Project: MENTAL MATH - SQUARES OF FIVES (sof0)

To implement a programmatic solution (ie simulation) of a real life process- the mental math trick of computing the square of any number ending with 5.

The allure of using (and learning) a programming language is to be able to effectively use it to solve problems, which in and of themselves are simulations of some process we can do in “the real world”.

In this case, we will be writing a program which will implement the mental math techniques for computing the square of any one, two-, or three-digit number that ends with 5.

Mental Math constitutes an intersection of mental techniques and math- instead of utilizing a purely math-only solution, textual manipulations or simplifications in the computational process may take place enabling an individual to, once having learned the process, solve such problems in their head, and typically without the use of a calculating device.

The process in this case is one of numeric manipulation and simple (reduced) multiplication. To wit:

Squaring is essentially multiplying a number by itself-

• 5 squared (5^2) is 5*5 or 25
• 8 squared (8^2) is 8*8 or 64

While not outwardly a difficult procedure, the nature of multiplying multiple digit numbers in your head can quickly result in more steps (and more steps means more time, if doing things the traditional way).

Finding a shortcut through this process enables it to remain solidly within the realm of mental math, and makes for a good algorithm to practice implementing on the computer.

This particular trick relies on a subset of the squares: those ending with a 5 (a five in the ones place).

The implementational scope of this trick will be just values of one-, two-, and three-digits ending with 5:

• 5
• 15
• 25
• 35
• 45
• 55
• 65
• 75
• 85
• 95
• 105
• 115
• 125
• …
• 235
• 245
• …
• 485
• 495
• 505
• …
• 995

The trick here is two-fold. First, we separate the one's place 5 from the rest of the number (which can be accomplished in our mind's easily enough, but on the computer we must resort to some math).

We then take that isolated five and square it; we'll get 25. That is how our result will end (so bam! we now have our tens and ones place already solved)

Next, we take the remaining digits of the original value, and multiply it by its increment:

• 1's increment (1+1) is 2, so 1*2
• 2's increment (2+1) is 3, so 2*3
• 3's increment (3+1) is 4, so 3*4
• 4's increment (4+1) is 5, so 4*5
• …
• 9's increment (9+1) is 10, so 9*10

We take this result and append the 25 after it.

For example:

15 * 15 = 1*(1+1) 5*5
        = 1*2     5*5
        = 2       25
        = 225

and:

75 * 75 = 7*(7+1) 5*5
        = 7*8     5*5
        = 56      25
        = 5625

For a single digit number like 5, when you take the 5 away, what do you get? ZERO. Zero times anything is zero, so the result is 0 25, or 25 (ie this process still works).

For three digit numbers like 105, we have 10, and its increment is 11, so 10 x 11 = 110.

105 * 105 = 10*(10+1) 5*5
          = 10*11     5*5
          = 110       25
          = 11025

It is your task to write the program that will use the above method to compute the square of the input value ending with a 5 (you are to input the entire number, including the 5 at the end).

Your program should:

• prompt the user for the number (input)
  • input number as an unsigned short integer
• perform the task (process)
  • isolate one's digit mathematically, store in a variable (unsigned short int)
  • isolate remaining digits mathematically, store in another variable (unsigned short int)
  • perform the algorithm on the two pieces, storing their results in two separate variables (of type unsigned short int)
• display the final value (output)
  • display the beginning and ending parts together (but stored in separate variables)
  • display the resulting number to STDOUT (right-justified in a space supporting the largest possible value – see output example below)
  • display any supporting text to STDERR (display of source values left-justified in a space supporting 3-digit values – see output example below).
• because we have not officially learned how to do selection/have the computer react to conditions, please implement with the assumption that the user will ALWAYS input a correct value. Do not worry about having to check for invalid or illegal input values (I will not be checking for such when I evaluate your project).

yourpi:~/src/SEMESTER/cprog/sof0$ ./sof0.armv7l
Enter value: 75
75  x 75  =   5625
yourpi:~/src/SEMESTER/cprog/sof0$ 

The execution of the program is short and simple- obtain the input, do the processing, produce the output, and then terminate.

Note how the two “75” values are left-justified within a 3-space slot (with the multiplication 'x' and equal sign '=' being padded with a space on either side). This information should all be displayed to STDERR.

Similarly, here's an example of 105×105:

yourpi:~/src/SEMESTER/cprog/sof0$ ./sof0.armv7l
Enter value: 105
105 x 105 =  11025
yourpi:~/src/SEMESTER/cprog/sof0$ 

The 'x' and '=' padding persists, but because we're squaring a 3-digit value vs. a 2-digit value, we occupy the entire allocated space on the screen.

If you'd like to verify successful output to STDOUT/STDERR, you can perform the following tests. First, verify that the answer (and ONLY the answer), is being sent to STDOUT – we do this by eliminating STDERR entirely:

yourpi:~/src/SEMESTER/cprog/sof0$ ./sof0.armv7l 2> /dev/null <<< 105
 11025
yourpi:~/src/SEMESTER/cprog/sof0$ 

What we are doing here is two-fold:

• We are using command-line I/O redirection to redirect STDERR (which is bound to file descriptor #2) to the system bit-bucket.
• We are “redirecting” STDIN using a here string, providing the program's input of 105 right on the command-line at time of execution.

Similarly, if we were to eliminate STDOUT entirely (for verifying STDERR output):

yourpi:~/src/SEMESTER/cprog/sof0$ ./sof0.armv7l 1> /dev/null
Enter value: 75
75  x 75  = yourpi:~/src/SEMESTER/cprog/sof0$ 

What we are doing here:

• We are using command-line I/O redirection to redirect STDOUT (which is bound to file descriptor #1) to the system bit-bucket.

One of the tests I will perform for output compliance of your code will involve comparing your program's output against a range of input values, to see if they all output in conformance with project specifications.

I will make use of a checksum to verify exactness.

You will need to run this from your sof0 project directory with a compiled and operational binary by the name of sof0.

You can check your project by typing in the following at the prompt:

lab46:~/src/SEMESTER/cprog/sof0$ pchk cprog sof0

If all aligns, you will see this:

==================================================
=   CPROG sof0 project output validation tool    =
==================================================
sof0 checksum is: 822a47fb2a45845500b6c10878045bd5
your checksum is: 822a47fb2a45845500b6c10878045bd5
==================================================
    verification: SUCCESS!
==================================================

If something is off, your checksum will not match the sof0 checksum, and verification will instead say “MISMATCH”, like follows (note that a mismatched checksum can be anything, and likely not what is seen in this example):

==================================================
=   CPROG sof0 project output validation tool    =
==================================================
sof0 checksum is: 822a47fb2a45845500b6c10878045bd5
your checksum is: 92af264c86823a61529948caaeac53e0
==================================================
    verification: MISMATCH
==================================================

These are things I'd like you to contemplate, even use as potential material on your weekly journal entry. The more you think about and understand the problem, the better your ability to solve it and other problems.

• Why/how does this trick work for 1-digit numbers?
• Considering our 1-, 2-, and 3-digit domain restriction for this project, how many candidate values are there for input?
• What is the smallest input value?
• What is the largest input value?
• How many input values are there that end in 5?
• What is the largest square that can be calculated given the project input restrictions?
• How many digits is the largest square?
• How can knowing how many digits the largest square is help you implement your solution?

Just to review the compilation/execution process for working with your source code, if we had a file, hello.c, that we wished to compile to a binary called hello, we'd first want to compile the code, as follows.

If compiling on lab46:

lab46:~/src/SEMESTER/cprog/PROJECT$ gcc -Wall --std=gnu99 -funsigned-char -o PROJECT.x86_64 PROJECT.c
lab46:~/src/SEMESTER/cprog/PROJECT$ 

If compiling on your pi system:

yourpi:~/src/SEMESTER/cprog/PROJECT$ gcc -Wall --std=gnu99 -funsigned-char -o PROJECT.armv7l PROJECT.c
yourpi:~/src/SEMESTER/cprog/PROJECT$ 

Assuming there are no syntax errors or warnings, and everything compiled correctly, you should just get your prompt back. In the event of problems, the compiler will be sure to tell you about them.

Conceptually, the arrangement is as follows:

gcc -Wall --std=gnu99 -funsigned-char -o BINARY_FILE SOURCE_FILE

The BINARY_FILE comes immediately after the -o, NOT the SOURCE_FILE (the source file must never immediately follow a -o). It can precede, and such is perfectly valid (especially if you feel that way more intuitive).

The -Wall (treat all warnings as errors, increase general verbosity about warnings) and --std=gnu99 (switch compiler to use the C99 standard of the C language, with GNU extensions) are options given to the compiler. The -funsigned-char flag forces “char” types lacking a signed/unsigned qualifier to default to unsigned.

To execute your binary, we need to specify a path to it, so we use ./, which basically references the current directory.

On lab46:

lab46:~/src/SEMESTER/cprog/PROJECT$ ./PROJECT.x86_64

On your pi system:

yourpi:~/src/SEMESTER/cprog/PROJECT$ ./PROJECT.armv7l

To successfully complete this project, the following criteria must be met:

• Code must compile cleanly (no warnings or errors)
  • Use the -Wall and --std=gnu99 flags when compiling.
• Executed program must display a total of 2 lines, one for input, one for output.
  • The computed number must be output to STDOUT
  • Any supporting output must be output to STDERR
  • Output is formatted in the manner in the sample above
• Output must be correct, and match the form given in the sample output above.
• Code must be nicely and consistently indented
• Code must implement solution using the mental math technique described above
• Code must be commented
  • have a properly filled-out comment banner at the top
  • have at least 20% of your program consist of //-style descriptive comments
• Output Formatting (including spacing) of program must conform to the provided output (see above).
• Track/version the source code in a repository
• 33% late penalty per day after deadline
• Program is submit in a C source file called sof0.c and compiles without warning, note, nor error with gcc on lab46.
• Submit a copy of your source code to me using the submit tool.

To submit this program to me using the submit tool, run the following command at your lab46 prompt:

lab46:~/src/SEMESTER/cprog/sof0$ submit cprog sof0 sof0.c
Submitting cprog project "sof0":
    -> sof0.c(OK)

SUCCESSFULLY SUBMITTED

You should get some sort of confirmation indicating successful submission if all went according to plan. If not, check for typos and or locational mismatches.

I'll be looking for the following:

39:sof0:final tally of results (39/39)
*:sof0:obtained via grabit by Sunday before deadline [3/3]
*:sof0:program compiles successfully, no errors [3/3]
*:sof0:program compiles with no warnings [3/3]
*:sof0:program performs stated task/algorithm [3/3]
*:sof0:program output conforms to formatting expectations [3/3]
*:sof0:proper error checking and status reporting performed [3/3]
*:sof0:code implements solution using relevant concepts [3/3]
*:sof0:code updates committed/pushed to lab46 semester repo [3/3]
*:sof0:code uses correct variable types and name lengths [3/3]
*:sof0:project is submitted with relevant and complete source [3/3]
*:sof0:project is submitted on lab46 using 'make submit' [3/3]
*:sof0:project is submitted with pi and lab46 binaries [3/3]
*:sof0:runtime tests of submitted program succeed [3/3]

Additionally:

• Solutions not abiding by SPIRIT of project will be subject to a 25% overall deduction
• Solutions not utilizing descriptive why and how COMMENTS will be subject to a 25% overall deduction
• Solutions not utilizing INDENTATION to promote scope and clarity will be subject to a 25% overall deduction
• Solutions lacking ORGANIZATION and are not easy to read (within 90 char width) are subject to a 25% overall deduction