
Intensive Computation  Calcolo Intensivo
Annalisa Massini Office Hours: appointment by email 
News
Dear students, this year I have updated the program of the course, making some changes to the order of the topics, making some additions, addressing some topics in more detail, and less in detail others that I had dealt with indepth in previous years. In particular, the course will start from the part dedicated to computer architectures, and will place greater emphasis on interconnection topologies for HPC and PD systems and the related communication problems. Quantum computing will be included as a new topic, with particular regard to quantum arithmetic circuits, in order to compare the classical solutions (which I will describe) with those currently being studied for quantum computers. Theses will be proposed on the topics of this first part of the course. In the second part of the course, the remaining topics will be treated (in previous years they were treated in the first period of the course): sparse matrices, errors, linear systems, eigenvalues and eigenvectors, molecular dynamics. Depending on how the course will proceed, it is possible that some of these latter topics are only mentioned or completely skipped. Important information

Lectures 20212022
Lecture 1, February 23rd, 2022 Introduction to the course.
Lecture1  Introduction
Lecture 2, February 25th, 2022 Summary of computer organization and architecture.
Lecture2  Computer overview  Part1
Lecture 3, March 2nd, 2022 Circuits for arithmetic operations. Lecture 3  Computer arithmetic  Slides 138
Lecture 4, March 16th, 2022 Pipelined addition. Pipelined unsigned and signed multiplication. Evaluation of circuit area and delay. Lecture 4  Computer arithmetic  Slides 3959
Lecture 5, March 18th, 2022 Redundant Number systems. Lecture 5  Redundant number systems  Slide 1052
Lecture 6, March 23rd, 2022 Residue Number systems. Lecture 6  Residue Number System Slides are UPDATED
Lecture 7, March 25th, 2022 Motivation to parallel architectures. Classifications of (parallel) architectures. Lecture 7  Motivation to parallel architectures.
Lecture 8, March 30th, 2022 The SIMD class: Vector architectures Lecture 8  Vector Architectures  Slide 148
Lecture 9, April 1st, 2022 The SIMD class. Vector architectures continued. Lecture 8  Vector Architectures  Slide 4968 Graphics Processing Units. Lecture 9  GPUs  Slide 141
Lecture 10, April 6th, 2022 Graphics Processing Units. Lecture 10  GPUs  Slide 4271
Lecture 11, April 8th, 2022 Graphics Processing Units. Exercises. Lecture 11  GPUs  Slide 72112
Lecture 12, April 13th, 2022 Speedup and performance. Lesson 12  Speedup and Performance
Midterm  April 20th, April
Lecture 13, April 22nd, 2022 Performance. Lesson 13  Performance Part2
Lecture 14, April 27th, 2022 Interconnection networks Lesson 14  Interconnection networks  Slide 145
Lecture 15, April 29th, 2022 Interconnection networks Lesson 15  Interconnection networks  Slide 46109
Lecture 16, May 4th, 2022 Interconnection networks: Fat trees and exrcises. Lesson 16  Interconnection networks  Slide 109123
Lecture 17, May 6th, 2022 Introduction to Quantum Computing. Qubits and Onequbit gates Lesson 17  Quantum Computing  Slide 152
Lecture 18, May 11th, 2022 Quantum Computing: MultipleQubit gates and Quantum circuits Lesson 18  Quantum Computing  Slide 5392 UPDATED slides after class. The last slides have been corrected (Bell state representation).
Lecture 19, May 13th, 2022 Quantum Computing: Adders. Lecture 19 Quantum Computing: adders UPDATED slides
Lecture 20, May 18th, 2022 Exercises on quantum circuits.
Lecture 21, May 20th, 2022 Sparse Matrices Lesson 21  Sparse Matrices Lecture 22, May 25th, 2022 Exercises on quantum circuits, sparse matrices and fat trees

Lectures 20202021 Lecture 1, February 24th, 2021 Introduction to the course. Lecture 1  Introduction
Lecture 2, February 26th, 2021 Introduction to Matlab  Part 1  Lecture 2  Matlab
Lecture 3, March 3rd, 2021 Introduction to Matlab  Part 2  Lecture 3  Matlab Lecture 4, March 5th, 2021 Sparse matrices: definitions and motivation of compact formats. Compact storage methods for sparse matrix: Coordinate, Skyline, Compact Sparse Row CSR, Compact Sparse Column CSC, Modified Sparse Row MSR. Lecture 4  SparseMatrices.pdf
Lecture 5, March 10th, 2021 Exercises on Sparse matrices.
Lecture 6, March 12th, 2021 Lecture by Dr. Viviana Arrigoni. Linear systems. Gaussian elimination for solving systems of linear equations. Pivoting. Methods to avoid pivoting. Random Butterfly Transformations and Transpose methods. Lecture 7  Linear Systems Part 1
Lecture 7, March 17th, 2021 Lecture by Dr. Viviana Arrigoni. Linear systems. Cholesky factorization. Jacobi iterative method. GaussSeidel iterative method. Lecture 7  Linear Systems Part 2
Lecture 8, March 19th, 2021 Errors: Computational errors, Data errors, Truncation errors, Rounding errors. Forward error and backward error. Sensitivity and condition number. Stability and accuracy. Errors in floatingpoint representation. Uncertainty in measurements. Lecture 8  Errors
Lecture 9, March 24th, 2021 Discussion on Homework 1: student's solutions. Exercises on linear systems and errors: Exercise 3 from Midterm exam 18 April 2018 (continued); Exercise 3 from Midterm exam 17 April 2019.
Lecture 10, March 26th, 2021 Eigenvalues and eigenvectors. The Power method. The Deflation methods.
Applications: Gould Index  Eigenvector Centrality in a Graph; the Fiedler Eigenvector and the Graph Partitioning; the Steady State of a Markov Chain using eigenvalues and eigenvectors; covariance matrix and eigenvectors. Lecture 10  Eigenvalues, Eigenvectors and applications
Lecture 11, March 31st, 2021 Molecular Dynamics: Introduction, Hooke's Law Model, LennardJones Model, Motion Equations. Lecture11  MolecularDynamicsMolecular Dynamics  L. Fosdick.
Lecture 12, April 7th, 2021 Molecular Dynamics: Euler's method and Verlet's method for Hooke's Law Model and LennardJones Model. Solution of motion equations for the 1D Hard Sphere Model. Lecture12  Molecular Dynamics Part 2  slide 137
Exact solution for Hooke's Law Model. Molecular Dynamics  L. Fosdick.
Lecture 13, April 9th, 2021 Molecular dynamics: Solution of motion equations for the 1D Hard Sphere Model. Exact solution of motion equations for the Hooke's Law Model. Lecture12  Molecular Dynamics Part 2  slide 3865
Midterm test  April 16th, 2021
Lecture 15, April 23rd, 2021 Circuits for arithmetic operations. Pipeline of arithmetic operations. Circuit evaluation: delay and area.
Lecture15  Computer arithmetic
Lecture 16, April 28th, 2021 Representations for Fast Arithmetic. Redundant number representations for carryfree addition. Modified Signed Digit (MSB) and Redundant Binary. Lecture16  Representations for Fast Arithmetic  Slides 131
Lecture 17, April 30th, 2021 Representations for Fast Arithmetic: Residue number system. Lecture17  Representations for Fast Arithmetic  Slides 3255
Lecture 18, May 5th, 2021 SIMD class: vector architecture. Lecture 18  Vector Architectures
Lecture 19, May 7th, 2021 Graphics Processing Units. Matrix multiplication on GPUs. Lecture19  GPUs
Lecture 20, May 12th, 2021 Interconnection networks. Lecture 20  Interconnection networks  Slides 1  39 Lecture 21, May 14th, 2021 Interconnection networks: Equivalence of log N stage and (2log N 1) stage MINs; alltoall personalized communication on log N stage and (2log N 1) stage MINs  Lecture 20  Interconnection networks  Slides 40  102
Lecture 22, May 19th, 2021 Exercises on Interconnection networks and GPUs.
Lecture 23, May 21st, 2021 Performance evaluation of computer architectures. Amdahl law. Performance equation. Lesson 23  Performance
Lecture 24, May 26st, 2021 Exercises on GPUs, Amdahl law, and Performance equation. Discussion on Projects and Homework.
Some papers proposed for past exam projects  Articoli proposti per esami passati

Past year lectures

Exam
The exam consists of two parts:
There will also be homework assignments. Homeworks will contribute to the final grade.
Text of exams
Grades

Textbooks  Testi di riferimento

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