CPEG 852 Advanced Topics in Computing Systems The Dataflow Model of Computation
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1 CPEG 852 Advanced Topics in Computing Systems The Dataflow Model of Computation Stéphane Zuckerman Computer Architecture & Parallel Systems Laboratory Electrical & Computer Engineering Dept. University of Delaware 140 Evans Hall Newark,DE 19716, United States September 8, 2015 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 1 / 46
2 Outline 1 A Quick Reminder on Execution Models 2 Dataflow Models of Computation 3 Dataflow Graphs and Properties 4 Static Dataflow Introduction Static Dataflow Examples Static Dataflow Features Static Dataflow Activity Templates 5 Recursive Program Graphs Introduction Ordinary and Tail Recursions Features of Recursive Program Graphs 6 Homework S.Zuckerman CPEG852 Fall 15 Dataflow MoC 2 / 46
3 Outline 1 A Quick Reminder on Execution Models 2 Dataflow Models of Computation 3 Dataflow Graphs and Properties 4 Static Dataflow Introduction Static Dataflow Examples Static Dataflow Features Static Dataflow Activity Templates 5 Recursive Program Graphs Introduction Ordinary and Tail Recursions Features of Recursive Program Graphs 6 Homework S.Zuckerman CPEG852 Fall 15 Dataflow MoC 3 / 46
4 High-Level View of a Computer System S.Zuckerman Figure: High-Level View CPEG852 of afall Computer 15 DataflowSystem MoC 4 / 46
5 A Representative View of Current Compute Nodes Hardware Figure: S.Zuckerman A Representative View CPEG852 of Current Fall 15 Compute Dataflow MoC Nodes Hardware 5 / 46
6 A Representative View of Current Compute Nodes Software Mess Figure: S.Zuckerman A Representative View of CPEG852 Current Fall Compute 15 Dataflow Nodes MoC Software Mess 6 / 46
7 Terminology Definition: Parallel Model of Computation Parallel models for algorithms designers Parallel models for system designers Parallel programming models Parallel execution models Parallel architecture models S.Zuckerman CPEG852 Fall 15 Dataflow MoC 7 / 46
8 An Alternate Program Execution Model Definition (Dr. Gao s) Definition: Program Execution Model The program execution model (PXM) is the basic low-level abstraction of the underlying system architecture upon which our programming model, compilation strategy, runtime system, and other software components are developed. The PXM (and its API) serves as an interface between the architecture and the software. Unlike an instruction set architecture (ISA) specification, which usually focuses on lower level details (such as instruction encoding and organization of registers for a specific processor), the PXM refers to machine organization at a higher level for a whole class of high-end machines as viewed by the users S.Zuckerman CPEG852 Fall 15 Dataflow MoC 8 / 46
9 Horizontal Conception of a PXM S.Zuckerman Figure: Horizontal CPEG852 Conception Fall 15 of Dataflow a PXM MoC 9 / 46
10 Vertical Conception of a PXM S.Zuckerman Figure: VerticalCPEG852 Conception Fall 15 of Dataflow a PXMMoC 10 / 46
11 Outline 1 A Quick Reminder on Execution Models 2 Dataflow Models of Computation 3 Dataflow Graphs and Properties 4 Static Dataflow Introduction Static Dataflow Examples Static Dataflow Features Static Dataflow Activity Templates 5 Recursive Program Graphs Introduction Ordinary and Tail Recursions Features of Recursive Program Graphs 6 Homework S.Zuckerman CPEG852 Fall 15 Dataflow MoC 11 / 46
12 The Dataflow Model of Computation A Pragmatic Approach S.Zuckerman CPEG852 Fall 15 Dataflow MoC 12 / 46
13 The Dataflow Model of Computation A Pragmatic Approach S.Zuckerman CPEG852 Fall 15 Dataflow MoC 12 / 46
14 The Dataflow Model of Computation A Pragmatic Approach S.Zuckerman CPEG852 Fall 15 Dataflow MoC 12 / 46
15 The Dataflow Model of Computation A Pragmatic Approach S.Zuckerman CPEG852 Fall 15 Dataflow MoC 12 / 46
16 The Dataflow Model of Computation A Pragmatic Approach S.Zuckerman CPEG852 Fall 15 Dataflow MoC 12 / 46
17 Dataflow Graphs For J.B. Dennis, the role of Dataflow Graphs (DFGs) is two-fold: Serve as an intermediate-level language for high-level languages Serve as a machine language for parallel machine S.Zuckerman CPEG852 Fall 15 Dataflow MoC 13 / 46
18 A Brief History of Dataflow MIT, April 1974: Symposium on Programming, Paris. Dennis: First Version of a Data Flow Procedure Language. January 1975: Second Annual Symposium on Computer Architecture, Houston. Dennis and Misunas: A Preliminary Architecture for a Basic Data-Flow Processor. August 1975: Sagamore Computer Conference on Parallel Processing: Rumbaugh: Data Flow Languages Rumbaugh: A Data Flow Multiprocessor Bryant & Dennis: Packet Communication Architecture Misunas: Structure Processing in a Data-Flow Computer S.Zuckerman CPEG852 Fall 15 Dataflow MoC 14 / 46
19 Eearly Roots on Dataflow Work MIT in the 70 s Asynchronous Digital Logic (D. E. Muller and Bartky, 1957; David E Muller, 1963) Control Structures for Parallel Programming (Conway, 1963; McIlroy, 1969; Dijkstra, 1971) Abstract Models for Concurrent Systems (Petri, 1966; Holt, 1978) Theory of Program Schemes (Ianov, 1958; Paterson and Hewitt, 1970) Structured Programming (Dahl, Dijkstra, and Hoare, 1972) Functional Programming (McCarthy, 1960; Landin, 1964) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 15 / 46
20 Outline 1 A Quick Reminder on Execution Models 2 Dataflow Models of Computation 3 Dataflow Graphs and Properties 4 Static Dataflow Introduction Static Dataflow Examples Static Dataflow Features Static Dataflow Activity Templates 5 Recursive Program Graphs Introduction Ordinary and Tail Recursions Features of Recursive Program Graphs 6 Homework S.Zuckerman CPEG852 Fall 15 Dataflow MoC 16 / 46
21 Dataflow Graphs Dataflow tokens Values in dataflow graphs are represented as tokens. Tokens are tuples < s, d, v >, where s is the instruction pointer, d is the port, and v represents the actual value (data). Operator Execution An operator executes when all its input tokens are present; copies of the result token are distributed to the destination operators. S.Zuckerman CPEG852 Fall 15 Dataflow MoC 17 / 46
22 Dataflow Graphs Dataflow tokens Values in dataflow graphs are represented as tokens. Tokens are tuples < s, d, v >, where s is the instruction pointer, d is the port, and v represents the actual value (data). Operator Execution An operator executes when all its input tokens are present; copies of the result token are distributed to the destination operators. S.Zuckerman CPEG852 Fall 15 Dataflow MoC 17 / 46
23 Dataflow Graphs Dataflow tokens Values in dataflow graphs are represented as tokens. Tokens are tuples < s, d, v >, where s is the instruction pointer, d is the port, and v represents the actual value (data). Operator Execution An operator executes when all its input tokens are present; copies of the result token are distributed to the destination operators. S.Zuckerman CPEG852 Fall 15 Dataflow MoC 17 / 46
24 Operational Semantics I Firing Rules Overview of Operational Semantics Values are represented by tokens Tokens are placed (assigned) on the arcs Snapshot/configuration: state Computation: Configuration configuration S.Zuckerman CPEG852 Fall 15 Dataflow MoC 18 / 46
25 Operational Semantics II Firing Rules Details on Operational Semantics Tokens Data Assignment Placing a token on the output arc Snapshot/configuration: state Computation The intermediate step between snapshots / configurations S.Zuckerman CPEG852 Fall 15 Dataflow MoC 19 / 46
26 Operational Semantics III Firing Rules Actors States An actor in a DFG is enabled if there is a token on each of its input arcs Any enabled actor may be fired to define the next state of the computation When an actor is fired, then: All of its input tokens are removed from the input arcs A token is placed on each of the actor s output arcs Computation Sequence of snapshots Many possible sequences, as long as firing rules are obeyed This is called determinacy Provides locality of effect S.Zuckerman CPEG852 Fall 15 Dataflow MoC 20 / 46
27 General Firing Rules A switch actor is enabled if: A token is available on its control input arc A token is available on its data input arc(s) Firing a switch actor: Removes input tokens Delivers the input data value as an output token on the corresponding output arc A (possibly unconditional) merge actor is enabled if There is a token available on any of its input arcs A conditional merge need to have a control token placed on its input control arc An enabled (unconditional) merge actor may be fired It will put (possibly non-deterministically) one of the input tokens on the output arc. S.Zuckerman CPEG852 Fall 15 Dataflow MoC 21 / 46
28 Conditional Expressions Figure: if/else construct S.Zuckerman CPEG852 Fall 15 Dataflow MoC 22 / 46
29 Conditional Expressions Figure: if/else schema S.Zuckerman CPEG852 Fall 15 Dataflow MoC 22 / 46
30 Conditional Expressions Figure: loop schema S.Zuckerman CPEG852 Fall 15 Dataflow MoC 22 / 46
31 Remarks on Dataflow Models The dataflow model of computation is fundamentally sound and simple Very few other parallel MoCs can claim this Few dataflow architecture projects survived past the early 1990 s. However, dataflow principles were heavily reused in both software and hardware With the advent of the new multi and many core era, we have many (good!) reasons to re-examine and explore the original dataflow models It never hurts to learn from the past! As a side-note: Jack Dennis s dataflow model was finally recognized on a world-scale level: he was awarded the John Von Neumann Medal (the IEEE equivalent to the ACM Turing Award) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 23 / 46
32 Outline 1 A Quick Reminder on Execution Models 2 Dataflow Models of Computation 3 Dataflow Graphs and Properties 4 Static Dataflow Introduction Static Dataflow Examples Static Dataflow Features Static Dataflow Activity Templates 5 Recursive Program Graphs Introduction Ordinary and Tail Recursions Features of Recursive Program Graphs 6 Homework S.Zuckerman CPEG852 Fall 15 Dataflow MoC 24 / 46
33 Static Dataflow Static dataflow was the first dataflow model It was developed in Jack Dennis team S.Zuckerman CPEG852 Fall 15 Dataflow MoC 25 / 46
34 Static Dataflow The Golden Rule Static Dataflow s Golden Rule... for any actor to be enabled, there must be no tokens on any of its output arcs... S.Zuckerman CPEG852 Fall 15 Dataflow MoC 26 / 46
35 Example Power Function long power ( i n t x, i n t n) { i n t y = 1; f o r ( i n t i = n; i > 0; --i) y *= x; r e t u r n y; } Figure: Computation: y = x n S.Zuckerman CPEG852 Fall 15 Dataflow MoC 27 / 46
36 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
37 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
38 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
39 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
40 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
41 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
42 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
43 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
44 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
45 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
46 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
47 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
48 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
49 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
50 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
51 Example Power Function Computing y = 2 3 S.Zuckerman CPEG852 Fall 15 Dataflow MoC 28 / 46
52 Example Vector Addition: CN = A N + B N S.Zuckerman CPEG852 Fall 15 Dataflow MoC 29 / 46
53 Static Dataflow Features One-token-per-arc Deterministic merge Conditional/iteration construction Consecutive iterations of a loop can only be pipelined A dataflow graph activity templates Opcode of the represented instruction Operand slots for holding operand values Destination address fields Token value + destination S.Zuckerman CPEG852 Fall 15 Dataflow MoC 30 / 46
54 Static Dataflow Activity Templates S.Zuckerman CPEG852 Fall 15 Dataflow MoC 31 / 46
55 Static Dataflow Activity Templates S.Zuckerman CPEG852 Fall 15 Dataflow MoC 32 / 46
56 Static Dataflow Limitations The static dataflow model has the advantage of being very simple. However, it is also fairly limited: Due to acknowledgment tokens, the token traffic is doubled Lack of support for programming constructs that are essential to modern programming languages No procedure calls No recursion S.Zuckerman CPEG852 Fall 15 Dataflow MoC 33 / 46
57 Outline 1 A Quick Reminder on Execution Models 2 Dataflow Models of Computation 3 Dataflow Graphs and Properties 4 Static Dataflow Introduction Static Dataflow Examples Static Dataflow Features Static Dataflow Activity Templates 5 Recursive Program Graphs Introduction Ordinary and Tail Recursions Features of Recursive Program Graphs 6 Homework S.Zuckerman CPEG852 Fall 15 Dataflow MoC 34 / 46
58 Recursive Program Graphs Extension over static dataflow concepts Graph must be acyclic (DAG, directed acyclic graph) One-token-per-arc-per-invocation Iteration is expressed in terms of tail recursion S.Zuckerman CPEG852 Fall 15 Dataflow MoC 35 / 46
59 Examples of Ordinary Recursion Factorial long factorial ( long n) { i f (n == 0) r e t u r n 1; e l s e r e t u r n n * fact (n -1); } S.Zuckerman CPEG852 Fall 15 Dataflow MoC 36 / 46
60 Examples of Tail Recursion Factorial long fact_tail_rec ( long n, long acc ) { i f (n == 0) r e t u r n acc ; e l s e r e t u r n fact (n -1, acc *n); } long factorial ( long n) { r e t u r n fact_tail_rec (n,1); } S.Zuckerman CPEG852 Fall 15 Dataflow MoC 37 / 46
61 Example Factorial Hand Simulation: fact(3) long f a c t o r i a l ( long n ) { return n == 0? 1 : n f a c t ( n 1); } S.Zuckerman CPEG852 Fall 15 Dataflow MoC 38 / 46
62 Example Factorial DFG for fact(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 39 / 46
63 Example Factorial DFG for fact(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 39 / 46
64 Example Factorial DFG for fact(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 39 / 46
65 Example Factorial DFG for fact(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 39 / 46
66 Example Factorial DFG for fact(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 39 / 46
67 Example Factorial DFG for fact(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 39 / 46
68 Example Factorial DFG for fact(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 39 / 46
69 Example Factorial DFG for fact(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 39 / 46
70 Example Factorial DFG for fact(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 39 / 46
71 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
72 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
73 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
74 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
75 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
76 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
77 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
78 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
79 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
80 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
81 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
82 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
83 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
84 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
85 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
86 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
87 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
88 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
89 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
90 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
91 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
92 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
93 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
94 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
95 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
96 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
97 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
98 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
99 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
100 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
101 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
102 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
103 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
104 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
105 Factorial Tail Recursive version factorial(3) S.Zuckerman CPEG852 Fall 15 Dataflow MoC 40 / 46
106 Recursive Program Graph Features Acyclic One-token-per-link-in-lifetime Tags No deterministic merge needed Recursion is expressed by runtime copying S.Zuckerman CPEG852 Fall 15 Dataflow MoC 41 / 46
107 Outline 1 A Quick Reminder on Execution Models 2 Dataflow Models of Computation 3 Dataflow Graphs and Properties 4 Static Dataflow Introduction Static Dataflow Examples Static Dataflow Features Static Dataflow Activity Templates 5 Recursive Program Graphs Introduction Ordinary and Tail Recursions Features of Recursive Program Graphs 6 Homework S.Zuckerman CPEG852 Fall 15 Dataflow MoC 42 / 46
108 Homework factorial function: Convert the recursive form of factorial into an iterative form Create/draw the corresponding static dataflow graph power function: Convert the iterative form of the power function into its recursive form Create/draw its recursive program graph S.Zuckerman CPEG852 Fall 15 Dataflow MoC 43 / 46
109 References I Conway, Melvin E. (1963). A Multiprocessor System Design. In: Proceedings of the November 12-14, 1963, Fall Joint Computer Conference. AFIPS 63 (Fall). Las Vegas, Nevada: ACM, pp doi: / url: Dahl, O. J., E. W. Dijkstra, and C. A. R. Hoare, eds. (1972). Structured Programming. London, UK, UK: Academic Press Ltd. isbn: Dijkstra, E. W. (1971). Hierarchical Ordering of Sequential Processes. In: Acta Inf. 1.2, pp issn: doi: /BF url: Holt, Richard C (1978). Structured concurrent programming with operating systems applications. Vol Reading, Mass.; Don Mills, Ont.: Addison-Wesley Publishing Company. S.Zuckerman CPEG852 Fall 15 Dataflow MoC 44 / 46
110 References II Ianov, Iu I. (1958). On the Equivalence and Transformation of Program Schemes. In: Commun. ACM 1.10, pp issn: doi: / url: Landin, Peter J (1964). The mechanical evaluation of expressions. In: The Computer Journal 6.4, pp McCarthy, John (1960). Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I. In: Commun. ACM 3.4, pp issn: doi: / url: McIlroy, M. D. (1969). Alternatives to Extensible Languages. In: SIGPLAN Not. 4.8, pp issn: doi: / url: S.Zuckerman CPEG852 Fall 15 Dataflow MoC 45 / 46
111 References III Muller, D. E. and W. Scott Bartky (1957). A Theory of Asynchronous Circuits. Report 78. University of Illinois, Graduate College, Digital Computer Laboratory. Muller, David E (1963). Asynchronous logics and application to information processing. In: Switching Theory in Space Technology, pp Paterson, Michael S. and Carl E. Hewitt (1970). Record of the Project MAC Conference on Concurrent Systems and Parallel Computation. In: ed. by Jack B. Dennis. New York, NY, USA: ACM. Chap. Comparative Schematology, pp doi: / url: Petri, Carl Adam (1966). Communication with automata. eng. PhD thesis. Universität Hamburg. S.Zuckerman CPEG852 Fall 15 Dataflow MoC 46 / 46
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