Description
Scale each cumulative endpoint by current width and add current lower for the next lower and upper bounds.
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.
Scale each cumulative endpoint by current width and add current lower for the next lower and upper bounds.
When to use this tool
Use Arithmetic Code Single Symbol Subinterval when you need one ideal interval-update or termination-budget term.
How to use the tool and how it works
- Enter lower, upper, cumulativeLower, cumulativeUpper. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read lower, upper. Use the output convention below.
Require ordered current and cumulative intervals within [0, 1]. Scale each cumulative endpoint by current width and add current lower for the next lower and upper bounds.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lower | Lower | Required. Finite number; minimum 0. |
| upper | Upper | Required. Finite number; maximum 1. |
| cumulativeLower | Cumulative Lower | Required. Finite number; minimum 0. |
| cumulativeUpper | Cumulative Upper | Required. Finite number; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
{
"input": {
"lower": 0.25,
"upper": 0.75,
"cumulativeLower": 0.25,
"cumulativeUpper": 0.5
},
"output": {
"lower": 0.375,
"upper": 0.5
}
}Limitations and assumptions
- This updates one ideal interval using floating point, without coder renormalization, integer range handling, or emitted bits.
- 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.
- Arithmetic Code Interval Bit Bound
For width in (0, 1], return idealBits = -log2(width) and sufficientBits = ceil(idealBits) + 1.