Description
Audit a measured cosine-rescaling discrepancy against a caller-supplied absolute roundoff budget.
A similarity term depends on the comparison universe, missing-value policy, treatment of repeated features, and normalization. A score can also have a caller-selected value when its mathematical denominator vanishes. Those conventions matter before interpreting a threshold or comparing methods.
Audit a measured cosine-rescaling discrepancy against a caller-supplied absolute roundoff budget.
When to use this tool
Use Cosine Rescale Roundoff Envelope when you need this particular comparison term, normalization, domain condition, or empty-result policy in a larger matching workflow.
How to use the tool and how it works
- Enter originalCosine, rescaledCosine, suppliedAbsoluteBudget. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read absoluteGap, withinBudget. Inspect withinBudget before interpreting the associated values.
Return absoluteGap=abs(rescaledCosine-originalCosine) and withinBudget for inclusive comparison with suppliedAbsoluteBudget. Require bounded input cosines and nonnegative budget.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| originalCosine | Original Cosine | Required. Finite number. |
| rescaledCosine | Rescaled Cosine | Required. Finite number. |
| suppliedAbsoluteBudget | Supplied Absolute Budget | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| absoluteGap | Absolute Gap | Required. Finite number. |
| withinBudget | Within Budget | Required. Boolean. |
{
"input": {
"originalCosine": 0.5,
"rescaledCosine": 0.5000000000000001,
"suppliedAbsoluteBudget": 1e-15
},
"output": {
"absoluteGap": 1.1102230246251565e-16,
"withinBudget": true
}
}Limitations and assumptions
- The tool compares supplied results without rescaling vectors or deriving a floating-point error bound. Passing the budget does not establish exact invariance or semantic agreement.
- 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
Compare methods only after aligning feature definitions, missingness, empty policies, multiplicities, and normalizers. Use a complete comparison when the tool returns only one contribution or count check.
References
Similar or alternative tools
- Cosine Dot Product Roundoff Clamp
Clamp cosine to minus one through one when it is within the supplied tolerance outside that interval.
- Cosine Norm Rescale Invariance Residual
Return cosine=dot/(firstNorm*secondNorm), scaledCosine=sign(firstScale*secondScale)*cosine, and their residual.