/* * Copyright (c) Facebook, Inc. and its affiliates. * * 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. */ /** * @author Philip Pronin (philipp@fb.com) * * Based on the paper by Sebastiano Vigna, * "Quasi-succinct indices" (arxiv:1206.4300). */ #pragma once #include #include #include #include #include #include #include #include #include #include #include #include #include #if !FOLLY_X64 #error EliasFanoCoding.h requires x86_64 #endif namespace folly { namespace compression { static_assert(kIsLittleEndian, "EliasFanoCoding.h requires little endianness"); constexpr size_t kCacheLineSize = 64; template struct EliasFanoCompressedListBase { EliasFanoCompressedListBase() = default; template EliasFanoCompressedListBase( const EliasFanoCompressedListBase& other) : size(other.size), numLowerBits(other.numLowerBits), upperSizeBytes(other.upperSizeBytes), data(other.data), skipPointers(reinterpret_cast(other.skipPointers)), forwardPointers(reinterpret_cast(other.forwardPointers)), lower(reinterpret_cast(other.lower)), upper(reinterpret_cast(other.upper)) {} template auto free() -> decltype(::free(T(nullptr))) { return ::free(data.data()); } size_t size = 0; uint8_t numLowerBits = 0; size_t upperSizeBytes = 0; // WARNING: EliasFanoCompressedList has no ownership of data. The 7 bytes // following the last byte should be readable if kUpperFirst = false, 8 bytes // otherwise. folly::Range data; Pointer skipPointers = nullptr; Pointer forwardPointers = nullptr; Pointer lower = nullptr; Pointer upper = nullptr; }; typedef EliasFanoCompressedListBase EliasFanoCompressedList; typedef EliasFanoCompressedListBase MutableEliasFanoCompressedList; template < class Value, // SkipValue must be wide enough to be able to represent the list length. class SkipValue = uint64_t, size_t kSkipQuantum = 0, // 0 = disabled size_t kForwardQuantum = 0, // 0 = disabled bool kUpperFirst = false> struct EliasFanoEncoderV2 { static_assert( std::is_integral::value && std::is_unsigned::value, "Value should be unsigned integral"); typedef EliasFanoCompressedList CompressedList; typedef MutableEliasFanoCompressedList MutableCompressedList; typedef Value ValueType; typedef SkipValue SkipValueType; struct Layout; static constexpr size_t skipQuantum = kSkipQuantum; static constexpr size_t forwardQuantum = kForwardQuantum; static uint8_t defaultNumLowerBits(size_t upperBound, size_t size) { if (UNLIKELY(size == 0 || upperBound < size)) { return 0; } // Result that should be returned is "floor(log(upperBound / size))". // In order to avoid expensive division, we rely on // "floor(a) - floor(b) - 1 <= floor(a - b) <= floor(a) - floor(b)". // Assuming "candidate = floor(log(upperBound)) - floor(log(upperBound))", // then result is either "candidate - 1" or "candidate". auto candidate = folly::findLastSet(upperBound) - folly::findLastSet(size); // NOTE: As size != 0, "candidate" is always < 64. return (size > (upperBound >> candidate)) ? candidate - 1 : candidate; } // Requires: input range (begin, end) is sorted (encoding // crashes if it's not). // WARNING: encode() mallocates EliasFanoCompressedList::data. As // EliasFanoCompressedList has no ownership of it, you need to call // free() explicitly. template static MutableCompressedList encode( RandomAccessIterator begin, RandomAccessIterator end) { if (begin == end) { return MutableCompressedList(); } EliasFanoEncoderV2 encoder(size_t(end - begin), *(end - 1)); for (; begin != end; ++begin) { encoder.add(*begin); } return encoder.finish(); } explicit EliasFanoEncoderV2(const MutableCompressedList& result) : lower_(result.lower), upper_(result.upper), skipPointers_(reinterpret_cast(result.skipPointers)), forwardPointers_( reinterpret_cast(result.forwardPointers)), result_(result) { std::fill(result.data.begin(), result.data.end(), '\0'); } EliasFanoEncoderV2(size_t size, ValueType upperBound) : EliasFanoEncoderV2( Layout::fromUpperBoundAndSize(upperBound, size).allocList()) {} void add(ValueType value) { CHECK_LT(value, std::numeric_limits::max()); CHECK_GE(value, lastValue_); const auto numLowerBits = result_.numLowerBits; const ValueType upperBits = value >> numLowerBits; // Upper sequence consists of upperBits 0-bits and (size_ + 1) 1-bits. const size_t pos = upperBits + size_; upper_[pos / 8] |= 1U << (pos % 8); // Append numLowerBits bits to lower sequence. if (numLowerBits != 0) { const ValueType lowerBits = value & ((ValueType(1) << numLowerBits) - 1); writeBits56(lower_, size_ * numLowerBits, numLowerBits, lowerBits); } fillSkipPointersUpTo(upperBits); if /* constexpr */ (forwardQuantum != 0) { if ((size_ + 1) % forwardQuantum == 0) { const auto k = size_ / forwardQuantum; // Store the number of preceding 0-bits. forwardPointers_[k] = upperBits; } } lastValue_ = value; ++size_; } const MutableCompressedList& finish() { CHECK_EQ(size_, result_.size); const ValueType upperBitsUniverse = (8 * result_.upperSizeBytes - result_.size); if (upperBitsUniverse > 0) { // Populate skip pointers up to the universe upper bound. fillSkipPointersUpTo(upperBitsUniverse - 1); } return result_; } private: void fillSkipPointersUpTo(ValueType fillBoundary) { if /* constexpr */ (skipQuantum != 0) { while ((skipPointersSize_ + 1) * skipQuantum <= fillBoundary) { // Store the number of preceding 1-bits. skipPointers_[skipPointersSize_++] = static_cast(size_); } } } // Writes value (with len up to 56 bits) to data starting at pos-th bit. static void writeBits56(unsigned char* data, size_t pos, uint8_t len, uint64_t value) { DCHECK_LE(uint32_t(len), 56); DCHECK_EQ(0, value & ~((uint64_t(1) << len) - 1)); unsigned char* const ptr = data + (pos / 8); uint64_t ptrv = folly::loadUnaligned(ptr); ptrv |= value << (pos % 8); folly::storeUnaligned(ptr, ptrv); } unsigned char* lower_ = nullptr; unsigned char* upper_ = nullptr; SkipValueType* skipPointers_ = nullptr; SkipValueType* forwardPointers_ = nullptr; ValueType lastValue_ = 0; size_t size_ = 0; size_t skipPointersSize_ = 0; MutableCompressedList result_; }; template < class Value, class SkipValue, size_t kSkipQuantum, size_t kForwardQuantum, bool kUpperFirst> struct EliasFanoEncoderV2< Value, SkipValue, kSkipQuantum, kForwardQuantum, kUpperFirst>::Layout { static Layout fromUpperBoundAndSize(size_t upperBound, size_t size) { // numLowerBits can be at most 56 because of detail::writeBits56. const uint8_t numLowerBits = std::min(defaultNumLowerBits(upperBound, size), uint8_t(56)); // *** Upper bits. // Upper bits are stored using unary delta encoding. // For example, (3 5 5 9) will be encoded as 1000011001000_2. const size_t upperSizeBits = (upperBound >> numLowerBits) + // Number of 0-bits to be stored. size; // 1-bits. const size_t upper = (upperSizeBits + 7) / 8; // *** Validity checks. // Shift by numLowerBits must be valid. CHECK_LT(numLowerBits, 8 * sizeof(Value)); CHECK_LT(size, std::numeric_limits::max()); CHECK_LT( upperBound >> numLowerBits, std::numeric_limits::max()); return fromInternalSizes(numLowerBits, upper, size); } static Layout fromInternalSizes(uint8_t numLowerBits, size_t upper, size_t size) { Layout layout; layout.size = size; layout.numLowerBits = numLowerBits; layout.lower = (numLowerBits * size + 7) / 8; layout.upper = upper; // *** Skip pointers. // Store (1-indexed) position of every skipQuantum-th // 0-bit in upper bits sequence. if /* constexpr */ (skipQuantum != 0) { // 8 * upper is used here instead of upperSizeBits, as that is // more serialization-friendly way (upperSizeBits doesn't need // to be known by this function, unlike upper). size_t numSkipPointers = (8 * upper - size) / skipQuantum; layout.skipPointers = numSkipPointers * sizeof(SkipValueType); } // *** Forward pointers. // Store (1-indexed) position of every forwardQuantum-th // 1-bit in upper bits sequence. if /* constexpr */ (forwardQuantum != 0) { size_t numForwardPointers = size / forwardQuantum; layout.forwardPointers = numForwardPointers * sizeof(SkipValueType); } return layout; } size_t bytes() const { return lower + upper + skipPointers + forwardPointers; } template EliasFanoCompressedListBase openList( Range& buf) const { EliasFanoCompressedListBase result; result.size = size; result.numLowerBits = numLowerBits; result.upperSizeBytes = upper; result.data = buf.subpiece(0, bytes()); auto advance = [&](size_t n) { auto begin = buf.data(); buf.advance(n); return begin; }; result.skipPointers = advance(skipPointers); result.forwardPointers = advance(forwardPointers); if /* constexpr */ (kUpperFirst) { result.upper = advance(upper); result.lower = advance(lower); } else { result.lower = advance(lower); result.upper = advance(upper); } return result; } MutableCompressedList allocList() const { uint8_t* buf = nullptr; // WARNING: Current read/write logic assumes that the 7 bytes // following the upper bytes and the 8 bytes following the lower bytes // sequences are readable (stored value doesn't matter and won't be // changed), so we allocate additional 8 bytes, but do not include them in // size of returned value. if (size > 0) { buf = static_cast(malloc(bytes() + 8)); } folly::MutableByteRange bufRange(buf, bytes()); return openList(bufRange); } size_t size = 0; uint8_t numLowerBits = 0; // Sizes in bytes. size_t lower = 0; size_t upper = 0; size_t skipPointers = 0; size_t forwardPointers = 0; }; namespace detail { template class UpperBitsReader : ForwardPointers, SkipPointers { typedef typename Encoder::SkipValueType SkipValueType; public: typedef typename Encoder::ValueType ValueType; explicit UpperBitsReader(const typename Encoder::CompressedList& list) : ForwardPointers(list.forwardPointers), SkipPointers(list.skipPointers), start_(list.upper) { reset(); } void reset() { // Pretend the bitvector is prefixed by a block of zeroes. block_ = 0; position_ = static_cast(-1); outer_ = static_cast(-sizeof(block_t)); value_ = 0; } SizeType position() const { return position_; } ValueType value() const { return value_; } ValueType previous() { size_t inner; block_t block; getPreviousInfo(block, inner, outer_); block_ = folly::loadUnaligned(start_ + outer_); block_ ^= block; --position_; return setValue(inner); } ValueType next() { // Skip to the first non-zero block. while (block_ == 0) { outer_ += sizeof(block_t); block_ = folly::loadUnaligned(start_ + outer_); } ++position_; size_t inner = Instructions::ctz(block_); block_ = Instructions::blsr(block_); return setValue(inner); } ValueType skip(SizeType n) { DCHECK_GT(n, 0); position_ += n; // n 1-bits will be read. // Use forward pointer. if (Encoder::forwardQuantum > 0 && n > Encoder::forwardQuantum) { const size_t steps = position_ / Encoder::forwardQuantum; const size_t dest = folly::loadUnaligned( this->forwardPointers_ + (steps - 1) * sizeof(SkipValueType)); reposition(dest + steps * Encoder::forwardQuantum); n = position_ + 1 - steps * Encoder::forwardQuantum; // n is > 0. } size_t cnt; // Find necessary block. while ((cnt = Instructions::popcount(block_)) < n) { n -= cnt; outer_ += sizeof(block_t); block_ = folly::loadUnaligned(start_ + outer_); } // Skip to the n-th one in the block. DCHECK_GT(n, 0); size_t inner = select64(block_, n - 1); block_ &= (block_t(-1) << inner) << 1; return setValue(inner); } // Skip to the first element that is >= v and located *after* the current // one (so even if current value equals v, position will be increased by 1). ValueType skipToNext(ValueType v) { DCHECK_GE(v, value_); // Use skip pointer. if (Encoder::skipQuantum > 0 && v >= value_ + Encoder::skipQuantum) { const size_t steps = v / Encoder::skipQuantum; const size_t dest = folly::loadUnaligned( this->skipPointers_ + (steps - 1) * sizeof(SkipValueType)); reposition(dest + Encoder::skipQuantum * steps); position_ = dest - 1; // Correct value_ will be set during the next() call at the end. // NOTE: Corresponding block of lower bits sequence may be // prefetched here (via __builtin_prefetch), but experiments // didn't show any significant improvements. } // Skip by blocks. size_t cnt; size_t skip = v - (8 * outer_ - position_ - 1); constexpr size_t kBitsPerBlock = 8 * sizeof(block_t); while ((cnt = Instructions::popcount(~block_)) < skip) { skip -= cnt; position_ += kBitsPerBlock - cnt; outer_ += sizeof(block_t); block_ = folly::loadUnaligned(start_ + outer_); } if (LIKELY(skip)) { auto inner = select64(~block_, skip - 1); position_ += inner - skip + 1; block_ &= block_t(-1) << inner; } next(); return value_; } /** * Prepare to skip to `value`. This is a constant-time operation that will * prefetch memory required for a `skipTo(value)` call. * * @return position of reader */ SizeType prepareSkipTo(ValueType v) const { auto position = position_; if (Encoder::skipQuantum > 0 && v >= value_ + Encoder::skipQuantum) { auto outer = outer_; const size_t steps = v / Encoder::skipQuantum; const size_t dest = folly::loadUnaligned( this->skipPointers_ + (steps - 1) * sizeof(SkipValueType)); position = dest - 1; outer = (dest + Encoder::skipQuantum * steps) / 8; // Prefetch up to the beginning of where we linear search. After that, // hardware prefetching will outperform our own. In addition, this // simplifies calculating what to prefetch as we don't have to calculate // the entire destination address. Two cache lines are prefetched because // this results in fewer cycles used (based on practical results) than // one. However, three cache lines does not have any additional effect. const auto addr = start_ + outer; __builtin_prefetch(addr); __builtin_prefetch(addr + kCacheLineSize); } return position; } ValueType previousValue() const { block_t block; size_t inner; OuterType outer; getPreviousInfo(block, inner, outer); return static_cast(8 * outer + inner - (position_ - 1)); } // Returns true if we're at the beginning of the list, or previousValue() != // value(). bool isAtBeginningOfRun() const { DCHECK_NE(position(), static_cast(-1)); if (position_ == 0) { return true; } size_t bitPos = size_t(value_) + position_ - 1; return (start_[bitPos / 8] & (1 << (bitPos % 8))) == 0; } void setDone(SizeType endPos) { position_ = endPos; } private: ValueType setValue(size_t inner) { value_ = static_cast(8 * outer_ + inner - position_); return value_; } void reposition(SizeType dest) { outer_ = dest / 8; block_ = folly::loadUnaligned(start_ + outer_); block_ &= ~((block_t(1) << (dest % 8)) - 1); } using block_t = uint64_t; // The size in bytes of the upper bits is limited by n + universe / 8, // so a type that can hold either sizes or values is sufficient. using OuterType = typename std::common_type::type; void getPreviousInfo(block_t& block, size_t& inner, OuterType& outer) const { DCHECK_NE(position(), std::numeric_limits::max()); DCHECK_GT(position(), 0); outer = outer_; block = folly::loadUnaligned(start_ + outer); inner = size_t(value_) - 8 * outer_ + position_; block &= (block_t(1) << inner) - 1; while (UNLIKELY(block == 0)) { DCHECK_GT(outer, 0); outer -= std::min(sizeof(block_t), outer); block = folly::loadUnaligned(start_ + outer); } inner = 8 * sizeof(block_t) - 1 - Instructions::clz(block); } const unsigned char* const start_; block_t block_; SizeType position_; // Index of current value (= #reads - 1). OuterType outer_; // Outer offset: number of consumed bytes in upper. ValueType value_; }; } // namespace detail // If kUnchecked = true the caller must guarantee that all the operations return // valid elements, i.e., they would never return false if checked. // // If the list length is known to be representable with a type narrower than the // SkipValueType used in the format, the reader footprint can be reduced by // passing the type as SizeType. template < class Encoder, class Instructions = instructions::Default, bool kUnchecked = false, class SizeType = typename Encoder::SkipValueType> class EliasFanoReader { public: typedef Encoder EncoderType; typedef typename Encoder::ValueType ValueType; explicit EliasFanoReader(const typename Encoder::CompressedList& list) : upper_(list), lower_(list.lower), size_(list.size), numLowerBits_(list.numLowerBits) { DCHECK(Instructions::supported()); // To avoid extra branching during skipTo() while reading // upper sequence we need to know the last element. // If kUnchecked == true, we do not check that skipTo() is called // within the bounds, so we can avoid initializing lastValue_. if (kUnchecked || UNLIKELY(list.size == 0)) { lastValue_ = 0; return; } ValueType lastUpperValue = ValueType(8 * list.upperSizeBytes - size_); auto it = list.upper + list.upperSizeBytes - 1; DCHECK_NE(*it, 0); lastUpperValue -= 8 - folly::findLastSet(*it); lastValue_ = readLowerPart(size_ - 1) | (lastUpperValue << numLowerBits_); } void reset() { upper_.reset(); value_ = kInvalidValue; } bool previous() { if (!kUnchecked && UNLIKELY(position() == 0)) { reset(); return false; } upper_.previous(); value_ = readLowerPart(upper_.position()) | (upper_.value() << numLowerBits_); return true; } bool next() { if (!kUnchecked && UNLIKELY(position() + 1 >= size_)) { return setDone(); } upper_.next(); value_ = readLowerPart(upper_.position()) | (upper_.value() << numLowerBits_); return true; } /** * Advances by n elements. n = 0 is allowed and has no effect. Returns false * if the end of the list is reached. */ bool skip(SizeType n) { if (n == 0) { return valid(); } if (kUnchecked || LIKELY(position() + n < size_)) { if (LIKELY(n < kLinearScanThreshold)) { for (SizeType i = 0; i < n; ++i) { upper_.next(); } } else { upper_.skip(n); } value_ = readLowerPart(upper_.position()) | (upper_.value() << numLowerBits_); return true; } return setDone(); } /** * Skips to the first element >= value whose position is greater or equal to * the current position. Requires that value >= value() (or that the reader is * at position -1). Returns false if no such element exists. */ bool skipTo(ValueType value) { if (value != kInvalidValue) { DCHECK_GE(value + 1, value_ + 1); } if (!kUnchecked && value > lastValue_) { return setDone(); } else if (value == value_) { return true; } ValueType upperValue = (value >> numLowerBits_); ValueType upperSkip = upperValue - upper_.value(); // The average density of ones in upper bits is 1/2. // LIKELY here seems to make things worse, even for small skips. if (upperSkip < 2 * kLinearScanThreshold) { do { upper_.next(); } while (UNLIKELY(upper_.value() < upperValue)); } else { upper_.skipToNext(upperValue); } iterateTo(value); return true; } /** * Prepare to skip to `value` by prefetching appropriate memory in both the * upper and lower bits. */ void prepareSkipTo(ValueType value) const { // Also works when value_ == kInvalidValue. if (value != kInvalidValue) { DCHECK_GE(value + 1, value_ + 1); } if ((!kUnchecked && value > lastValue_) || (value == value_)) { return; } // Do minimal computation required to prefetch address used in // `readLowerPart()`. ValueType upperValue = (value >> numLowerBits_); const auto upperPosition = upper_.prepareSkipTo(upperValue); const auto addr = lower_ + (upperPosition * numLowerBits_ / 8); __builtin_prefetch(addr); __builtin_prefetch(addr + kCacheLineSize); } /** * Jumps to the element at position n. The reader can be in any state. Returns * false if n >= size(). */ bool jump(SizeType n) { if (n + 1 < upper_.position() + 1) { // Also works if position() == -1. reset(); n += 1; // Initial position is -1. } else { n -= upper_.position(); } return skip(n); } /** * Jumps to the first element >= value. The reader can be in any * state. Returns false if no such element exists. * * If all the values in the list can be assumed distinct, setting * assumeDistinct = true can enable some optimizations. */ bool jumpTo(ValueType value, bool assumeDistinct = false) { if (value == value_) { if (assumeDistinct == true) { return true; } // We might be in the middle of a run, iterate backwards to the beginning. auto valueLower = Instructions::bzhi(value_, numLowerBits_); while (!upper_.isAtBeginningOfRun() && readLowerPart(upper_.position() - 1) == valueLower) { upper_.previous(); } return true; } // We need to reset if we're not in the initial state and the jump is // backwards. if (position() != static_cast(-1) && value < value_) { // If position() == size() value_ is kInvalidValue. reset(); } return skipTo(value); } ValueType lastValue() const { CHECK(!kUnchecked); return lastValue_; } ValueType previousValue() const { DCHECK_GT(position(), 0); DCHECK_LT(position(), size()); return readLowerPart(upper_.position() - 1) | (upper_.previousValue() << numLowerBits_); } SizeType size() const { return size_; } bool valid() const { return position() < size(); // Also checks that position() != -1. } SizeType position() const { return upper_.position(); } ValueType value() const { DCHECK(valid()); return value_; } private: // Must hold kInvalidValue + 1 == 0. constexpr static ValueType kInvalidValue = -1; bool setDone() { value_ = kInvalidValue; upper_.setDone(size_); return false; } ValueType readLowerPart(SizeType i) const { DCHECK_LT(i, size_); const size_t pos = i * numLowerBits_; const unsigned char* ptr = lower_ + (pos / 8); const uint64_t ptrv = folly::loadUnaligned(ptr); // This removes the branch in the fallback implementation of // bzhi. The condition is verified at encoding time. assume(numLowerBits_ < sizeof(ValueType) * 8); return Instructions::bzhi(ptrv >> (pos % 8), numLowerBits_); } void iterateTo(ValueType value) { while (true) { value_ = readLowerPart(upper_.position()) | (upper_.value() << numLowerBits_); if (LIKELY(value_ >= value)) { break; } upper_.next(); } } constexpr static size_t kLinearScanThreshold = 8; detail::UpperBitsReader upper_; const uint8_t* lower_; SizeType size_; ValueType value_ = kInvalidValue; ValueType lastValue_; uint8_t numLowerBits_; }; } // namespace compression } // namespace folly