Decimal Quantum Neighbor Values
Exact decimal quantum bounding neighbors; signed arithmetic uses floor rather than truncation.
Description
Exact decimal quantum bounding neighbors; signed arithmetic uses floor rather than truncation.
The two neighboring multiples of a quantum bracket an exact decimal value. An exact member has the same lower and upper neighbor.
When to use this tool
Exact decimal quantum bounding neighbors; signed arithmetic uses floor rather than truncation.
- Prepare the supplied value, quantum 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 value, quantum. 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.lower, result.upper. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Parse value and positive quantum as exact fractions. Floor their ratio for the lower multiple; use the same multiple if exact and the next one otherwise for upper. Return reduced fractions.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| value | value. | Text; at most 8,192 UTF-16 code units, subject to the grammar above |
| quantum | quantum. | Text; at most 8,192 UTF-16 code units, subject to the grammar above |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.lower | The lower value under the stated formula or text convention. |
| result.upper | The upper value under the stated formula or text convention. |
{
"input": {
"value": "0.25",
"quantum": "0.1"
},
"output": {
"result": {
"lower": {
"numerator": "1",
"denominator": "5"
},
"upper": {
"numerator": "3",
"denominator": "10"
}
}
}
}Limitations and assumptions
- These are grid neighbors rather than floating-point nextafter values. No storage-width range or preferred rounding policy is imposed.
- Exact decimal-spelling operations require digits before the optional decimal point and allow a signed exponent. Decimal text is bounded to 256 code units and effective scale to minus 256 through 256; integer-string fields allow a sign and up to 256 digits.
- 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.
- Lists are limited to 128 entries. JSON text must meet bounded size and depth checks, and numeric outputs beyond the safe finite magnitude are rejected. Exact large integers use decimal strings.
- 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
Preserve decimal and integer strings when exact comparisons matter. Select signedness, scale, rounding and overflow policies separately, and use the matching encoder/decoder rather than a floating-point approximation.
References
Similar or alternative tools
- Decimal Quantum Membership
Exact decimal quantum membership; signed arithmetic uses floor rather than truncation.
- Decimal Negative Zero Policy
Apply an explicit negative-zero spelling policy without treating negative zero as a different numerical value.