erf
erf(x)Input: x · Output: no output
What it is
The error function and its complement (erfc(x) = 1 - erf(x), computed directly rather than by subtraction so it stays accurate for large x, where erf(x) itself has already saturated to 1.0). x is a real scalar, Vec, or Mat/Signal; defined everywhere, no pole.
Overloads
One call shape — this function is not overloaded.
| Code | Input | Output | Description |
erf(x) | x scalar, Vec, Mat, or Signalnot documented yet | not documented yet | — |
Examples
No documentation example calls this form yet. The Core maths chapter is where one belongs.
How it works
erf/erfc: defined on the whole real line, no pole. erfc (x) = 1 - erf(x) mathematically, but computing it that way loses precision for large positive x: erf(x) saturates to 1.0 at double precision well before erfc(x) itself underflows to zero (erfc(6) is order 2e-17, nowhere near where 1.0 - erf(6) would still have any correct digits). libm::erfc computes the complementary form directly rather than subtracting, so it keeps precision into that tail -- see the erfc_of_large_x_does_not_cancel_to_nothing test below, which is exactly the case a naive 1.0 - erf(x) implementation gets wrong.
From the note above this builtin in the interpreter, where the reasoning was written down as it was built.
See also
erfc — documented in the same entry.