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notes:discrete:fall2021:projects:pnf0 [2021/09/01 00:06] – [Display] mpronti2notes:discrete:fall2021:projects:pnf0 [2021/09/05 12:05] (current) – [Submission] wedge
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 =====Objective===== =====Objective=====
 +
 Using the TIC-80 fantasy console simulator on your pi, implement a program that visually displays a range of values (lower and upper bounds adjustable by the user) that colorfully displays whether each value is a **prime** or **composite** value. Using the TIC-80 fantasy console simulator on your pi, implement a program that visually displays a range of values (lower and upper bounds adjustable by the user) that colorfully displays whether each value is a **prime** or **composite** value.
  
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 Once a language is selected, a developer will need to include a `TIC()` function. This is essentially the "main" function as many other programs would have, and is called automatically once the `run` command is issued on the cart 60 times per second. This can be relied on to provide synchronous 60fps display and physics or other necessary mechanics. Additionally, the `spr()`, `print()`, and `cls()` functions will prove essential. The `spr()` (Sprite) function is used to call upon sprites designed in the sprite editor and place them at some location on-screen. `print()` (Print) is more clear: this will print text directly to screen in the default font. It should be noted that the print function can also accept additional arguments for text position, size, and color. `cls` (Clear Screen) simply clears the screen of all pixel Once a language is selected, a developer will need to include a `TIC()` function. This is essentially the "main" function as many other programs would have, and is called automatically once the `run` command is issued on the cart 60 times per second. This can be relied on to provide synchronous 60fps display and physics or other necessary mechanics. Additionally, the `spr()`, `print()`, and `cls()` functions will prove essential. The `spr()` (Sprite) function is used to call upon sprites designed in the sprite editor and place them at some location on-screen. `print()` (Print) is more clear: this will print text directly to screen in the default font. It should be noted that the print function can also accept additional arguments for text position, size, and color. `cls` (Clear Screen) simply clears the screen of all pixel
 data and resets to blank. data and resets to blank.
 +
 ====Priminality==== ====Priminality====
 +
 =====Specifications===== =====Specifications=====
  
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     - If prime, positive output (e.g. rainbow/green/bright)     - If prime, positive output (e.g. rainbow/green/bright)
     - If composite, negative/neutral output (e.g. monochrome/red/dull)     - If composite, negative/neutral output (e.g. monochrome/red/dull)
 +
 +====Input====
 +
 ====Prime Detection Algorithm==== ====Prime Detection Algorithm====
 +
 +Before we can jump into how to //program// our prime number detection algorithm, we must understand the basic rules of prime numbers.
 +
 +Prime Numbers Must Be:
 +  * In the set of natural/counting numbers.
 +  * Greater than the number 1.
 +  * Factorable by only two natural/counting numbers: itself and 1.
 +
 +With your knowledge of programming and the rules of prime numbers, you should be able to make a detection algorithm now!  There are different computational methods for figuring out the primality of a number, we will take a look at one of the simplest ones first (more may be added in the future to this page).
 +
 +===Trial-By-Division Algorithm===
 +
 +One of the most basic methods of checking the primality of a number, this method relies on dividing a given number by the numbers in a set range. This is to see if any numbers in that range divide the given number cleanly; //no remainders exist in the mathematical output//. Clean division is a sign of a **composite** number.
 +
 +Let's assume we have an integer, //n//, in order to see if //n// is a prime number we should first determine our lower and upper bounds for the division test(s):
 +  * Lower bound: 2
 +  * Upper bound: <m>sqrt{n}</m>
 +     * If taking unoptimized route, upper bound can just be //n - 1//.
 +
 +Both of these bounds may be confusing, let me explain...
 +
 +For our lower bound, we most definitely want to start on the lowest number possible. Since we know that the potential factors for our integer, //n//, must be natural/counting numbers that means the lowest we could try to start at is 0. Is there an issue with this? Yes. Perhaps we can start at 1? No.
 +
 +Hopefully, you understand why starting at 0 for **division tests** would not be such a good idea. Starting at 1 would be superfluous; everything is divisible by 1. At this point, having our lower bound set to 2 ensures no issues and is the lowest we can go for our lower bound.
 +
 +For our upper bound, we want to prioritize testing to what we //absolutely// must test. Testing all values until //n// would be highly inefficient. One important rule to remember is that one of the two factors generated from //n// will be less than or equal to the square root of //n//. Knowing this rule, testing numbers after the square root of //n// is pointless.
 +
 +Now that you understand the general process of this algorithm, and what its lower and upper bounds should be, you can finally get into writing this algorithm. Here are a few concluding questions:
 +  * How can we test if a number divides cleanly by //n//?
 +     * Hint: remainder "%"
 +  * How can we implement a square root in our code for the upper bound?
 +  * How do we deal with testing the numbers 0 and 1?
  
 ====Display==== ====Display====
  
 The `print` function can be used to print text on the screen, but it also returns the width of the text. For example, `local string=print("Hello, World!",0,0,12)` would not only print the text on the screen, but it would also give the local variable `string` a value equal to the width of "Hello, World!" in pixels. This is especially helpful if you want to display a sprite after a string, but you don't feel like counting out how much space you need manually. The `print` function can be used to print text on the screen, but it also returns the width of the text. For example, `local string=print("Hello, World!",0,0,12)` would not only print the text on the screen, but it would also give the local variable `string` a value equal to the width of "Hello, World!" in pixels. This is especially helpful if you want to display a sprite after a string, but you don't feel like counting out how much space you need manually.
 +
 +Additionally, text can be appended to `print` alongside variables without the need for two separate lines of code/statements using `..`. For example, if you wanted to print "Times iterated: " and then a number contained within a variable, instead of doing two `print`s for the text and variable individually, you could do `print("Times iterated: "..variable,0,0,12)'.
  
 The `time` function returns the current run-time of the program in milliseconds. This is useful in a variety of circumstances; having something happen at a specific timestamp, having things refresh at a certain interval, etc. For pnf0, specifically, expertly utilizing `print()` alongside `time()` would display the current run-time in seconds, which is a requirement. The `time` function returns the current run-time of the program in milliseconds. This is useful in a variety of circumstances; having something happen at a specific timestamp, having things refresh at a certain interval, etc. For pnf0, specifically, expertly utilizing `print()` alongside `time()` would display the current run-time in seconds, which is a requirement.
- 
  
 =====References===== =====References=====
  
 https://github.com/nesbox/TIC-80/wiki https://github.com/nesbox/TIC-80/wiki
 +
 +http://lua-users.org/wiki/MathLibraryTutorial
 +
 +=====Submission=====
 +To submit, provide your tic file using the **submit** tool on lab46.
 +
 +I'll be looking for the following:
 +
 +<code>
 +65:pnf0:final tally of results (65/65)
 +*:pnf0:no errors, program runs in TIC-80 [13/13]
 +*:pnf0:user can specify lower and upper bounds at runtime [13/13]
 +*:pnf0:specified algorithms are implemented and functional [13/13]
 +*:pnf0:timing information is displayed [13/13]
 +*:pnf0:project page contributions as per project specifications [13/13]
 +</code>
 +
 +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
notes/discrete/fall2021/projects/pnf0.1630454817.txt.gz · Last modified: 2021/09/01 00:06 by mpronti2

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