gh-116968: Reimplement Tier 2 counters (#117144)

Introduce a unified 16-bit backoff counter type (``_Py_BackoffCounter``),
shared between the Tier 1 adaptive specializer and the Tier 2 optimizer. The
API used for adaptive specialization counters is changed but the behavior is
(supposed to be) identical.

The behavior of the Tier 2 counters is changed:
- There are no longer dynamic thresholds (we never varied these).
- All counters now use the same exponential backoff.
- The counter for ``JUMP_BACKWARD`` starts counting down from 16.
- The ``temperature`` in side exits starts counting down from 64.

Include/internal/pycore_backoff.h

@@ -0,0 +1,128 @@
+
+#ifndef Py_INTERNAL_BACKOFF_H
+#define Py_INTERNAL_BACKOFF_H
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef Py_BUILD_CORE
+#  error "this header requires Py_BUILD_CORE define"
+#endif
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stdint.h>
+
+/* 16-bit countdown counters using exponential backoff.
+
+   These are used by the adaptive specializer to count down until
+   it is time to specialize an instruction. If specialization fails
+   the counter is reset using exponential backoff.
+
+   Another use is for the Tier 2 optimizer to decide when to create
+   a new Tier 2 trace (executor). Again, exponential backoff is used.
+
+   The 16-bit counter is structured as a 12-bit unsigned 'value'
+   and a 4-bit 'backoff' field. When resetting the counter, the
+   backoff field is incremented (until it reaches a limit) and the
+   value is set to a bit mask representing the value 2**backoff - 1.
+   The maximum backoff is 12 (the number of value bits).
+
+   There is an exceptional value which must not be updated, 0xFFFF.
+*/
+
+#define UNREACHABLE_BACKOFF 0xFFFF
+
+static inline bool
+is_unreachable_backoff_counter(_Py_BackoffCounter counter)
+{
+    return counter.as_counter == UNREACHABLE_BACKOFF;
+}
+
+static inline _Py_BackoffCounter
+make_backoff_counter(uint16_t value, uint16_t backoff)
+{
+    assert(backoff <= 15);
+    assert(value <= 0xFFF);
+    return (_Py_BackoffCounter){.value = value, .backoff = backoff};
+}
+
+static inline _Py_BackoffCounter
+forge_backoff_counter(uint16_t counter)
+{
+    return (_Py_BackoffCounter){.as_counter = counter};
+}
+
+static inline _Py_BackoffCounter
+restart_backoff_counter(_Py_BackoffCounter counter)
+{
+    assert(!is_unreachable_backoff_counter(counter));
+    if (counter.backoff < 12) {
+        return make_backoff_counter((1 << (counter.backoff + 1)) - 1, counter.backoff + 1);
+    }
+    else {
+        return make_backoff_counter((1 << 12) - 1, 12);
+    }
+}
+
+static inline _Py_BackoffCounter
+pause_backoff_counter(_Py_BackoffCounter counter)
+{
+    return make_backoff_counter(counter.value | 1, counter.backoff);
+}
+
+static inline _Py_BackoffCounter
+advance_backoff_counter(_Py_BackoffCounter counter)
+{
+    if (!is_unreachable_backoff_counter(counter)) {
+        return make_backoff_counter((counter.value - 1) & 0xFFF, counter.backoff);
+    }
+    else {
+        return counter;
+    }
+}
+
+static inline bool
+backoff_counter_triggers(_Py_BackoffCounter counter)
+{
+    return counter.value == 0;
+}
+
+/* Initial JUMP_BACKWARD counter.
+ * This determines when we create a trace for a loop.
+* Backoff sequence 16, 32, 64, 128, 256, 512, 1024, 2048, 4096. */
+#define JUMP_BACKWARD_INITIAL_VALUE 16
+#define JUMP_BACKWARD_INITIAL_BACKOFF 4
+static inline _Py_BackoffCounter
+initial_jump_backoff_counter(void)
+{
+    return make_backoff_counter(JUMP_BACKWARD_INITIAL_VALUE,
+                                JUMP_BACKWARD_INITIAL_BACKOFF);
+}
+
+/* Initial exit temperature.
+ * Must be larger than ADAPTIVE_COOLDOWN_VALUE,
+ * otherwise when a side exit warms up we may construct
+ * a new trace before the Tier 1 code has properly re-specialized.
+ * Backoff sequence 64, 128, 256, 512, 1024, 2048, 4096. */
+#define COLD_EXIT_INITIAL_VALUE 64
+#define COLD_EXIT_INITIAL_BACKOFF 6
+
+static inline _Py_BackoffCounter
+initial_temperature_backoff_counter(void)
+{
+    return make_backoff_counter(COLD_EXIT_INITIAL_VALUE,
+                                COLD_EXIT_INITIAL_BACKOFF);
+}
+
+/* Unreachable backoff counter. */
+static inline _Py_BackoffCounter
+initial_unreachable_backoff_counter(void)
+{
+    return forge_backoff_counter(UNREACHABLE_BACKOFF);
+}
+
+#ifdef __cplusplus
+}
+#endif
+#endif /* !Py_INTERNAL_BACKOFF_H */