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α-wwwiki :: history/fibonacci/20130909-104607.txt

editor : alpha [83.158.157.173] 2013/09/09 10:46:07
_h1 fibonacci
_p This page shows how to compute and to display the first N numbers of [[Fibonacci|http://en.wikipedia.org/wiki/Fibonacci_number]]. This can be done directly in the page's code, via a mini-console integrated in the page or in an external Lisp console.

_h3 1) using the define operator
_p The lambdatalk {b define} operator allows to define user functions directly in the wiki page's code.

_h5 a) code
{pre °°
{define fibonacci (m)
  function fibo(n) {
    return (function fib(a,b,i) {
      return (i==0)? b : fib(a+b,a,i-1) })(1,0,n)  
  }
  return m + ': ' + fibo(m) + '\n';
}

{pre fibonacci numbers from 0 to 12 : 
 {map fibonacci {serie 0 12}}
}
°°}
_p The display is done via lambdatalk built-in operators. The alternate {b defun} operator using lambdatalk syntax can't be used here, because this operator can't define recursive functions. So we must work with the {b define} operator using a JS syntax. A loss in elegance but a gain in speed !

_h5 b) result
{div {@ style="display:none;"}
{define fibonacci (m)
  function fibo(n) {
    return (function fib(a,b,i) {
      return (i==0)? b : fib(a+b,a,i-1) })(1,0,n)  
  }
  return m + ': ' + fibo(m) + '\n';
}
}
{pre fibonacci numbers from 0 to 12 : 
 {map fibonacci {serie 0 12}}
}
_p Note that the page's code  must be edited to modify the value of N.

_h3 2) using the input operator
_p Sometimes it can be better to build a mini-console in order to test different values without editing the pages's code : the {b input} operator is adapted for this purpose. 
 
_h5 a) code  
_p The interface written in the wiki page is made of three parts, the input, the output and a button.
 
_ul 1) The number N will be entered in an input field made with an {b input} operator :
{pre °° {input {@ id="input" value="" placeHolder="enter a number"}} °°}

_ul 2) the result will be displayed in a HTML {b pre}(format) container :
{pre °° {pre {@ id="output"}} °°}

_ul 3) the JS code will be included in an {b input} operator via an {b onclick} attribute :
{pre °°{input {@ type="submit" value="fibonacci" onclick="••

_h5 b) result
_p These are the three elements ready for test any values of N :
{center 
{input {@ id="input" value="" placeHolder="enter a number"}}
{input {@ type="submit" value="fibonacci" onclick="°°
function fibs(n) {
  function fibonacci(n) {
    return (function fib(a,b,i) {
      return (i==0)? b : fib(a+b,a,i-1) })(1,0,n)  
  }
  var t0 = new Date().getTime();
  for (var r ='', i=0; i< n; i++) {
    r += '\n' + i + ': ' + fibonacci(i);
  }
  var t1 = new Date().getTime();
  return '\ntime = ' + (t1-t0) + 'ms\n' + r;
}
getId('output').innerHTML = fibs(getId('input').value) 
°°"}}
}
{pre {@ id="output"}}

_h3 3) using an external console
_p The Fibonacci sequence can be computed using an outside Lisp console, see for instance [[monodicolisp|data/monodicolisp/]] or [[alphalisp|data/alphalisp/]] and test this :
{pre
(define fast_fib
  (lambda (n)
    (begin
      (define ifib
        (lambda (n a b)
          (if (= n 0) b
            (if (= n 1) a
              (ifib (- n 1) (+ a b) a)
      ) ) ) )
      (ifib n 1 0)
) ) )
> [fast_fib]

(fast_fib 12)
> 144                     // time : 1ms
(fast_fib 123)
> 2.269837405200687e+25   // time : 17ms
(fast_fib 1234)
> 3.4774673918037014e+257 // time : 127ms
}