From: Robert Klemme <bob.news@...>
Date: 2005-05-05T02:09:57+09:00
Subject: Re: Fixnum's binary representation


<camsight@gmail.com> schrieb im Newsbeitrag 
news:1115223668.955656.66750@o13g2000cwo.googlegroups.com...
> Thanks, Robert!
>
>> For which numbers do you have problems?  I don't see any so far
>
> I mean...
> If Bignum#[] is made to simulate 32-bit signed integers, it can't show
> numbers with more than 32-bit representation.
> Well, positive numbers will be okay.
> But what about negative numbers?
> When can I expect the sign bit?

Well, since Bignums can be arbitrary size, you have to decide.  The values 
returned by Fixnum#[] and Bignum#[] represent bits of a two complement's 
arbitrary size binary number.  If you view it from this perspective, you'll 
see that there is no single sign bit.  Negative numbers have *all* the 
higher bits set to 1.

> I assume that numbers beyond 32-bit are not suitable for Bignum#[].
> Do you agree?

Not at all.

>> n = -(1<<100)
=> -1267650600228229401496703205376
>> 200.times{|i| print i, " ", n[i], "\n"}
0 0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
....
95 0
96 0
97 0
98 0
99 0
100 1
101 1
102 1
103 1
104 1
....
195 1
196 1
197 1
198 1
199 1
=> 200

As you clearly see, the representation is ok.

Btw, you'll notice the same effect with Fixnum#[] - because these methods do 
not represent the actual binary representation in mem but try to represent 
the general concept of signed binary numbers:

>> (-1)[100]
=> 1
>> (-1)[1<<100]
=> 1

Kind regards

    robert