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 // 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
 
 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.
   */
 const 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.
   */
 const int DynamicIndex = 0xffffff;
 
 /** This value means that the increment to go from one value to another in a sequence is not constant for each step.
   */
 const int UndefinedIncr = 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.
   */
 const 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.
   */
 const 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 */
 const unsigned int RowMajorBit = 0x1;
 
 /** \ingroup flags
   * means the expression should be evaluated by the calling expression */
 const unsigned int EvalBeforeNestingBit = 0x2;
 
 /** \ingroup flags
   * \deprecated
   * means the expression should be evaluated before any assignment */
 EIGEN_DEPRECATED
 const 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.
   */
 const 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.
   */
 const unsigned int ActualPacketAccessBit = PacketAccessBit;
 #else
 const 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.
   */
 const 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 note
   * 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.
   */
 const 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 referencable, do not have such a regular memory layout.
   *
   * See the comment on LvalueBit for an explanation of how LvalueBit and DirectAccessBit are mutually orthogonal.
   */
 const 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 const unsigned int AlignedBit = 0x80;
 
 const 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 */
 const 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
   */
 const unsigned int CompressedAccessBit = 0x400;
 
 
 // list of flags that are inherited by default
 const 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 {
   /** Do not specify what is to be done if the SVD of a non-square matrix is asked for. */
   NoQRPreconditioner,
   /** Use a QR decomposition without pivoting as the first step. */
   HouseholderQRPreconditioner,
   /** Use a QR decomposition with column pivoting as the first step. */
   ColPivHouseholderQRPreconditioner,
   /** Use a QR decomposition with full pivoting as the first step. */
   FullPivHouseholderQRPreconditioner
 };
 
 #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,
 #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
 #else
     Target = Generic
 #endif
   };
 }
 
 /** \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 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 {
   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

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