Merge other basic circuits here

circuits/comparators.circom

@@ -0,0 +1,55 @@
+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;
+}