from nmigen.hdl.ast import Assign
from abc import ABCMeta, abstractmethod
from nmigen.cli import main
+from functools import reduce
+from operator import or_
class PartitionPoints(dict):
: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):
return m
+class MaskedFullAdder(Elaboratable):
+ """Masked Full Adder.
+
+ :attribute mask: the carry partition mask
+ :attribute in0: the first input
+ :attribute in1: the second input
+ :attribute in2: the third input
+ :attribute sum: the sum output
+ :attribute mcarry: the masked carry output
+
+ FullAdders are always used with a "mask" on the output. To keep
+ the graphviz "clean", this class performs the masking here rather
+ than inside a large for-loop.
+
+ See the following discussion as to why this is no longer derived
+ from FullAdder. Each carry is shifted here *before* being ANDed
+ with the mask, so that an AOI cell may be used (which is more
+ gate-efficient)
+ https://en.wikipedia.org/wiki/AND-OR-Invert
+ https://groups.google.com/d/msg/comp.arch/fcq-GLQqvas/vTxmcA0QAgAJ
+ """
+
+ def __init__(self, width):
+ """Create a ``MaskedFullAdder``.
+
+ :param width: the bit width of the input and output
+ """
+ self.width = width
+ self.mask = Signal(width, reset_less=True)
+ self.mcarry = Signal(width, reset_less=True)
+ 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)
+
+ def elaborate(self, platform):
+ """Elaborate this module."""
+ m = Module()
+ s1 = Signal(self.width, reset_less=True)
+ s2 = Signal(self.width, reset_less=True)
+ s3 = Signal(self.width, reset_less=True)
+ c1 = Signal(self.width, reset_less=True)
+ c2 = Signal(self.width, reset_less=True)
+ c3 = Signal(self.width, reset_less=True)
+ m.d.comb += self.sum.eq(self.in0 ^ self.in1 ^ self.in2)
+ m.d.comb += s1.eq(Cat(0, self.in0))
+ m.d.comb += s2.eq(Cat(0, self.in1))
+ m.d.comb += s3.eq(Cat(0, self.in2))
+ m.d.comb += c1.eq(s1 & s2 & self.mask)
+ m.d.comb += c2.eq(s2 & s3 & self.mask)
+ m.d.comb += c3.eq(s3 & s1 & self.mask)
+ m.d.comb += self.mcarry.eq(c1 | c2 | c3)
+ return m
+
+
class PartitionedAdder(Elaboratable):
"""Partitioned Adder.
+ Performs the final add. The partition points are included in the
+ actual add (in one of the operands only), which causes a carry over
+ to the next bit. Then the final output *removes* the extra bits from
+ the result.
+
+ partition: .... P... P... P... P... (32 bits)
+ a : .... .... .... .... .... (32 bits)
+ b : .... .... .... .... .... (32 bits)
+ exp-a : ....P....P....P....P.... (32+4 bits, P=1 if no partition)
+ exp-b : ....0....0....0....0.... (32 bits plus 4 zeros)
+ exp-o : ....xN...xN...xN...xN... (32+4 bits - x to be discarded)
+ o : .... N... N... N... N... (32 bits - x ignored, N is carry-over)
+
:attribute width: the bit width of the input and output. Read-only.
:attribute a: the first input to the adder
:attribute b: the second input to the adder
expanded_width += 1
expanded_width += 1
self._expanded_width = expanded_width
- self._expanded_a = Signal(expanded_width)
- self._expanded_b = Signal(expanded_width)
- self._expanded_output = Signal(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_index = 0
+ # store bits in a list, use Cat later. graphviz is much cleaner
+ al, bl, ol, ea, eb, eo = [],[],[],[],[],[]
+
+ # partition points are "breaks" (extra zeros or 1s) in what would
+ # otherwise be a massive long add. when the "break" points are 0,
+ # whatever is in it (in the output) is discarded. however when
+ # there is a "1", it causes a roll-over carry to the *next* bit.
+ # we still ignore the "break" bit in the [intermediate] output,
+ # however by that time we've got the effect that we wanted: the
+ # carry has been carried *over* the break point.
+
for i in range(self.width):
if i in self.partition_points:
# add extra bit set to 0 + 0 for enabled partition points
# and 1 + 0 for disabled partition points
- m.d.comb += self._expanded_a[expanded_index].eq(
- ~self.partition_points[i])
- m.d.comb += self._expanded_b[expanded_index].eq(0)
- expanded_index += 1
- m.d.comb += self._expanded_a[expanded_index].eq(self.a[i])
- m.d.comb += self._expanded_b[expanded_index].eq(self.b[i])
- m.d.comb += self.output[i].eq(
- self._expanded_output[expanded_index])
+ 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])
+ 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])
+ al.append(self.a[i])
+ bl.append(self.b[i])
+ ol.append(self.output[i])
expanded_index += 1
+
+ # combine above using Cat
+ m.d.comb += Cat(*ea).eq(Cat(*al))
+ m.d.comb += Cat(*eb).eq(Cat(*bl))
+ m.d.comb += Cat(*ol).eq(Cat(*eo))
+
# use only one addition to take advantage of look-ahead carry and
# special hardware on FPGAs
- m.d.comb += self._expanded_output.eq(
+ m.d.comb += self._expanded_o.eq(
self._expanded_a + self._expanded_b)
return m
FULL_ADDER_INPUT_COUNT = 3
-class AddReduce(Elaboratable):
+class AddReduceSingle(Elaboratable):
"""Add list of numbers together.
:attribute inputs: input ``Signal``s to be summed. Modification not
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.
pipeline registers.
:param partition_points: the input partition points.
"""
+ self.part_ops = part_ops
+ self.out_part_ops = [Signal(2, name=f"out_part_ops_{i}")
+ for i in range(len(part_ops))]
self.inputs = list(inputs)
self._resized_inputs = [
Signal(output_width, name=f"resized_inputs[{i}]")
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 = AddReduce.get_max_level(len(self.inputs))
+
+ max_level = AddReduceSingle.get_max_level(len(self.inputs))
for level in self.register_levels:
if level > max_level:
raise ValueError(
"not enough adder levels for specified register levels")
+ # this is annoying. we have to create the modules (and terms)
+ # because we need to know what they are (in order to set up the
+ # interconnects back in AddReduce), but cannot do the m.d.comb +=
+ # etc because this is not in elaboratable.
+ self.groups = AddReduceSingle.full_adder_groups(len(self.inputs))
+ self._intermediate_terms = []
+ if len(self.groups) != 0:
+ self.create_next_terms()
+
@staticmethod
def get_max_level(input_count):
"""Get the maximum level.
"""
retval = 0
while True:
- groups = AddReduce.full_adder_groups(input_count)
+ groups = AddReduceSingle.full_adder_groups(input_count)
if len(groups) == 0:
return retval
input_count %= FULL_ADDER_INPUT_COUNT
input_count += 2 * len(groups)
retval += 1
- def next_register_levels(self):
- """``Iterable`` of ``register_levels`` for next recursive level."""
- for level in self.register_levels:
- if level > 0:
- yield level - 1
-
@staticmethod
def full_adder_groups(input_count):
"""Get ``inputs`` indices for which a full adder should be built."""
# pipeline registers
resized_input_assignments = [self._resized_inputs[i].eq(self.inputs[i])
for i in range(len(self.inputs))]
+ copy_part_ops = [self.out_part_ops[i].eq(self.part_ops[i])
+ for i in range(len(self.part_ops))]
if 0 in self.register_levels:
+ m.d.sync += copy_part_ops
m.d.sync += resized_input_assignments
m.d.sync += self._reg_partition_points.eq(self.partition_points)
else:
+ m.d.comb += copy_part_ops
m.d.comb += resized_input_assignments
m.d.comb += self._reg_partition_points.eq(self.partition_points)
- groups = AddReduce.full_adder_groups(len(self.inputs))
+ 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(groups) == 0:
+ if len(self.groups) == 0:
if len(self.inputs) == 0:
# use 0 as the default output value
m.d.comb += self.output.eq(0)
# handle single input
m.d.comb += self.output.eq(self._resized_inputs[0])
else:
- # base case for adding 2 or more inputs, which get recursively
- # reduced to 2 inputs
+ # base case for adding 2 inputs
assert len(self.inputs) == 2
adder = PartitionedAdder(len(self.output),
self._reg_partition_points)
m.d.comb += adder.b.eq(self._resized_inputs[1])
m.d.comb += self.output.eq(adder.output)
return m
- # go on to handle recursive case
- intermediate_terms: List[Signal]
+
+ 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)
- m.d.comb += intermediate_term.eq(value)
- part_mask = self._reg_partition_points.as_mask(len(self.output))
+ # store mask in intermediary (simplifies graph)
+ self.part_mask = Signal(len(self.output), reset_less=True)
# create full adders for this recursive level.
# this shrinks N terms to 2 * (N // 3) plus the remainder
- for i in groups:
- adder_i = FullAdder(len(self.output))
- setattr(m.submodules, f"adder_{i}", adder_i)
- m.d.comb += adder_i.in0.eq(self._resized_inputs[i])
- m.d.comb += adder_i.in1.eq(self._resized_inputs[i + 1])
- m.d.comb += adder_i.in2.eq(self._resized_inputs[i + 2])
+ self.adders = []
+ for i in self.groups:
+ adder_i = MaskedFullAdder(len(self.output))
+ self.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)
- shifted_carry = adder_i.carry << 1
- # mask out carry bits to prevent carries between partitions
- add_intermediate_term((adder_i.carry << 1) & part_mask)
+ add_intermediate_term(adder_i.mcarry)
# handle the remaining inputs.
if len(self.inputs) % FULL_ADDER_INPUT_COUNT == 1:
add_intermediate_term(self._resized_inputs[-1])
add_intermediate_term(self._resized_inputs[-1])
else:
assert len(self.inputs) % FULL_ADDER_INPUT_COUNT == 0
- # recursive invocation of ``AddReduce``
- next_level = AddReduce(intermediate_terms,
- len(self.output),
- self.next_register_levels(),
- self._reg_partition_points)
- m.submodules.next_level = next_level
+
+ self.intermediate_terms = intermediate_terms
+ self._intermediate_terms = _intermediate_terms
+
+
+class AddReduce(Elaboratable):
+ """Recursively Add list of numbers together.
+
+ :attribute inputs: input ``Signal``s to be summed. Modification not
+ supported, except for by ``Signal.eq``.
+ :attribute register_levels: List of nesting levels that should have
+ pipeline registers.
+ :attribute output: output sum.
+ :attribute partition_points: the input partition points. Modification not
+ supported, except for by ``Signal.eq``.
+ """
+
+ def __init__(self, inputs, output_width, register_levels, partition_points,
+ part_ops):
+ """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.inputs = inputs
+ self.part_ops = part_ops
+ self.out_part_ops = [Signal(2, name=f"out_part_ops_{i}")
+ for i in range(len(part_ops))]
+ self.output = Signal(output_width)
+ 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."""
+ for level in register_levels:
+ if level > 0:
+ yield level - 1
+
+ def create_levels(self):
+ """creates reduction levels"""
+
+ mods = []
+ next_levels = self.register_levels
+ partition_points = self.partition_points
+ inputs = self.inputs
+ part_ops = self.part_ops
+ while True:
+ next_level = AddReduceSingle(inputs, self.output_width, next_levels,
+ partition_points, part_ops)
+ mods.append(next_level)
+ if len(next_level.groups) == 0:
+ break
+ next_levels = list(AddReduce.next_register_levels(next_levels))
+ partition_points = next_level._reg_partition_points
+ inputs = next_level.intermediate_terms
+ part_ops = next_level.out_part_ops
+
+ self.levels = mods
+
+ def elaborate(self, platform):
+ """Elaborate this module."""
+ m = Module()
+
+ for i, next_level in enumerate(self.levels):
+ setattr(m.submodules, "next_level%d" % i, next_level)
+
+ # output comes from last module
m.d.comb += self.output.eq(next_level.output)
+ copy_part_ops = [self.out_part_ops[i].eq(next_level.out_part_ops[i])
+ for i in range(len(self.part_ops))]
+ m.d.comb += copy_part_ops
+
return m
OP_MUL_UNSIGNED_HIGH = 3
+def get_term(value, shift=0, enabled=None):
+ if enabled is not None:
+ value = Mux(enabled, value, 0)
+ if shift > 0:
+ value = Cat(Repl(C(0, 1), shift), value)
+ else:
+ assert shift == 0
+ return value
+
+
+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)
+
+ self.tl = tl = []
+ min_index = min(self.a_index, self.b_index)
+ max_index = max(self.a_index, self.b_index)
+ for i in range(min_index, max_index):
+ tl.append(self.pb_en[i])
+ name = "te_%d_%d" % (self.a_index, self.b_index)
+ if len(tl) > 0:
+ term_enabled = Signal(name=name, reset_less=True)
+ else:
+ term_enabled = None
+ self.enabled = term_enabled
+ self.term.name = "term_%d_%d" % (a_index, b_index) # rename
+
+ def elaborate(self, platform):
+
+ m = Module()
+ if self.enabled is not None:
+ m.d.comb += self.enabled.eq(~(Cat(*self.tl).bool()))
+
+ bsa = Signal(self.width, reset_less=True)
+ 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.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))
+ """
+ #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.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)
+ 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
+ self.pwidth = width
+ self.twidth = twidth
+ self.pbwid = pbwid
+ self.a = Signal(twidth//2, reset_less=True)
+ self.b = Signal(twidth//2, reset_less=True)
+ self.pb_en = Signal(pbwid, reset_less=True)
+ self.terms = [Signal(twidth, name="term%d"%i, reset_less=True) \
+ for i in range(blen)]
+
+ def elaborate(self, platform):
+
+ m = Module()
+
+ for b_index in range(self.blen):
+ t = ProductTerm(self.pwidth, self.twidth, self.pbwid,
+ self.a_index, b_index)
+ setattr(m.submodules, "term_%d" % b_index, t)
+
+ m.d.comb += t.a.eq(self.a)
+ m.d.comb += t.b.eq(self.b)
+ m.d.comb += t.pb_en.eq(self.pb_en)
+
+ m.d.comb += self.terms[b_index].eq(t.term)
+
+ 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.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)
+
+ 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)
+ 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
+
+ byte_width = 8 // len(parts) # byte width
+ bit_wid = 8 * byte_width # bit width
+ nat, nbt, nla, nlb = [], [], [], []
+ for i in range(len(parts)):
+ # 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.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)
+ 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.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)
+ 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)),
+ neg_lsb_b_term.eq(Cat(*nlb)),
+ ]
+
+ return m
+
+
+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
+ self.delayed_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)
+
+ def elaborate(self, platform):
+ m = Module()
+
+ ol = []
+ w = self.width
+ sel = w // 8
+ 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.part(i * w*2, w),
+ self.intermed.part(i * w*2 + w, w)))
+ ol.append(op)
+ m.d.comb += self.output.eq(Cat(*ol))
+
+ 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.part(i * 8, 8),
+ self.i16.part(i * 8, 8)),
+ Mux(self.d32[i // 4], self.i32.part(i * 8, 8),
+ self.i64.part(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)
+ for i in range(4)]
+ self.orout = Signal(wid, reset_less=True)
+
+ def elaborate(self, platform):
+ m = Module()
+ or1 = Signal(self.wid, reset_less=True)
+ or2 = Signal(self.wid, reset_less=True)
+ m.d.comb += or1.eq(self.orin[0] | self.orin[1])
+ m.d.comb += or2.eq(self.orin[2] | self.orin[3])
+ m.d.comb += self.orout.eq(or1 | or2)
+
+ 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)
+
+ # 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)
- self.output = Signal(64)
- self.register_levels = list(register_levels)
+
+ # intermediates (needed for unit tests)
self._intermediate_output = Signal(128)
- self._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))]
- self._part_8 = [Signal(name=f"_part_8_{i}") for i in range(8)]
- self._part_16 = [Signal(name=f"_part_16_{i}") for i in range(4)]
- self._part_32 = [Signal(name=f"_part_32_{i}") for i in range(2)]
- self._part_64 = [Signal(name=f"_part_64")]
- self._delayed_part_8 = [
- [Signal(name=f"_delayed_part_8_{delay}_{i}")
- for i in range(8)]
- for delay in range(1 + len(self.register_levels))]
- self._delayed_part_16 = [
- [Signal(name=f"_delayed_part_16_{delay}_{i}")
- for i in range(4)]
- for delay in range(1 + len(self.register_levels))]
- self._delayed_part_32 = [
- [Signal(name=f"_delayed_part_32_{delay}_{i}")
- for i in range(2)]
- for delay in range(1 + len(self.register_levels))]
- self._delayed_part_64 = [
- [Signal(name=f"_delayed_part_64_{delay}")]
- for delay in range(1 + len(self.register_levels))]
- self._output_64 = Signal(64)
- self._output_32 = Signal(64)
- self._output_16 = Signal(64)
- self._output_8 = 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._not_a_term_8 = Signal(128)
- self._neg_lsb_a_term_8 = Signal(128)
- self._not_b_term_8 = Signal(128)
- self._neg_lsb_b_term_8 = Signal(128)
- self._not_a_term_16 = Signal(128)
- self._neg_lsb_a_term_16 = Signal(128)
- self._not_b_term_16 = Signal(128)
- self._neg_lsb_b_term_16 = Signal(128)
- self._not_a_term_32 = Signal(128)
- self._neg_lsb_a_term_32 = Signal(128)
- self._not_b_term_32 = Signal(128)
- self._neg_lsb_b_term_32 = Signal(128)
- self._not_a_term_64 = Signal(128)
- self._neg_lsb_a_term_64 = Signal(128)
- self._not_b_term_64 = Signal(128)
- self._neg_lsb_b_term_64 = Signal(128)
+
+ # output
+ self.output = Signal(64)
def _part_byte(self, index):
if index == -1 or index == 7:
def elaborate(self, platform):
m = Module()
- for i in range(len(self.part_ops)):
- m.d.comb += self._delayed_part_ops[0][i].eq(self.part_ops[i])
- m.d.sync += [self._delayed_part_ops[j + 1][i]
- .eq(self._delayed_part_ops[j][i])
- for j in range(len(self.register_levels))]
-
- for parts, delayed_parts in [(self._part_64, self._delayed_part_64),
- (self._part_32, self._delayed_part_32),
- (self._part_16, self._delayed_part_16),
- (self._part_8, self._delayed_part_8)]:
- byte_count = 8 // len(parts)
- for i in range(len(parts)):
- value = self._part_byte(i * byte_count - 1)
- for j in range(i * byte_count, (i + 1) * byte_count - 1):
- value &= ~self._part_byte(j)
- value &= self._part_byte((i + 1) * byte_count - 1)
- m.d.comb += parts[i].eq(value)
- 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(self.register_levels))]
-
- products = [[
- Signal(16, name=f"products_{i}_{j}")
- for j in range(8)]
- for i in range(8)]
+ # 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))
+ tl.append(pb)
+ m.d.comb += pbs.eq(Cat(*tl))
- for a_index in range(8):
- for b_index in range(8):
- a = self.a.part(a_index * 8, 8)
- b = self.b.part(b_index * 8, 8)
- m.d.comb += products[a_index][b_index].eq(a * b)
+ # local variables
+ 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])
+
+ 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)
+ 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)
+ 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)
+ nla_l.append(mod.neg_lsb_a_term)
+ nlb_l.append(mod.neg_lsb_b_term)
terms = []
- def add_term(value, shift=0, enabled=None):
- term = Signal(128)
- terms.append(term)
- if enabled is not None:
- value = Mux(enabled, value, 0)
- if shift > 0:
- value = Cat(Repl(C(0, 1), shift), value)
- else:
- assert shift == 0
- m.d.comb += term.eq(value)
-
for a_index in range(8):
- for b_index in range(8):
- term_enabled: Value = C(True, 1)
- min_index = min(a_index, b_index)
- max_index = max(a_index, b_index)
- for i in range(min_index, max_index):
- term_enabled &= ~self._part_byte(i)
- add_term(products[a_index][b_index],
- 8 * (a_index + b_index),
- term_enabled)
+ t = ProductTerms(8, 128, 8, a_index, 8)
+ setattr(m.submodules, "terms_%d" % a_index, t)
- for i in range(8):
- a_signed = self.part_ops[i] != OP_MUL_UNSIGNED_HIGH
- b_signed = (self.part_ops[i] == OP_MUL_LOW) \
- | (self.part_ops[i] == OP_MUL_SIGNED_HIGH)
- m.d.comb += self._a_signed[i].eq(a_signed)
- m.d.comb += self._b_signed[i].eq(b_signed)
+ m.d.comb += t.a.eq(self.a)
+ m.d.comb += t.b.eq(self.b)
+ m.d.comb += t.pb_en.eq(pbs)
- # it's fine to bitwise-or these together since they are never enabled
+ for term in t.terms:
+ terms.append(term)
+
+ # it's fine to bitwise-or data together since they are never enabled
# at the same time
- add_term(self._not_a_term_8 | self._not_a_term_16
- | self._not_a_term_32 | self._not_a_term_64)
- add_term(self._neg_lsb_a_term_8 | self._neg_lsb_a_term_16
- | self._neg_lsb_a_term_32 | self._neg_lsb_a_term_64)
- add_term(self._not_b_term_8 | self._not_b_term_16
- | self._not_b_term_32 | self._not_b_term_64)
- add_term(self._neg_lsb_b_term_8 | self._neg_lsb_b_term_16
- | self._neg_lsb_b_term_32 | self._neg_lsb_b_term_64)
-
- for not_a_term, \
- neg_lsb_a_term, \
- not_b_term, \
- neg_lsb_b_term, \
- parts in [
- (self._not_a_term_8,
- self._neg_lsb_a_term_8,
- self._not_b_term_8,
- self._neg_lsb_b_term_8,
- self._part_8),
- (self._not_a_term_16,
- self._neg_lsb_a_term_16,
- self._not_b_term_16,
- self._neg_lsb_b_term_16,
- self._part_16),
- (self._not_a_term_32,
- self._neg_lsb_a_term_32,
- self._not_b_term_32,
- self._neg_lsb_b_term_32,
- self._part_32),
- (self._not_a_term_64,
- self._neg_lsb_a_term_64,
- self._not_b_term_64,
- self._neg_lsb_b_term_64,
- self._part_64),
- ]:
- byte_width = 8 // len(parts)
- bit_width = 8 * byte_width
- for i in range(len(parts)):
- b_enabled = parts[i] & self.a[(i + 1) * bit_width - 1] \
- & self._a_signed[i * byte_width]
- a_enabled = parts[i] & self.b[(i + 1) * bit_width - 1] \
- & self._b_signed[i * byte_width]
-
- # 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.
- m.d.comb += [
- not_a_term.part(bit_width * 2 * i, bit_width * 2)
- .eq(Mux(a_enabled,
- Cat(Repl(0, bit_width),
- ~self.a.part(bit_width * i, bit_width)),
- 0)),
-
- neg_lsb_a_term.part(bit_width * 2 * i, bit_width * 2)
- .eq(Cat(Repl(0, bit_width), a_enabled)),
-
- not_b_term.part(bit_width * 2 * i, bit_width * 2)
- .eq(Mux(b_enabled,
- Cat(Repl(0, bit_width),
- ~self.b.part(bit_width * i, bit_width)),
- 0)),
-
- neg_lsb_b_term.part(bit_width * 2 * i, bit_width * 2)
- .eq(Cat(Repl(0, bit_width), b_enabled))]
+ m.submodules.nat_or = nat_or = OrMod(128)
+ m.submodules.nbt_or = nbt_or = OrMod(128)
+ m.submodules.nla_or = nla_or = OrMod(128)
+ m.submodules.nlb_or = nlb_or = OrMod(128)
+ for l, mod in [(nat_l, nat_or),
+ (nbt_l, nbt_or),
+ (nla_l, nla_or),
+ (nlb_l, nlb_or)]:
+ for i in range(len(l)):
+ 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}")
+ signal = Signal(name=f"expanded_part_pts_{i*2}", reset_less=True)
expanded_part_pts[i * 2] = signal
m.d.comb += signal.eq(v)
add_reduce = AddReduce(terms,
128,
self.register_levels,
- expanded_part_pts)
+ expanded_part_pts,
+ self.part_ops)
+
+ out_part_ops = add_reduce.levels[-1].out_part_ops
+
m.submodules.add_reduce = add_reduce
m.d.comb += self._intermediate_output.eq(add_reduce.output)
- m.d.comb += self._output_64.eq(
- Mux(self._delayed_part_ops[-1][0] == OP_MUL_LOW,
- self._intermediate_output.part(0, 64),
- self._intermediate_output.part(64, 64)))
- for i in range(2):
- m.d.comb += self._output_32.part(i * 32, 32).eq(
- Mux(self._delayed_part_ops[-1][4 * i] == OP_MUL_LOW,
- self._intermediate_output.part(i * 64, 32),
- self._intermediate_output.part(i * 64 + 32, 32)))
- for i in range(4):
- m.d.comb += self._output_16.part(i * 16, 16).eq(
- Mux(self._delayed_part_ops[-1][2 * i] == OP_MUL_LOW,
- self._intermediate_output.part(i * 32, 16),
- self._intermediate_output.part(i * 32 + 16, 16)))
+ # create _output_64
+ m.submodules.io64 = io64 = IntermediateOut(64, 128, 1)
+ m.d.comb += io64.intermed.eq(self._intermediate_output)
for i in range(8):
- m.d.comb += self._output_8.part(i * 8, 8).eq(
- Mux(self._delayed_part_ops[-1][i] == OP_MUL_LOW,
- self._intermediate_output.part(i * 16, 8),
- self._intermediate_output.part(i * 16 + 8, 8)))
+ m.d.comb += io64.delayed_part_ops[i].eq(out_part_ops[i])
+
+ # 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(out_part_ops[i])
+
+ # 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 += self.output.part(i * 8, 8).eq(
- Mux(self._delayed_part_8[-1][i]
- | self._delayed_part_16[-1][i // 2],
- Mux(self._delayed_part_8[-1][i],
- self._output_8.part(i * 8, 8),
- self._output_16.part(i * 8, 8)),
- Mux(self._delayed_part_32[-1][i // 4],
- self._output_32.part(i * 8, 8),
- self._output_64.part(i * 8, 8))))
+ m.d.comb += io16.delayed_part_ops[i].eq(out_part_ops[i])
+
+ # 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(out_part_ops[i])
+
+ # 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.d.comb += self.output.eq(finalout.out)
+
return m
projects / ieee754fpu.git / blobdiff