sign(exp(2009)) --> floating point overflow

Am Samstag, den 17.10.2009, 17:12 -0500 schrieb Barton Willis: 
> In sign1, I see some code that looks broken. I commented it out and
> then sign(exp(2009)) --> pos. I'm not claiming that a good fix is to
> comment out this code--it's just a place I might start looking. Also,
> the signbfloat scheme is fundamentally broken.
> 
> (defun sign1 (x)
>   (setq x (specrepcheck x))
>   (setq x (infsimp* x))
>   (when (and *complexsign* (atom x) (eq x '$infinity))
>     ;; In Complex Mode the sign of infinity is complex.
>     (when *debug-compar* (format t "~& in sign1 detect $infintiy.~%"))
>     (return-from sign1 '$complex))
>   (if (member x '($und $ind $infinity) :test #'eq)
>       (if limitp '$pnz (merror (intl:gettext "sign: sign of ~:M is
>       undefined.") x)))
>   (prog (dum exp)
>      (setq dum (constp x) exp x)
>      (cond ((or (numberp x) (ratnump x)))
>     ((eq dum 'bigfloat)
>      (if (prog2 (setq dum ($bfloat x)) ($bfloatp dum))
>   (setq exp dum)))
>     ((eq dum 'float)
>      (if (and (setq dum (numer x)) (numberp dum)) (setq exp dum)))
>     ((and (member dum '(numer symbol) :test #'eq) ;; <---- looks bogus to
>     me (especially the (< (abs dum) 1.0e-6))
>    (prog2 (setq dum (numer x))
>        (or (null dum)
>     (and (numberp dum)
>          (prog2 (setq exp dum)
>       (< (abs dum) 1.0e-6)))))) ;; <---- surely this is bogus.
>      (cond ($signbfloat
>      (and (setq dum ($bfloat x)) ($bfloatp dum) (setq exp dum)))
>     (t (setq sign '$pnz evens nil odds (ncons x) minus nil)
>        (return sign)))))
>      (or (and (not (atom x)) (not (mnump x)) (equal x exp)
>        (let (s o e m lhs rhs)
>   (compsplt x)
>   (dcompare lhs rhs)
>   (cond ((member sign '($pos $neg $zero) :test #'eq))
>         ((eq sign '$pnz) nil)
>         (t (setq s sign o odds e evens m minus)
>     (sign x)
>     (if (not (strongp sign s))
>         (if (and (eq sign '$pnz) (eq s '$pn))
>      (setq sign s)
>      (setq sign s odds o evens e minus m)))
>     t))))
>   (sign exp))
>      (return sign)))

Because of the line
  
   (member dum '(numer symbol) :test #'eq)

all expressions with a constant like %e, %pi, ... are converted to a
float. Therefore, we have the bug for sign(%pi^2009) too.

This code is needed to get answers for expressions which involve the
numerical constants.

Interestingly, it is working in Maxima 19.2 (GCL on Windows). But if I
trace the routines sign1, constp, numer, $float I get a Lisp Error too.

Perhaps we have to look at the routine $float and the return value for
the case we have an overflow.

Dieter Kaiser