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From: Raymond Toy <rtoy@us...>  20041109 15:04:47

Update of /cvsroot/maxima/maxima/src In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv20276 Modified Files: simp.lisp Log Message: o Reindent expta nicely. o Partial fix for bug 586688: Make float(exp(2)) return a doublefloat, not singlefloat result, because exptb was computing (exp 2), not (exp (coerc 2 'doublefloat)). Index: simp.lisp =================================================================== RCS file: /cvsroot/maxima/maxima/src/simp.lisp,v retrieving revision 1.8 retrieving revision 1.9 diff u d r1.8 r1.9  simp.lisp 15 Oct 2004 16:48:09 0000 1.8 +++ simp.lisp 9 Nov 2004 15:04:35 0000 1.9 @@ 693,19 +693,31 @@ ;; ;; Does the LISPM have FSC? ;; (*QUO (FLOAT NU) D))) (defun expta (x y) (cond ((equal y 1) x)  ((numberp x) (exptb x (num1 y)))  (($bfloatp x) ($bfloat (list '(mexpt) x y)))  ((minusp (num1 y))  (*red (exptb (caddr x) (minus (num1 y)))  (exptb (cadr x) (minus (num1 y)))))  (t (*red (exptb (cadr x) (num1 y))  (exptb (caddr x) (num1 y)))))) +(defun expta (x y) + (cond ((equal y 1) + x) + ((numberp x) + (exptb x (num1 y))) + (($bfloatp x) + ($bfloat (list '(mexpt) x y))) + ((minusp (num1 y)) + (*red (exptb (caddr x) (minus (num1 y))) + (exptb (cadr x) (minus (num1 y))))) + (t + (*red (exptb (cadr x) (num1 y)) + (exptb (caddr x) (num1 y)))))) +;; I (rtoy) think EXPTB is meant to compute a^b, where b is an +;; integer. (defun exptb (a b)  (cond ((equal a %eval) (exp b))  ((or (floatp a) (not (minusp b))) (expt a b))  (t (setq b (expt a (minus b))) (*red 1 b)))) + (cond ((equal a %eval) + ;; Make B a float so we'll get doubleprecision result. + (exp (float b))) + ((or (floatp a) (not (minusp b))) + (expt a b)) + (t + (setq b (expt a (minus b))) + (*red 1 b)))) (defmfun simplus (x w z) ; W must be 1 (prog (res check eqnflag matrixflag sumflag) 
From: Raymond Toy <rtoy@us...>  20041109 14:53:53

Update of /cvsroot/maxima/maxima/src In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv18057/src Modified Files: float.lisp Log Message: Fix Bug 617021: Add support for bfloat(%gamma). Index: float.lisp =================================================================== RCS file: /cvsroot/maxima/maxima/src/float.lisp,v retrieving revision 1.10 retrieving revision 1.11 diff u d r1.10 r1.11  float.lisp 4 Oct 2004 02:25:55 0000 1.10 +++ float.lisp 9 Nov 2004 14:53:43 0000 1.11 @@ 102,7 +102,8 @@ "Bigfloat representation of %E") (defmvar bigfloat%pi '((bigfloat simp 56.) 56593902016227522. 2) "Bigfloat representation of %PI")  +(defmvar bigfloat%gamma '((bigfloat simp 56.) 41592772053807304. 0) + "Bigfloat representation of %GAMMA") ;; Internal specials ;; Number of bits of precision in the mantissa of newly created bigfloats. @@ 129,6 +130,7 @@ (defvar maxbfloat%pi bigfloat%pi) (defvar maxbfloat%e bigfloat%e) +(defvar maxbfloat%gamma bigfloat%gamma) (declaretop (special *cancelled $float $bfloat $ratprint $ratepsilon $domain $m1pbranch adjust)) @@ 432,7 +434,8 @@ (defmfun $bfloat (x) (let (y) (cond ((bigfloatp x))  ((or (numberp x) (memq x '($%e $%pi))) + ((or (numberp x) + (memq x '($%e $%pi $%gamma))) (bcons (intofp x))) ((or (atom x) (memq 'array (cdar x))) (if (eq x '$%phi) @@ 554,6 +557,7 @@ ((equal 0 l) '(0 0)) ((eq l '$%pi) (fppi)) ((eq l '$%e) (fpe)) + ((eq l '$%gamma) (fpgamma)) (t (list (fpround l) (plus *m fpprec))))) ;; It seems to me that this function gets called on an integer @@ 725,6 +729,16 @@ (cdr (setq bigfloat%pi (bigfloatp maxbfloat%pi)))) (t (cdr (setq maxbfloat%pi (setq bigfloat%pi (fppi1))))))) +(defun fpgamma () + (cond ((= fpprec (caddar bigfloat%gamma)) + (cdr bigfloat%gamma)) + ((< fpprec (caddar bigfloat%gamma)) + (cdr (setq bigfloat%gamma (bigfloatp bigfloat%gamma)))) + ((< fpprec (caddar maxbfloat%gamma)) + (cdr (setq bigfloat%gamma (bigfloatp maxbfloat%gamma)))) + (t + (cdr (setq maxbfloat%gamma (setq bigfloat%gamma (fpgamma1))))))) + (defun fpone nil (cond (*decfp (intofp 1)) ((= fpprec (caddar bigfloatone)) (cdr bigfloatone)) (t (intofp 1)))) @@ 746,6 +760,105 @@ (defun fppi1 nil (bcons (list (fpround (comppi (plus fpprec 3))) (plus 3 *m)))) +;; Compute the main part of the EulerMascheroni constant using the +;; Bessel function approach. See +;; http://numbers.computation.free.fr/Constants/Gamma/gamma.html for a +;; description of the algorithm. +;; Roughly, we have +;; +;; %gamma = A(N)/B(N)  log(N) + O(e^(4*N)) +;; +;; where +;; +;; +;; b*N +;; A(N) = sum (N^2/n!)^2*H(n) +;; n=0 +;; +;; b*N +;; B(N) = sum (N^2/n!)^2 +;; n=0 +;; +;; n +;; H(n) = sum 1/k +;; k=1 +;; +;; with H(0) = 0 +;; +;; and b = 4.970625759... where b*(log(b)1) = 3. +;; +;; This formula can be easily justified by looking at the value +;; K0(2*N)/I0(2*N), where K0 and I0 are the modified Bessel functions. +;; From A&S 9.6.12 and 9.6.13, We see that +;; +;; inf +;; I0(2*N) = sum (N^2/n!)^2 +;; n=0 +;; +;; +;; inf +;; K0(2*N) = (log(N) + %gamma)*I0(2*N) + sum (N^2/n!)^2*H(n) +;; n=0 +;; +;; So +;; +;; K0(2*N)/I0(2*N) = log(N)  %gamma + C +;; +;; where +;; +;; C = [sum (N^2/n!)^2*H(n)]/sum (N^2/n!)^2 +;; +;; or +;; +;; For N large, A&S gives +;; +;; I0(2*N) = exp(2*N)/sqrt(4*%pi*N) +;; +;; K0(2*N) = sqrt(%pi/(4*N))*exp(2*N) +;; +;; So K0(2*N)/I0(2*N) = %pi*exp(4*N) and +;; +;; O(exp(4*N)) = log(N)  %gamma + C +;; +;; or +;; +;; %gamma = C  log(N) + O(exp(4*N)) +;; +;; And C is approximately A(N)/B(N) if we take enough terms in the +;; sum. +;; +(defun compbf%gamma (prec) + ;; Prec is the number of digits we want. We assume the remainder is + ;; really e^(4*N) and not O(e^(4*N)). So choose N such that + ;; exp(4*N) is less than the number of digits of precision we want. + ;; + ;; We also assume don't need a really precise value of beta because + ;; our N's are not so big that we need more. + (let* ((bign (floor (* 1/4 prec (log 2d0)))) + (bignsq (cdr ($bfloat (* bign bign)))) + (beta 4.9706257595442319023d0) + (limit (floor (* beta bign))) + (term (cdr bigfloatone)) + (harmonic (cdr bigfloatzero)) + (asum (cdr bigfloatzero)) + (bsum (cdr bigfloatone))) + (do ((n 1 (1+ n))) + ((> n limit)) + (let ((bfn (cdr ($bfloat n)))) + (setf term (fpquotient (fptimes* term bignsq) + (fptimes* bfn bfn))) + (setf harmonic (fpplus harmonic + (fpquotient (fpone) bfn))) + (setf asum (fpplus asum + (fptimes* term harmonic))) + (setf bsum (fpplus bsum term)))) + (fpplus (fpquotient asum bsum) + (fpminus (cdr ($bfloat (list '(%log simp) bign))))))) + +(defun fpgamma1 () + ;; Use a few extra bits of precision + (bcons (list (fpround (first (compbf%gamma (plus fpprec 5)))) 0))) + (defmfun fpmax na (prog (max) (setq max (arg 1)) 
From: Robert Dodier <robert_dodier@us...>  20041109 05:55:52

Update of /cvsroot/maxima/maxima/doc/info In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv12957/doc/info Modified Files: Command.texi Log Message: Strike out @defun %TH which is redundant with identically named item in Input.texi. Strike out description of obsolete function RESTORE (broken, but still in dskfn.lisp). Index: Command.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/Command.texi,v retrieving revision 1.11 retrieving revision 1.12 diff u d r1.11 r1.12  Command.texi 4 Nov 2004 05:12:25 0000 1.11 +++ Command.texi 9 Nov 2004 05:55:42 0000 1.12 @@ 5,16 +5,6 @@ @node Introduction to Command Line, Definitions for Command Line, Command Line, Command Line @section Introduction to Command Line @... @node %TH @... @unnumberedsec phony @... %TH (i) is the ith previous computation. That is, if the next expression to be computed is D(j) this is D(ji). This is useful in BATCH files or for referring to a group of D expressions. For example, if SUM is initialized to 0 then FOR I:1 THRU 10 DO SUM:SUM+%TH(I) will set SUM to the sum of the last ten D expressions.  @... defun @c @node operator @c @unnumberedsec phony @deffn operator "'" @@ 391,15 +381,6 @@ considered to be computational features of Maxima.) @end defun @... @node RESTORE @... @unnumberedsec phony @... RESTORE (filespecification) reinitializes all quantities filed away by a use of the SAVE or STORE functions, in a prior Maxima session, from the file given by filespecification without bringing them into core.  @... defun @c @node SHOWTIME @c @unnumberedsec phony @defvar SHOWTIME 
From: Robert Dodier <robert_dodier@us...>  20041109 05:55:12

Update of /cvsroot/maxima/maxima/doc/info In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv12791/doc/info Modified Files: Input.texi Log Message: Strike out discussion of obsolete systems and commands from introductory section. Strike out @section PLAYBACK which described an obsolete key binding. (There exists a description of nonobsolete function PLAYBACK elsewhere.) Update and expand somewhat the descriptions of % and %%. Update description of %TH. Revise and expand description of SAVE. Minor changes to LOAD. Index: Input.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/Input.texi,v retrieving revision 1.20 retrieving revision 1.21 diff u d r1.20 r1.21  Input.texi 5 Nov 2004 03:37:39 0000 1.20 +++ Input.texi 9 Nov 2004 05:55:01 0000 1.21 @@ 1,50 +1,68 @@ @menu * Introduction to Input and Output:: * FILES:: * PLAYBACK:: * Definitions for Input and Output:: @end menu @node Introduction to Input and Output, FILES, Input and Output, Input and Output @section Introduction to Input and Output @... FILES, PLAYBACK, Introduction to Input and Output, Input and Output +@node FILES, Definitions for Input and Output, Introduction to Input and Output, Input and Output @section FILES   A file is simply an area on a particular storage device which contains data or text. The only storage devices which are used on the MC machine are disks and tapes. Files on the disks are figuratively grouped into "directories". A directory is just a list of all the files stored under a given user name. Do DESCRIBE(FILEOP); for details of how you may inspect your files using Maxima. Other commands which deal with files are: SAVE, STORE, LOAD, LOADFILE, RESTORE, UNSTORE, STRINGOUT, BATCH, BATCON, DEMO, WRITEFILE, CLOSEFILE, DELFILE, REMFILE, and APPENDFILE.  @... PLAYBACK, Definitions for Input and Output, FILES, Input and Output @... PLAYBACK  It is possible to play back the input lines in a temporary scroll down window, and so not lose ones current work. This can be done by typing Function E. A numeric argument tells it the line number to start at, otherwise it will go back about 40 lines. +A file is simply an area on a particular storage device which contains data or text. +Files on the disks are figuratively grouped into "directories". +A directory is just a list of files. +Commands which deal with files are: +SAVE, LOAD, LOADFILE, STRINGOUT, BATCH, DEMO, WRITEFILE, CLOSEFILE, and APPENDFILE. @c end concepts Input and Output @... Definitions for Input and Output, , PLAYBACK, Input and Output +@node Definitions for Input and Output, , FILES, Input and Output @section Definitions for Input and Output @defvar %  The last Dline computed by Maxima (whether or not it was printed out). (See also %%.) +The output label (e.g., @code{%o1}, @code{%o2}, @code{%o3}, ...) +most recently computed by Maxima, +whether or not it was displayed. +See also @code{%%}. @end defvar @defvar %%  The value of the last computation performed while in a Maxima break. Also may be used in compound statements in the nth statement to refer to the value of the (n1)th statement. E.g. F(N):=(INTEGRATE(X^N,X),SUBST(3,X,%%)SUBST(2,X,%%)); is in essence equivalent to F(N):=BLOCK([%%], %%:INTEGRATE(X^N,X), SUBST(3,X,%%)SUBST(2,X,%%)); This will also work for communicating between the (n1)th and nth (nonatomic) BLOCK statements. +In a compound statement comprising two or more statements, +@code{%%} is the value of the previous statement. +For example, + +@example +block (integrate (x^5, x), ev (%%, x=2)  ev (%%, x=1)); +block ([prev], prev: integrate (x^5, x), ev (prev, x=2)  ev (prev, x=1)); +@end example + +yield the same result, namely @code{21/2}. + +A compound statement may comprise other compound statements. +Whether a statement be simple or compound, +@code{%%} is the value of the previous statement. +For example, + +@example +block (block (a^n, %%*42), %%/6) +@end example + +yields @code{7*a^n}. + +Within a compound statement, the value of @code{%%} may be inspected at a break prompt, +which is opened by executing the BREAK function. +For example, at the break prompt opened by + +@example +block (a: 42, break ())$ +@end example + +entering @code{%%;} yields @code{42}. + +At the first statement in a compound statement, +or outside of a compound statement, +@code{%%} is undefined. @end defvar @@ 55,11 +73,18 @@ @end defvar @defun %TH (i) is the ith previous computation. That is, if the next expression to be computed is D(j) this is D(ji). This is useful in BATCH files or for referring to a group of D expressions. For example, if SUM is initialized to 0 then FOR I:1 THRU 10 DO SUM:SUM+%TH(I) will set SUM to the sum of the last ten D expressions. +The value of the i'th previous output label. +That is, if the next expression to be computed is the n'th output, +@code{%TH (m)} is the (nm)'th output. + +@code{%TH} is useful in BATCH files or for referring to a group of output labels. +For example, + +@example +block (s: 0, for i:1 thru 10 do s: s + %th (i))$ +@end example + +sets @code{s} to the sum of the last ten output labels. @end defun @@ 498,7 +523,9 @@ @end defvar @defun LOAD (filename) Evaluates expressions in @code{filename}, thus bringing new variables and functions into Maxima. +Evaluates expressions in @code{filename}, +thus bringing variables, functions, and other objects into Maxima. +The binding of any existing object is clobbered by the binding recovered from @code{filename}. To find the file, LOAD calls FILE_SEARCH with FILE_SEARCH_MAXIMA and FILE_SEARCH_LISP as the search directories. @@ 509,8 +536,8 @@ Files created by SAVE, TRANSLATE_FILE, and COMPILE_FILE, which create Lisp code, and STRINGOUT, which creates Maxima code, can all be processed by LOAD. See also LOADFILE, RESTORE, BATCH, and DEMO. LOADFILE and RESTORE process Lisp files; +See also LOADFILE, BATCH, and DEMO. +LOADFILE processes Lisp files; BATCH and DEMO process Maxima files. See FILE_SEARCH for more detail about the file search mechanism. @@ 640,21 +667,65 @@ @end defvar @... IN GREAT NEED OF UPDATING AND CLARIFICATION !!! @... SAVE (filename,arg1, arg2,...,argi) saves quantities described by its arguments on disk and keeps them in core also. The arg's are the expressions to be SAVEd. ALL is the simplest, but note that saving ALL will save the entire contents of your Maxima, which in the case of a large computation may result in a large file. VALUES, FUNCTIONS, or any other items on the INFOLISTS (do DESCRIBE(INFOLISTS); for the list) may be SAVEd, as may functions and variables by name. C and D lines may also be saved, but it is better to give them explicit names, which may be done in the command line, e.g. SAVE(RES1=%o15); Files saved with SAVE should be reloaded with LOADFILE. SAVE returns the pathname where the items were saved. +@defun SAVE (filename, name_1, name_2, name_3, ...) +@defunx SAVE (filename, VALUES, FUNCTIONS, LABELS, ...) +@defunx SAVE (filename, [m, n]) +@defunx SAVE (filename, new_1=old_1, new_2=old_2, ...) +@defunx SAVE (filename, ALL) +Stores the current values of @code{name_1}, @code{name_2}, @code{name_3}, ..., in @code{filename}. +The arguments must be names of variables, functions, or other objects. +SAVE returns @code{filename}. + +SAVE stores data in the form of Lisp expressions. +The data stored by SAVE may be recovered by @code{LOAD (filename)}. +The effect of executing SAVE when @code{filename} already exists +depends on the underlying Lisp implementation; +the file may be clobbered, or SAVE may complain with an error message. + +The special form @code{SAVE (filename, VALUES, FUNCTIONS, LABELS, ...)} +stores the items named by VALUES, FUNCTIONS, LABELS, etc. +The names may be any specified by the variable INFOLISTS. +VALUES comprises all userdefined variables. + +The special form @code{SAVE (filename, [m, n])} stores the values of +input and output labels @code{m} through @code{n}. +Note that @code{m} and @code{n} must be literal integers or doublequoted symbols. +Input and output labels may also be stored one by one, e.g., @code{SAVE ("foo.1", %i42, %o42)}. +@code{SAVE (filename, LABELS)} will store all input and output labels. +When the stored labels are recovered, they will clobber existing labels. + +The special form @code{SAVE (filename, name_1=expr_1, name_2=expr_2, ...)} +stores the values of @code{expr_1}, @code{expr_2}, ..., +with names @code{name_1}, @code{name_2}, .... +It is useful to apply this form to input and output labels, e.g., @code{SAVE ("foo.1", aa=%o88)}. +The righthand side of the equality in this form may be any expression, which is evaluated. +This form does not introduce the new names into the current Maxima environment, +but only stores them in @code{filename}. +These special forms and the general form of SAVE may be mixed at will. +For example, @code{SAVE (filename, aa, bb, cc=42, FUNCTIONS, [11, 17])}. + +The special form @code{SAVE (filename, ALL)} stores the current state of Maxima. +This includes all userdefined variables, functions, arrays, etc., as well +as some automatically defined items. +The saved items include system variables, +such as FILE_SEARCH_MAXIMA or SHOWTIME, if assigned new values by the user. + +SAVE quotes its arguments. +@code{filename} must be a string, not a string variable. +The first and last labels to save, if specified, must be integers. +The double quote operator will evaluate a string variable to its string value, +e.g., @code{s: "foo.1"$ SAVE (''s, ALL)$}, +and integer variables to their integer values, e.g., @code{m: 5$ n: 12$ SAVE ("foo.1", [''m, ''n])$}. + +@c ANY USE FOR THE FOLLOWING ??? +@c The following device constructs a list of variables to save and saves them. +@c +@c @example +@c s: "foo.1"$ +@c l: ['aa, 'bb, 'cc, 'dd]$ +@c apply (save, append ([s], l))$ +@c @end example @end defun @defvar SAVEDEF @@ 783,7 +854,7 @@ system("xgraph bar brw .7 nl < _hist.out")); @end example In order to make the plot be done in the background (returning control to maxima) +In order to make the plot be done in the background (returning control to Maxima) and remove the temporary file after it is done do: @example 
From: Robert Dodier <robert_dodier@us...>  20041109 05:54:25

Update of /cvsroot/maxima/maxima/doc/info In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv12644/doc/info Modified Files: maxima.texi Log Message: Strike out PLAYBACK from list of topics for Input and Output (section struck out of Input.texi). Index: maxima.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/maxima.texi,v retrieving revision 1.12 retrieving revision 1.13 diff u d r1.12 r1.13  maxima.texi 4 Nov 2004 15:34:15 0000 1.12 +++ maxima.texi 9 Nov 2004 05:54:00 0000 1.13 @@ 161,7 +161,6 @@ * Introduction to Input and Output:: * FILES:: * PLAYBACK:: * Definitions for Input and Output:: Floating Point 