Sample Grid Endpoint Count

Count a regular sample grid starting at start, with end inclusion explicit; a nonaligned end is not invented as an extra sample.

Description

Count a regular sample grid starting at start, with end inclusion explicit; a nonaligned end is not invented as an extra sample.

Regular sampling places observations at start plus integer multiples of step. An endpoint policy determines the count, but an off-grid endpoint is not an additional sample.

When to use this tool

Count a regular sample grid starting at start, with end inclusion explicit; a nonaligned end is not invented as an extra sample.

Prepare the supplied start, end, step, includeEnd fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter start, end, step, includeEnd. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.count, result.lastSample. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Require ordered start/end and positive step. Let q equal (end-start)/step. With includeEnd, use floor(q)+1 samples; otherwise use ceil(q). Return the count and final grid value, or null when the count is zero.^[1]

Input field	Meaning and representation	Accepted input
start	start.	Finite number
end	end.	Finite number
step	step.	Finite number; greater than zero
includeEnd	Explicit choice for include end; supply a boolean rather than a text label.	true or false

Output field	Interpretation
result	Object containing the named outputs below.
result.count	The count value under the stated formula or text convention.
result.lastSample	The last sample value under the stated formula or text convention.

json

{
  "input": {
    "start": 0,
    "end": 4,
    "step": 2,
    "includeEnd": true
  },
  "output": {
    "result": {
      "count": 3,
      "lastSample": 4
    }
  }
}

Limitations and assumptions

includeEnd permits a grid point exactly at end; it does not append end when off grid. The grid is bounded and uses floating-point arithmetic without a rounding tolerance.
Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
Ordinary string lists have at most 128 entries of at most 128 code units each; numeric lists and matrices have separate bounded size checks. Nonfinite results and excessively large serialized outputs are rejected.
Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.

Alternative or Complementary methods

Choose a sampling model before combining results. Earlier-sample hold, linear interpolation and index-only differences answer different questions; event cooldown, debounce and rolling limits also use different acceptance rules.

References

Tool behavior and example: Sample Grid Endpoint Count — tool.io

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