diff options
Diffstat (limited to 'third_party/highway/hwy/contrib/sort/vqsort-inl.h')
| -rw-r--r-- | third_party/highway/hwy/contrib/sort/vqsort-inl.h | 1484 |
1 files changed, 1484 insertions, 0 deletions
diff --git a/third_party/highway/hwy/contrib/sort/vqsort-inl.h b/third_party/highway/hwy/contrib/sort/vqsort-inl.h new file mode 100644 index 0000000000..edebe4af11 --- /dev/null +++ b/third_party/highway/hwy/contrib/sort/vqsort-inl.h @@ -0,0 +1,1484 @@ +// Copyright 2021 Google LLC +// SPDX-License-Identifier: Apache-2.0 +// +// 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. + +// Normal include guard for target-independent parts +#ifndef HIGHWAY_HWY_CONTRIB_SORT_VQSORT_INL_H_ +#define HIGHWAY_HWY_CONTRIB_SORT_VQSORT_INL_H_ + +#ifndef VQSORT_PRINT +#define VQSORT_PRINT 0 +#endif + +// Makes it harder for adversaries to predict our sampling locations, at the +// cost of 1-2% increased runtime. +#ifndef VQSORT_SECURE_RNG +#define VQSORT_SECURE_RNG 0 +#endif + +#if VQSORT_SECURE_RNG +#include "third_party/absl/random/random.h" +#endif + +#include <stdio.h> // unconditional #include so we can use if(VQSORT_PRINT). +#include <string.h> // memcpy + +#include "hwy/cache_control.h" // Prefetch +#include "hwy/contrib/sort/vqsort.h" // Fill24Bytes + +#if HWY_IS_MSAN +#include <sanitizer/msan_interface.h> +#endif + +#endif // HIGHWAY_HWY_CONTRIB_SORT_VQSORT_INL_H_ + +// Per-target +#if defined(HIGHWAY_HWY_CONTRIB_SORT_VQSORT_TOGGLE) == \ + defined(HWY_TARGET_TOGGLE) +#ifdef HIGHWAY_HWY_CONTRIB_SORT_VQSORT_TOGGLE +#undef HIGHWAY_HWY_CONTRIB_SORT_VQSORT_TOGGLE +#else +#define HIGHWAY_HWY_CONTRIB_SORT_VQSORT_TOGGLE +#endif + +#if VQSORT_PRINT +#include "hwy/print-inl.h" +#endif + +#include "hwy/contrib/sort/shared-inl.h" +#include "hwy/contrib/sort/sorting_networks-inl.h" +// Placeholder for internal instrumentation. Do not remove. +#include "hwy/highway.h" + +HWY_BEFORE_NAMESPACE(); +namespace hwy { +namespace HWY_NAMESPACE { +namespace detail { + +using Constants = hwy::SortConstants; + +// Wrappers to avoid #if in user code (interferes with code folding) + +HWY_INLINE void UnpoisonIfMemorySanitizer(void* p, size_t bytes) { +#if HWY_IS_MSAN + __msan_unpoison(p, bytes); +#else + (void)p; + (void)bytes; +#endif +} + +template <class D> +HWY_INLINE void MaybePrintVector(D d, const char* label, Vec<D> v, + size_t start = 0, size_t max_lanes = 16) { +#if VQSORT_PRINT >= 2 // Print is only defined #if + Print(d, label, v, start, max_lanes); +#else + (void)d; + (void)label; + (void)v; + (void)start; + (void)max_lanes; +#endif +} + +// ------------------------------ HeapSort + +template <class Traits, typename T> +void SiftDown(Traits st, T* HWY_RESTRICT lanes, const size_t num_lanes, + size_t start) { + constexpr size_t N1 = st.LanesPerKey(); + const FixedTag<T, N1> d; + + while (start < num_lanes) { + const size_t left = 2 * start + N1; + const size_t right = 2 * start + 2 * N1; + if (left >= num_lanes) break; + size_t idx_larger = start; + const auto key_j = st.SetKey(d, lanes + start); + if (AllTrue(d, st.Compare(d, key_j, st.SetKey(d, lanes + left)))) { + idx_larger = left; + } + if (right < num_lanes && + AllTrue(d, st.Compare(d, st.SetKey(d, lanes + idx_larger), + st.SetKey(d, lanes + right)))) { + idx_larger = right; + } + if (idx_larger == start) break; + st.Swap(lanes + start, lanes + idx_larger); + start = idx_larger; + } +} + +// Heapsort: O(1) space, O(N*logN) worst-case comparisons. +// Based on LLVM sanitizer_common.h, licensed under Apache-2.0. +template <class Traits, typename T> +void HeapSort(Traits st, T* HWY_RESTRICT lanes, const size_t num_lanes) { + constexpr size_t N1 = st.LanesPerKey(); + + if (num_lanes < 2 * N1) return; + + // Build heap. + for (size_t i = ((num_lanes - N1) / N1 / 2) * N1; i != (~N1 + 1); i -= N1) { + SiftDown(st, lanes, num_lanes, i); + } + + for (size_t i = num_lanes - N1; i != 0; i -= N1) { + // Swap root with last + st.Swap(lanes + 0, lanes + i); + + // Sift down the new root. + SiftDown(st, lanes, i, 0); + } +} + +#if VQSORT_ENABLED || HWY_IDE + +// ------------------------------ BaseCase + +// Sorts `keys` within the range [0, num) via sorting network. +template <class D, class Traits, typename T> +HWY_INLINE void BaseCase(D d, Traits st, T* HWY_RESTRICT keys, + T* HWY_RESTRICT keys_end, size_t num, + T* HWY_RESTRICT buf) { + const size_t N = Lanes(d); + using V = decltype(Zero(d)); + + // _Nonzero32 requires num - 1 != 0. + if (HWY_UNLIKELY(num <= 1)) return; + + // Reshape into a matrix with kMaxRows rows, and columns limited by the + // 1D `num`, which is upper-bounded by the vector width (see BaseCaseNum). + const size_t num_pow2 = size_t{1} + << (32 - Num0BitsAboveMS1Bit_Nonzero32( + static_cast<uint32_t>(num - 1))); + HWY_DASSERT(num <= num_pow2 && num_pow2 <= Constants::BaseCaseNum(N)); + const size_t cols = + HWY_MAX(st.LanesPerKey(), num_pow2 >> Constants::kMaxRowsLog2); + HWY_DASSERT(cols <= N); + + // We can avoid padding and load/store directly to `keys` after checking the + // original input array has enough space. Except at the right border, it's OK + // to sort more than the current sub-array. Even if we sort across a previous + // partition point, we know that keys will not migrate across it. However, we + // must use the maximum size of the sorting network, because the StoreU of its + // last vector would otherwise write invalid data starting at kMaxRows * cols. + const size_t N_sn = Lanes(CappedTag<T, Constants::kMaxCols>()); + if (HWY_LIKELY(keys + N_sn * Constants::kMaxRows <= keys_end)) { + SortingNetwork(st, keys, N_sn); + return; + } + + // Copy `keys` to `buf`. + size_t i; + for (i = 0; i + N <= num; i += N) { + Store(LoadU(d, keys + i), d, buf + i); + } + SafeCopyN(num - i, d, keys + i, buf + i); + i = num; + + // Fill with padding - last in sort order, not copied to keys. + const V kPadding = st.LastValue(d); + // Initialize an extra vector because SortingNetwork loads full vectors, + // which may exceed cols*kMaxRows. + for (; i < (cols * Constants::kMaxRows + N); i += N) { + StoreU(kPadding, d, buf + i); + } + + SortingNetwork(st, buf, cols); + + for (i = 0; i + N <= num; i += N) { + StoreU(Load(d, buf + i), d, keys + i); + } + SafeCopyN(num - i, d, buf + i, keys + i); +} + +// ------------------------------ Partition + +// Consumes from `keys` until a multiple of kUnroll*N remains. +// Temporarily stores the right side into `buf`, then moves behind `num`. +// Returns the number of keys consumed from the left side. +template <class D, class Traits, class T> +HWY_INLINE size_t PartitionToMultipleOfUnroll(D d, Traits st, + T* HWY_RESTRICT keys, size_t& num, + const Vec<D> pivot, + T* HWY_RESTRICT buf) { + constexpr size_t kUnroll = Constants::kPartitionUnroll; + const size_t N = Lanes(d); + size_t readL = 0; + T* HWY_RESTRICT posL = keys; + size_t bufR = 0; + // Partition requires both a multiple of kUnroll*N and at least + // 2*kUnroll*N for the initial loads. If less, consume all here. + const size_t num_rem = + (num < 2 * kUnroll * N) ? num : (num & (kUnroll * N - 1)); + size_t i = 0; + for (; i + N <= num_rem; i += N) { + const Vec<D> vL = LoadU(d, keys + readL); + readL += N; + + const auto comp = st.Compare(d, pivot, vL); + posL += CompressBlendedStore(vL, Not(comp), d, posL); + bufR += CompressStore(vL, comp, d, buf + bufR); + } + // Last iteration: only use valid lanes. + if (HWY_LIKELY(i != num_rem)) { + const auto mask = FirstN(d, num_rem - i); + const Vec<D> vL = LoadU(d, keys + readL); + + const auto comp = st.Compare(d, pivot, vL); + posL += CompressBlendedStore(vL, AndNot(comp, mask), d, posL); + bufR += CompressStore(vL, And(comp, mask), d, buf + bufR); + } + + // MSAN seems not to understand CompressStore. buf[0, bufR) are valid. + UnpoisonIfMemorySanitizer(buf, bufR * sizeof(T)); + + // Everything we loaded was put into buf, or behind the current `posL`, after + // which there is space for bufR items. First move items from `keys + num` to + // `posL` to free up space, then copy `buf` into the vacated `keys + num`. + // A loop with masked loads from `buf` is insufficient - we would also need to + // mask from `keys + num`. Combining a loop with memcpy for the remainders is + // slower than just memcpy, so we use that for simplicity. + num -= bufR; + memcpy(posL, keys + num, bufR * sizeof(T)); + memcpy(keys + num, buf, bufR * sizeof(T)); + return static_cast<size_t>(posL - keys); // caller will shrink num by this. +} + +template <class V> +V OrXor(const V o, const V x1, const V x2) { + // TODO(janwas): add op so we can benefit from AVX-512 ternlog? + return Or(o, Xor(x1, x2)); +} + +// Note: we could track the OrXor of v and pivot to see if the entire left +// partition is equal, but that happens rarely and thus is a net loss. +template <class D, class Traits, typename T> +HWY_INLINE void StoreLeftRight(D d, Traits st, const Vec<D> v, + const Vec<D> pivot, T* HWY_RESTRICT keys, + size_t& writeL, size_t& remaining) { + const size_t N = Lanes(d); + + const auto comp = st.Compare(d, pivot, v); + + remaining -= N; + if (hwy::HWY_NAMESPACE::CompressIsPartition<T>::value || + (HWY_MAX_BYTES == 16 && st.Is128())) { + // Non-native Compress (e.g. AVX2): we are able to partition a vector using + // a single Compress+two StoreU instead of two Compress[Blended]Store. The + // latter are more expensive. Because we store entire vectors, the contents + // between the updated writeL and writeR are ignored and will be overwritten + // by subsequent calls. This works because writeL and writeR are at least + // two vectors apart. + const auto lr = st.CompressKeys(v, comp); + const size_t num_left = N - CountTrue(d, comp); + StoreU(lr, d, keys + writeL); + // Now write the right-side elements (if any), such that the previous writeR + // is one past the end of the newly written right elements, then advance. + StoreU(lr, d, keys + remaining + writeL); + writeL += num_left; + } else { + // Native Compress[Store] (e.g. AVX3), which only keep the left or right + // side, not both, hence we require two calls. + const size_t num_left = CompressStore(v, Not(comp), d, keys + writeL); + writeL += num_left; + + (void)CompressBlendedStore(v, comp, d, keys + remaining + writeL); + } +} + +template <class D, class Traits, typename T> +HWY_INLINE void StoreLeftRight4(D d, Traits st, const Vec<D> v0, + const Vec<D> v1, const Vec<D> v2, + const Vec<D> v3, const Vec<D> pivot, + T* HWY_RESTRICT keys, size_t& writeL, + size_t& remaining) { + StoreLeftRight(d, st, v0, pivot, keys, writeL, remaining); + StoreLeftRight(d, st, v1, pivot, keys, writeL, remaining); + StoreLeftRight(d, st, v2, pivot, keys, writeL, remaining); + StoreLeftRight(d, st, v3, pivot, keys, writeL, remaining); +} + +// Moves "<= pivot" keys to the front, and others to the back. pivot is +// broadcasted. Time-critical! +// +// Aligned loads do not seem to be worthwhile (not bottlenecked by load ports). +template <class D, class Traits, typename T> +HWY_INLINE size_t Partition(D d, Traits st, T* HWY_RESTRICT keys, size_t num, + const Vec<D> pivot, T* HWY_RESTRICT buf) { + using V = decltype(Zero(d)); + const size_t N = Lanes(d); + + // StoreLeftRight will CompressBlendedStore ending at `writeR`. Unless all + // lanes happen to be in the right-side partition, this will overrun `keys`, + // which triggers asan errors. Avoid by special-casing the last vector. + HWY_DASSERT(num > 2 * N); // ensured by HandleSpecialCases + num -= N; + size_t last = num; + const V vlast = LoadU(d, keys + last); + + const size_t consumedL = + PartitionToMultipleOfUnroll(d, st, keys, num, pivot, buf); + keys += consumedL; + last -= consumedL; + num -= consumedL; + constexpr size_t kUnroll = Constants::kPartitionUnroll; + + // Partition splits the vector into 3 sections, left to right: Elements + // smaller or equal to the pivot, unpartitioned elements and elements larger + // than the pivot. To write elements unconditionally on the loop body without + // overwriting existing data, we maintain two regions of the loop where all + // elements have been copied elsewhere (e.g. vector registers.). I call these + // bufferL and bufferR, for left and right respectively. + // + // These regions are tracked by the indices (writeL, writeR, left, right) as + // presented in the diagram below. + // + // writeL writeR + // \/ \/ + // | <= pivot | bufferL | unpartitioned | bufferR | > pivot | + // \/ \/ + // left right + // + // In the main loop body below we choose a side, load some elements out of the + // vector and move either `left` or `right`. Next we call into StoreLeftRight + // to partition the data, and the partitioned elements will be written either + // to writeR or writeL and the corresponding index will be moved accordingly. + // + // Note that writeR is not explicitly tracked as an optimization for platforms + // with conditional operations. Instead we track writeL and the number of + // elements left to process (`remaining`). From the diagram above we can see + // that: + // writeR - writeL = remaining => writeR = remaining + writeL + // + // Tracking `remaining` is advantageous because each iteration reduces the + // number of unpartitioned elements by a fixed amount, so we can compute + // `remaining` without data dependencies. + // + size_t writeL = 0; + size_t remaining = num; + + const T* HWY_RESTRICT readL = keys; + const T* HWY_RESTRICT readR = keys + num; + // Cannot load if there were fewer than 2 * kUnroll * N. + if (HWY_LIKELY(num != 0)) { + HWY_DASSERT(num >= 2 * kUnroll * N); + HWY_DASSERT((num & (kUnroll * N - 1)) == 0); + + // Make space for writing in-place by reading from readL/readR. + const V vL0 = LoadU(d, readL + 0 * N); + const V vL1 = LoadU(d, readL + 1 * N); + const V vL2 = LoadU(d, readL + 2 * N); + const V vL3 = LoadU(d, readL + 3 * N); + readL += kUnroll * N; + readR -= kUnroll * N; + const V vR0 = LoadU(d, readR + 0 * N); + const V vR1 = LoadU(d, readR + 1 * N); + const V vR2 = LoadU(d, readR + 2 * N); + const V vR3 = LoadU(d, readR + 3 * N); + + // readL/readR changed above, so check again before the loop. + while (readL != readR) { + V v0, v1, v2, v3; + + // Data-dependent but branching is faster than forcing branch-free. + const size_t capacityL = + static_cast<size_t>((readL - keys) - static_cast<ptrdiff_t>(writeL)); + HWY_DASSERT(capacityL <= num); // >= 0 + // Load data from the end of the vector with less data (front or back). + // The next paragraphs explain how this works. + // + // let block_size = (kUnroll * N) + // On the loop prelude we load block_size elements from the front of the + // vector and an additional block_size elements from the back. On each + // iteration k elements are written to the front of the vector and + // (block_size - k) to the back. + // + // This creates a loop invariant where the capacity on the front + // (capacityL) and on the back (capacityR) always add to 2 * block_size. + // In other words: + // capacityL + capacityR = 2 * block_size + // capacityR = 2 * block_size - capacityL + // + // This means that: + // capacityL < capacityR <=> + // capacityL < 2 * block_size - capacityL <=> + // 2 * capacityL < 2 * block_size <=> + // capacityL < block_size + // + // Thus the check on the next line is equivalent to capacityL > capacityR. + // + if (kUnroll * N < capacityL) { + readR -= kUnroll * N; + v0 = LoadU(d, readR + 0 * N); + v1 = LoadU(d, readR + 1 * N); + v2 = LoadU(d, readR + 2 * N); + v3 = LoadU(d, readR + 3 * N); + hwy::Prefetch(readR - 3 * kUnroll * N); + } else { + v0 = LoadU(d, readL + 0 * N); + v1 = LoadU(d, readL + 1 * N); + v2 = LoadU(d, readL + 2 * N); + v3 = LoadU(d, readL + 3 * N); + readL += kUnroll * N; + hwy::Prefetch(readL + 3 * kUnroll * N); + } + + StoreLeftRight4(d, st, v0, v1, v2, v3, pivot, keys, writeL, remaining); + } + + // Now finish writing the saved vectors to the middle. + StoreLeftRight4(d, st, vL0, vL1, vL2, vL3, pivot, keys, writeL, remaining); + StoreLeftRight4(d, st, vR0, vR1, vR2, vR3, pivot, keys, writeL, remaining); + } + + // We have partitioned [left, right) such that writeL is the boundary. + HWY_DASSERT(remaining == 0); + // Make space for inserting vlast: move up to N of the first right-side keys + // into the unused space starting at last. If we have fewer, ensure they are + // the last items in that vector by subtracting from the *load* address, + // which is safe because we have at least two vectors (checked above). + const size_t totalR = last - writeL; + const size_t startR = totalR < N ? writeL + totalR - N : writeL; + StoreU(LoadU(d, keys + startR), d, keys + last); + + // Partition vlast: write L, then R, into the single-vector gap at writeL. + const auto comp = st.Compare(d, pivot, vlast); + writeL += CompressBlendedStore(vlast, Not(comp), d, keys + writeL); + (void)CompressBlendedStore(vlast, comp, d, keys + writeL); + + return consumedL + writeL; +} + +// Returns true and partitions if [keys, keys + num) contains only {valueL, +// valueR}. Otherwise, sets third to the first differing value; keys may have +// been reordered and a regular Partition is still necessary. +// Called from two locations, hence NOINLINE. +template <class D, class Traits, typename T> +HWY_NOINLINE bool MaybePartitionTwoValue(D d, Traits st, T* HWY_RESTRICT keys, + size_t num, const Vec<D> valueL, + const Vec<D> valueR, Vec<D>& third, + T* HWY_RESTRICT buf) { + const size_t N = Lanes(d); + + size_t i = 0; + size_t writeL = 0; + + // As long as all lanes are equal to L or R, we can overwrite with valueL. + // This is faster than first counting, then backtracking to fill L and R. + for (; i + N <= num; i += N) { + const Vec<D> v = LoadU(d, keys + i); + // It is not clear how to apply OrXor here - that can check if *both* + // comparisons are true, but here we want *either*. Comparing the unsigned + // min of differences to zero works, but is expensive for u64 prior to AVX3. + const Mask<D> eqL = st.EqualKeys(d, v, valueL); + const Mask<D> eqR = st.EqualKeys(d, v, valueR); + // At least one other value present; will require a regular partition. + // On AVX-512, Or + AllTrue are folded into a single kortest if we are + // careful with the FindKnownFirstTrue argument, see below. + if (HWY_UNLIKELY(!AllTrue(d, Or(eqL, eqR)))) { + // If we repeat Or(eqL, eqR) here, the compiler will hoist it into the + // loop, which is a pessimization because this if-true branch is cold. + // We can defeat this via Not(Xor), which is equivalent because eqL and + // eqR cannot be true at the same time. Can we elide the additional Not? + // FindFirstFalse instructions are generally unavailable, but we can + // fuse Not and Xor/Or into one ExclusiveNeither. + const size_t lane = FindKnownFirstTrue(d, ExclusiveNeither(eqL, eqR)); + third = st.SetKey(d, keys + i + lane); + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "found 3rd value at vec %zu; writeL %zu\n", i, writeL); + } + // 'Undo' what we did by filling the remainder of what we read with R. + for (; writeL + N <= i; writeL += N) { + StoreU(valueR, d, keys + writeL); + } + BlendedStore(valueR, FirstN(d, i - writeL), d, keys + writeL); + return false; + } + StoreU(valueL, d, keys + writeL); + writeL += CountTrue(d, eqL); + } + + // Final vector, masked comparison (no effect if i == num) + const size_t remaining = num - i; + SafeCopyN(remaining, d, keys + i, buf); + const Vec<D> v = Load(d, buf); + const Mask<D> valid = FirstN(d, remaining); + const Mask<D> eqL = And(st.EqualKeys(d, v, valueL), valid); + const Mask<D> eqR = st.EqualKeys(d, v, valueR); + // Invalid lanes are considered equal. + const Mask<D> eq = Or(Or(eqL, eqR), Not(valid)); + // At least one other value present; will require a regular partition. + if (HWY_UNLIKELY(!AllTrue(d, eq))) { + const size_t lane = FindKnownFirstTrue(d, Not(eq)); + third = st.SetKey(d, keys + i + lane); + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "found 3rd value at partial vec %zu; writeL %zu\n", i, + writeL); + } + // 'Undo' what we did by filling the remainder of what we read with R. + for (; writeL + N <= i; writeL += N) { + StoreU(valueR, d, keys + writeL); + } + BlendedStore(valueR, FirstN(d, i - writeL), d, keys + writeL); + return false; + } + BlendedStore(valueL, valid, d, keys + writeL); + writeL += CountTrue(d, eqL); + + // Fill right side + i = writeL; + for (; i + N <= num; i += N) { + StoreU(valueR, d, keys + i); + } + BlendedStore(valueR, FirstN(d, num - i), d, keys + i); + + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "Successful MaybePartitionTwoValue\n"); + } + return true; +} + +// Same as above, except that the pivot equals valueR, so scan right to left. +template <class D, class Traits, typename T> +HWY_INLINE bool MaybePartitionTwoValueR(D d, Traits st, T* HWY_RESTRICT keys, + size_t num, const Vec<D> valueL, + const Vec<D> valueR, Vec<D>& third, + T* HWY_RESTRICT buf) { + const size_t N = Lanes(d); + + HWY_DASSERT(num >= N); + size_t pos = num - N; // current read/write position + size_t countR = 0; // number of valueR found + + // For whole vectors, in descending address order: as long as all lanes are + // equal to L or R, overwrite with valueR. This is faster than counting, then + // filling both L and R. Loop terminates after unsigned wraparound. + for (; pos < num; pos -= N) { + const Vec<D> v = LoadU(d, keys + pos); + // It is not clear how to apply OrXor here - that can check if *both* + // comparisons are true, but here we want *either*. Comparing the unsigned + // min of differences to zero works, but is expensive for u64 prior to AVX3. + const Mask<D> eqL = st.EqualKeys(d, v, valueL); + const Mask<D> eqR = st.EqualKeys(d, v, valueR); + // If there is a third value, stop and undo what we've done. On AVX-512, + // Or + AllTrue are folded into a single kortest, but only if we are + // careful with the FindKnownFirstTrue argument - see prior comment on that. + if (HWY_UNLIKELY(!AllTrue(d, Or(eqL, eqR)))) { + const size_t lane = FindKnownFirstTrue(d, ExclusiveNeither(eqL, eqR)); + third = st.SetKey(d, keys + pos + lane); + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "found 3rd value at vec %zu; countR %zu\n", pos, + countR); + MaybePrintVector(d, "third", third, 0, st.LanesPerKey()); + } + pos += N; // rewind: we haven't yet committed changes in this iteration. + // We have filled [pos, num) with R, but only countR of them should have + // been written. Rewrite [pos, num - countR) to L. + HWY_DASSERT(countR <= num - pos); + const size_t endL = num - countR; + for (; pos + N <= endL; pos += N) { + StoreU(valueL, d, keys + pos); + } + BlendedStore(valueL, FirstN(d, endL - pos), d, keys + pos); + return false; + } + StoreU(valueR, d, keys + pos); + countR += CountTrue(d, eqR); + } + + // Final partial (or empty) vector, masked comparison. + const size_t remaining = pos + N; + HWY_DASSERT(remaining <= N); + const Vec<D> v = LoadU(d, keys); // Safe because num >= N. + const Mask<D> valid = FirstN(d, remaining); + const Mask<D> eqL = st.EqualKeys(d, v, valueL); + const Mask<D> eqR = And(st.EqualKeys(d, v, valueR), valid); + // Invalid lanes are considered equal. + const Mask<D> eq = Or(Or(eqL, eqR), Not(valid)); + // At least one other value present; will require a regular partition. + if (HWY_UNLIKELY(!AllTrue(d, eq))) { + const size_t lane = FindKnownFirstTrue(d, Not(eq)); + third = st.SetKey(d, keys + lane); + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "found 3rd value at partial vec %zu; writeR %zu\n", pos, + countR); + MaybePrintVector(d, "third", third, 0, st.LanesPerKey()); + } + pos += N; // rewind: we haven't yet committed changes in this iteration. + // We have filled [pos, num) with R, but only countR of them should have + // been written. Rewrite [pos, num - countR) to L. + HWY_DASSERT(countR <= num - pos); + const size_t endL = num - countR; + for (; pos + N <= endL; pos += N) { + StoreU(valueL, d, keys + pos); + } + BlendedStore(valueL, FirstN(d, endL - pos), d, keys + pos); + return false; + } + const size_t lastR = CountTrue(d, eqR); + countR += lastR; + + // First finish writing valueR - [0, N) lanes were not yet written. + StoreU(valueR, d, keys); // Safe because num >= N. + + // Fill left side (ascending order for clarity) + const size_t endL = num - countR; + size_t i = 0; + for (; i + N <= endL; i += N) { + StoreU(valueL, d, keys + i); + } + Store(valueL, d, buf); + SafeCopyN(endL - i, d, buf, keys + i); // avoids asan overrun + + if (VQSORT_PRINT >= 2) { + fprintf(stderr, + "MaybePartitionTwoValueR countR %zu pos %zu i %zu endL %zu\n", + countR, pos, i, endL); + } + + return true; +} + +// `idx_second` is `first_mismatch` from `AllEqual` and thus the index of the +// second key. This is the first path into `MaybePartitionTwoValue`, called +// when all samples are equal. Returns false if there are at least a third +// value and sets `third`. Otherwise, partitions the array and returns true. +template <class D, class Traits, typename T> +HWY_INLINE bool PartitionIfTwoKeys(D d, Traits st, const Vec<D> pivot, + T* HWY_RESTRICT keys, size_t num, + const size_t idx_second, const Vec<D> second, + Vec<D>& third, T* HWY_RESTRICT buf) { + // True if second comes before pivot. + const bool is_pivotR = AllFalse(d, st.Compare(d, pivot, second)); + if (VQSORT_PRINT >= 1) { + fprintf(stderr, "Samples all equal, diff at %zu, isPivotR %d\n", idx_second, + is_pivotR); + } + HWY_DASSERT(AllFalse(d, st.EqualKeys(d, second, pivot))); + + // If pivot is R, we scan backwards over the entire array. Otherwise, + // we already scanned up to idx_second and can leave those in place. + return is_pivotR ? MaybePartitionTwoValueR(d, st, keys, num, second, pivot, + third, buf) + : MaybePartitionTwoValue(d, st, keys + idx_second, + num - idx_second, pivot, second, + third, buf); +} + +// Second path into `MaybePartitionTwoValue`, called when not all samples are +// equal. `samples` is sorted. +template <class D, class Traits, typename T> +HWY_INLINE bool PartitionIfTwoSamples(D d, Traits st, T* HWY_RESTRICT keys, + size_t num, T* HWY_RESTRICT samples) { + constexpr size_t kSampleLanes = 3 * 64 / sizeof(T); + constexpr size_t N1 = st.LanesPerKey(); + const Vec<D> valueL = st.SetKey(d, samples); + const Vec<D> valueR = st.SetKey(d, samples + kSampleLanes - N1); + HWY_DASSERT(AllTrue(d, st.Compare(d, valueL, valueR))); + HWY_DASSERT(AllFalse(d, st.EqualKeys(d, valueL, valueR))); + const Vec<D> prev = st.PrevValue(d, valueR); + // If the sample has more than two values, then the keys have at least that + // many, and thus this special case is inapplicable. + if (HWY_UNLIKELY(!AllTrue(d, st.EqualKeys(d, valueL, prev)))) { + return false; + } + + // Must not overwrite samples because if this returns false, caller wants to + // read the original samples again. + T* HWY_RESTRICT buf = samples + kSampleLanes; + Vec<D> third; // unused + return MaybePartitionTwoValue(d, st, keys, num, valueL, valueR, third, buf); +} + +// ------------------------------ Pivot sampling + +template <class Traits, class V> +HWY_INLINE V MedianOf3(Traits st, V v0, V v1, V v2) { + const DFromV<V> d; + // Slightly faster for 128-bit, apparently because not serially dependent. + if (st.Is128()) { + // Median = XOR-sum 'minus' the first and last. Calling First twice is + // slightly faster than Compare + 2 IfThenElse or even IfThenElse + XOR. + const auto sum = Xor(Xor(v0, v1), v2); + const auto first = st.First(d, st.First(d, v0, v1), v2); + const auto last = st.Last(d, st.Last(d, v0, v1), v2); + return Xor(Xor(sum, first), last); + } + st.Sort2(d, v0, v2); + v1 = st.Last(d, v0, v1); + v1 = st.First(d, v1, v2); + return v1; +} + +#if VQSORT_SECURE_RNG +using Generator = absl::BitGen; +#else +// Based on https://github.com/numpy/numpy/issues/16313#issuecomment-641897028 +#pragma pack(push, 1) +class Generator { + public: + Generator(const void* heap, size_t num) { + Sorter::Fill24Bytes(heap, num, &a_); + k_ = 1; // stream index: must be odd + } + + explicit Generator(uint64_t seed) { + a_ = b_ = w_ = seed; + k_ = 1; + } + + uint64_t operator()() { + const uint64_t b = b_; + w_ += k_; + const uint64_t next = a_ ^ w_; + a_ = (b + (b << 3)) ^ (b >> 11); + const uint64_t rot = (b << 24) | (b >> 40); + b_ = rot + next; + return next; + } + + private: + uint64_t a_; + uint64_t b_; + uint64_t w_; + uint64_t k_; // increment +}; +#pragma pack(pop) + +#endif // !VQSORT_SECURE_RNG + +// Returns slightly biased random index of a chunk in [0, num_chunks). +// See https://www.pcg-random.org/posts/bounded-rands.html. +HWY_INLINE size_t RandomChunkIndex(const uint32_t num_chunks, uint32_t bits) { + const uint64_t chunk_index = (static_cast<uint64_t>(bits) * num_chunks) >> 32; + HWY_DASSERT(chunk_index < num_chunks); + return static_cast<size_t>(chunk_index); +} + +// Writes samples from `keys[0, num)` into `buf`. +template <class D, class Traits, typename T> +HWY_INLINE void DrawSamples(D d, Traits st, T* HWY_RESTRICT keys, size_t num, + T* HWY_RESTRICT buf, Generator& rng) { + using V = decltype(Zero(d)); + const size_t N = Lanes(d); + + // Power of two + constexpr size_t kLanesPerChunk = Constants::LanesPerChunk(sizeof(T)); + + // Align start of keys to chunks. We always have at least 2 chunks because the + // base case would have handled anything up to 16 vectors, i.e. >= 4 chunks. + HWY_DASSERT(num >= 2 * kLanesPerChunk); + const size_t misalign = + (reinterpret_cast<uintptr_t>(keys) / sizeof(T)) & (kLanesPerChunk - 1); + if (misalign != 0) { + const size_t consume = kLanesPerChunk - misalign; + keys += consume; + num -= consume; + } + + // Generate enough random bits for 9 uint32 + uint64_t* bits64 = reinterpret_cast<uint64_t*>(buf); + for (size_t i = 0; i < 5; ++i) { + bits64[i] = rng(); + } + const uint32_t* bits = reinterpret_cast<const uint32_t*>(buf); + + const size_t num_chunks64 = num / kLanesPerChunk; + // Clamp to uint32 for RandomChunkIndex + const uint32_t num_chunks = + static_cast<uint32_t>(HWY_MIN(num_chunks64, 0xFFFFFFFFull)); + + const size_t offset0 = RandomChunkIndex(num_chunks, bits[0]) * kLanesPerChunk; + const size_t offset1 = RandomChunkIndex(num_chunks, bits[1]) * kLanesPerChunk; + const size_t offset2 = RandomChunkIndex(num_chunks, bits[2]) * kLanesPerChunk; + const size_t offset3 = RandomChunkIndex(num_chunks, bits[3]) * kLanesPerChunk; + const size_t offset4 = RandomChunkIndex(num_chunks, bits[4]) * kLanesPerChunk; + const size_t offset5 = RandomChunkIndex(num_chunks, bits[5]) * kLanesPerChunk; + const size_t offset6 = RandomChunkIndex(num_chunks, bits[6]) * kLanesPerChunk; + const size_t offset7 = RandomChunkIndex(num_chunks, bits[7]) * kLanesPerChunk; + const size_t offset8 = RandomChunkIndex(num_chunks, bits[8]) * kLanesPerChunk; + for (size_t i = 0; i < kLanesPerChunk; i += N) { + const V v0 = Load(d, keys + offset0 + i); + const V v1 = Load(d, keys + offset1 + i); + const V v2 = Load(d, keys + offset2 + i); + const V medians0 = MedianOf3(st, v0, v1, v2); + Store(medians0, d, buf + i); + + const V v3 = Load(d, keys + offset3 + i); + const V v4 = Load(d, keys + offset4 + i); + const V v5 = Load(d, keys + offset5 + i); + const V medians1 = MedianOf3(st, v3, v4, v5); + Store(medians1, d, buf + i + kLanesPerChunk); + + const V v6 = Load(d, keys + offset6 + i); + const V v7 = Load(d, keys + offset7 + i); + const V v8 = Load(d, keys + offset8 + i); + const V medians2 = MedianOf3(st, v6, v7, v8); + Store(medians2, d, buf + i + kLanesPerChunk * 2); + } +} + +// For detecting inputs where (almost) all keys are equal. +template <class D, class Traits> +HWY_INLINE bool UnsortedSampleEqual(D d, Traits st, + const TFromD<D>* HWY_RESTRICT samples) { + constexpr size_t kSampleLanes = 3 * 64 / sizeof(TFromD<D>); + const size_t N = Lanes(d); + using V = Vec<D>; + + const V first = st.SetKey(d, samples); + // OR of XOR-difference may be faster than comparison. + V diff = Zero(d); + size_t i = 0; + for (; i + N <= kSampleLanes; i += N) { + const V v = Load(d, samples + i); + diff = OrXor(diff, first, v); + } + // Remainder, if any. + const V v = Load(d, samples + i); + const auto valid = FirstN(d, kSampleLanes - i); + diff = IfThenElse(valid, OrXor(diff, first, v), diff); + + return st.NoKeyDifference(d, diff); +} + +template <class D, class Traits, typename T> +HWY_INLINE void SortSamples(D d, Traits st, T* HWY_RESTRICT buf) { + // buf contains 192 bytes, so 16 128-bit vectors are necessary and sufficient. + constexpr size_t kSampleLanes = 3 * 64 / sizeof(T); + const CappedTag<T, 16 / sizeof(T)> d128; + const size_t N128 = Lanes(d128); + constexpr size_t kCols = HWY_MIN(16 / sizeof(T), Constants::kMaxCols); + constexpr size_t kBytes = kCols * Constants::kMaxRows * sizeof(T); + static_assert(192 <= kBytes, ""); + // Fill with padding - last in sort order. + const auto kPadding = st.LastValue(d128); + // Initialize an extra vector because SortingNetwork loads full vectors, + // which may exceed cols*kMaxRows. + for (size_t i = kSampleLanes; i <= kBytes / sizeof(T); i += N128) { + StoreU(kPadding, d128, buf + i); + } + + SortingNetwork(st, buf, kCols); + + if (VQSORT_PRINT >= 2) { + const size_t N = Lanes(d); + fprintf(stderr, "Samples:\n"); + for (size_t i = 0; i < kSampleLanes; i += N) { + MaybePrintVector(d, "", Load(d, buf + i), 0, N); + } + } +} + +// ------------------------------ Pivot selection + +enum class PivotResult { + kDone, // stop without partitioning (all equal, or two-value partition) + kNormal, // partition and recurse left and right + kIsFirst, // partition but skip left recursion + kWasLast, // partition but skip right recursion +}; + +HWY_INLINE const char* PivotResultString(PivotResult result) { + switch (result) { + case PivotResult::kDone: + return "done"; + case PivotResult::kNormal: + return "normal"; + case PivotResult::kIsFirst: + return "first"; + case PivotResult::kWasLast: + return "last"; + } + return "unknown"; +} + +template <class Traits, typename T> +HWY_INLINE size_t PivotRank(Traits st, const T* HWY_RESTRICT samples) { + constexpr size_t kSampleLanes = 3 * 64 / sizeof(T); + constexpr size_t N1 = st.LanesPerKey(); + + constexpr size_t kRankMid = kSampleLanes / 2; + static_assert(kRankMid % N1 == 0, "Mid is not an aligned key"); + + // Find the previous value not equal to the median. + size_t rank_prev = kRankMid - N1; + for (; st.Equal1(samples + rank_prev, samples + kRankMid); rank_prev -= N1) { + // All previous samples are equal to the median. + if (rank_prev == 0) return 0; + } + + size_t rank_next = rank_prev + N1; + for (; st.Equal1(samples + rank_next, samples + kRankMid); rank_next += N1) { + // The median is also the largest sample. If it is also the largest key, + // we'd end up with an empty right partition, so choose the previous key. + if (rank_next == kSampleLanes - N1) return rank_prev; + } + + // If we choose the median as pivot, the ratio of keys ending in the left + // partition will likely be rank_next/kSampleLanes (if the sample is + // representative). This is because equal-to-pivot values also land in the + // left - it's infeasible to do an in-place vectorized 3-way partition. + // Check whether prev would lead to a more balanced partition. + const size_t excess_if_median = rank_next - kRankMid; + const size_t excess_if_prev = kRankMid - rank_prev; + return excess_if_median < excess_if_prev ? kRankMid : rank_prev; +} + +// Returns pivot chosen from `samples`. It will never be the largest key +// (thus the right partition will never be empty). +template <class D, class Traits, typename T> +HWY_INLINE Vec<D> ChoosePivotByRank(D d, Traits st, + const T* HWY_RESTRICT samples) { + const size_t pivot_rank = PivotRank(st, samples); + const Vec<D> pivot = st.SetKey(d, samples + pivot_rank); + if (VQSORT_PRINT >= 2) { + fprintf(stderr, " Pivot rank %zu = %f\n", pivot_rank, + static_cast<double>(GetLane(pivot))); + } + // Verify pivot is not equal to the last sample. + constexpr size_t kSampleLanes = 3 * 64 / sizeof(T); + constexpr size_t N1 = st.LanesPerKey(); + const Vec<D> last = st.SetKey(d, samples + kSampleLanes - N1); + const bool all_neq = AllTrue(d, st.NotEqualKeys(d, pivot, last)); + (void)all_neq; + HWY_DASSERT(all_neq); + return pivot; +} + +// Returns true if all keys equal `pivot`, otherwise returns false and sets +// `*first_mismatch' to the index of the first differing key. +template <class D, class Traits, typename T> +HWY_INLINE bool AllEqual(D d, Traits st, const Vec<D> pivot, + const T* HWY_RESTRICT keys, size_t num, + size_t* HWY_RESTRICT first_mismatch) { + const size_t N = Lanes(d); + // Ensures we can use overlapping loads for the tail; see HandleSpecialCases. + HWY_DASSERT(num >= N); + const Vec<D> zero = Zero(d); + + // Vector-align keys + i. + const size_t misalign = + (reinterpret_cast<uintptr_t>(keys) / sizeof(T)) & (N - 1); + HWY_DASSERT(misalign % st.LanesPerKey() == 0); + const size_t consume = N - misalign; + { + const Vec<D> v = LoadU(d, keys); + // Only check masked lanes; consider others to be equal. + const Mask<D> diff = And(FirstN(d, consume), st.NotEqualKeys(d, v, pivot)); + if (HWY_UNLIKELY(!AllFalse(d, diff))) { + const size_t lane = FindKnownFirstTrue(d, diff); + *first_mismatch = lane; + return false; + } + } + size_t i = consume; + HWY_DASSERT(((reinterpret_cast<uintptr_t>(keys + i) / sizeof(T)) & (N - 1)) == + 0); + + // Sticky bits registering any difference between `keys` and the first key. + // We use vector XOR because it may be cheaper than comparisons, especially + // for 128-bit. 2x unrolled for more ILP. + Vec<D> diff0 = zero; + Vec<D> diff1 = zero; + + // We want to stop once a difference has been found, but without slowing + // down the loop by comparing during each iteration. The compromise is to + // compare after a 'group', which consists of kLoops times two vectors. + constexpr size_t kLoops = 8; + const size_t lanes_per_group = kLoops * 2 * N; + + for (; i + lanes_per_group <= num; i += lanes_per_group) { + HWY_DEFAULT_UNROLL + for (size_t loop = 0; loop < kLoops; ++loop) { + const Vec<D> v0 = Load(d, keys + i + loop * 2 * N); + const Vec<D> v1 = Load(d, keys + i + loop * 2 * N + N); + diff0 = OrXor(diff0, v0, pivot); + diff1 = OrXor(diff1, v1, pivot); + } + + // If there was a difference in the entire group: + if (HWY_UNLIKELY(!st.NoKeyDifference(d, Or(diff0, diff1)))) { + // .. then loop until the first one, with termination guarantee. + for (;; i += N) { + const Vec<D> v = Load(d, keys + i); + const Mask<D> diff = st.NotEqualKeys(d, v, pivot); + if (HWY_UNLIKELY(!AllFalse(d, diff))) { + const size_t lane = FindKnownFirstTrue(d, diff); + *first_mismatch = i + lane; + return false; + } + } + } + } + + // Whole vectors, no unrolling, compare directly + for (; i + N <= num; i += N) { + const Vec<D> v = Load(d, keys + i); + const Mask<D> diff = st.NotEqualKeys(d, v, pivot); + if (HWY_UNLIKELY(!AllFalse(d, diff))) { + const size_t lane = FindKnownFirstTrue(d, diff); + *first_mismatch = i + lane; + return false; + } + } + // Always re-check the last (unaligned) vector to reduce branching. + i = num - N; + const Vec<D> v = LoadU(d, keys + i); + const Mask<D> diff = st.NotEqualKeys(d, v, pivot); + if (HWY_UNLIKELY(!AllFalse(d, diff))) { + const size_t lane = FindKnownFirstTrue(d, diff); + *first_mismatch = i + lane; + return false; + } + + if (VQSORT_PRINT >= 1) { + fprintf(stderr, "All keys equal\n"); + } + return true; // all equal +} + +// Called from 'two locations', but only one is active (IsKV is constexpr). +template <class D, class Traits, typename T> +HWY_INLINE bool ExistsAnyBefore(D d, Traits st, const T* HWY_RESTRICT keys, + size_t num, const Vec<D> pivot) { + const size_t N = Lanes(d); + HWY_DASSERT(num >= N); // See HandleSpecialCases + + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "Scanning for before\n"); + } + + size_t i = 0; + + constexpr size_t kLoops = 16; + const size_t lanes_per_group = kLoops * N; + + Vec<D> first = pivot; + + // Whole group, unrolled + for (; i + lanes_per_group <= num; i += lanes_per_group) { + HWY_DEFAULT_UNROLL + for (size_t loop = 0; loop < kLoops; ++loop) { + const Vec<D> curr = LoadU(d, keys + i + loop * N); + first = st.First(d, first, curr); + } + + if (HWY_UNLIKELY(!AllFalse(d, st.Compare(d, first, pivot)))) { + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "Stopped scanning at end of group %zu\n", + i + lanes_per_group); + } + return true; + } + } + // Whole vectors, no unrolling + for (; i + N <= num; i += N) { + const Vec<D> curr = LoadU(d, keys + i); + if (HWY_UNLIKELY(!AllFalse(d, st.Compare(d, curr, pivot)))) { + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "Stopped scanning at %zu\n", i); + } + return true; + } + } + // If there are remainders, re-check the last whole vector. + if (HWY_LIKELY(i != num)) { + const Vec<D> curr = LoadU(d, keys + num - N); + if (HWY_UNLIKELY(!AllFalse(d, st.Compare(d, curr, pivot)))) { + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "Stopped scanning at last %zu\n", num - N); + } + return true; + } + } + + return false; // pivot is the first +} + +// Called from 'two locations', but only one is active (IsKV is constexpr). +template <class D, class Traits, typename T> +HWY_INLINE bool ExistsAnyAfter(D d, Traits st, const T* HWY_RESTRICT keys, + size_t num, const Vec<D> pivot) { + const size_t N = Lanes(d); + HWY_DASSERT(num >= N); // See HandleSpecialCases + + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "Scanning for after\n"); + } + + size_t i = 0; + + constexpr size_t kLoops = 16; + const size_t lanes_per_group = kLoops * N; + + Vec<D> last = pivot; + + // Whole group, unrolled + for (; i + lanes_per_group <= num; i += lanes_per_group) { + HWY_DEFAULT_UNROLL + for (size_t loop = 0; loop < kLoops; ++loop) { + const Vec<D> curr = LoadU(d, keys + i + loop * N); + last = st.Last(d, last, curr); + } + + if (HWY_UNLIKELY(!AllFalse(d, st.Compare(d, pivot, last)))) { + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "Stopped scanning at end of group %zu\n", + i + lanes_per_group); + } + return true; + } + } + // Whole vectors, no unrolling + for (; i + N <= num; i += N) { + const Vec<D> curr = LoadU(d, keys + i); + if (HWY_UNLIKELY(!AllFalse(d, st.Compare(d, pivot, curr)))) { + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "Stopped scanning at %zu\n", i); + } + return true; + } + } + // If there are remainders, re-check the last whole vector. + if (HWY_LIKELY(i != num)) { + const Vec<D> curr = LoadU(d, keys + num - N); + if (HWY_UNLIKELY(!AllFalse(d, st.Compare(d, pivot, curr)))) { + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "Stopped scanning at last %zu\n", num - N); + } + return true; + } + } + + return false; // pivot is the last +} + +// Returns pivot chosen from `keys[0, num)`. It will never be the largest key +// (thus the right partition will never be empty). +template <class D, class Traits, typename T> +HWY_INLINE Vec<D> ChoosePivotForEqualSamples(D d, Traits st, + T* HWY_RESTRICT keys, size_t num, + T* HWY_RESTRICT samples, + Vec<D> second, Vec<D> third, + PivotResult& result) { + const Vec<D> pivot = st.SetKey(d, samples); // the single unique sample + + // Early out for mostly-0 arrays, where pivot is often FirstValue. + if (HWY_UNLIKELY(AllTrue(d, st.EqualKeys(d, pivot, st.FirstValue(d))))) { + result = PivotResult::kIsFirst; + return pivot; + } + if (HWY_UNLIKELY(AllTrue(d, st.EqualKeys(d, pivot, st.LastValue(d))))) { + result = PivotResult::kWasLast; + return st.PrevValue(d, pivot); + } + + // If key-value, we didn't run PartitionIfTwo* and thus `third` is unknown and + // cannot be used. + if (st.IsKV()) { + // If true, pivot is either middle or last. + const bool before = !AllFalse(d, st.Compare(d, second, pivot)); + if (HWY_UNLIKELY(before)) { + // Not last, so middle. + if (HWY_UNLIKELY(ExistsAnyAfter(d, st, keys, num, pivot))) { + result = PivotResult::kNormal; + return pivot; + } + + // We didn't find anything after pivot, so it is the last. Because keys + // equal to the pivot go to the left partition, the right partition would + // be empty and Partition will not have changed anything. Instead use the + // previous value in sort order, which is not necessarily an actual key. + result = PivotResult::kWasLast; + return st.PrevValue(d, pivot); + } + + // Otherwise, pivot is first or middle. Rule out it being first: + if (HWY_UNLIKELY(ExistsAnyBefore(d, st, keys, num, pivot))) { + result = PivotResult::kNormal; + return pivot; + } + // It is first: fall through to shared code below. + } else { + // Check if pivot is between two known values. If so, it is not the first + // nor the last and we can avoid scanning. + st.Sort2(d, second, third); + HWY_DASSERT(AllTrue(d, st.Compare(d, second, third))); + const bool before = !AllFalse(d, st.Compare(d, second, pivot)); + const bool after = !AllFalse(d, st.Compare(d, pivot, third)); + // Only reached if there are three keys, which means pivot is either first, + // last, or in between. Thus there is another key that comes before or + // after. + HWY_DASSERT(before || after); + if (HWY_UNLIKELY(before)) { + // Neither first nor last. + if (HWY_UNLIKELY(after || ExistsAnyAfter(d, st, keys, num, pivot))) { + result = PivotResult::kNormal; + return pivot; + } + + // We didn't find anything after pivot, so it is the last. Because keys + // equal to the pivot go to the left partition, the right partition would + // be empty and Partition will not have changed anything. Instead use the + // previous value in sort order, which is not necessarily an actual key. + result = PivotResult::kWasLast; + return st.PrevValue(d, pivot); + } + + // Has after, and we found one before: in the middle. + if (HWY_UNLIKELY(ExistsAnyBefore(d, st, keys, num, pivot))) { + result = PivotResult::kNormal; + return pivot; + } + } + + // Pivot is first. We could consider a special partition mode that only + // reads from and writes to the right side, and later fills in the left + // side, which we know is equal to the pivot. However, that leads to more + // cache misses if the array is large, and doesn't save much, hence is a + // net loss. + result = PivotResult::kIsFirst; + return pivot; +} + +// ------------------------------ Quicksort recursion + +template <class D, class Traits, typename T> +HWY_NOINLINE void PrintMinMax(D d, Traits st, const T* HWY_RESTRICT keys, + size_t num, T* HWY_RESTRICT buf) { + if (VQSORT_PRINT >= 2) { + const size_t N = Lanes(d); + if (num < N) return; + + Vec<D> first = st.LastValue(d); + Vec<D> last = st.FirstValue(d); + + size_t i = 0; + for (; i + N <= num; i += N) { + const Vec<D> v = LoadU(d, keys + i); + first = st.First(d, v, first); + last = st.Last(d, v, last); + } + if (HWY_LIKELY(i != num)) { + HWY_DASSERT(num >= N); // See HandleSpecialCases + const Vec<D> v = LoadU(d, keys + num - N); + first = st.First(d, v, first); + last = st.Last(d, v, last); + } + + first = st.FirstOfLanes(d, first, buf); + last = st.LastOfLanes(d, last, buf); + MaybePrintVector(d, "first", first, 0, st.LanesPerKey()); + MaybePrintVector(d, "last", last, 0, st.LanesPerKey()); + } +} + +// keys_end is the end of the entire user input, not just the current subarray +// [keys, keys + num). +template <class D, class Traits, typename T> +HWY_NOINLINE void Recurse(D d, Traits st, T* HWY_RESTRICT keys, + T* HWY_RESTRICT keys_end, const size_t num, + T* HWY_RESTRICT buf, Generator& rng, + const size_t remaining_levels) { + HWY_DASSERT(num != 0); + + if (HWY_UNLIKELY(num <= Constants::BaseCaseNum(Lanes(d)))) { + BaseCase(d, st, keys, keys_end, num, buf); + return; + } + + // Move after BaseCase so we skip printing for small subarrays. + if (VQSORT_PRINT >= 1) { + fprintf(stderr, "\n\n=== Recurse depth=%zu len=%zu\n", remaining_levels, + num); + PrintMinMax(d, st, keys, num, buf); + } + + DrawSamples(d, st, keys, num, buf, rng); + + Vec<D> pivot; + PivotResult result = PivotResult::kNormal; + if (HWY_UNLIKELY(UnsortedSampleEqual(d, st, buf))) { + pivot = st.SetKey(d, buf); + size_t idx_second = 0; + if (HWY_UNLIKELY(AllEqual(d, st, pivot, keys, num, &idx_second))) { + return; + } + HWY_DASSERT(idx_second % st.LanesPerKey() == 0); + // Must capture the value before PartitionIfTwoKeys may overwrite it. + const Vec<D> second = st.SetKey(d, keys + idx_second); + MaybePrintVector(d, "pivot", pivot, 0, st.LanesPerKey()); + MaybePrintVector(d, "second", second, 0, st.LanesPerKey()); + + Vec<D> third; + // Not supported for key-value types because two 'keys' may be equivalent + // but not interchangeable (their values may differ). + if (HWY_UNLIKELY(!st.IsKV() && + PartitionIfTwoKeys(d, st, pivot, keys, num, idx_second, + second, third, buf))) { + return; // Done, skip recursion because each side has all-equal keys. + } + + // We can no longer start scanning from idx_second because + // PartitionIfTwoKeys may have reordered keys. + pivot = ChoosePivotForEqualSamples(d, st, keys, num, buf, second, third, + result); + // If kNormal, `pivot` is very common but not the first/last. It is + // tempting to do a 3-way partition (to avoid moving the =pivot keys a + // second time), but that is a net loss due to the extra comparisons. + } else { + SortSamples(d, st, buf); + + // Not supported for key-value types because two 'keys' may be equivalent + // but not interchangeable (their values may differ). + if (HWY_UNLIKELY(!st.IsKV() && + PartitionIfTwoSamples(d, st, keys, num, buf))) { + return; + } + + pivot = ChoosePivotByRank(d, st, buf); + } + + // Too many recursions. This is unlikely to happen because we select pivots + // from large (though still O(1)) samples. + if (HWY_UNLIKELY(remaining_levels == 0)) { + if (VQSORT_PRINT >= 1) { + fprintf(stderr, "HeapSort reached, size=%zu\n", num); + } + HeapSort(st, keys, num); // Slow but N*logN. + return; + } + + const size_t bound = Partition(d, st, keys, num, pivot, buf); + if (VQSORT_PRINT >= 2) { + fprintf(stderr, "bound %zu num %zu result %s\n", bound, num, + PivotResultString(result)); + } + // The left partition is not empty because the pivot is one of the keys + // (unless kWasLast, in which case the pivot is PrevValue, but we still + // have at least one value <= pivot because AllEqual ruled out the case of + // only one unique value, and there is exactly one value after pivot). + HWY_DASSERT(bound != 0); + // ChoosePivot* ensure pivot != last, so the right partition is never empty. + HWY_DASSERT(bound != num); + + if (HWY_LIKELY(result != PivotResult::kIsFirst)) { + Recurse(d, st, keys, keys_end, bound, buf, rng, remaining_levels - 1); + } + if (HWY_LIKELY(result != PivotResult::kWasLast)) { + Recurse(d, st, keys + bound, keys_end, num - bound, buf, rng, + remaining_levels - 1); + } +} + +// Returns true if sorting is finished. +template <class D, class Traits, typename T> +HWY_INLINE bool HandleSpecialCases(D d, Traits st, T* HWY_RESTRICT keys, + size_t num) { + const size_t N = Lanes(d); + const size_t base_case_num = Constants::BaseCaseNum(N); + + // 128-bit keys require vectors with at least two u64 lanes, which is always + // the case unless `d` requests partial vectors (e.g. fraction = 1/2) AND the + // hardware vector width is less than 128bit / fraction. + const bool partial_128 = !IsFull(d) && N < 2 && st.Is128(); + // Partition assumes its input is at least two vectors. If vectors are huge, + // base_case_num may actually be smaller. If so, which is only possible on + // RVV, pass a capped or partial d (LMUL < 1). Use HWY_MAX_BYTES instead of + // HWY_LANES to account for the largest possible LMUL. + constexpr bool kPotentiallyHuge = + HWY_MAX_BYTES / sizeof(T) > Constants::kMaxRows * Constants::kMaxCols; + const bool huge_vec = kPotentiallyHuge && (2 * N > base_case_num); + if (partial_128 || huge_vec) { + if (VQSORT_PRINT >= 1) { + fprintf(stderr, "WARNING: using slow HeapSort: partial %d huge %d\n", + partial_128, huge_vec); + } + HeapSort(st, keys, num); + return true; + } + + // Small arrays are already handled by Recurse. + + // We could also check for already sorted/reverse/equal, but that's probably + // counterproductive if vqsort is used as a base case. + + return false; // not finished sorting +} + +#endif // VQSORT_ENABLED +} // namespace detail + +// Sorts `keys[0..num-1]` according to the order defined by `st.Compare`. +// In-place i.e. O(1) additional storage. Worst-case N*logN comparisons. +// Non-stable (order of equal keys may change), except for the common case where +// the upper bits of T are the key, and the lower bits are a sequential or at +// least unique ID. +// There is no upper limit on `num`, but note that pivots may be chosen by +// sampling only from the first 256 GiB. +// +// `d` is typically SortTag<T> (chooses between full and partial vectors). +// `st` is SharedTraits<Traits*<Order*>>. This abstraction layer bridges +// differences in sort order and single-lane vs 128-bit keys. +template <class D, class Traits, typename T> +void Sort(D d, Traits st, T* HWY_RESTRICT keys, size_t num, + T* HWY_RESTRICT buf) { + if (VQSORT_PRINT >= 1) { + fprintf(stderr, "=============== Sort num %zu\n", num); + } + +#if VQSORT_ENABLED || HWY_IDE +#if !HWY_HAVE_SCALABLE + // On targets with fixed-size vectors, avoid _using_ the allocated memory. + // We avoid (potentially expensive for small input sizes) allocations on + // platforms where no targets are scalable. For 512-bit vectors, this fits on + // the stack (several KiB). + HWY_ALIGN T storage[SortConstants::BufNum<T>(HWY_LANES(T))] = {}; + static_assert(sizeof(storage) <= 8192, "Unexpectedly large, check size"); + buf = storage; +#endif // !HWY_HAVE_SCALABLE + + if (detail::HandleSpecialCases(d, st, keys, num)) return; + +#if HWY_MAX_BYTES > 64 + // sorting_networks-inl and traits assume no more than 512 bit vectors. + if (HWY_UNLIKELY(Lanes(d) > 64 / sizeof(T))) { + return Sort(CappedTag<T, 64 / sizeof(T)>(), st, keys, num, buf); + } +#endif // HWY_MAX_BYTES > 64 + + detail::Generator rng(keys, num); + + // Introspection: switch to worst-case N*logN heapsort after this many. + const size_t max_levels = 2 * hwy::CeilLog2(num) + 4; + detail::Recurse(d, st, keys, keys + num, num, buf, rng, max_levels); +#else + (void)d; + (void)buf; + if (VQSORT_PRINT >= 1) { + fprintf(stderr, "WARNING: using slow HeapSort because vqsort disabled\n"); + } + return detail::HeapSort(st, keys, num); +#endif // VQSORT_ENABLED +} + +// NOLINTNEXTLINE(google-readability-namespace-comments) +} // namespace HWY_NAMESPACE +} // namespace hwy +HWY_AFTER_NAMESPACE(); + +#endif // HIGHWAY_HWY_CONTRIB_SORT_VQSORT_TOGGLE |