What I'm looking for is a way to explain/understand simply how SmallInteger are
implemented.
>> Two's complement is a platform representation of integers not (necessarily)
>> a smalltalk one. The concept of negative numbers has nothing to do with the
>> radix a number is expressed in.
Yes I learned that
>>
>> There are convenient extensions to the ByteArray protocol added by FFI which
>> allow easy conversion though. I don't have time this second to list them,
>> but will do so in a few hours.
>
> That's true, but the internal implementation leaks out the bitAnd:
> bitOr: and other bit operations...
I want to explain two's complement then Smalltalk smallinteger
\section{Two's complement of a number}
....
Creating a two complement version of a number equals negating the number bits
and adding one.
\begin{code}{Calculating two complement of 3}
3 bitString '0000000000000000000000000000011'
3 bitInvert bitString '1111111111111111111111111111100'
(3 bitInvert + 1) bitString '1111111111111111111111111111101'
-3 bitString '1111111111111111111111111111101'
\end{code}
....
\section{SmallIntegers in Smalltalk}
Smalltalk small integers uses a two's complement arithmetic on 31 bits.
An N-bit two's-complement numeral system can represent every integer in the
range $-1 * 2^{N-1}\ to\ 2^{N-1}-1$. So for 32 bits Smalltalk systems, small
integers values are the range -1073741824 to 1073741823. Let's check that a
bit (this is the occasion to say it).
\begin{code}{}
2 raisedTo: 29
returns 536870912
536870912 class
returns SmallInteger
2 raisedTo: 30
returns 1073741824
1073741824 class
returns LargePositiveInteger
-1073741824 class
returns SmallInteger
2 class maxVal
returns 1073741823
-1 * (2 raisedTo: (31-1))
returns -1073741824
(2 raisedTo: 30) - 1
returns 1073741823
