Adding upstream version 1:115.7.0.upstream/1%115.7.0upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

37 files changed, 7263 insertions, 0 deletions

diff --git a/third_party/highway/hwy/contrib/sort/BUILD b/third_party/highway/hwy/contrib/sort/BUILD
new file mode 100644
index 0000000000..af4ed78837
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/BUILD
@@ -0,0 +1,193 @@
+package(
+    default_applicable_licenses = ["//:license"],
+    default_visibility = ["//visibility:public"],
+)
+
+licenses(["notice"])
+
+# Unused on Bazel builds, where this is not defined/known; Copybara replaces
+# usages with an empty list.
+COMPAT = [
+    "//buildenv/target:non_prod",  # includes mobile/vendor.
+]
+
+# cc_library(
+#     name = "vxsort",
+#     srcs = [
+#         "vxsort/isa_detection.cpp",
+#         "vxsort/isa_detection_msvc.cpp",
+#         "vxsort/isa_detection_sane.cpp",
+#         "vxsort/machine_traits.avx2.cpp",
+#         "vxsort/smallsort/avx2_load_mask_tables.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX2.double.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX2.float.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX2.int32_t.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX2.int64_t.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX2.uint32_t.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX2.uint64_t.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX512.double.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX512.float.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX512.int32_t.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX512.int64_t.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX512.uint32_t.generated.cpp",
+#         "vxsort/smallsort/bitonic_sort.AVX512.uint64_t.generated.cpp",
+#         "vxsort/vxsort_stats.cpp",
+#     ],
+#     hdrs = [
+#         "vxsort/alignment.h",
+#         "vxsort/defs.h",
+#         "vxsort/isa_detection.h",
+#         "vxsort/machine_traits.avx2.h",
+#         "vxsort/machine_traits.avx512.h",
+#         "vxsort/machine_traits.h",
+#         "vxsort/packer.h",
+#         "vxsort/smallsort/bitonic_sort.AVX2.double.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX2.float.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX2.int32_t.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX2.int64_t.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX2.uint32_t.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX2.uint64_t.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX512.double.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX512.float.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX512.int32_t.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX512.int64_t.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX512.uint32_t.generated.h",
+#         "vxsort/smallsort/bitonic_sort.AVX512.uint64_t.generated.h",
+#         "vxsort/smallsort/bitonic_sort.h",
+#         "vxsort/vxsort.h",
+#         "vxsort/vxsort_stats.h",
+#     ],
+#     compatible_with = [],
+#     textual_hdrs = [
+#         "vxsort/vxsort_targets_disable.h",
+#         "vxsort/vxsort_targets_enable_avx2.h",
+#         "vxsort/vxsort_targets_enable_avx512.h",
+#     ],
+# )
+
+cc_library(
+    name = "vqsort",
+    srcs = [
+        # Split into separate files to reduce MSVC build time.
+        "vqsort.cc",
+        "vqsort_128a.cc",
+        "vqsort_128d.cc",
+        "vqsort_f32a.cc",
+        "vqsort_f32d.cc",
+        "vqsort_f64a.cc",
+        "vqsort_f64d.cc",
+        "vqsort_i16a.cc",
+        "vqsort_i16d.cc",
+        "vqsort_i32a.cc",
+        "vqsort_i32d.cc",
+        "vqsort_i64a.cc",
+        "vqsort_i64d.cc",
+        "vqsort_kv64a.cc",
+        "vqsort_kv64d.cc",
+        "vqsort_kv128a.cc",
+        "vqsort_kv128d.cc",
+        "vqsort_u16a.cc",
+        "vqsort_u16d.cc",
+        "vqsort_u32a.cc",
+        "vqsort_u32d.cc",
+        "vqsort_u64a.cc",
+        "vqsort_u64d.cc",
+    ],
+    hdrs = [
+        "vqsort.h",  # public interface
+    ],
+    compatible_with = [],
+    local_defines = ["hwy_contrib_EXPORTS"],
+    textual_hdrs = [
+        "shared-inl.h",
+        "sorting_networks-inl.h",
+        "traits-inl.h",
+        "traits128-inl.h",
+        "vqsort-inl.h",
+        # Placeholder for internal instrumentation. Do not remove.
+    ],
+    deps = [
+        # Only if VQSORT_SECURE_RNG is set.
+        # "//third_party/absl/random",
+        "//:hwy",
+        # ":vxsort",  # required if HAVE_VXSORT
+    ],
+)
+
+# -----------------------------------------------------------------------------
+# Internal-only targets
+
+cc_library(
+    name = "helpers",
+    testonly = 1,
+    textual_hdrs = [
+        "algo-inl.h",
+        "result-inl.h",
+    ],
+    deps = [
+        ":vqsort",
+        "//:nanobenchmark",
+        # Required for HAVE_PDQSORT, but that is unused and this is
+        # unavailable to Bazel builds, hence commented out.
+        # "//third_party/boost/allowed",
+        # Avoid ips4o and thus TBB to work around hwloc build failure.
+    ],
+)
+
+cc_binary(
+    name = "print_network",
+    testonly = 1,
+    srcs = ["print_network.cc"],
+    deps = [
+        ":helpers",
+        ":vqsort",
+        "//:hwy",
+    ],
+)
+
+cc_test(
+    name = "sort_test",
+    size = "medium",
+    srcs = ["sort_test.cc"],
+    # Do not enable fully_static_link (pthread crash on bazel)
+    local_defines = ["HWY_IS_TEST"],
+    # for test_suite.
+    tags = ["hwy_ops_test"],
+    deps = [
+        ":helpers",
+        ":vqsort",
+        "@com_google_googletest//:gtest_main",
+        "//:hwy",
+        "//:hwy_test_util",
+    ],
+)
+
+cc_binary(
+    name = "bench_sort",
+    testonly = 1,
+    srcs = ["bench_sort.cc"],
+    # Do not enable fully_static_link (pthread crash on bazel)
+    local_defines = ["HWY_IS_TEST"],
+    deps = [
+        ":helpers",
+        ":vqsort",
+        "@com_google_googletest//:gtest_main",
+        "//:hwy",
+        "//:hwy_test_util",
+    ],
+)
+
+cc_binary(
+    name = "bench_parallel",
+    testonly = 1,
+    srcs = ["bench_parallel.cc"],
+    # Do not enable fully_static_link (pthread crash on bazel)
+    local_defines = ["HWY_IS_TEST"],
+    deps = [
+        ":helpers",
+        ":vqsort",
+        "@com_google_googletest//:gtest_main",
+        "//:hwy",
+        "//:hwy_test_util",
+    ],
+)
diff --git a/third_party/highway/hwy/contrib/sort/README.md b/third_party/highway/hwy/contrib/sort/README.md
new file mode 100644
index 0000000000..a0051414d3
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/README.md
@@ -0,0 +1,87 @@
+# Vectorized and performance-portable Quicksort
+
+## Introduction
+
+As of 2022-06-07 this sorts large arrays of built-in types about ten times as
+fast as `std::sort`. See also our
+[blog post](https://opensource.googleblog.com/2022/06/Vectorized%20and%20performance%20portable%20Quicksort.html)
+and [paper](https://arxiv.org/abs/2205.05982).
+
+## Instructions
+
+Here are instructions for reproducing our results on Linux and AWS (SVE, NEON).
+
+### Linux
+
+Please first ensure golang, and Clang (tested with 13.0.1) are installed via
+your system's package manager.
+
+```
+go install github.com/bazelbuild/bazelisk@latest
+git clone https://github.com/google/highway
+cd highway
+CC=clang CXX=clang++ ~/go/bin/bazelisk build -c opt hwy/contrib/sort:all
+bazel-bin/hwy/contrib/sort/sort_test
+bazel-bin/hwy/contrib/sort/bench_sort
+```
+
+### AWS Graviton3
+
+Instance config: amazon linux 5.10 arm64, c7g.8xlarge (largest allowed config is
+32 vCPU). Initial launch will fail. Wait a few minutes for an email saying the
+config is verified, then re-launch. See IPv4 hostname in list of instances.
+
+`ssh -i /path/key.pem ec2-user@hostname`
+
+Note that the AWS CMake package is too old for llvm, so we build it first:
+```
+wget https://cmake.org/files/v3.23/cmake-3.23.2.tar.gz
+tar -xvzf cmake-3.23.2.tar.gz && cd cmake-3.23.2/
+./bootstrap -- -DCMAKE_USE_OPENSSL=OFF
+make -j8 && sudo make install
+cd ..
+```
+
+AWS clang is at version 11.1, which generates unnecessary `AND` instructions
+which slow down the sort by 1.15x. We tested with clang trunk as of June 13
+(which reports Git hash 8f6512fea000c3a0d394864bb94e524bee375069). To build:
+
+```
+git clone --depth 1 https://github.com/llvm/llvm-project.git
+cd llvm-project
+mkdir -p build && cd build
+/usr/local/bin/cmake ../llvm -DLLVM_ENABLE_PROJECTS="clang" -DLLVM_ENABLE_RUNTIMES="libcxx;libcxxabi" -DCMAKE_BUILD_TYPE=Release
+make -j32 && sudo make install
+```
+
+```
+sudo yum install go
+go install github.com/bazelbuild/bazelisk@latest
+git clone https://github.com/google/highway
+cd highway
+CC=/usr/local/bin/clang CXX=/usr/local/bin/clang++ ~/go/bin/bazelisk build -c opt --copt=-march=armv8.2-a+sve hwy/contrib/sort:all
+bazel-bin/hwy/contrib/sort/sort_test
+bazel-bin/hwy/contrib/sort/bench_sort
+```
+
+The above command line enables SVE, which is currently only available on
+Graviton 3. You can also test NEON on the same processor, or other Arm CPUs, by
+changing the `-march=` option to `--copt=-march=armv8.2-a+crypto`. Note that
+such flags will be unnecessary once Clang supports `#pragma target` for NEON and
+SVE intrinsics, as it does for x86.
+
+## Results
+
+`bench_sort` outputs the instruction set (AVX3 refers to AVX-512), the sort
+algorithm (std for `std::sort`, vq for our vqsort), the type of keys being
+sorted (f32 is float), the distribution of keys (uniform32 for uniform random
+with range 0-2^32), the number of keys, then the throughput of sorted keys (i.e.
+number of key bytes output per second).
+
+Example excerpt from Xeon 6154 (Skylake-X) CPU clocked at 3 GHz:
+
+```
+[ RUN      ] BenchSortGroup/BenchSort.BenchAllSort/AVX3
+      AVX3:          std:     f32: uniform32: 1.00E+06   54 MB/s ( 1 threads)
+      AVX3:           vq:     f32: uniform32: 1.00E+06 1143 MB/s ( 1 threads)
+```
diff --git a/third_party/highway/hwy/contrib/sort/algo-inl.h b/third_party/highway/hwy/contrib/sort/algo-inl.h
new file mode 100644
index 0000000000..1ebbbd5745
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/algo-inl.h
@@ -0,0 +1,513 @@
+// 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_ALGO_INL_H_
+#define HIGHWAY_HWY_CONTRIB_SORT_ALGO_INL_H_
+
+#include <stdint.h>
+#include <string.h>  // memcpy
+
+#include <algorithm>   // std::sort, std::min, std::max
+#include <functional>  // std::less, std::greater
+#include <thread>      // NOLINT
+#include <vector>
+
+#include "hwy/base.h"
+#include "hwy/contrib/sort/vqsort.h"
+
+// Third-party algorithms
+#define HAVE_AVX2SORT 0
+#define HAVE_IPS4O 0
+// When enabling, consider changing max_threads (required for Table 1a)
+#define HAVE_PARALLEL_IPS4O (HAVE_IPS4O && 1)
+#define HAVE_PDQSORT 0
+#define HAVE_SORT512 0
+#define HAVE_VXSORT 0
+
+#if HAVE_AVX2SORT
+HWY_PUSH_ATTRIBUTES("avx2,avx")
+#include "avx2sort.h"  //NOLINT
+HWY_POP_ATTRIBUTES
+#endif
+#if HAVE_IPS4O || HAVE_PARALLEL_IPS4O
+#include "third_party/ips4o/include/ips4o.hpp"
+#include "third_party/ips4o/include/ips4o/thread_pool.hpp"
+#endif
+#if HAVE_PDQSORT
+#include "third_party/boost/allowed/sort/sort.hpp"
+#endif
+#if HAVE_SORT512
+#include "sort512.h"  //NOLINT
+#endif
+
+// vxsort is difficult to compile for multiple targets because it also uses
+// .cpp files, and we'd also have to #undef its include guards. Instead, compile
+// only for AVX2 or AVX3 depending on this macro.
+#define VXSORT_AVX3 1
+#if HAVE_VXSORT
+// inlined from vxsort_targets_enable_avx512 (must close before end of header)
+#ifdef __GNUC__
+#ifdef __clang__
+#if VXSORT_AVX3
+#pragma clang attribute push(__attribute__((target("avx512f,avx512dq"))), \
+                             apply_to = any(function))
+#else
+#pragma clang attribute push(__attribute__((target("avx2"))), \
+                             apply_to = any(function))
+#endif  // VXSORT_AVX3
+
+#else
+#pragma GCC push_options
+#if VXSORT_AVX3
+#pragma GCC target("avx512f,avx512dq")
+#else
+#pragma GCC target("avx2")
+#endif  // VXSORT_AVX3
+#endif
+#endif
+
+#if VXSORT_AVX3
+#include "vxsort/machine_traits.avx512.h"
+#else
+#include "vxsort/machine_traits.avx2.h"
+#endif  // VXSORT_AVX3
+#include "vxsort/vxsort.h"
+#ifdef __GNUC__
+#ifdef __clang__
+#pragma clang attribute pop
+#else
+#pragma GCC pop_options
+#endif
+#endif
+#endif  // HAVE_VXSORT
+
+namespace hwy {
+
+enum class Dist { kUniform8, kUniform16, kUniform32 };
+
+static inline std::vector<Dist> AllDist() {
+  return {/*Dist::kUniform8, Dist::kUniform16,*/ Dist::kUniform32};
+}
+
+static inline const char* DistName(Dist dist) {
+  switch (dist) {
+    case Dist::kUniform8:
+      return "uniform8";
+    case Dist::kUniform16:
+      return "uniform16";
+    case Dist::kUniform32:
+      return "uniform32";
+  }
+  return "unreachable";
+}
+
+template <typename T>
+class InputStats {
+ public:
+  void Notify(T value) {
+    min_ = std::min(min_, value);
+    max_ = std::max(max_, value);
+    // Converting to integer would truncate floats, multiplying to save digits
+    // risks overflow especially when casting, so instead take the sum of the
+    // bit representations as the checksum.
+    uint64_t bits = 0;
+    static_assert(sizeof(T) <= 8, "Expected a built-in type");
+    CopyBytes<sizeof(T)>(&value, &bits);  // not same size
+    sum_ += bits;
+    count_ += 1;
+  }
+
+  bool operator==(const InputStats& other) const {
+    if (count_ != other.count_) {
+      HWY_ABORT("count %d vs %d\n", static_cast<int>(count_),
+                static_cast<int>(other.count_));
+    }
+
+    if (min_ != other.min_ || max_ != other.max_) {
+      HWY_ABORT("minmax %f/%f vs %f/%f\n", static_cast<double>(min_),
+                static_cast<double>(max_), static_cast<double>(other.min_),
+                static_cast<double>(other.max_));
+    }
+
+    // Sum helps detect duplicated/lost values
+    if (sum_ != other.sum_) {
+      HWY_ABORT("Sum mismatch %g %g; min %g max %g\n",
+                static_cast<double>(sum_), static_cast<double>(other.sum_),
+                static_cast<double>(min_), static_cast<double>(max_));
+    }
+
+    return true;
+  }
+
+ private:
+  T min_ = hwy::HighestValue<T>();
+  T max_ = hwy::LowestValue<T>();
+  uint64_t sum_ = 0;
+  size_t count_ = 0;
+};
+
+enum class Algo {
+#if HAVE_AVX2SORT
+  kSEA,
+#endif
+#if HAVE_IPS4O
+  kIPS4O,
+#endif
+#if HAVE_PARALLEL_IPS4O
+  kParallelIPS4O,
+#endif
+#if HAVE_PDQSORT
+  kPDQ,
+#endif
+#if HAVE_SORT512
+  kSort512,
+#endif
+#if HAVE_VXSORT
+  kVXSort,
+#endif
+  kStd,
+  kVQSort,
+  kHeap,
+};
+
+static inline const char* AlgoName(Algo algo) {
+  switch (algo) {
+#if HAVE_AVX2SORT
+    case Algo::kSEA:
+      return "sea";
+#endif
+#if HAVE_IPS4O
+    case Algo::kIPS4O:
+      return "ips4o";
+#endif
+#if HAVE_PARALLEL_IPS4O
+    case Algo::kParallelIPS4O:
+      return "par_ips4o";
+#endif
+#if HAVE_PDQSORT
+    case Algo::kPDQ:
+      return "pdq";
+#endif
+#if HAVE_SORT512
+    case Algo::kSort512:
+      return "sort512";
+#endif
+#if HAVE_VXSORT
+    case Algo::kVXSort:
+      return "vxsort";
+#endif
+    case Algo::kStd:
+      return "std";
+    case Algo::kVQSort:
+      return "vq";
+    case Algo::kHeap:
+      return "heap";
+  }
+  return "unreachable";
+}
+
+}  // namespace hwy
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_ALGO_INL_H_
+
+// Per-target
+#if defined(HIGHWAY_HWY_CONTRIB_SORT_ALGO_TOGGLE) == \
+    defined(HWY_TARGET_TOGGLE)
+#ifdef HIGHWAY_HWY_CONTRIB_SORT_ALGO_TOGGLE
+#undef HIGHWAY_HWY_CONTRIB_SORT_ALGO_TOGGLE
+#else
+#define HIGHWAY_HWY_CONTRIB_SORT_ALGO_TOGGLE
+#endif
+
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/traits128-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"  // HeapSort
+#include "hwy/tests/test_util-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+class Xorshift128Plus {
+  static HWY_INLINE uint64_t SplitMix64(uint64_t z) {
+    z = (z ^ (z >> 30)) * 0xBF58476D1CE4E5B9ull;
+    z = (z ^ (z >> 27)) * 0x94D049BB133111EBull;
+    return z ^ (z >> 31);
+  }
+
+ public:
+  // Generates two vectors of 64-bit seeds via SplitMix64 and stores into
+  // `seeds`. Generating these afresh in each ChoosePivot is too expensive.
+  template <class DU64>
+  static void GenerateSeeds(DU64 du64, TFromD<DU64>* HWY_RESTRICT seeds) {
+    seeds[0] = SplitMix64(0x9E3779B97F4A7C15ull);
+    for (size_t i = 1; i < 2 * Lanes(du64); ++i) {
+      seeds[i] = SplitMix64(seeds[i - 1]);
+    }
+  }
+
+  // Need to pass in the state because vector cannot be class members.
+  template <class VU64>
+  static VU64 RandomBits(VU64& state0, VU64& state1) {
+    VU64 s1 = state0;
+    VU64 s0 = state1;
+    const VU64 bits = Add(s1, s0);
+    state0 = s0;
+    s1 = Xor(s1, ShiftLeft<23>(s1));
+    state1 = Xor(s1, Xor(s0, Xor(ShiftRight<18>(s1), ShiftRight<5>(s0))));
+    return bits;
+  }
+};
+
+template <class D, class VU64, HWY_IF_NOT_FLOAT_D(D)>
+Vec<D> RandomValues(D d, VU64& s0, VU64& s1, const VU64 mask) {
+  const VU64 bits = Xorshift128Plus::RandomBits(s0, s1);
+  return BitCast(d, And(bits, mask));
+}
+
+// It is important to avoid denormals, which are flushed to zero by SIMD but not
+// scalar sorts, and NaN, which may be ordered differently in scalar vs. SIMD.
+template <class DF, class VU64, HWY_IF_FLOAT_D(DF)>
+Vec<DF> RandomValues(DF df, VU64& s0, VU64& s1, const VU64 mask) {
+  using TF = TFromD<DF>;
+  const RebindToUnsigned<decltype(df)> du;
+  using VU = Vec<decltype(du)>;
+
+  const VU64 bits64 = And(Xorshift128Plus::RandomBits(s0, s1), mask);
+
+#if HWY_TARGET == HWY_SCALAR  // Cannot repartition u64 to smaller types
+  using TU = MakeUnsigned<TF>;
+  const VU bits = Set(du, static_cast<TU>(GetLane(bits64) & LimitsMax<TU>()));
+#else
+  const VU bits = BitCast(du, bits64);
+#endif
+  // Avoid NaN/denormal by only generating values in [1, 2), i.e. random
+  // mantissas with the exponent taken from the representation of 1.0.
+  const VU k1 = BitCast(du, Set(df, TF{1.0}));
+  const VU mantissa_mask = Set(du, MantissaMask<TF>());
+  const VU representation = OrAnd(k1, bits, mantissa_mask);
+  return BitCast(df, representation);
+}
+
+template <class DU64>
+Vec<DU64> MaskForDist(DU64 du64, const Dist dist, size_t sizeof_t) {
+  switch (sizeof_t) {
+    case 2:
+      return Set(du64, (dist == Dist::kUniform8) ? 0x00FF00FF00FF00FFull
+                                                 : 0xFFFFFFFFFFFFFFFFull);
+    case 4:
+      return Set(du64, (dist == Dist::kUniform8)    ? 0x000000FF000000FFull
+                       : (dist == Dist::kUniform16) ? 0x0000FFFF0000FFFFull
+                                                    : 0xFFFFFFFFFFFFFFFFull);
+    case 8:
+      return Set(du64, (dist == Dist::kUniform8)    ? 0x00000000000000FFull
+                       : (dist == Dist::kUniform16) ? 0x000000000000FFFFull
+                                                    : 0x00000000FFFFFFFFull);
+    default:
+      HWY_ABORT("Logic error");
+      return Zero(du64);
+  }
+}
+
+template <typename T>
+InputStats<T> GenerateInput(const Dist dist, T* v, size_t num) {
+  SortTag<uint64_t> du64;
+  using VU64 = Vec<decltype(du64)>;
+  const size_t N64 = Lanes(du64);
+  auto seeds = hwy::AllocateAligned<uint64_t>(2 * N64);
+  Xorshift128Plus::GenerateSeeds(du64, seeds.get());
+  VU64 s0 = Load(du64, seeds.get());
+  VU64 s1 = Load(du64, seeds.get() + N64);
+
+#if HWY_TARGET == HWY_SCALAR
+  const Sisd<T> d;
+#else
+  const Repartition<T, decltype(du64)> d;
+#endif
+  using V = Vec<decltype(d)>;
+  const size_t N = Lanes(d);
+  const VU64 mask = MaskForDist(du64, dist, sizeof(T));
+  auto buf = hwy::AllocateAligned<T>(N);
+
+  size_t i = 0;
+  for (; i + N <= num; i += N) {
+    const V values = RandomValues(d, s0, s1, mask);
+    StoreU(values, d, v + i);
+  }
+  if (i < num) {
+    const V values = RandomValues(d, s0, s1, mask);
+    StoreU(values, d, buf.get());
+    memcpy(v + i, buf.get(), (num - i) * sizeof(T));
+  }
+
+  InputStats<T> input_stats;
+  for (size_t i = 0; i < num; ++i) {
+    input_stats.Notify(v[i]);
+  }
+  return input_stats;
+}
+
+struct ThreadLocal {
+  Sorter sorter;
+};
+
+struct SharedState {
+#if HAVE_PARALLEL_IPS4O
+  const unsigned max_threads = hwy::LimitsMax<unsigned>();  // 16 for Table 1a
+  ips4o::StdThreadPool pool{static_cast<int>(
+      HWY_MIN(max_threads, std::thread::hardware_concurrency() / 2))};
+#endif
+  std::vector<ThreadLocal> tls{1};
+};
+
+// Bridge from keys (passed to Run) to lanes as expected by HeapSort. For
+// non-128-bit keys they are the same:
+template <class Order, typename KeyType, HWY_IF_NOT_LANE_SIZE(KeyType, 16)>
+void CallHeapSort(KeyType* HWY_RESTRICT keys, const size_t num_keys) {
+  using detail::TraitsLane;
+  using detail::SharedTraits;
+  if (Order().IsAscending()) {
+    const SharedTraits<TraitsLane<detail::OrderAscending<KeyType>>> st;
+    return detail::HeapSort(st, keys, num_keys);
+  } else {
+    const SharedTraits<TraitsLane<detail::OrderDescending<KeyType>>> st;
+    return detail::HeapSort(st, keys, num_keys);
+  }
+}
+
+#if VQSORT_ENABLED
+template <class Order>
+void CallHeapSort(hwy::uint128_t* HWY_RESTRICT keys, const size_t num_keys) {
+  using detail::SharedTraits;
+  using detail::Traits128;
+  uint64_t* lanes = reinterpret_cast<uint64_t*>(keys);
+  const size_t num_lanes = num_keys * 2;
+  if (Order().IsAscending()) {
+    const SharedTraits<Traits128<detail::OrderAscending128>> st;
+    return detail::HeapSort(st, lanes, num_lanes);
+  } else {
+    const SharedTraits<Traits128<detail::OrderDescending128>> st;
+    return detail::HeapSort(st, lanes, num_lanes);
+  }
+}
+
+template <class Order>
+void CallHeapSort(K64V64* HWY_RESTRICT keys, const size_t num_keys) {
+  using detail::SharedTraits;
+  using detail::Traits128;
+  uint64_t* lanes = reinterpret_cast<uint64_t*>(keys);
+  const size_t num_lanes = num_keys * 2;
+  if (Order().IsAscending()) {
+    const SharedTraits<Traits128<detail::OrderAscendingKV128>> st;
+    return detail::HeapSort(st, lanes, num_lanes);
+  } else {
+    const SharedTraits<Traits128<detail::OrderDescendingKV128>> st;
+    return detail::HeapSort(st, lanes, num_lanes);
+  }
+}
+#endif  // VQSORT_ENABLED
+
+template <class Order, typename KeyType>
+void Run(Algo algo, KeyType* HWY_RESTRICT inout, size_t num,
+         SharedState& shared, size_t thread) {
+  const std::less<KeyType> less;
+  const std::greater<KeyType> greater;
+
+  switch (algo) {
+#if HAVE_AVX2SORT
+    case Algo::kSEA:
+      return avx2::quicksort(inout, static_cast<int>(num));
+#endif
+
+#if HAVE_IPS4O
+    case Algo::kIPS4O:
+      if (Order().IsAscending()) {
+        return ips4o::sort(inout, inout + num, less);
+      } else {
+        return ips4o::sort(inout, inout + num, greater);
+      }
+#endif
+
+#if HAVE_PARALLEL_IPS4O
+    case Algo::kParallelIPS4O:
+      if (Order().IsAscending()) {
+        return ips4o::parallel::sort(inout, inout + num, less, shared.pool);
+      } else {
+        return ips4o::parallel::sort(inout, inout + num, greater, shared.pool);
+      }
+#endif
+
+#if HAVE_SORT512
+    case Algo::kSort512:
+      HWY_ABORT("not supported");
+      //    return Sort512::Sort(inout, num);
+#endif
+
+#if HAVE_PDQSORT
+    case Algo::kPDQ:
+      if (Order().IsAscending()) {
+        return boost::sort::pdqsort_branchless(inout, inout + num, less);
+      } else {
+        return boost::sort::pdqsort_branchless(inout, inout + num, greater);
+      }
+#endif
+
+#if HAVE_VXSORT
+    case Algo::kVXSort: {
+#if (VXSORT_AVX3 && HWY_TARGET != HWY_AVX3) || \
+    (!VXSORT_AVX3 && HWY_TARGET != HWY_AVX2)
+      fprintf(stderr, "Do not call for target %s\n",
+              hwy::TargetName(HWY_TARGET));
+      return;
+#else
+#if VXSORT_AVX3
+      vxsort::vxsort<KeyType, vxsort::AVX512> vx;
+#else
+      vxsort::vxsort<KeyType, vxsort::AVX2> vx;
+#endif
+      if (Order().IsAscending()) {
+        return vx.sort(inout, inout + num - 1);
+      } else {
+        fprintf(stderr, "Skipping VX - does not support descending order\n");
+        return;
+      }
+#endif  // enabled for this target
+    }
+#endif  // HAVE_VXSORT
+
+    case Algo::kStd:
+      if (Order().IsAscending()) {
+        return std::sort(inout, inout + num, less);
+      } else {
+        return std::sort(inout, inout + num, greater);
+      }
+
+    case Algo::kVQSort:
+      return shared.tls[thread].sorter(inout, num, Order());
+
+    case Algo::kHeap:
+      return CallHeapSort<Order>(inout, num);
+
+    default:
+      HWY_ABORT("Not implemented");
+  }
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_ALGO_TOGGLE
diff --git a/third_party/highway/hwy/contrib/sort/bench_parallel.cc b/third_party/highway/hwy/contrib/sort/bench_parallel.cc
new file mode 100644
index 0000000000..1c8c928e21
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/bench_parallel.cc
@@ -0,0 +1,238 @@
+// 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.
+
+// Concurrent, independent sorts for generating more memory traffic and testing
+// scalability.
+
+#include <stdint.h>
+#include <stdio.h>
+
+#include <condition_variable>  //NOLINT
+#include <functional>
+#include <memory>
+#include <mutex>   //NOLINT
+#include <thread>  //NOLINT
+#include <utility>
+#include <vector>
+
+// clang-format off
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/bench_parallel.cc"  //NOLINT
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/algo-inl.h"
+#include "hwy/contrib/sort/result-inl.h"
+#include "hwy/aligned_allocator.h"
+// Last
+#include "hwy/tests/test_util-inl.h"
+// clang-format on
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+namespace {
+
+class ThreadPool {
+ public:
+  // Starts the given number of worker threads and blocks until they are ready.
+  explicit ThreadPool(
+      const size_t num_threads = std::thread::hardware_concurrency())
+      : num_threads_(num_threads) {
+    HWY_ASSERT(num_threads_ > 0);
+    threads_.reserve(num_threads_);
+    for (size_t i = 0; i < num_threads_; ++i) {
+      threads_.emplace_back(ThreadFunc, this, i);
+    }
+
+    WorkersReadyBarrier();
+  }
+
+  ThreadPool(const ThreadPool&) = delete;
+  ThreadPool& operator&(const ThreadPool&) = delete;
+
+  // Waits for all threads to exit.
+  ~ThreadPool() {
+    StartWorkers(kWorkerExit);
+
+    for (std::thread& thread : threads_) {
+      thread.join();
+    }
+  }
+
+  size_t NumThreads() const { return threads_.size(); }
+
+  template <class Func>
+  void RunOnThreads(size_t max_threads, const Func& func) {
+    task_ = &CallClosure<Func>;
+    data_ = &func;
+    StartWorkers(max_threads);
+    WorkersReadyBarrier();
+  }
+
+ private:
+  // After construction and between calls to Run, workers are "ready", i.e.
+  // waiting on worker_start_cv_. They are "started" by sending a "command"
+  // and notifying all worker_start_cv_ waiters. (That is why all workers
+  // must be ready/waiting - otherwise, the notification will not reach all of
+  // them and the main thread waits in vain for them to report readiness.)
+  using WorkerCommand = uint64_t;
+
+  static constexpr WorkerCommand kWorkerWait = ~1ULL;
+  static constexpr WorkerCommand kWorkerExit = ~2ULL;
+
+  // Calls a closure (lambda with captures).
+  template <class Closure>
+  static void CallClosure(const void* f, size_t thread) {
+    (*reinterpret_cast<const Closure*>(f))(thread);
+  }
+
+  void WorkersReadyBarrier() {
+    std::unique_lock<std::mutex> lock(mutex_);
+    // Typically only a single iteration.
+    while (workers_ready_ != threads_.size()) {
+      workers_ready_cv_.wait(lock);
+    }
+    workers_ready_ = 0;
+
+    // Safely handle spurious worker wakeups.
+    worker_start_command_ = kWorkerWait;
+  }
+
+  // Precondition: all workers are ready.
+  void StartWorkers(const WorkerCommand worker_command) {
+    std::unique_lock<std::mutex> lock(mutex_);
+    worker_start_command_ = worker_command;
+    // Workers will need this lock, so release it before they wake up.
+    lock.unlock();
+    worker_start_cv_.notify_all();
+  }
+
+  static void ThreadFunc(ThreadPool* self, size_t thread) {
+    // Until kWorkerExit command received:
+    for (;;) {
+      std::unique_lock<std::mutex> lock(self->mutex_);
+      // Notify main thread that this thread is ready.
+      if (++self->workers_ready_ == self->num_threads_) {
+        self->workers_ready_cv_.notify_one();
+      }
+    RESUME_WAIT:
+      // Wait for a command.
+      self->worker_start_cv_.wait(lock);
+      const WorkerCommand command = self->worker_start_command_;
+      switch (command) {
+        case kWorkerWait:    // spurious wakeup:
+          goto RESUME_WAIT;  // lock still held, avoid incrementing ready.
+        case kWorkerExit:
+          return;  // exits thread
+        default:
+          break;
+      }
+
+      lock.unlock();
+      // Command is the maximum number of threads that should run the task.
+      HWY_ASSERT(command < self->NumThreads());
+      if (thread < command) {
+        self->task_(self->data_, thread);
+      }
+    }
+  }
+
+  const size_t num_threads_;
+
+  // Unmodified after ctor, but cannot be const because we call thread::join().
+  std::vector<std::thread> threads_;
+
+  std::mutex mutex_;  // guards both cv and their variables.
+  std::condition_variable workers_ready_cv_;
+  size_t workers_ready_ = 0;
+  std::condition_variable worker_start_cv_;
+  WorkerCommand worker_start_command_;
+
+  // Written by main thread, read by workers (after mutex lock/unlock).
+  std::function<void(const void*, size_t)> task_;  // points to CallClosure
+  const void* data_;                               // points to caller's Func
+};
+
+template <class Traits>
+void RunWithoutVerify(Traits st, const Dist dist, const size_t num_keys,
+                      const Algo algo, SharedState& shared, size_t thread) {
+  using LaneType = typename Traits::LaneType;
+  using KeyType = typename Traits::KeyType;
+  using Order = typename Traits::Order;
+  const size_t num_lanes = num_keys * st.LanesPerKey();
+  auto aligned = hwy::AllocateAligned<LaneType>(num_lanes);
+
+  (void)GenerateInput(dist, aligned.get(), num_lanes);
+
+  const Timestamp t0;
+  Run<Order>(algo, reinterpret_cast<KeyType*>(aligned.get()), num_keys, shared,
+             thread);
+  HWY_ASSERT(aligned[0] < aligned[num_lanes - 1]);
+}
+
+void BenchParallel() {
+  // Not interested in benchmark results for other targets on x86
+  if (HWY_ARCH_X86 && (HWY_TARGET != HWY_AVX2 && HWY_TARGET != HWY_AVX3)) {
+    return;
+  }
+
+  ThreadPool pool;
+  const size_t NT = pool.NumThreads();
+
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscending<int64_t>>> st;
+  using KeyType = typename decltype(st)::KeyType;
+  const size_t num_keys = size_t{100} * 1000 * 1000;
+
+#if HAVE_IPS4O
+  const Algo algo = Algo::kIPS4O;
+#else
+  const Algo algo = Algo::kVQSort;
+#endif
+  const Dist dist = Dist::kUniform32;
+
+  SharedState shared;
+  shared.tls.resize(NT);
+
+  std::vector<Result> results;
+  for (size_t nt = 1; nt < NT; nt += HWY_MAX(1, NT / 16)) {
+    Timestamp t0;
+    // Default capture because MSVC wants algo/dist but clang does not.
+    pool.RunOnThreads(nt, [=, &shared](size_t thread) {
+      RunWithoutVerify(st, dist, num_keys, algo, shared, thread);
+    });
+    const double sec = SecondsSince(t0);
+    results.emplace_back(algo, dist, num_keys, nt, sec, sizeof(KeyType),
+                         st.KeyString());
+    results.back().Print();
+  }
+}
+
+}  // namespace
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+
+namespace hwy {
+namespace {
+HWY_BEFORE_TEST(BenchParallel);
+HWY_EXPORT_AND_TEST_P(BenchParallel, BenchParallel);
+}  // namespace
+}  // namespace hwy
+
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/bench_sort.cc b/third_party/highway/hwy/contrib/sort/bench_sort.cc
new file mode 100644
index 0000000000..a668fde907
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/bench_sort.cc
@@ -0,0 +1,310 @@
+// 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.
+
+#include <stdint.h>
+#include <stdio.h>
+
+#include <vector>
+
+// clang-format off
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/bench_sort.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/algo-inl.h"
+#include "hwy/contrib/sort/result-inl.h"
+#include "hwy/contrib/sort/sorting_networks-inl.h"  // SharedTraits
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/traits128-inl.h"
+#include "hwy/tests/test_util-inl.h"
+// clang-format on
+
+// Mode for larger sorts because M1 is able to access more than the per-core
+// share of L2, so 1M elements might still be in cache.
+#define SORT_100M 0
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+// Defined within HWY_ONCE, used by BenchAllSort.
+extern int64_t first_sort_target;
+
+namespace HWY_NAMESPACE {
+namespace {
+using detail::TraitsLane;
+using detail::OrderAscending;
+using detail::OrderDescending;
+using detail::SharedTraits;
+
+#if VQSORT_ENABLED || HWY_IDE
+using detail::OrderAscending128;
+using detail::OrderAscendingKV128;
+using detail::Traits128;
+
+template <class Traits>
+HWY_NOINLINE void BenchPartition() {
+  using LaneType = typename Traits::LaneType;
+  using KeyType = typename Traits::KeyType;
+  const SortTag<LaneType> d;
+  detail::SharedTraits<Traits> st;
+  const Dist dist = Dist::kUniform8;
+  double sum = 0.0;
+
+  detail::Generator rng(&sum, 123);  // for ChoosePivot
+
+  const size_t max_log2 = AdjustedLog2Reps(20);
+  for (size_t log2 = max_log2; log2 < max_log2 + 1; ++log2) {
+    const size_t num_lanes = 1ull << log2;
+    const size_t num_keys = num_lanes / st.LanesPerKey();
+    auto aligned = hwy::AllocateAligned<LaneType>(num_lanes);
+    auto buf = hwy::AllocateAligned<LaneType>(
+        HWY_MAX(hwy::SortConstants::PartitionBufNum(Lanes(d)),
+                hwy::SortConstants::PivotBufNum(sizeof(LaneType), Lanes(d))));
+
+    std::vector<double> seconds;
+    const size_t num_reps = (1ull << (14 - log2 / 2)) * 30;
+    for (size_t rep = 0; rep < num_reps; ++rep) {
+      (void)GenerateInput(dist, aligned.get(), num_lanes);
+
+      // The pivot value can influence performance. Do exactly what vqsort will
+      // do so that the performance (influenced by prefetching and branch
+      // prediction) is likely to predict the actual performance inside vqsort.
+      detail::DrawSamples(d, st, aligned.get(), num_lanes, buf.get(), rng);
+      detail::SortSamples(d, st, buf.get());
+      auto pivot = detail::ChoosePivotByRank(d, st, buf.get());
+
+      const Timestamp t0;
+      detail::Partition(d, st, aligned.get(), num_lanes - 1, pivot, buf.get());
+      seconds.push_back(SecondsSince(t0));
+      // 'Use' the result to prevent optimizing out the partition.
+      sum += static_cast<double>(aligned.get()[num_lanes / 2]);
+    }
+
+    Result(Algo::kVQSort, dist, num_keys, 1, SummarizeMeasurements(seconds),
+           sizeof(KeyType), st.KeyString())
+        .Print();
+  }
+  HWY_ASSERT(sum != 999999);  // Prevent optimizing out
+}
+
+HWY_NOINLINE void BenchAllPartition() {
+  // Not interested in benchmark results for these targets
+  if (HWY_TARGET == HWY_SSSE3) {
+    return;
+  }
+
+  BenchPartition<TraitsLane<OrderDescending<float>>>();
+  BenchPartition<TraitsLane<OrderDescending<int32_t>>>();
+  BenchPartition<TraitsLane<OrderDescending<int64_t>>>();
+  BenchPartition<Traits128<OrderAscending128>>();
+  // BenchPartition<Traits128<OrderDescending128>>();
+  BenchPartition<Traits128<OrderAscendingKV128>>();
+}
+
+template <class Traits>
+HWY_NOINLINE void BenchBase(std::vector<Result>& results) {
+  // Not interested in benchmark results for these targets
+  if (HWY_TARGET == HWY_SSSE3 || HWY_TARGET == HWY_SSE4) {
+    return;
+  }
+
+  using LaneType = typename Traits::LaneType;
+  using KeyType = typename Traits::KeyType;
+  const SortTag<LaneType> d;
+  detail::SharedTraits<Traits> st;
+  const Dist dist = Dist::kUniform32;
+
+  const size_t N = Lanes(d);
+  const size_t num_lanes = SortConstants::BaseCaseNum(N);
+  const size_t num_keys = num_lanes / st.LanesPerKey();
+  auto keys = hwy::AllocateAligned<LaneType>(num_lanes);
+  auto buf = hwy::AllocateAligned<LaneType>(num_lanes + N);
+
+  std::vector<double> seconds;
+  double sum = 0;                             // prevents elision
+  constexpr size_t kMul = AdjustedReps(600);  // ensures long enough to measure
+
+  for (size_t rep = 0; rep < 30; ++rep) {
+    InputStats<LaneType> input_stats =
+        GenerateInput(dist, keys.get(), num_lanes);
+
+    const Timestamp t0;
+    for (size_t i = 0; i < kMul; ++i) {
+      detail::BaseCase(d, st, keys.get(), keys.get() + num_lanes, num_lanes,
+                       buf.get());
+      sum += static_cast<double>(keys[0]);
+    }
+    seconds.push_back(SecondsSince(t0));
+    // printf("%f\n", seconds.back());
+
+    HWY_ASSERT(VerifySort(st, input_stats, keys.get(), num_lanes, "BenchBase"));
+  }
+  HWY_ASSERT(sum < 1E99);
+  results.emplace_back(Algo::kVQSort, dist, num_keys * kMul, 1,
+                       SummarizeMeasurements(seconds), sizeof(KeyType),
+                       st.KeyString());
+}
+
+HWY_NOINLINE void BenchAllBase() {
+  // Not interested in benchmark results for these targets
+  if (HWY_TARGET == HWY_SSSE3) {
+    return;
+  }
+
+  std::vector<Result> results;
+  BenchBase<TraitsLane<OrderAscending<float>>>(results);
+  BenchBase<TraitsLane<OrderDescending<int64_t>>>(results);
+  BenchBase<Traits128<OrderAscending128>>(results);
+  for (const Result& r : results) {
+    r.Print();
+  }
+}
+
+#else
+void BenchAllPartition() {}
+void BenchAllBase() {}
+#endif  // VQSORT_ENABLED
+
+std::vector<Algo> AlgoForBench() {
+  return {
+#if HAVE_AVX2SORT
+    Algo::kSEA,
+#endif
+#if HAVE_PARALLEL_IPS4O
+        Algo::kParallelIPS4O,
+#elif HAVE_IPS4O
+        Algo::kIPS4O,
+#endif
+#if HAVE_PDQSORT
+        Algo::kPDQ,
+#endif
+#if HAVE_SORT512
+        Algo::kSort512,
+#endif
+// Only include if we're compiling for the target it supports.
+#if HAVE_VXSORT && ((VXSORT_AVX3 && HWY_TARGET == HWY_AVX3) || \
+                    (!VXSORT_AVX3 && HWY_TARGET == HWY_AVX2))
+        Algo::kVXSort,
+#endif
+
+#if !HAVE_PARALLEL_IPS4O
+#if !SORT_100M
+        // These are 10-20x slower, but that's OK for the default size when we
+        // are not testing the parallel nor 100M modes.
+        Algo::kStd, Algo::kHeap,
+#endif
+
+        Algo::kVQSort,  // only ~4x slower, but not required for Table 1a
+#endif
+  };
+}
+
+template <class Traits>
+HWY_NOINLINE void BenchSort(size_t num_keys) {
+  if (first_sort_target == 0) first_sort_target = HWY_TARGET;
+
+  SharedState shared;
+  detail::SharedTraits<Traits> st;
+  using Order = typename Traits::Order;
+  using LaneType = typename Traits::LaneType;
+  using KeyType = typename Traits::KeyType;
+  const size_t num_lanes = num_keys * st.LanesPerKey();
+  auto aligned = hwy::AllocateAligned<LaneType>(num_lanes);
+
+  const size_t reps = num_keys > 1000 * 1000 ? 10 : 30;
+
+  for (Algo algo : AlgoForBench()) {
+    // Other algorithms don't depend on the vector instructions, so only run
+    // them for the first target.
+#if !HAVE_VXSORT
+    if (algo != Algo::kVQSort && HWY_TARGET != first_sort_target) {
+      continue;
+    }
+#endif
+
+    for (Dist dist : AllDist()) {
+      std::vector<double> seconds;
+      for (size_t rep = 0; rep < reps; ++rep) {
+        InputStats<LaneType> input_stats =
+            GenerateInput(dist, aligned.get(), num_lanes);
+
+        const Timestamp t0;
+        Run<Order>(algo, reinterpret_cast<KeyType*>(aligned.get()), num_keys,
+                   shared, /*thread=*/0);
+        seconds.push_back(SecondsSince(t0));
+        // printf("%f\n", seconds.back());
+
+        HWY_ASSERT(
+            VerifySort(st, input_stats, aligned.get(), num_lanes, "BenchSort"));
+      }
+      Result(algo, dist, num_keys, 1, SummarizeMeasurements(seconds),
+             sizeof(KeyType), st.KeyString())
+          .Print();
+    }  // dist
+  }    // algo
+}
+
+HWY_NOINLINE void BenchAllSort() {
+  // Not interested in benchmark results for these targets
+  if (HWY_TARGET == HWY_SSSE3 || HWY_TARGET == HWY_SSE4) {
+    return;
+  }
+
+  constexpr size_t K = 1000;
+  constexpr size_t M = K * K;
+  (void)K;
+  (void)M;
+  for (size_t num_keys : {
+#if HAVE_PARALLEL_IPS4O || SORT_100M
+         100 * M,
+#else
+        1 * M,
+#endif
+       }) {
+    BenchSort<TraitsLane<OrderAscending<float>>>(num_keys);
+    // BenchSort<TraitsLane<OrderDescending<double>>>(num_keys);
+    // BenchSort<TraitsLane<OrderAscending<int16_t>>>(num_keys);
+    BenchSort<TraitsLane<OrderDescending<int32_t>>>(num_keys);
+    BenchSort<TraitsLane<OrderAscending<int64_t>>>(num_keys);
+    // BenchSort<TraitsLane<OrderDescending<uint16_t>>>(num_keys);
+    // BenchSort<TraitsLane<OrderDescending<uint32_t>>>(num_keys);
+    // BenchSort<TraitsLane<OrderAscending<uint64_t>>>(num_keys);
+
+#if !HAVE_VXSORT && VQSORT_ENABLED
+    BenchSort<Traits128<OrderAscending128>>(num_keys);
+    BenchSort<Traits128<OrderAscendingKV128>>(num_keys);
+#endif
+  }
+}
+
+}  // namespace
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+
+namespace hwy {
+int64_t first_sort_target = 0;  // none run yet
+namespace {
+HWY_BEFORE_TEST(BenchSort);
+HWY_EXPORT_AND_TEST_P(BenchSort, BenchAllPartition);
+HWY_EXPORT_AND_TEST_P(BenchSort, BenchAllBase);
+HWY_EXPORT_AND_TEST_P(BenchSort, BenchAllSort);
+}  // namespace
+}  // namespace hwy
+
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/print_network.cc b/third_party/highway/hwy/contrib/sort/print_network.cc
new file mode 100644
index 0000000000..59cfebcfbd
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/print_network.cc
@@ -0,0 +1,191 @@
+// 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.
+
+#include <stdio.h>
+
+#include <algorithm>
+
+#include "hwy/base.h"
+
+// Based on A.7 in "Entwurf und Implementierung vektorisierter
+// Sortieralgorithmen" and code by Mark Blacher.
+void PrintMergeNetwork16x2() {
+  for (int i = 8; i < 16; ++i) {
+    printf("v%x = st.SwapAdjacent(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 8; ++i) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, 15 - i);
+  }
+  for (int i = 0; i < 4; ++i) {
+    printf("v%x = st.SwapAdjacent(d, v%x);\n", i + 4, i + 4);
+    printf("v%x = st.SwapAdjacent(d, v%x);\n", i + 12, i + 12);
+  }
+  for (int i = 0; i < 4; ++i) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, 7 - i);
+    printf("st.Sort2(d, v%x, v%x);\n", i + 8, 15 - i);
+  }
+  for (int i = 0; i < 16; i += 4) {
+    printf("v%x = st.SwapAdjacent(d, v%x);\n", i + 2, i + 2);
+    printf("v%x = st.SwapAdjacent(d, v%x);\n", i + 3, i + 3);
+  }
+  for (int i = 0; i < 16; i += 4) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, i + 3);
+    printf("st.Sort2(d, v%x, v%x);\n", i + 1, i + 2);
+  }
+  for (int i = 0; i < 16; i += 2) {
+    printf("v%x = st.SwapAdjacent(d, v%x);\n", i + 1, i + 1);
+  }
+  for (int i = 0; i < 16; i += 2) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, i + 1);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsDistance1<kOrder>(d, v%x);\n", i, i);
+  }
+  printf("\n");
+}
+
+void PrintMergeNetwork16x4() {
+  printf("\n");
+
+  for (int i = 8; i < 16; ++i) {
+    printf("v%x = st.Reverse4(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 8; ++i) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, 15 - i);
+  }
+  for (int i = 0; i < 4; ++i) {
+    printf("v%x = st.Reverse4(d, v%x);\n", i + 4, i + 4);
+    printf("v%x = st.Reverse4(d, v%x);\n", i + 12, i + 12);
+  }
+  for (int i = 0; i < 4; ++i) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, 7 - i);
+    printf("st.Sort2(d, v%x, v%x);\n", i + 8, 15 - i);
+  }
+  for (int i = 0; i < 16; i += 4) {
+    printf("v%x = st.Reverse4(d, v%x);\n", i + 2, i + 2);
+    printf("v%x = st.Reverse4(d, v%x);\n", i + 3, i + 3);
+  }
+  for (int i = 0; i < 16; i += 4) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, i + 3);
+    printf("st.Sort2(d, v%x, v%x);\n", i + 1, i + 2);
+  }
+  for (int i = 0; i < 16; i += 2) {
+    printf("v%x = st.Reverse4(d, v%x);\n", i + 1, i + 1);
+  }
+  for (int i = 0; i < 16; i += 2) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, i + 1);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsReverse4(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsDistance1<kOrder>(d, v%x);\n", i, i);
+  }
+}
+
+void PrintMergeNetwork16x8() {
+  printf("\n");
+
+  for (int i = 8; i < 16; ++i) {
+    printf("v%x = st.ReverseKeys8(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 8; ++i) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, 15 - i);
+  }
+  for (int i = 0; i < 4; ++i) {
+    printf("v%x = st.ReverseKeys8(d, v%x);\n", i + 4, i + 4);
+    printf("v%x = st.ReverseKeys8(d, v%x);\n", i + 12, i + 12);
+  }
+  for (int i = 0; i < 4; ++i) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, 7 - i);
+    printf("st.Sort2(d, v%x, v%x);\n", i + 8, 15 - i);
+  }
+  for (int i = 0; i < 16; i += 4) {
+    printf("v%x = st.ReverseKeys8(d, v%x);\n", i + 2, i + 2);
+    printf("v%x = st.ReverseKeys8(d, v%x);\n", i + 3, i + 3);
+  }
+  for (int i = 0; i < 16; i += 4) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, i + 3);
+    printf("st.Sort2(d, v%x, v%x);\n", i + 1, i + 2);
+  }
+  for (int i = 0; i < 16; i += 2) {
+    printf("v%x = st.ReverseKeys8(d, v%x);\n", i + 1, i + 1);
+  }
+  for (int i = 0; i < 16; i += 2) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, i + 1);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsReverse8(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsDistance2<kOrder>(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsDistance1<kOrder>(d, v%x);\n", i, i);
+  }
+}
+
+void PrintMergeNetwork16x16() {
+  printf("\n");
+
+  for (int i = 8; i < 16; ++i) {
+    printf("v%x = st.ReverseKeys16(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 8; ++i) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, 15 - i);
+  }
+  for (int i = 0; i < 4; ++i) {
+    printf("v%x = st.ReverseKeys16(d, v%x);\n", i + 4, i + 4);
+    printf("v%x = st.ReverseKeys16(d, v%x);\n", i + 12, i + 12);
+  }
+  for (int i = 0; i < 4; ++i) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, 7 - i);
+    printf("st.Sort2(d, v%x, v%x);\n", i + 8, 15 - i);
+  }
+  for (int i = 0; i < 16; i += 4) {
+    printf("v%x = st.ReverseKeys16(d, v%x);\n", i + 2, i + 2);
+    printf("v%x = st.ReverseKeys16(d, v%x);\n", i + 3, i + 3);
+  }
+  for (int i = 0; i < 16; i += 4) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, i + 3);
+    printf("st.Sort2(d, v%x, v%x);\n", i + 1, i + 2);
+  }
+  for (int i = 0; i < 16; i += 2) {
+    printf("v%x = st.ReverseKeys16(d, v%x);\n", i + 1, i + 1);
+  }
+  for (int i = 0; i < 16; i += 2) {
+    printf("st.Sort2(d, v%x, v%x);\n", i, i + 1);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsReverse16<kOrder>(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsDistance4<kOrder>(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsDistance2<kOrder>(d, v%x);\n", i, i);
+  }
+  for (int i = 0; i < 16; ++i) {
+    printf("v%x = st.SortPairsDistance1<kOrder>(d, v%x);\n", i, i);
+  }
+}
+
+int main(int argc, char** argv) {
+  PrintMergeNetwork16x2();
+  PrintMergeNetwork16x4();
+  PrintMergeNetwork16x8();
+  PrintMergeNetwork16x16();
+  return 0;
+}
diff --git a/third_party/highway/hwy/contrib/sort/result-inl.h b/third_party/highway/hwy/contrib/sort/result-inl.h
new file mode 100644
index 0000000000..f3d842dfbd
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/result-inl.h
@@ -0,0 +1,139 @@
+// 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.
+
+#include "hwy/contrib/sort/algo-inl.h"
+
+// Normal include guard for non-SIMD parts
+#ifndef HIGHWAY_HWY_CONTRIB_SORT_RESULT_INL_H_
+#define HIGHWAY_HWY_CONTRIB_SORT_RESULT_INL_H_
+
+#include <time.h>
+
+#include <algorithm>  // std::sort
+#include <string>
+
+#include "hwy/base.h"
+#include "hwy/nanobenchmark.h"
+
+namespace hwy {
+
+struct Timestamp {
+  Timestamp() { t = platform::Now(); }
+  double t;
+};
+
+static inline double SecondsSince(const Timestamp& t0) {
+  const Timestamp t1;
+  return t1.t - t0.t;
+}
+
+// Returns trimmed mean (we don't want to run an out-of-L3-cache sort often
+// enough for the mode to be reliable).
+static inline double SummarizeMeasurements(std::vector<double>& seconds) {
+  std::sort(seconds.begin(), seconds.end());
+  double sum = 0;
+  int count = 0;
+  const size_t num = seconds.size();
+  for (size_t i = num / 4; i < num / 2; ++i) {
+    sum += seconds[i];
+    count += 1;
+  }
+  return sum / count;
+}
+
+}  // namespace hwy
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_RESULT_INL_H_
+
+// Per-target
+#if defined(HIGHWAY_HWY_CONTRIB_SORT_RESULT_TOGGLE) == \
+    defined(HWY_TARGET_TOGGLE)
+#ifdef HIGHWAY_HWY_CONTRIB_SORT_RESULT_TOGGLE
+#undef HIGHWAY_HWY_CONTRIB_SORT_RESULT_TOGGLE
+#else
+#define HIGHWAY_HWY_CONTRIB_SORT_RESULT_TOGGLE
+#endif
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+struct Result {
+  Result() {}
+  Result(const Algo algo, Dist dist, size_t num_keys, size_t num_threads,
+         double sec, size_t sizeof_key, const std::string& key_name)
+      : target(HWY_TARGET),
+        algo(algo),
+        dist(dist),
+        num_keys(num_keys),
+        num_threads(num_threads),
+        sec(sec),
+        sizeof_key(sizeof_key),
+        key_name(key_name) {}
+
+  void Print() const {
+    const double bytes = static_cast<double>(num_keys) *
+                         static_cast<double>(num_threads) *
+                         static_cast<double>(sizeof_key);
+    printf("%10s: %12s: %7s: %9s: %.2E %4.0f MB/s (%2zu threads)\n",
+           hwy::TargetName(target), AlgoName(algo), key_name.c_str(),
+           DistName(dist), static_cast<double>(num_keys), bytes * 1E-6 / sec,
+           num_threads);
+  }
+
+  int64_t target;
+  Algo algo;
+  Dist dist;
+  size_t num_keys = 0;
+  size_t num_threads = 0;
+  double sec = 0.0;
+  size_t sizeof_key = 0;
+  std::string key_name;
+};
+
+template <class Traits, typename LaneType>
+bool VerifySort(Traits st, const InputStats<LaneType>& input_stats,
+                const LaneType* out, size_t num_lanes, const char* caller) {
+  constexpr size_t N1 = st.LanesPerKey();
+  HWY_ASSERT(num_lanes >= N1);
+
+  InputStats<LaneType> output_stats;
+  // Ensure it matches the sort order
+  for (size_t i = 0; i < num_lanes - N1; i += N1) {
+    output_stats.Notify(out[i]);
+    if (N1 == 2) output_stats.Notify(out[i + 1]);
+    // Reverse order instead of checking !Compare1 so we accept equal keys.
+    if (st.Compare1(out + i + N1, out + i)) {
+      printf("%s: i=%d of %d lanes: N1=%d %5.0f %5.0f vs. %5.0f %5.0f\n\n",
+             caller, static_cast<int>(i), static_cast<int>(num_lanes),
+             static_cast<int>(N1), static_cast<double>(out[i + 1]),
+             static_cast<double>(out[i + 0]),
+             static_cast<double>(out[i + N1 + 1]),
+             static_cast<double>(out[i + N1]));
+      HWY_ABORT("%d-bit sort is incorrect\n",
+                static_cast<int>(sizeof(LaneType) * 8 * N1));
+    }
+  }
+  output_stats.Notify(out[num_lanes - N1]);
+  if (N1 == 2) output_stats.Notify(out[num_lanes - N1 + 1]);
+
+  return input_stats == output_stats;
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_RESULT_TOGGLE
diff --git a/third_party/highway/hwy/contrib/sort/shared-inl.h b/third_party/highway/hwy/contrib/sort/shared-inl.h
new file mode 100644
index 0000000000..735f95ee22
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/shared-inl.h
@@ -0,0 +1,134 @@
+// 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.
+
+// Definitions shared between vqsort-inl and sorting_networks-inl.
+
+// Normal include guard for target-independent parts
+#ifndef HIGHWAY_HWY_CONTRIB_SORT_SHARED_INL_H_
+#define HIGHWAY_HWY_CONTRIB_SORT_SHARED_INL_H_
+
+#include "hwy/base.h"
+
+namespace hwy {
+
+// Internal constants - these are to avoid magic numbers/literals and cannot be
+// changed without also changing the associated code.
+struct SortConstants {
+// SortingNetwork reshapes its input into a matrix. This is the maximum number
+// of *keys* per vector.
+#if HWY_COMPILER_MSVC || HWY_IS_DEBUG_BUILD
+  static constexpr size_t kMaxCols = 8;  // avoid build timeout/stack overflow
+#else
+  static constexpr size_t kMaxCols = 16;  // enough for u32 in 512-bit vector
+#endif
+
+  // 16 rows is a compromise between using the 32 AVX-512/SVE/RVV registers,
+  // fitting within 16 AVX2 registers with only a few spills, keeping BaseCase
+  // code size reasonable (7 KiB for AVX-512 and 16 cols), and minimizing the
+  // extra logN factor for larger networks (for which only loose upper bounds
+  // on size are known).
+  static constexpr size_t kMaxRowsLog2 = 4;
+  static constexpr size_t kMaxRows = size_t{1} << kMaxRowsLog2;
+
+  static constexpr HWY_INLINE size_t BaseCaseNum(size_t N) {
+    return kMaxRows * HWY_MIN(N, kMaxCols);
+  }
+
+  // Unrolling is important (pipelining and amortizing branch mispredictions);
+  // 2x is sufficient to reach full memory bandwidth on SKX in Partition, but
+  // somewhat slower for sorting than 4x.
+  //
+  // To change, must also update left + 3 * N etc. in the loop.
+  static constexpr size_t kPartitionUnroll = 4;
+
+  static constexpr HWY_INLINE size_t PartitionBufNum(size_t N) {
+    // The main loop reads kPartitionUnroll vectors, and first loads from
+    // both left and right beforehand, so it requires min = 2 *
+    // kPartitionUnroll vectors. To handle smaller amounts (only guaranteed
+    // >= BaseCaseNum), we partition the right side into a buffer. We need
+    // another vector at the end so CompressStore does not overwrite anything.
+    return (2 * kPartitionUnroll + 1) * N;
+  }
+
+  // Chunk := group of keys loaded for sampling a pivot. Matches the typical
+  // cache line size of 64 bytes to get maximum benefit per L2 miss. Sort()
+  // ensures vectors are no larger than that, so this can be independent of the
+  // vector size and thus constexpr.
+  static constexpr HWY_INLINE size_t LanesPerChunk(size_t sizeof_t) {
+    return 64 / sizeof_t;
+  }
+
+  static constexpr HWY_INLINE size_t PivotBufNum(size_t sizeof_t, size_t N) {
+    // 3 chunks of medians, 1 chunk of median medians plus two padding vectors.
+    return (3 + 1) * LanesPerChunk(sizeof_t) + 2 * N;
+  }
+
+  template <typename T>
+  static constexpr HWY_INLINE size_t BufNum(size_t N) {
+    // One extra for padding plus another for full-vector loads.
+    return HWY_MAX(BaseCaseNum(N) + 2 * N,
+                   HWY_MAX(PartitionBufNum(N), PivotBufNum(sizeof(T), N)));
+  }
+
+  template <typename T>
+  static constexpr HWY_INLINE size_t BufBytes(size_t vector_size) {
+    return sizeof(T) * BufNum<T>(vector_size / sizeof(T));
+  }
+};
+
+}  // namespace hwy
+
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_SHARED_INL_H_
+
+// Per-target
+#if defined(HIGHWAY_HWY_CONTRIB_SORT_SHARED_TOGGLE) == \
+    defined(HWY_TARGET_TOGGLE)
+#ifdef HIGHWAY_HWY_CONTRIB_SORT_SHARED_TOGGLE
+#undef HIGHWAY_HWY_CONTRIB_SORT_SHARED_TOGGLE
+#else
+#define HIGHWAY_HWY_CONTRIB_SORT_SHARED_TOGGLE
+#endif
+
+#include "hwy/highway.h"
+
+// vqsort isn't available on HWY_SCALAR, and builds time out on MSVC opt and
+// Arm v7 debug.
+#undef VQSORT_ENABLED
+#if (HWY_TARGET == HWY_SCALAR) ||                 \
+    (HWY_COMPILER_MSVC && !HWY_IS_DEBUG_BUILD) || \
+    (HWY_ARCH_ARM_V7 && HWY_IS_DEBUG_BUILD)
+#define VQSORT_ENABLED 0
+#else
+#define VQSORT_ENABLED 1
+#endif
+
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+// Default tag / vector width selector.
+#if HWY_TARGET == HWY_RVV
+// Use LMUL = 1/2; for SEW=64 this ends up emulated via vsetvl.
+template <typename T>
+using SortTag = ScalableTag<T, -1>;
+#else
+template <typename T>
+using SortTag = ScalableTag<T>;
+#endif
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_SHARED_TOGGLE
diff --git a/third_party/highway/hwy/contrib/sort/sort_test.cc b/third_party/highway/hwy/contrib/sort/sort_test.cc
new file mode 100644
index 0000000000..2d1f1d5169
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/sort_test.cc
@@ -0,0 +1,626 @@
+// 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.
+
+#ifndef __STDC_FORMAT_MACROS
+#define __STDC_FORMAT_MACROS  // before inttypes.h
+#endif
+#include <inttypes.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <string.h>  // memcpy
+
+#include <unordered_map>
+#include <vector>
+
+// clang-format off
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/sort_test.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+#include "hwy/contrib/sort/vqsort.h"
+// After foreach_target
+#include "hwy/contrib/sort/algo-inl.h"
+#include "hwy/contrib/sort/traits128-inl.h"
+#include "hwy/contrib/sort/result-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"  // BaseCase
+#include "hwy/tests/test_util-inl.h"
+// clang-format on
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+namespace {
+
+using detail::OrderAscending;
+using detail::OrderDescending;
+using detail::SharedTraits;
+using detail::TraitsLane;
+#if VQSORT_ENABLED || HWY_IDE
+using detail::OrderAscending128;
+using detail::OrderAscendingKV128;
+using detail::OrderAscendingKV64;
+using detail::OrderDescending128;
+using detail::OrderDescendingKV128;
+using detail::OrderDescendingKV64;
+using detail::Traits128;
+
+template <class Traits>
+static HWY_NOINLINE void TestMedian3() {
+  using LaneType = typename Traits::LaneType;
+  using D = CappedTag<LaneType, 1>;
+  SharedTraits<Traits> st;
+  const D d;
+  using V = Vec<D>;
+  for (uint32_t bits = 0; bits < 8; ++bits) {
+    const V v0 = Set(d, LaneType{(bits & (1u << 0)) ? 1u : 0u});
+    const V v1 = Set(d, LaneType{(bits & (1u << 1)) ? 1u : 0u});
+    const V v2 = Set(d, LaneType{(bits & (1u << 2)) ? 1u : 0u});
+    const LaneType m = GetLane(detail::MedianOf3(st, v0, v1, v2));
+    // If at least half(rounded up) of bits are 1, so is the median.
+    const size_t count = PopCount(bits);
+    HWY_ASSERT_EQ((count >= 2) ? static_cast<LaneType>(1) : 0, m);
+  }
+}
+
+HWY_NOINLINE void TestAllMedian() {
+  TestMedian3<TraitsLane<OrderAscending<uint64_t> > >();
+}
+
+template <class Traits>
+static HWY_NOINLINE void TestBaseCaseAscDesc() {
+  using LaneType = typename Traits::LaneType;
+  SharedTraits<Traits> st;
+  const SortTag<LaneType> d;
+  const size_t N = Lanes(d);
+  const size_t base_case_num = SortConstants::BaseCaseNum(N);
+  const size_t N1 = st.LanesPerKey();
+
+  constexpr int kDebug = 0;
+  auto aligned_lanes = hwy::AllocateAligned<LaneType>(N + base_case_num + N);
+  auto buf = hwy::AllocateAligned<LaneType>(base_case_num + 2 * N);
+
+  std::vector<size_t> lengths;
+  lengths.push_back(HWY_MAX(1, N1));
+  lengths.push_back(3 * N1);
+  lengths.push_back(base_case_num / 2);
+  lengths.push_back(base_case_num / 2 + N1);
+  lengths.push_back(base_case_num - N1);
+  lengths.push_back(base_case_num);
+
+  std::vector<size_t> misalignments;
+  misalignments.push_back(0);
+  misalignments.push_back(1);
+  if (N >= 6) misalignments.push_back(N / 2 - 1);
+  misalignments.push_back(N / 2);
+  misalignments.push_back(N / 2 + 1);
+  misalignments.push_back(HWY_MIN(2 * N / 3 + 3, size_t{N - 1}));
+
+  for (bool asc : {false, true}) {
+    for (size_t len : lengths) {
+      for (size_t misalign : misalignments) {
+        LaneType* HWY_RESTRICT lanes = aligned_lanes.get() + misalign;
+        if (kDebug) {
+          printf("============%s asc %d N1 %d len %d misalign %d\n",
+                 st.KeyString().c_str(), asc, static_cast<int>(N1),
+                 static_cast<int>(len), static_cast<int>(misalign));
+        }
+
+        for (size_t i = 0; i < misalign; ++i) {
+          aligned_lanes[i] = hwy::LowestValue<LaneType>();
+        }
+        InputStats<LaneType> input_stats;
+        for (size_t i = 0; i < len; ++i) {
+          lanes[i] = asc ? static_cast<LaneType>(LaneType(i) + 1)
+                         : static_cast<LaneType>(LaneType(len) - LaneType(i));
+          input_stats.Notify(lanes[i]);
+          if (kDebug >= 2) {
+            printf("%3zu: %f\n", i, static_cast<double>(lanes[i]));
+          }
+        }
+        for (size_t i = len; i < base_case_num + N; ++i) {
+          lanes[i] = hwy::LowestValue<LaneType>();
+        }
+
+        detail::BaseCase(d, st, lanes, lanes + len, len, buf.get());
+
+        if (kDebug >= 2) {
+          printf("out>>>>>>\n");
+          for (size_t i = 0; i < len; ++i) {
+            printf("%3zu: %f\n", i, static_cast<double>(lanes[i]));
+          }
+        }
+
+        HWY_ASSERT(VerifySort(st, input_stats, lanes, len, "BaseAscDesc"));
+        for (size_t i = 0; i < misalign; ++i) {
+          if (aligned_lanes[i] != hwy::LowestValue<LaneType>())
+            HWY_ABORT("Overrun misalign at %d\n", static_cast<int>(i));
+        }
+        for (size_t i = len; i < base_case_num + N; ++i) {
+          if (lanes[i] != hwy::LowestValue<LaneType>())
+            HWY_ABORT("Overrun right at %d\n", static_cast<int>(i));
+        }
+      }  // misalign
+    }    // len
+  }      // asc
+}
+
+template <class Traits>
+static HWY_NOINLINE void TestBaseCase01() {
+  using LaneType = typename Traits::LaneType;
+  SharedTraits<Traits> st;
+  const SortTag<LaneType> d;
+  const size_t N = Lanes(d);
+  const size_t base_case_num = SortConstants::BaseCaseNum(N);
+  const size_t N1 = st.LanesPerKey();
+
+  constexpr int kDebug = 0;
+  auto lanes = hwy::AllocateAligned<LaneType>(base_case_num + N);
+  auto buf = hwy::AllocateAligned<LaneType>(base_case_num + 2 * N);
+
+  std::vector<size_t> lengths;
+  lengths.push_back(HWY_MAX(1, N1));
+  lengths.push_back(3 * N1);
+  lengths.push_back(base_case_num / 2);
+  lengths.push_back(base_case_num / 2 + N1);
+  lengths.push_back(base_case_num - N1);
+  lengths.push_back(base_case_num);
+
+  for (size_t len : lengths) {
+    if (kDebug) {
+      printf("============%s 01 N1 %d len %d\n", st.KeyString().c_str(),
+             static_cast<int>(N1), static_cast<int>(len));
+    }
+    const uint64_t kMaxBits = AdjustedLog2Reps(HWY_MIN(len, size_t{14}));
+    for (uint64_t bits = 0; bits < ((1ull << kMaxBits) - 1); ++bits) {
+      InputStats<LaneType> input_stats;
+      for (size_t i = 0; i < len; ++i) {
+        lanes[i] = (i < 64 && (bits & (1ull << i))) ? 1 : 0;
+        input_stats.Notify(lanes[i]);
+        if (kDebug >= 2) {
+          printf("%3zu: %f\n", i, static_cast<double>(lanes[i]));
+        }
+      }
+      for (size_t i = len; i < base_case_num + N; ++i) {
+        lanes[i] = hwy::LowestValue<LaneType>();
+      }
+
+      detail::BaseCase(d, st, lanes.get(), lanes.get() + len, len, buf.get());
+
+      if (kDebug >= 2) {
+        printf("out>>>>>>\n");
+        for (size_t i = 0; i < len; ++i) {
+          printf("%3zu: %f\n", i, static_cast<double>(lanes[i]));
+        }
+      }
+
+      HWY_ASSERT(VerifySort(st, input_stats, lanes.get(), len, "Base01"));
+      for (size_t i = len; i < base_case_num + N; ++i) {
+        if (lanes[i] != hwy::LowestValue<LaneType>())
+          HWY_ABORT("Overrun right at %d\n", static_cast<int>(i));
+      }
+    }  // bits
+  }    // len
+}
+
+template <class Traits>
+static HWY_NOINLINE void TestBaseCase() {
+  TestBaseCaseAscDesc<Traits>();
+  TestBaseCase01<Traits>();
+}
+
+HWY_NOINLINE void TestAllBaseCase() {
+  // Workaround for stack overflow on MSVC debug.
+#if defined(_MSC_VER)
+  return;
+#endif
+  TestBaseCase<TraitsLane<OrderAscending<int32_t> > >();
+  TestBaseCase<TraitsLane<OrderDescending<int64_t> > >();
+  TestBaseCase<Traits128<OrderAscending128> >();
+  TestBaseCase<Traits128<OrderDescending128> >();
+}
+
+template <class Traits>
+static HWY_NOINLINE void VerifyPartition(
+    Traits st, typename Traits::LaneType* HWY_RESTRICT lanes, size_t left,
+    size_t border, size_t right, const size_t N1,
+    const typename Traits::LaneType* pivot) {
+  /* for (size_t i = left; i < right; ++i) {
+     if (i == border) printf("--\n");
+     printf("%4zu: %3d\n", i, lanes[i]);
+   }*/
+
+  HWY_ASSERT(left % N1 == 0);
+  HWY_ASSERT(border % N1 == 0);
+  HWY_ASSERT(right % N1 == 0);
+  const bool asc = typename Traits::Order().IsAscending();
+  for (size_t i = left; i < border; i += N1) {
+    if (st.Compare1(pivot, lanes + i)) {
+      HWY_ABORT(
+          "%s: asc %d left[%d] piv %.0f %.0f compares before %.0f %.0f "
+          "border %d",
+          st.KeyString().c_str(), asc, static_cast<int>(i),
+          static_cast<double>(pivot[1]), static_cast<double>(pivot[0]),
+          static_cast<double>(lanes[i + 1]), static_cast<double>(lanes[i + 0]),
+          static_cast<int>(border));
+    }
+  }
+  for (size_t i = border; i < right; i += N1) {
+    if (!st.Compare1(pivot, lanes + i)) {
+      HWY_ABORT(
+          "%s: asc %d right[%d] piv %.0f %.0f compares after %.0f %.0f "
+          "border %d",
+          st.KeyString().c_str(), asc, static_cast<int>(i),
+          static_cast<double>(pivot[1]), static_cast<double>(pivot[0]),
+          static_cast<double>(lanes[i + 1]), static_cast<double>(lanes[i]),
+          static_cast<int>(border));
+    }
+  }
+}
+
+template <class Traits>
+static HWY_NOINLINE void TestPartition() {
+  using LaneType = typename Traits::LaneType;
+  const SortTag<LaneType> d;
+  SharedTraits<Traits> st;
+  const bool asc = typename Traits::Order().IsAscending();
+  const size_t N = Lanes(d);
+  constexpr int kDebug = 0;
+  const size_t base_case_num = SortConstants::BaseCaseNum(N);
+  // left + len + align
+  const size_t total = 32 + (base_case_num + 4 * HWY_MAX(N, 4)) + 2 * N;
+  auto aligned_lanes = hwy::AllocateAligned<LaneType>(total);
+  auto buf = hwy::AllocateAligned<LaneType>(SortConstants::PartitionBufNum(N));
+
+  const size_t N1 = st.LanesPerKey();
+  for (bool in_asc : {false, true}) {
+    for (int left_i : {0, 1, 4, 6, 7, 8, 12, 15, 22, 28, 30, 31}) {
+      const size_t left = static_cast<size_t>(left_i) & ~(N1 - 1);
+      for (size_t ofs : {N, N + 1, N + 3, 2 * N, 2 * N + 2, 2 * N + 3,
+                         3 * N - 1, 4 * N - 3, 4 * N - 2}) {
+        const size_t len = (base_case_num + ofs) & ~(N1 - 1);
+        for (LaneType pivot1 :
+             {LaneType(0), LaneType(len / 3), LaneType(len / 2),
+              LaneType(2 * len / 3), LaneType(len)}) {
+          const LaneType pivot2[2] = {pivot1, 0};
+          const auto pivot = st.SetKey(d, pivot2);
+          for (size_t misalign = 0; misalign < N;
+               misalign += st.LanesPerKey()) {
+            LaneType* HWY_RESTRICT lanes = aligned_lanes.get() + misalign;
+            const size_t right = left + len;
+            if (kDebug) {
+              printf(
+                  "=========%s asc %d left %d len %d right %d piv %.0f %.0f\n",
+                  st.KeyString().c_str(), asc, static_cast<int>(left),
+                  static_cast<int>(len), static_cast<int>(right),
+                  static_cast<double>(pivot2[1]),
+                  static_cast<double>(pivot2[0]));
+            }
+
+            for (size_t i = 0; i < misalign; ++i) {
+              aligned_lanes[i] = hwy::LowestValue<LaneType>();
+            }
+            for (size_t i = 0; i < left; ++i) {
+              lanes[i] = hwy::LowestValue<LaneType>();
+            }
+            std::unordered_map<LaneType, int> counts;
+            for (size_t i = left; i < right; ++i) {
+              lanes[i] = static_cast<LaneType>(
+                  in_asc ? LaneType(i + 1) - static_cast<LaneType>(left)
+                         : static_cast<LaneType>(right) - LaneType(i));
+              ++counts[lanes[i]];
+              if (kDebug >= 2) {
+                printf("%3zu: %f\n", i, static_cast<double>(lanes[i]));
+              }
+            }
+            for (size_t i = right; i < total - misalign; ++i) {
+              lanes[i] = hwy::LowestValue<LaneType>();
+            }
+
+            size_t border =
+                left + detail::Partition(d, st, lanes + left, right - left,
+                                         pivot, buf.get());
+
+            if (kDebug >= 2) {
+              printf("out>>>>>>\n");
+              for (size_t i = left; i < right; ++i) {
+                printf("%3zu: %f\n", i, static_cast<double>(lanes[i]));
+              }
+              for (size_t i = right; i < total - misalign; ++i) {
+                printf("%3zu: sentinel %f\n", i, static_cast<double>(lanes[i]));
+              }
+            }
+            for (size_t i = left; i < right; ++i) {
+              --counts[lanes[i]];
+            }
+            for (auto kv : counts) {
+              if (kv.second != 0) {
+                PrintValue(kv.first);
+                HWY_ABORT("Incorrect count %d\n", kv.second);
+              }
+            }
+            VerifyPartition(st, lanes, left, border, right, N1, pivot2);
+            for (size_t i = 0; i < misalign; ++i) {
+              if (aligned_lanes[i] != hwy::LowestValue<LaneType>())
+                HWY_ABORT("Overrun misalign at %d\n", static_cast<int>(i));
+            }
+            for (size_t i = 0; i < left; ++i) {
+              if (lanes[i] != hwy::LowestValue<LaneType>())
+                HWY_ABORT("Overrun left at %d\n", static_cast<int>(i));
+            }
+            for (size_t i = right; i < total - misalign; ++i) {
+              if (lanes[i] != hwy::LowestValue<LaneType>())
+                HWY_ABORT("Overrun right at %d\n", static_cast<int>(i));
+            }
+          }  // misalign
+        }    // pivot
+      }      // len
+    }        // left
+  }          // asc
+}
+
+HWY_NOINLINE void TestAllPartition() {
+  TestPartition<TraitsLane<OrderDescending<int32_t> > >();
+  TestPartition<Traits128<OrderAscending128> >();
+
+#if !HWY_IS_DEBUG_BUILD
+  TestPartition<TraitsLane<OrderAscending<int16_t> > >();
+  TestPartition<TraitsLane<OrderAscending<int64_t> > >();
+  TestPartition<TraitsLane<OrderDescending<float> > >();
+#if HWY_HAVE_FLOAT64
+  TestPartition<TraitsLane<OrderDescending<double> > >();
+#endif
+  TestPartition<Traits128<OrderDescending128> >();
+#endif
+}
+
+// (used for sample selection for choosing a pivot)
+template <typename TU>
+static HWY_NOINLINE void TestRandomGenerator() {
+  static_assert(!hwy::IsSigned<TU>(), "");
+  SortTag<TU> du;
+  const size_t N = Lanes(du);
+
+  detail::Generator rng(&N, N);
+
+  const size_t lanes_per_block = HWY_MAX(64 / sizeof(TU), N);  // power of two
+
+  for (uint32_t num_blocks = 2; num_blocks < 100000;
+       num_blocks = 3 * num_blocks / 2) {
+    // Generate some numbers and ensure all are in range
+    uint64_t sum = 0;
+    constexpr size_t kReps = 10000;
+    for (size_t rep = 0; rep < kReps; ++rep) {
+      const uint32_t bits = rng() & 0xFFFFFFFF;
+      const size_t index = detail::RandomChunkIndex(num_blocks, bits);
+      HWY_ASSERT(((index + 1) * lanes_per_block) <=
+                 num_blocks * lanes_per_block);
+
+      sum += index;
+    }
+
+    // Also ensure the mean is near the middle of the range
+    const double expected = (num_blocks - 1) / 2.0;
+    const double actual = static_cast<double>(sum) / kReps;
+    HWY_ASSERT(0.9 * expected <= actual && actual <= 1.1 * expected);
+  }
+}
+
+HWY_NOINLINE void TestAllGenerator() {
+  TestRandomGenerator<uint32_t>();
+  TestRandomGenerator<uint64_t>();
+}
+
+#else
+static void TestAllMedian() {}
+static void TestAllBaseCase() {}
+static void TestAllPartition() {}
+static void TestAllGenerator() {}
+#endif  // VQSORT_ENABLED
+
+// Remembers input, and compares results to that of a reference algorithm.
+template <class Traits>
+class CompareResults {
+  using LaneType = typename Traits::LaneType;
+  using KeyType = typename Traits::KeyType;
+
+ public:
+  CompareResults(const LaneType* in, size_t num_lanes) {
+    copy_.resize(num_lanes);
+    memcpy(copy_.data(), in, num_lanes * sizeof(LaneType));
+  }
+
+  bool Verify(const LaneType* output) {
+#if HAVE_PDQSORT
+    const Algo reference = Algo::kPDQ;
+#else
+    const Algo reference = Algo::kStd;
+#endif
+    SharedState shared;
+    using Order = typename Traits::Order;
+    const Traits st;
+    const size_t num_keys = copy_.size() / st.LanesPerKey();
+    Run<Order>(reference, reinterpret_cast<KeyType*>(copy_.data()), num_keys,
+               shared, /*thread=*/0);
+#if VQSORT_PRINT >= 3
+    fprintf(stderr, "\nExpected:\n");
+    for (size_t i = 0; i < copy_.size(); ++i) {
+      PrintValue(copy_[i]);
+    }
+    fprintf(stderr, "\n");
+#endif
+    for (size_t i = 0; i < copy_.size(); ++i) {
+      if (copy_[i] != output[i]) {
+        if (sizeof(KeyType) == 16) {
+          fprintf(stderr,
+                  "%s Asc %d mismatch at %d of %d: %" PRIu64 " %" PRIu64 "\n",
+                  st.KeyString().c_str(), Order().IsAscending(),
+                  static_cast<int>(i), static_cast<int>(copy_.size()),
+                  static_cast<uint64_t>(copy_[i]),
+                  static_cast<uint64_t>(output[i]));
+        } else {
+          fprintf(stderr, "Type %s Asc %d mismatch at %d of %d: ",
+                  st.KeyString().c_str(), Order().IsAscending(),
+                  static_cast<int>(i), static_cast<int>(copy_.size()));
+          PrintValue(copy_[i]);
+          PrintValue(output[i]);
+          fprintf(stderr, "\n");
+        }
+        return false;
+      }
+    }
+    return true;
+  }
+
+ private:
+  std::vector<LaneType> copy_;
+};
+
+std::vector<Algo> AlgoForTest() {
+  return {
+#if HAVE_AVX2SORT
+    Algo::kSEA,
+#endif
+#if HAVE_IPS4O
+        Algo::kIPS4O,
+#endif
+#if HAVE_PDQSORT
+        Algo::kPDQ,
+#endif
+#if HAVE_SORT512
+        Algo::kSort512,
+#endif
+        Algo::kHeap, Algo::kVQSort,
+  };
+}
+
+template <class Traits>
+void TestSort(size_t num_lanes) {
+// Workaround for stack overflow on clang-cl (/F 8388608 does not help).
+#if defined(_MSC_VER)
+  return;
+#endif
+  using Order = typename Traits::Order;
+  using LaneType = typename Traits::LaneType;
+  using KeyType = typename Traits::KeyType;
+  SharedState shared;
+  SharedTraits<Traits> st;
+
+  // Round up to a whole number of keys.
+  num_lanes += (st.Is128() && (num_lanes & 1));
+  const size_t num_keys = num_lanes / st.LanesPerKey();
+
+  constexpr size_t kMaxMisalign = 16;
+  auto aligned =
+      hwy::AllocateAligned<LaneType>(kMaxMisalign + num_lanes + kMaxMisalign);
+  for (Algo algo : AlgoForTest()) {
+    for (Dist dist : AllDist()) {
+      for (size_t misalign : {size_t{0}, size_t{st.LanesPerKey()},
+                              size_t{3 * st.LanesPerKey()}, kMaxMisalign / 2}) {
+        LaneType* lanes = aligned.get() + misalign;
+
+        // Set up red zones before/after the keys to sort
+        for (size_t i = 0; i < misalign; ++i) {
+          aligned[i] = hwy::LowestValue<LaneType>();
+        }
+        for (size_t i = 0; i < kMaxMisalign; ++i) {
+          lanes[num_lanes + i] = hwy::HighestValue<LaneType>();
+        }
+#if HWY_IS_MSAN
+        __msan_poison(aligned.get(), misalign * sizeof(LaneType));
+        __msan_poison(lanes + num_lanes, kMaxMisalign * sizeof(LaneType));
+#endif
+        InputStats<LaneType> input_stats =
+            GenerateInput(dist, lanes, num_lanes);
+
+        CompareResults<Traits> compare(lanes, num_lanes);
+        Run<Order>(algo, reinterpret_cast<KeyType*>(lanes), num_keys, shared,
+                   /*thread=*/0);
+        HWY_ASSERT(compare.Verify(lanes));
+        HWY_ASSERT(VerifySort(st, input_stats, lanes, num_lanes, "TestSort"));
+
+        // Check red zones
+#if HWY_IS_MSAN
+        __msan_unpoison(aligned.get(), misalign * sizeof(LaneType));
+        __msan_unpoison(lanes + num_lanes, kMaxMisalign * sizeof(LaneType));
+#endif
+        for (size_t i = 0; i < misalign; ++i) {
+          if (aligned[i] != hwy::LowestValue<LaneType>())
+            HWY_ABORT("Overrun left at %d\n", static_cast<int>(i));
+        }
+        for (size_t i = num_lanes; i < num_lanes + kMaxMisalign; ++i) {
+          if (lanes[i] != hwy::HighestValue<LaneType>())
+            HWY_ABORT("Overrun right at %d\n", static_cast<int>(i));
+        }
+      }  // misalign
+    }    // dist
+  }      // algo
+}
+
+void TestAllSort() {
+  for (int num : {129, 504, 3 * 1000, 34567}) {
+    const size_t num_lanes = AdjustedReps(static_cast<size_t>(num));
+    TestSort<TraitsLane<OrderAscending<int16_t> > >(num_lanes);
+    TestSort<TraitsLane<OrderDescending<uint16_t> > >(num_lanes);
+
+    TestSort<TraitsLane<OrderDescending<int32_t> > >(num_lanes);
+    TestSort<TraitsLane<OrderDescending<uint32_t> > >(num_lanes);
+
+    TestSort<TraitsLane<OrderAscending<int64_t> > >(num_lanes);
+    TestSort<TraitsLane<OrderAscending<uint64_t> > >(num_lanes);
+
+    // WARNING: for float types, SIMD comparisons will flush denormals to
+    // zero, causing mismatches with scalar sorts. In this test, we avoid
+    // generating denormal inputs.
+    TestSort<TraitsLane<OrderAscending<float> > >(num_lanes);
+#if HWY_HAVE_FLOAT64  // protects algo-inl's GenerateRandom
+    if (Sorter::HaveFloat64()) {
+      TestSort<TraitsLane<OrderDescending<double> > >(num_lanes);
+    }
+#endif
+
+// Our HeapSort does not support 128-bit keys.
+#if VQSORT_ENABLED
+    TestSort<Traits128<OrderAscending128> >(num_lanes);
+    TestSort<Traits128<OrderDescending128> >(num_lanes);
+
+    TestSort<TraitsLane<OrderAscendingKV64> >(num_lanes);
+    TestSort<TraitsLane<OrderDescendingKV64> >(num_lanes);
+
+    TestSort<Traits128<OrderAscendingKV128> >(num_lanes);
+    TestSort<Traits128<OrderDescendingKV128> >(num_lanes);
+#endif
+  }
+}
+
+}  // namespace
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+
+namespace hwy {
+namespace {
+HWY_BEFORE_TEST(SortTest);
+HWY_EXPORT_AND_TEST_P(SortTest, TestAllMedian);
+HWY_EXPORT_AND_TEST_P(SortTest, TestAllBaseCase);
+HWY_EXPORT_AND_TEST_P(SortTest, TestAllPartition);
+HWY_EXPORT_AND_TEST_P(SortTest, TestAllGenerator);
+HWY_EXPORT_AND_TEST_P(SortTest, TestAllSort);
+}  // namespace
+}  // namespace hwy
+
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/sorting_networks-inl.h b/third_party/highway/hwy/contrib/sort/sorting_networks-inl.h
new file mode 100644
index 0000000000..2615a04b68
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/sorting_networks-inl.h
@@ -0,0 +1,707 @@
+// 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.
+
+// Per-target
+#if defined(HIGHWAY_HWY_CONTRIB_SORT_SORTING_NETWORKS_TOGGLE) == \
+    defined(HWY_TARGET_TOGGLE)
+#ifdef HIGHWAY_HWY_CONTRIB_SORT_SORTING_NETWORKS_TOGGLE
+#undef HIGHWAY_HWY_CONTRIB_SORT_SORTING_NETWORKS_TOGGLE
+#else
+#define HIGHWAY_HWY_CONTRIB_SORT_SORTING_NETWORKS_TOGGLE
+#endif
+
+#include "hwy/contrib/sort/shared-inl.h"  // SortConstants
+#include "hwy/highway.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+namespace detail {
+
+#if VQSORT_ENABLED
+
+using Constants = hwy::SortConstants;
+
+// ------------------------------ SharedTraits
+
+// Code shared between all traits. It's unclear whether these can profitably be
+// specialized for Lane vs Block, or optimized like SortPairsDistance1 using
+// Compare/DupOdd.
+template <class Base>
+struct SharedTraits : public Base {
+  // Conditionally swaps lane 0 with 2, 1 with 3 etc.
+  template <class D>
+  HWY_INLINE Vec<D> SortPairsDistance2(D d, Vec<D> v) const {
+    const Base* base = static_cast<const Base*>(this);
+    Vec<D> swapped = base->SwapAdjacentPairs(d, v);
+    base->Sort2(d, v, swapped);
+    return base->OddEvenPairs(d, swapped, v);
+  }
+
+  // Swaps with the vector formed by reversing contiguous groups of 8 keys.
+  template <class D>
+  HWY_INLINE Vec<D> SortPairsReverse8(D d, Vec<D> v) const {
+    const Base* base = static_cast<const Base*>(this);
+    Vec<D> swapped = base->ReverseKeys8(d, v);
+    base->Sort2(d, v, swapped);
+    return base->OddEvenQuads(d, swapped, v);
+  }
+
+  // Swaps with the vector formed by reversing contiguous groups of 8 keys.
+  template <class D>
+  HWY_INLINE Vec<D> SortPairsReverse16(D d, Vec<D> v) const {
+    const Base* base = static_cast<const Base*>(this);
+    static_assert(Constants::kMaxCols <= 16, "Need actual Reverse16");
+    Vec<D> swapped = base->ReverseKeys(d, v);
+    base->Sort2(d, v, swapped);
+    return ConcatUpperLower(d, swapped, v);  // 8 = half of the vector
+  }
+};
+
+// ------------------------------ Sorting network
+
+// (Green's irregular) sorting network for independent columns in 16 vectors.
+template <class D, class Traits, class V = Vec<D>>
+HWY_INLINE void Sort16(D d, Traits st, V& v0, V& v1, V& v2, V& v3, V& v4, V& v5,
+                       V& v6, V& v7, V& v8, V& v9, V& va, V& vb, V& vc, V& vd,
+                       V& ve, V& vf) {
+  st.Sort2(d, v0, v1);
+  st.Sort2(d, v2, v3);
+  st.Sort2(d, v4, v5);
+  st.Sort2(d, v6, v7);
+  st.Sort2(d, v8, v9);
+  st.Sort2(d, va, vb);
+  st.Sort2(d, vc, vd);
+  st.Sort2(d, ve, vf);
+  st.Sort2(d, v0, v2);
+  st.Sort2(d, v1, v3);
+  st.Sort2(d, v4, v6);
+  st.Sort2(d, v5, v7);
+  st.Sort2(d, v8, va);
+  st.Sort2(d, v9, vb);
+  st.Sort2(d, vc, ve);
+  st.Sort2(d, vd, vf);
+  st.Sort2(d, v0, v4);
+  st.Sort2(d, v1, v5);
+  st.Sort2(d, v2, v6);
+  st.Sort2(d, v3, v7);
+  st.Sort2(d, v8, vc);
+  st.Sort2(d, v9, vd);
+  st.Sort2(d, va, ve);
+  st.Sort2(d, vb, vf);
+  st.Sort2(d, v0, v8);
+  st.Sort2(d, v1, v9);
+  st.Sort2(d, v2, va);
+  st.Sort2(d, v3, vb);
+  st.Sort2(d, v4, vc);
+  st.Sort2(d, v5, vd);
+  st.Sort2(d, v6, ve);
+  st.Sort2(d, v7, vf);
+  st.Sort2(d, v5, va);
+  st.Sort2(d, v6, v9);
+  st.Sort2(d, v3, vc);
+  st.Sort2(d, v7, vb);
+  st.Sort2(d, vd, ve);
+  st.Sort2(d, v4, v8);
+  st.Sort2(d, v1, v2);
+  st.Sort2(d, v1, v4);
+  st.Sort2(d, v7, vd);
+  st.Sort2(d, v2, v8);
+  st.Sort2(d, vb, ve);
+  st.Sort2(d, v2, v4);
+  st.Sort2(d, v5, v6);
+  st.Sort2(d, v9, va);
+  st.Sort2(d, vb, vd);
+  st.Sort2(d, v3, v8);
+  st.Sort2(d, v7, vc);
+  st.Sort2(d, v3, v5);
+  st.Sort2(d, v6, v8);
+  st.Sort2(d, v7, v9);
+  st.Sort2(d, va, vc);
+  st.Sort2(d, v3, v4);
+  st.Sort2(d, v5, v6);
+  st.Sort2(d, v7, v8);
+  st.Sort2(d, v9, va);
+  st.Sort2(d, vb, vc);
+  st.Sort2(d, v6, v7);
+  st.Sort2(d, v8, v9);
+}
+
+// ------------------------------ Merging networks
+
+// Blacher's hybrid bitonic/odd-even networks, generated by print_network.cc.
+
+template <class D, class Traits, class V = Vec<D>>
+HWY_INLINE void Merge2(D d, Traits st, V& v0, V& v1, V& v2, V& v3, V& v4, V& v5,
+                       V& v6, V& v7, V& v8, V& v9, V& va, V& vb, V& vc, V& vd,
+                       V& ve, V& vf) {
+  v8 = st.ReverseKeys2(d, v8);
+  v9 = st.ReverseKeys2(d, v9);
+  va = st.ReverseKeys2(d, va);
+  vb = st.ReverseKeys2(d, vb);
+  vc = st.ReverseKeys2(d, vc);
+  vd = st.ReverseKeys2(d, vd);
+  ve = st.ReverseKeys2(d, ve);
+  vf = st.ReverseKeys2(d, vf);
+  st.Sort2(d, v0, vf);
+  st.Sort2(d, v1, ve);
+  st.Sort2(d, v2, vd);
+  st.Sort2(d, v3, vc);
+  st.Sort2(d, v4, vb);
+  st.Sort2(d, v5, va);
+  st.Sort2(d, v6, v9);
+  st.Sort2(d, v7, v8);
+  v4 = st.ReverseKeys2(d, v4);
+  vc = st.ReverseKeys2(d, vc);
+  v5 = st.ReverseKeys2(d, v5);
+  vd = st.ReverseKeys2(d, vd);
+  v6 = st.ReverseKeys2(d, v6);
+  ve = st.ReverseKeys2(d, ve);
+  v7 = st.ReverseKeys2(d, v7);
+  vf = st.ReverseKeys2(d, vf);
+  st.Sort2(d, v0, v7);
+  st.Sort2(d, v8, vf);
+  st.Sort2(d, v1, v6);
+  st.Sort2(d, v9, ve);
+  st.Sort2(d, v2, v5);
+  st.Sort2(d, va, vd);
+  st.Sort2(d, v3, v4);
+  st.Sort2(d, vb, vc);
+  v2 = st.ReverseKeys2(d, v2);
+  v3 = st.ReverseKeys2(d, v3);
+  v6 = st.ReverseKeys2(d, v6);
+  v7 = st.ReverseKeys2(d, v7);
+  va = st.ReverseKeys2(d, va);
+  vb = st.ReverseKeys2(d, vb);
+  ve = st.ReverseKeys2(d, ve);
+  vf = st.ReverseKeys2(d, vf);
+  st.Sort2(d, v0, v3);
+  st.Sort2(d, v1, v2);
+  st.Sort2(d, v4, v7);
+  st.Sort2(d, v5, v6);
+  st.Sort2(d, v8, vb);
+  st.Sort2(d, v9, va);
+  st.Sort2(d, vc, vf);
+  st.Sort2(d, vd, ve);
+  v1 = st.ReverseKeys2(d, v1);
+  v3 = st.ReverseKeys2(d, v3);
+  v5 = st.ReverseKeys2(d, v5);
+  v7 = st.ReverseKeys2(d, v7);
+  v9 = st.ReverseKeys2(d, v9);
+  vb = st.ReverseKeys2(d, vb);
+  vd = st.ReverseKeys2(d, vd);
+  vf = st.ReverseKeys2(d, vf);
+  st.Sort2(d, v0, v1);
+  st.Sort2(d, v2, v3);
+  st.Sort2(d, v4, v5);
+  st.Sort2(d, v6, v7);
+  st.Sort2(d, v8, v9);
+  st.Sort2(d, va, vb);
+  st.Sort2(d, vc, vd);
+  st.Sort2(d, ve, vf);
+  v0 = st.SortPairsDistance1(d, v0);
+  v1 = st.SortPairsDistance1(d, v1);
+  v2 = st.SortPairsDistance1(d, v2);
+  v3 = st.SortPairsDistance1(d, v3);
+  v4 = st.SortPairsDistance1(d, v4);
+  v5 = st.SortPairsDistance1(d, v5);
+  v6 = st.SortPairsDistance1(d, v6);
+  v7 = st.SortPairsDistance1(d, v7);
+  v8 = st.SortPairsDistance1(d, v8);
+  v9 = st.SortPairsDistance1(d, v9);
+  va = st.SortPairsDistance1(d, va);
+  vb = st.SortPairsDistance1(d, vb);
+  vc = st.SortPairsDistance1(d, vc);
+  vd = st.SortPairsDistance1(d, vd);
+  ve = st.SortPairsDistance1(d, ve);
+  vf = st.SortPairsDistance1(d, vf);
+}
+
+template <class D, class Traits, class V = Vec<D>>
+HWY_INLINE void Merge4(D d, Traits st, V& v0, V& v1, V& v2, V& v3, V& v4, V& v5,
+                       V& v6, V& v7, V& v8, V& v9, V& va, V& vb, V& vc, V& vd,
+                       V& ve, V& vf) {
+  v8 = st.ReverseKeys4(d, v8);
+  v9 = st.ReverseKeys4(d, v9);
+  va = st.ReverseKeys4(d, va);
+  vb = st.ReverseKeys4(d, vb);
+  vc = st.ReverseKeys4(d, vc);
+  vd = st.ReverseKeys4(d, vd);
+  ve = st.ReverseKeys4(d, ve);
+  vf = st.ReverseKeys4(d, vf);
+  st.Sort2(d, v0, vf);
+  st.Sort2(d, v1, ve);
+  st.Sort2(d, v2, vd);
+  st.Sort2(d, v3, vc);
+  st.Sort2(d, v4, vb);
+  st.Sort2(d, v5, va);
+  st.Sort2(d, v6, v9);
+  st.Sort2(d, v7, v8);
+  v4 = st.ReverseKeys4(d, v4);
+  vc = st.ReverseKeys4(d, vc);
+  v5 = st.ReverseKeys4(d, v5);
+  vd = st.ReverseKeys4(d, vd);
+  v6 = st.ReverseKeys4(d, v6);
+  ve = st.ReverseKeys4(d, ve);
+  v7 = st.ReverseKeys4(d, v7);
+  vf = st.ReverseKeys4(d, vf);
+  st.Sort2(d, v0, v7);
+  st.Sort2(d, v8, vf);
+  st.Sort2(d, v1, v6);
+  st.Sort2(d, v9, ve);
+  st.Sort2(d, v2, v5);
+  st.Sort2(d, va, vd);
+  st.Sort2(d, v3, v4);
+  st.Sort2(d, vb, vc);
+  v2 = st.ReverseKeys4(d, v2);
+  v3 = st.ReverseKeys4(d, v3);
+  v6 = st.ReverseKeys4(d, v6);
+  v7 = st.ReverseKeys4(d, v7);
+  va = st.ReverseKeys4(d, va);
+  vb = st.ReverseKeys4(d, vb);
+  ve = st.ReverseKeys4(d, ve);
+  vf = st.ReverseKeys4(d, vf);
+  st.Sort2(d, v0, v3);
+  st.Sort2(d, v1, v2);
+  st.Sort2(d, v4, v7);
+  st.Sort2(d, v5, v6);
+  st.Sort2(d, v8, vb);
+  st.Sort2(d, v9, va);
+  st.Sort2(d, vc, vf);
+  st.Sort2(d, vd, ve);
+  v1 = st.ReverseKeys4(d, v1);
+  v3 = st.ReverseKeys4(d, v3);
+  v5 = st.ReverseKeys4(d, v5);
+  v7 = st.ReverseKeys4(d, v7);
+  v9 = st.ReverseKeys4(d, v9);
+  vb = st.ReverseKeys4(d, vb);
+  vd = st.ReverseKeys4(d, vd);
+  vf = st.ReverseKeys4(d, vf);
+  st.Sort2(d, v0, v1);
+  st.Sort2(d, v2, v3);
+  st.Sort2(d, v4, v5);
+  st.Sort2(d, v6, v7);
+  st.Sort2(d, v8, v9);
+  st.Sort2(d, va, vb);
+  st.Sort2(d, vc, vd);
+  st.Sort2(d, ve, vf);
+  v0 = st.SortPairsReverse4(d, v0);
+  v1 = st.SortPairsReverse4(d, v1);
+  v2 = st.SortPairsReverse4(d, v2);
+  v3 = st.SortPairsReverse4(d, v3);
+  v4 = st.SortPairsReverse4(d, v4);
+  v5 = st.SortPairsReverse4(d, v5);
+  v6 = st.SortPairsReverse4(d, v6);
+  v7 = st.SortPairsReverse4(d, v7);
+  v8 = st.SortPairsReverse4(d, v8);
+  v9 = st.SortPairsReverse4(d, v9);
+  va = st.SortPairsReverse4(d, va);
+  vb = st.SortPairsReverse4(d, vb);
+  vc = st.SortPairsReverse4(d, vc);
+  vd = st.SortPairsReverse4(d, vd);
+  ve = st.SortPairsReverse4(d, ve);
+  vf = st.SortPairsReverse4(d, vf);
+  v0 = st.SortPairsDistance1(d, v0);
+  v1 = st.SortPairsDistance1(d, v1);
+  v2 = st.SortPairsDistance1(d, v2);
+  v3 = st.SortPairsDistance1(d, v3);
+  v4 = st.SortPairsDistance1(d, v4);
+  v5 = st.SortPairsDistance1(d, v5);
+  v6 = st.SortPairsDistance1(d, v6);
+  v7 = st.SortPairsDistance1(d, v7);
+  v8 = st.SortPairsDistance1(d, v8);
+  v9 = st.SortPairsDistance1(d, v9);
+  va = st.SortPairsDistance1(d, va);
+  vb = st.SortPairsDistance1(d, vb);
+  vc = st.SortPairsDistance1(d, vc);
+  vd = st.SortPairsDistance1(d, vd);
+  ve = st.SortPairsDistance1(d, ve);
+  vf = st.SortPairsDistance1(d, vf);
+}
+
+template <class D, class Traits, class V = Vec<D>>
+HWY_INLINE void Merge8(D d, Traits st, V& v0, V& v1, V& v2, V& v3, V& v4, V& v5,
+                       V& v6, V& v7, V& v8, V& v9, V& va, V& vb, V& vc, V& vd,
+                       V& ve, V& vf) {
+  v8 = st.ReverseKeys8(d, v8);
+  v9 = st.ReverseKeys8(d, v9);
+  va = st.ReverseKeys8(d, va);
+  vb = st.ReverseKeys8(d, vb);
+  vc = st.ReverseKeys8(d, vc);
+  vd = st.ReverseKeys8(d, vd);
+  ve = st.ReverseKeys8(d, ve);
+  vf = st.ReverseKeys8(d, vf);
+  st.Sort2(d, v0, vf);
+  st.Sort2(d, v1, ve);
+  st.Sort2(d, v2, vd);
+  st.Sort2(d, v3, vc);
+  st.Sort2(d, v4, vb);
+  st.Sort2(d, v5, va);
+  st.Sort2(d, v6, v9);
+  st.Sort2(d, v7, v8);
+  v4 = st.ReverseKeys8(d, v4);
+  vc = st.ReverseKeys8(d, vc);
+  v5 = st.ReverseKeys8(d, v5);
+  vd = st.ReverseKeys8(d, vd);
+  v6 = st.ReverseKeys8(d, v6);
+  ve = st.ReverseKeys8(d, ve);
+  v7 = st.ReverseKeys8(d, v7);
+  vf = st.ReverseKeys8(d, vf);
+  st.Sort2(d, v0, v7);
+  st.Sort2(d, v8, vf);
+  st.Sort2(d, v1, v6);
+  st.Sort2(d, v9, ve);
+  st.Sort2(d, v2, v5);
+  st.Sort2(d, va, vd);
+  st.Sort2(d, v3, v4);
+  st.Sort2(d, vb, vc);
+  v2 = st.ReverseKeys8(d, v2);
+  v3 = st.ReverseKeys8(d, v3);
+  v6 = st.ReverseKeys8(d, v6);
+  v7 = st.ReverseKeys8(d, v7);
+  va = st.ReverseKeys8(d, va);
+  vb = st.ReverseKeys8(d, vb);
+  ve = st.ReverseKeys8(d, ve);
+  vf = st.ReverseKeys8(d, vf);
+  st.Sort2(d, v0, v3);
+  st.Sort2(d, v1, v2);
+  st.Sort2(d, v4, v7);
+  st.Sort2(d, v5, v6);
+  st.Sort2(d, v8, vb);
+  st.Sort2(d, v9, va);
+  st.Sort2(d, vc, vf);
+  st.Sort2(d, vd, ve);
+  v1 = st.ReverseKeys8(d, v1);
+  v3 = st.ReverseKeys8(d, v3);
+  v5 = st.ReverseKeys8(d, v5);
+  v7 = st.ReverseKeys8(d, v7);
+  v9 = st.ReverseKeys8(d, v9);
+  vb = st.ReverseKeys8(d, vb);
+  vd = st.ReverseKeys8(d, vd);
+  vf = st.ReverseKeys8(d, vf);
+  st.Sort2(d, v0, v1);
+  st.Sort2(d, v2, v3);
+  st.Sort2(d, v4, v5);
+  st.Sort2(d, v6, v7);
+  st.Sort2(d, v8, v9);
+  st.Sort2(d, va, vb);
+  st.Sort2(d, vc, vd);
+  st.Sort2(d, ve, vf);
+  v0 = st.SortPairsReverse8(d, v0);
+  v1 = st.SortPairsReverse8(d, v1);
+  v2 = st.SortPairsReverse8(d, v2);
+  v3 = st.SortPairsReverse8(d, v3);
+  v4 = st.SortPairsReverse8(d, v4);
+  v5 = st.SortPairsReverse8(d, v5);
+  v6 = st.SortPairsReverse8(d, v6);
+  v7 = st.SortPairsReverse8(d, v7);
+  v8 = st.SortPairsReverse8(d, v8);
+  v9 = st.SortPairsReverse8(d, v9);
+  va = st.SortPairsReverse8(d, va);
+  vb = st.SortPairsReverse8(d, vb);
+  vc = st.SortPairsReverse8(d, vc);
+  vd = st.SortPairsReverse8(d, vd);
+  ve = st.SortPairsReverse8(d, ve);
+  vf = st.SortPairsReverse8(d, vf);
+  v0 = st.SortPairsDistance2(d, v0);
+  v1 = st.SortPairsDistance2(d, v1);
+  v2 = st.SortPairsDistance2(d, v2);
+  v3 = st.SortPairsDistance2(d, v3);
+  v4 = st.SortPairsDistance2(d, v4);
+  v5 = st.SortPairsDistance2(d, v5);
+  v6 = st.SortPairsDistance2(d, v6);
+  v7 = st.SortPairsDistance2(d, v7);
+  v8 = st.SortPairsDistance2(d, v8);
+  v9 = st.SortPairsDistance2(d, v9);
+  va = st.SortPairsDistance2(d, va);
+  vb = st.SortPairsDistance2(d, vb);
+  vc = st.SortPairsDistance2(d, vc);
+  vd = st.SortPairsDistance2(d, vd);
+  ve = st.SortPairsDistance2(d, ve);
+  vf = st.SortPairsDistance2(d, vf);
+  v0 = st.SortPairsDistance1(d, v0);
+  v1 = st.SortPairsDistance1(d, v1);
+  v2 = st.SortPairsDistance1(d, v2);
+  v3 = st.SortPairsDistance1(d, v3);
+  v4 = st.SortPairsDistance1(d, v4);
+  v5 = st.SortPairsDistance1(d, v5);
+  v6 = st.SortPairsDistance1(d, v6);
+  v7 = st.SortPairsDistance1(d, v7);
+  v8 = st.SortPairsDistance1(d, v8);
+  v9 = st.SortPairsDistance1(d, v9);
+  va = st.SortPairsDistance1(d, va);
+  vb = st.SortPairsDistance1(d, vb);
+  vc = st.SortPairsDistance1(d, vc);
+  vd = st.SortPairsDistance1(d, vd);
+  ve = st.SortPairsDistance1(d, ve);
+  vf = st.SortPairsDistance1(d, vf);
+}
+
+// Unused on MSVC, see below
+#if !HWY_COMPILER_MSVC
+
+template <class D, class Traits, class V = Vec<D>>
+HWY_INLINE void Merge16(D d, Traits st, V& v0, V& v1, V& v2, V& v3, V& v4,
+                        V& v5, V& v6, V& v7, V& v8, V& v9, V& va, V& vb, V& vc,
+                        V& vd, V& ve, V& vf) {
+  v8 = st.ReverseKeys16(d, v8);
+  v9 = st.ReverseKeys16(d, v9);
+  va = st.ReverseKeys16(d, va);
+  vb = st.ReverseKeys16(d, vb);
+  vc = st.ReverseKeys16(d, vc);
+  vd = st.ReverseKeys16(d, vd);
+  ve = st.ReverseKeys16(d, ve);
+  vf = st.ReverseKeys16(d, vf);
+  st.Sort2(d, v0, vf);
+  st.Sort2(d, v1, ve);
+  st.Sort2(d, v2, vd);
+  st.Sort2(d, v3, vc);
+  st.Sort2(d, v4, vb);
+  st.Sort2(d, v5, va);
+  st.Sort2(d, v6, v9);
+  st.Sort2(d, v7, v8);
+  v4 = st.ReverseKeys16(d, v4);
+  vc = st.ReverseKeys16(d, vc);
+  v5 = st.ReverseKeys16(d, v5);
+  vd = st.ReverseKeys16(d, vd);
+  v6 = st.ReverseKeys16(d, v6);
+  ve = st.ReverseKeys16(d, ve);
+  v7 = st.ReverseKeys16(d, v7);
+  vf = st.ReverseKeys16(d, vf);
+  st.Sort2(d, v0, v7);
+  st.Sort2(d, v8, vf);
+  st.Sort2(d, v1, v6);
+  st.Sort2(d, v9, ve);
+  st.Sort2(d, v2, v5);
+  st.Sort2(d, va, vd);
+  st.Sort2(d, v3, v4);
+  st.Sort2(d, vb, vc);
+  v2 = st.ReverseKeys16(d, v2);
+  v3 = st.ReverseKeys16(d, v3);
+  v6 = st.ReverseKeys16(d, v6);
+  v7 = st.ReverseKeys16(d, v7);
+  va = st.ReverseKeys16(d, va);
+  vb = st.ReverseKeys16(d, vb);
+  ve = st.ReverseKeys16(d, ve);
+  vf = st.ReverseKeys16(d, vf);
+  st.Sort2(d, v0, v3);
+  st.Sort2(d, v1, v2);
+  st.Sort2(d, v4, v7);
+  st.Sort2(d, v5, v6);
+  st.Sort2(d, v8, vb);
+  st.Sort2(d, v9, va);
+  st.Sort2(d, vc, vf);
+  st.Sort2(d, vd, ve);
+  v1 = st.ReverseKeys16(d, v1);
+  v3 = st.ReverseKeys16(d, v3);
+  v5 = st.ReverseKeys16(d, v5);
+  v7 = st.ReverseKeys16(d, v7);
+  v9 = st.ReverseKeys16(d, v9);
+  vb = st.ReverseKeys16(d, vb);
+  vd = st.ReverseKeys16(d, vd);
+  vf = st.ReverseKeys16(d, vf);
+  st.Sort2(d, v0, v1);
+  st.Sort2(d, v2, v3);
+  st.Sort2(d, v4, v5);
+  st.Sort2(d, v6, v7);
+  st.Sort2(d, v8, v9);
+  st.Sort2(d, va, vb);
+  st.Sort2(d, vc, vd);
+  st.Sort2(d, ve, vf);
+  v0 = st.SortPairsReverse16(d, v0);
+  v1 = st.SortPairsReverse16(d, v1);
+  v2 = st.SortPairsReverse16(d, v2);
+  v3 = st.SortPairsReverse16(d, v3);
+  v4 = st.SortPairsReverse16(d, v4);
+  v5 = st.SortPairsReverse16(d, v5);
+  v6 = st.SortPairsReverse16(d, v6);
+  v7 = st.SortPairsReverse16(d, v7);
+  v8 = st.SortPairsReverse16(d, v8);
+  v9 = st.SortPairsReverse16(d, v9);
+  va = st.SortPairsReverse16(d, va);
+  vb = st.SortPairsReverse16(d, vb);
+  vc = st.SortPairsReverse16(d, vc);
+  vd = st.SortPairsReverse16(d, vd);
+  ve = st.SortPairsReverse16(d, ve);
+  vf = st.SortPairsReverse16(d, vf);
+  v0 = st.SortPairsDistance4(d, v0);
+  v1 = st.SortPairsDistance4(d, v1);
+  v2 = st.SortPairsDistance4(d, v2);
+  v3 = st.SortPairsDistance4(d, v3);
+  v4 = st.SortPairsDistance4(d, v4);
+  v5 = st.SortPairsDistance4(d, v5);
+  v6 = st.SortPairsDistance4(d, v6);
+  v7 = st.SortPairsDistance4(d, v7);
+  v8 = st.SortPairsDistance4(d, v8);
+  v9 = st.SortPairsDistance4(d, v9);
+  va = st.SortPairsDistance4(d, va);
+  vb = st.SortPairsDistance4(d, vb);
+  vc = st.SortPairsDistance4(d, vc);
+  vd = st.SortPairsDistance4(d, vd);
+  ve = st.SortPairsDistance4(d, ve);
+  vf = st.SortPairsDistance4(d, vf);
+  v0 = st.SortPairsDistance2(d, v0);
+  v1 = st.SortPairsDistance2(d, v1);
+  v2 = st.SortPairsDistance2(d, v2);
+  v3 = st.SortPairsDistance2(d, v3);
+  v4 = st.SortPairsDistance2(d, v4);
+  v5 = st.SortPairsDistance2(d, v5);
+  v6 = st.SortPairsDistance2(d, v6);
+  v7 = st.SortPairsDistance2(d, v7);
+  v8 = st.SortPairsDistance2(d, v8);
+  v9 = st.SortPairsDistance2(d, v9);
+  va = st.SortPairsDistance2(d, va);
+  vb = st.SortPairsDistance2(d, vb);
+  vc = st.SortPairsDistance2(d, vc);
+  vd = st.SortPairsDistance2(d, vd);
+  ve = st.SortPairsDistance2(d, ve);
+  vf = st.SortPairsDistance2(d, vf);
+  v0 = st.SortPairsDistance1(d, v0);
+  v1 = st.SortPairsDistance1(d, v1);
+  v2 = st.SortPairsDistance1(d, v2);
+  v3 = st.SortPairsDistance1(d, v3);
+  v4 = st.SortPairsDistance1(d, v4);
+  v5 = st.SortPairsDistance1(d, v5);
+  v6 = st.SortPairsDistance1(d, v6);
+  v7 = st.SortPairsDistance1(d, v7);
+  v8 = st.SortPairsDistance1(d, v8);
+  v9 = st.SortPairsDistance1(d, v9);
+  va = st.SortPairsDistance1(d, va);
+  vb = st.SortPairsDistance1(d, vb);
+  vc = st.SortPairsDistance1(d, vc);
+  vd = st.SortPairsDistance1(d, vd);
+  ve = st.SortPairsDistance1(d, ve);
+  vf = st.SortPairsDistance1(d, vf);
+}
+
+#endif  // !HWY_COMPILER_MSVC
+
+// Reshapes `buf` into a matrix, sorts columns independently, and then merges
+// into a sorted 1D array without transposing.
+//
+// `st` is SharedTraits<Traits*<Order*>>. This abstraction layer bridges
+//   differences in sort order and single-lane vs 128-bit keys.
+//
+// References:
+// https://drops.dagstuhl.de/opus/volltexte/2021/13775/pdf/LIPIcs-SEA-2021-3.pdf
+// https://github.com/simd-sorting/fast-and-robust/blob/master/avx2_sort_demo/avx2sort.h
+// "Entwurf und Implementierung vektorisierter Sortieralgorithmen" (M. Blacher)
+template <class Traits, class V>
+HWY_INLINE void SortingNetwork(Traits st, size_t cols, V& v0, V& v1, V& v2,
+                               V& v3, V& v4, V& v5, V& v6, V& v7, V& v8, V& v9,
+                               V& va, V& vb, V& vc, V& vd, V& ve, V& vf) {
+  const CappedTag<typename Traits::LaneType, Constants::kMaxCols> d;
+
+  HWY_DASSERT(cols <= Constants::kMaxCols);
+
+  // The network width depends on the number of keys, not lanes.
+  constexpr size_t kLanesPerKey = st.LanesPerKey();
+  const size_t keys = cols / kLanesPerKey;
+  constexpr size_t kMaxKeys = MaxLanes(d) / kLanesPerKey;
+
+  Sort16(d, st, v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, va, vb, vc, vd, ve, vf);
+
+  // Checking MaxLanes avoids generating HWY_ASSERT code for the unreachable
+  // code paths: if MaxLanes < 2, then keys <= cols < 2.
+  if (HWY_LIKELY(keys >= 2 && kMaxKeys >= 2)) {
+    Merge2(d, st, v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, va, vb, vc, vd, ve,
+           vf);
+
+    if (HWY_LIKELY(keys >= 4 && kMaxKeys >= 4)) {
+      Merge4(d, st, v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, va, vb, vc, vd, ve,
+             vf);
+
+      if (HWY_LIKELY(keys >= 8 && kMaxKeys >= 8)) {
+        Merge8(d, st, v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, va, vb, vc, vd,
+               ve, vf);
+
+        // Avoids build timeout. Must match #if condition in kMaxCols.
+#if !HWY_COMPILER_MSVC && !HWY_IS_DEBUG_BUILD
+        if (HWY_LIKELY(keys >= 16 && kMaxKeys >= 16)) {
+          Merge16(d, st, v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, va, vb, vc, vd,
+                  ve, vf);
+
+          static_assert(Constants::kMaxCols <= 16, "Add more branches");
+        }
+#endif
+      }
+    }
+  }
+}
+
+// As above, but loads from/stores to `buf`. This ensures full vectors are
+// aligned, and enables loads/stores without bounds checks.
+//
+// NOINLINE because this is large and called twice from vqsort-inl.h.
+template <class Traits, typename T>
+HWY_NOINLINE void SortingNetwork(Traits st, T* HWY_RESTRICT buf, size_t cols) {
+  const CappedTag<T, Constants::kMaxCols> d;
+  using V = decltype(Zero(d));
+
+  HWY_DASSERT(cols <= Constants::kMaxCols);
+
+  // These are aligned iff cols == Lanes(d). We prefer unaligned/non-constexpr
+  // offsets to duplicating this code for every value of cols.
+  static_assert(Constants::kMaxRows == 16, "Update loads/stores/args");
+  V v0 = LoadU(d, buf + 0x0 * cols);
+  V v1 = LoadU(d, buf + 0x1 * cols);
+  V v2 = LoadU(d, buf + 0x2 * cols);
+  V v3 = LoadU(d, buf + 0x3 * cols);
+  V v4 = LoadU(d, buf + 0x4 * cols);
+  V v5 = LoadU(d, buf + 0x5 * cols);
+  V v6 = LoadU(d, buf + 0x6 * cols);
+  V v7 = LoadU(d, buf + 0x7 * cols);
+  V v8 = LoadU(d, buf + 0x8 * cols);
+  V v9 = LoadU(d, buf + 0x9 * cols);
+  V va = LoadU(d, buf + 0xa * cols);
+  V vb = LoadU(d, buf + 0xb * cols);
+  V vc = LoadU(d, buf + 0xc * cols);
+  V vd = LoadU(d, buf + 0xd * cols);
+  V ve = LoadU(d, buf + 0xe * cols);
+  V vf = LoadU(d, buf + 0xf * cols);
+
+  SortingNetwork(st, cols, v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, va, vb, vc,
+                 vd, ve, vf);
+
+  StoreU(v0, d, buf + 0x0 * cols);
+  StoreU(v1, d, buf + 0x1 * cols);
+  StoreU(v2, d, buf + 0x2 * cols);
+  StoreU(v3, d, buf + 0x3 * cols);
+  StoreU(v4, d, buf + 0x4 * cols);
+  StoreU(v5, d, buf + 0x5 * cols);
+  StoreU(v6, d, buf + 0x6 * cols);
+  StoreU(v7, d, buf + 0x7 * cols);
+  StoreU(v8, d, buf + 0x8 * cols);
+  StoreU(v9, d, buf + 0x9 * cols);
+  StoreU(va, d, buf + 0xa * cols);
+  StoreU(vb, d, buf + 0xb * cols);
+  StoreU(vc, d, buf + 0xc * cols);
+  StoreU(vd, d, buf + 0xd * cols);
+  StoreU(ve, d, buf + 0xe * cols);
+  StoreU(vf, d, buf + 0xf * cols);
+}
+
+#else
+template <class Base>
+struct SharedTraits : public Base {};
+#endif  // VQSORT_ENABLED
+
+}  // namespace detail
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_SORTING_NETWORKS_TOGGLE
diff --git a/third_party/highway/hwy/contrib/sort/traits-inl.h b/third_party/highway/hwy/contrib/sort/traits-inl.h
new file mode 100644
index 0000000000..8dfc639bbd
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/traits-inl.h
@@ -0,0 +1,568 @@
+// 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.
+
+// Per-target
+#if defined(HIGHWAY_HWY_CONTRIB_SORT_TRAITS_TOGGLE) == \
+    defined(HWY_TARGET_TOGGLE)
+#ifdef HIGHWAY_HWY_CONTRIB_SORT_TRAITS_TOGGLE
+#undef HIGHWAY_HWY_CONTRIB_SORT_TRAITS_TOGGLE
+#else
+#define HIGHWAY_HWY_CONTRIB_SORT_TRAITS_TOGGLE
+#endif
+
+#include <string>
+
+#include "hwy/contrib/sort/shared-inl.h"  // SortConstants
+#include "hwy/contrib/sort/vqsort.h"      // SortDescending
+#include "hwy/highway.h"
+#include "hwy/print.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+namespace detail {
+
+#if VQSORT_ENABLED || HWY_IDE
+
+// Highway does not provide a lane type for 128-bit keys, so we use uint64_t
+// along with an abstraction layer for single-lane vs. lane-pair, which is
+// independent of the order.
+template <typename T>
+struct KeyLane {
+  static constexpr bool Is128() { return false; }
+  // False indicates the entire key (i.e. lane) should be compared. KV stands
+  // for key-value.
+  static constexpr bool IsKV() { return false; }
+  constexpr size_t LanesPerKey() const { return 1; }
+
+  // What type bench_sort should allocate for generating inputs.
+  using LaneType = T;
+  // What type to pass to Sorter::operator().
+  using KeyType = T;
+
+  std::string KeyString() const {
+    char string100[100];
+    hwy::detail::TypeName(hwy::detail::MakeTypeInfo<KeyType>(), 1, string100);
+    return string100;
+  }
+
+  // For HeapSort
+  HWY_INLINE void Swap(T* a, T* b) const {
+    const T temp = *a;
+    *a = *b;
+    *b = temp;
+  }
+
+  template <class V, class M>
+  HWY_INLINE V CompressKeys(V keys, M mask) const {
+    return CompressNot(keys, mask);
+  }
+
+  // Broadcasts one key into a vector
+  template <class D>
+  HWY_INLINE Vec<D> SetKey(D d, const T* key) const {
+    return Set(d, *key);
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> EqualKeys(D /*tag*/, Vec<D> a, Vec<D> b) const {
+    return Eq(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> NotEqualKeys(D /*tag*/, Vec<D> a, Vec<D> b) const {
+    return Ne(a, b);
+  }
+
+  // For keys=lanes, any difference counts.
+  template <class D>
+  HWY_INLINE bool NoKeyDifference(D /*tag*/, Vec<D> diff) const {
+    // Must avoid floating-point comparisons (for -0)
+    const RebindToUnsigned<D> du;
+    return AllTrue(du, Eq(BitCast(du, diff), Zero(du)));
+  }
+
+  HWY_INLINE bool Equal1(const T* a, const T* b) const { return *a == *b; }
+
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys(D d, Vec<D> v) const {
+    return Reverse(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys2(D d, Vec<D> v) const {
+    return Reverse2(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys4(D d, Vec<D> v) const {
+    return Reverse4(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys8(D d, Vec<D> v) const {
+    return Reverse8(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys16(D d, Vec<D> v) const {
+    static_assert(SortConstants::kMaxCols <= 16, "Assumes u32x16 = 512 bit");
+    return ReverseKeys(d, v);
+  }
+
+  template <class V>
+  HWY_INLINE V OddEvenKeys(const V odd, const V even) const {
+    return OddEven(odd, even);
+  }
+
+  template <class D, HWY_IF_LANE_SIZE_D(D, 2)>
+  HWY_INLINE Vec<D> SwapAdjacentPairs(D d, const Vec<D> v) const {
+    const Repartition<uint32_t, D> du32;
+    return BitCast(d, Shuffle2301(BitCast(du32, v)));
+  }
+  template <class D, HWY_IF_LANE_SIZE_D(D, 4)>
+  HWY_INLINE Vec<D> SwapAdjacentPairs(D /* tag */, const Vec<D> v) const {
+    return Shuffle1032(v);
+  }
+  template <class D, HWY_IF_LANE_SIZE_D(D, 8)>
+  HWY_INLINE Vec<D> SwapAdjacentPairs(D /* tag */, const Vec<D> v) const {
+    return SwapAdjacentBlocks(v);
+  }
+
+  template <class D, HWY_IF_NOT_LANE_SIZE_D(D, 8)>
+  HWY_INLINE Vec<D> SwapAdjacentQuads(D d, const Vec<D> v) const {
+#if HWY_HAVE_FLOAT64  // in case D is float32
+    const RepartitionToWide<D> dw;
+#else
+    const RepartitionToWide<RebindToUnsigned<D> > dw;
+#endif
+    return BitCast(d, SwapAdjacentPairs(dw, BitCast(dw, v)));
+  }
+  template <class D, HWY_IF_LANE_SIZE_D(D, 8)>
+  HWY_INLINE Vec<D> SwapAdjacentQuads(D d, const Vec<D> v) const {
+    // Assumes max vector size = 512
+    return ConcatLowerUpper(d, v, v);
+  }
+
+  template <class D, HWY_IF_NOT_LANE_SIZE_D(D, 8)>
+  HWY_INLINE Vec<D> OddEvenPairs(D d, const Vec<D> odd,
+                                 const Vec<D> even) const {
+#if HWY_HAVE_FLOAT64  // in case D is float32
+    const RepartitionToWide<D> dw;
+#else
+    const RepartitionToWide<RebindToUnsigned<D> > dw;
+#endif
+    return BitCast(d, OddEven(BitCast(dw, odd), BitCast(dw, even)));
+  }
+  template <class D, HWY_IF_LANE_SIZE_D(D, 8)>
+  HWY_INLINE Vec<D> OddEvenPairs(D /* tag */, Vec<D> odd, Vec<D> even) const {
+    return OddEvenBlocks(odd, even);
+  }
+
+  template <class D, HWY_IF_NOT_LANE_SIZE_D(D, 8)>
+  HWY_INLINE Vec<D> OddEvenQuads(D d, Vec<D> odd, Vec<D> even) const {
+#if HWY_HAVE_FLOAT64  // in case D is float32
+    const RepartitionToWide<D> dw;
+#else
+    const RepartitionToWide<RebindToUnsigned<D> > dw;
+#endif
+    return BitCast(d, OddEvenPairs(dw, BitCast(dw, odd), BitCast(dw, even)));
+  }
+  template <class D, HWY_IF_LANE_SIZE_D(D, 8)>
+  HWY_INLINE Vec<D> OddEvenQuads(D d, Vec<D> odd, Vec<D> even) const {
+    return ConcatUpperLower(d, odd, even);
+  }
+};
+
+// Anything order-related depends on the key traits *and* the order (see
+// FirstOfLanes). We cannot implement just one Compare function because Lt128
+// only compiles if the lane type is u64. Thus we need either overloaded
+// functions with a tag type, class specializations, or separate classes.
+// We avoid overloaded functions because we want all functions to be callable
+// from a SortTraits without per-function wrappers. Specializing would work, but
+// we are anyway going to specialize at a higher level.
+template <typename T>
+struct OrderAscending : public KeyLane<T> {
+  using Order = SortAscending;
+
+  HWY_INLINE bool Compare1(const T* a, const T* b) { return *a < *b; }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D /* tag */, Vec<D> a, Vec<D> b) const {
+    return Lt(a, b);
+  }
+
+  // Two halves of Sort2, used in ScanMinMax.
+  template <class D>
+  HWY_INLINE Vec<D> First(D /* tag */, const Vec<D> a, const Vec<D> b) const {
+    return Min(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> Last(D /* tag */, const Vec<D> a, const Vec<D> b) const {
+    return Max(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> FirstOfLanes(D d, Vec<D> v,
+                                 T* HWY_RESTRICT /* buf */) const {
+    return MinOfLanes(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastOfLanes(D d, Vec<D> v,
+                                T* HWY_RESTRICT /* buf */) const {
+    return MaxOfLanes(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> FirstValue(D d) const {
+    return Set(d, hwy::LowestValue<T>());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastValue(D d) const {
+    return Set(d, hwy::HighestValue<T>());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> PrevValue(D d, Vec<D> v) const {
+    return Sub(v, Set(d, hwy::Epsilon<T>()));
+  }
+};
+
+template <typename T>
+struct OrderDescending : public KeyLane<T> {
+  using Order = SortDescending;
+
+  HWY_INLINE bool Compare1(const T* a, const T* b) { return *b < *a; }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D /* tag */, Vec<D> a, Vec<D> b) const {
+    return Lt(b, a);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> First(D /* tag */, const Vec<D> a, const Vec<D> b) const {
+    return Max(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> Last(D /* tag */, const Vec<D> a, const Vec<D> b) const {
+    return Min(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> FirstOfLanes(D d, Vec<D> v,
+                                 T* HWY_RESTRICT /* buf */) const {
+    return MaxOfLanes(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastOfLanes(D d, Vec<D> v,
+                                T* HWY_RESTRICT /* buf */) const {
+    return MinOfLanes(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> FirstValue(D d) const {
+    return Set(d, hwy::HighestValue<T>());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastValue(D d) const {
+    return Set(d, hwy::LowestValue<T>());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> PrevValue(D d, Vec<D> v) const {
+    return Add(v, Set(d, hwy::Epsilon<T>()));
+  }
+};
+
+struct KeyValue64 : public KeyLane<uint64_t> {
+  // True indicates only part of the key (i.e. lane) should be compared. KV
+  // stands for key-value.
+  static constexpr bool IsKV() { return true; }
+
+  template <class D>
+  HWY_INLINE Mask<D> EqualKeys(D /*tag*/, Vec<D> a, Vec<D> b) const {
+    return Eq(ShiftRight<32>(a), ShiftRight<32>(b));
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> NotEqualKeys(D /*tag*/, Vec<D> a, Vec<D> b) const {
+    return Ne(ShiftRight<32>(a), ShiftRight<32>(b));
+  }
+
+  HWY_INLINE bool Equal1(const uint64_t* a, const uint64_t* b) const {
+    return (*a >> 32) == (*b >> 32);
+  }
+
+  // Only count differences in the actual key, not the value.
+  template <class D>
+  HWY_INLINE bool NoKeyDifference(D /*tag*/, Vec<D> diff) const {
+    // Must avoid floating-point comparisons (for -0)
+    const RebindToUnsigned<D> du;
+    const Vec<decltype(du)> zero = Zero(du);
+    const Vec<decltype(du)> keys = ShiftRight<32>(diff);  // clear values
+    return AllTrue(du, Eq(BitCast(du, keys), zero));
+  }
+};
+
+struct OrderAscendingKV64 : public KeyValue64 {
+  using Order = SortAscending;
+
+  HWY_INLINE bool Compare1(const LaneType* a, const LaneType* b) {
+    return (*a >> 32) < (*b >> 32);
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D /* tag */, Vec<D> a, Vec<D> b) const {
+    return Lt(ShiftRight<32>(a), ShiftRight<32>(b));
+  }
+
+  // Not required to be stable (preserving the order of equivalent keys), so
+  // we can include the value in the comparison.
+  template <class D>
+  HWY_INLINE Vec<D> First(D /* tag */, const Vec<D> a, const Vec<D> b) const {
+    return Min(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> Last(D /* tag */, const Vec<D> a, const Vec<D> b) const {
+    return Max(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> FirstOfLanes(D d, Vec<D> v,
+                                 uint64_t* HWY_RESTRICT /* buf */) const {
+    return MinOfLanes(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastOfLanes(D d, Vec<D> v,
+                                uint64_t* HWY_RESTRICT /* buf */) const {
+    return MaxOfLanes(d, v);
+  }
+
+  // Same as for regular lanes.
+  template <class D>
+  HWY_INLINE Vec<D> FirstValue(D d) const {
+    return Set(d, hwy::LowestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastValue(D d) const {
+    return Set(d, hwy::HighestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> PrevValue(D d, Vec<D> v) const {
+    return Sub(v, Set(d, uint64_t{1}));
+  }
+};
+
+struct OrderDescendingKV64 : public KeyValue64 {
+  using Order = SortDescending;
+
+  HWY_INLINE bool Compare1(const LaneType* a, const LaneType* b) {
+    return (*b >> 32) < (*a >> 32);
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D /* tag */, Vec<D> a, Vec<D> b) const {
+    return Lt(ShiftRight<32>(b), ShiftRight<32>(a));
+  }
+
+  // Not required to be stable (preserving the order of equivalent keys), so
+  // we can include the value in the comparison.
+  template <class D>
+  HWY_INLINE Vec<D> First(D /* tag */, const Vec<D> a, const Vec<D> b) const {
+    return Max(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> Last(D /* tag */, const Vec<D> a, const Vec<D> b) const {
+    return Min(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> FirstOfLanes(D d, Vec<D> v,
+                                 uint64_t* HWY_RESTRICT /* buf */) const {
+    return MaxOfLanes(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastOfLanes(D d, Vec<D> v,
+                                uint64_t* HWY_RESTRICT /* buf */) const {
+    return MinOfLanes(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> FirstValue(D d) const {
+    return Set(d, hwy::HighestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastValue(D d) const {
+    return Set(d, hwy::LowestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> PrevValue(D d, Vec<D> v) const {
+    return Add(v, Set(d, uint64_t{1}));
+  }
+};
+
+// Shared code that depends on Order.
+template <class Base>
+struct TraitsLane : public Base {
+  // For each lane i: replaces a[i] with the first and b[i] with the second
+  // according to Base.
+  // Corresponds to a conditional swap, which is one "node" of a sorting
+  // network. Min/Max are cheaper than compare + blend at least for integers.
+  template <class D>
+  HWY_INLINE void Sort2(D d, Vec<D>& a, Vec<D>& b) const {
+    const Base* base = static_cast<const Base*>(this);
+
+    const Vec<D> a_copy = a;
+    // Prior to AVX3, there is no native 64-bit Min/Max, so they compile to 4
+    // instructions. We can reduce it to a compare + 2 IfThenElse.
+#if HWY_AVX3 < HWY_TARGET && HWY_TARGET <= HWY_SSSE3
+    if (sizeof(TFromD<D>) == 8) {
+      const Mask<D> cmp = base->Compare(d, a, b);
+      a = IfThenElse(cmp, a, b);
+      b = IfThenElse(cmp, b, a_copy);
+      return;
+    }
+#endif
+    a = base->First(d, a, b);
+    b = base->Last(d, a_copy, b);
+  }
+
+  // Conditionally swaps even-numbered lanes with their odd-numbered neighbor.
+  template <class D, HWY_IF_LANE_SIZE_D(D, 8)>
+  HWY_INLINE Vec<D> SortPairsDistance1(D d, Vec<D> v) const {
+    const Base* base = static_cast<const Base*>(this);
+    Vec<D> swapped = base->ReverseKeys2(d, v);
+    // Further to the above optimization, Sort2+OddEvenKeys compile to four
+    // instructions; we can save one by combining two blends.
+#if HWY_AVX3 < HWY_TARGET && HWY_TARGET <= HWY_SSSE3
+    const Vec<D> cmp = VecFromMask(d, base->Compare(d, v, swapped));
+    return IfVecThenElse(DupOdd(cmp), swapped, v);
+#else
+    Sort2(d, v, swapped);
+    return base->OddEvenKeys(swapped, v);
+#endif
+  }
+
+  // (See above - we use Sort2 for non-64-bit types.)
+  template <class D, HWY_IF_NOT_LANE_SIZE_D(D, 8)>
+  HWY_INLINE Vec<D> SortPairsDistance1(D d, Vec<D> v) const {
+    const Base* base = static_cast<const Base*>(this);
+    Vec<D> swapped = base->ReverseKeys2(d, v);
+    Sort2(d, v, swapped);
+    return base->OddEvenKeys(swapped, v);
+  }
+
+  // Swaps with the vector formed by reversing contiguous groups of 4 keys.
+  template <class D>
+  HWY_INLINE Vec<D> SortPairsReverse4(D d, Vec<D> v) const {
+    const Base* base = static_cast<const Base*>(this);
+    Vec<D> swapped = base->ReverseKeys4(d, v);
+    Sort2(d, v, swapped);
+    return base->OddEvenPairs(d, swapped, v);
+  }
+
+  // Conditionally swaps lane 0 with 4, 1 with 5 etc.
+  template <class D>
+  HWY_INLINE Vec<D> SortPairsDistance4(D d, Vec<D> v) const {
+    const Base* base = static_cast<const Base*>(this);
+    Vec<D> swapped = base->SwapAdjacentQuads(d, v);
+    // Only used in Merge16, so this will not be used on AVX2 (which only has 4
+    // u64 lanes), so skip the above optimization for 64-bit AVX2.
+    Sort2(d, v, swapped);
+    return base->OddEvenQuads(d, swapped, v);
+  }
+};
+
+#else
+
+// Base class shared between OrderAscending, OrderDescending.
+template <typename T>
+struct KeyLane {
+  constexpr bool Is128() const { return false; }
+  constexpr size_t LanesPerKey() const { return 1; }
+
+  using LaneType = T;
+  using KeyType = T;
+
+  std::string KeyString() const {
+    char string100[100];
+    hwy::detail::TypeName(hwy::detail::MakeTypeInfo<KeyType>(), 1, string100);
+    return string100;
+  }
+};
+
+template <typename T>
+struct OrderAscending : public KeyLane<T> {
+  using Order = SortAscending;
+
+  HWY_INLINE bool Compare1(const T* a, const T* b) { return *a < *b; }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D /* tag */, Vec<D> a, Vec<D> b) {
+    return Lt(a, b);
+  }
+};
+
+template <typename T>
+struct OrderDescending : public KeyLane<T> {
+  using Order = SortDescending;
+
+  HWY_INLINE bool Compare1(const T* a, const T* b) { return *b < *a; }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D /* tag */, Vec<D> a, Vec<D> b) {
+    return Lt(b, a);
+  }
+};
+
+template <class Order>
+struct TraitsLane : public Order {
+  // For HeapSort
+  template <typename T>  // MSVC doesn't find typename Order::LaneType.
+  HWY_INLINE void Swap(T* a, T* b) const {
+    const T temp = *a;
+    *a = *b;
+    *b = temp;
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> SetKey(D d, const TFromD<D>* key) const {
+    return Set(d, *key);
+  }
+};
+
+#endif  // VQSORT_ENABLED
+
+}  // namespace detail
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_TRAITS_TOGGLE
diff --git a/third_party/highway/hwy/contrib/sort/traits128-inl.h b/third_party/highway/hwy/contrib/sort/traits128-inl.h
new file mode 100644
index 0000000000..d889140868
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/traits128-inl.h
@@ -0,0 +1,517 @@
+// 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.
+
+// Per-target
+#if defined(HIGHWAY_HWY_CONTRIB_SORT_TRAITS128_TOGGLE) == \
+    defined(HWY_TARGET_TOGGLE)
+#ifdef HIGHWAY_HWY_CONTRIB_SORT_TRAITS128_TOGGLE
+#undef HIGHWAY_HWY_CONTRIB_SORT_TRAITS128_TOGGLE
+#else
+#define HIGHWAY_HWY_CONTRIB_SORT_TRAITS128_TOGGLE
+#endif
+
+#include <string>
+
+#include "hwy/contrib/sort/shared-inl.h"
+#include "hwy/contrib/sort/vqsort.h"  // SortDescending
+#include "hwy/highway.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+namespace detail {
+
+#if VQSORT_ENABLED || HWY_IDE
+
+// Highway does not provide a lane type for 128-bit keys, so we use uint64_t
+// along with an abstraction layer for single-lane vs. lane-pair, which is
+// independent of the order.
+struct KeyAny128 {
+  static constexpr bool Is128() { return true; }
+  constexpr size_t LanesPerKey() const { return 2; }
+
+  // What type bench_sort should allocate for generating inputs.
+  using LaneType = uint64_t;
+  // KeyType and KeyString are defined by derived classes.
+
+  HWY_INLINE void Swap(LaneType* a, LaneType* b) const {
+    const FixedTag<LaneType, 2> d;
+    const auto temp = LoadU(d, a);
+    StoreU(LoadU(d, b), d, a);
+    StoreU(temp, d, b);
+  }
+
+  template <class V, class M>
+  HWY_INLINE V CompressKeys(V keys, M mask) const {
+    return CompressBlocksNot(keys, mask);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> SetKey(D d, const TFromD<D>* key) const {
+    return LoadDup128(d, key);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys(D d, Vec<D> v) const {
+    return ReverseBlocks(d, v);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys2(D /* tag */, const Vec<D> v) const {
+    return SwapAdjacentBlocks(v);
+  }
+
+  // Only called for 4 keys because we do not support >512-bit vectors.
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys4(D d, const Vec<D> v) const {
+    HWY_DASSERT(Lanes(d) <= 64 / sizeof(TFromD<D>));
+    return ReverseKeys(d, v);
+  }
+
+  // Only called for 4 keys because we do not support >512-bit vectors.
+  template <class D>
+  HWY_INLINE Vec<D> OddEvenPairs(D d, const Vec<D> odd,
+                                 const Vec<D> even) const {
+    HWY_DASSERT(Lanes(d) <= 64 / sizeof(TFromD<D>));
+    return ConcatUpperLower(d, odd, even);
+  }
+
+  template <class V>
+  HWY_INLINE V OddEvenKeys(const V odd, const V even) const {
+    return OddEvenBlocks(odd, even);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys8(D, Vec<D>) const {
+    HWY_ASSERT(0);  // not supported: would require 1024-bit vectors
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> ReverseKeys16(D, Vec<D>) const {
+    HWY_ASSERT(0);  // not supported: would require 2048-bit vectors
+  }
+
+  // This is only called for 8/16 col networks (not supported).
+  template <class D>
+  HWY_INLINE Vec<D> SwapAdjacentPairs(D, Vec<D>) const {
+    HWY_ASSERT(0);
+  }
+
+  // This is only called for 16 col networks (not supported).
+  template <class D>
+  HWY_INLINE Vec<D> SwapAdjacentQuads(D, Vec<D>) const {
+    HWY_ASSERT(0);
+  }
+
+  // This is only called for 8 col networks (not supported).
+  template <class D>
+  HWY_INLINE Vec<D> OddEvenQuads(D, Vec<D>, Vec<D>) const {
+    HWY_ASSERT(0);
+  }
+};
+
+// Base class shared between OrderAscending128, OrderDescending128.
+struct Key128 : public KeyAny128 {
+  // False indicates the entire key should be compared. KV means key-value.
+  static constexpr bool IsKV() { return false; }
+
+  // What type to pass to Sorter::operator().
+  using KeyType = hwy::uint128_t;
+
+  std::string KeyString() const { return "U128"; }
+
+  template <class D>
+  HWY_INLINE Mask<D> EqualKeys(D d, Vec<D> a, Vec<D> b) const {
+    return Eq128(d, a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> NotEqualKeys(D d, Vec<D> a, Vec<D> b) const {
+    return Ne128(d, a, b);
+  }
+
+  // For keys=entire 128 bits, any difference counts.
+  template <class D>
+  HWY_INLINE bool NoKeyDifference(D /*tag*/, Vec<D> diff) const {
+    // Must avoid floating-point comparisons (for -0)
+    const RebindToUnsigned<D> du;
+    return AllTrue(du, Eq(BitCast(du, diff), Zero(du)));
+  }
+
+  HWY_INLINE bool Equal1(const LaneType* a, const LaneType* b) const {
+    return a[0] == b[0] && a[1] == b[1];
+  }
+};
+
+// Anything order-related depends on the key traits *and* the order (see
+// FirstOfLanes). We cannot implement just one Compare function because Lt128
+// only compiles if the lane type is u64. Thus we need either overloaded
+// functions with a tag type, class specializations, or separate classes.
+// We avoid overloaded functions because we want all functions to be callable
+// from a SortTraits without per-function wrappers. Specializing would work, but
+// we are anyway going to specialize at a higher level.
+struct OrderAscending128 : public Key128 {
+  using Order = SortAscending;
+
+  HWY_INLINE bool Compare1(const LaneType* a, const LaneType* b) {
+    return (a[1] == b[1]) ? a[0] < b[0] : a[1] < b[1];
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D d, Vec<D> a, Vec<D> b) const {
+    return Lt128(d, a, b);
+  }
+
+  // Used by CompareTop
+  template <class V>
+  HWY_INLINE Mask<DFromV<V> > CompareLanes(V a, V b) const {
+    return Lt(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> First(D d, const Vec<D> a, const Vec<D> b) const {
+    return Min128(d, a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> Last(D d, const Vec<D> a, const Vec<D> b) const {
+    return Max128(d, a, b);
+  }
+
+  // Same as for regular lanes because 128-bit lanes are u64.
+  template <class D>
+  HWY_INLINE Vec<D> FirstValue(D d) const {
+    return Set(d, hwy::LowestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastValue(D d) const {
+    return Set(d, hwy::HighestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> PrevValue(D d, Vec<D> v) const {
+    const Vec<D> k0 = Zero(d);
+    const Vec<D> k1 = OddEven(k0, Set(d, uint64_t{1}));
+    const Mask<D> borrow = Eq(v, k0);  // don't-care, lo == 0
+    // lo == 0? 1 : 0, 0
+    const Vec<D> adjust = ShiftLeftLanes<1>(IfThenElseZero(borrow, k1));
+    return Sub(Sub(v, k1), adjust);
+  }
+};
+
+struct OrderDescending128 : public Key128 {
+  using Order = SortDescending;
+
+  HWY_INLINE bool Compare1(const LaneType* a, const LaneType* b) {
+    return (a[1] == b[1]) ? b[0] < a[0] : b[1] < a[1];
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D d, Vec<D> a, Vec<D> b) const {
+    return Lt128(d, b, a);
+  }
+
+  // Used by CompareTop
+  template <class V>
+  HWY_INLINE Mask<DFromV<V> > CompareLanes(V a, V b) const {
+    return Lt(b, a);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> First(D d, const Vec<D> a, const Vec<D> b) const {
+    return Max128(d, a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> Last(D d, const Vec<D> a, const Vec<D> b) const {
+    return Min128(d, a, b);
+  }
+
+  // Same as for regular lanes because 128-bit lanes are u64.
+  template <class D>
+  HWY_INLINE Vec<D> FirstValue(D d) const {
+    return Set(d, hwy::HighestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastValue(D d) const {
+    return Set(d, hwy::LowestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> PrevValue(D d, Vec<D> v) const {
+    const Vec<D> k1 = OddEven(Zero(d), Set(d, uint64_t{1}));
+    const Vec<D> added = Add(v, k1);
+    const Mask<D> overflowed = Lt(added, v);  // false, overflowed
+    // overflowed? 1 : 0, 0
+    const Vec<D> adjust = ShiftLeftLanes<1>(IfThenElseZero(overflowed, k1));
+    return Add(added, adjust);
+  }
+};
+
+// Base class shared between OrderAscendingKV128, OrderDescendingKV128.
+struct KeyValue128 : public KeyAny128 {
+  // True indicates only part of the key (the more significant lane) should be
+  // compared. KV stands for key-value.
+  static constexpr bool IsKV() { return true; }
+
+  // What type to pass to Sorter::operator().
+  using KeyType = K64V64;
+
+  std::string KeyString() const { return "KV128"; }
+
+  template <class D>
+  HWY_INLINE Mask<D> EqualKeys(D d, Vec<D> a, Vec<D> b) const {
+    return Eq128Upper(d, a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> NotEqualKeys(D d, Vec<D> a, Vec<D> b) const {
+    return Ne128Upper(d, a, b);
+  }
+
+  // Only count differences in the actual key, not the value.
+  template <class D>
+  HWY_INLINE bool NoKeyDifference(D /*tag*/, Vec<D> diff) const {
+    // Must avoid floating-point comparisons (for -0)
+    const RebindToUnsigned<D> du;
+    const Vec<decltype(du)> zero = Zero(du);
+    const Vec<decltype(du)> keys = OddEven(diff, zero);  // clear values
+    return AllTrue(du, Eq(BitCast(du, keys), zero));
+  }
+
+  HWY_INLINE bool Equal1(const LaneType* a, const LaneType* b) const {
+    return a[1] == b[1];
+  }
+};
+
+struct OrderAscendingKV128 : public KeyValue128 {
+  using Order = SortAscending;
+
+  HWY_INLINE bool Compare1(const LaneType* a, const LaneType* b) {
+    return a[1] < b[1];
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D d, Vec<D> a, Vec<D> b) const {
+    return Lt128Upper(d, a, b);
+  }
+
+  // Used by CompareTop
+  template <class V>
+  HWY_INLINE Mask<DFromV<V> > CompareLanes(V a, V b) const {
+    return Lt(a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> First(D d, const Vec<D> a, const Vec<D> b) const {
+    return Min128Upper(d, a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> Last(D d, const Vec<D> a, const Vec<D> b) const {
+    return Max128Upper(d, a, b);
+  }
+
+  // Same as for regular lanes because 128-bit lanes are u64.
+  template <class D>
+  HWY_INLINE Vec<D> FirstValue(D d) const {
+    return Set(d, hwy::LowestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastValue(D d) const {
+    return Set(d, hwy::HighestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> PrevValue(D d, Vec<D> v) const {
+    const Vec<D> k1 = OddEven(Set(d, uint64_t{1}), Zero(d));
+    return Sub(v, k1);
+  }
+};
+
+struct OrderDescendingKV128 : public KeyValue128 {
+  using Order = SortDescending;
+
+  HWY_INLINE bool Compare1(const LaneType* a, const LaneType* b) {
+    return b[1] < a[1];
+  }
+
+  template <class D>
+  HWY_INLINE Mask<D> Compare(D d, Vec<D> a, Vec<D> b) const {
+    return Lt128Upper(d, b, a);
+  }
+
+  // Used by CompareTop
+  template <class V>
+  HWY_INLINE Mask<DFromV<V> > CompareLanes(V a, V b) const {
+    return Lt(b, a);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> First(D d, const Vec<D> a, const Vec<D> b) const {
+    return Max128Upper(d, a, b);
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> Last(D d, const Vec<D> a, const Vec<D> b) const {
+    return Min128Upper(d, a, b);
+  }
+
+  // Same as for regular lanes because 128-bit lanes are u64.
+  template <class D>
+  HWY_INLINE Vec<D> FirstValue(D d) const {
+    return Set(d, hwy::HighestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastValue(D d) const {
+    return Set(d, hwy::LowestValue<TFromD<D> >());
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> PrevValue(D d, Vec<D> v) const {
+    const Vec<D> k1 = OddEven(Set(d, uint64_t{1}), Zero(d));
+    return Add(v, k1);
+  }
+};
+
+// Shared code that depends on Order.
+template <class Base>
+class Traits128 : public Base {
+  // Special case for >= 256 bit vectors
+#if HWY_TARGET <= HWY_AVX2 || HWY_TARGET == HWY_SVE_256
+  // Returns vector with only the top u64 lane valid. Useful when the next step
+  // is to replicate the mask anyway.
+  template <class D>
+  HWY_INLINE HWY_MAYBE_UNUSED Vec<D> CompareTop(D d, Vec<D> a, Vec<D> b) const {
+    const Base* base = static_cast<const Base*>(this);
+    const Mask<D> eqHL = Eq(a, b);
+    const Vec<D> ltHL = VecFromMask(d, base->CompareLanes(a, b));
+#if HWY_TARGET == HWY_SVE_256
+    return IfThenElse(eqHL, DupEven(ltHL), ltHL);
+#else
+    const Vec<D> ltLX = ShiftLeftLanes<1>(ltHL);
+    return OrAnd(ltHL, VecFromMask(d, eqHL), ltLX);
+#endif
+  }
+
+  // We want to swap 2 u128, i.e. 4 u64 lanes, based on the 0 or FF..FF mask in
+  // the most-significant of those lanes (the result of CompareTop), so
+  // replicate it 4x. Only called for >= 256-bit vectors.
+  template <class V>
+  HWY_INLINE V ReplicateTop4x(V v) const {
+#if HWY_TARGET == HWY_SVE_256
+    return svdup_lane_u64(v, 3);
+#elif HWY_TARGET <= HWY_AVX3
+    return V{_mm512_permutex_epi64(v.raw, _MM_SHUFFLE(3, 3, 3, 3))};
+#else  // AVX2
+    return V{_mm256_permute4x64_epi64(v.raw, _MM_SHUFFLE(3, 3, 3, 3))};
+#endif
+  }
+#endif  // HWY_TARGET
+
+ public:
+  template <class D>
+  HWY_INLINE Vec<D> FirstOfLanes(D d, Vec<D> v,
+                                 TFromD<D>* HWY_RESTRICT buf) const {
+    const Base* base = static_cast<const Base*>(this);
+    const size_t N = Lanes(d);
+    Store(v, d, buf);
+    v = base->SetKey(d, buf + 0);  // result must be broadcasted
+    for (size_t i = base->LanesPerKey(); i < N; i += base->LanesPerKey()) {
+      v = base->First(d, v, base->SetKey(d, buf + i));
+    }
+    return v;
+  }
+
+  template <class D>
+  HWY_INLINE Vec<D> LastOfLanes(D d, Vec<D> v,
+                                TFromD<D>* HWY_RESTRICT buf) const {
+    const Base* base = static_cast<const Base*>(this);
+    const size_t N = Lanes(d);
+    Store(v, d, buf);
+    v = base->SetKey(d, buf + 0);  // result must be broadcasted
+    for (size_t i = base->LanesPerKey(); i < N; i += base->LanesPerKey()) {
+      v = base->Last(d, v, base->SetKey(d, buf + i));
+    }
+    return v;
+  }
+
+  template <class D>
+  HWY_INLINE void Sort2(D d, Vec<D>& a, Vec<D>& b) const {
+    const Base* base = static_cast<const Base*>(this);
+
+    const Vec<D> a_copy = a;
+    const auto lt = base->Compare(d, a, b);
+    a = IfThenElse(lt, a, b);
+    b = IfThenElse(lt, b, a_copy);
+  }
+
+  // Conditionally swaps even-numbered lanes with their odd-numbered neighbor.
+  template <class D>
+  HWY_INLINE Vec<D> SortPairsDistance1(D d, Vec<D> v) const {
+    const Base* base = static_cast<const Base*>(this);
+    Vec<D> swapped = base->ReverseKeys2(d, v);
+
+#if HWY_TARGET <= HWY_AVX2 || HWY_TARGET == HWY_SVE_256
+    const Vec<D> select = ReplicateTop4x(CompareTop(d, v, swapped));
+    return IfVecThenElse(select, swapped, v);
+#else
+    Sort2(d, v, swapped);
+    return base->OddEvenKeys(swapped, v);
+#endif
+  }
+
+  // Swaps with the vector formed by reversing contiguous groups of 4 keys.
+  template <class D>
+  HWY_INLINE Vec<D> SortPairsReverse4(D d, Vec<D> v) const {
+    const Base* base = static_cast<const Base*>(this);
+    Vec<D> swapped = base->ReverseKeys4(d, v);
+
+    // Only specialize for AVX3 because this requires 512-bit vectors.
+#if HWY_TARGET <= HWY_AVX3
+    const Vec512<uint64_t> outHx = CompareTop(d, v, swapped);
+    // Similar to ReplicateTop4x, we want to gang together 2 comparison results
+    // (4 lanes). They are not contiguous, so use permute to replicate 4x.
+    alignas(64) uint64_t kIndices[8] = {7, 7, 5, 5, 5, 5, 7, 7};
+    const Vec512<uint64_t> select =
+        TableLookupLanes(outHx, SetTableIndices(d, kIndices));
+    return IfVecThenElse(select, swapped, v);
+#else
+    Sort2(d, v, swapped);
+    return base->OddEvenPairs(d, swapped, v);
+#endif
+  }
+
+  // Conditionally swaps lane 0 with 4, 1 with 5 etc.
+  template <class D>
+  HWY_INLINE Vec<D> SortPairsDistance4(D, Vec<D>) const {
+    // Only used by Merge16, which would require 2048 bit vectors (unsupported).
+    HWY_ASSERT(0);
+  }
+};
+
+#endif  // VQSORT_ENABLED
+
+}  // namespace detail
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_TRAITS128_TOGGLE
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
diff --git a/third_party/highway/hwy/contrib/sort/vqsort.cc b/third_party/highway/hwy/contrib/sort/vqsort.cc
new file mode 100644
index 0000000000..b3bac0720a
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort.cc
@@ -0,0 +1,184 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#include <string.h>  // memset
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/shared-inl.h"
+
+// Architectures for which we know HWY_HAVE_SCALABLE == 0. This opts into an
+// optimization that replaces dynamic allocation with stack storage.
+#ifndef VQSORT_STACK
+#if HWY_ARCH_X86 || HWY_ARCH_WASM
+#define VQSORT_STACK 1
+#else
+#define VQSORT_STACK 0
+#endif
+#endif  // VQSORT_STACK
+
+#if !VQSORT_STACK
+#include "hwy/aligned_allocator.h"
+#endif
+
+// Check if we have sys/random.h. First skip some systems on which the check
+// itself (features.h) might be problematic.
+#if defined(ANDROID) || defined(__ANDROID__) || HWY_ARCH_RVV
+#define VQSORT_GETRANDOM 0
+#endif
+
+#if !defined(VQSORT_GETRANDOM) && HWY_OS_LINUX
+#include <features.h>
+
+// ---- which libc
+#if defined(__UCLIBC__)
+#define VQSORT_GETRANDOM 1  // added Mar 2015, before uclibc-ng 1.0
+
+#elif defined(__GLIBC__) && defined(__GLIBC_PREREQ)
+#if __GLIBC_PREREQ(2, 25)
+#define VQSORT_GETRANDOM 1
+#else
+#define VQSORT_GETRANDOM 0
+#endif
+
+#else
+// Assume MUSL, which has getrandom since 2018. There is no macro to test, see
+// https://www.openwall.com/lists/musl/2013/03/29/13.
+#define VQSORT_GETRANDOM 1
+
+#endif  // ---- which libc
+#endif  // linux
+
+#if !defined(VQSORT_GETRANDOM)
+#define VQSORT_GETRANDOM 0
+#endif
+
+// Seed source for SFC generator: 1=getrandom, 2=CryptGenRandom
+// (not all Android support the getrandom wrapper)
+#ifndef VQSORT_SECURE_SEED
+
+#if VQSORT_GETRANDOM
+#define VQSORT_SECURE_SEED 1
+#elif defined(_WIN32) || defined(_WIN64)
+#define VQSORT_SECURE_SEED 2
+#else
+#define VQSORT_SECURE_SEED 0
+#endif
+
+#endif  // VQSORT_SECURE_SEED
+
+#if !VQSORT_SECURE_RNG
+
+#include <time.h>
+#if VQSORT_SECURE_SEED == 1
+#include <sys/random.h>
+#elif VQSORT_SECURE_SEED == 2
+#include <windows.h>
+#pragma comment(lib, "advapi32.lib")
+// Must come after windows.h.
+#include <wincrypt.h>
+#endif  // VQSORT_SECURE_SEED
+
+#endif  // !VQSORT_SECURE_RNG
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+size_t VectorSize() { return Lanes(ScalableTag<uint8_t, 3>()); }
+bool HaveFloat64() { return HWY_HAVE_FLOAT64; }
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(VectorSize);
+HWY_EXPORT(HaveFloat64);
+
+}  // namespace
+
+Sorter::Sorter() {
+#if VQSORT_STACK
+  ptr_ = nullptr;  // Sort will use stack storage instead
+#else
+  // Determine the largest buffer size required for any type by trying them all.
+  // (The capping of N in BaseCaseNum means that smaller N but larger sizeof_t
+  // may require a larger buffer.)
+  const size_t vector_size = HWY_DYNAMIC_DISPATCH(VectorSize)();
+  const size_t max_bytes =
+      HWY_MAX(HWY_MAX(SortConstants::BufBytes<uint16_t>(vector_size),
+                      SortConstants::BufBytes<uint32_t>(vector_size)),
+              SortConstants::BufBytes<uint64_t>(vector_size));
+  ptr_ = hwy::AllocateAlignedBytes(max_bytes, nullptr, nullptr);
+
+  // Prevent msan errors by initializing.
+  memset(ptr_, 0, max_bytes);
+#endif
+}
+
+void Sorter::Delete() {
+#if !VQSORT_STACK
+  FreeAlignedBytes(ptr_, nullptr, nullptr);
+  ptr_ = nullptr;
+#endif
+}
+
+#if !VQSORT_SECURE_RNG
+
+void Sorter::Fill24Bytes(const void* seed_heap, size_t seed_num, void* bytes) {
+#if VQSORT_SECURE_SEED == 1
+  // May block if urandom is not yet initialized.
+  const ssize_t ret = getrandom(bytes, 24, /*flags=*/0);
+  if (ret == 24) return;
+#elif VQSORT_SECURE_SEED == 2
+  HCRYPTPROV hProvider{};
+  if (CryptAcquireContextA(&hProvider, nullptr, nullptr, PROV_RSA_FULL,
+                           CRYPT_VERIFYCONTEXT)) {
+    const BOOL ok =
+        CryptGenRandom(hProvider, 24, reinterpret_cast<BYTE*>(bytes));
+    CryptReleaseContext(hProvider, 0);
+    if (ok) return;
+  }
+#endif
+
+  // VQSORT_SECURE_SEED == 0, or one of the above failed. Get some entropy from
+  // stack/heap/code addresses and the clock() timer.
+  uint64_t* words = reinterpret_cast<uint64_t*>(bytes);
+  uint64_t** seed_stack = &words;
+  void (*seed_code)(const void*, size_t, void*) = &Fill24Bytes;
+  const uintptr_t bits_stack = reinterpret_cast<uintptr_t>(seed_stack);
+  const uintptr_t bits_heap = reinterpret_cast<uintptr_t>(seed_heap);
+  const uintptr_t bits_code = reinterpret_cast<uintptr_t>(seed_code);
+  const uint64_t bits_time = static_cast<uint64_t>(clock());
+  words[0] = bits_stack ^ bits_time ^ seed_num;
+  words[1] = bits_heap ^ bits_time ^ seed_num;
+  words[2] = bits_code ^ bits_time ^ seed_num;
+}
+
+#endif  // !VQSORT_SECURE_RNG
+
+bool Sorter::HaveFloat64() { return HWY_DYNAMIC_DISPATCH(HaveFloat64)(); }
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort.h b/third_party/highway/hwy/contrib/sort/vqsort.h
new file mode 100644
index 0000000000..88d78ac7f9
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort.h
@@ -0,0 +1,108 @@
+// Copyright 2022 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.
+
+// Interface to vectorized quicksort with dynamic dispatch.
+// Blog post: https://tinyurl.com/vqsort-blog
+// Paper with measurements: https://arxiv.org/abs/2205.05982
+//
+// To ensure the overhead of using wide vectors (e.g. AVX2 or AVX-512) is
+// worthwhile, we recommend using this code for sorting arrays whose size is at
+// least 512 KiB.
+
+#ifndef HIGHWAY_HWY_CONTRIB_SORT_VQSORT_H_
+#define HIGHWAY_HWY_CONTRIB_SORT_VQSORT_H_
+
+#include "hwy/base.h"
+
+namespace hwy {
+
+// Tag arguments that determine the sort order.
+struct SortAscending {
+  constexpr bool IsAscending() const { return true; }
+};
+struct SortDescending {
+  constexpr bool IsAscending() const { return false; }
+};
+
+// Allocates O(1) space. Type-erased RAII wrapper over hwy/aligned_allocator.h.
+// This allows amortizing the allocation over multiple sorts.
+class HWY_CONTRIB_DLLEXPORT Sorter {
+ public:
+  Sorter();
+  ~Sorter() { Delete(); }
+
+  // Move-only
+  Sorter(const Sorter&) = delete;
+  Sorter& operator=(const Sorter&) = delete;
+  Sorter(Sorter&& other) {
+    Delete();
+    ptr_ = other.ptr_;
+    other.ptr_ = nullptr;
+  }
+  Sorter& operator=(Sorter&& other) {
+    Delete();
+    ptr_ = other.ptr_;
+    other.ptr_ = nullptr;
+    return *this;
+  }
+
+  // Sorts keys[0, n). Dispatches to the best available instruction set,
+  // and does not allocate memory.
+  void operator()(uint16_t* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(uint16_t* HWY_RESTRICT keys, size_t n, SortDescending) const;
+  void operator()(uint32_t* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(uint32_t* HWY_RESTRICT keys, size_t n, SortDescending) const;
+  void operator()(uint64_t* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(uint64_t* HWY_RESTRICT keys, size_t n, SortDescending) const;
+
+  void operator()(int16_t* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(int16_t* HWY_RESTRICT keys, size_t n, SortDescending) const;
+  void operator()(int32_t* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(int32_t* HWY_RESTRICT keys, size_t n, SortDescending) const;
+  void operator()(int64_t* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(int64_t* HWY_RESTRICT keys, size_t n, SortDescending) const;
+
+  void operator()(float* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(float* HWY_RESTRICT keys, size_t n, SortDescending) const;
+  void operator()(double* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(double* HWY_RESTRICT keys, size_t n, SortDescending) const;
+
+  void operator()(uint128_t* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(uint128_t* HWY_RESTRICT keys, size_t n, SortDescending) const;
+
+  void operator()(K64V64* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(K64V64* HWY_RESTRICT keys, size_t n, SortDescending) const;
+
+  void operator()(K32V32* HWY_RESTRICT keys, size_t n, SortAscending) const;
+  void operator()(K32V32* HWY_RESTRICT keys, size_t n, SortDescending) const;
+
+  // For internal use only
+  static void Fill24Bytes(const void* seed_heap, size_t seed_num, void* bytes);
+  static bool HaveFloat64();
+
+ private:
+  void Delete();
+
+  template <typename T>
+  T* Get() const {
+    return static_cast<T*>(ptr_);
+  }
+
+  void* ptr_ = nullptr;
+};
+
+}  // namespace hwy
+
+#endif  // HIGHWAY_HWY_CONTRIB_SORT_VQSORT_H_
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_128a.cc b/third_party/highway/hwy/contrib/sort/vqsort_128a.cc
new file mode 100644
index 0000000000..40daea85c7
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_128a.cc
@@ -0,0 +1,62 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_128a.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits128-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void Sort128Asc(uint64_t* HWY_RESTRICT keys, size_t num,
+                uint64_t* HWY_RESTRICT buf) {
+#if VQSORT_ENABLED
+  SortTag<uint64_t> d;
+  detail::SharedTraits<detail::Traits128<detail::OrderAscending128>> st;
+  Sort(d, st, keys, num, buf);
+#else
+  (void) keys;
+  (void) num;
+  (void) buf;
+  HWY_ASSERT(0);
+#endif
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(Sort128Asc);
+}  // namespace
+
+void Sorter::operator()(uint128_t* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(Sort128Asc)
+  (reinterpret_cast<uint64_t*>(keys), n * 2, Get<uint64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_128d.cc b/third_party/highway/hwy/contrib/sort/vqsort_128d.cc
new file mode 100644
index 0000000000..357da840c1
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_128d.cc
@@ -0,0 +1,62 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_128d.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits128-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void Sort128Desc(uint64_t* HWY_RESTRICT keys, size_t num,
+                 uint64_t* HWY_RESTRICT buf) {
+#if VQSORT_ENABLED
+  SortTag<uint64_t> d;
+  detail::SharedTraits<detail::Traits128<detail::OrderDescending128>> st;
+  Sort(d, st, keys, num, buf);
+#else
+  (void) keys;
+  (void) num;
+  (void) buf;
+  HWY_ASSERT(0);
+#endif
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(Sort128Desc);
+}  // namespace
+
+void Sorter::operator()(uint128_t* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(Sort128Desc)
+  (reinterpret_cast<uint64_t*>(keys), n * 2, Get<uint64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_f32a.cc b/third_party/highway/hwy/contrib/sort/vqsort_f32a.cc
new file mode 100644
index 0000000000..3856eea5dd
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_f32a.cc
@@ -0,0 +1,53 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_f32a.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortF32Asc(float* HWY_RESTRICT keys, size_t num, float* HWY_RESTRICT buf) {
+  SortTag<float> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscending<float>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortF32Asc);
+}  // namespace
+
+void Sorter::operator()(float* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortF32Asc)(keys, n, Get<float>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_f32d.cc b/third_party/highway/hwy/contrib/sort/vqsort_f32d.cc
new file mode 100644
index 0000000000..7f5f97cdf2
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_f32d.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_f32d.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortF32Desc(float* HWY_RESTRICT keys, size_t num,
+                 float* HWY_RESTRICT buf) {
+  SortTag<float> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderDescending<float>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortF32Desc);
+}  // namespace
+
+void Sorter::operator()(float* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortF32Desc)(keys, n, Get<float>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_f64a.cc b/third_party/highway/hwy/contrib/sort/vqsort_f64a.cc
new file mode 100644
index 0000000000..287d5214e5
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_f64a.cc
@@ -0,0 +1,61 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_f64a.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortF64Asc(double* HWY_RESTRICT keys, size_t num,
+                double* HWY_RESTRICT buf) {
+#if HWY_HAVE_FLOAT64
+  SortTag<double> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscending<double>>> st;
+  Sort(d, st, keys, num, buf);
+#else
+  (void)keys;
+  (void)num;
+  (void)buf;
+  HWY_ASSERT(0);
+#endif
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortF64Asc);
+}  // namespace
+
+void Sorter::operator()(double* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortF64Asc)(keys, n, Get<double>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_f64d.cc b/third_party/highway/hwy/contrib/sort/vqsort_f64d.cc
new file mode 100644
index 0000000000..74d40c1ed3
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_f64d.cc
@@ -0,0 +1,61 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_f64d.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortF64Desc(double* HWY_RESTRICT keys, size_t num,
+                 double* HWY_RESTRICT buf) {
+#if HWY_HAVE_FLOAT64
+  SortTag<double> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderDescending<double>>> st;
+  Sort(d, st, keys, num, buf);
+#else
+  (void)keys;
+  (void)num;
+  (void)buf;
+  HWY_ASSERT(0);
+#endif
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortF64Desc);
+}  // namespace
+
+void Sorter::operator()(double* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortF64Desc)(keys, n, Get<double>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_i16a.cc b/third_party/highway/hwy/contrib/sort/vqsort_i16a.cc
new file mode 100644
index 0000000000..ef4bb75bc4
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_i16a.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_i16a.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortI16Asc(int16_t* HWY_RESTRICT keys, size_t num,
+                int16_t* HWY_RESTRICT buf) {
+  SortTag<int16_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscending<int16_t>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortI16Asc);
+}  // namespace
+
+void Sorter::operator()(int16_t* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortI16Asc)(keys, n, Get<int16_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_i16d.cc b/third_party/highway/hwy/contrib/sort/vqsort_i16d.cc
new file mode 100644
index 0000000000..6507ed6080
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_i16d.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_i16d.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortI16Desc(int16_t* HWY_RESTRICT keys, size_t num,
+                 int16_t* HWY_RESTRICT buf) {
+  SortTag<int16_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderDescending<int16_t>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortI16Desc);
+}  // namespace
+
+void Sorter::operator()(int16_t* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortI16Desc)(keys, n, Get<int16_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_i32a.cc b/third_party/highway/hwy/contrib/sort/vqsort_i32a.cc
new file mode 100644
index 0000000000..ae65be997e
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_i32a.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_i32a.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortI32Asc(int32_t* HWY_RESTRICT keys, size_t num,
+                int32_t* HWY_RESTRICT buf) {
+  SortTag<int32_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscending<int32_t>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortI32Asc);
+}  // namespace
+
+void Sorter::operator()(int32_t* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortI32Asc)(keys, n, Get<int32_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_i32d.cc b/third_party/highway/hwy/contrib/sort/vqsort_i32d.cc
new file mode 100644
index 0000000000..3ce276ee9c
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_i32d.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_i32d.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortI32Desc(int32_t* HWY_RESTRICT keys, size_t num,
+                 int32_t* HWY_RESTRICT buf) {
+  SortTag<int32_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderDescending<int32_t>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortI32Desc);
+}  // namespace
+
+void Sorter::operator()(int32_t* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortI32Desc)(keys, n, Get<int32_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_i64a.cc b/third_party/highway/hwy/contrib/sort/vqsort_i64a.cc
new file mode 100644
index 0000000000..901b8ead8a
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_i64a.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_i64a.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortI64Asc(int64_t* HWY_RESTRICT keys, size_t num,
+                int64_t* HWY_RESTRICT buf) {
+  SortTag<int64_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscending<int64_t>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortI64Asc);
+}  // namespace
+
+void Sorter::operator()(int64_t* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortI64Asc)(keys, n, Get<int64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_i64d.cc b/third_party/highway/hwy/contrib/sort/vqsort_i64d.cc
new file mode 100644
index 0000000000..7713f2eb89
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_i64d.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_i64d.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortI64Desc(int64_t* HWY_RESTRICT keys, size_t num,
+                 int64_t* HWY_RESTRICT buf) {
+  SortTag<int64_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderDescending<int64_t>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortI64Desc);
+}  // namespace
+
+void Sorter::operator()(int64_t* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortI64Desc)(keys, n, Get<int64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_kv128a.cc b/third_party/highway/hwy/contrib/sort/vqsort_kv128a.cc
new file mode 100644
index 0000000000..1e02742ef1
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_kv128a.cc
@@ -0,0 +1,65 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+// clang-format off
+// (avoid line break, which would prevent Copybara rules from matching)
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_kv128a.cc"  //NOLINT
+// clang-format on
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits128-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortKV128Asc(uint64_t* HWY_RESTRICT keys, size_t num,
+                  uint64_t* HWY_RESTRICT buf) {
+#if VQSORT_ENABLED
+  SortTag<uint64_t> d;
+  detail::SharedTraits<detail::Traits128<detail::OrderAscendingKV128>> st;
+  Sort(d, st, keys, num, buf);
+#else
+  (void) keys;
+  (void) num;
+  (void) buf;
+  HWY_ASSERT(0);
+#endif
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortKV128Asc);
+}  // namespace
+
+void Sorter::operator()(K64V64* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortKV128Asc)
+  (reinterpret_cast<uint64_t*>(keys), n * 2, Get<uint64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_kv128d.cc b/third_party/highway/hwy/contrib/sort/vqsort_kv128d.cc
new file mode 100644
index 0000000000..3dd53b5da3
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_kv128d.cc
@@ -0,0 +1,65 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+// clang-format off
+// (avoid line break, which would prevent Copybara rules from matching)
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_kv128d.cc"  //NOLINT
+// clang-format on
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits128-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortKV128Desc(uint64_t* HWY_RESTRICT keys, size_t num,
+                   uint64_t* HWY_RESTRICT buf) {
+#if VQSORT_ENABLED
+  SortTag<uint64_t> d;
+  detail::SharedTraits<detail::Traits128<detail::OrderDescendingKV128>> st;
+  Sort(d, st, keys, num, buf);
+#else
+  (void) keys;
+  (void) num;
+  (void) buf;
+  HWY_ASSERT(0);
+#endif
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortKV128Desc);
+}  // namespace
+
+void Sorter::operator()(K64V64* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortKV128Desc)
+  (reinterpret_cast<uint64_t*>(keys), n * 2, Get<uint64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_kv64a.cc b/third_party/highway/hwy/contrib/sort/vqsort_kv64a.cc
new file mode 100644
index 0000000000..c513e3c4ce
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_kv64a.cc
@@ -0,0 +1,65 @@
+// Copyright 2022 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+// clang-format off
+// (avoid line break, which would prevent Copybara rules from matching)
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_kv64a.cc"  //NOLINT
+// clang-format on
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortKV64Asc(uint64_t* HWY_RESTRICT keys, size_t num,
+                 uint64_t* HWY_RESTRICT buf) {
+#if VQSORT_ENABLED
+  SortTag<uint64_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscendingKV64>> st;
+  Sort(d, st, keys, num, buf);
+#else
+  (void) keys;
+  (void) num;
+  (void) buf;
+  HWY_ASSERT(0);
+#endif
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortKV64Asc);
+}  // namespace
+
+void Sorter::operator()(K32V32* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortKV64Asc)
+  (reinterpret_cast<uint64_t*>(keys), n, Get<uint64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_kv64d.cc b/third_party/highway/hwy/contrib/sort/vqsort_kv64d.cc
new file mode 100644
index 0000000000..c6c5fdcf74
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_kv64d.cc
@@ -0,0 +1,65 @@
+// Copyright 2022 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+// clang-format off
+// (avoid line break, which would prevent Copybara rules from matching)
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_kv64d.cc"  //NOLINT
+// clang-format on
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortKV64Desc(uint64_t* HWY_RESTRICT keys, size_t num,
+                  uint64_t* HWY_RESTRICT buf) {
+#if VQSORT_ENABLED
+  SortTag<uint64_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderDescendingKV64>> st;
+  Sort(d, st, keys, num, buf);
+#else
+  (void) keys;
+  (void) num;
+  (void) buf;
+  HWY_ASSERT(0);
+#endif
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortKV64Desc);
+}  // namespace
+
+void Sorter::operator()(K32V32* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortKV64Desc)
+  (reinterpret_cast<uint64_t*>(keys), n, Get<uint64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_u16a.cc b/third_party/highway/hwy/contrib/sort/vqsort_u16a.cc
new file mode 100644
index 0000000000..0a97ffa923
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_u16a.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_u16a.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortU16Asc(uint16_t* HWY_RESTRICT keys, size_t num,
+                uint16_t* HWY_RESTRICT buf) {
+  SortTag<uint16_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscending<uint16_t>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortU16Asc);
+}  // namespace
+
+void Sorter::operator()(uint16_t* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortU16Asc)(keys, n, Get<uint16_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_u16d.cc b/third_party/highway/hwy/contrib/sort/vqsort_u16d.cc
new file mode 100644
index 0000000000..286ebbba65
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_u16d.cc
@@ -0,0 +1,55 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_u16d.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortU16Desc(uint16_t* HWY_RESTRICT keys, size_t num,
+                 uint16_t* HWY_RESTRICT buf) {
+  SortTag<uint16_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderDescending<uint16_t>>>
+      st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortU16Desc);
+}  // namespace
+
+void Sorter::operator()(uint16_t* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortU16Desc)(keys, n, Get<uint16_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_u32a.cc b/third_party/highway/hwy/contrib/sort/vqsort_u32a.cc
new file mode 100644
index 0000000000..b6a69e6e28
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_u32a.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_u32a.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortU32Asc(uint32_t* HWY_RESTRICT keys, size_t num,
+                uint32_t* HWY_RESTRICT buf) {
+  SortTag<uint32_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscending<uint32_t>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortU32Asc);
+}  // namespace
+
+void Sorter::operator()(uint32_t* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortU32Asc)(keys, n, Get<uint32_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_u32d.cc b/third_party/highway/hwy/contrib/sort/vqsort_u32d.cc
new file mode 100644
index 0000000000..38fc1e1bfe
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_u32d.cc
@@ -0,0 +1,55 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_u32d.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortU32Desc(uint32_t* HWY_RESTRICT keys, size_t num,
+                 uint32_t* HWY_RESTRICT buf) {
+  SortTag<uint32_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderDescending<uint32_t>>>
+      st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortU32Desc);
+}  // namespace
+
+void Sorter::operator()(uint32_t* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortU32Desc)(keys, n, Get<uint32_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_u64a.cc b/third_party/highway/hwy/contrib/sort/vqsort_u64a.cc
new file mode 100644
index 0000000000..a29824a6f9
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_u64a.cc
@@ -0,0 +1,54 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_u64a.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortU64Asc(uint64_t* HWY_RESTRICT keys, size_t num,
+                uint64_t* HWY_RESTRICT buf) {
+  SortTag<uint64_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderAscending<uint64_t>>> st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortU64Asc);
+}  // namespace
+
+void Sorter::operator()(uint64_t* HWY_RESTRICT keys, size_t n,
+                        SortAscending) const {
+  HWY_DYNAMIC_DISPATCH(SortU64Asc)(keys, n, Get<uint64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE
diff --git a/third_party/highway/hwy/contrib/sort/vqsort_u64d.cc b/third_party/highway/hwy/contrib/sort/vqsort_u64d.cc
new file mode 100644
index 0000000000..d692458623
--- /dev/null
+++ b/third_party/highway/hwy/contrib/sort/vqsort_u64d.cc
@@ -0,0 +1,55 @@
+// 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.
+
+#include "hwy/contrib/sort/vqsort.h"
+
+#undef HWY_TARGET_INCLUDE
+#define HWY_TARGET_INCLUDE "hwy/contrib/sort/vqsort_u64d.cc"
+#include "hwy/foreach_target.h"  // IWYU pragma: keep
+
+// After foreach_target
+#include "hwy/contrib/sort/traits-inl.h"
+#include "hwy/contrib/sort/vqsort-inl.h"
+
+HWY_BEFORE_NAMESPACE();
+namespace hwy {
+namespace HWY_NAMESPACE {
+
+void SortU64Desc(uint64_t* HWY_RESTRICT keys, size_t num,
+                 uint64_t* HWY_RESTRICT buf) {
+  SortTag<uint64_t> d;
+  detail::SharedTraits<detail::TraitsLane<detail::OrderDescending<uint64_t>>>
+      st;
+  Sort(d, st, keys, num, buf);
+}
+
+// NOLINTNEXTLINE(google-readability-namespace-comments)
+}  // namespace HWY_NAMESPACE
+}  // namespace hwy
+HWY_AFTER_NAMESPACE();
+
+#if HWY_ONCE
+namespace hwy {
+namespace {
+HWY_EXPORT(SortU64Desc);
+}  // namespace
+
+void Sorter::operator()(uint64_t* HWY_RESTRICT keys, size_t n,
+                        SortDescending) const {
+  HWY_DYNAMIC_DISPATCH(SortU64Desc)(keys, n, Get<uint64_t>());
+}
+
+}  // namespace hwy
+#endif  // HWY_ONCE