From 39292ed736663d9e516b4420d7037dd696c73fd5 Mon Sep 17 00:00:00 2001
From: Mike Jarvis <michael@jarvis.net>
Date: Fri, 11 Jul 2025 21:55:46 -0400
Subject: [PATCH 1/3] Implement binary version of make_index_sequence

---
 include/pybind11/detail/common.h | 38 +++++++++++++++++++++++++++-----
 1 file changed, 33 insertions(+), 5 deletions(-)

diff --git a/include/pybind11/detail/common.h b/include/pybind11/detail/common.h
index 6f3de41458..b087092e64 100644
--- a/include/pybind11/detail/common.h
+++ b/include/pybind11/detail/common.h
@@ -720,14 +720,42 @@ using std::make_index_sequence;
 #else
 template <size_t...>
 struct index_sequence {};
-template <size_t N, size_t... S>
-struct make_index_sequence_impl : make_index_sequence_impl<N - 1, N - 1, S...> {};
-template <size_t... S>
-struct make_index_sequence_impl<0, S...> {
+// Comments about the algorithm below.
+//
+// Credit: This is based on an algorithm by taocpp here:
+//    https://github.com/taocpp/sequences/blob/main/include/tao/seq/make_integer_sequence.hpp
+// but significantly simplified.
+//
+// We build up a sequence S by repeatedly doubling its length and sometimes adding 1 to the end.
+// E.g. if the current S is 0...3, then we either go to 0...7 or 0...8 on the next pass.
+// The goal is to end with S = 0...N-1.
+// The key insight is that the times we need to add an additional digit to S correspond
+// exactly to the 1's in the binary representation of the number N.
+//
+// Invariants:
+// - digit is a power of 2
+// - N_digit_is_1 is whether N's binary representation has a 1 in that digit's position.
+// - end <= N
+// - S is 0...end-1.
+// - if digit > 0, end * digit * 2 <= N < (end+1) * digit * 2
+//
+// The process starts with digit > N, end = 0, and S is empty.
+// Ths process concludes with digit=0, in which case, end == N and S is 0...N-1.
+
+template <size_t digit, bool N_digit_is_1, size_t N, size_t end, size_t... S> // N_digit_is_1=false
+struct make_index_sequence_impl :
+    make_index_sequence_impl<digit/2, (N&(digit/2))!=0, N, 2*end, S..., (S+end)...> {};
+template <size_t digit, size_t N, size_t end, size_t... S>
+struct make_index_sequence_impl<digit, true, N, end, S...> :
+    make_index_sequence_impl<digit/2, (N&(digit/2))!=0, N, 2*end+1, S..., (S+end)..., 2*end> {};
+template <size_t N, size_t end, size_t... S>
+struct make_index_sequence_impl<0, false, N, end, S...> {
     using type = index_sequence<S...>;
 };
+constexpr size_t next_power_of_2(size_t N)
+{ return N == 0 ? 1 : next_power_of_2(N>>1)<<1; }
 template <size_t N>
-using make_index_sequence = typename make_index_sequence_impl<N>::type;
+using make_index_sequence = typename make_index_sequence_impl<next_power_of_2(N), false, N, 0>::type;
 #endif
 
 /// Make an index sequence of the indices of true arguments

From 7eef026d7ef16c608194af0631abd449c2571a6c Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sat, 12 Jul 2025 02:40:16 +0000
Subject: [PATCH 2/3] style: pre-commit fixes

---
 include/pybind11/detail/common.h | 21 ++++++++++++++-------
 1 file changed, 14 insertions(+), 7 deletions(-)

diff --git a/include/pybind11/detail/common.h b/include/pybind11/detail/common.h
index b087092e64..3cfd80ec93 100644
--- a/include/pybind11/detail/common.h
+++ b/include/pybind11/detail/common.h
@@ -743,19 +743,26 @@ struct index_sequence {};
 // Ths process concludes with digit=0, in which case, end == N and S is 0...N-1.
 
 template <size_t digit, bool N_digit_is_1, size_t N, size_t end, size_t... S> // N_digit_is_1=false
-struct make_index_sequence_impl :
-    make_index_sequence_impl<digit/2, (N&(digit/2))!=0, N, 2*end, S..., (S+end)...> {};
+struct make_index_sequence_impl
+    : make_index_sequence_impl<digit / 2, (N & (digit / 2)) != 0, N, 2 * end, S..., (S + end)...> {
+};
 template <size_t digit, size_t N, size_t end, size_t... S>
-struct make_index_sequence_impl<digit, true, N, end, S...> :
-    make_index_sequence_impl<digit/2, (N&(digit/2))!=0, N, 2*end+1, S..., (S+end)..., 2*end> {};
+struct make_index_sequence_impl<digit, true, N, end, S...>
+    : make_index_sequence_impl<digit / 2,
+                               (N & (digit / 2)) != 0,
+                               N,
+                               2 * end + 1,
+                               S...,
+                               (S + end)...,
+                               2 * end> {};
 template <size_t N, size_t end, size_t... S>
 struct make_index_sequence_impl<0, false, N, end, S...> {
     using type = index_sequence<S...>;
 };
-constexpr size_t next_power_of_2(size_t N)
-{ return N == 0 ? 1 : next_power_of_2(N>>1)<<1; }
+constexpr size_t next_power_of_2(size_t N) { return N == 0 ? 1 : next_power_of_2(N >> 1) << 1; }
 template <size_t N>
-using make_index_sequence = typename make_index_sequence_impl<next_power_of_2(N), false, N, 0>::type;
+using make_index_sequence =
+    typename make_index_sequence_impl<next_power_of_2(N), false, N, 0>::type;
 #endif
 
 /// Make an index sequence of the indices of true arguments

From df0e730bbea6b4e6a0ab898c96a9f9ca1add22e1 Mon Sep 17 00:00:00 2001
From: Mike Jarvis <michael@jarvis.net>
Date: Fri, 11 Jul 2025 22:43:52 -0400
Subject: [PATCH 3/3] typo

---
 include/pybind11/detail/common.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/include/pybind11/detail/common.h b/include/pybind11/detail/common.h
index 3cfd80ec93..126e428c30 100644
--- a/include/pybind11/detail/common.h
+++ b/include/pybind11/detail/common.h
@@ -740,7 +740,7 @@ struct index_sequence {};
 // - if digit > 0, end * digit * 2 <= N < (end+1) * digit * 2
 //
 // The process starts with digit > N, end = 0, and S is empty.
-// Ths process concludes with digit=0, in which case, end == N and S is 0...N-1.
+// The process concludes with digit=0, in which case, end == N and S is 0...N-1.
 
 template <size_t digit, bool N_digit_is_1, size_t N, size_t end, size_t... S> // N_digit_is_1=false
 struct make_index_sequence_impl