**SmileBoom**(the company that made SmileBASIC) decided to add functions to a dead language in order to "modernize" it a bit. Seriously though, functions... they're SUPER important. Next tutorial (part 9)

# Math Functions

So there's a bunch of*definitions*and

*theory*and a whole load of other BS that goes with functions in mathematics... but screw all that crap. Functions are

*easy*.

**Mathematical Functions**are just a way of

__transforming one number into another__. For instance, it might transform 2 into 4, 3 into 6, etc. Functions transform numbers in such a way that you can see the pattern of the transformation; for instance, a function might transform 1, 2, 3, 4, 5 into 3, 6, 9, 12, 15 (the function transformation is 'times 3'). The important thing about functions is that the transformation is ALWAYS the same for a given number. So if a function turns 2 into 4, it will ALWAYS turn 2 into 4.

## How to write functions

Functions are written as equations. You know what equations are:**equations**just show that two things are equal. For instance, 2+2=4. You know that the left side (2+2) is equal to the right side (4) because (a) you know know to count and (b) there's A BIG OL' EQUALS SIGN BETWEEN THEM. This works nicely with

**constants**(values that don't change; numbers like 4, 2, etc.), but you can also put in

**variables**(unknown values; this should sound familiar) to make the equation more interesting. Variables are usually written as letters. For instance, we could write 2+X=7. We know the left side of the equation (2+X) must be the same as the right (7), so we can kinda figure out that the "unknown" value is actually 5. Remember, mathematical variables are just

**placeholders**for numbers (pretty much like they are in code). Function equations are written like so:

f(x)=(transformation of x)where

**f(x)**is "function of x" and x is the

**input**(value given to a function) to be transformed. "Transformation of x" is just some math to apply to x. Remember, functions are just a way to transform numbers. So let's say that our transformation is simply to double the number. Our mathematical function would look like:

f(x)=2*xNow remember, f() is the function, so we can write f(10) to say "apply the function to 10". Here's what it would look like:

f(x) =2*x 'The function equation f(10)=2*10 'Notice we replaced all x's with our "input" f(10)=20 'This is the answerThat's really all a function is. You plug in a number and it spits out another one. A function can also take more than 1 input; for instance, you may be familiar with the distance formula (used to find the distance between two points, (x

_{1},y

_{1}) and (x

_{2},y

_{2})): f(x

_{1}, y

_{1}, x

_{2}, y

_{2}) = √((x

_{2}- x

_{1})

^{2}+ (y

_{2}- y

_{1})

^{2}) This may look complicated if you've never seen it before, but all we have to do is plug in 4 actual numbers to the equation and we'll get one final number (in this case, the distance). This is another important point:

__functions can have many inputs but ONLY one output__. It transforms a number (or multiple numbers) into a new number.

## Functions practice

OK, let's try to come up with math functions ourselves. I'll describe what I want and you should try to come up with the function equation. Try to come up with the equation without looking at the answer (otherwise it's kinda useless). Here we go: A function to square a number; ie 5 becomes 25## answer

f(x) = x^{2}

## answer

f(x) = x + 3## answer

f(x) = 2 * x + 1## answer

f(x) = sin(x)# Programming Functions

## SmileBASIC Built-ins

Functions in programming work in almost the same way: you give the function some**inputs**and it

**returns**a single number (thus transforming input to output). However, unlike math functions, programming functions can do anything you want since it's actually just running code to compute the

**return value**. So really, a

**programming function**is

__an isolated, reusable block of code that accepts inputs and (may) return a value when finished__. Let's take a look at some of the built-in functions for SmileBASIC:

SQR(X) 'Returns the square root of X POW(X,E) 'Returns X raised to the E power SIN(X) 'Returns the sin of X (where X is in radians) COS(X) 'Returns the cos of X (where X is in radians) PI() 'Returns the value of PI (always 3.14159 etc...) RND(X) 'Returns a random number from 0 to X-1Notice here that some functions don't have any inputs. Functions in programming aren't bound by the same rules as mathematical functions; they don't HAVE to have an input and furthermore, they don't even need to produce the same output for the same input. For instance, that RND function returns a different value every time, even though we keep passing in the same value for X. And here's how you might

**call**(pass the input value(s) and retrieve the output value from) some of these functions:

PRINT SQR(25) 'Prints 5 PRINT POW(2,5) 'Prints 32 (2 to the power of 5) PRINT SIN(PI()/2) 'Prints 1 PRINT RND(10) 'Prints some random number from 0 to 9Notice here that we can give functions and equations as inputs (as with the SIN example). In programming, the

**parameters**(inputs) are

**evaluated**(computed/reduced to a single number) before the function is called. Before SIN is called, it has to know what PI()/2 is, so it evaluates that first then passes the computed value (1.571) to SIN.

### SmileBASIC Silliness

Programming functions don't HAVE to return values, actually. This is true in any language; a function can simply be a piece of code that runs and then... that's it. For instance, PRINT is a function that accepts inputs (strings and stuff to display on the screen) but it doesn't return anything. In code, you can't do:DIM A = PRINT "THING" 'this doesn't workYou'd get a syntax error because PRINT doesn't produce a value like the functions SQR or SIN do. Same with some other stuff we've used before like INPUT: it's only running code; it doesn't give back anything when you call it. In nearly all other programming languages, there is no distinction between functions that return values and functions that do not. They are written the same, called the same... they are EXACTLY the same. However, SmileBASIC is

*SSSSPEEEEESHHHHULLLL*. Functions that return values include the parenthesis, like:

'These are standard functions which return values DIM A=SQR(5) DIM B=POW(4,2)Functions that do NOT return values do NOT have parenthesis and will fail if you use them, like:

'These functions don't return values and thus don't use parenthesis PRINT "HELLO" INPUT "GIVE ME NUMBER";N

### Functions in the SB Manual

There are many more functions built-in to SmileBASIC; we'll go over a few more in later lessons, or you can look them up in the SmileBASIC manual. The manual explains how to call the function and what parameters it expects. You can also press the ? button in the upper-right corner of the keyboard when the top screen cursor is on a function name to get information on that function. For instance, open up a program, type SQR , then press the ? in the upper-right corner of the keyboard to see information about that function. The top line shows how to use the function (Variable=SQR(Num)), and the rest explain the function and its parameters. If you find yourself confused about a function we use in the future, try looking it up in the manual while writing your program. Sometimes you'l look up a function and the manual will show weird stuff. For instance, type RND and bring up the in-game help (the question mark thing). The line that shows how to use the function looks something likeVariable=RND([Seed,] Max)When a parameter is surrounded by square brackets, it's an

**optional parameter**. Just like it sounds, optional parameters don't HAVE to be passed to a function. In the case of RND, you can call it like RND(5) and 5 will be the "max" parameter, or you can call it like RND(123,7) with 123 being the "seed" and 7 being the "max". Now look up PRINT in the in-game manual; it should look something like

PRINT [Expression [; or, Expression...]]This one is a little uglier but don't worry, it's not that bad. Remember, things inside square brackets are optional, so since the entire parameter list of PRINT is within square brackets, you can call PRINT by itself and it'll still work (it'll just print an empty line). "Expression" means you can put basically anything there that produces a value, like 5+5, SQR(49), "MONKEYS", etc. Then we have ANOTHER set of square brackets inside the outer ones with "; or,", another Expression, and then an ellipsis (...). The ellipsis means you can repeat whatever is inside the square brackets as many times as you want, and the "; or," means each expression is separated by semicolons or commas. So, this means PRINT can take 0 or more expressions with each expression separated by semicolons or commas. Here's some examples:

PRINT PRINT "Hello World" PRINT "First","Second" PRINT 55;"apples" PRINT B$,"things";4*8You may also see some functions with they keyword OUT in the call. Sometimes, a function just HAS to produce more than one value. In this case, instead of calling the function like V=FUNC(X), you'd do something more like FUNC(X) OUT V. This way, the function can produce more than one value. An example is retrieving the X and Y position of a sprite:

SPOFS I OUT X,YDon't worry, you don't need to know how sprites work yet. This function just needs to return both the X AND the Y position of a sprite, so this function uses OUT to return two values (stored into variables called X and Y, which can be named anything of course). Also, don't worry so much about OUT parameters right now; we won't be using them very much right now, and when we do I'll explain them again. Most of the things you use in SmileBASIC are functions, like XSCREEN, ACLS, SPDEF, etc. If you just keep in mind how to use functions and remember to use the in-game manual, you can write SmileBASIC code pretty easily! You just have to... you know... know what the functions actually do.

# Conclusion

Mathematical functions are a way of transforming one or more numbers into another single number. They are written as equations, for example: f(x) = x^{2}(a function which squares inputs: 3 becomes 9, 7 becomes 49, etc). Programming functions are about the same as math functions: they receive inputs (parameters) and

*may*produce an output value (return value). SmileBASIC built-in functions like SQR and POW are like math functions in that they have a list of inputs and produce a single output value, but other built-ins like PRINT and INPUT do not return any values and simply perform some task. Within programming functions are just little pieces of isolated code that can be reused to perform tasks. We only

*use*(not alter) built-ins like SQR and PRINT because we can't see their inner code, but in a later lesson we'll learn to write our own functions to extend the functionality of SmileBASIC. There are no "do it yourself" examples here because the next lesson will be all about using what we've learned to actually make something! If I don't make it in a reasonable amount of time, just keep bugging me until I do lol. Next tutorial (part 9)