src/gromacs/ewald/tests/pmegathertest.cpp

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  35 /*! \internal \file
  36  * \brief
  37  * Implements PME force gathering tests.
  38  *
  39  * \author Aleksei Iupinov <a.yupinov@gmail.com>
  40  * \ingroup module_ewald
  41  */
  42
  43 #include "gmxpre.h"
  44
  45 #include <string>
  46
  47 #include <gmock/gmock.h>
  48
  49 #include "gromacs/mdtypes/inputrec.h"
  50 #include "gromacs/utility/stringutil.h"
  51
  52 #include "testutils/refdata.h"
  53 #include "testutils/testasserts.h"
  54
  55 #include "pmetestcommon.h"
  56
  57 namespace gmx
  58 {
  59 namespace test
  60 {
  61 namespace
  62 {
  63
  64 /* Valid input instances */
  65
  66 //! A couple of valid inputs for boxes.
  67 static std::vector<Matrix3x3> const c_sampleBoxes
  68 {
  69     // normal box
  70     Matrix3x3 {{
  71                    8.0f, 0.0f, 0.0f,
  72                    0.0f, 3.4f, 0.0f,
  73                    0.0f, 0.0f, 2.0f
  74                }},
  75     // triclinic box
  76     Matrix3x3 {{
  77                    7.0f, 0.0f, 0.0f,
  78                    0.0f, 4.1f, 0.0f,
  79                    3.5f, 2.0f, 12.2f
  80                }},
  81 };
  82
  83 //! A couple of valid inputs for grid sizes
  84 static std::vector<IVec> const c_sampleGridSizes
  85 {
  86     IVec {
  87         16, 12, 14
  88     },
  89     IVec {
  90         13, 15, 11
  91     }
  92 };
  93 //! Random charges
  94 static std::vector<real> const c_sampleChargesFull
  95 {
  96     4.95f, 3.11f, 3.97f, 1.08f, 2.09f, 1.1f, 4.13f, 3.31f, 2.8f, 5.83f, 5.09f, 6.1f, 2.86f, 0.24f, 5.76f, 5.19f, 0.72f
  97 };
  98
  99 //! All the input atom gridline indices
 100 static std::vector<IVec> const c_sampleGridLineIndicesFull
 101 {
 102     IVec {
 103         4, 2, 6
 104     },
 105     IVec {
 106         1, 4, 10
 107     },
 108     IVec {
 109         0, 6, 6
 110     },
 111     IVec {
 112         0, 1, 4
 113     },
 114     IVec {
 115         6, 3, 0
 116     },
 117     IVec {
 118         7, 2, 2
 119     },
 120     IVec {
 121         8, 3, 1
 122     },
 123     IVec {
 124         4, 0, 3
 125     },
 126     IVec {
 127         0, 0, 0
 128     },
 129     IVec {
 130         8, 5, 8
 131     },
 132     IVec {
 133         4, 4, 2
 134     },
 135     IVec {
 136         7, 1, 7
 137     },
 138     IVec {
 139         8, 5, 5
 140     },
 141     IVec {
 142         2, 6, 5
 143     },
 144     IVec {
 145         1, 6, 2
 146     },
 147     IVec {
 148         7, 1, 8
 149     },
 150     IVec {
 151         3, 5, 1
 152     },
 153 };
 154
 155 // Spline values/derivatives below are also generated randomly, so they are bogus,
 156 // but that should not affect the reproducibility, which we're after
 157
 158 //! A lot of bogus input spline values - should have at list (max PME order = 5) * (DIM = 3) * (total unique atom number in all test cases = 16) values
 159 static std::vector<real> const c_sampleSplineValuesFull
 160 {
 161     0.12f, 0.81f, 0.29f, 0.22f, 0.13f, 0.19f, 0.12f, 0.8f, 0.44f, 0.38f, 0.32f, 0.36f, 0.27f, 0.11f, 0.17f, 0.94f, 0.07f, 0.9f, 0.98f, 0.96f, 0.07f, 0.94f, 0.77f, 0.24f, 0.84f, 0.16f, 0.77f, 0.57f, 0.52f, 0.27f, 0.39f, 0.45f, 0.6f, 0.59f, 0.44f, 0.91f, 0.97f, 0.43f, 0.24f, 0.52f, 0.73f, 0.55f, 0.99f, 0.39f, 0.97f, 0.35f, 0.1f, 0.68f, 0.19f, 0.1f, 0.77f, 0.2f, 0.43f, 0.69f, 0.76f, 0.32f, 0.31f, 0.94f, 0.53f, 0.6f, 0.93f, 0.57f, 0.94f, 0.88f, 0.75f, 0.77f, 0.91f, 0.72f, 0.07f, 0.78f, 0.09f, 0.02f, 0.48f, 0.97f, 0.89f, 0.39f, 0.48f, 0.19f, 0.02f, 0.92f, 0.8f, 0.41f, 0.53f, 0.32f, 0.38f, 0.58f, 0.36f, 0.46f, 0.92f, 0.91f, 0.01f, 0.86f, 0.54f, 0.86f, 0.94f, 0.37f, 0.35f, 0.81f, 0.89f, 0.48f,
 162     0.34f, 0.18f, 0.11f, 0.02f, 0.87f, 0.95f, 0.66f, 0.67f, 0.38f, 0.45f, 0.04f, 0.94f, 0.54f, 0.76f, 0.58f, 0.83f, 0.31f, 0.73f, 0.71f, 0.06f, 0.35f, 0.32f, 0.35f, 0.61f, 0.27f, 0.98f, 0.83f, 0.11f, 0.3f, 0.42f, 0.95f, 0.69f, 0.58f, 0.29f, 0.1f, 0.68f, 0.94f, 0.62f, 0.51f, 0.47f, 0.04f, 0.47f, 0.34f, 0.71f, 0.52f, 0.19f, 0.69f, 0.5f, 0.59f, 0.05f, 0.74f, 0.11f, 0.4f, 0.81f, 0.24f, 0.53f, 0.71f, 0.07f, 0.17f, 0.41f, 0.23f, 0.78f, 0.27f, 0.1f, 0.71f, 0.36f, 0.67f, 0.6f, 0.94f, 0.69f, 0.19f, 0.58f, 0.68f, 0.5f, 0.62f, 0.38f, 0.29f, 0.44f, 0.04f, 0.89f, 0.0f, 0.76f, 0.22f, 0.16f, 0.08f, 0.62f, 0.51f, 0.62f, 0.83f, 0.72f, 0.96f, 0.99f, 0.4f, 0.79f, 0.83f, 0.21f, 0.43f, 0.32f, 0.44f, 0.72f,
 163     0.21f, 0.4f, 0.93f, 0.07f, 0.11f, 0.41f, 0.24f, 0.04f, 0.36f, 0.15f, 0.92f, 0.08f, 0.99f, 0.35f, 0.42f, 0.7f, 0.17f, 0.39f, 0.69f, 0.0f, 0.86f, 0.89f, 0.59f, 0.81f, 0.77f, 0.15f, 0.89f, 0.17f, 0.76f, 0.67f, 0.58f, 0.78f, 0.26f, 0.19f, 0.69f, 0.18f, 0.46f, 0.6f, 0.69f, 0.23f, 0.34f, 0.3f, 0.64f, 0.34f, 0.6f, 0.99f, 0.69f, 0.57f, 0.75f, 0.07f, 0.36f, 0.75f, 0.81f, 0.8f, 0.42f, 0.09f, 0.94f, 0.66f, 0.35f, 0.67f, 0.34f, 0.66f, 0.02f, 0.47f, 0.78f, 0.21f, 0.02f, 0.18f, 0.42f, 0.2f, 0.46f, 0.34f, 0.4f, 0.46f, 0.96f, 0.86f, 0.25f, 0.25f, 0.22f, 0.37f, 0.59f, 0.19f, 0.45f, 0.61f, 0.04f, 0.71f, 0.77f, 0.51f, 0.77f, 0.15f, 0.78f, 0.36f, 0.62f, 0.24f, 0.86f, 0.2f, 0.77f, 0.08f, 0.09f, 0.3f,
 164     0.0f, 0.6f, 0.99f, 0.69f,
 165 };
 166
 167 //! A lot of bogus input spline derivatives - should have at list (max PME order = 5) * (DIM = 3) * (total unique atom number in all test cases = 16) values
 168 static std::vector<real> const c_sampleSplineDerivativesFull
 169 {
 170     0.82f, 0.88f, 0.83f, 0.11f, 0.93f, 0.32f, 0.71f, 0.37f, 0.69f, 0.88f, 0.11f, 0.38f, 0.25f, 0.5f, 0.36f, 0.81f, 0.78f, 0.31f, 0.66f, 0.32f, 0.27f, 0.35f, 0.53f, 0.83f, 0.08f, 0.08f, 0.94f, 0.71f, 0.65f, 0.24f, 0.13f, 0.01f, 0.33f, 0.65f, 0.24f, 0.53f, 0.45f, 0.84f, 0.33f, 0.97f, 0.31f, 0.7f, 0.03f, 0.31f, 0.41f, 0.76f, 0.12f, 0.3f, 0.57f, 0.65f, 0.87f, 0.99f, 0.42f, 0.97f, 0.32f, 0.39f, 0.73f, 0.23f, 0.03f, 0.67f, 0.97f, 0.57f, 0.42f, 0.38f, 0.54f, 0.17f, 0.53f, 0.54f, 0.18f, 0.8f, 0.76f, 0.13f, 0.29f, 0.83f, 0.77f, 0.56f, 0.4f, 0.87f, 0.36f, 0.18f, 0.59f, 0.04f, 0.05f, 0.61f, 0.26f, 0.91f, 0.62f, 0.16f, 0.89f, 0.23f, 0.26f, 0.59f, 0.33f, 0.2f, 0.49f, 0.41f, 0.25f, 0.4f, 0.16f, 0.83f,
 171     0.44f, 0.82f, 0.21f, 0.95f, 0.14f, 0.8f, 0.37f, 0.31f, 0.41f, 0.53f, 0.15f, 0.85f, 0.78f, 0.17f, 0.92f, 0.03f, 0.13f, 0.2f, 0.03f, 0.33f, 0.87f, 0.38f, 0, 0.08f, 0.79f, 0.36f, 0.53f, 0.05f, 0.07f, 0.94f, 0.23f, 0.85f, 0.13f, 0.27f, 0.23f, 0.22f, 0.26f, 0.38f, 0.15f, 0.48f, 0.18f, 0.33f, 0.23f, 0.62f, 0.1f, 0.36f, 0.99f, 0.07f, 0.02f, 0.04f, 0.09f, 0.29f, 0.52f, 0.29f, 0.83f, 0.97f, 0.61f, 0.81f, 0.49f, 0.56f, 0.08f, 0.09f, 0.03f, 0.65f, 0.46f, 0.1f, 0.06f, 0.06f, 0.39f, 0.29f, 0.04f, 0.03f, 0.1f, 0.83f, 0.94f, 0.59f, 0.97f, 0.82f, 0.2f, 0.66f, 0.23f, 0.11f, 0.03f, 0.16f, 0.27f, 0.53f, 0.94f, 0.46f, 0.43f, 0.29f, 0.97f, 0.64f, 0.46f, 0.37f, 0.43f, 0.48f, 0.37f, 0.93f, 0.5f, 0.2f,
 172     0.92f, 0.09f, 0.74f, 0.55f, 0.44f, 0.05f, 0.13f, 0.17f, 0.79f, 0.44f, 0.11f, 0.6f, 0.64f, 0.05f, 0.96f, 0.3f, 0.45f, 0.47f, 0.42f, 0.74f, 0.91f, 0.06f, 0.89f, 0.24f, 0.26f, 0.68f, 0.4f, 0.88f, 0.5f, 0.65f, 0.48f, 0.15f, 0.0f, 0.41f, 0.67f, 0.4f, 0.31f, 0.73f, 0.77f, 0.36f, 0.26f, 0.74f, 0.46f, 0.56f, 0.78f, 0.92f, 0.32f, 0.9f, 0.06f, 0.55f, 0.6f, 0.13f, 0.38f, 0.93f, 0.5f, 0.92f, 0.96f, 0.82f, 0.0f, 0.04f, 0.9f, 0.55f, 0.97f, 1.0f, 0.23f, 0.46f, 0.52f, 0.49f, 0.0f, 0.32f, 0.16f, 0.4f, 0.62f, 0.36f, 0.03f, 0.63f, 0.16f, 0.58f, 0.97f, 0.03f, 0.44f, 0.07f, 0.22f, 0.75f, 0.32f, 0.61f, 0.94f, 0.33f, 0.7f, 0.57f, 0.5f, 0.84f, 0.7f, 0.47f, 0.18f, 0.09f, 0.25f, 0.77f, 0.94f, 0.85f,
 173     0.09f, 0.83f, 0.02f, 0.91f,
 174 };
 175
 176 //! 2 c_sample grids - only non-zero values have to be listed
 177 static std::vector<SparseRealGridValuesInput> const c_sampleGrids
 178 {
 179     SparseRealGridValuesInput {{
 180                                    IVec {
 181                                        0, 0, 0
 182                                    }, 3.5f
 183                                }, {
 184                                    IVec {
 185                                        7, 0, 0
 186                                    }, -2.5f
 187                                },
 188                                {
 189                                    IVec {
 190                                        3, 5, 7
 191                                    }, -0.006f
 192                                }, {
 193                                    IVec {
 194                                        1, 6, 7
 195                                    }, -2.76f
 196                                }, {
 197                                    IVec {
 198                                        3, 1, 2
 199                                    }, 0.6f
 200                                },  {
 201                                    IVec {
 202                                        6, 2, 4
 203                                    }, 7.1f
 204                                }, {
 205                                    IVec {
 206                                        4, 5, 6
 207                                    }, 4.1f
 208                                }, {
 209                                    IVec {
 210                                        4, 4, 6
 211                                    }, -3.7f
 212                                }, },
 213     SparseRealGridValuesInput {{
 214                                    IVec {
 215                                        0, 4, 0
 216                                    }, 6.f
 217                                }, {
 218                                    IVec {
 219                                        4, 2, 7
 220                                    }, 13.76f
 221                                }, {
 222                                    IVec {
 223                                        0, 6, 7
 224                                    }, 3.6f
 225                                }, {
 226                                    IVec {
 227                                        3, 2, 8
 228                                    }, 0.61f
 229                                },
 230                                {
 231                                    IVec {
 232                                        5, 4, 3
 233                                    }, 2.1f
 234                                },
 235                                {
 236                                    IVec {
 237                                        2, 5, 10
 238                                    }, 3.6f
 239                                }, {
 240                                    IVec {
 241                                        5, 3, 6
 242                                    }, 2.1f
 243                                }, {
 244                                    IVec {
 245                                        6, 6, 6
 246                                    }, 6.1f
 247                                }, }
 248 };
 249
 250 //! Input forces for reduction
 251 static std::vector<RVec> const c_sampleForcesFull {
 252     RVec {
 253         0.02f, 0.87f, 0.95f
 254     }, RVec {
 255         0.66f, 0.67f, 0.38f
 256     }, RVec {
 257         0.45f, 0.04f, 0.94f
 258     }, RVec {
 259         0.54f, 0.76f, 0.58f
 260     },
 261     RVec {
 262         0.83f, 0.31f, 0.73f
 263     }, RVec {
 264         0.71f, 0.06f, 0.35f
 265     }, RVec {
 266         0.32f, 0.35f, 0.61f
 267     }, RVec {
 268         0.27f, 0.98f, 0.83f
 269     },
 270     RVec {
 271         0.11f, 0.3f, 0.42f
 272     }, RVec {
 273         0.95f, 0.69f, 0.58f
 274     }, RVec {
 275         0.29f, 0.1f, 0.68f
 276     }, RVec {
 277         0.94f, 0.62f, 0.51f
 278     },
 279     RVec {
 280         0.47f, 0.04f, 0.47f
 281     }, RVec {
 282         0.34f, 0.71f, 0.52f
 283     }
 284 };
 285
 286 //! PME orders to test
 287 static std::vector<int> const pmeOrders {
 288     3, 4, 5
 289 };
 290 //! Atom counts to test
 291 static std::vector<size_t> const atomCounts {
 292     1, 2, 13
 293 };
 294
 295 /* Helper structures for test input */
 296
 297 //! A structure for all the spline data which depends in size both on the PME order and atom count
 298 struct AtomAndPmeOrderSizedData
 299 {
 300     //! Spline values
 301     SplineParamsVector splineValues;
 302     //! Spline derivatives
 303     SplineParamsVector splineDerivatives;
 304 };
 305
 306 //! A structure for all the input atom data which depends in size on atom count - including a range of spline data for different PME orders
 307 struct AtomSizedData
 308 {
 309     //! Gridline indices
 310     GridLineIndicesVector                   gridLineIndices;
 311     //! Charges
 312     ChargesVector                           charges;
 313     //! Coordinates
 314     CoordinatesVector                       coordinates;
 315     //! Spline data for different orders
 316     std::map<int, AtomAndPmeOrderSizedData> splineDataByPmeOrder;
 317 };
 318
 319 //! A range of the test input data sets, uniquely identified by the atom count
 320 typedef std::map<size_t, AtomSizedData> InputDataByAtomCount;
 321
 322 /*! \brief Convenience typedef of the test input parameters - unit cell box, PME interpolation order, grid dimensions,
 323  *  grid values, overwriting/reducing the input forces, atom count.
 324  *
 325  * The rest of the atom-related input data - gridline indices, spline theta values, spline dtheta values, atom charges -
 326  * is looked up in the inputAtomDataSets_ test fixture variable.
 327  */
 328 typedef std::tuple<Matrix3x3, int, IVec, SparseRealGridValuesInput, PmeForceOutputHandling, size_t> GatherInputParameters;
 329
 330 //! Test fixture
 331 class PmeGatherTest : public ::testing::TestWithParam<GatherInputParameters>
 332 {
 333     private:
 334         //! Storage of all the input atom datasets
 335         static InputDataByAtomCount s_inputAtomDataSets_;
 336
 337     public:
 338         //! Default constructor
 339         PmeGatherTest()  = default;
 340         //! Sets the input atom data references once
 341         static void SetUpTestCase()
 342         {
 343             size_t start = 0;
 344             for (auto atomCount : atomCounts)
 345             {
 346                 AtomSizedData atomData;
 347                 atomData.gridLineIndices = GridLineIndicesVector(c_sampleGridLineIndicesFull).subArray(start, atomCount);
 348                 atomData.charges         = ChargesVector(c_sampleChargesFull).subArray(start, atomCount);
 349                 start                   += atomCount;
 350                 atomData.coordinates.resize(atomCount, RVec {1e6, 1e7, -1e8});
 351                 /* The coordinates are intentionally bogus in this test - only the size matters; the gridline indices are fed directly as inputs */
 352                 for (auto pmeOrder : pmeOrders)
 353                 {
 354                     AtomAndPmeOrderSizedData splineData;
 355                     const size_t             dimSize = atomCount * pmeOrder;
 356                     for (int dimIndex = 0; dimIndex < DIM; dimIndex++)
 357                     {
 358                         splineData.splineValues[dimIndex]      = SplineParamsDimVector(c_sampleSplineValuesFull).subArray(dimIndex * dimSize, dimSize);
 359                         splineData.splineDerivatives[dimIndex] = SplineParamsDimVector(c_sampleSplineDerivativesFull).subArray(dimIndex * dimSize, dimSize);
 360                     }
 361                     atomData.splineDataByPmeOrder[pmeOrder] = splineData;
 362                 }
 363                 s_inputAtomDataSets_[atomCount] = atomData;
 364             }
 365         }
 366         //! The test
 367         void runTest()
 368         {
 369             /* Getting the input */
 370             Matrix3x3                 box;
 371             int                       pmeOrder;
 372             IVec                      gridSize;
 373             size_t                    atomCount;
 374             SparseRealGridValuesInput nonZeroGridValues;
 375             PmeForceOutputHandling    inputForceTreatment;
 376             std::tie(box, pmeOrder, gridSize, nonZeroGridValues, inputForceTreatment, atomCount) = GetParam();
 377             auto inputAtomData       = s_inputAtomDataSets_[atomCount];
 378             auto inputAtomSplineData = inputAtomData.splineDataByPmeOrder[pmeOrder];
 379
 380             /* Storing the input where it's needed, running the test */
 381             t_inputrec inputRec;
 382             inputRec.nkx         = gridSize[XX];
 383             inputRec.nky         = gridSize[YY];
 384             inputRec.nkz         = gridSize[ZZ];
 385             inputRec.pme_order   = pmeOrder;
 386             inputRec.coulombtype = eelPME;
 387             inputRec.epsilon_r   = 1.0;
 388
 389             TestReferenceData                     refData;
 390             const std::map<CodePath, std::string> modesToTest = {{CodePath::CPU, "CPU"},
 391                                                                  {CodePath::CUDA, "CUDA"}};
 392             for (const auto &mode : modesToTest)
 393             {
 394                 const bool supportedInput = pmeSupportsInputForMode(&inputRec, mode.first);
 395                 if (!supportedInput)
 396                 {
 397                     /* Testing the failure for the unsupported input */
 398                     EXPECT_THROW(pmeInitAtoms(&inputRec, mode.first, nullptr, inputAtomData.coordinates, inputAtomData.charges, box), NotImplementedError);
 399                     continue;
 400                 }
 401
 402                 const auto contextsToTest = getPmeTestEnv()->getHardwareContexts(mode.first);
 403                 for (const auto &context : contextsToTest)
 404                 {
 405                     /* Describing the test uniquely */
 406                     SCOPED_TRACE(formatString("Testing force gathering with %s %sfor PME grid size %d %d %d"
 407                                               ", order %d, %zu atoms, %s",
 408                                               mode.second.c_str(), context.getDescription().c_str(),
 409                                               gridSize[XX], gridSize[YY], gridSize[ZZ],
 410                                               pmeOrder,
 411                                               atomCount,
 412                                               (inputForceTreatment == PmeForceOutputHandling::ReduceWithInput) ? "with reduction" : "without reduction"
 413                                               ));
 414
 415                     PmeSafePointer pmeSafe = pmeInitAtoms(&inputRec, mode.first, context.getDeviceInfo(), inputAtomData.coordinates, inputAtomData.charges, box);
 416
 417                     /* Setting some more inputs */
 418                     pmeSetRealGrid(pmeSafe.get(), mode.first, nonZeroGridValues);
 419                     pmeSetGridLineIndices(pmeSafe.get(), mode.first, inputAtomData.gridLineIndices);
 420                     for (int dimIndex = 0; dimIndex < DIM; dimIndex++)
 421                     {
 422                         pmeSetSplineData(pmeSafe.get(), mode.first, inputAtomSplineData.splineValues[dimIndex], PmeSplineDataType::Values, dimIndex);
 423                         pmeSetSplineData(pmeSafe.get(), mode.first, inputAtomSplineData.splineDerivatives[dimIndex], PmeSplineDataType::Derivatives, dimIndex);
 424                     }
 425
 426                     /* Explicitly copying the sample forces to be able to modify them */
 427                     auto inputForcesFull(c_sampleForcesFull);
 428                     GMX_RELEASE_ASSERT(inputForcesFull.size() >= atomCount, "Bad input forces size");
 429                     auto forces = ForcesVector(inputForcesFull).subArray(0, atomCount);
 430
 431                     /* Running the force gathering itself */
 432                     pmePerformGather(pmeSafe.get(), mode.first, inputForceTreatment, forces);
 433                     pmeFinalizeTest(pmeSafe.get(), mode.first);
 434
 435                     /* Check the output forces correctness */
 436                     TestReferenceChecker forceChecker(refData.rootChecker());
 437                     const auto           ulpTolerance = 3 * pmeOrder;
 438                     forceChecker.setDefaultTolerance(relativeToleranceAsUlp(1.0, ulpTolerance));
 439                     forceChecker.checkSequence(forces.begin(), forces.end(), "Forces");
 440                 }
 441             }
 442         }
 443 };
 444
 445 // An instance of static atom data
 446 InputDataByAtomCount PmeGatherTest::s_inputAtomDataSets_;
 447
 448 //! Test for PME force gathering
 449 TEST_P(PmeGatherTest, ReproducesOutputs)
 450 {
 451     EXPECT_NO_THROW(runTest());
 452 }
 453
 454 //! Instantiation of the PME gathering test
 455 INSTANTIATE_TEST_CASE_P(SaneInput, PmeGatherTest, ::testing::Combine(::testing::ValuesIn(c_sampleBoxes),
 456                                                                          ::testing::ValuesIn(pmeOrders),
 457                                                                          ::testing::ValuesIn(c_sampleGridSizes),
 458                                                                          ::testing::ValuesIn(c_sampleGrids),
 459                                                                          ::testing::Values(PmeForceOutputHandling::Set, PmeForceOutputHandling::ReduceWithInput),
 460                                                                          ::testing::ValuesIn(atomCounts)));
 461
 462 }
 463 }
 464 }