Addressing Data in Memory
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Lab 7: Floating-Point Addition 0.0
Lab 7: Floating-Point Addition 0.0 Introduction In this lab, you will write a MIPS assembly language function that performs floating-point addition. You will then run your program using PCSpim (just as you did in Lab 6). For testing, you are provided a program that calls your function to compute the value of the mathematical constant e. For those with no assembly language experience, this will be a long lab, so plan your time accordingly. Background You should be familiar with the IEEE 754 Floating-Point Standard, which is described in Section 3.6 of your book. (Hopefully you have read that section carefully!) Here we will be dealing only with single precision floating- point values, which are formatted as follows (this is also described in the “Floating-Point Representation” subsec- tion of Section 3.6 in your book): Sign Exponent (8 bits) Significand (23 bits) 31 30 29 ... 24 23 22 21 ... 0 Remember that the exponent is biased by 127, which means that an exponent of zero is represented by 127 (01111111). The exponent is not encoded using 2s-complement. The significand is always positive, and the sign bit is kept separately. Note that the actual significand is 24 bits long; the first bit is always a 1 and thus does not need to be stored explicitly. This will be important to remember when you write your function! There are several details of IEEE 754 that you will not have to worry about in this lab. For example, the expo- nents 00000000 and 11111111 are reserved for special purposes that are described in your book (representing zero, denormalized numbers and NaNs). -
The Hexadecimal Number System and Memory Addressing
C5537_App C_1107_03/16/2005 APPENDIX C The Hexadecimal Number System and Memory Addressing nderstanding the number system and the coding system that computers use to U store data and communicate with each other is fundamental to understanding how computers work. Early attempts to invent an electronic computing device met with disappointing results as long as inventors tried to use the decimal number sys- tem, with the digits 0–9. Then John Atanasoff proposed using a coding system that expressed everything in terms of different sequences of only two numerals: one repre- sented by the presence of a charge and one represented by the absence of a charge. The numbering system that can be supported by the expression of only two numerals is called base 2, or binary; it was invented by Ada Lovelace many years before, using the numerals 0 and 1. Under Atanasoff’s design, all numbers and other characters would be converted to this binary number system, and all storage, comparisons, and arithmetic would be done using it. Even today, this is one of the basic principles of computers. Every character or number entered into a computer is first converted into a series of 0s and 1s. Many coding schemes and techniques have been invented to manipulate these 0s and 1s, called bits for binary digits. The most widespread binary coding scheme for microcomputers, which is recog- nized as the microcomputer standard, is called ASCII (American Standard Code for Information Interchange). (Appendix B lists the binary code for the basic 127- character set.) In ASCII, each character is assigned an 8-bit code called a byte. -
POINTER (IN C/C++) What Is a Pointer?
POINTER (IN C/C++) What is a pointer? Variable in a program is something with a name, the value of which can vary. The way the compiler and linker handles this is that it assigns a specific block of memory within the computer to hold the value of that variable. • The left side is the value in memory. • The right side is the address of that memory Dereferencing: • int bar = *foo_ptr; • *foo_ptr = 42; // set foo to 42 which is also effect bar = 42 • To dereference ted, go to memory address of 1776, the value contain in that is 25 which is what we need. Differences between & and * & is the reference operator and can be read as "address of“ * is the dereference operator and can be read as "value pointed by" A variable referenced with & can be dereferenced with *. • Andy = 25; • Ted = &andy; All expressions below are true: • andy == 25 // true • &andy == 1776 // true • ted == 1776 // true • *ted == 25 // true How to declare pointer? • Type + “*” + name of variable. • Example: int * number; • char * c; • • number or c is a variable is called a pointer variable How to use pointer? • int foo; • int *foo_ptr = &foo; • foo_ptr is declared as a pointer to int. We have initialized it to point to foo. • foo occupies some memory. Its location in memory is called its address. &foo is the address of foo Assignment and pointer: • int *foo_pr = 5; // wrong • int foo = 5; • int *foo_pr = &foo; // correct way Change the pointer to the next memory block: • int foo = 5; • int *foo_pr = &foo; • foo_pr ++; Pointer arithmetics • char *mychar; // sizeof 1 byte • short *myshort; // sizeof 2 bytes • long *mylong; // sizeof 4 byts • mychar++; // increase by 1 byte • myshort++; // increase by 2 bytes • mylong++; // increase by 4 bytes Increase pointer is different from increase the dereference • *P++; // unary operation: go to the address of the pointer then increase its address and return a value • (*P)++; // get the value from the address of p then increase the value by 1 Arrays: • int array[] = {45,46,47}; • we can call the first element in the array by saying: *array or array[0]. -
Subtyping Recursive Types
ACM Transactions on Programming Languages and Systems, 15(4), pp. 575-631, 1993. Subtyping Recursive Types Roberto M. Amadio1 Luca Cardelli CNRS-CRIN, Nancy DEC, Systems Research Center Abstract We investigate the interactions of subtyping and recursive types, in a simply typed λ-calculus. The two fundamental questions here are whether two (recursive) types are in the subtype relation, and whether a term has a type. To address the first question, we relate various definitions of type equivalence and subtyping that are induced by a model, an ordering on infinite trees, an algorithm, and a set of type rules. We show soundness and completeness between the rules, the algorithm, and the tree semantics. We also prove soundness and a restricted form of completeness for the model. To address the second question, we show that to every pair of types in the subtype relation we can associate a term whose denotation is the uniquely determined coercion map between the two types. Moreover, we derive an algorithm that, when given a term with implicit coercions, can infer its least type whenever possible. 1This author's work has been supported in part by Digital Equipment Corporation and in part by the Stanford-CNR Collaboration Project. Page 1 Contents 1. Introduction 1.1 Types 1.2 Subtypes 1.3 Equality of Recursive Types 1.4 Subtyping of Recursive Types 1.5 Algorithm outline 1.6 Formal development 2. A Simply Typed λ-calculus with Recursive Types 2.1 Types 2.2 Terms 2.3 Equations 3. Tree Ordering 3.1 Subtyping Non-recursive Types 3.2 Folding and Unfolding 3.3 Tree Expansion 3.4 Finite Approximations 4. -
A Variable Precision Hardware Acceleration for Scientific Computing Andrea Bocco
A variable precision hardware acceleration for scientific computing Andrea Bocco To cite this version: Andrea Bocco. A variable precision hardware acceleration for scientific computing. Discrete Mathe- matics [cs.DM]. Université de Lyon, 2020. English. NNT : 2020LYSEI065. tel-03102749 HAL Id: tel-03102749 https://tel.archives-ouvertes.fr/tel-03102749 Submitted on 7 Jan 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. N°d’ordre NNT : 2020LYSEI065 THÈSE de DOCTORAT DE L’UNIVERSITÉ DE LYON Opérée au sein de : CEA Grenoble Ecole Doctorale InfoMaths EDA N17° 512 (Informatique Mathématique) Spécialité de doctorat :Informatique Soutenue publiquement le 29/07/2020, par : Andrea Bocco A variable precision hardware acceleration for scientific computing Devant le jury composé de : Frédéric Pétrot Président et Rapporteur Professeur des Universités, TIMA, Grenoble, France Marc Dumas Rapporteur Professeur des Universités, École Normale Supérieure de Lyon, France Nathalie Revol Examinatrice Docteure, École Normale Supérieure de Lyon, France Fabrizio Ferrandi Examinateur Professeur associé, Politecnico di Milano, Italie Florent de Dinechin Directeur de thèse Professeur des Universités, INSA Lyon, France Yves Durand Co-directeur de thèse Docteur, CEA Grenoble, France Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2020LYSEI065/these.pdf © [A. -
CS31 Discussion 1E Spring 17’: Week 08
CS31 Discussion 1E Spring 17’: week 08 TA: Bo-Jhang Ho [email protected] Credit to former TA Chelsea Ju Project 5 - Map cipher to crib } Approach 1: For each pair of positions, check two letters in cipher and crib are both identical or different } For each pair of positions pos1 and pos2, cipher[pos1] == cipher[pos2] should equal to crib[pos1] == crib[pos2] } Approach 2: Get the positions of the letter and compare } For each position pos, indexes1 = getAllPositions(cipher, pos, cipher[pos]) indexes2 = getAllPositions(crib, pos, crib[pos]) indexes1 should equal to indexes2 Project 5 - Map cipher to crib } Approach 3: Generate the mapping } We first have a mapping array char cipher2crib[128] = {‘\0’}; } Then whenever we attempt to map letterA in cipher to letterB in crib, we first check whether it violates the previous setup: } Is cipher2crib[letterA] != ‘\0’? // implies letterA has been used } Then cipher2crib[letterA] should equal to letterB } If no violation happens, } cipher2crib[letterA] = letterB; Road map of CS31 String Array Function Class Variable If / else Loops Pointer!! Cheat sheet Data type } int *a; } a is a variable, whose data type is int * } a stores an address of some integer “Use as verbs” } & - address-of operator } &b means I want to get the memory address of variable b } * - dereference operator } *c means I want to retrieve the value in address c Memory model Address Memory Contents 1000 1 byte 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 Memory model Address Memory -
CS 351: Systems Programming
Virtual Memory CS 351: Systems Programming Michael Saelee <[email protected]> Computer Science Science registers cache (SRAM) main memory (DRAM) local hard disk drive (HDD/SSD) remote storage (networked drive / cloud) previously: SRAM ⇔ DRAM Computer Science Science registers cache (SRAM) main memory (DRAM) local hard disk drive (HDD/SSD) remote storage (networked drive / cloud) next: DRAM ⇔ HDD, SSD, etc. i.e., memory as a “cache” for disk Computer Science Science main goals: 1. maximize memory throughput 2. maximize memory utilization 3. provide address space consistency & memory protection to processes Computer Science Science throughput = # bytes per second - depends on access latencies (DRAM, HDD) and “hit rate” Computer Science Science utilization = fraction of allocated memory that contains “user” data (aka payload) - vs. metadata and other overhead required for memory management Computer Science Science address space consistency → provide a uniform “view” of memory to each process 0xffffffff Computer Science Science Kernel virtual memory Memory (code, data, heap, stack) invisible to 0xc0000000 user code User stack (created at runtime) %esp (stack pointer) Memory mapped region for shared libraries 0x40000000 brk Run-time heap (created by malloc) Read/write segment ( , ) .data .bss Loaded from the Read-only segment executable file (.init, .text, .rodata) 0x08048000 0 Unused address space consistency → provide a uniform “view” of memory to each process Computer Science Science memory protection → prevent processes from directly accessing -
Chapter 9: Memory Management
Chapter 9: Memory Management I Background I Swapping I Contiguous Allocation I Paging I Segmentation I Segmentation with Paging Operating System Concepts 9.1 Silberschatz, Galvin and Gagne 2002 Background I Program must be brought into memory and placed within a process for it to be run. I Input queue – collection of processes on the disk that are waiting to be brought into memory to run the program. I User programs go through several steps before being run. Operating System Concepts 9.2 Silberschatz, Galvin and Gagne 2002 Binding of Instructions and Data to Memory Address binding of instructions and data to memory addresses can happen at three different stages. I Compile time: If memory location known a priori, absolute code can be generated; must recompile code if starting location changes. I Load time: Must generate relocatable code if memory location is not known at compile time. I Execution time: Binding delayed until run time if the process can be moved during its execution from one memory segment to another. Need hardware support for address maps (e.g., base and limit registers). Operating System Concepts 9.3 Silberschatz, Galvin and Gagne 2002 Multistep Processing of a User Program Operating System Concepts 9.4 Silberschatz, Galvin and Gagne 2002 Logical vs. Physical Address Space I The concept of a logical address space that is bound to a separate physical address space is central to proper memory management. ✦ Logical address – generated by the CPU; also referred to as virtual address. ✦ Physical address – address seen by the memory unit. I Logical and physical addresses are the same in compile- time and load-time address-binding schemes; logical (virtual) and physical addresses differ in execution-time address-binding scheme. -
Memory Hierarchies.Pages
CPS311 Lecture: Memory Hierarchies Last Revised October 21, 2019 Objectives: 1. To introduce cache memory 2. To introduce logical-physical address mapping 3. To introduce virtual memory Materials 1. Memory System Demo 2. Files for demo: CAMCache1ByteLine.parameters, CAMCache8ByteLine.parameters, DMCache.parameters, SACache.parameters, WBCache.parameters, NonVirtualNoTLB.parameters, NonVirtualWithTLB.system, Virtual.parameters, Full.parameters 3. AMAT Calculation example handout I. Introduction A.In the previous lecture, we looked at the basic building blocks of memory systems: the individual devices. We now focus on complete memory systems. B. Since every instruction executed by the CPU requires at least one memory access (to fetch the instruction) and often more, the performance of memory has a strong impact on system performance. In fact, the overall system cannot perform better than its memory system. 1. Note that we are distinguishing between the CPU and the memory system on a functional basis. The CPU accesses memory both when fetching an instruction, and as a result of executing instructions that reference memory (such as lw and sw on MIPS). 2. We will consider the memory system to be a logical unit separate from the CPU, even though it is often the case that, for performance reasons, some portions of it physically reside on the same chip as the CPU. !1 C. At one point in time, the speed of the dominant technology used for memory was well matched to the speed of the CPU. This, however, is not the case today (and has not been the case - in at least some portions of the computer system landscape - for decades). -
Objective-C Internals Realmac Software
André Pang Objective-C Internals Realmac Software 1 Nice license plate, eh? In this talk, we peek under the hood and have a look at Objective-C’s engine: how objects are represented in memory, and how message sending works. What is an object? 2 To understand what an object really is, we dive down to the lowest-level of the object: what it actually looks like in memory. And to understand Objective-C’s memory model, one must first understand C’s memory model… What is an object? int i; i = 0xdeadbeef; de ad be ef 3 Simple example: here’s how an int is represented in C on a 32-bit machine. 32 bits = 4 bytes, so the int might look like this. What is an object? int i; i = 0xdeadbeef; ef be af de 4 Actually, the int will look like this on Intel-Chip Based Macs (or ICBMs, as I like to call them), since ICBMs are little- endian. What is an object? int i; i = 0xdeadbeef; de ad be ef 5 … but for simplicity, we’ll assume memory layout is big-endian for this presentation, since it’s easier to read. What is an object? typedef struct _IntContainer { int i; } IntContainer; IntContainer ic; ic.i = 0xdeadbeef; de ad be ef 6 This is what a C struct that contains a single int looks like. In terms of memory layout, a struct with a single int looks exactly the same as just an int[1]. This is very important, because it means that you can cast between an IntContainer and an int for a particular value with no loss of precision. -
CS/COE1541: Introduction to Computer Architecture Dept
CS/COE1541: Introduction to Computer Architecture Dept. of Computer Science University of Pittsburgh http://www.cs.pitt.edu/~melhem/courses/1541p/index.html Chapter 5: Exploiting the Memory Hierarchy Lecture 2 Lecturer: Rami Melhem 1 The Basics of Caches • Until specified otherwise, it will be assumed that a block is one word of data • Three issues: – How do we know if a data item is in the cache? – If it is, how do we find it? address – If it is not, what do we do? Main CPU Cache memory • It boils down to – where do we put an item in the cache? – how do we identify the items in the cache? data • Two solutions – put item anywhere in cache (associative cache) – associate specific locations to specific items (direct mapped cache) Note: we will assume that memory requests are for words (4 Bytes) although an instruction can address a byte 2 Fully associative cache 00000 00001 To cache a data word, d, whose memory address is L: 00010 00011 •Put d in any location in the cache 00100 00101 • Tag the data with the memory address L. 00110 00111 01000 Cache index 01001 01010 01011 000 01001000 01100 Example: 001 001 01101 010 010 01110 • An 8-word cache 011 011 01111 (indexed by 000, … , 111) 100 11000100 10000 101 101 10001 • A 32-words memory 110 01110110 10010 111 111 10011 (addresses 00000, … , 11111) Tags Data 10100 10101 Cache 10110 10111 11000 Advantage: can fully utilize the cache capacity 11001 11010 Disadvantage: need to search all tags to find data 11011 11100 Memory word addresses 11101 11110 (without the 2-bits byte offset) 11111 Memory 3 Direct Mapped Cache (direct hashing) 00000 Assume that the size of the cache is N words. -
IA-32 Architecture
Outline IA-32 Architecture Intel Microprocessors IA-32 Registers Computer Organization Instruction Execution Cycle & IA-32 Memory Management Assembly Language Programming Dr Adnan Gutub aagutub ‘at’ uqu.edu.sa [Adapted from slides of Dr. Kip Irvine: Assembly Language for Intel-Based Computers] Most Slides contents have been arranged by Dr Muhamed Mudawar & Dr Aiman El-Maleh from Computer Engineering Dept. at KFUPM 45/٢ IA-32 Architecture Computer Organization and Assembly Language slide Intel Microprocessors Intel 80286 and 80386 Processors Intel introduced the 8086 microprocessor in 1979 80286 was introduced in 1982 8086, 8087, 8088, and 80186 processors 24-bit address bus ⇒ 224 bytes = 16 MB address space 16-bit processors with 16-bit registers Introduced protected mode 16-bit data bus and 20-bit address bus Segmentation in protected mode is different from the real mode Physical address space = 220 bytes = 1 MB 80386 was introduced in 1985 8087 Floating-Point co-processor First 32-bit processor with 32-bit general-purpose registers Uses segmentation and real-address mode to address memory First processor to define the IA-32 architecture Each segment can address 216 bytes = 64 KB 32-bit data bus and 32-bit address bus 8088 is a less expensive version of 8086 232 bytes ⇒ 4 GB address space Uses an 8-bit data bus Introduced paging , virtual memory , and the flat memory model 80186 is a faster version of 8086 Segmentation can be turned off 45/٤ 45 IA-32 Architecture Computer Organization and Assembly Language slide/٣