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       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                 :     3885762 : static inline uint32_t FastRange32(uint32_t x, uint32_t n)
      20                 :             : {
      21         [ +  + ]:     3885762 :     return (uint64_t{x} * n) >> 32;
      22                 :             : }
      23                 :             : 
      24                 :             : /** Fast range reduction with 64-bit input and 64-bit range. */
      25                 :       10538 : static inline uint64_t FastRange64(uint64_t x, uint64_t n)
      26                 :             : {
      27                 :             : #ifdef __SIZEOF_INT128__
      28                 :       10538 :     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