Eigen/src/Core/arch/ZVector/PacketMath.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0

#ifndef EIGEN_PACKET_MATH_ZVECTOR_H
#define EIGEN_PACKET_MATH_ZVECTOR_H

// IWYU pragma: private
#include "../../InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 16
#endif

#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#endif

#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
#endif

typedef __vector int Packet4i;
typedef __vector unsigned int Packet4ui;
typedef __vector __bool int Packet4bi;
typedef __vector short int Packet8i;
typedef __vector unsigned char Packet16uc;
typedef __vector double Packet2d;
typedef __vector unsigned long long Packet2ul;
typedef __vector long long Packet2l;

// Z14 has builtin support for float vectors
typedef __vector float Packet4f;

typedef union {
  numext::int32_t i[4];
  numext::uint32_t ui[4];
  numext::int64_t l[2];
  numext::uint64_t ul[2];
  double d[2];
  float f[4];
  Packet4i v4i;
  Packet4ui v4ui;
  Packet2l v2l;
  Packet2ul v2ul;
  Packet2d v2d;
  Packet4f v4f;
} Packet;

// We don't want to write the same code all the time, but we need to reuse the constants
// and it doesn't really work to declare them global, so we define macros instead

#define EIGEN_DECLARE_CONST_FAST_Packet4i(NAME, X) Packet4i p4i_##NAME = reinterpret_cast<Packet4i>(vec_splat_s32(X))

#define EIGEN_DECLARE_CONST_FAST_Packet2d(NAME, X) Packet2d p2d_##NAME = reinterpret_cast<Packet2d>(vec_splat_s64(X))

#define EIGEN_DECLARE_CONST_FAST_Packet2l(NAME, X) Packet2l p2l_##NAME = reinterpret_cast<Packet2l>(vec_splat_s64(X))

#define EIGEN_DECLARE_CONST_Packet4i(NAME, X) Packet4i p4i_##NAME = pset1<Packet4i>(X)

#define EIGEN_DECLARE_CONST_Packet2d(NAME, X) Packet2d p2d_##NAME = pset1<Packet2d>(X)

#define EIGEN_DECLARE_CONST_Packet2l(NAME, X) Packet2l p2l_##NAME = pset1<Packet2l>(X)

// These constants are endian-agnostic
static EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0);  //{ 0, 0, 0, 0,}
static EIGEN_DECLARE_CONST_FAST_Packet4i(ONE, 1);   //{ 1, 1, 1, 1}

static EIGEN_DECLARE_CONST_FAST_Packet2d(ZERO, 0);
static EIGEN_DECLARE_CONST_FAST_Packet2l(ZERO, 0);
static EIGEN_DECLARE_CONST_FAST_Packet2l(ONE, 1);

static Packet2d p2d_ONE = {1.0, 1.0};
static Packet2d p2d_ZERO_ = {numext::bit_cast<double>(0x8000000000000000ull),
                             numext::bit_cast<double>(0x8000000000000000ull)};

#define EIGEN_DECLARE_CONST_FAST_Packet4f(NAME, X) Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(vec_splat_s32(X))

#define EIGEN_DECLARE_CONST_Packet4f(NAME, X) Packet4f p4f_##NAME = pset1<Packet4f>(X)

#define EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME, X) \
  const Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(pset1<Packet4i>(X))

static EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0);     //{ 0.0, 0.0, 0.0, 0.0}
static EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1, -1);  //{ -1, -1, -1, -1}
static Packet4f p4f_MZERO = {0x80000000, 0x80000000, 0x80000000, 0x80000000};

static Packet4i p4i_COUNTDOWN = {0, 1, 2, 3};
static Packet4f p4f_COUNTDOWN = {0.0, 1.0, 2.0, 3.0};
static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(
    vec_sld(reinterpret_cast<Packet16uc>(p2d_ZERO), reinterpret_cast<Packet16uc>(p2d_ONE), 8));

static Packet16uc p16uc_PSET64_HI = {0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7};
static Packet16uc p16uc_DUPLICATE32_HI = {0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 6, 7, 4, 5, 6, 7};

// Mask alignment
#define EIGEN_MASK_ALIGNMENT 0xfffffffffffffff0

#define EIGEN_ALIGNED_PTR(x) ((std::ptrdiff_t)(x) & EIGEN_MASK_ALIGNMENT)

// Handle endianness properly while loading constants
// Define global static constants:

static Packet16uc p16uc_FORWARD = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
static Packet16uc p16uc_REVERSE32 = {12, 13, 14, 15, 8, 9, 10, 11, 4, 5, 6, 7, 0, 1, 2, 3};
static Packet16uc p16uc_REVERSE64 = {8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7};

static Packet16uc p16uc_PSET32_WODD =
    vec_sld((Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 2),
            8);  //{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
static Packet16uc p16uc_PSET32_WEVEN = vec_sld(p16uc_DUPLICATE32_HI, (Packet16uc)vec_splat((Packet4ui)p16uc_FORWARD, 3),
                                               8);  //{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
static Packet16uc p16uc_PSET64_LO = (Packet16uc)vec_mergel(
    (Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);  //{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };
static Packet16uc p16uc_TRANSPOSE64_HI = {0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23};
static Packet16uc p16uc_TRANSPOSE64_LO = {8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31};

static Packet16uc p16uc_COMPLEX32_REV =
    vec_sld(p16uc_REVERSE32, p16uc_REVERSE32, 8);  //{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };

static Packet16uc p16uc_COMPLEX32_REV2 =
    vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8);  //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };

#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
#define EIGEN_ZVECTOR_PREFETCH(ADDR) __builtin_prefetch(ADDR);
#else
#define EIGEN_ZVECTOR_PREFETCH(ADDR) asm("   pfd [%[addr]]\n" ::[addr] "r"(ADDR) : "cc");
#endif

template <>
struct packet_traits<int> : default_packet_traits {
  typedef Packet4i type;
  typedef Packet4i half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 4,

    HasAdd = 1,
    HasSub = 1,
    HasMul = 1,
    HasDiv = 1,
  };
};

template <>
struct packet_traits<float> : default_packet_traits {
  typedef Packet4f type;
  typedef Packet4f half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 4,

    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasMul = 1,
    HasDiv = 1,
    HasMin = 1,
    HasMax = 1,
    HasAbs = 1,
    HasSin = 0,
    HasCos = 0,
    HasLog = 0,
    HasExp = 1,
    HasSqrt = 1,
    HasRsqrt = 1,
    HasTanh = 1,
    HasErf = 1,
    HasNegate = 1,
  };
};

template <>
struct packet_traits<double> : default_packet_traits {
  typedef Packet2d type;
  typedef Packet2d half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 2,

    HasAdd = 1,
    HasSub = 1,
    HasMul = 1,
    HasDiv = 1,
    HasMin = 1,
    HasMax = 1,
    HasAbs = 1,
    HasSin = 0,
    HasCos = 0,
    HasLog = 0,
    HasExp = 1,
    HasSqrt = 1,
    HasRsqrt = 1,
    HasNegate = 1,
  };
};

template <>
struct unpacket_traits<Packet4i> {
  typedef int type;
  enum {
    size = 4,
    alignment = Aligned16,
    vectorizable = true,
    masked_load_available = false,
    masked_store_available = false
  };
  typedef Packet4i half;
};
template <>
struct unpacket_traits<Packet4f> {
  typedef float type;
  enum {
    size = 4,
    alignment = Aligned16,
    vectorizable = true,
    masked_load_available = false,
    masked_store_available = false
  };
  typedef Packet4f half;
  typedef Packet4i integer_packet;
};
template <>
struct unpacket_traits<Packet2d> {
  typedef double type;
  enum {
    size = 2,
    alignment = Aligned16,
    vectorizable = true,
    masked_load_available = false,
    masked_store_available = false
  };
  typedef Packet2d half;
  typedef Packet2l integer_packet;
};
// The integer_packet of Packet2d, for the generic bit-manipulation paths; int64 is not vectorized.
template <>
struct unpacket_traits<Packet2l> {
  using type = numext::int64_t;
  using half = Packet2l;
  static constexpr int size = 2;
  static constexpr int alignment = Aligned16;
  static constexpr bool vectorizable = false;
  static constexpr bool masked_load_available = false;
  static constexpr bool masked_store_available = false;
};

/* Forward declaration */
EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4f, 4>& kernel);

inline std::ostream& operator<<(std::ostream& s, const Packet4i& v) {
  Packet vt;
  vt.v4i = v;
  s << vt.i[0] << ", " << vt.i[1] << ", " << vt.i[2] << ", " << vt.i[3];
  return s;
}

inline std::ostream& operator<<(std::ostream& s, const Packet4ui& v) {
  Packet vt;
  vt.v4ui = v;
  s << vt.ui[0] << ", " << vt.ui[1] << ", " << vt.ui[2] << ", " << vt.ui[3];
  return s;
}

inline std::ostream& operator<<(std::ostream& s, const Packet2l& v) {
  Packet vt;
  vt.v2l = v;
  s << vt.l[0] << ", " << vt.l[1];
  return s;
}

inline std::ostream& operator<<(std::ostream& s, const Packet2ul& v) {
  Packet vt;
  vt.v2ul = v;
  s << vt.ul[0] << ", " << vt.ul[1];
  return s;
}

inline std::ostream& operator<<(std::ostream& s, const Packet2d& v) {
  Packet vt;
  vt.v2d = v;
  s << vt.d[0] << ", " << vt.d[1];
  return s;
}

inline std::ostream& operator<<(std::ostream& s, const Packet4f& v) {
  Packet vt;
  vt.v4f = v;
  s << vt.f[0] << ", " << vt.f[1] << ", " << vt.f[2] << ", " << vt.f[3];
  return s;
}

template <>
EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) {
  EIGEN_DEBUG_ALIGNED_LOAD
  return vec_xl(0, from);
}

template <>
EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) {
  EIGEN_DEBUG_ALIGNED_LOAD
  return vec_xl(0, from);
}

template <>
EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) {
  EIGEN_DEBUG_ALIGNED_STORE
  vec_xst(from, 0, to);
}

template <>
EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) {
  EIGEN_DEBUG_ALIGNED_STORE
  vec_xst(from, 0, to);
}

template <>
EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) {
  return pfrexp_generic(a, exponent);
}

template <>
EIGEN_STRONG_INLINE Packet2d pfrexp<Packet2d>(const Packet2d& a, Packet2d& exponent) {
  return pfrexp_generic(a, exponent);
}

template <>
EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) {
  return vec_splats(from);
}
template <>
EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) {
  return vec_splats(from);
}
template <>
EIGEN_STRONG_INLINE Packet2l pset1<Packet2l>(const numext::int64_t& from) {
  return vec_splats(static_cast<long long>(from));
}

template <>
EIGEN_STRONG_INLINE void pbroadcast4<Packet4i>(const int* a, Packet4i& a0, Packet4i& a1, Packet4i& a2, Packet4i& a3) {
  a3 = pload<Packet4i>(a);
  a0 = vec_splat(a3, 0);
  a1 = vec_splat(a3, 1);
  a2 = vec_splat(a3, 2);
  a3 = vec_splat(a3, 3);
}

template <>
EIGEN_STRONG_INLINE void pbroadcast4<Packet2d>(const double* a, Packet2d& a0, Packet2d& a1, Packet2d& a2,
                                               Packet2d& a3) {
  a1 = pload<Packet2d>(a);
  a0 = vec_splat(a1, 0);
  a1 = vec_splat(a1, 1);
  a3 = pload<Packet2d>(a + 2);
  a2 = vec_splat(a3, 0);
  a3 = vec_splat(a3, 1);
}

template <>
EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride) {
  EIGEN_ALIGN16 int ai[4];
  ai[0] = from[0 * stride];
  ai[1] = from[1 * stride];
  ai[2] = from[2 * stride];
  ai[3] = from[3 * stride];
  return pload<Packet4i>(ai);
}

template <>
EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride) {
  EIGEN_ALIGN16 double af[2];
  af[0] = from[0 * stride];
  af[1] = from[1 * stride];
  return pload<Packet2d>(af);
}

template <>
EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride) {
  EIGEN_ALIGN16 int ai[4];
  pstore<int>((int*)ai, from);
  to[0 * stride] = ai[0];
  to[1 * stride] = ai[1];
  to[2 * stride] = ai[2];
  to[3 * stride] = ai[3];
}

template <>
EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride) {
  EIGEN_ALIGN16 double af[2];
  pstore<double>(af, from);
  to[0 * stride] = af[0];
  to[1 * stride] = af[1];
}

template <>
EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return (a + b);
}
template <>
EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return (a + b);
}

template <>
EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return (a - b);
}
template <>
EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return (a - b);
}

template <>
EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return (a * b);
}
template <>
EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return (a * b);
}

template <>
EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return (a / b);
}
template <>
EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return (a / b);
}

template <>
EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) {
  return (-a);
}
template <>
EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) {
  return (-a);
}

template <>
EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) {
  return padd<Packet4i>(pmul<Packet4i>(a, b), c);
}
template <>
EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) {
  return vec_madd(a, b, c);
}

template <>
EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) {
  return padd<Packet4i>(pset1<Packet4i>(a), p4i_COUNTDOWN);
}
template <>
EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) {
  return padd<Packet2d>(pset1<Packet2d>(a), p2d_COUNTDOWN);
}

template <>
EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vec_min(a, b);
}
// pmin/pmax follow std::min/std::max: they return a whenever either operand is NaN, so a NaN in a propagates through
// clamps such as pmax(pmin(x, hi), lo). vec_min/vec_max (VFMIN/VFMAX mode 0 on z14) drop it.
template <>
EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return __builtin_s390_vfmindb(a, b, 3);  // mode 3: std::min
}

template <>
EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vec_max(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return __builtin_s390_vfmaxdb(a, b, 3);  // mode 3: std::max
}

template <>
EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vec_and(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vec_and(a, b);
}

template <>
EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vec_or(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vec_or(a, b);
}

template <>
EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vec_xor(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vec_xor(a, b);
}

template <>
EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return pand<Packet4i>(a, vec_nor(b, b));
}
template <>
EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vec_and(a, vec_nor(b, b));
}

template <>
EIGEN_STRONG_INLINE Packet2l padd<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return (a + b);
}
template <>
EIGEN_STRONG_INLINE Packet2l psub<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return (a - b);
}
template <>
EIGEN_STRONG_INLINE Packet2l pand<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vec_and(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l por<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vec_or(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l pxor<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vec_xor(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l pandnot<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vec_and(a, vec_nor(b, b));
}
template <>
EIGEN_STRONG_INLINE Packet2l pcmp_eq<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return reinterpret_cast<Packet2l>(vec_cmpeq(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet2l pcmp_lt<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return reinterpret_cast<Packet2l>(vec_cmplt(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet2l pcmp_le<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return reinterpret_cast<Packet2l>(vec_cmple(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet2l pselect<Packet2l>(const Packet2l& mask, const Packet2l& a, const Packet2l& b) {
  return vec_sel(b, a, reinterpret_cast<Packet2ul>(mask));
}

template <>
struct cast_impl<Packet2l, Packet2d> {
  EIGEN_DEVICE_FUNC static inline Packet2d run(const Packet2l& a) { return vec_double(a); }
};

template <>
struct cast_impl<Packet2d, Packet2l> {
  EIGEN_DEVICE_FUNC static inline Packet2l run(const Packet2d& a) {
    return vec_signed(vec_sel(p2d_ZERO, a, vec_cmpeq(a, a)));  // A NaN lane converts to 0.
  }
};

template <>
EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) {
  /* Uses non-default rounding for vec_round */
  return __builtin_s390_vfidb(a, 0, 1);
}
template <>
EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) {
  return vec_ceil(a);
}
template <>
EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) {
  return vec_floor(a);
}
template <>
EIGEN_STRONG_INLINE Packet2d print<Packet2d>(const Packet2d& a) {
  // M5 = 4: round to nearest, ties to even.
  return __builtin_s390_vfidb(a, 4, 4);
}
template <>
EIGEN_STRONG_INLINE Packet2d ptrunc<Packet2d>(const Packet2d& a) {
  // M5 = 5: round toward zero.
  return __builtin_s390_vfidb(a, 4, 5);
}
template <>
EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return pnot(pcmp_le(b, a));
}

template <>
EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from) {
  return pload<Packet4i>(from);
}
template <>
EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) {
  return pload<Packet2d>(from);
}

template <>
EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from) {
  Packet4i p = pload<Packet4i>(from);
  return vec_perm(p, p, p16uc_DUPLICATE32_HI);
}

template <>
EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from) {
  Packet2d p = pload<Packet2d>(from);
  return vec_perm(p, p, p16uc_PSET64_HI);
}

template <>
EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from) {
  pstore<int>(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) {
  pstore<double>(to, from);
}

template <>
EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) {
  EIGEN_ZVECTOR_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) {
  EIGEN_ZVECTOR_PREFETCH(addr);
}

template <int N>
EIGEN_STRONG_INLINE Packet2l parithmetic_shift_right(const Packet2l& a) {
  return Packet2l{parithmetic_shift_right<N>(a[0]), parithmetic_shift_right<N>(a[1])};
}
template <int N>
EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(const Packet4i& a) {
  return Packet4i{parithmetic_shift_right<N>(a[0]), parithmetic_shift_right<N>(a[1]), parithmetic_shift_right<N>(a[2]),
                  parithmetic_shift_right<N>(a[3])};
}

template <int N>
EIGEN_STRONG_INLINE Packet2l plogical_shift_right(const Packet2l& a) {
  return Packet2l{plogical_shift_right<N>(a[0]), plogical_shift_right<N>(a[1])};
}
template <int N>
EIGEN_STRONG_INLINE Packet4i plogical_shift_right(const Packet4i& a) {
  return Packet4i{plogical_shift_right<N>(a[0]), plogical_shift_right<N>(a[1]), plogical_shift_right<N>(a[2]),
                  plogical_shift_right<N>(a[3])};
}

template <int N>
EIGEN_STRONG_INLINE Packet2l plogical_shift_left(const Packet2l& a) {
  return Packet2l{plogical_shift_left<N>(a[0]), plogical_shift_left<N>(a[1])};
}
template <int N>
EIGEN_STRONG_INLINE Packet4i plogical_shift_left(const Packet4i& a) {
  return Packet4i{plogical_shift_left<N>(a[0]), plogical_shift_left<N>(a[1]), plogical_shift_left<N>(a[2]),
                  plogical_shift_left<N>(a[3])};
}

template <>
EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) {
  EIGEN_ALIGN16 int x[4];
  pstore(x, a);
  return x[0];
}
template <>
EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) {
  EIGEN_ALIGN16 double x[2];
  pstore(x, a);
  return x[0];
}

template <>
EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) {
  return reinterpret_cast<Packet4i>(
      vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
}

template <>
EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) {
  return reinterpret_cast<Packet2d>(
      vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE64));
}

template <>
EIGEN_STRONG_INLINE Packet4i pabs<Packet4i>(const Packet4i& a) {
  return vec_abs(a);
}
template <>
EIGEN_STRONG_INLINE Packet2d pabs<Packet2d>(const Packet2d& a) {
  return vec_abs(a);
}

template <>
EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a) {
  Packet4i b, sum;
  b = vec_sld(a, a, 8);
  sum = padd<Packet4i>(a, b);
  b = vec_sld(sum, sum, 4);
  sum = padd<Packet4i>(sum, b);
  return pfirst(sum);
}

template <>
EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) {
  Packet2d b, sum;
  b = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8));
  sum = padd<Packet2d>(a, b);
  return pfirst(sum);
}

template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet2d& a) {
  const Packet2ul zero = {0, 0};
  return vec_any_ne(reinterpret_cast<Packet2ul>(a), zero);
}

// Other reduction functions:
// mul
template <>
EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a) {
  EIGEN_ALIGN16 int aux[4];
  pstore(aux, a);
  return aux[0] * aux[1] * aux[2] * aux[3];
}

template <>
EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) {
  return pfirst(
      pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));
}

// min
template <>
EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a) {
  Packet4i b, res;
  b = pmin<Packet4i>(a, vec_sld(a, a, 8));
  res = pmin<Packet4i>(b, vec_sld(b, b, 4));
  return pfirst(res);
}

template <>
EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a) {
  return pfirst(pmin<Packet2d>(
      a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));
}

// max
template <>
EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a) {
  Packet4i b, res;
  b = pmax<Packet4i>(a, vec_sld(a, a, 8));
  res = pmax<Packet4i>(b, vec_sld(b, b, 4));
  return pfirst(res);
}

// max
template <>
EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a) {
  return pfirst(pmax<Packet2d>(
      a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));
}

EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4i, 4>& kernel) {
  Packet4i t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
  Packet4i t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
  Packet4i t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
  Packet4i t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
  kernel.packet[0] = vec_mergeh(t0, t2);
  kernel.packet[1] = vec_mergel(t0, t2);
  kernel.packet[2] = vec_mergeh(t1, t3);
  kernel.packet[3] = vec_mergel(t1, t3);
}

EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet2d, 2>& kernel) {
  Packet2d t0 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_HI);
  Packet2d t1 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_LO);
  kernel.packet[0] = t0;
  kernel.packet[1] = t1;
}

template <>
EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) {
  EIGEN_DEBUG_ALIGNED_LOAD
  return vec_xl(0, from);
}

template <>
EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) {
  EIGEN_DEBUG_ALIGNED_STORE
  vec_xst(from, 0, to);
}

template <>
EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) {
  return vec_splats(from);
}

template <>
EIGEN_STRONG_INLINE void pbroadcast4<Packet4f>(const float* a, Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3) {
  a3 = pload<Packet4f>(a);
  a0 = vec_splat(a3, 0);
  a1 = vec_splat(a3, 1);
  a2 = vec_splat(a3, 2);
  a3 = vec_splat(a3, 3);
}

template <>
EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride) {
  EIGEN_ALIGN16 float af[4];
  af[0] = from[0 * stride];
  af[1] = from[1 * stride];
  af[2] = from[2 * stride];
  af[3] = from[3 * stride];
  return pload<Packet4f>(af);
}

template <>
EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride) {
  EIGEN_ALIGN16 float af[4];
  pstore<float>((float*)af, from);
  to[0 * stride] = af[0];
  to[1 * stride] = af[1];
  to[2 * stride] = af[2];
  to[3 * stride] = af[3];
}

template <>
EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return (a + b);
}
template <>
EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return (a - b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return (a * b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return (a / b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pnegate<Packet4f>(const Packet4f& a) {
  return (-a);
}
template <>
EIGEN_STRONG_INLINE Packet4f pmadd<Packet4f>(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
  return vec_madd(a, b, c);
}
template <>
EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return __builtin_s390_vfminsb(a, b, 3);  // mode 3: std::min
}
template <>
EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return __builtin_s390_vfmaxsb(a, b, 3);  // mode 3: std::max
}
template <>
EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vec_and(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vec_or(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vec_xor(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vec_and(a, vec_nor(b, b));
}
template <>
EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) {
  /* Uses non-default rounding for vec_round */
  return __builtin_s390_vfisb(a, 0, 1);
}
template <>
EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) {
  return vec_ceil(a);
}
template <>
EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) {
  return vec_floor(a);
}
template <>
EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a) {
  // M5 = 4: round to nearest, ties to even.
  return __builtin_s390_vfisb(a, 4, 4);
}
template <>
EIGEN_STRONG_INLINE Packet4f ptrunc<Packet4f>(const Packet4f& a) {
  // M5 = 5: round toward zero.
  return __builtin_s390_vfisb(a, 4, 5);
}
template <>
EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return pnot(pcmp_le(b, a));
}
template <>
EIGEN_STRONG_INLINE Packet4f pabs<Packet4f>(const Packet4f& a) {
  return vec_abs(a);
}
template <>
EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) {
  EIGEN_ALIGN16 float x[4];
  pstore(x, a);
  return x[0];
}

template <>
EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from) {
  Packet4f p = pload<Packet4f>(from);
  return vec_perm(p, p, p16uc_DUPLICATE32_HI);
}

template <>
EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) {
  return reinterpret_cast<Packet4f>(
      vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
}

template <>
EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a) {
  Packet4f b, sum;
  b = vec_sld(a, a, 8);
  sum = padd<Packet4f>(a, b);
  b = vec_sld(sum, sum, 4);
  sum = padd<Packet4f>(sum, b);
  return pfirst(sum);
}

template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet4f& a) {
  const Packet4ui zero = {0, 0, 0, 0};
  return vec_any_ne(reinterpret_cast<Packet4ui>(a), zero);
}

// Other reduction functions:
// mul
template <>
EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a) {
  Packet4f prod;
  prod = pmul(a, vec_sld(a, a, 8));
  return pfirst(pmul(prod, vec_sld(prod, prod, 4)));
}

// min
template <>
EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a) {
  Packet4f b, res;
  b = pmin<Packet4f>(a, vec_sld(a, a, 8));
  res = pmin<Packet4f>(b, vec_sld(b, b, 4));
  return pfirst(res);
}

// max
template <>
EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a) {
  Packet4f b, res;
  b = pmax<Packet4f>(a, vec_sld(a, a, 8));
  res = pmax<Packet4f>(b, vec_sld(b, b, 4));
  return pfirst(res);
}

EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4f, 4>& kernel) {
  Packet4f t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
  Packet4f t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
  Packet4f t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
  Packet4f t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
  kernel.packet[0] = vec_mergeh(t0, t2);
  kernel.packet[1] = vec_mergel(t0, t2);
  kernel.packet[2] = vec_mergeh(t1, t3);
  kernel.packet[3] = vec_mergel(t1, t3);
}

template <>
EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) {
  return pldexp_generic(a, exponent);
}

template <>
EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent) {
  // The single-rounding split of pldexp_generic on int64 exponents.
  const Packet2d max_exponent = pset1<Packet2d>(2099.0);
  const Packet2d last_max = pset1<Packet2d>(1022.0);
  const Packet2l e = pcast<Packet2d, Packet2l>(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));
  const Packet2l b = pcast<Packet2d, Packet2l>(pmin(pmax(exponent, pnegate(last_max)), last_max));
  const Packet2l bias = {1023, 1023};
  const Packet2l even = {-2, -2};
  const Packet2l t = psub(e, b) & even;
  const Packet2d c1 = reinterpret_cast<Packet2d>(plogical_shift_left<51>(t + bias + bias));    // 2^(t/2)
  const Packet2d c2 = reinterpret_cast<Packet2d>(plogical_shift_left<52>(psub(e, t) + bias));  // 2^(e - t)
  return pldexp_apply_factors(a, c1, c2);                                                      // a * 2^e
}

template <>
EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) {
  EIGEN_ZVECTOR_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) {
  return pload<Packet4f>(from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) {
  pstore<float>(to, from);
}
template <>
EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) {
  return padd<Packet4f>(pset1<Packet4f>(a), p4f_COUNTDOWN);
}

#if !defined(vec_float) || !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ < 13)
#pragma GCC warning "float->int and int->float conversion is simulated. compile for z15 for improved performance"
template <>
struct cast_impl<Packet4i, Packet4f> {
  EIGEN_DEVICE_FUNC static inline Packet4f run(const Packet4i& a) {
    return Packet4f{float(a[0]), float(a[1]), float(a[2]), float(a[3])};
  }
};

template <>
struct cast_impl<Packet4f, Packet4i> {
  // A NaN lane converts to 0: the scalar conversion would be undefined, and pexp's clamp lets NaN through.
  EIGEN_DEVICE_FUNC static inline Packet4i run(const Packet4f& a) {
    return Packet4i{to_int(a[0]), to_int(a[1]), to_int(a[2]), to_int(a[3])};
  }
  EIGEN_DEVICE_FUNC static inline int to_int(float x) { return x == x ? int(x) : 0; }
};
#else
template <>
struct cast_impl<Packet4i, Packet4f> {
  EIGEN_DEVICE_FUNC static inline Packet4f run(const Packet4i& a) { return vec_float(a); }
};

template <>
struct cast_impl<Packet4f, Packet4i> {
  EIGEN_DEVICE_FUNC static inline Packet4i run(const Packet4f& a) {
    return vec_signed(vec_sel(p4f_ZERO, a, vec_cmpeq(a, a)));  // A NaN lane converts to 0.
  }
};
#endif

template <>
EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(uint32_t from) {
  return pset1<Packet4f>(Eigen::numext::bit_cast<float>(from));
}
template <>
EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(uint64_t from) {
  return pset1<Packet2d>(Eigen::numext::bit_cast<double>(from));
}

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_PACKET_MATH_ZVECTOR_H