MVSIS

1
MVSIS

• MVSIS Group
• Minxi Gao,, Jie-Hong Jiang, Yunjian Jiang,
  Yinghua Li, Subarna Sinha and Robert K. Brayton
• Dept. of Electrical Engineering and Computer
  Science University of California, Berkeley

2
Outline

• Motivation From binary to multi-value
• Design specification
• MVSIS optimizations
• Node simplification
• Kernel and cube extraction
• Pairing and encoding
• Network manipulation
• Demo
• Conclusions

3
History

• Multi-valued logic

Incomplete references
E. L. Post, Introdution to a general theory of
elementary propositions,Amer. J. Math., Jun 1921
J. C. Muzio and D. M. Miller, On the
minimization of many-valued functions,Proc. 9th
Int. Symp. Multiple-valued Logic, 1979
S. L. Hurst, Multiple-valued logic its status
and its future, IEEE Trans. On Computers, Jun
1984
J. C. Muzio and T. C. Wesselkamper,
Multiple-valued switching theoryBristol
Hilger, 1986
R. K. Brayton and S. P. Khatri, Multi-valued
logic synthesis,Proc. 12th Int. Conf. On VLSI
Design, Jan 1999
4
Motivations

• Synchronous hardware synthesis
• Software synthesis from synchronous
  specifications
• Asynchronous hardware synthesis
• Multi-valued devices?
• Current-mode CMOS devices
• Optical logic circuits

5
Motivation synchronous hardware

• Design and synthesis from multi-valued logic
• Natural method of specification
• Larger design space

Verilog-MV
vl2mv
BLIF-MV
Two-level MV-PLA synthesis R.Rudell, et al
Espresso-MV, 1987
MV-Optimize
Multi-level FSM synthesis (single MV) L.Lavagno,
et al MIS-MV, 1990
Opt-Encode
Encode
FSM state encoding T.Villa, et al, Nova,
1990 E.Goldberg, et al, Minsk, 1999
MVSIS
SIS
6
Motivation software synthesis

• Synchronous programming of embedded systems
• Esterel/Lustre/Signal
• Interactive FSM semantics
• Code generation from logic

FSMs
POLIS F.Balerin, et al, Synthesis of software
programsfor embedded control applications, TCAD
1999
MV-Optimize
ESTEREL G.Berry, The foundations of Esterel,
2000
Code Gen
POLISVCC
MVSIS
MVSIS Y.Jiang, et al, Logic optimization and
code generationfor embedded control
applications, CODES 2000
C/Assembly
7
Motivation multi-valued devices

• Multi-valued current-mode MOS
• signed digit arithmetic
• High-speed, Low supply voltage

Building blocks
Current source Linear sum PMOS current mirror Threshold detector

Iy
Ix
IT
x
y1
y2
T. Hanyu and M. Kameyama, A 200 MHz pipelined
multiplier using 1.5 V-supplymultiple-valued MOS
current-mode circuits with dual-rail
source-coupled logic, IEEE Journal of
Solid-Statee Circuits, 1995
8
Functional Semantics
F

• Network of MV-nodes
• Each variable xn has its own range0, 1,,
  Pn-1
• Values are treated uniformly
• MV-literal X0,2
• MV-cube X0,2Z0,1
• MV-function

Latch
9
Design Specification
.model simple .inputs a b .outputs f .mv f 3 .mv
x 3 .table x a b -gt f .def 0 0 1 1 1 1 0 - 1 1
1 1 2 0 - 0 2 .reset x 0 .latch f
x .exdc .inputs a b .outputs f .table a b -gt
f .def 0 0 0 1 .end

• BLIF-MV subset
• Deterministic (no pseudo inputs)
• Single output MV nodes
• Flat network, no hierarchy
• Constant initial states (.reset)
• Extension
• External dont care networks (.exdc)

10
MVSIS Optimization

• MVSIS optimizations
• Node simplification
• Kernel and cube extraction
• Pairing
• Encoding
• Network manipulations

11
Node Simplification
a b c d z
100 11 011 101 0 101 10 111 011 0 110 10 110
110 0
100 11 111 101 1 111 01 100 111 1 100 11 110
110 1

• Two-level Espresso-MV
• Multi-level

ltdefaultgt 2
101 01 100 001 - 010 01 001 101 -
Minimize each i-set independently Dont care
input minterm that produces all output
values Partial care input minterm that produces
a subset of output values
Compatible observability dont cares(CODC) Satisf
iability dont cares (SDC) External dont cares
(XDC)
mvsisgt simplify mvsisgt fullsimp mvsisgt
reset_default
12
Algebraic Decomposition
M. Gao and R. K. Brayton, Multi-valued
Multi-level Network Decomposition, IWLS, June
2001.

• Kernel extraction
• Semi-algebraic division
• Resubstitution
• Factoring/Decomposition

F a0,1,2 b0,1,2,3c3 b1,2,3 c3
a0b1,2,3 c0 a0 b0,1,2,3c1
-q Two-cube divisors -g Best divisors
(c3 a0c0,1)(a0,1,2 c1,3 b1,2,3
c0,3)
mvsisgt fx -q -g mvsisgt decomp mvsisgt
factor mvsisgt resub
13
Pairing and Encoding

• Pair_decode/Merge
• Encode
• Merge some i-sets

Bit-pairing to create multi-valued node Explore
different encodings
SOP further simplified Output literal count
reduced
mvsisgt pair_decode mvsisgt merge mvsisgt
encode mvsisgt elim_part
14
Other Commands

• Network manipulations
• IO interface
• Verification

• Printing
• Sequential

mvsisgt eliminate mvsisgt collapse Mvsisgt sweep
mvsisgt print_stats mvsisgt print_factor mvsisgt
print_range mvsisgt print_io mvsisgt
print_value mvsisgt print_part_value
mvsisgt read_blifmv mvsisgt read_blif mvsisgt
write_blifmv
mvsisgt extract_seq_dc
mvsisgt validate m mddsimu mvsisgt
gen_vec mvsisgt simulate mvsisgt qcheck
15
Design Flow

• Typical design flow

mvsisgt source mvsis.script mvsisgt encode
-i mvsisgt source mvsis.scriptb
16
Example 1

• Matrix multiplication (3 values)

.table a21 a22 b12 b22 c22 0 0 - - 0 0 1 - -
b22 0 2 - 0 0 0 2 - 1 2 0 2 - 2 1 1 0 - -
b12 1 1 0 0 0 1 1 0 1 1 1 1 0 2 2 1 1 1 0
1 .end
2 X 2 matrix mult over the ring Z_3 .model
matmul .inputs a11 a12 a21 a22 .inputs b11
b12 b21 b22 .outputs c11 c12 c21 c22 .mv
a11, a12, a21, a22 3 .mv b11, b12, b21,
b22 3 .mv c11, c12, c21, c22 3 .table a11
a12 b11 b21 c11 0 0 - - 0 0 1 - - b21 0 2 - 0
0 0 2 - 1 2 0 2 - 2 1 1 0 - - b11 1 1 0 0
0 1 1 0 1 1 1 1 0 2 2 1 1 1 0 1 .table a11
a12 b12 b22 c12 0 0 - - 0 0 1 - - b22 0 2 - 0
0 0 2 - 1 2 0 2 - 2 1
1 0 - - b12 1 1 0 0 0 1 1 0 1 1 1 1 0 2 2
.table a21 a22 b11 b21 c21 0 0 - - 0 0 1 - -
b21 0 2 - 0 0 0 2 - 1 2 0 2 - 2 1 1 0 - -
b11 1 1 0 0 0 1 1 0 1 1 1 1 0 2 2 1 1 1 0
1 1 1 1 1 2 1 1 1 2 0 1 1 2 0 2 1 1 2 1 0 1 1
2 2 1 1 2 0 0 0 1 2 0 1 2 1 2 0 2 1 1 2 1 0
1 1 2 1 1 0
17
cadntws11/home/wjiang/mvsis/examples/bob
mvsis UC Berkeley, MVSIS 0.95 (compiled 24-May-01
at 219 PM) mvsisgt help alias
chng_name collapse
decomp delete
echo elim_part
eliminate encode
extract_seq_dc factor
fullsimp fx
gen_vec help
history
merge pair_decode
print print_altname
print_factor print_io
print_level
print_part_value print_range
print_stats print_value
qcheck quit
read_blif read_blifmv
reset_default reset_name
resub runtime
set
simplify simulate
source sweep
unalias undo
unset usage
validate
write_blifmv mvsisgt
mvsisgt read_blifmv matmul-c mvsisgt
mvsisgt chng_name changing to short-name mode
mvsisgt print_stats matmul 4 nodes, 4 POs, 128
cubes(sop), 480 lits(sop) mvsisgt
18
mvsisgt print_io primary inputs a b c d e f g
h primary outputs i j k l mvsisgt
mvsisgt set autoexec pfs matmul 4 nodes, 4 POs,
128 cubes(sop), 480 lits(sop), 216
lits(fact.) mvsisgt
mvsisgt print_range i 3 j 3 k 3 l 3 a
3 b 3 c 3 d 3 e 3 f 3 g 3 h 3 matmul 4
nodes, 4 POs, 128 cubes(sop), 480 lits(sop),
216 lits(fact.) mvsisgt
mvsisgt simplify matmul 4 nodes, 4 POs, 96
cubes(sop), 320 lits(sop), 160
lits(fact.) mvsisgt
mvsisgt reset_default matmul 4 nodes, 4 POs,
96 cubes(sop), 320 lits(sop), 160
lits(fact.) mvsisgt
19
mvsisgt fullsimp matmul 4 nodes, 4 POs, 96
cubes(sop), 320 lits(sop), 160
lits(fact.) mvsisgt
mvsisgt pair_decode 1 m0 a0e2 e0 m1
a0e1 m3 a1e2 a2e1 n0
a0f2 f0 n1 a0f1 n3 a1f2
a2f1 o0 e0c2 c0 o1
e0c1 o3 e1c2 e2c1 p0
f0c2 c0 p1 f0c1 p3 f1c2
f2c1 q0 b0g2 g0 q1
b0g1 q3 b1g2 b2g1 r0
b0h2 h0 r1 b0h1 r3 b1h2
b2h1 s0 g0d2 d0 s1
g0d1 s3 g1d2 g2d1 t0
h0d2 d0 t1 h0d1 t3 h1d2
h2d1 matmul 12 nodes, 4 POs, 64
cubes(sop), 184 lits(sop), 160
lits(fact.) mvsisgt
20
mvsisgt simplify matmul 12 nodes, 4 POs, 56
cubes(sop), 96 lits(sop), 96 lits(fact.) mvsisgt
mvsisgt reset_default matmul 12 nodes, 4 POs,
56 cubes(sop), 96 lits(sop), 96
lits(fact.) mvsisgt
mvsisgt fullsimp matmul 12 nodes, 4 POs, 56
cubes(sop), 96 lits(sop), 96 lits(fact.) mvsisgt
21
mvsisgt print_factor i1 m2q2 m1q0
m0q1 i2 m2q0 m1q1
m0q2 j1 n2r2 n1r0
n0r1 j2 n2r0 n1r1
n0r2 k1 o2s2 o1s0
o0s1 k2 o2s0 o1s1
o0s2 l1 p2t2 p1t0
p0t1 l2 p2t0 p1t1
p0t2 m0 a0 e0 m2 a2e1
a1e2 n0 a0 f0 n2 a2f1
a1f2 o0 c0 e0 o2 c2e1
c1e2 p0 c0 f0 p2 c2f1
c1f2 q0 b0 g0 q2 b2g1
b1g2 r0 b0 h0 r2 b2h1
b1h2 s0 d0 g0 s2 d2g1
d1g2 t0 d0 h0 t2 d2h1
d1h2 matmul 12 nodes, 4 POs, 56
cubes(sop), 96 lits(sop), 96 lits(fact.) mvsisgt
22
mvsisgt validate -m mdd matmul-c Networks are
combinationally equivalent according to MDD
method. matmul 12 nodes, 4 POs, 56
cubes(sop), 96 lits(sop), 96 lits(fact.) mvsisgt
23
cadntws11/home/wjiang/mvsis/examples/bob
mvsis UC Berkeley, MVSIS 0.95 (compiled 24-May-01
at 219 PM) mvsisgt mvsisgt read_blifmv
red-add.mv mvsisgt
mvsisgt chng_name changing to short-name
mode mvsisgt
mvsisgt print_io primary inputs a b c d
e primary outputs f g h mvsisgt
mvsisgt set autoexec pfs red_adder 3 nodes, 3
POs, 48 cubes(sop), 240 lits(sop), 69
lits(fact.) mvsisgt
mvsisgt reset_default red_adder 3 nodes, 3 POs,
48 cubes(sop), 240 lits(sop), 69
lits(fact.) mvsisgt
mvsisgt simplify red_adder 3 nodes, 3 POs, 15
cubes(sop), 44 lits(sop), 28 lits(fact.) mvsisgt
mvsisgt fullsimp red_adder 3 nodes, 3 POs, 15
cubes(sop), 44 lits(sop), 28 lits(fact.) mvsisgt
24
mvsisgt print_range f 2 g 2 h 2 a 8 b 8
c 8 d 8 e 8 red_adder 3 nodes, 3 POs, 15
cubes(sop), 44 lits(sop), 28 lits(fact.) mvsisgt
mvsisgt encode red_adder 3 nodes, 3 POs, 15
cubes(sop), 44 lits(sop), 28 lits(fact.) mvsisgt
mvsisgt print_range f 2 o 2 g 2 p 2 h
2 q 2 i 2 r 2 j 2 s 2 k 2 t 2 l 2 u
2 m 2 v 2 n 2 w 2 red_adder 3 nodes, 3
POs, 15 cubes(sop), 44 lits(sop), 28
lits(fact.) mvsisgt
25
mvsisgt simplify red_adder 3 nodes, 3 POs, 15
cubes(sop), 44 lits(sop), 28 lits(fact.) mvsisgt
mvsisgt fullsimp red_adder 3 nodes, 3 POs, 15
cubes(sop), 44 lits(sop), 28 lits(fact.) mvsisgt
mvsisgt print_io primary inputs i j k l m n o p
q r s t u v w primary outputs f g
h red_adder 3 nodes, 3 POs, 15 cubes(sop),
44 lits(sop), 28 lits(fact.) mvsisgt
26
mvsisgt read_blifmv red-add.mv red_adder 3
nodes, 3 POs, 48 cubes(sop), 240 lits(sop),
69 lits(fact.) mvsisgt
mvsisgt help encode Feb 16, 2001
MVSIS(1)
encode -i -n -s Encode the whole
network into a binary one, considering both
output and input constraints. For
sequential networks, a latch is encoded with
constraints generated from both its inputs and
outputs -i keep primary inputs and
outputs as multi-valued add interface
nodes between the internal encoded binary network
and PI/POs. This option allows
validation of the result. -n use natural
code -s use NO_COMP rather than ESPRESSO
as the intermediate minimization
method. The difference is only in performance.
Ordinary users should not be concerned
with this option. red_adder 3 nodes, 3 POs,
48 cubes(sop), 240 lits(sop), 69
lits(fact.) mvsisgt
mvsisgt encode -n red_adder 3 nodes, 3 POs,
1251 cubes(sop), 9432 lits(sop), 577
lits(fact.) mvsisgt
27
mvsisgt simplify -t 1000 red_adder 3 nodes, 3
POs, 315 cubes(sop), 2010 lits(sop), 156
lits(fact.) mvsisgt
mvsisgt simplify -t 1000 -m exact red_adder 3
nodes, 3 POs, 300 cubes(sop), 1989 lits(sop),
130 lits(fact.) mvsisgt
mvsisgt validate -m mdd red-add-bin.mv Networks
differ on (at least) primary output s1 i-set
0 Incorrect input is 0 x1_b0 1 x1_b1 1 x1_b2 0
x0_b0 0 x0_b1 0 x0_b2 0 y1_b0 0 y1_b1 0 y1_b2 0
y0_b0 0 y0_b1 0 y0_b2 0 cin_b0 0 cin_b1 0
cin_b2 Networks are NOT combinationally
equivalent. red_adder 3 nodes, 3 POs, 300
cubes(sop), 1989 lits(sop), 130
lits(fact.) mvsisgt
28
Conclusions

• Multi-valued logic important in various
  applications
• Presented MVSIS, an multi-valued logic synthesis
  software infrastructure
• Release 1.0 on Linux platform (as of June, 2001)
• Support registers
• Support external dont care networks
• External dont cares from incomplete
  specification
• Sequential dont care extraction
• Verification based on MDD representations
• Bug fixes

http//www-cad.eecs.berkeley.edu/Respep/Research/m
vsis