Integer Nearest Multiple Tie Policy Tool

Description

For positive integer step compute q=floor(integer/step) and r=integer-q*step.

Exact integer arithmetic and finite numeric arithmetic have different range limits. A safe integer number is bounded by +/-9007199254740991, while supported decimal-integer text can represent larger values. Division and remainder also need a signed convention: truncating quotients and Euclidean nonnegative remainders can give different results.

For positive integer step compute q=floor(integer/step) and r=integer-q*step.

When to use this tool

Use Integer Nearest Multiple Tie Policy when you need this exact stated integer sign, bound, division, comparison, or factor component.

How to use the tool and how it works

Enter integer, step, tiesUp. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read multiple, tied. Inspect tied before interpreting the associated values.

For positive integer step compute q=floor(integer/step) and r=integer-q*step. Return tied when 2*r==step; choose the upper multiple when 2*r>step or tied and tiesUp, otherwise the lower multiple.^[1]

Input field	Meaning and units	Accepted input
integer	Safe integer number or exact signed decimal-integer text as declared below.	Required. Safe integer.
step	Step	Required. Safe integer; minimum 1.
tiesUp	At a midpoint choose toward positive infinity when true, otherwise the lower multiple.	Required. Boolean.

Output field	Interpretation	Returned shape
multiple	Multiple	Required. Safe integer.
tied	Tied	Required. Boolean.

json

{
  "input": {
    "integer": 15,
    "step": 10,
    "tiesUp": false
  },
  "output": {
    "multiple": 10,
    "tied": true
  }
}

Limitations and assumptions

TiesUp means toward positive infinity, including negative inputs, rather than away from zero. Numeric intermediate products and results remain subject to safe-integer range and precision limits.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
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. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use exact decimal-integer tools when the range exceeds safe numeric integers. State the division, remainder, midpoint, and zero convention before combining results from different operations.

References

Calculation and input contract: number/integer-nearest-multiple-tie-policy — tool.io

Similar or alternative tools

Integer Multiple Nearest Lower Upper
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