> Can different iterations of this loop run independently?

I'm not a compiler guy, but vectorisation algorithms typically analyze loop-carried dependencies and can vectorise loops that are not trivially data parallel as is the case in the post. Allen & Kennedy (MK, 2002) discusses the classical methods.

Here's an example, I'm not sure whether the post's algorithm would handle it:

  phase = 0.0
  inc = 0.12345678899

  for i in [0, n):
    out[i] = table[phase % TABLE_LEN]
    phase = phase + inc

Assuming n%4 == 0, this can be trivially 4 lane vectorised as:

  phasev = [phase, phase+inc, phase+inc+inc, phase+inc+inc+inc]
  incv = [inc, inc, inc, inc]

  for i in [0, n) step 4:
    out[i..i+3] = table[phasev % TABLE_LEN]
    phasev = phasev + incv

When I read Allan and Kennedy my impression was that vectorising arbitrary imperative code is a much harder problem than designing a language that only allows for vectorisable constructs to be expressed in the first place. For example maybe it's better to express trivially data parallel kernels as pure functions over buffers and buffer indices. That's how shader programs work isn't it? In my example that would produce different code, requiring a multiplication:

  lambda i: table[(phase0 + i*inc) % TABLE_LEN]

Look into the Eigen library. They use template meta programming to chain linear algebra operations in a way that the compiler should be able to optimize memory layout and kernels for vector instructions. Might give you some ideas.

https://libeigen.gitlab.io/

Though you can expect very verbose compiler output. (I had 35 pages of compiler output output for a single type error once). Probably Nbd with llms.