what math do i need to convert this number

Question

given an X, what math is needed to find its Y, using this table?

x->y
0->1
1->0
2->6
3->5
4->4
5->3
6->2

language agnostic problem

and no, i dont/cant just store the array, and do the lookup.

yes, the input will always be the finite set of 0 to 6. it wont be scaling later.

Answer 1

unsigned short convertNumber(unsigned short input) {
  if (input <= 1) { return !input; } //convert 0 => 1, 1 => 0
  return (8-input); //convert 2 => 6 ... 6 => 2
}

Answer 2

It looks like:

y = (x * 6 + 1) % 7

Answer 3

Homework?

How about:

y = (x <= 1 ? 1 : 8) - x

Answer 4

This:

y = (8 - x) % 7

This is how I arrived at that:

x  8-x  (8-x)%7
----------------
0   8     1
1   7     0
2   6     6
3   5     5
4   4     4
5   3     3
6   2     2

Answer 5

and no, i dont/cant just store the array, and do the lookup.

Why not?

yes, the input will always be the finite set of 0 to 6. it wont be scaling later.

Just use a bunch of conditionals then.

if (input == 0) return 1;
else if (input == 1) return 0;
else if (input == 2) return 6;
...

Or find a formula if it's easy to see one, and it is here:

if (input == 0) return 1;
else if (input == 1) return 0;
else return 8 - input;

Here's a way to avoid both modulo and conditionals, going from this:

y = (8 - x) % 7

We know that x % y = x - floor(x/y)*y

So we can use y = 8 - x - floor((8 - x) / 7) * 7

Answer 6

Combining the ideas in Dave and Paul's answer gives the rather elegant:

y = (8 - x) % 7`

(though I see I was beaten to the punch with this)

Answer 7

0.048611x^6 - 0.9625x^5 + 7.340278x^4 - 26.6875x^3 + (45 + 1/9)x^2 - 25.85x + 1

Sometimes the simple ways are best. ;)

Answer 8

Though it seems a bunch of correct answers have already appeared, I figured I'd post this just to show another way to have worked it out (they're all basically variations on the same thing):

Well, the underlying pattern is pretty simple:

x y
0 6
1 5
2 4
3 3
4 2 
5 1
6 0

y = 6 - x

Your data just happens to have the y values shifted "down" by two indices (or to have the x values shifted "up").

So you need a function to shift the x value. This should do it:

x = (x + 5) % 7;

Resulting equation:

y = 6 - ((x + 5) % 7);

Answer 9

int f(int x)
{
    return x["I@Velcro"] & 7;
}

Answer 10

What about some bit-fu ?

You can get the result using only minus, logical operators and shifts.

b = (x >> 2) | ((x >> 1) & 1)
y = ((b << 3)|(b ^ 1)) - x