feat(pps): add adaptive disciplined timing loop

soc/software/pps_python/test_pps_model.py

@@ -79,6 +79,27 @@ class PpsModelTests(unittest.TestCase):
             1000.0 * np.median(np.abs(timing_error)),
         )
 
+    def test_fractional_code_phase_is_applied_to_capture_counter(self):
+        _, _, epochs = make_simulation(70.0)
+        mature = [epoch for epoch in epochs if epoch.transmit_true_s >= 50.0]
+        applied_s = np.asarray(
+            [
+                (
+                    epoch.reference_tracking_tick_raw
+                    - epoch.reference_tracking_tick
+                )
+                / TRACKING_HZ
+                for epoch in mature
+            ]
+        )
+        self.assertGreater(np.max(applied_s), 40.0e-9)
+        self.assertTrue(np.all(applied_s >= 0.0))
+        self.assertTrue(np.all(applied_s <= 64.0e-9))
+        # The integer mailbox can represent the correction only on the 8 ns
+        # PPS grid; the model must use the same nearest-tick quantization.
+        applied_ticks = applied_s * TRACKING_HZ
+        self.assertLess(np.max(np.abs(applied_ticks - np.rint(applied_ticks))), 1.0e-9)
+
     def test_timestamped_pi_rejects_apb_latency_as_phase(self):
         _, tracking, epochs = make_simulation(70.0)
         config = PIConfig(natural_frequency_hz=0.035, damping=0.9, max_slew_ppm=20.0)