Agena

agena >> `The Power of Procedural Programming` 6.6.10 Shiraz, January 28, 2026 - The binary operators, `dual.hypot` and `dual.arctan2` now accept a mix of hyper-dual numbers and Agena numbers. In this case the Agena number will be treated as a hyper-dual constant. To implement the inverse square root, just type: > dual.recipsqrt := <: x :: dual -> 1/sqrt(x) :> - The new package function `dual.const` allows to explicitly define constants. An alternative implementation of the inverse square root might look like this: > dual.recipsqrt := <: x :: dual -> dual.const(1)/sqrt(x) :> - Added various predefined constants to the `dual` package, check the end of Chapter 11.7 of the Agena Reference for a list. - With hyper-dual numbers, the `/` operator now explicitly checks for division by zero and the `^` operator checks for non-positive bases. - With hyper-dual numbers, the `recip` operator has been tweaked a bit. - With hyper-dual numbers, the following functions and operators have been protected against internal rounding errors that would wrongfully trigger out-of-domain errors: `arcsin`, `arccos`, `arcsec`, `dual.arccsc`, `dual.arcsinh`, `dual.arccosh`, `dual.arccsch`, `dual.arcsech`. - The `sqrt` and `arcsec` operators incorrectly computed the second derivative. Same with `dual.arccsc` and `dual.arccsch`. This has all been fixed. - `dual.diff` did not work when the computation resulted in a domain error. This has been fixed. - Extended the regression tests.