extended lattice based memory allocation
play

Extended Lattice-Based Memory Allocation Alain Darte Tomofumi Yuki - PowerPoint PPT Presentation

Apr 28, 2023 •358 likes •845 views

Extended Lattice-Based Memory Allocation Alain Darte Tomofumi Yuki Alexandre Isoard Laboratoire de lInformatique du Paralllisme Lyon, France 25th International Conference on Compiler Construction March 1718, 2016 Barcelona Spain A.

  1. Extended Lattice-Based Memory Allocation Alain Darte Tomofumi Yuki Alexandre Isoard Laboratoire de l’Informatique du Parallélisme Lyon, France 25th International Conference on Compiler Construction March 17–18, 2016 Barcelona Spain A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 1 / 20

  2. Motivation We want to automatically find compact memory allocations. Because: domain specific languages (DSL) abstract away memory allocation: ◮ Alpha ◮ Single Assignment C ◮ . . . array expansion increases parallelism but also memory footprint ◮ Parallelizing/optimizing compilers useful for programming memory hierarchy ◮ Kernel offloading to GPU ◮ High level synthesis for FPGA ◮ Flat-mode of Xeon Phi A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 2 / 20

  3. Static intra-array optimization Principle: Reuse memory locations (values without overlapping lifetimes) Reuse within a given array (element wise) Reduce memory of temporary arrays Static optimization (at compile time) for ( int t = 0; t < n-1; ++t) for ( int i = 0; i < n; ++i) A[t+1][i] = f(A[t][i-1], A[t][i], A[t][i+1]); Uses n 2 storage. for ( int t = 0; t < n-1; ++t) for ( int i = 0; i < n; ++i) A[(t+1)%2][i] = f(A[t%2][i-1], A[t%2][i], A[t%2][i+1]); Uses 2 n storage. A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 3 / 20

  4. Static intra-array optimization Principle: Reuse memory locations (values without overlapping lifetimes) Reuse within a given array (element wise) Reduce memory of temporary arrays Static optimization (at compile time) for ( int t = 0; t < n-1; ++t) for ( int i = 0; i < n; ++i) A[t+1][i] = f(A[t][i-1], A[t][i], A[t][i+1]); Uses n 2 storage. for ( int t = 0; t < n-1; ++t) for ( int i = 0; i < n; ++i) int x = i-t; int b = n+1; A[x%b] = f(A[x%b], A[(x+1)%b], A[(x+2)%b]); Uses n + 1 storage! A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 3 / 20

  5. History: shift in approach Schedule-based approaches: Wilde & Rajopadhye (1996) De Greef, Cathoor & al. (1997) Lefebvre-Feautrier (1998) Quilleré & Rajopadhye (2000) Thies, Amarasinghe, & al. (2007) Separation of concerns (live-range conflict vs. modular mapping search) Universal Occupancy Vectors, Strout & al. (1998) Lattice-based, Darte & al. (2005) SMO, Bhaskaracharya & al. (2015) Extended Lattice-based, Darte & al. (this paper) A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 4 / 20

  6. Our contribution Basis selection heuristic driven by reuse vectors Provides: Support for wide range of languages (cf. our paper at IMPACT’16) Method to optimize mapping for size Natural treatment of non-convex union of polyhedra Parametric analysis and parametric modular mapping Simple to use (only requires conflict difference set) Scope: Intra-array optimization ☛ Inter-array? Size focused ☛ Locality? Affine mapping ☛ Redundant storage, live-range splitting? A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 5 / 20

  7. Successive modulo for ( int t = 0; t < n; ++t) for ( int i = 0; i < n; ++i) A[t][i] = A[t-1][i-1] + A[t-1][i] + A[t-1][i+1]; i Canonical basis: (Lefebvre-Feautrier) A[t][i] �→ A[t % 2][i % n] t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 6 / 20

  8. Successive modulo for ( int t = 0; t < n; ++t) for ( int i = 0; i < n; ++i) A[t][i] = A[t-1][i-1] + A[t-1][i] + A[t-1][i+1]; i Canonical basis: (Lefebvre-Feautrier) A[t][i] �→ A[t % 2][i % n] t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 6 / 20

  9. Successive modulo for ( int t = 0; t < n; ++t) for ( int i = 0; i < n; ++i) A[t][i] = A[t-1][i-1] + A[t-1][i] + A[t-1][i+1]; i Canonical basis: (Lefebvre-Feautrier) A[t][i] �→ A[t % 2][i % n] t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 6 / 20

  10. Successive modulo for ( int t = 0; t < n; ++t) for ( int i = 0; i < n; ++i) A[t][i] = A[t-1][i-1] + A[t-1][i] + A[t-1][i+1]; i Canonical basis: (Lefebvre-Feautrier) A[t][i] �→ A[t % 2][i % n] Skewed basis: A[t][i] �→ A[(i-t) % (n+1)] t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 6 / 20

  11. Successive modulo for ( int t = 0; t < n; ++t) for ( int i = 0; i < n; ++i) A[t][i] = A[t-1][i-1] + A[t-1][i] + A[t-1][i+1]; i Canonical basis: (Lefebvre-Feautrier) A[t][i] �→ A[t % 2][i % n] Skewed basis: A[t][i] �→ A[(i-t) % (n+1)] t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 6 / 20

  12. Tiling case We usually get this kind of conflicts (live-out set) after tiling: i t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 7 / 20

  13. Tiling case We usually get this kind of conflicts (live-out set) after tiling: i Canonical basis: t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 7 / 20

  14. Tiling case We usually get this kind of conflicts (live-out set) after tiling: i Canonical basis: A[t][i] �→ A[t % n][i % n] t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 7 / 20

  15. Tiling case We usually get this kind of conflicts (live-out set) after tiling: i Canonical basis: A[t][i] �→ A[t % n][i % n] Skewed basis: t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 7 / 20

  16. Tiling case We usually get this kind of conflicts (live-out set) after tiling: i Canonical basis: A[t][i] �→ A[t % n][i % n] Skewed basis: A[t][i] �→ A[(i-t) % (2n-1)] t Bhaskaracharya & al.: Looks for hyperplanes interecting at most one point A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 7 / 20

  17. Tiling in general (with longer dependences) We also get this kind of conflicts (live-out set) after tiling: i t Bhaskaracharya & al.: Looks for hyperplanes interecting at most one point A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 8 / 20

  18. Tiling in general (with longer dependences) We also get this kind of conflicts (live-out set) after tiling: i Bhaskaracharya & al. basis: A[t][i] �→ A[(i-2t) % (5n-4)] t Bhaskaracharya & al.: Looks for hyperplanes interecting at most one point A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 8 / 20

  19. Tiling in general (with longer dependences) We also get this kind of conflicts (live-out set) after tiling: i Bhaskaracharya & al. basis: A[t][i] �→ A[(i-2t) % (5n-4)] Best basis: A[t][i] �→ A[t%2][(i-t)%(2n-1)] t Bhaskaracharya & al.: Looks for hyperplanes interecting at most one point Ours: Finds the basis that minimizes reuse distance A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 8 / 20

  20. Running example i for ( int t = 0; t < n; ++t) for ( int i = 0; i < n; ++i) A[t][i] = A[t-1][i-1] + A[t-1][i] + A[t-1][i+1] + A[t-2][i]; ֒ → t A[t][i] �→ A[t%2][i] A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 9 / 20

  21. Running example (skewed) i for ( int t = 0; t < n; ++t) for ( int i = t; i < n+t; ++i) int j = i-t; A[t][j] = A[t-1][j-1] + A[t-1][j] + A[t-1][j+1] + A[t-2][j]; ֒ → t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 10 / 20

  22. Running example (tiled) i t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 11 / 20

  23. Running example (tiled) i t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 11 / 20

  24. Running example (tiled) i t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 11 / 20

  25. Conflict set to conflict differences (visualization) δ i i δ t t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 12 / 20

  26. Running example (successive modulo) δ i Canonical basis: � � � � 1 0 � x mod 0 1 m 0 δ t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 13 / 20

  27. Running example (successive modulo) δ i Canonical basis: � � � � 1 0 n � x mod 0 1 n − 1 m 0 δ t A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 13 / 20

  28. Running example (successive modulo) δ i Canonical basis: � � � � 1 0 n � x mod 0 1 n − 1 m 0 δ t slice A. Darte, A. Isoard, T. Yuki (LIP, Lyon) Extended Lattice-Based Memory Allocation Compiler Construction 2016 13 / 20

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

CSE 351: Section 10 Memory Allocation Memory Allocation Must allocate any memory you need to

CSE 351: Section 10 Memory Allocation Memory Allocation Must allocate any memory you need to

CSE 351: Section 10 Memory Allocation Memory Allocation Must allocate any memory you need to use Allocating memory = designating a block of it as 'used' This way, you don't overwrite your data The memory isn't changed, but

417 views • 15 slides
Dynamic Memory Allocation Today Dynamic memory allocation mechanisms &amp; policies

Dynamic Memory Allocation Today Dynamic memory allocation mechanisms &amp; policies

Dynamic Memory Allocation Today Dynamic memory allocation mechanisms &amp; policies Memory bugs Chris Riesbeck, Spring 2010 Original: Fabian Bustamante Wednesday, November 2, 2011 Dynamic memory allocation Application Dynamic

1.2k views • 47 slides
Memory Management 5A. Memory Management and Address Spaces 5B. Allocation Algorithms Operating

Memory Management 5A. Memory Management and Address Spaces 5B. Allocation Algorithms Operating

4/10/2016 Memory Management 5A. Memory Management and Address Spaces 5B. Allocation Algorithms Operating Systems Principles 5C. Advanced Allocation Techniques Memory Management 5D. Segment Relocation 5E. Garbage Collection Mark Kampe

711 views • 9 slides
Automatic Memory Management Storage Allocation Static Allocation Bind names at compile

Automatic Memory Management Storage Allocation Static Allocation Bind names at compile

Automatic Memory Management Storage Allocation Static Allocation Bind names at compile time Pros: Fast (no run time allocation, no indirection) Safety : memory requirements known in advance Cons: Sizes must be

417 views • 14 slides
1 Allocation Example Assumptions Made in These Slides Memory is word addressed. p1 =

1 Allocation Example Assumptions Made in These Slides Memory is word addressed. p1 =

Today Basic concepts Dynamic Memory Allocation: Performance concerns Approach 1: implicit free lists Basic Concepts CSci 2021: Machine Architecture and Organization April 24th-27th, 2020 Your instructor: Stephen McCamant Based on

603 views • 6 slides
Dynamic Memory Allocation Lecture 14 COP 3014 Spring 2018 April 4, 2018 Allocating memory

Dynamic Memory Allocation Lecture 14 COP 3014 Spring 2018 April 4, 2018 Allocating memory

Dynamic Memory Allocation Lecture 14 COP 3014 Spring 2018 April 4, 2018 Allocating memory There are two ways that memory gets allocated for data storage: 1. Compile Time (or static) Allocation Memory for named variables is allocated by the

783 views • 10 slides
Dynamic Memory Allocation Lecture 14 COP 3014 Fall 2019 November 20, 2019 Allocating memory

Dynamic Memory Allocation Lecture 14 COP 3014 Fall 2019 November 20, 2019 Allocating memory

Dynamic Memory Allocation Lecture 14 COP 3014 Fall 2019 November 20, 2019 Allocating memory There are two ways that memory gets allocated for data storage: 1. Compile Time (or static) Allocation Memory for named variables is allocated by

987 views • 10 slides
Dynamic Memory Allocation Lecture 27 COP 3014 Spring 2017 March 23, 2017 Allocating memory

Dynamic Memory Allocation Lecture 27 COP 3014 Spring 2017 March 23, 2017 Allocating memory

Dynamic Memory Allocation Lecture 27 COP 3014 Spring 2017 March 23, 2017 Allocating memory There are two ways that memory gets allocated for data storage: 1. Compile Time (or static) Allocation Memory for named variables is allocated by

340 views • 10 slides
Dynamic Memory Allocation in the Heap (malloc and free) Explicit allocators (a.k.a. manual memory

Dynamic Memory Allocation in the Heap (malloc and free) Explicit allocators (a.k.a. manual memory

Dynamic Memory Allocation in the Heap (malloc and free) Explicit allocators (a.k.a. manual memory management) Heap Allocation Addr Perm Contents Managed by Initialized Stack 2 N -1 RW Procedure context Compiler Run-time Programmer,

565 views • 31 slides
Memory: Hardware and Allocation Summer 2011 Cornell University 1 Today How the memory is

Memory: Hardware and Allocation Summer 2011 Cornell University 1 Today How the memory is

CS 4410 Operating Systems Memory: Hardware and Allocation Summer 2011 Cornell University 1 Today How the memory is shared among the ready processes? Memory Address protection Logical vs Physical Address Contiguous memory

321 views • 17 slides
Memory Allocation Nima Honarmand (Based on slides by Don Porter and Mike Ferdman) Fall 2014 ::

Memory Allocation Nima Honarmand (Based on slides by Don Porter and Mike Ferdman) Fall 2014 ::

Fall 2014 :: CSE 506 :: Section 2 (PhD) Memory Allocation Nima Honarmand (Based on slides by Don Porter and Mike Ferdman) Fall 2014 :: CSE 506 :: Section 2 (PhD) Lecture goal Understand how memory allocators work In both kernel and

508 views • 22 slides
Memory Management Guest lecture by Junfeng Yang Outline Dynamic memory allocation Stack

Memory Management Guest lecture by Junfeng Yang Outline Dynamic memory allocation Stack

COMS 3995: Networks, Operating Systems and Security Memory Management Guest lecture by Junfeng Yang Outline Dynamic memory allocation Stack Heap Heap allocation strategies Intro to memory management Paging 1 Dynamic

770 views • 43 slides
Manual Allocation Dynamic memory allocation is an obvious necessity in a programming environment.

Manual Allocation Dynamic memory allocation is an obvious necessity in a programming environment.

11/26/2012 Manual Allocation Dynamic memory allocation is an obvious necessity in a programming environment. CS 1622: Many programming languages expose some functions or keywords to manage runtime allocations: C: malloc/free Garbage

406 views • 6 slides
Detecting and Eliminating Memory Leaks Using Cyclic Memory Allocation Huu Hai Nguyen and Martin

Detecting and Eliminating Memory Leaks Using Cyclic Memory Allocation Huu Hai Nguyen and Martin

Introduction Implementation Experiments Conclusion Detecting and Eliminating Memory Leaks Using Cyclic Memory Allocation Huu Hai Nguyen and Martin Rinard Massachusetts Institute of Technology presented by: Hannes Payer Computational Systems

224 views • 20 slides
Memory Allocation Memory What is memory? Storage for variables, data, code etc. How is

Memory Allocation Memory What is memory? Storage for variables, data, code etc. How is

Memory Allocation Memory What is memory? Storage for variables, data, code etc. How is memory organized? Text Text (Code) Data Data (Constants) BSS BSS (Global and static variables) Heap Stack (Local variables)

597 views • 25 slides
Vector and Free Store (Pointers and Memory Allocation) Marco Chiarandini Department of

Vector and Free Store (Pointers and Memory Allocation) Marco Chiarandini Department of

DM560 Introduction to Programming in C++ Vector and Free Store (Pointers and Memory Allocation) Marco Chiarandini Department of Mathematics &amp; Computer Science University of Southern Denmark [ Based on slides by Bjarne Stroustrup ] Outline

1.42k views • 39 slides
Nominal Exchange Rate Variability, Nominal Wage Rigidity, and the Pattern of Trade ISHISE,

Nominal Exchange Rate Variability, Nominal Wage Rigidity, and the Pattern of Trade ISHISE,

Nominal Exchange Rate Variability, Nominal Wage Rigidity, and the Pattern of Trade ISHISE, Hirokazu ishise@osipp.osaka-u.ac.jp Osaka School of International Public Policy Osaka University Dec 2019 Exchange rate &amp; trade pattern Hiro

587 views • 57 slides
k =0 structures (Type I or III MSG symmetry). The most interesting ones for magneto-structural

k =0 structures (Type I or III MSG symmetry). The most interesting ones for magneto-structural

MAGNDATA: A collection/database of magnetic structures using symmetry and portable CIF-type files Bilbao : Samuel V. Gallego, J. Manuel Perez-Mato, L. Elcoro, Mois I. Aroyo, G. Madariaga Ankara: Emre S. Tasci Tsukuba: Koichi Momma

697 views • 40 slides
Simula and Smalltalk First object-oriented language Designed for simulation Later

Simula and Smalltalk First object-oriented language Designed for simulation Later

CS 242 Simula 67 Simula and Smalltalk First object-oriented language Designed for simulation Later recognized as general-purpose prog language Extension of Algol 60 John Mitchell Standardized as Simula (no 67) in 1977

405 views • 6 slides
Linear Algebra Chapter 2. Dimension, Rank, and Linear Transformations Section 2.5. Lines, Planes,

Linear Algebra Chapter 2. Dimension, Rank, and Linear Transformations Section 2.5. Lines, Planes,

Linear Algebra Chapter 2. Dimension, Rank, and Linear Transformations Section 2.5. Lines, Planes, and Other FlatsProofs of Theorems June 20, 2019 () Linear Algebra June 20, 2019 1 / 11 Table of contents Page 176 Number 8 1 Page 176

347 views • 30 slides
Machine Learning for NLP Supervised Learning Aurlie Herbelot 2019 Centre for Mind/Brain

Machine Learning for NLP Supervised Learning Aurlie Herbelot 2019 Centre for Mind/Brain

Machine Learning for NLP Supervised Learning Aurlie Herbelot 2019 Centre for Mind/Brain Sciences University of Trento 1 Supervised learning Supervised: you know the result of the task you want to perform. Supervised learning mostly

832 views • 61 slides
Investigation of OM/OC Using Ambient Measurements CMAS 2009 Conference Heather Simon, Prakash

Investigation of OM/OC Using Ambient Measurements CMAS 2009 Conference Heather Simon, Prakash

Investigation of OM/OC Using Ambient Measurements CMAS 2009 Conference Heather Simon, Prakash Bhave, Jenise Swall, and Neil Frank Photo image area measures 2 H x 6.93 W and can be masked by a collage strip of one, two or three images.

469 views • 27 slides
Low Cost 3D Rotational Input Devices: the Stationary Spinball and the Stationary Spinball and

Low Cost 3D Rotational Input Devices: the Stationary Spinball and the Stationary Spinball and

Low Cost 3D Rotational Input Devices: the Stationary Spinball and the Stationary Spinball and the Mobile Soap3D Marcus Tnnis, Florian Echtler, Manuel Huber, Gudrun Klinker Fachgebiet Augmented Reality T Technische Universitt Mnchen,

660 views • 21 slides
Causal inference Part II: Difference In Difference and Instrumental Variables Difference in

Causal inference Part II: Difference In Difference and Instrumental Variables Difference in

Causal inference Part II: Difference In Difference and Instrumental Variables Difference in difference Card &amp; Krueger (1995,AER) Rise in minimum wage from 4,2$ to 5,05$ in April 1992 in the State of New Jersey. Research question:

405 views • 28 slides

More recommend