DOCSLIB.ORG

Object Flow Integrity

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Object Flow Integrity Session I2: Information Flow CCS’17, October 30-November 3, 2017, Dallas, TX, USA Object Flow Integrity Wenhao Wang Xiaoyang Xu Kevin W. Hamlen [email protected] [email protected] [email protected] The University of Texas at Dallas The University of Texas at Dallas The University of Texas at Dallas ABSTRACT CFI and SFI frameworks work by statically instrumenting control- Object flow integrity (OFI) augments control-flow integrity (CFI) flow transfer instructions in vulnerable software with extra guard and software fault isolation (SFI) protections with secure, first-class code that validates each computed jump destination at runtime. support for binary object exchange across inter-module trust bound- The instrumentation can be performed at compile-time (e.g., [2, 4– aries. This extends both source-aware and source-free CFI and SFI 6, 32, 36, 43–46, 55, 57, 71]) or on sourceless binaries (e.g., [40, 48, 58, technologies to a large class of previously unsupported software: 62, 65, 72–74]). This facility to harden source-free binary software those containing immutable system modules with large, object- is important for securing software in-flight—allowing third parties oriented APIs—which are particularly common in component-based, to secure dynamically procured binary software on-demand in a event-driven consumer software. It also helps to protect these inter- way that is transparent to code producers and consumers—and for module object exchanges against confused deputy-assisted vtable securing the large quantity of software that is closed-source, or that corruption and counterfeit object-oriented programming attacks. incorporates software components (e.g., binary libraries) whose A prototype implementation for Microsoft Component Object source code is unavailable to code consumers. Model demonstrates that OFI is scalable to large interfaces on the While the past decade has witnessed rapid progress toward more order of tens of thousands of methods, and exhibits low overheads of under 1% for some common-case applications. Significant elements powerful, higher performance, and more flexible CFI enforcement of the implementation are synthesized automatically through a strategies, there still remain large classes of consumer software principled design inspired by type-based contracts. to which these technologies are extremely difficult to apply using existing methods. Such limitations often stem from many source- CCS CONCEPTS aware CFI algorithms’ need for full source code for the entire soft- • Security and privacy → Software security engineering; • ware ecosystem (e.g., even for the OS kernel, device drivers, and Software and its engineering → Classes and objects; Incre- complete runtime system) in order to properly analyze application mental compilers; control-flows, or the difficulty of analyzing complex flows common to certain well-entrenched consumer software paradigms, such as KEYWORDS GUI-interactive, event-driven, and component-based software ap- security; control-flow integrity; object-oriented programming; bi- plications. For example, although CFI has been applied successfully nary transformation to some large applications, in our experience no CFI/SFI algorithm published in the literature to date (see §6) successfully preserves and secures the full functionality of Windows Notepad—one of the 1 INTRODUCTION most ubiquitous consumer software products available. Control-flow integrity (CFI) [2] and software fault isolation (SFI) [61] The central problem is a lack of first-class support for archi- secure software against control-flow hijacking attacks by confining tectures in which immutable, trusted software components have its flows to a whitelist of permissible control-flow edges. Theap- huge object-oriented interfaces. Programs like Notepad interact with proach has proven successful against some of the most dangerous, users by displaying windows, monitoring mouse events, and send- cutting-edge attack classes, including return-oriented programming (ROP) [51] and other code-reuse attacks (CRAs) [5]. Attacks in these ing printer commands. At the binary level, this is achieved by calling families typically exploit dataflow vulnerabilities (e.g., buffer over- runtime system API methods that expect binary objects as input. flows) to corrupt code pointers and thereby redirect control to The app-provided binary object contains a virtual method table attacker-chosen program subroutines. By validating each impend- (vtable), whose members are subsequently called by the runtime ing control-flow target at runtime before it is reached, CFI guards system to notify the app of window, mouse, and printer events. The can often thwart these hijackings. call sites that target untrusted code, and that CFI algorithms must instrument, are therefore not exclusively located within the untrusted Permission to make digital or hard copies of all or part of this work for personal or app code classroom use is granted without fee provided that copies are not made or distributed —many are within trusted system libraries that cannot be for profit or commercial advantage and that copies bear this notice and the full citation modified (or sometimes even examined) by the instrumentation on the first page. Copyrights for components of this work owned by others than the process, since they are part of the protected runtime system. author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission Most CFI algorithms demand write-access to all system soft- and/or a fee. Request permissions from [email protected]. ware components that may contain unguarded, computed jumps— CCS’17, October 30 – November 3, 2017, Dallas, TX, USA © 2017 Copyright held by the owner/author(s). Publication rights licensed to Associa- including the OS, all dynamically loaded libraries, and all future tion for Computing Machinery. updates to them—in order to ensure safety. In component-driven ACM ISBN 978-1-4503-4946-8/17/10...$15.00 https://doi.org/10.1145/3133956.3133986 settings, where modules are dynamically procured on-demand via 1 1909 Session I2: Information Flow CCS’17, October 30-November 3, 2017, Dallas, TX, USA a distributed network or cloud, this is often impractical. Unfortu- Untrusted Module 1 h i;:::; h i nately, such settings comprise >98% of the world’s software mar- CoCreateInstance( clsid iid1 , &o1); 2 o !Show(:::); ket,1 including many mission-critical infrastructures that incorpo- 1 Trusted Module rate consumer software components. 3 o1!QueryInterface(hiid2 i, &o2); One approach for coping with this pervasive problem has been to 4 o2!GetOptions(:::); secure objects passed to uninstrumented modules at call sites within 5 o2!Release(); ! the instrumented modules, before the trusted module receives them 6 o1 GetResult(&o3); 7 o !GetDisplayName(:::); (e.g., [57]). But this approach fails when trusted modules retain 3 8 o3!Release(); persistent references to the object, or when their code executes 9 o1!Release(); concurrently with untrusted module code. In these cases, verifying the object at the point of exchange does not prevent the untrusted Listing 1: Code that opens a file-save dialog box module from subsequently modifying the vtable pointer to which the trusted module’s reference points (e.g., as part of a data corrup- of optimizing the performance of the underlying CFI enforcement tion attack). We refer to such attacks as COnfused DEputy-assisted mechanism, deriving suitable control-flow policies for CFI mecha- Counterfeit Object-Oriented Programming (CODE-COOP) attacks, nisms to enforce (cf., [54]), or obtaining accurate native code dis- since they turn recipients of counterfeit objects [54] into confused assemblies without source code (cf., [66]). Our goal is to enhance deputies [31] who unwittingly invoke policy-prohibited code on existing CFI/SFI systems with support for a much larger class of behalf of callers. target application programs and architectures without exacerbating Faced with such difficulties, many CFI systems conservatively any of these challenges, which are the focuses of related works. resort to disallowing untrusted module accesses to trusted, object- In summary, our contributions are as follows: oriented APIs to ensure safety. This confines such approaches to • We introduce a general methodology for safely exchanging architectures with few trusted object-oriented system APIs (e.g., binary objects across inter-module trust boundaries in CFI/SFI- Linux), applications that make little or no use of such APIs (e.g., protected programs without varying trusted module code. benchmark or command-line utilities), or platforms where the ma- • A prototype implementation for Microsoft COM demonstrates jority of the OS can be rewritten (e.g., ChromeOS [57]). The ma- that the approach is feasible for large, complex, object-oriented jority of present-day software architectures that fall outside these APIs on the order of tens of thousands of methods. restrictive parameters have remained unsupported or receive only • A significant portion of the implementation is shown to besyn- incomplete CFI security. thesizable automatically through a novel approach to reflective To bridge this longstanding gap, we introduce object flow integrity C++ programming. (OFI)—a systematic methodology for imbuing CFI and SFI systems • Experimental evaluation indicates that OFI imposes negligi- with first-class support for immutable, trusted
Load more

Recommended publications
  • 7. Control Flow First?
    Copyright (C) R.A. van Engelen, FSU Department of Computer Science, 2000-2004 Ordering Program Execution: What is Done 7. Control Flow First? Overview Categories for specifying ordering in programming languages: Expressions 1. Sequencing: the execution of statements and evaluation of Evaluation order expressions is usually in the order in which they appear in a Assignments program text Structured and unstructured flow constructs 2. Selection (or alternation): a run-time condition determines the Goto's choice among two or more statements or expressions Sequencing 3. Iteration: a statement is repeated a number of times or until a Selection run-time condition is met Iteration and iterators 4. Procedural abstraction: subroutines encapsulate collections of Recursion statements and subroutine calls can be treated as single Nondeterminacy statements 5. Recursion: subroutines which call themselves directly or indirectly to solve a problem, where the problem is typically defined in terms of simpler versions of itself 6. Concurrency: two or more program fragments executed in parallel, either on separate processors or interleaved on a single processor Note: Study Chapter 6 of the textbook except Section 7. Nondeterminacy: the execution order among alternative 6.6.2. constructs is deliberately left unspecified, indicating that any alternative will lead to a correct result Expression Syntax Expression Evaluation Ordering: Precedence An expression consists of and Associativity An atomic object, e.g. number or variable The use of infix, prefix, and postfix notation leads to ambiguity An operator applied to a collection of operands (or as to what is an operand of what arguments) which are expressions Fortran example: a+b*c**d**e/f Common syntactic forms for operators: The choice among alternative evaluation orders depends on Function call notation, e.g.
    [Show full text]
  • A Survey of Hardware-Based Control Flow Integrity (CFI)
    A survey of Hardware-based Control Flow Integrity (CFI) RUAN DE CLERCQ∗ and INGRID VERBAUWHEDE, KU Leuven Control Flow Integrity (CFI) is a computer security technique that detects runtime attacks by monitoring a program’s branching behavior. This work presents a detailed analysis of the security policies enforced by 21 recent hardware-based CFI architectures. The goal is to evaluate the security, limitations, hardware cost, performance, and practicality of using these policies. We show that many architectures are not suitable for widespread adoption, since they have practical issues, such as relying on accurate control flow model (which is difficult to obtain) or they implement policies which provide only limited security. CCS Concepts: • Security and privacy → Hardware-based security protocols; Information flow control; • General and reference → Surveys and overviews; Additional Key Words and Phrases: control-flow integrity, control-flow hijacking, return oriented programming, shadow stack ACM Reference format: Ruan de Clercq and Ingrid Verbauwhede. YYYY. A survey of Hardware-based Control Flow Integrity (CFI). ACM Comput. Surv. V, N, Article A (January YYYY), 27 pages. https://doi.org/10.1145/nnnnnnn.nnnnnnn 1 INTRODUCTION Today, a lot of software is written in memory unsafe languages, such as C and C++, which introduces memory corruption bugs. This makes software vulnerable to attack, since attackers exploit these bugs to make the software misbehave. Modern Operating Systems (OSs) and microprocessors are equipped with security mechanisms to protect against some classes of attacks. However, these mechanisms cannot defend against all attack classes. In particular, Code Reuse Attacks (CRAs), which re-uses pre-existing software for malicious purposes, is an important threat that is difficult to protect against.
    [Show full text]
  • Control-Flow Analysis of Functional Programs
    Control-flow analysis of functional programs JAN MIDTGAARD Department of Computer Science, Aarhus University We present a survey of control-flow analysis of functional programs, which has been the subject of extensive investigation throughout the past 30 years. Analyses of the control flow of functional programs have been formulated in multiple settings and have led to many different approximations, starting with the seminal works of Jones, Shivers, and Sestoft. In this paper, we survey control-flow analysis of functional programs by structuring the multitude of formulations and approximations and comparing them. Categories and Subject Descriptors: D.3.2 [Programming Languages]: Language Classifica- tions—Applicative languages; F.3.1 [Logics and Meanings of Programs]: Specifying and Ver- ifying and Reasoning about Programs General Terms: Languages, Theory, Verification Additional Key Words and Phrases: Control-flow analysis, higher-order functions 1. INTRODUCTION Since the introduction of high-level languages and compilers, much work has been devoted to approximating, at compile time, which values the variables of a given program may denote at run time. The problem has been named data-flow analysis or just flow analysis. In a language without higher-order functions, the operator of a function call is apparent from the text of the program: it is a lexically visible identifier and therefore the called function is available at compile time. One can thus base an analysis for such a language on the textual structure of the program, since it determines the exact control flow of the program, e.g., as a flow chart. On the other hand, in a language with higher-order functions, the operator of a function call may not be apparent from the text of the program: it can be the result of a computation and therefore the called function may not be available until run time.
    [Show full text]
  • Obfuscating C++ Programs Via Control Flow Flattening
    Annales Univ. Sci. Budapest., Sect. Comp. 30 (2009) 3-19 OBFUSCATING C++ PROGRAMS VIA CONTROL FLOW FLATTENING T. L¶aszl¶oand A.¶ Kiss (Szeged, Hungary) Abstract. Protecting a software from unauthorized access is an ever de- manding task. Thus, in this paper, we focus on the protection of source code by means of obfuscation and discuss the adaptation of a control flow transformation technique called control flow flattening to the C++ lan- guage. In addition to the problems of adaptation and the solutions pro- posed for them, a formal algorithm of the technique is given as well. A prototype implementation of the algorithm presents that the complexity of a program can show an increase as high as 5-fold due to the obfuscation. 1. Introduction Protecting a software from unauthorized access is an ever demanding task. Unfortunately, it is impossible to guarantee complete safety, since with enough time given, there is no unbreakable code. Thus, the goal is usually to make the job of the attacker as di±cult as possible. Systems can be protected at several levels, e.g., hardware, operating system or source code. In this paper, we focus on the protection of source code by means of obfuscation. Several code obfuscation techniques exist. Their common feature is that they change programs to make their comprehension di±cult, while keep- ing their original behaviour. The simplest technique is layout transformation [1], which scrambles identi¯ers in the code, removes comments and debug informa- tion. Another technique is data obfuscation [2], which changes data structures, 4 T. L¶aszl¶oand A.¶ Kiss e.g., by changing variable visibilities or by reordering and restructuring arrays.
    [Show full text]
  • Control Flow Statements
    Control Flow Statements Christopher M. Harden Contents 1 Some more types 2 1.1 Undefined and null . .2 1.2 Booleans . .2 1.2.1 Creating boolean values . .3 1.2.2 Combining boolean values . .4 2 Conditional statements 5 2.1 if statement . .5 2.1.1 Using blocks . .5 2.2 else statement . .6 2.3 Tertiary operator . .7 2.4 switch statement . .8 3 Looping constructs 10 3.1 while loop . 10 3.2 do while loop . 11 3.3 for loop . 11 3.4 Further loop control . 12 4 Try it yourself 13 1 1 Some more types 1.1 Undefined and null The undefined type has only one value, undefined. Similarly, the null type has only one value, null. Since both types have only one value, there are no operators on these types. These types exist to represent the absence of data, and their difference is only in intent. • undefined represents data that is accidentally missing. • null represents data that is intentionally missing. In general, null is to be used over undefined in your scripts. undefined is given to you by the JavaScript interpreter in certain situations, and it is useful to be able to notice these situations when they appear. Listing 1 shows the difference between the two. Listing 1: Undefined and Null 1 var name; 2 // Will say"Hello undefined" 3 a l e r t( "Hello" + name); 4 5 name= prompt( "Do not answer this question" ); 6 // Will say"Hello null" 7 a l e r t( "Hello" + name); 1.2 Booleans The Boolean type has two values, true and false.
    [Show full text]
  • Control Flow Statements in Java Tutorials Point
    Control Flow Statements In Java Tutorials Point Cnidarian and Waldenses Bubba pillar inclemently and excorticated his mong troublesomely and hereabout. andRounding convective and conversational when energises Jodi some cudgelled Anderson some very prokaryote intertwiningly so wearily! and pardi? Is Gordon always scaphocephalous Go a certain section, commercial use will likely somewhere in java, but is like expression representation of flow control for loop conditionals are independent prognostic factors In this disease let's delve deep into Java Servlets and understand when this. Java Control Flow Statements CoreJavaGuru. Loops in Java Tutorialspointdev. Advantages of Java programming Language. Matlab object On what Kitchen Floor. The flow of controls cursor positioning of files correctly for the python and we represent the location of our java entry points and times as when exploits are handled by minimizing the. The basic control flow standpoint the typecase construct one be seen to realize similar to. Example- Circumference of Circle 227 x Diameter Here This technique. GPGPU GPU Java JCuda For example charity is not discount to control utiliza- com A. There are 3 types of two flow statements supported by the Java programming language Decision-making statements if-then they-then-else switch Looping. Java IfElse Tutorial W3Schools. Spring batch passing data between steps. The tutorial in? Remove that will need to point handling the tutorial will be used or run unit of discipline when using this statement, easing the blinking effect. Either expressed or database systems support for tcl as a controlling source listing applies to a sending field identifier names being part and production.
    [Show full text]
  • Control Flow Analysis
    SIGPLAN Notices 1970 July Control Flow Analysis Frances E. Allen IBM CORPORATION INTRODUCTION Any static, global analysis of the expression and data relation- ships in a program requires a knowledge of the control flow of the program. Since one of the primary reasons for doing such a global analysis in a compiler is to produce optimized programs, control flow analysis has been embedded in many compilers and has been described in several papers. An early paper by Prosser [5] described the use of Boolean matrices (or, more particularly, connectivity matrices) in flow analysis. The use of "dominance" relationships in flow analysis was first introduced by Prosser and much expanded by Lowry and Medlock [6]. References [6,8,9] describe compilers which use various forms of control flow analysis for optimization. Some recent develop- ments in the area are reported in [4] and in [7]. The underlying motivation in all the different types of control flow analysis is the need to codify the flow relationships in the program. The codification may be in connectivity matrices, in predecessor-successor tables, in dominance lists, etc. Whatever the form, the purpose is to facilitate determining what the flow relation- ships are; in other words to facilitate answering such questions as: is this an inner loop?, if an expression is removed from the loop where can it be correctly and profitably placed?, which variable definitions can affect this use? In this paper the basic control flow relationships are expressed in a directed graph. Various graph constructs are then found and shown to codify interesting global relationships.
    [Show full text]
  • Code Based Analysis of Object-Oriented Systems Using Extended Control Flow Graph
    CORE Metadata, citation and similar papers at core.ac.uk Provided by ethesis@nitr Code Based Analysis of Object-Oriented Systems Using Extended Control Flow Graph A thesis submitted in partial fulfillment for the degree of Bachelor of Technology by Shariq Islam 109CS0324 Under the supervision of Prof. S. K. Rath DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA, ORISSA, INDIA-769008 May 2013 Certificate This is to certify that the thesis entitled \Code Based Analysis of Object-Oriented Systems using Extended Control Flow Graph" submitted by Shariq Islam, in the partial fulfillment of the requirements for the award of Bachelor of Technology Degree in Computer Science & Engineering at National Institute of Technology Rourkela is an authentic work carried out by him under my supervision and guidance. To best of my knowledge, The matter embodied in the thesis has not been submitted to any other university / institution for the award of any Degree or Diploma. Date: Dr. S. K. Rath ||||||||||||||||||||{ Acknowledgements I am grateful to numerous peers who have contributed toward shaping this project. At the outset, I would like to express my sincere thanks to Prof. S. K. Rath for his advice during my project work. As my supervisor, he has constantly encouraged me to remain focused on achieving my goal. His observation and comments helped me to move forward with investigation depth. He has helped me greatly and always been a source of knowledge. I am thankful to all my friends. I sincerely thank everyone who has provided me with inspirational words, a welcome ear, new ideas, constructive criticism, and their invaluable time.
    [Show full text]
  • Computer Science 2. Conditionals and Loops
    COMPUTER SCIENCE COMPUTER SCIENCE SEDGEWICK/WAYNE SEDGEWICK/WAYNE PART I: PROGRAMMING IN JAVA PART I: PROGRAMMING IN JAVA Computer Science 2. Conditionals & Loops •Conditionals: the if statement Computer 2. Conditionals and loops •Loops: the while statement Science •An alternative: the for loop An Interdisciplinary Approach •Nesting R O B E R T S E D G E W I C K 1.3 KEVIN WAYNE •Debugging http://introcs.cs.princeton.edu CS.2.A.Loops.If Context: basic building blocks for programming Conditionals and Loops Control flow • The sequence of statements that are actually executed in a program. any program you might want to write • Conditionals and loops enable us to choreograph control flow. objects true boolean 1 functions and modules statement 1 graphics, sound, and image I/O false statement 2 statement 1 arrays boolean 2 true statement 2 conditionalsconditionals and loops statement 3 Math text I/O false statement 4 statement 3 primitive data types assignment statements This lecture: to infinity and beyond! Previous lecture: straight-line control flow control flow with conditionals and a loop equivalent to a calculator [ previous lecture ] [this lecture] 3 4 The if statement Example of if statement use: simulate a coin flip Execute certain statements depending on the values of certain variables. • Evaluate a boolean expression. public class Flip • If true, execute a statement. { • The else option: If false, execute a different statement. public static void main(String[] args) { if (Math.random() < 0.5) System.out.println("Heads"); Example: if (x > y) max = x; Example: if (x < 0) x = -x; else else max = y; System.out.println("Tails"); % java Flip } Heads } true true x < 0 ? false x > y ? false % java Flip Heads x = -x; max = x; max = y; % java Flip Tails % java Flip Heads Replaces x with the absolute value of x Computes the maximum of x and y 5 6 Example of if statement use: 2-sort Pop quiz on if statements Q.
    [Show full text]
  • Statement-Level Control Structures
    Chapter 7 Levels of Control Flow: 1. Within expressions 2. Among program units 3. Among program statements Evolution: - FORTRAN I control statements were based directly on IBM 704 hardware - Much research and argument in the1960s about the issue - One important result: It was proven that all flowcharts can be coded with only two-way selection and pretest logical loops Def: A control structure is a control statement and the statements whose execution it controls Overall Design Question: What control statements should a language have, beyond selection and pretest logical loops? Copyright © 1998 by Addison Wesley Longman, Inc. 1 Chapter 7 Compound statements - introduced by ALGOL 60 in the form of begin...end A block is a compound statement that can define a new scope (with local variables) Selection Statements Design Issues: 1. What is the form and type of the control expression? 2. What is the selectable segment form (single statement, statement sequence, compound statement)? 3. How should the meaning of nested selectors be specified? Single-Way Examples FORTRAN IF: IF (boolean_expr) statement Problem: can select only a single statement; to select more, a goto must be used, as in the following example Copyright © 1998 by Addison Wesley Longman, Inc. 2 Chapter 7 FORTRAN example: IF (.NOT. condition) GOTO 20 ... ... 20 CONTINUE ALGOL 60 if: if (boolean_expr) then begin ... end Two-way Selector Examples ALGOL 60 if: if (boolean_expr) then statement (the then clause) else statement (the else clause) - The statements could be single or compound Copyright © 1998 by Addison Wesley Longman, Inc. 3 Chapter 7 Nested Selectors e.g.
    [Show full text]
  • Stimulus Structures and Mental Representations in Expert Comprehension of Computer Programs By: Nancy Pennington Presented By: Michael John Decker Author & Journal
    Stimulus Structures and Mental Representations in Expert Comprehension of Computer Programs By: Nancy Pennington Presented by: Michael John Decker Author & Journal • Nancy Pennington - No internet presence • Journal: Cognitive Psychology - Is. 19, Pg: 295-341 (1987) • 2013 JIF: 3.571 • Paper Citations: 525 Research Question • What mental model best describe how an expert programmer builds up knowledge of a program? • When studying the code? • When performing maintenance activities? Motivation • Study of program comprehension means studying role of particular kinds of knowledge in cognitive skill domains • Estimated 50% of professional programmers time is spent on program maintenance • comprehension is a significant part of maintenance • Increased understanding of how knowledge is obtained and applied then use for higher productivity and decreased maintenance costs Computer Program Text Abstractions • Goal hierarchy - functional achievements of program • Data flow - transformations applied to data objects • Control flow - sequences of program actions and the passage of control between them • Conditionalized Actions - representation specifying states of the program and the actions invoked Programming Knowledge • Text Structure Knowledge • Plan Knowledge Text Structure Knowledge • Decomposition of a program’s text into text structure units • Segmentation of statements into phrase-like grouping that are combined into higher-order groupings • Syntactic markings provide clues into the boundary of segments • Segmentation reflects the control structure
    [Show full text]
  • Control Flow
    Control Flow Stephen A. Edwards Columbia University Fall 2012 Control Flow “Time is Nature’s way of preventing everything from happening at once.” Scott identifies seven manifestations of this: 1. Sequencing foo(); bar(); 2. Selection if (a) foo(); 3. Iteration while (i<10) foo(i); 4. Procedures foo(10,20); 5. Recursion foo(int i) { foo(i-1); } 6. Concurrency foo() bar() jj 7. Nondeterminism do a -> foo(); [] b -> bar(); Ordering Within Expressions What code does a compiler generate for a = b + c + d; Most likely something like tmp = b + c; a = tmp + d; (Assumes left-to-right evaluation of expressions.) Order of Evaluation Why would you care? Expression evaluation can have side-effects. Floating-point numbers don’t behave like numbers. GCC returned 25. Sun’s C compiler returned 20. C says expression evaluation order is implementation-dependent. Side-effects int x = 0; int foo() { x += 5; return x; } int bar() { int a = foo() + x + foo(); return a; } What does bar() return? Side-effects int x = 0; int foo() { x += 5; return x; } int bar() { int a = foo() + x + foo(); return a; } What does bar() return? GCC returned 25. Sun’s C compiler returned 20. C says expression evaluation order is implementation-dependent. Side-effects Java prescribes left-to-right evaluation. class Foo { static int x; static int foo() { x += 5; return x; } public static void main(String args[]) { int a = foo() + x + foo(); System.out.println(a); } } Always prints 20. Number Behavior Basic number axioms: a x a if and only if x 0 Additive identity Å Æ Æ (a b) c a (b c) Associative Å Å Æ Å Å a(b c) ab ac Distributive Å Æ Å Misbehaving Floating-Point Numbers 1e20 + 1e-20 = 1e20 1e-20 1e20 ¿ (1 + 9e-7) + 9e-7 1 + (9e-7 + 9e-7) 6Æ 9e-7 1, so it is discarded, however, 1.8e-6 is large enough ¿ 1.00001(1.000001 1) 1.00001 1.000001 1.00001 1 ¡ 6Æ ¢ ¡ ¢ 1.00001 1.000001 1.00001100001 requires too much intermediate ¢ Æ precision.
    [Show full text]