Re: Differentiable Forth

In fact, dl^ has too many use cases.
in the last post I've given a definition for dl^, it works for
calculating the values (real part)
but it fails to get the eps part (that gives the derivative).
Here a new definition that 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 is_even_integer? 0=
    dlover dl>rl f0< and if
      dldrop dldrop
      cr ." Can't be defined for Real numbers!"
      exit
    then
    dldup  dl>rl f0=  if dldrop dldrop 1e 0e   exit then
    dldup dl>eps f0=
    dlover f0= and
    f0< and
    dldup  dl>rl is_even_integer? and
    if
      dlswap
      dlnegate
      dlln dl* dlexp
      fdrop 0e
      exit
    then
    dlover f0=
    f0< and
    dldup  dl>rl is_even_integer? and
    if
      dlover
      dlnegate
      dlln dl* dlexp
      dlswap dl>rl fln fnip
      exit
    then
    dlover f0<>
    f0< and
    dldup  dl>rl is_even_integer? and
     if
      dlswap
      dlnegate
      dlln dl* dlexp
      exit
    then
    dlover dl>rl f0<> if dlswap dlln dl* dlexp exit then
    dldrop dldrop 0e 0e
;
And here, some examples:
-1e f>dl 2e f>dl dl^ dl. 1. + eps 0.  ok
-1e f>dl_d 2e f>dl dl^ dl. 1. + eps -2.  ok
-1e f>dl 2e f>dl_d dl^ dl. 1. + eps NaN ok
-1e f>dl 2.2e f>dl dl^
Can't be defined for Real numbers! ok
-1.2e f>dl 2e f>dl dl^ dl. 1.44 + eps 0.  ok
-1.2e f>dl_d 2e f>dl dl^ dl. 1.44 + eps -2.4  ok
-1.2e f>dl 2e f>dl_d dl^ dl. 1.44 + eps NaN ok
-1.2e f>dl 2.2e f>dl_d dl^
Can't be defined for Real numbers! ok
-1.2e f>dl -2.2e f>dl dl^
Can't be defined for Real numbers! ok
-1.2e f>dl -2e f>dl dl^ dl. 0.694444444444445 + eps 0.  ok
-1.2e f>dl_d -2e f>dl dl^  dl. 0.694444444444445 + eps 1.15740740740741 ok
-1.2e f>dl -2e f>dl_d dl^   dl. 0.694444444444445 + eps NaN ok
-1.2e f>dl 0e f>dl_d dl^   dl. 1. + eps 0.  ok
-1.2e f>dl 0e f>dl dl^   dl. 1. + eps 0.  ok
-1.2e f>dl_d 0e f>dl dl^   dl. 1. + eps 0.  ok
0e f>dl_d 0e f>dl dl^   dl. 1. + eps 0.  ok
It is ok for the real part and the eps part.
It is not optimized.
Ahmed