Place indirect contractions once per assignment

[pbrubeck]

TLDR

This is the TSFC half of firedrakeproject/fiat#286. It places the indirect
contraction pass once per finished assignment, and lowers the view it
leaves behind without copying it.

Stacked on #5362, which carries the TSFC halves of fiat#284 and fiat#281.
Needs firedrakeproject/fiat#286.

What this does

Place the pass once per assignment (tsfc/spectral.py,
tsfc/coffee_mode.py).

tabulate_indirect_contractions rewrites a contraction that reads a table
through a map into one tabulation over the table's rows, followed by a gather.
It used to run at the tail of gem.coffee.optimise_monomial_sum, which
sum_factorise calls recursively, so it re-walked the same subtrees once per
level of recursion: 754 calls over 75,497 nodes for a Johnson--Mercier matrix
in 3D.

It now runs once on each finished assignment, in _factorise and in
optimise_expressions. Placing it there also keeps it inside plan costing, so
the two plans #5362 compares are costed with the tabulation applied.

Lower the view without a copy (tsfc/loopy.py).

The rewrite leaves its result behind a ComponentTensor view of a temporary
that code generation has already emitted. Indexing that view used to
materialise a second array and copy into it. _expression_indexed now reads
the existing temporary through the view's own indices.

Effect

Flops are unchanged; this is placement, not a new rewrite. TSFC compile time
falls 1.4-2.4x on the zany elements, and the copy the view lowering removes is
one array per tabulated contraction.

The rewrite itself is what recovers the Johnson--Mercier and Argyris actions
that #5362 alone regresses -- see the tables there. Without this PR the pass is
present in GEM but never reaches a whole assignment.

Benchmarks

Measured 2026-09-08 against today's main, with the whole stack installed
(fiat#282 -> #284 -> #281 -> #286 paired with the two firedrake PRs). Minimum of
25 timed assemblies, three interleaved repetitions. NCE degree 3 on a prism is
the control: the stack cannot touch it, and it is flat, so the harness is
honest.

Action

element	dim	flops main	flops stack	assemble main	assemble stack
Argyris	2	6,508	3,938	0.890 ms	0.796 ms	11% faster
Johnson--Mercier	2	3,753	3,129	1.151 ms	1.151 ms	unchanged
Johnson--Mercier	3	44,248	32,806	8.348 ms	10.191 ms	22% slower
Guzman--Neilan	2	3,549	2,586	1.044 ms	0.965 ms	8% faster
Guzman--Neilan	3	106,236	51,296	26.882 ms	7.806 ms	3.4x faster
NCE degree 3 (control)	3	110,019	110,052	1.608 ms	1.621 ms	1.01

Bilinear form

element	dim	flops main	flops stack	assemble main	assemble stack
Argyris	2	38,611	53,286	3.532 ms	4.053 ms	15% slower
Johnson--Mercier	2	21,660	21,645	3.384 ms	3.543 ms	5% slower
Johnson--Mercier	3	686,329	494,893	53.466 ms	50.410 ms	6% faster
Guzman--Neilan	2	10,041	10,963	2.300 ms	2.506 ms	9% slower
Guzman--Neilan	3	384,767	344,078	47.364 ms	43.073 ms	9% faster
NCE degree 3 (control)	3	1,639,009	1,639,042	27.664 ms	27.733 ms	1.00

The assembled action vectors agree with main to 12 digits on Johnson--Mercier
and Guzman--Neilan in 2D and 3D, so the Guzman--Neilan win is real work and not
dropped work.

Generated code

The stack replaces unrolled scalar arithmetic with tables and loops, so it moves
storage out of working temporaries and into read-only tables. Working
temporaries are the ones that matter, and they fall.

element	dim	working elements main	working stack	C lines main	C lines stack
Argyris (action)	2	63	113	387	352
Johnson--Mercier (action)	3	798	224	2,127	771
Johnson--Mercier (matrix)	3	4,704	4,676	2,315	364
Guzman--Neilan (action)	3	144	91	1,559	851
Guzman--Neilan (matrix)	3	288	347	1,803	432

AI assistance

Claude Code was used for the split, the benchmarking and this description. The
human contributor remains responsible for understanding, validating and
maintaining the changes.

🤖 Generated with Claude Code

https://claude.ai/code/session_01A1NNAv95LANgpBX61ozPE2