1 /// Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at 2 /// the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights 3 /// reserved. See files LICENSE and NOTICE for details. 4 /// 5 /// This file is part of CEED, a collection of benchmarks, miniapps, software 6 /// libraries and APIs for efficient high-order finite element and spectral 7 /// element discretizations for exascale applications. For more information and 8 /// source code availability see http://github.com/ceed. 9 /// 10 /// The CEED research is supported by the Exascale Computing Project 17-SC-20-SC, 11 /// a collaborative effort of two U.S. Department of Energy organizations (Office 12 /// of Science and the National Nuclear Security Administration) responsible for 13 /// the planning and preparation of a capable exascale ecosystem, including 14 /// software, applications, hardware, advanced system engineering and early 15 /// testbed platforms, in support of the nation's exascale computing imperative. 16 17 /// @file 18 /// Public header for user and utility components of libCEED 19 #ifndef _ceed_h 20 #define _ceed_h 21 22 /// @defgroup Ceed Ceed: core components 23 /// @defgroup CeedVector CeedVector: storing and manipulating vectors 24 /// @defgroup CeedElemRestriction CeedElemRestriction: restriction from local vectors to elements 25 /// @defgroup CeedBasis CeedBasis: fully discrete finite element-like objects 26 /// @defgroup CeedQFunction CeedQFunction: independent operations at quadrature points 27 /// @defgroup CeedOperator CeedOperator: composed FE-type operations on vectors 28 /// 29 /// @page FunctionCategories libCEED: Types of Functions 30 /// libCEED provides three different header files depending upon the type of 31 /// functions a user requires. 32 /// @section Utility Utility Functions 33 /// These functions are intended general utilities that may be useful to 34 /// libCEED developers and users. These functions can generally be found in 35 /// "ceed.h". 36 /// @section Basic User Functions 37 /// These functions are intended to be used by general users of the libCEED 38 /// interface. These functions can generally be found in "ceed.h". 39 /// @section Advanced Backend Developer Functions 40 /// These functions are intended to be used by backend developers of the 41 /// libCEED interface. These functions can generally be found in 42 /// "ceed-backend.h". 43 /// @section Developer Frontend Developer Functions 44 /// These functions are intended to be used by frontend developers of the 45 /// libCEED interface. These functions can generally be found in "ceed-impl.h". 46 47 /** 48 CEED_EXTERN is used in this header to denote all publicly visible symbols. 49 50 No other file should declare publicly visible symbols, thus it should never be 51 used outside ceed.h. 52 */ 53 #ifdef __cplusplus 54 # define CEED_EXTERN extern "C" 55 #else 56 # define CEED_EXTERN extern 57 #endif 58 59 #ifndef CEED_QFUNCTION 60 #define CEED_QFUNCTION(name) \ 61 static const char name ## _loc[] = __FILE__ ":" #name; \ 62 static int name 63 #endif 64 65 #ifndef CeedPragmaSIMD 66 # if defined(__INTEL_COMPILER) &&__INTEL_COMPILER >= 900 67 # define CeedPragmaSIMD _Pragma("simd") 68 # elif defined(__GNUC__) && __GNUC__ >= 5 69 # define CeedPragmaSIMD _Pragma("GCC ivdep") 70 # elif defined(_OPENMP) && _OPENMP >= 201307 // OpenMP-4.0 (July, 2013) 71 # define CeedPragmaSIMD _Pragma("omp simd") 72 # else 73 # define CeedPragmaSIMD 74 # endif 75 #endif 76 77 #include <assert.h> 78 #include <stdint.h> 79 #include <stddef.h> 80 #include <stdarg.h> 81 #include <stdio.h> 82 #include <stdbool.h> 83 84 /// We can discuss ways to avoid forcing these to be compile-time decisions, 85 /// but let's leave that for later. 86 /// Integer type, used for indexing 87 /// @ingroup Ceed 88 typedef int32_t CeedInt; 89 /// Scalar (floating point) type 90 /// @ingroup Ceed 91 typedef double CeedScalar; 92 93 /// Library context created by CeedInit() 94 /// @ingroup Ceed 95 typedef struct Ceed_private *Ceed; 96 /// Non-blocking Ceed interfaces return a CeedRequest. 97 /// To perform an operation immediately, pass \ref CEED_REQUEST_IMMEDIATE instead. 98 /// @ingroup Ceed 99 typedef struct CeedRequest_private *CeedRequest; 100 /// Handle for vectors over the field \ref CeedScalar 101 /// @ingroup CeedVector 102 typedef struct CeedVector_private *CeedVector; 103 /// Handle for object describing restriction to elements 104 /// @ingroup CeedElemRestriction 105 typedef struct CeedElemRestriction_private *CeedElemRestriction; 106 /// Handle for object describing discrete finite element evaluations 107 /// @ingroup CeedBasis 108 typedef struct CeedBasis_private *CeedBasis; 109 /// Handle for object describing functions evaluated independently at quadrature points 110 /// @ingroup CeedQFunction 111 typedef struct CeedQFunction_private *CeedQFunction; 112 /// Handle for object describing FE-type operators acting on vectors 113 /// 114 /// Given an element restriction \f$E\f$, basis evaluator \f$B\f$, and 115 /// quadrature function\f$f\f$, a CeedOperator expresses operations of the form 116 /// $$ E^T B^T f(B E u) $$ 117 /// acting on the vector \f$u\f$. 118 /// @ingroup CeedOperator 119 typedef struct CeedOperator_private *CeedOperator; 120 121 CEED_EXTERN int CeedInit(const char *resource, Ceed *ceed); 122 CEED_EXTERN int CeedGetResource(Ceed ceed, const char **resource); 123 CEED_EXTERN int CeedDestroy(Ceed *ceed); 124 125 CEED_EXTERN int CeedErrorImpl(Ceed, const char *, int, const char *, int, 126 const char *, ...); 127 /// Raise an error on ceed object 128 /// 129 /// @param ceed Ceed library context or NULL 130 /// @param ecode Error code (int) 131 /// @param ... printf-style format string followed by arguments as needed 132 /// 133 /// @ingroup Ceed 134 /// @sa CeedSetErrorHandler() 135 #if defined(__clang__) 136 /// Use nonstandard ternary to convince the compiler/clang-tidy that this 137 /// function never returns zero. 138 # define CeedError(ceed, ecode, ...) \ 139 (CeedErrorImpl((ceed), __FILE__, __LINE__, __func__, (ecode), __VA_ARGS__) ?: (ecode)) 140 #else 141 # define CeedError(ceed, ecode, ...) \ 142 CeedErrorImpl((ceed), __FILE__, __LINE__, __func__, (ecode), __VA_ARGS__) ?: (ecode) 143 #endif 144 /// Specify memory type 145 /// 146 /// Many Ceed interfaces take or return pointers to memory. This enum is used to 147 /// specify where the memory being provided or requested must reside. 148 /// @ingroup Ceed 149 typedef enum { 150 /// Memory resides on the host 151 CEED_MEM_HOST, 152 /// Memory resides on a device (corresponding to \ref Ceed resource) 153 CEED_MEM_DEVICE, 154 } CeedMemType; 155 156 CEED_EXTERN const char *const CeedMemTypes[]; 157 158 CEED_EXTERN int CeedGetPreferredMemType(Ceed ceed, CeedMemType *type); 159 160 /// Conveys ownership status of arrays passed to Ceed interfaces. 161 /// @ingroup Ceed 162 typedef enum { 163 /// Implementation will copy the values and not store the passed pointer. 164 CEED_COPY_VALUES, 165 /// Implementation can use and modify the data provided by the user, but does 166 /// not take ownership. 167 CEED_USE_POINTER, 168 /// Implementation takes ownership of the pointer and will free using 169 /// CeedFree() when done using it. The user should not assume that the 170 /// pointer remains valid after ownership has been transferred. Note that 171 /// arrays allocated using C++ operator new or other allocators cannot 172 /// generally be freed using CeedFree(). CeedFree() is capable of freeing any 173 /// memory that can be freed using free(3). 174 CEED_OWN_POINTER, 175 } CeedCopyMode; 176 177 /// Denotes type of vector norm to be computed 178 /// @ingroup CeedVector 179 typedef enum { 180 /// L_1 norm: sum_i |x_i| 181 CEED_NORM_1, 182 /// L_2 norm: sqrt(sum_i |x_i|^2) 183 CEED_NORM_2, 184 /// L_Infinity norm: max_i |x_i| 185 CEED_NORM_MAX, 186 } CeedNormType; 187 188 CEED_EXTERN const char *const CeedCopyModes[]; 189 190 CEED_EXTERN int CeedVectorCreate(Ceed ceed, CeedInt len, CeedVector *vec); 191 CEED_EXTERN int CeedVectorSetArray(CeedVector vec, CeedMemType mtype, 192 CeedCopyMode cmode, CeedScalar *array); 193 CEED_EXTERN int CeedVectorSetValue(CeedVector vec, CeedScalar value); 194 CEED_EXTERN int CeedVectorSyncArray(CeedVector vec, CeedMemType mtype); 195 CEED_EXTERN int CeedVectorGetArray(CeedVector vec, CeedMemType mtype, 196 CeedScalar **array); 197 CEED_EXTERN int CeedVectorGetArrayRead(CeedVector vec, CeedMemType mtype, 198 const CeedScalar **array); 199 CEED_EXTERN int CeedVectorRestoreArray(CeedVector vec, CeedScalar **array); 200 CEED_EXTERN int CeedVectorRestoreArrayRead(CeedVector vec, 201 const CeedScalar **array); 202 CEED_EXTERN int CeedVectorNorm(CeedVector vec, CeedNormType type, 203 CeedScalar *norm); 204 CEED_EXTERN int CeedVectorView(CeedVector vec, const char *fpfmt, FILE *stream); 205 CEED_EXTERN int CeedVectorGetLength(CeedVector vec, CeedInt *length); 206 CEED_EXTERN int CeedVectorDestroy(CeedVector *vec); 207 208 CEED_EXTERN CeedRequest *const CEED_REQUEST_IMMEDIATE; 209 CEED_EXTERN CeedRequest *const CEED_REQUEST_ORDERED; 210 CEED_EXTERN int CeedRequestWait(CeedRequest *req); 211 212 /// Argument for CeedOperatorSetField that vector is collocated with 213 /// quadrature points, used with QFunction eval mode CEED_EVAL_NONE 214 /// or CEED_EVAL_INTERP only, not with CEED_EVAL_GRAD, CEED_EVAL_DIV, 215 /// or CEED_EVAL_CURL 216 /// @ingroup CeedBasis 217 CEED_EXTERN CeedBasis CEED_BASIS_COLLOCATED; 218 219 /// Argument for CeedOperatorSetField to use active input or output 220 /// @ingroup CeedVector 221 CEED_EXTERN CeedVector CEED_VECTOR_ACTIVE; 222 223 /// Argument for CeedOperatorSetField to use no vector, used with 224 /// qfunction input with eval mode CEED_EVAL_WEIGHTS 225 /// @ingroup CeedVector 226 CEED_EXTERN CeedVector CEED_VECTOR_NONE; 227 228 /// Argument for CeedOperatorCreate that QFunction is not created by user. 229 /// Only used for QFunctions dqf and dqfT. If implemented, a backend may 230 /// attempt to provide the action of these QFunctions. 231 /// @ingroup CeedQFunction 232 CEED_EXTERN CeedQFunction CEED_QFUNCTION_NONE; 233 234 /// Denotes whether a linear transformation or its transpose should be applied 235 /// @ingroup CeedBasis 236 typedef enum { 237 /// Apply the linear transformation 238 CEED_NOTRANSPOSE, 239 /// Apply the transpose 240 CEED_TRANSPOSE 241 } CeedTransposeMode; 242 243 CEED_EXTERN const char *const CeedTransposeModes[]; 244 245 /// Denotes whether a L-vector is ordered [component, node] or [node, component] 246 /// with the right-most index being contiguous in memory 247 /// @ingroup CeedElemRestriction 248 typedef enum { 249 /// L-vector data is not interlaced, ordered [component, node] 250 CEED_NONINTERLACED, 251 /// L-vector data is interlaced, ordered [node, component] 252 CEED_INTERLACED 253 } CeedInterlaceMode; 254 255 CEED_EXTERN const char *const CeedInterlaceModes[]; 256 257 CEED_EXTERN int CeedElemRestrictionCreate(Ceed ceed, CeedInterlaceMode imode, 258 CeedInt nelem, CeedInt elemsize, CeedInt nnodes, CeedInt ncomp, 259 CeedMemType mtype, CeedCopyMode cmode, const CeedInt *indices, 260 CeedElemRestriction *rstr); 261 CEED_EXTERN int CeedElemRestrictionCreateIdentity(Ceed ceed, 262 CeedInterlaceMode imode,CeedInt nelem, CeedInt elemsize, CeedInt nnodes, 263 CeedInt ncomp, CeedElemRestriction *rstr); 264 CEED_EXTERN int CeedElemRestrictionCreateBlocked(Ceed ceed, 265 CeedInterlaceMode imode,CeedInt nelem, CeedInt elemsize, CeedInt blksize, 266 CeedInt nnodes, CeedInt ncomp, CeedMemType mtype, CeedCopyMode cmode, 267 const CeedInt *indices, CeedElemRestriction *rstr); 268 CEED_EXTERN int CeedElemRestrictionCreateVector(CeedElemRestriction rstr, 269 CeedVector *lvec, CeedVector *evec); 270 CEED_EXTERN int CeedElemRestrictionApply(CeedElemRestriction rstr, 271 CeedTransposeMode tmode, CeedVector u, CeedVector ru, CeedRequest *request); 272 CEED_EXTERN int CeedElemRestrictionApplyBlock(CeedElemRestriction rstr, 273 CeedInt block, CeedTransposeMode tmode, CeedVector u, CeedVector ru, 274 CeedRequest *request); 275 CEED_EXTERN int CeedElemRestrictionGetIMode(CeedElemRestriction rstr, 276 CeedInterlaceMode *Imode); 277 CEED_EXTERN int CeedElemRestrictionGetNumElements(CeedElemRestriction rstr, 278 CeedInt *numelem); 279 CEED_EXTERN int CeedElemRestrictionGetElementSize(CeedElemRestriction rstr, 280 CeedInt *elemsize); 281 CEED_EXTERN int CeedElemRestrictionGetNumNodes(CeedElemRestriction rstr, 282 CeedInt *numnodes); 283 CEED_EXTERN int CeedElemRestrictionGetNumComponents(CeedElemRestriction rstr, 284 CeedInt *numcomp); 285 CEED_EXTERN int CeedElemRestrictionGetNumBlocks(CeedElemRestriction rstr, 286 CeedInt *numblk); 287 CEED_EXTERN int CeedElemRestrictionGetBlockSize(CeedElemRestriction rstr, 288 CeedInt *blksize); 289 CEED_EXTERN int CeedElemRestrictionGetMultiplicity(CeedElemRestriction rstr, 290 CeedVector mult); 291 CEED_EXTERN int CeedElemRestrictionView(CeedElemRestriction rstr, FILE *stream); 292 CEED_EXTERN int CeedElemRestrictionDestroy(CeedElemRestriction *rstr); 293 294 /// The formalism here is that we have the structure 295 /// \int_\Omega v^T f_0(u, \nabla u, qdata) + (\nabla v)^T f_1(u, \nabla u, qdata) 296 /// where gradients are with respect to the reference element. 297 298 /// Basis evaluation mode 299 /// 300 /// Modes can be bitwise ORed when passing to most functions. 301 /// @ingroup CeedBasis 302 typedef enum { 303 /// Perform no evaluation (either because there is no data or it is already at 304 /// quadrature points) 305 CEED_EVAL_NONE = 0, 306 /// Interpolate from nodes to quadrature points 307 CEED_EVAL_INTERP = 1, 308 /// Evaluate gradients at quadrature points from input in a nodal basis 309 CEED_EVAL_GRAD = 2, 310 /// Evaluate divergence at quadrature points from input in a nodal basis 311 CEED_EVAL_DIV = 4, 312 /// Evaluate curl at quadrature points from input in a nodal basis 313 CEED_EVAL_CURL = 8, 314 /// Using no input, evaluate quadrature weights on the reference element 315 CEED_EVAL_WEIGHT = 16, 316 } CeedEvalMode; 317 318 CEED_EXTERN const char *const CeedEvalModes[]; 319 320 /// Type of quadrature; also used for location of nodes 321 /// @ingroup CeedBasis 322 typedef enum { 323 /// Gauss-Legendre quadrature 324 CEED_GAUSS = 0, 325 /// Gauss-Legendre-Lobatto quadrature 326 CEED_GAUSS_LOBATTO = 1, 327 } CeedQuadMode; 328 329 CEED_EXTERN const char *const CeedQuadModes[]; 330 331 /// Type of basis shape to create non-tensor H1 element basis 332 /// 333 /// Dimension can be extracted with bitwise AND 334 /// (CeedElemTopology & 2**(dim + 2)) == TRUE 335 /// @ingroup CeedBasis 336 typedef enum { 337 /// Line 338 CEED_LINE = 1 << 16 | 0, 339 /// Triangle - 2D shape 340 CEED_TRIANGLE = 2 << 16 | 1, 341 /// Quadralateral - 2D shape 342 CEED_QUAD = 2 << 16 | 2, 343 /// Tetrahedron - 3D shape 344 CEED_TET = 3 << 16 | 3, 345 /// Pyramid - 3D shape 346 CEED_PYRAMID = 3 << 16 | 4, 347 /// Prism - 3D shape 348 CEED_PRISM = 3 << 16 | 5, 349 /// Hexehedron - 3D shape 350 CEED_HEX = 3 << 16 | 6, 351 } CeedElemTopology; 352 353 CEED_EXTERN const char *const CeedElemTopologies[]; 354 355 CEED_EXTERN int CeedBasisCreateTensorH1Lagrange(Ceed ceed, CeedInt dim, 356 CeedInt ncomp, CeedInt P, CeedInt Q, CeedQuadMode qmode, CeedBasis *basis); 357 CEED_EXTERN int CeedBasisCreateTensorH1(Ceed ceed, CeedInt dim, CeedInt ncomp, 358 CeedInt P1d, CeedInt Q1d, 359 const CeedScalar *interp1d, 360 const CeedScalar *grad1d, 361 const CeedScalar *qref1d, 362 const CeedScalar *qweight1d, 363 CeedBasis *basis); 364 CEED_EXTERN int CeedBasisCreateH1(Ceed ceed, CeedElemTopology topo, 365 CeedInt ncomp, 366 CeedInt nnodes, CeedInt nqpts, 367 const CeedScalar *interp, 368 const CeedScalar *grad, 369 const CeedScalar *qref, 370 const CeedScalar *qweight, CeedBasis *basis); 371 CEED_EXTERN int CeedBasisView(CeedBasis basis, FILE *stream); 372 CEED_EXTERN int CeedBasisGetNumNodes(CeedBasis basis, CeedInt *P); 373 CEED_EXTERN int CeedBasisGetNumQuadraturePoints(CeedBasis basis, CeedInt *Q); 374 CEED_EXTERN int CeedBasisApply(CeedBasis basis, CeedInt nelem, 375 CeedTransposeMode tmode, 376 CeedEvalMode emode, CeedVector u, CeedVector v); 377 CEED_EXTERN int CeedBasisDestroy(CeedBasis *basis); 378 379 CEED_EXTERN int CeedGaussQuadrature(CeedInt Q, CeedScalar *qref1d, 380 CeedScalar *qweight1d); 381 CEED_EXTERN int CeedLobattoQuadrature(CeedInt Q, CeedScalar *qref1d, 382 CeedScalar *qweight1d); 383 CEED_EXTERN int CeedQRFactorization(Ceed ceed, CeedScalar *mat, CeedScalar *tau, 384 CeedInt m, CeedInt n); 385 CEED_EXTERN int CeedSymmetricSchurDecomposition(Ceed ceed, CeedScalar *mat, 386 CeedScalar *lambda, CeedInt n); 387 CEED_EXTERN int CeedSimultaneousDiagonalization(Ceed ceed, CeedScalar *matA, 388 CeedScalar *matB, CeedScalar *x, CeedScalar *lambda, CeedInt n); 389 390 /** Handle for the object describing the user CeedQFunction 391 392 @param ctx user-defined context set using CeedQFunctionSetContext() or NULL 393 394 @param Q number of quadrature points at which to evaluate 395 396 @param in array of pointers to each input argument in the order provided 397 by the user in CeedQFunctionAddInput(). Each array has shape 398 `[dim, ncomp, Q]` where `dim` is the geometric dimension for 399 \ref CEED_EVAL_GRAD (`dim=1` for \ref CEED_EVAL_INTERP) and 400 `ncomp` is the number of field components (`ncomp=1` for 401 scalar fields). This results in indexing the `i`th input at 402 quadrature point `j` as `in[i][(d*ncomp + c)*Q + j]`. 403 404 @param out array of pointers to each output array in the order provided 405 using CeedQFunctionAddOutput(). The shapes are as above for 406 \a in. 407 408 @return An error code: 0 - success, otherwise - failure 409 410 @ingroup CeedQFunction 411 **/ 412 typedef int (*CeedQFunctionUser)(void *ctx, const CeedInt Q, 413 const CeedScalar *const *in, 414 CeedScalar *const *out); 415 416 CEED_EXTERN int CeedQFunctionCreateInterior(Ceed ceed, CeedInt vlength, 417 CeedQFunctionUser f, const char *source, CeedQFunction *qf); 418 CEED_EXTERN int CeedQFunctionCreateInteriorByName(Ceed ceed, const char *name, 419 CeedQFunction *qf); 420 CEED_EXTERN int CeedQFunctionCreateIdentity(Ceed ceed, CeedInt size, 421 CeedEvalMode inmode, CeedEvalMode outmode, CeedQFunction *qf); 422 CEED_EXTERN int CeedQFunctionAddInput(CeedQFunction qf, const char *fieldname, 423 CeedInt size, CeedEvalMode emode); 424 CEED_EXTERN int CeedQFunctionAddOutput(CeedQFunction qf, const char *fieldname, 425 CeedInt size, CeedEvalMode emode); 426 CEED_EXTERN int CeedQFunctionSetContext(CeedQFunction qf, void *ctx, 427 size_t ctxsize); 428 CEED_EXTERN int CeedQFunctionView(CeedQFunction qf, FILE *stream); 429 CEED_EXTERN int CeedQFunctionApply(CeedQFunction qf, CeedInt Q, 430 CeedVector *u, CeedVector *v); 431 CEED_EXTERN int CeedQFunctionDestroy(CeedQFunction *qf); 432 433 CEED_EXTERN int CeedOperatorCreate(Ceed ceed, CeedQFunction qf, 434 CeedQFunction dqf, CeedQFunction dqfT, 435 CeedOperator *op); 436 CEED_EXTERN int CeedCompositeOperatorCreate(Ceed ceed, CeedOperator *op); 437 CEED_EXTERN int CeedOperatorSetField(CeedOperator op, const char *fieldname, 438 CeedElemRestriction r, CeedBasis b, 439 CeedVector v); 440 CEED_EXTERN int CeedCompositeOperatorAddSub(CeedOperator compositeop, 441 CeedOperator subop); 442 CEED_EXTERN int CeedOperatorAssembleLinearQFunction(CeedOperator op, 443 CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request); 444 CEED_EXTERN int CeedOperatorAssembleLinearDiagonal(CeedOperator op, 445 CeedVector *assembled, CeedRequest *request); 446 CEED_EXTERN int CeedOperatorView(CeedOperator op, FILE *stream); 447 CEED_EXTERN int CeedOperatorCreateFDMElementInverse(CeedOperator op, 448 CeedOperator *fdminv, CeedRequest *request); 449 CEED_EXTERN int CeedOperatorApply(CeedOperator op, CeedVector in, 450 CeedVector out, CeedRequest *request); 451 CEED_EXTERN int CeedOperatorApplyAdd(CeedOperator op, CeedVector in, 452 CeedVector out, CeedRequest *request); 453 CEED_EXTERN int CeedOperatorDestroy(CeedOperator *op); 454 455 /** 456 @brief Return integer power 457 458 @param[in] base The base to exponentiate 459 @param[in] power The power to raise the base to 460 461 @return base^power 462 463 @ref Utility 464 **/ 465 static inline CeedInt CeedIntPow(CeedInt base, CeedInt power) { 466 CeedInt result = 1; 467 while (power) { 468 if (power & 1) result *= base; 469 power >>= 1; 470 base *= base; 471 } 472 return result; 473 } 474 475 /** 476 @brief Return minimum of two integers 477 478 @param[in] a The first integer to compare 479 @param[in] b The second integer to compare 480 481 @return The minimum of the two integers 482 483 @ref Utility 484 **/ 485 static inline CeedInt CeedIntMin(CeedInt a, CeedInt b) { return a < b ? a : b; } 486 487 #endif 488