Compile interpolation through the GEM optimisation pipeline

[pbrubeck]

Description

assemble(interpolate) now contracts over the points with the same GEM optimisations as in assemble(Form).

Depends on firedrakeproject/fiat#288

Benchmark

Interpolation into CG on a 16x16x16 extruded hex mesh, minimum of 15 timed
batches. f scalar, u vector, A tensor, all CG of the given degree.

case	flops main	flops PR	ratio	time main	time PR	ratio
f*f*f -> S (CG1)	96	96	1.00x	0.85 ms	0.85 ms	1.00x
dot(u,u)*u -> V (CG1)	520	304	1.71x	1.49 ms	1.43 ms	1.04x
inner(A,A) -> S (CG1)	792	792	1.00x	1.48 ms	1.52 ms	0.97x
dot(A,A) -> T (CG1)	1728	1080	1.60x	2.18 ms	2.04 ms	1.07x
dot(A,dot(A,u)) -> V (CG1)	1776	1128	1.57x	2.15 ms	2.08 ms	1.03x
dot(A,dot(A,A)) -> T (CG1)	2736	1440	1.90x	2.72 ms	2.47 ms	1.10x
f*f*f -> S (CG2)	486	486	1.00x	1.13 ms	1.16 ms	0.97x
dot(u,u)*u -> V (CG2)	2727	1512	1.80x	2.76 ms	2.43 ms	1.14x
inner(A,A) -> S (CG2)	4131	4131	1.00x	2.94 ms	2.93 ms	1.01x
dot(A,A) -> T (CG2)	8748	5103	1.71x	6.83 ms	6.63 ms	1.03x
dot(A,dot(A,u)) -> V (CG2)	9396	5751	1.63x	6.35 ms	5.61 ms	1.13x
dot(A,dot(A,A)) -> T (CG2)	13608	6318	2.15x	9.42 ms	7.29 ms	1.29x
f*f*f -> S (CG3)	1728	1728	1.00x	2.65 ms	2.80 ms	0.95x
dot(u,u)*u -> V (CG3)	9920	5312	1.87x	11.25 ms	7.55 ms	1.49x
inner(A,A) -> S (CG3)	14976	14976	1.00x	6.45 ms	6.51 ms	0.99x
dot(A,A) -> T (CG3)	31104	17280	1.80x	27.49 ms	15.93 ms	1.73x
dot(A,dot(A,u)) -> V (CG3)	34368	20544	1.67x	23.89 ms	14.43 ms	1.66x
dot(A,dot(A,A)) -> T (CG3)	47808	20160	2.37x	33.72 ms	16.91 ms	1.99x

Speed up comes from Delta cancellation that was missing for tensor-valued expressions.

f*f*f and inner(A,A) have an empty value shape, so this change cannot
affect them: they are the control, and come out at 1.00x flops and
0.95-1.01x time. Every case with a value shape improves.

Temporaries rise in two cases (81 to 120 at CG2 dot(A,A), 44 to 65 at CG1
dot(A,A)), and both are still faster, so the extra register pressure does
not cost anything measurable.

Generated with Claude Code

[connorjward]

How much of this code is the same as in compile_form? Ideally they would be the same code path no?

[pbrubeck]

How much of this code is the same as in compile_form? Ideally they would be the same code path no?

Ideally we would have a unified assembler that would deal with compositions of same-mesh interpolate and Form.

#5258

I suggest we take this as the first step.

[connorjward]

This seems fine

[connorjward]

How much of this code is the same as in compile_form? Ideally they would be the same code path no?

Ideally we would have a unified assembler that would deal with compositions of same-mesh interpolate and Form.

#5258

I suggest we take this as the first step.

Agreed. Fine to do in pieces.