High Performance Embedded Computing © 2007 Elsevier Lecture 4: Models of Computation Embedded Computing Systems Mikko Lipasti, adapted from M. Schulte Based on slides and textbook from Wayne Wolf

© 2006 Elsevier Topics Why models of computation? Structural models. Finite-state machines. Turing machines. Petri nets. Control flow graphs. Data flow models. Task graphs. Control flow models.

© 2006 Elsevier Models of computation Models of computation:  Define the basic capabilities of an abstract computer  Affect programming style No one model of computation is good for all algorithms.  Systems that use multiple programming languages are called heterogeneously programmed.

© 2006 Elsevier Aspects of models of computation Large systems may require different models of computation for different parts.  Models must communicate with one another Models of computation can be distinguished by:  Finite state vs. infinite state  Control vs. data  Sequential vs. parallel Introduce models now, cover in more detail later

© 2006 Elsevier Processor graph M1M1 L1L1 M2M2 M3M3 M4M4 L2L2 L3L3

© 2006 Elsevier Finite state machines State transition graph and table are equivalent: s3 s1s2 0/0 0/1 1/0 0/0 1/1 1/0 0s1s20 1s1 0 0s2 1 1 s s11 I S Δ O

© 2006 Elsevier Nondeterministic FSM Several transitions out of a state for a given input.  Equivalent to executing all alternatives in parallel.  Future inputs may cause some paths to be pruned Can allow  moves---goes to next state without input. Also known as nondeterministic finite automata (NFA) s1s2 a a

© 2006 Elsevier Deterministic FSM from NFA Any NFA can be transformed into a deterministic FSM. Add states for the various combinations of non-determinism. So why use NFAs? s1s2 a a s3 nondeterministic b s4 c s1s12 a s3 b s4 c c deterministic

© 2006 Elsevier Turing machine General model of computing: program head tape state

© 2006 Elsevier Turing machine step 1. Read current square. 2. Erase current square. 3. Take state-dependent action: 1. Print new value. 2. Move to adjacent cell. 3. Set machine to next state.

© 2006 Elsevier Turing machine properties Example program:  If (state = 2 and cell = 0): print 0, move left, state = 4.  If (state = 2 and cell = 1): print 1, move left, state = 3. Can be implemented on many physical devices. Turing machine is a general model of computability. Can be extended to probabilistic behavior.

© 2006 Elsevier Turing machine properties Infinite tape = infinite state machine. Basic model of computability.  Lambda calculus is alternative model.  Other models of computing can be shown to be equivalent to or proper subset of Turing machine. What advantages and disadvantages do Turing machines have compared to finite state machines?

© 2006 Elsevier Control flow graph (CFG) Commonly used to model program structure. Nodes are unconditionally or conditionally executed. Is this a finite state or infinite state model of computation? x = a - b y = c + d x = a i = 0?

© 2006 Elsevier Data flow graph (DFG) Partially-ordered computations: +- * + -, * +, -, * -, +, *

© 2006 Elsevier Data flow streams Captures sequence but not time. Totally-ordered set of values.  New values are appended at the end as they appear. May be infinite

© 2006 Elsevier Firing rules A node may have one or more firing rules. Firing rules determine when tokens are consumed and produced.  Firing consumes a set of tokens at inputs, generates token at output.

© 2006 Elsevier Example firing rules Basic rule fires when tokens are available at all inputs: Conditional firing rule depends on control input: + a b c a b T

© 2006 Elsevier Data flow graph properties Finite state model. Basic data flow graph is acyclic. Scheduling provides a total ordering of operations.

© 2006 Elsevier Synchronous data flow (SDF) Lee/Messerschmitt: Relate data flow graph properties to schedulability.  Synchronous communication between data flow nodes.  Nodes may communicate at multiple rates.

© 2006 Elsevier SDF notation Nodes may have rates at which data are produced or consumed. Edges may have delays

© 2006 Elsevier SDF example What are the input and output rates of each node? separate outputs

© 2006 Elsevier Delays in SDF graphs Delays do not change rates, only the amount of data stored in the system. Changes system start-up

© 2006 Elsevier Kahn process network Process has unbounded FIFO at each input: Each channel carries a possibly infinite sequence or stream. A process maps one or more input sequences to one or more output sequences. processchannel

© 2006 Elsevier Monotonicity of Khan processes If F(X) is the output of a processor for input stream X, the system is monotonic if: X in X’ => F(X) in F(X’)

© 2006 Elsevier Networks of processes A network of processes relates the streams of several processes. If I = input sequences, X = internal sequences + outputs, then network behavior fixed point behavior is  X = F(X,I) A network of monotonic processes is a monotonic process.  Even in the presence of feedback loops.

© 2006 Elsevier Task graph Used to model parallelism. 11 22 P1P1 P2P2 P3P3 P4P4 P5P5

© 2006 Elsevier Task graph properties Not a Turning machine.  No branching behavior.  May be extended to provide conditionals, but still FSMs Possible models of execution time:  Constant.  Min-max bounds.  Statistical. Can model late arrivals, early departures by adding dummy processes.

© 2006 Elsevier Petri net Parallel model of computation. place arc token transition

© 2006 Elsevier Firing rule A transition is enabled if each place at its inputs have at least one token.  A transition doesn’t have to fire right away. Firing a transition removes tokens from inputs and adds a token to each output place. In general, may require multiple tokens to enable firing.

© 2006 Elsevier Properties of Petri nets Turing complete. Arbitrary number of tokens.  Nondeterministic behavior.  Naturally model parallelism.

© 2006 Elsevier Communication models Buffered communication – assumes memory is available to store a values if the receiver is not ready to receive it Unbuffered communication – assumes no memory between the sender and receiver Blocking communication – sender waits until the receiver has the data Nonblocking communication – does no require the sender to wait until the receiver has the data

© 2006 Elsevier Sources of parallelism Instruction-level parallelism – from executing independent instructions in parallel Data-level parallelism – from executing the same operation on multiple pieces of data in parallel Task-level parallelism – from performing multiple tasks in parallel What are mechanisms used to exploit each type of parallelism?