3 First Steps in C Programming
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
TI 83/84: Scientific Notation on Your Calculator
TI 83/84: Scientific Notation on your calculator this is above the comma, next to the square root! choose the proper MODE : Normal or Sci entering numbers: 2.39 x 106 on calculator: 2.39 2nd EE 6 ENTER reading numbers: 2.39E6 on the calculator means for us. • When you're in Normal mode, the calculator will write regular numbers unless they get too big or too small, when it will switch to scientific notation. • In Sci mode, the calculator displays every answer as scientific notation. • In both modes, you can type in numbers in scientific notation or as regular numbers. Humans should never, ever, ever write scientific notation using the calculator’s E notation! Try these problems. Answer in scientific notation, and round decimals to two places. 2.39 x 1016 (5) 2.39 x 109+ 4.7 x 10 10 (4) 4.7 x 10−3 3.01 103 1.07 10 0 2.39 10 5 4.94 10 10 5.09 1018 − 3.76 10−− 1 2.39 10 5 7.93 10 8 Remember to change your MODE back to Normal when you're done. Using the STORE key: Let's say that you want to store a number so that you can use it later, or that you want to store answers for several different variables, and then use them together in one problem. Here's how: Enter the number, then press STO (above the ON key), then press ALPHA and the letter you want. (The letters are in alphabetical order above the other keys.) Then press ENTER. -
Fortran 90 Overview
1 Fortran 90 Overview J.E. Akin, Copyright 1998 This overview of Fortran 90 (F90) features is presented as a series of tables that illustrate the syntax and abilities of F90. Frequently comparisons are made to similar features in the C++ and F77 languages and to the Matlab environment. These tables show that F90 has significant improvements over F77 and matches or exceeds newer software capabilities found in C++ and Matlab for dynamic memory management, user defined data structures, matrix operations, operator definition and overloading, intrinsics for vector and parallel pro- cessors and the basic requirements for object-oriented programming. They are intended to serve as a condensed quick reference guide for programming in F90 and for understanding programs developed by others. List of Tables 1 Comment syntax . 4 2 Intrinsic data types of variables . 4 3 Arithmetic operators . 4 4 Relational operators (arithmetic and logical) . 5 5 Precedence pecking order . 5 6 Colon Operator Syntax and its Applications . 5 7 Mathematical functions . 6 8 Flow Control Statements . 7 9 Basic loop constructs . 7 10 IF Constructs . 8 11 Nested IF Constructs . 8 12 Logical IF-ELSE Constructs . 8 13 Logical IF-ELSE-IF Constructs . 8 14 Case Selection Constructs . 9 15 F90 Optional Logic Block Names . 9 16 GO TO Break-out of Nested Loops . 9 17 Skip a Single Loop Cycle . 10 18 Abort a Single Loop . 10 19 F90 DOs Named for Control . 10 20 Looping While a Condition is True . 11 21 Function definitions . 11 22 Arguments and return values of subprograms . 12 23 Defining and referring to global variables . -
Quick Overview: Complex Numbers
Quick Overview: Complex Numbers February 23, 2012 1 Initial Definitions Definition 1 The complex number z is defined as: z = a + bi (1) p where a, b are real numbers and i = −1. Remarks about the definition: • Engineers typically use j instead of i. • Examples of complex numbers: p 5 + 2i; 3 − 2i; 3; −5i • Powers of i: i2 = −1 i3 = −i i4 = 1 i5 = i i6 = −1 i7 = −i . • All real numbers are also complex (by taking b = 0). 2 Visualizing Complex Numbers A complex number is defined by it's two real numbers. If we have z = a + bi, then: Definition 2 The real part of a + bi is a, Re(z) = Re(a + bi) = a The imaginary part of a + bi is b, Im(z) = Im(a + bi) = b 1 Im(z) 4i 3i z = a + bi 2i r b 1i θ Re(z) a −1i Figure 1: Visualizing z = a + bi in the complex plane. Shown are the modulus (or length) r and the argument (or angle) θ. To visualize a complex number, we use the complex plane C, where the horizontal (or x-) axis is for the real part, and the vertical axis is for the imaginary part. That is, a + bi is plotted as the point (a; b). In Figure 1, we can see that it is also possible to represent the point a + bi, or (a; b) in polar form, by computing its modulus (or size), and angle (or argument): p r = jzj = a2 + b2 θ = arg(z) We have to be a bit careful defining φ, since there are many ways to write φ (and we could add multiples of 2π as well). -
Primitive Number Types
Primitive number types Values of each of the primitive number types Java has these 4 primitive integral types: byte: A value occupies 1 byte (8 bits). The range of values is -2^7..2^7-1, or -128..127 short: A value occupies 2 bytes (16 bits). The range of values is -2^15..2^15-1 int: A value occupies 4 bytes (32 bits). The range of values is -2^31..2^31-1 long: A value occupies 8 bytes (64 bits). The range of values is -2^63..2^63-1 and two “floating-point” types, whose values are approximations to the real numbers: float: A value occupies 4 bytes (32 bits). double: A value occupies 8 bytes (64 bits). Values of the integral types are maintained in two’s complement notation (see the dictionary entry for two’s complement notation). A discussion of floating-point values is outside the scope of this website, except to say that some bits are used for the mantissa and some for the exponent and that infinity and NaN (not a number) are both floating-point values. We don’t discuss this further. Generally, one uses mainly types int and double. But if you are declaring a large array and you know that the values fit in a byte, you can save ¾ of the space using a byte array instead of an int array, e.g. byte[] b= new byte[1000]; Operations on the primitive integer types Types byte and short have no operations. Instead, operations on their values int and long operations are treated as if the values were of type int. -
Fortran Math Special Functions Library
IMSL® Fortran Math Special Functions Library Version 2021.0 Copyright 1970-2021 Rogue Wave Software, Inc., a Perforce company. Visual Numerics, IMSL, and PV-WAVE are registered trademarks of Rogue Wave Software, Inc., a Perforce company. IMPORTANT NOTICE: Information contained in this documentation is subject to change without notice. Use of this docu- ment is subject to the terms and conditions of a Rogue Wave Software License Agreement, including, without limitation, the Limited Warranty and Limitation of Liability. ACKNOWLEDGMENTS Use of the Documentation and implementation of any of its processes or techniques are the sole responsibility of the client, and Perforce Soft- ware, Inc., assumes no responsibility and will not be liable for any errors, omissions, damage, or loss that might result from any use or misuse of the Documentation PERFORCE SOFTWARE, INC. MAKES NO REPRESENTATION ABOUT THE SUITABILITY OF THE DOCUMENTATION. THE DOCU- MENTATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND. PERFORCE SOFTWARE, INC. HEREBY DISCLAIMS ALL WARRANTIES AND CONDITIONS WITH REGARD TO THE DOCUMENTATION, WHETHER EXPRESS, IMPLIED, STATUTORY, OR OTHERWISE, INCLUDING WITHOUT LIMITATION ANY IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PAR- TICULAR PURPOSE, OR NONINFRINGEMENT. IN NO EVENT SHALL PERFORCE SOFTWARE, INC. BE LIABLE, WHETHER IN CONTRACT, TORT, OR OTHERWISE, FOR ANY SPECIAL, CONSEQUENTIAL, INDIRECT, PUNITIVE, OR EXEMPLARY DAMAGES IN CONNECTION WITH THE USE OF THE DOCUMENTATION. The Documentation is subject to change at any time without notice. IMSL https://www.imsl.com/ Contents Introduction The IMSL Fortran Numerical Libraries . 1 Getting Started . 2 Finding the Right Routine . 3 Organization of the Documentation . 4 Naming Conventions . -
C++ Data Types
Software Design & Programming I Starting Out with C++ (From Control Structures through Objects) 7th Edition Written by: Tony Gaddis Pearson - Addison Wesley ISBN: 13-978-0-132-57625-3 Chapter 2 (Part II) Introduction to C++ The char Data Type (Sample Program) Character and String Constants The char Data Type Program 2-12 assigns character constants to the variable letter. Anytime a program works with a character, it internally works with the code used to represent that character, so this program is still assigning the values 65 and 66 to letter. Character constants can only hold a single character. To store a series of characters in a constant we need a string constant. In the following example, 'H' is a character constant and "Hello" is a string constant. Notice that a character constant is enclosed in single quotation marks whereas a string constant is enclosed in double quotation marks. cout << ‘H’ << endl; cout << “Hello” << endl; The char Data Type Strings, which allow a series of characters to be stored in consecutive memory locations, can be virtually any length. This means that there must be some way for the program to know how long the string is. In C++ this is done by appending an extra byte to the end of string constants. In this last byte, the number 0 is stored. It is called the null terminator or null character and marks the end of the string. Don’t confuse the null terminator with the character '0'. If you look at Appendix A you will see that the character '0' has ASCII code 48, whereas the null terminator has ASCII code 0. -
Floating Point Numbers
Floating Point Numbers CS031 September 12, 2011 Motivation We’ve seen how unsigned and signed integers are represented by a computer. We’d like to represent decimal numbers like 3.7510 as well. By learning how these numbers are represented in hardware, we can understand and avoid pitfalls of using them in our code. Fixed-Point Binary Representation Fractional numbers are represented in binary much like integers are, but negative exponents and a decimal point are used. 3.7510 = 2+1+0.5+0.25 1 0 -1 -2 = 2 +2 +2 +2 = 11.112 Not all numbers have a finite representation: 0.110 = 0.0625+0.03125+0.0078125+… -4 -5 -8 -9 = 2 +2 +2 +2 +… = 0.00011001100110011… 2 Computer Representation Goals Fixed-point representation assumes no space limitations, so it’s infeasible here. Assume we have 32 bits per number. We want to represent as many decimal numbers as we can, don’t want to sacrifice range. Adding two numbers should be as similar to adding signed integers as possible. Comparing two numbers should be straightforward and intuitive in this representation. The Challenges How many distinct numbers can we represent with 32 bits? Answer: 232 We must decide which numbers to represent. Suppose we want to represent both 3.7510 = 11.112 and 7.510 = 111.12. How will the computer distinguish between them in our representation? Excursus – Scientific Notation 913.8 = 91.38 x 101 = 9.138 x 102 = 0.9138 x 103 We call the final 3 representations scientific notation. It’s standard to use the format 9.138 x 102 (exactly one non-zero digit before the decimal point) for a unique representation. -
Floating Point Numbers and Arithmetic
Overview Floating Point Numbers & • Floating Point Numbers Arithmetic • Motivation: Decimal Scientific Notation – Binary Scientific Notation • Floating Point Representation inside computer (binary) – Greater range, precision • Decimal to Floating Point conversion, and vice versa • Big Idea: Type is not associated with data • MIPS floating point instructions, registers CS 160 Ward 1 CS 160 Ward 2 Review of Numbers Other Numbers •What about other numbers? • Computers are made to deal with –Very large numbers? (seconds/century) numbers 9 3,155,760,00010 (3.1557610 x 10 ) • What can we represent in N bits? –Very small numbers? (atomic diameter) -8 – Unsigned integers: 0.0000000110 (1.010 x 10 ) 0to2N -1 –Rationals (repeating pattern) 2/3 (0.666666666. .) – Signed Integers (Two’s Complement) (N-1) (N-1) –Irrationals -2 to 2 -1 21/2 (1.414213562373. .) –Transcendentals e (2.718...), π (3.141...) •All represented in scientific notation CS 160 Ward 3 CS 160 Ward 4 Scientific Notation Review Scientific Notation for Binary Numbers mantissa exponent Mantissa exponent 23 -1 6.02 x 10 1.0two x 2 decimal point radix (base) “binary point” radix (base) •Computer arithmetic that supports it called •Normalized form: no leadings 0s floating point, because it represents (exactly one digit to left of decimal point) numbers where binary point is not fixed, as it is for integers •Alternatives to representing 1/1,000,000,000 –Declare such variable in C as float –Normalized: 1.0 x 10-9 –Not normalized: 0.1 x 10-8, 10.0 x 10-10 CS 160 Ward 5 CS 160 Ward 6 Floating -
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 -
A Practical Introduction to Python Programming
A Practical Introduction to Python Programming Brian Heinold Department of Mathematics and Computer Science Mount St. Mary’s University ii ©2012 Brian Heinold Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported Li- cense Contents I Basics1 1 Getting Started 3 1.1 Installing Python..............................................3 1.2 IDLE......................................................3 1.3 A first program...............................................4 1.4 Typing things in...............................................5 1.5 Getting input.................................................6 1.6 Printing....................................................6 1.7 Variables...................................................7 1.8 Exercises...................................................9 2 For loops 11 2.1 Examples................................................... 11 2.2 The loop variable.............................................. 13 2.3 The range function............................................ 13 2.4 A Trickier Example............................................. 14 2.5 Exercises................................................... 15 3 Numbers 19 3.1 Integers and Decimal Numbers.................................... 19 3.2 Math Operators............................................... 19 3.3 Order of operations............................................ 21 3.4 Random numbers............................................. 21 3.5 Math functions............................................... 21 3.6 Getting -
Princeton University COS 217: Introduction to Programming Systems C Primitive Data Types
Princeton University COS 217: Introduction to Programming Systems C Primitive Data Types Type: int Description: A (positive or negative) integer. Size: System dependent. On CourseLab with gcc217: 4 bytes. Example Variable Declarations: int iFirst; signed int iSecond; Example Literals (assuming size is 4 bytes): C Literal Binary Representation Note 123 00000000 00000000 00000000 01111011 decimal form -123 11111111 11111111 11111111 10000101 negative form 0173 00000000 00000000 00000000 01111011 octal form 0x7B 00000000 00000000 00000000 01111011 hexadecimal form 2147483647 01111111 11111111 11111111 11111111 largest -2147483648 10000000 00000000 00000000 00000000 smallest Type: unsigned int Description: A non-negative integer. Size: System dependent. sizeof(unsigned int) == sizeof(int). On CourseLab with gcc217: 4 bytes. Example Variable Declaration: unsigned int uiFirst; unsigned uiSecond; Example Literals (assuming size is 4 bytes): C Literal Binary Representation Note 123U 00000000 00000000 00000000 01111011 decimal form 0173U 00000000 00000000 00000000 01111011 octal form 0x7BU 00000000 00000000 00000000 01111011 hexadecimal form 4294967295U 11111111 11111111 11111111 11111111 largest 0U 00000000 00000000 00000000 00000000 smallest Type: long Description: A (positive or negative) integer. Size: System dependent. sizeof(long) >= sizeof(int). On CourseLab with gcc217: 8 bytes. Example Variable Declarations: long lFirst; long int iSecond; signed long lThird; signed long int lFourth; Page 1 of 5 Example Literals (assuming size is 8 bytes): -
A Fast-Start Method for Computing the Inverse Tangent
A Fast-Start Method for Computing the Inverse Tangent Peter Markstein Hewlett-Packard Laboratories 1501 Page Mill Road Palo Alto, CA 94062, U.S.A. [email protected] Abstract duction method is handled out-of-loop because its use is rarely required.) In a search for an algorithm to compute atan(x) For short latency, it is often desirable to use many in- which has both low latency and few floating point in- structions. Different sequences may be optimal over var- structions, an interesting variant of familiar trigonom- ious subdomains of the function, and in each subdomain, etry formulas was discovered that allow the start of ar- instruction level parallelism, such as Estrin’s method of gument reduction to commence before any references to polynomial evaluation [3] reduces latency at the cost of tables stored in memory are needed. Low latency makes additional intermediate calculations. the method suitable for a closed subroutine, and few In searching for an inverse tangent algorithm, an un- floating point operations make the method advantageous usual method was discovered that permits a floating for a software-pipelined implementation. point argument reduction computation to begin at the first cycle, without first examining a table of values. While a table is used, the table access is overlapped with 1Introduction most of the argument reduction, helping to contain la- tency. The table is designed to allow a low degree odd Short latency and high throughput are two conflict- polynomial to complete the approximation. A new ap- ing goals in transcendental function evaluation algo- proach to the logarithm routine [1] which motivated this rithm design.