from functools import reduce
from operator import or_
+
class PartitionPoints(dict):
"""Partition points and corresponding ``Value``s.
:attribute in2: the third input
:attribute sum: the sum output
:attribute carry: the carry output
+
+ Rather than do individual full adders (and have an array of them,
+ which would be very slow to simulate), this module can specify the
+ bit width of the inputs and outputs: in effect it performs multiple
+ Full 3-2 Add operations "in parallel".
"""
def __init__(self, width):
expanded_width += 1
expanded_width += 1
self._expanded_width = expanded_width
+ # XXX these have to remain here due to some horrible nmigen
+ # simulation bugs involving sync. it is *not* necessary to
+ # have them here, they should (under normal circumstances)
+ # be moved into elaborate, as they are entirely local
self._expanded_a = Signal(expanded_width)
self._expanded_b = Signal(expanded_width)
self._expanded_output = Signal(expanded_width)
m = Module()
expanded_index = 0
# store bits in a list, use Cat later. graphviz is much cleaner
- al = []
- bl = []
- ol = []
- ea = []
- eb = []
- eo = []
+ al, bl, ol, ea, eb, eo = [],[],[],[],[],[]
+
# partition points are "breaks" (extra zeros) in what would otherwise
# be a massive long add.
for i in range(self.width):
return value
-class Term(Elaboratable):
- def __init__(self, width, twidth, shift=0, enabled=None):
- self.width = width
- self.shift = shift
- self.enabled = enabled
- self.ti = Signal(width, reset_less=True)
- self.term = Signal(twidth, reset_less=True)
-
- def elaborate(self, platform):
-
- m = Module()
- m.d.comb += self.term.eq(get_term(self.ti, self.shift, self.enabled))
-
- return m
-
-
class ProductTerm(Elaboratable):
+ """ this class creates a single product term (a[..]*b[..]).
+ it has a design flaw in that is the *output* that is selected,
+ where the multiplication(s) are combinatorially generated
+ all the time.
+ """
+
def __init__(self, width, twidth, pbwid, a_index, b_index):
self.a_index = a_index
self.b_index = b_index
shift = 8 * (self.a_index + self.b_index)
self.pwidth = width
+ self.twidth = twidth
+ self.width = width*2
+ self.shift = shift
+
+ self.ti = Signal(self.width, reset_less=True)
+ self.term = Signal(twidth, reset_less=True)
self.a = Signal(twidth//2, reset_less=True)
self.b = Signal(twidth//2, reset_less=True)
self.pb_en = Signal(pbwid, reset_less=True)
term_enabled = Signal(name=name, reset_less=True)
else:
term_enabled = None
-
- Term.__init__(self, width*2, twidth, shift, term_enabled)
+ self.enabled = term_enabled
self.term.name = "term_%d_%d" % (a_index, b_index) # rename
def elaborate(self, platform):
- m = Term.elaborate(self, platform)
+ m = Module()
if self.enabled is not None:
m.d.comb += self.enabled.eq(~(Cat(*self.tl).bool()))
m.d.comb += bsa.eq(self.a.bit_select(a_index * pwidth, pwidth))
m.d.comb += bsb.eq(self.b.bit_select(b_index * pwidth, pwidth))
m.d.comb += self.ti.eq(bsa * bsb)
+ m.d.comb += self.term.eq(get_term(self.ti, self.shift, self.enabled))
+ """
+ #TODO: sort out width issues, get inputs a/b switched on/off.
+ #data going into Muxes is 1/2 the required width
+
+ pwidth = self.pwidth
+ width = self.width
+ bsa = Signal(self.twidth//2, reset_less=True)
+ bsb = Signal(self.twidth//2, reset_less=True)
+ asel = Signal(width, reset_less=True)
+ bsel = Signal(width, reset_less=True)
+ a_index, b_index = self.a_index, self.b_index
+ m.d.comb += asel.eq(self.a.bit_select(a_index * pwidth, pwidth))
+ m.d.comb += bsel.eq(self.b.bit_select(b_index * pwidth, pwidth))
+ m.d.comb += bsa.eq(get_term(asel, self.shift, self.enabled))
+ m.d.comb += bsb.eq(get_term(bsel, self.shift, self.enabled))
+ m.d.comb += self.ti.eq(bsa * bsb)
+ m.d.comb += self.term.eq(self.ti)
+ """
return m
class ProductTerms(Elaboratable):
-
+ """ creates a bank of product terms. also performs the actual bit-selection
+ this class is to be wrapped with a for-loop on the "a" operand.
+ it creates a second-level for-loop on the "b" operand.
+ """
def __init__(self, width, twidth, pbwid, a_index, blen):
self.a_index = a_index
self.blen = blen
return m
+class LSBNegTerm(Elaboratable):
+
+ def __init__(self, bit_width):
+ self.bit_width = bit_width
+ self.part = Signal(reset_less=True)
+ self.signed = Signal(reset_less=True)
+ self.op = Signal(bit_width, reset_less=True)
+ self.msb = Signal(reset_less=True)
+ self.nt = Signal(bit_width*2, reset_less=True)
+ self.nl = Signal(bit_width*2, reset_less=True)
+
+ def elaborate(self, platform):
+ m = Module()
+ comb = m.d.comb
+ bit_wid = self.bit_width
+ ext = Repl(0, bit_wid) # extend output to HI part
+
+ # determine sign of each incoming number *in this partition*
+ enabled = Signal(reset_less=True)
+ m.d.comb += enabled.eq(self.part & self.msb & self.signed)
+
+ # for 8-bit values: form a * 0xFF00 by using -a * 0x100, the
+ # negation operation is split into a bitwise not and a +1.
+ # likewise for 16, 32, and 64-bit values.
+
+ # width-extended 1s complement if a is signed, otherwise zero
+ comb += self.nt.eq(Mux(enabled, Cat(ext, ~self.op), 0))
+
+ # add 1 if signed, otherwise add zero
+ comb += self.nl.eq(Cat(ext, enabled, Repl(0, bit_wid-1)))
+
+ return m
+
class Part(Elaboratable):
+ """ a key class which, depending on the partitioning, will determine
+ what action to take when parts of the output are signed or unsigned.
+
+ this requires 2 pieces of data *per operand, per partition*:
+ whether the MSB is HI/LO (per partition!), and whether a signed
+ or unsigned operation has been *requested*.
+
+ once that is determined, signed is basically carried out
+ by splitting 2's complement into 1's complement plus one.
+ 1's complement is just a bit-inversion.
+
+ the extra terms - as separate terms - are then thrown at the
+ AddReduce alongside the multiplication part-results.
+ """
def __init__(self, width, n_parts, n_levels, pbwid):
# inputs
self.a = Signal(64)
self.b = Signal(64)
- self._a_signed = [Signal(name=f"_a_signed_{i}") for i in range(8)]
- self._b_signed = [Signal(name=f"_b_signed_{i}") for i in range(8)]
+ self.a_signed = [Signal(name=f"a_signed_{i}") for i in range(8)]
+ self.b_signed = [Signal(name=f"_b_signed_{i}") for i in range(8)]
self.pbs = Signal(pbwid, reset_less=True)
# outputs
self.parts = [Signal(name=f"part_{i}") for i in range(n_parts)]
self.delayed_parts = [
- [Signal(name=f"delayed_part_8_{delay}_{i}")
+ [Signal(name=f"delayed_part_{delay}_{i}")
for i in range(n_parts)]
for delay in range(n_levels)]
+ # XXX REALLY WEIRD BUG - have to take a copy of the last delayed_parts
+ self.dplast = [Signal(name=f"dplast_{i}")
+ for i in range(n_parts)]
self.not_a_term = Signal(width)
self.neg_lsb_a_term = Signal(width)
m = Module()
pbs, parts, delayed_parts = self.pbs, self.parts, self.delayed_parts
+ # negated-temporary copy of partition bits
+ npbs = Signal.like(pbs, reset_less=True)
+ m.d.comb += npbs.eq(~pbs)
byte_count = 8 // len(parts)
for i in range(len(parts)):
pbl = []
- pbl.append(~pbs[i * byte_count - 1])
+ pbl.append(npbs[i * byte_count - 1])
for j in range(i * byte_count, (i + 1) * byte_count - 1):
pbl.append(pbs[j])
- pbl.append(~pbs[(i + 1) * byte_count - 1])
- value = Signal(len(pbl), reset_less=True)
+ pbl.append(npbs[(i + 1) * byte_count - 1])
+ value = Signal(len(pbl), name="value_%di" % i, reset_less=True)
m.d.comb += value.eq(Cat(*pbl))
m.d.comb += parts[i].eq(~(value).bool())
m.d.comb += delayed_parts[0][i].eq(parts[i])
m.d.sync += [delayed_parts[j + 1][i].eq(delayed_parts[j][i])
for j in range(len(delayed_parts)-1)]
+ m.d.comb += self.dplast[i].eq(delayed_parts[-1][i])
not_a_term, neg_lsb_a_term, not_b_term, neg_lsb_b_term = \
self.not_a_term, self.neg_lsb_a_term, \
self.not_b_term, self.neg_lsb_b_term
- byte_width = 8 // len(parts)
- bit_width = 8 * byte_width
+ byte_width = 8 // len(parts) # byte width
+ bit_wid = 8 * byte_width # bit width
nat, nbt, nla, nlb = [], [], [], []
for i in range(len(parts)):
- be = parts[i] & self.a[(i + 1) * bit_width - 1] \
- & self._a_signed[i * byte_width]
- ae = parts[i] & self.b[(i + 1) * bit_width - 1] \
- & self._b_signed[i * byte_width]
- a_enabled = Signal(name="a_en_%d" % i, reset_less=True)
- b_enabled = Signal(name="b_en_%d" % i, reset_less=True)
- m.d.comb += a_enabled.eq(ae)
- m.d.comb += b_enabled.eq(be)
-
- # for 8-bit values: form a * 0xFF00 by using -a * 0x100, the
- # negation operation is split into a bitwise not and a +1.
- # likewise for 16, 32, and 64-bit values.
- nat.append(Mux(a_enabled,
- Cat(Repl(0, bit_width),
- ~self.a.bit_select(bit_width * i, bit_width)),
- 0))
-
- nla.append(Cat(Repl(0, bit_width), a_enabled,
- Repl(0, bit_width-1)))
-
- nbt.append(Mux(b_enabled,
- Cat(Repl(0, bit_width),
- ~self.b.bit_select(bit_width * i, bit_width)),
- 0))
-
- nlb.append(Cat(Repl(0, bit_width), b_enabled,
- Repl(0, bit_width-1)))
-
+ # work out bit-inverted and +1 term for a.
+ pa = LSBNegTerm(bit_wid)
+ setattr(m.submodules, "lnt_%d_a_%d" % (bit_wid, i), pa)
+ m.d.comb += pa.part.eq(parts[i])
+ m.d.comb += pa.op.eq(self.a.bit_select(bit_wid * i, bit_wid))
+ m.d.comb += pa.signed.eq(self.b_signed[i * byte_width]) # yes b
+ m.d.comb += pa.msb.eq(self.b[(i + 1) * bit_wid - 1]) # really, b
+ nat.append(pa.nt)
+ nla.append(pa.nl)
+
+ # work out bit-inverted and +1 term for b
+ pb = LSBNegTerm(bit_wid)
+ setattr(m.submodules, "lnt_%d_b_%d" % (bit_wid, i), pb)
+ m.d.comb += pb.part.eq(parts[i])
+ m.d.comb += pb.op.eq(self.b.bit_select(bit_wid * i, bit_wid))
+ m.d.comb += pb.signed.eq(self.a_signed[i * byte_width]) # yes a
+ m.d.comb += pb.msb.eq(self.a[(i + 1) * bit_wid - 1]) # really, a
+ nbt.append(pb.nt)
+ nlb.append(pb.nl)
+
+ # concatenate together and return all 4 results.
m.d.comb += [not_a_term.eq(Cat(*nat)),
not_b_term.eq(Cat(*nbt)),
neg_lsb_a_term.eq(Cat(*nla)),
class IntermediateOut(Elaboratable):
+ """ selects the HI/LO part of the multiplication, for a given bit-width
+ the output is also reconstructed in its SIMD (partition) lanes.
+ """
def __init__(self, width, out_wid, n_parts):
self.width = width
self.n_parts = n_parts
w = self.width
sel = w // 8
for i in range(self.n_parts):
- op = Signal(w, reset_less=True, name="op32_%d" % i)
+ op = Signal(w, reset_less=True, name="op%d_%d" % (w, i))
m.d.comb += op.eq(
Mux(self.delayed_part_ops[sel * i] == OP_MUL_LOW,
self.intermed.bit_select(i * w*2, w),
return m
+
+class FinalOut(Elaboratable):
+ """ selects the final output based on the partitioning.
+
+ each byte is selectable independently, i.e. it is possible
+ that some partitions requested 8-bit computation whilst others
+ requested 16 or 32 bit.
+ """
+ def __init__(self, out_wid):
+ # inputs
+ self.d8 = [Signal(name=f"d8_{i}", reset_less=True) for i in range(8)]
+ self.d16 = [Signal(name=f"d16_{i}", reset_less=True) for i in range(4)]
+ self.d32 = [Signal(name=f"d32_{i}", reset_less=True) for i in range(2)]
+
+ self.i8 = Signal(out_wid, reset_less=True)
+ self.i16 = Signal(out_wid, reset_less=True)
+ self.i32 = Signal(out_wid, reset_less=True)
+ self.i64 = Signal(out_wid, reset_less=True)
+
+ # output
+ self.out = Signal(out_wid, reset_less=True)
+
+ def elaborate(self, platform):
+ m = Module()
+ ol = []
+ for i in range(8):
+ # select one of the outputs: d8 selects i8, d16 selects i16
+ # d32 selects i32, and the default is i64.
+ # d8 and d16 are ORed together in the first Mux
+ # then the 2nd selects either i8 or i16.
+ # if neither d8 nor d16 are set, d32 selects either i32 or i64.
+ op = Signal(8, reset_less=True, name="op_%d" % i)
+ m.d.comb += op.eq(
+ Mux(self.d8[i] | self.d16[i // 2],
+ Mux(self.d8[i], self.i8.bit_select(i * 8, 8),
+ self.i16.bit_select(i * 8, 8)),
+ Mux(self.d32[i // 4], self.i32.bit_select(i * 8, 8),
+ self.i64.bit_select(i * 8, 8))))
+ ol.append(op)
+ m.d.comb += self.out.eq(Cat(*ol))
+ return m
+
+
class OrMod(Elaboratable):
+ """ ORs four values together in a hierarchical tree
+ """
def __init__(self, wid):
self.wid = wid
self.orin = [Signal(wid, name="orin%d" % i, reset_less=True)
return m
+class Signs(Elaboratable):
+ """ determines whether a or b are signed numbers
+ based on the required operation type (OP_MUL_*)
+ """
+
+ def __init__(self):
+ self.part_ops = Signal(2, reset_less=True)
+ self.a_signed = Signal(reset_less=True)
+ self.b_signed = Signal(reset_less=True)
+
+ def elaborate(self, platform):
+
+ m = Module()
+
+ asig = self.part_ops != OP_MUL_UNSIGNED_HIGH
+ bsig = (self.part_ops == OP_MUL_LOW) \
+ | (self.part_ops == OP_MUL_SIGNED_HIGH)
+ m.d.comb += self.a_signed.eq(asig)
+ m.d.comb += self.b_signed.eq(bsig)
+
+ return m
+
+
class Mul8_16_32_64(Elaboratable):
"""Signed/Unsigned 8/16/32/64-bit partitioned integer multiplier.
instruction.
"""
- def __init__(self, register_levels= ()):
+ def __init__(self, register_levels=()):
+ """ register_levels: specifies the points in the cascade at which
+ flip-flops are to be inserted.
+ """
# parameter(s)
self.register_levels = list(register_levels)
m.d.comb += pbs.eq(Cat(*tl))
# local variables
- output_64 = Signal(64)
- output_32 = Signal(64)
- output_16 = Signal(64)
- output_8 = Signal(64)
- a_signed = [Signal(name=f"_a_signed_{i}") for i in range(8)]
- b_signed = [Signal(name=f"_b_signed_{i}") for i in range(8)]
+ signs = []
+ for i in range(8):
+ s = Signs()
+ signs.append(s)
+ setattr(m.submodules, "signs%d" % i, s)
+ m.d.comb += s.part_ops.eq(self.part_ops[i])
delayed_part_ops = [
[Signal(2, name=f"_delayed_part_ops_{delay}_{i}")
for mod in [part_8, part_16, part_32, part_64]:
m.d.comb += mod.a.eq(self.a)
m.d.comb += mod.b.eq(self.b)
- for i in range(len(a_signed)):
- m.d.comb += mod._a_signed[i].eq(a_signed[i])
- for i in range(len(b_signed)):
- m.d.comb += mod._b_signed[i].eq(b_signed[i])
+ for i in range(len(signs)):
+ m.d.comb += mod.a_signed[i].eq(signs[i].a_signed)
+ m.d.comb += mod.b_signed[i].eq(signs[i].b_signed)
m.d.comb += mod.pbs.eq(pbs)
nat_l.append(mod.not_a_term)
nbt_l.append(mod.not_b_term)
for term in t.terms:
terms.append(term)
- for i in range(8):
- asig = self.part_ops[i] != OP_MUL_UNSIGNED_HIGH
- bsig = (self.part_ops[i] == OP_MUL_LOW) \
- | (self.part_ops[i] == OP_MUL_SIGNED_HIGH)
- m.d.comb += a_signed[i].eq(asig)
- m.d.comb += b_signed[i].eq(bsig)
-
# it's fine to bitwise-or data together since they are never enabled
# at the same time
m.submodules.nat_or = nat_or = OrMod(128)
m.d.comb += io64.intermed.eq(self._intermediate_output)
for i in range(8):
m.d.comb += io64.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
- m.d.comb += output_64.eq(io64.output)
# create _output_32
m.submodules.io32 = io32 = IntermediateOut(32, 128, 2)
m.d.comb += io32.intermed.eq(self._intermediate_output)
for i in range(8):
m.d.comb += io32.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
- m.d.comb += output_32.eq(io32.output)
# create _output_16
m.submodules.io16 = io16 = IntermediateOut(16, 128, 4)
m.d.comb += io16.intermed.eq(self._intermediate_output)
for i in range(8):
m.d.comb += io16.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
- m.d.comb += output_16.eq(io16.output)
# create _output_8
m.submodules.io8 = io8 = IntermediateOut(8, 128, 8)
m.d.comb += io8.intermed.eq(self._intermediate_output)
for i in range(8):
m.d.comb += io8.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
- m.d.comb += output_8.eq(io8.output)
# final output
- ol = []
- for i in range(8):
- op = Signal(8, reset_less=True, name="op%d" % i)
- m.d.comb += op.eq(
- Mux(part_8.delayed_parts[-1][i]
- | part_16.delayed_parts[-1][i // 2],
- Mux(part_8.delayed_parts[-1][i],
- output_8.bit_select(i * 8, 8),
- output_16.bit_select(i * 8, 8)),
- Mux(part_32.delayed_parts[-1][i // 4],
- output_32.bit_select(i * 8, 8),
- output_64.bit_select(i * 8, 8))))
- ol.append(op)
- m.d.comb += self.output.eq(Cat(*ol))
+ m.submodules.finalout = finalout = FinalOut(64)
+ for i in range(len(part_8.delayed_parts[-1])):
+ m.d.comb += finalout.d8[i].eq(part_8.dplast[i])
+ for i in range(len(part_16.delayed_parts[-1])):
+ m.d.comb += finalout.d16[i].eq(part_16.dplast[i])
+ for i in range(len(part_32.delayed_parts[-1])):
+ m.d.comb += finalout.d32[i].eq(part_32.dplast[i])
+ m.d.comb += finalout.i8.eq(io8.output)
+ m.d.comb += finalout.i16.eq(io16.output)
+ m.d.comb += finalout.i32.eq(io32.output)
+ m.d.comb += finalout.i64.eq(io64.output)
+ m.d.comb += self.output.eq(finalout.out)
+
return m