CSE 333 24au Exercise 0

Due: Mon, Sep 30th, 2024 by 10:00 am; No late exercises will be accepted.
Goals: Write a C program from scratch including a function declaration, learn how to process command-line arguments, and explore some basic C libraries for handling I/O, strings, and numeric conversions.

Description: One way to estimate π is to use the following infinite series, which was discovered by Nilakantha in the 15th century:

      π = 3 + (4 / (2 x 3 x 4)) - (4 / (4 x 5 x 6)) + (4 / (6 x 7 x 8)) - ...

Breaking the series down:

• the zero'th term in the series is 3.0
• the first term in the series is +(4 / (2 x 3 x 4))
• the second term in the series is -(4 / (4 x 5 x 6))
• the nth term in the series is (-1)⁽ⁿ⁺¹⁾ x (4 / (2n x (2n+1) x (2n+2)))

Write a C program that estimates π by adding together terms 0 through n, inclusive, in the Nilakantha series, and prints out that estimate to 20 decimal places. "n" is provided to your program as a command-line argument. Your program, when compiled, should be called "ex0" and an example of how the user should invoke it, and the resulting output, which you should match, is:

    bash$ gcc -Wall -g -std=c17 -o ex0 ex0.c
    bash$ ls
    ex0     ex0.c
    bash$ ./ex0 100
    Our estimate of Pi is 3.14159241097198238535
    bash$

You should use C's double type for the floating-point arithmetic and you should add the terms in increasing order (ie, add the 1st term to the 0th term, then the 2nd term to the previous sum). Different floating-point types or adding up the terms in a different order may yield different results. Since the point of this exercise is to create and run a simple C program, not to explore the nuances of floating-point arithmetic, please use double and add the terms in increasing order.

As part of this exercise, you will need to explore the standard C libraries and conventions for accessing the command line argument (ie, the string of digit characters), converting that digit string to a binary int value, and printing the result. The course Resources page contains a link to cplusplus.com, which is a good source for information about the C and C++ libraries; ignore the C++ information for now. In particular, you will find it useful to look at the stdio.h library for basic input and output, string.h for handling C strings (null-terminated arrays of characters), and stdlib.h for assorted functions (including multiple options for parsing (converting) strings of digit characters to int values.

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Your code must:

• Compile without errors or warnings on CSE Linux machines (lab workstations, attu, or CSE home VM) with gcc -Wall -g -std=c17 -o ex0 ex0.c -- do not submit a Makefile.
  
  Note that this means that you are free to use any standard library functions and also that these libraries must not require you to add options to the command line. In particular, using <math.h> requires the addition of the -lm option to the compilation command, so you may not use this library.
• Have no crashes, memory leaks, or memory errors on CSE linux machines. (Suggestion: valgrind)
• Follow the quality guidelines we covered in class, including the formatting, modularization, variable and function names, and so on. If in doubt, follow the Google C++ style guide. We also suggest using cpplint --clint.
• Be robust: you should think about handling bogus input from the user (if any), and you should handle hard-to-handle cases (if there are any) gracefully. For example, if the program argument is not an integer or is too large or too small to be handled properly, the program should do something sensible, and this behavior should be (briefly) documented in the code.
• Have a comment at the top of each source file with your name, and CSE or UW email address.

You should submit your exercise to the course Gradescope.