Closed Integer Interval Overlap Count

Count shared integers in closed integer endpoint intervals, including one-point contact.

Description

Count shared integers in closed integer endpoint intervals, including one-point contact.

Closed integer ranges count both boundary integers. Their overlap count differs from continuous length because a shared endpoint contributes one integer.

When to use this tool

Count shared integers in closed integer endpoint intervals, including one-point contact.

Prepare the supplied aStart, aEnd, bStart, bEnd 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 aStart, aEnd, bStart, bEnd. 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.sharedIntegerCount. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Validate ordered bounded integer endpoints, take the larger start and smaller end, and return the larger of zero and end-start+1.^[1]

Input field	Meaning and representation	Accepted input
aStart	a start.	Finite number
aEnd	a end.	Finite number
bStart	b start.	Finite number
bEnd	b end.	Finite number

Output field	Interpretation
result	Object containing the named outputs below.
result.sharedIntegerCount	The shared integer count value under the stated formula or text convention.

json

{
  "input": {
    "aStart": 0,
    "aEnd": 2,
    "bStart": 2,
    "bEnd": 3
  },
  "output": {
    "result": {
      "sharedIntegerCount": 1
    }
  }
}

Limitations and assumptions

This is a count of shared integers, not an interval length. It assumes unit-spaced integers and does not accept arbitrary real-valued bounds.
Interval-array rows contain exactly two finite endpoints in start/end order, with at most 128 intervals per collection. Individual operations state when positive length, integer endpoints or explicit inclusion flags are required.
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

Retain the endpoint convention with every result. Continuous length, integer point counts and open/closed membership differ; merge returned cells separately when a canonical minimal interval collection is required.

References

Tool behavior and example: Closed Integer Interval Overlap Count — tool.io

Similar or alternative tools

Half Open Interval Overlap Length
Compute Lebesgue overlap length of half-open finite intervals; touching and empty intervals have zero length.
Integer Range Residue Count
Count congruent integers in an inclusive closed range using Euclidean residues, including negative endpoints.