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- /*
- * Copyright 2015-present Facebook, Inc.
- *
- * Licensed under the Apache License, Version 2.0 (the "License");
- * you may not use this file except in compliance with the License.
- * You may obtain a copy of the License at
- *
- * http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
- #pragma once
- #include <array>
- #include <glog/logging.h>
- #include <folly/Portability.h>
- #include <folly/experimental/Instructions.h>
- namespace folly {
- namespace detail {
- // kSelectInByte
- //
- // Described in:
- // http://dsiutils.di.unimi.it/docs/it/unimi/dsi/bits/Fast.html#selectInByte
- //
- // A precomputed tabled containing the positions of the set bits in the binary
- // representations of all 8-bit unsigned integers.
- //
- // For i: [0, 256) ranging over all 8-bit unsigned integers and for j: [0, 8)
- // ranging over all 0-based bit positions in an 8-bit unsigned integer, the
- // table entry kSelectInByte[i][j] is the 0-based bit position of the j-th set
- // bit in the binary representation of i, or 8 if it has fewer than j set bits.
- //
- // Example: i: 17 (b00010001), j: [0, 8)
- // kSelectInByte[b00010001][0] = 0
- // kSelectInByte[b00010001][1] = 4
- // kSelectInByte[b00010001][2] = 8
- // ...
- // kSelectInByte[b00010001][7] = 8
- extern std::array<std::array<std::uint8_t, 256>, 8> const kSelectInByte;
- } // namespace detail
- /**
- * Returns the position of the k-th 1 in the 64-bit word x.
- * k is 0-based, so k=0 returns the position of the first 1.
- *
- * Uses the broadword selection algorithm by Vigna [1], improved by Gog
- * and Petri [2] and Vigna [3].
- *
- * [1] Sebastiano Vigna. Broadword Implementation of Rank/Select
- * Queries. WEA, 2008
- *
- * [2] Simon Gog, Matthias Petri. Optimized succinct data structures
- * for massive data. Softw. Pract. Exper., 2014
- *
- * [3] Sebastiano Vigna. MG4J 5.2.1. http://mg4j.di.unimi.it/
- */
- template <class Instructions>
- inline uint64_t select64(uint64_t x, uint64_t k) {
- DCHECK_LT(k, Instructions::popcount(x));
- constexpr uint64_t kOnesStep4 = 0x1111111111111111ULL;
- constexpr uint64_t kOnesStep8 = 0x0101010101010101ULL;
- constexpr uint64_t kMSBsStep8 = 0x80ULL * kOnesStep8;
- auto s = x;
- s = s - ((s & 0xA * kOnesStep4) >> 1);
- s = (s & 0x3 * kOnesStep4) + ((s >> 2) & 0x3 * kOnesStep4);
- s = (s + (s >> 4)) & 0xF * kOnesStep8;
- uint64_t byteSums = s * kOnesStep8;
- uint64_t kStep8 = k * kOnesStep8;
- uint64_t geqKStep8 = (((kStep8 | kMSBsStep8) - byteSums) & kMSBsStep8);
- uint64_t place = Instructions::popcount(geqKStep8) * 8;
- uint64_t byteRank = k - (((byteSums << 8) >> place) & uint64_t(0xFF));
- return place + detail::kSelectInByte[byteRank][((x >> place) & 0xFF)];
- }
- template <>
- FOLLY_ALWAYS_INLINE uint64_t
- select64<compression::instructions::Haswell>(uint64_t x, uint64_t k) {
- #if defined(__GNUC__) || defined(__clang__)
- // GCC and Clang won't inline the intrinsics.
- uint64_t result = uint64_t(1) << k;
- asm("pdep %1, %0, %0\n\t"
- "tzcnt %0, %0"
- : "+r"(result)
- : "r"(x));
- return result;
- #else
- return _tzcnt_u64(_pdep_u64(1ULL << k, x));
- #endif
- }
- } // namespace folly
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