changing floating point number input.. (was realroots...)

I like this. There is a problem that I encountered doing something similar
with Allegro CL. Namely the integer-decode-float program failed on a NaN --
I reported it as a bug and was told that a NaN was not a float and they
meant to do that.  So I had to write an Allegro-specific version of
integer-decode-float. It may also be necessary to do such a thing for other
CLs.
One should also be able to define $float_inf  to create an inf etc.

RJF


> -----Original Message-----
> From: maxima-bounces at math.utexas.edu 
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Robert Dodier
> Sent: Monday, August 28, 2006 10:38 PM
> To: Richard Fateman
> Cc: maxima
> Subject: Re: [Maxima] changing floating point number input.. 
> (was realroots...)
> 
> Richard,
> 
> Here's an attempt at a implementation-neutral modification of 
> nformat to print nan's and inf's. Here's a sample session 
> (after loading the code) using GCL:
> 
> (%i1) obase : 16.;
> (%o1)                          10
> (%i2) a : ?most\-positive\-short\-float;
> (%o2)                     3.4028235S+38
> (%i3) 2 * a;
> (%o3)               float_inf(1, 69, 800000)
> (%i4) -2 * a;
> (%o4)              float_inf(- 1, 69, 800000)
> (%i5) 2 * a - 3 * a;
> (%o5)              float_nan(- 1, 69, C00000)
> (%i6) b : ?most\-positive\-double\-float;
> (%o6)                1.7976931348623157E+308
> (%i7) 2 * b;
> (%o7)           float_inf(1, 3CC, 10000000000000)
> (%i8) -2 * b;
> (%o8)          float_inf(- 1, 3CC, 10000000000000)
> (%i9) 2 * b - 3 * b;
> (%o9)          float_nan(- 1, 3CC, 18000000000000)
> 
> Printing the sign, exponent, and significand makes the result 
> theoretically readable ....
> 
> FWIW
> Robert
> 
> PS. Here's the code. Doubtless this can be improved.
> 
> (defun significand-bits (x) (nth-value 0 (integer-decode-float x)))
> 
> (defun exponent-bits (x) (nth-value 1 (integer-decode-float x)))
> 
> (defun float-special-value-p (x)
>   (and (floatp x)
>     (let
>       ((max-exponent
>          (typecase x
>            (short-float (exponent-bits most-positive-short-float))
>            (single-float (exponent-bits most-positive-single-float))
>            (double-float (exponent-bits most-positive-double-float))
>            (long-float (exponent-bits most-positive-long-float)))))
>         (= (exponent-bits x) (1+ max-exponent)))))
> 
> (defun float-inf-p (x)
>   (and
>     (float-special-value-p x)
>     (= (significand-bits x) (lsh 1 (1- (float-digits x))))))
> 
> (defun float-nan-p (x)
>   (and
>     (float-special-value-p x)
>     (not (= (significand-bits x) (lsh 1 (1- (float-digits x)))))))
> 
> (let ((save-nformat #'nformat))
>   (defun nformat (x)
>     (cond
>       ((float-inf-p x)
>        (apply save-nformat (list `(($float_inf) ,@(reverse 
> (multiple-value-list (integer-decode-float x)))))))
>       ((float-nan-p x)
>        (apply save-nformat (list `(($float_nan) ,@(reverse 
> (multiple-value-list (integer-decode-float x)))))))
>       (t
>         (apply save-nformat (list x)))))) 
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