Question

Task 1: Machine Epsilon (10 pts) Machine epsilon e is a characteristic of the CPU in ones computer. This machine constant is used extensively when writing computer code to help make ones algorithms CPU insensitive. Machine epsilon e is the smallest number e such that 1 +e>1 in floating-point arithmetic. For any smaller value of e, round-off error would return 1+e = 1. Machine epsilon is defined by the formula b-where b is the base number used by your computer in its construction of a floating-point number (b-2 in computers that run Intel chips), and a is the total number of digits in the mantissa (adjustable and fixed). Note: 1 m is the power of base b because the first bit in a mantissa is fixed (ef. Homework 2). The fixed bit does. not appear explicitly in the bit array representing a floating-point number 1) Write a Python function that Computes machine epsilon (m). Use a while loop to accomplish this. Start with m equalling 1. In each successive loop compute em/2. Exit the loop when variable 1 m equals 1. Multiply the result coming out of this loop by 2 and you have computed machine epsilon. This function should have the following structure: def sachinelps epailen 1.o return epsilon Script files are executable files. 2) Write a Python script that Calls the function for computing machine epsilon, and then prints out (to the command window in Spyder) the answer in a readable format; specifi cally, the written output this script is to produce should look like = <the number> machine epsilon The above output is what your grader will grade! This seript file must have the interface: 6/9/2019 def runTask1) in which you will call your function machineEps and primt out the answer in the format specified above Call this script file a3taskl.py

use python

Answer 1

#The executable file is as follows. It also contains the function to be defined in part 1:

################################ Code Starts Here ####################################

def machineEps():

epsilon = 1.0 # Assigning initial value of epsilon
  
while (1.0 + epsilon) != 1.0:

epsilon = epsilon / 2.0 # Dividing epsilon by 2 in every iteration of while loop
  
machine_epsilon = epsilon * 2 # Getting machine epsilon by multiplying final value of epsilon with 2

return machine_epsilon

def runTask1():

print("machine epsilon = ", machineEps()) # calling machineEps() function to print the statement in the prescribed format

if __name__ == '__main__':

   runTask1()

############################## Code ends here ###################################

# Save the file as "a3task1.py"

# Then execute it from the command prompt using command python "a3task1.py"

# Sample run: