t = ts.utc(2020, 7, 17, 8, 51, [0, 1])
[   93s]         r = np.array([(1, 0, 0), (1, 0, 0)]).T
[   93s]         v = np.array([(0, 0, 0), (0, 0, 0)]).T
[   93s]     
[   93s]         r, v = ITRF_to_GCRS2(t, r, v, True)
[   93s]     
[   93s]         # Rotate back to equinox-of-date before applying correction.
[   93s]         r = mxv(t.M, r)
[   93s]         v = mxv(t.M, v)
[   93s]     
[   93s]         r0, r1 = r.T
[   93s]         v0 = v[:,0]
[   93s]     
[   93s]         # Apply a correction: the instantaneous velocity does not in fact
[   93s]         # carry the position in a straight line, but in an arc around the
[   93s]         # origin; so use trigonometry to move the destination point to where
[   93s]         # linear motion would have carried it.
[   93s]         angvel = (t.gast[1] - t.gast[0]) / 24.0 * tau
[   93s]         r1 = mxv(rot_z(np.arctan(angvel) - angvel), r1)
[   93s]         r1 *= np.sqrt(1 + angvel*angvel)
[   93s]     
[   93s]         actual_motion = r1 - r0
[   93s]         predicted_motion = v0 / DAY_S
[   93s]     
[   93s]         relative_error = (length_of(actual_motion - predicted_motion)
[   93s]                           / length_of(actual_motion))
[   93s]     
[   93s] >       assert relative_error < 2e-12
[   93s] E       assert 3.866305785983307e-12 < 2e-12
[   93s] 
[   93s] skyfield/tests/test_positions.py:129: AssertionError
[   93s] =========================== short test summary info ============================
[   93s] FAILED skyfield/tests/test_positions.py::test_velocity_in_ITRF_to_GCRS2 - ass...
[   93s] ======================== 1 failed, 452 passed in 14.92s ========================

[bnavigator]

Can confirm, tests now pass using assay on i586

[brandon-rhodes]

I have adjusted the test tolerances so that they should now all pass under 32-bit Linux! I do not have anything running under 32-bit in CI, but I now have a local command I can run before each Skyfield release (hopefully I remember!) that should hopefully keep the tests of future versions also running under 32-bit operating systems.

I plan to release a new Skyfield 1.25 within the next few hours that includes the improvement. Once you have the chance to try it out, let me know if you have any further problems that need to be tracked down for your openSUSE build!