ECE 8473 - Assignment #5 - Due: 27 Oct 2022

Programs must compile with no warnings or errors using: gcc -std=c11 -pedantic -Wall

Shell scripts should run correctly using dash.

Each source file must start with a comment containing your name and a description.

1. [50] a5/p1.c - approximating math.h functions

   Each student has been randomly assigned one of the functions from math.h to approximate using a cubic polynomial over a specified range.

   The assigned function and range are listed in a comment at the top of your initial a5p1.c file in the Assignment Results.

   Write a main program which uses the provided llsq() function (llsq.h, llsq.c) to determine the linear least-square-error cubic polynomial coefficients and then print the function x,y values and polynomial estimates.

   The program output must consist of only the math function x,y values, double-spaced, followed by the polynomial estimates for each x value, single-spaced, so the results can easily be plotted for comparison.

   program outline, sample output, sample plot

   ---

2. [25] a5/p2.c and [25] a5/p2.sh - substitution cipher

   First write a C program p2.c which produces a random permutation of the upper-case alphabetic characters A...Z.

   Sample runs:

     $ ./p2
     IWDJUMCFEBXPQGNZLAYRKVTOSH
     $ ./p2
     WXBRVYKNCIGHFLAUMSOEPTDJZQ
     $ ./p2
     YKZMRLJQNUFXBOAVIEDGSPCHWT
     $
   

   Use srand(time(0)) to initialize rand(), and starting with an array of characters "ABCDEFGHIJKLMNOPQRSTUVWXYZ", put the array into random order using the following algorithm with len=26:

     for j = len, len-1, ..., 2
     {
       i = random index from 0 to j-1
   
       swap array elements i and j-1
     }
   

   A random integer from 0 to n-1 is generated using either rand()%n or (int)(n*(rand()/(RAND_MAX+1.0)))

   Then write a shell script p2.sh which uses p2 to generate a random permutation, then uses tr to encrypt a random upper-case fortune using the permutation for letter substitution, then decrypts and tests that the decrypted result is correct.

   To create an upper-case random fortune input file use:

     fortune | cat -v | tr '[:lower:]' '[:upper:]' > plaintext
   

   Sample runs:

     $ dash ./p2.sh # with no bugs
     generating random fortune > plaintext
     encrypting > ciphertext
     decrypting > p2.tmp
     it worked, p2.tmp matches the plaintext!
     plaintext:
     ONE FAMILY BUILDS A WALL, TWO FAMILIES ENJOY IT.
     ciphertext:
     UJE RAQTXP BNTXIS A ZAXX, WZU RAQTXTES EJFUP TW.
     p2.tmp:
     ONE FAMILY BUILDS A WALL, TWO FAMILIES ENJOY IT.
     
     $ dash ./p2.sh # with bug somewhere
     generating random fortune > plaintext
     encrypting > ciphertext
     decrypting > p2.tmp
     it didn't work, p2.tmp does not match the plaintext
     plaintext:
     BIOLOGY IS THE ONLY SCIENCE IN WHICH MULTIPLICATION MEANS THE SAME THING
     AS DIVISION.
     ciphertext:
     ZSUNULY SA CEO UQNY AKSOQKO SQ RESKE XINCSBNSKFCSUQ XOFQA CEO AFXO CESQL
     FA MSGSASUQ.
     p2.tmp:
     PYEOEQS YR GIX EMOS RUYXMUX YM TIYUI KAOGYJOYUHGYEM KXHMR GIX RHKX GIYMQ
     HR FYNYRYEM.
   

   Manual example using tr:

     $ tr "ABCDEFGHIJKLMNOPQRSTUVWXYZ" "IWDJUMCFEBXPQGNZLAYRKVTOSH" < plaintext > ciphertext
     $ cat ciphertext
     SNKA WUYR DNGYNPIRENG EY RFU FNZU RFIR RFU RFEGCY SNK MIEPUJ RN CUR TUAUG'R
     AUIPPS TNARF FIVEGC.
     $ tr "IWDJUMCFEBXPQGNZLAYRKVTOSH" "ABCDEFGHIJKLMNOPQRSTUVWXYZ" < ciphertext
     YOUR BEST CONSOLATION IS THE HOPE THAT THE THINGS YOU FAILED TO GET WEREN'T
     REALLY WORTH HAVING.
     $