University of Alicante - Specialized Processor Architectures Lab

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- University of Alicante - Specialized Processor Architectures Lab. ‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’. Contents introduction research motivations background method: “special purpose processor design for scientific computing calculations” - PowerPoint PPT Presentation

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The Role of Algebraic Models and Type-2 Theory of Effectivity in Special Purpose Processor Design‘The Role of Algebraic Models and Type-2 Theory of Effectivity in Special Purpose Processor Design’
Gregorio de Miguel Casado Juan Manuel García Chamizo
-Computability in Europe- July, 4th 2006
- University of Alicante -
Specialized Processor Architectures Lab
introduction method application conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Contents
introduction
Computable Analysis Type-2 Theory of Effectivity
Formal VLSI design Algebraic Models of Processors
application: “processor design for computable convolution operation in ”
conclusions
introduction motivation background method application conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Research Motivation
research line: Scientific Computing
integral transforms
CIE 2006
introduction motivation background method application conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Background
Scientific Computing
Computable Analysis: Type-2 Theory of Effectivity [Wei00]…
VLSI design
correctness in specification and verification of processors [McT90] and [MöT98]
Formal Methods: Algebraic Models of Processors [HaT97], [FoH03]…
Computer Arithmetic
limited hardware support for arithmetic precision management (IEEE 754) [Lyn95]…
signed-digit arithmetic [ErL04]
memory integration improvements
introduction method Type-2 Theory of Effectivity Algebraic Models sketch application conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Type-2 Theory of Effectivity
Presents a realistic model of computation based on Type-2 machines
Provides a concrete computability concept based on naming systems and realizations
Allows the definition of computable functions on the set of all real numbers
Allows a natural complexity theory
The representations based on signed-digit notation are feasible for developing ad-hoc hardware arithmetic support (precision criteria)
The amount of memory available limits the feasibility of representation implementation
CIE 2006
introduction method Type-2 Theory of Effectivity Algebraic Models sketch application conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Algebraic Models of Processors
Isolation of some fundamental scientific structural features of processor computation (behavior over time and of data representation and operation)
Used for the specification and verification of computer architectures. Techniques: microprogramming, pipelined and superscalar processors
Connection with verification tools such as Maude and HOL
Algebraic abstraction for complex computer architecture approaches
Realistic approach by levels: Programmer & Abstract Circuit
CIE 2006
introduction method Type-2 Theory of Effectivity Algebraic Models sketch application conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Sketch of the method
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Application
Overview of the system architecture
CIE 2006
application
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Formalization of the problem
INPUT: informal problem description
Processor requirements and restrictions
symbolic calculation programs
Support for scalability features by introducing several levels of parallelization of the calculation
Support for variable precision capabilities in order to cover a wide range of precision requirements
Support for calculation time restrictions and result quality management
Test scenarios
CIE 2006
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Computability Analysis (i)
TTE-Computable convolution operation between Lebesgue integrable functions in spaces
TTE-Representation for the set of rational step functions
“Countable dense subset of “. Every integrable measurable function can be approximated by measurable step functions in the norm |·| and every measurable subset of can be approximated from above by open sets with respect to the Lebesgue measure [Klu04]
CIE 2006
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Computability Analysis (ii)
TTE-Computable convolution operation between Lebesgue integrable functions in spaces
TTE-Representation for the set of rational step functions
normalized signed digit notation based on the vsd notation for the rational numbers [Wei00]
Complexity Analysis
CIE 2006
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Specification
INPUTS
OUTPUT: algebraic specification of the processor
Functional specification Algebraic specification
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Functional Specification
CIE 2006
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Algebraic Specification
machine algebra
Abstract circuit level
control unit
machine algebra
CIE 2006
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Algebraic Specification. Data memory organization
Mapping functions: phead_name, paddrF, paddrRSF, pheadStep, paddrRangeStep, paddrLint, paddrHint, paddrA, paddrB, paddrCr, paddrCi, pRangeStep, plInterval, pHinterval, pa, pb, pCr, pCi
Data memory mapping
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Algebraic Specification. Data memory storage
Normalized signed-digit representation
introduction method application problem formalization computability analysis specification conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Algebraic Specification. Rational Step Function Unit
CIE 2006
introduction method application conclusions
‘The Role of Algebraic Models and TTE in Special Purpose Processor Design’
Conclusions
Novel theoretical approach for designing a processor for computable scientific computing calculations
Type-2 Theory of Effectivity
Algebraic Models of Processors
TTE provides criteria about data precision management
TTE representations for rational step functions based on rational signed digit notation can be mapped into conventional memories
Algebraic models provide a suitable general framework for the specification of special purpose processors
Online arithmetic provides feasible circuit designs for the simple arithmetic operations involved in the calculation (addition, multiplication and comparison)
Research in progress
Prototype implementation and performance evaluation
CIE 2006
conclusions
introduction
method
application
‘The Role of Algebraic Models and Type-2 Theory of Effectivity in Special Purpose Processor Design’
Gregorio de Miguel Casado Juan Manuel García Chamizo
-Computability in Europe- July, 4th 2006
- University of Alicante -