@seberg I think it is not necessary to initialize h[1]. In the first iteration of the outer loop: L115-L132 (when j = 1), h[1] is assigned at L130 without being read up to that point.

• the inner loop - for (int p = 0; p < j; p++) { hh[p] = h[p]; } does not be executed, so h[1] is not referenced.
• the inner loop - for (n = 1; n <= j; n++) { ... } assigns h[1] at h[n] = w * (xp - xa); when n = 1.

@asi1024 OK, I think I found the actual issue, I guess... This one looks like a clear typo and makes a lot more sense.

I won't claim to have understood why this issue leads to the above observations or the algorithm, but it's clear that x[n] must be filled in...

We should wait a bit for @ev-br, we have been chatting a bit and he is looking at the SciPy code. SciPy has the same code although it (recently) started to zero the input.

But... let's see maybe @ev-br finds something more here. It still looks like a typo to me, but it sounds like there may be a bit more complexity here.

OK, I think we agreed to (and Evgeni found a bit more to back it up), that deBoors formula has a funny "use zero when it would be divide by zero" which is the reason for the path, so that the fix is right.
(It is still surprising that this error seems very subtle since the test suite doesn't notice a thing here for example!)

Evgeni figures the reason why this is that it is practically impossible to hit this path to begin with: The test is very strange.

/test mini

To summarize, I indeed believe this is the right fix. A typo (mu<->n) led to using uninitialized memory in some cases.
The typo originates from scipy, where it traces back to the original commit which introduced the de_boor_d function, in 2007.
The spirit of the fix is indeed to enforce the "result is zero if denominator is zero" caveat for the recursive definition of b-splines.
Why tests do not catch it otherwise: it is rather difficult to hit this code path. The flaky test which caught it in CuPy has several features which helped catching it (mostly by chance): for a quadratic spline (k=2), it has a triple knot, and there are only two boundary knots next to it.

@seberg Many thanks for looking into the flaky failure! LGTM!