Description
Set max=max(left,right) and return logSum=max+ln(exp(left-max)+exp(right-max)).
Products of small probabilities can round to zero in floating-point arithmetic. Natural logarithms turn products into sums, and centering or expm1-based expressions can reduce avoidable numerical loss. A finite log weight is different from a raw probability and cannot directly represent an exact zero probability.
Set max=max(left,right) and return logSum=max+ln(exp(left-max)+exp(right-max)).
When to use this tool
Use Log Probability Logsum Two Weights when you need the stated natural-log contribution or stable conversion between a finite log representation and an ordinary value.
How to use the tool and how it works
- Enter left, right. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read logSum. Use the output convention below.
Set max=max(left,right) and return logSum=max+ln(exp(left-max)+exp(right-max)).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Finite number. |
| right | Right | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| logSum | Log Sum | Required. Finite number. |
{
"input": {
"left": 1000,
"right": 1000
},
"output": {
"logSum": 1000.6931471805599
}
}Limitations and assumptions
- Inputs are finite natural log weights, not raw probabilities. This stable two-term expression does not accept infinities, and extreme final sums can still exceed the output contract.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Keep long products or normalizations in the log domain when feasible. Check whether exact zeros need a separate flag and whether the final ordinary-scale result is representable.
References
Similar or alternative tools
- Log Probability Weight Centering Offset
For a nonempty finite logWeights list take offset=max(logWeights) and return centered values logWeights-offset.
- Normal Density Log Ratio Two Points
Return logRatio=((second-mean)^2-(first-mean)^2)/(2*deviation^2), requiring positive deviation.