Description
For width in (0, 1], return idealBits = -log2(width) and sufficientBits = ceil(idealBits) + 1.
Arithmetic coding narrows an interval according to cumulative symbol probabilities. Choosing a point or bit budget for that interval differs from implementing a practical integer range coder.
For width in (0, 1], return idealBits = -log2(width) and sufficientBits = ceil(idealBits) + 1.
When to use this tool
Use Arithmetic Code Interval Bit Bound when you need one ideal interval-update or termination-budget term.
How to use the tool and how it works
- Enter width. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read idealBits, sufficientBits. Use the output convention below.
For width in (0, 1], return idealBits = -log2(width) and sufficientBits = ceil(idealBits) + 1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| width | Width, count, or interval span under the stated formula. | Required. Finite number; maximum 1; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| idealBits | Ideal Bits | Required. Finite number. |
| sufficientBits | Sufficient Bits | Required. Safe integer. |
{
"input": {
"width": 0.125
},
"output": {
"idealBits": 3,
"sufficientBits": 4
}
}Limitations and assumptions
- This is a conservative ideal interval-selection budget, not the exact emitted length of a particular coder or termination format.
- 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
Use a complete coding implementation with explicit precision, renormalization, and stream-termination rules.
References
Similar or alternative tools
- Arithmetic Code Final Interval Midpoint
Reject when that midpoint is not representably inside [lower, upper); otherwise return midpoint and width.
- Information: Ideal Codeword Length Integer Gap
Compute -ln(probability)/ln(radix) for idealLength, ceil it for integerLength, and return their gap.