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Suppose you have a number $N$ and an interval: $[\min, \max]$–where $\min$ and $\max$ are two known numbers creating a closed interval (including themselves).

I want to have a function that for a given $N$ will return the same $\text{result}$ number located in the specified interval ($\min \le \text{result} \le \max$), but preferably to cover the whole interval (at least, as much as possible).

Are there any known implementations/solutions/algorithms for this kind of problem?


I'm currently thinking if using modulo-n classes would be a solution:

$$f (N, \min, \max) = N \mathbin{\%} (\max + 1 - \min) + \min$$

($x \mathbin{\%} y$ being the rest of $x / y$)

Example:

\begin{align} f(42, 4, 6) & = 4 \\ f(43, 4, 6) & = 5 \\ f(44, 4, 6) & = 6 \\ f(45, 4, 6) & = 4 \\ & \ \ \vdots \end{align}

This is covering the entire interval which is great.


Can this be improved? What other solutions are there?

It's not a problem if there are multiple $N$ values for which the result is same as long the function is not a very general thing (e.g. constant) or the interval is not covered (possible return values are not part of the whole interval. e.g. last/first digit–that will be a value between $0$ and $9$, so obviously not something I'm looking for).


Currently I need only integers, but I'm open to see how this can be extended to real/complex numbers.

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  • $\begingroup$ Could you give an example, as I feel your question is not very clear, for a given N in a range, gives you the same result, What do you mean by that? $\endgroup$ – Satish Ramanathan Dec 19 '15 at 20:13
  • $\begingroup$ @satishramanathan I updated the question. I'm a developer, and there we have a random function. I don't want this to be random or depend on anything that changes (e.g. time). I want for a given $N$ and range to get the same result now and after one day and after one year. $\endgroup$ – Ionică Bizău Dec 19 '15 at 20:37
  • $\begingroup$ @IonicăBizău if you want a random number generator to give you always the same sequence, use the same inital seed? Or what is your problem? $\endgroup$ – Adrian Dec 19 '15 at 22:38
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A way to generalize this to the real numbers is to define a function

$$f(x)=x+a$$

where the domain is $[0,b-a]$ and the range is $[a,b]$. If you want your program to output a value for any real number, simply have it subtract $b-a$ from your input until your input lies in the domain of $f(x)$.

Because the complex numbers contain two real components, any complex number $z$ in the interval $$\{z=x+iy\,|\, x\in[a,b],y\in[a,b]\}$$ can be mapped to $\mathbb{R}^2$ with the function $$g(x,y)=f(x)+if(y)$$ which has a domain $0\leq x \leq b-a,\ 0\leq y \leq b-a$.

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