Lesson 11 - Mathematical functions in Swift
In the previous lesson, Multidimensional arrays in Swift, we introduced multidimensional arrays. Learning Swift actually starts from now on, however, this online course of the most basic constructs of the language will be finished today. I'm glad that we successfully got until here, the next online course will be about "object oriented programming". We'll be creating really interesting applications and even one game. We'll end this course with a simple article about mathematical functions that will certainly come in handy in our future programs.
In Swift, the basic math functions are contained in the
Foundation module which you need for bunch of other features as
well. We've already encountered the
sqrt() function to get the
We are also provided with the following math constants:
M_PI is, of course, the number pi
E is the Euler's number, i.e. the base
of natural logarithm (
2.7182...). We can access the
constant on the
Float types as well.
print("Pi: \(Double.pi)\ne: \(M_E)")
Pi: 3.14159265358979 e: 2.71828182845905
Now, let's go over available math functions.
Available math functions
Let's start with the simple ones Both functions take two numbers of any data type as parameters. The
min() function returns the smallest number, the
function returns the greatest one.
round(), ceil(), floor() and trunc()
All these functions are related to rounding.
round() takes a
decimal number as a parameter and returns the rounded number of the
Double type in the way we learned in school (from
0.5 it rounds upwards, otherwise downwards).
rounds always upwards and
floor() rounds downwards no matter what.
trunc() (truncate) doesn't round, it just cuts the part after the
decimal point off. All these functions are expecting the
Float, there are alternatives with the
suffix, for example:
We'll certainly be using
round() very often. I practically used
the other functions e.g. in determining the number of pages of a guestbook. When
we've 33 comments and we print only 10 comments per page, they'll, therefore,
occupy 3.3 pages. The result must be rounded up since there will be actually 4
If you think that
trunc() do the same
thing, think again! They behave differently for negative numbers.
floor() rounds negative numbers down to the next "more negative"
trunc() always rounds to zero when the input is
We round decimal numbers and store them in
Int variables like
let d = 2.72 let a: Int = Int(round(d))
Int is necessary; even though
returns a whole number. However, it's still of the
Double type, due
to the fact that all mathematical functions work with
abs(), sign, and signum()
You'll probably use
abs() more, which takes any number of any
type as a parameter and returns its absolute (in other words positive) value.
sign property and the
signum() method return
1 depending on the sign of the
number (whether it's negative, zero, or positive). The difference is data types.
sign is a property of decimal numbers,
signum() can be
sin(), cos(), tan()
The classic trigonometric functions, they all take an angle in radians as
Double as a parameter, remember they don't work with degrees. To
convert degrees to radians we multiply them by
* (M_PI / 180). The
output is a
Double again. The functions have also
acos(), asin(), atan()
The classic inverse trigonometric functions (arcus, sometimes cyclometric
functions), which return the original angle according to the trigonometric
value. The parameter is the value as
Double, the output is the
angle in radians (also a
Double). If we wish to have an angle in
degrees, we have to divide the radians by
/ (180 / PI). The
functions have also
pow() and sqrt()
pow() takes two parameters of the
Double type. The
first is the base of the power and the second is the exponent. Again, we have
Float alternatives. If we wanted to calculate, for example,
23, the code would look like this:
sqrt() is an abbreviation of SQuare
RooT, which returns the square root of the
number given as
Double. Both functions return the result as
Double. There's the
sqrtf() function for the
exp(), log(), log10()
exp() returns the Euler's number raised to a given exponent.
log() returns the natural logarithm of a given number.
log10() then returns the decadic logarithm (the base is
10) of a given number.
Hopefully, you noticed that the method list lacks any general root function. We, however, can calculate it using the provided math functions.
We know that roots work like this: 3rd root of 8 = 8^(1/3). So we can write:
It's very important that we write at least one number with a decimal point when dividing, otherwise Swift will assume an integer division, resulting in 80 = 1.
Programming languages often differ in how they perform the division of numbers. You need to be aware of these issues to avoid being, unpleasantly, surprised afterwards. Let's write a simple program:
let a : Int = 5 / 2 let b : Double = 5 / 2 let c : Double = 5.0 / 2 let d : Double = 5 / 2.0 let e : Double = 5.0 / 2.0 // let f : Int = 5 / 2.0 print("\(a)\n\(b)\n\(c)\n\(d)\n\(e)")
We divide 5/2 for several times in the code, which is mathematically 2.5. Nonetheless, the results will not be the same in all cases. Can you guess what we'll get in each case? Go ahead, give it a try
The code wouldn't compile because of the line with the
variable, which we commented. The problem is that in this case the result is a
decimal number which we're trying to store into an integer (
The program's output is as follows:
2 2.5 2.5 2.5 2.5
We see the result of this division is in the first case whole and in other
cases decimal. It depends in which type we store to. Although in the second case
the division is the same as in the first one, the result is
because it's the type we store to. The last case (with the
variable) won't work because we divide by 2.0 and Swift tries to store
Double to the integer variable.
For example, the PHP language always returns the decimal result of the division. When you divide in different programming languages make sure you check how division works there first before you use it.
The remainder after division
In our applications, we often need the remainder after integer division (i.e. modulo). In our example 5/2, the integer result is 2 and modulo is 1 (what left over). Modulo is often used to determine whether a number is even (remainder of division by 2 is 0). Modulo is useful if you want, for example, to draw a checkerboard and fill in the fields based on whether they are even or odd, to calculate the deviance of your position from some square grid, and so on.
In Swift and C-like languages in general, modulo is a percent sign, i.e.
print(5 % 2) // Prints 1
Well, that's all I've got for you in this course. The course continues with the Basics of Object-Oriented Programming in Swift course. Next time, we'll introduce the world of objects and understand a lot of things that remained unrevealed until now You should surely try the exercises too.
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