src/ieee754/part_mul_add/multiply.py

   1 # SPDX-License-Identifier: LGPL-2.1-or-later
   2 # See Notices.txt for copyright information
   3 """Integer Multiplication."""
   4
   5 from nmigen import Signal, Module, Value, Elaboratable, Cat, C, Mux, Repl
   6 from nmigen.hdl.ast import Assign
   7 from abc import ABCMeta, abstractmethod
   8 from nmigen.cli import main
   9 from functools import reduce
  10 from operator import or_
  11
  12 class PartitionPoints(dict):
  13     """Partition points and corresponding ``Value``s.
  14
  15     The points at where an ALU is partitioned along with ``Value``s that
  16     specify if the corresponding partition points are enabled.
  17
  18     For example: ``{1: True, 5: True, 10: True}`` with
  19     ``width == 16`` specifies that the ALU is split into 4 sections:
  20     * bits 0 <= ``i`` < 1
  21     * bits 1 <= ``i`` < 5
  22     * bits 5 <= ``i`` < 10
  23     * bits 10 <= ``i`` < 16
  24
  25     If the partition_points were instead ``{1: True, 5: a, 10: True}``
  26     where ``a`` is a 1-bit ``Signal``:
  27     * If ``a`` is asserted:
  28         * bits 0 <= ``i`` < 1
  29         * bits 1 <= ``i`` < 5
  30         * bits 5 <= ``i`` < 10
  31         * bits 10 <= ``i`` < 16
  32     * Otherwise
  33         * bits 0 <= ``i`` < 1
  34         * bits 1 <= ``i`` < 10
  35         * bits 10 <= ``i`` < 16
  36     """
  37
  38     def __init__(self, partition_points=None):
  39         """Create a new ``PartitionPoints``.
  40
  41         :param partition_points: the input partition points to values mapping.
  42         """
  43         super().__init__()
  44         if partition_points is not None:
  45             for point, enabled in partition_points.items():
  46                 if not isinstance(point, int):
  47                     raise TypeError("point must be a non-negative integer")
  48                 if point < 0:
  49                     raise ValueError("point must be a non-negative integer")
  50                 self[point] = Value.wrap(enabled)
  51
  52     def like(self, name=None, src_loc_at=0):
  53         """Create a new ``PartitionPoints`` with ``Signal``s for all values.
  54
  55         :param name: the base name for the new ``Signal``s.
  56         """
  57         if name is None:
  58             name = Signal(src_loc_at=1+src_loc_at).name  # get variable name
  59         retval = PartitionPoints()
  60         for point, enabled in self.items():
  61             retval[point] = Signal(enabled.shape(), name=f"{name}_{point}")
  62         return retval
  63
  64     def eq(self, rhs):
  65         """Assign ``PartitionPoints`` using ``Signal.eq``."""
  66         if set(self.keys()) != set(rhs.keys()):
  67             raise ValueError("incompatible point set")
  68         for point, enabled in self.items():
  69             yield enabled.eq(rhs[point])
  70
  71     def as_mask(self, width):
  72         """Create a bit-mask from `self`.
  73
  74         Each bit in the returned mask is clear only if the partition point at
  75         the same bit-index is enabled.
  76
  77         :param width: the bit width of the resulting mask
  78         """
  79         bits = []
  80         for i in range(width):
  81             if i in self:
  82                 bits.append(~self[i])
  83             else:
  84                 bits.append(True)
  85         return Cat(*bits)
  86
  87     def get_max_partition_count(self, width):
  88         """Get the maximum number of partitions.
  89
  90         Gets the number of partitions when all partition points are enabled.
  91         """
  92         retval = 1
  93         for point in self.keys():
  94             if point < width:
  95                 retval += 1
  96         return retval
  97
  98     def fits_in_width(self, width):
  99         """Check if all partition points are smaller than `width`."""
 100         for point in self.keys():
 101             if point >= width:
 102                 return False
 103         return True
 104
 105
 106 class FullAdder(Elaboratable):
 107     """Full Adder.
 108
 109     :attribute in0: the first input
 110     :attribute in1: the second input
 111     :attribute in2: the third input
 112     :attribute sum: the sum output
 113     :attribute carry: the carry output
 114     """
 115
 116     def __init__(self, width):
 117         """Create a ``FullAdder``.
 118
 119         :param width: the bit width of the input and output
 120         """
 121         self.in0 = Signal(width)
 122         self.in1 = Signal(width)
 123         self.in2 = Signal(width)
 124         self.sum = Signal(width)
 125         self.carry = Signal(width)
 126
 127     def elaborate(self, platform):
 128         """Elaborate this module."""
 129         m = Module()
 130         m.d.comb += self.sum.eq(self.in0 ^ self.in1 ^ self.in2)
 131         m.d.comb += self.carry.eq((self.in0 & self.in1)
 132                                   | (self.in1 & self.in2)
 133                                   | (self.in2 & self.in0))
 134         return m
 135
 136
 137 class PartitionedAdder(Elaboratable):
 138     """Partitioned Adder.
 139
 140     :attribute width: the bit width of the input and output. Read-only.
 141     :attribute a: the first input to the adder
 142     :attribute b: the second input to the adder
 143     :attribute output: the sum output
 144     :attribute partition_points: the input partition points. Modification not
 145         supported, except for by ``Signal.eq``.
 146     """
 147
 148     def __init__(self, width, partition_points):
 149         """Create a ``PartitionedAdder``.
 150
 151         :param width: the bit width of the input and output
 152         :param partition_points: the input partition points
 153         """
 154         self.width = width
 155         self.a = Signal(width)
 156         self.b = Signal(width)
 157         self.output = Signal(width)
 158         self.partition_points = PartitionPoints(partition_points)
 159         if not self.partition_points.fits_in_width(width):
 160             raise ValueError("partition_points doesn't fit in width")
 161         expanded_width = 0
 162         for i in range(self.width):
 163             if i in self.partition_points:
 164                 expanded_width += 1
 165             expanded_width += 1
 166         self._expanded_width = expanded_width
 167
 168     def elaborate(self, platform):
 169         """Elaborate this module."""
 170         m = Module()
 171
 172         # intermediates
 173         expanded_a = Signal(self._expanded_width)
 174         expanded_b = Signal(self._expanded_width)
 175         expanded_output = Signal(self._expanded_width)
 176
 177         expanded_index = 0
 178         # store bits in a list, use Cat later.  graphviz is much cleaner
 179         al = []
 180         bl = []
 181         ol = []
 182         ea = []
 183         eb = []
 184         eo = []
 185         # partition points are "breaks" (extra zeros) in what would otherwise
 186         # be a massive long add.
 187         for i in range(self.width):
 188             if i in self.partition_points:
 189                 # add extra bit set to 0 + 0 for enabled partition points
 190                 # and 1 + 0 for disabled partition points
 191                 ea.append(expanded_a[expanded_index])
 192                 al.append(~self.partition_points[i])
 193                 eb.append(expanded_b[expanded_index])
 194                 bl.append(C(0))
 195                 expanded_index += 1
 196             ea.append(expanded_a[expanded_index])
 197             al.append(self.a[i])
 198             eb.append(expanded_b[expanded_index])
 199             bl.append(self.b[i])
 200             eo.append(expanded_output[expanded_index])
 201             ol.append(self.output[i])
 202             expanded_index += 1
 203         # combine above using Cat
 204         m.d.comb += Cat(*ea).eq(Cat(*al))
 205         m.d.comb += Cat(*eb).eq(Cat(*bl))
 206         m.d.comb += Cat(*ol).eq(Cat(*eo))
 207         # use only one addition to take advantage of look-ahead carry and
 208         # special hardware on FPGAs
 209         m.d.comb += expanded_output.eq( expanded_a + expanded_b)
 210         return m
 211
 212
 213 FULL_ADDER_INPUT_COUNT = 3
 214
 215
 216 class AddReduce(Elaboratable):
 217     """Add list of numbers together.
 218
 219     :attribute inputs: input ``Signal``s to be summed. Modification not
 220         supported, except for by ``Signal.eq``.
 221     :attribute register_levels: List of nesting levels that should have
 222         pipeline registers.
 223     :attribute output: output sum.
 224     :attribute partition_points: the input partition points. Modification not
 225         supported, except for by ``Signal.eq``.
 226     """
 227
 228     def __init__(self, inputs, output_width, register_levels, partition_points):
 229         """Create an ``AddReduce``.
 230
 231         :param inputs: input ``Signal``s to be summed.
 232         :param output_width: bit-width of ``output``.
 233         :param register_levels: List of nesting levels that should have
 234             pipeline registers.
 235         :param partition_points: the input partition points.
 236         """
 237         self.inputs = list(inputs)
 238         self._resized_inputs = [
 239             Signal(output_width, name=f"resized_inputs[{i}]")
 240             for i in range(len(self.inputs))]
 241         self.register_levels = list(register_levels)
 242         self.output = Signal(output_width)
 243         self.partition_points = PartitionPoints(partition_points)
 244         if not self.partition_points.fits_in_width(output_width):
 245             raise ValueError("partition_points doesn't fit in output_width")
 246         self._reg_partition_points = self.partition_points.like()
 247         max_level = AddReduce.get_max_level(len(self.inputs))
 248         for level in self.register_levels:
 249             if level > max_level:
 250                 raise ValueError(
 251                     "not enough adder levels for specified register levels")
 252
 253     @staticmethod
 254     def get_max_level(input_count):
 255         """Get the maximum level.
 256
 257         All ``register_levels`` must be less than or equal to the maximum
 258         level.
 259         """
 260         retval = 0
 261         while True:
 262             groups = AddReduce.full_adder_groups(input_count)
 263             if len(groups) == 0:
 264                 return retval
 265             input_count %= FULL_ADDER_INPUT_COUNT
 266             input_count += 2 * len(groups)
 267             retval += 1
 268
 269     def next_register_levels(self):
 270         """``Iterable`` of ``register_levels`` for next recursive level."""
 271         for level in self.register_levels:
 272             if level > 0:
 273                 yield level - 1
 274
 275     @staticmethod
 276     def full_adder_groups(input_count):
 277         """Get ``inputs`` indices for which a full adder should be built."""
 278         return range(0,
 279                      input_count - FULL_ADDER_INPUT_COUNT + 1,
 280                      FULL_ADDER_INPUT_COUNT)
 281
 282     def elaborate(self, platform):
 283         """Elaborate this module."""
 284         m = Module()
 285
 286         # resize inputs to correct bit-width and optionally add in
 287         # pipeline registers
 288         resized_input_assignments = [self._resized_inputs[i].eq(self.inputs[i])
 289                                      for i in range(len(self.inputs))]
 290         if 0 in self.register_levels:
 291             m.d.sync += resized_input_assignments
 292             m.d.sync += self._reg_partition_points.eq(self.partition_points)
 293         else:
 294             m.d.comb += resized_input_assignments
 295             m.d.comb += self._reg_partition_points.eq(self.partition_points)
 296
 297         groups = AddReduce.full_adder_groups(len(self.inputs))
 298         # if there are no full adders to create, then we handle the base cases
 299         # and return, otherwise we go on to the recursive case
 300         if len(groups) == 0:
 301             if len(self.inputs) == 0:
 302                 # use 0 as the default output value
 303                 m.d.comb += self.output.eq(0)
 304             elif len(self.inputs) == 1:
 305                 # handle single input
 306                 m.d.comb += self.output.eq(self._resized_inputs[0])
 307             else:
 308                 # base case for adding 2 or more inputs, which get recursively
 309                 # reduced to 2 inputs
 310                 assert len(self.inputs) == 2
 311                 adder = PartitionedAdder(len(self.output),
 312                                          self._reg_partition_points)
 313                 m.submodules.final_adder = adder
 314                 m.d.comb += adder.a.eq(self._resized_inputs[0])
 315                 m.d.comb += adder.b.eq(self._resized_inputs[1])
 316                 m.d.comb += self.output.eq(adder.output)
 317             return m
 318         # go on to handle recursive case
 319         intermediate_terms = []
 320
 321         def add_intermediate_term(value):
 322             intermediate_term = Signal(
 323                 len(self.output),
 324                 name=f"intermediate_terms[{len(intermediate_terms)}]")
 325             intermediate_terms.append(intermediate_term)
 326             m.d.comb += intermediate_term.eq(value)
 327
 328         # store mask in intermediary (simplifies graph)
 329         part_mask = Signal(len(self.output), reset_less=True)
 330         mask = self._reg_partition_points.as_mask(len(self.output))
 331         m.d.comb += part_mask.eq(mask)
 332
 333         # create full adders for this recursive level.
 334         # this shrinks N terms to 2 * (N // 3) plus the remainder
 335         for i in groups:
 336             adder_i = FullAdder(len(self.output))
 337             setattr(m.submodules, f"adder_{i}", adder_i)
 338             m.d.comb += adder_i.in0.eq(self._resized_inputs[i])
 339             m.d.comb += adder_i.in1.eq(self._resized_inputs[i + 1])
 340             m.d.comb += adder_i.in2.eq(self._resized_inputs[i + 2])
 341             add_intermediate_term(adder_i.sum)
 342             shifted_carry = adder_i.carry << 1
 343             # mask out carry bits to prevent carries between partitions
 344             add_intermediate_term((adder_i.carry << 1) & part_mask)
 345         # handle the remaining inputs.
 346         if len(self.inputs) % FULL_ADDER_INPUT_COUNT == 1:
 347             add_intermediate_term(self._resized_inputs[-1])
 348         elif len(self.inputs) % FULL_ADDER_INPUT_COUNT == 2:
 349             # Just pass the terms to the next layer, since we wouldn't gain
 350             # anything by using a half adder since there would still be 2 terms
 351             # and just passing the terms to the next layer saves gates.
 352             add_intermediate_term(self._resized_inputs[-2])
 353             add_intermediate_term(self._resized_inputs[-1])
 354         else:
 355             assert len(self.inputs) % FULL_ADDER_INPUT_COUNT == 0
 356         # recursive invocation of ``AddReduce``
 357         next_level = AddReduce(intermediate_terms,
 358                                len(self.output),
 359                                self.next_register_levels(),
 360                                self._reg_partition_points)
 361         m.submodules.next_level = next_level
 362         m.d.comb += self.output.eq(next_level.output)
 363         return m
 364
 365
 366 OP_MUL_LOW = 0
 367 OP_MUL_SIGNED_HIGH = 1
 368 OP_MUL_SIGNED_UNSIGNED_HIGH = 2  # a is signed, b is unsigned
 369 OP_MUL_UNSIGNED_HIGH = 3
 370
 371
 372 def get_term(value, shift=0, enabled=None):
 373     if enabled is not None:
 374         value = Mux(enabled, value, 0)
 375     if shift > 0:
 376         value = Cat(Repl(C(0, 1), shift), value)
 377     else:
 378         assert shift == 0
 379     return value
 380
 381
 382 class ProductTerm(Elaboratable):
 383
 384     def __init__(self, width, twidth, pbwid, a_index, b_index):
 385         self.a_index = a_index
 386         self.b_index = b_index
 387         shift = 8 * (self.a_index + self.b_index)
 388         self.pwidth = width
 389         self.width = width*2
 390         self.shift = shift
 391
 392         self.ti = Signal(self.width, reset_less=True)
 393         self.term = Signal(twidth, reset_less=True)
 394         self.a = Signal(twidth//2, reset_less=True)
 395         self.b = Signal(twidth//2, reset_less=True)
 396         self.pb_en = Signal(pbwid, reset_less=True)
 397
 398         self.tl = tl = []
 399         min_index = min(self.a_index, self.b_index)
 400         max_index = max(self.a_index, self.b_index)
 401         for i in range(min_index, max_index):
 402             tl.append(self.pb_en[i])
 403         name = "te_%d_%d" % (self.a_index, self.b_index)
 404         if len(tl) > 0:
 405             term_enabled = Signal(name=name, reset_less=True)
 406         else:
 407             term_enabled = None
 408         self.enabled = term_enabled
 409         self.term.name = "term_%d_%d" % (a_index, b_index) # rename
 410
 411     def elaborate(self, platform):
 412
 413         m = Module()
 414         if self.enabled is not None:
 415             m.d.comb += self.enabled.eq(~(Cat(*self.tl).bool()))
 416
 417         bsa = Signal(self.width, reset_less=True)
 418         bsb = Signal(self.width, reset_less=True)
 419         a_index, b_index = self.a_index, self.b_index
 420         pwidth = self.pwidth
 421         m.d.comb += bsa.eq(self.a.bit_select(a_index * pwidth, pwidth))
 422         m.d.comb += bsb.eq(self.b.bit_select(b_index * pwidth, pwidth))
 423         m.d.comb += self.ti.eq(bsa * bsb)
 424         m.d.comb += self.term.eq(get_term(self.ti, self.shift, self.enabled))
 425
 426         return m
 427
 428
 429 class ProductTerms(Elaboratable):
 430
 431     def __init__(self, width, twidth, pbwid, a_index, blen):
 432         self.a_index = a_index
 433         self.blen = blen
 434         self.pwidth = width
 435         self.twidth = twidth
 436         self.pbwid = pbwid
 437         self.a = Signal(twidth//2, reset_less=True)
 438         self.b = Signal(twidth//2, reset_less=True)
 439         self.pb_en = Signal(pbwid, reset_less=True)
 440         self.terms = [Signal(twidth, name="term%d"%i, reset_less=True) \
 441                             for i in range(blen)]
 442
 443     def elaborate(self, platform):
 444
 445         m = Module()
 446
 447         for b_index in range(self.blen):
 448             t = ProductTerm(self.pwidth, self.twidth, self.pbwid,
 449                             self.a_index, b_index)
 450             setattr(m.submodules, "term_%d" % b_index, t)
 451
 452             m.d.comb += t.a.eq(self.a)
 453             m.d.comb += t.b.eq(self.b)
 454             m.d.comb += t.pb_en.eq(self.pb_en)
 455
 456             m.d.comb += self.terms[b_index].eq(t.term)
 457
 458         return m
 459
 460
 461 class Part(Elaboratable):
 462     def __init__(self, width, n_parts, n_levels, pbwid):
 463
 464         # inputs
 465         self.a = Signal(64)
 466         self.b = Signal(64)
 467         self.a_signed = [Signal(name=f"a_signed_{i}") for i in range(8)]
 468         self.b_signed = [Signal(name=f"_b_signed_{i}") for i in range(8)]
 469         self.pbs = Signal(pbwid, reset_less=True)
 470
 471         # outputs
 472         self.parts = [Signal(name=f"part_{i}") for i in range(n_parts)]
 473         self.delayed_parts = [
 474             [Signal(name=f"delayed_part_{delay}_{i}")
 475              for i in range(n_parts)]
 476                 for delay in range(n_levels)]
 477         # XXX REALLY WEIRD BUG - have to take a copy of the last delayed_parts
 478         self.dplast = [Signal(name=f"dplast_{i}")
 479                          for i in range(n_parts)]
 480
 481         self.not_a_term = Signal(width)
 482         self.neg_lsb_a_term = Signal(width)
 483         self.not_b_term = Signal(width)
 484         self.neg_lsb_b_term = Signal(width)
 485
 486     def elaborate(self, platform):
 487         m = Module()
 488
 489         pbs, parts, delayed_parts = self.pbs, self.parts, self.delayed_parts
 490         byte_count = 8 // len(parts)
 491         for i in range(len(parts)):
 492             pbl = []
 493             pbl.append(~pbs[i * byte_count - 1])
 494             for j in range(i * byte_count, (i + 1) * byte_count - 1):
 495                 pbl.append(pbs[j])
 496             pbl.append(~pbs[(i + 1) * byte_count - 1])
 497             value = Signal(len(pbl), reset_less=True)
 498             m.d.comb += value.eq(Cat(*pbl))
 499             m.d.comb += parts[i].eq(~(value).bool())
 500             m.d.comb += delayed_parts[0][i].eq(parts[i])
 501             m.d.sync += [delayed_parts[j + 1][i].eq(delayed_parts[j][i])
 502                          for j in range(len(delayed_parts)-1)]
 503             m.d.comb += self.dplast[i].eq(delayed_parts[-1][i])
 504
 505         not_a_term, neg_lsb_a_term, not_b_term, neg_lsb_b_term = \
 506                 self.not_a_term, self.neg_lsb_a_term, \
 507                 self.not_b_term, self.neg_lsb_b_term
 508
 509         byte_width = 8 // len(parts)
 510         bit_width = 8 * byte_width
 511         nat, nbt, nla, nlb = [], [], [], []
 512         for i in range(len(parts)):
 513             be = parts[i] & self.a[(i + 1) * bit_width - 1] \
 514                 & self.a_signed[i * byte_width]
 515             ae = parts[i] & self.b[(i + 1) * bit_width - 1] \
 516                 & self.b_signed[i * byte_width]
 517             a_enabled = Signal(name="a_en_%d" % i, reset_less=True)
 518             b_enabled = Signal(name="b_en_%d" % i, reset_less=True)
 519             m.d.comb += a_enabled.eq(ae)
 520             m.d.comb += b_enabled.eq(be)
 521
 522             # for 8-bit values: form a * 0xFF00 by using -a * 0x100, the
 523             # negation operation is split into a bitwise not and a +1.
 524             # likewise for 16, 32, and 64-bit values.
 525             nat.append(Mux(a_enabled,
 526                     Cat(Repl(0, bit_width),
 527                         ~self.a.bit_select(bit_width * i, bit_width)),
 528                     0))
 529
 530             nla.append(Cat(Repl(0, bit_width), a_enabled,
 531                            Repl(0, bit_width-1)))
 532
 533             nbt.append(Mux(b_enabled,
 534                     Cat(Repl(0, bit_width),
 535                         ~self.b.bit_select(bit_width * i, bit_width)),
 536                     0))
 537
 538             nlb.append(Cat(Repl(0, bit_width), b_enabled,
 539                            Repl(0, bit_width-1)))
 540
 541         m.d.comb += [not_a_term.eq(Cat(*nat)),
 542                      not_b_term.eq(Cat(*nbt)),
 543                      neg_lsb_a_term.eq(Cat(*nla)),
 544                      neg_lsb_b_term.eq(Cat(*nlb)),
 545                     ]
 546
 547         return m
 548
 549
 550 class IntermediateOut(Elaboratable):
 551     def __init__(self, width, out_wid, n_parts):
 552         self.width = width
 553         self.n_parts = n_parts
 554         self.delayed_part_ops = [Signal(2, name="dpop%d" % i, reset_less=True)
 555                                      for i in range(8)]
 556         self.intermed = Signal(out_wid, reset_less=True)
 557         self.output = Signal(out_wid//2, reset_less=True)
 558
 559     def elaborate(self, platform):
 560         m = Module()
 561
 562         ol = []
 563         w = self.width
 564         sel = w // 8
 565         for i in range(self.n_parts):
 566             op = Signal(w, reset_less=True, name="op%d_%d" % (w, i))
 567             m.d.comb += op.eq(
 568                 Mux(self.delayed_part_ops[sel * i] == OP_MUL_LOW,
 569                     self.intermed.bit_select(i * w*2, w),
 570                     self.intermed.bit_select(i * w*2 + w, w)))
 571             ol.append(op)
 572         m.d.comb += self.output.eq(Cat(*ol))
 573
 574         return m
 575
 576
 577 class FinalOut(Elaboratable):
 578     def __init__(self, out_wid):
 579         # inputs
 580         self.d8 = [Signal(name=f"d8_{i}", reset_less=True) for i in range(8)]
 581         self.d16 = [Signal(name=f"d16_{i}", reset_less=True) for i in range(4)]
 582         self.d32 = [Signal(name=f"d32_{i}", reset_less=True) for i in range(2)]
 583
 584         self.i8 = Signal(out_wid, reset_less=True)
 585         self.i16 = Signal(out_wid, reset_less=True)
 586         self.i32 = Signal(out_wid, reset_less=True)
 587         self.i64 = Signal(out_wid, reset_less=True)
 588
 589         # output
 590         self.out = Signal(out_wid, reset_less=True)
 591
 592     def elaborate(self, platform):
 593         m = Module()
 594         ol = []
 595         for i in range(8):
 596             op = Signal(8, reset_less=True, name="op_%d" % i)
 597             m.d.comb += op.eq(
 598                 Mux(self.d8[i] | self.d16[i // 2],
 599                     Mux(self.d8[i], self.i8.bit_select(i * 8, 8),
 600                                      self.i16.bit_select(i * 8, 8)),
 601                     Mux(self.d32[i // 4], self.i32.bit_select(i * 8, 8),
 602                                           self.i64.bit_select(i * 8, 8))))
 603             ol.append(op)
 604         m.d.comb += self.out.eq(Cat(*ol))
 605         return m
 606
 607
 608 class OrMod(Elaboratable):
 609     def __init__(self, wid):
 610         self.wid = wid
 611         self.orin = [Signal(wid, name="orin%d" % i, reset_less=True)
 612                      for i in range(4)]
 613         self.orout = Signal(wid, reset_less=True)
 614
 615     def elaborate(self, platform):
 616         m = Module()
 617         or1 = Signal(self.wid, reset_less=True)
 618         or2 = Signal(self.wid, reset_less=True)
 619         m.d.comb += or1.eq(self.orin[0] | self.orin[1])
 620         m.d.comb += or2.eq(self.orin[2] | self.orin[3])
 621         m.d.comb += self.orout.eq(or1 | or2)
 622
 623         return m
 624
 625
 626 class Signs(Elaboratable):
 627
 628     def __init__(self):
 629         self.part_ops = Signal(2, reset_less=True)
 630         self.a_signed = Signal(reset_less=True)
 631         self.b_signed = Signal(reset_less=True)
 632
 633     def elaborate(self, platform):
 634
 635         m = Module()
 636
 637         asig = self.part_ops != OP_MUL_UNSIGNED_HIGH
 638         bsig = (self.part_ops == OP_MUL_LOW) \
 639                     | (self.part_ops == OP_MUL_SIGNED_HIGH)
 640         m.d.comb += self.a_signed.eq(asig)
 641         m.d.comb += self.b_signed.eq(bsig)
 642
 643         return m
 644
 645
 646 class Mul8_16_32_64(Elaboratable):
 647     """Signed/Unsigned 8/16/32/64-bit partitioned integer multiplier.
 648
 649     Supports partitioning into any combination of 8, 16, 32, and 64-bit
 650     partitions on naturally-aligned boundaries. Supports the operation being
 651     set for each partition independently.
 652
 653     :attribute part_pts: the input partition points. Has a partition point at
 654         multiples of 8 in 0 < i < 64. Each partition point's associated
 655         ``Value`` is a ``Signal``. Modification not supported, except for by
 656         ``Signal.eq``.
 657     :attribute part_ops: the operation for each byte. The operation for a
 658         particular partition is selected by assigning the selected operation
 659         code to each byte in the partition. The allowed operation codes are:
 660
 661         :attribute OP_MUL_LOW: the LSB half of the product. Equivalent to
 662             RISC-V's `mul` instruction.
 663         :attribute OP_MUL_SIGNED_HIGH: the MSB half of the product where both
 664             ``a`` and ``b`` are signed. Equivalent to RISC-V's `mulh`
 665             instruction.
 666         :attribute OP_MUL_SIGNED_UNSIGNED_HIGH: the MSB half of the product
 667             where ``a`` is signed and ``b`` is unsigned. Equivalent to RISC-V's
 668             `mulhsu` instruction.
 669         :attribute OP_MUL_UNSIGNED_HIGH: the MSB half of the product where both
 670             ``a`` and ``b`` are unsigned. Equivalent to RISC-V's `mulhu`
 671             instruction.
 672     """
 673
 674     def __init__(self, register_levels= ()):
 675
 676         # parameter(s)
 677         self.register_levels = list(register_levels)
 678
 679         # inputs
 680         self.part_pts = PartitionPoints()
 681         for i in range(8, 64, 8):
 682             self.part_pts[i] = Signal(name=f"part_pts_{i}")
 683         self.part_ops = [Signal(2, name=f"part_ops_{i}") for i in range(8)]
 684         self.a = Signal(64)
 685         self.b = Signal(64)
 686
 687         # intermediates (needed for unit tests)
 688         self._intermediate_output = Signal(128)
 689
 690         # output
 691         self.output = Signal(64)
 692
 693     def _part_byte(self, index):
 694         if index == -1 or index == 7:
 695             return C(True, 1)
 696         assert index >= 0 and index < 8
 697         return self.part_pts[index * 8 + 8]
 698
 699     def elaborate(self, platform):
 700         m = Module()
 701
 702         # collect part-bytes
 703         pbs = Signal(8, reset_less=True)
 704         tl = []
 705         for i in range(8):
 706             pb = Signal(name="pb%d" % i, reset_less=True)
 707             m.d.comb += pb.eq(self._part_byte(i))
 708             tl.append(pb)
 709         m.d.comb += pbs.eq(Cat(*tl))
 710
 711         # local variables
 712         signs = []
 713         for i in range(8):
 714             s = Signs()
 715             signs.append(s)
 716             setattr(m.submodules, "signs%d" % i, s)
 717             m.d.comb += s.part_ops.eq(self.part_ops[i])
 718
 719         delayed_part_ops = [
 720             [Signal(2, name=f"_delayed_part_ops_{delay}_{i}")
 721              for i in range(8)]
 722             for delay in range(1 + len(self.register_levels))]
 723         for i in range(len(self.part_ops)):
 724             m.d.comb += delayed_part_ops[0][i].eq(self.part_ops[i])
 725             m.d.sync += [delayed_part_ops[j + 1][i].eq(delayed_part_ops[j][i])
 726                          for j in range(len(self.register_levels))]
 727
 728         n_levels = len(self.register_levels)+1
 729         m.submodules.part_8 = part_8 = Part(128, 8, n_levels, 8)
 730         m.submodules.part_16 = part_16 = Part(128, 4, n_levels, 8)
 731         m.submodules.part_32 = part_32 = Part(128, 2, n_levels, 8)
 732         m.submodules.part_64 = part_64 = Part(128, 1, n_levels, 8)
 733         nat_l, nbt_l, nla_l, nlb_l = [], [], [], []
 734         for mod in [part_8, part_16, part_32, part_64]:
 735             m.d.comb += mod.a.eq(self.a)
 736             m.d.comb += mod.b.eq(self.b)
 737             for i in range(len(signs)):
 738                 m.d.comb += mod.a_signed[i].eq(signs[i].a_signed)
 739                 m.d.comb += mod.b_signed[i].eq(signs[i].b_signed)
 740             m.d.comb += mod.pbs.eq(pbs)
 741             nat_l.append(mod.not_a_term)
 742             nbt_l.append(mod.not_b_term)
 743             nla_l.append(mod.neg_lsb_a_term)
 744             nlb_l.append(mod.neg_lsb_b_term)
 745
 746         terms = []
 747
 748         for a_index in range(8):
 749             t = ProductTerms(8, 128, 8, a_index, 8)
 750             setattr(m.submodules, "terms_%d" % a_index, t)
 751
 752             m.d.comb += t.a.eq(self.a)
 753             m.d.comb += t.b.eq(self.b)
 754             m.d.comb += t.pb_en.eq(pbs)
 755
 756             for term in t.terms:
 757                 terms.append(term)
 758
 759         # it's fine to bitwise-or data together since they are never enabled
 760         # at the same time
 761         m.submodules.nat_or = nat_or = OrMod(128)
 762         m.submodules.nbt_or = nbt_or = OrMod(128)
 763         m.submodules.nla_or = nla_or = OrMod(128)
 764         m.submodules.nlb_or = nlb_or = OrMod(128)
 765         for l, mod in [(nat_l, nat_or),
 766                              (nbt_l, nbt_or),
 767                              (nla_l, nla_or),
 768                              (nlb_l, nlb_or)]:
 769             for i in range(len(l)):
 770                 m.d.comb += mod.orin[i].eq(l[i])
 771             terms.append(mod.orout)
 772
 773         expanded_part_pts = PartitionPoints()
 774         for i, v in self.part_pts.items():
 775             signal = Signal(name=f"expanded_part_pts_{i*2}", reset_less=True)
 776             expanded_part_pts[i * 2] = signal
 777             m.d.comb += signal.eq(v)
 778
 779         add_reduce = AddReduce(terms,
 780                                128,
 781                                self.register_levels,
 782                                expanded_part_pts)
 783         m.submodules.add_reduce = add_reduce
 784         m.d.comb += self._intermediate_output.eq(add_reduce.output)
 785         # create _output_64
 786         m.submodules.io64 = io64 = IntermediateOut(64, 128, 1)
 787         m.d.comb += io64.intermed.eq(self._intermediate_output)
 788         for i in range(8):
 789             m.d.comb += io64.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
 790
 791         # create _output_32
 792         m.submodules.io32 = io32 = IntermediateOut(32, 128, 2)
 793         m.d.comb += io32.intermed.eq(self._intermediate_output)
 794         for i in range(8):
 795             m.d.comb += io32.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
 796
 797         # create _output_16
 798         m.submodules.io16 = io16 = IntermediateOut(16, 128, 4)
 799         m.d.comb += io16.intermed.eq(self._intermediate_output)
 800         for i in range(8):
 801             m.d.comb += io16.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
 802
 803         # create _output_8
 804         m.submodules.io8 = io8 = IntermediateOut(8, 128, 8)
 805         m.d.comb += io8.intermed.eq(self._intermediate_output)
 806         for i in range(8):
 807             m.d.comb += io8.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
 808
 809         # final output
 810         m.submodules.fo = fo = FinalOut(64)
 811         for i in range(len(part_8.delayed_parts[-1])):
 812             m.d.comb += fo.d8[i].eq(part_8.dplast[i])
 813         for i in range(len(part_16.delayed_parts[-1])):
 814             m.d.comb += fo.d16[i].eq(part_16.dplast[i])
 815         for i in range(len(part_32.delayed_parts[-1])):
 816             m.d.comb += fo.d32[i].eq(part_32.dplast[i])
 817         m.d.comb += fo.i8.eq(io8.output)
 818         m.d.comb += fo.i16.eq(io16.output)
 819         m.d.comb += fo.i32.eq(io32.output)
 820         m.d.comb += fo.i64.eq(io64.output)
 821         m.d.comb += self.output.eq(fo.out)
 822
 823         return m
 824
 825
 826 if __name__ == "__main__":
 827     m = Mul8_16_32_64()
 828     main(m, ports=[m.a,
 829                    m.b,
 830                    m._intermediate_output,
 831                    m.output,
 832                    *m.part_ops,
 833                    *m.part_pts.values()])