PR #5381 makes some SciPy tests fail

[mattip]

I discovered that latest develop is failing tests in SciPy, where 0.3.30 passes. Bisecting back, it seems #5381 changed some results in SciPy's root finding. xref MacPython/openblas-libs#242.

• scipy/interpolate/tests/test_interpolate.py::TestPPoly::test_roots_croots fails, increasing the atol from 1e-10 to 1e-8 makes the test pass
• scipy/linalg/tests/test_solvers.py::TestSolveContinuousAre::test_solve_continuous_are fails, the test arrays are ill-conditioned when solve_discrete_are is called, the error is in calling tsgen which returns info==1, raising an error "Reordering of (A, B) failed because the transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is very ill-conditioned. (A, B) may have been partially reordered"

I can try to whittle these failures down, but wanted to open the issue first in case someone has a better idea of what is going on. CC @Mousius.

[martin-frbg]

Do the failing tests involve any bfloat16 math at all ? Otherwise I do not see how #5381 could be related

[martin-frbg]

Also, are you building with BUILD_BFLOAT16 enabled on x86_64 ? Otherwise the newly added function pointers should have no bearing at all, and in particular would not be able to affect parameter assignment through changed offsets (which should lead to compilation errors or at least warnings anyway)

[martin-frbg]

the only inadvertent inaccuracy I think the PR may have introduced would potentially affect DSCAL, as the alpha argument is copied to a 32bit float instead of the adjustible FLOAT type - but AFAICT this would only affect its subsequent comparison against a constant 1.0 of either single or double precision

[mattip]

alpha argument is copied to a 32bit float instead of the adjustible FLOAT type

Bingo. See #5571