Error function¶
Description¶
The integral is
\[\mathrm{erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x \exp(-t^2) dt.\]
The magnitude of \(x\) is limited to \(9.231948545\) for DEC arithmetic; \(1\) or \(-1\) is returned outside this range.
For \(0 <= |x| < 1\), \(\mathrm{erf}(x) = x * P4(x**2)/Q5(x**2)\); otherwise \(\mathrm{erf}(x) = 1 - \mathrm{erfc}(x)\).
Accuracy¶
| Relative error | ||||
|---|---|---|---|---|
| arithmetic | domain | # trials | peak | rms |
| DEC | 0, 1 | 14000 | 4.7e-17 | 1.5e-17 |
| IEEE | 0, 1 | 30000 | 3.7e-16 | 1.0e-16 |