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

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
Last class: Memory Management Today: Paging Memory Management Basics Allocation

Last class: Memory Management Today: Paging Memory Management Basics Allocation

Last class: Memory Management Today: Paging Memory Management Basics Allocation Previously Allocate arbitrary-sized chunks (e.g., in old days, a process; now the heap) Challenges Fragmentation and performance

360 views • 31 slides
Project 1: -allocator Computation structures October 9, 2018 Memory allocation Static

Project 1: -allocator Computation structures October 9, 2018 Memory allocation Static

Project 1: -allocator Computation structures October 9, 2018 Memory allocation Static allocation : size must be known at compile-time, handled by compilers in high-level languages. In -assembly: | static allocation on the stack |

261 views • 9 slides
Effiziente Programmierung in c Dynamic Memory Allocation A presentation from : Marcel Ellermann

Effiziente Programmierung in c Dynamic Memory Allocation A presentation from : Marcel Ellermann

Effiziente Programmierung in c Dynamic Memory Allocation A presentation from : Marcel Ellermann Seminar Effizientes Programmieren in C Dynamic Memory Allocation Marcel Ellermann 1 Agenda Introduction to Memory Management

582 views • 34 slides
Dynamic Memory Allocation in the Heap (malloc and free) Now: Explicit allocators (a.k.a. manual

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

Dynamic Memory Allocation in the Heap (malloc and free) Now: Explicit allocators (a.k.a. manual memory management) Later: implicit allocators (a.k.a. automatic memory management) Heap Allocation Addr Perm Contents Managed by Initialized

420 views • 31 slides
Lattice-based Signcryption without Random Oracles

Lattice-based Signcryption without Random Oracles

Lattice-based Signcryption without Random Oracles Junji Shikata Graduate School of Environment and Information Sciences, Yokohama National University, Japan Overview Lattice-based Cryptography

277 views • 26 slides
A Dynamic Memory Allocation Library for High-Level Synthesis Nicholas V. Giamblanco and Jason H.

A Dynamic Memory Allocation Library for High-Level Synthesis Nicholas V. Giamblanco and Jason H.

A Dynamic Memory Allocation Library for High-Level Synthesis Nicholas V. Giamblanco and Jason H. Anderson University of Toronto, Canada Dept. of Electrical and Computer Engineering FPL 2019 Dynamic Memory Allocation in HLS: Current Problems

1.2k views • 13 slides
A History of Lattice-Based Encryption (in order of increasing efficiency) Vadim Lyubashevsky

A History of Lattice-Based Encryption (in order of increasing efficiency) Vadim Lyubashevsky

A History of Lattice-Based Encryption (in order of increasing efficiency) Vadim Lyubashevsky INRIA / ENS, Paris Lattice-Based Crypto &amp; Applications 1 Bar-Ilan University, Israel 2012 Lattice-Based Encryption Schemes 1. NTRU [Hoffstein,

849 views • 47 slides
Lists Intro A list is a data structure based on usage of pointers and dynamic allocation of

Lists Intro A list is a data structure based on usage of pointers and dynamic allocation of

Advanced Programming Lists Lists Intro A list is a data structure based on usage of pointers and dynamic allocation of memory. With respect to other ADT (like arrays), a list: provides more flexibility in memory usage but it is less

450 views • 14 slides

More recommend