1/*
2 * Copyright 2015-present Facebook, Inc.
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 * http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 * See the License for the specific language governing permissions and
14 * limitations under the License.
15 */
16
17#pragma once
18
19#include <array>
20
21#include <glog/logging.h>
22
23#include <folly/Portability.h>
24#include <folly/experimental/Instructions.h>
25
26namespace folly {
27
28namespace detail {
29
30// kSelectInByte
31//
32// Described in:
33// http://dsiutils.di.unimi.it/docs/it/unimi/dsi/bits/Fast.html#selectInByte
34//
35// A precomputed tabled containing the positions of the set bits in the binary
36// representations of all 8-bit unsigned integers.
37//
38// For i: [0, 256) ranging over all 8-bit unsigned integers and for j: [0, 8)
39// ranging over all 0-based bit positions in an 8-bit unsigned integer, the
40// table entry kSelectInByte[i][j] is the 0-based bit position of the j-th set
41// bit in the binary representation of i, or 8 if it has fewer than j set bits.
42//
43// Example: i: 17 (b00010001), j: [0, 8)
44// kSelectInByte[b00010001][0] = 0
45// kSelectInByte[b00010001][1] = 4
46// kSelectInByte[b00010001][2] = 8
47// ...
48// kSelectInByte[b00010001][7] = 8
49extern std::array<std::array<std::uint8_t, 256>, 8> const kSelectInByte;
50
51} // namespace detail
52
53/**
54 * Returns the position of the k-th 1 in the 64-bit word x.
55 * k is 0-based, so k=0 returns the position of the first 1.
56 *
57 * Uses the broadword selection algorithm by Vigna [1], improved by Gog
58 * and Petri [2] and Vigna [3].
59 *
60 * [1] Sebastiano Vigna. Broadword Implementation of Rank/Select
61 * Queries. WEA, 2008
62 *
63 * [2] Simon Gog, Matthias Petri. Optimized succinct data structures
64 * for massive data. Softw. Pract. Exper., 2014
65 *
66 * [3] Sebastiano Vigna. MG4J 5.2.1. http://mg4j.di.unimi.it/
67 */
68template <class Instructions>
69inline uint64_t select64(uint64_t x, uint64_t k) {
70 DCHECK_LT(k, Instructions::popcount(x));
71
72 constexpr uint64_t kOnesStep4 = 0x1111111111111111ULL;
73 constexpr uint64_t kOnesStep8 = 0x0101010101010101ULL;
74 constexpr uint64_t kMSBsStep8 = 0x80ULL * kOnesStep8;
75
76 auto s = x;
77 s = s - ((s & 0xA * kOnesStep4) >> 1);
78 s = (s & 0x3 * kOnesStep4) + ((s >> 2) & 0x3 * kOnesStep4);
79 s = (s + (s >> 4)) & 0xF * kOnesStep8;
80 uint64_t byteSums = s * kOnesStep8;
81
82 uint64_t kStep8 = k * kOnesStep8;
83 uint64_t geqKStep8 = (((kStep8 | kMSBsStep8) - byteSums) & kMSBsStep8);
84 uint64_t place = Instructions::popcount(geqKStep8) * 8;
85 uint64_t byteRank = k - (((byteSums << 8) >> place) & uint64_t(0xFF));
86 return place + detail::kSelectInByte[byteRank][((x >> place) & 0xFF)];
87}
88
89template <>
90FOLLY_ALWAYS_INLINE uint64_t
91select64<compression::instructions::Haswell>(uint64_t x, uint64_t k) {
92#if defined(__GNUC__) || defined(__clang__)
93 // GCC and Clang won't inline the intrinsics.
94 uint64_t result = uint64_t(1) << k;
95
96 asm("pdep %1, %0, %0\n\t"
97 "tzcnt %0, %0"
98 : "+r"(result)
99 : "r"(x));
100
101 return result;
102#else
103 return _tzcnt_u64(_pdep_u64(1ULL << k, x));
104#endif
105}
106
107} // namespace folly
108