Relational Verification Using Product Programs
Total Page:16
File Type:pdf, Size:1020Kb

Load more
Recommended publications
-
CSE 582 – Compilers
CSE P 501 – Compilers Optimizing Transformations Hal Perkins Autumn 2011 11/8/2011 © 2002-11 Hal Perkins & UW CSE S-1 Agenda A sampler of typical optimizing transformations Mostly a teaser for later, particularly once we’ve looked at analyzing loops 11/8/2011 © 2002-11 Hal Perkins & UW CSE S-2 Role of Transformations Data-flow analysis discovers opportunities for code improvement Compiler must rewrite the code (IR) to realize these improvements A transformation may reveal additional opportunities for further analysis & transformation May also block opportunities by obscuring information 11/8/2011 © 2002-11 Hal Perkins & UW CSE S-3 Organizing Transformations in a Compiler Typically middle end consists of many individual transformations that filter the IR and produce rewritten IR No formal theory for order to apply them Some rules of thumb and best practices Some transformations can be profitably applied repeatedly, particularly if others transformations expose more opportunities 11/8/2011 © 2002-11 Hal Perkins & UW CSE S-4 A Taxonomy Machine Independent Transformations Realized profitability may actually depend on machine architecture, but are typically implemented without considering this Machine Dependent Transformations Most of the machine dependent code is in instruction selection & scheduling and register allocation Some machine dependent code belongs in the optimizer 11/8/2011 © 2002-11 Hal Perkins & UW CSE S-5 Machine Independent Transformations Dead code elimination Code motion Specialization Strength reduction -
ICS803 Elective – III Multicore Architecture Teacher Name: Ms
ICS803 Elective – III Multicore Architecture Teacher Name: Ms. Raksha Pandey Course Structure L T P 3 1 0 4 Prerequisite: Course Content: Unit-I: Multi-core Architectures Introduction to multi-core architectures, issues involved into writing code for multi-core architectures, Virtual Memory, VM addressing, VA to PA translation, Page fault, TLB- Parallel computers, Instruction level parallelism (ILP) vs. thread level parallelism (TLP), Performance issues, OpenMP and other message passing libraries, threads, mutex etc. Unit-II: Multi-threaded Architectures Brief introduction to cache hierarchy - Caches: Addressing a Cache, Cache Hierarchy, States of Cache line, Inclusion policy, TLB access, Memory Op latency, MLP, Memory Wall, communication latency, Shared memory multiprocessors, General architectures and the problem of cache coherence, Synchronization primitives: Atomic primitives; locks: TTS, ticket, array; barriers: central and tree; performance implications in shared memory programs; Chip multiprocessors: Why CMP (Moore's law, wire delay); shared L2 vs. tiled CMP; core complexity; power/performance; Snoopy coherence: invalidate vs. update, MSI, MESI, MOESI, MOSI; performance trade-offs; pipelined snoopy bus design; Memory consistency models: SC, PC, TSO, PSO, WO/WC, RC; Chip multiprocessor case studies: Intel Montecito and dual-core, Pentium4, IBM Power4, Sun Niagara Unit-III: Compiler Optimization Issues Code optimizations: Copy Propagation, dead Code elimination , Loop Optimizations-Loop Unrolling, Induction variable Simplification, Loop Jamming, Loop Unswitching, Techniques to improve detection of parallelism: Scalar Processors, Special locality, Temporal locality, Vector machine, Strip mining, Shared memory model, SIMD architecture, Dopar loop, Dosingle loop. Unit-IV: Control Flow analysis Control flow analysis, Flow graph, Loops in Flow graphs, Loop Detection, Approaches to Control Flow Analysis, Reducible Flow Graphs, Node Splitting. -
CS153: Compilers Lecture 19: Optimization
CS153: Compilers Lecture 19: Optimization Stephen Chong https://www.seas.harvard.edu/courses/cs153 Contains content from lecture notes by Steve Zdancewic and Greg Morrisett Announcements •HW5: Oat v.2 out •Due in 2 weeks •HW6 will be released next week •Implementing optimizations! (and more) Stephen Chong, Harvard University 2 Today •Optimizations •Safety •Constant folding •Algebraic simplification • Strength reduction •Constant propagation •Copy propagation •Dead code elimination •Inlining and specialization • Recursive function inlining •Tail call elimination •Common subexpression elimination Stephen Chong, Harvard University 3 Optimizations •The code generated by our OAT compiler so far is pretty inefficient. •Lots of redundant moves. •Lots of unnecessary arithmetic instructions. •Consider this OAT program: int foo(int w) { var x = 3 + 5; var y = x * w; var z = y - 0; return z * 4; } Stephen Chong, Harvard University 4 Unoptimized vs. Optimized Output .globl _foo _foo: •Hand optimized code: pushl %ebp movl %esp, %ebp _foo: subl $64, %esp shlq $5, %rdi __fresh2: movq %rdi, %rax leal -64(%ebp), %eax ret movl %eax, -48(%ebp) movl 8(%ebp), %eax •Function foo may be movl %eax, %ecx movl -48(%ebp), %eax inlined by the compiler, movl %ecx, (%eax) movl $3, %eax so it can be implemented movl %eax, -44(%ebp) movl $5, %eax by just one instruction! movl %eax, %ecx addl %ecx, -44(%ebp) leal -60(%ebp), %eax movl %eax, -40(%ebp) movl -44(%ebp), %eax Stephen Chong,movl Harvard %eax,University %ecx 5 Why do we need optimizations? •To help programmers… •They write modular, clean, high-level programs •Compiler generates efficient, high-performance assembly •Programmers don’t write optimal code •High-level languages make avoiding redundant computation inconvenient or impossible •e.g. -
Fast-Path Loop Unrolling of Non-Counted Loops to Enable Subsequent Compiler Optimizations∗
Fast-Path Loop Unrolling of Non-Counted Loops to Enable Subsequent Compiler Optimizations∗ David Leopoldseder Roland Schatz Lukas Stadler Johannes Kepler University Linz Oracle Labs Oracle Labs Austria Linz, Austria Linz, Austria [email protected] [email protected] [email protected] Manuel Rigger Thomas Würthinger Hanspeter Mössenböck Johannes Kepler University Linz Oracle Labs Johannes Kepler University Linz Austria Zurich, Switzerland Austria [email protected] [email protected] [email protected] ABSTRACT Non-Counted Loops to Enable Subsequent Compiler Optimizations. In 15th Java programs can contain non-counted loops, that is, loops for International Conference on Managed Languages & Runtimes (ManLang’18), September 12–14, 2018, Linz, Austria. ACM, New York, NY, USA, 13 pages. which the iteration count can neither be determined at compile https://doi.org/10.1145/3237009.3237013 time nor at run time. State-of-the-art compilers do not aggressively optimize them, since unrolling non-counted loops often involves 1 INTRODUCTION duplicating also a loop’s exit condition, which thus only improves run-time performance if subsequent compiler optimizations can Generating fast machine code for loops depends on a selective appli- optimize the unrolled code. cation of different loop optimizations on the main optimizable parts This paper presents an unrolling approach for non-counted loops of a loop: the loop’s exit condition(s), the back edges and the loop that uses simulation at run time to determine whether unrolling body. All these parts must be optimized to generate optimal code such loops enables subsequent compiler optimizations. Simulat- for a loop. -
Compiler Optimization for Configurable Accelerators Betul Buyukkurt Zhi Guo Walid A
Compiler Optimization for Configurable Accelerators Betul Buyukkurt Zhi Guo Walid A. Najjar University of California Riverside University of California Riverside University of California Riverside Computer Science Department Electrical Engineering Department Computer Science Department Riverside, CA 92521 Riverside, CA 92521 Riverside, CA 92521 [email protected] [email protected] [email protected] ABSTRACT such as constant propagation, constant folding, dead code ROCCC (Riverside Optimizing Configurable Computing eliminations that enables other optimizations. Then, loop Compiler) is an optimizing C to HDL compiler targeting level optimizations such as loop unrolling, loop invariant FPGA and CSOC (Configurable System On a Chip) code motion, loop fusion and other such transforms are architectures. ROCCC system is built on the SUIF- applied. MACHSUIF compiler infrastructure. Our system first This paper is organized as follows. Next section discusses identifies frequently executed kernel loops inside programs on the related work. Section 3 gives an in depth description and then compiles them to VHDL after optimizing the of the ROCCC system. SUIF2 level optimizations are kernels to make best use of FPGA resources. This paper described in Section 4 followed by the compilation done at presents an overview of the ROCCC project as well as the MACHSUIF level in Section 5. Section 6 mentions our optimizations performed inside the ROCCC compiler. early results. Finally Section 7 concludes the paper. 1. INTRODUCTION 2. RELATED WORK FPGAs (Field Programmable Gate Array) can boost There are several projects and publications on translating C software performance due to the large amount of or other high level languages to different HDLs. Streams- parallelism they offer. -
Strength Reduction of Induction Variables and Pointer Analysis – Induction Variable Elimination
Loop optimizations • Optimize loops – Loop invariant code motion [last time] Loop Optimizations – Strength reduction of induction variables and Pointer Analysis – Induction variable elimination CS 412/413 Spring 2008 Introduction to Compilers 1 CS 412/413 Spring 2008 Introduction to Compilers 2 Strength Reduction Induction Variables • Basic idea: replace expensive operations (multiplications) with • An induction variable is a variable in a loop, cheaper ones (additions) in definitions of induction variables whose value is a function of the loop iteration s = 3*i+1; number v = f(i) while (i<10) { while (i<10) { j = 3*i+1; //<i,3,1> j = s; • In compilers, this a linear function: a[j] = a[j] –2; a[j] = a[j] –2; i = i+2; i = i+2; f(i) = c*i + d } s= s+6; } •Observation:linear combinations of linear • Benefit: cheaper to compute s = s+6 than j = 3*i functions are linear functions – s = s+6 requires an addition – Consequence: linear combinations of induction – j = 3*i requires a multiplication variables are induction variables CS 412/413 Spring 2008 Introduction to Compilers 3 CS 412/413 Spring 2008 Introduction to Compilers 4 1 Families of Induction Variables Representation • Basic induction variable: a variable whose only definition in the • Representation of induction variables in family i by triples: loop body is of the form – Denote basic induction variable i by <i, 1, 0> i = i + c – Denote induction variable k=i*a+b by triple <i, a, b> where c is a loop-invariant value • Derived induction variables: Each basic induction variable i defines -
Lecture Notes on Peephole Optimizations and Common Subexpression Elimination
Lecture Notes on Peephole Optimizations and Common Subexpression Elimination 15-411: Compiler Design Frank Pfenning and Jan Hoffmann Lecture 18 October 31, 2017 1 Introduction In this lecture, we discuss common subexpression elimination and a class of optimiza- tions that is called peephole optimizations. The idea of common subexpression elimination is to avoid to perform the same operation twice by replacing (binary) operations with variables. To ensure that these substitutions are sound we intro- duce dominance, which ensures that substituted variables are always defined. Peephole optimizations are optimizations that are performed locally on a small number of instructions. The name is inspired from the picture that we look at the code through a peephole and make optimization that only involve the small amount code we can see and that are indented of the rest of the program. There is a large number of possible peephole optimizations. The LLVM com- piler implements for example more than 1000 peephole optimizations [LMNR15]. In this lecture, we discuss three important and representative peephole optimiza- tions: constant folding, strength reduction, and null sequences. 2 Constant Folding Optimizations have two components: (1) a condition under which they can be ap- plied and the (2) code transformation itself. The optimization of constant folding is a straightforward example of this. The code transformation itself replaces a binary operation with a single constant, and applies whenever c1 c2 is defined. l : x c1 c2 −! l : x c (where c = -
Efficient Symbolic Analysis for Optimizing Compilers*
Efficient Symbolic Analysis for Optimizing Compilers? Robert A. van Engelen Dept. of Computer Science, Florida State University, Tallahassee, FL 32306-4530 [email protected] Abstract. Because most of the execution time of a program is typically spend in loops, loop optimization is the main target of optimizing and re- structuring compilers. An accurate determination of induction variables and dependencies in loops is of paramount importance to many loop opti- mization and parallelization techniques, such as generalized loop strength reduction, loop parallelization by induction variable substitution, and loop-invariant expression elimination. In this paper we present a new method for induction variable recognition. Existing methods are either ad-hoc and not powerful enough to recognize some types of induction variables, or existing methods are powerful but not safe. The most pow- erful method known is the symbolic differencing method as demonstrated by the Parafrase-2 compiler on parallelizing the Perfect Benchmarks(R). However, symbolic differencing is inherently unsafe and a compiler that uses this method may produce incorrectly transformed programs without issuing a warning. In contrast, our method is safe, simpler to implement in a compiler, better adaptable for controlling loop transformations, and recognizes a larger class of induction variables. 1 Introduction It is well known that the optimization and parallelization of scientific applica- tions by restructuring compilers requires extensive analysis of induction vari- ables and dependencies -
Functional Array Programming in Sac
Functional Array Programming in SaC Sven-Bodo Scholz Dept of Computer Science, University of Hertfordshire, United Kingdom [email protected] Abstract. These notes present an introduction into array-based pro- gramming from a functional, i.e., side-effect-free perspective. The first part focuses on promoting arrays as predominant, stateless data structure. This leads to a programming style that favors compo- sitions of generic array operations that manipulate entire arrays over specifications that are made in an element-wise fashion. An algebraicly consistent set of such operations is defined and several examples are given demonstrating the expressiveness of the proposed set of operations. The second part shows how such a set of array operations can be defined within the first-order functional array language SaC.Itdoes not only discuss the language design issues involved but it also tackles implementation issues that are crucial for achieving acceptable runtimes from such genericly specified array operations. 1 Introduction Traditionally, binary lists and algebraic data types are the predominant data structures in functional programming languages. They fit nicely into the frame- work of recursive program specifications, lazy evaluation and demand driven garbage collection. Support for arrays in most languages is confined to a very resricted set of basic functionality similar to that found in imperative languages. Even if some languages do support more advanced specificational means such as array comprehensions, these usualy do not provide the same genericity as can be found in array programming languages such as Apl,J,orNial. Besides these specificational issues, typically, there is also a performance issue. -
Loop Transformations and Parallelization
Loop transformations and parallelization Claude Tadonki LAL/CNRS/IN2P3 University of Paris-Sud [email protected] December 2010 Claude Tadonki Loop transformations and parallelization C. Tadonki – Loop transformations Introduction Most of the time, the most time consuming part of a program is on loops. Thus, loops optimization is critical in high performance computing. Depending on the target architecture, the goal of loops transformations are: improve data reuse and data locality efficient use of memory hierarchy reducing overheads associated with executing loops instructions pipeline maximize parallelism Loop transformations can be performed at different levels by the programmer, the compiler, or specialized tools. At high level, some well known transformations are commonly considered: loop interchange loop (node) splitting loop unswitching loop reversal loop fusion loop inversion loop skewing loop fission loop vectorization loop blocking loop unrolling loop parallelization Claude Tadonki Loop transformations and parallelization C. Tadonki – Loop transformations Dependence analysis Extract and analyze the dependencies of a computation from its polyhedral model is a fundamental step toward loop optimization or scheduling. Definition For a given variable V and given indexes I1, I2, if the computation of X(I1) requires the value of X(I2), then I1 ¡ I2 is called a dependence vector for variable V . Drawing all the dependence vectors within the computation polytope yields the so-called dependencies diagram. Example The dependence vectors are (1; 0); (0; 1); (¡1; 1). Claude Tadonki Loop transformations and parallelization C. Tadonki – Loop transformations Scheduling Definition The computation on the entire domain of a given loop can be performed following any valid schedule.A timing function tV for variable V yields a valid schedule if and only if t(x) > t(x ¡ d); 8d 2 DV ; (1) where DV is the set of all dependence vectors for variable V . -
Code Optimizations Recap Peephole Optimization
7/23/2016 Program Analysis Recap https://www.cse.iitb.ac.in/~karkare/cs618/ • Optimizations Code Optimizations – To improve efficiency of generated executable (time, space, resources …) Amey Karkare – Maintain semantic equivalence Dept of Computer Science and Engg • Two levels IIT Kanpur – Machine Independent Visiting IIT Bombay [email protected] – Machine Dependent [email protected] 2 Peephole Optimization Peephole optimization examples… • target code often contains redundant Redundant loads and stores instructions and suboptimal constructs • Consider the code sequence • examine a short sequence of target instruction (peephole) and replace by a Move R , a shorter or faster sequence 0 Move a, R0 • peephole is a small moving window on the target systems • Instruction 2 can always be removed if it does not have a label. 3 4 1 7/23/2016 Peephole optimization examples… Unreachable code example … Unreachable code constant propagation • Consider following code sequence if 0 <> 1 goto L2 int debug = 0 print debugging information if (debug) { L2: print debugging info } Evaluate boolean expression. Since if condition is always true the code becomes this may be translated as goto L2 if debug == 1 goto L1 goto L2 print debugging information L1: print debugging info L2: L2: The print statement is now unreachable. Therefore, the code Eliminate jumps becomes if debug != 1 goto L2 print debugging information L2: L2: 5 6 Peephole optimization examples… Peephole optimization examples… • flow of control: replace jump over jumps • Strength reduction -
Compiler-Based Code-Improvement Techniques
Compiler-Based Code-Improvement Techniques KEITH D. COOPER, KATHRYN S. MCKINLEY, and LINDA TORCZON Since the earliest days of compilation, code quality has been recognized as an important problem [18]. A rich literature has developed around the issue of improving code quality. This paper surveys one part of that literature: code transformations intended to improve the running time of programs on uniprocessor machines. This paper emphasizes transformations intended to improve code quality rather than analysis methods. We describe analytical techniques and specific data-flow problems to the extent that they are necessary to understand the transformations. Other papers provide excellent summaries of the various sub-fields of program analysis. The paper is structured around a simple taxonomy that classifies transformations based on how they change the code. The taxonomy is populated with example transformations drawn from the literature. Each transformation is described at a depth that facilitates broad understanding; detailed references are provided for deeper study of individual transformations. The taxonomy provides the reader with a framework for thinking about code-improving transformations. It also serves as an organizing principle for the paper. Copyright 1998, all rights reserved. You may copy this article for your personal use in Comp 512. Further reproduction or distribution requires written permission from the authors. 1INTRODUCTION This paper presents an overview of compiler-based methods for improving the run-time behavior of programs — often mislabeled code optimization. These techniques have a long history in the literature. For example, Backus makes it quite clear that code quality was a major concern to the implementors of the first Fortran compilers [18].