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