Theory

For a stochastic result with lanes (R_i), DSArith computes:

[ \bar{R} = \frac{1}{N}\sumi Ri, \quad \sigma^2 = \frac{1}{N-1}\sumi (Ri-\bar{R})^2 ]

[ CR = \log{10}\left(\frac{\sqrt{N}|\bar{R}|}{\sigma\tau_\beta}\right) ]

Where:

• (N): number of stochastic lanes,
• (\tau_\beta): Student-(t) quantile for confidence level (1-\beta),
• (C_R): estimated number of significant decimal digits.

Interpretation

• Larger (C_R) means more reliable digits.
• accuracy(x) is the clamped integer form of (C_R).
• iscomputedzero(x) indicates results interpreted as computational zero.

Computational zero criterion

DSArith marks a result as computational zero when:

1. all lanes are exactly zero, or
2. significance is negative / insufficient under the DSA estimate.

This is the mechanism behind @.0 output in unstable cancellation scenarios.