Download Production Rule

Compiling Communicating
Processes into Delay-Insensitive
VLSI Circuits
Alain J. Martin
Department of Computer Science
California Institute of Technology
Production Rule
Production rules:
if C then A
if condition C is true then Perform action A
Example:
if A and B then C
Production rule: A B  C
Production Rule
• CMOS transistors can be modeled by a set of PRs.
Example: inverter:
a b 
a  b 
Pull-up network
a
b
Pull-down network
Production Rule
General Model
• Pull-up network: a PR that makes z=true
• Pull-down network: a PR that makes z=false
Pull-up network
Z
Pull-down network
Production Rule
One-input operators:
• Wire
a b 
a  b 
• Fork
a b c 
a  b  c 
• inverter
a b 
a  b 
a
b
a
b
c
a
b
Production Rule
Two-input operators:
1
1
• And
a
b
a b  c 
c
a  b  c 
0
1
• OR
a
b
ab c
c a  b  c 
0
0
Production Rule
• Nand
a
b
c
a b  c 
a  b  c 
1
1
0
1
• Nor
a
b
c
ab  c 
 a  b  c 
0
0
Production Rule
• XOR
a b c 
a  b c 
• EQ
a b c 
a  b c 
a
• C-element
a b  c 
a  b  c 
c
b
Production Rule
• Switch
a b  c 
a  b  c 
a
SW
c
b
• SR-latch
s q
r q
r
s
SR
q
q’
Production Rule
Multi-input operators:
• Multiplexer
( s  a )( s b ) c 
( s  a )( s  b ) c 
a
b
mux
s
c
Arbiter:ME
Arbiter 
*[[x u ;[x];u 
|y  v ;[y]; v 
]]
0
x
u
v
y
0
Arbiter:ME
• No request: x=0 y=0 ==> u=0 v=0
0
x 0
y
1
u0
v 0
0
1
0
Arbiter:ME
• Request on x: x=1 y=0 ==> u=1 v=0
• Similar to request on y.
0
x 1
y
0
u1
v 0
0
1
0
Arbiter:ME
• Request on both x and y: x=1 y=1 ==> either u=1 or v=1
• xu and yv will be both zero at some time
• Depend on the race one of them will be 1.
For example xu=0 propagates fast than yv
0
then yv will be locked at 1
and u=1 and v=0.
xu
x 1
u -->
y
v -->
1
yv
0
CHP: Compilation Method
• CHP specification
• Process decomposition
• Handshaking expansion
• Reshuffling
• Production rule expansion
• Circuit Implementation
CHP: CHP specification
*[ FETCH : i, pc := imem[pc], pc+1
[ off(i) -->offset, pc := imem[pc], pc+1;
[] not off(i) -->skip ];
EXEC : [ alu(i) -->(reg[i.z], f) := aluf(reg[i.x], reg[i.y], i.op, f)
[] ld(i) -->reg[i.z] := dmem[reg[i.x]+reg[i.y]]
[] st(i) -->dmem[reg[i.x] + reg[i.y]] := reg[i.z]
[] ldx(i) -->reg[i.z] := dmem[offset + reg[i.y]]
[] stx(i) -->dmem[offset + reg[i.y]] := reg[i.z]
[] lda(i) -->reg[i.z] := offset + reg[i.y]
[] stpc(i) -->reg[i.z] := pc
[] jmp(i) -->pc := reg[i.y]
[] brch(i) -->[ cond(f, i.cc) -->pc := pc + offset
[] not cond(f, i.cc) -->skip ] ] ]
CHP: CHP specification
• CPU: *[[Fetch; Exec]]
• i:instruction being executed.
• All instructions contain an op field.
• The parameter fields depend on the types of instruct
instruction for alu = record
op : alu.15..alu.12
x : alu.11..alu.8
y : alu.7..alu.4
z : alu.3..alu.0
end
Example. Add, and, …, load and store.
CHP: CHP specification
• f: flags generated by the execution of an alu
instruction
• cc: condition code field of branch instructions.
• Memory: 1. imem: instruction memory
2. dmem: data memory
• offset: two-word instructions
• reg[0] always contains the value zero.
• (z,f) := aluf(x,y,op,f)
evaluate an alu instrution with the opcode op,
parameters x,y
current flag f.
CHP: Process decomposition
P
P1
X
Y
P2
Chan(X,Y)
P=BS;S;AS
P1=BS;X;AS
P2=*[[Y-->S;Y]]
or (Y/S) call operator
• S can be a selection, repetition or assignment command.
CHP: Process decomposition
P
X
P1
Y
P2
Chan(X,Y)
P=BS;S;AS
P1=BS;X;AS
P2=*[[Y-->S;Y]]
or (Y/S) call operator
• S is a selection
• S  [ B1  S 1[] B 2  S 2 ]
P 2  *[[ Y  B1  S 1;Y []Y  B 2  S 2;Y ]
CHP: Process decomposition
P
X
P1
Y
P2
Chan(X,Y)
P=A;S;B
P1=A;X;B
• S is a repetition
• S  *[ B1  S 1[] B 2

S2]
P 2  *[[ Y  B1  S 1
[]Y  B 2

S2
[]Y  B1  B 2

Y ]]
P2=*[[Y-->S;Y]]
or (Y/S) call operator
CHP: Process decomposition
P
X
P1
Y
P2
Chan(X,Y)
P=BS;S;AS
P1=BS;X;AS
P2=*[[Y-->S;Y]]
or (Y/S) call operator
• S is an assignment (B is an arbitrary boolean function)
•
SxB
P 2  *[[ Y  B  x 
[]Y  B  x  ]]
CHP: Process decomposition
• Process decomposition can reduce a process
with an arbitrary control structure to a set of
subprocesses of only two different types:
• Sequences of communication actions
• Repetition of the types shown in
the previous 3 slides.
CHP: Process decomposition
• Example
: Simple Logic Unit
X
Y
SLU
Z
OP
* [ OP ? op;
[ op  ( X ? x || Y ? y ); z : x  y ; Z ! z
[]op  ( X ? x || Y ? y ); z : x  y ; Z ! z ]]
CHP: Process decomposition
* [ OP ? op ;
[ op  ( X ? x || Y ? y ); z : x  y ; Z ! z
[]op  ( X ? x || Y ? y ); z : x  y ; Z ! z ]]

* [ A; B ]
|| *[[ A  OP ? op ; A ]]
|| *[[ B  op  ( X ? x || Y ? y ); z : x  y ; Z ! z ; B
[] B  op  ( X ? x || Y ? y ); z : x  y ; Z ! z ; B ]]
CHP: Process decomposition
* [[ B  op  ( X ? x || Y ? y ); z : x  y ; Z ! z ; B
[] B  op  ( X ? x || Y ? y ); z : x  y ; Z ! z ; B ]]

* [[ B  op  ( C || D ); z : x  y ; E ; B
[] B  op  ( C || D ); z : x  y ; E ; B ]]
|| *[[ C  X ? x; C ]]
|| *[[ D  Y ? y ; D ]]
|| *[[ E  Z ! z ; E ]]
CHP: Process decomposition
* [[ B  op  ( C || D ); z : x  y ; E ; B
[] B  op  ( C || D ); z : x  y ; E ; B ]]

* [[ B  op  ( C || D ); F ; E ; B
[] B  op  ( C || D ); G ; E ; B ]]
|| *[ [ F  (x  y)  z ; F
[] F  ( x  y)  z ; F
[] G  (x  y)  z ; G
[] G  (x  y)  z ; G ] ]
CHP: Process decomposition
* [ A; B ] || *[[ A  OP ? op ; A ]]
|| *[[ B  op  ( C || D ); F ; E ; B
[] B  op  ( C || D ); G ; E ; B ]]
|| *[[ C  X ? x ; C ]]
|| *[[ D  Y ? y ; D ]]
• Decomposed SLU
|| *[[ E  Z ! z ; E ]]
|| *[ [ F  (x  y)  z ; F
[] F  ( x  y)  z ; F
[] G  (x  y)  z ; G
[] G  (x  y)  z ; G ] ]
CHP: Handshaking Expansion
• Handshaking Expansion:
P1
X
Y
x0
P2
P1
P2
xi
P1   ; X ; 
yi
yo
P 2   ;Y ;
P1   ; xo ; [ xi ]; 
P2   ; [ yi ]; yo ;
• P1:Active P2: passive
CHP: Handshaking Expansion
• Handshaking Expansion: 2-phase
P1
X
Y
x0
P2
P1
P2
xi
P1   ; X ; 
yi
yo
P 2   ;Y ;
P1   ; xo  xo; [ xi  xo ]; 
P 2   ; [ yi  yo ]; yo  yo;
CHP: Handshaking Expansion
• Handshaking Expansion: 4-phase
P1
X
Y
x0
P2
P1
P2
xi
P1   ; X ; 
yi
yo
P 2   ;Y ;
P1   ; xo ; [ xi ]; xo ; [ xi ]; 
P2   ; [ yi ]; yo ; [ yi ]; yo ;
• P1:Active P2: passive
CHP: Handshaking Expansion
• Handshaking Expansion:
ao
OP?op
SLU
* [ A; B ]
ai
|| *[[ A  OP ? op ; A ]]

* [ ao ; [ ai ] ; ao  [ai];
bo ; [bi]; bo  [bi] ]
|| *[[ ao  OP ? op ; ai  ; [ ao ]; ai  ]]
CHP: Handshaking Expansion
• Handshaking Expansion:
bo
(C||D);...
SLU
bi
* [[ B  op  ( C || D ); F ; E ; B
[] B  op  ( C || D ); G ; E ; B ]]

* [[ bo  op  ( C || D ); F ; E ; bi  ; [ bo ]; bi 
[]boop  ( C || D ); G ; E ; bi  ; [ bo ]; bi  ]]
CHP: Reshuffling
• ...; xo ; [ xi ];...
...; [ yi ]; yo ;...
are only used to reset to zero
they can be inserted anywhere
as long as cyclic order is maintained.
• WARNING: Reshuffling can introduce deadlock.
•
...; xo ; [ xi ]; xo ; [ xi ]; S ;... 
...; xo ; [ xi ]; S ; xo ; [ xi ];...
does not introduce deadlock when:
1. S contains no communication action, or
2. X is an internal channel created by process decomposition
CHP: Lazy-active protocol
• Active protocol X:
...; xo ; [ xi ]; xo ; [ xi ];...
• Passive protocol Y:
...; [ yi ]; yo ; [ yi ]; yo ;...
• Lazy active protocol X:
...[ xi ]; xo ; [ xi ]; xo ;...
1.[ xi ] is postponed to next X command
2. First [ xi ] is vacuous.
CHP: Reshulffling
• Active protocol:
* [ ao ; [ ai ] ; ao  [ai]; bo ; [bi]; bo  [bi] ]
• Reshuffing
* [ ao ; [ ai ] ; bo ; [bi] ;( ao || bo  );( [ai]  [bi] )]
• Lazy active
* [ [ai] ; ao ; [ ai ] ; [bi] ; bo ; [bi] ;( ao || bo  )]
Simple Logic Unit
Simple Logic Unit:Block
diagram
OPreg
OP
A?(and,or)
Control
F
C D
X
Y
Xreg
Yreg
G
E
x
y
And/Or
Unit
z
Zreg
Z
Simple Logic Unit:Block
diagram
Ao and or
Co
Ci
Do
Di
Control
Fo Fi Go Gi
Eo
Ei
Simple Logic Unit:
Simple Logic Unit:
• Extracting the control signals: data transfer
Simple Logic Unit:
• Extracting the control signals: data operations
Simple Logic Unit:Control HSE
CHP: Production rule
expansion
• Production rule expansion:
A. a handshaking expansion ==> a set of PRs
B. consist of 3 Steps:
state assignment,
guard strengthening
symmetrization
CHP: Production rule
expansion
• state assignment: keep the execution sequence
* [[li]; ro ; [ri]; ro ;[ri]; lo ;[li]; lo ]
x  li  ro 
state
ri  ro  assignment
ri  x 
li
lo
L/R
li  ro 
ri  lo 
x  ri  lo 
li  lo 
li  x 
x  ro 
x  lo 
* [[li]; ro ; [ri]; x ;[x]; ro ;[ri]; lo ;[li]; x ;[x]; lo ]
ro
ri
CHP: Production rule
expansion
• Symmetrization: Combinational vs state holding
x  li  ro 
x  li  ro 
ri  x 
li  x 
x  ri  lo 
x  ri  lo 
li
ro lo
li
x
ri
li
x
ri
F/F
x
lo
L/R
ro
ri