sys/ztimer: properly initialize intermediate extension callback

sys/include/ztimer.h

@@ -485,6 +485,23 @@ void ztimer_update_head_offset(ztimer_clock_t *clock);
  */
 void ztimer_init(void);
 
+/**
+ * @brief   Initialize possible ztimer extension intermediate timer
+ *
+ * This will basically just set a timer to (clock->max_value >> 1), *if*
+ * max_value is not UINT32_MAX.
+ *
+ * This is called automatically by all ztimer backends and extension modules.
+ *
+ * @internal
+ */
+static inline void ztimer_init_extend(ztimer_clock_t *clock)
+{
+    if (clock->max_value < UINT32_MAX) {
+        clock->ops->set(clock, clock->max_value >> 1);
+    }
+}
+
 /* default ztimer virtual devices */
 /**
  * @brief   Default ztimer microsecond clock

sys/ztimer/convert_frac.c

@@ -91,6 +91,7 @@ void ztimer_convert_frac_init(ztimer_convert_frac_t *self, ztimer_clock_t *lower
     ztimer_convert_frac_compute_scale(self, freq_self, freq_lower);
     if (freq_self < freq_lower) {
         self->super.super.max_value = frac_scale(&self->scale_set, UINT32_MAX);
+        ztimer_init_extend(&self->super.super);
     }
     else {
         DEBUG("ztimer_convert_frac_init: rounding up val:%" PRIu32"\n",

sys/ztimer/convert_muldiv64.c

@@ -120,4 +120,5 @@ void ztimer_convert_muldiv64_init(
     ztimer_convert_muldiv64->super.super.ops = &_ztimer_convert_muldiv64_ops;
     ztimer_convert_muldiv64->div = div;
     ztimer_convert_muldiv64->mul = mul;
+    ztimer_init_extend(&ztimer_convert_muldiv64->super.super);
 }

sys/ztimer/periph_rtt.c

@@ -88,4 +88,5 @@ void ztimer_periph_rtt_init(ztimer_periph_rtt_t *clock)
     clock->max_value = RTT_MAX_VALUE;
     rtt_init();
     rtt_poweron();
+    ztimer_init_extend(clock);
 }

sys/ztimer/periph_timer.c

@@ -79,4 +79,5 @@ void ztimer_periph_timer_init(ztimer_periph_timer_t *clock, tim_t dev, unsigned
     clock->super.ops = &_ztimer_periph_timer_ops;
     clock->super.max_value = max_val;
     timer_init(dev, freq, _ztimer_periph_timer_callback, clock);
+    ztimer_init_extend(&clock->super);
 }