Chapter 2 : Computational tools

Transcription

1 Chapter 2 : Computational tools 1 Inside the box : computer architecture Integrated circuits (chips) connected via printed-circuit boards memory made of millions of individual transistors processor(s) storage media : hard disk, CD-rom, mass storage device, 3.5 diskette,... interfaces : screen, keyboard, mouse,...

2 1.1 Memory Composed of millions of transistors in the OFF (non-conducting) state or in the ON (conducting) state Smallest unit of storage bit with value 0 or 1 Types of memories : RAM (random access memory), accessible for reading and writing ROM (read only memory) PROM (programmable read only memory)

3 The data stored in memory provide all the information that controls the actions of the computer One bit contains the minimum information possible : 0 or 1 1. First stage of organisation : Data bits are grouped 1. by 8 in bytes : for instance : by (usually) 32 in words for instance Memory are divided in blocks (typically 512 octets) or pages (4096 octets)

4 2. Second stage of organisation of the memory : Each word is given an address unique identifying number RAM chip transistors + circuitry Example : 1 Mbit chip can be arranged in 32-bit words, numbered from 0 to Mbit = 2 20 = /2 5 = 2 15 = Address binary number, specified to the chip by 15 connections to the address lines Higher bits of the address specify different chips is the data read from the chip or written to it?

5 1.2 Processors Processor central processing unit (cpu) Executes programs by performing arithmetical or logical operations on data Creates new information by combining or modifying existing information Includes a control unit with memory for 2 very important words instruction unit holding the action to execute in numerical form program counter holding the address of the instruction to perform data registers : memory to store numbers (integer and real registers) arithmetical/logical units : execute integer, real or logical instructions Each unit has its own data registers

6 Program long list of numerical instructions 1. Program counter initialised to the entry point first address 2. CPU executes the instructions by repeating a 4 steps cycle (a) Fill the instruction register with the content of the memory at the address given by the program counter (b) Decode and carry out the action specified in the instruction register (c) Increment the program counter so it points to the next instruction (d) Return to step 1 Instructions can alter the program counter!! i.e. the address of the following instruction program is not necessarily executed in sequence 3. Counter loaded with the address of a system program that frees the memory

7 Types of processor 1. Scalar processors CISC processor : Complex Instruction Set Computer, voluntarily complex but accessing memory less often Examples : AMD Athlon, Intel Pentium,... RISC processor : Reduced Instruction Set Computer, with a limited set of instructions of equal length (the program counter is increased by 1 word or 4 bytes each cycle), executed very quickly executes several instructions per clock cycle super scalar processors Examples : IBM Power2 et Power PC, MIPS R12000 (Motorola), Vectorial processors able to execute an instruction on a vector of operands Examples : Cray, Fujitsu, NEC,...

8 Speed of processor clock cycle = shortest time interval for an operation Unit Hertz (Hz) Typical speed : 1 3 Gigahertz (GHz) Number of instructions per second (mips = millions instructions per second) Instruction task executed by the processor Number of floating operations per second flops Floating operation operation on real numbers Operation : at least one cycle Possibility to execute simultaneously several operations of different types Floating point operations : often longer to execute than integer operations Multiplication : 4 cycles Division : clock cycles

9 Performance in Mflops LINPACK Benchmark : solution of a system of n linear equations Processor Theoretical Peak n = 1000 n = 100 NEC SX Futjitsu VPP IBM eserver pseries 690 Turbo 1.3 GHz 5200 IBM RS/6000 SP Power MHz Intel P GHz Intel Itanium 800 MHz Sun Ultra SPARC III 750 MHz Computer Theoretical Peak n = 1000 NEC SX-6/8 (8 processors) Cray T932 (4 processors) Cray T932 (32 processors)

10 Organisation of the memory : 1. level 1 cache : located in the cpu, very fast (access time 10 nsec) but very expensive. Typically, a cpu has a cache of 128 Kb to 256 Kb 2. level 2 cache (optional) : located on the memory card buffer between the cpu and the primary memory 3. primary memory : slower than the cache memory (access times nsec), cheaper (typically 128 Mbytes to 256 Mbytes for a PC, 1 Gbytes for a workstation and several Gbytes for supercomputers calcul) The information between different modules (cpu, memories,...) is transfered by buses Transfert rate band width measured in bits/sec or bps, can vary from 10 Mbps to 500 Mbps

11 1.3 Storage media Hard disks magnetic media for data storage accessible for reading or writing Size : 20 Gbytes 100 Gbytes Access times : 8 12 msec Rate of transfer onto the disk : 80 Mbps Size of CD : 800 Mbyte, size of DVD : 4.7 Gbytes 1.4 Interface in the (not good) old times : paper tapes, punched cards printer keyboard, screen mouse, pointer, touchpad microphone

12 2 Software 1. Operating System (OS) Control the running of other programs Examples : Unix (Linux), Windows, Mac/OS (Macintosh),... Unix globaly independent of the architecture 2. Stand-alone packages Examples : text editors, word processors, spreadsheets, CAD programs, Graphical interfaces : important role for user s comfort Examples : X-windows, KDE, Gnome, Windows,... visualisation of data Examples : xmgr, Data Explorer, AVS, PV-Wave,...

13 4. Programming languages Assembler Assembler equivalent Acorn Archimedes LDR R1,c LDR R2,b MUL R3,R2,R1 LDR R4,a ADD R3,R3,R4 STR R3,x Machine-language equivalent (HEX) Archimedes RISC processor E59F101C E59F2014 E E59F4008 E E58F300C High-level language equivalent : x = a + b c

14 Fortran (Formula Translation) for intensive scientific calculation C, C++ Pascal (teaching) Lisp (artificial intelligence), ADA, Java, Perl, Eiffel, Scientific libraries Machine optimised Portability Parallel version Examples : BLAS (Basic Linear Algebra Subroutines) LAPACK (Linear Algebra Package) Commercial libraries (NAG, ESSL,...) STAT

15 6. Computing environments for mathematics and sciences Examples : Mathematica, Matlab, Maple, Macsima,... Manipulate character strings rather than numbers Useful for analytical evaluation of series, integrals, derivatives, reduction of polynomials and search of zeroes, matrix manipulation,... Numerical mode Results in graphic form 7. Communication : Modem : PPP (Point to Point Protocol) TCP/IP (Transmission Control Protocol/Internet Protocol) : FTP (File Transfer Protocol) : transfer of data files Telnet, rlogin : remote login HTTP (hypertext transfer protocol) : for web browsers

16 Information on the computer used during the tutorials PC with 2 Intel Pentium II processors, 400MHz 512 Kbytes cache, 192 Mbytes memory Disks : /home : 3 Gbytes /etu : 9 Gbytes Operating system : LINUX kernel , Mandrake distribution KDE graphical interface

17 3 Programming 3.1 Why do you want to write your own program? Software not available Improve understanding Improve performance Want to check Professional (or semi-professional) aim Curiosity

18 3.2 How to write a good program? A. Clarity Use meaningful names of variables Indent commands to show the structure of the code Document the code by useful comments : objectives, author s name, date of last up-date, task description, B. User-friendliness (interaction with the user) Simple and clear input data Verify the validity of input data Provide understandable and helpful error messages Simple and clear output data Portable

19 PROGRAM solve This program solves quadratic equations Written by M Dunseath, REAL:: a, b, bp, c, discri, xminus, xplus WRITE (6,*) Please enter a,b,c with ax**2 + bx + c = 0 READ (5,*) a,b,c bp = 0.5 * b discri = sqrt(bp * bp - a * c) xminus = (- bp - discri) / a xplus = (- bp + discri) / a WRITE (6, ( xminus =,d13.5, xplus =,d13.5) ) xminus, xplus END PROGRAM solve

20 FORTRAN90 File containg the program : solve.f90 1. Compilation : f90 -c solve.f90 object module : solve.o 2. Edition of links : f90 -o solve.exe solve executable : solve.exe 1. & 2. Compilation and edition of links : f90 -o solve.exe solve.f90 3. Run : solve.exe C++ File containg the program : solve.cpp 1. Compilation : g++ -c solve.cpp object module : solve.o 2. Edition of links : g++ -o solve.exe solve executable : solve.exe 1. & 2. Compilation and edition of links : g++ -o solve solve.cpp 3. Run : solve

21 // C++ version #include <iostream.h> #include <math.h> main() { // This program solves one-variable second-order equations // Written by M Dunseath, float a, b, bp, c, discri, xminus, xplus; cout >> Please enter a,b,c with ax**2 + bx + c = 0 \n ; cin << a << b << c; bp = 0.5 * b; discri = sqrt(bp * bp - a * c); xminus = (- bp - discri) / a; xplus = (- bp + discri) / a; cout >> xminus = >> xminus >> xplus = >> xplus >> \n ; return 0; }

22 PROGRAM PROG IMPLICIT REAL(A-H,O-Z) READ (5,*) VAR1,VAR2,VAR3 TITI=SQRT(VAR2**2-4*VAR1*VAR3) TATA=(-VAR2+TITI)/2/VAR1 TOTO=(-VAR2-TITI)/2/VAR1 WRITE (6,*) TATA,TOTO END PROGRAM PROG

23 PROGRAM solvequadeq Purpose of the program This program solves one-variable second-order equations 2 a * x + bx + c = 0 Author of the program Mr Toomuch Office number 123, building P Date: 17th of January 2003 Declaration of variables REAL :: a, b, c, discriminant, halfofb, xminus, xplus Ask data to user WRITE (6,*) Please enter a,b,c with ax**2 + bx + c = 0 Read in data READ (5,*) a,b,c Here start the real job Calculate half of b and store in halfofb halfofb = 0.5 * b Calculate discriminant of second order equation discriminant = sqrt(halfofb * halfofb - a * c) Calculate first solution (smallest one) xminus = (- halfofb - discriminant) / a Calculate second solution (largest one) xplus = (- halfofb + discriminant) / a Print solutions WRITE (6, ( xminus =,d13.5, xplus =,d13.5) ) xminus, xplus End of the program END PROGRAM solvequadeq