Description
Return -log2(collisionProbability), log2(support), and their difference.
Entropy summarizes uncertainty under a specified probability model and logarithm convention. Support indicators, one-symbol terms, and exponentiated entropies are components with different meanings.
Return -log2(collisionProbability), log2(support), and their difference.
When to use this tool
Use Collision Entropy Uniform Support Gap when you need one explicitly scoped entropy or support calculation.
How to use the tool and how it works
- Enter collisionProbability, support. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read entropyBits, maximumBits, gapBits. Use the output convention below.
Require support at least one and collisionProbability in (0, 1] no smaller than 1/support minus 1e-12. Return -log2(collisionProbability), log2(support), and their difference.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| collisionProbability | Collision Probability | Required. Finite number; maximum 1; strictly above 0. |
| support | Support | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| entropyBits | Information entropy in bits on the same per-symbol basis as the code cost. | Required. Finite number. |
| maximumBits | Maximum Bits | Required. Finite number. |
| gapBits | Gap Bits | Required. Finite number. |
{
"input": {
"collisionProbability": 0.5,
"support": 4
},
"output": {
"entropyBits": 1,
"maximumBits": 2,
"gapBits": 1
}
}Limitations and assumptions
- The bound has an absolute tolerance, so a tiny negative gap is possible; the underlying distribution and exact support are supplied rather than verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Validate and align complete probability distributions before aggregating terms or interpreting an uncertainty estimate.
References
Similar or alternative tools
- Collision Probability Single Symbol Term
Validate probability in [0, 1] and square it for contribution.
- Min Entropy Maxsymbol Contribution
Require maximumProbability in (0, 1] and return -log2(maximumProbability) as bits.