1. Topic B (Cont’d) Dataflow Model of Computation
Guang R. Gao
ACM Fellow and IEEE Fellow
Endowed Distinguished Professor
Electrical & Computer Engineering
University of Delaware
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

2. Outline Parallel Program Execution Models
Dataflow Models of Computation
Dataflow Graphs and Properties
Three Dataflow Models
Static
Recursive Program Graph
Dynamic
Dataflow Architectures and Evolution of Multithreading
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

3. Dataflow Models Static Dataflow Model Recursive Program Graphs
Tagged Token Dataflow Model
Also known as dynamic
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

4. Static Dataflow Model
“...for any actor to be enabled, there must be no tokens on any of its output arcs...”
So-called: at most “one-token-per-arc” rule
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

5. Conditional Expressiony p
if (p(y)){
f(x,y); }
else{
g(y); T T F
FIFO f g T F
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

6. Example Power Function
long power(int x, int n){
int y = 1;
for(int i = n; i > 0; --i)
y *= x;
return y; }
y = xn
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

7. Power Function y = xn * -1 x 1 n T F T F T F x y f f i f i>0 T T T
return
y = xn
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

8. Power Function y = 23 * -1 2 1 3 T F T F T F x y f f i f i>0 T T T
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

9. Power Function y = 23 * -1 T F T F T F 2 1 3 3 i>0 T T T F return
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

10. Power Function y = 23 * -1 T F T F T F t t t i>0 1 3 2 t t t T T T
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

11. Power Function y = 23 * -1 T F T F T F t t t i>0 T T T F 3 2 2 1
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

12. Power Function y = 23 * -1 T F T F T F t 2 t i>0 2 2 T T T F return
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

13. Power Function y = 23 * -1 T F T F T F 2 2 2 i>0 2 T T T F return
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

14. Power Function y = 23 * -1 T F T F T F t t t i>0 2 2 2 t t t T T T
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

15. Power Function y = 23 * -1 T F T F T F t t t i>0 T T T F 2 2 2 2
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

16. Power Function y = 23 * -1 T F T F T F t t 2 i>0 4 1 T T T F return
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

17. Power Function y = 23 * -1 T F T F T F 1 1 4 i>0 2 T T T F return
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

18. Power Function y = 23 * -1 T F T F T F t t t i>0 4 1 2 t t t T T T
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

19. Power Function y = 23 * -1 T F T F T F t t t i>0 T T T F 1 2 2 4
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

20. Power Function y = 23 * -1 T F T F T F t t 2 i>0 8 T T T F returnT T T F * -1
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

21. Power Function y = 23 * -1 T F T F T F 8 i>0 2 T T T F return8
i>0 2 T T T F * -1
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

22. Power Function y = 23 * -1 T F T F T F f f f i>0 f 2 8 f f T T T F2 8 f f T T T F * -1
return
y = 23
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

23. Power Function y = 23 * -1 T F T F T F f f f i>0 T T T F 8
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

24. DFG Vector Addition for(i = 0; i < N; ++i) c[i] = a[i] + b[i]; a b
NULL N T F T F T F T F T F
< T T T F T T +1
Select
Select
Assign
for(i = 0; i < N; ++i)
c[i] = a[i] + b[i]; + c
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

25. Static Dataflow Model Features
One-token-per-arc
Deterministic merge
Conditional/iteration construction
Consecutive iterations of a loop appear to be only subjected to sequential execution (?)
A dataflow graph  activity templates
Opcode of the represented instruction
Operand slots for holding operand values
Destination address fields
Token  value + destination
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

26. Static Dataflow Model Features
Deficiencies:
Due to acknowledgment tokens, the token traffic is doubled.
Lack of support for programming constructs that are essential to modern programming language
no procedure calls,
no recursion.
Advantage:
simple model
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

27. MIT Static Dataflow Processor Architecture
and Program Activity Templates
Operation units
Update
unit
queue
Fetch
unit
Activity
store + a b *
Z = (a + b) * (c - d) z - c
Gao and Theobald: The Static
Dataflow Enable Memory Chip
(fall, 1984) d
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

28. Instructions in a Static Dataflow Architecture
mult2
2 3 a c
sub
2 3
ac-bd
mult2
opcode
2 3 b d
EC RC
Destination list
operand1
operand2
mult2
2 3 a d
plus
2 3
ad+bc
result arc
mult2
2 3 b c
signal arc
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

29. Dataflow Software Pipelining
X[I]
Y[I]
U[I]
V[I]
T[i] *
for I in [1, n]
H[i] = a * X[i] + Y[i]
G[i] = b * U[i] + V[i]
Z[i]= T[i] * H[i] + S[i] * G[i]
end for + *
H[i] b * +
Z[i]
G[i] + *
S[i]
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

30. Recursive Program Graphs
Outlaw iterations :
Graph must be acyclic
One-token-per-arc-per-invocation
Iteration is expressed in terms of a tail recursion
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

31. Tail Function Application
Tail-procedure application
a procedure application that occurs as the last statement in another procedure;
Tail-function application is a function application (appears in the body expression) whose result value is also returned as the value of the entire functions
Consider the role of stack
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

32. Factorial long fact(n){ if(n == 0) return 1;
else return n * fact(n-1); }
Normal Recursive
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
Tail Recursive
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

33. Factorial The Normal Version1
n==0 F T
Hand Simulate fact(3) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

34. Factorial The Normal Version3 1
n==0 F T
Hand Simulate fact(3) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

35. Factorial The Normal Version3 n 1
n==0 3 F T
Hand Simulate fact(3) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

36. Factorial The Normal Version1
n==0 3 F F T
Hand Simulate fact(3) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

37. Factorial The Normal Version1
n==0 3 F T F F
Hand Simulate fact(3) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

38. Factorial The Normal Version1
n==0 F T 3
Hand Simulate fact(3) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

39. Factorial The Normal Version1
n==0 F T
Hand Simulate fact(3) 3 -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact 3 *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

40. Factorial The Normal Version1
n==0 F T
Hand Simulate fact(3) -1 2
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact 3 *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

41. Factorial The Normal Version2 1
n==0 F T
3 * fact(2) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

42. Factorial The Normal Version2 n 1
n==0 2 F T
3 * fact(2) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

43. Factorial The Normal Version1
n==0 2 F F T
3 * fact(2) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

44. Factorial The Normal Version1
n==0 2 F T F F
3 * fact(2) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

45. Factorial The Normal Version1
n==0 F T 2
3 * fact(2) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

46. Factorial The Normal Version1
n==0 F T
3 * fact(2) 2 -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact 2 *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

47. Factorial The Normal Version1
n==0 F T
3 * fact(2) -1 1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact 2 *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

48. Factorial The Normal Version1 1
n==0 F T
3 * fact(2 * fact(1)) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

49. Factorial The Normal Version1 n 1
n==0 1 F T
3 * fact(2 * fact(1)) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

50. Factorial The Normal Version1
n==0 1 F F T
3 * fact(2 * fact(1)) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

51. Factorial The Normal Version1
n==0 1 F T F F
3 * fact(2 * fact(1)) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

52. Factorial The Normal Version1
n==0 F T 1
3 * fact(2 * fact(1)) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

53. Factorial The Normal Version1
n==0 F T
3 * fact(2 * fact(1)) 1 -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact 1 *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

54. Factorial The Normal Version1
n==0 F T
3 * fact(2 * fact(1)) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact 1 *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

55. Factorial The Normal Version1
n==0 F T
3 * fact(2 * fact(1 * fact(0))) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

56. Factorial The Normal Versionn 1
n==0 F T
3 * fact(2 * fact(1 * fact(0))) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

57. Factorial The Normal Version1
n==0 T F T
3 * fact(2 * fact(1 * fact(0))) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

58. Factorial The Normal Version1
n==0 F T T T
3 * fact(2 * fact(1 * fact(0))) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

59. Factorial The Normal Version
3 * fact(2 * fact(1 * fact(0))) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact * 1
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

60. Factorial The Normal Version1
n==0 F T
3 * fact(2 * fact(1 * 1)) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact 1 1 *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

61. Factorial The Normal Version1
n==0 F T
3 * fact(2 * fact(1 * 1)) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact * 1
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

62. Factorial The Normal Version1
n==0 F T
3 * fact(2 * 1) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact 2 1 *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

63. Factorial The Normal Version1
n==0 F T
3 * fact(2 * 1) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact * 2
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

64. Factorial The Normal Version1
n==0 F T
3 * 2 -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact 3 2 *
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

65. Factorial The Normal Version1
n==0 F T
3 * 2 -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact * 6
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

66. Factorial The Normal Version1
n==0 F T 6 -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact * 6
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

67. Can you see where is the problem ??
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

68. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1
Call fact_1(3,1)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

69. Factorial The Tail Recursion Version3 1
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1
fact_1(3,1)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

70. Factorial The Tail Recursion Version3 n 1
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 3 F F T -1 *
Apply fact_1
fact_1(3,1)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

71. Factorial The Tail Recursion Version1
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 3 F F T F F -1 *
Apply fact_1
fact_1(3,1)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

72. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T 3 1 -1 *
Apply fact_1
fact_1(3,1)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

73. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T 3 3 1 -1 *
Apply fact_1
fact_1(3,1)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

74. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 * 2
Apply fact_1 3
fact_1(3,1)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

75. Factorial The Tail Recursion Version2 3
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1
Call fact_1(2,3)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

76. Factorial The Tail Recursion Version2 n 3
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 2 F F T -1 *
Apply fact_1
fact_1(2,3)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

77. Factorial The Tail Recursion Version3
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 2 F F T F F -1 *
Apply fact_1
fact_1(2,3)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

78. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T 2 3 -1 *
Apply fact_1
fact_1(2,3)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

79. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T 2 2 3 -1 *
Apply fact_1
fact_1(2,3)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

80. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 * 1
Apply fact_1 6
Call fact_1 (1,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

81. Factorial The Tail Recursion Version1 6
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1
fact_1(1,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

82. Factorial The Tail Recursion Version1 n 6
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 1 F F T -1 *
Apply fact_1
fact_1(1,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

83. Factorial The Tail Recursion Version6
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 1 F F T F F -1 *
Apply fact_1
fact_1(1,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

84. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T 1 6 -1 *
Apply fact_1
fact_1(1,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

85. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T 1 1 6 -1 *
Apply fact_1
fact_1(1,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

86. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1 6
fact_1(1,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

87. Factorial The Tail Recursion Version6
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1
Call fact(0,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

88. Factorial The Tail Recursion Versionn 6
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1
fact_1(0,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

89. Factorial The Tail Recursion Version6
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T T T -1 *
Apply fact_1
fact_1(0,6)
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

90. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1
fact_1(0,6) returns 6 6
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

91. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1
fact_1(1,6) returns 6 6
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

92. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1
fact_1(3,1) returns 6 6
09/07/2011
CPEG F-Topic-B-Dataflow-Part2

93. Factorial The Tail Recursion Versionp
long fact_1(n, p){
if(n == 0) return p;
else return fact_1(n-1, n*p); }
n==0 F F T -1 *
Apply fact_1 6 6
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94. Recursive Program Graph Features
Acyclic
One-token-per-link-in-lifetime
Tags
No deterministic merge needed
Recursion is expressed by runtime copying
No matching is needed (why?)
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95. A Quiz: y = x ^ n ?
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96. A Recursive Version of Power (not tail recursive)x x n
x > 0 T T
Function Rec-Power (x, n : integer
returns integer)
Returns
If n = 0 then 1
else
x * rec-power (x, n - 1)
endif
endfun -1 n
apply rec-power 1 * 20
Note: tail-recursive = iterations:
i.e. the states of the computation are captured
explicitly by the set of iteration variables.
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97. The power function as a recursive program graph1
apply (Rec) x n y X
F T T
> 0
Rec -1
function Rec (x,y,n)
if n = 0 then y
else
Rec (x, x*y, n-1)
endif
end function
Rec (x,1,n)
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98. Dynamic Dataflow Static Dataflow Dynamic Dataflow
Only one token per arc
Problems with Function calls, nested loops and data structures
A signal is needed to allow the parent’s operator to fire
Dynamic Dataflow
No limitations on number of tokens per arc
Tokens have tags – new firing rules and tag matching
The MIT tagged token dataflow model
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99. The Token in Dynamic Dataflow
Token  Tag + Value
[v, <u, s>, d]
v : Value
u : activation instance
s : destination actor
d : operand slot
Different from Static Dataflow that it needs the tag <u,s>
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100. Dynamic Dataflow Loops and function calls
Should be executed in parallel as instances of the same graph
Arc  a container with different token that have different tags
A node can fire as soon that all tokens with identical tags are presented in its input arcs
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101. Tags and Colors Concept of colors
In a tag <u,s> - which is the color ?
When a new color is generated ?
When an old color is revovered ?
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102. Factorial The Normal Version – Dynamic Dataflow1
n==0 F T
fact(3) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
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103. Factorial The Normal Version – Dynamic Dataflow3 1
n==0 F T
fact(3) -1
long fact(n){
if(n == 0) return 1;
else return n * fact(n-1); }
Apply fact *
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104. Example of Dynamic Dataflow
Example A
Example B
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105. The Apply Operator CPEG867-2011-F-Topic-B-Dataflow-Apply-Operator
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106. The Apply Operator CPEG867-2011-F-Topic-B-Dataflow-Apply-Operator
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107. The Apply Operator CPEG867-2011-F-Topic-B-Dataflow-Apply-Operator
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108. The Apply Operator CPEG867-2011-F-Topic-B-Dataflow-Apply-Operator
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109. The Apply Operator CPEG867-2011-F-Topic-B-Dataflow-Apply-Operator
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110. The Apply Operator CPEG867-2011-F-Topic-B-Dataflow-Apply-Operator
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111. The Apply Operator CPEG867-2011-F-Topic-B-Dataflow-Apply-Operator
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112. Dynamic Dataflow Advantages Disadvantages More Parallelism
Handle arbitrary recursion
Disadvantages
Implementation of the token tag matching unit
Associative Memory would be ideal
Not cost effective
Hashing is used
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113. Features of Data Flow Computation Model
Not history-sensitive
Semantics
(determinate)
Parallelism
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114. Interpreting function invocation as module substitution+2 - u v
apply(F) y z X w x +2 - w x X y z
(a) (b) (c)
Function F Function G Function G’
Interpreting function invocation
as module substitution
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115. ... ... ... ... The Apply Actor u1 un (a) Notation for apply u1 unV1 Vm
apply
... u1 un
(a) Notation for apply
“F” V1 Vm
apply
... u1 un V1
... Vm
(b) Firing Rule
F is an (m,n)
schema
... u1 un
The Apply Actor
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116. Concept of Strictness
Intuitive:
a mechanism that requires all arguments to be evaluated before evaluation of the body of a function may begin
Formal :
A function f is strict if
f =
nonstrict = not strict
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117. Comment on Strict “Apply” Actor
Advantage - Parallelism
Call-by-value semantics
Disadvantage:
Lose “substitution” property or “referential transparency” property
to avoid it, need strictness analysis
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118. Referential Transparency
“...The only thing that matters about an expression is its value, and any subexpression can be replaced by any other equal in value...”
“...Moreover, the value of an expression is, within certain limits, the same when ever it occurs...”
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119. “Referential Transparency” or “Property of Substitution”
Let f,g be two procedures/functions such that f appears as an application inside of g; let g’ be the procedure obtained from g by substituting the text of f in place of the application;
In the languages which are “ referential transparent”, the specification of the function for g will not depend on any terminating property of f, or g=g’.
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120. Concept of Non-Strictness
Lenient evaluation model
Lazy evaluation model
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121. Outline Parallel Program Execution Models
Dataflow Models of Computation
Dataflow Graphs and Properties
Three Dataflow Models
Static
Recursive Program Graph
Dynamic
Dataflow Architectures: Evolution of Multithreading
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122. MIT Tagged Token Dataflow Architecture Processor
Wait-Match
Unit
Waiting token
memory (associative)
Instruction
Fetch
Program memory
Token
Queue
Execute OP
Form Tokens
Output
To network
From network
Wait-Match Unit:
Tokens for unary ops go straight through
Tokens for binary ops: try to match incoming token and a waiting token with same instruction address and context id
Success: Both tokens forwarded
Fail: Incoming token  Waiting Token Mem, Bubble (no-op) forwarded

123. Memory Model and Dataflow
What is “memory” in dataflow model ?
What is “memory model” under dataflow model ?
Concept of functional programming
Concept of single-assignment and single-assignmen programming languages
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124. The I Structures Single Assignment Rule and Complex Data structures
Consume the entire data structure after each access
The Concept of the I Structure
Only consume the entry on a write
A data repository that obeys the Single Assignment Rule
Written only once, read many times
Elements are associated with status bits and a queue of deferred reads
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125. I-Structure Memory
Extending dataflow abstract Machine model with I-Structure Memory
Use a data structure before it is completely defined
Incremental creating or reading of data structures
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126. Dataflow The I Structures
An element of a I-structure becomes defined on a write and it only happens only once
At this moment all deferred reads will be satisfied
Use a I-structure before it is completely defined
Incremental creating or reading of data structures
Lenient evaluation model - revisited
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127. The I Structures: state transitions
States
Present: The element of an I-structure (e.g. A[i]) can be read but not written
Absent: The element has been attempted to be read but the element has not been written yet (initial state)
Waiting: At least one read request has been deferred
Absent r w w
Waiting
Present r r w
Error
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128. I Structures Elementary Used to create construct nodes:
Allocate: reserves space for the new I-Structure
I-fetch: Get the value of the new I-structure (deferred)
I-store: Writes a value into the specified I structure element
Used to create construct nodes:
SELECT
ASSIGN
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