Circular left shift

[sylau]

Hello,

I am trying to implement a circular left shift in set /a. Regular left shift works well, but I cannot rotate the front bits back.

For example

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set /a x=0xAA00FF00

x is now

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in binary:      10101010000000001111111100000000
in hexadecimal: AA00FF00

If I circularly left shifted it by 4 bits, x should be

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in binary:      10100000000011111111000000001010
in hexadecimal: A00FF00A

I'd prefer it if there were no string manipulation involved.

Thanks, WOLGA

[Aacini]

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@echo off
setlocal

set /A x=0xAA00FF00

set /A "shift=x<<4 | x>>28&0xF"

echo Result  = %shift%

set /A correct=0xA00FF00A

echo Correct = %correct%

Output:

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Result  = -1609568246
Correct = -1609568246

Antonio

[sylau]

Aacini, is there a way to make it so that the number of bits I am shifting by is variable?

[aGerman]

You could extend Antonio's equation a little.

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@echo off &setlocal

set /a "x=0xAA00FF00, sh=-28"
call :printhex %x%

set /a "sh=((sh %% 32) + 32) %% 32, y=(x << sh) | ( (x >> (32 - sh)) & ((1 << sh) - 1) )"
call :printhex %y%

pause
exit /b


:printhex
cmd /c exit %~1
echo %=exitcode%
exit /b

%sh% is the bits to shift.
The 2nd SET /A command consists of two comma-separated equations.
- The first normalizes %sh% to result in a positive value in range 0...31. Thus, values greater than 32 will work as well as negative values.
- The second is Antonio's equation, generalized to work with any normalized %sh% value.

There are some extra parentheses that hopefully make it easier to understand.

Steffen

[Aacini]

Aacini, is there a way to make it so that the number of bits I am shifting by is variable?

Yes. Instead "4" put the desired bits, instead "28" put "32-bits" and adjust the mask:

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set /A "bits=4, shift=x<<bits | x>>32-bits&(1<<bits)-1"

Antonio

[sylau]

Aacini, is there a way to make it so that the number of bits I am shifting by is variable?

Yes. Instead "4" put the desired bits, instead "28" put "32-bits" and adjust the mask:

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set /A "bits=4, shift=x<<bits | x>>32-bits&(1<<bits)-1"

Antonio

Thank you! If you don't mind me asking, how does it work? It's hard for me to wrap my head around the logic.

[aGerman]

For binary operations you need to think binary
In your example the binary equivalent of 0xAA00FF00 is 10101010000000001111111100000000

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left OR operand:
        10101010000000001111111100000000
<<  4   10100000000011111111000000000000

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

right OR operand:
        10100000000011111111000000000000
>> 28   11111111111111111111111111111010  (where 28 is 32-4)
&  15   00000000000000000000000000001111  (where 15 is (1<<4)-1)
result  00000000000000000000000000001010

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

OR operation
        10100000000011111111000000000000
|       00000000000000000000000000001010
result  10100000000011111111000000001010

The reason why you need the bitwise AND is that numbers in batch are 32bit signed integers. Right-shifting is implemented as two's complement arithmetic shifting. Thus, ones are shifted in for negative numbers.

Steffen

[IcarusLives]

For binary operations you need to think binary
In your example the binary equivalent of 0xAA00FF00 is 10101010000000001111111100000000

Code: Select all

left OR operand:
        10101010000000001111111100000000
<<  4   10100000000011111111000000000000

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

right OR operand:
        10100000000011111111000000000000
>> 28   11111111111111111111111111111010  (where 28 is 32-4)
&  15   00000000000000000000000000001111  (where 15 is (1<<4)-1)
result  00000000000000000000000000001010

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

OR operation
        10100000000011111111000000000000
|       00000000000000000000000000001010
result  10100000000011111111000000001010

The reason why you need the bitwise AND is that numbers in batch are 32bit signed integers. Right-shifting is implemented as two's complement arithmetic shifting. Thus, ones are shifted in for negative numbers.

Steffen

This is excellent information! Thank you for sharing!

OP, what is the purpose of this project? The responses for this are interesting, and I'm learning a lot.