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--- notes:discrete:fall2021:projects:pnf0 [2021/08/28 14:21] – additional usage section work aholmes9
+++ notes:discrete:fall2021:projects:pnf0 [2021/09/05 12:05] (current) – [Submission] wedge
@@ Line 7: / Line 7: @@
 =====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.
@@ Line 24: / Line 25: @@
 ====TIC80====
-TIC80 works on a system of **carts**. The carts present on a system can be listed via a familiar call to `ls`, or, at a more involved level, the system folder which TIC80 uses to store its data can be accessed via the `folder` command in the TIC80 terminal. The code content of these cards after `load`ing them can be accessed by pressing [ESC] from the terminal, opening the included basic IDE equipped with a code, sprite, map, sfx, and music editor.
+TIC80 works on a system of **carts**. The carts present on a system can be listed via a familiar call to `ls`, or, at a more involved level, the system folder which TIC80 uses to store its data can be accessed via the `folder` command in the TIC80 terminal. A new cart can be made with the `new` command, and the loaded cart can be saved via the `save` command. The code content of these cards after `load`ing them can be accessed by pressing [ESC] from the terminal, opening the included basic IDE equipped with a code, sprite, map, sfx, and music editor.
 The **code editor** is relatively simple: 64KB are allotted for a script written in any of: Lua, JavaScript, Moonscript, Wren, Fennel, and Squirrel. External packages may also be used to allow for the usage of more languages. The first step in writing a basic program in TIC80 is to supply a series of comments (formatted in the choice language) which allow TIC80 to ascertain four pieces of metadata, as in:
@@ Line 41: / Line 42: @@
 for JavaScript, and so on.
-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 `clr()` 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. `clr` (Clear) 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.
 ====Priminality====
 =====Specifications=====
@@ Line 57: / Line 60: @@
     - If prime, positive output (e.g. rainbow/green/bright)
     - If composite, negative/neutral output (e.g. monochrome/red/dull)
+====Input====
 ====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====
+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.
 =====References=====
+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>
+: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

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