Programming Assignment I

Due on Friday, September 26, 2008 @ 11pm

100 points

The cosine function cos(x) can be represented as an infinite series as shown below. An obvious way of computing cos(x) is to sum the terms until a term is less than certain tolerance value, say 0.0000005, in single precision.

This is not a good method to compute cos(x) accurately and Fortran 90 does not use it to implement the COS(x) intrinsic function, because there could be so many numerical problems. However, this is a very good chance for you to gain some experience in finite precision arithmetic.

The problem you should solve is very simple:

Input and Output

1000.0
0.5
-20.5
0.0
+3.1456

For each x, your program should print the following four output lines. The first line shows the input value x, the second is the COS(x) computed using the infinite series (i.e., your COS(x)), the third shows the result computed by Fortran 90's intrinsic function COS(x), and the fourth is the absolute value of the difference of the two computed values.

Input Value    = x
My cos(x)      = cos(x) computed using the above infinite series
Fortran cos(x) = Result from Fortran 90 intrinsic function COS(x)
Error          = The absolute difference of the two computed value

The above four output lines should be repeated for each input value with a blank line between two groups. The complete output should look like the following:

*** CS3911 Programming Assignment #1 ***
***   COS(x) Computation Experiment  ***

--- the above four lines for the first input value ---

--- the above four lines for the second input value ---

--- output for other input values ---

*** Done due to end-of-file ***

The following is a possible input file, which will be used as a sample testing input:

-70000.0
-10000.0
-1500.0
-50.0
-10.0
-1.0
0.0
1.5
3.14156
7.0
15.0
100.0
1000.0
100000.0
500000.0

1. All programs must be written in ANSI Fortran 90.
2. Use the submit command to submit your work. You can submit as many times as you want, but only the last on-time one will be graded.
3. Your program should be named as prog1.f90. Note that Unix filename is case sensitive. As a result, PROG1.f90, prog1.F90, pROG1.f90, etc are not acceptable.
4. We will use the following approach to compile and test your programs:

   f90 prog1.f90 -o prog1  <-- compile your program
   prog1 < our-test-file   <-- test your program
   

   This procedure may be repeated a number of times with different input files to see if your program works correctly.
5. Your implementation should fulfill the program specification as stated. Any deviation from the specification will cause you to receive zero point.
6. No late submission will be graded.
7. My rule of grading is deduction based. I assume you always receive 100%. If you missed something, some points will be deducted based on the following rules. Read these rules carefully. Otherwise, you may receive low or very low grade.
• Your programs must contain enough comments. Programs without comments or with insufficient and/or vague comments will cost you 30%.
• For each program, the first piece should be a program header to identify yourself like this:

  ! ----------------------------------------------------------- 
  ! NAME : John Smith                         User ID: xxxxxxxx 
  ! DUE DATE : mm/dd/yyyy                                       
  ! PROGRAM ASSIGNMENT #                                        
  ! FILE NAME : xxxx.yyyy.zzzz (your unix file name)            
  ! PROGRAM PURPOSE :                                           
  !    A couple of lines describing your program briefly        
  ! ----------------------------------------------------------- 
  

  Here, User ID is the one you use to login. It is not your social security number!

  For each function in your program, include a simple description like this:

  ! ----------------------------------------------------------- 
  ! FUNCTION  xxyyzz : (function name)                          
  !     the purpose of this function                            
  ! PARAMETER USAGE :                                           
  !    a list of all parameters and their meaning               
  ! FUNCTION CALLED :                                           
  !    a list of functions that are called by this one          
  ! ----------------------------------------------------------- 
  

  Bad programming style and missing headers will cost you 30%.

• Not-compile programs receive 0 point. By not-compile, I mean any reason that could cause an unsuccessful compilation, including missing files, incorrect filenames, syntax errors in your programs, and so on. Double check your files before you submit, since I will not change your program to make it work. Note again: Unix filenames are case sensitive.
• Compile-but-not-run programs receive no more than 50%. Compile-but-not-run means you have attempted to solve the problem to certain extent but you failed to make it working properly. A meaningless or vague program receives no credit even though it compiles successfully.
• Programs delivering incorrect results, incomplete results, or incompatible output/format receive no more than 70%.
• All deductions mentioned above are cumulative! This means that even though you have turned in a correct program, you could get very low grade. For example, if your submission does not have the necessary program and function headings (30% off), does not have enough comments (30% off), poorly written and/or nearly contentless README (30% off), then you will receive 100-30-30-30=10 points.
• Your submission should include the following files:
  1. File prog1.f90 that contains your Fortran 90 source program.
  2. A file named README to answer the following questions:
     • What is your approach to ensure the computed error to be small? Elaborate your approach and provide a convincing "theory." Don't repeat what your program statements say, because that is not a "theory." (Actually, it is an implementation.) You should explain why your approach works.
     • Why are some errors so large in your implementation? Your program will not always compute cos(x) accurately. It may produce ridiculous output for some input. Explain why. Note that vague answers such as "because of cancellation and/or rounding" receive no credit. You have to back up your claim correctly and accurately.
     • Would the use of double precision help bring accuracy better with your implementation? Provide an analysis. A yes/no answer receives no credit.
     You should elaborate your answer and provide details.

     Note that the file name has to be README rather than readme or Readme. Note also that there is no filename extension, which means filename such as README.TXT is NOT acceptable.

     README must be a plain text file. We do not accept files produced by any word processor. Moreover, watch for very long lines. More precisely, limit the length of each line to no more than 80 characters with the Return key for line separation. Missing this file, submitting non-text file, file with long lines, or providing incorrect and/or vague answers costs you 40%. Suggestion: Use a Unix text editor to prepare your README rather than a word processor.

• Programs submitted to wrong class and/or wrong section will not be graded.
• Always start early, because I will not grant any extension if your home machine, network connection, your phone line or the department machines crash in the last minute.
8. Since the rules are all clearly stated, no leniency will be given and none of the above conditions is negotiable. So, if you have anything in doubt, please ask for clarification.
9. Click here to see how your program will be graded.