What Does 1 (Mod N) Mean?
I Am Trying to Implement a Simple Algorithm in Javascript. Wherever I Look, It Calls for the Code to Work out 1 (Mod N). as Far as I Can Tell, 1 Modulo...
I am trying to implement a simple algorithm in JavaScript. Wherever I look, it calls for the code to work out 1 (mod N). As far as I can tell, 1 modulo anything (or 1%N) is 1.
What am I missing? Is it always 1, and if so, why not just use 1?
2 Answers
The algorithm probably says something like:
x ≡ 1 (mod N) # x is congruent to 1 (modulo N)
The (mod N) and the triple equals sign denote that you're working with modular arithmetic, not normal arithmetic. Think of it like the hands of a clock. In modular arithmetic, x ≡ 1 means that x and 1 belong to the same residue class. If you have a clock with N hour divisions, turning the hand 1 time or x times will bring the hand to the same end position.
For your specific case, x ≡ 1 (mod N) can be represented as x % N === 1 in JavaScript if x is never negative. Otherwise, your equality will not hold even though it should: for example, -1 ≡ 1 (mod 2) but (-1) % 2 === -1, which isn't equal to 1 even though they're "equal" in the modular arithmetic sense.
If you expect x to be negative, you can just rearrange the congruence relation:
x ≡ 1 (mod N)
⇒ x - 1 ≡ 0 (mod N)
x - 1 being congruent to 0 means that it's divisible by N itself, so you can use the modulo operator safely:
if ((x - 1) % N === 0) {
...
}
How the modulo (%) operator works is defined in ECMA-262 §11.5.3. There are a few quirks, the ECMAScript modulo operator accepts floats as well as integers:
For integers:
1 % -Infinity returns 1
...
1 % -2 returns 1
1 % -1 returns 0
1 % 0 returns NaN
1 % 1 returns 0
1 % 2 returns 1
...
1 % Infinity returns 1
For floats,
1 % -1.1 returns 1
1 % 0.1 returns 0.09999999999999995
1 % 0.6 returns 0.4
1 % 0.5 returns 0
1 % 0.4 returns 0.19999999999999996
1 % 0.9 returns 0.09999999999999998
1 % 1.1 returns 1
So without the context of how the modulo operator is being applied, it's very difficult to determine why it's being used. Best of all would be documentation of the code, but I suppose that's not available.
One use is, where an integer is expected, to evaluate 0 and 1 as false and everything else as true, so:
if (1 % n) {
// do this if n is something other than 0 or 1
}
Maya is a hardware enthusiast who tests and reviews smart home devices, smartphones, wearables, and audio gear. She focuses on practical consumer value and build quality.
