src/ieee754/part/layout_experiment.py

   1 #!/usr/bin/env python3
   2 # SPDX-License-Identifier: LGPL-3-or-later
   3 # See Notices.txt for copyright information
   4 """
   5 Links:
   6 * https://libre-soc.org/3d_gpu/architecture/dynamic_simd/shape/
   7 * https://bugs.libre-soc.org/show_bug.cgi?id=713#c20
   8 * https://bugs.libre-soc.org/show_bug.cgi?id=713#c30
   9 * https://bugs.libre-soc.org/show_bug.cgi?id=713#c34
  10 * https://bugs.libre-soc.org/show_bug.cgi?id=713#c47
  11 * https://bugs.libre-soc.org/show_bug.cgi?id=713#c22
  12 * https://bugs.libre-soc.org/show_bug.cgi?id=713#c67
  13 """
  14
  15 from nmigen import Signal, Module, Elaboratable, Mux, Cat, Shape, Repl
  16 from nmigen.back.pysim import Simulator, Delay, Settle
  17 from nmigen.cli import rtlil
  18
  19 from collections.abc import Mapping
  20 from functools import reduce
  21 import operator
  22 from collections import defaultdict
  23 from pprint import pprint
  24
  25 from ieee754.part_mul_add.partpoints import PartitionPoints
  26
  27
  28 # main fn, which started out here in the bugtracker:
  29 # https://bugs.libre-soc.org/show_bug.cgi?id=713#c20
  30 # note that signed is **NOT** part of the layout, and will NOT
  31 # be added (because it is not relevant or appropriate).
  32 # sign belongs in ast.Shape and is the only appropriate location.
  33 # there is absolutely nothing within this function that in any
  34 # way requires a sign.  it is *purely* performing numerical width
  35 # computations that have absolutely nothing to do with whether the
  36 # actual data is signed or unsigned.
  37 def layout(elwid, vec_el_counts, lane_shapes=None, fixed_width=None):
  38     """calculate a SIMD layout.
  39
  40     Glossary:
  41     * element: a single scalar value that is an element of a SIMD vector.
  42         it has a width in bits. Every element is made of 1 or
  43         more parts.
  44     * ElWid: the element-width (really the element type) of an instruction.
  45         Either an integer or a FP type. Integer `ElWid`s are sign-agnostic.
  46         In Python, `ElWid` is either an enum type or is `int`.
  47         Example `ElWid` definition for integers:
  48
  49         class ElWid(Enum):
  50             I64 = ...       # SVP64 value 0b00
  51             I32 = ...       # SVP64 value 0b01
  52             I16 = ...       # SVP64 value 0b10
  53             I8 = ...        # SVP64 value 0b11
  54
  55         Example `ElWid` definition for floats:
  56
  57         class ElWid(Enum):
  58             F64 = ...    # SVP64 value 0b00
  59             F32 = ...    # SVP64 value 0b01
  60             F16 = ...    # SVP64 value 0b10
  61             BF16 = ...   # SVP64 value 0b11
  62
  63     * elwid: ElWid or nmigen Value with ElWid as the shape
  64         the current element-width
  65
  66     * vec_el_counts: dict[ElWid, int]
  67         a map from `ElWid` values `k` to the number of vector elements
  68         required within a partition when `elwid == k`.
  69
  70         Example:
  71         vec_el_counts = {ElWid.I8(==0b11): 8, # 8 vector elements
  72                        ElWid.I16(==0b10): 4,  # 4 vector elements
  73                        ElWid.I32(==0b01): 2,  # 2 vector elements
  74                        ElWid.I64(==0b00): 1}  # 1 vector (aka scalar) element
  75
  76         Another Example:
  77         vec_el_counts = {ElWid.BF16(==0b11): 4, # 4 vector elements
  78                          ElWid.F16(==0b10): 4,  # 4 vector elements
  79                          ElWid.F32(==0b01): 2,  # 2 vector elements
  80                          ElWid.F64(==0b00): 1}  # 1 (aka scalar) vector element
  81
  82     * lane_shapes: int or Mapping[ElWid, int] (optional)
  83         the bit-width of all elements in a SIMD layout.
  84         if not provided, the lane_shapes are computed from fixed_width
  85         and vec_el_counts at each elwidth.
  86
  87     * fixed_width: int (optional)
  88         the total width of a SIMD vector. One or both of lane_shapes or
  89         fixed_width may be provided.  Both may not be left out.
  90     """
  91     # when there are no lane_shapes specified, this indicates a
  92     # desire to use the maximum available space based on the fixed width
  93     # https://bugs.libre-soc.org/show_bug.cgi?id=713#c67
  94     if lane_shapes is None:
  95         assert fixed_width is not None, \
  96             "both fixed_width and lane_shapes cannot be None"
  97         lane_shapes = {i: fixed_width // vec_el_counts[i]
  98                        for i in vec_el_counts}
  99         print("lane_shapes", fixed_width, lane_shapes)
 100
 101     # identify if the lane_shapes is a mapping (dict, etc.)
 102     # if not, then assume that it is an integer (width) that
 103     # needs to be requested across all partitions
 104     if not isinstance(lane_shapes, Mapping):
 105         lane_shapes = {i: lane_shapes for i in vec_el_counts}
 106
 107     # compute a set of partition widths
 108     print("lane_shapes", lane_shapes, "vec_el_counts", vec_el_counts)
 109     cpart_wid = 0
 110     width = 0
 111     for i, lwid in lane_shapes.items():
 112         required_width = lwid * vec_el_counts[i]
 113         print("     required width", cpart_wid, i, lwid, required_width)
 114         if required_width > width:
 115             cpart_wid = lwid
 116             width = required_width
 117
 118     # calculate the minumum width required if fixed_width specified
 119     part_count = max(vec_el_counts.values())
 120     print("width", width, cpart_wid, part_count)
 121     if fixed_width is not None:  # override the width and part_wid
 122         assert width <= fixed_width, "not enough space to fit partitions"
 123         part_wid = fixed_width // part_count
 124         assert part_wid * part_count == fixed_width, \
 125             "calculated width not aligned multiples"
 126         width = fixed_width
 127         print("part_wid", part_wid, "count", part_count, "width", width)
 128
 129     # create the breakpoints dictionary.
 130     # do multi-stage version https://bugs.libre-soc.org/show_bug.cgi?id=713#c34
 131     # https://stackoverflow.com/questions/26367812/
 132     dpoints = defaultdict(list)  # if empty key, create a (empty) list
 133     for i, c in vec_el_counts.items():
 134         print("dpoints", i, "count", c)
 135         # calculate part_wid based on overall width divided by number
 136         # of elements.
 137         part_wid = width // c
 138
 139         def add_p(msg, start, p):
 140             print("    adding dpoint", msg, start, part_wid, i, c, p)
 141             dpoints[p].append(i)  # auto-creates list if key non-existent
 142         # for each elwidth, create the required number of vector elements
 143         for start in range(c):
 144             add_p("start", start, start * part_wid)  # start of lane
 145             add_p("end  ", start, start * part_wid +
 146                   lane_shapes[i])  # end lane
 147
 148     # deduplicate dpoints lists
 149     for k in dpoints.keys():
 150         dpoints[k] = list({i: None for i in dpoints[k]}.keys())
 151
 152     # do not need the breakpoints at the very start or the very end
 153     dpoints.pop(0, None)
 154     dpoints.pop(width, None)
 155     plist = list(dpoints.keys())
 156     plist.sort()
 157     print("dpoints")
 158     pprint(dict(dpoints))
 159
 160     # second stage, add (map to) the elwidth==i expressions.
 161     # TODO: use nmutil.treereduce?
 162     points = {}
 163     for p in plist:
 164         points[p] = map(lambda i: elwid == i, dpoints[p])
 165         points[p] = reduce(operator.or_, points[p])
 166
 167     # third stage, create the binary values which *if* elwidth is set to i
 168     # *would* result in the mask at that elwidth being set to this value
 169     # these can easily be double-checked through Assertion
 170     bitp = {}
 171     for i in vec_el_counts.keys():
 172         bitp[i] = 0
 173         for p, elwidths in dpoints.items():
 174             if i in elwidths:
 175                 bitpos = plist.index(p)
 176                 bitp[i] |= 1 << bitpos
 177
 178     # fourth stage: determine which partitions are 100% unused.
 179     # these can then be "blanked out"
 180     bmask = (1 << len(plist))-1
 181     for p in bitp.values():
 182         bmask &= ~p
 183     return (PartitionPoints(points), bitp, bmask, width, lane_shapes,
 184             part_wid)
 185
 186
 187 if __name__ == '__main__':
 188
 189     # for each element-width (elwidth 0-3) the number of Vector Elements is:
 190     # elwidth=0b00 QTY 1 partitions:   |          ?          |
 191     # elwidth=0b01 QTY 1 partitions:   |          ?          |
 192     # elwidth=0b10 QTY 2 partitions:   |    ?     |     ?    |
 193     # elwidth=0b11 QTY 4 partitions:   | ?  |  ?  |  ?  | ?  |
 194     # actual widths of Signals *within* those partitions is given separately
 195     vec_el_counts = {
 196         0: 1,
 197         1: 1,
 198         2: 2,
 199         3: 4,
 200     }
 201
 202     # width=3 indicates "same width Vector Elements (3) at all elwidths"
 203     # elwidth=0b00 1x 5-bit     |  unused xx      ..3 |
 204     # elwidth=0b01 1x 6-bit     |  unused xx      ..3 |
 205     # elwidth=0b10 2x 12-bit    | xxx  ..3 | xxx  ..3 |
 206     # elwidth=0b11 3x 24-bit    | ..3| ..3 | ..3 |..3 |
 207     # expected partitions      (^)   |     |     |   (^)
 208     # to be at these points:   (|)   |     |     |    |
 209     width_in_all_parts = 3
 210
 211     for i in range(4):
 212         pprint((i, layout(i, vec_el_counts, width_in_all_parts)))
 213
 214     # specify that the Vector Element lengths are to be *different* at
 215     # each of the elwidths.
 216     # combined with vec_el_counts we have:
 217     # elwidth=0b00 1x 5-bit    |<----unused---------->....5|
 218     # elwidth=0b01 1x 6-bit    |<----unused--------->.....6|
 219     # elwidth=0b10 2x 6-bit    |unused>.....6|unused>.....6|
 220     # elwidth=0b11 4x 6-bit    |.....6|.....6|.....6|.....6|
 221     # expected partitions     (^)     ^      ^      ^^    (^)
 222     # to be at these points:  (|)     |      |      ||    (|)
 223     #                         (24)   18     12      65    (0)
 224     widths_at_elwidth = {
 225         0: 5,
 226         1: 6,
 227         2: 6,
 228         3: 6
 229     }
 230
 231     print("5,6,6,6 elements", widths_at_elwidth)
 232     for i in range(4):
 233         pp, bitp, bm, b, c, d = \
 234             layout(i, vec_el_counts, widths_at_elwidth)
 235         pprint((i, (pp, bitp, bm, b, c, d)))
 236     # now check that the expected partition points occur
 237     print("5,6,6,6 ppt keys", pp.keys())
 238     assert list(pp.keys()) == [5, 6, 12, 18]
 239
 240     # this example was probably what the 5,6,6,6 one was supposed to be.
 241     # combined with vec_el_counts {0:1, 1:1, 2:2, 3:4} we have:
 242     # elwidth=0b00 1x 24-bit    |.........................24|
 243     # elwidth=0b01 1x 12-bit    |<--unused--->|...........12|
 244     # elwidth=0b10 2x 5 -bit    |unused>|....5|unused>|....5|
 245     # elwidth=0b11 4x 6 -bit    |.....6|.....6|.....6|.....6|
 246     # expected partitions      (^)     ^^     ^       ^^    (^)
 247     # to be at these points:   (|)     ||     |       ||    (|)
 248     #                          (24)   1817   12       65    (0)
 249     widths_at_elwidth = {
 250         0: 24,  # QTY 1x 24
 251         1: 12,  # QTY 1x 12
 252         2: 5,   # QTY 2x 5
 253         3: 6    # QTY 4x 6
 254     }
 255
 256     print("24,12,5,6 elements", widths_at_elwidth)
 257     for i in range(4):
 258         pp, bitp, bm, b, c, d = \
 259             layout(i, vec_el_counts, widths_at_elwidth)
 260         pprint((i, (pp, bitp, bm, b, c, d)))
 261     # now check that the expected partition points occur
 262     print("24,12,5,6 ppt keys", pp.keys())
 263     assert list(pp.keys()) == [5, 6, 12, 17, 18]
 264
 265     # this tests elwidth as an actual Signal. layout is allowed to
 266     # determine arbitrarily the overall length
 267     # https://bugs.libre-soc.org/show_bug.cgi?id=713#c30
 268
 269     elwid = Signal(2)
 270     pp, bitp, bm, b, c, d = layout(
 271         elwid, vec_el_counts, widths_at_elwidth)
 272     pprint((pp, b, c, d))
 273     for k, v in bitp.items():
 274         print("bitp elwidth=%d" % k, bin(v))
 275     print("bmask", bin(bm))
 276
 277     m = Module()
 278
 279     def process():
 280         for i in range(4):
 281             yield elwid.eq(i)
 282             yield Settle()
 283             ppt = []
 284             for pval in list(pp.values()):
 285                 val = yield pval  # get nmigen to evaluate pp
 286                 ppt.append(val)
 287             pprint((i, (ppt, b, c, d)))
 288             # check the results against bitp static-expected partition points
 289             # https://bugs.libre-soc.org/show_bug.cgi?id=713#c47
 290             # https://stackoverflow.com/a/27165694
 291             ival = int(''.join(map(str, ppt[::-1])), 2)
 292             assert ival == bitp[i]
 293
 294     sim = Simulator(m)
 295     sim.add_process(process)
 296     sim.run()
 297
 298     # this tests elwidth as an actual Signal. layout is *not* allowed to
 299     # determine arbitrarily the overall length, it is fixed to 64
 300     # https://bugs.libre-soc.org/show_bug.cgi?id=713#c22
 301
 302     elwid = Signal(2)
 303     pp, bitp, bm, b, c, d = layout(elwid, vec_el_counts,
 304                                    widths_at_elwidth,
 305                                    fixed_width=64)
 306     pprint((pp, b, c, d))
 307     for k, v in bitp.items():
 308         print("bitp elwidth=%d" % k, bin(v))
 309     print("bmask", bin(bm))
 310
 311     m = Module()
 312
 313     def process():
 314         for i in range(4):
 315             yield elwid.eq(i)
 316             yield Settle()
 317             ppt = []
 318             for pval in list(pp.values()):
 319                 val = yield pval  # get nmigen to evaluate pp
 320                 ppt.append(val)
 321             print("test elwidth=%d" % i)
 322             pprint((i, (ppt, b, c, d)))
 323             # check the results against bitp static-expected partition points
 324             # https://bugs.libre-soc.org/show_bug.cgi?id=713#c47
 325             # https://stackoverflow.com/a/27165694
 326             ival = int(''.join(map(str, ppt[::-1])), 2)
 327             assert ival == bitp[i], "ival %s actual %s" % (bin(ival),
 328                                                            bin(bitp[i]))
 329
 330     sim = Simulator(m)
 331     sim.add_process(process)
 332     sim.run()
 333
 334     # fixed_width=32 and no lane_widths says "allocate maximum"
 335     # i.e. Vector Element Widths are auto-allocated
 336     # elwidth=0b00 1x 32-bit    | .................32 |
 337     # elwidth=0b01 1x 32-bit    | .................32 |
 338     # elwidth=0b10 2x 12-bit    | ......16 | ......16 |
 339     # elwidth=0b11 3x 24-bit    | ..8| ..8 | ..8 |..8 |
 340     # expected partitions      (^)   |     |     |   (^)
 341     # to be at these points:   (|)   |     |     |    |
 342
 343     # TODO, fix this so that it is correct.  put it at the end so it
 344     # shows that things break and doesn't stop the other tests.
 345     print("maximum allocation from fixed_width=32")
 346     for i in range(4):
 347         pprint((i, layout(i, vec_el_counts, fixed_width=32)))
 348
 349     # example "exponent"
 350     #  https://libre-soc.org/3d_gpu/architecture/dynamic_simd/shape/
 351     # 1xFP64: 11 bits, one exponent
 352     # 2xFP32: 8 bits, two exponents
 353     # 4xFP16: 5 bits, four exponents
 354     # 4xBF16: 8 bits, four exponents
 355     vec_el_counts = {
 356         0: 1,  # QTY 1x FP64
 357         1: 2,  # QTY 2x FP32
 358         2: 4,  # QTY 4x FP16
 359         3: 4,  # QTY 4x BF16
 360     }
 361     widths_at_elwidth = {
 362         0: 11,  # FP64 ew=0b00
 363         1: 8,  # FP32 ew=0b01
 364         2: 5,  # FP16 ew=0b10
 365         3: 8   # BF16 ew=0b11
 366     }
 367
 368     # expected results:
 369     #
 370     #        |31|  |  |24|     16|15  |  |   8|7     0 |
 371     #        |31|28|26|24| |20|16|  12|  |10|8|5|4   0 |
 372     #  32bit | x| x| x|  |      x|   x| x|10 ....    0 |
 373     #  16bit | x| x|26    ... 16 |   x| x|10 ....    0 |
 374     #  8bit  | x|28 .. 24|  20.16|   x|11 .. 8|x|4.. 0 |
 375     #  unused  x                     x
 376
 377     print("11,8,5,8 elements (FP64/32/16/BF exponents)", widths_at_elwidth)
 378     for i in range(4):
 379         pp, bitp, bm, b, c, d = \
 380             layout(i, vec_el_counts, widths_at_elwidth,
 381                    fixed_width=32)
 382         pprint((i, (pp, bitp, bin(bm), b, c, d)))
 383     # now check that the expected partition points occur
 384     print("11,8,5,8 pp keys", pp.keys())
 385     #assert list(pp.keys()) == [5,6,12,18]
 386
 387     ######                                                           ######
 388     ###### 2nd test, different from the above, elwid=0b10 ==> 11 bit ######
 389     ######                                                           ######
 390
 391     # example "exponent"
 392     vec_el_counts = {
 393         0: 1,  # QTY 1x FP64
 394         1: 2,  # QTY 2x FP32
 395         2: 4,  # QTY 4x FP16
 396         3: 4,  # QTY 4x BF16
 397     }
 398     widths_at_elwidth = {
 399         0: 11,  # FP64 ew=0b00
 400         1: 11,  # FP32 ew=0b01
 401         2: 5,  # FP16 ew=0b10
 402         3: 8   # BF16 ew=0b11
 403     }
 404
 405     # expected results:
 406     #
 407     #        |31|  |  |24|     16|15  |  |   8|7     0 |
 408     #        |31|28|26|24| |20|16|  12|  |10|8|5|4   0 |
 409     #  32bit | x| x| x|  |      x|   x| x|10 ....    0 |
 410     #  16bit | x| x|26    ... 16 |   x| x|10 ....    0 |
 411     #  8bit  | x|28 .. 24|  20.16|   x|11 .. 8|x|4.. 0 |
 412     #  unused  x                     x
 413
 414     print("11,8,5,8 elements (FP64/32/16/BF exponents)", widths_at_elwidth)
 415     for i in range(4):
 416         pp, bitp, bm, b, c, d = \
 417             layout(i, vec_el_counts, widths_at_elwidth,
 418                    fixed_width=32)
 419         pprint((i, (pp, bitp, bin(bm), b, c, d)))
 420     # now check that the expected partition points occur
 421     print("11,8,5,8 pp keys", pp.keys())
 422     #assert list(pp.keys()) == [5,6,12,18]