The lpm_add_sub and lpm_mult both have option to select input type as signed/unsigned

--- Quote Start ---

Yes it does with respect to carry bit for example [001] +[111] (+1-1) should be zero if signed but would be 8 [1000] if unsigned. Apart from that they are same.

--- Quote End ---

That's not how lpm_add_sub works. Carry bit generation is the same for signed and unsigned, please try. The only difference is in the generation of optional overflow bit.

Your example isn't quite right. In case of signed number you'll either add 3 bit number, then the there's no fourth result bit. Or you have four bit numbers, then you get [0001]+[1111] = [0000].