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+// Copyright (c) 2018-2020 The Bitcoin Core developers
+// Distributed under the MIT software license, see the accompanying
+// file COPYING or http://www.opensource.org/licenses/mit-license.php.
+
+#ifndef BITCOIN_UTIL_FASTRANGE_H
+#define BITCOIN_UTIL_FASTRANGE_H
+
+#include <cstdint>
+
+/* This file offers implementations of the fast range reduction technique described
+ * in https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
+ *
+ * In short, they take an integer x and a range n, and return the upper bits of
+ * (x * n). If x is uniformly distributed over its domain, the result is as close to
+ * uniformly distributed over [0, n) as (x mod n) would be, but significantly faster.
+ */
+
+/** Fast range reduction with 32-bit input and 32-bit range. */
+static inline uint32_t FastRange32(uint32_t x, uint32_t n)
+{
+ return (uint64_t{x} * n) >> 32;
+}
+
+/** Fast range reduction with 64-bit input and 64-bit range. */
+static inline uint64_t FastRange64(uint64_t x, uint64_t n)
+{
+#ifdef __SIZEOF_INT128__
+ return (static_cast<unsigned __int128>(x) * static_cast<unsigned __int128>(n)) >> 64;
+#else
+ // To perform the calculation on 64-bit numbers without losing the
+ // result to overflow, split the numbers into the most significant and
+ // least significant 32 bits and perform multiplication piece-wise.
+ //
+ // See: https://stackoverflow.com/a/26855440
+ const uint64_t x_hi = x >> 32;
+ const uint64_t x_lo = x & 0xFFFFFFFF;
+ const uint64_t n_hi = n >> 32;
+ const uint64_t n_lo = n & 0xFFFFFFFF;
+
+ const uint64_t ac = x_hi * n_hi;
+ const uint64_t ad = x_hi * n_lo;
+ const uint64_t bc = x_lo * n_hi;
+ const uint64_t bd = x_lo * n_lo;
+
+ const uint64_t mid34 = (bd >> 32) + (bc & 0xFFFFFFFF) + (ad & 0xFFFFFFFF);
+ const uint64_t upper64 = ac + (bc >> 32) + (ad >> 32) + (mid34 >> 32);
+ return upper64;
+#endif
+}
+
+#endif // BITCOIN_UTIL_FASTRANGE_H