from ieee754.part_mul_add.partpoints import PartitionPoints
+# XXX MAKE SURE TO PRESERVE ALL THESE COMMENTS XXX
+
# main fn, which started out here in the bugtracker:
# https://bugs.libre-soc.org/show_bug.cgi?id=713#c20
-def layout(elwid, signed, part_counts, lane_shapes=None, fixed_width=None):
+# note that signed is **NOT** part of the layout, and will NOT
+# be added (because it is not relevant or appropriate).
+# sign belongs in ast.Shape and is the only appropriate location.
+# there is absolutely nothing within this function that in any
+# way requires a sign. it is *purely* performing numerical width
+# computations that have absolutely nothing to do with whether the
+# actual data is signed or unsigned.
+#
+# context for parameters:
+# http://lists.libre-soc.org/pipermail/libre-soc-dev/2021-October/003921.html
+def layout(elwid, # comes from SimdScope constructor
+ vec_el_counts, # comes from SimdScope constructor
+ lane_shapes=None, # from SimdScope.Signal via a SimdShape
+ fixed_width=None): # from SimdScope.Signal via a SimdShape
"""calculate a SIMD layout.
Glossary:
* element: a single scalar value that is an element of a SIMD vector.
- it has a width in bits, and a signedness. Every element is made of 1 or
+ it has a width in bits. Every element is made of 1 or
more parts.
* ElWid: the element-width (really the element type) of an instruction.
Either an integer or a FP type. Integer `ElWid`s are sign-agnostic.
F16 = ... # SVP64 value 0b10
BF16 = ... # SVP64 value 0b11
- * part: A piece of a SIMD vector, every SIMD vector is made of a
- non-negative integer of parts. Elements are made of a power-of-two
- number of parts. A part is a fixed number of bits wide for each
- different SIMD layout, it doesn't vary when `elwid` changes. A part
- can have a bit width of any non-negative integer, it is not restricted
- to power-of-two. SIMD vectors should have as few parts as necessary,
- since some circuits have size proportional to the number of parts.
-
-
* elwid: ElWid or nmigen Value with ElWid as the shape
the current element-width
- * signed: bool
- the signedness of all elements in a SIMD layout
- * part_counts: dict[ElWid, int]
- a map from `ElWid` values `k` to the number of parts in an element
- when `elwid == k`. Values should be minimized, since higher values
- often create bigger circuits.
+
+ * vec_el_counts: dict[ElWid, int]
+ a map from `ElWid` values `k` to the number of vector elements
+ required within a partition when `elwid == k`.
Example:
- # here, an I8 element is 1 part wide
- part_counts = {ElWid.I8: 1,
- ElWid.I16: 2,
- ElWid.I32: 4,
- ElWid.I64: 8}
+ vec_el_counts = {ElWid.I8(==0b11): 8, # 8 vector elements
+ ElWid.I16(==0b10): 4, # 4 vector elements
+ ElWid.I32(==0b01): 2, # 2 vector elements
+ ElWid.I64(==0b00): 1} # 1 vector (aka scalar) element
Another Example:
- # here, an F16 element is 1 part wide
- part_counts = {ElWid.F16: 1, ElWid.BF16: 1, ElWid.F32: 2, ElWid.F64: 4}
+ vec_el_counts = {ElWid.BF16(==0b11): 4, # 4 vector elements
+ ElWid.F16(==0b10): 4, # 4 vector elements
+ ElWid.F32(==0b01): 2, # 2 vector elements
+ ElWid.F64(==0b00): 1} # 1 (aka scalar) vector element
+
* lane_shapes: int or Mapping[ElWid, int] (optional)
the bit-width of all elements in a SIMD layout.
+ if not provided, the lane_shapes are computed from fixed_width
+ and vec_el_counts at each elwidth.
+
* fixed_width: int (optional)
- the total width of a SIMD vector. One of lane_shapes and fixed_width
- must be provided.
+ the total width of a SIMD vector. One or both of lane_shapes or
+ fixed_width may be provided. Both may not be left out.
"""
# when there are no lane_shapes specified, this indicates a
# desire to use the maximum available space based on the fixed width
if lane_shapes is None:
assert fixed_width is not None, \
"both fixed_width and lane_shapes cannot be None"
- lane_shapes = {i: fixed_width // part_counts[i] for i in part_counts}
+ lane_shapes = {i: fixed_width // vec_el_counts[i]
+ for i in vec_el_counts}
print("lane_shapes", fixed_width, lane_shapes)
+
# identify if the lane_shapes is a mapping (dict, etc.)
# if not, then assume that it is an integer (width) that
# needs to be requested across all partitions
if not isinstance(lane_shapes, Mapping):
- lane_shapes = {i: lane_shapes for i in part_counts}
+ lane_shapes = {i: lane_shapes for i in vec_el_counts}
+
# compute a set of partition widths
- print("lane_shapes", lane_shapes, "part_counts", part_counts)
- cpart_wid = max(lane_shapes.values())
- part_count = max(part_counts.values())
- # calculate the minumum width required
- width = cpart_wid * part_count
+ print("lane_shapes", lane_shapes, "vec_el_counts", vec_el_counts)
+ cpart_wid = 0
+ width = 0
+ for i, lwid in lane_shapes.items():
+ required_width = lwid * vec_el_counts[i]
+ print(" required width", cpart_wid, i, lwid, required_width)
+ if required_width > width:
+ cpart_wid = lwid
+ width = required_width
+
+ # calculate the minumum width required if fixed_width specified
+ part_count = max(vec_el_counts.values())
print("width", width, cpart_wid, part_count)
if fixed_width is not None: # override the width and part_wid
- assert width < fixed_width, "not enough space to fit partitions"
+ assert width <= fixed_width, "not enough space to fit partitions"
part_wid = fixed_width // part_count
assert part_wid * part_count == fixed_width, \
"calculated width not aligned multiples"
width = fixed_width
- print("part_wid", part_wid, "count", part_count)
- else:
- # go with computed width
- part_wid = cpart_wid
+ print("part_wid", part_wid, "count", part_count, "width", width)
+
# create the breakpoints dictionary.
# do multi-stage version https://bugs.libre-soc.org/show_bug.cgi?id=713#c34
# https://stackoverflow.com/questions/26367812/
dpoints = defaultdict(list) # if empty key, create a (empty) list
- for i, c in part_counts.items():
- def add_p(p):
+ padding_masks = {}
+ always_padding_mask = (1 << width) - 1 # start with all bits padding
+ for i, c in vec_el_counts.items():
+ print("dpoints", i, "count", c)
+ # calculate part_wid based on overall width divided by number
+ # of elements.
+ part_wid = width // c
+
+ padding_mask = (1 << width) - 1 # start with all bits padding
+
+ def add_p(msg, start, p):
+ print(" adding dpoint", msg, start, part_wid, i, c, p)
dpoints[p].append(i) # auto-creates list if key non-existent
- for start in range(0, part_count, c):
- add_p(start * part_wid) # start of lane
- add_p(start * part_wid + lane_shapes[i]) # start of padding
+ # for each elwidth, create the required number of vector elements
+ for start in range(c):
+ start_bit = start * part_wid
+ end_bit = start_bit + lane_shapes[i]
+ element_mask = (1 << end_bit) - (1 << start_bit)
+ padding_mask &= ~element_mask # remove element from padding_mask
+ add_p("start", start, start_bit) # start of lane
+ add_p("end ", start, end_bit) # end lane
+ padding_masks[i] = padding_mask
+ always_padding_mask &= padding_mask
+
+ # deduplicate dpoints lists
+ for k in dpoints.keys():
+ dpoints[k] = list({i: None for i in dpoints[k]}.keys())
+
# do not need the breakpoints at the very start or the very end
dpoints.pop(0, None)
dpoints.pop(width, None)
- plist = list(dpoints.keys())
- plist.sort()
+
+ # sort dpoints keys
+ dpoints = dict(sorted(dpoints.items(), key=lambda i: i[0]))
+
print("dpoints")
- pprint(dict(dpoints))
+ pprint(dpoints)
+
# second stage, add (map to) the elwidth==i expressions.
# TODO: use nmutil.treereduce?
points = {}
- for p in plist:
+ for p in dpoints.keys():
points[p] = map(lambda i: elwid == i, dpoints[p])
points[p] = reduce(operator.or_, points[p])
+
# third stage, create the binary values which *if* elwidth is set to i
# *would* result in the mask at that elwidth being set to this value
# these can easily be double-checked through Assertion
bitp = {}
- for i in part_counts.keys():
+ for i in vec_el_counts.keys():
bitp[i] = 0
- for p, elwidths in dpoints.items():
+ for bit_index, (p, elwidths) in enumerate(dpoints.items()):
if i in elwidths:
- bitpos = plist.index(p)
- bitp[i] |= 1 << bitpos
+ bitp[i] |= 1 << bit_index
+
# fourth stage: determine which partitions are 100% unused.
# these can then be "blanked out"
- bmask = (1 << len(plist))-1
- for p in bitp.values():
- bmask &= ~p
+
+ # points are the partition separators, not partition indexes
+ partition_ends = [*dpoints.keys(), width]
+ bmask = 0
+ partition_start = 0
+ for bit_index, partition_end in enumerate(partition_ends):
+ pmask = (1 << partition_end) - (1 << partition_start)
+ always_padding = (always_padding_mask & pmask) == pmask
+ if always_padding:
+ bmask |= 1 << bit_index
+ partition_start = partition_end
return (PartitionPoints(points), bitp, bmask, width, lane_shapes,
- part_wid, part_count)
+ part_wid)
+# XXX XXX XXX XXX quick tests TODO convert to proper ones but kinda good
+# enough for now. if adding new tests do not alter or delete the old ones
+# XXX XXX XXX XXX
if __name__ == '__main__':
# elwidth=0b10 QTY 2 partitions: | ? | ? |
# elwidth=0b11 QTY 4 partitions: | ? | ? | ? | ? |
# actual widths of Signals *within* those partitions is given separately
- part_counts = {
+ vec_el_counts = {
0: 1,
1: 1,
2: 2,
width_in_all_parts = 3
for i in range(4):
- pprint((i, layout(i, True, part_counts, width_in_all_parts)))
-
- # fixed_width=32 and no lane_widths says "allocate maximum"
- # i.e. Vector Element Widths are auto-allocated
- # elwidth=0b00 1x 32-bit | .................32 |
- # elwidth=0b01 1x 32-bit | .................32 |
- # elwidth=0b10 2x 12-bit | ......16 | ......16 |
- # elwidth=0b11 3x 24-bit | ..8| ..8 | ..8 |..8 |
- # expected partitions (^) | | | (^)
- # to be at these points: (|) | | | |
-
- # TODO, fix this so that it is correct
- #print ("maximum allocation from fixed_width=32")
- # for i in range(4):
- # pprint((i, layout(i, True, part_counts, fixed_width=32)))
+ pprint((i, layout(i, vec_el_counts, width_in_all_parts)))
# specify that the Vector Element lengths are to be *different* at
# each of the elwidths.
- # combined with part_counts we have:
- # elwidth=0b00 1x 5-bit | <-- unused -->....5 |
- # elwidth=0b01 1x 6-bit | <-- unused -->.....6 |
- # elwidth=0b10 2x 12-bit | unused .....6 | unused .....6 |
- # elwidth=0b11 3x 24-bit | .....6 | .....6 | .....6 | .....6 |
- # expected partitions (^) ^ ^ ^^ (^)
- # to be at these points: (|) | | || (|)
+ # combined with vec_el_counts we have:
+ # elwidth=0b00 1x 5-bit |<----unused---------->....5|
+ # elwidth=0b01 1x 6-bit |<----unused--------->.....6|
+ # elwidth=0b10 2x 6-bit |unused>.....6|unused>.....6|
+ # elwidth=0b11 4x 6-bit |.....6|.....6|.....6|.....6|
+ # expected partitions (^) ^ ^ ^^ (^)
+ # to be at these points: (|) | | || (|)
+ # (24) 18 12 65 (0)
widths_at_elwidth = {
0: 5,
1: 6,
3: 6
}
- print ("5,6,6,6 elements", widths_at_elwidth)
+ print("5,6,6,6 elements", widths_at_elwidth)
for i in range(4):
- pprint((i, layout(i, False, part_counts, widths_at_elwidth)))
+ pp, bitp, bm, b, c, d = \
+ layout(i, vec_el_counts, widths_at_elwidth)
+ pprint((i, (pp, bitp, bm, b, c, d)))
+ # now check that the expected partition points occur
+ print("5,6,6,6 ppt keys", pp.keys())
+ assert list(pp.keys()) == [5, 6, 12, 18]
+ assert bm == 0 # no unused partitions
+
+ # this example was probably what the 5,6,6,6 one was supposed to be.
+ # combined with vec_el_counts {0:1, 1:1, 2:2, 3:4} we have:
+ # elwidth=0b00 1x 24-bit |.........................24|
+ # elwidth=0b01 1x 12-bit |<--unused--->|...........12|
+ # elwidth=0b10 2x 5 -bit |unused>|....5|unused>|....5|
+ # elwidth=0b11 4x 6 -bit |.....6|.....6|.....6|.....6|
+ # expected partitions (^) ^^ ^ ^^ (^)
+ # to be at these points: (|) || | || (|)
+ # (24) 1817 12 65 (0)
+ widths_at_elwidth = {
+ 0: 24, # QTY 1x 24
+ 1: 12, # QTY 1x 12
+ 2: 5, # QTY 2x 5
+ 3: 6 # QTY 4x 6
+ }
+
+ print("24,12,5,6 elements", widths_at_elwidth)
+ for i in range(4):
+ pp, bitp, bm, b, c, d = \
+ layout(i, vec_el_counts, widths_at_elwidth)
+ pprint((i, (pp, bitp, bm, b, c, d)))
+ # now check that the expected partition points occur
+ print("24,12,5,6 ppt keys", pp.keys())
+ assert list(pp.keys()) == [5, 6, 12, 17, 18]
+ print("bmask", bin(bm))
+ assert bm == 0 # no unused partitions
# this tests elwidth as an actual Signal. layout is allowed to
# determine arbitrarily the overall length
# https://bugs.libre-soc.org/show_bug.cgi?id=713#c30
elwid = Signal(2)
- pp, bitp, bm, b, c, d, e = layout(
- elwid, False, part_counts, widths_at_elwidth)
- pprint((pp, b, c, d, e))
+ pp, bitp, bm, b, c, d = layout(
+ elwid, vec_el_counts, widths_at_elwidth)
+ pprint((pp, b, c, d))
for k, v in bitp.items():
print("bitp elwidth=%d" % k, bin(v))
print("bmask", bin(bm))
+ assert bm == 0 # no unused partitions
m = Module()
for pval in list(pp.values()):
val = yield pval # get nmigen to evaluate pp
ppt.append(val)
- pprint((i, (ppt, b, c, d, e)))
+ pprint((i, (ppt, b, c, d)))
# check the results against bitp static-expected partition points
# https://bugs.libre-soc.org/show_bug.cgi?id=713#c47
# https://stackoverflow.com/a/27165694
# determine arbitrarily the overall length, it is fixed to 64
# https://bugs.libre-soc.org/show_bug.cgi?id=713#c22
+ # combined with vec_el_counts {0:1, 1:1, 2:2, 3:4} we have:
+ # elwidth=0b00 1x 24-bit
+ # elwidth=0b01 1x 12-bit
+ # elwidth=0b10 2x 5-bit
+ # elwidth=0b11 4x 6-bit
+ #
+ # bmask<--------1<----0<---------10<---0<-------1<0<----0<---0<----00<---0
+ # always unused:| | | || | | | | | | || |
+ # 1111111111000000 1111111111000000 1111111100000000 0000000000000000
+ # | | | || | | | | | | || |
+ # 0b00 xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxx........ ..............24|
+ # 0b01 xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxx..........12|
+ # 0b10 xxxxxxxxxxxxxxxx xxxxxxxxxxx....5|xxxxxxxxxxxxxxxx xxxxxxxxxxx....5|
+ # 0b11 xxxxxxxxxx.....6|xxxxxxxxxx.....6|xxxxxxxxxx.....6|xxxxxxxxxx.....6|
+ # ^ ^ ^^ ^ ^ ^ ^ ^ ^^
+ # ppoints: | | || | | | | | ||
+ # | bit-48 /\ | bit-24-/ | | bit-12 /\-bit-5
+ # bit-54 bit-38-/ \ bit-32 | bit-16 /
+ # bit-37 bit-22 bit-6
+
elwid = Signal(2)
- pp, bitp, bm, b, c, d, e = layout(elwid, False, part_counts,
- widths_at_elwidth,
- fixed_width=64)
- pprint((pp, b, c, d, e))
+ pp, bitp, bm, b, c, d = layout(elwid, vec_el_counts,
+ widths_at_elwidth,
+ fixed_width=64)
+ pprint((pp, b, c, d))
for k, v in bitp.items():
print("bitp elwidth=%d" % k, bin(v))
print("bmask", bin(bm))
+ assert bm == 0b101001000000
m = Module()
val = yield pval # get nmigen to evaluate pp
ppt.append(val)
print("test elwidth=%d" % i)
- pprint((i, (ppt, b, c, d, e)))
+ pprint((i, (ppt, b, c, d)))
# check the results against bitp static-expected partition points
# https://bugs.libre-soc.org/show_bug.cgi?id=713#c47
# https://stackoverflow.com/a/27165694
sim = Simulator(m)
sim.add_process(process)
sim.run()
+
+ # fixed_width=32 and no lane_widths says "allocate maximum"
+ # i.e. Vector Element Widths are auto-allocated
+ # elwidth=0b00 1x 32-bit | .................32 |
+ # elwidth=0b01 1x 32-bit | .................32 |
+ # elwidth=0b10 2x 12-bit | ......16 | ......16 |
+ # elwidth=0b11 3x 24-bit | ..8| ..8 | ..8 |..8 |
+ # expected partitions (^) | | | (^)
+ # to be at these points: (|) | | | |
+
+ # TODO, fix this so that it is correct. put it at the end so it
+ # shows that things break and doesn't stop the other tests.
+ print("maximum allocation from fixed_width=32")
+ for i in range(4):
+ pprint((i, layout(i, vec_el_counts, fixed_width=32)))
+
+ # example "exponent"
+ # https://libre-soc.org/3d_gpu/architecture/dynamic_simd/shape/
+ # 1xFP64: 11 bits, one exponent
+ # 2xFP32: 8 bits, two exponents
+ # 4xFP16: 5 bits, four exponents
+ # 4xBF16: 8 bits, four exponents
+ vec_el_counts = {
+ 0: 1, # QTY 1x FP64
+ 1: 2, # QTY 2x FP32
+ 2: 4, # QTY 4x FP16
+ 3: 4, # QTY 4x BF16
+ }
+ widths_at_elwidth = {
+ 0: 11, # FP64 ew=0b00
+ 1: 8, # FP32 ew=0b01
+ 2: 5, # FP16 ew=0b10
+ 3: 8 # BF16 ew=0b11
+ }
+
+ # expected results:
+ #
+ # |31| | |24| 16|15 | | 8|7 0 |
+ # |31|28|26|24| |20|16| 12| |10|8|5|4 0 |
+ # 32bit | x| x| x| | x| x| x|10 .... 0 |
+ # 16bit | x| x|26 ... 16 | x| x|10 .... 0 |
+ # 8bit | x|28 .. 24| 20.16| x|11 .. 8|x|4.. 0 |
+ # unused x x
+
+ print("11,8,5,8 elements (FP64/32/16/BF exponents)", widths_at_elwidth)
+ for i in range(4):
+ pp, bitp, bm, b, c, d = \
+ layout(i, vec_el_counts, widths_at_elwidth,
+ fixed_width=32)
+ pprint((i, (pp, bitp, bin(bm), b, c, d)))
+ # now check that the expected partition points occur
+ print("11,8,5,8 pp keys", pp.keys())
+ #assert list(pp.keys()) == [5,6,12,18]
+
+ ###### ######
+ ###### 2nd test, different from the above, elwid=0b10 ==> 11 bit ######
+ ###### ######
+
+ # example "exponent"
+ vec_el_counts = {
+ 0: 1, # QTY 1x FP64
+ 1: 2, # QTY 2x FP32
+ 2: 4, # QTY 4x FP16
+ 3: 4, # QTY 4x BF16
+ }
+ widths_at_elwidth = {
+ 0: 11, # FP64 ew=0b00
+ 1: 11, # FP32 ew=0b01
+ 2: 5, # FP16 ew=0b10
+ 3: 8 # BF16 ew=0b11
+ }
+
+ # expected results:
+ #
+ # |31| | |24| 16|15 | | 8|7 0 |
+ # |31|28|26|24| |20|16| 12| |10|8|5|4 0 |
+ # 32bit | x| x| x| | x| x| x|10 .... 0 |
+ # 16bit | x| x|26 ... 16 | x| x|10 .... 0 |
+ # 8bit | x|28 .. 24| 20.16| x|11 .. 8|x|4.. 0 |
+ # unused x x
+
+ print("11,8,5,8 elements (FP64/32/16/BF exponents)", widths_at_elwidth)
+ for i in range(4):
+ pp, bitp, bm, b, c, d = \
+ layout(i, vec_el_counts, widths_at_elwidth,
+ fixed_width=32)
+ pprint((i, (pp, bitp, bin(bm), b, c, d)))
+ # now check that the expected partition points occur
+ print("11,8,5,8 pp keys", pp.keys())
+ #assert list(pp.keys()) == [5,6,12,18]
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