three-body-algorithm

Why is it that an additional half of pairs can be skipped in the three-body potentials such as sw and tersoff in addition to the newton’s third law savings? The part of the code I’m wondering about is pasted below starting with the if block.

// two-body interactions, skip half of them

jlist = firstneigh[i];
jnum = numneigh[i];

for (jj = 0; jj < jnum; jj++) {
j = jlist[jj];
j &= NEIGHMASK;
jtag = tag[j];

if (itag > jtag) {
if ((itag+jtag) 2 == 0) continue; } else if (itag < jtag) { if ((itag+jtag) 2 == 1) continue;
} else {
if (x[j][2] < ztmp) continue;
if (x[j][2] == ztmp && x[j][1] < ytmp) continue;
if (x[j][2] == ztmp && x[j][1] == ytmp && x[j][0] < xtmp) continue;
}