Two's Complement and Squeak Integers

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

Integer readFrom: '11111111' readStream base: 2.  ?

Best,

Karl

On Tue, Jun 16, 2020 at 6:36 PM Eric Gade <[hidden email]> 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

Try loading package TwosComplement from the SqueakMap loader, or
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,
>
> Integer readFrom: '11111111' readStream base: 2.  ?
> >
>
> 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 <[hidden email]> wrote:
>
> > Integer readFrom: '11111111' readStream base: 2.  ?
> >
> > Best,
> > Karl
> >
> >
> >
> >
> > On Tue, Jun 16, 2020 at 6:36 PM Eric Gade <[hidden email]> 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

>

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 <[hidden email]> wrote:

Try loading package TwosComplement from the SqueakMap loader, or
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,
>
> Integer readFrom: '11111111' readStream base: 2.  ?
> >
>
> 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 <[hidden email]> wrote:
>
> > Integer readFrom: '11111111' readStream base: 2.  ?
> >
> > Best,
> > Karl
> >
> >
> >
> >
> > On Tue, Jun 16, 2020 at 6:36 PM Eric Gade <[hidden email]> 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

Le mar. 16 juin 2020 à 23:20, Nicolas Cellier <[hidden email]> 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

    ^self bitAnd: AllOnesMask.

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

    ^1 + (self bitXor: AllOnesMask) bitAnd: AllOnesMask

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 <[hidden email]> 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 <[hidden email]> wrote:

Try loading package TwosComplement from the SqueakMap loader, or
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,
>
> Integer readFrom: '11111111' readStream base: 2.  ?
> >
>
> 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 <[hidden email]> wrote:
>
> > Integer readFrom: '11111111' readStream base: 2.  ?
> >
> > Best,
> > Karl
> >
> >
> >
> >
> > On Tue, Jun 16, 2020 at 6:36 PM Eric Gade <[hidden email]> 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