Re: Differentiable Forth

There is another problem with dl^.
The definition of dl^ given previously has problems:
  a b dl^ doesn't work when:
     - a is a dual number with negative real part ( for example: a =
-5.6 + eps c, c in R)
and (in the same time)
     - b is a dual number with real part is integer and even ( for
example: b = 8 + eps d, d in R)
For floats, we have -5.6e 8e f** f.  967173.11574016  ok
But with dl^, we get : -5.6e f>dl 8e f>dl dl^ dl. NaN+ eps NaN ok
Here is the new definition of dl^, it corrects this problem.
: is_even_integer? ( f: a --) ( -- f)
    fdup f>s dup s>f f=
    swap 2 mod 0= and
;
: dl^  ( dl: a b -- a^b) \ a^b = exp(b*ln(a))
    dldup  dl>rl f0=  if dldrop dldrop 1e 0e   exit then
    dldup  dl>rl is_even_integer? if
      dlswap
      fswap fabs fswap
      dlln dl* dlexp exit
    then
    dlover dl>rl f0<> if dlswap dlln dl* dlexp exit then
    dldrop dldrop 0e 0e
;
For the same example, it gives
-5.6e f>dl 8e f>dl dl^ dl. 967173.11574016 + eps 0.
which is ok.
Ahmed