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_mic.c

@@ -2,13 +2,12 @@
 //
 // UNVERIFIED AGAINST REAL HARDWARE. Written against ESP-IDF's documented
 // `driver/i2s_std.h` API (the current idiomatic I2S driver, superseding the
-// older monolithic `driver/i2s.h`) and the INMP441 family's well-documented
-// output format: 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," so
+// older monolithic `driver/i2s.h`). This file owns only the I2S traffic;
+// the RMS -> dBFS maths, the 24-bit-in-32-bit-slot shift and the honesty
+// notes about both live in mems_level.h/.c, which is ESP-IDF-free and
+// unit-tested on a host with plain gcc (see ../test/).
+//
+// "Commonly documented" is not "verified against this specific board," so
 // treat the very first real readings as a sanity check, not a given: talk
 // near the mic and confirm the reported level actually rises before
 // trusting it unattended.
@@ -18,6 +17,7 @@
 #include <math.h>
 #include <stdlib.h>
 #include "mems_mic.h"
+#include "mems_level.h"
 #include "driver/i2s_std.h"
 #include "esp_log.h"
 #include "freertos/FreeRTOS.h"
@@ -25,8 +25,7 @@
 
 static const char *TAG = "mems_mic";
 
-// dBFS reference: full-scale magnitude of a 24-bit signed sample.
-#define FULL_SCALE_24BIT (8388608.0) // 2^23
+// dBFS reference level and noise floor live in mems_level.h.
 
 static i2s_chan_handle_t s_rx_chan = NULL;
 static bool s_ready = false;
@@ -119,26 +118,9 @@ esp_err_t mems_mic_read(sensor_reading_t *out, size_t max_out, size_t *out_count
         return ESP_OK;
     }
 
-    // RMS over the block. The mic's 24-bit sample is left-justified in the
-    // 32-bit I2S slot -- shift right 8 to recover it before squaring, so
-    // the magnitude lines up with FULL_SCALE_24BIT below.
-    double sum_sq = 0.0;
-    for (size_t i = 0; i < n_samples; i++) {
-        double sample = (double)(s_sample_buf[i] >> 8);
-        sum_sq += sample * sample;
-    }
-    double rms = sqrt(sum_sq / (double)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 dbfs;
-    if (rms < 1.0) {
-        dbfs = -120.0; // effective noise floor
-    } else {
-        dbfs = 20.0 * log10(rms / FULL_SCALE_24BIT);
-        if (dbfs < -120.0) dbfs = -120.0;
-    }
+    // All level arithmetic is in the pure, host-tested unit.
+    double rms = mems_level_rms(s_sample_buf, n_samples);
+    double dbfs = mems_level_dbfs(rms);
 
     memset(&out[0], 0, sizeof(out[0]));
     strncpy(out[0].sensor_type, "evp", SENSOR_READING_TYPE_MAXLEN - 1);