gh-141498: Change backoff counter to use prime numbers instead of powers of 2 (GH-141591)

Include/internal/pycore_backoff.h

@@ -22,33 +22,48 @@ extern "C" {
    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
+   The 16-bit counter is structured as a 13-bit unsigned 'value'
+   and a 3-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 bits in the value).
+   value is set to a bit mask representing some prime value - 1.
+   New values and backoffs for each backoff are calculated once
+   at compile time and saved to value_and_backoff_next table.
+   The maximum backoff is 6, since 7 is an UNREACHABLE_BACKOFF.
 
    There is an exceptional value which must not be updated, 0xFFFF.
 */
 
-#define BACKOFF_BITS 4
-#define MAX_BACKOFF 12
-#define UNREACHABLE_BACKOFF 15
+#define BACKOFF_BITS 3
+#define BACKOFF_MASK 7
+#define MAX_BACKOFF 6
+#define UNREACHABLE_BACKOFF 7
+#define MAX_VALUE 0x1FFF
 
-static inline bool
-is_unreachable_backoff_counter(_Py_BackoffCounter counter)
-{
-    return counter.value_and_backoff == UNREACHABLE_BACKOFF;
-}
+#define MAKE_VALUE_AND_BACKOFF(value, backoff) \
+    ((value << BACKOFF_BITS) | backoff)
+
+// For previous backoff b we use value x such that
+// x + 1 is near to 2**(2*b+1) and x + 1 is prime.
+static const uint16_t value_and_backoff_next[] = {
+    MAKE_VALUE_AND_BACKOFF(1, 1),
+    MAKE_VALUE_AND_BACKOFF(6, 2),
+    MAKE_VALUE_AND_BACKOFF(30, 3),
+    MAKE_VALUE_AND_BACKOFF(126, 4),
+    MAKE_VALUE_AND_BACKOFF(508, 5),
+    MAKE_VALUE_AND_BACKOFF(2052, 6),
+    // We use the same backoff counter for all backoffs >= MAX_BACKOFF.
+    MAKE_VALUE_AND_BACKOFF(8190, 6),
+    MAKE_VALUE_AND_BACKOFF(8190, 6),
+};
 
 static inline _Py_BackoffCounter
 make_backoff_counter(uint16_t value, uint16_t backoff)
 {
-    assert(backoff <= 15);
-    assert(value <= 0xFFF);
-    _Py_BackoffCounter result;
-    result.value_and_backoff = (value << BACKOFF_BITS) | backoff;
-    return result;
+    assert(backoff <= UNREACHABLE_BACKOFF);
+    assert(value <= MAX_VALUE);
+    return ((_Py_BackoffCounter){
+        .value_and_backoff = MAKE_VALUE_AND_BACKOFF(value, backoff)
+    });
 }
 
 static inline _Py_BackoffCounter
@@ -62,14 +77,11 @@ forge_backoff_counter(uint16_t counter)
 static inline _Py_BackoffCounter
 restart_backoff_counter(_Py_BackoffCounter counter)
 {
-    assert(!is_unreachable_backoff_counter(counter));
-    int backoff = counter.value_and_backoff & 15;
-    if (backoff < MAX_BACKOFF) {
-        return make_backoff_counter((1 << (backoff + 1)) - 1, backoff + 1);
-    }
-    else {
-        return make_backoff_counter((1 << MAX_BACKOFF) - 1, MAX_BACKOFF);
-    }
+    uint16_t backoff = counter.value_and_backoff & BACKOFF_MASK;
+    assert(backoff <= MAX_BACKOFF);
+    return ((_Py_BackoffCounter){
+        .value_and_backoff = value_and_backoff_next[backoff]
+    });
 }
 
 static inline _Py_BackoffCounter
@@ -113,7 +125,7 @@ trigger_backoff_counter(void)
 // as we always end up tracing the loop iteration's
 // exhaustion iteration. Which aborts our current tracer.
 #define JUMP_BACKWARD_INITIAL_VALUE 4000
-#define JUMP_BACKWARD_INITIAL_BACKOFF 12
+#define JUMP_BACKWARD_INITIAL_BACKOFF 6
 static inline _Py_BackoffCounter
 initial_jump_backoff_counter(void)
 {
@@ -126,7 +138,7 @@ initial_jump_backoff_counter(void)
  * otherwise when a side exit warms up we may construct
  * a new trace before the Tier 1 code has properly re-specialized. */
 #define SIDE_EXIT_INITIAL_VALUE 4000
-#define SIDE_EXIT_INITIAL_BACKOFF 12
+#define SIDE_EXIT_INITIAL_BACKOFF 6
 
 static inline _Py_BackoffCounter
 initial_temperature_backoff_counter(void)

Lib/test/test_opcache.py

@@ -590,7 +590,7 @@ def make_deferred_ref_count_obj():
 class TestRacesDoNotCrash(TestBase):
     # Careful with these. Bigger numbers have a higher chance of catching bugs,
     # but you can also burn through a *ton* of type/dict/function versions:
-    ITEMS = 1000
+    ITEMS = 1400
     LOOPS = 4
     WRITERS = 2
 

Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst

@@ -0,0 +1,3 @@
+Change ``backoff counter`` to use prime numbers instead of powers of 2.
+Use only 3 bits for ``counter`` and 13 bits for ``value``.
+This allows to support values up to 8191. Patch by Mikhail Efimov.