[nicolas-maman]

The pairs phase brought to 1.1-1.2x Box3D e77352c (it was 1.45-1.6x), a wide separating axis test, and a bug from #157. The golden trace is unchanged bit for bit.

The broad phase (#151):

• The dynamic tree's boxes and the world's fat boxes are single precision, rounded outward from double, as the reference's large-world build keeps them (math.aabb_round_out, its b3RoundDownFloat and b3RoundUpFloat). That gives 32-byte nodes.
• The insertion costs and the rays are measured on the widened boxes, which is exact. Storage, refit and overlaps are float.
• A tree query compares the double box against the widened nodes, so a query pays no rounding at all.
• The rounding is the bit step nextafterf takes, inline in the native header and branch-free. It is checked against libm's at zero, the denormals and the largest float.
• Measured alone, the float boxes did not move the pairs phase. The profile showed why: two thirds of the walk was the pair set's probe, a cache miss per candidate. So candidates are now batched 32 at a time with every hash slot prefetched before any probe, as the reference does (b3FlushCandidatePairs). The walk also reads a leaf's shape index from the node rather than the proxy array.
• Pairs phase, ms per step: convex pile 1.82 to 1.44 (Box3D 1.24), junkyard 2.88 to 2.21 (2.00), washer 2.65 to 2.21 (1.83), spinner 0.403 to 0.353 (0.284).

The separating axis test (#150, in part):

• Every hull carries single-precision rows of its vertices and normals, padded to eight lanes, and its edges' cosines. The HULL_VERSION changed, and hull_bytes_valid checks the new sections.
• Support searches run eight vertices a pass. A hull of 16 vertices or fewer is searched one vertex at a time in double, where the lanes' reduction cost more than it saved.
• Edge candidates are culled with the stored cosines and then by the best faces' probe points (b3FilterEdgeCandidates). Edge pairs run eight a pass, with the axis and separation in lanes.
• Every winner is measured again in double.
• SAT runs, µs: cylinder/cylinder 4.73 to 2.58 (Box3D 1.41), complex/cylinder 2.77 to 2.02 (1.06), complex/complex 1.76 to 1.60 (0.95).
• Hull SAT: e77352c's wide separating axis (convex_manifold_wide.inl); the convex pile's collide is 1.38x #150 stays open for the rest: the face dots, the transform of B and the reduction, done in lanes. The reduction waits on aether#2603, filed here: std.lanes has no bit reinterpretation for the reference's embedded-index minimum.

A bug fixed (#158): hull_bytes_valid (from #157) bounded half-edges by MAX_HULL_EDGES, half what the builder allows. A compound holding a hull of more than 64 edges failed its byte round trip. It is fixed, and the round trip is now tested on a 240-half-edge cylinder.

Whole step, ours before and after, ms per step:

• convex pile 11.84 to 11.26, junkyard 28.3 to 25.0, washer 17.6 to 16.7, spinner 4.31 to 4.08, sleep 2.40 to 2.33;
• trees25 1.589 to 1.587, trees100 unchanged, trees50 +2.8%.

The trees scenes pay for rounding the fat boxes of fast shapes, which leave them every step. Details are in bench/RESULTS.md, "The pairs phase and the wide separating axis test".

Also:

• scripts/profile.sh passes ae cflags whole, since 0.795's include directories come as -idirafter <dir> pairs.
• Tests:
  • centimetre boxes at 1e7, each held by its leaf and found by every query that touches them;
  • the rounding's properties and its agreement with libm;
  • the broad phase's brute force over the stored boxes;
  • the big-hull byte round trip.

Local gate on Aether 0.795.0: all 34 suites pass with no warnings, and the golden trace matches bit for bit (1,256 steps). Pins: Aether 0.795.0 and aeb v0.325, the latest releases.

Closes #151. Closes #158. Refs #150, #121.