Hi there,
Grab a pencil and paper and get ready for some serious number crunching.
I was poking around my system for something new and came across a
scripting language presumably launched by the FSF. As you might guess,
anything out of FSF has to have RMS's blessings to be a success. This
one undoubtadly was inspired by GNU Emacs, and is built as a replacement
(or work along-side) for the common scripting languages such as Perl,
Python, Tcl, and even bash.
It's called Guile. Like the Info page says:
"Guile" (which can stand for _GNU Ubiquitous Intelligent Language
Extension_) is the GNU extension language. It started out as an
embeddable Scheme interpreter, and has rapidly evolved into a
kitchen-sink package including a standalone Scheme interpreter, an
embeddable Scheme interpreter, several graphics options, other
languages that can be used along with Scheme (for now just _ctax_
and _Tcl_), and hooks for much more.
Now, Scheme is a dialect of Lisp. What's Lisp famous for? Recursion.
I coded a simple factorial program (this one comes with the Tutorial).
Note: `=>' denotes return value in Lisp lingo, and `-|' denotes messages
printed other than the output.
(define (fact n)
(if (zero? n)
1
(* n (fact (- n 1)))))
=> fact
OK, everything went well and I got the answer as the tutorial said:
(fact 5)
=> 120
A bigger number was met with an error message:
(fact 500)
-|
ERROR: Stack overflow
ABORT: (stack-overflow)
But what surprised me was when the tutorial gave another factorial
example. Its called "Tail Recursive Factorization":
(define (nfact n)
(define (loop k l)
(if (zero? k) l
(loop (- k 1) (* k l))))
(loop n 1))
=> nfact
(nfact 500)
=>1220136825991110068701238785423046926253574342803192842192413588385845
373153881997605496447502203281863013616477148203584163378722078177200480
785205159329285477907571939330603772960859086270429174547882424912726344
305670173270769461062802310452644218878789465754777149863494367781037644
274033827365397471386477878495438489595537537990423241061271326984327745
715546309977202781014561081188373709531016356324432987029563896628911658
974769572087926928871281780070265174507768410719624390394322536422605234
945850129918571501248706961568141625359056693423813008856249246891564126
775654481886506593847951775360894005745238940335798476363944905313062323
749066445048824665075946735862074637925184200459369692981022263971952597
190945217823331756934581508552332820762820023402626907898342451712006207
714640979456116127629145951237229913340169552363850942885592018727433795
173014586357570828355780158735432768888680120399882384702151467605445407
663535984174430480128938313896881639487469658817504506926365338175055478
128640000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000
(Numbers are broken at 72 column width for formating.)
My box is a Celeron 634MHz, 2 x 64MB RAM.
Now any one with a common sense and basic machine architecture knowledge
knows that after a certain limit any variable used for numerical purpose
has a tendancy to overflow. How can a 32-bit machine handle such a big
number escapes me. That too, prints the result in less than
half-a-second!!
Or is it that Stallman really *IS* God??? Gosh! Now I'm starting to
believe that GNU/Linux _is_ the next best thing since sliced bread.
To double check (whether this is a unique feature of Lisp) I immediatly
converted the program to the easily accesible Lisp machine I had -- GNU
Emacs. Note: Emacs Lisp is another dialect with slight syntax change.
(defun fact (n)
(if (zerop n)
1
(* n (fact (- n 1)))))
=> fact
(fact 10)
=> 3628800
Yup, everything went well. Now the other loop.
(defun nfact (n)
(defun loop (k l)
(if (zerop k)
l
(loop (- k 1) (* k l))))
(loop n 1))
=> fact
(nfact 10)
=> 3628800
(nfact 500)
Oh no, that horrible hairy Emacs debugger chased me away with a stack
overflow error. Ok, so this ain't a Lisp feature. It's unique to
Scheme/Guile.
Dear fellow Linux hackers (esp. Lisp hackers),
Could you please please enlighten this GNUbie as to what makes this
miracle. I am a Lisp novice, but this clearly fascinates me. I would
like to have some logical explanation.
Revelation: I remember reading somewhere that a tail recursion is
nothing but a `goto' that can return values. That isn't helping me
either.
Any help would be very much appreciated.
Regards,
Mahesh Aravind.
--
And the Grand Finale.
(nfact 5000)
=>4228577926605543522201064200233584405390786674626646748849782402181358
052708108200690899047871706387537084746657300685445878486066683812736337
210893772787631279390363058462160643904478986982239871929708896211612652
968321775500399242196837031469072644728787897904047548841622152266719284
109692369104495659717363529484002238403811206448202308576711045023061748
947554283097617817240408053248099278093287840554861993645482912118762582
488021891739779000502132125980436392446264607705113588465951086754705858
339246552255890354744359883473831789880346330084586315102090915099356538
200109330479657425567419309170551728052002360750859911976352287559079020
433697431235069168312119244959715562674075214621989862330886259983028598
648575787494459631152869708867100462684236481789899054546908613916132183
441741488071862344481148312094903611965468727677556178868287202691048140
924564103418359756042764581615131785759016610717825441569808833593727299
956033713712004710494376562911424886053352994996423006999722049181201008
190594391406750532650047755338508990979451015510914869070044071195723360
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