test: make firmware logic bugs catchable without hardware (Workstream F)

The firmware has never been flashed, and a real bug already reached the
repo because of it: RD03E_FRAME_LEN was 5 for a 6-byte frame, so the footer
check collided with the distance high byte and EVERY distance reading was
garbage — always `lo | 0x5500`, about 218 metres, regardless of what the
sensor saw. That was pure logic with no hardware dependency. It should have
been catchable on a laptop, and there was simply no way to run the code.

Extracted the hardware-free logic out of the three drivers — rd03e_parse,
bmp280_compensate, mems_level — as moves rather than rewrites, carrying the
explanatory comments along with the code they explain. The drivers now own
only their bus I/O and call into the pure units, so nothing changes for the
real device.

`./run_tests.sh` builds them with gcc -Wall -Wextra -Werror plus a
dependency-free assert harness: 175 checks, 0 failed, from a clean tree.

Proven to catch the actual bug rather than assumed to: reintroducing
FRAME_LEN 5 fails four checks, including one that reads "a simple-report
frame is 6 bytes, not 5", plus the truncated-frame and 5-byte-window cases.
Restored, green again.

This does NOT make the firmware verified, and the README says so plainly —
it is called a narrow exception and scoped to pure logic. Wiring, timing,
real register behaviour and the reconstructed RD-03E frame format all still
need the physical board.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

firmware/esp32p4-sensor-node/main/mems_level.h

@@ -0,0 +1,47 @@
+// I2S MEMS microphone level maths (RMS -> dBFS) — PURE LOGIC.
+//
+// ESP-IDF-free by design: no I2S, no esp_err_t, no logging. Only
+// <stdint.h>/<stddef.h> and <math.h> in the .c, so it compiles and is
+// testable on a host with plain gcc (see ../test/). `mems_mic.c` does the
+// I2S read and calls in here for the arithmetic.
+//
+// The INMP441 family outputs 24-bit signed PCM, MSB-first, left-justified
+// in a 32-bit I2S slot (Philips/standard I2S timing). The right-shift-by-8
+// used below to recover the 24-bit sample from the 32-bit slot, and the
+// dBFS reference level (2^23, a 24-bit signed sample's full-scale
+// magnitude), are the commonly-documented values for this exact mic family
+// — but "commonly documented" is not "verified against this specific
+// board." Host tests prove the arithmetic (full scale reads ~0 dBFS,
+// silence reads the floor and never -inf/NaN); they cannot prove the shift
+// amount matches this module revision's real bit alignment.
+
+#pragma once
+
+#include <stddef.h>
+#include <stdint.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+// dBFS reference: full-scale magnitude of a 24-bit signed sample.
+#define MEMS_FULL_SCALE_24BIT (8388608.0) // 2^23
+
+// Level reported for a true-silent (or sub-LSB) input, and the clamp
+// applied to anything quieter.
+#define MEMS_DBFS_FLOOR (-120.0)
+
+// RMS over a block of raw 32-bit I2S slots. The mic's 24-bit sample is
+// left-justified in the 32-bit slot -- shift right 8 to recover it before
+// squaring, so the magnitude lines up with MEMS_FULL_SCALE_24BIT.
+// Returns 0.0 for an empty block.
+double mems_level_rms(const int32_t *samples, size_t n_samples);
+
+// dBFS: 20*log10(rms / full_scale). A true-silent input gives rms=0,
+// which is -inf in dB -- clamp to a floor rather than emit a value the
+// JSON encoder/backend can't handle.
+double mems_level_dbfs(double rms);
+
+#ifdef __cplusplus
+}
+#endif