raise ValueError("point must be a non-negative integer")
self[point] = Value.wrap(enabled)
- def like(self, name=None, src_loc_at=0):
+ def like(self, name=None, src_loc_at=0, mul=1):
"""Create a new ``PartitionPoints`` with ``Signal``s for all values.
:param name: the base name for the new ``Signal``s.
+ :param mul: a multiplication factor on the indices
"""
if name is None:
name = Signal(src_loc_at=1+src_loc_at).name # get variable name
retval = PartitionPoints()
for point, enabled in self.items():
+ point *= mul
retval[point] = Signal(enabled.shape(), name=f"{name}_{point}")
return retval
for point, enabled in self.items():
yield enabled.eq(rhs[point])
- def as_mask(self, width):
+ def as_mask(self, width, mul=1):
"""Create a bit-mask from `self`.
Each bit in the returned mask is clear only if the partition point at
the same bit-index is enabled.
:param width: the bit width of the resulting mask
+ :param mul: a "multiplier" which in-place expands the partition points
+ typically set to "2" when used for multipliers
"""
bits = []
for i in range(width):
- if i in self:
+ i /= mul
+ if i.is_integer() and int(i) in self:
bits.append(~self[i])
else:
bits.append(True)
return False
return True
+ def part_byte(self, index, mfactor=1): # mfactor used for "expanding"
+ if index == -1 or index == 7:
+ return C(True, 1)
+ assert index >= 0 and index < 8
+ return self[(index * 8 + 8)*mfactor]
+
class FullAdder(Elaboratable):
"""Full Adder.
:param width: the bit width of the input and output
"""
- self.in0 = Signal(width)
- self.in1 = Signal(width)
- self.in2 = Signal(width)
- self.sum = Signal(width)
- self.carry = Signal(width)
+ self.in0 = Signal(width, reset_less=True)
+ self.in1 = Signal(width, reset_less=True)
+ self.in2 = Signal(width, reset_less=True)
+ self.sum = Signal(width, reset_less=True)
+ self.carry = Signal(width, reset_less=True)
def elaborate(self, platform):
"""Elaborate this module."""
supported, except for by ``Signal.eq``.
"""
- def __init__(self, width, partition_points):
+ def __init__(self, width, partition_points, partition_step=1):
"""Create a ``PartitionedAdder``.
:param width: the bit width of the input and output
:param partition_points: the input partition points
+ :param partition_step: a multiplier (typically double) step
+ which in-place "expands" the partition points
"""
self.width = width
- self.a = Signal(width)
- self.b = Signal(width)
- self.output = Signal(width)
+ self.pmul = partition_step
+ self.a = Signal(width, reset_less=True)
+ self.b = Signal(width, reset_less=True)
+ self.output = Signal(width, reset_less=True)
self.partition_points = PartitionPoints(partition_points)
if not self.partition_points.fits_in_width(width):
raise ValueError("partition_points doesn't fit in 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) # includes extra part-points
- self._expanded_b = Signal(expanded_width) # likewise.
- self._expanded_o = Signal(expanded_width) # likewise.
def elaborate(self, platform):
"""Elaborate this module."""
m = Module()
+ expanded_a = Signal(self._expanded_width, reset_less=True)
+ expanded_b = Signal(self._expanded_width, reset_less=True)
+ expanded_o = Signal(self._expanded_width, reset_less=True)
+
expanded_index = 0
# store bits in a list, use Cat later. graphviz is much cleaner
al, bl, ol, ea, eb, eo = [],[],[],[],[],[]
# carry has been carried *over* the break point.
for i in range(self.width):
- if i in self.partition_points:
+ pi = i/self.pmul # double the range of the partition point test
+ if pi.is_integer() and pi in self.partition_points:
# add extra bit set to 0 + 0 for enabled partition points
# and 1 + 0 for disabled partition points
- ea.append(self._expanded_a[expanded_index])
- al.append(~self.partition_points[i]) # add extra bit in a
- eb.append(self._expanded_b[expanded_index])
+ ea.append(expanded_a[expanded_index])
+ al.append(~self.partition_points[pi]) # add extra bit in a
+ eb.append(expanded_b[expanded_index])
bl.append(C(0)) # yes, add a zero
expanded_index += 1 # skip the extra point. NOT in the output
- ea.append(self._expanded_a[expanded_index])
- eb.append(self._expanded_b[expanded_index])
- eo.append(self._expanded_o[expanded_index])
+ ea.append(expanded_a[expanded_index])
+ eb.append(expanded_b[expanded_index])
+ eo.append(expanded_o[expanded_index])
al.append(self.a[i])
bl.append(self.b[i])
ol.append(self.output[i])
# use only one addition to take advantage of look-ahead carry and
# special hardware on FPGAs
- m.d.comb += self._expanded_o.eq(
- self._expanded_a + self._expanded_b)
+ m.d.comb += expanded_o.eq(expanded_a + expanded_b)
return m
FULL_ADDER_INPUT_COUNT = 3
+class AddReduceData:
+
+ def __init__(self, part_pts, n_inputs, output_width, n_parts):
+ self.part_ops = [Signal(2, name=f"part_ops_{i}", reset_less=True)
+ for i in range(n_parts)]
+ self.terms = [Signal(output_width, name=f"inputs_{i}",
+ reset_less=True)
+ for i in range(n_inputs)]
+ self.part_pts = part_pts.like()
+
+ def eq_from(self, part_pts, inputs, part_ops):
+ return [self.part_pts.eq(part_pts)] + \
+ [self.terms[i].eq(inputs[i])
+ for i in range(len(self.terms))] + \
+ [self.part_ops[i].eq(part_ops[i])
+ for i in range(len(self.part_ops))]
+
+ def eq(self, rhs):
+ return self.eq_from(rhs.part_pts, rhs.terms, rhs.part_ops)
+
+
+class FinalReduceData:
+
+ def __init__(self, part_pts, output_width, n_parts):
+ self.part_ops = [Signal(2, name=f"part_ops_{i}", reset_less=True)
+ for i in range(n_parts)]
+ self.output = Signal(output_width, reset_less=True)
+ self.part_pts = part_pts.like()
+
+ def eq_from(self, part_pts, output, part_ops):
+ return [self.part_pts.eq(part_pts)] + \
+ [self.output.eq(output)] + \
+ [self.part_ops[i].eq(part_ops[i])
+ for i in range(len(self.part_ops))]
+
+ def eq(self, rhs):
+ return self.eq_from(rhs.part_pts, rhs.output, rhs.part_ops)
+
+
+class FinalAdd(Elaboratable):
+ """ Final stage of add reduce
+ """
+
+ def __init__(self, n_inputs, output_width, n_parts, register_levels,
+ partition_points):
+ self.i = AddReduceData(partition_points, n_inputs,
+ output_width, n_parts)
+ self.o = FinalReduceData(partition_points, output_width, n_parts)
+ self.output_width = output_width
+ self.n_inputs = n_inputs
+ self.n_parts = n_parts
+ self.register_levels = list(register_levels)
+ self.partition_points = PartitionPoints(partition_points)
+ if not self.partition_points.fits_in_width(output_width):
+ raise ValueError("partition_points doesn't fit in output_width")
+
+ def elaborate(self, platform):
+ """Elaborate this module."""
+ m = Module()
+
+ output_width = self.output_width
+ output = Signal(output_width, reset_less=True)
+ if self.n_inputs == 0:
+ # use 0 as the default output value
+ m.d.comb += output.eq(0)
+ elif self.n_inputs == 1:
+ # handle single input
+ m.d.comb += output.eq(self.i.terms[0])
+ else:
+ # base case for adding 2 inputs
+ assert self.n_inputs == 2
+ adder = PartitionedAdder(output_width,
+ self.i.part_pts, 2)
+ m.submodules.final_adder = adder
+ m.d.comb += adder.a.eq(self.i.terms[0])
+ m.d.comb += adder.b.eq(self.i.terms[1])
+ m.d.comb += output.eq(adder.output)
+
+ # create output
+ m.d.comb += self.o.eq_from(self.i.part_pts, output,
+ self.i.part_ops)
+
+ return m
+
class AddReduceSingle(Elaboratable):
"""Add list of numbers together.
supported, except for by ``Signal.eq``.
"""
- def __init__(self, inputs, output_width, register_levels, partition_points):
+ def __init__(self, n_inputs, output_width, n_parts, register_levels,
+ partition_points):
"""Create an ``AddReduce``.
:param inputs: input ``Signal``s to be summed.
pipeline registers.
:param partition_points: the input partition points.
"""
- self.inputs = list(inputs)
- self._resized_inputs = [
- Signal(output_width, name=f"resized_inputs[{i}]")
- for i in range(len(self.inputs))]
+ self.n_inputs = n_inputs
+ self.n_parts = n_parts
+ self.output_width = output_width
+ self.i = AddReduceData(partition_points, n_inputs,
+ output_width, n_parts)
self.register_levels = list(register_levels)
- self.output = Signal(output_width)
self.partition_points = PartitionPoints(partition_points)
if not self.partition_points.fits_in_width(output_width):
raise ValueError("partition_points doesn't fit in output_width")
- self._reg_partition_points = self.partition_points.like()
- max_level = AddReduceSingle.get_max_level(len(self.inputs))
+ max_level = AddReduceSingle.get_max_level(n_inputs)
for level in self.register_levels:
if level > max_level:
raise ValueError(
"not enough adder levels for specified register levels")
- self.groups = AddReduceSingle.full_adder_groups(len(self.inputs))
- self._intermediate_terms = []
- if len(self.groups) != 0:
- self.create_next_terms()
+ self.groups = AddReduceSingle.full_adder_groups(n_inputs)
+ n_terms = AddReduceSingle.calc_n_inputs(n_inputs, self.groups)
+ self.o = AddReduceData(partition_points, n_terms, output_width, n_parts)
+
+ @staticmethod
+ def calc_n_inputs(n_inputs, groups):
+ retval = len(groups)*2
+ if n_inputs % FULL_ADDER_INPUT_COUNT == 1:
+ retval += 1
+ elif n_inputs % FULL_ADDER_INPUT_COUNT == 2:
+ retval += 2
+ else:
+ assert n_inputs % FULL_ADDER_INPUT_COUNT == 0
+ return retval
@staticmethod
def get_max_level(input_count):
input_count - FULL_ADDER_INPUT_COUNT + 1,
FULL_ADDER_INPUT_COUNT)
- def elaborate(self, platform):
- """Elaborate this module."""
- m = Module()
-
- # resize inputs to correct bit-width and optionally add in
- # pipeline registers
- resized_input_assignments = [self._resized_inputs[i].eq(self.inputs[i])
- for i in range(len(self.inputs))]
- if 0 in self.register_levels:
- m.d.sync += resized_input_assignments
- m.d.sync += self._reg_partition_points.eq(self.partition_points)
- else:
- m.d.comb += resized_input_assignments
- m.d.comb += self._reg_partition_points.eq(self.partition_points)
-
- for (value, term) in self._intermediate_terms:
- m.d.comb += term.eq(value)
-
- # if there are no full adders to create, then we handle the base cases
- # and return, otherwise we go on to the recursive case
- if len(self.groups) == 0:
- if len(self.inputs) == 0:
- # use 0 as the default output value
- m.d.comb += self.output.eq(0)
- elif len(self.inputs) == 1:
- # handle single input
- m.d.comb += self.output.eq(self._resized_inputs[0])
- else:
- # base case for adding 2 inputs
- assert len(self.inputs) == 2
- adder = PartitionedAdder(len(self.output),
- self._reg_partition_points)
- m.submodules.final_adder = adder
- m.d.comb += adder.a.eq(self._resized_inputs[0])
- m.d.comb += adder.b.eq(self._resized_inputs[1])
- m.d.comb += self.output.eq(adder.output)
- return m
-
- mask = self._reg_partition_points.as_mask(len(self.output))
- m.d.comb += self.part_mask.eq(mask)
-
- # add and link the intermediate term modules
- for i, (iidx, adder_i) in enumerate(self.adders):
- setattr(m.submodules, f"adder_{i}", adder_i)
-
- m.d.comb += adder_i.in0.eq(self._resized_inputs[iidx])
- m.d.comb += adder_i.in1.eq(self._resized_inputs[iidx + 1])
- m.d.comb += adder_i.in2.eq(self._resized_inputs[iidx + 2])
- m.d.comb += adder_i.mask.eq(self.part_mask)
-
- return m
-
def create_next_terms(self):
-
- # go on to prepare recursive case
- intermediate_terms = []
- _intermediate_terms = []
-
- def add_intermediate_term(value):
- intermediate_term = Signal(
- len(self.output),
- name=f"intermediate_terms[{len(intermediate_terms)}]")
- _intermediate_terms.append((value, intermediate_term))
- intermediate_terms.append(intermediate_term)
-
- # store mask in intermediary (simplifies graph)
- self.part_mask = Signal(len(self.output), reset_less=True)
+ """ create next intermediate terms, for linking up in elaborate, below
+ """
+ terms = []
+ adders = []
# create full adders for this recursive level.
# this shrinks N terms to 2 * (N // 3) plus the remainder
- self.adders = []
for i in self.groups:
- adder_i = MaskedFullAdder(len(self.output))
- self.adders.append((i, adder_i))
+ adder_i = MaskedFullAdder(self.output_width)
+ adders.append((i, adder_i))
# add both the sum and the masked-carry to the next level.
# 3 inputs have now been reduced to 2...
- add_intermediate_term(adder_i.sum)
- add_intermediate_term(adder_i.mcarry)
+ terms.append(adder_i.sum)
+ terms.append(adder_i.mcarry)
# handle the remaining inputs.
- if len(self.inputs) % FULL_ADDER_INPUT_COUNT == 1:
- add_intermediate_term(self._resized_inputs[-1])
- elif len(self.inputs) % FULL_ADDER_INPUT_COUNT == 2:
+ if self.n_inputs % FULL_ADDER_INPUT_COUNT == 1:
+ terms.append(self.i.terms[-1])
+ elif self.n_inputs % FULL_ADDER_INPUT_COUNT == 2:
# Just pass the terms to the next layer, since we wouldn't gain
# anything by using a half adder since there would still be 2 terms
# and just passing the terms to the next layer saves gates.
- add_intermediate_term(self._resized_inputs[-2])
- add_intermediate_term(self._resized_inputs[-1])
+ terms.append(self.i.terms[-2])
+ terms.append(self.i.terms[-1])
else:
- assert len(self.inputs) % FULL_ADDER_INPUT_COUNT == 0
+ assert self.n_inputs % FULL_ADDER_INPUT_COUNT == 0
- self.intermediate_terms = intermediate_terms
- self._intermediate_terms = _intermediate_terms
+ return terms, adders
+
+ def elaborate(self, platform):
+ """Elaborate this module."""
+ m = Module()
+
+ terms, adders = self.create_next_terms()
+
+ # copy the intermediate terms to the output
+ for i, value in enumerate(terms):
+ m.d.comb += self.o.terms[i].eq(value)
+
+ # copy reg part points and part ops to output
+ m.d.comb += self.o.part_pts.eq(self.i.part_pts)
+ m.d.comb += [self.o.part_ops[i].eq(self.i.part_ops[i])
+ for i in range(len(self.i.part_ops))]
+
+ # set up the partition mask (for the adders)
+ part_mask = Signal(self.output_width, reset_less=True)
+
+ # get partition points as a mask
+ mask = self.i.part_pts.as_mask(self.output_width, mul=2)
+ m.d.comb += part_mask.eq(mask)
+
+ # add and link the intermediate term modules
+ for i, (iidx, adder_i) in enumerate(adders):
+ setattr(m.submodules, f"adder_{i}", adder_i)
+
+ m.d.comb += adder_i.in0.eq(self.i.terms[iidx])
+ m.d.comb += adder_i.in1.eq(self.i.terms[iidx + 1])
+ m.d.comb += adder_i.in2.eq(self.i.terms[iidx + 2])
+ m.d.comb += adder_i.mask.eq(part_mask)
+
+ return m
class AddReduce(Elaboratable):
supported, except for by ``Signal.eq``.
"""
- def __init__(self, inputs, output_width, register_levels, partition_points):
+ def __init__(self, inputs, output_width, register_levels, partition_points,
+ part_ops):
"""Create an ``AddReduce``.
:param inputs: input ``Signal``s to be summed.
:param partition_points: the input partition points.
"""
self.inputs = inputs
- self.output = Signal(output_width)
+ self.part_ops = part_ops
+ n_parts = len(part_ops)
+ self.o = FinalReduceData(partition_points, output_width, n_parts)
self.output_width = output_width
self.register_levels = register_levels
self.partition_points = partition_points
self.create_levels()
+ @staticmethod
+ def get_max_level(input_count):
+ return AddReduceSingle.get_max_level(input_count)
+
@staticmethod
def next_register_levels(register_levels):
"""``Iterable`` of ``register_levels`` for next recursive level."""
mods = []
next_levels = self.register_levels
partition_points = self.partition_points
+ part_ops = self.part_ops
+ n_parts = len(part_ops)
inputs = self.inputs
+ ilen = len(inputs)
while True:
- next_level = AddReduceSingle(inputs, self.output_width, next_levels,
- partition_points)
- mods.append(next_level)
- if len(next_level.groups) == 0:
+ groups = AddReduceSingle.full_adder_groups(len(inputs))
+ if len(groups) == 0:
break
+ next_level = AddReduceSingle(ilen, self.output_width, n_parts,
+ next_levels, partition_points)
+ mods.append(next_level)
next_levels = list(AddReduce.next_register_levels(next_levels))
- partition_points = next_level._reg_partition_points
- inputs = next_level.intermediate_terms
+ partition_points = next_level.i.part_pts
+ inputs = next_level.o.terms
+ ilen = len(inputs)
+ part_ops = next_level.i.part_ops
+
+ next_level = FinalAdd(ilen, self.output_width, n_parts,
+ next_levels, partition_points)
+ mods.append(next_level)
self.levels = mods
for i, next_level in enumerate(self.levels):
setattr(m.submodules, "next_level%d" % i, next_level)
+ partition_points = self.partition_points
+ inputs = self.inputs
+ part_ops = self.part_ops
+ n_parts = len(part_ops)
+ n_inputs = len(inputs)
+ output_width = self.output_width
+ i = AddReduceData(partition_points, n_inputs, output_width, n_parts)
+ m.d.comb += i.eq_from(partition_points, inputs, part_ops)
+ for idx in range(len(self.levels)):
+ mcur = self.levels[idx]
+ if 0 in mcur.register_levels:
+ m.d.sync += mcur.i.eq(i)
+ else:
+ m.d.comb += mcur.i.eq(i)
+ i = mcur.o # for next loop
+
# output comes from last module
- m.d.comb += self.output.eq(next_level.output)
+ m.d.comb += self.o.eq(i)
return m
bsb = Signal(self.width, reset_less=True)
a_index, b_index = self.a_index, self.b_index
pwidth = self.pwidth
- 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 += bsa.eq(self.a.part(a_index * pwidth, pwidth))
+ m.d.comb += bsb.eq(self.b.part(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))
"""
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 += asel.eq(self.a.part(a_index * pwidth, pwidth))
+ m.d.comb += bsel.eq(self.b.part(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)
return m
+
class LSBNegTerm(Elaboratable):
def __init__(self, bit_width):
return m
+class Parts(Elaboratable):
+
+ def __init__(self, pbwid, part_pts, n_parts):
+ self.pbwid = pbwid
+ # inputs
+ self.part_pts = PartitionPoints.like(part_pts)
+ # outputs
+ self.parts = [Signal(name=f"part_{i}", reset_less=True)
+ for i in range(n_parts)]
+
+ def elaborate(self, platform):
+ m = Module()
+
+ part_pts, parts = self.part_pts, self.parts
+ # collect part-bytes (double factor because the input is extended)
+ pbs = Signal(self.pbwid, reset_less=True)
+ tl = []
+ for i in range(self.pbwid):
+ pb = Signal(name="pb%d" % i, reset_less=True)
+ m.d.comb += pb.eq(part_pts.part_byte(i))
+ tl.append(pb)
+ m.d.comb += pbs.eq(Cat(*tl))
+
+ # 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(npbs[i * byte_count - 1])
+ for j in range(i * byte_count, (i + 1) * byte_count - 1):
+ pbl.append(pbs[j])
+ pbl.append(npbs[(i + 1) * byte_count - 1])
+ value = Signal(len(pbl), name="value_%d" % i, reset_less=True)
+ m.d.comb += value.eq(Cat(*pbl))
+ m.d.comb += parts[i].eq(~(value).bool())
+
+ 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.
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):
+ def __init__(self, part_pts, width, n_parts, n_levels, pbwid):
+
+ self.pbwid = pbwid
+ self.part_pts = part_pts
# 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 = Signal(64, reset_less=True)
+ self.b = Signal(64, reset_less=True)
+ self.a_signed = [Signal(name=f"a_signed_{i}", reset_less=True)
+ for i in range(8)]
+ self.b_signed = [Signal(name=f"_b_signed_{i}", reset_less=True)
+ 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_{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)
- self.not_b_term = Signal(width)
- self.neg_lsb_b_term = Signal(width)
+ self.parts = [Signal(name=f"part_{i}", reset_less=True)
+ for i in range(n_parts)]
+
+ self.not_a_term = Signal(width, reset_less=True)
+ self.neg_lsb_a_term = Signal(width, reset_less=True)
+ self.not_b_term = Signal(width, reset_less=True)
+ self.neg_lsb_b_term = Signal(width, reset_less=True)
def elaborate(self, platform):
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)
+ pbs, parts = self.pbs, self.parts
+ part_pts = self.part_pts
+ m.submodules.p = p = Parts(self.pbwid, part_pts, len(parts))
+ m.d.comb += p.part_pts.eq(part_pts)
+ parts = p.parts
+
byte_count = 8 // len(parts)
- for i in range(len(parts)):
- pbl = []
- 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(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
+ 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) # byte width
bit_wid = 8 * byte_width # bit width
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.op.eq(self.a.part(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)
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.op.eq(self.b.part(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)
def __init__(self, width, out_wid, n_parts):
self.width = width
self.n_parts = n_parts
- self.delayed_part_ops = [Signal(2, name="dpop%d" % i, reset_less=True)
+ self.part_ops = [Signal(2, name="dpop%d" % i, reset_less=True)
for i in range(8)]
self.intermed = Signal(out_wid, reset_less=True)
self.output = Signal(out_wid//2, reset_less=True)
for i in range(self.n_parts):
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),
- self.intermed.bit_select(i * w*2 + w, w)))
+ Mux(self.part_ops[sel * i] == OP_MUL_LOW,
+ self.intermed.part(i * w*2, w),
+ self.intermed.part(i * w*2 + w, w)))
ol.append(op)
m.d.comb += self.output.eq(Cat(*ol))
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)
-
+ def __init__(self, output_width, n_parts, part_pts):
+ self.part_pts = part_pts
+ self.i = IntermediateData(part_pts, output_width, n_parts)
+ self.out_wid = output_width//2
# output
- self.out = Signal(out_wid, reset_less=True)
+ self.out = Signal(self.out_wid, reset_less=True)
+ self.intermediate_output = Signal(output_width, reset_less=True)
def elaborate(self, platform):
m = Module()
+
+ part_pts = self.part_pts
+ m.submodules.p_8 = p_8 = Parts(8, part_pts, 8)
+ m.submodules.p_16 = p_16 = Parts(8, part_pts, 4)
+ m.submodules.p_32 = p_32 = Parts(8, part_pts, 2)
+ m.submodules.p_64 = p_64 = Parts(8, part_pts, 1)
+
+ out_part_pts = self.i.part_pts
+
+ # temporaries
+ d8 = [Signal(name=f"d8_{i}", reset_less=True) for i in range(8)]
+ d16 = [Signal(name=f"d16_{i}", reset_less=True) for i in range(4)]
+ d32 = [Signal(name=f"d32_{i}", reset_less=True) for i in range(2)]
+
+ i8 = Signal(self.out_wid, reset_less=True)
+ i16 = Signal(self.out_wid, reset_less=True)
+ i32 = Signal(self.out_wid, reset_less=True)
+ i64 = Signal(self.out_wid, reset_less=True)
+
+ m.d.comb += p_8.part_pts.eq(out_part_pts)
+ m.d.comb += p_16.part_pts.eq(out_part_pts)
+ m.d.comb += p_32.part_pts.eq(out_part_pts)
+ m.d.comb += p_64.part_pts.eq(out_part_pts)
+
+ for i in range(len(p_8.parts)):
+ m.d.comb += d8[i].eq(p_8.parts[i])
+ for i in range(len(p_16.parts)):
+ m.d.comb += d16[i].eq(p_16.parts[i])
+ for i in range(len(p_32.parts)):
+ m.d.comb += d32[i].eq(p_32.parts[i])
+ m.d.comb += i8.eq(self.i.outputs[0])
+ m.d.comb += i16.eq(self.i.outputs[1])
+ m.d.comb += i32.eq(self.i.outputs[2])
+ m.d.comb += i64.eq(self.i.outputs[3])
+
ol = []
for i in range(8):
# select one of the outputs: d8 selects i8, d16 selects 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))))
+ Mux(d8[i] | d16[i // 2],
+ Mux(d8[i], i8.part(i * 8, 8), i16.part(i * 8, 8)),
+ Mux(d32[i // 4], i32.part(i * 8, 8), i64.part(i * 8, 8))))
ol.append(op)
m.d.comb += self.out.eq(Cat(*ol))
+ m.d.comb += self.intermediate_output.eq(self.i.intermediate_output)
return m
return m
-class Mul8_16_32_64(Elaboratable):
- """Signed/Unsigned 8/16/32/64-bit partitioned integer multiplier.
+class IntermediateData:
- Supports partitioning into any combination of 8, 16, 32, and 64-bit
- partitions on naturally-aligned boundaries. Supports the operation being
- set for each partition independently.
+ def __init__(self, part_pts, output_width, n_parts):
+ self.part_ops = [Signal(2, name=f"part_ops_{i}", reset_less=True)
+ for i in range(n_parts)]
+ self.part_pts = part_pts.like()
+ self.outputs = [Signal(output_width, name="io%d" % i, reset_less=True)
+ for i in range(4)]
+ # intermediates (needed for unit tests)
+ self.intermediate_output = Signal(output_width)
- :attribute part_pts: the input partition points. Has a partition point at
- multiples of 8 in 0 < i < 64. Each partition point's associated
- ``Value`` is a ``Signal``. Modification not supported, except for by
- ``Signal.eq``.
- :attribute part_ops: the operation for each byte. The operation for a
- particular partition is selected by assigning the selected operation
- code to each byte in the partition. The allowed operation codes are:
+ def eq_from(self, part_pts, outputs, intermediate_output,
+ part_ops):
+ return [self.part_pts.eq(part_pts)] + \
+ [self.intermediate_output.eq(intermediate_output)] + \
+ [self.outputs[i].eq(outputs[i])
+ for i in range(4)] + \
+ [self.part_ops[i].eq(part_ops[i])
+ for i in range(len(self.part_ops))]
- :attribute OP_MUL_LOW: the LSB half of the product. Equivalent to
- RISC-V's `mul` instruction.
- :attribute OP_MUL_SIGNED_HIGH: the MSB half of the product where both
- ``a`` and ``b`` are signed. Equivalent to RISC-V's `mulh`
- instruction.
- :attribute OP_MUL_SIGNED_UNSIGNED_HIGH: the MSB half of the product
- where ``a`` is signed and ``b`` is unsigned. Equivalent to RISC-V's
- `mulhsu` instruction.
- :attribute OP_MUL_UNSIGNED_HIGH: the MSB half of the product where both
- ``a`` and ``b`` are unsigned. Equivalent to RISC-V's `mulhu`
- instruction.
- """
+ def eq(self, rhs):
+ return self.eq_from(rhs.part_pts, rhs.outputs,
+ rhs.intermediate_output, rhs.part_ops)
- 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)
+class AllTermsData:
- # inputs
- self.part_pts = PartitionPoints()
- for i in range(8, 64, 8):
- self.part_pts[i] = Signal(name=f"part_pts_{i}")
- self.part_ops = [Signal(2, name=f"part_ops_{i}") for i in range(8)]
+ def __init__(self, partition_points):
self.a = Signal(64)
self.b = Signal(64)
+ self.part_pts = partition_points.like()
+ self.part_ops = [Signal(2, name=f"part_ops_{i}") for i in range(8)]
- # intermediates (needed for unit tests)
- self._intermediate_output = Signal(128)
+ def eq_from(self, part_pts, inputs, part_ops):
+ return [self.part_pts.eq(part_pts)] + \
+ [self.a.eq(a), self.b.eq(b)] + \
+ [self.part_ops[i].eq(part_ops[i])
+ for i in range(len(self.part_ops))]
- # output
- self.output = Signal(64)
+ def eq(self, rhs):
+ return self.eq_from(rhs.part_pts, rhs.a, rhs.b, rhs.part_ops)
- def _part_byte(self, index):
- if index == -1 or index == 7:
- return C(True, 1)
- assert index >= 0 and index < 8
- return self.part_pts[index * 8 + 8]
+
+class AllTerms(Elaboratable):
+ """Set of terms to be added together
+ """
+
+ def __init__(self, n_inputs, output_width, n_parts, register_levels,
+ partition_points):
+ """Create an ``AddReduce``.
+
+ :param inputs: input ``Signal``s to be summed.
+ :param output_width: bit-width of ``output``.
+ :param register_levels: List of nesting levels that should have
+ pipeline registers.
+ :param partition_points: the input partition points.
+ """
+ self.i = AllTermsData(partition_points)
+ self.register_levels = register_levels
+ self.n_inputs = n_inputs
+ self.n_parts = n_parts
+ self.output_width = output_width
+ self.o = AddReduceData(self.i.part_pts, n_inputs,
+ output_width, n_parts)
def elaborate(self, platform):
m = Module()
+ eps = self.i.part_pts
+
# collect part-bytes
pbs = Signal(8, reset_less=True)
tl = []
for i in range(8):
pb = Signal(name="pb%d" % i, reset_less=True)
- m.d.comb += pb.eq(self._part_byte(i))
+ m.d.comb += pb.eq(eps.part_byte(i))
tl.append(pb)
m.d.comb += pbs.eq(Cat(*tl))
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 i in range(8)]
- for delay in range(1 + len(self.register_levels))]
- for i in range(len(self.part_ops)):
- m.d.comb += delayed_part_ops[0][i].eq(self.part_ops[i])
- m.d.sync += [delayed_part_ops[j + 1][i].eq(delayed_part_ops[j][i])
- for j in range(len(self.register_levels))]
+ m.d.comb += s.part_ops.eq(self.i.part_ops[i])
n_levels = len(self.register_levels)+1
- m.submodules.part_8 = part_8 = Part(128, 8, n_levels, 8)
- m.submodules.part_16 = part_16 = Part(128, 4, n_levels, 8)
- m.submodules.part_32 = part_32 = Part(128, 2, n_levels, 8)
- m.submodules.part_64 = part_64 = Part(128, 1, n_levels, 8)
+ m.submodules.part_8 = part_8 = Part(eps, 128, 8, n_levels, 8)
+ m.submodules.part_16 = part_16 = Part(eps, 128, 4, n_levels, 8)
+ m.submodules.part_32 = part_32 = Part(eps, 128, 2, n_levels, 8)
+ m.submodules.part_64 = part_64 = Part(eps, 128, 1, n_levels, 8)
nat_l, nbt_l, nla_l, nlb_l = [], [], [], []
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)
+ m.d.comb += mod.a.eq(self.i.a)
+ m.d.comb += mod.b.eq(self.i.b)
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)
t = ProductTerms(8, 128, 8, a_index, 8)
setattr(m.submodules, "terms_%d" % a_index, t)
- m.d.comb += t.a.eq(self.a)
- m.d.comb += t.b.eq(self.b)
+ m.d.comb += t.a.eq(self.i.a)
+ m.d.comb += t.b.eq(self.i.b)
m.d.comb += t.pb_en.eq(pbs)
for term in t.terms:
m.d.comb += mod.orin[i].eq(l[i])
terms.append(mod.orout)
- expanded_part_pts = PartitionPoints()
- for i, v in self.part_pts.items():
- signal = Signal(name=f"expanded_part_pts_{i*2}", reset_less=True)
- expanded_part_pts[i * 2] = signal
- m.d.comb += signal.eq(v)
+ # copy the intermediate terms to the output
+ for i, value in enumerate(terms):
+ m.d.comb += self.o.terms[i].eq(value)
+
+ # copy reg part points and part ops to output
+ m.d.comb += self.o.part_pts.eq(eps)
+ m.d.comb += [self.o.part_ops[i].eq(self.i.part_ops[i])
+ for i in range(len(self.i.part_ops))]
+
+ return m
+
+
+class Intermediates(Elaboratable):
+ """ Intermediate output modules
+ """
+
+ def __init__(self, output_width, n_parts, partition_points):
+ self.i = FinalReduceData(partition_points, output_width, n_parts)
+ self.o = IntermediateData(partition_points, output_width, n_parts)
+
+ def elaborate(self, platform):
+ m = Module()
+
+ out_part_ops = self.i.part_ops
+ out_part_pts = self.i.part_pts
- add_reduce = AddReduce(terms,
- 128,
- self.register_levels,
- expanded_part_pts)
- m.submodules.add_reduce = add_reduce
- m.d.comb += self._intermediate_output.eq(add_reduce.output)
# create _output_64
m.submodules.io64 = io64 = IntermediateOut(64, 128, 1)
- m.d.comb += io64.intermed.eq(self._intermediate_output)
+ m.d.comb += io64.intermed.eq(self.i.output)
for i in range(8):
- m.d.comb += io64.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
+ m.d.comb += io64.part_ops[i].eq(out_part_ops[i])
+ m.d.comb += self.o.outputs[3].eq(io64.output)
# create _output_32
m.submodules.io32 = io32 = IntermediateOut(32, 128, 2)
- m.d.comb += io32.intermed.eq(self._intermediate_output)
+ m.d.comb += io32.intermed.eq(self.i.output)
for i in range(8):
- m.d.comb += io32.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
+ m.d.comb += io32.part_ops[i].eq(out_part_ops[i])
+ m.d.comb += self.o.outputs[2].eq(io32.output)
# create _output_16
m.submodules.io16 = io16 = IntermediateOut(16, 128, 4)
- m.d.comb += io16.intermed.eq(self._intermediate_output)
+ m.d.comb += io16.intermed.eq(self.i.output)
for i in range(8):
- m.d.comb += io16.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
+ m.d.comb += io16.part_ops[i].eq(out_part_ops[i])
+ m.d.comb += self.o.outputs[1].eq(io16.output)
# create _output_8
m.submodules.io8 = io8 = IntermediateOut(8, 128, 8)
- m.d.comb += io8.intermed.eq(self._intermediate_output)
+ m.d.comb += io8.intermed.eq(self.i.output)
+ for i in range(8):
+ m.d.comb += io8.part_ops[i].eq(out_part_ops[i])
+ m.d.comb += self.o.outputs[0].eq(io8.output)
+
+ for i in range(8):
+ m.d.comb += self.o.part_ops[i].eq(out_part_ops[i])
+ m.d.comb += self.o.part_pts.eq(out_part_pts)
+ m.d.comb += self.o.intermediate_output.eq(self.i.output)
+
+ return m
+
+
+class Mul8_16_32_64(Elaboratable):
+ """Signed/Unsigned 8/16/32/64-bit partitioned integer multiplier.
+
+ Supports partitioning into any combination of 8, 16, 32, and 64-bit
+ partitions on naturally-aligned boundaries. Supports the operation being
+ set for each partition independently.
+
+ :attribute part_pts: the input partition points. Has a partition point at
+ multiples of 8 in 0 < i < 64. Each partition point's associated
+ ``Value`` is a ``Signal``. Modification not supported, except for by
+ ``Signal.eq``.
+ :attribute part_ops: the operation for each byte. The operation for a
+ particular partition is selected by assigning the selected operation
+ code to each byte in the partition. The allowed operation codes are:
+
+ :attribute OP_MUL_LOW: the LSB half of the product. Equivalent to
+ RISC-V's `mul` instruction.
+ :attribute OP_MUL_SIGNED_HIGH: the MSB half of the product where both
+ ``a`` and ``b`` are signed. Equivalent to RISC-V's `mulh`
+ instruction.
+ :attribute OP_MUL_SIGNED_UNSIGNED_HIGH: the MSB half of the product
+ where ``a`` is signed and ``b`` is unsigned. Equivalent to RISC-V's
+ `mulhsu` instruction.
+ :attribute OP_MUL_UNSIGNED_HIGH: the MSB half of the product where both
+ ``a`` and ``b`` are unsigned. Equivalent to RISC-V's `mulhu`
+ instruction.
+ """
+
+ 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)
+
+ # inputs
+ self.part_pts = PartitionPoints()
+ for i in range(8, 64, 8):
+ self.part_pts[i] = Signal(name=f"part_pts_{i}")
+ self.part_ops = [Signal(2, name=f"part_ops_{i}") for i in range(8)]
+ self.a = Signal(64)
+ self.b = Signal(64)
+
+ # intermediates (needed for unit tests)
+ self.intermediate_output = Signal(128)
+
+ # output
+ self.output = Signal(64)
+
+ def elaborate(self, platform):
+ m = Module()
+
+ part_pts = self.part_pts
+
+ n_inputs = 64 + 4
+ n_parts = 8 #len(self.part_pts)
+ t = AllTerms(n_inputs, 128, n_parts, self.register_levels, part_pts)
+ m.submodules.allterms = t
+ m.d.comb += t.i.a.eq(self.a)
+ m.d.comb += t.i.b.eq(self.b)
+ m.d.comb += t.i.part_pts.eq(part_pts)
for i in range(8):
- m.d.comb += io8.delayed_part_ops[i].eq(delayed_part_ops[-1][i])
+ m.d.comb += t.i.part_ops[i].eq(self.part_ops[i])
+
+ terms = t.o.terms
+
+ add_reduce = AddReduce(terms,
+ 128,
+ self.register_levels,
+ t.o.part_pts,
+ t.o.part_ops)
+
+ out_part_ops = add_reduce.o.part_ops
+ out_part_pts = add_reduce.o.part_pts
+
+ m.submodules.add_reduce = add_reduce
+
+ interm = Intermediates(128, 8, part_pts)
+ m.submodules.intermediates = interm
+ m.d.comb += interm.i.eq(add_reduce.o)
# final output
- 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.submodules.finalout = finalout = FinalOut(128, 8, part_pts)
+ m.d.comb += finalout.i.eq(interm.o)
m.d.comb += self.output.eq(finalout.out)
+ m.d.comb += self.intermediate_output.eq(finalout.intermediate_output)
return m
m = Mul8_16_32_64()
main(m, ports=[m.a,
m.b,
- m._intermediate_output,
+ m.intermediate_output,
m.output,
*m.part_ops,
*m.part_pts.values()])
projects / ieee754fpu.git / blobdiff