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Multiset Count Signed Update Underflow Tool

Calculate multiset count signed update underflow from explicit caller-supplied inputs.

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Description

Add signed integer delta to nonnegative count.

A finite set records membership, while a multiset also records multiplicity. An ordered set adds an ordering rule, and an interval adds endpoint-closure choices. A witness for one element, a count budget, and equality of complete sets establish different facts.

Add signed integer delta to nonnegative count.

When to use this tool

Use Multiset Count Signed Update Underflow when you need the stated finite-set, interval, multiplicity, membership, or ordering operation under the given equality convention.

How to use the tool and how it works

  1. Enter count, delta, clamp. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read count, underflow. Inspect underflow before interpreting the associated values.

Add signed integer delta to nonnegative count. Reject a negative raw result unless clamp is true; otherwise floor it at zero and report underflow.1

Input fieldMeaning and unitsAccepted input
countCount under the stated input or output convention.Required. Safe integer; minimum 0.
deltaSigned integer count change.Required. Safe integer.
clampClampRequired. Boolean.
Output fieldInterpretationReturned shape
countCount under the stated input or output convention.Required. Safe integer.
underflowWhether the raw updated count was negative, even when clamped.Required. Boolean.
json
{
  "input": {
    "count": 3,
    "delta": -5,
    "clamp": true
  },
  "output": {
    "count": 0,
    "underflow": true
  }
}

Limitations and assumptions

  • Underflow records the raw sign even when clamped. This is a supplied count transition without an actual map update, event provenance, or capacity check.
  • 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

Use a full set operation when one element or count cannot establish the required relation. Preserve the distinction between strings, typed scalar atoms, nested sets, ordered lists, and multisets.

References

  1. Calculation and input contract: set/multiset-count-signed-update-underflow — tool.io

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