Description
Accumulate positive integer run lengths until zero-based position falls in a run, then return that run's zero-based index and offset within it.
A sequence rule specifies an index origin, state order, and relation among terms. Advancing one step, mapping an index, and checking a local residual answer different questions. Supplied coefficients or periods define a model; they do not establish that observations follow it.
Accumulate positive integer run lengths until zero-based position falls in a run, then return that run's zero-based index and offset within it.
When to use this tool
Use Sequence Run Length Decoded Position when you need this particular index map, recurrence step, count, or local algebraic term under supplied sequence conventions.
How to use the tool and how it works
- Enter lengths, position. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read run, offset. Use the output convention below.
Accumulate positive integer run lengths until zero-based position falls in a run, then return that run's zero-based index and offset within it.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lengths | Lengths | Required. Array of safe integer; maximum items 256. |
| position | Zero-based decoded position. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| run | Zero-based run index. | Required. Safe integer. |
| offset | Zero-based offset within that run. | Required. Safe integer. |
{
"input": {
"lengths": [
2,
3,
1
],
"position": 4
},
"output": {
"run": 1,
"offset": 2
}
}Limitations and assumptions
- Position must fit the total decoded length. No values are decoded or stored, and floating-point output and safe-integer limits still constrain very large aggregate lengths.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Choose exact integer arithmetic when the index or coefficient range requires it. A complete sequence analysis needs actual terms and a consistent index and state-order convention beyond one local step.
References
Similar or alternative tools
- Interleaved Sequence Odd Even Length
Return evenPositions=ceil(length/2) and oddPositions=floor(length/2) for nonnegative integer length.
- Run Boundary Alternation Parity
Count alternations in an explicitly supplied two-label run-length encoding, preserving empty-stream status.