A Floating-Point Numerical Sanitizer
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Type-Safe Composition of Object Modules*
International Conference on Computer Systems and Education I ISc Bangalore Typ esafe Comp osition of Ob ject Mo dules Guruduth Banavar Gary Lindstrom Douglas Orr Department of Computer Science University of Utah Salt LakeCity Utah USA Abstract Intro duction It is widely agreed that strong typing in We describ e a facility that enables routine creases the reliability and eciency of soft typ echecking during the linkage of exter ware However compilers for statically typ ed nal declarations and denitions of separately languages suchasC and C in tradi compiled programs in ANSI C The primary tional nonintegrated programming environ advantage of our serverstyle typ echecked ments guarantee complete typ esafety only linkage facility is the ability to program the within a compilation unit but not across comp osition of ob ject mo dules via a suite of suchunits Longstanding and widely avail strongly typ ed mo dule combination op era able linkers comp ose separately compiled tors Such programmability enables one to units bymatching symb ols purely byname easily incorp orate programmerdened data equivalence with no regard to their typ es format conversion stubs at linktime In ad Such common denominator linkers accom dition our linkage facility is able to automat mo date ob ject mo dules from various source ically generate safe co ercion stubs for com languages by simply ignoring the static se patible encapsulated data mantics of the language Moreover com monly used ob ject le formats are not de signed to incorp orate source language typ e -
Faster Ffts in Medium Precision
Faster FFTs in medium precision Joris van der Hoevena, Grégoire Lecerfb Laboratoire d’informatique, UMR 7161 CNRS Campus de l’École polytechnique 1, rue Honoré d’Estienne d’Orves Bâtiment Alan Turing, CS35003 91120 Palaiseau a. Email: [email protected] b. Email: [email protected] November 10, 2014 In this paper, we present new algorithms for the computation of fast Fourier transforms over complex numbers for “medium” precisions, typically in the range from 100 until 400 bits. On the one hand, such precisions are usually not supported by hardware. On the other hand, asymptotically fast algorithms for multiple precision arithmetic do not pay off yet. The main idea behind our algorithms is to develop efficient vectorial multiple precision fixed point arithmetic, capable of exploiting SIMD instructions in modern processors. Keywords: floating point arithmetic, quadruple precision, complexity bound, FFT, SIMD A.C.M. subject classification: G.1.0 Computer-arithmetic A.M.S. subject classification: 65Y04, 65T50, 68W30 1. Introduction Multiple precision arithmetic [4] is crucial in areas such as computer algebra and cryptography, and increasingly useful in mathematical physics and numerical analysis [2]. Early multiple preci- sion libraries appeared in the seventies [3], and nowadays GMP [11] and MPFR [8] are typically very efficient for large precisions of more than, say, 1000 bits. However, for precisions which are only a few times larger than the machine precision, these libraries suffer from a large overhead. For instance, the MPFR library for arbitrary precision and IEEE-style standardized floating point arithmetic is typically about a factor 100 slower than double precision machine arithmetic. -
Exploring C Semantics and Pointer Provenance
Exploring C Semantics and Pointer Provenance KAYVAN MEMARIAN, University of Cambridge VICTOR B. F. GOMES, University of Cambridge BROOKS DAVIS, SRI International STEPHEN KELL, University of Cambridge ALEXANDER RICHARDSON, University of Cambridge ROBERT N. M. WATSON, University of Cambridge PETER SEWELL, University of Cambridge The semantics of pointers and memory objects in C has been a vexed question for many years. C values cannot be treated as either purely abstract or purely concrete entities: the language exposes their representations, 67 but compiler optimisations rely on analyses that reason about provenance and initialisation status, not just runtime representations. The ISO WG14 standard leaves much of this unclear, and in some respects differs with de facto standard usage — which itself is difficult to investigate. In this paper we explore the possible source-language semantics for memory objects and pointers, in ISO C and in C as it is used and implemented in practice, focussing especially on pointer provenance. We aim to, as far as possible, reconcile the ISO C standard, mainstream compiler behaviour, and the semantics relied on by the corpus of existing C code. We present two coherent proposals, tracking provenance via integers and not; both address many design questions. We highlight some pros and cons and open questions, and illustrate the discussion with a library of test cases. We make our semantics executable as a test oracle, integrating it with the Cerberus semantics for much of the rest of C, which we have made substantially more complete and robust, and equipped with a web-interface GUI. This allows us to experimentally assess our proposals on those test cases. -
Timur Doumler @Timur Audio
Type punning in modern C++ version 1.1 Timur Doumler @timur_audio C++ Russia 30 October 2019 Image: ESA/Hubble Type punning in modern C++ 2 How not to do type punning in modern C++ 3 How to write portable code that achieves the same effect as type punning in modern C++ 4 How to write portable code that achieves the same effect as type punning in modern C++ without causing undefined behaviour 5 6 7 � 8 � (�) 9 10 11 12 struct Widget { virtual void doSomething() { printf("Widget"); } }; struct Gizmo { virtual void doSomethingCompletelyDifferent() { printf("Gizmo"); } }; int main() { Gizmo g; Widget* w = (Widget*)&g; w->doSomething(); } Example from Luna @lunasorcery 13 struct Widget { virtual void doSomething() { printf("Widget"); } }; struct Gizmo { virtual void doSomethingCompletelyDifferent() { printf("Gizmo"); } }; int main() { Gizmo g; Widget* w = (Widget*)&g; w->doSomething(); } Example from Luna @lunasorcery 14 15 Don’t use C-style casts. 16 struct Widget { virtual void doSomething() { printf("Widget"); } }; struct Gizmo { virtual void doSomethingCompletelyDifferent() { printf("Gizmo"); } }; int main() { Gizmo g; Widget* w = (Widget*)&g; w->doSomething(); } Example from Luna @lunasorcery 17 18 19 20 float F0 00 80 01 int F0 00 80 01 21 float F0 00 80 01 int F0 00 80 01 float F0 00 80 01 char* std::byte* F0 00 80 01 22 float F0 00 80 01 int F0 00 80 01 float F0 00 80 01 char* std::byte* F0 00 80 01 Widget F0 00 80 01 01 BD 83 E3 float[2] F0 00 80 01 01 BD 83 E3 23 float F0 00 80 01 int F0 00 80 01 float F0 00 80 01 char* std::byte* -
Effective Types: Examples (P1796R0) 2 3 4 PETER SEWELL, University of Cambridge 5 KAYVAN MEMARIAN, University of Cambridge 6 VICTOR B
1 Effective types: examples (P1796R0) 2 3 4 PETER SEWELL, University of Cambridge 5 KAYVAN MEMARIAN, University of Cambridge 6 VICTOR B. F. GOMES, University of Cambridge 7 JENS GUSTEDT, INRIA 8 HUBERT TONG 9 10 11 This is a collection of examples exploring the semantics that should be allowed for objects 12 and subobjects in allocated regions – especially, where the defined/undefined-behaviour 13 boundary should be, and how that relates to compiler alias analysis. The examples are in 14 C, but much should be similar in C++. We refer to the ISO C notion of effective types, 15 but that turns out to be quite flawed. Some examples at the end (from Hubert Tong) show 16 that existing compiler behaviour is not consistent with type-changing updates. 17 This is an updated version of part of n2294 C Memory Object Model Study Group: 18 Progress Report, 2018-09-16. 19 1 INTRODUCTION 20 21 Paragraphs 6.5p{6,7} of the standard introduce effective types. These were added to 22 C in C99 to permit compilers to do optimisations driven by type-based alias analysis, 23 by ruling out programs involving unannotated aliasing of references to different types 24 (regarding them as having undefined behaviour). However, this is one of the less clear, 25 less well-understood, and more controversial aspects of the standard, as one can see from 1 2 26 various GCC and Linux Kernel mailing list threads , blog postings , and the responses to 3 4 27 Questions 10, 11, and 15 of our survey . See also earlier committee discussion . -
GNU MPFR the Multiple Precision Floating-Point Reliable Library Edition 4.1.0 July 2020
GNU MPFR The Multiple Precision Floating-Point Reliable Library Edition 4.1.0 July 2020 The MPFR team [email protected] This manual documents how to install and use the Multiple Precision Floating-Point Reliable Library, version 4.1.0. Copyright 1991, 1993-2020 Free Software Foundation, Inc. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, with no Front-Cover Texts, and with no Back- Cover Texts. A copy of the license is included in Appendix A [GNU Free Documentation License], page 59. i Table of Contents MPFR Copying Conditions ::::::::::::::::::::::::::::::::::::::: 1 1 Introduction to MPFR :::::::::::::::::::::::::::::::::::::::: 2 1.1 How to Use This Manual::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 2 2 Installing MPFR ::::::::::::::::::::::::::::::::::::::::::::::: 3 2.1 How to Install ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3 2.2 Other `make' Targets :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 4 2.3 Build Problems :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 4 2.4 Getting the Latest Version of MPFR ::::::::::::::::::::::::::::::::::::::::::::::: 4 3 Reporting Bugs::::::::::::::::::::::::::::::::::::::::::::::::: 5 4 MPFR Basics ::::::::::::::::::::::::::::::::::::::::::::::::::: 6 4.1 Headers and Libraries :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 6 -
IEEE Standard 754 for Binary Floating-Point Arithmetic
Work in Progress: Lecture Notes on the Status of IEEE 754 October 1, 1997 3:36 am Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic Prof. W. Kahan Elect. Eng. & Computer Science University of California Berkeley CA 94720-1776 Introduction: Twenty years ago anarchy threatened floating-point arithmetic. Over a dozen commercially significant arithmetics boasted diverse wordsizes, precisions, rounding procedures and over/underflow behaviors, and more were in the works. “Portable” software intended to reconcile that numerical diversity had become unbearably costly to develop. Thirteen years ago, when IEEE 754 became official, major microprocessor manufacturers had already adopted it despite the challenge it posed to implementors. With unprecedented altruism, hardware designers had risen to its challenge in the belief that they would ease and encourage a vast burgeoning of numerical software. They did succeed to a considerable extent. Anyway, rounding anomalies that preoccupied all of us in the 1970s afflict only CRAY X-MPs — J90s now. Now atrophy threatens features of IEEE 754 caught in a vicious circle: Those features lack support in programming languages and compilers, so those features are mishandled and/or practically unusable, so those features are little known and less in demand, and so those features lack support in programming languages and compilers. To help break that circle, those features are discussed in these notes under the following headings: Representable Numbers, Normal and Subnormal, Infinite -
Aliasing Restrictions of C11 Formalized in Coq
Aliasing restrictions of C11 formalized in Coq Robbert Krebbers Radboud University Nijmegen December 11, 2013 @ CPP, Melbourne, Australia int f(int *p, int *q) { int x = *p; *q = 314; return x; } If p and q alias, the original value n of *p is returned n p q Optimizing x away is unsound: 314 would be returned Alias analysis: to determine whether pointers can alias Aliasing Aliasing: multiple pointers referring to the same object Optimizing x away is unsound: 314 would be returned Alias analysis: to determine whether pointers can alias Aliasing Aliasing: multiple pointers referring to the same object int f(int *p, int *q) { int x = *p; *q = 314; return x; } If p and q alias, the original value n of *p is returned n p q Alias analysis: to determine whether pointers can alias Aliasing Aliasing: multiple pointers referring to the same object int f(int *p, int *q) { int x = *p; *q = 314; return x *p; } If p and q alias, the original value n of *p is returned n p q Optimizing x away is unsound: 314 would be returned Aliasing Aliasing: multiple pointers referring to the same object int f(int *p, int *q) { int x = *p; *q = 314; return x; } If p and q alias, the original value n of *p is returned n p q Optimizing x away is unsound: 314 would be returned Alias analysis: to determine whether pointers can alias It can still be called with aliased pointers: x union { int x; float y; } u; y u.x = 271; return h(&u.x, &u.y); &u.x &u.y C89 allows p and q to be aliased, and thus requires it to return 271 C99/C11 allows type-based alias analysis: I A compiler -
SATE V Ockham Sound Analysis Criteria
NISTIR 8113 SATE V Ockham Sound Analysis Criteria Paul E. Black Athos Ribeiro This publication is available free of charge from: https://doi.org/10.6028/NIST.IR.8113 NISTIR 8113 SATE V Ockham Sound Analysis Criteria Paul E. Black Software and Systems Division Information Technology Laboratory Athos Ribeiro Department of Computer Science University of Sao˜ Paulo Sao˜ Paulo, SP Brazil This publication is available free of charge from: https://doi.org/10.6028/NIST.IR.8113 March 2016 Including updates as of June 2017 U.S. Department of Commerce Wilbur L. Ross, Jr., Secretary National Institute of Standards and Technology Kent Rochford, Acting NIST Director and Under Secretary of Commerce for Standards and Technology Abstract Static analyzers examine the source or executable code of programs to find problems. Many static analyzers use heuristics or approximations to handle programs up to millions of lines of code. We established the Ockham Sound Analysis Criteria to recognize static analyzers whose findings are always correct. In brief the criteria are (1) the analyzer’s findings are claimed to always be correct, (2) it produces findings for most of a program, and (3) even one incorrect finding disqualifies an analyzer. This document begins by explaining the background and requirements of the Ockham Criteria. In Static Analysis Tool Exposition (SATE) V, only one tool was submitted to be re- viewed. Pascal Cuoq and Florent Kirchner ran the August 2013 development version of Frama-C on pertinent parts of the Juliet 1.2 test suite. We divided the warnings into eight classes, including improper buffer access, NULL pointer dereference, integer overflow, and use of uninitialized variable. -
Effectiveness of Floating-Point Precision on the Numerical Approximation by Spectral Methods
Mathematical and Computational Applications Article Effectiveness of Floating-Point Precision on the Numerical Approximation by Spectral Methods José A. O. Matos 1,2,† and Paulo B. Vasconcelos 1,2,∗,† 1 Center of Mathematics, University of Porto, R. Dr. Roberto Frias, 4200-464 Porto, Portugal; [email protected] 2 Faculty of Economics, University of Porto, R. Dr. Roberto Frias, 4200-464 Porto, Portugal * Correspondence: [email protected] † These authors contributed equally to this work. Abstract: With the fast advances in computational sciences, there is a need for more accurate compu- tations, especially in large-scale solutions of differential problems and long-term simulations. Amid the many numerical approaches to solving differential problems, including both local and global methods, spectral methods can offer greater accuracy. The downside is that spectral methods often require high-order polynomial approximations, which brings numerical instability issues to the prob- lem resolution. In particular, large condition numbers associated with the large operational matrices, prevent stable algorithms from working within machine precision. Software-based solutions that implement arbitrary precision arithmetic are available and should be explored to obtain higher accu- racy when needed, even with the higher computing time cost associated. In this work, experimental results on the computation of approximate solutions of differential problems via spectral methods are detailed with recourse to quadruple precision arithmetic. Variable precision arithmetic was used in Tau Toolbox, a mathematical software package to solve integro-differential problems via the spectral Tau method. Citation: Matos, J.A.O.; Vasconcelos, Keywords: floating-point arithmetic; variable precision arithmetic; IEEE 754-2008 standard; quadru- P.B. -
Direct to SOM
Direct to SOM Contents General Description Header Requirements Language Restrictions MacSOM Pragmas General Description MrCpp and SCpp support Direct-To-SOM programming in C++. You can write MacSOM based classes directly using C++, that is, without using the IDL language or the IDL compiler. To use the compiler’s Direct-To-SOM feature, combine the replacement SOMObjects headers (described below) from CIncludes, and the MrCpp/SCpp tools from the Tools found in the folder Past&Future:PreRelease:Direct SOMObjects for Mac OS, with an MPW installation that already has SOM 2.0.8 (or greater) installed. Look in the SOMExamples folder for build scripts called DTS.build.script . The -som command line option enables Direct-To-SOM support. When this flag is specified, classes which are derived (directly or indirectly) from the special class named SOMObject will be processed differently than ordinary C++ classes—for these classes, the compiler will generate the MacSOM enabling class meta-data instead of standard C++ vtables. Also when -som is specified on the command line, the preprocessor symbol __SOM_ENABLED__ is defined as 1. MrCpp and SCpp ship with new, replacement MacSOM header files. The header files have been upgraded to support Direct-To-SOM. Two new header files are of special interest: Header Requirements MrCpp and SCpp ship with new, replacement MacSOM header files. The header files have been upgraded to support Direct-To-SOM. Two new header files are of special interest: • somobj.hh Defines the root MacSOM class SOMObject. It should be included when subclassing from SOMObject. If you are converting from IDL with C++ to Direct-To-SOM C++, then this file can be thought of as a replacement for both somobj.idl and somobj.xh . -
C Language Features
C Language Features 5.4 SUPPORTED DATA TYPES AND VARIABLES 5.4.1 Identifiers A C variable identifier (the following is also true for function identifiers) is a sequence of letters and digits, where the underscore character “_” counts as a letter. Identifiers cannot start with a digit. Although they can start with an underscore, such identifiers are reserved for the compiler’s use and should not be defined by your programs. Such is not the case for assembly domain identifiers, which often begin with an underscore, see Section 5.12.3.1 “Equivalent Assembly Symbols”. Identifiers are case sensitive, so main is different to Main. Not every character is significant in an identifier. The maximum number of significant characters can be set using an option, see Section 4.8.8 “-N: Identifier Length”. If two identifiers differ only after the maximum number of significant characters, then the compiler will consider them to be the same symbol. 5.4.2 Integer Data Types The MPLAB XC8 compiler supports integer data types with 1, 2, 3 and 4 byte sizes as well as a single bit type. Table 5-1 shows the data types and their corresponding size and arithmetic type. The default type for each type is underlined. TABLE 5-1: INTEGER DATA TYPES Type Size (bits) Arithmetic Type bit 1 Unsigned integer signed char 8 Signed integer unsigned char 8 Unsigned integer signed short 16 Signed integer unsigned short 16 Unsigned integer signed int 16 Signed integer unsigned int 16 Unsigned integer signed short long 24 Signed integer unsigned short long 24 Unsigned integer signed long 32 Signed integer unsigned long 32 Unsigned integer signed long long 32 Signed integer unsigned long long 32 Unsigned integer The bit and short long types are non-standard types available in this implementa- tion.