From 281009cad94119a78b73302f2b0c3be216f6b26c Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 19:03:39 +0200
Subject: [PATCH 01/21] bpo-29782: Consolidate _Py_Bit_Length()

In GH-2866, _Py_Bit_Length() was added to pymath.h for lack of a better
location. GH-20518 added a more appropriate header file for bit utilities. It
also shows how to properly use intrinsics. This allows reconsidering bpo-29782.

* Move the function to the new header.
* Changed return type to match __builtin_clzl and reviewed usage.
* Use intrinsics where available.
* Pick a (mostly theoretical) fallback implementation suitable for
  inlining.
---
 Include/internal/pycore_bitutils.h | 32 ++++++++++++++++++++++++++----
 Include/pymath.h                   |  8 --------
 Modules/mathmodule.c               |  1 +
 Python/pymath.c                    | 15 --------------
 4 files changed, 29 insertions(+), 27 deletions(-)

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 36ffe23b9ff264..814876747b9b97 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -7,8 +7,8 @@
    - _Py_bswap64(uint64_t)
 */
 
-#ifndef Py_INTERNAL_BSWAP_H
-#define Py_INTERNAL_BSWAP_H
+#ifndef Py_INTERNAL_BITUTILS_H
+#define Py_INTERNAL_BITUTILS_H
 #ifdef __cplusplus
 extern "C" {
 #endif
@@ -131,8 +131,32 @@ _Py_popcount32(uint32_t x)
 }
 
 
+// Return the index of the most significant 1 bit in 'x'. This is the smallest
+// integer k such that x < 2**k. Equivalent to floor(log2(x)) + 1 for x != 0.
+static inline int
+_Py_bit_length(unsigned long x) {
+    if (!x) {
+        return 0;
+    }
+#if (defined(__clang__) || defined(__GNUC__))
+    return sizeof(unsigned long) * 8 - __builtin_clzl(x);
+#elif defined(_MSC_VER)
+    Py_BUILD_ASSERT(4 == sizeof(unsigned long));
+    unsigned long msb;
+    _BitScanReverse(&msb, x);
+    return 32 - msb;
+#else
+    int msb = 0;
+    while (x != 0) {
+        msb += 1;
+        x >>= 1;
+    }
+    return msb;
+#endif
+}
+
+
 #ifdef __cplusplus
 }
 #endif
-#endif /* !Py_INTERNAL_BSWAP_H */
-
+#endif /* !Py_INTERNAL_BITUTILS_H */
diff --git a/Include/pymath.h b/Include/pymath.h
index 63ca972784e311..f869724334a4c4 100644
--- a/Include/pymath.h
+++ b/Include/pymath.h
@@ -227,12 +227,4 @@ PyAPI_FUNC(void) _Py_set_387controlword(unsigned short);
  * behavior. */
 #define _Py_InIntegralTypeRange(type, v) (_Py_IntegralTypeMin(type) <= v && v <= _Py_IntegralTypeMax(type))
 
-/* Return the smallest integer k such that n < 2**k, or 0 if n == 0.
- * Equivalent to floor(log2(x))+1.  Also equivalent to: bitwidth_of_type -
- * count_leading_zero_bits(x)
- */
-#ifndef Py_LIMITED_API
-PyAPI_FUNC(unsigned int) _Py_bit_length(unsigned long d);
-#endif
-
 #endif /* Py_PYMATH_H */
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index cb05ce7c509625..89b395a7d38852 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -53,6 +53,7 @@ raised for division by zero and mod by zero.
  */
 
 #include "Python.h"
+#include "pycore_bitutils.h"
 #include "pycore_dtoa.h"
 #include "_math.h"
 
diff --git a/Python/pymath.c b/Python/pymath.c
index a08a0e796156f7..24b804223eef19 100644
--- a/Python/pymath.c
+++ b/Python/pymath.c
@@ -79,18 +79,3 @@ round(double x)
     return copysign(y, x);
 }
 #endif /* HAVE_ROUND */
-
-static const unsigned int BitLengthTable[32] = {
-    0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
-    5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
-};
-
-unsigned int _Py_bit_length(unsigned long d) {
-   unsigned int d_bits = 0;
-   while (d >= 32) {
-       d_bits += 6;
-       d >>= 6;
-   }
-   d_bits += BitLengthTable[d];
-   return d_bits;
-}

From 65abb8304d41c82efee2f64f2a0d126ed7e3013b Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 21:03:05 +0200
Subject: [PATCH 02/21] Specify required gcc version for __builtin_clzl

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

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 814876747b9b97..a7e157eff41c6f 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -138,7 +138,7 @@ _Py_bit_length(unsigned long x) {
     if (!x) {
         return 0;
     }
-#if (defined(__clang__) || defined(__GNUC__))
+#if (defined(__clang__) || (defined(__GNUC__) && (((__GNUC__ == 3) && (__GNUC_MINOR__ >= 4)) || (__GNUC__ >= 4))))
     return sizeof(unsigned long) * 8 - __builtin_clzl(x);
 #elif defined(_MSC_VER)
     Py_BUILD_ASSERT(4 == sizeof(unsigned long));

From ce45ff2a8d0a131839942dd78fa0952ccff42bae Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 21:04:49 +0200
Subject: [PATCH 03/21] Fix _BitScanReverse usage

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

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index a7e157eff41c6f..6d1de7223935e8 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -144,7 +144,7 @@ _Py_bit_length(unsigned long x) {
     Py_BUILD_ASSERT(4 == sizeof(unsigned long));
     unsigned long msb;
     _BitScanReverse(&msb, x);
-    return 32 - msb;
+    return msb + 1;
 #else
     int msb = 0;
     while (x != 0) {

From 6464ca6001409512ea15c7d4ea732b4b84a96dfa Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 21:14:35 +0200
Subject: [PATCH 04/21] Document reason for include

---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 89b395a7d38852..b7dcb66723f10e 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -53,7 +53,7 @@ raised for division by zero and mod by zero.
  */
 
 #include "Python.h"
-#include "pycore_bitutils.h"
+#include "pycore_bitutils.h" // _Py_bit_length()
 #include "pycore_dtoa.h"
 #include "_math.h"
 

From 0bd42652dfed7b06dc0fe9e6732e327b717f1618 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 21:41:03 +0200
Subject: [PATCH 05/21] Ensure future compatibility

---
 Include/internal/pycore_bitutils.h | 18 +++++++++++++-----
 Objects/longobject.c               | 18 +++++++++---------
 2 files changed, 22 insertions(+), 14 deletions(-)

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 6d1de7223935e8..c6d03b96cf83e3 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -135,26 +135,34 @@ _Py_popcount32(uint32_t x)
 // integer k such that x < 2**k. Equivalent to floor(log2(x)) + 1 for x != 0.
 static inline int
 _Py_bit_length(unsigned long x) {
-    if (!x) {
+    if (x == 0) {
         return 0;
     }
 #if (defined(__clang__) || (defined(__GNUC__) && (((__GNUC__ == 3) && (__GNUC_MINOR__ >= 4)) || (__GNUC__ >= 4))))
+    // Undefined behavior for x == 0.
     return sizeof(unsigned long) * 8 - __builtin_clzl(x);
 #elif defined(_MSC_VER)
-    Py_BUILD_ASSERT(4 == sizeof(unsigned long));
+    Py_BUILD_ASSERT(sizeof(unsigned long) <= 4);
+    // Does not write to msb if x == 0.
     unsigned long msb;
     _BitScanReverse(&msb, x);
-    return msb + 1;
+    return (int)msb + 1;
 #else
     int msb = 0;
-    while (x != 0) {
+    do {
         msb += 1;
         x >>= 1;
-    }
+    } while (x != 0);
     return msb;
 #endif
 }
 
+static inline int
+_Py_bit_length_digit(digit x) {
+    Py_BUILD_ASSERT(PyLong_SHIFT <= sizeof(unsigned long) * 8);
+    return _Py_popcount32((unsigned long)x);
+}
+
 
 #ifdef __cplusplus
 }
diff --git a/Objects/longobject.c b/Objects/longobject.c
index ce10c4f66586a1..a55171b543d126 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -712,7 +712,7 @@ _PyLong_NumBits(PyObject *vv)
         if ((size_t)(ndigits - 1) > SIZE_MAX / (size_t)PyLong_SHIFT)
             goto Overflow;
         result = (size_t)(ndigits - 1) * (size_t)PyLong_SHIFT;
-        msd_bits = _Py_bit_length(msd);
+        msd_bits = _Py_bit_length_digit(msd);
         if (SIZE_MAX - msd_bits < result)
             goto Overflow;
         result += msd_bits;
@@ -1822,7 +1822,7 @@ long_format_binary(PyObject *aa, int base, int alternate,
             return -1;
         }
         size_a_in_bits = (size_a - 1) * PyLong_SHIFT +
-                         _Py_bit_length(a->ob_digit[size_a - 1]);
+                         _Py_bit_length_digit(a->ob_digit[size_a - 1]);
         /* Allow 1 character for a '-' sign. */
         sz = negative + (size_a_in_bits + (bits - 1)) / bits;
     }
@@ -2642,7 +2642,7 @@ x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem)
 
     /* normalize: shift w1 left so that its top digit is >= PyLong_BASE/2.
        shift v1 left by the same amount.  Results go into w and v. */
-    d = PyLong_SHIFT - _Py_bit_length(w1->ob_digit[size_w-1]);
+    d = PyLong_SHIFT - _Py_bit_length_digit(w1->ob_digit[size_w-1]);
     carry = v_lshift(w->ob_digit, w1->ob_digit, size_w, d);
     assert(carry == 0);
     carry = v_lshift(v->ob_digit, v1->ob_digit, size_v, d);
@@ -2764,7 +2764,7 @@ _PyLong_Frexp(PyLongObject *a, Py_ssize_t *e)
         *e = 0;
         return 0.0;
     }
-    a_bits = _Py_bit_length(a->ob_digit[a_size-1]);
+    a_bits = _Py_bit_length_digit(a->ob_digit[a_size-1]);
     /* The following is an overflow-free version of the check
        "if ((a_size - 1) * PyLong_SHIFT + a_bits > PY_SSIZE_T_MAX) ..." */
     if (a_size >= (PY_SSIZE_T_MAX - 1) / PyLong_SHIFT + 1 &&
@@ -3857,8 +3857,8 @@ long_true_divide(PyObject *v, PyObject *w)
         /* Extreme underflow */
         goto underflow_or_zero;
     /* Next line is now safe from overflowing a Py_ssize_t */
-    diff = diff * PyLong_SHIFT + _Py_bit_length(a->ob_digit[a_size - 1]) -
-        _Py_bit_length(b->ob_digit[b_size - 1]);
+    diff = diff * PyLong_SHIFT + _Py_bit_length_digit(a->ob_digit[a_size - 1]) -
+        _Py_bit_length_digit(b->ob_digit[b_size - 1]);
     /* Now diff = a_bits - b_bits. */
     if (diff > DBL_MAX_EXP)
         goto overflow;
@@ -3934,7 +3934,7 @@ long_true_divide(PyObject *v, PyObject *w)
     }
     x_size = Py_ABS(Py_SIZE(x));
     assert(x_size > 0); /* result of division is never zero */
-    x_bits = (x_size-1)*PyLong_SHIFT+_Py_bit_length(x->ob_digit[x_size-1]);
+    x_bits = (x_size-1)*PyLong_SHIFT+_Py_bit_length_digit(x->ob_digit[x_size-1]);
 
     /* The number of extra bits that have to be rounded away. */
     extra_bits = Py_MAX(x_bits, DBL_MIN_EXP - shift) - DBL_MANT_DIG;
@@ -4748,7 +4748,7 @@ _PyLong_GCD(PyObject *aarg, PyObject *barg)
     alloc_b = Py_SIZE(b);
     /* reduce until a fits into 2 digits */
     while ((size_a = Py_SIZE(a)) > 2) {
-        nbits = _Py_bit_length(a->ob_digit[size_a-1]);
+        nbits = _Py_bit_length_digit(a->ob_digit[size_a-1]);
         /* extract top 2*PyLong_SHIFT bits of a into x, along with
            corresponding bits of b into y */
         size_b = Py_SIZE(b);
@@ -5269,7 +5269,7 @@ int_bit_length_impl(PyObject *self)
         return PyLong_FromLong(0);
 
     msd = ((PyLongObject *)self)->ob_digit[ndigits-1];
-    msd_bits = _Py_bit_length(msd);
+    msd_bits = _Py_bit_length_digit(msd);
 
     if (ndigits <= PY_SSIZE_T_MAX/PyLong_SHIFT)
         return PyLong_FromSsize_t((ndigits-1)*PyLong_SHIFT + msd_bits);

From fbaca66885fdfb64edcbe5ec45ec590405e98e79 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 22:01:18 +0200
Subject: [PATCH 06/21] Do not try to support GCC < 3.4

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

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index c6d03b96cf83e3..f24bec3b09c9cb 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -138,7 +138,8 @@ _Py_bit_length(unsigned long x) {
     if (x == 0) {
         return 0;
     }
-#if (defined(__clang__) || (defined(__GNUC__) && (((__GNUC__ == 3) && (__GNUC_MINOR__ >= 4)) || (__GNUC__ >= 4))))
+#if (defined(__clang__) || defined(__GNUC__))
+    // __builtin_clzl() is available since GCC 3.4.
     // Undefined behavior for x == 0.
     return sizeof(unsigned long) * 8 - __builtin_clzl(x);
 #elif defined(_MSC_VER)

From 436f68b26f776a5fd80375122c44c00c9710dd70 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 22:03:40 +0200
Subject: [PATCH 07/21] Coding style

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

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index f24bec3b09c9cb..8196c167ce0396 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -134,7 +134,8 @@ _Py_popcount32(uint32_t x)
 // Return the index of the most significant 1 bit in 'x'. This is the smallest
 // integer k such that x < 2**k. Equivalent to floor(log2(x)) + 1 for x != 0.
 static inline int
-_Py_bit_length(unsigned long x) {
+_Py_bit_length(unsigned long x)
+{
     if (x == 0) {
         return 0;
     }
@@ -159,7 +160,8 @@ _Py_bit_length(unsigned long x) {
 }
 
 static inline int
-_Py_bit_length_digit(digit x) {
+_Py_bit_length_digit(digit x)
+{
     Py_BUILD_ASSERT(PyLong_SHIFT <= sizeof(unsigned long) * 8);
     return _Py_popcount32((unsigned long)x);
 }

From ac664bc555efa89e309e1bfcfd51243ccb055205 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 22:04:51 +0200
Subject: [PATCH 08/21] Fix comment indent

Co-authored-by: Victor Stinner <vstinner@python.org>
---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index b7dcb66723f10e..4450ce18941020 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -53,7 +53,7 @@ raised for division by zero and mod by zero.
  */
 
 #include "Python.h"
-#include "pycore_bitutils.h" // _Py_bit_length()
+#include "pycore_bitutils.h"      // _Py_bit_length()
 #include "pycore_dtoa.h"
 #include "_math.h"
 

From 3279d1750e25d7589e6f2d92391578ab41d613cb Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 22:08:28 +0200
Subject: [PATCH 09/21] Do not factor out x != 0

---
 Include/internal/pycore_bitutils.h | 25 +++++++++++++++----------
 1 file changed, 15 insertions(+), 10 deletions(-)

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 8196c167ce0396..0c1b306a7280f0 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -136,25 +136,30 @@ _Py_popcount32(uint32_t x)
 static inline int
 _Py_bit_length(unsigned long x)
 {
-    if (x == 0) {
+#if (defined(__clang__) || defined(__GNUC__))
+    if (x != 0) {
+        // __builtin_clzl() is available since GCC 3.4.
+        // Undefined behavior for x == 0.
+        return sizeof(unsigned long) * 8 - __builtin_clzl(x);
+    }
+    else {
         return 0;
     }
-#if (defined(__clang__) || defined(__GNUC__))
-    // __builtin_clzl() is available since GCC 3.4.
-    // Undefined behavior for x == 0.
-    return sizeof(unsigned long) * 8 - __builtin_clzl(x);
 #elif defined(_MSC_VER)
     Py_BUILD_ASSERT(sizeof(unsigned long) <= 4);
-    // Does not write to msb if x == 0.
     unsigned long msb;
-    _BitScanReverse(&msb, x);
-    return (int)msb + 1;
+    if (_BitScanReverse(&msb, x)) {
+        return (int)msb + 1;
+    }
+    else {
+        return 0;
+    }
 #else
     int msb = 0;
-    do {
+    while (x != 0) {
         msb += 1;
         x >>= 1;
-    } while (x != 0);
+    }
     return msb;
 #endif
 }

From 525da3d1f77d0b34a81ad18a32cbf65f3b677eb8 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 22:13:30 +0200
Subject: [PATCH 10/21] Fix and move _Py_bit_length_digit()

---
 Include/internal/pycore_bitutils.h | 7 -------
 Objects/longobject.c               | 7 +++++++
 2 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 0c1b306a7280f0..1a17d8aa400840 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -164,13 +164,6 @@ _Py_bit_length(unsigned long x)
 #endif
 }
 
-static inline int
-_Py_bit_length_digit(digit x)
-{
-    Py_BUILD_ASSERT(PyLong_SHIFT <= sizeof(unsigned long) * 8);
-    return _Py_popcount32((unsigned long)x);
-}
-
 
 #ifdef __cplusplus
 }
diff --git a/Objects/longobject.c b/Objects/longobject.c
index a55171b543d126..b5112a62c1a70d 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -695,6 +695,13 @@ _PyLong_Sign(PyObject *vv)
     return Py_SIZE(v) == 0 ? 0 : (Py_SIZE(v) < 0 ? -1 : 1);
 }
 
+static int
+_Py_bit_length_digit(digit x)
+{
+    Py_BUILD_ASSERT(PyLong_SHIFT <= sizeof(unsigned long) * 8);
+    return _Py_bit_length((unsigned long)x);
+}
+
 size_t
 _PyLong_NumBits(PyObject *vv)
 {

From e4876228c203758ee3e512c0dbfe04019901dd9a Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 22:33:22 +0200
Subject: [PATCH 11/21] Add unit test for _Py_bit_length()

---
 Modules/_testinternalcapi.c | 38 +++++++++++++++++++++++++++++++++++++
 1 file changed, 38 insertions(+)

diff --git a/Modules/_testinternalcapi.c b/Modules/_testinternalcapi.c
index 6d5af5917f1f07..65f235f326e40e 100644
--- a/Modules/_testinternalcapi.c
+++ b/Modules/_testinternalcapi.c
@@ -102,6 +102,43 @@ test_popcount(PyObject *self, PyObject *Py_UNUSED(args))
 }
 
 
+static int
+check_bit_length(unsigned long x, int expected)
+{
+    int len = _Py_bit_length(x);
+    if (len != expected) {
+        PyErr_Format(PyExc_AssertionError,
+                     "_Py_bit_length(%lu) returns %i, expected %i",
+                     (unsigned long)x, len, expected);
+        return -1;
+    }
+    return 0;
+}
+
+
+static PyObject*
+test_bit_length(PyObject *self, PyObject *Py_UNUSED(args))
+{
+#define CHECK(X, RESULT) \
+    do { \
+        if (check_bit_length(X, RESULT) < 0) { \
+            return NULL; \
+        } \
+    } while (0)
+
+    CHECK(0, 0);
+    CHECK(1, 1);
+    CHECK(0x08080808, 28);
+    CHECK(0x10101010, 29);
+    CHECK(0x10204080, 29);
+    CHECK(0xDEADCAFE, 32);
+    CHECK(0xFFFFFFFF, 32);
+    Py_RETURN_NONE;
+
+#undef CHECK
+}
+
+
 #define TO_PTR(ch) ((void*)(uintptr_t)ch)
 #define FROM_PTR(ptr) ((uintptr_t)ptr)
 #define VALUE(key) (1 + ((int)(key) - 'a'))
@@ -197,6 +234,7 @@ static PyMethodDef TestMethods[] = {
     {"get_recursion_depth", get_recursion_depth, METH_NOARGS},
     {"test_bswap", test_bswap, METH_NOARGS},
     {"test_popcount", test_popcount, METH_NOARGS},
+    {"test_bit_length", test_bit_length, METH_NOARGS},
     {"test_hashtable", test_hashtable, METH_NOARGS},
     {NULL, NULL} /* sentinel */
 };

From a338761dd9d47dec671b1711c526cca551fb2ad5 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 22:39:49 +0200
Subject: [PATCH 12/21] Remove useless cast in test

---
 Modules/_testinternalcapi.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/_testinternalcapi.c b/Modules/_testinternalcapi.c
index 65f235f326e40e..4f6ff9dd2fcfd5 100644
--- a/Modules/_testinternalcapi.c
+++ b/Modules/_testinternalcapi.c
@@ -109,7 +109,7 @@ check_bit_length(unsigned long x, int expected)
     if (len != expected) {
         PyErr_Format(PyExc_AssertionError,
                      "_Py_bit_length(%lu) returns %i, expected %i",
-                     (unsigned long)x, len, expected);
+                     x, len, expected);
         return -1;
     }
     return 0;

From 5a146f7cc3b4377d188463f4134b77524d7c9d39 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 22:53:46 +0200
Subject: [PATCH 13/21] Use original implementation as fallback

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

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 1a17d8aa400840..fb33b042f688bd 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -136,7 +136,7 @@ _Py_popcount32(uint32_t x)
 static inline int
 _Py_bit_length(unsigned long x)
 {
-#if (defined(__clang__) || defined(__GNUC__))
+#if 0 && (defined(__clang__) || defined(__GNUC__))
     if (x != 0) {
         // __builtin_clzl() is available since GCC 3.4.
         // Undefined behavior for x == 0.
@@ -155,11 +155,16 @@ _Py_bit_length(unsigned long x)
         return 0;
     }
 #else
+    const int BIT_LENGTH_TABLE[32] = {
+        0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
+        5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
+    };
     int msb = 0;
-    while (x != 0) {
-        msb += 1;
-        x >>= 1;
+    while (x >= 32) {
+        msb += 6;
+        x >>= 6;
     }
+    msb += BIT_LENGTH_TABLE[x];
     return msb;
 #endif
 }

From 8e3ce6615c0f053c5e0186423e59ecfc041095e2 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 22:54:53 +0200
Subject: [PATCH 14/21] Re-enable intrinsics

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

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index fb33b042f688bd..55e3dbd6e80e37 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -136,7 +136,7 @@ _Py_popcount32(uint32_t x)
 static inline int
 _Py_bit_length(unsigned long x)
 {
-#if 0 && (defined(__clang__) || defined(__GNUC__))
+#if (defined(__clang__) || defined(__GNUC__))
     if (x != 0) {
         // __builtin_clzl() is available since GCC 3.4.
         // Undefined behavior for x == 0.

From 86241f6ecb36e07ba76fc8c1162d76ab3c0e6ac4 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 23:12:29 +0200
Subject: [PATCH 15/21] Explicitly cast sizeof

Co-authored-by: Victor Stinner <vstinner@python.org>
---
 Include/internal/pycore_bitutils.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 55e3dbd6e80e37..1297f75245e48d 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -140,7 +140,7 @@ _Py_bit_length(unsigned long x)
     if (x != 0) {
         // __builtin_clzl() is available since GCC 3.4.
         // Undefined behavior for x == 0.
-        return sizeof(unsigned long) * 8 - __builtin_clzl(x);
+        return (int)sizeof(unsigned long) * 8 - __builtin_clzl(x);
     }
     else {
         return 0;

From c7ccbe206269a79fc73c7ab1bfe3183e2a21fc62 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 23:16:26 +0200
Subject: [PATCH 16/21] Better tests

Co-authored-by: Victor Stinner <vstinner@python.org>
---
 Modules/_testinternalcapi.c | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/Modules/_testinternalcapi.c b/Modules/_testinternalcapi.c
index 4f6ff9dd2fcfd5..f13c20271c7aa1 100644
--- a/Modules/_testinternalcapi.c
+++ b/Modules/_testinternalcapi.c
@@ -128,10 +128,10 @@ test_bit_length(PyObject *self, PyObject *Py_UNUSED(args))
 
     CHECK(0, 0);
     CHECK(1, 1);
-    CHECK(0x08080808, 28);
-    CHECK(0x10101010, 29);
-    CHECK(0x10204080, 29);
-    CHECK(0xDEADCAFE, 32);
+    CHECK(0x1000, 12);
+    CHECK(0x1234, 12);
+    CHECK(0x54321, 19);    
+    CHECK(0x7FFFFFFF, 31);    
     CHECK(0xFFFFFFFF, 32);
     Py_RETURN_NONE;
 

From dfceaf205ed74b9a229cc92c53d7247ad7c5b9eb Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 23:13:02 +0200
Subject: [PATCH 17/21] Explain Py_BUILD_ASSERT(sizeof(unsigned long) <= 4)

---
 Include/internal/pycore_bitutils.h | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 1297f75245e48d..0bd3270fe82e5c 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -146,6 +146,7 @@ _Py_bit_length(unsigned long x)
         return 0;
     }
 #elif defined(_MSC_VER)
+    // _BitScanReverse() is documented to search 32 bits.
     Py_BUILD_ASSERT(sizeof(unsigned long) <= 4);
     unsigned long msb;
     if (_BitScanReverse(&msb, x)) {

From fbf01ae0c98156b3f9692453af6c739dedaf4f14 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 23:15:19 +0200
Subject: [PATCH 18/21] Use volatile so test actually runs intrinsic

---
 Modules/_testinternalcapi.c | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/Modules/_testinternalcapi.c b/Modules/_testinternalcapi.c
index f13c20271c7aa1..42e0c570073c6e 100644
--- a/Modules/_testinternalcapi.c
+++ b/Modules/_testinternalcapi.c
@@ -105,7 +105,9 @@ test_popcount(PyObject *self, PyObject *Py_UNUSED(args))
 static int
 check_bit_length(unsigned long x, int expected)
 {
-    int len = _Py_bit_length(x);
+    // Use volatile to prevent the compiler to optimize out the whole test
+    volatile unsigned long u = x;
+    int len = _Py_bit_length(u);
     if (len != expected) {
         PyErr_Format(PyExc_AssertionError,
                      "_Py_bit_length(%lu) returns %i, expected %i",

From 991622b6d5542b9d446aee609a4a70504b5c58a8 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 23:17:04 +0200
Subject: [PATCH 19/21] Remove trailing spaces

---
 Modules/_testinternalcapi.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Modules/_testinternalcapi.c b/Modules/_testinternalcapi.c
index 42e0c570073c6e..ff4c5ecdd14e32 100644
--- a/Modules/_testinternalcapi.c
+++ b/Modules/_testinternalcapi.c
@@ -132,8 +132,8 @@ test_bit_length(PyObject *self, PyObject *Py_UNUSED(args))
     CHECK(1, 1);
     CHECK(0x1000, 12);
     CHECK(0x1234, 12);
-    CHECK(0x54321, 19);    
-    CHECK(0x7FFFFFFF, 31);    
+    CHECK(0x54321, 19);
+    CHECK(0x7FFFFFFF, 31);
     CHECK(0xFFFFFFFF, 32);
     Py_RETURN_NONE;
 

From 462d995f073215309cbd9afc1aa93658cf683777 Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 23:18:22 +0200
Subject: [PATCH 20/21] _Py_bit_length_digit -> bit_length_digit

---
 Objects/longobject.c | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/Objects/longobject.c b/Objects/longobject.c
index b5112a62c1a70d..81baada7a0a769 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -696,7 +696,7 @@ _PyLong_Sign(PyObject *vv)
 }
 
 static int
-_Py_bit_length_digit(digit x)
+bit_length_digit(digit x)
 {
     Py_BUILD_ASSERT(PyLong_SHIFT <= sizeof(unsigned long) * 8);
     return _Py_bit_length((unsigned long)x);
@@ -719,7 +719,7 @@ _PyLong_NumBits(PyObject *vv)
         if ((size_t)(ndigits - 1) > SIZE_MAX / (size_t)PyLong_SHIFT)
             goto Overflow;
         result = (size_t)(ndigits - 1) * (size_t)PyLong_SHIFT;
-        msd_bits = _Py_bit_length_digit(msd);
+        msd_bits = bit_length_digit(msd);
         if (SIZE_MAX - msd_bits < result)
             goto Overflow;
         result += msd_bits;
@@ -1829,7 +1829,7 @@ long_format_binary(PyObject *aa, int base, int alternate,
             return -1;
         }
         size_a_in_bits = (size_a - 1) * PyLong_SHIFT +
-                         _Py_bit_length_digit(a->ob_digit[size_a - 1]);
+                         bit_length_digit(a->ob_digit[size_a - 1]);
         /* Allow 1 character for a '-' sign. */
         sz = negative + (size_a_in_bits + (bits - 1)) / bits;
     }
@@ -2649,7 +2649,7 @@ x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem)
 
     /* normalize: shift w1 left so that its top digit is >= PyLong_BASE/2.
        shift v1 left by the same amount.  Results go into w and v. */
-    d = PyLong_SHIFT - _Py_bit_length_digit(w1->ob_digit[size_w-1]);
+    d = PyLong_SHIFT - bit_length_digit(w1->ob_digit[size_w-1]);
     carry = v_lshift(w->ob_digit, w1->ob_digit, size_w, d);
     assert(carry == 0);
     carry = v_lshift(v->ob_digit, v1->ob_digit, size_v, d);
@@ -2771,7 +2771,7 @@ _PyLong_Frexp(PyLongObject *a, Py_ssize_t *e)
         *e = 0;
         return 0.0;
     }
-    a_bits = _Py_bit_length_digit(a->ob_digit[a_size-1]);
+    a_bits = bit_length_digit(a->ob_digit[a_size-1]);
     /* The following is an overflow-free version of the check
        "if ((a_size - 1) * PyLong_SHIFT + a_bits > PY_SSIZE_T_MAX) ..." */
     if (a_size >= (PY_SSIZE_T_MAX - 1) / PyLong_SHIFT + 1 &&
@@ -3864,8 +3864,8 @@ long_true_divide(PyObject *v, PyObject *w)
         /* Extreme underflow */
         goto underflow_or_zero;
     /* Next line is now safe from overflowing a Py_ssize_t */
-    diff = diff * PyLong_SHIFT + _Py_bit_length_digit(a->ob_digit[a_size - 1]) -
-        _Py_bit_length_digit(b->ob_digit[b_size - 1]);
+    diff = diff * PyLong_SHIFT + bit_length_digit(a->ob_digit[a_size - 1]) -
+        bit_length_digit(b->ob_digit[b_size - 1]);
     /* Now diff = a_bits - b_bits. */
     if (diff > DBL_MAX_EXP)
         goto overflow;
@@ -3941,7 +3941,7 @@ long_true_divide(PyObject *v, PyObject *w)
     }
     x_size = Py_ABS(Py_SIZE(x));
     assert(x_size > 0); /* result of division is never zero */
-    x_bits = (x_size-1)*PyLong_SHIFT+_Py_bit_length_digit(x->ob_digit[x_size-1]);
+    x_bits = (x_size-1)*PyLong_SHIFT+bit_length_digit(x->ob_digit[x_size-1]);
 
     /* The number of extra bits that have to be rounded away. */
     extra_bits = Py_MAX(x_bits, DBL_MIN_EXP - shift) - DBL_MANT_DIG;
@@ -4755,7 +4755,7 @@ _PyLong_GCD(PyObject *aarg, PyObject *barg)
     alloc_b = Py_SIZE(b);
     /* reduce until a fits into 2 digits */
     while ((size_a = Py_SIZE(a)) > 2) {
-        nbits = _Py_bit_length_digit(a->ob_digit[size_a-1]);
+        nbits = bit_length_digit(a->ob_digit[size_a-1]);
         /* extract top 2*PyLong_SHIFT bits of a into x, along with
            corresponding bits of b into y */
         size_b = Py_SIZE(b);
@@ -5276,7 +5276,7 @@ int_bit_length_impl(PyObject *self)
         return PyLong_FromLong(0);
 
     msd = ((PyLongObject *)self)->ob_digit[ndigits-1];
-    msd_bits = _Py_bit_length_digit(msd);
+    msd_bits = bit_length_digit(msd);
 
     if (ndigits <= PY_SSIZE_T_MAX/PyLong_SHIFT)
         return PyLong_FromSsize_t((ndigits-1)*PyLong_SHIFT + msd_bits);

From 98fc7a867ede94c2ba2b2077c4deb0227dc8ce7f Mon Sep 17 00:00:00 2001
From: Niklas Fiekas <niklas.fiekas@backscattering.de>
Date: Mon, 8 Jun 2020 23:56:02 +0200
Subject: [PATCH 21/21] Fixup test expectations

---
 Modules/_testinternalcapi.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Modules/_testinternalcapi.c b/Modules/_testinternalcapi.c
index ff4c5ecdd14e32..7970e2f4f443fd 100644
--- a/Modules/_testinternalcapi.c
+++ b/Modules/_testinternalcapi.c
@@ -130,8 +130,8 @@ test_bit_length(PyObject *self, PyObject *Py_UNUSED(args))
 
     CHECK(0, 0);
     CHECK(1, 1);
-    CHECK(0x1000, 12);
-    CHECK(0x1234, 12);
+    CHECK(0x1000, 13);
+    CHECK(0x1234, 13);
     CHECK(0x54321, 19);
     CHECK(0x7FFFFFFF, 31);
     CHECK(0xFFFFFFFF, 32);