Eigen/src/Core/util/Constants.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) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2020, Arm Limited and Contributors
//
// 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/.

#ifndef EIGEN_CONSTANTS_H
#define EIGEN_CONSTANTS_H

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

namespace Eigen {

/** This value means that a positive quantity (e.g., a size) is not known at compile-time, and that instead the value is
 * stored in some runtime variable.
 *
 * Changing the value of Dynamic breaks the ABI, as Dynamic is often used as a template parameter for Matrix.
 */
constexpr int Dynamic = -1;

/** This value means that a signed quantity (e.g., a signed index) is not known at compile-time, and that instead its
 * value has to be specified at runtime.
 */
constexpr int DynamicIndex = 0xffffff;

/** This value means that the requested value is not defined.
 */
constexpr int Undefined = 0xfffffe;

/** This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>().
 * The value Infinity there means the L-infinity norm.
 */
constexpr int Infinity = -1;

/** This value means that the cost to evaluate an expression coefficient is either very expensive or
 * cannot be known at compile time.
 *
 * This value has to be positive to (1) simplify cost computation, and (2) allow to distinguish between a very expensive
 * and very very expensive expressions. It thus must also be large enough to make sure unrolling won't happen and that
 * sub expressions will be evaluated, but not too large to avoid overflow.
 */
constexpr int HugeCost = 10000;

/** \defgroup flags Flags
 * \ingroup Core_Module
 *
 * These are the possible bits which can be OR'ed to constitute the flags of a matrix or
 * expression.
 *
 * It is important to note that these flags are a purely compile-time notion. They are a compile-time property of
 * an expression type, implemented as enum's. They are not stored in memory at runtime, and they do not incur any
 * runtime overhead.
 *
 * \sa MatrixBase::Flags
 */

/** \ingroup flags
 *
 * for a matrix, this means that the storage order is row-major.
 * If this bit is not set, the storage order is column-major.
 * For an expression, this determines the storage order of
 * the matrix created by evaluation of that expression.
 * \sa \blank  \ref TopicStorageOrders */
constexpr unsigned int RowMajorBit = 0x1;

/** \ingroup flags
 * means the expression should be evaluated by the calling expression */
constexpr unsigned int EvalBeforeNestingBit = 0x2;

/** \ingroup flags
 * \deprecated
 * means the expression should be evaluated before any assignment */
EIGEN_DEPRECATED constexpr unsigned int EvalBeforeAssigningBit = 0x4;  // FIXME deprecated

/** \ingroup flags
 *
 * Short version: means the expression might be vectorized
 *
 * Long version: means that the coefficients can be handled by packets
 * and start at a memory location whose alignment meets the requirements
 * of the present CPU architecture for optimized packet access. In the fixed-size
 * case, there is the additional condition that it be possible to access all the
 * coefficients by packets (this implies the requirement that the size be a multiple of 16 bytes,
 * and that any nontrivial strides don't break the alignment). In the dynamic-size case,
 * there is no such condition on the total size and strides, so it might not be possible to access
 * all coeffs by packets.
 *
 * \note This bit can be set regardless of whether vectorization is actually enabled.
 *       To check for actual vectorizability, see \a ActualPacketAccessBit.
 */
constexpr unsigned int PacketAccessBit = 0x8;

#ifdef EIGEN_VECTORIZE
/** \ingroup flags
 *
 * If vectorization is enabled (EIGEN_VECTORIZE is defined) this constant
 * is set to the value \a PacketAccessBit.
 *
 * If vectorization is not enabled (EIGEN_VECTORIZE is not defined) this constant
 * is set to the value 0.
 */
constexpr unsigned int ActualPacketAccessBit = PacketAccessBit;
#else
constexpr unsigned int ActualPacketAccessBit = 0x0;
#endif

/** \ingroup flags
 *
 * Short version: means the expression can be seen as 1D vector.
 *
 * Long version: means that one can access the coefficients
 * of this expression by coeff(int), and coeffRef(int) in the case of a lvalue expression. These
 * index-based access methods are guaranteed
 * to not have to do any runtime computation of a (row, col)-pair from the index, so that it
 * is guaranteed that whenever it is available, index-based access is at least as fast as
 * (row,col)-based access. Expressions for which that isn't possible don't have the LinearAccessBit.
 *
 * If both PacketAccessBit and LinearAccessBit are set, then the
 * packets of this expression can be accessed by packet(int), and writePacket(int) in the case of a
 * lvalue expression.
 *
 * Typically, all vector expressions have the LinearAccessBit, but there is one exception:
 * Product expressions don't have it, because it would be troublesome for vectorization, even when the
 * Product is a vector expression. Thus, vector Product expressions allow index-based coefficient access but
 * not index-based packet access, so they don't have the LinearAccessBit.
 */
constexpr unsigned int LinearAccessBit = 0x10;

/** \ingroup flags
 *
 * Means the expression has a coeffRef() method, i.e. is writable as its individual coefficients are directly
 * addressable. This rules out read-only expressions.
 *
 * Note that DirectAccessBit and LvalueBit are mutually orthogonal, as there are examples of expression having one but
 * not the other: \li writable expressions that don't have a very simple memory layout as a strided array, have
 * LvalueBit but not DirectAccessBit \li Map-to-const expressions, for example Map<const Matrix>, have DirectAccessBit
 * but not LvalueBit
 *
 * Expressions having LvalueBit also have their coeff() method returning a const reference instead of returning a new
 * value.
 */
constexpr unsigned int LvalueBit = 0x20;

/** \ingroup flags
 *
 * Means that the underlying array of coefficients can be directly accessed as a plain strided array. The memory layout
 * of the array of coefficients must be exactly the natural one suggested by rows(), cols(),
 * outerStride(), innerStride(), and the RowMajorBit. This rules out expressions such as Diagonal, whose coefficients,
 * though referenceable, do not have such a regular memory layout.
 *
 * See the comment on LvalueBit for an explanation of how LvalueBit and DirectAccessBit are mutually orthogonal.
 */
constexpr unsigned int DirectAccessBit = 0x40;

/** \deprecated \ingroup flags
 *
 * means the first coefficient packet is guaranteed to be aligned.
 * An expression cannot have the AlignedBit without the PacketAccessBit flag.
 * In other words, this means we are allow to perform an aligned packet access to the first element regardless
 * of the expression kind:
 * \code
 * expression.packet<Aligned>(0);
 * \endcode
 */
EIGEN_DEPRECATED constexpr unsigned int AlignedBit = 0x80;

constexpr unsigned int NestByRefBit = 0x100;

/** \ingroup flags
 *
 * for an expression, this means that the storage order
 * can be either row-major or column-major.
 * The precise choice will be decided at evaluation time or when
 * combined with other expressions.
 * \sa \blank  \ref RowMajorBit, \ref TopicStorageOrders */
constexpr unsigned int NoPreferredStorageOrderBit = 0x200;

/** \ingroup flags
  *
  * Means that the underlying coefficients can be accessed through pointers to the sparse (un)compressed storage format,
  * that is, the expression provides:
  * \code
    inline const Scalar* valuePtr() const;
    inline const Index* innerIndexPtr() const;
    inline const Index* outerIndexPtr() const;
    inline const Index* innerNonZeroPtr() const;
    \endcode
  */
constexpr unsigned int CompressedAccessBit = 0x400;

// list of flags that are inherited by default
constexpr unsigned int HereditaryBits = RowMajorBit | EvalBeforeNestingBit;

/** \defgroup enums Enumerations
 * \ingroup Core_Module
 *
 * Various enumerations used in %Eigen. Many of these are used as template parameters.
 */

/** \ingroup enums
 * Enum containing possible values for the \c Mode or \c UpLo parameter of
 * MatrixBase::selfadjointView() and MatrixBase::triangularView(), and selfadjoint solvers. */
enum UpLoType {
  /** View matrix as a lower triangular matrix. */
  Lower = 0x1,
  /** View matrix as an upper triangular matrix. */
  Upper = 0x2,
  /** %Matrix has ones on the diagonal; to be used in combination with #Lower or #Upper. */
  UnitDiag = 0x4,
  /** %Matrix has zeros on the diagonal; to be used in combination with #Lower or #Upper. */
  ZeroDiag = 0x8,
  /** View matrix as a lower triangular matrix with ones on the diagonal. */
  UnitLower = UnitDiag | Lower,
  /** View matrix as an upper triangular matrix with ones on the diagonal. */
  UnitUpper = UnitDiag | Upper,
  /** View matrix as a lower triangular matrix with zeros on the diagonal. */
  StrictlyLower = ZeroDiag | Lower,
  /** View matrix as an upper triangular matrix with zeros on the diagonal. */
  StrictlyUpper = ZeroDiag | Upper,
  /** Used in BandMatrix and SelfAdjointView to indicate that the matrix is self-adjoint. */
  SelfAdjoint = 0x10,
  /** Used to support symmetric, non-selfadjoint, complex matrices. */
  Symmetric = 0x20
};

/** \ingroup enums
 * Enum for indicating whether a buffer is aligned or not. */
enum AlignmentType {
  Unaligned = 0,    /**< Data pointer has no specific alignment. */
  Aligned8 = 8,     /**< Data pointer is aligned on a 8 bytes boundary. */
  Aligned16 = 16,   /**< Data pointer is aligned on a 16 bytes boundary. */
  Aligned32 = 32,   /**< Data pointer is aligned on a 32 bytes boundary. */
  Aligned64 = 64,   /**< Data pointer is aligned on a 64 bytes boundary. */
  Aligned128 = 128, /**< Data pointer is aligned on a 128 bytes boundary. */
  AlignedMask = 255,
  Aligned = 16, /**< \deprecated Synonym for Aligned16. */
#if EIGEN_MAX_ALIGN_BYTES == 128
  AlignedMax = Aligned128
#elif EIGEN_MAX_ALIGN_BYTES == 64
  AlignedMax = Aligned64
#elif EIGEN_MAX_ALIGN_BYTES == 32
  AlignedMax = Aligned32
#elif EIGEN_MAX_ALIGN_BYTES == 16
  AlignedMax = Aligned16
#elif EIGEN_MAX_ALIGN_BYTES == 8
  AlignedMax = Aligned8
#elif EIGEN_MAX_ALIGN_BYTES == 0
  AlignedMax = Unaligned
#else
#error Invalid value for EIGEN_MAX_ALIGN_BYTES
#endif
};

/** \ingroup enums
 * Enum containing possible values for the \p Direction parameter of
 * Reverse, PartialReduxExpr and VectorwiseOp. */
enum DirectionType {
  /** For Reverse, all columns are reversed;
   * for PartialReduxExpr and VectorwiseOp, act on columns. */
  Vertical,
  /** For Reverse, all rows are reversed;
   * for PartialReduxExpr and VectorwiseOp, act on rows. */
  Horizontal,
  /** For Reverse, both rows and columns are reversed;
   * not used for PartialReduxExpr and VectorwiseOp. */
  BothDirections
};

/** \internal \ingroup enums
 * Enum to specify how to traverse the entries of a matrix. */
enum TraversalType {
  /** \internal Default traversal, no vectorization, no index-based access */
  DefaultTraversal,
  /** \internal No vectorization, use index-based access to have only one for loop instead of 2 nested loops */
  LinearTraversal,
  /** \internal Equivalent to a slice vectorization for fixed-size matrices having good alignment
   * and good size */
  InnerVectorizedTraversal,
  /** \internal Vectorization path using a single loop plus scalar loops for the
   * unaligned boundaries */
  LinearVectorizedTraversal,
  /** \internal Generic vectorization path using one vectorized loop per row/column with some
   * scalar loops to handle the unaligned boundaries */
  SliceVectorizedTraversal,
  /** \internal Special case to properly handle incompatible scalar types or other defecting cases*/
  InvalidTraversal,
  /** \internal Evaluate all entries at once */
  AllAtOnceTraversal
};

/** \internal \ingroup enums
 * Enum to specify whether to unroll loops when traversing over the entries of a matrix. */
enum UnrollingType {
  /** \internal Do not unroll loops. */
  NoUnrolling,
  /** \internal Unroll only the inner loop, but not the outer loop. */
  InnerUnrolling,
  /** \internal Unroll both the inner and the outer loop. If there is only one loop,
   * because linear traversal is used, then unroll that loop. */
  CompleteUnrolling
};

/** \internal \ingroup enums
 * Enum to specify whether to use the default (built-in) implementation or the specialization. */
enum SpecializedType { Specialized, BuiltIn };

/** \ingroup enums
 * Enum containing possible values for the \p Options_ template parameter of
 * Matrix, Array and BandMatrix. */
enum StorageOptions {
  /** Storage order is column major (see \ref TopicStorageOrders). */
  ColMajor = 0,
  /** Storage order is row major (see \ref TopicStorageOrders). */
  RowMajor = 0x1,  // it is only a coincidence that this is equal to RowMajorBit -- don't rely on that
  /** Align the matrix itself if it is vectorizable fixed-size */
  AutoAlign = 0,
  /** Don't require alignment for the matrix itself (the array of coefficients, if dynamically allocated, may still be requested to be aligned) */ // FIXME --- clarify the situation
  DontAlign = 0x2
};

/** \ingroup enums
 * Enum for specifying whether to apply or solve on the left or right. */
enum SideType {
  /** Apply transformation on the left. */
  OnTheLeft = 1,
  /** Apply transformation on the right. */
  OnTheRight = 2
};

/** \ingroup enums
 * Enum for specifying NaN-propagation behavior, e.g. for coeff-wise min/max. */
enum NaNPropagationOptions {
  /**  Implementation defined behavior if NaNs are present. */
  PropagateFast = 0,
  /**  Always propagate NaNs. */
  PropagateNaN,
  /**  Always propagate not-NaNs. */
  PropagateNumbers
};

/* the following used to be written as:
 *
 *   struct NoChange_t {};
 *   namespace {
 *     EIGEN_UNUSED NoChange_t NoChange;
 *   }
 *
 * on the ground that it feels dangerous to disambiguate overloaded functions on enum/integer types.
 * However, this leads to "variable declared but never referenced" warnings on Intel Composer XE,
 * and we do not know how to get rid of them (bug 450).
 */

enum NoChange_t { NoChange };
enum Sequential_t { Sequential };
enum Default_t { Default };

/** \internal \ingroup enums
 * Used in AmbiVector. */
enum AmbiVectorMode { IsDense = 0, IsSparse };

/** \ingroup enums
 * Used as template parameter in DenseCoeffBase and MapBase to indicate
 * which accessors should be provided. */
enum AccessorLevels {
  /** Read-only access via a member function. */
  ReadOnlyAccessors,
  /** Read/write access via member functions. */
  WriteAccessors,
  /** Direct read-only access to the coefficients. */
  DirectAccessors,
  /** Direct read/write access to the coefficients. */
  DirectWriteAccessors
};

/** \ingroup enums
 * Enum with options to give to various decompositions. */
enum DecompositionOptions {
  /** \internal Not used (meant for LDLT?). */
  Pivoting = 0x01,
  /** \internal Not used (meant for LDLT?). */
  NoPivoting = 0x02,
  /** Used in JacobiSVD to indicate that the square matrix U is to be computed. */
  ComputeFullU = 0x04,
  /** Used in JacobiSVD to indicate that the thin matrix U is to be computed. */
  ComputeThinU = 0x08,
  /** Used in JacobiSVD to indicate that the square matrix V is to be computed. */
  ComputeFullV = 0x10,
  /** Used in JacobiSVD to indicate that the thin matrix V is to be computed. */
  ComputeThinV = 0x20,
  /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
   * that only the eigenvalues are to be computed and not the eigenvectors. */
  EigenvaluesOnly = 0x40,
  /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
   * that both the eigenvalues and the eigenvectors are to be computed. */
  ComputeEigenvectors = 0x80,
  /** \internal */
  EigVecMask = EigenvaluesOnly | ComputeEigenvectors,
  /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
   * solve the generalized eigenproblem \f$ Ax = \lambda B x \f$. */
  Ax_lBx = 0x100,
  /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
   * solve the generalized eigenproblem \f$ ABx = \lambda x \f$. */
  ABx_lx = 0x200,
  /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
   * solve the generalized eigenproblem \f$ BAx = \lambda x \f$. */
  BAx_lx = 0x400,
  /** \internal */
  GenEigMask = Ax_lBx | ABx_lx | BAx_lx
};

/** \ingroup enums
 * Possible values for the \p QRPreconditioner template parameter of JacobiSVD. */
enum QRPreconditioners {
  /** Use a QR decomposition with column pivoting as the first step. */
  ColPivHouseholderQRPreconditioner = 0x0,
  /** Do not specify what is to be done if the SVD of a non-square matrix is asked for. */
  NoQRPreconditioner = 0x40,
  /** Use a QR decomposition without pivoting as the first step. */
  HouseholderQRPreconditioner = 0x80,
  /** Use a QR decomposition with full pivoting as the first step. */
  FullPivHouseholderQRPreconditioner = 0xC0,
  /** Used to disable the QR Preconditioner in BDCSVD. */
  DisableQRDecomposition = NoQRPreconditioner
};

#ifdef Success
#error The preprocessor symbol 'Success' is defined, possibly by the X11 header file X.h
#endif

/** \ingroup enums
 * Enum for reporting the status of a computation. */
enum ComputationInfo {
  /** Computation was successful. */
  Success = 0,
  /** The provided data did not satisfy the prerequisites. */
  NumericalIssue = 1,
  /** Iterative procedure did not converge. */
  NoConvergence = 2,
  /** The inputs are invalid, or the algorithm has been improperly called.
   * When assertions are enabled, such errors trigger an assert. */
  InvalidInput = 3
};

/** \ingroup enums
 * Enum used to specify how a particular transformation is stored in a matrix.
 * \sa Transform, Hyperplane::transform(). */
enum TransformTraits {
  /** Transformation is an isometry. */
  Isometry = 0x1,
  /** Transformation is an affine transformation stored as a (Dim+1)^2 matrix whose last row is
   * assumed to be [0 ... 0 1]. */
  Affine = 0x2,
  /** Transformation is an affine transformation stored as a (Dim) x (Dim+1) matrix. */
  AffineCompact = 0x10 | Affine,
  /** Transformation is a general projective transformation stored as a (Dim+1)^2 matrix. */
  Projective = 0x20
};

/** \internal \ingroup enums
 * Enum used to choose between implementation depending on the computer architecture. */
namespace Architecture {
enum Type {
  Generic = 0x0,
  SSE = 0x1,
  AltiVec = 0x2,
  VSX = 0x3,
  NEON = 0x4,
  MSA = 0x5,
  SVE = 0x6,
  HVX = 0x7,
  LSX = 0x8,
  RVV10 = 0x9,
#if defined EIGEN_VECTORIZE_SSE
  Target = SSE
#elif defined EIGEN_VECTORIZE_ALTIVEC
  Target = AltiVec
#elif defined EIGEN_VECTORIZE_VSX
  Target = VSX
#elif defined EIGEN_VECTORIZE_NEON
  Target = NEON
#elif defined EIGEN_VECTORIZE_SVE
  Target = SVE
#elif defined EIGEN_VECTORIZE_MSA
  Target = MSA
#elif defined EIGEN_VECTORIZE_HVX
  Target = HVX
#elif defined EIGEN_VECTORIZE_LSX
  Target = LSX
#elif defined EIGEN_VECTORIZE_RVV10
  Target = RVV10
#else
  Target = Generic
#endif
};
}  // namespace Architecture

/** \internal \ingroup enums
 * Enum used as template parameter in Product and product evaluators. */
enum ProductImplType {
  DefaultProduct = 0,
  LazyProduct,
  AliasFreeProduct,
  CoeffBasedProductMode,
  LazyCoeffBasedProductMode,
  OuterProduct,
  InnerProduct,
  GemvProduct,
  GemmProduct
};

/** \internal \ingroup enums
 * Enum used in experimental parallel implementation. */
enum Action { GetAction, SetAction };

/** The type used to identify a dense storage. */
struct Dense {};

/** The type used to identify a general sparse storage. */
struct Sparse {};

/** The type used to identify a general solver (factored) storage. */
struct SolverStorage {};

/** The type used to identify a permutation storage. */
struct PermutationStorage {};

/** The type used to identify a permutation storage. */
struct TranspositionsStorage {};

/** The type used to identify a matrix expression */
struct MatrixXpr {};

/** The type used to identify an array expression */
struct ArrayXpr {};

// An evaluator must define its shape. By default, it can be one of the following:
struct DenseShape {
  static std::string debugName() { return "DenseShape"; }
};
struct SolverShape {
  static std::string debugName() { return "SolverShape"; }
};
struct HomogeneousShape {
  static std::string debugName() { return "HomogeneousShape"; }
};
struct DiagonalShape {
  static std::string debugName() { return "DiagonalShape"; }
};
struct SkewSymmetricShape {
  static std::string debugName() { return "SkewSymmetricShape"; }
};
struct BandShape {
  static std::string debugName() { return "BandShape"; }
};
struct TriangularShape {
  static std::string debugName() { return "TriangularShape"; }
};
struct SelfAdjointShape {
  static std::string debugName() { return "SelfAdjointShape"; }
};
struct PermutationShape {
  static std::string debugName() { return "PermutationShape"; }
};
struct TranspositionsShape {
  static std::string debugName() { return "TranspositionsShape"; }
};
struct SparseShape {
  static std::string debugName() { return "SparseShape"; }
};

namespace internal {

// random access iterators based on coeff*() accessors.
struct IndexBased {};

// evaluator based on iterators to access coefficients.
struct IteratorBased {};

/** \internal
 * Constants for comparison functors
 */
enum ComparisonName : unsigned int {
  cmp_EQ = 0,
  cmp_LT = 1,
  cmp_LE = 2,
  cmp_UNORD = 3,
  cmp_NEQ = 4,
  cmp_GT = 5,
  cmp_GE = 6
};
}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_CONSTANTS_H