The Fibonacci sequence of numbers was described in a mathematics book by Leonardo da Pisa (Fibonacci) called
Lisp, second edition Lisp, second edition Weinreb, Daniel 1987-08-01 00:00:00 Winston and Horn's Lisp is a textbook on symbolic computation and the Lisp language. It was originally published in 1981, based on a set of course notes developed for the introductory course in artificial intelligence at MIT. Two excellent Common LISP references include, 'LISP' by Patrick Henry Winston and Bertold Klaus Paul Horn Winston, 1989 and 'Common LISP - The Language' by Guy L. Steele Steele, 1990. Common Music is accompanied by voluminous electronic documentation, much of it in HTML. Lisp Winston Horn Pdf. Books by Patrick Henry Winston and Friends. Textbooks in the On To Series On To Java, Third Edition Sundar Narasimhan, Coauthor. Basedirectory List 2.3 Small - Free ebook download as Text File (.txt), PDF File (.pdf) or read. New therapeutic targets warrant further evaluation in these cancers. Despite the encouraging results achieved with antiepidermal growth factor receptor therapy, particularly with cetuximab, targeted therapy trials conducted in head and neck cancers.
Liber Abaci. The LISP by Winston, Patrick Henry; Horn, Berthold. Publication date 1984 Topics LISP (Computer program language), Programming Languages, LISP (Langage de programmation), LISP Publisher Reading, Mass.: Addison-Wesley Collection. Borrow this book to access EPUB and PDF files. IN COLLECTIONS. Books to Borrow. Books for People with Print Disabilities.
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n-th element of the sequence represents the number of pairs of rabbits at the start of the n-th month, beginning with a single pair, given that in every month each pair bears a new pair which becomes productive from the second month on. It is a common example used in education to teach recursion.Here are the first 14 Fibonacci numbers, starting with F(0):
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, .
and various Common Lisp implementations for the computation of the nth element of the sequence, structured similarly to the Factorial page: Ethernet driver for mac os high sierra.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, .
and various Common Lisp implementations for the computation of the nth element of the sequence, structured similarly to the Factorial page: Ethernet driver for mac os high sierra.
(defun fib (n)'Naive recursive computation of the nth element of the Fibonacci sequence'(check-type n (integer 0 *))(if(< n 2) n (+(fib (1- n))(fib (- n 2)))))
(defun fib (n)'Tail-recursive computation of the nth element of the Fibonacci sequence'(check-type n (integer 0 *))(labels((fib-aux (n f1 f2)(if(zerop n) f1 (fib-aux (1- n) f2 (+ f1 f2)))))(fib-aux n 0 1)))
This loop-based implementation probably written by Nicolas Neuss ([email protected]):
(defun fib (n)'loop-based iterative computation of the nth element of the Fibonacci sequence'(check-type n (integer 0 *))(loop for f1 = 0 then f2 and f2 = 1 then (+ f1 f2) repeat n finally (return f1)))
(defun fib (n)'do-based iterative computation of the nth element of the Fibonacci sequence'(check-type n (integer 0 *))(do((i n (1- i))(f1 0 f2)(f2 1 (+ f1 f2)))((= i 0) f1)))
(defun fib (n)'CPS computation of the nth element of the Fibonacci sequence'(check-type n (integer 0 *))(labels((fib-aux (n k)(if(zerop n)(funcall k 0 1)(fib-aux (1- n)(lambda(x y)(funcall k y (+ x y)))))))(fib-aux n #'(lambda(a b) a))))
It is worth mentioning that the initial (lambda (a b) a), or λab.a in lambda calculus notation, is one of the two Church booleans: true.You can use multiple values for a truly recursive implementation:
(defun fib (n)(labels((fib2 (n)(cond((= n 0)(values 1 0))(t(multiple-value-bind(val prev-val)(fib2 (- n 1))(values(+ val prev-val) val))))))(nth-value 0 (fib2 n))))
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Of course, this is in some sense equivalent to the CPS version, but with thecontinuation left implicit. (Author: Drew McDermott, [email protected])A 'successive squaring' method suggested in Structure and Interpretation of Computer Programs, which runs in a logarithmic number of steps:
(defun fib (n)'Successive squaring method from SICP'(check-type n (integer 0 *))(labels((fib-aux (a b p q count)(cond((= count 0) b)(()(fib-aux a b (+(* p p)(* q q))(+(* q q)(* 2 p q))(/ count 2)))(t(fib-aux (+(* b q)(* a q)(* a p))(+(* b p)(* a q)) p q (-count 1))))))(fib-aux 1 0 0 1 n)))
Note that the 'clever algorithm' mentioned but not cited in SICP is described in an 'EWD note' entitled In honour of Fibonacci by Edsger Wybe Dijkstra.Another successive squaring method based on these formulas: F(2n-1)=F(n)^2+F(n-1)^2, F(2n)=(2F(n-1)+F(n))*F(n). See the end of this section from the Wikipedia article, or see the same EWD note as above, In honour of Fibonacci by Edsger Wybe Dijkstra.
(defun fib (n)(if(< n 2) n (if(oddp n)(let((k (/ (1+ n) 2)))(+(expt(fib k) 2)(expt(fib (1- k)) 2)))(let*((k (/ n 2))(fk (fib k)))(*(+(* 2 (fib (1- k))) fk) fk)))))
And now for something completely different, a generator version, inspired by a Python snippet.Python | Lisp | Ruby | Javascript |
---|
def fib (): a, b = 0, 1 while 1: yield a a, b = b, a+b
(let((a 0)(b 1))(defun fib ()(prog1 a (psetf a b b (+ a b)))))
def make_fib() a = 0; b = 1 lambda { v = a a, b = b, a + b v }end
var fib; ( function (){ var a=0; var b=1; fib=function (){ b=a+(a=b); return a; }})();
Upon successive calls, (fib) will return the next number in the sequence.JavaScript version by Cosmin Branescu, [email protected].;; Taken from Winston's Lisp, 3rd edition, this is a tail-recursive version, w/o an auxiliary function(defun fib (n &optional (i 1)(previous-month 0)(this-month 1))(if(<= n i) this-month (fib n (+ 1 i) this-month (+ this-month previous-month))))
;;;Original code by Arnold Schoenhage, ;;;translated to Scheme by Bradley J. Lucier (2004), ;;;and adapted to Common Lisp by Nicolas Neuss.(defun fast-fib-pair (n)'Returns f_n f_{n+1}.'(case n ((0)(values 0 1))((1)(values 1 1))(t(let((m (floor n 2)))(multiple-value-bind(f_m f_m+1)(fast-fib-pair m)(let((f_m^2 (* f_m f_m))(f_m+1^2 (* f_m+1 f_m+1)))(if(evenp n)(values(-(* 2 f_m+1^2)(* 3 f_m^2)(if(oddp m) -2 2))(+ f_m^2 f_m+1^2))(values(+ f_m^2 f_m+1^2)(-(* 3 f_m+1^2)(* 2 f_m^2)(if(oddp m) -2 2))))))))))
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;; Fibonacci - Binet's Formula(defun fib (n)(*(/ 1 (sqrt 5))(-(expt(/ (+ 1 (sqrt 5)) 2) n)(expt(/ (- 1 (sqrt 5)) 2) n))))
or
(defun fib (n)(/ (-(expt(/ (+ 1 (sqrt 5)) 2) n)(expt(/ (- 1 (sqrt 5)) 2) n))(sqrt 5)))
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(defun fib (n)(prog1(round(/ (expt(/ (+ 1 (sqrt 5)) 2) n)(sqrt 5)))))
Free mp3 lagu julio iglesias. Q: In the Winston & Horn book, n for the two above functions is n+1. Is there some reason for NOT having e.g.
A: Some authors still use a deprecated definition of the Fibonacci sequence, the one that begins with 1, 1 instead of 0, 1. Please see the definition and especially the closed form.Also, most books that touch on this topic (Donald Knuth's TAOCP for instance).
(expt (/ (- 1 (sqrt 5)) 2) (+ n 1)))
?A: Some authors still use a deprecated definition of the Fibonacci sequence, the one that begins with 1, 1 instead of 0, 1. Please see the definition and especially the closed form.Also, most books that touch on this topic (Donald Knuth's TAOCP for instance).
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Q: Do we have any reason to keep the first implementation instead of the second one based on the Binet formula? Gta sa mega download. --Cornel
Final fantasy x ost download. Caution: Due to limitations in floating-point representation precision, this last version works - (truncate (fib n)) is correct - only for n < 32.
From that point on, the error rises exponentially approximately like this: new_error = old_error * (5 / 3)
So, if for n = 32 the error is 1.25, for n = 99 the error is 4.2221247E14. I determined this using CLISP 2.33.2 under GNU Linux on IA32.
This can be improved by using 5.0d0 instead of 5, which ensures the use ofdouble-float. CLISP 2.33.2 computes correct values (using (round (fib n)) forn ≤ 75.
From that point on, the error rises exponentially approximately like this: new_error = old_error * (5 / 3)
So, if for n = 32 the error is 1.25, for n = 99 the error is 4.2221247E14. I determined this using CLISP 2.33.2 under GNU Linux on IA32.
This can be improved by using 5.0d0 instead of 5, which ensures the use ofdouble-float. CLISP 2.33.2 computes correct values (using (round (fib n)) forn ≤ 75.