Computer ArchitectureDataflow Machines

Data Flow• Conventional programming models are

control driven• Instruction sequence is precisely specified• Sequence specifies control

• which instruction the CPU will execute next• Execution rule:

• Execute an instruction when its predecessor has completed

s1: r = a*b;s2: s = c*d;s3: y = r + s;

s2 executes when s1 is completes3 executes when s2 is complete

Data Flow• Consider the calculation

• y = a*b + c*d• Represent it by

a graph• Nodes represent

computations• Data flows along

arcs• Execution rule:

• Execute an instruction when its data is available

• Data driven rule

a b

x

+

d c

x

y

Data Flow• Dataflow firing rule

• An instruction fires (executes)when its data is available

• Exposes all possible parallelism• Either multiplication can

fire as soon as data arrives• Addition must wait

• Data dependence analysis!• Instruction issue units:

• Fire (issue) each instructionwhen its operands (registers) have been written a b

x

+

d c

x

y

Data Flow - Realisations• Several Experimental Machines built

• Manchester Gurd & Watson• Tagged Token Arvind, MIT• Sigma ETL, Tsukuba• EMC-4 ETL, Tsukuba• Monsoon Arvind, MIT• EMX ETL, Tsukuba• RAPID Osaka/Sharp/Mitsubishi

(Asynchronous!)• Naiad Tasmania

and some others

Data Flow - Realisations• Manchester

Data Flow - Program• Program word

• Matching Store Entry

• When both Presence Flags are Y,this packet is despatched to a PE (any PE!)

Operation+, -, *, /

etc

Left, RightOperands Presence

Flags

DestinationAddress

DestinationLeft or Right

Data Flow - Matching Store• Special purpose memory

• Limited processing capability• Detects full slots• Despatches operation packets to any idle PE

Operation+, -, *, /

etc

Left, RightOperands Presence

Flags

DestinationAddress

DestinationLeft or Right

Data Flow - Processing Elements• Receive operation packets

• Generate result• Form result packet• Despatch to matching store

Data Flow - EM4• Architects

• Yamaguchi,Sakai, Kodama,Sato et al

• ElectroTechnicalLaboratory,Tsukuba,Japan

• PE (EM-Y)• CMOS Gate Array• 80k gates / 1.0• f = 20MHz• ~1992

Data Flow - Monsoon• Architects

• Papadopoulos, Culleret al

• MIT, Cambridge

• PE • f = 10MHz• ~1990

• I-StructureProcessor

Data Flow - I-Structures• Memory with a presence bit

• Tag each memory location with a bitindicating its validity

• Valid bit set -> normal read (no wait)• Data not yet written (valid bit not set)

WaitRead requests queued

Data driven execution• Operations proceed when data is available

valid validdata data valid data

Data Flow - Monsoon Pipeline

• 8 stage pipeline• “Presence bits”

checks operandavailability

• Frame (coarse grain)basis

Data Flow - Summary• Fine-Grain Dataflow

• Suffered from comms network overload!• Coarse-Grain Dataflow

• Monsoon ...• Overtaken by commercial technology!!• A sad “fact-of-life”

• It’s almost impossible to generate the fundsfor non-”mainstream” computer architecture research

• $n x 108 required • Non-mainstream = interesting!

Data Flow - Summary• As a software model …

• Functional languages • Dataflow in a different guise! • Theoretically

• important• Practically?

• Inefficient ( = slow!!) • ….. Ask your CS colleagues!

• Cilk - based on C• Used on CIIPS Myrmidons• Uses a dataflow model

• Threads become ready for execution when their data is generated• Message passing efficiency

• Without explicit data transfer & synchronisation!

Networks• Network Topology (or shape)

• Vital to efficient parallel algorithms• Communication is the limiting factor!

• Ideal• Cross-bar

• Any-to-any• Non-blocking

• Except two sources to same receiver

• Realisable• But only for limited order (number of ports)

Networks• Cross-bars

• Achilles• 8 x 8• Full duplex

• Simultaneous Input and Outputat each port

• 32 bit data-path• Target :

1Gbyte / second total throughput but we needed the 3-D arrangement to achieve

• bandwidth• high order

Networks• Cross-bars

• Achilles• Hardware

almost trivial!• Single FPGA

on each level• Programmable

• VHDL Models• Several topologies• Just by changing the

software!

Networks - More than 8 PEs

• Simple• Use 2 8x8 routers!

but ….This linkgets a lot of traffic!

Networks - Fat tree

• Problem:• High-traffic links between PEs can become a bottleneck

• Solution: Fat-tree• Links higher up the tree are “fatter”• Sustainable bandwidth between all PEs is the same

Networks - Performance Metrics

• Metrics for comparing network topologies• Diameter

• Maximum distance between any pair of nodes• Determines latency

• Bisection Bandwidth• Aggregate bandwidth over any “cut”

which divides the network in half• Determines throughput

• Crossbar• Diameter: 1

• Every PE is directly connected to routerso a single “hop” suffices

• Bisection Bandwidth: b bytes/sec• b is the bandwidth of a single link

Networks - Performance Metrics

• Metrics for comparing network topologies• To connect n PEs with mxm crossbars• Single link bandwidth b bytes/s

• Simple: n = 14 (2 switches)• Diameter 3

• Bisection Bandwidth b

1

2

3

Networks - Performance Metrics

• Fat-tree• Diameter: 2 logmn

• Height is logmn• Worst case distance - up and down

• Bisection Bandwidth: b n/2 bytes/sec• Links are fatter higher up the tree

logmn

Networks - Performance Metrics

• Mesh• Diameter: 2n-2• Bisection Bandwidth: b n bytes/sec• Order: 4

Networks - Performance Metrics

• Hypercube• Hypercube of order m• Link 2 order m-1 hypercubes with 2m-1 links• Number of PEs: n = 2m

• Order: log2n = m

Order 2 Hypercube Order 2

Hypercube

Order 3 Hypercube

Networks - Hypercubes

• Embedding property• In an n PE hypercube,

we have hypercubes of size n/2, n/4, …• Number PEs with binary numbers

• 000, 001, 010, 011, 100, …• Joining two hypercubes

• add one binary digitto the numbering

• Each PE is connectedto every PE whoseindex differs in only one bit

Networks - Hypercubes

• Embedding property• Partitioning tasks

• Allocate to sub-cubes• Sub-tasks allocated to

sub-cubes of that cube,etc