Lab# 3 IEEE Floating Point Representation

CST8233: Lab# 3
IEEE Floating Point Representation
Objectives
The objective of this lab is to get the student familiar with the theory components covered
in week 2.
Earning
To earn your mark for this lab, each student should finish the lab’s requirements
within the lab session and demonstrate the working code to the instructor.
Laboratory Problem Description
Part A:
The following program demonstrate the overflow and underflow
Task A.1: Copy and paste the following code to your Visual Studio environment.
Task A.2: Run the code and notice the output of the program. Explain what happens to
the
instructor.
Task A.3: Change the loop’s determinant “i” to few numbers higher than 127 and notice
the output. Explain the results to the lab instructor.
#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include<math.h>
int main()
{
int i;
float n, x;
n = 1.0;
for (i = 0; i <= 127; i++)
{
n = n * 2.0;
x = 1.0 / n;
printf("%d %e %E\n", i, x, n);
}
return 0;
}
Part B:
Truncation error occurs when the numerical methods used for solving mathematical
problem. The numerical method approximates your function using a finite number of
terms.
The difference between the exact and approximate solution is called truncation error. The
following task demonstrate the truncation error to compute the famous factorial function.
there is a famous numerical approximate formula, named after the Scottish mathematician
James Stirling (1692-1770), that gives an approximate evaluation for n!.
𝒏! = √𝟐 ∗ 𝝅 ∗ 𝒏 ∗ 𝒏
𝒏
∗ 𝒆
−𝒏
Task B :
Write a program to output a table with the following formate, you may use the factorial
function from Lab#1 to calculate the analytical value of factorial function at each step.
n n! Stirling’s
approximation
Absolute error Relative error
for n = 1,2,...,10.
Hint: If your computer system does not have a predefined value for π,
Use either π = acos(-1.0) or π = 4.0*atan(1.0)
Sample output:
Enter the number to calculate its factorial: 10
N n! Stirling’s
approximation
Absolute error
error
Relative error
1 1 0.922137 0.077863 0.077863
2 2 1.919004 0.080996 0.040498
3 6 5.836210 0.163790 0.027298
4 24 23.506175 0.493825 0.020576
5 120 118.019168 1.980832 0.016507
6 720 710.078185 9.921815 0.013780
7 5040 4980.395832 59.604168 0.011826
8 40320 39902.395453 417.604547 0.010357
9 362880 359536.872842 3343.127158 0.009213
10 3628800 3598695.618741 30104.381259 0.008296
Your numbers may be slightly different depending on the computer system and
the precision used. Judging from the results, does the accuracy increase or
decrease with increasing n.