Question: Question #2 - 6 marks. If a and y are floating-point numbers, then the evaluation of f(x, y) = -1 - VT? - 4 in

Question #2 - 6 marks. If a and y are floating-point numbers, then the evaluation of f(x, y) = -1 - VT? - 4 in a floating point system may be very inaccurate due to cancellation. To illustrate, use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic for parts (a) and (b) below. (a) Let x = 123.4 = 0.1234 x 10' and y = -1.234 = -0.1234 x 10', evaluate f(f(,y)) and determine the relative error. (b) Now let r = -123.4 = -0.1234 x 10' and y = 1.234 = 0.1234 x 10', evaluate f(f(x,y)) and determine the relative error. (c) Based on the above results and similar kinds of computations you might do some more computations, but it is not necessary to hand them in), specify which ranges of values of r and y are such that the computation of f (x,y)) will always be very inaccurate? (Your ranges can be loosely deifned, that is, you do not have to give specific numeric bounds. You may say things like "large x", or "large y", or "small positive x", etc.) Question #2 - 6 marks. If a and y are floating-point numbers, then the evaluation of f(x, y) = -1 - VT? - 4 in a floating point system may be very inaccurate due to cancellation. To illustrate, use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic for parts (a) and (b) below. (a) Let x = 123.4 = 0.1234 x 10' and y = -1.234 = -0.1234 x 10', evaluate f(f(,y)) and determine the relative error. (b) Now let r = -123.4 = -0.1234 x 10' and y = 1.234 = 0.1234 x 10', evaluate f(f(x,y)) and determine the relative error. (c) Based on the above results and similar kinds of computations you might do some more computations, but it is not necessary to hand them in), specify which ranges of values of r and y are such that the computation of f (x,y)) will always be very inaccurate? (Your ranges can be loosely deifned, that is, you do not have to give specific numeric bounds. You may say things like "large x", or "large y", or "small positive x", etc.)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

i) Consider the floating-point number system that have binary representa- tions of the form (0.b1b2)2 x 2*, where k, b,b = {0,1}. a) Write down all the numbers which can be represented in this...

If x and y are floating - point numbers, then the evaluation off ( x , y ) = x x 2 yin a floating point system may be very inaccurate due to cancellation. To illustrate, use baseb = 1 0 , precision k...

clarifications: math.h functions may not be used in this project math.h was included in to the source code to provide the INFINITY constant needed by your get_fp() function for returning...

In this question assume that p and q are atomic formulae. (a) Compare and contrast path formulae and state formulae in temporal logic. [4 marks] (b) Describe and contrast the meanings of F(G p) and...

A discrete sequence {xn} can be converted into a continuous representation x(t) = ts X n= (t n ts) xn, where ts is the sampling period. (a) State two characteristic properties of Dirac's function. [2...

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

Let r and s be solutions to the quadratic equation x 2 b x + c = 0. For n N, define d0 = 0 d1 = r s dn = b dn1 c dn2 (n 2) Prove that dn = r n s n for all n N. [4 marks] (b) Recall that a commutative...

Predictive text entry systems are familiar on touch screens and mobile phones. This question asks you to consider how the same principles might be used in a programming editor for creating Java code....

Give the typing rules for Peano natural numbers and their eliminator.(ii) Using the rules given above, define the addition function.] (iii) Let a binary tree be either a leaf Leaf or a node...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

Additionally, explain why you think this is the best case for you by identifying the most important lesson you learned from this case. How can you apply this lesson to manage an organization of your...

Discuss how XBRL addresses transparency, quality, and timeliness issues.

The process may look up information that should not be available to the _ _ _ _ _ attacker coder executable command

The first scenario will be a Verbal Judo scenario in which your scenario follows the standard Verbal Judo interaction: You need to ask somebody to modify their behavior either to do something or to...

3. What constructive coping skills do you want to develop or enhance? Do you want to, for example, start exercising more, learn meditation, manage your time better, develop a new hobby or activity,...

3. If some adjustments are in order, then first consider how you might eliminate some activities or time spent on doing things that are less important or out of balance. Then identify some specific...

3. Where and how would you begin to work toward getting such an innovation implemented? What factors do you think will support its adoption? What might be the significant barriers?