GPSL5I construction: preallocate code matrix and speed up gen_l5i_code (LFSR)

[giove-a]

Summary

GPSL5I builds its 10230×37 code matrix at construction via gen_l5i_code per PRN. Profiling (done while implementing Galileo E5a, which uses a similar LFSR generator) shows two independent optimization opportunities in src/gps/l5i.jl:

1. mapreduce(…, hcat, 1:37) accumulation in read_gpsl5i_codes — modest time cost, large allocation cost.
2. gen_l5i_code internals — the actual dominant cost.

Neither is on a runtime hot path (gen_code!/get_code operate on the prebuilt matrix); this only affects one-time construction. Filing for visibility — not urgent.

Measurements (read_gpsl5i_codes, 37 PRNs, steady-state median)

variant	time	allocations
current mapreduce(…, hcat, …)	3.45 ms	7.57 MB
preallocated column-fill	3.03 ms	0.76 MB
gain	1.14× (~0.42 ms)	10× (−6.8 MB)

So the hcat accumulation (which reallocates a growing matrix 37 times) leaves only ~0.42 ms / ~12% on the table time-wise, but ~6.8 MB of needless allocation churn.

The bigger opportunity: gen_l5i_code

The hcat is not the bottleneck — gen_l5i_code is. Pure LFSR work is ~3.0 ms (37 × ~81 µs/PRN). For contrast, the new Galileo E5a generator produces 50 PRNs in ~0.7 ms, while L5-I produces 37 in ~3 ms — roughly 5–6× slower per code.

Likely causes in gen_l5i_code / shift_register:

• Per-call allocation of tap-index arrays ([9, 10, 12, 13], [1, 3, 4, 6, 7, 8, 12, 13]) and the weight vector [4096, …, 1].
• Array/index-based shift register instead of bitmask taps.

The E5a generator (src/galileo/e5a.jl, _e5_lfsr_bits) uses bitmask taps with count_ones for the feedback parity, which is much faster. Porting L5-I to the same style would recover most of the ~2.5 ms.

Suggested fix

1. Preallocate the matrix in read_gpsl5i_codes and fill columns in place (10× allocation drop, ~0.4 ms).
2. Rewrite gen_l5i_code/shift_register to a bitmask LFSR (hoist the constant tap masks out of the loop), mirroring _e5_lfsr_bits in e5a.jl.

Notes

• Found while adding Galileo E5a; deliberately left out of that change to keep it focused.
• Measured on Julia 1.12, --project, steady-state median of 11 runs (first-call compilation excluded).