2 * Copyright 2016 Facebook, Inc.
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
8 * http://www.apache.org/licenses/LICENSE-2.0
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.
18 * @author Philip Pronin (philipp@fb.com)
20 * Based on the paper by Sebastiano Vigna,
21 * "Quasi-succinct indices" (arxiv:1206.4300).
29 #include <type_traits>
31 #include <folly/Bits.h>
32 #include <folly/Likely.h>
33 #include <folly/Portability.h>
34 #include <folly/Range.h>
35 #include <folly/experimental/Instructions.h>
36 #include <folly/experimental/Select64.h>
37 #include <glog/logging.h>
40 #error EliasFanoCoding.h requires GCC
44 #error EliasFanoCoding.h requires x86_64
47 #if __BYTE_ORDER__ != __ORDER_LITTLE_ENDIAN__
48 #error EliasFanoCoding.h requires little endianness
51 namespace folly { namespace compression {
53 template <class Pointer>
54 struct EliasFanoCompressedListBase {
55 EliasFanoCompressedListBase() = default;
57 template <class OtherPointer>
58 EliasFanoCompressedListBase(
59 const EliasFanoCompressedListBase<OtherPointer>& other)
61 numLowerBits(other.numLowerBits),
63 skipPointers(reinterpret_cast<Pointer>(other.skipPointers)),
64 forwardPointers(reinterpret_cast<Pointer>(other.forwardPointers)),
65 lower(reinterpret_cast<Pointer>(other.lower)),
66 upper(reinterpret_cast<Pointer>(other.upper)) { }
68 template <class T = Pointer>
69 auto free() -> decltype(::free(T(nullptr))) {
70 return ::free(data.data());
73 size_t upperSize() const { return data.end() - upper; }
76 uint8_t numLowerBits = 0;
78 // WARNING: EliasFanoCompressedList has no ownership of data. The 7
79 // bytes following the last byte should be readable.
80 folly::Range<Pointer> data;
82 Pointer skipPointers = nullptr;
83 Pointer forwardPointers = nullptr;
84 Pointer lower = nullptr;
85 Pointer upper = nullptr;
88 typedef EliasFanoCompressedListBase<const uint8_t*> EliasFanoCompressedList;
89 typedef EliasFanoCompressedListBase<uint8_t*> MutableEliasFanoCompressedList;
91 template <class Value,
92 class SkipValue = size_t,
93 size_t kSkipQuantum = 0, // 0 = disabled
94 size_t kForwardQuantum = 0> // 0 = disabled
95 struct EliasFanoEncoderV2 {
96 static_assert(std::is_integral<Value>::value &&
97 std::is_unsigned<Value>::value,
98 "Value should be unsigned integral");
100 typedef EliasFanoCompressedList CompressedList;
101 typedef MutableEliasFanoCompressedList MutableCompressedList;
103 typedef Value ValueType;
104 typedef SkipValue SkipValueType;
107 static constexpr size_t skipQuantum = kSkipQuantum;
108 static constexpr size_t forwardQuantum = kForwardQuantum;
110 static uint8_t defaultNumLowerBits(size_t upperBound, size_t size) {
111 if (size == 0 || upperBound < size) {
114 // floor(log(upperBound / size));
115 return folly::findLastSet(upperBound / size) - 1;
118 // Requires: input range (begin, end) is sorted (encoding
119 // crashes if it's not).
120 // WARNING: encode() mallocates EliasFanoCompressedList::data. As
121 // EliasFanoCompressedList has no ownership of it, you need to call
122 // free() explicitly.
123 template <class RandomAccessIterator>
124 static MutableCompressedList encode(RandomAccessIterator begin,
125 RandomAccessIterator end) {
127 return MutableCompressedList();
129 EliasFanoEncoderV2 encoder(end - begin, *(end - 1));
130 for (; begin != end; ++begin) {
133 return encoder.finish();
136 explicit EliasFanoEncoderV2(const MutableCompressedList& result)
137 : lower_(result.lower),
138 upper_(result.upper),
139 skipPointers_(reinterpret_cast<SkipValueType*>(
140 result.skipPointers)),
141 forwardPointers_(reinterpret_cast<SkipValueType*>(
142 result.forwardPointers)),
144 std::fill(result.data.begin(), result.data.end(), 0);
147 EliasFanoEncoderV2(size_t size, ValueType upperBound)
148 : EliasFanoEncoderV2(
149 Layout::fromUpperBoundAndSize(upperBound, size).allocList()) { }
151 void add(ValueType value) {
152 CHECK_LT(value, std::numeric_limits<ValueType>::max());
153 CHECK_GE(value, lastValue_);
155 const auto numLowerBits = result_.numLowerBits;
156 const ValueType upperBits = value >> numLowerBits;
158 // Upper sequence consists of upperBits 0-bits and (size_ + 1) 1-bits.
159 const size_t pos = upperBits + size_;
160 upper_[pos / 8] |= 1U << (pos % 8);
161 // Append numLowerBits bits to lower sequence.
162 if (numLowerBits != 0) {
163 const ValueType lowerBits = value & ((ValueType(1) << numLowerBits) - 1);
164 writeBits56(lower_, size_ * numLowerBits, numLowerBits, lowerBits);
167 /* static */ if (skipQuantum != 0) {
168 while ((skipPointersSize_ + 1) * skipQuantum <= upperBits) {
169 // Store the number of preceding 1-bits.
170 skipPointers_[skipPointersSize_++] = size_;
174 /* static */ if (forwardQuantum != 0) {
175 if ((size_ + 1) % forwardQuantum == 0) {
176 const auto pos = size_ / forwardQuantum;
177 // Store the number of preceding 0-bits.
178 forwardPointers_[pos] = upperBits;
186 const MutableCompressedList& finish() const {
187 CHECK_EQ(size_, result_.size);
192 // Writes value (with len up to 56 bits) to data starting at pos-th bit.
193 static void writeBits56(unsigned char* data, size_t pos,
194 uint8_t len, uint64_t value) {
195 DCHECK_LE(uint32_t(len), 56);
196 DCHECK_EQ(0, value & ~((uint64_t(1) << len) - 1));
197 unsigned char* const ptr = data + (pos / 8);
198 uint64_t ptrv = folly::loadUnaligned<uint64_t>(ptr);
199 ptrv |= value << (pos % 8);
200 folly::storeUnaligned<uint64_t>(ptr, ptrv);
203 unsigned char* lower_ = nullptr;
204 unsigned char* upper_ = nullptr;
205 SkipValueType* skipPointers_ = nullptr;
206 SkipValueType* forwardPointers_ = nullptr;
208 ValueType lastValue_ = 0;
210 size_t skipPointersSize_ = 0;
212 MutableCompressedList result_;
215 template <class Value,
218 size_t kForwardQuantum>
219 struct EliasFanoEncoderV2<Value,
222 kForwardQuantum>::Layout {
223 static Layout fromUpperBoundAndSize(size_t upperBound, size_t size) {
224 // numLowerBits can be at most 56 because of detail::writeBits56.
225 const uint8_t numLowerBits = std::min(defaultNumLowerBits(upperBound,
229 // Upper bits are stored using unary delta encoding.
230 // For example, (3 5 5 9) will be encoded as 1000011001000_2.
231 const size_t upperSizeBits =
232 (upperBound >> numLowerBits) + // Number of 0-bits to be stored.
234 const size_t upper = (upperSizeBits + 7) / 8;
236 // *** Validity checks.
237 // Shift by numLowerBits must be valid.
238 CHECK_LT(numLowerBits, 8 * sizeof(Value));
239 CHECK_LT(size, std::numeric_limits<SkipValueType>::max());
240 CHECK_LT(upperBound >> numLowerBits,
241 std::numeric_limits<SkipValueType>::max());
243 return fromInternalSizes(numLowerBits, upper, size);
246 static Layout fromInternalSizes(uint8_t numLowerBits,
251 layout.numLowerBits = numLowerBits;
253 layout.lower = (numLowerBits * size + 7) / 8;
254 layout.upper = upper;
256 // *** Skip pointers.
257 // Store (1-indexed) position of every skipQuantum-th
258 // 0-bit in upper bits sequence.
259 /* static */ if (skipQuantum != 0) {
260 // 8 * upper is used here instead of upperSizeBits, as that is
261 // more serialization-friendly way (upperSizeBits doesn't need
262 // to be known by this function, unlike upper).
264 // '?: 1' is a workaround for false 'division by zero'
265 // compile-time error.
266 size_t numSkipPointers = (8 * upper - size) / (skipQuantum ?: 1);
267 layout.skipPointers = numSkipPointers * sizeof(SkipValueType);
270 // *** Forward pointers.
271 // Store (1-indexed) position of every forwardQuantum-th
272 // 1-bit in upper bits sequence.
273 /* static */ if (forwardQuantum != 0) {
274 size_t numForwardPointers = size / (forwardQuantum ?: 1);
275 layout.forwardPointers = numForwardPointers * sizeof(SkipValueType);
281 size_t bytes() const {
282 return lower + upper + skipPointers + forwardPointers;
285 template <class Range>
286 EliasFanoCompressedListBase<typename Range::iterator>
287 openList(Range& buf) const {
288 EliasFanoCompressedListBase<typename Range::iterator> result;
290 result.numLowerBits = numLowerBits;
291 result.data = buf.subpiece(0, bytes());
293 auto advance = [&] (size_t n) {
294 auto begin = buf.data();
299 result.skipPointers = advance(skipPointers);
300 result.forwardPointers = advance(forwardPointers);
301 result.lower = advance(lower);
302 result.upper = advance(upper);
307 MutableCompressedList allocList() const {
308 uint8_t* buf = nullptr;
309 // WARNING: Current read/write logic assumes that the 7 bytes
310 // following the last byte of lower and upper sequences are
311 // readable (stored value doesn't matter and won't be changed), so
312 // we allocate additional 7 bytes, but do not include them in size
313 // of returned value.
315 buf = static_cast<uint8_t*>(malloc(bytes() + 7));
317 folly::MutableByteRange bufRange(buf, bytes());
318 return openList(bufRange);
322 uint8_t numLowerBits = 0;
327 size_t skipPointers = 0;
328 size_t forwardPointers = 0;
333 template <class Encoder, class Instructions>
334 class UpperBitsReader {
335 typedef typename Encoder::SkipValueType SkipValueType;
337 typedef typename Encoder::ValueType ValueType;
339 explicit UpperBitsReader(const typename Encoder::CompressedList& list)
340 : forwardPointers_(list.forwardPointers),
341 skipPointers_(list.skipPointers),
347 block_ = start_ != nullptr ? folly::loadUnaligned<block_t>(start_) : 0;
354 size_t position() const { return position_; }
355 ValueType value() const { return value_; }
358 // Skip to the first non-zero block.
359 while (block_ == 0) {
360 outer_ += sizeof(block_t);
361 block_ = folly::loadUnaligned<block_t>(start_ + outer_);
365 inner_ = Instructions::ctz(block_);
366 block_ = Instructions::blsr(block_);
371 ValueType skip(size_t n) {
374 position_ += n; // n 1-bits will be read.
376 // Use forward pointer.
377 if (Encoder::forwardQuantum > 0 && n > Encoder::forwardQuantum) {
378 // Workaround to avoid 'division by zero' compile-time error.
379 constexpr size_t q = Encoder::forwardQuantum ?: 1;
381 const size_t steps = position_ / q;
383 folly::loadUnaligned<SkipValueType>(
384 forwardPointers_ + (steps - 1) * sizeof(SkipValueType));
386 reposition(dest + steps * q);
387 n = position_ + 1 - steps * q; // n is > 0.
388 // Correct inner_ will be set at the end.
392 // Find necessary block.
393 while ((cnt = Instructions::popcount(block_)) < n) {
395 outer_ += sizeof(block_t);
396 block_ = folly::loadUnaligned<block_t>(start_ + outer_);
399 // Skip to the n-th one in the block.
401 inner_ = select64<Instructions>(block_, n - 1);
402 block_ &= (block_t(-1) << inner_) << 1;
407 // Skip to the first element that is >= v and located *after* the current
408 // one (so even if current value equals v, position will be increased by 1).
409 ValueType skipToNext(ValueType v) {
410 DCHECK_GE(v, value_);
413 if (Encoder::skipQuantum > 0 && v >= value_ + Encoder::skipQuantum) {
414 // Workaround to avoid 'division by zero' compile-time error.
415 constexpr size_t q = Encoder::skipQuantum ?: 1;
417 const size_t steps = v / q;
419 folly::loadUnaligned<SkipValueType>(
420 skipPointers_ + (steps - 1) * sizeof(SkipValueType));
422 reposition(dest + q * steps);
423 position_ = dest - 1;
425 // Correct inner_ and value_ will be set during the next()
428 // NOTE: Corresponding block of lower bits sequence may be
429 // prefetched here (via __builtin_prefetch), but experiments
430 // didn't show any significant improvements.
435 size_t skip = v - (8 * outer_ - position_ - 1);
437 constexpr size_t kBitsPerBlock = 8 * sizeof(block_t);
438 while ((cnt = Instructions::popcount(~block_)) < skip) {
440 position_ += kBitsPerBlock - cnt;
441 outer_ += sizeof(block_t);
442 block_ = folly::loadUnaligned<block_t>(start_ + outer_);
446 auto inner = select64<Instructions>(~block_, skip - 1);
447 position_ += inner - skip + 1;
448 block_ &= block_t(-1) << inner;
455 ValueType jump(size_t n) {
456 if (Encoder::forwardQuantum == 0 || n <= Encoder::forwardQuantum) {
459 position_ = -1; // Avoid reading the head, skip() will reposition.
464 ValueType jumpToNext(ValueType v) {
465 if (Encoder::skipQuantum == 0 || v < Encoder::skipQuantum) {
468 value_ = 0; // Avoid reading the head, skipToNext() will reposition.
470 return skipToNext(v);
473 ValueType previousValue() const {
474 DCHECK_NE(position(), -1);
475 DCHECK_GT(position(), 0);
477 size_t outer = outer_;
478 block_t block = folly::loadUnaligned<block_t>(start_ + outer);
479 block &= (block_t(1) << inner_) - 1;
481 while (UNLIKELY(block == 0)) {
482 DCHECK_GE(outer, sizeof(block_t));
483 outer -= sizeof(block_t);
484 block = folly::loadUnaligned<block_t>(start_ + outer);
487 auto inner = 8 * sizeof(block_t) - 1 - Instructions::clz(block);
488 return static_cast<ValueType>(8 * outer + inner - (position_ - 1));
491 void setDone(size_t endPos) {
496 ValueType setValue() {
497 value_ = static_cast<ValueType>(8 * outer_ + inner_ - position_);
501 void reposition(size_t dest) {
503 block_ = folly::loadUnaligned<block_t>(start_ + outer_);
504 block_ &= ~((block_t(1) << (dest % 8)) - 1);
507 typedef uint64_t block_t;
508 const unsigned char* const forwardPointers_;
509 const unsigned char* const skipPointers_;
510 const unsigned char* const start_;
512 size_t outer_; // Outer offset: number of consumed bytes in upper.
513 size_t inner_; // Inner offset: (bit) position in current block.
514 size_t position_; // Index of current value (= #reads - 1).
518 } // namespace detail
520 // If kUnchecked = true the caller must guarantee that all the
521 // operations return valid elements, i.e., they would never return
523 template <class Encoder,
524 class Instructions = instructions::Default,
525 bool kUnchecked = false>
526 class EliasFanoReader {
528 typedef Encoder EncoderType;
529 typedef typename Encoder::ValueType ValueType;
531 explicit EliasFanoReader(const typename Encoder::CompressedList& list)
535 lowerMask_((ValueType(1) << list.numLowerBits) - 1),
536 numLowerBits_(list.numLowerBits) {
537 DCHECK(Instructions::supported());
538 // To avoid extra branching during skipTo() while reading
539 // upper sequence we need to know the last element.
540 // If kUnchecked == true, we do not check that skipTo() is called
541 // within the bounds, so we can avoid initializing lastValue_.
542 if (kUnchecked || UNLIKELY(list.size == 0)) {
546 ValueType lastUpperValue = 8 * list.upperSize() - size_;
547 auto it = list.upper + list.upperSize() - 1;
549 lastUpperValue -= 8 - folly::findLastSet(*it);
550 lastValue_ = readLowerPart(size_ - 1) | (lastUpperValue << numLowerBits_);
555 value_ = kInvalidValue;
559 if (!kUnchecked && UNLIKELY(position() + 1 >= size_)) {
563 value_ = readLowerPart(upper_.position()) |
564 (upper_.value() << numLowerBits_);
568 bool skip(size_t n) {
571 if (kUnchecked || LIKELY(position() + n < size_)) {
572 if (LIKELY(n < kLinearScanThreshold)) {
573 for (size_t i = 0; i < n; ++i) upper_.next();
577 value_ = readLowerPart(upper_.position()) |
578 (upper_.value() << numLowerBits_);
585 bool skipTo(ValueType value) {
586 // Also works when value_ == kInvalidValue.
587 if (value != kInvalidValue) { DCHECK_GE(value + 1, value_ + 1); }
589 if (!kUnchecked && value > lastValue_) {
591 } else if (value == value_) {
595 size_t upperValue = (value >> numLowerBits_);
596 size_t upperSkip = upperValue - upper_.value();
597 // The average density of ones in upper bits is 1/2.
598 // LIKELY here seems to make things worse, even for small skips.
599 if (upperSkip < 2 * kLinearScanThreshold) {
602 } while (UNLIKELY(upper_.value() < upperValue));
604 upper_.skipToNext(upperValue);
611 bool jump(size_t n) {
612 if (LIKELY(n < size_)) { // Also checks that n != -1.
613 value_ = readLowerPart(n) | (upper_.jump(n + 1) << numLowerBits_);
619 bool jumpTo(ValueType value) {
620 if (!kUnchecked && value > lastValue_) {
624 upper_.jumpToNext(value >> numLowerBits_);
629 ValueType previousValue() const {
630 DCHECK_GT(position(), 0);
631 DCHECK_LT(position(), size());
632 return readLowerPart(upper_.position() - 1) |
633 (upper_.previousValue() << numLowerBits_);
636 size_t size() const { return size_; }
639 return position() < size(); // Also checks that position() != -1.
642 size_t position() const { return upper_.position(); }
643 ValueType value() const {
649 constexpr static ValueType kInvalidValue =
650 std::numeric_limits<ValueType>::max(); // Must hold kInvalidValue + 1 == 0.
653 value_ = kInvalidValue;
654 upper_.setDone(size_);
658 ValueType readLowerPart(size_t i) const {
660 const size_t pos = i * numLowerBits_;
661 const unsigned char* ptr = lower_ + (pos / 8);
662 const uint64_t ptrv = folly::loadUnaligned<uint64_t>(ptr);
663 return lowerMask_ & (ptrv >> (pos % 8));
666 void iterateTo(ValueType value) {
668 value_ = readLowerPart(upper_.position()) |
669 (upper_.value() << numLowerBits_);
670 if (LIKELY(value_ >= value)) break;
675 constexpr static size_t kLinearScanThreshold = 8;
678 const uint8_t* lower_;
679 detail::UpperBitsReader<Encoder, Instructions> upper_;
680 const ValueType lowerMask_;
681 ValueType value_ = kInvalidValue;
682 ValueType lastValue_;
683 uint8_t numLowerBits_;