EECC756 - Shaaban #1 lec # 1 Spring 2003 3-11-2003 Systolic Architectures Replace single processor with an array of regular processing elements Orchestrate.

Slides:

Advertisements

Similar presentations

2.3 Modeling Real World Data with Matrices

Advertisements

Section 13-4: Matrix Multiplication

Systolic Arrays & Their Applications

CS 201 Compiler Construction

ECE669 L3: Design Issues February 5, 2004 ECE 669 Parallel Computer Architecture Lecture 3 Design Issues.

Memory Address Decoding

EECC551 - Shaaban #1 Fall 2005 lec# Static Compiler Optimization Techniques We examined the following static ISA/compiler techniques aimed.

Matrices A matrix is a rectangular array of quantities (numbers, expressions or function), arranged in m rows and n columns x 3y.

Application Specific Massive Parallelism Systolic and Instruction Systolic Computing Heiko Schröder, 2003 LOCOMAP.

Maths for Computer Graphics

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Why Systolic Architecture ? VLSI Signal Processing 台灣大學電機系吳安宇.

Advanced Topics in Algorithms and Data Structures An overview of the lecture 2 Models of parallel computation Characteristics of SIMD models Design issue.

Examples of Two- Dimensional Systolic Arrays. Obvious Matrix Multiply Rows of a distributed to each PE in row. Columns of b distributed to each PE in.

Supporting Systolic and Memory Communication in iWarp (Borkar et al. 1990) presented by Vasily Volkov CS258, Spring 2008, UC Berkeley.

EECC551 - Shaaban #1 Spring 2004 lec# Static Compiler Optimization Techniques We already examined the following static compiler techniques aimed.

\course\eleg652-03F\Topic1a- 03F.ppt1 Vector and SIMD Computers Vector computers SIMD.

Programming SA --- Systolic Array SIMD --- Single Instruction Multiple Data ISA --- Instruction Systolic Array MIMD --- Multiple Instruction Multiple Data.

EECC722 - Shaaban #1 Lec # 10 Fall Conventional & Block-based Trace Caches In high performance superscalar processors the instruction fetch.

(Page 554 – 564) Ping Perez CS 147 Summer 2001 Alternative Parallel Architectures  Dataflow  Systolic arrays  Neural networks.

Synthesizable, Space and Time Efficient Algorithms for String Editing Problem. Vamsi K. Kundeti.

Models of Parallel Computation Advanced Algorithms & Data Structures Lecture Theme 12 Prof. Dr. Th. Ottmann Summer Semester 2006.

EECC756 - Shaaban #1 lec # 1 Spring Parallel Computer Architecture A parallel computer is a collection of processing elements that cooperate.

EECC756 - Shaaban #1 lec # 1 Spring Parallel Computer Architecture A parallel computer is a collection of processing elements that cooperate.

EECC722 - Shaaban #1 Lec # 9 Fall Conventional & Block-based Trace Caches In high performance superscalar processors the instruction fetch.

Determinants 2 x 2 and 3 x 3 Matrices. Matrices A matrix is an array of numbers that are arranged in rows and columns. A matrix is “square” if it has.

HSDSL, Technion Spring 2014 Preliminary Design Review Matrix Multiplication on FPGA Project No. : 1998 Project B By: Zaid Abassi Supervisor: Rolf.

Anshul Kumar, CSE IITD CS718 : Data Parallel Processors 27 th April, 2006.

Parallel Algorithms Sorting and more. Keep hardware in mind When considering ‘parallel’ algorithms, – We have to have an understanding of the hardware.

Softcore Vector Processor Team ASP Brandon Harris Arpith Jacob.

Chapter One Introduction to Pipelined Processors.

Slides for Parallel Programming Techniques & Applications Using Networked Workstations & Parallel Computers 2nd ed., by B. Wilkinson & M

CSE Advanced Computer Architecture Week-1 Week of Jan 12, 2004 engr.smu.edu/~rewini/8383.

Data Structure CS 322. What is an array? Initializing arrays Accessing the values of an array Multidimensional arrays LAB#1 : Arrays.

4/25/2013 CS152, Spring 2013 CS 152 Computer Architecture and Engineering Lecture 22: Putting it All Together Krste Asanovic Electrical Engineering and.

COARSE GRAINED RECONFIGURABLE ARCHITECTURES 04/18/2014 Aditi Sharma Dhiraj Chaudhary Pruthvi Gowda Rachana Raj Sunku DAY

Slide Copyright © 2009 Pearson Education, Inc. 7.3 Matrices.

Matrix Operations.

Vector and symbolic processors

CprE / ComS 583 Reconfigurable Computing Prof. Joseph Zambreno Department of Electrical and Computer Engineering Iowa State University Lecture #12 – Systolic.

3.4 Solution by Matrices. What is a Matrix? matrix A matrix is a rectangular array of numbers.

Lecture 3: Computer Architectures

Parallel Processing Presented by: Wanki Ho CS147, Section 1.

A New Class of High Performance FFTs Dr. J. Greg Nash Centar ( High Performance Embedded Computing (HPEC) Workshop.

Matrix Multiplication The Introduction. Look at the matrix sizes.

Matrix Multiplication. Row 1 x Column X 25 = Jeff Bivin -- LZHS.

Fast VLSI Implementation of Sorting Algorithm for Standard Median Filters Hyeong-Seok Yu SungKyunKwan Univ. Dept. of ECE, Vada Lab.

Table of Contents Matrices - Definition and Notation A matrix is a rectangular array of numbers. Consider the following matrix: Matrix B has 3 rows and.

Notes Over 4.2 Finding the Product of Two Matrices Find the product. If it is not defined, state the reason. To multiply matrices, the number of columns.

C.E. Goutis V.I.Kelefouras University of Patras Department of Electrical and Computer Engineering VLSI lab Date: 20/11/2015 Compilers for Embedded Systems.

VLSI SP Course 2001 台大電機吳安宇 1 Why Systolic Architecture ? H. T. Kung Carnegie-Mellon University.

Matrices. Variety of engineering problems lead to the need to solve systems of linear equations matrixcolumn vectors.

A rectangular array of numeric or algebraic quantities subject to mathematical operations. The regular formation of elements into columns and rows.

Processor Level Parallelism 1

GPU Architecture and Its Application

Design of Digital Circuits Lecture 24: Systolic Arrays and Beyond

Lesson 43: Working with Matrices: Multiplication

12-1 Organizing Data Using Matrices

CS140 Lecture 03: The Machinery of Computation: Combinational Logic

How does an SIMD computer work?

Laxmi Narayan Bhuyan SIMD Architectures Laxmi Narayan Bhuyan

Array Processor.

فصل نهم از کتاب طراحی آموزشی تألیف :آر.ام گانیه

A Survey of Recent Media Processors

Parallel Matrix Operations

MATRICES MATRIX OPERATIONS.

Parallel Computer Architecture

COMPUTER ARCHITECTURES FOR PARALLEL ROCESSING

Matrix A matrix is a rectangular arrangement of numbers in rows and columns Each number in a matrix is called an Element. The dimensions of a matrix are.

Presentation transcript:

EECC756 - Shaaban #1 lec # 1 Spring Systolic Architectures Replace single processor with an array of regular processing elements Orchestrate data flow for high throughput with less memory access Different from pipelining –Nonlinear array structure, multidirection data flow, each PE may have (small) local instruction and data memory Different from SIMD: each PE may do something different Initial motivation: VLSI enables inexpensive special-purpose chips Represent algorithms directly by chips connected in regular pattern Slides from Shaaban

EECC756 - Shaaban #2 lec # 1 Spring Systolic Array Example: 3x3 Systolic Array Matrix Multiplication b2,2 b2,1 b1,2 b2,0 b1,1 b0,2 b1,0 b0,1 b0,0 a0,2 a0,1 a0,0 a1,2 a1,1 a1,0 a2,2 a2,1 a2,0 Alignments in time Processors arranged in a 2-D grid Each processor accumulates one element of the product Rows of A Columns of B T = 0 Example source:

EECC756 - Shaaban #3 lec # 1 Spring Systolic Array Example: 3x3 Systolic Array Matrix Multiplication b2,2 b2,1 b1,2 b2,0 b1,1 b0,2 b1,0 b0,1 a0,2 a0,1 a1,2 a1,1 a1,0 a2,2 a2,1 a2,0 Alignments in time Processors arranged in a 2-D grid Each processor accumulates one element of the product T = 1 b0,0 a0,0 a0,0*b0,0 Example source:

EECC756 - Shaaban #4 lec # 1 Spring Systolic Array Example: 3x3 Systolic Array Matrix Multiplication b2,2 b2,1 b1,2 b2,0 b1,1 b0,2 a0,2 a1,2 a1,1 a2,2 a2,1 a2,0 Alignments in time Processors arranged in a 2-D grid Each processor accumulates one element of the product T = 2 b1,0 a0,1 a0,0*b0,0 + a0,1*b1,0 a1,0 a0,0 b0,1 b0,0 a0,0*b0,1 a1,0*b0,0 Example source:

EECC756 - Shaaban #5 lec # 1 Spring Systolic Array Example: 3x3 Systolic Array Matrix Multiplication b2,2 b2,1 b1,2 a1,2 a2,2 a2,1 Alignments in time Processors arranged in a 2-D grid Each processor accumulates one element of the product T = 3 b2,0 a0,2 a0,0*b0,0 + a0,1*b1,0 + a0,2*b2,0 a1,1 a0,1 b1,1 b1,0 a0,0*b0,1 + a0,1*b1,1 a1,0*b0,0 + a1,1*b1,0 a1,0 b0,1 a0,0 b0,0 b0,2 a2,0 a1,0*b0,1 a0,0*b0,2 a2,0*b0,0 Example source:

EECC756 - Shaaban #6 lec # 1 Spring Systolic Array Example: 3x3 Systolic Array Matrix Multiplication b2,2 a2,2 Alignments in time Processors arranged in a 2-D grid Each processor accumulates one element of the product T = 4 a0,0*b0,0 + a0,1*b1,0 + a0,2*b2,0 a1,2 a0,2 b2,1 b2,0 a0,0*b0,1 + a0,1*b1,1 + a0,2*b2,1 a1,0*b0,0 + a1,1*b1,0 + a1,2*a2,0 a1,1 b1,1 a0,1 b1,0 b1,2 a2,1 a1,0*b0,1 +a1,1*b1,1 a0,0*b0,2 + a0,1*b1,2 a2,0*b0,0 + a2,1*b1,0 b0,1 a1,0 b0,2 a2,0 a2,0*b0,1 a1,0*b0,2 a2,2 Example source:

EECC756 - Shaaban #7 lec # 1 Spring Systolic Array Example: 3x3 Systolic Array Matrix Multiplication Alignments in time Processors arranged in a 2-D grid Each processor accumulates one element of the product T = 5 a0,0*b0,0 + a0,1*b1,0 + a0,2*b2,0 a0,0*b0,1 + a0,1*b1,1 + a0,2*b2,1 a1,0*b0,0 + a1,1*b1,0 + a1,2*a2,0 a1,2 b2,1 a0,2 b2,0 b2,2 a2,2 a1,0*b0,1 +a1,1*b1,1 + a1,2*b2,1 a0,0*b0,2 + a0,1*b1,2 + a0,2*b2,2 a2,0*b0,0 + a2,1*b1,0 + a2,2*b2,0 b1,1 a1,1 b1,2 a2,1 a2,0*b0,1 + a2,1*b1,1 a1,0*b0,2 + a1,1*b1,2 b0,2 a2,0 a2,0*b0,2 Example source:

EECC756 - Shaaban #8 lec # 1 Spring Systolic Array Example: 3x3 Systolic Array Matrix Multiplication Alignments in time Processors arranged in a 2-D grid Each processor accumulates one element of the product T = 6 a0,0*b0,0 + a0,1*b1,0 + a0,2*b2,0 a0,0*b0,1 + a0,1*b1,1 + a0,2*b2,1 a1,0*b0,0 + a1,1*b1,0 + a1,2*a2,0 a1,0*b0,1 +a1,1*b1,1 + a1,2*b2,1 a0,0*b0,2 + a0,1*b1,2 + a0,2*b2,2 a2,0*b0,0 + a2,1*b1,0 + a2,2*b2,0 b2,1 a1,2 b2,2 a2,2 a2,0*b0,1 + a2,1*b1,1 + a2,2*b2,1 a1,0*b0,2 + a1,1*b1,2 + a1,2*b2,2 b1,2 a2,1 a2,0*b0,2 + a2,1*b1,2 Example source:

EECC756 - Shaaban #9 lec # 1 Spring Systolic Array Example: 3x3 Systolic Array Matrix Multiplication Alignments in time Processors arranged in a 2-D grid Each processor accumulates one element of the product T = 7 a0,0*b0,0 + a0,1*b1,0 + a0,2*b2,0 a0,0*b0,1 + a0,1*b1,1 + a0,2*b2,1 a1,0*b0,0 + a1,1*b1,0 + a1,2*a2,0 a1,0*b0,1 +a1,1*b1,1 + a1,2*b2,1 a0,0*b0,2 + a0,1*b1,2 + a0,2*b2,2 a2,0*b0,0 + a2,1*b1,0 + a2,2*b2,0 a2,0*b0,1 + a2,1*b1,1 + a2,2*b2,1 a1,0*b0,2 + a1,1*b1,2 + a1,2*b2,2 b2,2 a2,2 a2,0*b0,2 + a2,1*b1,2 + a2,2*b2,2 Done Example source: