/***************************************************************************
 * Copyright (c) Johan Mabille, Sylvain Corlay, Wolf Vollprecht and         *
 * Martin Renou                                                             *
 * Copyright (c) QuantStack                                                 *
 * Copyright (c) Serge Guelton                                              *
 *                                                                          *
 * Distributed under the terms of the BSD 3-Clause License.                 *
 *                                                                          *
 * The full license is in the file LICENSE, distributed with this software. *
 ****************************************************************************/

#ifndef XSIMD_AVX512F_HPP
#define XSIMD_AVX512F_HPP

#include <complex>
#include <limits>
#include <type_traits>

#include "../types/xsimd_avx512f_register.hpp"

namespace xsimd
{

    namespace kernel
    {
        using namespace types;

        namespace detail
        {
            inline void split_avx512(__m512 val, __m256& low, __m256& high) noexcept
            {
                low = _mm512_castps512_ps256(val);
                high = _mm512_extractf32x8_ps(val, 1);
            }
            inline void split_avx512(__m512d val, __m256d& low, __m256d& high) noexcept
            {
                low = _mm512_castpd512_pd256(val);
                high = _mm512_extractf64x4_pd(val, 1);
            }
            inline void split_avx512(__m512i val, __m256i& low, __m256i& high) noexcept
            {
                low = _mm512_castsi512_si256(val);
                high = _mm512_extracti64x4_epi64(val, 1);
            }
            inline __m512i merge_avx(__m256i low, __m256i high) noexcept
            {
                return _mm512_inserti64x4(_mm512_castsi256_si512(low), high, 1);
            }
            inline __m512 merge_avx(__m256 low, __m256 high) noexcept
            {
                return _mm512_castpd_ps(_mm512_insertf64x4(_mm512_castpd256_pd512(_mm256_castps_pd(low)), _mm256_castps_pd(high), 1));
            }
            inline __m512d merge_avx(__m256d low, __m256d high) noexcept
            {
                return _mm512_insertf64x4(_mm512_castpd256_pd512(low), high, 1);
            }
            template <class F>
            __m512i fwd_to_avx(F f, __m512i self)
            {
                __m256i self_low, self_high;
                split_avx512(self, self_low, self_high);
                __m256i res_low = f(self_low);
                __m256i res_high = f(self_high);
                return merge_avx(res_low, res_high);
            }
            template <class F>
            __m512i fwd_to_avx(F f, __m512i self, __m512i other)
            {
                __m256i self_low, self_high, other_low, other_high;
                split_avx512(self, self_low, self_high);
                split_avx512(other, other_low, other_high);
                __m256i res_low = f(self_low, other_low);
                __m256i res_high = f(self_high, other_high);
                return merge_avx(res_low, res_high);
            }
            template <class F>
            __m512i fwd_to_avx(F f, __m512i self, int32_t other)
            {
                __m256i self_low, self_high;
                split_avx512(self, self_low, self_high);
                __m256i res_low = f(self_low, other);
                __m256i res_high = f(self_high, other);
                return merge_avx(res_low, res_high);
            }
        }
        namespace detail
        {

            inline uint32_t morton(uint16_t x, uint16_t y) noexcept
            {

                static const unsigned short MortonTable256[256] = {
                    0x0000, 0x0001, 0x0004, 0x0005, 0x0010, 0x0011, 0x0014, 0x0015,
                    0x0040, 0x0041, 0x0044, 0x0045, 0x0050, 0x0051, 0x0054, 0x0055,
                    0x0100, 0x0101, 0x0104, 0x0105, 0x0110, 0x0111, 0x0114, 0x0115,
                    0x0140, 0x0141, 0x0144, 0x0145, 0x0150, 0x0151, 0x0154, 0x0155,
                    0x0400, 0x0401, 0x0404, 0x0405, 0x0410, 0x0411, 0x0414, 0x0415,
                    0x0440, 0x0441, 0x0444, 0x0445, 0x0450, 0x0451, 0x0454, 0x0455,
                    0x0500, 0x0501, 0x0504, 0x0505, 0x0510, 0x0511, 0x0514, 0x0515,
                    0x0540, 0x0541, 0x0544, 0x0545, 0x0550, 0x0551, 0x0554, 0x0555,
                    0x1000, 0x1001, 0x1004, 0x1005, 0x1010, 0x1011, 0x1014, 0x1015,
                    0x1040, 0x1041, 0x1044, 0x1045, 0x1050, 0x1051, 0x1054, 0x1055,
                    0x1100, 0x1101, 0x1104, 0x1105, 0x1110, 0x1111, 0x1114, 0x1115,
                    0x1140, 0x1141, 0x1144, 0x1145, 0x1150, 0x1151, 0x1154, 0x1155,
                    0x1400, 0x1401, 0x1404, 0x1405, 0x1410, 0x1411, 0x1414, 0x1415,
                    0x1440, 0x1441, 0x1444, 0x1445, 0x1450, 0x1451, 0x1454, 0x1455,
                    0x1500, 0x1501, 0x1504, 0x1505, 0x1510, 0x1511, 0x1514, 0x1515,
                    0x1540, 0x1541, 0x1544, 0x1545, 0x1550, 0x1551, 0x1554, 0x1555,
                    0x4000, 0x4001, 0x4004, 0x4005, 0x4010, 0x4011, 0x4014, 0x4015,
                    0x4040, 0x4041, 0x4044, 0x4045, 0x4050, 0x4051, 0x4054, 0x4055,
                    0x4100, 0x4101, 0x4104, 0x4105, 0x4110, 0x4111, 0x4114, 0x4115,
                    0x4140, 0x4141, 0x4144, 0x4145, 0x4150, 0x4151, 0x4154, 0x4155,
                    0x4400, 0x4401, 0x4404, 0x4405, 0x4410, 0x4411, 0x4414, 0x4415,
                    0x4440, 0x4441, 0x4444, 0x4445, 0x4450, 0x4451, 0x4454, 0x4455,
                    0x4500, 0x4501, 0x4504, 0x4505, 0x4510, 0x4511, 0x4514, 0x4515,
                    0x4540, 0x4541, 0x4544, 0x4545, 0x4550, 0x4551, 0x4554, 0x4555,
                    0x5000, 0x5001, 0x5004, 0x5005, 0x5010, 0x5011, 0x5014, 0x5015,
                    0x5040, 0x5041, 0x5044, 0x5045, 0x5050, 0x5051, 0x5054, 0x5055,
                    0x5100, 0x5101, 0x5104, 0x5105, 0x5110, 0x5111, 0x5114, 0x5115,
                    0x5140, 0x5141, 0x5144, 0x5145, 0x5150, 0x5151, 0x5154, 0x5155,
                    0x5400, 0x5401, 0x5404, 0x5405, 0x5410, 0x5411, 0x5414, 0x5415,
                    0x5440, 0x5441, 0x5444, 0x5445, 0x5450, 0x5451, 0x5454, 0x5455,
                    0x5500, 0x5501, 0x5504, 0x5505, 0x5510, 0x5511, 0x5514, 0x5515,
                    0x5540, 0x5541, 0x5544, 0x5545, 0x5550, 0x5551, 0x5554, 0x5555
                };

                uint32_t z = MortonTable256[y >> 8] << 17 | MortonTable256[x >> 8] << 16 | MortonTable256[y & 0xFF] << 1 | MortonTable256[x & 0xFF];
                return z;
            }

            template <class A, class T, int Cmp>
            inline batch_bool<T, A> compare_int_avx512f(batch<T, A> const& self, batch<T, A> const& other) noexcept
            {
                using register_type = typename batch_bool<T, A>::register_type;
                if (std::is_signed<T>::value)
                {
                    XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
                    {
                        // shifting to take sign into account
                        uint64_t mask_low0 = _mm512_cmp_epi32_mask((batch<int32_t, A>(self.data) & batch<int32_t, A>(0x000000FF)) << 24,
                                                                   (batch<int32_t, A>(other.data) & batch<int32_t, A>(0x000000FF)) << 24,
                                                                   Cmp);
                        uint64_t mask_low1 = _mm512_cmp_epi32_mask((batch<int32_t, A>(self.data) & batch<int32_t, A>(0x0000FF00)) << 16,
                                                                   (batch<int32_t, A>(other.data) & batch<int32_t, A>(0x0000FF00)) << 16,
                                                                   Cmp);
                        uint64_t mask_high0 = _mm512_cmp_epi32_mask((batch<int32_t, A>(self.data) & batch<int32_t, A>(0x00FF0000)) << 8,
                                                                    (batch<int32_t, A>(other.data) & batch<int32_t, A>(0x00FF0000)) << 8,
                                                                    Cmp);
                        uint64_t mask_high1 = _mm512_cmp_epi32_mask((batch<int32_t, A>(self.data) & batch<int32_t, A>(0xFF000000)),
                                                                    (batch<int32_t, A>(other.data) & batch<int32_t, A>(0xFF000000)),
                                                                    Cmp);
                        uint64_t mask = 0;
                        for (unsigned i = 0; i < 16; ++i)
                        {
                            mask |= (mask_low0 & (uint64_t(1) << i)) << (3 * i + 0);
                            mask |= (mask_low1 & (uint64_t(1) << i)) << (3 * i + 1);
                            mask |= (mask_high0 & (uint64_t(1) << i)) << (3 * i + 2);
                            mask |= (mask_high1 & (uint64_t(1) << i)) << (3 * i + 3);
                        }
                        return (register_type)mask;
                    }
                    else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
                    {
                        // shifting to take sign into account
                        uint16_t mask_low = _mm512_cmp_epi32_mask((batch<int32_t, A>(self.data) & batch<int32_t, A>(0x0000FFFF)) << 16,
                                                                  (batch<int32_t, A>(other.data) & batch<int32_t, A>(0x0000FFFF)) << 16,
                                                                  Cmp);
                        uint16_t mask_high = _mm512_cmp_epi32_mask((batch<int32_t, A>(self.data) & batch<int32_t, A>(0xFFFF0000)),
                                                                   (batch<int32_t, A>(other.data) & batch<int32_t, A>(0xFFFF0000)),
                                                                   Cmp);
                        return static_cast<register_type>(morton(mask_low, mask_high));
                    }
                    else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                    {
                        return (register_type)_mm512_cmp_epi32_mask(self, other, Cmp);
                    }
                    else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                    {
                        return (register_type)_mm512_cmp_epi64_mask(self, other, Cmp);
                    }
                }
                else
                {
                    XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
                    {
                        uint64_t mask_low0 = _mm512_cmp_epu32_mask((batch<uint32_t, A>(self.data) & batch<uint32_t, A>(0x000000FF)), (batch<uint32_t, A>(other.data) & batch<uint32_t, A>(0x000000FF)), Cmp);
                        uint64_t mask_low1 = _mm512_cmp_epu32_mask((batch<uint32_t, A>(self.data) & batch<uint32_t, A>(0x0000FF00)), (batch<uint32_t, A>(other.data) & batch<uint32_t, A>(0x0000FF00)), Cmp);
                        uint64_t mask_high0 = _mm512_cmp_epu32_mask((batch<uint32_t, A>(self.data) & batch<uint32_t, A>(0x00FF0000)), (batch<uint32_t, A>(other.data) & batch<uint32_t, A>(0x00FF0000)), Cmp);
                        uint64_t mask_high1 = _mm512_cmp_epu32_mask((batch<uint32_t, A>(self.data) & batch<uint32_t, A>(0xFF000000)), (batch<uint32_t, A>(other.data) & batch<uint32_t, A>(0xFF000000)), Cmp);
                        uint64_t mask = 0;
                        for (unsigned i = 0; i < 16; ++i)
                        {
                            mask |= (mask_low0 & (uint64_t(1) << i)) << (3 * i + 0);
                            mask |= (mask_low1 & (uint64_t(1) << i)) << (3 * i + 1);
                            mask |= (mask_high0 & (uint64_t(1) << i)) << (3 * i + 2);
                            mask |= (mask_high1 & (uint64_t(1) << i)) << (3 * i + 3);
                        }
                        return (register_type)mask;
                    }
                    else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
                    {
                        uint16_t mask_low = _mm512_cmp_epu32_mask((batch<uint32_t, A>(self.data) & batch<uint32_t, A>(0x0000FFFF)), (batch<uint32_t, A>(other.data) & batch<uint32_t, A>(0x0000FFFF)), Cmp);
                        uint16_t mask_high = _mm512_cmp_epu32_mask((batch<uint32_t, A>(self.data) & batch<uint32_t, A>(0xFFFF0000)), (batch<uint32_t, A>(other.data) & batch<uint32_t, A>(0xFFFF0000)), Cmp);
                        return static_cast<register_type>(morton(mask_low, mask_high));
                    }
                    else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                    {
                        return (register_type)_mm512_cmp_epu32_mask(self, other, Cmp);
                    }
                    else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                    {
                        return (register_type)_mm512_cmp_epu64_mask(self, other, Cmp);
                    }
                }
            }
        }

        // abs
        template <class A>
        inline batch<float, A> abs(batch<float, A> const& self, requires_arch<avx512f>) noexcept
        {
            __m512 self_asf = (__m512)self;
            __m512i self_asi = *reinterpret_cast<__m512i*>(&self_asf);
            __m512i res_asi = _mm512_and_epi32(_mm512_set1_epi32(0x7FFFFFFF), self_asi);
            return *reinterpret_cast<__m512*>(&res_asi);
        }
        template <class A>
        inline batch<double, A> abs(batch<double, A> const& self, requires_arch<avx512f>) noexcept
        {
            __m512d self_asd = (__m512d)self;
            __m512i self_asi = *reinterpret_cast<__m512i*>(&self_asd);
            __m512i res_asi = _mm512_and_epi64(_mm512_set1_epi64(0x7FFFFFFFFFFFFFFF),
                                               self_asi);
            return *reinterpret_cast<__m512d*>(&res_asi);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> abs(batch<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            if (std::is_unsigned<T>::value)
            {
                return self;
            }

            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
            {
                return detail::fwd_to_avx([](__m256i s) noexcept
                                          { return abs(batch<T, avx2>(s)); },
                                          self);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
            {
                return detail::fwd_to_avx([](__m256i s) noexcept
                                          { return abs(batch<T, avx2>(s)); },
                                          self);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                return _mm512_abs_epi32(self);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
            {
                return _mm512_abs_epi64(self);
            }
            else
            {
                assert(false && "unsupported arch/op combination");
                return {};
            }
        }

        // add
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> add(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
            {
                return detail::fwd_to_avx([](__m256i s, __m256i o) noexcept
                                          { return add(batch<T, avx2>(s), batch<T, avx2>(o)); },
                                          self, other);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
            {
                return detail::fwd_to_avx([](__m256i s, __m256i o) noexcept
                                          { return add(batch<T, avx2>(s), batch<T, avx2>(o)); },
                                          self, other);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                return _mm512_add_epi32(self, other);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
            {
                return _mm512_add_epi64(self, other);
            }
            else
            {
                assert(false && "unsupported arch/op combination");
                return {};
            }
        }
        template <class A>
        inline batch<float, A> add(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_add_ps(self, other);
        }
        template <class A>
        inline batch<double, A> add(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_add_pd(self, other);
        }

        // all
        template <class A, class T>
        inline bool all(batch_bool<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            return self.data == register_type(-1);
        }

        // any
        template <class A, class T>
        inline bool any(batch_bool<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            return self.data != register_type(0);
        }

        // batch_bool_cast
        template <class A, class T_out, class T_in>
        inline batch_bool<T_out, A> batch_bool_cast(batch_bool<T_in, A> const& self, batch_bool<T_out, A> const&, requires_arch<avx512f>) noexcept
        {
            return self.data;
        }

        // bitwise_and
        template <class A>
        inline batch<float, A> bitwise_and(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
#if defined(_MSC_VER)
            return _mm512_and_ps(self, other);
#else
            return _mm512_castsi512_ps(_mm512_and_si512(_mm512_castps_si512(self), _mm512_castps_si512(other)));
#endif
        }
        template <class A>
        inline batch<double, A> bitwise_and(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_pd(_mm512_and_si512(_mm512_castpd_si512(self), _mm512_castpd_si512(other)));
        }

        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> bitwise_and(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_and_si512(self, other);
        }

        template <class A, class T>
        inline batch_bool<T, A> bitwise_and(batch_bool<T, A> const& self, batch_bool<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            return register_type(self.data & other.data);
        }

        // bitwise_andnot
        template <class A>
        inline batch<float, A> bitwise_andnot(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_ps(_mm512_andnot_si512(_mm512_castps_si512(other), _mm512_castps_si512(self)));
        }
        template <class A>
        inline batch<double, A> bitwise_andnot(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_pd(_mm512_andnot_si512(_mm512_castpd_si512(other), _mm512_castpd_si512(self)));
        }

        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> bitwise_andnot(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_andnot_si512(other, self);
        }

        template <class A, class T>
        inline batch_bool<T, A> bitwise_andnot(batch_bool<T, A> const& self, batch_bool<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            return register_type(self.data & ~other.data);
        }

        // bitwise_lshift
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> bitwise_lshift(batch<T, A> const& self, int32_t other, requires_arch<avx512f>) noexcept
        {
            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
            {
#if defined(XSIMD_AVX512_SHIFT_INTRINSICS_IMM_ONLY)
                __m512i tmp = _mm512_sllv_epi32(self, _mm512_set1_epi32(other));
#else
                __m512i tmp = _mm512_slli_epi32(self, other);
#endif
                return _mm512_and_si512(_mm512_set1_epi8(0xFF << other), tmp);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
            {
                return detail::fwd_to_avx([](__m256i s, int32_t o) noexcept
                                          { return bitwise_lshift(batch<T, avx2>(s), o, avx2 {}); },
                                          self, other);
#if defined(XSIMD_AVX512_SHIFT_INTRINSICS_IMM_ONLY)
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                return _mm512_sllv_epi32(self, _mm512_set1_epi32(other));
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
            {
                return _mm512_sllv_epi64(self, _mm512_set1_epi64(other));
#else
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                return _mm512_slli_epi32(self, other);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
            {
                return _mm512_slli_epi64(self, other);
#endif
            }
            else
            {
                assert(false && "unsupported arch/op combination");
                return {};
            }
        }

        // bitwise_not
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> bitwise_not(batch<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_xor_si512(self, _mm512_set1_epi32(-1));
        }
        template <class A, class T>
        inline batch_bool<T, A> bitwise_not(batch_bool<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            return register_type(~self.data);
        }

        template <class A>
        inline batch<float, A> bitwise_not(batch<float, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_ps(_mm512_xor_si512(_mm512_castps_si512(self), _mm512_set1_epi32(-1)));
        }
        template <class A>
        inline batch<double, A> bitwise_not(batch<double, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_pd(_mm512_xor_si512(_mm512_castpd_si512(self), _mm512_set1_epi32(-1)));
        }

        // bitwise_or
        template <class A>
        inline batch<float, A> bitwise_or(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_ps(_mm512_or_si512(_mm512_castps_si512(self), _mm512_castps_si512(other)));
        }
        template <class A>
        inline batch<double, A> bitwise_or(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_pd(_mm512_or_si512(_mm512_castpd_si512(self), _mm512_castpd_si512(other)));
        }

        template <class A, class T>
        inline batch_bool<T, A> bitwise_or(batch_bool<T, A> const& self, batch_bool<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            return register_type(self.data | other.data);
        }

        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> bitwise_or(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_or_si512(self, other);
        }

        // bitwise_rshift
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> bitwise_rshift(batch<T, A> const& self, int32_t other, requires_arch<avx512f>) noexcept
        {
            if (std::is_signed<T>::value)
            {
#if defined(XSIMD_AVX512_SHIFT_INTRINSICS_IMM_ONLY)
                XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                {
                    return _mm512_srav_epi32(self, _mm512_set1_epi32(other));
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                {
                    return _mm512_srav_epi64(self, _mm512_set1_epi64(other));
#else
                XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                {
                    return _mm512_srai_epi32(self, other);
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                {
                    return _mm512_srai_epi64(self, other);
#endif
                }
                else
                {
                    return detail::fwd_to_avx([](__m256i s, int32_t o) noexcept
                                              { return bitwise_rshift(batch<T, avx2>(s), o, avx2 {}); },
                                              self, other);
                }
            }
            else
            {
                XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
                {
#if defined(XSIMD_AVX512_SHIFT_INTRINSICS_IMM_ONLY)
                    __m512i tmp = _mm512_srlv_epi32(self, _mm512_set1_epi32(other));
#else
                    __m512i tmp = _mm512_srli_epi32(self, other);
#endif
                    return _mm512_and_si512(_mm512_set1_epi8(0xFF >> other), tmp);
#if defined(XSIMD_AVX512_SHIFT_INTRINSICS_IMM_ONLY)
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                {
                    return _mm512_srlv_epi32(self, _mm512_set1_epi32(other));
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                {
                    return _mm512_srlv_epi64(self, _mm512_set1_epi64(other));
#else
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                {
                    return _mm512_srli_epi32(self, other);
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                {
                    return _mm512_srli_epi64(self, other);
#endif
                }
                else
                {
                    return detail::fwd_to_avx([](__m256i s, int32_t o) noexcept
                                              { return bitwise_rshift(batch<T, avx2>(s), o, avx2 {}); },
                                              self, other);
                }
            }
        }

        // bitwise_xor
        template <class A>
        inline batch<float, A> bitwise_xor(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_ps(_mm512_xor_si512(_mm512_castps_si512(self), _mm512_castps_si512(other)));
        }
        template <class A>
        inline batch<double, A> bitwise_xor(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_pd(_mm512_xor_si512(_mm512_castpd_si512(self), _mm512_castpd_si512(other)));
        }

        template <class A, class T>
        inline batch_bool<T, A> bitwise_xor(batch_bool<T, A> const& self, batch_bool<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            return register_type(self.data | other.data);
        }

        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> bitwise_xor(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_xor_si512(self, other);
        }

        // bitwise_cast
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<float, A> bitwise_cast(batch<T, A> const& self, batch<float, A> const&, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_ps(self);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<double, A> bitwise_cast(batch<T, A> const& self, batch<double, A> const&, requires_arch<avx512f>) noexcept
        {
            return _mm512_castsi512_pd(self);
        }
        template <class A, class T, class Tp, class = typename std::enable_if<std::is_integral<typename std::common_type<T, Tp>::type>::value, void>::type>
        inline batch<Tp, A> bitwise_cast(batch<T, A> const& self, batch<Tp, A> const&, requires_arch<avx512f>) noexcept
        {
            return batch<Tp, A>(self.data);
        }
        template <class A>
        inline batch<double, A> bitwise_cast(batch<float, A> const& self, batch<double, A> const&, requires_arch<avx512f>) noexcept
        {
            return _mm512_castps_pd(self);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> bitwise_cast(batch<float, A> const& self, batch<T, A> const&, requires_arch<avx512f>) noexcept
        {
            return _mm512_castps_si512(self);
        }
        template <class A>
        inline batch<float, A> bitwise_cast(batch<double, A> const& self, batch<float, A> const&, requires_arch<avx512f>) noexcept
        {
            return _mm512_castpd_ps(self);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> bitwise_cast(batch<double, A> const& self, batch<T, A> const&, requires_arch<avx512f>) noexcept
        {
            return _mm512_castpd_si512(self);
        }

        // broadcast
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> broadcast(T val, requires_arch<avx512f>) noexcept
        {
            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
            {
                return _mm512_set1_epi8(val);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
            {
                return _mm512_set1_epi16(val);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                return _mm512_set1_epi32(val);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
            {
                return _mm512_set1_epi64(val);
            }
            else
            {
                assert(false && "unsupported");
                return {};
            }
        }
        template <class A>
        inline batch<float, A> broadcast(float val, requires_arch<avx512f>) noexcept
        {
            return _mm512_set1_ps(val);
        }
        template <class A>
        batch<double, A> inline broadcast(double val, requires_arch<avx512f>) noexcept
        {
            return _mm512_set1_pd(val);
        }

        // ceil
        template <class A>
        inline batch<float, A> ceil(batch<float, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_roundscale_ps(self, _MM_FROUND_TO_POS_INF);
        }
        template <class A>
        inline batch<double, A> ceil(batch<double, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_roundscale_pd(self, _MM_FROUND_TO_POS_INF);
        }

        // convert
        namespace detail
        {
            template <class A>
            inline batch<float, A> fast_cast(batch<int32_t, A> const& self, batch<float, A> const&, requires_arch<avx512f>) noexcept
            {
                return _mm512_cvtepi32_ps(self);
            }

            template <class A>
            inline batch<int32_t, A> fast_cast(batch<float, A> const& self, batch<int32_t, A> const&, requires_arch<avx512f>) noexcept
            {
                return _mm512_cvttps_epi32(self);
            }

            template <class A>
            inline batch<float, A> fast_cast(batch<uint32_t, A> const& self, batch<float, A> const&, requires_arch<avx512f>) noexcept
            {
                return _mm512_cvtepu32_ps(self);
            }

            template <class A>
            batch<uint32_t, A> fast_cast(batch<float, A> const& self, batch<uint32_t, A> const&, requires_arch<avx512f>)
            {
                return _mm512_cvttps_epu32(self);
            }
        }

        namespace detail
        {
            // complex_low
            template <class A>
            inline batch<float, A> complex_low(batch<std::complex<float>, A> const& self, requires_arch<avx512f>) noexcept
            {
                __m512i idx = _mm512_setr_epi32(0, 16, 1, 17, 2, 18, 3, 19, 4, 20, 5, 21, 6, 22, 7, 23);
                return _mm512_permutex2var_ps(self.real(), idx, self.imag());
            }
            template <class A>
            inline batch<double, A> complex_low(batch<std::complex<double>, A> const& self, requires_arch<avx512f>) noexcept
            {
                __m512i idx = _mm512_setr_epi64(0, 8, 1, 9, 2, 10, 3, 11);
                return _mm512_permutex2var_pd(self.real(), idx, self.imag());
            }

            // complex_high
            template <class A>
            inline batch<float, A> complex_high(batch<std::complex<float>, A> const& self, requires_arch<avx512f>) noexcept
            {
                __m512i idx = _mm512_setr_epi32(8, 24, 9, 25, 10, 26, 11, 27, 12, 28, 13, 29, 14, 30, 15, 31);
                return _mm512_permutex2var_ps(self.real(), idx, self.imag());
            }
            template <class A>
            inline batch<double, A> complex_high(batch<std::complex<double>, A> const& self, requires_arch<avx512f>) noexcept
            {
                __m512i idx = _mm512_setr_epi64(4, 12, 5, 13, 6, 14, 7, 15);
                return _mm512_permutex2var_pd(self.real(), idx, self.imag());
            }
        }

        // div
        template <class A>
        inline batch<float, A> div(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_div_ps(self, other);
        }
        template <class A>
        inline batch<double, A> div(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_div_pd(self, other);
        }

        // eq
        template <class A>
        inline batch_bool<float, A> eq(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_ps_mask(self, other, _CMP_EQ_OQ);
        }
        template <class A>
        inline batch_bool<double, A> eq(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_pd_mask(self, other, _CMP_EQ_OQ);
        }

        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch_bool<T, A> eq(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return detail::compare_int_avx512f<A, T, _MM_CMPINT_EQ>(self, other);
        }
        template <class A, class T>
        inline batch_bool<T, A> eq(batch_bool<T, A> const& self, batch_bool<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            return register_type(~self.data ^ other.data);
        }

        // floor
        template <class A>
        inline batch<float, A> floor(batch<float, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_roundscale_ps(self, _MM_FROUND_TO_NEG_INF);
        }
        template <class A>
        inline batch<double, A> floor(batch<double, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_roundscale_pd(self, _MM_FROUND_TO_NEG_INF);
        }

        // fnma
        template <class A>
        inline batch<float, A> fnma(batch<float, A> const& x, batch<float, A> const& y, batch<float, A> const& z, requires_arch<avx512f>) noexcept
        {
            return _mm512_fnmadd_ps(x, y, z);
        }

        template <class A>
        inline batch<double, A> fnma(batch<double, A> const& x, batch<double, A> const& y, batch<double, A> const& z, requires_arch<avx512f>) noexcept
        {
            return _mm512_fnmadd_pd(x, y, z);
        }

        // fma
        template <class A>
        inline batch<float, A> fma(batch<float, A> const& x, batch<float, A> const& y, batch<float, A> const& z, requires_arch<avx512f>) noexcept
        {
            return _mm512_fmadd_ps(x, y, z);
        }

        template <class A>
        inline batch<double, A> fma(batch<double, A> const& x, batch<double, A> const& y, batch<double, A> const& z, requires_arch<avx512f>) noexcept
        {
            return _mm512_fmadd_pd(x, y, z);
        }

        // fms
        template <class A>
        inline batch<float, A> fms(batch<float, A> const& x, batch<float, A> const& y, batch<float, A> const& z, requires_arch<avx512f>) noexcept
        {
            return _mm512_fmsub_ps(x, y, z);
        }

        template <class A>
        inline batch<double, A> fms(batch<double, A> const& x, batch<double, A> const& y, batch<double, A> const& z, requires_arch<avx512f>) noexcept
        {
            return _mm512_fmsub_pd(x, y, z);
        }

        // from bool
        template <class A, class T>
        inline batch<T, A> from_bool(batch_bool<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            return select(self, batch<T, A>(1), batch<T, A>(0));
        }

        // from_mask
        template <class T, class A>
        inline batch_bool<T, A> from_mask(batch_bool<T, A> const&, uint64_t mask, requires_arch<avx512f>) noexcept
        {
            return static_cast<typename batch_bool<T, A>::register_type>(mask);
        }

        // gather
        template <class T, class A, class U, detail::enable_sized_integral_t<T, 4> = 0, detail::enable_sized_integral_t<U, 4> = 0>
        inline batch<T, A> gather(batch<T, A> const&, T const* src, batch<U, A> const& index,
                                  kernel::requires_arch<avx512f>) noexcept
        {
            return _mm512_i32gather_epi32(index, static_cast<const void*>(src), sizeof(T));
        }

        template <class T, class A, class U, detail::enable_sized_integral_t<T, 8> = 0, detail::enable_sized_integral_t<U, 8> = 0>
        inline batch<T, A> gather(batch<T, A> const&, T const* src, batch<U, A> const& index,
                                  kernel::requires_arch<avx512f>) noexcept
        {
            return _mm512_i64gather_epi64(index, static_cast<const void*>(src), sizeof(T));
        }

        template <class A, class U, detail::enable_sized_integral_t<U, 4> = 0>
        inline batch<float, A> gather(batch<float, A> const&, float const* src,
                                      batch<U, A> const& index,
                                      kernel::requires_arch<avx512f>) noexcept
        {
            return _mm512_i32gather_ps(index, src, sizeof(float));
        }

        template <class A, class U, detail::enable_sized_integral_t<U, 8> = 0>
        inline batch<double, A>
        gather(batch<double, A> const&, double const* src, batch<U, A> const& index,
               kernel::requires_arch<avx512f>) noexcept
        {
            return _mm512_i64gather_pd(index, src, sizeof(double));
        }

        // gather: handmade conversions
        template <class A, class V, detail::enable_sized_integral_t<V, 4> = 0>
        inline batch<float, A> gather(batch<float, A> const&, double const* src,
                                      batch<V, A> const& index,
                                      requires_arch<avx512f>) noexcept
        {
            const batch<double, A> low(_mm512_i32gather_pd(_mm512_castsi512_si256(index.data), src, sizeof(double)));
            const batch<double, A> high(_mm512_i32gather_pd(_mm256_castpd_si256(_mm512_extractf64x4_pd(_mm512_castsi512_pd(index.data), 1)), src, sizeof(double)));
            return detail::merge_avx(_mm512_cvtpd_ps(low.data), _mm512_cvtpd_ps(high.data));
        }

        template <class A, class V, detail::enable_sized_integral_t<V, 4> = 0>
        inline batch<int32_t, A> gather(batch<int32_t, A> const&, double const* src,
                                        batch<V, A> const& index,
                                        requires_arch<avx512f>) noexcept
        {
            const batch<double, A> low(_mm512_i32gather_pd(_mm512_castsi512_si256(index.data), src, sizeof(double)));
            const batch<double, A> high(_mm512_i32gather_pd(_mm256_castpd_si256(_mm512_extractf64x4_pd(_mm512_castsi512_pd(index.data), 1)), src, sizeof(double)));
            return detail::merge_avx(_mm512_cvtpd_epi32(low.data), _mm512_cvtpd_epi32(high.data));
        }

        // ge
        template <class A>
        inline batch_bool<float, A> ge(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_ps_mask(self, other, _CMP_GE_OQ);
        }
        template <class A>
        inline batch_bool<double, A> ge(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_pd_mask(self, other, _CMP_GE_OQ);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch_bool<T, A> ge(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return detail::compare_int_avx512f<A, T, _MM_CMPINT_GE>(self, other);
        }

        // gt
        template <class A>
        inline batch_bool<float, A> gt(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_ps_mask(self, other, _CMP_GT_OQ);
        }
        template <class A>
        inline batch_bool<double, A> gt(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_pd_mask(self, other, _CMP_GT_OQ);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch_bool<T, A> gt(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return detail::compare_int_avx512f<A, T, _MM_CMPINT_GT>(self, other);
        }

        // haddp
        template <class A>
        inline batch<float, A> haddp(batch<float, A> const* row, requires_arch<avx512f>) noexcept
        {
            // The following folds over the vector once:
            // tmp1 = [a0..8, b0..8]
            // tmp2 = [a8..f, b8..f]
#define XSIMD_AVX512_HADDP_STEP1(I, a, b)                                \
    batch<float, avx512f> res##I;                                        \
    {                                                                    \
        auto tmp1 = _mm512_shuffle_f32x4(a, b, _MM_SHUFFLE(1, 0, 1, 0)); \
        auto tmp2 = _mm512_shuffle_f32x4(a, b, _MM_SHUFFLE(3, 2, 3, 2)); \
        res##I = _mm512_add_ps(tmp1, tmp2);                              \
    }

            XSIMD_AVX512_HADDP_STEP1(0, row[0], row[2]);
            XSIMD_AVX512_HADDP_STEP1(1, row[4], row[6]);
            XSIMD_AVX512_HADDP_STEP1(2, row[1], row[3]);
            XSIMD_AVX512_HADDP_STEP1(3, row[5], row[7]);
            XSIMD_AVX512_HADDP_STEP1(4, row[8], row[10]);
            XSIMD_AVX512_HADDP_STEP1(5, row[12], row[14]);
            XSIMD_AVX512_HADDP_STEP1(6, row[9], row[11]);
            XSIMD_AVX512_HADDP_STEP1(7, row[13], row[15]);

#undef XSIMD_AVX512_HADDP_STEP1

            // The following flds the code and shuffles so that hadd_ps produces the correct result
            // tmp1 = [a0..4,  a8..12,  b0..4,  b8..12] (same for tmp3)
            // tmp2 = [a5..8, a12..16, b5..8, b12..16]  (same for tmp4)
            // tmp5 = [r1[0], r1[2], r2[0], r2[2], r1[4], r1[6] ...
#define XSIMD_AVX512_HADDP_STEP2(I, a, b, c, d)                                                                                                         \
    batch<float, avx2> halfx##I;                                                                                                                        \
    {                                                                                                                                                   \
        auto tmp1 = _mm512_shuffle_f32x4(a, b, _MM_SHUFFLE(2, 0, 2, 0));                                                                                \
        auto tmp2 = _mm512_shuffle_f32x4(a, b, _MM_SHUFFLE(3, 1, 3, 1));                                                                                \
                                                                                                                                                        \
        auto resx1 = _mm512_add_ps(tmp1, tmp2);                                                                                                         \
                                                                                                                                                        \
        auto tmp3 = _mm512_shuffle_f32x4(c, d, _MM_SHUFFLE(2, 0, 2, 0));                                                                                \
        auto tmp4 = _mm512_shuffle_f32x4(c, d, _MM_SHUFFLE(3, 1, 3, 1));                                                                                \
                                                                                                                                                        \
        auto resx2 = _mm512_add_ps(tmp3, tmp4);                                                                                                         \
                                                                                                                                                        \
        auto tmp5 = _mm512_shuffle_ps(resx1, resx2, _MM_SHUFFLE(2, 0, 2, 0));                                                                           \
        auto tmp6 = _mm512_shuffle_ps(resx1, resx2, _MM_SHUFFLE(3, 1, 3, 1));                                                                           \
                                                                                                                                                        \
        auto resx3 = _mm512_add_ps(tmp5, tmp6);                                                                                                         \
                                                                                                                                                        \
        halfx##I = _mm256_hadd_ps(_mm256_insertf128_ps(_mm256_castps128_ps256(_mm512_extractf32x4_ps(resx3, 0)), _mm512_extractf32x4_ps(resx3, 1), 1),  \
                                  _mm256_insertf128_ps(_mm256_castps128_ps256(_mm512_extractf32x4_ps(resx3, 2)), _mm512_extractf32x4_ps(resx3, 3), 1)); \
    }

            XSIMD_AVX512_HADDP_STEP2(0, res0, res1, res2, res3);
            XSIMD_AVX512_HADDP_STEP2(1, res4, res5, res6, res7);

#undef XSIMD_AVX512_HADDP_STEP2

            auto concat = _mm512_castps256_ps512(halfx0);
            concat = _mm512_castpd_ps(_mm512_insertf64x4(_mm512_castps_pd(concat), _mm256_castps_pd(halfx1), 1));
            return concat;
        }

        template <class A>
        inline batch<double, A> haddp(batch<double, A> const* row, requires_arch<avx512f>) noexcept
        {
#define step1(I, a, b)                                                   \
    batch<double, avx512f> res##I;                                       \
    {                                                                    \
        auto tmp1 = _mm512_shuffle_f64x2(a, b, _MM_SHUFFLE(1, 0, 1, 0)); \
        auto tmp2 = _mm512_shuffle_f64x2(a, b, _MM_SHUFFLE(3, 2, 3, 2)); \
        res##I = _mm512_add_pd(tmp1, tmp2);                              \
    }

            step1(1, row[0], row[2]);
            step1(2, row[4], row[6]);
            step1(3, row[1], row[3]);
            step1(4, row[5], row[7]);

#undef step1

            auto tmp5 = _mm512_shuffle_f64x2(res1, res2, _MM_SHUFFLE(2, 0, 2, 0));
            auto tmp6 = _mm512_shuffle_f64x2(res1, res2, _MM_SHUFFLE(3, 1, 3, 1));

            auto resx1 = _mm512_add_pd(tmp5, tmp6);

            auto tmp7 = _mm512_shuffle_f64x2(res3, res4, _MM_SHUFFLE(2, 0, 2, 0));
            auto tmp8 = _mm512_shuffle_f64x2(res3, res4, _MM_SHUFFLE(3, 1, 3, 1));

            auto resx2 = _mm512_add_pd(tmp7, tmp8);

            auto tmpx = _mm512_shuffle_pd(resx1, resx2, 0b00000000);
            auto tmpy = _mm512_shuffle_pd(resx1, resx2, 0b11111111);

            return _mm512_add_pd(tmpx, tmpy);
        }

        // isnan
        template <class A>
        inline batch_bool<float, A> isnan(batch<float, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_ps_mask(self, self, _CMP_UNORD_Q);
        }
        template <class A>
        inline batch_bool<double, A> isnan(batch<double, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_pd_mask(self, self, _CMP_UNORD_Q);
        }

        // ldexp
        template <class A>
        inline batch<float, A> ldexp(const batch<float, A>& self, const batch<as_integer_t<float>, A>& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_scalef_ps(self, _mm512_cvtepi32_ps(other));
        }

        template <class A>
        inline batch<double, A> ldexp(const batch<double, A>& self, const batch<as_integer_t<double>, A>& other, requires_arch<avx512f>) noexcept
        {
            // FIXME: potential data loss here when converting other elements to
            // int32 before converting them back to double.
            __m512d adjusted_index = _mm512_cvtepi32_pd(_mm512_cvtepi64_epi32(other));
            return _mm512_scalef_pd(self, adjusted_index);
        }

        // le
        template <class A>
        inline batch_bool<float, A> le(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_ps_mask(self, other, _CMP_LE_OQ);
        }
        template <class A>
        inline batch_bool<double, A> le(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_pd_mask(self, other, _CMP_LE_OQ);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch_bool<T, A> le(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return detail::compare_int_avx512f<A, T, _MM_CMPINT_LE>(self, other);
        }

        // load_aligned
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> load_aligned(T const* mem, convert<T>, requires_arch<avx512f>) noexcept
        {
            return _mm512_load_si512((__m512i const*)mem);
        }
        template <class A>
        inline batch<float, A> load_aligned(float const* mem, convert<float>, requires_arch<avx512f>) noexcept
        {
            return _mm512_load_ps(mem);
        }
        template <class A>
        inline batch<double, A> load_aligned(double const* mem, convert<double>, requires_arch<avx512f>) noexcept
        {
            return _mm512_load_pd(mem);
        }

        // load_complex
        namespace detail
        {
            template <class A>
            inline batch<std::complex<float>, A> load_complex(batch<float, A> const& hi, batch<float, A> const& lo, requires_arch<avx512f>) noexcept
            {
                __m512i real_idx = _mm512_setr_epi32(0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30);
                __m512i imag_idx = _mm512_setr_epi32(1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31);
                auto real = _mm512_permutex2var_ps(hi, real_idx, lo);
                auto imag = _mm512_permutex2var_ps(hi, imag_idx, lo);
                return { real, imag };
            }
            template <class A>
            inline batch<std::complex<double>, A> load_complex(batch<double, A> const& hi, batch<double, A> const& lo, requires_arch<avx512f>) noexcept
            {
                __m512i real_idx = _mm512_setr_epi64(0, 2, 4, 6, 8, 10, 12, 14);
                __m512i imag_idx = _mm512_setr_epi64(1, 3, 5, 7, 9, 11, 13, 15);
                auto real = _mm512_permutex2var_pd(hi, real_idx, lo);
                auto imag = _mm512_permutex2var_pd(hi, imag_idx, lo);
                return { real, imag };
            }
        }

        // load_unaligned
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> load_unaligned(T const* mem, convert<T>, requires_arch<avx512f>) noexcept
        {
            return _mm512_loadu_si512((__m512i const*)mem);
        }
        template <class A>
        inline batch<float, A> load_unaligned(float const* mem, convert<float>, requires_arch<avx512f>) noexcept
        {
            return _mm512_loadu_ps(mem);
        }
        template <class A>
        inline batch<double, A> load_unaligned(double const* mem, convert<double>, requires_arch<avx512f>) noexcept
        {
            return _mm512_loadu_pd(mem);
        }

        // lt
        template <class A>
        inline batch_bool<float, A> lt(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_ps_mask(self, other, _CMP_LT_OQ);
        }
        template <class A>
        inline batch_bool<double, A> lt(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_pd_mask(self, other, _CMP_LT_OQ);
        }

        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch_bool<T, A> lt(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return detail::compare_int_avx512f<A, T, _MM_CMPINT_LT>(self, other);
        }

        // mask
        template <class A, class T>
        inline uint64_t mask(batch_bool<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            return self.data;
        }

        // max
        template <class A>
        inline batch<float, A> max(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_max_ps(self, other);
        }
        template <class A>
        inline batch<double, A> max(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_max_pd(self, other);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> max(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            if (std::is_signed<T>::value)
            {
                XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                {
                    return _mm512_max_epi32(self, other);
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                {
                    return _mm512_max_epi64(self, other);
                }
                else
                {
                    return detail::fwd_to_avx([](__m256i s, __m256i o) noexcept
                                              { return max(batch<T, avx2>(s), batch<T, avx2>(o)); },
                                              self, other);
                }
            }
            else
            {
                XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                {
                    return _mm512_max_epu32(self, other);
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                {
                    return _mm512_max_epu64(self, other);
                }
                else
                {
                    return detail::fwd_to_avx([](__m256i s, __m256i o) noexcept
                                              { return max(batch<T, avx2>(s), batch<T, avx2>(o)); },
                                              self, other);
                }
            }
        }

        // min
        template <class A>
        inline batch<float, A> min(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_min_ps(self, other);
        }
        template <class A>
        inline batch<double, A> min(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_min_pd(self, other);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> min(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            if (std::is_signed<T>::value)
            {
                XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                {
                    return _mm512_min_epi32(self, other);
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                {
                    return _mm512_min_epi64(self, other);
                }
                else
                {
                    return detail::fwd_to_avx([](__m256i s, __m256i o) noexcept
                                              { return min(batch<T, avx2>(s), batch<T, avx2>(o)); },
                                              self, other);
                }
            }
            else
            {
                XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
                {
                    return _mm512_min_epu32(self, other);
                }
                else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
                {
                    return _mm512_min_epu64(self, other);
                }
                else
                {
                    return detail::fwd_to_avx([](__m256i s, __m256i o) noexcept
                                              { return min(batch<T, avx2>(s), batch<T, avx2>(o)); },
                                              self, other);
                }
            }
        }

        // mul
        template <class A>
        inline batch<float, A> mul(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_mul_ps(self, other);
        }
        template <class A>
        inline batch<double, A> mul(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_mul_pd(self, other);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> mul(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                return _mm512_mullo_epi32(self, other);
            }
            else
            {
                return detail::fwd_to_avx([](__m256i s, __m256i o) noexcept
                                          { return mul(batch<T, avx2>(s), batch<T, avx2>(o)); },
                                          self, other);
            }
        }

        // nearbyint
        template <class A>
        inline batch<float, A> nearbyint(batch<float, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_roundscale_round_ps(self, _MM_FROUND_TO_NEAREST_INT, _MM_FROUND_CUR_DIRECTION);
        }
        template <class A>
        inline batch<double, A> nearbyint(batch<double, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_roundscale_round_pd(self, _MM_FROUND_TO_NEAREST_INT, _MM_FROUND_CUR_DIRECTION);
        }

        // nearbyint_as_int
        template <class A>
        inline batch<int32_t, A> nearbyint_as_int(batch<float, A> const& self,
                                                  requires_arch<avx512f>) noexcept
        {
            return _mm512_cvtps_epi32(self);
        }

        // neg
        template <class A, class T>
        inline batch<T, A> neg(batch<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            return 0 - self;
        }

        // neq
        template <class A>
        inline batch_bool<float, A> neq(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_ps_mask(self, other, _CMP_NEQ_UQ);
        }
        template <class A>
        inline batch_bool<double, A> neq(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_cmp_pd_mask(self, other, _CMP_NEQ_UQ);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch_bool<T, A> neq(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            return ~(self == other);
        }

        template <class A, class T>
        inline batch_bool<T, A> neq(batch_bool<T, A> const& self, batch_bool<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            return register_type(self.data ^ other.data);
        }

        // reciprocal
        template <class A>
        inline batch<float, A>
        reciprocal(batch<float, A> const& self,
                   kernel::requires_arch<avx512f>) noexcept
        {
            return _mm512_rcp14_ps(self);
        }

        template <class A>
        inline batch<double, A>
        reciprocal(batch<double, A> const& self,
                   kernel::requires_arch<avx512f>) noexcept
        {
            return _mm512_rcp14_pd(self);
        }

        // reduce_add
        template <class A>
        inline float reduce_add(batch<float, A> const& rhs, requires_arch<avx512f>) noexcept
        {
            __m128 tmp1 = _mm512_extractf32x4_ps(rhs, 0);
            __m128 tmp2 = _mm512_extractf32x4_ps(rhs, 1);
            __m128 tmp3 = _mm512_extractf32x4_ps(rhs, 2);
            __m128 tmp4 = _mm512_extractf32x4_ps(rhs, 3);
            __m128 res1 = _mm_add_ps(tmp1, tmp2);
            __m128 res2 = _mm_add_ps(tmp3, tmp4);
            __m128 res3 = _mm_add_ps(res1, res2);
            return reduce_add(batch<float, sse4_2>(res3), sse4_2 {});
        }
        template <class A>
        inline double reduce_add(batch<double, A> const& rhs, requires_arch<avx512f>) noexcept
        {
            __m256d tmp1 = _mm512_extractf64x4_pd(rhs, 1);
            __m256d tmp2 = _mm512_extractf64x4_pd(rhs, 0);
            __m256d res1 = _mm256_add_pd(tmp1, tmp2);
            return reduce_add(batch<double, avx2>(res1), avx2 {});
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline T reduce_add(batch<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            __m256i low, high;
            detail::split_avx512(self, low, high);
            batch<T, avx2> blow(low), bhigh(high);
            return reduce_add(blow, avx2 {}) + reduce_add(bhigh, avx2 {});
        }

        // reduce_max
        template <class A, class T, class _ = typename std::enable_if<(sizeof(T) == 1), void>::type>
        inline T reduce_max(batch<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            constexpr batch_constant<batch<uint64_t, A>, 5, 6, 7, 8, 0, 0, 0, 0> mask;
            batch<T, A> step = _mm512_permutexvar_epi64((batch<uint64_t, A>)mask, self);
            batch<T, A> acc = max(self, step);
            __m256i low = _mm512_castsi512_si256(acc);
            return reduce_max(batch<T, avx2>(low));
        }

        // reduce_min
        template <class A, class T, class _ = typename std::enable_if<(sizeof(T) == 1), void>::type>
        inline T reduce_min(batch<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            constexpr batch_constant<batch<uint64_t, A>, 5, 6, 7, 8, 0, 0, 0, 0> mask;
            batch<T, A> step = _mm512_permutexvar_epi64((batch<uint64_t, A>)mask, self);
            batch<T, A> acc = min(self, step);
            __m256i low = _mm512_castsi512_si256(acc);
            return reduce_min(batch<T, avx2>(low));
        }

        // rsqrt
        template <class A>
        inline batch<float, A> rsqrt(batch<float, A> const& val, requires_arch<avx512f>) noexcept
        {
            return _mm512_rsqrt14_ps(val);
        }
        template <class A>
        inline batch<double, A> rsqrt(batch<double, A> const& val, requires_arch<avx512f>) noexcept
        {
            return _mm512_rsqrt14_pd(val);
        }

        // sadd
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> sadd(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            if (std::is_signed<T>::value)
            {
                auto mask = other < 0;
                auto self_pos_branch = min(std::numeric_limits<T>::max() - other, self);
                auto self_neg_branch = max(std::numeric_limits<T>::min() - other, self);
                return other + select(mask, self_neg_branch, self_pos_branch);
            }
            else
            {
                const auto diffmax = std::numeric_limits<T>::max() - self;
                const auto mindiff = min(diffmax, other);
                return self + mindiff;
            }
        }

        // scatter
        template <class A, class T,
                  class = typename std::enable_if<std::is_same<uint32_t, T>::value || std::is_same<int32_t, T>::value, void>::type>
        inline void scatter(batch<T, A> const& src, T* dst,
                            batch<int32_t, A> const& index,
                            kernel::requires_arch<avx512f>) noexcept
        {
            _mm512_i32scatter_epi32(dst, index, src, sizeof(T));
        }

        template <class A, class T,
                  class = typename std::enable_if<std::is_same<uint64_t, T>::value || std::is_same<int64_t, T>::value, void>::type>
        inline void scatter(batch<T, A> const& src, T* dst,
                            batch<int64_t, A> const& index,
                            kernel::requires_arch<avx512f>) noexcept
        {
            _mm512_i64scatter_epi64(dst, index, src, sizeof(T));
        }

        template <class A>
        inline void scatter(batch<float, A> const& src, float* dst,
                            batch<int32_t, A> const& index,
                            kernel::requires_arch<avx512f>) noexcept
        {
            _mm512_i32scatter_ps(dst, index, src, sizeof(float));
        }

        template <class A>
        inline void scatter(batch<double, A> const& src, double* dst,
                            batch<int64_t, A> const& index,
                            kernel::requires_arch<avx512f>) noexcept
        {
            _mm512_i64scatter_pd(dst, index, src, sizeof(double));
        }

        // select
        template <class A>
        inline batch<float, A> select(batch_bool<float, A> const& cond, batch<float, A> const& true_br, batch<float, A> const& false_br, requires_arch<avx512f>) noexcept
        {
            return _mm512_mask_blend_ps(cond, false_br, true_br);
        }
        template <class A>
        inline batch<double, A> select(batch_bool<double, A> const& cond, batch<double, A> const& true_br, batch<double, A> const& false_br, requires_arch<avx512f>) noexcept
        {
            return _mm512_mask_blend_pd(cond, false_br, true_br);
        }

        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> select(batch_bool<T, A> const& cond, batch<T, A> const& true_br, batch<T, A> const& false_br, requires_arch<avx512f>) noexcept
        {
            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
            {
                alignas(avx2::alignment()) uint8_t buffer[64];
                // FIXME: ultra inefficient
                for (int i = 0; i < 64; ++i)
                    buffer[i] = cond.data & (1ull << i) ? 0xFF : 0;
                __m256i cond_low = batch<uint8_t, avx2>::load_aligned(&buffer[0]);
                __m256i cond_hi = batch<uint8_t, avx2>::load_aligned(&buffer[32]);

                __m256i true_low, true_hi;
                detail::split_avx512(true_br, true_low, true_hi);

                __m256i false_low, false_hi;
                detail::split_avx512(false_br, false_low, false_hi);

                __m256i res_low = select(batch_bool<T, avx2>(cond_low), batch<T, avx2>(true_low), batch<T, avx2>(false_low), avx2 {});
                __m256i res_hi = select(batch_bool<T, avx2>(cond_hi), batch<T, avx2>(true_hi), batch<T, avx2>(false_hi), avx2 {});
                return detail::merge_avx(res_low, res_hi);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
            {
                __m256i cond_low = _mm512_maskz_cvtepi32_epi16((uint64_t)cond.data & 0xFFFF, _mm512_set1_epi32(~0));
                __m256i cond_hi = _mm512_maskz_cvtepi32_epi16((uint64_t)cond.data >> 16, _mm512_set1_epi32(~0));

                __m256i true_low, true_hi;
                detail::split_avx512(true_br, true_low, true_hi);

                __m256i false_low, false_hi;
                detail::split_avx512(false_br, false_low, false_hi);

                __m256i res_low = select(batch_bool<T, avx2>(cond_low), batch<T, avx2>(true_low), batch<T, avx2>(false_low), avx2 {});
                __m256i res_hi = select(batch_bool<T, avx2>(cond_hi), batch<T, avx2>(true_hi), batch<T, avx2>(false_hi), avx2 {});
                return detail::merge_avx(res_low, res_hi);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                return _mm512_mask_blend_epi32(cond, false_br, true_br);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
            {
                return _mm512_mask_blend_epi64(cond, false_br, true_br);
            }
            else
            {
                assert(false && "unsupported arch/type combination");
                return {};
            }
        }

        template <class A, class T, bool... Values, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> select(batch_bool_constant<batch<T, A>, Values...> const&, batch<T, A> const& true_br, batch<T, A> const& false_br, requires_arch<avx512f>) noexcept
        {
            return select(batch_bool<T, A> { Values... }, true_br, false_br, avx512f {});
        }

        namespace detail
        {
            template <class T>
            using enable_signed_integer_t = typename std::enable_if<std::is_integral<T>::value && std::is_signed<T>::value,
                                                                    int>::type;

            template <class T>
            using enable_unsigned_integer_t = typename std::enable_if<std::is_integral<T>::value && std::is_unsigned<T>::value,
                                                                      int>::type;
        }

        // set
        template <class A>
        inline batch<float, A> set(batch<float, A> const&, requires_arch<avx512f>, float v0, float v1, float v2, float v3, float v4, float v5, float v6, float v7, float v8, float v9, float v10, float v11, float v12, float v13, float v14, float v15) noexcept
        {
            return _mm512_setr_ps(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15);
        }

        template <class A>
        inline batch<double, A> set(batch<double, A> const&, requires_arch<avx512f>, double v0, double v1, double v2, double v3, double v4, double v5, double v6, double v7) noexcept
        {
            return _mm512_setr_pd(v0, v1, v2, v3, v4, v5, v6, v7);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> set(batch<T, A> const&, requires_arch<avx512f>, T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7) noexcept
        {
            return _mm512_set_epi64(v7, v6, v5, v4, v3, v2, v1, v0);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> set(batch<T, A> const&, requires_arch<avx512f>, T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7,
                               T v8, T v9, T v10, T v11, T v12, T v13, T v14, T v15) noexcept
        {
            return _mm512_setr_epi32(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15);
        }
        template <class A, class T, detail::enable_signed_integer_t<T> = 0>
        inline batch<T, A> set(batch<T, A> const&, requires_arch<avx512f>, T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7,
                               T v8, T v9, T v10, T v11, T v12, T v13, T v14, T v15,
                               T v16, T v17, T v18, T v19, T v20, T v21, T v22, T v23,
                               T v24, T v25, T v26, T v27, T v28, T v29, T v30, T v31) noexcept
        {
#if defined(__clang__) || __GNUC__
            return __extension__(__m512i)(__v32hi) {
                v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15,
                v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31
            };
#else
            return _mm512_set_epi16(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15,
                                    v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31);
#endif
        }

        template <class A, class T, detail::enable_unsigned_integer_t<T> = 0>
        inline batch<T, A> set(batch<T, A> const&, requires_arch<avx512f>, T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7,
                               T v8, T v9, T v10, T v11, T v12, T v13, T v14, T v15,
                               T v16, T v17, T v18, T v19, T v20, T v21, T v22, T v23,
                               T v24, T v25, T v26, T v27, T v28, T v29, T v30, T v31) noexcept
        {
#if defined(__clang__) || __GNUC__
            return __extension__(__m512i)(__v32hu) {
                v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15,
                v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31
            };
#else
            return _mm512_set_epi16(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15,
                                    v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31);
#endif
        }

        template <class A, class T, detail::enable_signed_integer_t<T> = 0>
        inline batch<T, A> set(batch<T, A> const&, requires_arch<avx512f>, T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7,
                               T v8, T v9, T v10, T v11, T v12, T v13, T v14, T v15,
                               T v16, T v17, T v18, T v19, T v20, T v21, T v22, T v23,
                               T v24, T v25, T v26, T v27, T v28, T v29, T v30, T v31,
                               T v32, T v33, T v34, T v35, T v36, T v37, T v38, T v39,
                               T v40, T v41, T v42, T v43, T v44, T v45, T v46, T v47,
                               T v48, T v49, T v50, T v51, T v52, T v53, T v54, T v55,
                               T v56, T v57, T v58, T v59, T v60, T v61, T v62, T v63) noexcept
        {

#if defined(__clang__) || __GNUC__
            return __extension__(__m512i)(__v64qi) {
                v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15,
                v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31,
                v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47,
                v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63
            };
#else
            return _mm512_set_epi8(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15,
                                   v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31,
                                   v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47,
                                   v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63);
#endif
        }
        template <class A, class T, detail::enable_unsigned_integer_t<T> = 0>
        inline batch<T, A> set(batch<T, A> const&, requires_arch<avx512f>, T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7,
                               T v8, T v9, T v10, T v11, T v12, T v13, T v14, T v15,
                               T v16, T v17, T v18, T v19, T v20, T v21, T v22, T v23,
                               T v24, T v25, T v26, T v27, T v28, T v29, T v30, T v31,
                               T v32, T v33, T v34, T v35, T v36, T v37, T v38, T v39,
                               T v40, T v41, T v42, T v43, T v44, T v45, T v46, T v47,
                               T v48, T v49, T v50, T v51, T v52, T v53, T v54, T v55,
                               T v56, T v57, T v58, T v59, T v60, T v61, T v62, T v63) noexcept
        {

#if defined(__clang__) || __GNUC__
            return __extension__(__m512i)(__v64qu) {
                v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15,
                v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31,
                v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47,
                v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63
            };
#else
            return _mm512_set_epi8(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15,
                                   v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31,
                                   v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47,
                                   v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63);
#endif
        }

        template <class A, class T, class... Values>
        inline batch_bool<T, A> set(batch_bool<T, A> const&, requires_arch<avx512f>, Values... values) noexcept
        {
            static_assert(sizeof...(Values) == batch_bool<T, A>::size, "consistent init");
            using register_type = typename batch_bool<T, A>::register_type;
            register_type r = 0;
            unsigned shift = 0;
            (void)std::initializer_list<register_type> { (r |= register_type(values ? 1 : 0) << (shift++))... };
            return r;
        }

        // slide_left
        template <size_t N, class A, class T>
        inline batch<T, A> slide_left(batch<T, A> const&, requires_arch<avx512f>) noexcept
        {
            static_assert(N == 0xDEAD, "not implemented yet");
            return {};
        }

        // slide_right
        template <size_t N, class A, class T>
        inline batch<T, A> slide_right(batch<T, A> const&, requires_arch<avx512f>) noexcept
        {
            static_assert(N == 0xDEAD, "not implemented yet");
            return {};
        }

        // sqrt
        template <class A>
        inline batch<float, A> sqrt(batch<float, A> const& val, requires_arch<avx512f>) noexcept
        {
            return _mm512_sqrt_ps(val);
        }
        template <class A>
        inline batch<double, A> sqrt(batch<double, A> const& val, requires_arch<avx512f>) noexcept
        {
            return _mm512_sqrt_pd(val);
        }

        // ssub
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> ssub(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            if (std::is_signed<T>::value)
            {
                return sadd(self, -other);
            }
            else
            {
                const auto diff = min(self, other);
                return self - diff;
            }
        }

        // store
        template <class T, class A>
        inline void store(batch_bool<T, A> const& self, bool* mem, requires_arch<avx512f>) noexcept
        {
            using register_type = typename batch_bool<T, A>::register_type;
            constexpr auto size = batch_bool<T, A>::size;
            for (std::size_t i = 0; i < size; ++i)
                mem[i] = self.data & (register_type(1) << i);
        }

        // store_aligned
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline void store_aligned(T* mem, batch<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_store_si512((__m512i*)mem, self);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline void store_aligned(T* mem, batch_bool<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_store_si512((__m512i*)mem, self);
        }
        template <class A>
        inline void store_aligned(float* mem, batch<float, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_store_ps(mem, self);
        }
        template <class A>
        inline void store_aligned(double* mem, batch<double, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_store_pd(mem, self);
        }

        // store_unaligned
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline void store_unaligned(T* mem, batch<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_storeu_si512((__m512i*)mem, self);
        }
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline void store_unaligned(T* mem, batch_bool<T, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_storeu_si512((__m512i*)mem, self);
        }
        template <class A>
        inline void store_unaligned(float* mem, batch<float, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_storeu_ps(mem, self);
        }
        template <class A>
        inline void store_unaligned(double* mem, batch<double, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_storeu_pd(mem, self);
        }

        // sub
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A> sub(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
            {
                return detail::fwd_to_avx([](__m256i s, __m256i o) noexcept
                                          { return sub(batch<T, avx2>(s), batch<T, avx2>(o)); },
                                          self, other);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
            {
                return detail::fwd_to_avx([](__m256i s, __m256i o) noexcept
                                          { return sub(batch<T, avx2>(s), batch<T, avx2>(o)); },
                                          self, other);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                return _mm512_sub_epi32(self, other);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
            {
                return _mm512_sub_epi64(self, other);
            }
            else
            {
                assert(false && "unsupported arch/op combination");
                return {};
            }
        }
        template <class A>
        inline batch<float, A> sub(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_sub_ps(self, other);
        }
        template <class A>
        inline batch<double, A> sub(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            return _mm512_sub_pd(self, other);
        }

        // swizzle
        template <class A, uint32_t... Vs>
        inline batch<float, A> swizzle(batch<float, A> const& self, batch_constant<batch<uint32_t, A>, Vs...> mask, requires_arch<avx512f>) noexcept
        {
            return _mm512_permutexvar_ps((batch<uint32_t, A>)mask, self);
        }

        template <class A, uint64_t... Vs>
        inline batch<double, A> swizzle(batch<double, A> const& self, batch_constant<batch<uint64_t, A>, Vs...> mask, requires_arch<avx512f>) noexcept
        {
            return _mm512_permutexvar_pd((batch<uint64_t, A>)mask, self);
        }

        template <class A, uint64_t... Vs>
        inline batch<uint64_t, A> swizzle(batch<uint64_t, A> const& self, batch_constant<batch<uint64_t, A>, Vs...> mask, requires_arch<avx512f>) noexcept
        {
            return _mm512_permutexvar_epi64((batch<uint64_t, A>)mask, self);
        }

        template <class A, uint64_t... Vs>
        inline batch<int64_t, A> swizzle(batch<int64_t, A> const& self, batch_constant<batch<uint64_t, A>, Vs...> mask, requires_arch<avx512f>) noexcept
        {
            return bitwise_cast<int64_t>(swizzle(bitwise_cast<uint64_t>(self), mask, avx512f {}));
        }

        template <class A, uint32_t... Vs>
        inline batch<uint32_t, A> swizzle(batch<uint32_t, A> const& self, batch_constant<batch<uint32_t, A>, Vs...> mask, requires_arch<avx512f>) noexcept
        {
            return _mm512_permutexvar_epi32((batch<uint32_t, A>)mask, self);
        }

        template <class A, uint32_t... Vs>
        inline batch<int32_t, A> swizzle(batch<int32_t, A> const& self, batch_constant<batch<uint32_t, A>, Vs...> mask, requires_arch<avx512f>) noexcept
        {
            return bitwise_cast<int32_t>(swizzle(bitwise_cast<uint32_t>(self), mask, avx512f {}));
        }

        namespace detail
        {
            template <class T, class A, T... Idx>
            struct is_pair_of_contiguous_indices;

            template <class T, class A>
            struct is_pair_of_contiguous_indices<T, A> : std::true_type
            {
            };

            template <class T, class A, T Idx0, T Idx1, T... Idx>
            struct is_pair_of_contiguous_indices<T, A, Idx0, Idx1, Idx...> : std::conditional<(Idx0 % 2 == 0) && (Idx0 + 1 == Idx1), is_pair_of_contiguous_indices<T, A, Idx...>, std::false_type>::type
            {
            };

            template <class A, uint16_t I0, uint16_t I1, uint16_t I2, uint16_t I3, uint16_t I4, uint16_t I5, uint16_t I6, uint16_t I7,
                      uint16_t I8, uint16_t I9, uint16_t I10, uint16_t I11, uint16_t I12, uint16_t I13, uint16_t I14, uint16_t I15,
                      uint16_t I16, uint16_t I17, uint16_t I18, uint16_t I19, uint16_t I20, uint16_t I21, uint16_t I22, uint16_t I23,
                      uint16_t I24, uint16_t I25, uint16_t I26, uint16_t I27, uint16_t I28, uint16_t I29, uint16_t I30, uint16_t I31>
            struct fold_batch_constant
            {
                using type = batch_constant<batch<uint32_t, A>, I0 / 2, I2 / 2, I4 / 2, I6 / 2, I8 / 2, I10 / 2, I12 / 2, I14 / 2,
                                            I16 / 2, I18 / 2, I20 / 2, I22 / 2, I24 / 2, I26 / 2, I28 / 2, I30 / 2>;
            };

        }

        template <class A, uint16_t... Idx, class _ = typename std::enable_if<detail::is_pair_of_contiguous_indices<uint16_t, A, Idx...>::value, void>::type>
        inline batch<uint16_t, A> swizzle(batch<uint16_t, A> const& self, batch_constant<batch<uint16_t, A>, Idx...>, requires_arch<avx512f>) noexcept
        {
            constexpr typename detail::fold_batch_constant<A, Idx...>::type mask32;
            return _mm512_permutexvar_epi32(static_cast<batch<uint32_t, A>>(mask32), self);
        }

        template <class A>
        inline batch<uint16_t, A>
        swizzle(batch<uint16_t, A> const& self, batch_constant<batch<uint16_t, A>, (uint16_t)1, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1, (uint16_t)0, (uint16_t)1>, requires_arch<avx512f>) noexcept
        {
            // FIXME: this sequence is very inefficient, but it's here to catch
            // a pattern generated by detail::reduce from xsimd_generic_math.hpp.
            // The whole pattern is actually decently folded by GCC and Clang,
            // so bare with it.
            constexpr batch_constant<batch<uint32_t, A>, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0> mask32;
            auto tmp = _mm512_permutexvar_epi32(static_cast<batch<uint32_t, A>>(mask32), self);

            alignas(A::alignment()) uint16_t buffer[32];
            _mm512_store_si512((__m512i*)&buffer[0], tmp);
            buffer[0] = buffer[1];
            return _mm512_load_si512(&buffer[0]);
        }

        template <class A, uint16_t... Vs>
        inline batch<int16_t, A>
        swizzle(batch<int16_t, A> const& self, batch_constant<batch<uint16_t, A>, Vs...> mask, requires_arch<avx512f>) noexcept
        {
            return bitwise_cast<int16_t>(swizzle(bitwise_cast<uint16_t>(self), mask, avx512f {}));
        }

        // trunc
        template <class A>
        inline batch<float, A>
        trunc(batch<float, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_roundscale_round_ps(self, _MM_FROUND_TO_ZERO, _MM_FROUND_CUR_DIRECTION);
        }
        template <class A>
        inline batch<double, A>
        trunc(batch<double, A> const& self, requires_arch<avx512f>) noexcept
        {
            return _mm512_roundscale_round_pd(self, _MM_FROUND_TO_ZERO, _MM_FROUND_CUR_DIRECTION);
        }

        // zip_hi
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A>
        zip_hi(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            __m512i lo, hi;
            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
            {
                assert(false && "not implemented yet");
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
            {
                assert(false && "not implemented yet");
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                lo = _mm512_unpacklo_epi32(self, other);
                hi = _mm512_unpackhi_epi32(self, other);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
            {
                lo = _mm512_unpacklo_epi64(self, other);
                hi = _mm512_unpackhi_epi64(self, other);
            }
            else
            {
                assert(false && "unsupported arch/op combination");
                return {};
            }
            return _mm512_inserti32x4(
                _mm512_inserti32x4(
                    _mm512_inserti32x4(hi, _mm512_extracti32x4_epi32(lo, 2), 0),
                    _mm512_extracti32x4_epi32(lo, 3),
                    2),
                _mm512_extracti32x4_epi32(hi, 2),
                1);
        }
        template <class A>
        inline batch<float, A>
        zip_hi(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            auto lo = _mm512_unpacklo_ps(self, other);
            auto hi = _mm512_unpackhi_ps(self, other);
            return _mm512_insertf32x4(
                _mm512_insertf32x4(
                    _mm512_insertf32x4(hi, _mm512_extractf32x4_ps(lo, 2), 0),
                    _mm512_extractf32x4_ps(lo, 3),
                    2),
                _mm512_extractf32x4_ps(hi, 2),
                1);
        }
        template <class A>
        inline batch<double, A>
        zip_hi(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            auto lo = _mm512_castpd_ps(_mm512_unpacklo_pd(self, other));
            auto hi = _mm512_castpd_ps(_mm512_unpackhi_pd(self, other));
            return _mm512_castps_pd(_mm512_insertf32x4(
                _mm512_insertf32x4(
                    _mm512_insertf32x4(hi, _mm512_extractf32x4_ps(lo, 2), 0),
                    _mm512_extractf32x4_ps(lo, 3),
                    2),
                _mm512_extractf32x4_ps(hi, 2),
                1));
        }

        // zip_lo
        template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
        inline batch<T, A>
        zip_lo(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
        {
            __m512i lo, hi;
            XSIMD_IF_CONSTEXPR(sizeof(T) == 1)
            {
                assert(false && "not implemented yet");
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 2)
            {
                assert(false && "not implemented yet");
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 4)
            {
                lo = _mm512_unpacklo_epi32(self, other);
                hi = _mm512_unpackhi_epi32(self, other);
            }
            else XSIMD_IF_CONSTEXPR(sizeof(T) == 8)
            {
                lo = _mm512_unpacklo_epi64(self, other);
                hi = _mm512_unpackhi_epi64(self, other);
            }
            else
            {
                assert(false && "unsupported arch/op combination");
                return {};
            }
            return _mm512_inserti32x4(
                _mm512_inserti32x4(
                    _mm512_inserti32x4(lo, _mm512_extracti32x4_epi32(hi, 0), 1),
                    _mm512_extracti32x4_epi32(hi, 1),
                    3),
                _mm512_extracti32x4_epi32(lo, 1),
                2);
        }
        template <class A>
        inline batch<float, A>
        zip_lo(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
        {
            auto lo = _mm512_unpacklo_ps(self, other);
            auto hi = _mm512_unpackhi_ps(self, other);
            return _mm512_insertf32x4(
                _mm512_insertf32x4(
                    _mm512_insertf32x4(lo, _mm512_extractf32x4_ps(hi, 0), 1),
                    _mm512_extractf32x4_ps(hi, 1),
                    3),
                _mm512_extractf32x4_ps(lo, 1),
                2);
        }
        template <class A>
        inline batch<double, A>
        zip_lo(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
        {
            auto lo = _mm512_castpd_ps(_mm512_unpacklo_pd(self, other));
            auto hi = _mm512_castpd_ps(_mm512_unpackhi_pd(self, other));
            return _mm512_castps_pd(_mm512_insertf32x4(
                _mm512_insertf32x4(
                    _mm512_insertf32x4(lo, _mm512_extractf32x4_ps(hi, 0), 1),
                    _mm512_extractf32x4_ps(hi, 1),
                    3),
                _mm512_extractf32x4_ps(lo, 1),
                2));
        }

    }

}

#endif
