1  // Copyright (c) 2018-2022 The Bitcoin Core developers
 2  // Distributed under the MIT software license, see the accompanying
 3  // file COPYING or http://www.opensource.org/licenses/mit-license.php.
 4  
 5  #ifndef BITCOIN_UTIL_FASTRANGE_H
 6  #define BITCOIN_UTIL_FASTRANGE_H
 7  
 8  #include <cstdint>
 9  
10  /* This file offers implementations of the fast range reduction technique described
11   * in https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
12   *
13   * In short, they take an integer x and a range n, and return the upper bits of
14   * (x * n). If x is uniformly distributed over its domain, the result is as close to
15   * uniformly distributed over [0, n) as (x mod n) would be, but significantly faster.
16   */
17  
18  /** Fast range reduction with 32-bit input and 32-bit range. */
19  static inline uint32_t FastRange32(uint32_t x, uint32_t n)
20  {
21      return (uint64_t{x} * n) >> 32;
22  }
23  
24  /** Fast range reduction with 64-bit input and 64-bit range. */
25  static inline uint64_t FastRange64(uint64_t x, uint64_t n)
26  {
27  #ifdef __SIZEOF_INT128__
28      return (static_cast<unsigned __int128>(x) * static_cast<unsigned __int128>(n)) >> 64;
29  #else
30      // To perform the calculation on 64-bit numbers without losing the
31      // result to overflow, split the numbers into the most significant and
32      // least significant 32 bits and perform multiplication piece-wise.
33      //
34      // See: https://stackoverflow.com/a/26855440
35      const uint64_t x_hi = x >> 32;
36      const uint64_t x_lo = x & 0xFFFFFFFF;
37      const uint64_t n_hi = n >> 32;
38      const uint64_t n_lo = n & 0xFFFFFFFF;
39  
40      const uint64_t ac = x_hi * n_hi;
41      const uint64_t ad = x_hi * n_lo;
42      const uint64_t bc = x_lo * n_hi;
43      const uint64_t bd = x_lo * n_lo;
44  
45      const uint64_t mid34 = (bd >> 32) + (bc & 0xFFFFFFFF) + (ad & 0xFFFFFFFF);
46      const uint64_t upper64 = ac + (bc >> 32) + (ad >> 32) + (mid34 >> 32);
47      return upper64;
48  #endif
49  }
50  
51  #endif // BITCOIN_UTIL_FASTRANGE_H