Description
Advance one multiplicative recurrence step and clamp it to supplied bounds.
A sequence rule specifies how terms relate. Checking one transition, advancing a recurrence, and bounding an infinite tail answer different questions. A calculation from supplied coefficients assumes that rule; it does not infer it from observations.
Advance one multiplicative recurrence step and clamp it to supplied bounds.
When to use this tool
Use it for bounded recurrence zero input step when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter previous, multiplier, lower, upper. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read next, clamped. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Multiply previous by multiplier with no added input, clamp the result to the inclusive lower/upper interval, and report whether clamping changed the raw product. Require lower no greater than upper.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| previous | Previous | Required. Finite number. |
| multiplier | Multiplier | Required. Finite number. |
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| next | Next | Required. Finite number. |
| clamped | Clamped | Required. Boolean. |
{
"input": {
"previous": 3,
"multiplier": 2,
"lower": 0,
"upper": 5
},
"output": {
"next": 5,
"clamped": true
}
}Limitations and assumptions
- This is one bounded recurrence step, not a convergence analysis. Saturation can hide a large raw product; inspect clamped rather than treating the result as an unconstrained prediction.
- The field tables describe structural bounds; the mechanics also state cross-field requirements. Malformed input shapes, disallowed keys, and invalid domains cause input errors. Results must remain finite and within the declared output contract. A successful false flag or zero placeholder is distinct from an error.
- Numeric arithmetic uses binary floating point. Exact comparisons have no hidden tolerance or decimal rounding; negative zero is exported as zero. Decimal-text integer operations retain the exactness specifically stated above.
Alternative or Complementary methods
For bounded recurrence zero input step, check the source records and the supplied rule before comparing the result with another method. Use exact integer or symbolic arithmetic when a numerical equality is insufficient.
References
Similar or alternative tools
- Affine Recurrence Two Step Constant
Return the coefficients obtained by composing a supplied affine recurrence twice.
- Arithmetic Progression Modular Residue Step
Advance a numeric residue by a supplied difference under floating-point modulo arithmetic.