How to do bit-wise operations on symbolic variables that may be very long possibly larger than inter 64

Below is something I was able to do with some smaller numbers in base 2 and I can do base 10 also. Using Min,Max I can do AND and OR but I haven't been able to understand the use of the Symbolic Tool Box to do this symbolically .

a=12345
b=9867
c=0
n=0
while a>0 |b>0
    digita=mod(a,2)
    digitb=mod(b,2)
    c=c+max(digita,digitb)*2^n
    n=n+1
    a=floor(a/2)
    b=floor(b/2)
end
c

[Steve]

I forgot to add that I want to try and use the normal bit-wise operations if possible.

Answer 1

[John D'Errico]

Why is there a problem? Just define the numbers as syms. Make sure that you don't make the mistake of computing 2^n as a DOUBLE. That would surely cause failure at some point if n grows large enough.

a = sym('1234566726356446657575412365654161131310325345345');
b = sym('9866848646846846864684635468141413513513511534146867');
c = sym(0);
n=0;
while a>0 || b>0
    digita=mod(a,2);
    digitb=mod(b,2);
    c=c+max(digita,digitb)*sym(2)^n;
    n=n+1;
    a=floor(a/2);
    b=floor(b/2);
end
n

n = 173

c

c = 

9868036217465768677971888683212354493291227772861811

a

a = 

0

b

b = 

0

Make sure you keep everything a sym, and you will have no problem. Note my use of the || operator in the while statement. It is not really that significant here, but it can improve the speed of your code.

However, did you really need to use a loop there? Of course not.

a = sym('1234566726356446657575412365654161131310325345345');
b = sym('9866848646846846864684635468141413513513511534146867');
% in case we need leading zero bits on the smaller number
% I could also pad the smaller, but this test is trivial.
if a > b
  abin = dec2bin(a);
  bbin = dec2bin(b,numel(abin));
else
  bbin = dec2bin(b);
  abin = dec2bin(a,numel(bbin));
end
abin

abin = '00000000000001101100000111111111000101111101101011100111010000101000000111111100011110010100001100111001010110101111100100010110110000011110100110001101110101010110001000001'

bbin

bbin = '11010010111110010101111111011011010001101111110000000000111110010010000110110110100111011111110001011110000110111011001010100010101101010001011100000110011110011010100110011'

% I could compute c here in many ways, but bin2dec does
% not generate a sym. In my large integer codes, I provided
% that as an option, but not hard to do.
cbin = abin;
cbin(bbin == '1') = '1';

nc = numel(cbin);
c = dot(cbin - '0',sym(2).^(nc-1:-1:0))

c = 

9868036217465768677971888683212354493291227772861811

Note that c is the same in both cases, but that a loop was never necessary.

Ok, could we have used direct bit operators here? For example, we can do this:

a = 12345;
b = 9867;
bitor(a,b)

ans = 14011

The problem is, bitor does not apply to symbolic numbers. Sorry.

[Steve]

Thanks very much for the explaination on that and for the example. I learned something new for which I am gratefull

Answer 2

[Walter Roberson]

a = sym(12345);
b = sym(9867);
c = sym(0);
n = sym(0);
while a>0 |b>0
    digita=mod(a,2);
    digitb=mod(b,2);
    c=c+max(digita,digitb)*2^n;
    n=n+1;
    a=floor(a/2);
    b=floor(b/2);
end
c

c = 

14011

n

n = 

14

Answer 3

[Sulaymon Eshkabilov]

Is this what you are trying to get:

syms a b c n   % Create symbols

a = 12345;
b = 9867;
c = sym(0);
n = 0;

while a > 0 || b > 0
    digita = mod(a, 2);
    digitb = mod(b, 2);
    c = c + max(digita, digitb) * 2^n;
    n = n + 1;
    a = floor(a / 2);
    b = floor(b / 2);
end

disp(c);

14011

[Walter Roberson]

syms a b c n   % Create symbols
a = 12345;
b = 9867;
c = sym(0);
n = 0;

Assigning double precision values to a and b and n effectively undoes the "syms a b n". Assigning symbolic 0 to c overrides the syms c with a different sym. The "syms a b c n" statement has no effect on the outcome.

[Steve]

I'm sorry I forgot to add that I was wantin to try normal bitwise operation to sym variables

[Steve]

should I repost this as a seperate question?

[John D'Errico]

@Steve - no. you asked the question. Your question is clear. Don't keep on posting it.

[John D'Errico]

@Sulaymon Eshkabilov

Um, predefining those variables as syms does NOTHING.

syms a b c n   % Create symbols
a = 12345;
b = 9867;

whos a b

  Name      Size            Bytes  Class     Attributes

  a         1x1                 8  double              
  b         1x1                 8  double              

Do you see that now, a and b are DOUBLES?

[Sulaymon Eshkabilov]

Yes, I overlooked. This is what it should be like:

a = sym(12345);
b = sym(9867);
c = sym(0);
n = sym(0);
while a > 0 || b > 0
    digita = mod(a, 2);
    digitb = mod(b, 2);
    c = c + max(digita, digitb) * 2^n;
    n = n + 1;
    a = floor(a / 2);
    b = floor(b / 2);
end
disp(c);

14011

whos a b c n

  Name      Size            Bytes  Class    Attributes

  a         1x1                 8  sym                
  b         1x1                 8  sym                
  c         1x1                 8  sym                
  n         1x1                 8  sym