How to add integers without correction?

when using integer class such as int8 in matlab, and some calculation result is bigger than the upper range (for int8 , the upper range is 127), matlab would automatically set the value to the maximum.

Help Center - Largest and Smallest Values for Integer Classes

eg.

a=int8(126);
b=int8(2);
c=a+b; % matlab would gives c=127, since 128 exceed the upper range of int8

but in some cases, i want to get a negetive result, like many programming languages do

i want c to be -128 because 01111110+00000010=10000000 and it's -128 for int8

this could be done by a "bitadd" like

function int1 = bitadd(int1,int2)

while (int2 ~=0)
    carry=bitand(int1,int2);
    int1=bitxor(int1,int2);
    int2=bitshift(carry,1);
end

end

however this is very inefficient, since a while loop in the function

Setting the result to maximum should be additional correction, so is there a faster method to do bitwise add without such correction?

Answer 1

[Jan]

a = int8(126);
b = int8(2);

tic
for k = 1:1e4
    c = bitadd1(a, b);
end
toc

Elapsed time is 0.141335 seconds.

tic
for k = 1:1e4
    c = bitadd2(a, b);
end
toc

Elapsed time is 0.068172 seconds.

function int1 = bitadd1(int1,int2)
while (int2 ~=0)
    carry = bitand(int1,int2);
    int1  = bitxor(int1,int2);
    int2  = bitshift(carry,1);
end
end

function c = bitadd2(a, b)
m = typecast(int16(a) + int16(b), 'int8');
c = m(1);
end

[DGM]

If it's important to support nonscalars, your version can do it with just a tiny modification:

function c = bitadd2(a, b)
	m = typecast(int16(a) + int16(b), 'int8');
	c = m(1:2:end);
end

Depending on how the rest of the code calls this adding function, using the vectorized approach may be the biggest part of time saving:

% emulate doing the same number of operations in vectorized form
aa = repmat(a,[1 1E4]);
bb = repmat(b,[1 1E4]);
tic
c = bitadd2(aa,bb);
toc

On my dumpster PC in R2019b, this takes about 210us. Compare that to 67ms and 25ms for the loop tests with bitadd1() and bitadd2() respectively.

[Dejia Kong]

thanks for your bitadd2 and introducing typecast to me

in fact i want some code as fast as

tic;
for i=1:1e4
    c=a+b;
end
toc;

since i think setting the result to maximum is additional correction and would take extra time.

But now i think when i have such performance requirement, it's better to use c++/fortran instead of matlab.

[Jan]

It will be much faster to use int16 in general and crop the higher bits during the addition. In my tests this is 10 times faster, but I did not get the correct results when the overflow appears.