How to Generate Unique, Deterministic Numbers with a 1:1 Mapping?

Constant Deterministic Number Generation with 1:1 Mapping

Objective

Generate a deterministic function that maps input numbers to unique output numbers within a specified range, without duplication.

Method

Utilize modular arithmetic based on the Affine cipher:

1. Transformation Formula: f(P) = (mP s) mod n

2. Parameters:

   • m: Must be coprime with n (not divisible by the same numbers as n).
   • s: A random number less than n.
   • n: The desired range of the output.

Example for uint64

• n = 2^64 (uint64 range)
• m = 39293 (an odd number)
• s = 75321908 (random number < 2^64)

Transformation Function:

func transform(p uint64) uint64 {
    return m * p + s  // implicitly mod'd 2^64 by the type's size
}

Example with int64

For signed numbers, convert input and output between uint64 and int64 to maintain the unique mapping:

func signedTransform(p int64) int64 {
    return int64(transform(uint64(p)))
}

Guarantees

• The function ensures a 1:1 mapping for all input numbers.
• No two input numbers will generate the same output number.
• The output numbers will be uniformly distributed within the specified range.
• The function is deterministic, always generating the same output for a given input.

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