Systolic Organization

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Systolic Organization

• A.R. Hurson
• Computer Science Department
• Missouri Science Technology
• hurson_at_mst.edu

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Systolic Organization

• To effectively utilize a given technology, the
  constraints of that technology must be well
  understood.
• System designers must consider the limitations of
  the technology to design a system where those
  limitations do not impact the overall performance
  significantly.

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Systolic Organization

• It is generally accepted that many computational
  tasks are by their very nature sequential, and
  for others the degree of parallelism varies.
• To maintain sufficient application flexibility
  and computational efficiency, a massively
  parallel computational architecture must offer
  reconfigurability, scalability, and
  programmability.

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Systolic Organization

• reconfigurable to exploit application
  dependent parallelisms,
• high level language programmable to provide
  task control and flexibility,
• scalable to easily extend the architecture to
  many applications,
• capable of supporting SIMD organizations for
  vector operations and MIMD for non homogeneous
  parallelism requirements.

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Systolic Organization

• Systolic operation and organization is a design
  philosophy that is aimed to satisfy the
  architectural constraints imposed by the advances
  in silicon technology.
• It offers simplicity, regularity, modularity, and
  localized communications.

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Systolic Organization

• Systolic arrays are typically characterized as
  having intensive local communications and
  computations yet, with decentralized parallelism
  in a compact package.
• Systolic arrays capitalize on processes which can
  be performed in a regular, modular, rhythmic,
  synchronous, and concurrent manner that require
  intensive repetitive computations.

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Systolic Organization

• Systolic arrays originally were proposed for
  fixed or special purpose instances, however, this
  concept has been extended to more general purpose
  SIMD and MIMD architectures.

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Systolic Organization

• What is a Systolic Arrays?
• There is no uniquely accepted definition for
  systolic arrays or systolic cells.
• The term systolic originated in the medical
  community where it is used to describe the human
  circulatory system.
• Systolic processes, like the circulatory system,
  perform the operations in a rhythmic,
  incremental, cellular, and repetitive manner much
  like the heart circulating blood through the
  arteries, veins, and capillaries.

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Systolic Organization

• What is a Systolic Arrays?
• The systolic computational rate is restricted by
  the array's I/O operations, much the same way
  that the heart controls blood flow to the cells.
• The term array originates from the observation
  that systolic arrays have balanced uniform
  architectures which typically look like grids
• Each line indicates a communication path.
• Each intersection represents a cell or a systolic
  element.

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Systolic Organization

• What is a Systolic Arrays?
• Systolic arrays are more than processor arrays
  which execute systolic algorithms.
• A systolic cell takes on one of the following
  forms
• A special purpose cell with hardwired functions,
• A vector-computer-like cell with instruction
  decoding and a processing element or,
• A systolic processor complete with a control unit
  and a processing unit.

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Systolic Organization

• General Systolic Organization

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Systolic Organization

• In 1978, the first systolic arrays were
  introduced as a feasible design for special
  purpose devices which meet the VLSI constraints.
• These special purpose devices were able to
  perform four types of matrix operations at high
  processing speeds
• matrix-vector multiplication,
• matrix-matrix multiplication,
• LU-decomposition of a matrix,
• Solution of triangular linear systems.

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Systolic Organization

• Although, systolic architectures originally, were
  motivated for high performance special purpose
  computational systems that meet the constraints
  of VLSI, however, it is possible to design
  systolic systems which have high throughputs and
  yet are not constrained to a single VLSI chip.

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Systolic Organization

• Systolic Characteristics
• Systolic architectures are composed of a few
  basic building blocks faster design time.
• Basic building blocks are replicated in a one,
  two, or possibly higher dimensional space.
• The systolic cells use simple and regular
  communication paths to their nearest neighbors
  To eliminate broadcasting of data throughout the
  system. Regular interconnections also lead to
  higher densities and shorter communication paths.

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Systolic Organization

• Systolic Characteristics
• The systolic cells are synchronized by a single
  global clock.
• The input data streams are fed to the systolic
  array only at its boundaries.
• Different data streams can flow in different
  directions at different speeds through the array.

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Systolic Organization

• Systolic Characteristics
• Systolic architectures have some characteristics
  similar to pipelined or array processor
  configurations.

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Systolic Organization

• Systolic Characteristics
• Systolic architectures differ from pipelined
  systems because
• Most of the stages are identical,
• Input data is not consumed,
• Input data streams can flow in different
  directions,
• Modules may be organized in a two-dimensional (or
  higher) configuration.

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Systolic Organization

• Systolic Characteristics
• Systolic architectures differ from array of
  processors because
• Processors in systolic organizations are
  synchronized by a single global clock, but are
  locally controlled different systolic cells can
  perform different operations at the same time.

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Systolic Organization

• Systolic Characteristics
• Systolic architecture have several advantages
  over conventional systems
• Systolic architectures make the design of special
  purpose systems easier cost-effective special
  purpose systems.
• Systolic architectures are also well suited for
  the constraints of many technologies especially
  VLSI.

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Systolic Organization

• Systolic Characteristics
• Systolic architectures allow higher throughputs
  concurrent operations of a large number of the
  processing cells.
• Ability to increase the execution speed of
  compute-bound applications without increasing the
  I/O requirements reusability of the input data.

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Systolic Organization

• Systolic Issues
• Algorithms and Mapping Designers must be
  intimately familiar with the algorithms that they
  are implementing on systolic arrays.
• The heuristic design of systolic arrays from an
  algorithm is slow, error prone, requires
  simulation for verification, and often results in
  a non optimum solution.
• Automatic array synthesis is a research area of
  interest. However, most array designs are based
  on heuristics.

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Systolic Organization

• Systolic Issues
• Integration into Existing Systems Generally,
  systolic processors are integrated into an
  existing host as a backend processor.

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Systolic Organization

• Systolic Issues
• Integration into Existing Systems
• System integration is often nontrivial because of
  the arrays high I/O requirements.
• Often, an additional memory subsystem is added
  between the existing host and the systolic array
  to support data access and data multiplexing and
  de-multiplexing since the existing I/O channel of
  the host rarely satisfies the bandwidth required
  by the systolic array.

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Systolic Organization

• Systolic Issues
• Cell Granularity Low level or high level cell
  granularity will directly affect the arrays
  throughput, flexibility, and the set of
  algorithms which may be efficiently executed.

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Systolic Organization

• Systolic Issues
• Cell Granularity
• The basic operation performed in each cycle by
  each cell can range from logical or bit wise
  operations to word level multiplication and
  addition to a complete program.
• Granularity is subject to technology capabilities
  and limitations as well as design goals.
• Packaging will also introduce input/output pin
  restrictions.

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Systolic Organization

• Systolic Issues
• Extensibility Since systolic arrays are built
  around the cellular building blocks, the cell
  design should be sufficiently flexible to allow
  it to be used in a wide variety of topologies
  implemented in a wide variety of substrate
  technologies.

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Systolic Organization

• Systolic Issues
• Clock Synchronization Clock lines of different
  lengths within integrated chips, as well as
  external to the chips, can introduce skews.
• Clock skew risk is greater when data flow within
  the systolic array is bi-directional.
• Wave-front arrays reduce the clock skew problem
  by introducing more complicated asynchronous
  inter cellular communications.

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Systolic Organization

• Systolic Issues
• Reliability As integrated circuits grow larger
  and larger, inherent fault tolerant abilities
  must be added if the same degree of reliability
  is to be maintained. Also diagnostics should be
  built in at design time so proper operation can
  more easily be verified.

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Systolic Organization

• Summary
• Systolic organization
• Definition
• Characteristics
• Issues
• Systolic vs. Pipelining
• Systolic vs. array of processor

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Systolic Organization

• Systolic Design Character Matching
• A straightforward approach to search for a
  pattern within a string of characters (string) is
  simple but time-consuming.
• The following algorithm shows the sequence of
  operations.
• The algorithm compares the characters in the
  pattern against the characters in the text from
  left to right.
• This simple algorithm has a time complexity of
  O(mn) where m and n are the lengths of the
  pattern and text.

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Systolic Organization

• Systolic Design Character Matching
• Search for a Pattern

T-index ? 0 While T-index lt (n-m1) DO Save ?
T-index P-index ? 0 While P-index lt m and
Textsave PatternP-index DO Save ? Save
1 P-index ? P-index 1 END If P-index m
then return T-index ? T-index 1 END
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Systolic Organization

• Systolic Design Character Matching
• Concept of the finite state automaton can be used
  to perform pattern matching operation in a time
  complexity of O(n).
• Knuth proposed an algorithm with the time
  complexity of O(mn).

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Systolic Organization

• Systolic Design Character Matching
• The proposed model is used for character matching
  (pattern Matching) operation.
• The model is composed of two kind of cells
• Comparator cells, and
• Accumulator cells.

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Systolic Organization

• Systolic Design Character Matching
• The comparator cells receive text and patterns
  from opposite directions and generate the
  Comparison results.
• The accumulator cells transmit information
  regarding delimiters and "don't care" signals.
  In addition, it accumulates the partial match
  results.

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Systolic Organization

• Systolic Design Character Matching

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Systolic Organization

• Systolic Design Character Matching
• Algorithm in C cells

Pout ? Pin Sout ? Sin dout ? (Pin Sin)
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Systolic Organization

• Systolic Design Character Matching
• Algorithm in A cells

lout ? lin Xout ? Xin IF lin THEN rout ? t t ?
True ELSE rout ? rin t ? t AND (Xin OR din)
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Systolic Organization

• Systolic Design Character Matching
• Detect pattern ISSI in text MISSISSIPPI in a
  systolic organization composed of seven cells.

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Systolic Organization

• Systolic Design Character Matching
• Initial configuration

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Systolic Organization

• Systolic Design Character Matching

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Systolic Organization

• Systolic Design Character Matching

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Systolic Organization

• Systolic Design Character Matching

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Systolic Organization

• Systolic Design Character Matching

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Systolic Organization

• Systolic Design Character Matching

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Systolic Organization

• Systolic Design Character Matching

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Systolic Organization

• Systolic Design Character Matching
• General Characteristics
• Hardware utilization is low, since during each
  clock pulse only half of the cells are active.
• Patterns have to be cycled through the array
  continuously to meet all the text characters.
• Possible detection of more hits in the input text.

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Systolic Organization

• Systolic Design Join Operation
• Within the scope of relational databases, join is
  one of the most time consuming operations.

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Systolic Organization

• Assume we have two product-compatible relations
  (sets) A and B. Each relation is composed of
  several tuples (records).
• Further, let ? ???, ?, ?, ...?, then the ?-Join
  of relation A on attribute X with relation B on
  attribute Y is a relation consist of tuples
  t(lta,bgt) from Cartesian product of A and B such
  that tx ? ty is true.

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Systolic Organization

• Systolic Design Join Operation
• Assume we have the following two relations

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Systolic Organization

• Systolic Design Join Operation

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Systolic Organization

• Systolic Design Join Operation
• In relational database system, join operation is
  used as a measure to evaluate the performance of
  the system. This is due to the
• Complexity of the join, and
• application of join in de-normalizing the
  relations.

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Systolic Organization

• Systolic Design Join Operation
• Let us look at a systolic model for join
  operation
• A collection of basic cells replicated in a two
  dimensional space.
• System is highly parallel and satisfies the
  constraints imposed by the VLSI technology.

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Systolic Organization

• Systolic Design Join Operation
• A Systolic Cell

as and bs are the attributes and t is a control
signal that reflects the comparison between a and
b.
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Systolic Organization

• Systolic Design Join Operation
• A Systolic Cell

Tout ? tin ? (ain ? bin) aout ? ain bout ? bin
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Systolic Organization

• Systolic Design Join Operation

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Systolic Organization

• Systolic Design Join Operation

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Systolic Organization

• Systolic Design Join Operation

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Systolic Organization

• Systolic Design Join Operation

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Systolic Organization

• Systolic Design Join Operation

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Systolic Organization

• Systolic Design Join Operation

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Systolic Organization

• Systolic Design Join Operation