define test_element_order(group) {
  a := random(group);
  o := order(group);
  b := a^o;
  CHECK(b == group(0));
}

define test_group_order() {
  CHECK(order(G1) == order(G2));
  CHECK(order(G2) == order(GT));
  a := pairing(random(G1), random(G2));
  o := order(GT);
  b := a^o;
  CHECK(b == GT(0));
}

define test_pairing_with_zero() {
  CHECK(GT(0) == GT(1));
  CHECK(pairing(G1(0), random(G2)) == GT(0));
  CHECK(pairing(random(G1), G2(0)) == GT(0));
  CHECK(pairing(G1(0), G2(0)) == GT(0));
}

define test_bilinear() {
  a1 := random(G1);
  b1 := random(G2);
  x := random(Zr);
  y := random(Zr);
  CHECK(pairing(a1^x, b1) == pairing(a1, b1^x));
  CHECK(pairing(a1^x, b1) == pairing(a1, b1)^x);
  CHECK(pairing(a1, b1^x) == pairing(a1, b1)^x);
  CHECK(pairing(a1^x, b1^y) == pairing(a1, b1)^(x*y));
}

define test(initfn) {
  initfn();
  test_element_order(G1);
  test_element_order(G2);
  test_element_order(GT);
  test_group_order();
  test_pairing_with_zero();
  test_bilinear();
}

test(init_pairing_a);
test(init_pairing_d);
test(init_pairing_e);
test(init_pairing_f);
test(init_pairing_g);
test(init_pairing_i);