include "bitify.circom";
include "binsum.circom";

template IsZero() {
    signal input in;
    signal output out;

    signal inv;

    inv <-- in!=0 ? 1/in : 0;

    out <== -in*inv +1;
    in*out === 0;
}


template IsEqual() {
    signal input in[2];
    signal output out;

    component isz = IsZero();

    in[1] - in[0] ==> isz.in;

    isz.out ==> out;
}


// N is the number of bits the input  have.
// The MSF is the sign bit.
template LessThan(n) {
    signal input in[2];
    signal output out;

    component num2Bits0;
    component num2Bits1;

    component adder;

    adder = BinSum(n, 2);

    num2Bits0 = Num2Bits(n);
    num2Bits1 = Num2BitsNeg(n);

    in[0] ==> num2Bits0.in;
    in[1] ==> num2Bits1.in;

    var i;
    for (i=0;i<n;i++) {
        num2Bits0.out[i] ==> adder.in[0][i];
        num2Bits1.out[i] ==> adder.in[1][i];
    }

    adder.out[n-1] ==> out;
}