ceed.h

/// Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
/// the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
/// reserved. See files LICENSE and NOTICE for details.
///
/// This file is part of CEED, a collection of benchmarks, miniapps, software
/// libraries and APIs for efficient high-order finite element and spectral
/// element discretizations for exascale applications. For more information and
/// source code availability see http://github.com/ceed.
///
/// The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
/// a collaborative effort of two U.S. Department of Energy organizations (Office
/// of Science and the National Nuclear Security Administration) responsible for
/// the planning and preparation of a capable exascale ecosystem, including
/// software, applications, hardware, advanced system engineering and early
/// testbed platforms, in support of the nation's exascale computing imperative.

/// @file
/// Public header for user and utility components of libCEED
#ifndef _ceed_h
#define _ceed_h

/// @defgroup Ceed Ceed: core components
/// @defgroup CeedVector CeedVector: storing and manipulating vectors
/// @defgroup CeedElemRestriction CeedElemRestriction: restriction from local vectors to elements
/// @defgroup CeedBasis CeedBasis: fully discrete finite element-like objects
/// @defgroup CeedQFunction CeedQFunction: independent operations at quadrature points
/// @defgroup CeedOperator CeedOperator: composed FE-type operations on vectors
///
/// @page FunctionCategories libCEED: Types of Functions
///    libCEED provides three different header files depending upon the type of
///    functions a user requires.
/// @section Utility Utility Functions
///    These functions are intended general utilities that may be useful to
///    libCEED developers and users. These functions can generally be found in
///    "ceed.h".
/// @section User User Functions
///    These functions are intended to be used by general users of libCEED
///    and can generally be found in "ceed.h".
/// @section Advanced Advanced Functions
///    These functions are intended to be used by advanced users of libCEED
///    and can generally be found in "ceed.h".
/// @section Backend Backend Developer Functions
///    These functions are intended to be used by backend developers of
///    libCEED and can generally be found in "ceed-backend.h".
/// @section Developer Library Developer Functions
///    These functions are intended to be used by library developers of
///    libCEED and can generally be found in "ceed-impl.h".

/**
  CEED_EXTERN is used in this header to denote all publicly visible symbols.

  No other file should declare publicly visible symbols, thus it should never be
  used outside ceed.h.
 */
#ifdef __cplusplus
#  define CEED_EXTERN extern "C"
#else
#  define CEED_EXTERN extern
#endif

/**
  @ingroup CeedQFunction
  This macro populates the correct function annotations for User QFunction
    source for code generation backends or populates default values for CPU
    backends. It also creates a variable `name_loc` populated with the correct
    source path for creating the respective User QFunction.
**/
#ifndef CEED_QFUNCTION
#define CEED_QFUNCTION(name) \
  static const char name ## _loc[] = __FILE__ ":" #name;        \
  static int name
#endif

/**
  @ingroup CeedQFunction
  This macro populates the correct function annotations for User QFunction
    helper function source for code generation backends or populates default
    values for CPU backends.
**/
#ifndef CEED_QFUNCTION_HELPER
#define CEED_QFUNCTION_HELPER static inline
#endif

/**
  @ingroup CeedQFunction
  Using VLA syntax to reshape User QFunction inputs and outputs can make
    user code more readable. VLA is a C99 feature that is not supported by
    the C++ dialect used by CUDA. This macro allows users to use the VLA
    syntax with the CUDA backends.
**/
#ifndef CEED_Q_VLA
#  define CEED_Q_VLA Q
#endif

/**
  @ingroup Ceed
  This macro provides the appropriate SIMD Pragma for the compilation
    environment. Code generation backends may redefine this macro, as needed.
**/
#ifndef CeedPragmaSIMD
#  if defined(__INTEL_COMPILER)
#    define CeedPragmaSIMD _Pragma("vector")
// Cannot use Intel pragma ivdep because it miscompiles unpacking symmetric tensors, as in
// Poisson2DApply, where the SIMD loop body contains temporaries such as the following.
//
//     const CeedScalar dXdxdXdxT[2][2] = {{qd[i+0*Q], qd[i+2*Q]},
//                                         {qd[i+2*Q], qd[i+1*Q]}};
//     for (int j=0; j<2; j++)
//        vg[i+j*Q] = (du[0] * dXdxdXdxT[0][j] + du[1] * dXdxdXdxT[1][j]);
//
// Miscompilation with pragma ivdep observed with icc (ICC) 19.0.5.281 20190815
// at -O2 and above.
#  elif defined(__GNUC__) && __GNUC__ >= 5
#    define CeedPragmaSIMD _Pragma("GCC ivdep")
#  elif defined(_OPENMP) && _OPENMP >= 201307 // OpenMP-4.0 (July, 2013)
#    define CeedPragmaSIMD _Pragma("omp simd")
#  else
#    define CeedPragmaSIMD
#  endif
#endif

#include <stdint.h>
#include <stdarg.h>
#include <stdio.h>
#include <stdbool.h>

/// Integer type, used for indexing
/// @ingroup Ceed
typedef int32_t CeedInt;

/// Scalar (floating point) types
///
/// @ingroup Ceed
typedef enum {
  /// Single precision
  CEED_SCALAR_FP32,
  /// Double precision
  CEED_SCALAR_FP64
} CeedScalarType;
/// Base scalar type for the library to use: change which header is
/// included to change the precision.
#include "ceed-f64.h"

/// Library context created by CeedInit()
/// @ingroup CeedUser
typedef struct Ceed_private *Ceed;
/// Non-blocking Ceed interfaces return a CeedRequest.
/// To perform an operation immediately, pass \ref CEED_REQUEST_IMMEDIATE instead.
/// @ingroup CeedUser
typedef struct CeedRequest_private *CeedRequest;
/// Handle for vectors over the field \ref CeedScalar
/// @ingroup CeedVectorUser
typedef struct CeedVector_private *CeedVector;
/// Handle for object describing restriction to elements
/// @ingroup CeedElemRestrictionUser
typedef struct CeedElemRestriction_private *CeedElemRestriction;
/// Handle for object describing discrete finite element evaluations
/// @ingroup CeedBasisUser
typedef struct CeedBasis_private *CeedBasis;
/// Handle for object describing CeedQFunction fields
/// @ingroup CeedQFunctionBackend
typedef struct CeedQFunctionField_private *CeedQFunctionField;
/// Handle for object describing functions evaluated independently at quadrature points
/// @ingroup CeedQFunctionUser
typedef struct CeedQFunction_private *CeedQFunction;
/// Handle for object describing CeedOperator fields
/// @ingroup CeedOperatorBackend
typedef struct CeedOperatorField_private *CeedOperatorField;
/// Handle for object describing context data for CeedQFunctions
/// @ingroup CeedQFunctionUser
typedef struct CeedQFunctionContext_private *CeedQFunctionContext;
/// Handle for object describing registered fields for CeedQFunctionContext
/// @ingroup CeedQFunctionUser
typedef struct CeedContextFieldLabel_private *CeedContextFieldLabel;
/// Handle for object describing FE-type operators acting on vectors
///
/// Given an element restriction \f$E\f$, basis evaluator \f$B\f$, and
///   quadrature function\f$f\f$, a CeedOperator expresses operations of the form
///   $$ E^T B^T f(B E u) $$
///   acting on the vector \f$u\f$.
/// @ingroup CeedOperatorUser
typedef struct CeedOperator_private *CeedOperator;

CEED_EXTERN int CeedRegistryGetList(size_t *n, char ***const resources, CeedInt **array);
CEED_EXTERN int CeedInit(const char *resource, Ceed *ceed);
CEED_EXTERN int CeedReferenceCopy(Ceed ceed, Ceed *ceed_copy);
CEED_EXTERN int CeedGetResource(Ceed ceed, const char **resource);
CEED_EXTERN int CeedIsDeterministic(Ceed ceed, bool *is_deterministic);
CEED_EXTERN int CeedView(Ceed ceed, FILE *stream);
CEED_EXTERN int CeedDestroy(Ceed *ceed);

CEED_EXTERN int CeedErrorImpl(Ceed, const char *, int, const char *, int,
                              const char *, ...);
/// Raise an error on ceed object
///
/// @param ceed Ceed library context or NULL
/// @param ecode Error code (int)
/// @param ... printf-style format string followed by arguments as needed
///
/// @ingroup Ceed
/// @sa CeedSetErrorHandler()
#if defined(__clang__)
/// Use nonstandard ternary to convince the compiler/clang-tidy that this
/// function never returns zero.
#  define CeedError(ceed, ecode, ...)                                     \
  (CeedErrorImpl((ceed), __FILE__, __LINE__, __func__, (ecode), __VA_ARGS__), (ecode))
#else
#  define CeedError(ceed, ecode, ...)                                     \
  CeedErrorImpl((ceed), __FILE__, __LINE__, __func__, (ecode), __VA_ARGS__) ?: (ecode)
#endif

/// Ceed error handlers
CEED_EXTERN int CeedErrorReturn(Ceed, const char *, int, const char *, int,
                                const char *, va_list *);
CEED_EXTERN int CeedErrorStore(Ceed, const char *, int, const char *, int,
                               const char *, va_list *);
CEED_EXTERN int CeedErrorAbort(Ceed, const char *, int, const char *, int,
                               const char *, va_list *);
CEED_EXTERN int CeedErrorExit(Ceed, const char *, int, const char *, int,
                              const char *, va_list *);
typedef int (*CeedErrorHandler)(Ceed, const char *, int,
                                const char *, int, const char *,
                                va_list *);
CEED_EXTERN int CeedSetErrorHandler(Ceed ceed, CeedErrorHandler eh);
CEED_EXTERN int CeedGetErrorMessage(Ceed, const char **err_msg);
CEED_EXTERN int CeedResetErrorMessage(Ceed, const char **err_msg);

/// libCEED library version numbering
/// @ingroup Ceed
#define CEED_VERSION_MAJOR 0
#define CEED_VERSION_MINOR 9
#define CEED_VERSION_PATCH 0
#define CEED_VERSION_RELEASE false

/// Compile-time check that the the current library version is at least as
/// recent as the specified version. This macro is typically used in
/// @code
/// #if CEED_VERSION_GE(0, 8, 0)
///   code path that needs at least 0.8.0
/// #else
///   fallback code for older versions
/// #endif
/// @endcode
///
/// A non-release version always compares as positive infinity.
///
/// @param major   Major version
/// @param minor   Minor version
/// @param patch   Patch (subminor) version
///
/// @ingroup Ceed
/// @sa CeedGetVersion()
#define CEED_VERSION_GE(major, minor, patch)                                   \
  (!CEED_VERSION_RELEASE ||                                                    \
   (CEED_VERSION_MAJOR > major ||                                              \
    (CEED_VERSION_MAJOR == major &&                                            \
     (CEED_VERSION_MINOR > minor ||                                            \
      (CEED_VERSION_MINOR == minor && CEED_VERSION_PATCH >= patch)))))

CEED_EXTERN int CeedGetVersion(int *major, int *minor, int *patch,
                               bool *release);

CEED_EXTERN int CeedGetScalarType(CeedScalarType *scalar_type);

/// Ceed Errors
///
/// This enum is used to specify the type of error returned by a function.
/// A zero error code is success, negative error codes indicate terminal errors
/// and positive error codes indicate nonterminal errors. With nonterminal errors
/// the object state has not been modifiend, but with terminal errors the object
/// data is likely modified or corrupted.
/// @ingroup Ceed
typedef enum {
  /// Success error code
  CEED_ERROR_SUCCESS      = 0,
  /// Minor error, generic
  CEED_ERROR_MINOR        = 1,
  /// Minor error, dimension mismatch in inputs
  CEED_ERROR_DIMENSION    = 2,
  /// Minor error, incomplete object setup
  CEED_ERROR_INCOMPLETE   = 3,
  /// Minor error, incompatible arguments/configuration
  CEED_ERROR_INCOMPATIBLE = 4,
  /// Minor error, access lock problem
  CEED_ERROR_ACCESS       = 5,
  /// Major error, generic
  CEED_ERROR_MAJOR        = -1,
  /// Major error, internal backend error
  CEED_ERROR_BACKEND      = -2,
  /// Major error, operation unsupported by current backend
  CEED_ERROR_UNSUPPORTED  = -3,
} CeedErrorType;
CEED_EXTERN const char *const *CeedErrorTypes;

/// Specify memory type
///
/// Many Ceed interfaces take or return pointers to memory.  This enum is used to
/// specify where the memory being provided or requested must reside.
/// @ingroup Ceed
typedef enum {
  /// Memory resides on the host
  CEED_MEM_HOST,
  /// Memory resides on a device (corresponding to \ref Ceed resource)
  CEED_MEM_DEVICE,
} CeedMemType;
CEED_EXTERN const char *const CeedMemTypes[];

CEED_EXTERN int CeedGetPreferredMemType(Ceed ceed, CeedMemType *type);

/// Conveys ownership status of arrays passed to Ceed interfaces.
/// @ingroup Ceed
typedef enum {
  /// Implementation will copy the values and not store the passed pointer.
  CEED_COPY_VALUES,
  /// Implementation can use and modify the data provided by the user, but does
  /// not take ownership.
  CEED_USE_POINTER,
  /// Implementation takes ownership of the pointer and will free using
  /// CeedFree() when done using it.  The user should not assume that the
  /// pointer remains valid after ownership has been transferred.  Note that
  /// arrays allocated using C++ operator new or other allocators cannot
  /// generally be freed using CeedFree().  CeedFree() is capable of freeing any
  /// memory that can be freed using free(3).
  CEED_OWN_POINTER,
} CeedCopyMode;
CEED_EXTERN const char *const CeedCopyModes[];

/// Denotes type of vector norm to be computed
/// @ingroup CeedVector
typedef enum {
  /// L_1 norm: sum_i |x_i|
  CEED_NORM_1,
  /// L_2 norm: sqrt(sum_i |x_i|^2)
  CEED_NORM_2,
  /// L_Infinity norm: max_i |x_i|
  CEED_NORM_MAX,
} CeedNormType;

CEED_EXTERN int CeedVectorCreate(Ceed ceed, CeedInt len, CeedVector *vec);
CEED_EXTERN int CeedVectorReferenceCopy(CeedVector vec, CeedVector *vec_copy);
CEED_EXTERN int CeedVectorSetArray(CeedVector vec, CeedMemType mem_type,
                                   CeedCopyMode copy_mode, CeedScalar *array);
CEED_EXTERN int CeedVectorSetValue(CeedVector vec, CeedScalar value);
CEED_EXTERN int CeedVectorSyncArray(CeedVector vec, CeedMemType mem_type);
CEED_EXTERN int CeedVectorTakeArray(CeedVector vec, CeedMemType mem_type,
                                    CeedScalar **array);
CEED_EXTERN int CeedVectorGetArray(CeedVector vec, CeedMemType mem_type,
                                   CeedScalar **array);
CEED_EXTERN int CeedVectorGetArrayRead(CeedVector vec, CeedMemType mem_type,
                                       const CeedScalar **array);
CEED_EXTERN int CeedVectorGetArrayWrite(CeedVector vec, CeedMemType mem_type,
                                        CeedScalar **array);
CEED_EXTERN int CeedVectorRestoreArray(CeedVector vec, CeedScalar **array);
CEED_EXTERN int CeedVectorRestoreArrayRead(CeedVector vec,
    const CeedScalar **array);
CEED_EXTERN int CeedVectorNorm(CeedVector vec, CeedNormType type,
                               CeedScalar *norm);
CEED_EXTERN int CeedVectorScale(CeedVector x, CeedScalar alpha);
CEED_EXTERN int CeedVectorAXPY(CeedVector y, CeedScalar alpha, CeedVector x);
CEED_EXTERN int CeedVectorPointwiseMult(CeedVector w, CeedVector x, CeedVector y);
CEED_EXTERN int CeedVectorReciprocal(CeedVector vec);
CEED_EXTERN int CeedVectorView(CeedVector vec, const char *fp_fmt, FILE *stream);
CEED_EXTERN int CeedVectorGetCeed(CeedVector vec, Ceed *ceed);
CEED_EXTERN int CeedVectorGetLength(CeedVector vec, CeedInt *length);
CEED_EXTERN int CeedVectorDestroy(CeedVector *vec);

CEED_EXTERN CeedRequest *const CEED_REQUEST_IMMEDIATE;
CEED_EXTERN CeedRequest *const CEED_REQUEST_ORDERED;
CEED_EXTERN int CeedRequestWait(CeedRequest *req);

/// Argument for CeedOperatorSetField that vector is collocated with
/// quadrature points, used with QFunction eval mode CEED_EVAL_NONE
/// or CEED_EVAL_INTERP only, not with CEED_EVAL_GRAD, CEED_EVAL_DIV,
/// or CEED_EVAL_CURL
/// @ingroup CeedBasis
CEED_EXTERN const CeedBasis CEED_BASIS_COLLOCATED;

/// Argument for CeedOperatorSetField to use active input or output
/// @ingroup CeedVector
CEED_EXTERN const CeedVector CEED_VECTOR_ACTIVE;

/// Argument for CeedOperatorSetField to use no vector, used with
/// qfunction input with eval mode CEED_EVAL_WEIGHT
/// @ingroup CeedVector
CEED_EXTERN const CeedVector CEED_VECTOR_NONE;

/// Argument for CeedOperatorSetField to use no ElemRestriction, only used with
/// eval mode CEED_EVAL_WEIGHT.
/// @ingroup CeedElemRestriction
CEED_EXTERN const CeedElemRestriction CEED_ELEMRESTRICTION_NONE;

/// Argument for CeedOperatorCreate that QFunction is not created by user.
/// Only used for QFunctions dqf and dqfT. If implemented, a backend may
/// attempt to provide the action of these QFunctions.
/// @ingroup CeedQFunction
CEED_EXTERN const CeedQFunction CEED_QFUNCTION_NONE;

/// Denotes whether a linear transformation or its transpose should be applied
/// @ingroup CeedBasis
typedef enum {
  /// Apply the linear transformation
  CEED_NOTRANSPOSE,
  /// Apply the transpose
  CEED_TRANSPOSE
} CeedTransposeMode;
CEED_EXTERN const char *const CeedTransposeModes[];

/// Argument for CeedElemRestrictionCreateStrided that L-vector is in
/// the Ceed backend's preferred layout. This argument should only be used
/// with vectors created by a Ceed backend.
/// @ingroup CeedElemRestriction
CEED_EXTERN const CeedInt CEED_STRIDES_BACKEND[3];

CEED_EXTERN int CeedElemRestrictionCreate(Ceed ceed, CeedInt num_elem,
    CeedInt elem_size, CeedInt num_comp, CeedInt comp_stride, CeedInt l_size,
    CeedMemType mem_type, CeedCopyMode copy_mode, const CeedInt *offsets,
    CeedElemRestriction *rstr);
CEED_EXTERN int CeedElemRestrictionCreateOriented(Ceed ceed, CeedInt num_elem,
    CeedInt elem_size, CeedInt num_comp, CeedInt comp_stride, CeedInt l_size,
    CeedMemType mem_type, CeedCopyMode copy_mode, const CeedInt *offsets,
    const bool *orient, CeedElemRestriction *rstr);
CEED_EXTERN int CeedElemRestrictionCreateStrided(Ceed ceed,
    CeedInt num_elem, CeedInt elem_size, CeedInt num_comp, CeedInt l_size,
    const CeedInt strides[3], CeedElemRestriction *rstr);
CEED_EXTERN int CeedElemRestrictionCreateBlocked(Ceed ceed, CeedInt num_elem,
    CeedInt elem_size, CeedInt blk_size, CeedInt num_comp, CeedInt comp_stride,
    CeedInt l_size, CeedMemType mem_type, CeedCopyMode copy_mode,
    const CeedInt *offsets, CeedElemRestriction *rstr);
CEED_EXTERN int CeedElemRestrictionCreateBlockedStrided(Ceed ceed,
    CeedInt num_elem, CeedInt elem_size, CeedInt blk_size, CeedInt num_comp,
    CeedInt l_size, const CeedInt strides[3], CeedElemRestriction *rstr);
CEED_EXTERN int CeedElemRestrictionReferenceCopy(CeedElemRestriction rstr,
    CeedElemRestriction *rstr_copy);
CEED_EXTERN int CeedElemRestrictionCreateVector(CeedElemRestriction rstr,
    CeedVector *lvec, CeedVector *evec);
CEED_EXTERN int CeedElemRestrictionApply(CeedElemRestriction rstr,
    CeedTransposeMode t_mode, CeedVector u, CeedVector ru, CeedRequest *request);
CEED_EXTERN int CeedElemRestrictionApplyBlock(CeedElemRestriction rstr,
    CeedInt block, CeedTransposeMode t_mode, CeedVector u, CeedVector ru,
    CeedRequest *request);
CEED_EXTERN int CeedElemRestrictionGetCeed(CeedElemRestriction rstr,
    Ceed *ceed);
CEED_EXTERN int CeedElemRestrictionGetCompStride(CeedElemRestriction rstr,
    CeedInt *comp_stride);
CEED_EXTERN int CeedElemRestrictionGetNumElements(CeedElemRestriction rstr,
    CeedInt *num_elem);
CEED_EXTERN int CeedElemRestrictionGetElementSize(CeedElemRestriction rstr,
    CeedInt *elem_size);
CEED_EXTERN int CeedElemRestrictionGetLVectorSize(CeedElemRestriction rstr,
    CeedInt *l_size);
CEED_EXTERN int CeedElemRestrictionGetNumComponents(CeedElemRestriction rstr,
    CeedInt *num_comp);
CEED_EXTERN int CeedElemRestrictionGetNumBlocks(CeedElemRestriction rstr,
    CeedInt *num_blk);
CEED_EXTERN int CeedElemRestrictionGetBlockSize(CeedElemRestriction rstr,
    CeedInt *blk_size);
CEED_EXTERN int CeedElemRestrictionGetMultiplicity(CeedElemRestriction rstr,
    CeedVector mult);
CEED_EXTERN int CeedElemRestrictionView(CeedElemRestriction rstr, FILE *stream);
CEED_EXTERN int CeedElemRestrictionDestroy(CeedElemRestriction *rstr);

// The formalism here is that we have the structure
//  \int_\Omega v^T f_0(u, \nabla u, qdata) + (\nabla v)^T f_1(u, \nabla u, qdata)
// where gradients are with respect to the reference element.

/// Basis evaluation mode
///
/// Modes can be bitwise ORed when passing to most functions.
/// @ingroup CeedBasis
typedef enum {
  /// Perform no evaluation (either because there is no data or it is already at
  /// quadrature points)
  CEED_EVAL_NONE   = 0,
  /// Interpolate from nodes to quadrature points
  CEED_EVAL_INTERP = 1,
  /// Evaluate gradients at quadrature points from input in a nodal basis
  CEED_EVAL_GRAD   = 2,
  /// Evaluate divergence at quadrature points from input in a nodal basis
  CEED_EVAL_DIV    = 4,
  /// Evaluate curl at quadrature points from input in a nodal basis
  CEED_EVAL_CURL   = 8,
  /// Using no input, evaluate quadrature weights on the reference element
  CEED_EVAL_WEIGHT = 16,
} CeedEvalMode;
CEED_EXTERN const char *const CeedEvalModes[];

/// Type of quadrature; also used for location of nodes
/// @ingroup CeedBasis
typedef enum {
  /// Gauss-Legendre quadrature
  CEED_GAUSS         = 0,
  /// Gauss-Legendre-Lobatto quadrature
  CEED_GAUSS_LOBATTO = 1,
} CeedQuadMode;
CEED_EXTERN const char *const CeedQuadModes[];

/// Type of basis shape to create non-tensor H1 element basis
///
/// Dimension can be extracted with bitwise AND
/// (CeedElemTopology & 2**(dim + 2)) == TRUE
/// @ingroup CeedBasis
typedef enum {
  /// Line
  CEED_TOPOLOGY_LINE     = 1 << 16 | 0,
  /// Triangle - 2D shape
  CEED_TOPOLOGY_TRIANGLE = 2 << 16 | 1,
  /// Quadralateral - 2D shape
  CEED_TOPOLOGY_QUAD     = 2 << 16 | 2,
  /// Tetrahedron - 3D shape
  CEED_TOPOLOGY_TET      = 3 << 16 | 3,
  /// Pyramid - 3D shape
  CEED_TOPOLOGY_PYRAMID  = 3 << 16 | 4,
  /// Prism - 3D shape
  CEED_TOPOLOGY_PRISM    = 3 << 16 | 5,
  /// Hexehedron - 3D shape
  CEED_TOPOLOGY_HEX      = 3 << 16 | 6,
} CeedElemTopology;
CEED_EXTERN const char *const CeedElemTopologies[];

CEED_EXTERN int CeedBasisCreateTensorH1Lagrange(Ceed ceed, CeedInt dim,
    CeedInt num_comp, CeedInt P, CeedInt Q, CeedQuadMode quad_mode, CeedBasis *basis);
CEED_EXTERN int CeedBasisCreateTensorH1(Ceed ceed, CeedInt dim, CeedInt num_comp,
                                        CeedInt P_1d, CeedInt Q_1d,
                                        const CeedScalar *interp_1d,
                                        const CeedScalar *grad_1d,
                                        const CeedScalar *q_ref_1d,
                                        const CeedScalar *q_weight_1d,
                                        CeedBasis *basis);
CEED_EXTERN int CeedBasisCreateH1(Ceed ceed, CeedElemTopology topo,
                                  CeedInt num_comp,
                                  CeedInt num_nodes, CeedInt nqpts,
                                  const CeedScalar *interp,
                                  const CeedScalar *grad,
                                  const CeedScalar *q_ref,
                                  const CeedScalar *q_weights, CeedBasis *basis);
CEED_EXTERN int CeedBasisCreateHdiv(Ceed ceed, CeedElemTopology topo,
                                    CeedInt num_comp,
                                    CeedInt num_nodes, CeedInt nqpts,
                                    const CeedScalar *interp,
                                    const CeedScalar *div,
                                    const CeedScalar *q_ref,
                                    const CeedScalar *q_weights, CeedBasis *basis);
CEED_EXTERN int CeedBasisReferenceCopy(CeedBasis basis, CeedBasis *basis_copy);
CEED_EXTERN int CeedBasisView(CeedBasis basis, FILE *stream);
CEED_EXTERN int CeedBasisApply(CeedBasis basis, CeedInt num_elem,
                               CeedTransposeMode t_mode,
                               CeedEvalMode eval_mode, CeedVector u, CeedVector v);
CEED_EXTERN int CeedBasisGetCeed(CeedBasis basis, Ceed *ceed);
CEED_EXTERN int CeedBasisGetDimension(CeedBasis basis, CeedInt *dim);
CEED_EXTERN int CeedBasisGetTopology(CeedBasis basis, CeedElemTopology *topo);
CEED_EXTERN int CeedBasisGetNumQuadratureComponents(CeedBasis basis, CeedInt *Q_comp);
CEED_EXTERN int CeedBasisGetNumComponents(CeedBasis basis, CeedInt *num_comp);
CEED_EXTERN int CeedBasisGetNumNodes(CeedBasis basis, CeedInt *P);
CEED_EXTERN int CeedBasisGetNumNodes1D(CeedBasis basis, CeedInt *P_1d);
CEED_EXTERN int CeedBasisGetNumQuadraturePoints(CeedBasis basis, CeedInt *Q);
CEED_EXTERN int CeedBasisGetNumQuadraturePoints1D(CeedBasis basis,
    CeedInt *Q_1d);
CEED_EXTERN int CeedBasisGetQRef(CeedBasis basis, const CeedScalar **q_ref);
CEED_EXTERN int CeedBasisGetQWeights(CeedBasis basis,
                                     const CeedScalar **q_weights);
CEED_EXTERN int CeedBasisGetInterp(CeedBasis basis, const CeedScalar **interp);
CEED_EXTERN int CeedBasisGetInterp1D(CeedBasis basis,
                                     const CeedScalar **interp_1d);
CEED_EXTERN int CeedBasisGetGrad(CeedBasis basis, const CeedScalar **grad);
CEED_EXTERN int CeedBasisGetGrad1D(CeedBasis basis, const CeedScalar **grad_1d);
CEED_EXTERN int CeedBasisGetDiv(CeedBasis basis, const CeedScalar **div);
CEED_EXTERN int CeedBasisDestroy(CeedBasis *basis);

CEED_EXTERN int CeedGaussQuadrature(CeedInt Q, CeedScalar *q_ref_1d,
                                    CeedScalar *q_weight_1d);
CEED_EXTERN int CeedLobattoQuadrature(CeedInt Q, CeedScalar *q_ref_1d,
                                      CeedScalar *q_weight_1d);
CEED_EXTERN int CeedHaleTrefethenStripMap(CeedScalar rho, CeedScalar s,
                                          CeedScalar *g, CeedScalar *g_prime);
CEED_EXTERN int CeedGaussHaleTrefethenQuadrature(CeedScalar rho, CeedInt Q,
                                                 CeedScalar *q_ref_1d, CeedScalar *q_weight_1d);
CEED_EXTERN int CeedQRFactorization(Ceed ceed, CeedScalar *mat, CeedScalar *tau,
                                    CeedInt m, CeedInt n);
CEED_EXTERN int CeedSymmetricSchurDecomposition(Ceed ceed, CeedScalar *mat,
    CeedScalar *lambda, CeedInt n);
CEED_EXTERN int CeedSimultaneousDiagonalization(Ceed ceed, CeedScalar *mat_A,
    CeedScalar *mat_B, CeedScalar *x, CeedScalar *lambda, CeedInt n);

/** Handle for the user provided CeedQFunction callback function

 @param[in,out] ctx  User-defined context set using CeedQFunctionSetContext() or NULL
 @param[in] Q        Number of quadrature points at which to evaluate
 @param[in] in       Array of pointers to each input argument in the order provided
                       by the user in CeedQFunctionAddInput().  Each array has shape
                       `[dim, num_comp, Q]` where `dim` is the geometric dimension for
                       \ref CEED_EVAL_GRAD (`dim=1` for \ref CEED_EVAL_INTERP) and
                       `num_comp` is the number of field components (`num_comp=1` for
                       scalar fields).  This results in indexing the `i`th input at
                       quadrature point `j` as `in[i][(d*num_comp + c)*Q + j]`.
 @param[out]   out   Array of pointers to each output array in the order provided
                       using CeedQFunctionAddOutput().  The shapes are as above for
                       \a in.

 @return An error code: 0 - success, otherwise - failure

 @ingroup CeedQFunction
**/
typedef int (*CeedQFunctionUser)(void *ctx, const CeedInt Q,
                                 const CeedScalar *const *in,
                                 CeedScalar *const *out);

CEED_EXTERN int CeedQFunctionCreateInterior(Ceed ceed, CeedInt vec_length,
    CeedQFunctionUser f, const char *source, CeedQFunction *qf);
CEED_EXTERN int CeedQFunctionCreateInteriorByName(Ceed ceed, const char *name,
    CeedQFunction *qf);
CEED_EXTERN int CeedQFunctionCreateIdentity(Ceed ceed, CeedInt size,
    CeedEvalMode in_mode, CeedEvalMode out_mode, CeedQFunction *qf);
CEED_EXTERN int CeedQFunctionReferenceCopy(CeedQFunction qf, CeedQFunction *qf_copy);
CEED_EXTERN int CeedQFunctionAddInput(CeedQFunction qf, const char *field_name,
                                      CeedInt size, CeedEvalMode eval_mode);
CEED_EXTERN int CeedQFunctionAddOutput(CeedQFunction qf, const char *field_name,
                                       CeedInt size, CeedEvalMode eval_mode);
CEED_EXTERN int CeedQFunctionGetFields(CeedQFunction qf,
                                       CeedInt *num_input_fields,
                                       CeedQFunctionField **input_fields,
                                       CeedInt *num_output_fields,
                                       CeedQFunctionField **output_fields);
CEED_EXTERN int CeedQFunctionSetContext(CeedQFunction qf,
                                        CeedQFunctionContext ctx);
CEED_EXTERN int CeedQFunctionSetContextWritable(CeedQFunction qf, bool is_writable);
CEED_EXTERN int CeedQFunctionView(CeedQFunction qf, FILE *stream);
CEED_EXTERN int CeedQFunctionGetCeed(CeedQFunction qf, Ceed *ceed);
CEED_EXTERN int CeedQFunctionApply(CeedQFunction qf, CeedInt Q,
                                   CeedVector *u, CeedVector *v);
CEED_EXTERN int CeedQFunctionDestroy(CeedQFunction *qf);

CEED_EXTERN int CeedQFunctionFieldGetName(CeedQFunctionField qf_field,
    char **field_name);
CEED_EXTERN int CeedQFunctionFieldGetSize(CeedQFunctionField qf_field,
    CeedInt *size);
CEED_EXTERN int CeedQFunctionFieldGetEvalMode(CeedQFunctionField qf_field,
    CeedEvalMode *eval_mode);

/// Denotes type of data stored in a CeedQFunctionContext field
/// @ingroup CeedQFunction
typedef enum {
  /// Double precision value
  CEED_CONTEXT_FIELD_DOUBLE = 1,
  /// 32 bit integer value
  CEED_CONTEXT_FIELD_INT32  = 2,
} CeedContextFieldType;
CEED_EXTERN const char *const CeedContextFieldTypes[];

CEED_EXTERN int CeedQFunctionContextCreate(Ceed ceed,
    CeedQFunctionContext *ctx);
CEED_EXTERN int CeedQFunctionContextReferenceCopy(CeedQFunctionContext ctx,
    CeedQFunctionContext *ctx_copy);
CEED_EXTERN int CeedQFunctionContextSetData(CeedQFunctionContext ctx,
    CeedMemType mem_type, CeedCopyMode copy_mode, size_t size, void *data);
CEED_EXTERN int CeedQFunctionContextTakeData(CeedQFunctionContext ctx,
    CeedMemType mem_type, void *data);
CEED_EXTERN int CeedQFunctionContextGetData(CeedQFunctionContext ctx,
    CeedMemType mem_type, void *data);
CEED_EXTERN int CeedQFunctionContextGetDataRead(CeedQFunctionContext ctx,
    CeedMemType mem_type, void *data);
CEED_EXTERN int CeedQFunctionContextRestoreData(CeedQFunctionContext ctx,
    void *data);
CEED_EXTERN int CeedQFunctionContextRestoreDataRead(CeedQFunctionContext ctx,
    void *data);
CEED_EXTERN int CeedQFunctionContextRegisterDouble(CeedQFunctionContext ctx,
    const char *field_name, size_t field_offset, size_t num_values,
    const char *field_description);
CEED_EXTERN int CeedQFunctionContextRegisterInt32(CeedQFunctionContext ctx,
    const char *field_name, size_t field_offset, size_t num_values,
    const char *field_description);
CEED_EXTERN int CeedQFunctionContextGetFieldLabel(CeedQFunctionContext ctx,
    const char *field_name, CeedContextFieldLabel *field_label);
CEED_EXTERN int CeedQFunctionContextGetAllFieldLabels(CeedQFunctionContext ctx,
    const CeedContextFieldLabel **field_labels, CeedInt *num_fields);
CEED_EXTERN int CeedContextFieldLabelGetDescription(CeedContextFieldLabel label,
    const char **field_name, const char **field_description, size_t *num_values,
    CeedContextFieldType *field_type);
CEED_EXTERN int CeedQFunctionContextSetDouble(CeedQFunctionContext ctx,
    CeedContextFieldLabel field_label, double *values);
CEED_EXTERN int CeedQFunctionContextSetInt32(CeedQFunctionContext ctx,
    CeedContextFieldLabel field_label, int *values);
CEED_EXTERN int CeedQFunctionContextGetContextSize(CeedQFunctionContext ctx,
    size_t *ctx_size);
CEED_EXTERN int CeedQFunctionContextView(CeedQFunctionContext ctx,
    FILE *stream);
CEED_EXTERN int CeedQFunctionContextDestroy(CeedQFunctionContext *ctx);

CEED_EXTERN int CeedOperatorCreate(Ceed ceed, CeedQFunction qf,
                                   CeedQFunction dqf, CeedQFunction dqfT,
                                   CeedOperator *op);
CEED_EXTERN int CeedCompositeOperatorCreate(Ceed ceed, CeedOperator *op);
CEED_EXTERN int CeedOperatorReferenceCopy(CeedOperator op, CeedOperator *op_copy);
CEED_EXTERN int CeedOperatorSetField(CeedOperator op, const char *field_name,
                                     CeedElemRestriction r, CeedBasis b,
                                     CeedVector v);
CEED_EXTERN int CeedOperatorGetFields(CeedOperator op,
                                      CeedInt *num_input_fields,
                                      CeedOperatorField **input_fields,
                                      CeedInt *num_output_fields,
                                      CeedOperatorField **output_fields);
CEED_EXTERN int CeedCompositeOperatorAddSub(CeedOperator composite_op,
    CeedOperator sub_op);
CEED_EXTERN int CeedOperatorCheckReady(CeedOperator op);
CEED_EXTERN int CeedOperatorLinearAssembleQFunction(CeedOperator op,
    CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request);
CEED_EXTERN int CeedOperatorLinearAssembleQFunctionBuildOrUpdate(CeedOperator op,
    CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request);
CEED_EXTERN int CeedOperatorLinearAssembleDiagonal(CeedOperator op,
    CeedVector assembled, CeedRequest *request);
CEED_EXTERN int CeedOperatorLinearAssembleAddDiagonal(CeedOperator op,
    CeedVector assembled, CeedRequest *request);
CEED_EXTERN int CeedOperatorLinearAssemblePointBlockDiagonal(CeedOperator op,
    CeedVector assembled, CeedRequest *request);
CEED_EXTERN int CeedOperatorLinearAssembleAddPointBlockDiagonal(CeedOperator op,
    CeedVector assembled, CeedRequest *request);
CEED_EXTERN int CeedOperatorLinearAssembleSymbolic(CeedOperator op,
    CeedInt *num_entries, CeedInt **rows, CeedInt **cols);
CEED_EXTERN int CeedOperatorLinearAssemble(CeedOperator op, CeedVector values);
CEED_EXTERN int CeedOperatorMultigridLevelCreate(CeedOperator op_fine,
    CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
    CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict);
CEED_EXTERN int CeedOperatorMultigridLevelCreateTensorH1(
  CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse,
  CeedBasis basis_coarse, const CeedScalar *interp_c_to_f, CeedOperator *op_coarse,
  CeedOperator *op_prolong, CeedOperator *op_restrict);
CEED_EXTERN int CeedOperatorMultigridLevelCreateH1(CeedOperator op_fine,
    CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
    const CeedScalar *interp_c_to_f, CeedOperator *op_coarse,
    CeedOperator *op_prolong, CeedOperator *op_restrict);
CEED_EXTERN int CeedOperatorCreateFDMElementInverse(CeedOperator op,
    CeedOperator *fdm_inv, CeedRequest *request);
CEED_EXTERN int CeedOperatorSetNumQuadraturePoints(CeedOperator op, CeedInt num_qpts);
CEED_EXTERN int CeedOperatorView(CeedOperator op, FILE *stream);
CEED_EXTERN int CeedOperatorGetCeed(CeedOperator op, Ceed *ceed);
CEED_EXTERN int CeedOperatorGetNumElements(CeedOperator op, CeedInt *num_elem);
CEED_EXTERN int CeedOperatorGetNumQuadraturePoints(CeedOperator op,
    CeedInt *num_qpts);
CEED_EXTERN int CeedOperatorContextGetFieldLabel(CeedOperator op,
    const char *field_name, CeedContextFieldLabel *field_label);
CEED_EXTERN int CeedOperatorContextSetDouble(CeedOperator op,
    CeedContextFieldLabel field_label, double *values);
CEED_EXTERN int CeedOperatorContextSetInt32(CeedOperator op,
    CeedContextFieldLabel field_label, int *values);
CEED_EXTERN int CeedOperatorApply(CeedOperator op, CeedVector in,
                                  CeedVector out, CeedRequest *request);
CEED_EXTERN int CeedOperatorApplyAdd(CeedOperator op, CeedVector in,
                                     CeedVector out, CeedRequest *request);
CEED_EXTERN int CeedOperatorDestroy(CeedOperator *op);

CEED_EXTERN int CeedOperatorFieldGetName(CeedOperatorField op_field,
    char **field_name);
CEED_EXTERN int CeedOperatorFieldGetElemRestriction(CeedOperatorField op_field,
    CeedElemRestriction *rstr);
CEED_EXTERN int CeedOperatorFieldGetBasis(CeedOperatorField op_field,
    CeedBasis *basis);
CEED_EXTERN int CeedOperatorFieldGetVector(CeedOperatorField op_field,
    CeedVector *vec);

/**
  @brief Return integer power

  @param[in] base   The base to exponentiate
  @param[in] power  The power to raise the base to

  @return base^power

  @ref Utility
**/
static inline CeedInt CeedIntPow(CeedInt base, CeedInt power) {
  CeedInt result = 1;
  while (power) {
    if (power & 1) result *= base;
    power >>= 1;
    base *= base;
  }
  return result;
}

/**
  @brief Return minimum of two integers

  @param[in] a  The first integer to compare
  @param[in] b  The second integer to compare

  @return The minimum of the two integers

  @ref Utility
**/
static inline CeedInt CeedIntMin(CeedInt a, CeedInt b) { return a < b ? a : b; }

/**
  @brief Return maximum of two integers

  @param[in] a  The first integer to compare
  @param[in] b  The second integer to compare

  @return The maximum of the two integers

  @ref Utility
**/
static inline CeedInt CeedIntMax(CeedInt a, CeedInt b) { return a > b ? a : b; }

// Used to ensure initialization before CeedInit()
CEED_EXTERN int CeedRegisterAll(void);
// Used to ensure initialization before CeedQFunctionCreate*()
CEED_EXTERN int CeedQFunctionRegisterAll(void);

#endif