Native CPU: a stage's forward transforms as one batched region (#560 item 4) #584

What

#560 item 4, on the CPU: a source's forward transforms as one batched region, each row of each transform a task for one team, in place of one threaded call per transform.

Why it may pay

On a host each forward transform of a stage (the state's, the plasma current's and its edge term's; the quadrature alarm's three) runs as its own threaded call over that transform's columns. With four modes, four of 16 threads have work.

The Julia backend experiment (#559) ran them as one pool's work, each block of each transform a task. On an Intel Xeon Gold 6240 at 16 threads it took rdw's commits from 12.3 ms to 5.8 ms and its source transforms from 8.7 ms to 3.8 ms (#560). After #576, Julia's remaining lead on an Apple M5 Max includes this idea, still untried in native.

SEP 46's calibration (#582) points the same way. On 16 cores of a Google Axion, a team of 8 ran the few-mode tracking cases 9–20 % faster (argon_blueshift_envelope 0.80, h2_raman_averaged 0.90, rdw 0.91) and the large ones up to 1.8 times slower. A process-wide narrower team cannot serve both; filling the team with more work per region can.

What native already has

The device path stacks a stage's forward rows into one buffer and one plan: packs_forward() and transform_forward_pack() in native/src/general.cpp, carrying the in-stage absorber's rows, the projection's (fine and coarse) and the held currents'. On a host packs_forward() returns false behind a compile-time #if. A CPU version can reuse the buffer layout and differ only in how the batch runs:

• one FFTW plan over all rows (howmany = the batch), threaded by FFTW; or
• blocks of single-threaded plans as tasks of one OpenMP region, as Julia does.

Plan

1. Probe (free hardware): enable the pack on a host behind a build switch; A/B rdw, ctc, line, h2_raman_averaged and argon_blueshift_envelope against the current build on one socket of an Intel Xeon Gold 6240, at 1 and 16 threads. Fields must agree to rounding.
2. If it pays, a PR stacked on SEP 46: calibrating the native backend to its machine #582: the batched region's width becomes an operation class of SEP 46's CpuExecution (a built-in threshold and calibrated candidates), qualified with the tracking set on the machines of SEP 46 section 7 item 1.

Done when

The probe's ratios are recorded with hardware and date. Then either the host batch lands with its grain calibrated, or this issue closes on the numbers.