Memory.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009 Kenneth Riddile <kfriddile@yahoo.com>
// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
// Copyright (C) 2010 Thomas Capricelli <orzel@freehackers.org>
// Copyright (C) 2013 Pavel Holoborodko <pavel@holoborodko.com>
//
// 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
 
/*****************************************************************************
*** Platform checks for aligned malloc functions                           ***
*****************************************************************************/
 
#ifndef EIGEN_MEMORY_H
#define EIGEN_MEMORY_H
 
#ifndef EIGEN_MALLOC_ALREADY_ALIGNED
 
// Try to determine automatically if malloc is already aligned.
 
// On 64-bit systems, glibc's malloc returns 16-byte-aligned pointers, see:
//   http://www.gnu.org/s/libc/manual/html_node/Aligned-Memory-Blocks.html
// This is true at least since glibc 2.8.
// This leaves the question how to detect 64-bit. According to this document,
//   http://gcc.fyxm.net/summit/2003/Porting%20to%2064%20bit.pdf
// page 114, "[The] LP64 model [...] is used by all 64-bit UNIX ports" so it's indeed
// quite safe, at least within the context of glibc, to equate 64-bit with LP64.
#if defined(__GLIBC__) && ((__GLIBC__ >= 2 && __GLIBC_MINOR__ >= 8) || __GLIBC__ > 2) && defined(__LP64__) && \
    !defined(__SANITIZE_ADDRESS__) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)
#define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 1
#else
#define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 0
#endif
 
// FreeBSD 6 seems to have 16-byte aligned malloc
//   See http://svn.freebsd.org/viewvc/base/stable/6/lib/libc/stdlib/malloc.c?view=markup
// FreeBSD 7 seems to have 16-byte aligned malloc except on ARM and MIPS architectures
//   See http://svn.freebsd.org/viewvc/base/stable/7/lib/libc/stdlib/malloc.c?view=markup
#if defined(__FreeBSD__) && !(EIGEN_ARCH_ARM || EIGEN_ARCH_MIPS) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)
#define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 1
#else
#define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 0
#endif
 
#if (EIGEN_OS_MAC && (EIGEN_DEFAULT_ALIGN_BYTES == 16)) || (EIGEN_OS_WIN64 && (EIGEN_DEFAULT_ALIGN_BYTES == 16)) || \
    EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED || EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED
#define EIGEN_MALLOC_ALREADY_ALIGNED 1
#else
#define EIGEN_MALLOC_ALREADY_ALIGNED 0
#endif
 
#endif
 
#ifndef EIGEN_MALLOC_CHECK_THREAD_LOCAL
 
// Check whether we can use the thread_local keyword to allow or disallow
// allocating memory with per-thread granularity, by means of the
// set_is_malloc_allowed() function.
#ifndef EIGEN_AVOID_THREAD_LOCAL
 
#if !defined(EIGEN_GPU_COMPILE_PHASE)
#define EIGEN_MALLOC_CHECK_THREAD_LOCAL thread_local
#else
#define EIGEN_MALLOC_CHECK_THREAD_LOCAL
#endif
 
#else  // EIGEN_AVOID_THREAD_LOCAL
#define EIGEN_MALLOC_CHECK_THREAD_LOCAL
#endif  // EIGEN_AVOID_THREAD_LOCAL
 
#endif
 
// IWYU pragma: private
#include "../InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
/*****************************************************************************
*** Implementation of portable aligned versions of malloc/free/realloc     ***
*****************************************************************************/
 
#ifdef EIGEN_NO_MALLOC
EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed() {
  eigen_assert(false && "heap allocation is forbidden (EIGEN_NO_MALLOC is defined)");
}
EIGEN_DEVICE_FUNC inline void check_that_free_is_allowed() {
  eigen_assert(false && "heap deallocation is forbidden (EIGEN_NO_MALLOC is defined)");
}
#elif defined EIGEN_RUNTIME_NO_MALLOC
EIGEN_DEVICE_FUNC inline bool is_malloc_allowed_impl(bool update, bool new_value = false) {
  EIGEN_MALLOC_CHECK_THREAD_LOCAL static bool value = true;
  if (update == 1) value = new_value;
  return value;
}
EIGEN_DEVICE_FUNC inline bool is_malloc_allowed() { return is_malloc_allowed_impl(false); }
EIGEN_DEVICE_FUNC inline bool set_is_malloc_allowed(bool new_value) { return is_malloc_allowed_impl(true, new_value); }
EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed() {
  eigen_assert(is_malloc_allowed() &&
               "heap allocation is forbidden (EIGEN_RUNTIME_NO_MALLOC is defined and set_is_malloc_allowed is false)");
}
EIGEN_DEVICE_FUNC inline bool is_free_allowed_impl(bool update, bool new_value = false) {
  EIGEN_MALLOC_CHECK_THREAD_LOCAL static bool value = true;
  if (update == 1) value = new_value;
  return value;
}
EIGEN_DEVICE_FUNC inline bool is_free_allowed() { return is_free_allowed_impl(false); }
EIGEN_DEVICE_FUNC inline bool set_is_free_allowed(bool new_value) { return is_free_allowed_impl(true, new_value); }
EIGEN_DEVICE_FUNC inline void check_that_free_is_allowed() {
  eigen_assert(is_free_allowed() &&
               "heap deallocation is forbidden (EIGEN_RUNTIME_NO_MALLOC is defined and set_is_free_allowed is false)");
}
#else
EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed() {}
EIGEN_DEVICE_FUNC inline void check_that_free_is_allowed() {}
#endif
 
EIGEN_DEVICE_FUNC inline void throw_std_bad_alloc() {
#ifdef EIGEN_EXCEPTIONS
  throw std::bad_alloc();
#else
  std::size_t huge = static_cast<std::size_t>(-1);
#if defined(EIGEN_HIPCC)
  //
  // calls to "::operator new" are to be treated as opaque function calls (i.e no inlining),
  // and as a consequence the code in the #else block triggers the hipcc warning :
  // "no overloaded function has restriction specifiers that are compatible with the ambient context"
  //
  // "throw_std_bad_alloc" has the EIGEN_DEVICE_FUNC attribute, so it seems that hipcc expects
  // the same on "operator new"
  // Reverting code back to the old version in this #if block for the hipcc compiler
  //
  new int[huge];
#else
  void* unused = ::operator new(huge);
  EIGEN_UNUSED_VARIABLE(unused);
#endif
#endif
}
 
/*****************************************************************************
*** Implementation of handmade aligned functions                           ***
*****************************************************************************/
 
/* ----- Hand made implementations of aligned malloc/free and realloc ----- */

EIGEN_DEVICE_FUNC inline void* handmade_aligned_malloc(std::size_t size,
                                                       std::size_t alignment = EIGEN_DEFAULT_ALIGN_BYTES) {
  eigen_assert(alignment >= sizeof(void*) && alignment <= 256 && (alignment & (alignment - 1)) == 0 &&
               "Alignment must be at least sizeof(void*), less than or equal to 256, and a power of 2");
 
  check_that_malloc_is_allowed();
  EIGEN_USING_STD(malloc)
  void* original = malloc(size + alignment);
  if (original == nullptr) return nullptr;
  std::size_t offset = alignment - (reinterpret_cast<std::size_t>(original) & (alignment - 1));
  void* aligned = static_cast<void*>(static_cast<uint8_t*>(original) + offset);
  // Store offset - 1, since it is guaranteed to be at least 1.
  *(static_cast<uint8_t*>(aligned) - 1) = static_cast<uint8_t>(offset - 1);
  return aligned;
}

EIGEN_DEVICE_FUNC inline void handmade_aligned_free(void* ptr) {
  if (ptr != nullptr) {
    std::size_t offset = static_cast<std::size_t>(*(static_cast<uint8_t*>(ptr) - 1)) + 1;
    void* original = static_cast<void*>(static_cast<uint8_t*>(ptr) - offset);
 
    check_that_free_is_allowed();
    EIGEN_USING_STD(free)
    free(original);
  }
}

EIGEN_DEVICE_FUNC inline void* handmade_aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size,
                                                        std::size_t alignment = EIGEN_DEFAULT_ALIGN_BYTES) {
  if (ptr == nullptr) return handmade_aligned_malloc(new_size, alignment);
  std::size_t old_offset = static_cast<std::size_t>(*(static_cast<uint8_t*>(ptr) - 1)) + 1;
  void* old_original = static_cast<uint8_t*>(ptr) - old_offset;
 
  check_that_malloc_is_allowed();
  EIGEN_USING_STD(realloc)
  void* original = realloc(old_original, new_size + alignment);
  if (original == nullptr) return nullptr;
  if (original == old_original) return ptr;
  std::size_t offset = alignment - (reinterpret_cast<std::size_t>(original) & (alignment - 1));
  void* aligned = static_cast<void*>(static_cast<uint8_t*>(original) + offset);
  if (offset != old_offset) {
    const void* src = static_cast<const void*>(static_cast<uint8_t*>(original) + old_offset);
    std::size_t count = (std::min)(new_size, old_size);
    std::memmove(aligned, src, count);
  }
  // Store offset - 1, since it is guaranteed to be at least 1.
  *(static_cast<uint8_t*>(aligned) - 1) = static_cast<uint8_t>(offset - 1);
  return aligned;
}

EIGEN_DEVICE_FUNC inline void* aligned_malloc(std::size_t size) {
  if (size == 0) return nullptr;
 
  void* result;
#if (EIGEN_DEFAULT_ALIGN_BYTES == 0) || EIGEN_MALLOC_ALREADY_ALIGNED
 
  check_that_malloc_is_allowed();
  EIGEN_USING_STD(malloc)
  result = malloc(size);
 
#if EIGEN_DEFAULT_ALIGN_BYTES == 16
  eigen_assert((size < 16 || (std::size_t(result) % 16) == 0) &&
               "System's malloc returned an unaligned pointer. Compile with EIGEN_MALLOC_ALREADY_ALIGNED=0 to fallback "
               "to handmade aligned memory allocator.");
#endif
#else
  result = handmade_aligned_malloc(size);
#endif
 
  if (!result && size) throw_std_bad_alloc();
 
  return result;
}

EIGEN_DEVICE_FUNC inline void aligned_free(void* ptr) {
#if (EIGEN_DEFAULT_ALIGN_BYTES == 0) || EIGEN_MALLOC_ALREADY_ALIGNED
 
  if (ptr != nullptr) {
    check_that_free_is_allowed();
    EIGEN_USING_STD(free)
    free(ptr);
  }
 
#else
  handmade_aligned_free(ptr);
#endif
}

EIGEN_DEVICE_FUNC inline void* aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size) {
  if (ptr == nullptr) return aligned_malloc(new_size);
  if (old_size == new_size) return ptr;
  if (new_size == 0) {
    aligned_free(ptr);
    return nullptr;
  }
 
  void* result;
#if (EIGEN_DEFAULT_ALIGN_BYTES == 0) || EIGEN_MALLOC_ALREADY_ALIGNED
  EIGEN_UNUSED_VARIABLE(old_size);
 
  check_that_malloc_is_allowed();
  EIGEN_USING_STD(realloc)
  result = realloc(ptr, new_size);
#else
  result = handmade_aligned_realloc(ptr, new_size, old_size);
#endif
 
  if (!result && new_size) throw_std_bad_alloc();
 
  return result;
}
 
/*****************************************************************************
*** Implementation of conditionally aligned functions                      ***
*****************************************************************************/

template <bool Align>
EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc(std::size_t size) {
  return aligned_malloc(size);
}
 
template <>
EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc<false>(std::size_t size) {
  if (size == 0) return nullptr;
 
  check_that_malloc_is_allowed();
  EIGEN_USING_STD(malloc)
  void* result = malloc(size);
 
  if (!result && size) throw_std_bad_alloc();
  return result;
}

template <bool Align>
EIGEN_DEVICE_FUNC inline void conditional_aligned_free(void* ptr) {
  aligned_free(ptr);
}
 
template <>
EIGEN_DEVICE_FUNC inline void conditional_aligned_free<false>(void* ptr) {
  if (ptr != nullptr) {
    check_that_free_is_allowed();
    EIGEN_USING_STD(free)
    free(ptr);
  }
}
 
template <bool Align>
EIGEN_DEVICE_FUNC inline void* conditional_aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size) {
  return aligned_realloc(ptr, new_size, old_size);
}
 
template <>
EIGEN_DEVICE_FUNC inline void* conditional_aligned_realloc<false>(void* ptr, std::size_t new_size,
                                                                  std::size_t old_size) {
  if (ptr == nullptr) return conditional_aligned_malloc<false>(new_size);
  if (old_size == new_size) return ptr;
  if (new_size == 0) {
    conditional_aligned_free<false>(ptr);
    return nullptr;
  }
 
  check_that_malloc_is_allowed();
  EIGEN_USING_STD(realloc)
  return realloc(ptr, new_size);
}
 
/*****************************************************************************
*** Construction/destruction of array elements                             ***
*****************************************************************************/

template <typename T>
EIGEN_DEVICE_FUNC inline void destruct_elements_of_array(T* ptr, std::size_t size) {
  // always destruct an array starting from the end.
  if (ptr)
    while (size) ptr[--size].~T();
}

template <typename T>
EIGEN_DEVICE_FUNC inline T* default_construct_elements_of_array(T* ptr, std::size_t size) {
  std::size_t i = 0;
  EIGEN_TRY {
    for (i = 0; i < size; ++i) ::new (ptr + i) T;
  }
  EIGEN_CATCH(...) {
    destruct_elements_of_array(ptr, i);
    EIGEN_THROW;
  }
  return ptr;
}

template <typename T>
EIGEN_DEVICE_FUNC inline T* copy_construct_elements_of_array(T* ptr, const T* src, std::size_t size) {
  std::size_t i = 0;
  EIGEN_TRY {
    for (i = 0; i < size; ++i) ::new (ptr + i) T(*(src + i));
  }
  EIGEN_CATCH(...) {
    destruct_elements_of_array(ptr, i);
    EIGEN_THROW;
  }
  return ptr;
}

template <typename T>
EIGEN_DEVICE_FUNC inline T* move_construct_elements_of_array(T* ptr, T* src, std::size_t size) {
  std::size_t i = 0;
  EIGEN_TRY {
    for (i = 0; i < size; ++i) ::new (ptr + i) T(std::move(*(src + i)));
  }
  EIGEN_CATCH(...) {
    destruct_elements_of_array(ptr, i);
    EIGEN_THROW;
  }
  return ptr;
}
 
/*****************************************************************************
*** Implementation of aligned new/delete-like functions                    ***
*****************************************************************************/
 
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void check_size_for_overflow(std::size_t size) {
  constexpr std::size_t max_elements = (std::numeric_limits<std::ptrdiff_t>::max)() / sizeof(T);
  if (size > max_elements) throw_std_bad_alloc();
}

template <typename T>
EIGEN_DEVICE_FUNC inline T* aligned_new(std::size_t size) {
  check_size_for_overflow<T>(size);
  T* result = static_cast<T*>(aligned_malloc(sizeof(T) * size));
  EIGEN_TRY { default_construct_elements_of_array(result, size); }
  EIGEN_CATCH(...) {
    aligned_free(result);
    EIGEN_THROW;
  }
  return result;
}
 
template <typename T, bool Align>
EIGEN_DEVICE_FUNC inline T* conditional_aligned_new(std::size_t size) {
  check_size_for_overflow<T>(size);
  T* result = static_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T) * size));
  EIGEN_TRY { default_construct_elements_of_array(result, size); }
  EIGEN_CATCH(...) {
    conditional_aligned_free<Align>(result);
    EIGEN_THROW;
  }
  return result;
}

template <typename T>
EIGEN_DEVICE_FUNC inline void aligned_delete(T* ptr, std::size_t size) {
  destruct_elements_of_array<T>(ptr, size);
  aligned_free(ptr);
}

template <typename T, bool Align>
EIGEN_DEVICE_FUNC inline void conditional_aligned_delete(T* ptr, std::size_t size) {
  destruct_elements_of_array<T>(ptr, size);
  conditional_aligned_free<Align>(ptr);
}
 
template <typename T, bool Align>
EIGEN_DEVICE_FUNC inline T* conditional_aligned_realloc_new(T* pts, std::size_t new_size, std::size_t old_size) {
  check_size_for_overflow<T>(new_size);
  check_size_for_overflow<T>(old_size);
 
  // If elements need to be explicitly initialized, we cannot simply realloc
  // (or memcpy) the memory block - each element needs to be reconstructed.
  // Otherwise, objects that contain internal pointers like mpfr or
  // AnnoyingScalar can be pointing to the wrong thing.
  T* result = static_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T) * new_size));
  EIGEN_TRY {
    // Move-construct initial elements.
    std::size_t copy_size = (std::min)(old_size, new_size);
    move_construct_elements_of_array(result, pts, copy_size);
 
    // Default-construct remaining elements.
    if (new_size > old_size) {
      default_construct_elements_of_array(result + copy_size, new_size - old_size);
    }
 
    // Delete old elements.
    conditional_aligned_delete<T, Align>(pts, old_size);
  }
  EIGEN_CATCH(...) {
    conditional_aligned_free<Align>(result);
    EIGEN_THROW;
  }
 
  return result;
}
 
template <typename T, bool Align>
EIGEN_DEVICE_FUNC inline T* conditional_aligned_new_auto(std::size_t size) {
  if (size == 0) return nullptr;  // short-cut. Also fixes Bug 884
  check_size_for_overflow<T>(size);
  T* result = static_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T) * size));
  EIGEN_IF_CONSTEXPR (NumTraits<T>::RequireInitialization) {
    EIGEN_TRY { default_construct_elements_of_array(result, size); }
    EIGEN_CATCH(...) {
      conditional_aligned_free<Align>(result);
      EIGEN_THROW;
    }
  }
  return result;
}
 
template <typename T, bool Align>
EIGEN_DEVICE_FUNC inline T* conditional_aligned_realloc_new_auto(T* pts, std::size_t new_size, std::size_t old_size) {
  EIGEN_IF_CONSTEXPR (NumTraits<T>::RequireInitialization) {
    return conditional_aligned_realloc_new<T, Align>(pts, new_size, old_size);
  }
 
  check_size_for_overflow<T>(new_size);
  check_size_for_overflow<T>(old_size);
  return static_cast<T*>(
      conditional_aligned_realloc<Align>(static_cast<void*>(pts), sizeof(T) * new_size, sizeof(T) * old_size));
}
 
template <typename T, bool Align>
EIGEN_DEVICE_FUNC inline void conditional_aligned_delete_auto(T* ptr, std::size_t size) {
  EIGEN_IF_CONSTEXPR (NumTraits<T>::RequireInitialization) destruct_elements_of_array<T>(ptr, size);
  conditional_aligned_free<Align>(ptr);
}
 
/****************************************************************************/

template <int Alignment, typename Scalar, typename Index>
EIGEN_DEVICE_FUNC inline Index first_aligned(const Scalar* array, Index size) {
  constexpr Index ScalarSize = sizeof(Scalar);
  constexpr Index AlignmentSize = Alignment / ScalarSize;
  constexpr Index AlignmentMask = AlignmentSize - 1;
 
  EIGEN_IF_CONSTEXPR (AlignmentSize <= 1) {
    // Either the requested alignment if smaller than a scalar, or it exactly match a 1 scalar
    // so that all elements of the array have the same alignment.
    return 0;
  } else EIGEN_IF_CONSTEXPR ((Alignment % ScalarSize) != 0) {
    // The requested alignment is not a multiple of the scalar size. Consequently, no element of the array is well
    // aligned.
    return size;
  } else if (std::uintptr_t(array) & (sizeof(Scalar) - 1)) {
    // The array is not aligned to the size of a single scalar. Consequently, no element of the array is well aligned.
    return size;
  } else {
    Index first = (AlignmentSize - (Index((std::uintptr_t(array) / sizeof(Scalar))) & AlignmentMask)) & AlignmentMask;
    return (first < size) ? first : size;
  }
}

template <typename Scalar, typename Index>
EIGEN_DEVICE_FUNC inline Index first_default_aligned(const Scalar* array, Index size) {
  using DefaultPacketType = typename packet_traits<Scalar>::type;
  return first_aligned<unpacket_traits<DefaultPacketType>::alignment>(array, size);
}

template <typename Index>
inline Index first_multiple(Index size, Index base) {
  return ((size + base - 1) / base) * base;
}
 
// std::copy is much slower than memcpy, so let's introduce a smart_copy which
// use memcpy on trivial types, i.e., on types that does not require an initialization ctor.
template <typename T, bool UseMemcpy>
struct smart_copy_helper;
 
template <typename T>
EIGEN_DEVICE_FUNC void smart_copy(const T* start, const T* end, T* target) {
  smart_copy_helper<T, !NumTraits<T>::RequireInitialization>::run(start, end, target);
}
 
template <typename T>
struct smart_copy_helper<T, true> {
  EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target) {
    std::ptrdiff_t count = end - start;
    if (count <= 0) return;
    eigen_internal_assert(start != 0 && end != 0 && target != 0);
    EIGEN_USING_STD(memcpy)
    memcpy(target, start, static_cast<std::size_t>(count) * sizeof(T));
  }
};
 
template <typename T>
struct smart_copy_helper<T, false> {
  EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target) { std::copy(start, end, target); }
};
 
// intelligent memmove. falls back to std::memmove for POD types, uses std::copy otherwise.
template <typename T, bool UseMemmove>
struct smart_memmove_helper;
 
template <typename T>
void smart_memmove(const T* start, const T* end, T* target) {
  smart_memmove_helper<T, !NumTraits<T>::RequireInitialization>::run(start, end, target);
}
 
template <typename T>
struct smart_memmove_helper<T, true> {
  static inline void run(const T* start, const T* end, T* target) {
    std::ptrdiff_t count = end - start;
    if (count <= 0) return;
    eigen_internal_assert(start != 0 && end != 0 && target != 0);
    std::memmove(target, start, static_cast<std::size_t>(count) * sizeof(T));
  }
};
 
template <typename T>
struct smart_memmove_helper<T, false> {
  static inline void run(const T* start, const T* end, T* target) {
    if (std::uintptr_t(target) < std::uintptr_t(start)) {
      std::copy(start, end, target);
    } else {
      std::ptrdiff_t count = (std::ptrdiff_t(end) - std::ptrdiff_t(start)) / sizeof(T);
      std::copy_backward(start, end, target + count);
    }
  }
};
 
/*****************************************************************************
*** Implementation of runtime stack allocation (falling back to malloc)    ***
*****************************************************************************/
 
// you can overwrite Eigen's default behavior regarding alloca by defining EIGEN_ALLOCA
// to the appropriate stack allocation function
#if !defined EIGEN_ALLOCA && !defined EIGEN_GPU_COMPILE_PHASE
#if EIGEN_OS_LINUX || EIGEN_OS_MAC || (defined alloca)
#define EIGEN_ALLOCA alloca
#elif EIGEN_COMP_MSVC
#define EIGEN_ALLOCA _alloca
#endif
#endif
 
// With clang -Oz -mthumb, alloca changes the stack pointer in a way that is
// not allowed in Thumb2. -DEIGEN_STACK_ALLOCATION_LIMIT=0 doesn't work because
// the compiler still emits bad code because stack allocation checks use "<=".
// TODO: Eliminate after https://bugs.llvm.org/show_bug.cgi?id=23772
// is fixed.
#if defined(__clang__) && defined(__thumb__)
#undef EIGEN_ALLOCA
#endif
 
// The SME GEMM kernel reads its packed panels a streaming vector at a time and slows down when they straddle
// 64-byte lines, so SME builds align the internal temporaries to 64 bytes, heap and stack alike.
#ifndef EIGEN_STACK_ALIGN_BYTES
#if defined(EIGEN_VECTORIZE_SME) && EIGEN_DEFAULT_ALIGN_BYTES < 64
#define EIGEN_STACK_ALIGN_BYTES 64
#else
#define EIGEN_STACK_ALIGN_BYTES EIGEN_DEFAULT_ALIGN_BYTES
#endif
#endif

EIGEN_DEVICE_FUNC inline void* scratch_malloc(std::size_t size) {
#if EIGEN_STACK_ALIGN_BYTES > EIGEN_DEFAULT_ALIGN_BYTES
  void* result = handmade_aligned_malloc(size, EIGEN_STACK_ALIGN_BYTES);
  if (!result && size) throw_std_bad_alloc();
  return result;
#else
  return aligned_malloc(size);
#endif
}
EIGEN_DEVICE_FUNC inline void scratch_free(void* ptr) {
#if EIGEN_STACK_ALIGN_BYTES > EIGEN_DEFAULT_ALIGN_BYTES
  handmade_aligned_free(ptr);
#else
  aligned_free(ptr);
#endif
}

template <typename T>
EIGEN_DEVICE_FUNC inline T* scratch_new(std::size_t size) {
  check_size_for_overflow<T>(size);
  T* result = static_cast<T*>(scratch_malloc(sizeof(T) * size));
  EIGEN_TRY { default_construct_elements_of_array(result, size); }
  EIGEN_CATCH(...) {
    scratch_free(result);
    EIGEN_THROW;
  }
  return result;
}

template <typename T>
EIGEN_DEVICE_FUNC inline void scratch_delete(T* ptr, std::size_t size) {
  destruct_elements_of_array<T>(ptr, size);
  scratch_free(ptr);
}
 
// This helper class construct the allocated memory, and takes care of destructing and freeing the handled data
// at destruction time. In practice this helper class is mainly useful to avoid memory leak in case of exceptions.
template <typename T>
class aligned_stack_memory_handler {
 public:
  aligned_stack_memory_handler(const aligned_stack_memory_handler&) = delete;
  aligned_stack_memory_handler& operator=(const aligned_stack_memory_handler&) = delete;
 
  /* Creates a stack_memory_handler responsible for the buffer \a ptr of size \a size.
   * Note that \a ptr can be 0 regardless of the other parameters.
   * This constructor takes care of constructing/initializing the elements of the buffer if required by the scalar type
   *T (see NumTraits<T>::RequireInitialization). In this case, the buffer elements will also be destructed when this
   *handler will be destructed. Finally, if \a dealloc is true, then the pointer \a ptr is freed.
   **/
  EIGEN_DEVICE_FUNC aligned_stack_memory_handler(T* ptr, std::size_t size, bool dealloc)
      : m_ptr(ptr), m_size(size), m_deallocate(dealloc) {
    EIGEN_IF_CONSTEXPR (NumTraits<T>::RequireInitialization) {
      if (m_ptr) Eigen::internal::default_construct_elements_of_array(m_ptr, size);
    }
  }
  EIGEN_DEVICE_FUNC ~aligned_stack_memory_handler() {
    EIGEN_IF_CONSTEXPR (NumTraits<T>::RequireInitialization) {
      if (m_ptr) Eigen::internal::destruct_elements_of_array<T>(m_ptr, m_size);
    }
    if (m_deallocate) Eigen::internal::scratch_free(m_ptr);
  }
 
 protected:
  T* m_ptr;
  std::size_t m_size;
  bool m_deallocate;
};
 
#ifdef EIGEN_ALLOCA
 
template <typename Xpr, int NbEvaluations,
          bool MapExternalBuffer = nested_eval<Xpr, NbEvaluations>::Evaluate && Xpr::MaxSizeAtCompileTime == Dynamic>
struct local_nested_eval_wrapper {
  static constexpr bool NeedExternalBuffer = false;
  using Scalar = typename Xpr::Scalar;
  using ObjectType = typename nested_eval<Xpr, NbEvaluations>::type;
  ObjectType object;
 
  EIGEN_DEVICE_FUNC local_nested_eval_wrapper(const Xpr& xpr, Scalar* ptr) : object(xpr) {
    EIGEN_UNUSED_VARIABLE(ptr);
    eigen_internal_assert(ptr == 0);
  }
};
 
template <typename Xpr, int NbEvaluations>
struct local_nested_eval_wrapper<Xpr, NbEvaluations, true> {
  static constexpr bool NeedExternalBuffer = true;
  using Scalar = typename Xpr::Scalar;
  using PlainObject = typename plain_object_eval<Xpr>::type;
  using ObjectType = Map<PlainObject, EIGEN_DEFAULT_ALIGN_BYTES>;
  ObjectType object;
 
  EIGEN_DEVICE_FUNC local_nested_eval_wrapper(const Xpr& xpr, Scalar* ptr)
      : object(ptr == 0 ? reinterpret_cast<Scalar*>(Eigen::internal::aligned_malloc(sizeof(Scalar) * xpr.size())) : ptr,
               xpr.rows(), xpr.cols()),
        m_deallocate(ptr == 0) {
    EIGEN_IF_CONSTEXPR (NumTraits<Scalar>::RequireInitialization) {
      if (object.data()) Eigen::internal::default_construct_elements_of_array(object.data(), object.size());
    }
    object = xpr;
  }
 
  EIGEN_DEVICE_FUNC ~local_nested_eval_wrapper() {
    EIGEN_IF_CONSTEXPR (NumTraits<Scalar>::RequireInitialization) {
      if (object.data()) Eigen::internal::destruct_elements_of_array(object.data(), object.size());
    }
    if (m_deallocate) Eigen::internal::aligned_free(object.data());
  }
 
 private:
  bool m_deallocate;
};
 
#endif  // EIGEN_ALLOCA
 
}  // end namespace internal

#if defined(EIGEN_ALLOCA) && !defined(EIGEN_NO_ALLOCA)
 
#if EIGEN_STACK_ALIGN_BYTES > 0
// We always manually re-align the result of EIGEN_ALLOCA.
// If alloca is already aligned, the compiler should be smart enough to optimize away the re-alignment.
 
#if ((EIGEN_COMP_GNUC || EIGEN_COMP_CLANG) && !EIGEN_COMP_NVHPC && !EIGEN_COMP_ICC)
#define EIGEN_ALIGNED_ALLOCA(SIZE) __builtin_alloca_with_align(SIZE, CHAR_BIT* EIGEN_STACK_ALIGN_BYTES)
#else
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void* eigen_aligned_alloca_helper(void* ptr) {
  constexpr std::uintptr_t mask = EIGEN_STACK_ALIGN_BYTES - 1;
  std::uintptr_t ptr_int = std::uintptr_t(ptr);
  std::uintptr_t aligned_ptr_int = (ptr_int + mask) & ~mask;
  std::uintptr_t offset = aligned_ptr_int - ptr_int;
  return static_cast<void*>(static_cast<uint8_t*>(ptr) + offset);
}
#define EIGEN_ALIGNED_ALLOCA(SIZE) eigen_aligned_alloca_helper(EIGEN_ALLOCA(SIZE + EIGEN_STACK_ALIGN_BYTES - 1))
#endif
 
#else
#define EIGEN_ALIGNED_ALLOCA(SIZE) EIGEN_ALLOCA(SIZE)
#endif
 
#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)                                       \
  Eigen::internal::check_size_for_overflow<TYPE>(SIZE);                                                               \
  TYPE* NAME = (BUFFER) != 0 ? (BUFFER)                                                                               \
                             : reinterpret_cast<TYPE*>((sizeof(TYPE) * (SIZE) <= EIGEN_STACK_ALLOCATION_LIMIT)        \
                                                           ? EIGEN_ALIGNED_ALLOCA(sizeof(TYPE) * (SIZE))              \
                                                           : Eigen::internal::scratch_malloc(sizeof(TYPE) * (SIZE))); \
  Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME, _stack_memory_destructor)(                      \
      (BUFFER) == 0 ? NAME : 0, SIZE, sizeof(TYPE) * (SIZE) > EIGEN_STACK_ALLOCATION_LIMIT)
 
#define ei_declare_local_nested_eval(XPR_T, XPR, N, NAME)                                        \
  Eigen::internal::local_nested_eval_wrapper<XPR_T, N> EIGEN_CAT(NAME, _wrapper)(                \
      XPR, reinterpret_cast<typename XPR_T::Scalar*>(                                            \
               ((Eigen::internal::local_nested_eval_wrapper<XPR_T, N>::NeedExternalBuffer) &&    \
                ((sizeof(typename XPR_T::Scalar) * XPR.size()) <= EIGEN_STACK_ALLOCATION_LIMIT)) \
                   ? EIGEN_ALIGNED_ALLOCA(sizeof(typename XPR_T::Scalar) * XPR.size())           \
                   : 0));                                                                        \
  typename Eigen::internal::local_nested_eval_wrapper<XPR_T, N>::ObjectType NAME(EIGEN_CAT(NAME, _wrapper).object)
 
#else
 
#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)                                 \
  Eigen::internal::check_size_for_overflow<TYPE>(SIZE);                                                         \
  TYPE* NAME =                                                                                                  \
      (BUFFER) != 0 ? BUFFER : reinterpret_cast<TYPE*>(Eigen::internal::scratch_malloc(sizeof(TYPE) * (SIZE))); \
  Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME, _stack_memory_destructor)(                \
      (BUFFER) == 0 ? NAME : 0, SIZE, true)
 
#define ei_declare_local_nested_eval(XPR_T, XPR, N, NAME) \
  typename Eigen::internal::nested_eval<XPR_T, N>::type NAME(XPR)
 
#endif
 
/*****************************************************************************
*** Implementation of EIGEN_MAKE_ALIGNED_OPERATOR_NEW [_IF]                ***
*****************************************************************************/
 
#if EIGEN_HAS_CXX17_OVERALIGN
 
// C++17 -> no need to bother about alignment anymore :)
 
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Size)
 
#else
 
// HIP does not support new/delete on device.
#if EIGEN_MAX_ALIGN_BYTES != 0 && !defined(EIGEN_HIP_DEVICE_COMPILE)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)                              \
  EIGEN_DEVICE_FUNC void* operator new(std::size_t size, const std::nothrow_t&) noexcept { \
    EIGEN_TRY { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); }  \
    EIGEN_CATCH(...) { return 0; }                                                         \
  }
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)                                                              \
  EIGEN_DEVICE_FUNC void* operator new(std::size_t size) {                                                            \
    return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size);                                           \
  }                                                                                                                   \
  EIGEN_DEVICE_FUNC void* operator new[](std::size_t size) {                                                          \
    return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size);                                           \
  }                                                                                                                   \
  EIGEN_DEVICE_FUNC void operator delete(void* ptr) noexcept {                                                        \
    Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                     \
  }                                                                                                                   \
  EIGEN_DEVICE_FUNC void operator delete[](void* ptr) noexcept {                                                      \
    Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                     \
  }                                                                                                                   \
  EIGEN_DEVICE_FUNC void operator delete(void* ptr, std::size_t /* sz */) noexcept {                                  \
    Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                     \
  }                                                                                                                   \
  EIGEN_DEVICE_FUNC void operator delete[](void* ptr, std::size_t /* sz */) noexcept {                                \
    Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                     \
  }                                                                                                                   \
  /* in-place new and delete. since (at least afaik) there is no actual   */                                          \
  /* memory allocated we can safely let the default implementation handle */                                          \
  /* this particular case. */                                                                                         \
  EIGEN_DEVICE_FUNC static void* operator new(std::size_t size, void* ptr) { return ::operator new(size, ptr); }      \
  EIGEN_DEVICE_FUNC static void* operator new[](std::size_t size, void* ptr) { return ::operator new[](size, ptr); }  \
  EIGEN_DEVICE_FUNC void operator delete(void* memory, void* ptr) noexcept { return ::operator delete(memory, ptr); } \
  EIGEN_DEVICE_FUNC void operator delete[](void* memory, void* ptr) noexcept {                                        \
    return ::operator delete[](memory, ptr);                                                                          \
  }                                                                                                                   \
  /* nothrow-new (returns zero instead of std::bad_alloc) */                                                          \
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)                                                               \
  EIGEN_DEVICE_FUNC void operator delete(void* ptr, const std::nothrow_t&) noexcept {                                 \
    Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                     \
  }                                                                                                                   \
  typedef void eigen_aligned_operator_new_marker_type;
#else
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
#endif
 
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(true)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Size)                                       \
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(                                                                                  \
      bool(((Size) != Eigen::Dynamic) &&                                                                               \
           (((EIGEN_MAX_ALIGN_BYTES >= 16) && ((sizeof(Scalar) * size_t(Size)) % (EIGEN_MAX_ALIGN_BYTES) == 0)) ||     \
            ((EIGEN_MAX_ALIGN_BYTES >= 32) && ((sizeof(Scalar) * size_t(Size)) % (EIGEN_MAX_ALIGN_BYTES / 2) == 0)) || \
            ((EIGEN_MAX_ALIGN_BYTES >= 64) && ((sizeof(Scalar) * size_t(Size)) % (EIGEN_MAX_ALIGN_BYTES / 4) == 0)))))
 
#endif
 
/****************************************************************************/

template <class T>
class aligned_allocator {
 public:
  using size_type = std::size_t;
  using difference_type = std::ptrdiff_t;
  using pointer = T*;
  using const_pointer = const T*;
  using reference = T&;
  using const_reference = const T&;
  using value_type = T;
 
  template <class U>
  struct rebind {
    using other = aligned_allocator<U>;
  };
 
  aligned_allocator() = default;
 
  aligned_allocator(const aligned_allocator&) = default;
 
  template <class U>
  aligned_allocator(const aligned_allocator<U>&) {}
 
  template <class U>
  constexpr bool operator==(const aligned_allocator<U>&) const noexcept {
    return true;
  }
  template <class U>
  constexpr bool operator!=(const aligned_allocator<U>&) const noexcept {
    return false;
  }
 
#if EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_STRICT_AT_LEAST(7, 0, 0)
  // In gcc std::allocator::max_size() is bugged making gcc triggers a warning:
  // eigen/Eigen/src/Core/util/Memory.h:189:12: warning: argument 1 value '18446744073709551612' exceeds maximum object
  // size 9223372036854775807 See https://gcc.gnu.org/bugzilla/show_bug.cgi?id=87544
  size_type max_size() const { return (std::numeric_limits<std::ptrdiff_t>::max)() / sizeof(T); }
#endif
 
  pointer allocate(size_type num, const void* /*hint*/ = 0) {
    internal::check_size_for_overflow<T>(num);
    return static_cast<pointer>(internal::aligned_malloc(num * sizeof(T)));
  }
 
  void deallocate(pointer p, size_type /*num*/) { internal::aligned_free(p); }
};
 
//---------- Cache sizes ----------
 
#if EIGEN_OS_LINUX && !defined(EIGEN_NO_CPU_CACHE_SYSFS)
// Linux publishes the cache topology under sysfs on every architecture.
#define EIGEN_CPU_CACHE_SYSFS 1
#endif
 
#if !defined(EIGEN_NO_CPUID)
#if EIGEN_COMP_GNUC && EIGEN_ARCH_i386_OR_x86_64
#if defined(__PIC__) && EIGEN_ARCH_i386
// Case for x86 with PIC
#define EIGEN_CPUID(abcd, func, id)                                                  \
  __asm__ __volatile__("xchgl %%ebx, %k1;cpuid; xchgl %%ebx,%k1"                     \
                       : "=a"(abcd[0]), "=&r"(abcd[1]), "=c"(abcd[2]), "=d"(abcd[3]) \
                       : "a"(func), "c"(id));
#elif defined(__PIC__) && EIGEN_ARCH_x86_64
// Case for x64 with PIC. In theory this is only a problem with recent gcc and with medium or large code model, not with
// the default small code model. However, we cannot detect which code model is used, and the xchg overhead is negligible
// anyway.
#define EIGEN_CPUID(abcd, func, id)                                                  \
  __asm__ __volatile__("xchg{q}\t{%%}rbx, %q1; cpuid; xchg{q}\t{%%}rbx, %q1"         \
                       : "=a"(abcd[0]), "=&r"(abcd[1]), "=c"(abcd[2]), "=d"(abcd[3]) \
                       : "0"(func), "2"(id));
#else
// Case for x86_64 or x86 w/o PIC
#define EIGEN_CPUID(abcd, func, id) \
  __asm__ __volatile__("cpuid" : "=a"(abcd[0]), "=b"(abcd[1]), "=c"(abcd[2]), "=d"(abcd[3]) : "0"(func), "2"(id));
#endif
#elif EIGEN_COMP_MSVC
#if EIGEN_ARCH_i386_OR_x86_64
#define EIGEN_CPUID(abcd, func, id) __cpuidex((int*)abcd, func, id)
#endif
#endif
#endif
 
namespace internal {
 
#ifdef EIGEN_CPUID
 
inline bool cpuid_is_vendor(int abcd[4], const int vendor[3]) {
  return abcd[1] == vendor[0] && abcd[3] == vendor[1] && abcd[2] == vendor[2];
}
 
inline void queryCacheSizes_intel_direct(std::ptrdiff_t& l1, std::ptrdiff_t& l2, std::ptrdiff_t& l3) {
  int abcd[4];
  l1 = l2 = l3 = 0;
  int cache_id = 0;
  int cache_type = 0;
  do {
    abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
    EIGEN_CPUID(abcd, 0x4, cache_id);
    cache_type = (abcd[0] & 0x0F) >> 0;
    if (cache_type == 1 || cache_type == 3)  // data or unified cache
    {
      int cache_level = (abcd[0] & 0xE0) >> 5;        // A[7:5]
      int ways = (abcd[1] & 0xFFC00000) >> 22;        // B[31:22]
      int partitions = (abcd[1] & 0x003FF000) >> 12;  // B[21:12]
      int line_size = (abcd[1] & 0x00000FFF) >> 0;    // B[11:0]
      int sets = (abcd[2]);                           // C[31:0]
 
      std::ptrdiff_t cache_size =
          static_cast<std::ptrdiff_t>(ways + 1) * (partitions + 1) * (line_size + 1) * (sets + 1);
 
      switch (cache_level) {
        case 1:
          l1 = cache_size;
          break;
        case 2:
          l2 = cache_size;
          break;
        case 3:
          l3 = cache_size;
          break;
        default:
          break;
      }
    }
    cache_id++;
  } while (cache_type > 0 && cache_id < 16);
}
 
inline void queryCacheSizes_intel_codes(std::ptrdiff_t& l1, std::ptrdiff_t& l2, std::ptrdiff_t& l3) {
  int abcd[4];
  abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
  l1 = l2 = l3 = 0;
  EIGEN_CPUID(abcd, 0x00000002, 0);
  unsigned char* bytes = reinterpret_cast<unsigned char*>(abcd) + 2;
  bool check_for_p2_core2 = false;
  for (int i = 0; i < 14; ++i) {
    switch (bytes[i]) {
      case 0x0A:
        l1 = 8;
        break;  // 0Ah   data L1 cache, 8 KB, 2 ways, 32 byte lines
      case 0x0C:
        l1 = 16;
        break;  // 0Ch   data L1 cache, 16 KB, 4 ways, 32 byte lines
      case 0x0E:
        l1 = 24;
        break;  // 0Eh   data L1 cache, 24 KB, 6 ways, 64 byte lines
      case 0x10:
        l1 = 16;
        break;  // 10h   data L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
      case 0x15:
        l1 = 16;
        break;  // 15h   code L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
      case 0x2C:
        l1 = 32;
        break;  // 2Ch   data L1 cache, 32 KB, 8 ways, 64 byte lines
      case 0x30:
        l1 = 32;
        break;  // 30h   code L1 cache, 32 KB, 8 ways, 64 byte lines
      case 0x60:
        l1 = 16;
        break;  // 60h   data L1 cache, 16 KB, 8 ways, 64 byte lines, sectored
      case 0x66:
        l1 = 8;
        break;  // 66h   data L1 cache, 8 KB, 4 ways, 64 byte lines, sectored
      case 0x67:
        l1 = 16;
        break;  // 67h   data L1 cache, 16 KB, 4 ways, 64 byte lines, sectored
      case 0x68:
        l1 = 32;
        break;  // 68h   data L1 cache, 32 KB, 4 ways, 64 byte lines, sectored
      case 0x1A:
        l2 = 96;
        break;  // code and data L2 cache, 96 KB, 6 ways, 64 byte lines (IA-64)
      case 0x22:
        l3 = 512;
        break;  // code and data L3 cache, 512 KB, 4 ways (!), 64 byte lines, dual-sectored
      case 0x23:
        l3 = 1024;
        break;  // code and data L3 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
      case 0x25:
        l3 = 2048;
        break;  // code and data L3 cache, 2048 KB, 8 ways, 64 byte lines, dual-sectored
      case 0x29:
        l3 = 4096;
        break;  // code and data L3 cache, 4096 KB, 8 ways, 64 byte lines, dual-sectored
      case 0x39:
        l2 = 128;
        break;  // code and data L2 cache, 128 KB, 4 ways, 64 byte lines, sectored
      case 0x3A:
        l2 = 192;
        break;  // code and data L2 cache, 192 KB, 6 ways, 64 byte lines, sectored
      case 0x3B:
        l2 = 128;
        break;  // code and data L2 cache, 128 KB, 2 ways, 64 byte lines, sectored
      case 0x3C:
        l2 = 256;
        break;  // code and data L2 cache, 256 KB, 4 ways, 64 byte lines, sectored
      case 0x3D:
        l2 = 384;
        break;  // code and data L2 cache, 384 KB, 6 ways, 64 byte lines, sectored
      case 0x3E:
        l2 = 512;
        break;  // code and data L2 cache, 512 KB, 4 ways, 64 byte lines, sectored
      case 0x40:
        l2 = 0;
        break;  // no integrated L2 cache (P6 core) or L3 cache (P4 core)
      case 0x41:
        l2 = 128;
        break;  // code and data L2 cache, 128 KB, 4 ways, 32 byte lines
      case 0x42:
        l2 = 256;
        break;  // code and data L2 cache, 256 KB, 4 ways, 32 byte lines
      case 0x43:
        l2 = 512;
        break;  // code and data L2 cache, 512 KB, 4 ways, 32 byte lines
      case 0x44:
        l2 = 1024;
        break;  // code and data L2 cache, 1024 KB, 4 ways, 32 byte lines
      case 0x45:
        l2 = 2048;
        break;  // code and data L2 cache, 2048 KB, 4 ways, 32 byte lines
      case 0x46:
        l3 = 4096;
        break;  // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines
      case 0x47:
        l3 = 8192;
        break;  // code and data L3 cache, 8192 KB, 8 ways, 64 byte lines
      case 0x48:
        l2 = 3072;
        break;  // code and data L2 cache, 3072 KB, 12 ways, 64 byte lines
      case 0x49:
        if (l2 != 0)
          l3 = 4096;
        else {
          check_for_p2_core2 = true;
          l3 = l2 = 4096;
        }
        break;  // code and data L3 cache, 4096 KB, 16 ways, 64 byte lines (P4) or L2 for core2
      case 0x4A:
        l3 = 6144;
        break;  // code and data L3 cache, 6144 KB, 12 ways, 64 byte lines
      case 0x4B:
        l3 = 8192;
        break;  // code and data L3 cache, 8192 KB, 16 ways, 64 byte lines
      case 0x4C:
        l3 = 12288;
        break;  // code and data L3 cache, 12288 KB, 12 ways, 64 byte lines
      case 0x4D:
        l3 = 16384;
        break;  // code and data L3 cache, 16384 KB, 16 ways, 64 byte lines
      case 0x4E:
        l2 = 6144;
        break;  // code and data L2 cache, 6144 KB, 24 ways, 64 byte lines
      case 0x78:
        l2 = 1024;
        break;  // code and data L2 cache, 1024 KB, 4 ways, 64 byte lines
      case 0x79:
        l2 = 128;
        break;  // code and data L2 cache, 128 KB, 8 ways, 64 byte lines, dual-sectored
      case 0x7A:
        l2 = 256;
        break;  // code and data L2 cache, 256 KB, 8 ways, 64 byte lines, dual-sectored
      case 0x7B:
        l2 = 512;
        break;  // code and data L2 cache, 512 KB, 8 ways, 64 byte lines, dual-sectored
      case 0x7C:
        l2 = 1024;
        break;  // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
      case 0x7D:
        l2 = 2048;
        break;  // code and data L2 cache, 2048 KB, 8 ways, 64 byte lines
      case 0x7E:
        l2 = 256;
        break;  // code and data L2 cache, 256 KB, 8 ways, 128 byte lines, sect. (IA-64)
      case 0x7F:
        l2 = 512;
        break;  // code and data L2 cache, 512 KB, 2 ways, 64 byte lines
      case 0x80:
        l2 = 512;
        break;  // code and data L2 cache, 512 KB, 8 ways, 64 byte lines
      case 0x81:
        l2 = 128;
        break;  // code and data L2 cache, 128 KB, 8 ways, 32 byte lines
      case 0x82:
        l2 = 256;
        break;  // code and data L2 cache, 256 KB, 8 ways, 32 byte lines
      case 0x83:
        l2 = 512;
        break;  // code and data L2 cache, 512 KB, 8 ways, 32 byte lines
      case 0x84:
        l2 = 1024;
        break;  // code and data L2 cache, 1024 KB, 8 ways, 32 byte lines
      case 0x85:
        l2 = 2048;
        break;  // code and data L2 cache, 2048 KB, 8 ways, 32 byte lines
      case 0x86:
        l2 = 512;
        break;  // code and data L2 cache, 512 KB, 4 ways, 64 byte lines
      case 0x87:
        l2 = 1024;
        break;  // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines
      case 0x88:
        l3 = 2048;
        break;  // code and data L3 cache, 2048 KB, 4 ways, 64 byte lines (IA-64)
      case 0x89:
        l3 = 4096;
        break;  // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines (IA-64)
      case 0x8A:
        l3 = 8192;
        break;  // code and data L3 cache, 8192 KB, 4 ways, 64 byte lines (IA-64)
      case 0x8D:
        l3 = 3072;
        break;  // code and data L3 cache, 3072 KB, 12 ways, 128 byte lines (IA-64)
 
      default:
        break;
    }
  }
  if (check_for_p2_core2 && l2 == l3) l3 = 0;
  l1 *= 1024;
  l2 *= 1024;
  l3 *= 1024;
}
 
inline void queryCacheSizes_intel(std::ptrdiff_t& l1, std::ptrdiff_t& l2, std::ptrdiff_t& l3, int max_std_funcs) {
  if (max_std_funcs >= 4)
    queryCacheSizes_intel_direct(l1, l2, l3);
  else if (max_std_funcs >= 2)
    queryCacheSizes_intel_codes(l1, l2, l3);
  else
    l1 = l2 = l3 = 0;
}
 
inline void queryCacheSizes_amd(std::ptrdiff_t& l1, std::ptrdiff_t& l2, std::ptrdiff_t& l3) {
  int abcd[4];
  abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
 
  // First query the max supported function.
  EIGEN_CPUID(abcd, 0x80000000, 0);
  if (static_cast<numext::uint32_t>(abcd[0]) >= static_cast<numext::uint32_t>(0x80000006)) {
    EIGEN_CPUID(abcd, 0x80000005, 0);
    l1 = (abcd[2] >> 24) * 1024;  // C[31:24] = L1 size in KB
    abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
    EIGEN_CPUID(abcd, 0x80000006, 0);
    l2 = (abcd[2] >> 16) * 1024;                                                 // C[31;16] = l2 cache size in KB
    l3 = static_cast<std::ptrdiff_t>((abcd[3] & 0xFFFC000) >> 18) * 512 * 1024;  // D[31;18] = l3 cache size in 512KB
  } else {
    l1 = l2 = l3 = 0;
  }
}
#endif
 
#ifdef EIGEN_CPU_CACHE_SYSFS

struct CpuCacheTopology {
  std::ptrdiff_t l1 = 0;
  std::ptrdiff_t l2 = 0;
  std::ptrdiff_t l3 = 0;
  std::ptrdiff_t l3_per_cpu = 0;
};

template <int Size>
inline bool readSysfsLine(const char* root, const char* relative, char (&value)[Size]) {
  char path[512];
  const int length = std::snprintf(path, sizeof(path), "%s/%s", root, relative);
  if (length <= 0 || length >= static_cast<int>(sizeof(path))) return false;
  const int fd = ::open(path, O_RDONLY | O_CLOEXEC);
  if (fd < 0) return false;
  const ssize_t bytes_read = ::read(fd, value, Size - 1);
  ::close(fd);
  if (bytes_read <= 0) return false;
  value[bytes_read] = '\0';
  char* newline = std::strchr(value, '\n');
  if (newline != nullptr) {
    newline[1] = '\0';
  }
  return true;
}

template <int Size>
inline bool readCpuCacheAttribute(const char* root, int cpu, int index, const char* name, char (&value)[Size]) {
  char relative[64];
  const int length = std::snprintf(relative, sizeof(relative), "cpu%d/cache/index%d/%s", cpu, index, name);
  return length > 0 && length < static_cast<int>(sizeof(relative)) && readSysfsLine(root, relative, value);
}

inline std::ptrdiff_t parseCpuCacheSize(const char* text) {
  char* suffix = nullptr;
  const std::ptrdiff_t value = std::strtol(text, &suffix, 10);
  if (value <= 0) return 0;
  // The kernel writes kibibytes ("%uK"), but only scale on an explicit unit: reading a bare byte
  // count as kibibytes would overstate a cache 1024x, which is much worse than the reverse.
  const std::ptrdiff_t multiplier = (*suffix == 'K' || *suffix == 'k')   ? 1024
                                    : (*suffix == 'M' || *suffix == 'm') ? 1024 * 1024
                                                                         : 1;
  return value * multiplier;
}

inline bool isCpuListTerminator(const char* text) { return *text == '\0' || *text == '\n' || *text == '\r'; }

template <typename Visitor>
inline bool parseCpuList(const char* text, Visitor&& visit) {
  if (isCpuListTerminator(text)) return false;
  // Far above the 8192 CPUs current kernels can number, so a larger id means the line is not a cpu list;
  // bounding it also keeps a caller that walks the ranges from visiting ids that cannot exist.
  const long max_cpu_id = 1 << 16;
  const char* cursor = text;
  for (;;) {
    char* end = nullptr;
    const long first = std::strtol(cursor, &end, 10);
    if (end == cursor || first < 0) return false;
    long last = first;
    if (*end == '-') {
      cursor = end + 1;
      last = std::strtol(cursor, &end, 10);
      if (end == cursor || last < first) return false;
    }
    if (last >= max_cpu_id) return false;
    visit(static_cast<int>(first), static_cast<int>(last));
    // A comma promises another range, so a list ending on one is malformed: going round the loop
    // lands on the terminator and fails the strtol above.
    if (*end == ',') {
      cursor = end + 1;
      continue;
    }
    // Anything other than a separator or the end of the line means the format is not what this
    // parser assumes.
    return isCpuListTerminator(end);
  }
}

inline int parseCpuListCount(const char* text) {
  int count = 0;
  return parseCpuList(text, [&count](int first, int last) { count += last - first + 1; }) ? count : 0;
}

inline CpuCacheTopology readCpuCacheTopologySysfs(const char* root, int cpu) {
  CpuCacheTopology topology;
  // One directory per cache, numbered contiguously from zero. The bound only guards a malformed
  // sysfs; it is far above what any current CPU reports.
  for (int index = 0; index < 16; ++index) {
    // A shared_cpu_list can be long on a large machine, and truncating it would undercount the
    // sharers and hand out too large a share.
    char value[512];
 
    if (!readCpuCacheAttribute(root, cpu, index, "level", value)) break;
    const long level = std::strtol(value, nullptr, 10);
    std::ptrdiff_t* target =
        level == 1 ? &topology.l1 : (level == 2 ? &topology.l2 : (level == 3 ? &topology.l3 : nullptr));
    if (target == nullptr || *target > 0) continue;
 
    // "Data", "Instruction", or "Unified". An instruction cache never holds the operands a product
    // blocks for, so it must not be mistaken for the L1 data cache.
    if (!readCpuCacheAttribute(root, cpu, index, "type", value) || value[0] == 'I') continue;
 
    if (!readCpuCacheAttribute(root, cpu, index, "size", value)) continue;
    const std::ptrdiff_t size = parseCpuCacheSize(value);
    if (size <= 0) continue;
    *target = size;
 
    if (level == 3 && readCpuCacheAttribute(root, cpu, index, "shared_cpu_list", value) &&
        std::strchr(value, '\n') != nullptr) {
      const int sharing = parseCpuListCount(value);
      if (sharing > 0) topology.l3_per_cpu = size / sharing;
    }
  }
  return topology;
}

inline std::ptrdiff_t smallerReportedCacheSize(std::ptrdiff_t a, std::ptrdiff_t b) {
  return a == 0 ? b : (b == 0 ? a : (std::min)(a, b));
}

template <typename IsAllowed>
inline CpuCacheTopology queryCpuCacheTopologySysfs(const char* root, IsAllowed&& is_allowed) {
  CpuCacheTopology topology;
  char online[512];
  if (!readSysfsLine(root, "online", online) || std::strchr(online, '\n') == nullptr) return topology;
  // Validate the whole line before acting on any range of it, so that a malformed list reads as "unknown".
  if (!parseCpuList(online, [](int, int) {})) return topology;
  parseCpuList(online, [&](int first, int last) {
    for (int cpu = first; cpu <= last; ++cpu) {
      if (!is_allowed(cpu)) continue;
      const CpuCacheTopology candidate = readCpuCacheTopologySysfs(root, cpu);
      topology.l1 = smallerReportedCacheSize(topology.l1, candidate.l1);
      topology.l2 = smallerReportedCacheSize(topology.l2, candidate.l2);
      topology.l3 = smallerReportedCacheSize(topology.l3, candidate.l3);
      topology.l3_per_cpu = smallerReportedCacheSize(topology.l3_per_cpu, candidate.l3_per_cpu);
    }
  });
  return topology;
}

inline CpuCacheTopology queryCpuCacheTopologySysfs(const char* root = "/sys/devices/system/cpu") {
#ifdef CPU_SETSIZE
  // The affinity API is a GNU extension that glibc, musl and bionic expose under _GNU_SOURCE, which g++ and
  // clang++ predefine for C++; CPU_SETSIZE is defined exactly when it is exposed. The query fails on a machine
  // with more CPU ids than cpu_set_t holds.
  cpu_set_t allowed;
  if (sched_getaffinity(0, sizeof(allowed), &allowed) == 0) {
    return queryCpuCacheTopologySysfs(root,
                                      [&allowed](int cpu) { return cpu < CPU_SETSIZE && CPU_ISSET(cpu, &allowed); });
  }
#endif
  return queryCpuCacheTopologySysfs(root, [](int) { return true; });
}
 
#endif  // EIGEN_CPU_CACHE_SYSFS

inline void queryCacheSizes(std::ptrdiff_t& l1, std::ptrdiff_t& l2, std::ptrdiff_t& l3, std::ptrdiff_t& l3_per_cpu) {
  l3_per_cpu = 0;
#ifdef EIGEN_CPUID
  int abcd[4];
  const int GenuineIntel[] = {0x756e6547, 0x49656e69, 0x6c65746e};
  const int AuthenticAMD[] = {0x68747541, 0x69746e65, 0x444d4163};
  const int AMDisbetter_[] = {0x69444d41, 0x74656273, 0x21726574};  // "AMDisbetter!"
  // Hygon Dhyana is a Zen-based joint-venture line that returns "HygonGenuine"
  // and shares AMD's CPUID layout for cache descriptors (AMD Family 17h).
  const int HygonGenuine[] = {0x6f677948, 0x6e65476e, 0x656e6975};  // "HygonGenuine"
 
  // identify the CPU vendor
  EIGEN_CPUID(abcd, 0x0, 0);
  int max_std_funcs = abcd[0];
  if (cpuid_is_vendor(abcd, GenuineIntel))
    queryCacheSizes_intel(l1, l2, l3, max_std_funcs);
  else if (cpuid_is_vendor(abcd, AuthenticAMD) || cpuid_is_vendor(abcd, AMDisbetter_) ||
           cpuid_is_vendor(abcd, HygonGenuine))
    queryCacheSizes_amd(l1, l2, l3);
  else
    // by default let's use Intel's API
    queryCacheSizes_intel(l1, l2, l3, max_std_funcs);
 
    // here is the list of other vendors:
    //   ||cpuid_is_vendor(abcd,"VIA VIA VIA ")
    //   ||cpuid_is_vendor(abcd,"CyrixInstead")
    //   ||cpuid_is_vendor(abcd,"CentaurHauls")
    //   ||cpuid_is_vendor(abcd,"GenuineTMx86")
    //   ||cpuid_is_vendor(abcd,"TransmetaCPU")
    //   ||cpuid_is_vendor(abcd,"RiseRiseRise")
    //   ||cpuid_is_vendor(abcd,"Geode by NSC")
    //   ||cpuid_is_vendor(abcd,"SiS SiS SiS ")
    //   ||cpuid_is_vendor(abcd,"UMC UMC UMC ")
    //   ||cpuid_is_vendor(abcd,"NexGenDriven")
#elif EIGEN_OS_MAC
  // On macOS (including Apple Silicon), use sysctlbyname to query cache sizes.
  // The sysctl values are 64-bit, so read into int64_t and convert.
  // For L1, prefer P-core (perflevel0) size since compute-heavy work like GEMM
  // is typically scheduled on performance cores. L1 is per-core so always safe.
  // For L2, use the generic hw.l2cachesize which is more conservative (reports
  // the smaller E-core cluster L2 on heterogeneous chips). The P-core L2 is
  // shared among all P-cores and would overestimate per-core capacity.
  {
    int64_t val = 0;
    std::size_t val_size = sizeof(val);
    l1 = -1;
    val_size = sizeof(val);
    if (sysctlbyname("hw.perflevel0.l1dcachesize", &val, &val_size, nullptr, 0) == 0 && val > 0)
      l1 = val;
    else {
      val_size = sizeof(val);
      if (sysctlbyname("hw.l1dcachesize", &val, &val_size, nullptr, 0) == 0) l1 = val;
    }
    l2 = -1;
    val_size = sizeof(val);
    if (sysctlbyname("hw.l2cachesize", &val, &val_size, nullptr, 0) == 0) l2 = val;
    l3 = -1;
    val_size = sizeof(val);
    if (sysctlbyname("hw.l3cachesize", &val, &val_size, nullptr, 0) == 0 && val > 0) l3 = val;
  }
#elif EIGEN_OS_UNIX && defined(_SC_LEVEL1_DCACHE_SIZE)
  // A glibc extension: POSIX specifies no cache queries, and musl defines none of these names.
  l1 = sysconf(_SC_LEVEL1_DCACHE_SIZE);
  l2 = sysconf(_SC_LEVEL2_CACHE_SIZE);
  l3 = sysconf(_SC_LEVEL3_CACHE_SIZE);
#else
  l1 = l2 = l3 = -1;
#endif
#ifdef EIGEN_CPU_CACHE_SYSFS
  // glibc answers the _SC_LEVEL*_CACHE_SIZE queries from CPUID and so only implements them on x86; every
  // other architecture gets 0, and musl has no such queries at all. Whatever the platform left unknown comes
  // from the topology Linux publishes on every architecture, as does the L3 share, so that all four numbers
  // describe the same CPUs.
  const CpuCacheTopology topology = queryCpuCacheTopologySysfs();
  if (l1 <= 0) l1 = topology.l1;
  if (l2 <= 0) l2 = topology.l2;
  if (l3 <= 0) l3 = topology.l3;
  l3_per_cpu = topology.l3_per_cpu;
#endif
}

inline void queryCacheSizes(std::ptrdiff_t& l1, std::ptrdiff_t& l2, std::ptrdiff_t& l3) {
  std::ptrdiff_t l3_per_cpu;
  queryCacheSizes(l1, l2, l3, l3_per_cpu);
}

inline std::ptrdiff_t queryL1CacheSize() {
  std::ptrdiff_t l1(-1), l2, l3;
  queryCacheSizes(l1, l2, l3);
  return l1;
}

inline std::ptrdiff_t queryTopLevelCacheSize() {
  std::ptrdiff_t l1, l2(-1), l3(-1);
  queryCacheSizes(l1, l2, l3);
  return (std::max)(l2, l3);
}

 
#if !defined(EIGEN_GPU_COMPILE_PHASE) && EIGEN_COMP_CXXVER >= 20 && defined(__cpp_lib_constexpr_dynamic_alloc) && \
    __cpp_lib_constexpr_dynamic_alloc >= 201907L
using std::construct_at;
#else
template <class T, class... Args>
EIGEN_DEVICE_FUNC T* construct_at(T* p, Args&&... args) {
  return ::new (const_cast<void*>(static_cast<const volatile void*>(p))) T(std::forward<Args>(args)...);
}
#endif

#if EIGEN_COMP_CXXVER >= 17
using std::destroy_at;
#else
template <class T>
EIGEN_DEVICE_FUNC void destroy_at(T* p) {
  p->~T();
}
#endif
 
// FIXME(rmlarsen): Work around missing linker symbol with msan on ARM.
#if !defined(EIGEN_DONT_ASSUME_ALIGNED) && __has_feature(memory_sanitizer) && (EIGEN_ARCH_ARM || EIGEN_ARCH_ARM64)
#define EIGEN_DONT_ASSUME_ALIGNED
#endif
 
#if !defined(EIGEN_DONT_ASSUME_ALIGNED) && defined(__cpp_lib_assume_aligned) && (__cpp_lib_assume_aligned >= 201811L)
template <std::size_t N, typename T>
EIGEN_DEVICE_FUNC constexpr T* assume_aligned(T* ptr) {
  return std::assume_aligned<N, T>(ptr);
}
#elif !defined(EIGEN_DONT_ASSUME_ALIGNED) && EIGEN_HAS_BUILTIN(__builtin_assume_aligned)
template <std::size_t N, typename T>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC T* assume_aligned(T* ptr) {
  return static_cast<T*>(__builtin_assume_aligned(ptr, N));
}
#else
template <std::size_t N, typename T>
EIGEN_DEVICE_FUNC constexpr T* assume_aligned(T* ptr) {
  return ptr;
}
#endif
 
}  // end namespace internal
 
}  // end namespace Eigen
 
#endif  // EIGEN_MEMORY_H