refactor: add overflow-safe `CeilDiv` helper

diff --git a/src/arith_uint256.cpp b/src/arith_uint256.cpp
index 392f052c..54513990 100644
--- a/src/arith_uint256.cpp
+++ b/src/arith_uint256.cpp
@@ -5,8 +5,9 @@
 
 #include <arith_uint256.h>
 
-#include <uint256.h>
 #include <crypto/common.h>
+#include <uint256.h>
+#include <util/overflow.h>
 
 #include <cassert>
 
@@ -194,7 +195,7 @@ arith_uint256& arith_uint256::SetCompact(uint32_t nCompact, bool* pfNegative, bo
 
 uint32_t arith_uint256::GetCompact(bool fNegative) const
 {
-    int nSize = (bits() + 7) / 8;
+    int nSize = CeilDiv(bits(), 8u);
     uint32_t nCompact = 0;
     if (nSize <= 3) {
         nCompact = GetLow64() << 8 * (3 - nSize);
diff --git a/src/common/bloom.cpp b/src/common/bloom.cpp
index efb4178c..3ee78994 100644
--- a/src/common/bloom.cpp
+++ b/src/common/bloom.cpp
@@ -12,6 +12,7 @@
 #include <span.h>
 #include <streams.h>
 #include <util/fastrange.h>
+#include <util/overflow.h>
 
 #include <algorithm>
 #include <cmath>
@@ -166,7 +167,7 @@ CRollingBloomFilter::CRollingBloomFilter(const unsigned int nElements, const dou
      * restrict it to the range 1-50. */
     nHashFuncs = std::max(1, std::min((int)round(logFpRate / log(0.5)), 50));
     /* In this rolling bloom filter, we'll store between 2 and 3 generations of nElements / 2 entries. */
-    nEntriesPerGeneration = (nElements + 1) / 2;
+    nEntriesPerGeneration = CeilDiv(nElements, 2u);
     uint32_t nMaxElements = nEntriesPerGeneration * 3;
     /* The maximum fpRate = pow(1.0 - exp(-nHashFuncs * nMaxElements / nFilterBits), nHashFuncs)
      * =>          pow(fpRate, 1.0 / nHashFuncs) = 1.0 - exp(-nHashFuncs * nMaxElements / nFilterBits)
@@ -182,7 +183,7 @@ CRollingBloomFilter::CRollingBloomFilter(const unsigned int nElements, const dou
      * treated as set in generation 1, 2, or 3 respectively.
      * These bits are stored in separate integers: position P corresponds to bit
      * (P & 63) of the integers data[(P >> 6) * 2] and data[(P >> 6) * 2 + 1]. */
-    data.resize(((nFilterBits + 63) / 64) << 1);
+    data.resize(CeilDiv(nFilterBits, 64u) << 1);
     reset();
 }
 
diff --git a/src/cuckoocache.h b/src/cuckoocache.h
index 281efbd0..e25f6913 100644
--- a/src/cuckoocache.h
+++ b/src/cuckoocache.h
@@ -6,6 +6,7 @@
 #define BITCOIN_CUCKOOCACHE_H
 
 #include <util/fastrange.h>
+#include <util/overflow.h>
 
 #include <algorithm>
 #include <array>
@@ -63,7 +64,7 @@ public:
     explicit bit_packed_atomic_flags(uint32_t size)
     {
         // pad out the size if needed
-        size = (size + 7) / 8;
+        size = CeilDiv(size, 8u);
         mem.reset(new std::atomic<uint8_t>[size]);
         for (uint32_t i = 0; i < size; ++i)
             mem[i].store(0xFF);
diff --git a/src/flatfile.cpp b/src/flatfile.cpp
index 056fb9c1..b1b1e045 100644
--- a/src/flatfile.cpp
+++ b/src/flatfile.cpp
@@ -8,6 +8,7 @@
 #include <tinyformat.h>
 #include <util/fs_helpers.h>
 #include <util/log.h>
+#include <util/overflow.h>
 
 #include <stdexcept>
 
@@ -59,8 +60,8 @@ size_t FlatFileSeq::Allocate(const FlatFilePos& pos, size_t add_size, bool& out_
 {
     out_of_space = false;
 
-    unsigned int n_old_chunks = (pos.nPos + m_chunk_size - 1) / m_chunk_size;
-    unsigned int n_new_chunks = (pos.nPos + add_size + m_chunk_size - 1) / m_chunk_size;
+    unsigned int n_old_chunks = CeilDiv(pos.nPos, m_chunk_size);
+    unsigned int n_new_chunks = CeilDiv(pos.nPos + add_size, m_chunk_size);
     if (n_new_chunks > n_old_chunks) {
         size_t old_size = pos.nPos;
         size_t new_size = n_new_chunks * m_chunk_size;
diff --git a/src/key_io.cpp b/src/key_io.cpp
index 3726d222..94964bdd 100644
--- a/src/key_io.cpp
+++ b/src/key_io.cpp
@@ -9,6 +9,7 @@
 #include <script/interpreter.h>
 #include <script/solver.h>
 #include <tinyformat.h>
+#include <util/overflow.h>
 #include <util/strencodings.h>
 
 #include <algorithm>
@@ -72,7 +73,7 @@ public:
             return {};
         }
         std::vector<unsigned char> data = {(unsigned char)id.GetWitnessVersion()};
-        data.reserve(1 + (program.size() * 8 + 4) / 5);
+        data.reserve(1 + CeilDiv(program.size() * 8, 5u));
         ConvertBits<8, 5, true>([&](unsigned char c) { data.push_back(c); }, program.begin(), program.end());
         return bech32::Encode(bech32::Encoding::BECH32M, m_params.Bech32HRP(), data);
     }
diff --git a/src/merkleblock.cpp b/src/merkleblock.cpp
index f6c474e0..6bb05a5e 100644
--- a/src/merkleblock.cpp
+++ b/src/merkleblock.cpp
@@ -5,13 +5,14 @@
 
 #include <merkleblock.h>
 
-#include <hash.h>
 #include <consensus/consensus.h>
+#include <hash.h>
+#include <util/overflow.h>
 
 
 std::vector<unsigned char> BitsToBytes(const std::vector<bool>& bits)
 {
-    std::vector<unsigned char> ret((bits.size() + 7) / 8);
+    std::vector<unsigned char> ret(CeilDiv(bits.size(), 8u));
     for (unsigned int p = 0; p < bits.size(); p++) {
         ret[p / 8] |= bits[p] << (p % 8);
     }
@@ -174,7 +175,7 @@ uint256 CPartialMerkleTree::ExtractMatches(std::vector<Txid> &vMatch, std::vecto
     if (fBad)
         return uint256();
     // verify that all bits were consumed (except for the padding caused by serializing it as a byte sequence)
-    if ((nBitsUsed+7)/8 != (vBits.size()+7)/8)
+    if (CeilDiv(nBitsUsed, 8u) != CeilDiv(vBits.size(), 8u))
         return uint256();
     // verify that all hashes were consumed
     if (nHashUsed != vHash.size())
diff --git a/src/rest.cpp b/src/rest.cpp
index f59dc1cb..899f0875 100644
--- a/src/rest.cpp
+++ b/src/rest.cpp
@@ -28,6 +28,7 @@
 #include <undo.h>
 #include <util/any.h>
 #include <util/check.h>
+#include <util/overflow.h>
 #include <util/strencodings.h>
 #include <validation.h>
 
@@ -993,7 +994,7 @@ static bool rest_getutxos(const std::any& context, HTTPRequest* req, const std::
     std::vector<CCoin> outs;
     std::string bitmapStringRepresentation;
     std::vector<bool> hits;
-    bitmap.resize((vOutPoints.size() + 7) / 8);
+    bitmap.resize(CeilDiv(vOutPoints.size(), 8u));
     ChainstateManager* maybe_chainman = GetChainman(context, req);
     if (!maybe_chainman) return false;
     ChainstateManager& chainman = *maybe_chainman;
diff --git a/src/serialize.h b/src/serialize.h
index 21b3325f..9c18c727 100644
--- a/src/serialize.h
+++ b/src/serialize.h
@@ -11,6 +11,7 @@
 #include <compat/endian.h>
 #include <prevector.h>
 #include <span.h>
+#include <util/overflow.h>
 
 #include <algorithm>
 #include <concepts>
@@ -425,7 +426,7 @@ template<typename Stream, VarIntMode Mode, typename I>
 void WriteVarInt(Stream& os, I n)
 {
     CheckVarIntMode<Mode, I>();
-    unsigned char tmp[(sizeof(n)*8+6)/7];
+    unsigned char tmp[CeilDiv(sizeof(n) * 8, 7u)];
     int len=0;
     while(true) {
         tmp[len] = (n & 0x7F) | (len ? 0x80 : 0x00);
diff --git a/src/support/allocators/pool.h b/src/support/allocators/pool.h
index d4ce68b9..e4b1acc6 100644
--- a/src/support/allocators/pool.h
+++ b/src/support/allocators/pool.h
@@ -15,6 +15,7 @@
 #include <utility>
 
 #include <util/check.h>
+#include <util/overflow.h>
 
 /**
  * A memory resource similar to std::pmr::unsynchronized_pool_resource, but
@@ -127,7 +128,7 @@ class PoolResource final
      */
     [[nodiscard]] static constexpr std::size_t NumElemAlignBytes(std::size_t bytes)
     {
-        return (bytes + ELEM_ALIGN_BYTES - 1) / ELEM_ALIGN_BYTES + (bytes == 0);
+        return CeilDiv(bytes, ELEM_ALIGN_BYTES) + (bytes == 0);
     }
 
     /**
diff --git a/src/test/util_tests.cpp b/src/test/util_tests.cpp
index 2b4e5330..103a55ab 100644
--- a/src/test/util_tests.cpp
+++ b/src/test/util_tests.cpp
@@ -1833,4 +1833,41 @@ BOOST_AUTO_TEST_CASE(mib_string_literal_test)
     BOOST_CHECK_EXCEPTION(operator""_MiB(static_cast<unsigned long long>(max_mib) + 1), std::overflow_error, HasReason("MiB value too large for size_t byte conversion"));
 }
 
+BOOST_AUTO_TEST_CASE(ceil_div_test)
+{
+    // Type combinations used by current CeilDiv callsites.
+    BOOST_CHECK((std::is_same_v<decltype(CeilDiv(uint32_t{0}, 8u)), uint32_t>));
+    BOOST_CHECK((std::is_same_v<decltype(CeilDiv(size_t{0}, 8u)), size_t>));
+    BOOST_CHECK((std::is_same_v<decltype(CeilDiv(unsigned{0}, size_t{1})), size_t>));
+
+    // `common/bloom.cpp` and `cuckoocache.h` patterns.
+    BOOST_CHECK_EQUAL(CeilDiv(uint32_t{3}, 2u), uint32_t{2});
+    BOOST_CHECK_EQUAL(CeilDiv(uint32_t{65}, 64u), uint32_t{2});
+    BOOST_CHECK_EQUAL(CeilDiv(uint32_t{9}, 8u), uint32_t{2});
+
+    // `key_io.cpp`, `rest.cpp`, `merkleblock.cpp`, `strencodings.cpp` patterns.
+    BOOST_CHECK_EQUAL(CeilDiv(size_t{9}, 8u), size_t{2});
+    BOOST_CHECK_EQUAL(CeilDiv(size_t{10}, 3u), size_t{4});
+    BOOST_CHECK_EQUAL(CeilDiv(size_t{11}, 5u), size_t{3});
+    BOOST_CHECK_EQUAL(CeilDiv(size_t{41} * 8, 5u), size_t{66});
+
+    // `flatfile.cpp` mixed unsigned/size_t pattern.
+    BOOST_CHECK_EQUAL(CeilDiv(unsigned{10}, size_t{4}), size_t{3});
+
+    // `util/feefrac.h` fast-path rounding-up pattern.
+    constexpr int64_t fee{12345};
+    constexpr int32_t at_size{67};
+    constexpr int32_t size{10};
+    BOOST_CHECK_EQUAL(CeilDiv(uint64_t(fee) * at_size, uint32_t(size)),
+                      (uint64_t(fee) * at_size + uint32_t(size) - 1) / uint32_t(size));
+
+    // `bitset.h` template parameter pattern.
+    constexpr unsigned bits{129};
+    constexpr size_t digits{std::numeric_limits<size_t>::digits};
+    BOOST_CHECK_EQUAL(CeilDiv(bits, digits), (bits + digits - 1) / digits);
+
+    // `serialize.h` varint scratch-buffer pattern.
+    BOOST_CHECK_EQUAL(CeilDiv(sizeof(uint64_t) * 8, 7u), (sizeof(uint64_t) * 8 + 6) / 7);
+}
+
 BOOST_AUTO_TEST_SUITE_END()
diff --git a/src/util/bitdeque.h b/src/util/bitdeque.h
index 70556a7d..294c42f4 100644
--- a/src/util/bitdeque.h
+++ b/src/util/bitdeque.h
@@ -11,6 +11,7 @@
 #include <limits>
 #include <stdexcept>
 #include <tuple>
+#include <util/overflow.h>
 
 /** Class that mimics std::deque<bool>, but with std::vector<bool>'s bit packing.
  *
@@ -211,7 +212,7 @@ public:
     void assign(size_type count, bool val)
     {
         m_deque.clear();
-        m_deque.resize((count + BITS_PER_WORD - 1) / BITS_PER_WORD);
+        m_deque.resize(CeilDiv(count, size_type{BITS_PER_WORD}));
         m_pad_begin = 0;
         m_pad_end = 0;
         if (val) {
diff --git a/src/util/bitset.h b/src/util/bitset.h
index 17ebc709..1e7ed440 100644
--- a/src/util/bitset.h
+++ b/src/util/bitset.h
@@ -6,6 +6,7 @@
 #define BITCOIN_UTIL_BITSET_H
 
 #include <util/check.h>
+#include <util/overflow.h>
 
 #include <array>
 #include <bit>
@@ -522,6 +523,6 @@ public:
 template<unsigned BITS>
 using BitSet = std::conditional_t<(BITS <= 32), bitset_detail::IntBitSet<uint32_t>,
                std::conditional_t<(BITS <= std::numeric_limits<size_t>::digits), bitset_detail::IntBitSet<size_t>,
-               bitset_detail::MultiIntBitSet<size_t, (BITS + std::numeric_limits<size_t>::digits - 1) / std::numeric_limits<size_t>::digits>>>;
+               bitset_detail::MultiIntBitSet<size_t, CeilDiv(BITS, size_t{std::numeric_limits<size_t>::digits})>>>;
 
 #endif // BITCOIN_UTIL_BITSET_H
diff --git a/src/util/feefrac.h b/src/util/feefrac.h
index 7577107e..25d87d34 100644
--- a/src/util/feefrac.h
+++ b/src/util/feefrac.h
@@ -7,6 +7,7 @@
 
 #include <span.h>
 #include <util/check.h>
+#include <util/overflow.h>
 
 #include <compare>
 #include <cstdint>
@@ -208,7 +209,7 @@ struct FeeFrac
             if constexpr (RoundDown) {
                 return (uint64_t(fee) * at_size) / uint32_t(size);
             } else {
-                return (uint64_t(fee) * at_size + size - 1U) / uint32_t(size);
+                return CeilDiv(uint64_t(fee) * at_size, uint32_t(size));
             }
         } else {
             // Otherwise, use Mul and Div.
diff --git a/src/util/overflow.h b/src/util/overflow.h
index 8b8511f8..76ad0bdc 100644
--- a/src/util/overflow.h
+++ b/src/util/overflow.h
@@ -5,6 +5,7 @@
 #ifndef BITCOIN_UTIL_OVERFLOW_H
 #define BITCOIN_UTIL_OVERFLOW_H
 
+#include <cassert>
 #include <climits>
 #include <concepts>
 #include <limits>
@@ -49,6 +50,21 @@ template <class T>
     return i + j;
 }
 
+/**
+ * @brief Integer ceiling division (for unsigned values).
+ *
+ * Computes the smallest integer q such that q * divisor >= dividend.
+ * Both dividend and divisor must be unsigned, and divisor must be non-zero.
+ *
+ * The implementation avoids overflow that can occur with `(dividend + divisor - 1) / divisor`.
+ */
+template <std::unsigned_integral Dividend, std::unsigned_integral Divisor>
+[[nodiscard]] constexpr auto CeilDiv(const Dividend dividend, const Divisor divisor)
+{
+    assert(divisor > 0);
+    return dividend / divisor + (dividend % divisor != 0);
+}
+
 /**
  * @brief Left bit shift with overflow checking.
  * @param input The input value to be left shifted.
diff --git a/src/util/strencodings.cpp b/src/util/strencodings.cpp
index 289f49d4..ff593885 100644
--- a/src/util/strencodings.cpp
+++ b/src/util/strencodings.cpp
@@ -7,6 +7,7 @@
 
 #include <crypto/hex_base.h>
 #include <span.h>
+#include <util/overflow.h>
 
 #include <array>
 #include <cassert>
@@ -100,7 +101,7 @@ std::string EncodeBase64(std::span<const unsigned char> input)
     static const char *pbase64 = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
 
     std::string str;
-    str.reserve(((input.size() + 2) / 3) * 4);
+    str.reserve(CeilDiv(input.size(), 3u) * 4);
     ConvertBits<8, 6, true>([&](int v) { str += pbase64[v]; }, input.begin(), input.end());
     while (str.size() % 4) str += '=';
     return str;
@@ -146,7 +147,7 @@ std::string EncodeBase32(std::span<const unsigned char> input, bool pad)
     static const char *pbase32 = "abcdefghijklmnopqrstuvwxyz234567";
 
     std::string str;
-    str.reserve(((input.size() + 4) / 5) * 8);
+    str.reserve(CeilDiv(input.size(), 5u) * 8);
     ConvertBits<8, 5, true>([&](int v) { str += pbase32[v]; }, input.begin(), input.end());
     if (pad) {
         while (str.size() % 8) {