spline_coeff: bound="zero" is silently treated as dct1 (bit-identical results)

[balbasty]

Found during an adversarial autograd review of fastfields-torch#28 (see fastfields-torch#29).

Problem

spline_coeff accepts bound=Bound.Zero (0) but produces results bit-identical to bound=Bound.DCT1 (2). The caller asks for zero-padding and silently gets whole-point mirroring instead — a wrong answer with no diagnostic.

Built the operator matrix column-by-column through the torch binding (N=16, float64):

order=2 max|M_zero - M_dct1| = 0.000e+00 bitwise identical: True
order=3 max|M_zero - M_dct1| = 0.000e+00 bitwise identical: True
order=5 max|M_zero - M_dct1| = 0.000e+00 bitwise identical: True
order=7 max|M_zero - M_dct1| = 0.000e+00 bitwise identical: True

For contrast, zero genuinely differs from the other bounds, so this is specifically an alias to dct1 and not a degenerate operator:

max|M_zero - M_dct2| = 5.885e-01
max|M_zero - M_replicate| = 5.885e-01
max|M_zero - M_dft| = 4.641e-01

Reference behaviour

jitfields does not have this problem because it refuses the bound outright — jitfields/splinc.py:

bounds_ok = ('dct1', 'dct2', 'dft', 'replicate')
...
raise ValueError(f'`spline_coeff` only implemented for bounds {bounds_ok} but got: {bound}')

So zero is simply not an implemented boundary condition for the prefilter, and the native layer should say so rather than falling through to the DCT-I path. dst1/dst2/nocheck already raise from the binding — zero is the one that slips through.

Impact

Silent wrong forward results for anyone passing bound="zero" to spline_coeff/spline_coeff_ on any backend. It also produced a wrong gradient on torch, though that half is now handled downstream.

Mitigation already in place (downstream only)

fastfields-torch#29 rejects the unimplemented bounds at the Python entry point, mirroring jitfields' checkbound. That protects the torch backend only — fastfields.numpy and fastfields.cupy still expose the aliased behaviour, and the right place for the check is the native/binding layer.

Suggested fix

Validate the bound in the splinc path and raise for anything outside {dct1, dct2, dft, replicate} (skipping the check for orders 0/1, where the prefilter is the identity and the bound is irrelevant).

🤖 Generated with Claude Code

https://claude.ai/code/session_016AjQcY78NgbagPSbPJRr6Z