Newbie questions

[Nick Linker]

Kostis Sagonas wrote:

>Nick Linter wrote:
>
>An example would have helped us understand better what the issue is.
>Currently, I get:
>
>Eshell V5.5  (abort with ^G)
>1> math:log(...).
>480.407
>
Well, I get the following result:

    43> math:log10(test:fib(1476)).
    308.116
    44> math:log10(test:fib(1477)).
     
    =ERROR REPORT==== 27-Mar-2006::10:57:47 ===
    Error in process <0.181.0> with exit value:
    {badarith,[{math,log10,[16#00012D269
    C3FA9D767CB55B0DDF8E6A2DE7B1D967FF8D0BE61EB16ACD02D1A53C95A370ABD95285998D226919

    D95DCA54298D92C348C27E635E1690E7858060F0DC14E885F0217413C55A1F820D6EB051F87C7C73

    818AC23E4A9A00A2072C08C6697A2FAD66FC7DEBEEB7A5F582D7639A431B9C99CEC6315A9ED1C652

    A81A6B59A39]},{erl_eval,do_apply,5},{shell,exprs,6},{shell,eval_loop,3}]}

     
    ** exited: {badarith,[{math,log10,
                               
    [211475298697902185255785861961179135570552502746803
    25217495622655863402432394766663713782393252439761186467156621190833026337742520

    45520741882086869936691237540043402509431087092122991804222930097654049305082429

    75773774612140021599477983006713536106549441161323499077298115887067363710153036

    315849480388057657]},
                          {erl_eval,do_apply,5},
                          {shell,exprs,6},
                          {shell,eval_loop,3}]} **

My system is Windows XP, Erlang R10B.

>fib(N) ->
>  trunc((1/sqrt(5)) * (pow(((1+sqrt(5))/2),N) - pow(((1-sqrt(5))/2),N))).
>  
>
Good solution :-)
Now I also have different idea without using recursion. It is based on 
the following equation
[F_n  ]   [1  1]   [F_n-1]
[     ] = [    ] * [     ]
[F_n-1]   [1  0]   [F_n-2]
And we just have to calculate k-th power of the matrix [[1,1],[1,0]]. It 
is possible to do within O(log(k)).

>PS. The performance you are experiencing in your version of fib/1
>    has nothing to do with tail recursion...
>
Yes, exponential number of recursive calls... Thank you.

I'm sorry, but most interesting question (2nd, about number of digits in 
an integer) remains unanswered. But I guess it is very rare problem with 
numbers, so if there is no answer, I will understand.

Best regards,
Linker Nick.
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