Binary Arithmetic and Bit Operations
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Bit Shifts Bit Operations, Logical Shifts, Arithmetic Shifts, Rotate Shifts
Why bit operations Assembly languages all provide ways to manipulate individual bits in multi-byte values Some of the coolest “tricks” in assembly rely on Bit Shifts bit operations With only a few instructions one can do a lot very quickly using judicious bit operations And you can do them in almost all high-level ICS312 programming languages! Let’s look at some of the common operations, Machine-Level and starting with shifts Systems Programming logical shifts arithmetic shifts Henri Casanova ([email protected]) rotate shifts Shift Operations Logical Shifts The simplest shifts: bits disappear at one end A shift moves the bits around in some data and zeros appear at the other A shift can be toward the left (i.e., toward the most significant bits), or toward the right (i.e., original byte 1 0 1 1 0 1 0 1 toward the least significant bits) left log. shift 0 1 1 0 1 0 1 0 left log. shift 1 1 0 1 0 1 0 0 left log. shift 1 0 1 0 1 0 0 0 There are two kinds of shifts: right log. shift 0 1 0 1 0 1 0 0 Logical Shifts right log. shift 0 0 1 0 1 0 1 0 Arithmetic Shifts right log. shift 0 0 0 1 0 1 0 1 Logical Shift Instructions Shifts and Numbers Two instructions: shl and shr The common use for shifts: quickly multiply and divide by powers of 2 One specifies by how many bits the data is shifted In decimal, for instance: multiplying 0013 by 10 amounts to doing one left shift to obtain 0130 Either by just passing a constant to the instruction multiplying by 100=102 amounts to doing two left shifts to obtain 1300 Or by using whatever -
Pdp11-40.Pdf
processor handbook digital equipment corporation Copyright© 1972, by Digital Equipment Corporation DEC, PDP, UNIBUS are registered trademarks of Digital Equipment Corporation. ii TABLE OF CONTENTS CHAPTER 1 INTRODUCTION 1·1 1.1 GENERAL ............................................. 1·1 1.2 GENERAL CHARACTERISTICS . 1·2 1.2.1 The UNIBUS ..... 1·2 1.2.2 Central Processor 1·3 1.2.3 Memories ........... 1·5 1.2.4 Floating Point ... 1·5 1.2.5 Memory Management .............................. .. 1·5 1.3 PERIPHERALS/OPTIONS ......................................... 1·5 1.3.1 1/0 Devices .......... .................................. 1·6 1.3.2 Storage Devices ...................................... .. 1·6 1.3.3 Bus Options .............................................. 1·6 1.4 SOFTWARE ..... .... ........................................... ............. 1·6 1.4.1 Paper Tape Software .......................................... 1·7 1.4.2 Disk Operating System Software ........................ 1·7 1.4.3 Higher Level Languages ................................... .. 1·7 1.5 NUMBER SYSTEMS ..................................... 1-7 CHAPTER 2 SYSTEM ARCHITECTURE. 2-1 2.1 SYSTEM DEFINITION .............. 2·1 2.2 UNIBUS ......................................... 2-1 2.2.1 Bidirectional Lines ...... 2-1 2.2.2 Master-Slave Relation .. 2-2 2.2.3 Interlocked Communication 2-2 2.3 CENTRAL PROCESSOR .......... 2-2 2.3.1 General Registers ... 2-3 2.3.2 Processor Status Word ....... 2-4 2.3.3 Stack Limit Register 2-5 2.4 EXTENDED INSTRUCTION SET & FLOATING POINT .. 2-5 2.5 CORE MEMORY . .... 2-6 2.6 AUTOMATIC PRIORITY INTERRUPTS .... 2-7 2.6.1 Using the Interrupts . 2-9 2.6.2 Interrupt Procedure 2-9 2.6.3 Interrupt Servicing ............ .. 2-10 2.7 PROCESSOR TRAPS ............ 2-10 2.7.1 Power Failure .............. -
Frequently Asked Questions in Mathematics
Frequently Asked Questions in Mathematics The Sci.Math FAQ Team. Editor: Alex L´opez-Ortiz e-mail: [email protected] Contents 1 Introduction 4 1.1 Why a list of Frequently Asked Questions? . 4 1.2 Frequently Asked Questions in Mathematics? . 4 2 Fundamentals 5 2.1 Algebraic structures . 5 2.1.1 Monoids and Groups . 6 2.1.2 Rings . 7 2.1.3 Fields . 7 2.1.4 Ordering . 8 2.2 What are numbers? . 9 2.2.1 Introduction . 9 2.2.2 Construction of the Number System . 9 2.2.3 Construction of N ............................... 10 2.2.4 Construction of Z ................................ 10 2.2.5 Construction of Q ............................... 11 2.2.6 Construction of R ............................... 11 2.2.7 Construction of C ............................... 12 2.2.8 Rounding things up . 12 2.2.9 What’s next? . 12 3 Number Theory 14 3.1 Fermat’s Last Theorem . 14 3.1.1 History of Fermat’s Last Theorem . 14 3.1.2 What is the current status of FLT? . 14 3.1.3 Related Conjectures . 15 3.1.4 Did Fermat prove this theorem? . 16 3.2 Prime Numbers . 17 3.2.1 Largest known Mersenne prime . 17 3.2.2 Largest known prime . 17 3.2.3 Largest known twin primes . 18 3.2.4 Largest Fermat number with known factorization . 18 3.2.5 Algorithms to factor integer numbers . 18 3.2.6 Primality Testing . 19 3.2.7 List of record numbers . 20 3.2.8 What is the current status on Mersenne primes? . -
Chapter 7 Expressions and Assignment Statements
Chapter 7 Expressions and Assignment Statements Chapter 7 Topics Introduction Arithmetic Expressions Overloaded Operators Type Conversions Relational and Boolean Expressions Short-Circuit Evaluation Assignment Statements Mixed-Mode Assignment Chapter 7 Expressions and Assignment Statements Introduction Expressions are the fundamental means of specifying computations in a programming language. To understand expression evaluation, need to be familiar with the orders of operator and operand evaluation. Essence of imperative languages is dominant role of assignment statements. Arithmetic Expressions Their evaluation was one of the motivations for the development of the first programming languages. Most of the characteristics of arithmetic expressions in programming languages were inherited from conventions that had evolved in math. Arithmetic expressions consist of operators, operands, parentheses, and function calls. The operators can be unary, or binary. C-based languages include a ternary operator, which has three operands (conditional expression). The purpose of an arithmetic expression is to specify an arithmetic computation. An implementation of such a computation must cause two actions: o Fetching the operands from memory o Executing the arithmetic operations on those operands. Design issues for arithmetic expressions: 1. What are the operator precedence rules? 2. What are the operator associativity rules? 3. What is the order of operand evaluation? 4. Are there restrictions on operand evaluation side effects? 5. Does the language allow user-defined operator overloading? 6. What mode mixing is allowed in expressions? Operator Evaluation Order 1. Precedence The operator precedence rules for expression evaluation define the order in which “adjacent” operators of different precedence levels are evaluated (“adjacent” means they are separated by at most one operand). -
Operators and Expressions
UNIT – 3 OPERATORS AND EXPRESSIONS Lesson Structure 3.0 Objectives 3.1 Introduction 3.2 Arithmetic Operators 3.3 Relational Operators 3.4 Logical Operators 3.5 Assignment Operators 3.6 Increment and Decrement Operators 3.7 Conditional Operator 3.8 Bitwise Operators 3.9 Special Operators 3.10 Arithmetic Expressions 3.11 Evaluation of Expressions 3.12 Precedence of Arithmetic Operators 3.13 Type Conversions in Expressions 3.14 Operator Precedence and Associability 3.15 Mathematical Functions 3.16 Summary 3.17 Questions 3.18 Suggested Readings 3.0 Objectives After going through this unit you will be able to: Define and use different types of operators in Java programming Understand how to evaluate expressions? Understand the operator precedence and type conversion And write mathematical functions. 3.1 Introduction Java supports a rich set of operators. We have already used several of them, such as =, +, –, and *. An operator is a symbol that tells the computer to perform certain mathematical or logical manipulations. Operators are used in programs to manipulate data and variables. They usually form a part of mathematical or logical expressions. Java operators can be classified into a number of related categories as below: 1. Arithmetic operators 2. Relational operators 1 3. Logical operators 4. Assignment operators 5. Increment and decrement operators 6. Conditional operators 7. Bitwise operators 8. Special operators 3.2 Arithmetic Operators Arithmetic operators are used to construct mathematical expressions as in algebra. Java provides all the basic arithmetic operators. They are listed in Tabled 3.1. The operators +, –, *, and / all works the same way as they do in other languages. -
Lecture 04 Linear Structures Sort
Algorithmics (6EAP) MTAT.03.238 Linear structures, sorting, searching, etc Jaak Vilo 2018 Fall Jaak Vilo 1 Big-Oh notation classes Class Informal Intuition Analogy f(n) ∈ ο ( g(n) ) f is dominated by g Strictly below < f(n) ∈ O( g(n) ) Bounded from above Upper bound ≤ f(n) ∈ Θ( g(n) ) Bounded from “equal to” = above and below f(n) ∈ Ω( g(n) ) Bounded from below Lower bound ≥ f(n) ∈ ω( g(n) ) f dominates g Strictly above > Conclusions • Algorithm complexity deals with the behavior in the long-term – worst case -- typical – average case -- quite hard – best case -- bogus, cheating • In practice, long-term sometimes not necessary – E.g. for sorting 20 elements, you dont need fancy algorithms… Linear, sequential, ordered, list … Memory, disk, tape etc – is an ordered sequentially addressed media. Physical ordered list ~ array • Memory /address/ – Garbage collection • Files (character/byte list/lines in text file,…) • Disk – Disk fragmentation Linear data structures: Arrays • Array • Hashed array tree • Bidirectional map • Heightmap • Bit array • Lookup table • Bit field • Matrix • Bitboard • Parallel array • Bitmap • Sorted array • Circular buffer • Sparse array • Control table • Sparse matrix • Image • Iliffe vector • Dynamic array • Variable-length array • Gap buffer Linear data structures: Lists • Doubly linked list • Array list • Xor linked list • Linked list • Zipper • Self-organizing list • Doubly connected edge • Skip list list • Unrolled linked list • Difference list • VList Lists: Array 0 1 size MAX_SIZE-1 3 6 7 5 2 L = int[MAX_SIZE] -
Specification of Bit Handling Routines AUTOSAR CP Release 4.3.1
Specification of Bit Handling Routines AUTOSAR CP Release 4.3.1 Document Title Specification of Bit Handling Routines Document Owner AUTOSAR Document Responsibility AUTOSAR Document Identification No 399 Document Status Final Part of AUTOSAR Standard Classic Platform Part of Standard Release 4.3.1 Document Change History Date Release Changed by Change Description 2017-12-08 4.3.1 AUTOSAR Addition on mnemonic for boolean Release as “u8”. Management Editorial changes 2016-11-30 4.3.0 AUTOSAR Removal of the requirement Release SWS_Bfx_00204 Management Updation of MISRA violation com- ment format Updation of unspecified value range for BitPn, BitStartPn, BitLn and ShiftCnt Clarifications 1 of 42 Document ID 399: AUTOSAR_SWS_BFXLibrary - AUTOSAR confidential - Specification of Bit Handling Routines AUTOSAR CP Release 4.3.1 Document Change History Date Release Changed by Change Description 2015-07-31 4.2.2 AUTOSAR Updated SWS_Bfx_00017 for the Release return type of Bfx_GetBit function Management from 1 and 0 to TRUE and FALSE Updated chapter 8.1 for the defini- tion of bit addressing and updated the examples of Bfx_SetBit, Bfx_ClrBit, Bfx_GetBit, Bfx_SetBits, Bfx_CopyBit, Bfx_PutBits, Bfx_PutBit Updated SWS_Bfx_00017 for the return type of Bfx_GetBit function from 1 and 0 to TRUE and FALSE without changing the formula Updated SWS_Bfx_00011 and SWS_Bfx_00022 for the review comments provided for the exam- ples In Table 2, replaced Boolean with boolean In SWS_Bfx_00029, in example re- placed BFX_GetBits_u16u8u8_u16 with Bfx_GetBits_u16u8u8_u16 2014-10-31 4.2.1 AUTOSAR Correct usage of const in function Release declarations Management Editoral changes 2014-03-31 4.1.3 AUTOSAR Editoral changes Release Management 2013-10-31 4.1.2 AUTOSAR Improve description of how to map Release functions to C-files Management Improve the definition of error classi- fication Editorial changes 2013-03-15 4.1.1 AUTOSAR Change return value of Test Bit API Administration to boolean. -
Designing PCI Cards and Drivers for Power Macintosh Computers
Designing PCI Cards and Drivers for Power Macintosh Computers Revised Edition Revised 3/26/99 Technical Publications © Apple Computer, Inc. 1999 Apple Computer, Inc. Adobe, Acrobat, and PostScript are Even though Apple has reviewed this © 1995, 1996 , 1999 Apple Computer, trademarks of Adobe Systems manual, APPLE MAKES NO Inc. All rights reserved. Incorporated or its subsidiaries and WARRANTY OR REPRESENTATION, EITHER EXPRESS OR IMPLIED, WITH No part of this publication may be may be registered in certain RESPECT TO THIS MANUAL, ITS reproduced, stored in a retrieval jurisdictions. QUALITY, ACCURACY, system, or transmitted, in any form America Online is a service mark of MERCHANTABILITY, OR FITNESS or by any means, mechanical, Quantum Computer Services, Inc. FOR A PARTICULAR PURPOSE. AS A electronic, photocopying, recording, Code Warrior is a trademark of RESULT, THIS MANUAL IS SOLD “AS or otherwise, without prior written Metrowerks. IS,” AND YOU, THE PURCHASER, ARE permission of Apple Computer, Inc., CompuServe is a registered ASSUMING THE ENTIRE RISK AS TO except to make a backup copy of any trademark of CompuServe, Inc. ITS QUALITY AND ACCURACY. documentation provided on Ethernet is a registered trademark of CD-ROM. IN NO EVENT WILL APPLE BE LIABLE Xerox Corporation. The Apple logo is a trademark of FOR DIRECT, INDIRECT, SPECIAL, FrameMaker is a registered Apple Computer, Inc. INCIDENTAL, OR CONSEQUENTIAL trademark of Frame Technology Use of the “keyboard” Apple logo DAMAGES RESULTING FROM ANY Corporation. (Option-Shift-K) for commercial DEFECT OR INACCURACY IN THIS purposes without the prior written Helvetica and Palatino are registered MANUAL, even if advised of the consent of Apple may constitute trademarks of Linotype-Hell AG possibility of such damages. -
Faster Base64 Encoding and Decoding Using AVX2 Instructions
Faster Base64 Encoding and Decoding using AVX2 Instructions WOJCIECH MUŁA, DANIEL LEMIRE, Universite´ du Quebec´ (TELUQ) Web developers use base64 formats to include images, fonts, sounds and other resources directly inside HTML, JavaScript, JSON and XML files. We estimate that billions of base64 messages are decoded every day. We are motivated to improve the efficiency of base64 encoding and decoding. Compared to state-of-the-art implementations, we multiply the speeds of both the encoding (≈ 10×) and the decoding (≈ 7×). We achieve these good results by using the single-instruction-multiple-data (SIMD) instructions available on recent Intel processors (AVX2). Our accelerated software abides by the specification and reports errors when encountering characters outside of the base64 set. It is available online as free software under a liberal license. CCS Concepts: •Theory of computation ! Vector / streaming algorithms; General Terms: Algorithms, Performance Additional Key Words and Phrases: Binary-to-text encoding, Vectorization, Data URI, Web Performance 1. INTRODUCTION We use base64 formats to represent arbitrary binary data as text. Base64 is part of the MIME email protocol [Linn 1993; Freed and Borenstein 1996], used to encode binary attachments. Base64 is included in the standard libraries of popular programming languages such as Java, C#, Swift, PHP, Python, Rust, JavaScript and Go. Major database systems such as Oracle and MySQL include base64 functions. On the Web, we often combine binary resources (images, videos, sounds) with text- only documents (XML, JavaScript, HTML). Before a Web page can be displayed, it is often necessary to retrieve not only the HTML document but also all of the separate binary resources it needs. -
RISC-V Bitmanip Extension Document Version 0.90
RISC-V Bitmanip Extension Document Version 0.90 Editor: Clifford Wolf Symbiotic GmbH [email protected] June 10, 2019 Contributors to all versions of the spec in alphabetical order (please contact editors to suggest corrections): Jacob Bachmeyer, Allen Baum, Alex Bradbury, Steven Braeger, Rogier Brussee, Michael Clark, Ken Dockser, Paul Donahue, Dennis Ferguson, Fabian Giesen, John Hauser, Robert Henry, Bruce Hoult, Po-wei Huang, Rex McCrary, Lee Moore, Jiˇr´ıMoravec, Samuel Neves, Markus Oberhumer, Nils Pipenbrinck, Xue Saw, Tommy Thorn, Andrew Waterman, Thomas Wicki, and Clifford Wolf. This document is released under a Creative Commons Attribution 4.0 International License. Contents 1 Introduction 1 1.1 ISA Extension Proposal Design Criteria . .1 1.2 B Extension Adoption Strategy . .2 1.3 Next steps . .2 2 RISC-V Bitmanip Extension 3 2.1 Basic bit manipulation instructions . .4 2.1.1 Count Leading/Trailing Zeros (clz, ctz)....................4 2.1.2 Count Bits Set (pcnt)...............................5 2.1.3 Logic-with-negate (andn, orn, xnor).......................5 2.1.4 Pack two XLEN/2 words in one register (pack).................6 2.1.5 Min/max instructions (min, max, minu, maxu)................7 2.1.6 Single-bit instructions (sbset, sbclr, sbinv, sbext)............8 2.1.7 Shift Ones (Left/Right) (slo, sloi, sro, sroi)...............9 2.2 Bit permutation instructions . 10 2.2.1 Rotate (Left/Right) (rol, ror, rori)..................... 10 2.2.2 Generalized Reverse (grev, grevi)....................... 11 2.2.3 Generalized Shuffleshfl ( , unshfl, shfli, unshfli).............. 14 2.3 Bit Extract/Deposit (bext, bdep)............................ 22 2.4 Carry-less multiply (clmul, clmulh, clmulr).................... -
Bit-Mask Based Compression of FPGA Bitstreams
International Journal of Soft Computing and Engineering (IJSCE) ISSN: 2231-2307, Volume-3 Issue-1, March 2013 Bit-Mask Based Compression of FPGA Bitstreams S.Vigneshwaran, S.Sreekanth The efficiency of bitstream compression is measured using Abstract— In this paper, bitmask based compression of FPGA Compression Ratio (CR). It is defined as the ratio between the bit-streams has been implemented. Reconfiguration system uses compressed bitstream size (CS) and the original bitstream bitstream compression to reduce bitstream size and memory size (OS) (ie CR=CS/OS). A smaller compression ratio requirement. It also improves communication bandwidth and implies a better compression technique. Among various thereby decreases reconfiguration time. The three major compression techniques that has been proposed compression contributions of this paper are; i) Efficient bitmask selection [5] seems to be attractive for bitstream compression, because technique that can create a large set of matching patterns; ii) Proposes a bitmask based compression using the bitmask and of its good compression ratio and relatively simple dictionary selection technique that can significantly reduce the decompression scheme. This approach combines the memory requirement iii) Efficient combination of bitmask-based advantages of previous compression techniques with good compression and G o l o m b coding of repetitive patterns. compression ratio and those with fast decompression. Index Terms—Bitmask-based compression, Decompression II. RELATED WORK engine, Golomb coding, Field Programmable Gate Array (FPGA). The existing bitstream compression techniques can be classified into two categories based on whether they need I. INTRODUCTION special hardware support during decompression. Some Field-Programmable Gate Arrays (Fpga) is widely used in approaches require special hardware features to access the reconfigurable systems. -
Chapter 17: Filters to Detect, Filters to Protect Page 1 of 11
Chapter 17: Filters to Detect, Filters to Protect Page 1 of 11 Chapter 17: Filters to Detect, Filters to Protect You learned about the concepts of discovering events of interest by configuring filters in Chapter 8, "Introduction to Filters and Signatures." That chapter showed you various different products with unique filtering languages to assist you in discovering malicious types of traffic. What if you are a do- it-yourself type, inclined to watch Bob Vila or "Men in Tool Belts?" The time-honored TCPdump program comes with an extensive filter language that you can use to look at any field, combination of fields, or bits found in an IP datagram. If you like puzzles and don’t mind a bit of tinkering, you can use TCPdump filters to extract different anomalous traffic. Mind you, this is not the tool for the faint of heart or for those of you who shy away from getting your brain a bit frazzled. Those who prefer a packaged solution might be better off using the commercial products and their GUIs or filters. This chapter introduces the concept of using TCPdump and TCPdump filters to detect events of interest. TCPdump and TCPdump filters are the backbone of Shadow, and so the recommended suggestion is to download the current version of Shadow at http://www.nswc.navy.mil/ISSEC/CID/ to examine and enhance its native filters. This takes care of automating the collection and processing of traffic, freeing you to concentrate on improving the TCPdump filters for better detects. Specifically, this chapter discusses the mechanics of creating TCPdump filters.