Description
Return a logarithmic reference ratio and its sign.
Conversion direction matters for reciprocal and logarithmic quantities. Frequencies, periods, phase coordinates and reference ratios use explicit origins, sign policies and denominator units, rather than a single ordinary length or time multiplier.
Return a logarithmic reference ratio and its sign.
When to use this tool
Use Log Ratio Reference Sign when converting the stated reciprocal, angular, phase or logarithmic convention.
How to use the tool and how it works
- Enter value, reference, logBase. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read logRatio, sign. Use the output convention below.
Return a logarithmic reference ratio and its sign. Require value/reference > 0 and logBase > 0 except one; logRatio = (ln(value)-ln(reference))/ln(base), sign uses (value-reference)/ln(base).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value | Required. Finite number; strictly above 0. |
| reference | Reference | Required. Finite number; strictly above 0. |
| logBase | Log Base | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| logRatio | Log Ratio | Required. Finite number. |
| sign | Sign | Required. Safe integer. |
{
"input": {
"value": 4,
"reference": 2,
"logBase": 2
},
"output": {
"logRatio": 1,
"sign": 1
}
}Limitations and assumptions
- Bases between zero and one reverse sign; input units must form a dimensionless ratio and no reference is selected.
- 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 the complete unit and origin definitions, and distinguish a coordinate conversion from a density Jacobian or a physical measurement.
References
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