1 # SPDX-License-Identifier: LGPL-2.1-or-later
2 # See Notices.txt for copyright information
3 """Integer Multiplication."""
5 from nmigen
import Signal
, Module
, Value
, Elaboratable
, Cat
, C
, Mux
, Repl
6 from nmigen
.hdl
.ast
import Assign
7 from abc
import ABCMeta
, abstractmethod
8 from nmigen
.cli
import main
9 from functools
import reduce
10 from operator
import or_
13 class PartitionPoints(dict):
14 """Partition points and corresponding ``Value``s.
16 The points at where an ALU is partitioned along with ``Value``s that
17 specify if the corresponding partition points are enabled.
19 For example: ``{1: True, 5: True, 10: True}`` with
20 ``width == 16`` specifies that the ALU is split into 4 sections:
23 * bits 5 <= ``i`` < 10
24 * bits 10 <= ``i`` < 16
26 If the partition_points were instead ``{1: True, 5: a, 10: True}``
27 where ``a`` is a 1-bit ``Signal``:
28 * If ``a`` is asserted:
31 * bits 5 <= ``i`` < 10
32 * bits 10 <= ``i`` < 16
35 * bits 1 <= ``i`` < 10
36 * bits 10 <= ``i`` < 16
39 def __init__(self
, partition_points
=None):
40 """Create a new ``PartitionPoints``.
42 :param partition_points: the input partition points to values mapping.
45 if partition_points
is not None:
46 for point
, enabled
in partition_points
.items():
47 if not isinstance(point
, int):
48 raise TypeError("point must be a non-negative integer")
50 raise ValueError("point must be a non-negative integer")
51 self
[point
] = Value
.wrap(enabled
)
53 def like(self
, name
=None, src_loc_at
=0):
54 """Create a new ``PartitionPoints`` with ``Signal``s for all values.
56 :param name: the base name for the new ``Signal``s.
59 name
= Signal(src_loc_at
=1+src_loc_at
).name
# get variable name
60 retval
= PartitionPoints()
61 for point
, enabled
in self
.items():
62 retval
[point
] = Signal(enabled
.shape(), name
=f
"{name}_{point}")
66 """Assign ``PartitionPoints`` using ``Signal.eq``."""
67 if set(self
.keys()) != set(rhs
.keys()):
68 raise ValueError("incompatible point set")
69 for point
, enabled
in self
.items():
70 yield enabled
.eq(rhs
[point
])
72 def as_mask(self
, width
):
73 """Create a bit-mask from `self`.
75 Each bit in the returned mask is clear only if the partition point at
76 the same bit-index is enabled.
78 :param width: the bit width of the resulting mask
81 for i
in range(width
):
88 def get_max_partition_count(self
, width
):
89 """Get the maximum number of partitions.
91 Gets the number of partitions when all partition points are enabled.
94 for point
in self
.keys():
99 def fits_in_width(self
, width
):
100 """Check if all partition points are smaller than `width`."""
101 for point
in self
.keys():
107 class FullAdder(Elaboratable
):
110 :attribute in0: the first input
111 :attribute in1: the second input
112 :attribute in2: the third input
113 :attribute sum: the sum output
114 :attribute carry: the carry output
116 Rather than do individual full adders (and have an array of them,
117 which would be very slow to simulate), this module can specify the
118 bit width of the inputs and outputs: in effect it performs multiple
119 Full 3-2 Add operations "in parallel".
122 def __init__(self
, width
):
123 """Create a ``FullAdder``.
125 :param width: the bit width of the input and output
127 self
.in0
= Signal(width
)
128 self
.in1
= Signal(width
)
129 self
.in2
= Signal(width
)
130 self
.sum = Signal(width
)
131 self
.carry
= Signal(width
)
133 def elaborate(self
, platform
):
134 """Elaborate this module."""
136 m
.d
.comb
+= self
.sum.eq(self
.in0 ^ self
.in1 ^ self
.in2
)
137 m
.d
.comb
+= self
.carry
.eq((self
.in0
& self
.in1
)
138 |
(self
.in1
& self
.in2
)
139 |
(self
.in2
& self
.in0
))
143 class PartitionedAdder(Elaboratable
):
144 """Partitioned Adder.
146 :attribute width: the bit width of the input and output. Read-only.
147 :attribute a: the first input to the adder
148 :attribute b: the second input to the adder
149 :attribute output: the sum output
150 :attribute partition_points: the input partition points. Modification not
151 supported, except for by ``Signal.eq``.
154 def __init__(self
, width
, partition_points
):
155 """Create a ``PartitionedAdder``.
157 :param width: the bit width of the input and output
158 :param partition_points: the input partition points
161 self
.a
= Signal(width
)
162 self
.b
= Signal(width
)
163 self
.output
= Signal(width
)
164 self
.partition_points
= PartitionPoints(partition_points
)
165 if not self
.partition_points
.fits_in_width(width
):
166 raise ValueError("partition_points doesn't fit in width")
168 for i
in range(self
.width
):
169 if i
in self
.partition_points
:
172 self
._expanded
_width
= expanded_width
173 # XXX these have to remain here due to some horrible nmigen
174 # simulation bugs involving sync. it is *not* necessary to
175 # have them here, they should (under normal circumstances)
176 # be moved into elaborate, as they are entirely local
177 self
._expanded
_a
= Signal(expanded_width
)
178 self
._expanded
_b
= Signal(expanded_width
)
179 self
._expanded
_output
= Signal(expanded_width
)
181 def elaborate(self
, platform
):
182 """Elaborate this module."""
185 # store bits in a list, use Cat later. graphviz is much cleaner
186 al
, bl
, ol
, ea
, eb
, eo
= [],[],[],[],[],[]
188 # partition points are "breaks" (extra zeros) in what would otherwise
189 # be a massive long add.
190 for i
in range(self
.width
):
191 if i
in self
.partition_points
:
192 # add extra bit set to 0 + 0 for enabled partition points
193 # and 1 + 0 for disabled partition points
194 ea
.append(self
._expanded
_a
[expanded_index
])
195 al
.append(~self
.partition_points
[i
])
196 eb
.append(self
._expanded
_b
[expanded_index
])
199 ea
.append(self
._expanded
_a
[expanded_index
])
201 eb
.append(self
._expanded
_b
[expanded_index
])
203 eo
.append(self
._expanded
_output
[expanded_index
])
204 ol
.append(self
.output
[i
])
206 # combine above using Cat
207 m
.d
.comb
+= Cat(*ea
).eq(Cat(*al
))
208 m
.d
.comb
+= Cat(*eb
).eq(Cat(*bl
))
209 m
.d
.comb
+= Cat(*ol
).eq(Cat(*eo
))
210 # use only one addition to take advantage of look-ahead carry and
211 # special hardware on FPGAs
212 m
.d
.comb
+= self
._expanded
_output
.eq(
213 self
._expanded
_a
+ self
._expanded
_b
)
217 FULL_ADDER_INPUT_COUNT
= 3
220 class AddReduce(Elaboratable
):
221 """Add list of numbers together.
223 :attribute inputs: input ``Signal``s to be summed. Modification not
224 supported, except for by ``Signal.eq``.
225 :attribute register_levels: List of nesting levels that should have
227 :attribute output: output sum.
228 :attribute partition_points: the input partition points. Modification not
229 supported, except for by ``Signal.eq``.
232 def __init__(self
, inputs
, output_width
, register_levels
, partition_points
):
233 """Create an ``AddReduce``.
235 :param inputs: input ``Signal``s to be summed.
236 :param output_width: bit-width of ``output``.
237 :param register_levels: List of nesting levels that should have
239 :param partition_points: the input partition points.
241 self
.inputs
= list(inputs
)
242 self
._resized
_inputs
= [
243 Signal(output_width
, name
=f
"resized_inputs[{i}]")
244 for i
in range(len(self
.inputs
))]
245 self
.register_levels
= list(register_levels
)
246 self
.output
= Signal(output_width
)
247 self
.partition_points
= PartitionPoints(partition_points
)
248 if not self
.partition_points
.fits_in_width(output_width
):
249 raise ValueError("partition_points doesn't fit in output_width")
250 self
._reg
_partition
_points
= self
.partition_points
.like()
251 max_level
= AddReduce
.get_max_level(len(self
.inputs
))
252 for level
in self
.register_levels
:
253 if level
> max_level
:
255 "not enough adder levels for specified register levels")
258 def get_max_level(input_count
):
259 """Get the maximum level.
261 All ``register_levels`` must be less than or equal to the maximum
266 groups
= AddReduce
.full_adder_groups(input_count
)
269 input_count
%= FULL_ADDER_INPUT_COUNT
270 input_count
+= 2 * len(groups
)
273 def next_register_levels(self
):
274 """``Iterable`` of ``register_levels`` for next recursive level."""
275 for level
in self
.register_levels
:
280 def full_adder_groups(input_count
):
281 """Get ``inputs`` indices for which a full adder should be built."""
283 input_count
- FULL_ADDER_INPUT_COUNT
+ 1,
284 FULL_ADDER_INPUT_COUNT
)
286 def elaborate(self
, platform
):
287 """Elaborate this module."""
290 # resize inputs to correct bit-width and optionally add in
292 resized_input_assignments
= [self
._resized
_inputs
[i
].eq(self
.inputs
[i
])
293 for i
in range(len(self
.inputs
))]
294 if 0 in self
.register_levels
:
295 m
.d
.sync
+= resized_input_assignments
296 m
.d
.sync
+= self
._reg
_partition
_points
.eq(self
.partition_points
)
298 m
.d
.comb
+= resized_input_assignments
299 m
.d
.comb
+= self
._reg
_partition
_points
.eq(self
.partition_points
)
301 groups
= AddReduce
.full_adder_groups(len(self
.inputs
))
302 # if there are no full adders to create, then we handle the base cases
303 # and return, otherwise we go on to the recursive case
305 if len(self
.inputs
) == 0:
306 # use 0 as the default output value
307 m
.d
.comb
+= self
.output
.eq(0)
308 elif len(self
.inputs
) == 1:
309 # handle single input
310 m
.d
.comb
+= self
.output
.eq(self
._resized
_inputs
[0])
312 # base case for adding 2 or more inputs, which get recursively
313 # reduced to 2 inputs
314 assert len(self
.inputs
) == 2
315 adder
= PartitionedAdder(len(self
.output
),
316 self
._reg
_partition
_points
)
317 m
.submodules
.final_adder
= adder
318 m
.d
.comb
+= adder
.a
.eq(self
._resized
_inputs
[0])
319 m
.d
.comb
+= adder
.b
.eq(self
._resized
_inputs
[1])
320 m
.d
.comb
+= self
.output
.eq(adder
.output
)
322 # go on to handle recursive case
323 intermediate_terms
= []
325 def add_intermediate_term(value
):
326 intermediate_term
= Signal(
328 name
=f
"intermediate_terms[{len(intermediate_terms)}]")
329 intermediate_terms
.append(intermediate_term
)
330 m
.d
.comb
+= intermediate_term
.eq(value
)
332 # store mask in intermediary (simplifies graph)
333 part_mask
= Signal(len(self
.output
), reset_less
=True)
334 mask
= self
._reg
_partition
_points
.as_mask(len(self
.output
))
335 m
.d
.comb
+= part_mask
.eq(mask
)
337 # create full adders for this recursive level.
338 # this shrinks N terms to 2 * (N // 3) plus the remainder
340 adder_i
= FullAdder(len(self
.output
))
341 setattr(m
.submodules
, f
"adder_{i}", adder_i
)
342 m
.d
.comb
+= adder_i
.in0
.eq(self
._resized
_inputs
[i
])
343 m
.d
.comb
+= adder_i
.in1
.eq(self
._resized
_inputs
[i
+ 1])
344 m
.d
.comb
+= adder_i
.in2
.eq(self
._resized
_inputs
[i
+ 2])
345 add_intermediate_term(adder_i
.sum)
346 shifted_carry
= adder_i
.carry
<< 1
347 # mask out carry bits to prevent carries between partitions
348 add_intermediate_term((adder_i
.carry
<< 1) & part_mask
)
349 # handle the remaining inputs.
350 if len(self
.inputs
) % FULL_ADDER_INPUT_COUNT
== 1:
351 add_intermediate_term(self
._resized
_inputs
[-1])
352 elif len(self
.inputs
) % FULL_ADDER_INPUT_COUNT
== 2:
353 # Just pass the terms to the next layer, since we wouldn't gain
354 # anything by using a half adder since there would still be 2 terms
355 # and just passing the terms to the next layer saves gates.
356 add_intermediate_term(self
._resized
_inputs
[-2])
357 add_intermediate_term(self
._resized
_inputs
[-1])
359 assert len(self
.inputs
) % FULL_ADDER_INPUT_COUNT
== 0
360 # recursive invocation of ``AddReduce``
361 next_level
= AddReduce(intermediate_terms
,
363 self
.next_register_levels(),
364 self
._reg
_partition
_points
)
365 m
.submodules
.next_level
= next_level
366 m
.d
.comb
+= self
.output
.eq(next_level
.output
)
371 OP_MUL_SIGNED_HIGH
= 1
372 OP_MUL_SIGNED_UNSIGNED_HIGH
= 2 # a is signed, b is unsigned
373 OP_MUL_UNSIGNED_HIGH
= 3
376 def get_term(value
, shift
=0, enabled
=None):
377 if enabled
is not None:
378 value
= Mux(enabled
, value
, 0)
380 value
= Cat(Repl(C(0, 1), shift
), value
)
386 class ProductTerm(Elaboratable
):
387 """ this class creates a single product term (a[..]*b[..]).
388 it has a design flaw in that is the *output* that is selected,
389 where the multiplication(s) are combinatorially generated
393 def __init__(self
, width
, twidth
, pbwid
, a_index
, b_index
):
394 self
.a_index
= a_index
395 self
.b_index
= b_index
396 shift
= 8 * (self
.a_index
+ self
.b_index
)
402 self
.ti
= Signal(self
.width
, reset_less
=True)
403 self
.term
= Signal(twidth
, reset_less
=True)
404 self
.a
= Signal(twidth
//2, reset_less
=True)
405 self
.b
= Signal(twidth
//2, reset_less
=True)
406 self
.pb_en
= Signal(pbwid
, reset_less
=True)
409 min_index
= min(self
.a_index
, self
.b_index
)
410 max_index
= max(self
.a_index
, self
.b_index
)
411 for i
in range(min_index
, max_index
):
412 tl
.append(self
.pb_en
[i
])
413 name
= "te_%d_%d" % (self
.a_index
, self
.b_index
)
415 term_enabled
= Signal(name
=name
, reset_less
=True)
418 self
.enabled
= term_enabled
419 self
.term
.name
= "term_%d_%d" % (a_index
, b_index
) # rename
421 def elaborate(self
, platform
):
424 if self
.enabled
is not None:
425 m
.d
.comb
+= self
.enabled
.eq(~
(Cat(*self
.tl
).bool()))
427 bsa
= Signal(self
.width
, reset_less
=True)
428 bsb
= Signal(self
.width
, reset_less
=True)
429 a_index
, b_index
= self
.a_index
, self
.b_index
431 m
.d
.comb
+= bsa
.eq(self
.a
.bit_select(a_index
* pwidth
, pwidth
))
432 m
.d
.comb
+= bsb
.eq(self
.b
.bit_select(b_index
* pwidth
, pwidth
))
433 m
.d
.comb
+= self
.ti
.eq(bsa
* bsb
)
434 m
.d
.comb
+= self
.term
.eq(get_term(self
.ti
, self
.shift
, self
.enabled
))
436 #TODO: sort out width issues, get inputs a/b switched on/off.
437 #data going into Muxes is 1/2 the required width
441 bsa = Signal(self.twidth//2, reset_less=True)
442 bsb = Signal(self.twidth//2, reset_less=True)
443 asel = Signal(width, reset_less=True)
444 bsel = Signal(width, reset_less=True)
445 a_index, b_index = self.a_index, self.b_index
446 m.d.comb += asel.eq(self.a.bit_select(a_index * pwidth, pwidth))
447 m.d.comb += bsel.eq(self.b.bit_select(b_index * pwidth, pwidth))
448 m.d.comb += bsa.eq(get_term(asel, self.shift, self.enabled))
449 m.d.comb += bsb.eq(get_term(bsel, self.shift, self.enabled))
450 m.d.comb += self.ti.eq(bsa * bsb)
451 m.d.comb += self.term.eq(self.ti)
457 class ProductTerms(Elaboratable
):
458 """ creates a bank of product terms. also performs the actual bit-selection
459 this class is to be wrapped with a for-loop on the "a" operand.
460 it creates a second-level for-loop on the "b" operand.
462 def __init__(self
, width
, twidth
, pbwid
, a_index
, blen
):
463 self
.a_index
= a_index
468 self
.a
= Signal(twidth
//2, reset_less
=True)
469 self
.b
= Signal(twidth
//2, reset_less
=True)
470 self
.pb_en
= Signal(pbwid
, reset_less
=True)
471 self
.terms
= [Signal(twidth
, name
="term%d"%i, reset_less
=True) \
472 for i
in range(blen
)]
474 def elaborate(self
, platform
):
478 for b_index
in range(self
.blen
):
479 t
= ProductTerm(self
.pwidth
, self
.twidth
, self
.pbwid
,
480 self
.a_index
, b_index
)
481 setattr(m
.submodules
, "term_%d" % b_index
, t
)
483 m
.d
.comb
+= t
.a
.eq(self
.a
)
484 m
.d
.comb
+= t
.b
.eq(self
.b
)
485 m
.d
.comb
+= t
.pb_en
.eq(self
.pb_en
)
487 m
.d
.comb
+= self
.terms
[b_index
].eq(t
.term
)
492 class Part(Elaboratable
):
493 """ a key class which, depending on the partitioning, will determine
494 what action to take when parts of the output are signed or unsigned.
496 this requires 2 pieces of data *per operand, per partition*:
497 whether the MSB is HI/LO (per partition!), and whether a signed
498 or unsigned operation has been *requested*.
500 once that is determined, signed is basically carried out
501 by splitting 2's complement into 1's complement plus one.
502 1's complement is just a bit-inversion.
504 the extra terms - as separate terms - are then thrown at the
505 AddReduce alongside the multiplication part-results.
507 def __init__(self
, width
, n_parts
, n_levels
, pbwid
):
512 self
.a_signed
= [Signal(name
=f
"a_signed_{i}") for i
in range(8)]
513 self
.b_signed
= [Signal(name
=f
"_b_signed_{i}") for i
in range(8)]
514 self
.pbs
= Signal(pbwid
, reset_less
=True)
517 self
.parts
= [Signal(name
=f
"part_{i}") for i
in range(n_parts
)]
518 self
.delayed_parts
= [
519 [Signal(name
=f
"delayed_part_{delay}_{i}")
520 for i
in range(n_parts
)]
521 for delay
in range(n_levels
)]
522 # XXX REALLY WEIRD BUG - have to take a copy of the last delayed_parts
523 self
.dplast
= [Signal(name
=f
"dplast_{i}")
524 for i
in range(n_parts
)]
526 self
.not_a_term
= Signal(width
)
527 self
.neg_lsb_a_term
= Signal(width
)
528 self
.not_b_term
= Signal(width
)
529 self
.neg_lsb_b_term
= Signal(width
)
531 def elaborate(self
, platform
):
534 pbs
, parts
, delayed_parts
= self
.pbs
, self
.parts
, self
.delayed_parts
535 byte_count
= 8 // len(parts
)
536 for i
in range(len(parts
)):
538 pbl
.append(~pbs
[i
* byte_count
- 1])
539 for j
in range(i
* byte_count
, (i
+ 1) * byte_count
- 1):
541 pbl
.append(~pbs
[(i
+ 1) * byte_count
- 1])
542 value
= Signal(len(pbl
), reset_less
=True)
543 m
.d
.comb
+= value
.eq(Cat(*pbl
))
544 m
.d
.comb
+= parts
[i
].eq(~
(value
).bool())
545 m
.d
.comb
+= delayed_parts
[0][i
].eq(parts
[i
])
546 m
.d
.sync
+= [delayed_parts
[j
+ 1][i
].eq(delayed_parts
[j
][i
])
547 for j
in range(len(delayed_parts
)-1)]
548 m
.d
.comb
+= self
.dplast
[i
].eq(delayed_parts
[-1][i
])
550 not_a_term
, neg_lsb_a_term
, not_b_term
, neg_lsb_b_term
= \
551 self
.not_a_term
, self
.neg_lsb_a_term
, \
552 self
.not_b_term
, self
.neg_lsb_b_term
554 byte_width
= 8 // len(parts
) # byte width
555 bit_wid
= 8 * byte_width
# bit width
556 ext
= Repl(0, bit_wid
) # extend output to HI part
557 nat
, nbt
, nla
, nlb
= [], [], [], []
558 for i
in range(len(parts
)):
559 # determine sign of each incoming number *in this partition*
560 be
= (parts
[i
] & self
.a
[(i
+ 1) * bit_wid
- 1] # MSB
561 & self
.a_signed
[i
* byte_width
]) # a op is signed?
562 ae
= (parts
[i
] & self
.b
[(i
+ 1) * bit_wid
- 1] # MSB
563 & self
.b_signed
[i
* byte_width
]) # b op is signed?
564 a_enabled
= Signal(name
="a_en_%d" % i
, reset_less
=True)
565 b_enabled
= Signal(name
="b_en_%d" % i
, reset_less
=True)
566 m
.d
.comb
+= a_enabled
.eq(ae
)
567 m
.d
.comb
+= b_enabled
.eq(be
)
569 # for 8-bit values: form a * 0xFF00 by using -a * 0x100, the
570 # negation operation is split into a bitwise not and a +1.
571 # likewise for 16, 32, and 64-bit values.
573 # a: width-extended 1s complement if a is signed, otherwise zero
574 nat
.append(Mux(a_enabled
,
575 Cat(ext
, ~self
.a
.bit_select(bit_wid
* i
, bit_wid
)),
578 # a: add 1 if a signed, otherwise add zero
579 nla
.append(Cat(ext
, a_enabled
, Repl(0, bit_wid
-1)))
581 # b: width-extended 1s complement if a is signed, otherwise zero
582 nbt
.append(Mux(b_enabled
,
583 Cat(ext
, ~self
.b
.bit_select(bit_wid
* i
, bit_wid
)),
586 # b: add 1 if b signed, otherwise add zero
587 nlb
.append(Cat(ext
, b_enabled
, Repl(0, bit_wid
-1)))
589 # concatenate together and return all 4 results.
590 m
.d
.comb
+= [not_a_term
.eq(Cat(*nat
)),
591 not_b_term
.eq(Cat(*nbt
)),
592 neg_lsb_a_term
.eq(Cat(*nla
)),
593 neg_lsb_b_term
.eq(Cat(*nlb
)),
599 class IntermediateOut(Elaboratable
):
600 """ selects the HI/LO part of the multiplication, for a given bit-width
601 the output is also reconstructed in its SIMD (partition) lanes.
603 def __init__(self
, width
, out_wid
, n_parts
):
605 self
.n_parts
= n_parts
606 self
.delayed_part_ops
= [Signal(2, name
="dpop%d" % i
, reset_less
=True)
608 self
.intermed
= Signal(out_wid
, reset_less
=True)
609 self
.output
= Signal(out_wid
//2, reset_less
=True)
611 def elaborate(self
, platform
):
617 for i
in range(self
.n_parts
):
618 op
= Signal(w
, reset_less
=True, name
="op%d_%d" % (w
, i
))
620 Mux(self
.delayed_part_ops
[sel
* i
] == OP_MUL_LOW
,
621 self
.intermed
.bit_select(i
* w
*2, w
),
622 self
.intermed
.bit_select(i
* w
*2 + w
, w
)))
624 m
.d
.comb
+= self
.output
.eq(Cat(*ol
))
629 class FinalOut(Elaboratable
):
630 """ selects the final output based on the partitioning.
632 each byte is selectable independently, i.e. it is possible
633 that some partitions requested 8-bit computation whilst others
634 requested 16 or 32 bit.
636 def __init__(self
, out_wid
):
638 self
.d8
= [Signal(name
=f
"d8_{i}", reset_less
=True) for i
in range(8)]
639 self
.d16
= [Signal(name
=f
"d16_{i}", reset_less
=True) for i
in range(4)]
640 self
.d32
= [Signal(name
=f
"d32_{i}", reset_less
=True) for i
in range(2)]
642 self
.i8
= Signal(out_wid
, reset_less
=True)
643 self
.i16
= Signal(out_wid
, reset_less
=True)
644 self
.i32
= Signal(out_wid
, reset_less
=True)
645 self
.i64
= Signal(out_wid
, reset_less
=True)
648 self
.out
= Signal(out_wid
, reset_less
=True)
650 def elaborate(self
, platform
):
654 # select one of the outputs: d8 selects i8, d16 selects i16
655 # d32 selects i32, and the default is i64.
656 # d8 and d16 are ORed together in the first Mux
657 # then the 2nd selects either i8 or i16.
658 # if neither d8 nor d16 are set, d32 selects either i32 or i64.
659 op
= Signal(8, reset_less
=True, name
="op_%d" % i
)
661 Mux(self
.d8
[i
] | self
.d16
[i
// 2],
662 Mux(self
.d8
[i
], self
.i8
.bit_select(i
* 8, 8),
663 self
.i16
.bit_select(i
* 8, 8)),
664 Mux(self
.d32
[i
// 4], self
.i32
.bit_select(i
* 8, 8),
665 self
.i64
.bit_select(i
* 8, 8))))
667 m
.d
.comb
+= self
.out
.eq(Cat(*ol
))
671 class OrMod(Elaboratable
):
672 """ ORs four values together in a hierarchical tree
674 def __init__(self
, wid
):
676 self
.orin
= [Signal(wid
, name
="orin%d" % i
, reset_less
=True)
678 self
.orout
= Signal(wid
, reset_less
=True)
680 def elaborate(self
, platform
):
682 or1
= Signal(self
.wid
, reset_less
=True)
683 or2
= Signal(self
.wid
, reset_less
=True)
684 m
.d
.comb
+= or1
.eq(self
.orin
[0] | self
.orin
[1])
685 m
.d
.comb
+= or2
.eq(self
.orin
[2] | self
.orin
[3])
686 m
.d
.comb
+= self
.orout
.eq(or1 | or2
)
691 class Signs(Elaboratable
):
692 """ determines whether a or b are signed numbers
693 based on the required operation type (OP_MUL_*)
697 self
.part_ops
= Signal(2, reset_less
=True)
698 self
.a_signed
= Signal(reset_less
=True)
699 self
.b_signed
= Signal(reset_less
=True)
701 def elaborate(self
, platform
):
705 asig
= self
.part_ops
!= OP_MUL_UNSIGNED_HIGH
706 bsig
= (self
.part_ops
== OP_MUL_LOW
) \
707 |
(self
.part_ops
== OP_MUL_SIGNED_HIGH
)
708 m
.d
.comb
+= self
.a_signed
.eq(asig
)
709 m
.d
.comb
+= self
.b_signed
.eq(bsig
)
714 class Mul8_16_32_64(Elaboratable
):
715 """Signed/Unsigned 8/16/32/64-bit partitioned integer multiplier.
717 Supports partitioning into any combination of 8, 16, 32, and 64-bit
718 partitions on naturally-aligned boundaries. Supports the operation being
719 set for each partition independently.
721 :attribute part_pts: the input partition points. Has a partition point at
722 multiples of 8 in 0 < i < 64. Each partition point's associated
723 ``Value`` is a ``Signal``. Modification not supported, except for by
725 :attribute part_ops: the operation for each byte. The operation for a
726 particular partition is selected by assigning the selected operation
727 code to each byte in the partition. The allowed operation codes are:
729 :attribute OP_MUL_LOW: the LSB half of the product. Equivalent to
730 RISC-V's `mul` instruction.
731 :attribute OP_MUL_SIGNED_HIGH: the MSB half of the product where both
732 ``a`` and ``b`` are signed. Equivalent to RISC-V's `mulh`
734 :attribute OP_MUL_SIGNED_UNSIGNED_HIGH: the MSB half of the product
735 where ``a`` is signed and ``b`` is unsigned. Equivalent to RISC-V's
736 `mulhsu` instruction.
737 :attribute OP_MUL_UNSIGNED_HIGH: the MSB half of the product where both
738 ``a`` and ``b`` are unsigned. Equivalent to RISC-V's `mulhu`
742 def __init__(self
, register_levels
=()):
743 """ register_levels: specifies the points in the cascade at which
744 flip-flops are to be inserted.
748 self
.register_levels
= list(register_levels
)
751 self
.part_pts
= PartitionPoints()
752 for i
in range(8, 64, 8):
753 self
.part_pts
[i
] = Signal(name
=f
"part_pts_{i}")
754 self
.part_ops
= [Signal(2, name
=f
"part_ops_{i}") for i
in range(8)]
758 # intermediates (needed for unit tests)
759 self
._intermediate
_output
= Signal(128)
762 self
.output
= Signal(64)
764 def _part_byte(self
, index
):
765 if index
== -1 or index
== 7:
767 assert index
>= 0 and index
< 8
768 return self
.part_pts
[index
* 8 + 8]
770 def elaborate(self
, platform
):
774 pbs
= Signal(8, reset_less
=True)
777 pb
= Signal(name
="pb%d" % i
, reset_less
=True)
778 m
.d
.comb
+= pb
.eq(self
._part
_byte
(i
))
780 m
.d
.comb
+= pbs
.eq(Cat(*tl
))
787 setattr(m
.submodules
, "signs%d" % i
, s
)
788 m
.d
.comb
+= s
.part_ops
.eq(self
.part_ops
[i
])
791 [Signal(2, name
=f
"_delayed_part_ops_{delay}_{i}")
793 for delay
in range(1 + len(self
.register_levels
))]
794 for i
in range(len(self
.part_ops
)):
795 m
.d
.comb
+= delayed_part_ops
[0][i
].eq(self
.part_ops
[i
])
796 m
.d
.sync
+= [delayed_part_ops
[j
+ 1][i
].eq(delayed_part_ops
[j
][i
])
797 for j
in range(len(self
.register_levels
))]
799 n_levels
= len(self
.register_levels
)+1
800 m
.submodules
.part_8
= part_8
= Part(128, 8, n_levels
, 8)
801 m
.submodules
.part_16
= part_16
= Part(128, 4, n_levels
, 8)
802 m
.submodules
.part_32
= part_32
= Part(128, 2, n_levels
, 8)
803 m
.submodules
.part_64
= part_64
= Part(128, 1, n_levels
, 8)
804 nat_l
, nbt_l
, nla_l
, nlb_l
= [], [], [], []
805 for mod
in [part_8
, part_16
, part_32
, part_64
]:
806 m
.d
.comb
+= mod
.a
.eq(self
.a
)
807 m
.d
.comb
+= mod
.b
.eq(self
.b
)
808 for i
in range(len(signs
)):
809 m
.d
.comb
+= mod
.a_signed
[i
].eq(signs
[i
].a_signed
)
810 m
.d
.comb
+= mod
.b_signed
[i
].eq(signs
[i
].b_signed
)
811 m
.d
.comb
+= mod
.pbs
.eq(pbs
)
812 nat_l
.append(mod
.not_a_term
)
813 nbt_l
.append(mod
.not_b_term
)
814 nla_l
.append(mod
.neg_lsb_a_term
)
815 nlb_l
.append(mod
.neg_lsb_b_term
)
819 for a_index
in range(8):
820 t
= ProductTerms(8, 128, 8, a_index
, 8)
821 setattr(m
.submodules
, "terms_%d" % a_index
, t
)
823 m
.d
.comb
+= t
.a
.eq(self
.a
)
824 m
.d
.comb
+= t
.b
.eq(self
.b
)
825 m
.d
.comb
+= t
.pb_en
.eq(pbs
)
830 # it's fine to bitwise-or data together since they are never enabled
832 m
.submodules
.nat_or
= nat_or
= OrMod(128)
833 m
.submodules
.nbt_or
= nbt_or
= OrMod(128)
834 m
.submodules
.nla_or
= nla_or
= OrMod(128)
835 m
.submodules
.nlb_or
= nlb_or
= OrMod(128)
836 for l
, mod
in [(nat_l
, nat_or
),
840 for i
in range(len(l
)):
841 m
.d
.comb
+= mod
.orin
[i
].eq(l
[i
])
842 terms
.append(mod
.orout
)
844 expanded_part_pts
= PartitionPoints()
845 for i
, v
in self
.part_pts
.items():
846 signal
= Signal(name
=f
"expanded_part_pts_{i*2}", reset_less
=True)
847 expanded_part_pts
[i
* 2] = signal
848 m
.d
.comb
+= signal
.eq(v
)
850 add_reduce
= AddReduce(terms
,
852 self
.register_levels
,
854 m
.submodules
.add_reduce
= add_reduce
855 m
.d
.comb
+= self
._intermediate
_output
.eq(add_reduce
.output
)
857 m
.submodules
.io64
= io64
= IntermediateOut(64, 128, 1)
858 m
.d
.comb
+= io64
.intermed
.eq(self
._intermediate
_output
)
860 m
.d
.comb
+= io64
.delayed_part_ops
[i
].eq(delayed_part_ops
[-1][i
])
863 m
.submodules
.io32
= io32
= IntermediateOut(32, 128, 2)
864 m
.d
.comb
+= io32
.intermed
.eq(self
._intermediate
_output
)
866 m
.d
.comb
+= io32
.delayed_part_ops
[i
].eq(delayed_part_ops
[-1][i
])
869 m
.submodules
.io16
= io16
= IntermediateOut(16, 128, 4)
870 m
.d
.comb
+= io16
.intermed
.eq(self
._intermediate
_output
)
872 m
.d
.comb
+= io16
.delayed_part_ops
[i
].eq(delayed_part_ops
[-1][i
])
875 m
.submodules
.io8
= io8
= IntermediateOut(8, 128, 8)
876 m
.d
.comb
+= io8
.intermed
.eq(self
._intermediate
_output
)
878 m
.d
.comb
+= io8
.delayed_part_ops
[i
].eq(delayed_part_ops
[-1][i
])
881 m
.submodules
.finalout
= finalout
= FinalOut(64)
882 for i
in range(len(part_8
.delayed_parts
[-1])):
883 m
.d
.comb
+= finalout
.d8
[i
].eq(part_8
.dplast
[i
])
884 for i
in range(len(part_16
.delayed_parts
[-1])):
885 m
.d
.comb
+= finalout
.d16
[i
].eq(part_16
.dplast
[i
])
886 for i
in range(len(part_32
.delayed_parts
[-1])):
887 m
.d
.comb
+= finalout
.d32
[i
].eq(part_32
.dplast
[i
])
888 m
.d
.comb
+= finalout
.i8
.eq(io8
.output
)
889 m
.d
.comb
+= finalout
.i16
.eq(io16
.output
)
890 m
.d
.comb
+= finalout
.i32
.eq(io32
.output
)
891 m
.d
.comb
+= finalout
.i64
.eq(io64
.output
)
892 m
.d
.comb
+= self
.output
.eq(finalout
.out
)
897 if __name__
== "__main__":
901 m
._intermediate
_output
,
904 *m
.part_pts
.values()])