## [squeak-dev] Two's Complement and Squeak Integers

Wed Jun 17 21:36:06 UTC 2020

```Nicolas,

Thanks so much for the examples. It's the (1 bitShift: n) - 1 trick that I
some of this same stuff a a couple of years ago). These are all useful
tidbits to have, both in my own work and especially for posterity here in
the list. Thanks again!

On Tue, Jun 16, 2020 at 5:52 PM Nicolas Cellier <
nicolas.cellier.aka.nice at gmail.com> wrote:

>
>
> Le mar. 16 juin 2020 à 23:20, Nicolas Cellier <
> nicolas.cellier.aka.nice at gmail.com> a écrit :
>
>> Hi Eric,
>> there are several simple snippets that might be useful.
>> One simple thing to transform n bits unsigned into n bits signed value is
>>     ^self - ((self bitAt: n) bitShift: n).
>>
>> Transforming a signed value into an unsigned bit pattern can be obtained
>> with a simple
>> where:
>>     AllOnesMask := (1 bitShift: n) - 1.
>>
>> Also note that #bitInvert definition assuming two complement is:
>>      ^ -1 - self
>>
>> Squeak assumes an infinite serie of bits. For limited register, that is:
>>      ^ -1 - self bitAnd: allOnesMask
>>
>> Inversely you can negate a 2 complement bit pattern thru
>>
>> Of course, you cannot negate AllOneMask, case of overflow...
>>
>> err, you can not negate  (1 bitShift: n-1) of course...
>
>>
>> Le mar. 16 juin 2020 à 21:40, Eric Gade <eric.gade at gmail.com> a écrit :
>>
>>> Thanks Dave!
>>>
>>> The TwosComplementRegister is a good package and will be a helpful guide
>>> -- thanks for pointing me to it.
>>>
>>> For posterity I want to post the key functionality here (which was in
>>> #asSignedInteger). It more or less describes how to take bits (as an
>>> ordered collection of some kind) that are already in two's complement
>>> negative format and convert them to a Squeak negative Integer:
>>>
>>> asSignedInteger
>>>
>>> self negative
>>> ifTrue: [^ ((bits reversed collect: [:e | e value not])
>>> inject: 0
>>> into: [:val :bit | bit value
>>> ifTrue: [val << 1 + 1]
>>> ifFalse: [val << 1]]) negated - 1]
>>> ifFalse: [^ self asUnsignedInteger]
>>>
>>> Thanks again,
>>>
>>> On Tue, Jun 16, 2020 at 2:19 PM David T. Lewis <lewis at mail.msen.com>
>>> wrote:
>>>
>>>> install it like this:
>>>>
>>>>   Installer ss project: 'TwosComplement';
>>>>       package: 'TwosComplement';
>>>>       install.
>>>>
>>>> Then inspect these:
>>>>
>>>>   TwosComplementRegister width: 8 value: -1.
>>>>
>>>>   255 asRegister: 8. "same as above but note the overflow bit is set"
>>>>
>>>>   TwosComplementRegister width: 64 value: -1.
>>>>
>>>> Dave
>>>>
>>>>
>>>> On Tue, Jun 16, 2020 at 02:09:15PM -0400, Eric Gade wrote:
>>>> > Hi Karl,
>>>> >
>>>> > >
>>>> >
>>>> > When I evaluate this in Squeak, the Integer produced is 255 (I need
>>>> to get
>>>> > from 255 to -1 -- and back again if possible).
>>>> >
>>>> > One hint that I've found in the image is that Integers respond to a
>>>> message
>>>> > #highBitOfMagnitude, which gives me the value of the most significant
>>>> bit
>>>> > in the integer. That is a starting point if I want to treat the bits
>>>> in
>>>> > twos-complement: I can determine if the desired representation should
>>>> be
>>>> > negative or positive. However, I'm not sure how to actually translate
>>>> the
>>>> > bits into a matching Squeak integer with the correct sign and value.
>>>> >
>>>> > Here is a more concrete explanation of my issue: In the
>>>> implementation /
>>>> > simulation, Register objects store their values as Squeak Integers,
>>>> and
>>>> > they are truncated at evaluation to be 32-bit integers. Some
>>>> instructions
>>>> > will treat a register as signed and others as unsigned. For unsigned
>>>> > treatment, there's no problem: Squeak always has the correct bit
>>>> values for
>>>> > what I need. I just need to figure out what to "do" with the integer
>>>> in the
>>>> > register when I want to treat it as signed. In the case of a value
>>>> like -1
>>>> > ('11111111') I can send that #highBitOfMagnitude to determine if it
>>>> should
>>>> > be a negative or positive value, but then what? I can't just send
>>>> > #negative, because that gives me -255
>>>> >
>>>> > PS - Perhaps at some point there was a #twosComplement method
>>>> implemented
>>>> > on Integers. There is an EToys object that is currently sending the
>>>> message
>>>> > (which has no implementors in 5.3 as far as I can see):
>>>> SecurityManager >>
>>>> > #asn1Integer:
>>>> >
>>>> > On Tue, Jun 16, 2020 at 1:44 PM karl ramberg <karlramberg at gmail.com>
>>>> wrote:
>>>> >
>>>> > >
>>>> > > Best,
>>>> > > Karl
>>>> > >
>>>> > >
>>>> > >
>>>> > >
>>>> > > On Tue, Jun 16, 2020 at 6:36 PM Eric Gade <eric.gade at gmail.com>
>>>> wrote:
>>>> > >
>>>> > >> Hi everyone,
>>>> > >>
>>>> > >> I'm smack in the middle of making some RISC-V tools in Squeak,
>>>> which
>>>> > >> means I'm dealing with a lot of low-level bit manipulation.
>>>> > >>
>>>> > >> One question I have is how best to deal with two's complement
>>>> > >> representations of integers in Squeak, and how to translate
>>>> between the
>>>> > >> different (positive v negative) values based on a given set of
>>>> bits (or a
>>>> > >> byteArray or whatever).
>>>> > >>
>>>> > >> For example, doing the following:
>>>> > >> -1 printStringBase: 2 nDigits: 8. "11111111"
>>>> > >> Gives the expected binary value "11111111"
>>>> > >>
>>>> > >> However (and as we should expect), evaluating the following:
>>>> > >> 2r11111111. "255"
>>>> > >>
>>>> > >> Gives the (again, expected) value 255.
>>>> > >>
>>>> > >> My question is: what is the best way to convert between the
>>>> complements
>>>> > >> in Squeak? How can I take 255, examine its bits, and get -1 as the
>>>> response
>>>> > >> (or convert in the reverse)? I'm assuming there are already ways
>>>> to deal
>>>> > >> with this, I just cannot find them.
>>>> > >>
>>>> > >> Thanks!
>>>> > >>
>>>> > >> --
>>>> > >> Eric
>>>> > >>
>>>> > >>
>>>> > >
>>>> >
>>>> > --
>>>> > Eric
>>>>
>>>> >
>>>>
>>>>
>>>>
>>>
>>> --
>>> Eric
>>>
>>>
>

--
Eric
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