ENH: Add AVX-512 based 64-bit dtype sort

5 files changed, 110 insertions, 839 deletions

diff --git a/numpy/core/setup.py b/numpy/core/setup.py
index e509b9d11..912867709 100644
--- a/numpy/core/setup.py
+++ b/numpy/core/setup.py
@@ -650,6 +650,7 @@ def configuration(parent_package='',top_path=None):
     config.add_include_dirs(join('src', 'multiarray'))
     config.add_include_dirs(join('src', 'umath'))
     config.add_include_dirs(join('src', 'npysort'))
+    config.add_include_dirs(join('src', 'npysort', 'x86-simd-sort', 'src'))
     config.add_include_dirs(join('src', '_simd'))
 
     config.add_define_macros([("NPY_INTERNAL_BUILD", "1")]) # this macro indicates that Numpy build is in process
@@ -942,7 +943,7 @@ def configuration(parent_package='',top_path=None):
             join('src', 'multiarray', 'usertypes.c'),
             join('src', 'multiarray', 'vdot.c'),
             join('src', 'common', 'npy_sort.h.src'),
-            join('src', 'npysort', 'x86-qsort.dispatch.cpp'),
+            join('src', 'npysort', 'x86-qsort-skx.dispatch.cpp'),
             join('src', 'npysort', 'quicksort.cpp'),
             join('src', 'npysort', 'mergesort.cpp'),
             join('src', 'npysort', 'timsort.cpp'),
diff --git a/numpy/core/src/npysort/quicksort.cpp b/numpy/core/src/npysort/quicksort.cpp
index 3e351dd84..06ac0c172 100644
--- a/numpy/core/src/npysort/quicksort.cpp
+++ b/numpy/core/src/npysort/quicksort.cpp
@@ -55,12 +55,12 @@
 #include "npysort_heapsort.h"
 #include "numpy_tag.h"
 
-#include "x86-qsort.h"
+#include "x86-qsort-skx.h"
 #include <cstdlib>
 #include <utility>
 
 #ifndef NPY_DISABLE_OPTIMIZATION
-#include "x86-qsort.dispatch.h"
+#include "x86-qsort-skx.dispatch.h"
 #endif
 
 #define NOT_USED NPY_UNUSED(unused)
@@ -87,6 +87,48 @@ struct x86_dispatch {
 };
 
 template <>
+struct x86_dispatch<npy::long_tag> {
+    static bool quicksort(npy_long *start, npy_intp num)
+    {
+        void (*dispfunc)(void *, npy_intp) = nullptr;
+        NPY_CPU_DISPATCH_CALL_XB(dispfunc = x86_quicksort_long);
+        if (dispfunc) {
+            (*dispfunc)(start, num);
+            return true;
+        }
+        return false;
+    }
+};
+
+template <>
+struct x86_dispatch<npy::ulong_tag> {
+    static bool quicksort(npy_ulong *start, npy_intp num)
+    {
+        void (*dispfunc)(void *, npy_intp) = nullptr;
+        NPY_CPU_DISPATCH_CALL_XB(dispfunc = x86_quicksort_ulong);
+        if (dispfunc) {
+            (*dispfunc)(start, num);
+            return true;
+        }
+        return false;
+    }
+};
+
+template <>
+struct x86_dispatch<npy::double_tag> {
+    static bool quicksort(npy_double *start, npy_intp num)
+    {
+        void (*dispfunc)(void *, npy_intp) = nullptr;
+        NPY_CPU_DISPATCH_CALL_XB(dispfunc = x86_quicksort_double);
+        if (dispfunc) {
+            (*dispfunc)(start, num);
+            return true;
+        }
+        return false;
+    }
+};
+
+template <>
 struct x86_dispatch<npy::int_tag> {
     static bool quicksort(npy_int *start, npy_intp num)
     {
diff --git a/numpy/core/src/npysort/x86-qsort-skx.dispatch.cpp b/numpy/core/src/npysort/x86-qsort-skx.dispatch.cpp
new file mode 100644
index 000000000..d26b8fc9f
--- /dev/null
+++ b/numpy/core/src/npysort/x86-qsort-skx.dispatch.cpp
@@ -0,0 +1,54 @@
+/*@targets
+ * $maxopt $keep_baseline avx512_skx
+ */
+// policy $keep_baseline is used to avoid skip building avx512_skx
+// when its part of baseline features (--cpu-baseline), since
+// 'baseline' option isn't specified within targets.
+
+#include "x86-qsort-skx.h"
+#define NPY_NO_DEPRECATED_API NPY_API_VERSION
+
+#ifdef NPY_HAVE_AVX512_SKX
+#include "avx512-32bit-qsort.hpp"
+#include "avx512-64bit-qsort.hpp"
+
+/***************************************
+ * C > C++ dispatch
+ ***************************************/
+NPY_NO_EXPORT void
+NPY_CPU_DISPATCH_CURFX(x86_quicksort_long)(void *arr, npy_intp arrsize)
+{
+    avx512_qsort<npy_long>((npy_long*)arr, arrsize);
+}
+
+NPY_NO_EXPORT void
+NPY_CPU_DISPATCH_CURFX(x86_quicksort_ulong)(void *arr, npy_intp arrsize)
+{
+    avx512_qsort<npy_ulong>((npy_ulong*)arr, arrsize);
+}
+
+NPY_NO_EXPORT void
+NPY_CPU_DISPATCH_CURFX(x86_quicksort_double)(void *arr, npy_intp arrsize)
+{
+    avx512_qsort<npy_double>((npy_double*)arr, arrsize);
+}
+
+NPY_NO_EXPORT void
+NPY_CPU_DISPATCH_CURFX(x86_quicksort_int)(void *arr, npy_intp arrsize)
+{
+    avx512_qsort<npy_int>((npy_int*)arr, arrsize);
+}
+
+NPY_NO_EXPORT void
+NPY_CPU_DISPATCH_CURFX(x86_quicksort_uint)(void *arr, npy_intp arrsize)
+{
+    avx512_qsort<npy_uint>((npy_uint*)arr, arrsize);
+}
+
+NPY_NO_EXPORT void
+NPY_CPU_DISPATCH_CURFX(x86_quicksort_float)(void *arr, npy_intp arrsize)
+{
+    avx512_qsort<npy_float>((npy_float*)arr, arrsize);
+}
+
+#endif  // NPY_HAVE_AVX512_SKX
diff --git a/numpy/core/src/npysort/x86-qsort.h b/numpy/core/src/npysort/x86-qsort-skx.h
index 6340e2bc7..9a5cb2c9d 100644
--- a/numpy/core/src/npysort/x86-qsort.h
+++ b/numpy/core/src/npysort/x86-qsort-skx.h
@@ -7,12 +7,21 @@
 #endif
 
 #ifndef NPY_DISABLE_OPTIMIZATION
-#include "x86-qsort.dispatch.h"
+#include "x86-qsort-skx.dispatch.h"
 #endif
 
 #ifdef __cplusplus
 extern "C" {
 #endif
+NPY_CPU_DISPATCH_DECLARE(NPY_NO_EXPORT void x86_quicksort_long,
+                         (void *start, npy_intp num))
+
+NPY_CPU_DISPATCH_DECLARE(NPY_NO_EXPORT void x86_quicksort_ulong,
+                         (void *start, npy_intp num))
+
+NPY_CPU_DISPATCH_DECLARE(NPY_NO_EXPORT void x86_quicksort_double,
+                         (void *start, npy_intp num))
+
 
 NPY_CPU_DISPATCH_DECLARE(NPY_NO_EXPORT void x86_quicksort_int,
                          (void *start, npy_intp num))
diff --git a/numpy/core/src/npysort/x86-qsort.dispatch.cpp b/numpy/core/src/npysort/x86-qsort.dispatch.cpp
deleted file mode 100644
index 8e88cc667..000000000
--- a/numpy/core/src/npysort/x86-qsort.dispatch.cpp
+++ /dev/null
@@ -1,835 +0,0 @@
-/*@targets
- * $maxopt $keep_baseline avx512_skx
- */
-// policy $keep_baseline is used to avoid skip building avx512_skx
-// when its part of baseline features (--cpu-baseline), since
-// 'baseline' option isn't specified within targets.
-
-#include "x86-qsort.h"
-#define NPY_NO_DEPRECATED_API NPY_API_VERSION
-
-#ifdef NPY_HAVE_AVX512_SKX
-#include "numpy/npy_math.h"
-
-#include "npy_sort.h"
-#include "numpy_tag.h"
-
-#include "simd/simd.h"
-#include <immintrin.h>
-
-template <typename Tag, typename type>
-NPY_NO_EXPORT int
-heapsort_(type *start, npy_intp n);
-
-/*
- * Quicksort using AVX-512 for int, uint32 and float. The ideas and code are
- * based on these two research papers:
- * (1) Fast and Robust Vectorized In-Place Sorting of Primitive Types
- *     https://drops.dagstuhl.de/opus/volltexte/2021/13775/
- * (2) A Novel Hybrid Quicksort Algorithm Vectorized using AVX-512 on Intel
- * Skylake https://arxiv.org/pdf/1704.08579.pdf
- *
- * High level idea: Vectorize the quicksort partitioning using AVX-512
- * compressstore instructions. The algorithm to pick the pivot is to use median
- * of 72 elements picked at random. If the array size is < 128, then use
- * Bitonic sorting network. Good resource for bitonic sorting network:
- * http://mitp-content-server.mit.edu:18180/books/content/sectbyfn?collid=books_pres_0&fn=Chapter%2027.pdf&id=8030
- *
- * Refer to https://github.com/numpy/numpy/pull/20133#issuecomment-958110340
- * for potential problems when converting this code to universal intrinsics
- * framework.
- */
-
-/*
- * Constants used in sorting 16 elements in a ZMM registers. Based on Bitonic
- * sorting network (see
- * https://en.wikipedia.org/wiki/Bitonic_sorter#/media/File:BitonicSort.svg)
- */
-#define NETWORK1 14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 0, 1
-#define NETWORK2 12, 13, 14, 15, 8, 9, 10, 11, 4, 5, 6, 7, 0, 1, 2, 3
-#define NETWORK3 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7
-#define NETWORK4 13, 12, 15, 14, 9, 8, 11, 10, 5, 4, 7, 6, 1, 0, 3, 2
-#define NETWORK5 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
-#define NETWORK6 11, 10, 9, 8, 15, 14, 13, 12, 3, 2, 1, 0, 7, 6, 5, 4
-#define NETWORK7 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8
-#define ZMM_MAX_FLOAT _mm512_set1_ps(NPY_INFINITYF)
-#define ZMM_MAX_UINT _mm512_set1_epi32(NPY_MAX_UINT32)
-#define ZMM_MAX_INT _mm512_set1_epi32(NPY_MAX_INT32)
-#define SHUFFLE_MASK(a, b, c, d) (a << 6) | (b << 4) | (c << 2) | d
-#define SHUFFLE_ps(ZMM, MASK) _mm512_shuffle_ps(zmm, zmm, MASK)
-#define SHUFFLE_epi32(ZMM, MASK) _mm512_shuffle_epi32(zmm, MASK)
-
-#define MAX(x, y) (((x) > (y)) ? (x) : (y))
-#define MIN(x, y) (((x) < (y)) ? (x) : (y))
-
-/*
- * Vectorized random number generator xoroshiro128+. Broken into 2 parts:
- * (1) vnext generates 2 64-bit random integers
- * (2) rnd_epu32 converts this to 4 32-bit random integers and bounds it to
- *     the length of the array
- */
-#define VROTL(x, k) /* rotate each uint64_t value in vector */ \
-    _mm256_or_si256(_mm256_slli_epi64((x), (k)),               \
-                    _mm256_srli_epi64((x), 64 - (k)))
-
-static inline __m256i
-vnext(__m256i *s0, __m256i *s1)
-{
-    *s1 = _mm256_xor_si256(*s0, *s1); /* modify vectors s1 and s0 */
-    *s0 = _mm256_xor_si256(_mm256_xor_si256(VROTL(*s0, 24), *s1),
-                           _mm256_slli_epi64(*s1, 16));
-    *s1 = VROTL(*s1, 37);
-    return _mm256_add_epi64(*s0, *s1); /* return random vector */
-}
-
-/* transform random numbers to the range between 0 and bound - 1 */
-static inline __m256i
-rnd_epu32(__m256i rnd_vec, __m256i bound)
-{
-    __m256i even = _mm256_srli_epi64(_mm256_mul_epu32(rnd_vec, bound), 32);
-    __m256i odd = _mm256_mul_epu32(_mm256_srli_epi64(rnd_vec, 32), bound);
-    return _mm256_blend_epi32(odd, even, 0b01010101);
-}
-
-template <typename type>
-struct vector;
-
-template <>
-struct vector<npy_int> {
-    using tag = npy::int_tag;
-    using type_t = npy_int;
-    using zmm_t = __m512i;
-    using ymm_t = __m256i;
-
-    static type_t type_max() { return NPY_MAX_INT32; }
-    static type_t type_min() { return NPY_MIN_INT32; }
-    static zmm_t zmm_max() { return _mm512_set1_epi32(type_max()); }
-
-    static __mmask16 ge(zmm_t x, zmm_t y)
-    {
-        return _mm512_cmp_epi32_mask(x, y, _MM_CMPINT_NLT);
-    }
-    template <int scale>
-    static ymm_t i64gather(__m512i index, void const *base)
-    {
-        return _mm512_i64gather_epi32(index, base, scale);
-    }
-    static zmm_t loadu(void const *mem) { return _mm512_loadu_si512(mem); }
-    static zmm_t max(zmm_t x, zmm_t y) { return _mm512_max_epi32(x, y); }
-    static void mask_compressstoreu(void *mem, __mmask16 mask, zmm_t x)
-    {
-        return _mm512_mask_compressstoreu_epi32(mem, mask, x);
-    }
-    static zmm_t mask_loadu(zmm_t x, __mmask16 mask, void const *mem)
-    {
-        return _mm512_mask_loadu_epi32(x, mask, mem);
-    }
-    static zmm_t mask_mov(zmm_t x, __mmask16 mask, zmm_t y)
-    {
-        return _mm512_mask_mov_epi32(x, mask, y);
-    }
-    static void mask_storeu(void *mem, __mmask16 mask, zmm_t x)
-    {
-        return _mm512_mask_storeu_epi32(mem, mask, x);
-    }
-    static zmm_t min(zmm_t x, zmm_t y) { return _mm512_min_epi32(x, y); }
-    static zmm_t permutexvar(__m512i idx, zmm_t zmm)
-    {
-        return _mm512_permutexvar_epi32(idx, zmm);
-    }
-    static type_t reducemax(zmm_t v) { return npyv_reduce_max_s32(v); }
-    static type_t reducemin(zmm_t v) { return npyv_reduce_min_s32(v); }
-    static zmm_t set1(type_t v) { return _mm512_set1_epi32(v); }
-    template<__mmask16 mask>
-    static zmm_t shuffle(zmm_t zmm)
-    {
-        return _mm512_shuffle_epi32(zmm, (_MM_PERM_ENUM)mask);
-    }
-    static void storeu(void *mem, zmm_t x)
-    {
-        return _mm512_storeu_si512(mem, x);
-    }
-
-    static ymm_t max(ymm_t x, ymm_t y) { return _mm256_max_epi32(x, y); }
-    static ymm_t min(ymm_t x, ymm_t y) { return _mm256_min_epi32(x, y); }
-};
-template <>
-struct vector<npy_uint> {
-    using tag = npy::uint_tag;
-    using type_t = npy_uint;
-    using zmm_t = __m512i;
-    using ymm_t = __m256i;
-
-    static type_t type_max() { return NPY_MAX_UINT32; }
-    static type_t type_min() { return 0; }
-    static zmm_t zmm_max() { return _mm512_set1_epi32(type_max()); }
-
-    template<int scale>
-    static ymm_t i64gather(__m512i index, void const *base)
-    {
-        return _mm512_i64gather_epi32(index, base, scale);
-    }
-    static __mmask16 ge(zmm_t x, zmm_t y)
-    {
-        return _mm512_cmp_epu32_mask(x, y, _MM_CMPINT_NLT);
-    }
-    static zmm_t loadu(void const *mem) { return _mm512_loadu_si512(mem); }
-    static zmm_t max(zmm_t x, zmm_t y) { return _mm512_max_epu32(x, y); }
-    static void mask_compressstoreu(void *mem, __mmask16 mask, zmm_t x)
-    {
-        return _mm512_mask_compressstoreu_epi32(mem, mask, x);
-    }
-    static zmm_t mask_loadu(zmm_t x, __mmask16 mask, void const *mem)
-    {
-        return _mm512_mask_loadu_epi32(x, mask, mem);
-    }
-    static zmm_t mask_mov(zmm_t x, __mmask16 mask, zmm_t y)
-    {
-        return _mm512_mask_mov_epi32(x, mask, y);
-    }
-    static void mask_storeu(void *mem, __mmask16 mask, zmm_t x)
-    {
-        return _mm512_mask_storeu_epi32(mem, mask, x);
-    }
-    static zmm_t min(zmm_t x, zmm_t y) { return _mm512_min_epu32(x, y); }
-    static zmm_t permutexvar(__m512i idx, zmm_t zmm)
-    {
-        return _mm512_permutexvar_epi32(idx, zmm);
-    }
-    static type_t reducemax(zmm_t v) { return npyv_reduce_max_u32(v); }
-    static type_t reducemin(zmm_t v) { return npyv_reduce_min_u32(v); }
-    static zmm_t set1(type_t v) { return _mm512_set1_epi32(v); }
-    template<__mmask16 mask>
-    static zmm_t shuffle(zmm_t zmm)
-    {
-        return _mm512_shuffle_epi32(zmm, (_MM_PERM_ENUM)mask);
-    }
-    static void storeu(void *mem, zmm_t x)
-    {
-        return _mm512_storeu_si512(mem, x);
-    }
-
-    static ymm_t max(ymm_t x, ymm_t y) { return _mm256_max_epu32(x, y); }
-    static ymm_t min(ymm_t x, ymm_t y) { return _mm256_min_epu32(x, y); }
-};
-template <>
-struct vector<npy_float> {
-    using tag = npy::float_tag;
-    using type_t = npy_float;
-    using zmm_t = __m512;
-    using ymm_t = __m256;
-
-    static type_t type_max() { return NPY_INFINITYF; }
-    static type_t type_min() { return -NPY_INFINITYF; }
-    static zmm_t zmm_max() { return _mm512_set1_ps(type_max()); }
-
-    static __mmask16 ge(zmm_t x, zmm_t y)
-    {
-        return _mm512_cmp_ps_mask(x, y, _CMP_GE_OQ);
-    }
-    template<int scale>
-    static ymm_t i64gather(__m512i index, void const *base)
-    {
-        return _mm512_i64gather_ps(index, base, scale);
-    }
-    static zmm_t loadu(void const *mem) { return _mm512_loadu_ps(mem); }
-    static zmm_t max(zmm_t x, zmm_t y) { return _mm512_max_ps(x, y); }
-    static void mask_compressstoreu(void *mem, __mmask16 mask, zmm_t x)
-    {
-        return _mm512_mask_compressstoreu_ps(mem, mask, x);
-    }
-    static zmm_t mask_loadu(zmm_t x, __mmask16 mask, void const *mem)
-    {
-        return _mm512_mask_loadu_ps(x, mask, mem);
-    }
-    static zmm_t mask_mov(zmm_t x, __mmask16 mask, zmm_t y)
-    {
-        return _mm512_mask_mov_ps(x, mask, y);
-    }
-    static void mask_storeu(void *mem, __mmask16 mask, zmm_t x)
-    {
-        return _mm512_mask_storeu_ps(mem, mask, x);
-    }
-    static zmm_t min(zmm_t x, zmm_t y) { return _mm512_min_ps(x, y); }
-    static zmm_t permutexvar(__m512i idx, zmm_t zmm)
-    {
-        return _mm512_permutexvar_ps(idx, zmm);
-    }
-    static type_t reducemax(zmm_t v) { return npyv_reduce_max_f32(v); }
-    static type_t reducemin(zmm_t v) { return npyv_reduce_min_f32(v); }
-    static zmm_t set1(type_t v) { return _mm512_set1_ps(v); }
-    template<__mmask16 mask>
-    static zmm_t shuffle(zmm_t zmm)
-    {
-        return _mm512_shuffle_ps(zmm, zmm, (_MM_PERM_ENUM)mask);
-    }
-    static void storeu(void *mem, zmm_t x) { return _mm512_storeu_ps(mem, x); }
-
-    static ymm_t max(ymm_t x, ymm_t y) { return _mm256_max_ps(x, y); }
-    static ymm_t min(ymm_t x, ymm_t y) { return _mm256_min_ps(x, y); }
-};
-
-/*
- * COEX == Compare and Exchange two registers by swapping min and max values
- */
-template <typename vtype, typename mm_t>
-void
-COEX(mm_t &a, mm_t &b)
-{
-    mm_t temp = a;
-    a = vtype::min(a, b);
-    b = vtype::max(temp, b);
-}
-
-template <typename vtype, typename zmm_t = typename vtype::zmm_t>
-static inline zmm_t
-cmp_merge(zmm_t in1, zmm_t in2, __mmask16 mask)
-{
-    zmm_t min = vtype::min(in2, in1);
-    zmm_t max = vtype::max(in2, in1);
-    return vtype::mask_mov(min, mask, max);  // 0 -> min, 1 -> max
-}
-
-/*
- * Assumes zmm is random and performs a full sorting network defined in
- * https://en.wikipedia.org/wiki/Bitonic_sorter#/media/File:BitonicSort.svg
- */
-template <typename vtype, typename zmm_t = typename vtype::zmm_t>
-static inline zmm_t
-sort_zmm(zmm_t zmm)
-{
-    zmm = cmp_merge<vtype>(zmm, vtype::template shuffle<SHUFFLE_MASK(2, 3, 0, 1)>(zmm),
-                           0xAAAA);
-    zmm = cmp_merge<vtype>(zmm, vtype::template shuffle<SHUFFLE_MASK(0, 1, 2, 3)>(zmm),
-                           0xCCCC);
-    zmm = cmp_merge<vtype>(zmm, vtype::template shuffle<SHUFFLE_MASK(2, 3, 0, 1)>(zmm),
-                           0xAAAA);
-    zmm = cmp_merge<vtype>(
-            zmm, vtype::permutexvar(_mm512_set_epi32(NETWORK3), zmm), 0xF0F0);
-    zmm = cmp_merge<vtype>(zmm, vtype::template shuffle<SHUFFLE_MASK(1, 0, 3, 2)>(zmm),
-                           0xCCCC);
-    zmm = cmp_merge<vtype>(zmm, vtype::template shuffle<SHUFFLE_MASK(2, 3, 0, 1)>(zmm),
-                           0xAAAA);
-    zmm = cmp_merge<vtype>(
-            zmm, vtype::permutexvar(_mm512_set_epi32(NETWORK5), zmm), 0xFF00);
-    zmm = cmp_merge<vtype>(
-            zmm, vtype::permutexvar(_mm512_set_epi32(NETWORK6), zmm), 0xF0F0);
-    zmm = cmp_merge<vtype>(zmm, vtype::template shuffle<SHUFFLE_MASK(1, 0, 3, 2)>(zmm),
-                           0xCCCC);
-    zmm = cmp_merge<vtype>(zmm, vtype::template shuffle<SHUFFLE_MASK(2, 3, 0, 1)>(zmm),
-                           0xAAAA);
-    return zmm;
-}
-
-// Assumes zmm is bitonic and performs a recursive half cleaner
-template <typename vtype, typename zmm_t = typename vtype::zmm_t>
-static inline zmm_t
-bitonic_merge_zmm(zmm_t zmm)
-{
-    // 1) half_cleaner[16]: compare 1-9, 2-10, 3-11 etc ..
-    zmm = cmp_merge<vtype>(
-            zmm, vtype::permutexvar(_mm512_set_epi32(NETWORK7), zmm), 0xFF00);
-    // 2) half_cleaner[8]: compare 1-5, 2-6, 3-7 etc ..
-    zmm = cmp_merge<vtype>(
-            zmm, vtype::permutexvar(_mm512_set_epi32(NETWORK6), zmm), 0xF0F0);
-    // 3) half_cleaner[4]
-    zmm = cmp_merge<vtype>(zmm, vtype::template shuffle<SHUFFLE_MASK(1, 0, 3, 2)>(zmm),
-                           0xCCCC);
-    // 3) half_cleaner[1]
-    zmm = cmp_merge<vtype>(zmm, vtype::template shuffle<SHUFFLE_MASK(2, 3, 0, 1)>(zmm),
-                           0xAAAA);
-    return zmm;
-}
-
-// Assumes zmm1 and zmm2 are sorted and performs a recursive half cleaner
-template <typename vtype, typename zmm_t = typename vtype::zmm_t>
-static inline void
-bitonic_merge_two_zmm(zmm_t *zmm1, zmm_t *zmm2)
-{
-    // 1) First step of a merging network: coex of zmm1 and zmm2 reversed
-    *zmm2 = vtype::permutexvar(_mm512_set_epi32(NETWORK5), *zmm2);
-    zmm_t zmm3 = vtype::min(*zmm1, *zmm2);
-    zmm_t zmm4 = vtype::max(*zmm1, *zmm2);
-    // 2) Recursive half cleaner for each
-    *zmm1 = bitonic_merge_zmm<vtype>(zmm3);
-    *zmm2 = bitonic_merge_zmm<vtype>(zmm4);
-}
-
-// Assumes [zmm0, zmm1] and [zmm2, zmm3] are sorted and performs a recursive
-// half cleaner
-template <typename vtype, typename zmm_t = typename vtype::zmm_t>
-static inline void
-bitonic_merge_four_zmm(zmm_t *zmm)
-{
-    zmm_t zmm2r = vtype::permutexvar(_mm512_set_epi32(NETWORK5), zmm[2]);
-    zmm_t zmm3r = vtype::permutexvar(_mm512_set_epi32(NETWORK5), zmm[3]);
-    zmm_t zmm_t1 = vtype::min(zmm[0], zmm3r);
-    zmm_t zmm_t2 = vtype::min(zmm[1], zmm2r);
-    zmm_t zmm_t3 = vtype::permutexvar(_mm512_set_epi32(NETWORK5),
-                                      vtype::max(zmm[1], zmm2r));
-    zmm_t zmm_t4 = vtype::permutexvar(_mm512_set_epi32(NETWORK5),
-                                      vtype::max(zmm[0], zmm3r));
-    zmm_t zmm0 = vtype::min(zmm_t1, zmm_t2);
-    zmm_t zmm1 = vtype::max(zmm_t1, zmm_t2);
-    zmm_t zmm2 = vtype::min(zmm_t3, zmm_t4);
-    zmm_t zmm3 = vtype::max(zmm_t3, zmm_t4);
-    zmm[0] = bitonic_merge_zmm<vtype>(zmm0);
-    zmm[1] = bitonic_merge_zmm<vtype>(zmm1);
-    zmm[2] = bitonic_merge_zmm<vtype>(zmm2);
-    zmm[3] = bitonic_merge_zmm<vtype>(zmm3);
-}
-
-template <typename vtype, typename zmm_t = typename vtype::zmm_t>
-static inline void
-bitonic_merge_eight_zmm(zmm_t *zmm)
-{
-    zmm_t zmm4r = vtype::permutexvar(_mm512_set_epi32(NETWORK5), zmm[4]);
-    zmm_t zmm5r = vtype::permutexvar(_mm512_set_epi32(NETWORK5), zmm[5]);
-    zmm_t zmm6r = vtype::permutexvar(_mm512_set_epi32(NETWORK5), zmm[6]);
-    zmm_t zmm7r = vtype::permutexvar(_mm512_set_epi32(NETWORK5), zmm[7]);
-    zmm_t zmm_t1 = vtype::min(zmm[0], zmm7r);
-    zmm_t zmm_t2 = vtype::min(zmm[1], zmm6r);
-    zmm_t zmm_t3 = vtype::min(zmm[2], zmm5r);
-    zmm_t zmm_t4 = vtype::min(zmm[3], zmm4r);
-    zmm_t zmm_t5 = vtype::permutexvar(_mm512_set_epi32(NETWORK5),
-                                      vtype::max(zmm[3], zmm4r));
-    zmm_t zmm_t6 = vtype::permutexvar(_mm512_set_epi32(NETWORK5),
-                                      vtype::max(zmm[2], zmm5r));
-    zmm_t zmm_t7 = vtype::permutexvar(_mm512_set_epi32(NETWORK5),
-                                      vtype::max(zmm[1], zmm6r));
-    zmm_t zmm_t8 = vtype::permutexvar(_mm512_set_epi32(NETWORK5),
-                                      vtype::max(zmm[0], zmm7r));
-    COEX<vtype>(zmm_t1, zmm_t3);
-    COEX<vtype>(zmm_t2, zmm_t4);
-    COEX<vtype>(zmm_t5, zmm_t7);
-    COEX<vtype>(zmm_t6, zmm_t8);
-    COEX<vtype>(zmm_t1, zmm_t2);
-    COEX<vtype>(zmm_t3, zmm_t4);
-    COEX<vtype>(zmm_t5, zmm_t6);
-    COEX<vtype>(zmm_t7, zmm_t8);
-    zmm[0] = bitonic_merge_zmm<vtype>(zmm_t1);
-    zmm[1] = bitonic_merge_zmm<vtype>(zmm_t2);
-    zmm[2] = bitonic_merge_zmm<vtype>(zmm_t3);
-    zmm[3] = bitonic_merge_zmm<vtype>(zmm_t4);
-    zmm[4] = bitonic_merge_zmm<vtype>(zmm_t5);
-    zmm[5] = bitonic_merge_zmm<vtype>(zmm_t6);
-    zmm[6] = bitonic_merge_zmm<vtype>(zmm_t7);
-    zmm[7] = bitonic_merge_zmm<vtype>(zmm_t8);
-}
-
-template <typename vtype, typename type_t>
-static inline void
-sort_16(type_t *arr, npy_int N)
-{
-    __mmask16 load_mask = (0x0001 << N) - 0x0001;
-    typename vtype::zmm_t zmm =
-            vtype::mask_loadu(vtype::zmm_max(), load_mask, arr);
-    vtype::mask_storeu(arr, load_mask, sort_zmm<vtype>(zmm));
-}
-
-template <typename vtype, typename type_t>
-static inline void
-sort_32(type_t *arr, npy_int N)
-{
-    if (N <= 16) {
-        sort_16<vtype>(arr, N);
-        return;
-    }
-    using zmm_t = typename vtype::zmm_t;
-    zmm_t zmm1 = vtype::loadu(arr);
-    __mmask16 load_mask = (0x0001 << (N - 16)) - 0x0001;
-    zmm_t zmm2 = vtype::mask_loadu(vtype::zmm_max(), load_mask, arr + 16);
-    zmm1 = sort_zmm<vtype>(zmm1);
-    zmm2 = sort_zmm<vtype>(zmm2);
-    bitonic_merge_two_zmm<vtype>(&zmm1, &zmm2);
-    vtype::storeu(arr, zmm1);
-    vtype::mask_storeu(arr + 16, load_mask, zmm2);
-}
-
-template <typename vtype, typename type_t>
-static inline void
-sort_64(type_t *arr, npy_int N)
-{
-    if (N <= 32) {
-        sort_32<vtype>(arr, N);
-        return;
-    }
-    using zmm_t = typename vtype::zmm_t;
-    zmm_t zmm[4];
-    zmm[0] = vtype::loadu(arr);
-    zmm[1] = vtype::loadu(arr + 16);
-    __mmask16 load_mask1 = 0xFFFF, load_mask2 = 0xFFFF;
-    if (N < 48) {
-        load_mask1 = (0x0001 << (N - 32)) - 0x0001;
-        load_mask2 = 0x0000;
-    }
-    else if (N < 64) {
-        load_mask2 = (0x0001 << (N - 48)) - 0x0001;
-    }
-    zmm[2] = vtype::mask_loadu(vtype::zmm_max(), load_mask1, arr + 32);
-    zmm[3] = vtype::mask_loadu(vtype::zmm_max(), load_mask2, arr + 48);
-    zmm[0] = sort_zmm<vtype>(zmm[0]);
-    zmm[1] = sort_zmm<vtype>(zmm[1]);
-    zmm[2] = sort_zmm<vtype>(zmm[2]);
-    zmm[3] = sort_zmm<vtype>(zmm[3]);
-    bitonic_merge_two_zmm<vtype>(&zmm[0], &zmm[1]);
-    bitonic_merge_two_zmm<vtype>(&zmm[2], &zmm[3]);
-    bitonic_merge_four_zmm<vtype>(zmm);
-    vtype::storeu(arr, zmm[0]);
-    vtype::storeu(arr + 16, zmm[1]);
-    vtype::mask_storeu(arr + 32, load_mask1, zmm[2]);
-    vtype::mask_storeu(arr + 48, load_mask2, zmm[3]);
-}
-
-template <typename vtype, typename type_t>
-static inline void
-sort_128(type_t *arr, npy_int N)
-{
-    if (N <= 64) {
-        sort_64<vtype>(arr, N);
-        return;
-    }
-    using zmm_t = typename vtype::zmm_t;
-    zmm_t zmm[8];
-    zmm[0] = vtype::loadu(arr);
-    zmm[1] = vtype::loadu(arr + 16);
-    zmm[2] = vtype::loadu(arr + 32);
-    zmm[3] = vtype::loadu(arr + 48);
-    zmm[0] = sort_zmm<vtype>(zmm[0]);
-    zmm[1] = sort_zmm<vtype>(zmm[1]);
-    zmm[2] = sort_zmm<vtype>(zmm[2]);
-    zmm[3] = sort_zmm<vtype>(zmm[3]);
-    __mmask16 load_mask1 = 0xFFFF, load_mask2 = 0xFFFF;
-    __mmask16 load_mask3 = 0xFFFF, load_mask4 = 0xFFFF;
-    if (N < 80) {
-        load_mask1 = (0x0001 << (N - 64)) - 0x0001;
-        load_mask2 = 0x0000;
-        load_mask3 = 0x0000;
-        load_mask4 = 0x0000;
-    }
-    else if (N < 96) {
-        load_mask2 = (0x0001 << (N - 80)) - 0x0001;
-        load_mask3 = 0x0000;
-        load_mask4 = 0x0000;
-    }
-    else if (N < 112) {
-        load_mask3 = (0x0001 << (N - 96)) - 0x0001;
-        load_mask4 = 0x0000;
-    }
-    else {
-        load_mask4 = (0x0001 << (N - 112)) - 0x0001;
-    }
-    zmm[4] = vtype::mask_loadu(vtype::zmm_max(), load_mask1, arr + 64);
-    zmm[5] = vtype::mask_loadu(vtype::zmm_max(), load_mask2, arr + 80);
-    zmm[6] = vtype::mask_loadu(vtype::zmm_max(), load_mask3, arr + 96);
-    zmm[7] = vtype::mask_loadu(vtype::zmm_max(), load_mask4, arr + 112);
-    zmm[4] = sort_zmm<vtype>(zmm[4]);
-    zmm[5] = sort_zmm<vtype>(zmm[5]);
-    zmm[6] = sort_zmm<vtype>(zmm[6]);
-    zmm[7] = sort_zmm<vtype>(zmm[7]);
-    bitonic_merge_two_zmm<vtype>(&zmm[0], &zmm[1]);
-    bitonic_merge_two_zmm<vtype>(&zmm[2], &zmm[3]);
-    bitonic_merge_two_zmm<vtype>(&zmm[4], &zmm[5]);
-    bitonic_merge_two_zmm<vtype>(&zmm[6], &zmm[7]);
-    bitonic_merge_four_zmm<vtype>(zmm);
-    bitonic_merge_four_zmm<vtype>(zmm + 4);
-    bitonic_merge_eight_zmm<vtype>(zmm);
-    vtype::storeu(arr, zmm[0]);
-    vtype::storeu(arr + 16, zmm[1]);
-    vtype::storeu(arr + 32, zmm[2]);
-    vtype::storeu(arr + 48, zmm[3]);
-    vtype::mask_storeu(arr + 64, load_mask1, zmm[4]);
-    vtype::mask_storeu(arr + 80, load_mask2, zmm[5]);
-    vtype::mask_storeu(arr + 96, load_mask3, zmm[6]);
-    vtype::mask_storeu(arr + 112, load_mask4, zmm[7]);
-}
-
-template <typename type_t>
-static inline void
-swap(type_t *arr, npy_intp ii, npy_intp jj)
-{
-    type_t temp = arr[ii];
-    arr[ii] = arr[jj];
-    arr[jj] = temp;
-}
-
-// Median of 3 strategy
-// template<typename type_t>
-// static inline
-// npy_intp get_pivot_index(type_t *arr, const npy_intp left, const npy_intp
-// right) {
-//    return (rand() % (right + 1 - left)) + left;
-//    //npy_intp middle = ((right-left)/2) + left;
-//    //type_t a = arr[left], b = arr[middle], c = arr[right];
-//    //if ((b >= a && b <= c) || (b <= a && b >= c))
-//    //    return middle;
-//    //if ((a >= b && a <= c) || (a <= b && a >= c))
-//    //    return left;
-//    //else
-//    //    return right;
-//}
-
-/*
- * Picking the pivot: Median of 72 array elements chosen at random.
- */
-
-template <typename vtype, typename type_t>
-static inline type_t
-get_pivot(type_t *arr, const npy_intp left, const npy_intp right)
-{
-    /* seeds for vectorized random number generator */
-    __m256i s0 = _mm256_setr_epi64x(8265987198341093849, 3762817312854612374,
-                                    1324281658759788278, 6214952190349879213);
-    __m256i s1 = _mm256_setr_epi64x(2874178529384792648, 1257248936691237653,
-                                    7874578921548791257, 1998265912745817298);
-    s0 = _mm256_add_epi64(s0, _mm256_set1_epi64x(left));
-    s1 = _mm256_sub_epi64(s1, _mm256_set1_epi64x(right));
-
-    npy_intp arrsize = right - left + 1;
-    __m256i bound =
-            _mm256_set1_epi32(arrsize > INT32_MAX ? INT32_MAX : arrsize);
-    __m512i left_vec = _mm512_set1_epi64(left);
-    __m512i right_vec = _mm512_set1_epi64(right);
-    using ymm_t = typename vtype::ymm_t;
-    ymm_t v[9];
-    /* fill 9 vectors with random numbers */
-    for (npy_int i = 0; i < 9; ++i) {
-        __m256i rand_64 = vnext(&s0, &s1); /* vector with 4 random uint64_t */
-        __m512i rand_32 = _mm512_cvtepi32_epi64(rnd_epu32(
-                rand_64, bound)); /* random numbers between 0 and bound - 1 */
-        __m512i indices;
-        if (i < 5)
-            indices =
-                    _mm512_add_epi64(left_vec, rand_32); /* indices for arr */
-        else
-            indices =
-                    _mm512_sub_epi64(right_vec, rand_32); /* indices for arr */
-
-        v[i] = vtype::template i64gather<sizeof(type_t)>(indices, arr);
-    }
-
-    /* median network for 9 elements */
-    COEX<vtype>(v[0], v[1]);
-    COEX<vtype>(v[2], v[3]);
-    COEX<vtype>(v[4], v[5]);
-    COEX<vtype>(v[6], v[7]);
-    COEX<vtype>(v[0], v[2]);
-    COEX<vtype>(v[1], v[3]);
-    COEX<vtype>(v[4], v[6]);
-    COEX<vtype>(v[5], v[7]);
-    COEX<vtype>(v[0], v[4]);
-    COEX<vtype>(v[1], v[2]);
-    COEX<vtype>(v[5], v[6]);
-    COEX<vtype>(v[3], v[7]);
-    COEX<vtype>(v[1], v[5]);
-    COEX<vtype>(v[2], v[6]);
-    COEX<vtype>(v[3], v[5]);
-    COEX<vtype>(v[2], v[4]);
-    COEX<vtype>(v[3], v[4]);
-    COEX<vtype>(v[3], v[8]);
-    COEX<vtype>(v[4], v[8]);
-
-    // technically v[4] needs to be sorted before we pick the correct median,
-    // picking the 4th element works just as well for performance
-    type_t *temp = (type_t *)&v[4];
-
-    return temp[4];
-}
-
-/*
- * Partition one ZMM register based on the pivot and returns the index of the
- * last element that is less than equal to the pivot.
- */
-template <typename vtype, typename type_t, typename zmm_t>
-static inline npy_int
-partition_vec(type_t *arr, npy_intp left, npy_intp right, const zmm_t curr_vec,
-              const zmm_t pivot_vec, zmm_t *smallest_vec, zmm_t *biggest_vec)
-{
-    /* which elements are larger than the pivot */
-    __mmask16 gt_mask = vtype::ge(curr_vec, pivot_vec);
-    npy_int amount_gt_pivot = _mm_popcnt_u32((npy_int)gt_mask);
-    vtype::mask_compressstoreu(arr + left, _mm512_knot(gt_mask), curr_vec);
-    vtype::mask_compressstoreu(arr + right - amount_gt_pivot, gt_mask,
-                               curr_vec);
-    *smallest_vec = vtype::min(curr_vec, *smallest_vec);
-    *biggest_vec = vtype::max(curr_vec, *biggest_vec);
-    return amount_gt_pivot;
-}
-
-/*
- * Partition an array based on the pivot and returns the index of the
- * last element that is less than equal to the pivot.
- */
-template <typename vtype, typename type_t>
-static inline npy_intp
-partition_avx512(type_t *arr, npy_intp left, npy_intp right, type_t pivot,
-                 type_t *smallest, type_t *biggest)
-{
-    /* make array length divisible by 16 , shortening the array */
-    for (npy_int i = (right - left) % 16; i > 0; --i) {
-        *smallest = MIN(*smallest, arr[left]);
-        *biggest = MAX(*biggest, arr[left]);
-        if (arr[left] > pivot) {
-            swap(arr, left, --right);
-        }
-        else {
-            ++left;
-        }
-    }
-
-    if (left == right)
-        return left; /* less than 16 elements in the array */
-
-    using zmm_t = typename vtype::zmm_t;
-    zmm_t pivot_vec = vtype::set1(pivot);
-    zmm_t min_vec = vtype::set1(*smallest);
-    zmm_t max_vec = vtype::set1(*biggest);
-
-    if (right - left == 16) {
-        zmm_t vec = vtype::loadu(arr + left);
-        npy_int amount_gt_pivot = partition_vec<vtype>(
-                arr, left, left + 16, vec, pivot_vec, &min_vec, &max_vec);
-        *smallest = vtype::reducemin(min_vec);
-        *biggest = vtype::reducemax(max_vec);
-        return left + (16 - amount_gt_pivot);
-    }
-
-    // first and last 16 values are partitioned at the end
-    zmm_t vec_left = vtype::loadu(arr + left);
-    zmm_t vec_right = vtype::loadu(arr + (right - 16));
-    // store points of the vectors
-    npy_intp r_store = right - 16;
-    npy_intp l_store = left;
-    // indices for loading the elements
-    left += 16;
-    right -= 16;
-    while (right - left != 0) {
-        zmm_t curr_vec;
-        /*
-         * if fewer elements are stored on the right side of the array,
-         * then next elements are loaded from the right side,
-         * otherwise from the left side
-         */
-        if ((r_store + 16) - right < left - l_store) {
-            right -= 16;
-            curr_vec = vtype::loadu(arr + right);
-        }
-        else {
-            curr_vec = vtype::loadu(arr + left);
-            left += 16;
-        }
-        // partition the current vector and save it on both sides of the array
-        npy_int amount_gt_pivot =
-                partition_vec<vtype>(arr, l_store, r_store + 16, curr_vec,
-                                     pivot_vec, &min_vec, &max_vec);
-        ;
-        r_store -= amount_gt_pivot;
-        l_store += (16 - amount_gt_pivot);
-    }
-
-    /* partition and save vec_left and vec_right */
-    npy_int amount_gt_pivot =
-            partition_vec<vtype>(arr, l_store, r_store + 16, vec_left,
-                                 pivot_vec, &min_vec, &max_vec);
-    l_store += (16 - amount_gt_pivot);
-    amount_gt_pivot =
-            partition_vec<vtype>(arr, l_store, l_store + 16, vec_right,
-                                 pivot_vec, &min_vec, &max_vec);
-    l_store += (16 - amount_gt_pivot);
-    *smallest = vtype::reducemin(min_vec);
-    *biggest = vtype::reducemax(max_vec);
-    return l_store;
-}
-
-template <typename vtype, typename type_t>
-static inline void
-qsort_(type_t *arr, npy_intp left, npy_intp right, npy_int max_iters)
-{
-    /*
-     * Resort to heapsort if quicksort isn't making any progress
-     */
-    if (max_iters <= 0) {
-        heapsort_<typename vtype::tag>(arr + left, right + 1 - left);
-        return;
-    }
-    /*
-     * Base case: use bitonic networks to sort arrays <= 128
-     */
-    if (right + 1 - left <= 128) {
-        sort_128<vtype>(arr + left, (npy_int)(right + 1 - left));
-        return;
-    }
-
-    type_t pivot = get_pivot<vtype>(arr, left, right);
-    type_t smallest = vtype::type_max();
-    type_t biggest = vtype::type_min();
-    npy_intp pivot_index = partition_avx512<vtype>(arr, left, right + 1, pivot,
-                                                   &smallest, &biggest);
-    if (pivot != smallest)
-        qsort_<vtype>(arr, left, pivot_index - 1, max_iters - 1);
-    if (pivot != biggest)
-        qsort_<vtype>(arr, pivot_index, right, max_iters - 1);
-}
-
-static inline npy_intp
-replace_nan_with_inf(npy_float *arr, npy_intp arrsize)
-{
-    npy_intp nan_count = 0;
-    __mmask16 loadmask = 0xFFFF;
-    while (arrsize > 0) {
-        if (arrsize < 16) {
-            loadmask = (0x0001 << arrsize) - 0x0001;
-        }
-        __m512 in_zmm = _mm512_maskz_loadu_ps(loadmask, arr);
-        __mmask16 nanmask = _mm512_cmp_ps_mask(in_zmm, in_zmm, _CMP_NEQ_UQ);
-        nan_count += _mm_popcnt_u32((npy_int)nanmask);
-        _mm512_mask_storeu_ps(arr, nanmask, ZMM_MAX_FLOAT);
-        arr += 16;
-        arrsize -= 16;
-    }
-    return nan_count;
-}
-
-static inline void
-replace_inf_with_nan(npy_float *arr, npy_intp arrsize, npy_intp nan_count)
-{
-    for (npy_intp ii = arrsize - 1; nan_count > 0; --ii) {
-        arr[ii] = NPY_NANF;
-        nan_count -= 1;
-    }
-}
-
-/***************************************
- * C > C++ dispatch
- ***************************************/
-
-NPY_NO_EXPORT void
-NPY_CPU_DISPATCH_CURFX(x86_quicksort_int)(void *arr, npy_intp arrsize)
-{
-    if (arrsize > 1) {
-        qsort_<vector<npy_int>, npy_int>((npy_int *)arr, 0, arrsize - 1,
-                                         2 * (npy_int)log2(arrsize));
-    }
-}
-
-NPY_NO_EXPORT void
-NPY_CPU_DISPATCH_CURFX(x86_quicksort_uint)(void *arr, npy_intp arrsize)
-{
-    if (arrsize > 1) {
-        qsort_<vector<npy_uint>, npy_uint>((npy_uint *)arr, 0, arrsize - 1,
-                                           2 * (npy_int)log2(arrsize));
-    }
-}
-
-NPY_NO_EXPORT void
-NPY_CPU_DISPATCH_CURFX(x86_quicksort_float)(void *arr, npy_intp arrsize)
-{
-    if (arrsize > 1) {
-        npy_intp nan_count = replace_nan_with_inf((npy_float *)arr, arrsize);
-        qsort_<vector<npy_float>, npy_float>((npy_float *)arr, 0, arrsize - 1,
-                                             2 * (npy_int)log2(arrsize));
-        replace_inf_with_nan((npy_float *)arr, arrsize, nan_count);
-    }
-}
-
-#endif  // NPY_HAVE_AVX512_SKX