From 86de63aa1f8cdc53550d750547c12c11cb181bc8 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Sat, 15 Nov 2025 13:34:42 +0300
Subject: [PATCH 01/21] Some refactor

---
 Include/internal/pycore_backoff.h | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index 71066f1bd9f19b..6b287568a3f80a 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -32,8 +32,10 @@ extern "C" {
 */
 
 #define BACKOFF_BITS 4
+#define BACKOFF_MASK 0xF
 #define MAX_BACKOFF 12
 #define UNREACHABLE_BACKOFF 15
+#define MAX_VALUE 0xFFF
 
 static inline bool
 is_unreachable_backoff_counter(_Py_BackoffCounter counter)
@@ -44,8 +46,8 @@ is_unreachable_backoff_counter(_Py_BackoffCounter counter)
 static inline _Py_BackoffCounter
 make_backoff_counter(uint16_t value, uint16_t backoff)
 {
-    assert(backoff <= 15);
-    assert(value <= 0xFFF);
+    assert(backoff <= UNREACHABLE_BACKOFF);
+    assert(value <= MAX_VALUE);
     _Py_BackoffCounter result;
     result.value_and_backoff = (value << BACKOFF_BITS) | backoff;
     return result;
@@ -63,7 +65,7 @@ static inline _Py_BackoffCounter
 restart_backoff_counter(_Py_BackoffCounter counter)
 {
     assert(!is_unreachable_backoff_counter(counter));
-    int backoff = counter.value_and_backoff & 15;
+    int backoff = counter.value_and_backoff & BACKOFF_MASK;
     if (backoff < MAX_BACKOFF) {
         return make_backoff_counter((1 << (backoff + 1)) - 1, backoff + 1);
     }

From 4eb3231710cdeaf9a0dcf48b35784bb193a040cf Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Sat, 15 Nov 2025 13:57:07 +0300
Subject: [PATCH 02/21] Changes in backoff bit pattern

---
 Include/internal/pycore_backoff.h | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index 6b287568a3f80a..d9d9efee96975f 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -22,20 +22,20 @@ 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 the value 2**(2*backoff+1) - 1.
+   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 BACKOFF_MASK 0xF
-#define MAX_BACKOFF 12
-#define UNREACHABLE_BACKOFF 15
-#define MAX_VALUE 0xFFF
+#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)
@@ -67,10 +67,10 @@ restart_backoff_counter(_Py_BackoffCounter counter)
     assert(!is_unreachable_backoff_counter(counter));
     int backoff = counter.value_and_backoff & BACKOFF_MASK;
     if (backoff < MAX_BACKOFF) {
-        return make_backoff_counter((1 << (backoff + 1)) - 1, backoff + 1);
+        return make_backoff_counter((1 << (2 * backoff + 3)) - 1, backoff + 1);
     }
     else {
-        return make_backoff_counter((1 << MAX_BACKOFF) - 1, MAX_BACKOFF);
+        return make_backoff_counter((1 << (2 * MAX_BACKOFF + 1)) - 1, MAX_BACKOFF);
     }
 }
 
@@ -115,7 +115,7 @@ 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)
 {
@@ -128,7 +128,7 @@ 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)

From 25816298feef931d941f4d21624760188ff8c20d Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Sat, 15 Nov 2025 14:04:38 +0300
Subject: [PATCH 03/21] Add NEWS

---
 .../2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst              | 2 ++
 1 file changed, 2 insertions(+)
 create mode 100644 Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst

diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst b/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst
new file mode 100644
index 00000000000000..a1637c6f2eb173
--- /dev/null
+++ b/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst
@@ -0,0 +1,2 @@
+Change ``backoff counter`` to use powers of 4 instead of powers of 2. Patch
+by Mikhail Efimov.

From 96de415869221eff5a3c70d50b31dbccde9515ec Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Sat, 15 Nov 2025 14:10:35 +0300
Subject: [PATCH 04/21] NEWS fix

---
 .../2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst            | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst b/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst
index a1637c6f2eb173..10c8d268e42994 100644
--- a/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst
+++ b/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst
@@ -1,2 +1,2 @@
-Change ``backoff counter`` to use powers of 4 instead of powers of 2. Patch
-by Mikhail Efimov.
+Change ``backoff counter`` to use powers of 4 instead of powers of 2.
+This allows to support values up to 8191. Patch by Mikhail Efimov.

From ce3e14f251b5f4c59cee318eb4c38f8443321fcb Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Sat, 15 Nov 2025 15:17:22 +0300
Subject: [PATCH 05/21] Change ITEMS count in test

---
 Lib/test/test_opcache.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Lib/test/test_opcache.py b/Lib/test/test_opcache.py
index c7eea75117de8c..4113b79ef5c80b 100644
--- a/Lib/test/test_opcache.py
+++ b/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
 

From e17b195eadfdddc39e89233ae7cfdda4e5932c05 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 16:28:08 +0300
Subject: [PATCH 06/21] Refactor restart_backoff_counter

---
 Include/internal/pycore_backoff.h | 12 +++++-------
 1 file changed, 5 insertions(+), 7 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index d9d9efee96975f..b7d5e1479dfe4c 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -65,13 +65,11 @@ static inline _Py_BackoffCounter
 restart_backoff_counter(_Py_BackoffCounter counter)
 {
     assert(!is_unreachable_backoff_counter(counter));
-    int backoff = counter.value_and_backoff & BACKOFF_MASK;
-    if (backoff < MAX_BACKOFF) {
-        return make_backoff_counter((1 << (2 * backoff + 3)) - 1, backoff + 1);
-    }
-    else {
-        return make_backoff_counter((1 << (2 * MAX_BACKOFF + 1)) - 1, MAX_BACKOFF);
-    }
+    uint16_t backoff = counter.value_and_backoff & BACKOFF_MASK;
+    assert(backoff <= MAX_BACKOFF);
+    backoff = (backoff == MAX_BACKOFF) ? backoff : backoff + 1;
+    uint16_t value = (1 << (2 * backoff + 1)) - 1;
+    return make_backoff_counter(value, backoff);
 }
 
 static inline _Py_BackoffCounter

From 44b4eb889186f8b727d1341c6cc73f63e8736885 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 16:29:43 +0300
Subject: [PATCH 07/21] Remove unneed assertion and function

---
 Include/internal/pycore_backoff.h | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index b7d5e1479dfe4c..f08bebe5168cb0 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -37,12 +37,6 @@ extern "C" {
 #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;
-}
-
 static inline _Py_BackoffCounter
 make_backoff_counter(uint16_t value, uint16_t backoff)
 {
@@ -64,7 +58,6 @@ forge_backoff_counter(uint16_t counter)
 static inline _Py_BackoffCounter
 restart_backoff_counter(_Py_BackoffCounter counter)
 {
-    assert(!is_unreachable_backoff_counter(counter));
     uint16_t backoff = counter.value_and_backoff & BACKOFF_MASK;
     assert(backoff <= MAX_BACKOFF);
     backoff = (backoff == MAX_BACKOFF) ? backoff : backoff + 1;

From 6d443334c47f99c93789411e9ea09956c4335ab0 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 16:55:24 +0300
Subject: [PATCH 08/21] Use lookup_table

---
 Include/internal/pycore_backoff.h | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index f08bebe5168cb0..d96815a32c371c 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -37,6 +37,9 @@ extern "C" {
 #define UNREACHABLE_BACKOFF 7
 #define MAX_VALUE 0x1FFF
 
+// We only use values x such that x + 1 is prime.
+static const int lookup_table[] = {1, 6, 30, 126, 508, 2052, 8190, 8190};
+
 static inline _Py_BackoffCounter
 make_backoff_counter(uint16_t value, uint16_t backoff)
 {
@@ -61,8 +64,7 @@ restart_backoff_counter(_Py_BackoffCounter counter)
     uint16_t backoff = counter.value_and_backoff & BACKOFF_MASK;
     assert(backoff <= MAX_BACKOFF);
     backoff = (backoff == MAX_BACKOFF) ? backoff : backoff + 1;
-    uint16_t value = (1 << (2 * backoff + 1)) - 1;
-    return make_backoff_counter(value, backoff);
+    return make_backoff_counter(lookup_table[backoff], backoff);
 }
 
 static inline _Py_BackoffCounter

From 0e057129d492549d2ea79927dc86fe3f292b17db Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 17:25:59 +0300
Subject: [PATCH 09/21] Use MAKE_BACKOFF_COUNTER macro

---
 Include/internal/pycore_backoff.h | 37 ++++++++++++++++---------------
 Include/internal/pycore_code.h    | 13 ++++-------
 2 files changed, 23 insertions(+), 27 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index d96815a32c371c..cfa46bfcb4b0b4 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -35,20 +35,21 @@ extern "C" {
 #define BACKOFF_MASK 7
 #define MAX_BACKOFF 6
 #define UNREACHABLE_BACKOFF 7
-#define MAX_VALUE 0x1FFF
 
-// We only use values x such that x + 1 is prime.
-static const int lookup_table[] = {1, 6, 30, 126, 508, 2052, 8190, 8190};
-
-static inline _Py_BackoffCounter
-make_backoff_counter(uint16_t value, uint16_t backoff)
-{
-    assert(backoff <= UNREACHABLE_BACKOFF);
-    assert(value <= MAX_VALUE);
-    _Py_BackoffCounter result;
-    result.value_and_backoff = (value << BACKOFF_BITS) | backoff;
-    return result;
-}
+#define MAKE_BACKOFF_COUNTER(value, backoff) \
+    ((_Py_BackoffCounter){ .value_and_backoff = (value << BACKOFF_BITS) | backoff })
+
+// We only use values x and backoffs b such that
+// x + 1 is prime and is near to 2**(2*b+1).
+static const _Py_BackoffCounter backoff_counter_table[] = {
+    MAKE_BACKOFF_COUNTER(1, 0),
+    MAKE_BACKOFF_COUNTER(6, 1),
+    MAKE_BACKOFF_COUNTER(30, 2),
+    MAKE_BACKOFF_COUNTER(126, 3),
+    MAKE_BACKOFF_COUNTER(508, 4),
+    MAKE_BACKOFF_COUNTER(2052, 5),
+    MAKE_BACKOFF_COUNTER(8190, 6),
+};
 
 static inline _Py_BackoffCounter
 forge_backoff_counter(uint16_t counter)
@@ -63,8 +64,8 @@ restart_backoff_counter(_Py_BackoffCounter counter)
 {
     uint16_t backoff = counter.value_and_backoff & BACKOFF_MASK;
     assert(backoff <= MAX_BACKOFF);
-    backoff = (backoff == MAX_BACKOFF) ? backoff : backoff + 1;
-    return make_backoff_counter(lookup_table[backoff], backoff);
+    backoff = (backoff >= MAX_BACKOFF) ? MAX_BACKOFF : backoff + 1;
+    return backoff_counter_table[backoff];
 }
 
 static inline _Py_BackoffCounter
@@ -112,7 +113,7 @@ trigger_backoff_counter(void)
 static inline _Py_BackoffCounter
 initial_jump_backoff_counter(void)
 {
-    return make_backoff_counter(JUMP_BACKWARD_INITIAL_VALUE,
+    return MAKE_BACKOFF_COUNTER(JUMP_BACKWARD_INITIAL_VALUE,
                                 JUMP_BACKWARD_INITIAL_BACKOFF);
 }
 
@@ -126,7 +127,7 @@ initial_jump_backoff_counter(void)
 static inline _Py_BackoffCounter
 initial_temperature_backoff_counter(void)
 {
-    return make_backoff_counter(SIDE_EXIT_INITIAL_VALUE,
+    return MAKE_BACKOFF_COUNTER(SIDE_EXIT_INITIAL_VALUE,
                                 SIDE_EXIT_INITIAL_BACKOFF);
 }
 
@@ -134,7 +135,7 @@ initial_temperature_backoff_counter(void)
 static inline _Py_BackoffCounter
 initial_unreachable_backoff_counter(void)
 {
-    return make_backoff_counter(0, UNREACHABLE_BACKOFF);
+    return MAKE_BACKOFF_COUNTER(0, UNREACHABLE_BACKOFF);
 }
 
 #ifdef __cplusplus
diff --git a/Include/internal/pycore_code.h b/Include/internal/pycore_code.h
index cb9c0aa27a1785..b5dfd471b5d8ce 100644
--- a/Include/internal/pycore_code.h
+++ b/Include/internal/pycore_code.h
@@ -466,21 +466,16 @@ write_location_entry_start(uint8_t *ptr, int code, int length)
 #  error  "Cold exit value should be larger than adaptive cooldown value"
 #endif
 
-static inline _Py_BackoffCounter
-adaptive_counter_bits(uint16_t value, uint16_t backoff) {
-    return make_backoff_counter(value, backoff);
-}
-
 static inline _Py_BackoffCounter
 adaptive_counter_warmup(void) {
-    return adaptive_counter_bits(ADAPTIVE_WARMUP_VALUE,
-                                 ADAPTIVE_WARMUP_BACKOFF);
+    return MAKE_BACKOFF_COUNTER(ADAPTIVE_WARMUP_VALUE,
+                                ADAPTIVE_WARMUP_BACKOFF);
 }
 
 static inline _Py_BackoffCounter
 adaptive_counter_cooldown(void) {
-    return adaptive_counter_bits(ADAPTIVE_COOLDOWN_VALUE,
-                                 ADAPTIVE_COOLDOWN_BACKOFF);
+    return MAKE_BACKOFF_COUNTER(ADAPTIVE_COOLDOWN_VALUE,
+                                ADAPTIVE_COOLDOWN_BACKOFF);
 }
 
 static inline _Py_BackoffCounter

From f3c92874741e6c04d001cc673718941ddd3577a2 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 17:28:42 +0300
Subject: [PATCH 10/21] Comment change

---
 Include/internal/pycore_backoff.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index cfa46bfcb4b0b4..3f43b398260f7a 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -40,7 +40,7 @@ extern "C" {
     ((_Py_BackoffCounter){ .value_and_backoff = (value << BACKOFF_BITS) | backoff })
 
 // We only use values x and backoffs b such that
-// x + 1 is prime and is near to 2**(2*b+1).
+// x + 1 is near to 2**(2*b+1) and x + 1 is prime.
 static const _Py_BackoffCounter backoff_counter_table[] = {
     MAKE_BACKOFF_COUNTER(1, 0),
     MAKE_BACKOFF_COUNTER(6, 1),

From e16b368f12b028462aba73b915a4324c599656cc Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 17:37:40 +0300
Subject: [PATCH 11/21] Fix Windows build: remove const keyword

---
 Include/internal/pycore_backoff.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index 3f43b398260f7a..ee2f1eb7ac1d38 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -41,7 +41,7 @@ extern "C" {
 
 // We only use values x and backoffs b such that
 // x + 1 is near to 2**(2*b+1) and x + 1 is prime.
-static const _Py_BackoffCounter backoff_counter_table[] = {
+static _Py_BackoffCounter backoff_counter_table[] = {
     MAKE_BACKOFF_COUNTER(1, 0),
     MAKE_BACKOFF_COUNTER(6, 1),
     MAKE_BACKOFF_COUNTER(30, 2),

From 6b1fe6674f01585faec273e8b2ab84ebf6ddfcd0 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 17:46:38 +0300
Subject: [PATCH 12/21] Simplify obtaining next backoff

---
 Include/internal/pycore_backoff.h | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index ee2f1eb7ac1d38..f155236980843f 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -41,14 +41,16 @@ extern "C" {
 
 // We only use values x and backoffs b such that
 // x + 1 is near to 2**(2*b+1) and x + 1 is prime.
-static _Py_BackoffCounter backoff_counter_table[] = {
-    MAKE_BACKOFF_COUNTER(1, 0),
+static _Py_BackoffCounter backoff_counter_next_table[] = {
     MAKE_BACKOFF_COUNTER(6, 1),
     MAKE_BACKOFF_COUNTER(30, 2),
     MAKE_BACKOFF_COUNTER(126, 3),
     MAKE_BACKOFF_COUNTER(508, 4),
     MAKE_BACKOFF_COUNTER(2052, 5),
     MAKE_BACKOFF_COUNTER(8190, 6),
+    // We use the same backoff counter for all backoffs >= MAX_BACKOFF.
+    MAKE_BACKOFF_COUNTER(8190, 6),
+    MAKE_BACKOFF_COUNTER(8190, 6),
 };
 
 static inline _Py_BackoffCounter
@@ -64,8 +66,7 @@ restart_backoff_counter(_Py_BackoffCounter counter)
 {
     uint16_t backoff = counter.value_and_backoff & BACKOFF_MASK;
     assert(backoff <= MAX_BACKOFF);
-    backoff = (backoff >= MAX_BACKOFF) ? MAX_BACKOFF : backoff + 1;
-    return backoff_counter_table[backoff];
+    return backoff_counter_next_table[backoff];
 }
 
 static inline _Py_BackoffCounter

From 2600236851d82903b0b8a83f9fa7d9dae2ffa83e Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 17:48:01 +0300
Subject: [PATCH 13/21] Remove forge_backoff_counter

---
 Include/internal/pycore_backoff.h | 8 --------
 Python/ceval_macros.h             | 2 +-
 2 files changed, 1 insertion(+), 9 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index f155236980843f..9bf779a7f87ef0 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -53,14 +53,6 @@ static _Py_BackoffCounter backoff_counter_next_table[] = {
     MAKE_BACKOFF_COUNTER(8190, 6),
 };
 
-static inline _Py_BackoffCounter
-forge_backoff_counter(uint16_t counter)
-{
-    _Py_BackoffCounter result;
-    result.value_and_backoff = counter;
-    return result;
-}
-
 static inline _Py_BackoffCounter
 restart_backoff_counter(_Py_BackoffCounter counter)
 {
diff --git a/Python/ceval_macros.h b/Python/ceval_macros.h
index 05a2760671e847..fce05c237a858a 100644
--- a/Python/ceval_macros.h
+++ b/Python/ceval_macros.h
@@ -315,7 +315,7 @@ GETITEM(PyObject *v, Py_ssize_t i) {
  * which is always an integral type. */
 // Force re-specialization when tracing a side exit to get good side exits.
 #define ADAPTIVE_COUNTER_TRIGGERS(COUNTER) \
-    backoff_counter_triggers(forge_backoff_counter((COUNTER)))
+    backoff_counter_triggers(MAKE_BACKOFF_COUNTER(0, (COUNTER)))
 
 #define ADVANCE_ADAPTIVE_COUNTER(COUNTER) \
     do { \

From ec27072724e7e6abeb5ca8d528b7204d59840986 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 18:19:33 +0300
Subject: [PATCH 14/21] Another try to fix Windows build

---
 Include/internal/pycore_backoff.h | 31 +++++++++++++++++++------------
 1 file changed, 19 insertions(+), 12 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index 9bf779a7f87ef0..0c3c36c0feed20 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -36,21 +36,26 @@ extern "C" {
 #define MAX_BACKOFF 6
 #define UNREACHABLE_BACKOFF 7
 
-#define MAKE_BACKOFF_COUNTER(value, backoff) \
-    ((_Py_BackoffCounter){ .value_and_backoff = (value << BACKOFF_BITS) | backoff })
+#define MAKE_VALUE_AND_BACKOFF(value, backoff) \
+    ((value << BACKOFF_BITS) | backoff)
+
+#define MAKE_BACKOFF_COUNTER(value, backoff)                        \
+    ((_Py_BackoffCounter){                                          \
+        .value_and_backoff = MAKE_VALUE_AND_BACKOFF(value, backoff) \
+    })
 
 // We only use values x and backoffs b such that
 // x + 1 is near to 2**(2*b+1) and x + 1 is prime.
-static _Py_BackoffCounter backoff_counter_next_table[] = {
-    MAKE_BACKOFF_COUNTER(6, 1),
-    MAKE_BACKOFF_COUNTER(30, 2),
-    MAKE_BACKOFF_COUNTER(126, 3),
-    MAKE_BACKOFF_COUNTER(508, 4),
-    MAKE_BACKOFF_COUNTER(2052, 5),
-    MAKE_BACKOFF_COUNTER(8190, 6),
+static uint16_t value_and_backoff_next[] = {
+    MAKE_VALUE_AND_BACKOFF(6, 1),
+    MAKE_VALUE_AND_BACKOFF(30, 2),
+    MAKE_VALUE_AND_BACKOFF(126, 3),
+    MAKE_VALUE_AND_BACKOFF(508, 4),
+    MAKE_VALUE_AND_BACKOFF(2052, 5),
+    MAKE_VALUE_AND_BACKOFF(8190, 6),
     // We use the same backoff counter for all backoffs >= MAX_BACKOFF.
-    MAKE_BACKOFF_COUNTER(8190, 6),
-    MAKE_BACKOFF_COUNTER(8190, 6),
+    MAKE_VALUE_AND_BACKOFF(8190, 6),
+    MAKE_VALUE_AND_BACKOFF(8190, 6),
 };
 
 static inline _Py_BackoffCounter
@@ -58,7 +63,9 @@ restart_backoff_counter(_Py_BackoffCounter counter)
 {
     uint16_t backoff = counter.value_and_backoff & BACKOFF_MASK;
     assert(backoff <= MAX_BACKOFF);
-    return backoff_counter_next_table[backoff];
+    return ((_Py_BackoffCounter){
+        .value_and_backoff = value_and_backoff_next[backoff]
+    });
 }
 
 static inline _Py_BackoffCounter

From 401b6da609c8ddd74fd0321dfee3a81e994cc78a Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 18:24:32 +0300
Subject: [PATCH 15/21] Revert make_backoff_counter

---
 Include/internal/pycore_backoff.h | 22 ++++++++++++++--------
 Include/internal/pycore_code.h    |  4 ++--
 Python/ceval_macros.h             |  2 +-
 3 files changed, 17 insertions(+), 11 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index 0c3c36c0feed20..b311cc3ba3e5d3 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -35,15 +35,11 @@ extern "C" {
 #define BACKOFF_MASK 7
 #define MAX_BACKOFF 6
 #define UNREACHABLE_BACKOFF 7
+#define MAX_VALUE 0x1FFF
 
 #define MAKE_VALUE_AND_BACKOFF(value, backoff) \
     ((value << BACKOFF_BITS) | backoff)
 
-#define MAKE_BACKOFF_COUNTER(value, backoff)                        \
-    ((_Py_BackoffCounter){                                          \
-        .value_and_backoff = MAKE_VALUE_AND_BACKOFF(value, backoff) \
-    })
-
 // We only use values x and backoffs b such that
 // x + 1 is near to 2**(2*b+1) and x + 1 is prime.
 static uint16_t value_and_backoff_next[] = {
@@ -58,6 +54,16 @@ static uint16_t value_and_backoff_next[] = {
     MAKE_VALUE_AND_BACKOFF(8190, 6),
 };
 
+static inline _Py_BackoffCounter
+make_backoff_counter(uint16_t value, uint16_t backoff)
+{
+    assert(backoff <= UNREACHABLE_BACKOFF);
+    assert(value <= MAX_VALUE);
+    return ((_Py_BackoffCounter){
+        .value_and_backoff = MAKE_VALUE_AND_BACKOFF(value, backoff)
+    });
+}
+
 static inline _Py_BackoffCounter
 restart_backoff_counter(_Py_BackoffCounter counter)
 {
@@ -113,7 +119,7 @@ trigger_backoff_counter(void)
 static inline _Py_BackoffCounter
 initial_jump_backoff_counter(void)
 {
-    return MAKE_BACKOFF_COUNTER(JUMP_BACKWARD_INITIAL_VALUE,
+    return make_backoff_counter(JUMP_BACKWARD_INITIAL_VALUE,
                                 JUMP_BACKWARD_INITIAL_BACKOFF);
 }
 
@@ -127,7 +133,7 @@ initial_jump_backoff_counter(void)
 static inline _Py_BackoffCounter
 initial_temperature_backoff_counter(void)
 {
-    return MAKE_BACKOFF_COUNTER(SIDE_EXIT_INITIAL_VALUE,
+    return make_backoff_counter(SIDE_EXIT_INITIAL_VALUE,
                                 SIDE_EXIT_INITIAL_BACKOFF);
 }
 
@@ -135,7 +141,7 @@ initial_temperature_backoff_counter(void)
 static inline _Py_BackoffCounter
 initial_unreachable_backoff_counter(void)
 {
-    return MAKE_BACKOFF_COUNTER(0, UNREACHABLE_BACKOFF);
+    return make_backoff_counter(0, UNREACHABLE_BACKOFF);
 }
 
 #ifdef __cplusplus
diff --git a/Include/internal/pycore_code.h b/Include/internal/pycore_code.h
index b5dfd471b5d8ce..b89de83fe4391e 100644
--- a/Include/internal/pycore_code.h
+++ b/Include/internal/pycore_code.h
@@ -468,13 +468,13 @@ write_location_entry_start(uint8_t *ptr, int code, int length)
 
 static inline _Py_BackoffCounter
 adaptive_counter_warmup(void) {
-    return MAKE_BACKOFF_COUNTER(ADAPTIVE_WARMUP_VALUE,
+    return make_backoff_counter(ADAPTIVE_WARMUP_VALUE,
                                 ADAPTIVE_WARMUP_BACKOFF);
 }
 
 static inline _Py_BackoffCounter
 adaptive_counter_cooldown(void) {
-    return MAKE_BACKOFF_COUNTER(ADAPTIVE_COOLDOWN_VALUE,
+    return make_backoff_counter(ADAPTIVE_COOLDOWN_VALUE,
                                 ADAPTIVE_COOLDOWN_BACKOFF);
 }
 
diff --git a/Python/ceval_macros.h b/Python/ceval_macros.h
index fce05c237a858a..14550d2307e2f5 100644
--- a/Python/ceval_macros.h
+++ b/Python/ceval_macros.h
@@ -315,7 +315,7 @@ GETITEM(PyObject *v, Py_ssize_t i) {
  * which is always an integral type. */
 // Force re-specialization when tracing a side exit to get good side exits.
 #define ADAPTIVE_COUNTER_TRIGGERS(COUNTER) \
-    backoff_counter_triggers(MAKE_BACKOFF_COUNTER(0, (COUNTER)))
+    backoff_counter_triggers(make_backoff_counter(0, (COUNTER)))
 
 #define ADVANCE_ADAPTIVE_COUNTER(COUNTER) \
     do { \

From 3418be123fa1bb836bed00c2324845d02de254c7 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 18:28:42 +0300
Subject: [PATCH 16/21] Revert changes to pycore_code.h

---
 Include/internal/pycore_code.h | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/Include/internal/pycore_code.h b/Include/internal/pycore_code.h
index b89de83fe4391e..cb9c0aa27a1785 100644
--- a/Include/internal/pycore_code.h
+++ b/Include/internal/pycore_code.h
@@ -466,16 +466,21 @@ write_location_entry_start(uint8_t *ptr, int code, int length)
 #  error  "Cold exit value should be larger than adaptive cooldown value"
 #endif
 
+static inline _Py_BackoffCounter
+adaptive_counter_bits(uint16_t value, uint16_t backoff) {
+    return make_backoff_counter(value, backoff);
+}
+
 static inline _Py_BackoffCounter
 adaptive_counter_warmup(void) {
-    return make_backoff_counter(ADAPTIVE_WARMUP_VALUE,
-                                ADAPTIVE_WARMUP_BACKOFF);
+    return adaptive_counter_bits(ADAPTIVE_WARMUP_VALUE,
+                                 ADAPTIVE_WARMUP_BACKOFF);
 }
 
 static inline _Py_BackoffCounter
 adaptive_counter_cooldown(void) {
-    return make_backoff_counter(ADAPTIVE_COOLDOWN_VALUE,
-                                ADAPTIVE_COOLDOWN_BACKOFF);
+    return adaptive_counter_bits(ADAPTIVE_COOLDOWN_VALUE,
+                                 ADAPTIVE_COOLDOWN_BACKOFF);
 }
 
 static inline _Py_BackoffCounter

From ceddb6a96714a02d3ae63b3ddd7ddffe56a08f21 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 18:30:39 +0300
Subject: [PATCH 17/21] Comment fix

---
 Include/internal/pycore_backoff.h | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index b311cc3ba3e5d3..873447bced6a25 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -25,7 +25,8 @@ extern "C" {
    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**(2*backoff+1) - 1.
+   value is set to a bit mask representing some prime value near
+   to 2**(2*backoff+1) - 1, see value_and_backoff_next.
    The maximum backoff is 6, since 7 is an UNREACHABLE_BACKOFF.
 
    There is an exceptional value which must not be updated, 0xFFFF.

From a89d6decfbbe4aeed4a49e14b930acf48b0cbc44 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 18:47:54 +0300
Subject: [PATCH 18/21] Temporarily disable assert

---
 Include/internal/pycore_backoff.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index 873447bced6a25..d4cfc70cacf107 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -58,7 +58,7 @@ static uint16_t value_and_backoff_next[] = {
 static inline _Py_BackoffCounter
 make_backoff_counter(uint16_t value, uint16_t backoff)
 {
-    assert(backoff <= UNREACHABLE_BACKOFF);
+    //assert(backoff <= UNREACHABLE_BACKOFF);
     assert(value <= MAX_VALUE);
     return ((_Py_BackoffCounter){
         .value_and_backoff = MAKE_VALUE_AND_BACKOFF(value, backoff)

From c7873c276668e56f4d8d94474e4eb767bff37e35 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 18:58:18 +0300
Subject: [PATCH 19/21] Revert forge_backoff_counter

---
 Include/internal/pycore_backoff.h | 10 +++++++++-
 Python/ceval_macros.h             |  2 +-
 2 files changed, 10 insertions(+), 2 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index d4cfc70cacf107..2391ecd760903a 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -58,13 +58,21 @@ static uint16_t value_and_backoff_next[] = {
 static inline _Py_BackoffCounter
 make_backoff_counter(uint16_t value, uint16_t backoff)
 {
-    //assert(backoff <= UNREACHABLE_BACKOFF);
+    assert(backoff <= UNREACHABLE_BACKOFF);
     assert(value <= MAX_VALUE);
     return ((_Py_BackoffCounter){
         .value_and_backoff = MAKE_VALUE_AND_BACKOFF(value, backoff)
     });
 }
 
+static inline _Py_BackoffCounter
+forge_backoff_counter(uint16_t counter)
+{
+    _Py_BackoffCounter result;
+    result.value_and_backoff = counter;
+    return result;
+}
+
 static inline _Py_BackoffCounter
 restart_backoff_counter(_Py_BackoffCounter counter)
 {
diff --git a/Python/ceval_macros.h b/Python/ceval_macros.h
index 14550d2307e2f5..05a2760671e847 100644
--- a/Python/ceval_macros.h
+++ b/Python/ceval_macros.h
@@ -315,7 +315,7 @@ GETITEM(PyObject *v, Py_ssize_t i) {
  * which is always an integral type. */
 // Force re-specialization when tracing a side exit to get good side exits.
 #define ADAPTIVE_COUNTER_TRIGGERS(COUNTER) \
-    backoff_counter_triggers(make_backoff_counter(0, (COUNTER)))
+    backoff_counter_triggers(forge_backoff_counter((COUNTER)))
 
 #define ADVANCE_ADAPTIVE_COUNTER(COUNTER) \
     do { \

From 5b7bfd9db3054669155efbeb0cade572b62982cf Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Wed, 19 Nov 2025 20:09:09 +0300
Subject: [PATCH 20/21] Fix CI, NEWS updated

---
 Include/internal/pycore_backoff.h                              | 2 +-
 .../2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst             | 3 ++-
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index 2391ecd760903a..c9b016cad18b39 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -43,7 +43,7 @@ extern "C" {
 
 // We only use values x and backoffs b such that
 // x + 1 is near to 2**(2*b+1) and x + 1 is prime.
-static uint16_t value_and_backoff_next[] = {
+static const uint16_t value_and_backoff_next[] = {
     MAKE_VALUE_AND_BACKOFF(6, 1),
     MAKE_VALUE_AND_BACKOFF(30, 2),
     MAKE_VALUE_AND_BACKOFF(126, 3),
diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst b/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst
index 10c8d268e42994..5eb0e0c8b89f7a 100644
--- a/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst
+++ b/Misc/NEWS.d/next/Core_and_Builtins/2025-11-15-14-04-35.gh-issue-141589.VfdMDD.rst
@@ -1,2 +1,3 @@
-Change ``backoff counter`` to use powers of 4 instead of powers of 2.
+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.

From dda4cdb215e7e0ec7eb340d72cf3b4445db8f900 Mon Sep 17 00:00:00 2001
From: Mikhail Efimov <efimov.mikhail@gmail.com>
Date: Thu, 20 Nov 2025 18:41:42 +0300
Subject: [PATCH 21/21] Review addressed: change values and comment

---
 Include/internal/pycore_backoff.h | 19 ++++++++++---------
 1 file changed, 10 insertions(+), 9 deletions(-)

diff --git a/Include/internal/pycore_backoff.h b/Include/internal/pycore_backoff.h
index c9b016cad18b39..7f60eb495080ae 100644
--- a/Include/internal/pycore_backoff.h
+++ b/Include/internal/pycore_backoff.h
@@ -25,8 +25,9 @@ extern "C" {
    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 some prime value near
-   to 2**(2*backoff+1) - 1, see value_and_backoff_next.
+   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.
@@ -41,15 +42,15 @@ extern "C" {
 #define MAKE_VALUE_AND_BACKOFF(value, backoff) \
     ((value << BACKOFF_BITS) | backoff)
 
-// We only use values x and backoffs b such that
+// 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(6, 1),
-    MAKE_VALUE_AND_BACKOFF(30, 2),
-    MAKE_VALUE_AND_BACKOFF(126, 3),
-    MAKE_VALUE_AND_BACKOFF(508, 4),
-    MAKE_VALUE_AND_BACKOFF(2052, 5),
-    MAKE_VALUE_AND_BACKOFF(8190, 6),
+    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),