108 lines
3.3 KiB
C++
108 lines
3.3 KiB
C++
/*
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* Copyright (c) Facebook, Inc. and its affiliates.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#pragma once
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#include <array>
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#include <glog/logging.h>
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#include <folly/Portability.h>
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#include <folly/experimental/Instructions.h>
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namespace folly {
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namespace detail {
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// kSelectInByte
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//
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// Described in:
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// http://dsiutils.di.unimi.it/docs/it/unimi/dsi/bits/Fast.html#selectInByte
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//
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// A precomputed tabled containing the positions of the set bits in the binary
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// representations of all 8-bit unsigned integers.
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//
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// For i: [0, 256) ranging over all 8-bit unsigned integers and for j: [0, 8)
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// ranging over all 0-based bit positions in an 8-bit unsigned integer, the
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// table entry kSelectInByte[i][j] is the 0-based bit position of the j-th set
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// bit in the binary representation of i, or 8 if it has fewer than j set bits.
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//
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// Example: i: 17 (b00010001), j: [0, 8)
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// kSelectInByte[b00010001][0] = 0
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// kSelectInByte[b00010001][1] = 4
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// kSelectInByte[b00010001][2] = 8
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// ...
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// kSelectInByte[b00010001][7] = 8
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extern std::array<std::array<std::uint8_t, 256>, 8> const kSelectInByte;
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} // namespace detail
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/**
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* Returns the position of the k-th 1 in the 64-bit word x.
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* k is 0-based, so k=0 returns the position of the first 1.
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*
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* Uses the broadword selection algorithm by Vigna [1], improved by Gog
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* and Petri [2] and Vigna [3].
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*
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* [1] Sebastiano Vigna. Broadword Implementation of Rank/Select
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* Queries. WEA, 2008
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*
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* [2] Simon Gog, Matthias Petri. Optimized succinct data structures
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* for massive data. Softw. Pract. Exper., 2014
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*
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* [3] Sebastiano Vigna. MG4J 5.2.1. http://mg4j.di.unimi.it/
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*/
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template <class Instructions>
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inline uint64_t select64(uint64_t x, uint64_t k) {
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DCHECK_LT(k, Instructions::popcount(x));
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constexpr uint64_t kOnesStep4 = 0x1111111111111111ULL;
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constexpr uint64_t kOnesStep8 = 0x0101010101010101ULL;
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constexpr uint64_t kMSBsStep8 = 0x80ULL * kOnesStep8;
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auto s = x;
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s = s - ((s & 0xA * kOnesStep4) >> 1);
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s = (s & 0x3 * kOnesStep4) + ((s >> 2) & 0x3 * kOnesStep4);
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s = (s + (s >> 4)) & 0xF * kOnesStep8;
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uint64_t byteSums = s * kOnesStep8;
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uint64_t kStep8 = k * kOnesStep8;
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uint64_t geqKStep8 = (((kStep8 | kMSBsStep8) - byteSums) & kMSBsStep8);
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uint64_t place = Instructions::popcount(geqKStep8) * 8;
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uint64_t byteRank = k - (((byteSums << 8) >> place) & uint64_t(0xFF));
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return place + detail::kSelectInByte[byteRank][((x >> place) & 0xFF)];
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}
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template <>
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FOLLY_ALWAYS_INLINE uint64_t
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select64<compression::instructions::Haswell>(uint64_t x, uint64_t k) {
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#if defined(__GNUC__)
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// GCC and Clang won't inline the intrinsics.
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uint64_t result = uint64_t(1) << k;
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asm("pdep %1, %0, %0\n\t"
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"tzcnt %0, %0"
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: "+r"(result)
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: "r"(x));
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return result;
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#else
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return _tzcnt_u64(_pdep_u64(1ULL << k, x));
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#endif
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}
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} // namespace folly
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