indexing.py 11.9 KB
Newer Older
1
import abc
2

3
4
5
6
7
8
import sympy as sp
import math
import pycuda.driver as cuda
import pycuda.autoinit

from pystencils.astnodes import Conditional, Block
9
from pystencils.slicing import normalizeSlice
10
11
12
13
14

BLOCK_IDX = list(sp.symbols("blockIdx.x blockIdx.y blockIdx.z"))
THREAD_IDX = list(sp.symbols("threadIdx.x threadIdx.y threadIdx.z"))


15
16
17
18
19
class AbstractIndexing(abc.ABCMeta('ABC', (object,), {})):
    """
    Abstract base class for all Indexing classes. An Indexing class defines how a multidimensional
    field is mapped to CUDA's block and grid system. It calculates indices based on CUDA's thread and block indices
    and computes the number of blocks and threads a kernel is started with. The Indexing class is created with
20
    a pystencils field, a slice to iterate over, and further optional parameters that must have default values.
21
    """
22

23
24
25
26
    @abc.abstractproperty
    def coordinates(self):
        """Returns a sequence of coordinate expressions for (x,y,z) depending on symbolic CUDA block and thread indices.
        These symbolic indices can be obtained with the method `indexVariables` """
27
28

    @property
29
30
31
    def indexVariables(self):
        """Sympy symbols for CUDA's block and thread indices"""
        return BLOCK_IDX + THREAD_IDX
32

33
    @abc.abstractmethod
34
    def getCallParameters(self, arrShape, functionToCall):
35
36
37
        """
        Determine grid and block size for kernel call
        :param arrShape: the numeric (not symbolic) shape of the array
38
39
        :param functionToCall: compile kernel function that should be called. Use this object to get information
                               about required resources like number of registers
40
41
42
43
44
45
46
47
48
49
50
51
52
        :return: dict with keys 'blocks' and 'threads' with tuple values for number of (x,y,z) threads and blocks
                 the kernel should be started with
        """

    @abc.abstractmethod
    def guard(self, kernelContent, arrShape):
        """
        In some indexing schemes not all threads of a block execute the kernel content.
        This function can return a Conditional ast node, defining this execution guard.
        :param kernelContent: the actual kernel contents which can e.g. be put into the Conditional node as true block
        :param arrShape: the numeric or symbolic shape of the field
        :return: ast node, which is put inside the kernel function
        """
53
54


55
# -------------------------------------------- Implementations ---------------------------------------------------------
56
57


58
59
class BlockIndexing(AbstractIndexing):
    """Generic indexing scheme that maps sub-blocks of an array to CUDA blocks."""
60

61
62
    def __init__(self, field, iterationSlice=None,
                 blockSize=(256, 8, 1), permuteBlockSizeDependentOnLayout=True):
63
64
65
        """
        Creates
        :param field: pystencils field (common to all Indexing classes)
66
        :param iterationSlice: slice that defines rectangular subarea which is iterated over
67
68
69
        :param permuteBlockSizeDependentOnLayout: if True the blockSize is permuted such that the fastest coordinate
                                                  gets the largest amount of threads
        """
70
71
72
73
74
75
        if field.spatialDimensions > 3:
            raise NotImplementedError("This indexing scheme supports at most 3 spatial dimensions")

        if permuteBlockSizeDependentOnLayout:
            blockSize = self.permuteBlockSizeAccordingToLayout(blockSize, field.layout)

76
77
        blockSize = self.limitBlockSizeToDeviceMaximum(blockSize)
        self._blockSize = blockSize
78
79
80
        self._iterationSlice = normalizeSlice(iterationSlice, field.spatialShape)
        self._dim = field.spatialDimensions
        self._symbolicShape = [e if isinstance(e, sp.Basic) else None for e in field.spatialShape]
81

82
83
    @property
    def coordinates(self):
84
85
86
87
88
        offsets = _getStartFromSlice(self._iterationSlice)
        coordinates = [blockIndex * bs + threadIdx + off
                       for blockIndex, bs, threadIdx, off in zip(BLOCK_IDX, self._blockSize, THREAD_IDX, offsets)]

        return coordinates[:self._dim]
89

90
    def getCallParameters(self, arrShape, functionToCall):
91
92
        substitutionDict = {sym: value for sym, value in zip(self._symbolicShape, arrShape) if sym is not None}

93
94
        widths = [end - start for start, end in zip(_getStartFromSlice(self._iterationSlice),
                                                    _getEndFromSlice(self._iterationSlice, arrShape))]
95
96
        widths = sp.Matrix(widths).subs(substitutionDict)

97
        grid = tuple(math.ceil(length / blockSize) for length, blockSize in zip(widths, self._blockSize))
98
99
        extendBs = (1,) * (3 - len(self._blockSize))
        extendGr = (1,) * (3 - len(grid))
100

101
102
103
104
        return {'block': self._blockSize + extendBs,
                'grid': grid + extendGr}

    def guard(self, kernelContent, arrShape):
105
        arrShape = arrShape[:self._dim]
106
        conditions = [c < end
107
                      for c, end in zip(self.coordinates, _getEndFromSlice(self._iterationSlice, arrShape))]
108
109
110
111
112
        condition = conditions[0]
        for c in conditions[1:]:
            condition = sp.And(condition, c)
        return Block([Conditional(condition, kernelContent)])

113
114
    @staticmethod
    def limitBlockSizeToDeviceMaximum(blockSize):
115
116
117
118
119
120
121
        """
        Changes blocksize according to match device limits according to the following rules:
        1) if the total amount of threads is too big for the current device, the biggest coordinate is divided by 2.
        2) next, if one component is still too big, the component which is too big is divided by 2 and the smallest
           component is multiplied by 2, such that the total amount of threads stays the same
        Returns the altered blockSize
        """
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
        # Get device limits
        da = cuda.device_attribute
        device = cuda.Context.get_device()

        blockSize = list(blockSize)
        maxThreads = device.get_attribute(da.MAX_THREADS_PER_BLOCK)
        maxBlockSize = [device.get_attribute(a)
                        for a in (da.MAX_BLOCK_DIM_X, da.MAX_BLOCK_DIM_Y, da.MAX_BLOCK_DIM_Z)]

        def prod(seq):
            result = 1
            for e in seq:
                result *= e
            return result

        def getIndexOfTooBigElement(blockSize):
            for i, bs in enumerate(blockSize):
                if bs > maxBlockSize[i]:
                    return i
            return None

        def getIndexOfTooSmallElement(blockSize):
            for i, bs in enumerate(blockSize):
                if bs // 2 <= maxBlockSize[i]:
                    return i
            return None

        # Reduce the total number of threads if necessary
        while prod(blockSize) > maxThreads:
            itemToReduce = blockSize.index(max(blockSize))
            for i, bs in enumerate(blockSize):
                if bs > maxBlockSize[i]:
                    itemToReduce = i
            blockSize[itemToReduce] //= 2

        # Cap individual elements
        tooBigElementIndex = getIndexOfTooBigElement(blockSize)
        while tooBigElementIndex is not None:
            tooSmallElementIndex = getIndexOfTooSmallElement(blockSize)
            blockSize[tooSmallElementIndex] *= 2
            blockSize[tooBigElementIndex] //= 2
            tooBigElementIndex = getIndexOfTooBigElement(blockSize)

        return tuple(blockSize)

167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
    @staticmethod
    def limitBlockSizeByRegisterRestriction(blockSize, requiredRegistersPerThread, device=None):
        """Shrinks the blockSize if there are too many registers used per multiprocessor.
        This is not done automatically, since the requiredRegistersPerThread are not known before compilation.
        They can be obtained by ``func.num_regs`` from a pycuda function.
        :returns smaller blockSize if too many registers are used.
        """
        da = cuda.device_attribute
        if device is None:
            device = cuda.Context.get_device()
        availableRegistersPerMP = device.get_attribute(da.MAX_REGISTERS_PER_MULTIPROCESSOR)

        block = blockSize

        while True:
            numThreads = 1
            for t in block:
                numThreads *= t
            requiredRegistersPerMT = numThreads * requiredRegistersPerThread
            if requiredRegistersPerMT <= availableRegistersPerMP:
                return block
            else:
                largestGridEntryIdx = max(range(len(block)), key=lambda e: block[e])
                assert block[largestGridEntryIdx] >= 2
                block[largestGridEntryIdx] //= 2

193
194
    @staticmethod
    def permuteBlockSizeAccordingToLayout(blockSize, layout):
195
        """Returns modified blockSize such that the fastest coordinate gets the biggest block dimension"""
196
197
198
199
200
201
202
203
204
205
        sortedBlockSize = list(sorted(blockSize, reverse=True))
        while len(sortedBlockSize) > len(layout):
            sortedBlockSize[0] *= sortedBlockSize[-1]
            sortedBlockSize = sortedBlockSize[:-1]

        result = list(blockSize)
        for l, bs in zip(reversed(layout), sortedBlockSize):
            result[l] = bs
        return tuple(result[:len(layout)])

206
207
208
209
210
211
212
213
214

class LineIndexing(AbstractIndexing):
    """
    Indexing scheme that assigns the innermost 'line' i.e. the elements which are adjacent in memory to a 1D CUDA block.
    The fastest coordinate is indexed with threadIdx.x, the remaining coordinates are mapped to blockIdx.{x,y,z}
    This indexing scheme supports up to 4 spatial dimensions, where the innermost dimensions is not larger than the
    maximum amount of threads allowed in a CUDA block (which depends on device).
    """

215
    def __init__(self, field, iterationSlice=None):
216
217
218
219
220
221
222
223
224
        availableIndices = [THREAD_IDX[0]] + BLOCK_IDX
        if field.spatialDimensions > 4:
            raise NotImplementedError("This indexing scheme supports at most 4 spatial dimensions")

        coordinates = availableIndices[:field.spatialDimensions]

        fastestCoordinate = field.layout[-1]
        coordinates[0], coordinates[fastestCoordinate] = coordinates[fastestCoordinate], coordinates[0]

225
        self._coordinates = coordinates
226
227
        self._iterationSlice = normalizeSlice(iterationSlice, field.spatialShape)
        self._symbolicShape = [e if isinstance(e, sp.Basic) else None for e in field.spatialShape]
228

229
230
    @property
    def coordinates(self):
231
        return [i + offset for i, offset in zip(self._coordinates, _getStartFromSlice(self._iterationSlice))]
232

233
    def getCallParameters(self, arrShape, functionToCall):
234
235
        substitutionDict = {sym: value for sym, value in zip(self._symbolicShape, arrShape) if sym is not None}

236
237
        widths = [end - start for start, end in zip(_getStartFromSlice(self._iterationSlice),
                                                    _getEndFromSlice(self._iterationSlice, arrShape))]
238
        widths = sp.Matrix(widths).subs(substitutionDict)
239

240
        def getShapeOfCudaIdx(cudaIdx):
241
            if cudaIdx not in self._coordinates:
242
243
                return 1
            else:
244
                idx = self._coordinates.index(cudaIdx)
245
                return int(widths[idx])
246

247
248
        return {'block': tuple([getShapeOfCudaIdx(idx) for idx in THREAD_IDX]),
                'grid': tuple([getShapeOfCudaIdx(idx) for idx in BLOCK_IDX])}
249

250
251
    def guard(self, kernelContent, arrShape):
        return kernelContent
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275


# -------------------------------------- Helper functions --------------------------------------------------------------

def _getStartFromSlice(iterationSlice):
    res = []
    for sliceComponent in iterationSlice:
        if type(sliceComponent) is slice:
            res.append(sliceComponent.start if sliceComponent.start is not None else 0)
        else:
            assert isinstance(sliceComponent, int)
            res.append(sliceComponent)
    return res


def _getEndFromSlice(iterationSlice, arrShape):
    iterSlice = normalizeSlice(iterationSlice, arrShape)
    res = []
    for sliceComponent in iterSlice:
        if type(sliceComponent) is slice:
            res.append(sliceComponent.stop)
        else:
            assert isinstance(sliceComponent, int)
            res.append(sliceComponent + 1)
276
277
    return res