Computer Science: An Overview (12th Edition)
12th Edition
ISBN: 9780133760064
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
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Chapter 8, Problem 3SI
In many application
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Write a program to calculate the function sin(x) or cos(x) using a Taylor series expansion around the point 0. In other words, you will program the sine or cosine function yourself, without using any existing solution. You can enter the angles in degrees or radians. The program must work for any input, e.g. -4500° or +8649°. The function will have two arguments:
float sinus(float radians, float epsilon);
For your own implementation, use one of the following relations (you only need to program either sine or cosine, you don't need both):
Tip 1: Of course, you cannot calculate the sum of an infinite series indefinitely. You can see (if not, look in the program) that the terms keep getting smaller, so there will definitely be a situation where adding another term will not change the result in any way (see problem 1.3 – machine epsilon). However, you can end the calculation even earlier – when the result changes by less than epsilon (a pre-specified, sufficiently small number, e.g.…
Write a C program that finds and prints the machine epsilon for the float and double data types. Also print the values of __FLT_EPSILON__ and __DBL_EPSILON__ defined in float.h. Reminder – the phrase data type tells how the compiler “understands” the ones and zeros you are working with. This identifies whether you are working with integers, letters, real numbers, and so on.
Another definition:Machine epsilon is the "distance" between the number 1 and its immediate right neighbor.
We work in binary (decimal is in parentheses):
1 + 0,1 = 1,1 (1 + 1/2 = 1,5)
1 + 0,01 = 1,01 (1 + 1/4 = 1,25)
1 + 0,001 = 1,001 (1 + 1/8 = 1,125)
then, due to the limited accuracy of the computer at a certain number of decimal places, a situation arises where 1 + 0.0…001 = 1 (instead of the correct 1.0…001). Then the previous number 0.0…01 is called the machine epsilon . It is obvious that its value may be different on different computers. However, the machine…
Write a program that performs a rotational bit shift to the right for a positive integer. The user enters a number, the number of bits to shift (and, if you want, the direction of the shift, but right is enough).
Example:The number 9 (in binary form 1001) when rotated to the right by 1 bit becomes 1100.
Tip : A bit rotation (also known as a cyclic shift) is an operation in which the bits in a binary number are shifted a certain number of places to the right or left, with bits that “fall out” at one end being returned to the opposite end. So, start with a bit shift operation. Write a few examples on paper before programming.Tip : Use the unsigned int data type.You can get the number of bits of this data type as follows: int bit_count = sizeof (unsigned int ) * 8
Chapter 8 Solutions
Computer Science: An Overview (12th Edition)
Ch. 8.1 - Give examples (outside of computer science) of...Ch. 8.1 - Prob. 2QECh. 8.1 - Prob. 3QECh. 8.1 - Prob. 4QECh. 8.1 - Prob. 5QECh. 8.2 - In what sense are data structures such as arrays,...Ch. 8.2 - Prob. 2QECh. 8.2 - Prob. 3QECh. 8.3 - Prob. 1QECh. 8.3 - Prob. 2QE
Ch. 8.3 - Prob. 3QECh. 8.3 - Prob. 4QECh. 8.3 - Modify the function in Figure 8.19 so that it...Ch. 8.3 - Prob. 7QECh. 8.3 - Prob. 8QECh. 8.3 - Draw a diagram representing how the tree below...Ch. 8.4 - Prob. 1QECh. 8.4 - Prob. 2QECh. 8.4 - Prob. 3QECh. 8.4 - Prob. 4QECh. 8.5 - Prob. 1QECh. 8.5 - Prob. 3QECh. 8.5 - Prob. 4QECh. 8.6 - In what ways are abstract data types and classes...Ch. 8.6 - What is the difference between a class and an...Ch. 8.6 - Prob. 3QECh. 8.7 - Suppose the Vole machine language (Appendix C) has...Ch. 8.7 - Prob. 2QECh. 8.7 - Using the extensions described at the end of this...Ch. 8.7 - In the chapter, we introduced a machine...Ch. 8 - Prob. 1CRPCh. 8 - Prob. 2CRPCh. 8 - (Asterisked problems are associated with optional...Ch. 8 - Prob. 4CRPCh. 8 - (Asterisked problems are associated with optional...Ch. 8 - Prob. 6CRPCh. 8 - Prob. 7CRPCh. 8 - Prob. 8CRPCh. 8 - Prob. 9CRPCh. 8 - Prob. 10CRPCh. 8 - Prob. 11CRPCh. 8 - Prob. 12CRPCh. 8 - Prob. 13CRPCh. 8 - Prob. 14CRPCh. 8 - Prob. 15CRPCh. 8 - Prob. 16CRPCh. 8 - Prob. 17CRPCh. 8 - Prob. 18CRPCh. 8 - Design a function to compare the contents of two...Ch. 8 - (Asterisked problems are associated with optional...Ch. 8 - (Asterisked problems are associated with optional...Ch. 8 - Prob. 22CRPCh. 8 - Prob. 23CRPCh. 8 - Prob. 24CRPCh. 8 - (Asterisked problems are associated with optional...Ch. 8 - Prob. 26CRPCh. 8 - Prob. 27CRPCh. 8 - Prob. 28CRPCh. 8 - Prob. 29CRPCh. 8 - Prob. 30CRPCh. 8 - Design a nonrecursive algorithm to replace the...Ch. 8 - Prob. 32CRPCh. 8 - Prob. 33CRPCh. 8 - Prob. 34CRPCh. 8 - Draw a diagram showing how the binary tree below...Ch. 8 - Prob. 36CRPCh. 8 - Prob. 37CRPCh. 8 - Prob. 38CRPCh. 8 - Prob. 39CRPCh. 8 - Prob. 40CRPCh. 8 - Modify the function in Figure 8.24 print the list...Ch. 8 - Prob. 42CRPCh. 8 - Prob. 43CRPCh. 8 - Prob. 44CRPCh. 8 - Prob. 45CRPCh. 8 - Prob. 46CRPCh. 8 - Using pseudocode similar to the Java class syntax...Ch. 8 - Prob. 48CRPCh. 8 - Identify the data structures and procedures that...Ch. 8 - Prob. 51CRPCh. 8 - In what way is a class more general than a...Ch. 8 - Prob. 53CRPCh. 8 - Prob. 54CRPCh. 8 - Prob. 55CRPCh. 8 - Prob. 1SICh. 8 - Prob. 2SICh. 8 - In many application programs, the size to which a...Ch. 8 - Prob. 4SICh. 8 - Prob. 5SICh. 8 - Prob. 6SICh. 8 - Prob. 7SICh. 8 - Prob. 8SI
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