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[Gcl-devel] Re: [Maxima] float(sin(2^2048))?
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From: |
Camm Maguire |
|
Subject: |
[Gcl-devel] Re: [Maxima] float(sin(2^2048))? |
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Date: |
Mon, 17 May 2010 11:49:13 -0400 |
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User-agent: |
Gnus/5.11 (Gnus v5.11) Emacs/22.2 (gnu/linux) |
Greetings!
Stavros Macrakis <address@hidden> writes:
> On Thu, May 13, 2010 at 14:27, Camm Maguire <address@hidden> wrote:
>
> ...
>
> (%i1) :lisp (setq si::*print-nans* t)
> T
> (%i1) :lisp (float (expt 2 2049) 1.0e0)
> #<inf>
>
> Thanks for the info! It prints a little differently in my copy of GCL, but
> basically OK.
> On the other hand, there are a couple of peculiarities in the floats (maybe
> controlled by other global
> vars?).
>
> Maxima 5.20.1 http://maxima.sourceforge.net
> using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
> (%i1) to_lisp();
> MAXIMA> (setq si:*print-nans* t)
> T
> MAXIMA> (setq inf (expt 2.0 2000))
> #<1.#INF00e+000> OK
> MAXIMA> (setq nan (- inf inf)) IND is OK, but why shown
> as negative?
> #<-1.#IND00e+000>
This is determined by the operating system:
{if (sSAprint_nansA->s.s_dbind !=Cnil)
{sprintf(s, "%e",d);
*sp = 2;
return;
We use whatever sprintf outputs, but this could be changed. I take it
you are using Windows?
> MAXIMA> (< nan 0) Oops.
> T
> MAXIMA> (< nan (- inf)) Oops.
> T
This is indeed a bug. I'll try to fix this. But see below for a
practical workaround.
> MAXIMA> (/ 1 inf) OK
> 0.0
> MAXIMA> (/ -1 inf) Shouldn't this be
> -0.0?
> 0.0
This also appears operating system dependent. Does mingw support
negative zero?
(/ -1 (expt 2.0 20000))
-0.0
>
> MAXIMA> (/ 1 0.0) Shouldn't this be INF?
> Maxima encountered a Lisp error:
> Error in EVAL [or a callee]: Zero divisor.
>
This has to throw an error in ANSI. Worse, ansi requires that
ignore-errors has to return nil. Maybe some fancy handler-bind might
work. 2.7 has the variable si::*ignore-floating-point-errors* which
currently steps around overflow and underflow to give the right inf or
nan. The compiler uses this in type propagation for the common
floating point functions. division-by-zero should be added here.
But at points like this I always go back to C (at some modest "unsafe*
compilation level) if I'm looking for the intuitive IEEE behavior:
(funcall (compile nil '(lambda (x y) (declare (long-float x y)) (/ x
y))) 1.0 0.0) --> #<inf>
It would be helpful if you could run the following file and inspect
the results. I've included the 2.6 and 2.7 results on my system too.
Take care,
=============================================================================
(setq si::*print-nans* t)
(when (setq tmp (find-symbol "+INF" 'si)) (import tmp))
(when (setq tmp (find-symbol "-INF" 'si)) (import tmp))
(when (setq tmp (find-symbol "NAN" 'si)) (import tmp))
(when (setq tmp (find-symbol "*IGNORE-FLOATING-POINT-ERRORS*" 'si)) (import
tmp))
(unless (boundp '+inf) (setq +inf (expt 2.0 20000)))
(unless (boundp '-inf) (setq -inf (- +inf)))
(unless (boundp 'nan)
(setq nan (funcall (compile nil '(lambda (x) (declare (long-float x)) (sqrt
x))) -1.0)))
(setq *ignore-floating-point-errors* t)
(setq *tops* '(+ - * / = /= <))
(setq *ctops* (mapcar (lambda (x)
(compile (eval `(defun ,(intern (concatenate 'string
"M" (symbol-name x))) (x y)
(declare (long-float x y))
(,x x y))))) *tops*))
(setq *oops* '(sqrt sin log exp))
(setq *coops* (mapcar (lambda (x)
(compile (eval `(defun ,(intern (concatenate 'string
"M" (symbol-name x))) (x)
(declare (long-float x))
(,x x))))) *oops*))
(setq *nums* `(0.0 1.0 -1.0 ,+inf ,-inf ,nan))
(mapcar (lambda (op)
(mapcar (lambda (x)
(mapcar (lambda (y)
(list op x y (ignore-errors (funcall op x y))))
*nums*)) *nums*)) *tops*)
(mapcar (lambda (op)
(mapcar (lambda (x)
(mapcar (lambda (y)
(list op x y (ignore-errors (funcall op x y))))
*nums*)) *nums*)) *ctops*)
(mapcar (lambda (op)
(mapcar (lambda (x)
(list op x (ignore-errors (funcall op x)))) *nums*)) *oops*)
(mapcar (lambda (op)
(mapcar (lambda (x)
(list op x (ignore-errors (funcall op x))))
*nums*)) *coops*)
=============================================================================
2.6:
=============================================================================
((((+ 0.0 0.0 0.0) (+ 0.0 1.0 1.0) (+ 0.0 -1.0 -1.0)
(+ 0.0 #<inf> #<inf>) (+ 0.0 #<-inf> #<-inf>) (+ 0.0 #<nan> #<nan>))
((+ 1.0 0.0 1.0) (+ 1.0 1.0 2.0) (+ 1.0 -1.0 0.0)
(+ 1.0 #<inf> #<inf>) (+ 1.0 #<-inf> #<-inf>) (+ 1.0 #<nan> #<nan>))
((+ -1.0 0.0 -1.0) (+ -1.0 1.0 0.0) (+ -1.0 -1.0 -2.0)
(+ -1.0 #<inf> #<inf>) (+ -1.0 #<-inf> #<-inf>)
(+ -1.0 #<nan> #<nan>))
((+ #<inf> 0.0 #<inf>) (+ #<inf> 1.0 #<inf>) (+ #<inf> -1.0 #<inf>)
(+ #<inf> #<inf> #<inf>) (+ #<inf> #<-inf> #<nan>)
(+ #<inf> #<nan> #<nan>))
((+ #<-inf> 0.0 #<-inf>) (+ #<-inf> 1.0 #<-inf>)
(+ #<-inf> -1.0 #<-inf>) (+ #<-inf> #<inf> #<nan>)
(+ #<-inf> #<-inf> #<-inf>) (+ #<-inf> #<nan> #<nan>))
((+ #<nan> 0.0 #<nan>) (+ #<nan> 1.0 #<nan>) (+ #<nan> -1.0 #<nan>)
(+ #<nan> #<inf> #<nan>) (+ #<nan> #<-inf> #<nan>)
(+ #<nan> #<nan> #<nan>)))
(((- 0.0 0.0 0.0) (- 0.0 1.0 -1.0) (- 0.0 -1.0 1.0)
(- 0.0 #<inf> #<-inf>) (- 0.0 #<-inf> #<inf>) (- 0.0 #<nan> #<nan>))
((- 1.0 0.0 1.0) (- 1.0 1.0 0.0) (- 1.0 -1.0 2.0)
(- 1.0 #<inf> #<-inf>) (- 1.0 #<-inf> #<inf>) (- 1.0 #<nan> #<nan>))
((- -1.0 0.0 -1.0) (- -1.0 1.0 -2.0) (- -1.0 -1.0 0.0)
(- -1.0 #<inf> #<-inf>) (- -1.0 #<-inf> #<inf>)
(- -1.0 #<nan> #<nan>))
((- #<inf> 0.0 #<inf>) (- #<inf> 1.0 #<inf>) (- #<inf> -1.0 #<inf>)
(- #<inf> #<inf> #<nan>) (- #<inf> #<-inf> #<inf>)
(- #<inf> #<nan> #<nan>))
((- #<-inf> 0.0 #<-inf>) (- #<-inf> 1.0 #<-inf>)
(- #<-inf> -1.0 #<-inf>) (- #<-inf> #<inf> #<-inf>)
(- #<-inf> #<-inf> #<nan>) (- #<-inf> #<nan> #<nan>))
((- #<nan> 0.0 #<nan>) (- #<nan> 1.0 #<nan>) (- #<nan> -1.0 #<nan>)
(- #<nan> #<inf> #<nan>) (- #<nan> #<-inf> #<nan>)
(- #<nan> #<nan> #<nan>)))
(((* 0.0 0.0 0.0) (* 0.0 1.0 0.0) (* 0.0 -1.0 -0.0)
(* 0.0 #<inf> #<nan>) (* 0.0 #<-inf> #<nan>) (* 0.0 #<nan> #<nan>))
((* 1.0 0.0 0.0) (* 1.0 1.0 1.0) (* 1.0 -1.0 -1.0)
(* 1.0 #<inf> #<inf>) (* 1.0 #<-inf> #<-inf>) (* 1.0 #<nan> #<nan>))
((* -1.0 0.0 -0.0) (* -1.0 1.0 -1.0) (* -1.0 -1.0 1.0)
(* -1.0 #<inf> #<-inf>) (* -1.0 #<-inf> #<inf>)
(* -1.0 #<nan> #<nan>))
((* #<inf> 0.0 #<nan>) (* #<inf> 1.0 #<inf>) (* #<inf> -1.0 #<-inf>)
(* #<inf> #<inf> #<inf>) (* #<inf> #<-inf> #<-inf>)
(* #<inf> #<nan> #<nan>))
((* #<-inf> 0.0 #<nan>) (* #<-inf> 1.0 #<-inf>)
(* #<-inf> -1.0 #<inf>) (* #<-inf> #<inf> #<-inf>)
(* #<-inf> #<-inf> #<inf>) (* #<-inf> #<nan> #<nan>))
((* #<nan> 0.0 #<nan>) (* #<nan> 1.0 #<nan>) (* #<nan> -1.0 #<nan>)
(* #<nan> #<inf> #<nan>) (* #<nan> #<-inf> #<nan>)
(* #<nan> #<nan> #<nan>)))
(((/ 0.0 0.0 NIL) (/ 0.0 1.0 0.0) (/ 0.0 -1.0 -0.0) (/ 0.0 #<inf> 0.0)
(/ 0.0 #<-inf> -0.0) (/ 0.0 #<nan> #<nan>))
((/ 1.0 0.0 NIL) (/ 1.0 1.0 1.0) (/ 1.0 -1.0 -1.0) (/ 1.0 #<inf> 0.0)
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((/ -1.0 0.0 NIL) (/ -1.0 1.0 -1.0) (/ -1.0 -1.0 1.0)
(/ -1.0 #<inf> -0.0) (/ -1.0 #<-inf> 0.0) (/ -1.0 #<nan> #<nan>))
((/ #<inf> 0.0 NIL) (/ #<inf> 1.0 #<inf>) (/ #<inf> -1.0 #<-inf>)
(/ #<inf> #<inf> #<nan>) (/ #<inf> #<-inf> #<nan>)
(/ #<inf> #<nan> #<nan>))
((/ #<-inf> 0.0 NIL) (/ #<-inf> 1.0 #<-inf>) (/ #<-inf> -1.0 #<inf>)
(/ #<-inf> #<inf> #<nan>) (/ #<-inf> #<-inf> #<nan>)
(/ #<-inf> #<nan> #<nan>))
((/ #<nan> 0.0 NIL) (/ #<nan> 1.0 #<nan>) (/ #<nan> -1.0 #<nan>)
(/ #<nan> #<inf> #<nan>) (/ #<nan> #<-inf> #<nan>)
(/ #<nan> #<nan> #<nan>)))
(((= 0.0 0.0 T) (= 0.0 1.0 NIL) (= 0.0 -1.0 NIL) (= 0.0 #<inf> NIL)
(= 0.0 #<-inf> NIL) (= 0.0 #<nan> NIL))
((= 1.0 0.0 NIL) (= 1.0 1.0 T) (= 1.0 -1.0 NIL) (= 1.0 #<inf> NIL)
(= 1.0 #<-inf> NIL) (= 1.0 #<nan> NIL))
((= -1.0 0.0 NIL) (= -1.0 1.0 NIL) (= -1.0 -1.0 T)
(= -1.0 #<inf> NIL) (= -1.0 #<-inf> NIL) (= -1.0 #<nan> NIL))
((= #<inf> 0.0 NIL) (= #<inf> 1.0 NIL) (= #<inf> -1.0 NIL)
(= #<inf> #<inf> T) (= #<inf> #<-inf> NIL) (= #<inf> #<nan> NIL))
((= #<-inf> 0.0 NIL) (= #<-inf> 1.0 NIL) (= #<-inf> -1.0 NIL)
(= #<-inf> #<inf> NIL) (= #<-inf> #<-inf> T) (= #<-inf> #<nan> NIL))
((= #<nan> 0.0 NIL) (= #<nan> 1.0 NIL) (= #<nan> -1.0 NIL)
(= #<nan> #<inf> NIL) (= #<nan> #<-inf> NIL) (= #<nan> #<nan> NIL)))
(((/= 0.0 0.0 NIL) (/= 0.0 1.0 T) (/= 0.0 -1.0 T) (/= 0.0 #<inf> T)
(/= 0.0 #<-inf> T) (/= 0.0 #<nan> T))
((/= 1.0 0.0 T) (/= 1.0 1.0 NIL) (/= 1.0 -1.0 T) (/= 1.0 #<inf> T)
(/= 1.0 #<-inf> T) (/= 1.0 #<nan> T))
((/= -1.0 0.0 T) (/= -1.0 1.0 T) (/= -1.0 -1.0 NIL)
(/= -1.0 #<inf> T) (/= -1.0 #<-inf> T) (/= -1.0 #<nan> T))
((/= #<inf> 0.0 T) (/= #<inf> 1.0 T) (/= #<inf> -1.0 T)
(/= #<inf> #<inf> NIL) (/= #<inf> #<-inf> T) (/= #<inf> #<nan> T))
((/= #<-inf> 0.0 T) (/= #<-inf> 1.0 T) (/= #<-inf> -1.0 T)
(/= #<-inf> #<inf> T) (/= #<-inf> #<-inf> NIL)
(/= #<-inf> #<nan> T))
((/= #<nan> 0.0 T) (/= #<nan> 1.0 T) (/= #<nan> -1.0 T)
(/= #<nan> #<inf> T) (/= #<nan> #<-inf> T) (/= #<nan> #<nan> T)))
(((< 0.0 0.0 NIL) (< 0.0 1.0 T) (< 0.0 -1.0 NIL) (< 0.0 #<inf> T)
(< 0.0 #<-inf> NIL) (< 0.0 #<nan> T))
((< 1.0 0.0 NIL) (< 1.0 1.0 NIL) (< 1.0 -1.0 NIL) (< 1.0 #<inf> T)
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((< -1.0 0.0 T) (< -1.0 1.0 T) (< -1.0 -1.0 NIL) (< -1.0 #<inf> T)
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((< #<-inf> 0.0 T) (< #<-inf> 1.0 T) (< #<-inf> -1.0 T)
(< #<-inf> #<inf> T) (< #<-inf> #<-inf> NIL) (< #<-inf> #<nan> T))
((< #<nan> 0.0 T) (< #<nan> 1.0 T) (< #<nan> -1.0 T)
(< #<nan> #<inf> T) (< #<nan> #<-inf> T) (< #<nan> #<nan> T))))
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=============================================================================
--
Camm Maguire address@hidden
==========================================================================
"The earth is but one country, and mankind its citizens." -- Baha'u'llah