cycle_group.test.cpp

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#include "barretenberg/stdlib/primitives/group/cycle_group.hpp"
#include "barretenberg/circuit_checker/circuit_checker.hpp"
#include "barretenberg/common/assert.hpp"
#include "barretenberg/common/ref_span.hpp"
#include "barretenberg/crypto/pedersen_commitment/pedersen.hpp"
#include "barretenberg/crypto/pedersen_hash/pedersen.hpp"
#include "barretenberg/numeric/random/engine.hpp"
#include "barretenberg/stdlib/primitives/bigfield/bigfield.hpp"
#include "barretenberg/stdlib/primitives/field/field.hpp"
#include "barretenberg/stdlib/primitives/test_utils.hpp"
#include "barretenberg/stdlib/primitives/witness/witness.hpp"
#include "barretenberg/stdlib_circuit_builders/mega_circuit_builder.hpp"
#include "barretenberg/stdlib_circuit_builders/plookup_tables/fixed_base/fixed_base.hpp"
#include "barretenberg/transcript/origin_tag.hpp"
#include <gtest/gtest.h>
 
#define STDLIB_TYPE_ALIASES                                                                                            \
    using Builder = TypeParam;                                                                                         \
    using cycle_group_ct = stdlib::cycle_group<Builder>;                                                               \
    using Curve = typename stdlib::cycle_group<Builder>::Curve;                                                        \
    using Element = typename Curve::Element;                                                                           \
    using AffineElement = typename Curve::AffineElement;                                                               \
    using Group = typename Curve::Group;                                                                               \
    using bool_ct = stdlib::bool_t<Builder>;                                                                           \
    using witness_ct = stdlib::witness_t<Builder>;                                                                     \
    using cycle_scalar_ct = cycle_group_ct::cycle_scalar;
 
using namespace bb;
 
namespace {
auto& engine = numeric::get_debug_randomness();
}
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
 
template <class Builder> class CycleGroupTest : public ::testing::Test {
  public:
    using Curve = typename stdlib::cycle_group<Builder>::Curve;
    using Group = typename Curve::Group;
 
    using Element = typename Curve::Element;
    using AffineElement = typename Curve::AffineElement;
 
    static constexpr size_t num_generators = 110;
    static inline std::array<AffineElement, num_generators> generators{};
 
    static void SetUpTestSuite()
    {
 
        for (size_t i = 0; i < num_generators; ++i) {
            generators[i] = Group::one * Curve::ScalarField::random_element(&engine);
        }
    };
};
 
using CircuitTypes = ::testing::Types<bb::UltraCircuitBuilder, bb::MegaCircuitBuilder>;
TYPED_TEST_SUITE(CycleGroupTest, CircuitTypes);
 
// Import the check_circuit_and_gate_count function from test_utils
using bb::stdlib::test_utils::check_circuit_and_gate_count;
 
STANDARD_TESTING_TAGS
TYPED_TEST(CycleGroupTest, TestBasicTagLogic)
{
    STDLIB_TYPE_ALIASES
    Builder builder;
 
    // Create field elements with specific tags before constructing the cycle_group
    auto lhs = TestFixture::generators[0];
    auto x = stdlib::field_t<Builder>::from_witness(&builder, lhs.x);
    auto y = stdlib::field_t<Builder>::from_witness(&builder, lhs.y);
 
    // Set tags on the individual field elements
    x.set_origin_tag(submitted_value_origin_tag);
    y.set_origin_tag(challenge_origin_tag);
 
    // Construct cycle_group from pre-tagged field elements
    // The 2-arg constructor auto-detects infinity from coordinates, so _is_infinity
    // will have a tag derived from x and y (since it's computed from x² + 5y²)
    cycle_group_ct a(x, y, /*assert_on_curve=*/true);
 
    // The tag of the cycle_group should be the union of x and y tags
    // (is_infinity is derived from x and y, so its tag is already included)
    EXPECT_EQ(a.get_origin_tag(), first_two_merged_tag);
 
#ifndef NDEBUG
    // Test that instant_death_tag on x coordinate propagates correctly
    auto x_death = stdlib::field_t<Builder>::from_witness(&builder, TestFixture::generators[1].x);
    auto y_normal = stdlib::field_t<Builder>::from_witness(&builder, TestFixture::generators[1].y);
 
    x_death.set_origin_tag(instant_death_tag);
    // Set constant tags on the other elements so they can be merged with instant_death_tag
    y_normal.set_origin_tag(constant_tag);
 
    // Use assert_on_curve=false to avoid triggering instant_death during validate_on_curve()
    cycle_group_ct b(x_death, y_normal, /*assert_on_curve=*/false);
    // Even requesting the tag of the whole structure can cause instant death
    EXPECT_THROW(b.get_origin_tag(), std::runtime_error);
#endif
}
 
TYPED_TEST(CycleGroupTest, TestInfConstantWintnessRegression)
{
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    auto lhs = TestFixture::generators[0] * 0;
    cycle_group_ct a = cycle_group_ct::from_constant_witness(&builder, lhs);
    (void)a;
    EXPECT_FALSE(builder.failed());
    check_circuit_and_gate_count(builder, 0);
}
 
TYPED_TEST(CycleGroupTest, TestWitnessSumRegression)
{
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    auto lhs = TestFixture::generators[0];
    auto rhs = TestFixture::generators[1];
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
    cycle_group_ct c = a + b;
    EXPECT_FALSE(c.is_constant());
    c = a - b;
    EXPECT_FALSE(c.is_constant());
}
 
TYPED_TEST(CycleGroupTest, TestOperatorNegRegression)
{
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    auto lhs = TestFixture::generators[0];
    auto rhs = TestFixture::generators[1];
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
    b = -b;
    cycle_group_ct c = a.unconditional_add(b);
    (void)c;
    EXPECT_FALSE(builder.failed());
    check_circuit_and_gate_count(builder, 23);
}
 
TYPED_TEST(CycleGroupTest, TestConstantWitnessMixupRegression)
{
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    auto c1 = cycle_group_ct(AffineElement::one());
    auto cw8 = cycle_group_ct::from_constant_witness(&builder, AffineElement::one() * 0);
    auto w11 = cycle_group_ct::from_witness(&builder, TestFixture::generators[0]);
 
    auto w9 = cw8 + c1;  // mixup happens here due to _is_infinity being a constant
    auto w26 = w9 + w11; // and here the circuit checker crashes
 
    auto w10 = cw8 - c1;
    auto w27 = w10 - w11; // and here
    (void)w26;
    (void)w27;
    check_circuit_and_gate_count(builder, 44);
}
 
TYPED_TEST(CycleGroupTest, TestConditionalAssignRegression)
{
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    auto c0 = cycle_group_ct(AffineElement::one() * 0);
    auto c1 = cycle_group_ct::conditional_assign(bool_ct(witness_ct(&builder, false)), c0, c0);
    auto w3 = c1.dbl();
    (void)w3;
    check_circuit_and_gate_count(builder, 1);
}
 
TYPED_TEST(CycleGroupTest, TestConditionalAssignSuperMixupRegression)
{
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    auto c0 = cycle_group_ct(TestFixture::generators[0]);
    auto c1 = cycle_group_ct(-TestFixture::generators[0]);
    auto w2 = cycle_group_ct::conditional_assign(bool_ct(witness_ct(&builder, true)), c0, c1);
    EXPECT_FALSE(w2.x().is_constant());
    EXPECT_FALSE(w2.y().is_constant());
    EXPECT_TRUE(w2.is_point_at_infinity().is_constant());
    auto w3 = w2.dbl();
    (void)w3;
    check_circuit_and_gate_count(builder, 5);
}
 
TYPED_TEST(CycleGroupTest, TestValidateOnCurveSucceed)
{
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    auto point_val = TestFixture::generators[0];
    auto x = stdlib::field_t<Builder>::from_witness(&builder, point_val.x);
    auto y = stdlib::field_t<Builder>::from_witness(&builder, point_val.y);
 
    // The 2-arg constructor auto-detects infinity from (x == 0 && y == 0).
    // For a generator point, this will correctly detect is_infinity = false.
    cycle_group_ct point(x, y, /*assert_on_curve=*/true);
    EXPECT_FALSE(builder.failed());
    // Gate count includes infinity auto-detection + validate_on_curve
    check_circuit_and_gate_count(builder, 10);
}
 
TYPED_TEST(CycleGroupTest, TestValidateOnCurveInfinitySucceed)
{
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, AffineElement::infinity());
    a.validate_on_curve();
    EXPECT_FALSE(builder.failed());
    check_circuit_and_gate_count(builder, 15);
}
 
TYPED_TEST(CycleGroupTest, TestValidateOnCurveFail)
{
    BB_DISABLE_ASSERTS(); // Avoid on_curve assertion failure in cycle_group constructor
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    auto x = stdlib::field_t<Builder>::from_witness(&builder, typename stdlib::field_t<Builder>::native(1));
    auto y = stdlib::field_t<Builder>::from_witness(&builder, typename stdlib::field_t<Builder>::native(1));
 
    // Point (1, 1) is not on the curve - validate_on_curve should fail
    // The 2-arg constructor auto-detects infinity as false for non-zero coordinates
    cycle_group_ct a(x, y, /*assert_on_curve=*/true);
    EXPECT_TRUE(builder.failed());
    EXPECT_FALSE(CircuitChecker::check(builder));
}
 
TYPED_TEST(CycleGroupTest, TestValidateOnCurveFail2)
{
    BB_DISABLE_ASSERTS(); // Avoid on_curve assertion failure in cycle_group constructor
    STDLIB_TYPE_ALIASES;
    Builder builder;
 
    auto x = stdlib::field_t<Builder>::from_witness(&builder, typename stdlib::field_t<Builder>::native(1));
    auto y = stdlib::field_t<Builder>::from_witness(&builder, typename stdlib::field_t<Builder>::native(1));
 
    // Point (1, 1) is not on the curve - validate_on_curve should fail
    // The 2-arg constructor auto-detects infinity from coordinates (1² + 5*1² ≠ 0, so not infinity)
    cycle_group_ct a(x, y, /*assert_on_curve=*/false);
    a.validate_on_curve();
    EXPECT_TRUE(builder.failed());
    EXPECT_FALSE(CircuitChecker::check(builder));
}
 
TYPED_TEST(CycleGroupTest, TestStandardForm)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto affine_infinity = cycle_group_ct::AffineElement::infinity();
    cycle_group_ct input_a = cycle_group_ct::from_witness(&builder, Element::random_element());
    cycle_group_ct input_b = cycle_group_ct::from_witness(&builder, affine_infinity);
    cycle_group_ct input_c = cycle_group_ct(Element::random_element());
    cycle_group_ct input_d = cycle_group_ct(affine_infinity);
 
    // Assign different tags to all inputs
    input_a.set_origin_tag(submitted_value_origin_tag);
    input_b.set_origin_tag(challenge_origin_tag);
    input_c.set_origin_tag(next_challenge_tag);
    input_d.set_origin_tag(first_two_merged_tag);
 
    input_a.standardize();
    auto standard_a = input_a;
    input_b.standardize();
    auto standard_b = input_b;
    input_c.standardize();
    auto standard_c = input_c;
    input_d.standardize();
    auto standard_d = input_d;
 
    EXPECT_EQ(standard_a.is_point_at_infinity().get_value(), false);
    EXPECT_EQ(standard_b.is_point_at_infinity().get_value(), true);
    EXPECT_EQ(standard_c.is_point_at_infinity().get_value(), false);
    EXPECT_EQ(standard_d.is_point_at_infinity().get_value(), true);
 
    // Ensure that the tags in the standard form remain the same
    EXPECT_EQ(standard_a.get_origin_tag(), submitted_value_origin_tag);
    EXPECT_EQ(standard_b.get_origin_tag(), challenge_origin_tag);
    EXPECT_EQ(standard_c.get_origin_tag(), next_challenge_tag);
    EXPECT_EQ(standard_d.get_origin_tag(), first_two_merged_tag);
 
    auto input_a_x = input_a.x().get_value();
    auto input_a_y = input_a.y().get_value();
    auto input_c_x = input_c.x().get_value();
    auto input_c_y = input_c.y().get_value();
 
    auto standard_a_x = standard_a.x().get_value();
    auto standard_a_y = standard_a.y().get_value();
 
    auto standard_b_x = standard_b.x().get_value();
    auto standard_b_y = standard_b.y().get_value();
 
    auto standard_c_x = standard_c.x().get_value();
    auto standard_c_y = standard_c.y().get_value();
 
    auto standard_d_x = standard_d.x().get_value();
    auto standard_d_y = standard_d.y().get_value();
 
    EXPECT_EQ(input_a_x, standard_a_x);
    EXPECT_EQ(input_a_y, standard_a_y);
    EXPECT_EQ(standard_b_x, 0);
    EXPECT_EQ(standard_b_y, 0);
    EXPECT_EQ(input_c_x, standard_c_x);
    EXPECT_EQ(input_c_y, standard_c_y);
    EXPECT_EQ(standard_d_x, 0);
    EXPECT_EQ(standard_d_y, 0);
 
    check_circuit_and_gate_count(builder, 24);
}
TYPED_TEST(CycleGroupTest, TestDbl)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct(lhs);
    // Assign two different tags
    a.set_origin_tag(submitted_value_origin_tag);
    b.set_origin_tag(challenge_origin_tag);
    cycle_group_ct c;
    cycle_group_ct d;
    for (size_t i = 0; i < 3; ++i) {
        c = a.dbl();
    }
    d = b.dbl();
    AffineElement expected(Element(lhs).dbl());
    AffineElement result = c.get_value();
    EXPECT_EQ(result, expected);
    EXPECT_EQ(d.get_value(), expected);
 
    check_circuit_and_gate_count(builder, 19);
 
    // Ensure the tags stay the same after doubling
    EXPECT_EQ(c.get_origin_tag(), submitted_value_origin_tag);
    EXPECT_EQ(d.get_origin_tag(), challenge_origin_tag);
}
 
TYPED_TEST(CycleGroupTest, TestDblNonConstantPoints)
{
    STDLIB_TYPE_ALIASES;
 
    // Test case 1: Witness point WITH hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[0];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
 
        Element doubled_element = Element(lhs).dbl();
        AffineElement hint(doubled_element);
 
        cycle_group_ct result = a.dbl(hint);
 
        EXPECT_EQ(result.get_value(), hint);
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 13);
    }
 
    // Test case 2: Witness point WITHOUT hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[1];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
 
        cycle_group_ct result = a.dbl();
 
        Element expected_element = Element(lhs).dbl();
        AffineElement expected(expected_element);
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        // Note: same gate count as with hint - hint is a witness generation optimization only
        check_circuit_and_gate_count(builder, 13);
    }
 
    // Test case 3: Witness infinity point WITHOUT hint
    {
        auto builder = Builder();
        AffineElement infinity_element;
        infinity_element.self_set_infinity();
 
        cycle_group_ct infinity = cycle_group_ct::from_witness(&builder, infinity_element);
 
        cycle_group_ct result = infinity.dbl();
 
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        // Note: from_witness sets x,y to witness(0,0) for infinity points
        // After doubling, y becomes -1 (0x3064...) due to the modified_y logic
        EXPECT_EQ(result.x().get_value(), 0);
 
        // Same gate count as regular witness points
        check_circuit_and_gate_count(builder, 13);
    }
}
 
TYPED_TEST(CycleGroupTest, TestDblConstantPoints)
{
    STDLIB_TYPE_ALIASES;
 
    // Test case 1: Constant point WITH hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[0];
        cycle_group_ct a(lhs);
 
        Element doubled_element = Element(lhs).dbl();
        AffineElement hint(doubled_element);
 
        cycle_group_ct result = a.dbl(hint);
 
        EXPECT_EQ(result.get_value(), hint);
        EXPECT_TRUE(result.is_constant());
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 0);
    }
 
    // Test case 2: Constant point WITHOUT hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[1];
        cycle_group_ct a(lhs);
 
        cycle_group_ct result = a.dbl();
 
        Element expected_element = Element(lhs).dbl();
        AffineElement expected(expected_element);
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_TRUE(result.is_constant());
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 0);
    }
 
    // Test case 3: Constant infinity point WITHOUT hint
    {
        auto builder = Builder();
        cycle_group_ct infinity = cycle_group_ct::constant_infinity(nullptr);
 
        cycle_group_ct result = infinity.dbl();
 
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        EXPECT_TRUE(result.is_constant());
        EXPECT_EQ(result.x().get_value(), 0);
        EXPECT_EQ(result.y().get_value(), 0);
 
        check_circuit_and_gate_count(builder, 0);
    }
 
    // Test case 4: Constant infinity point WITH hint
    {
        auto builder = Builder();
        cycle_group_ct infinity = cycle_group_ct::constant_infinity(nullptr);
 
        AffineElement hint;
        hint.self_set_infinity();
 
        cycle_group_ct result = infinity.dbl(hint);
 
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        EXPECT_TRUE(result.is_constant());
        EXPECT_EQ(result.x().get_value(), 0);
        EXPECT_EQ(result.y().get_value(), 0);
 
        check_circuit_and_gate_count(builder, 0);
    }
}
 
TYPED_TEST(CycleGroupTest, TestDblMixedConstantWitness)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    // Test doubling where x is constant but y is witness (edge case)
    auto point = TestFixture::generators[1];
    auto x = stdlib::field_t<Builder>(&builder, point.x);             // constant
    auto y = stdlib::field_t<Builder>(witness_ct(&builder, point.y)); // witness
 
    // Mixed constancy is remedied inside the constructor; x will be converted to a fixed witness
    // The point is known to be on the curve and not at infinity (it's a generator point)
    cycle_group_ct a(x, y, /*assert_on_curve=*/false);
 
    EXPECT_FALSE(a.x().is_constant());
    EXPECT_FALSE(a.y().is_constant());
 
    a.dbl();
 
    check_circuit_and_gate_count(builder, 8);
}
 
TYPED_TEST(CycleGroupTest, TestUnconditionalAddNonConstantPoints)
{
    STDLIB_TYPE_ALIASES;
 
    // Test case 1: Two witness points WITHOUT hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[0];
        auto rhs = TestFixture::generators[1];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
 
        cycle_group_ct result = a.unconditional_add(b);
 
        Element expected_element = Element(lhs) + Element(rhs);
        AffineElement expected(expected_element);
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 22);
    }
 
    // Test case 2: Two witness points WITH hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[2];
        auto rhs = TestFixture::generators[3];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
 
        Element sum_element = Element(lhs) + Element(rhs);
        AffineElement hint(sum_element);
 
        cycle_group_ct result = a.unconditional_add(b, hint);
 
        EXPECT_EQ(result.get_value(), hint);
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 22);
    }
 
    // Test case 3: Mixed witness and constant points
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[0];
        auto rhs = TestFixture::generators[1];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b(rhs); // constant
 
        cycle_group_ct result = a.unconditional_add(b);
 
        Element expected_element = Element(lhs) + Element(rhs);
        AffineElement expected(expected_element);
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_FALSE(result.is_constant());
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 14);
    }
}
 
TYPED_TEST(CycleGroupTest, TestUnconditionalAddConstantPoints)
{
    STDLIB_TYPE_ALIASES;
 
    // Test case 1: Two constant points WITHOUT hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[0];
        auto rhs = TestFixture::generators[1];
        cycle_group_ct a(lhs);
        cycle_group_ct b(rhs);
 
        cycle_group_ct result = a.unconditional_add(b);
 
        Element expected_element = Element(lhs) + Element(rhs);
        AffineElement expected(expected_element);
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_TRUE(result.is_constant());
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 0);
    }
 
    // Test case 2: Two constant points WITH hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[2];
        auto rhs = TestFixture::generators[3];
        cycle_group_ct a(lhs);
        cycle_group_ct b(rhs);
 
        Element sum_element = Element(lhs) + Element(rhs);
        AffineElement hint(sum_element);
 
        cycle_group_ct result = a.unconditional_add(b, hint);
 
        EXPECT_EQ(result.get_value(), hint);
        EXPECT_TRUE(result.is_constant());
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 0);
    }
}
 
TYPED_TEST(CycleGroupTest, TestUnconditionalSubtractNonConstantPoints)
{
    STDLIB_TYPE_ALIASES;
 
    // Test case 1: Two witness points WITHOUT hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[0];
        auto rhs = TestFixture::generators[1];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
 
        cycle_group_ct result = a.unconditional_subtract(b);
 
        Element expected_element = Element(lhs) - Element(rhs);
        AffineElement expected(expected_element);
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 22);
    }
 
    // Test case 2: Two witness points WITH hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[2];
        auto rhs = TestFixture::generators[3];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
 
        Element diff_element = Element(lhs) - Element(rhs);
        AffineElement hint(diff_element);
 
        cycle_group_ct result = a.unconditional_subtract(b, hint);
 
        EXPECT_EQ(result.get_value(), hint);
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        // Same gate count as without hint - hint is a witness generation optimization only
        check_circuit_and_gate_count(builder, 22);
    }
 
    // Test case 3: Mixed witness and constant points
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[0];
        auto rhs = TestFixture::generators[1];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b(rhs); // constant
 
        cycle_group_ct result = a.unconditional_subtract(b);
 
        Element expected_element = Element(lhs) - Element(rhs);
        AffineElement expected(expected_element);
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_FALSE(result.is_constant());
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 14);
    }
}
 
TYPED_TEST(CycleGroupTest, TestUnconditionalSubtractConstantPoints)
{
    STDLIB_TYPE_ALIASES;
 
    // Test case 1: Two constant points WITHOUT hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[0];
        auto rhs = TestFixture::generators[1];
        cycle_group_ct a(lhs);
        cycle_group_ct b(rhs);
 
        cycle_group_ct result = a.unconditional_subtract(b);
 
        Element expected_element = Element(lhs) - Element(rhs);
        AffineElement expected(expected_element);
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_TRUE(result.is_constant());
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 0);
    }
 
    // Test case 2: Two constant points WITH hint
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[2];
        auto rhs = TestFixture::generators[3];
        cycle_group_ct a(lhs);
        cycle_group_ct b(rhs);
 
        Element diff_element = Element(lhs) - Element(rhs);
        AffineElement hint(diff_element);
 
        cycle_group_ct result = a.unconditional_subtract(b, hint);
 
        EXPECT_EQ(result.get_value(), hint);
        EXPECT_TRUE(result.is_constant());
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        check_circuit_and_gate_count(builder, 0);
    }
}
 
TYPED_TEST(CycleGroupTest, TestUnconditionalAdd)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto add =
        [&](const AffineElement& lhs, const AffineElement& rhs, const bool lhs_constant, const bool rhs_constant) {
            cycle_group_ct a = lhs_constant ? cycle_group_ct(lhs) : cycle_group_ct::from_witness(&builder, lhs);
            cycle_group_ct b = rhs_constant ? cycle_group_ct(rhs) : cycle_group_ct::from_witness(&builder, rhs);
            // Assign two different tags
            a.set_origin_tag(submitted_value_origin_tag);
            b.set_origin_tag(challenge_origin_tag);
            cycle_group_ct c = a.unconditional_add(b);
            AffineElement expected(Element(lhs) + Element(rhs));
            AffineElement result = c.get_value();
            EXPECT_EQ(result, expected);
            // Ensure the tags in the result are merged
            EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
        };
 
    add(TestFixture::generators[0], TestFixture::generators[1], false, false);
    add(TestFixture::generators[0], TestFixture::generators[1], false, true);
    add(TestFixture::generators[0], TestFixture::generators[1], true, false);
    add(TestFixture::generators[0], TestFixture::generators[1], true, true);
 
    check_circuit_and_gate_count(builder, 50);
}
 
TYPED_TEST(CycleGroupTest, TestConstrainedUnconditionalAddSucceed)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
    auto rhs = TestFixture::generators[1];
 
    // case 1. valid unconditional add
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
    cycle_group_ct c = a.checked_unconditional_add(b);
    AffineElement expected(Element(lhs) + Element(rhs));
    AffineElement result = c.get_value();
    EXPECT_EQ(result, expected);
 
    check_circuit_and_gate_count(builder, 24);
}
 
TYPED_TEST(CycleGroupTest, TestConstrainedUnconditionalAddFail)
{
    BB_DISABLE_ASSERTS(); // Avoid on_curve assertion failure in cycle_group constructor
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
    auto rhs = -TestFixture::generators[0]; // ruh roh
 
    // case 2. invalid unconditional add
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
    a.checked_unconditional_add(b);
 
    EXPECT_TRUE(builder.failed());
    // No gate count check for failing test
    EXPECT_FALSE(CircuitChecker::check(builder));
}
 
// Test regular addition of witness points (no edge cases)
TYPED_TEST(CycleGroupTest, TestAddRegular)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
    auto rhs = -TestFixture::generators[1];
 
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
 
    // Test tag merging
    a.set_origin_tag(submitted_value_origin_tag);
    b.set_origin_tag(challenge_origin_tag);
 
    cycle_group_ct c = a + b;
 
    AffineElement expected(Element(lhs) + Element(rhs));
    EXPECT_EQ(c.get_value(), expected);
    EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
 
    check_circuit_and_gate_count(builder, 55);
}
 
// Test addition with LHS point at infinity
TYPED_TEST(CycleGroupTest, TestAddLhsInfinity)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto rhs = -TestFixture::generators[1];
    auto affine_infinity = cycle_group_ct::AffineElement::infinity();
 
    cycle_group_ct point_at_infinity = cycle_group_ct::from_witness(&builder, affine_infinity);
 
    cycle_group_ct a = point_at_infinity;
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
 
    a.set_origin_tag(submitted_value_origin_tag);
    b.set_origin_tag(challenge_origin_tag);
 
    cycle_group_ct c = a + b;
 
    // Result should be rhs since infinity + P = P
    EXPECT_EQ(c.get_value(), rhs);
    EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
 
    check_circuit_and_gate_count(builder, 55);
}
 
// Test addition with RHS point at infinity
TYPED_TEST(CycleGroupTest, TestAddRhsInfinity)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
    auto affine_infinity = cycle_group_ct::AffineElement::infinity();
 
    cycle_group_ct point_at_infinity = cycle_group_ct::from_witness(&builder, affine_infinity);
 
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = point_at_infinity;
 
    a.set_origin_tag(submitted_value_origin_tag);
    b.set_origin_tag(challenge_origin_tag);
 
    cycle_group_ct c = a + b;
 
    // Result should be lhs since P + infinity = P
    EXPECT_EQ(c.get_value(), lhs);
    EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
 
    // Addition with witness infinity point
    check_circuit_and_gate_count(builder, 55);
}
 
// Test addition with both points at infinity
TYPED_TEST(CycleGroupTest, TestAddBothInfinity)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto affine_infinity = cycle_group_ct::AffineElement::infinity();
 
    cycle_group_ct point_at_infinity1 = cycle_group_ct::from_witness(&builder, affine_infinity);
 
    cycle_group_ct point_at_infinity2 = cycle_group_ct::from_witness(&builder, affine_infinity);
 
    cycle_group_ct a = point_at_infinity1;
    cycle_group_ct b = point_at_infinity2;
 
    a.set_origin_tag(submitted_value_origin_tag);
    b.set_origin_tag(challenge_origin_tag);
 
    cycle_group_ct c = a + b;
 
    // Result should be infinity since infinity + infinity = infinity
    EXPECT_TRUE(c.is_point_at_infinity().get_value());
    EXPECT_TRUE(c.get_value().is_point_at_infinity());
    EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
 
    check_circuit_and_gate_count(builder, 55);
}
 
// Test addition of inverse points (result is infinity)
TYPED_TEST(CycleGroupTest, TestAddInversePoints)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
 
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, -lhs);
 
    a.set_origin_tag(submitted_value_origin_tag);
    b.set_origin_tag(challenge_origin_tag);
 
    cycle_group_ct c = a + b;
 
    EXPECT_TRUE(c.is_point_at_infinity().get_value());
    EXPECT_TRUE(c.get_value().is_point_at_infinity());
    EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
 
    check_circuit_and_gate_count(builder, 55);
}
 
// Test doubling (adding point to itself)
TYPED_TEST(CycleGroupTest, TestAddDoubling)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
 
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, lhs);
 
    a.set_origin_tag(submitted_value_origin_tag);
    b.set_origin_tag(challenge_origin_tag);
 
    cycle_group_ct c = a + b;
 
    AffineElement expected((Element(lhs)).dbl());
    EXPECT_EQ(c.get_value(), expected);
    EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
 
    check_circuit_and_gate_count(builder, 55);
}
 
TYPED_TEST(CycleGroupTest, TestAddConstantPoints)
{
    STDLIB_TYPE_ALIASES;
 
    // Test adding constant points - this takes a completely different path than witness points
    // The existing TestAdd only tests witness points
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[5];
        auto rhs = TestFixture::generators[6];
 
        cycle_group_ct a(lhs);
        cycle_group_ct b(rhs);
 
        cycle_group_ct result = a + b;
 
        AffineElement expected(Element(lhs) + Element(rhs));
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_TRUE(result.is_constant());
 
        // No gates needed for constant arithmetic
        check_circuit_and_gate_count(builder, 0);
    }
 
    // Test constant point + constant infinity (early return optimization)
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[7];
 
        cycle_group_ct a(lhs);
        cycle_group_ct b = cycle_group_ct::constant_infinity(&builder);
 
        cycle_group_ct result = a + b;
 
        EXPECT_EQ(result.get_value(), lhs);
        EXPECT_TRUE(result.is_constant());
 
        // Uses early return for constant infinity
        check_circuit_and_gate_count(builder, 0);
    }
}
 
TYPED_TEST(CycleGroupTest, TestAddMixedConstantWitness)
{
    STDLIB_TYPE_ALIASES;
 
    // Test mixed constant/witness operations which use different code paths than pure witness ops
    // The existing TestAdd doesn't cover these mixed scenarios
 
    // Test witness + constant infinity (early return path)
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[10];
 
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b = cycle_group_ct::constant_infinity(&builder);
 
        cycle_group_ct result = a + b;
 
        EXPECT_EQ(result.get_value(), lhs);
        EXPECT_FALSE(result.is_constant());
 
        // Early return optimization for constant infinity
        check_circuit_and_gate_count(builder, 10);
    }
 
    // Test constant + witness point (different gate count than witness + witness)
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[11];
        auto rhs = TestFixture::generators[12];
 
        cycle_group_ct a(lhs);                                          // constant
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs); // witness
 
        cycle_group_ct result = a + b;
 
        AffineElement expected(Element(lhs) + Element(rhs));
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_FALSE(result.is_constant());
 
        // Different gate count than pure witness addition
        check_circuit_and_gate_count(builder, 27);
    }
}
 
// Test the infinity result logic specifically
TYPED_TEST(CycleGroupTest, TestAddInfinityResultLogic)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    // Test Case 1: P + (-P) = O (infinity_predicate true, neither input is infinity)
    {
        auto point = TestFixture::generators[0];
        auto neg_point = -point;
 
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, point);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, neg_point);
 
        cycle_group_ct result = a + b;
 
        // Verify result is infinity
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        EXPECT_TRUE(result.get_value().is_point_at_infinity());
    }
 
    // Test Case 2: O + O = O (both inputs are infinity)
    {
        cycle_group_ct inf1 = cycle_group_ct::from_witness(&builder, Group::affine_point_at_infinity);
        cycle_group_ct inf2 = cycle_group_ct::from_witness(&builder, Group::affine_point_at_infinity);
 
        cycle_group_ct result = inf1 + inf2;
 
        // Verify result is infinity
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        EXPECT_TRUE(result.get_value().is_point_at_infinity());
    }
 
    // Test Case 3: P + O = P (only rhs is infinity, result should NOT be infinity)
    {
        auto point = TestFixture::generators[1];
 
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, point);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, Group::affine_point_at_infinity);
 
        cycle_group_ct result = a + b;
 
        // Verify result is NOT infinity
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
        EXPECT_EQ(result.get_value(), point);
    }
 
    // Test Case 4: O + P = P (only lhs is infinity, result should NOT be infinity)
    {
        auto point = TestFixture::generators[2];
 
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, Group::affine_point_at_infinity);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, point);
 
        cycle_group_ct result = a + b;
 
        // Verify result is NOT infinity
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
        EXPECT_EQ(result.get_value(), point);
    }
 
    // Test Case 5: P + P = 2P (doubling, result should NOT be infinity unless P is special)
    {
        auto point = TestFixture::generators[3];
 
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, point);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, point);
 
        cycle_group_ct result = a + b;
 
        // Verify result is NOT infinity (it's 2P)
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
 
        AffineElement expected(Element(point).dbl());
        EXPECT_EQ(result.get_value(), expected);
    }
 
    check_circuit_and_gate_count(builder, 275);
}
 
TYPED_TEST(CycleGroupTest, TestUnconditionalSubtract)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto subtract =
        [&](const AffineElement& lhs, const AffineElement& rhs, const bool lhs_constant, const bool rhs_constant) {
            cycle_group_ct a = lhs_constant ? cycle_group_ct(lhs) : cycle_group_ct::from_witness(&builder, lhs);
            cycle_group_ct b = rhs_constant ? cycle_group_ct(rhs) : cycle_group_ct::from_witness(&builder, rhs);
            // Assign two different tags
            a.set_origin_tag(submitted_value_origin_tag);
            b.set_origin_tag(challenge_origin_tag);
 
            cycle_group_ct c = a.unconditional_subtract(b);
            AffineElement expected(Element(lhs) - Element(rhs));
            AffineElement result = c.get_value();
            EXPECT_EQ(result, expected);
            // Expect tags to be merged in the result
            EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
        };
 
    subtract(TestFixture::generators[0], TestFixture::generators[1], false, false);
    subtract(TestFixture::generators[0], TestFixture::generators[1], false, true);
    subtract(TestFixture::generators[0], TestFixture::generators[1], true, false);
    subtract(TestFixture::generators[0], TestFixture::generators[1], true, true);
 
    check_circuit_and_gate_count(builder, 50);
}
 
TYPED_TEST(CycleGroupTest, TestConstrainedUnconditionalSubtractSucceed)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
    auto rhs = TestFixture::generators[1];
 
    // case 1. valid unconditional add
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
    cycle_group_ct c = a.checked_unconditional_subtract(b);
    AffineElement expected(Element(lhs) - Element(rhs));
    AffineElement result = c.get_value();
    EXPECT_EQ(result, expected);
 
    check_circuit_and_gate_count(builder, 24);
}
 
TYPED_TEST(CycleGroupTest, TestConstrainedUnconditionalSubtractFail)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
    auto rhs = -TestFixture::generators[0]; // ruh roh
 
    // case 2. invalid unconditional add
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
    cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
    a.checked_unconditional_subtract(b);
 
    EXPECT_TRUE(builder.failed());
    // No gate count check for failing test
    EXPECT_FALSE(CircuitChecker::check(builder));
}
 
TYPED_TEST(CycleGroupTest, TestSubtract)
{
    STDLIB_TYPE_ALIASES;
    using bool_ct = stdlib::bool_t<Builder>;
    using witness_ct = stdlib::witness_t<Builder>;
    auto builder = Builder();
 
    auto lhs = TestFixture::generators[0];
    auto rhs = -TestFixture::generators[1];
    auto affine_infinity = cycle_group_ct::AffineElement::infinity();
 
    cycle_group_ct point_at_infinity = cycle_group_ct::from_witness(&builder, affine_infinity);
 
    // case 1. no edge-cases triggered
    {
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
        // Here and in the following cases we set 2 different tags to a and b
        a.set_origin_tag(submitted_value_origin_tag);
        b.set_origin_tag(challenge_origin_tag);
 
        cycle_group_ct c = a - b;
        AffineElement expected(Element(lhs) - Element(rhs));
        AffineElement result = c.get_value();
        EXPECT_EQ(result, expected);
        // We expect the tag of the result to be the union of a and b tags
        EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
    }
 
    // case 2. lhs is point at infinity
    {
        cycle_group_ct a = point_at_infinity;
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, rhs);
        a.set_origin_tag(submitted_value_origin_tag);
        b.set_origin_tag(challenge_origin_tag);
 
        cycle_group_ct c = a - b;
        AffineElement result = c.get_value();
        EXPECT_EQ(result, -rhs);
        EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
    }
 
    // case 3. rhs is point at infinity
    {
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b = point_at_infinity;
        a.set_origin_tag(submitted_value_origin_tag);
        b.set_origin_tag(challenge_origin_tag);
 
        cycle_group_ct c = a - b;
        AffineElement result = c.get_value();
        EXPECT_EQ(result, lhs);
        EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
    }
 
    // case 4. both points are at infinity
    {
        cycle_group_ct a = point_at_infinity;
        cycle_group_ct b = point_at_infinity;
        a.set_origin_tag(submitted_value_origin_tag);
        b.set_origin_tag(challenge_origin_tag);
 
        cycle_group_ct c = a - b;
        EXPECT_TRUE(c.is_point_at_infinity().get_value());
        EXPECT_TRUE(c.get_value().is_point_at_infinity());
        EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
    }
 
    // case 5. lhs = -rhs
    {
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, -lhs);
        a.set_origin_tag(submitted_value_origin_tag);
        b.set_origin_tag(challenge_origin_tag);
 
        cycle_group_ct c = a - b;
        AffineElement expected((Element(lhs)).dbl());
        AffineElement result = c.get_value();
        EXPECT_EQ(result, expected);
        EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
    }
 
    // case 6. lhs = rhs
    {
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, lhs);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, lhs);
        a.set_origin_tag(submitted_value_origin_tag);
        b.set_origin_tag(challenge_origin_tag);
 
        cycle_group_ct c = a - b;
        EXPECT_TRUE(c.is_point_at_infinity().get_value());
        EXPECT_TRUE(c.get_value().is_point_at_infinity());
        EXPECT_EQ(c.get_origin_tag(), first_two_merged_tag);
    }
 
    check_circuit_and_gate_count(builder, 297);
}
 
TYPED_TEST(CycleGroupTest, TestSubtractConstantPoints)
{
    STDLIB_TYPE_ALIASES;
 
    // Test subtracting constant points - this takes a completely different path than witness points
    // The existing TestSubtract only tests witness points
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[5];
        auto rhs = TestFixture::generators[6];
 
        cycle_group_ct a(lhs);
        cycle_group_ct b(rhs);
 
        cycle_group_ct result = a - b;
 
        AffineElement expected(Element(lhs) - Element(rhs));
        EXPECT_EQ(result.get_value(), expected);
        EXPECT_TRUE(result.is_constant());
 
        // No gates needed for constant arithmetic
        check_circuit_and_gate_count(builder, 0);
    }
 
    // Test constant point - constant infinity (early return optimization)
    {
        auto builder = Builder();
        auto lhs = TestFixture::generators[7];
 
        cycle_group_ct a(lhs);
        cycle_group_ct b = cycle_group_ct::constant_infinity(&builder);
 
        cycle_group_ct result = a - b;
 
        EXPECT_EQ(result.get_value(), lhs);
        EXPECT_TRUE(result.is_constant());
 
        // Uses early return for constant infinity
        check_circuit_and_gate_count(builder, 0);
    }
 
    // Test constant infinity - constant point (early return optimization)
    {
        auto builder = Builder();
        auto rhs = TestFixture::generators[7];
 
        cycle_group_ct a = cycle_group_ct::constant_infinity(&builder);
        cycle_group_ct b(rhs);
 
        cycle_group_ct result = a - b;
 
        EXPECT_EQ(result.get_value(), -rhs);
        EXPECT_TRUE(result.is_constant());
 
        // Uses early return for constant infinity
        check_circuit_and_gate_count(builder, 0);
    }
}
 
template <typename T1, typename T2> auto assign_and_merge_tags(T1& points, T2& scalars)
{
    OriginTag merged_tag = OriginTag::constant(); // Initialize as CONSTANT so merging with input tags works correctly
    for (size_t i = 0; i < points.size(); i++) {
        const auto point_tag = OriginTag(/*parent_index=*/0, /*round_index=*/i, /*is_submitted=*/true);
        const auto scalar_tag = OriginTag(/*parent_index=*/0, /*round_index=*/i, /*is_submitted=*/false);
 
        merged_tag = OriginTag(merged_tag, OriginTag(point_tag, scalar_tag));
        points[i].set_origin_tag(point_tag);
        scalars[i].set_origin_tag(scalar_tag);
    }
    return merged_tag;
}
 
TYPED_TEST(CycleGroupTest, TestBatchMulGeneralMSM)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    const size_t num_muls = 1;
    // case 1, general MSM with inputs that are combinations of constant and witnesses
    std::vector<cycle_group_ct> points;
    std::vector<typename cycle_group_ct::cycle_scalar> scalars;
    Element expected = Group::point_at_infinity;
 
    for (size_t i = 0; i < num_muls; ++i) {
        auto element = TestFixture::generators[i];
        typename Group::Fr scalar = Group::Fr::random_element(&engine);
 
        // 1: add entry where point, scalar are witnesses
        expected += (element * scalar);
        points.emplace_back(cycle_group_ct::from_witness(&builder, element));
        scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
 
        // 2: add entry where point is constant, scalar is witness
        expected += (element * scalar);
        points.emplace_back(cycle_group_ct(element));
        scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
 
        // 3: add entry where point is witness, scalar is constant
        expected += (element * scalar);
        points.emplace_back(cycle_group_ct::from_witness(&builder, element));
        scalars.emplace_back(typename cycle_group_ct::cycle_scalar(scalar));
 
        // 4: add entry where point is constant, scalar is constant
        expected += (element * scalar);
        points.emplace_back(cycle_group_ct(element));
        scalars.emplace_back(typename cycle_group_ct::cycle_scalar(scalar));
    }
 
    // Here and in the following cases assign different tags to points and scalars and get the union of them back
    const auto expected_tag = assign_and_merge_tags(points, scalars);
 
    auto result = cycle_group_ct::batch_mul(points, scalars);
    EXPECT_EQ(result.get_value(), AffineElement(expected));
    // The tag should the union of all tags
    EXPECT_EQ(result.get_origin_tag(), expected_tag);
 
    if constexpr (std::is_same_v<TypeParam, bb::MegaCircuitBuilder>) {
        check_circuit_and_gate_count(builder, 4401); // Mega
    } else {
        check_circuit_and_gate_count(builder, 4404); // Ultra
    }
}
 
TYPED_TEST(CycleGroupTest, TestBatchMulProducesInfinity)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    // case 2, MSM that produces point at infinity
    std::vector<cycle_group_ct> points;
    std::vector<typename cycle_group_ct::cycle_scalar> scalars;
 
    auto element = TestFixture::generators[0];
    typename Group::Fr scalar = Group::Fr::random_element(&engine);
    points.emplace_back(cycle_group_ct::from_witness(&builder, element));
    scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
 
    points.emplace_back(cycle_group_ct::from_witness(&builder, element));
    scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, -scalar));
 
    const auto expected_tag = assign_and_merge_tags(points, scalars);
 
    auto result = cycle_group_ct::batch_mul(points, scalars);
    EXPECT_TRUE(result.is_point_at_infinity().get_value());
 
    EXPECT_EQ(result.get_origin_tag(), expected_tag);
 
    if constexpr (std::is_same_v<TypeParam, bb::MegaCircuitBuilder>) {
        check_circuit_and_gate_count(builder, 4027); // Mega
    } else {
        check_circuit_and_gate_count(builder, 4030); // Ultra
    }
}
 
TYPED_TEST(CycleGroupTest, TestBatchMulMultiplyByZero)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    // case 3. Multiply by zero
    std::vector<cycle_group_ct> points;
    std::vector<typename cycle_group_ct::cycle_scalar> scalars;
 
    auto element = TestFixture::generators[0];
    typename Group::Fr scalar = 0;
    points.emplace_back(cycle_group_ct::from_witness(&builder, element));
    scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
 
    const auto expected_tag = assign_and_merge_tags(points, scalars);
    auto result = cycle_group_ct::batch_mul(points, scalars);
    EXPECT_TRUE(result.is_point_at_infinity().get_value());
    EXPECT_EQ(result.get_origin_tag(), expected_tag);
 
    if constexpr (std::is_same_v<TypeParam, bb::MegaCircuitBuilder>) {
        check_circuit_and_gate_count(builder, 3533); // Mega
    } else {
        check_circuit_and_gate_count(builder, 3536); // Ultra
    }
}
 
TYPED_TEST(CycleGroupTest, TestBatchMulInputsAreInfinity)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    // Test batch_mul with witness point at infinity
    std::vector<cycle_group_ct> points;
    std::vector<typename cycle_group_ct::cycle_scalar> scalars;
 
    typename Group::Fr scalar = Group::Fr::random_element(&engine);
    auto affine_infinity = cycle_group_ct::AffineElement::infinity();
 
    // is_infinity = witness
    {
        cycle_group_ct point = cycle_group_ct::from_witness(&builder, affine_infinity);
        points.emplace_back(point);
        scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
    }
    // is_infinity = constant
    {
        cycle_group_ct point = cycle_group_ct(affine_infinity);
        points.emplace_back(point);
        scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
    }
 
    const auto expected_tag = assign_and_merge_tags(points, scalars);
    auto result = cycle_group_ct::batch_mul(points, scalars);
    EXPECT_TRUE(result.is_point_at_infinity().get_value());
    EXPECT_EQ(result.get_origin_tag(), expected_tag);
 
    // Gate count difference due to additional constants added by default in Mega builder
    if constexpr (std::is_same_v<TypeParam, bb::MegaCircuitBuilder>) {
        check_circuit_and_gate_count(builder, 3584); // Mega
    } else {
        check_circuit_and_gate_count(builder, 3587); // Ultra
    }
}
 
TYPED_TEST(CycleGroupTest, TestBatchMulFixedBaseInLookupTable)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    const size_t num_muls = 1;
    // case 5, fixed-base MSM with inputs that are combinations of constant and witnesses (group elements are in
    // lookup table)
    std::vector<cycle_group_ct> points;
    std::vector<typename cycle_group_ct::cycle_scalar> scalars;
    std::vector<typename Group::Fq> scalars_native;
    Element expected = Group::point_at_infinity;
    for (size_t i = 0; i < num_muls; ++i) {
        auto element = plookup::fixed_base::table::lhs_generator_point();
        typename Group::Fr scalar = Group::Fr::random_element(&engine);
 
        // 1: add entry where point is constant, scalar is witness
        expected += (element * scalar);
        points.emplace_back(element);
        scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
        scalars_native.emplace_back(uint256_t(scalar));
 
        // 2: add entry where point is constant, scalar is constant
        element = plookup::fixed_base::table::rhs_generator_point();
        expected += (element * scalar);
        points.emplace_back(element);
        scalars.emplace_back(typename cycle_group_ct::cycle_scalar(scalar));
        scalars_native.emplace_back(uint256_t(scalar));
    }
    const auto expected_tag = assign_and_merge_tags(points, scalars);
    auto result = cycle_group_ct::batch_mul(points, scalars);
    EXPECT_EQ(result.get_value(), AffineElement(expected));
    EXPECT_EQ(result.get_value(), crypto::pedersen_commitment::commit_native(scalars_native));
    EXPECT_EQ(result.get_origin_tag(), expected_tag);
 
    check_circuit_and_gate_count(builder, 2822);
}
 
TYPED_TEST(CycleGroupTest, TestBatchMulFixedBaseSomeInLookupTable)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    const size_t num_muls = 1;
    // case 6, fixed-base MSM with inputs that are combinations of constant and witnesses (some group elements are
    // in lookup table)
    std::vector<cycle_group_ct> points;
    std::vector<typename cycle_group_ct::cycle_scalar> scalars;
    std::vector<typename Group::Fr> scalars_native;
    Element expected = Group::point_at_infinity;
    for (size_t i = 0; i < num_muls; ++i) {
        auto element = plookup::fixed_base::table::lhs_generator_point();
        typename Group::Fr scalar = Group::Fr::random_element(&engine);
 
        // 1: add entry where point is constant, scalar is witness
        expected += (element * scalar);
        points.emplace_back(element);
        scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
        scalars_native.emplace_back(scalar);
 
        // 2: add entry where point is constant, scalar is constant
        element = plookup::fixed_base::table::rhs_generator_point();
        expected += (element * scalar);
        points.emplace_back(element);
        scalars.emplace_back(typename cycle_group_ct::cycle_scalar(scalar));
        scalars_native.emplace_back(scalar);
 
        // 3: add entry where point is constant, scalar is witness
        scalar = Group::Fr::random_element(&engine);
        element = Group::one * Group::Fr::random_element(&engine);
        expected += (element * scalar);
        points.emplace_back(element);
        scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
        scalars_native.emplace_back(scalar);
    }
    const auto expected_tag = assign_and_merge_tags(points, scalars);
    auto result = cycle_group_ct::batch_mul(points, scalars);
    EXPECT_EQ(result.get_value(), AffineElement(expected));
    EXPECT_EQ(result.get_origin_tag(), expected_tag);
 
    // Gate count difference due to additional constants added by default in Mega builder
    if constexpr (std::is_same_v<TypeParam, bb::MegaCircuitBuilder>) {
        check_circuit_and_gate_count(builder, 3395); // Mega
    } else {
        check_circuit_and_gate_count(builder, 3398); // Ultra
    }
}
 
TYPED_TEST(CycleGroupTest, TestBatchMulFixedBaseZeroScalars)
{
    STDLIB_TYPE_ALIASES;
    auto builder = Builder();
 
    const size_t num_muls = 1;
    // case 7, Fixed-base MSM where input scalars are 0
    std::vector<cycle_group_ct> points;
    std::vector<typename cycle_group_ct::cycle_scalar> scalars;
 
    for (size_t i = 0; i < num_muls; ++i) {
        auto element = plookup::fixed_base::table::lhs_generator_point();
        typename Group::Fr scalar = 0;
 
        // 1: add entry where point is constant, scalar is witness
        points.emplace_back((element));
        scalars.emplace_back(cycle_group_ct::cycle_scalar::from_witness(&builder, scalar));
 
        // 2: add entry where point is constant, scalar is constant
        points.emplace_back((element));
        scalars.emplace_back(typename cycle_group_ct::cycle_scalar(scalar));
    }
    const auto expected_tag = assign_and_merge_tags(points, scalars);
    auto result = cycle_group_ct::batch_mul(points, scalars);
    EXPECT_EQ(result.is_point_at_infinity().get_value(), true);
    EXPECT_EQ(result.get_origin_tag(), expected_tag);
 
    check_circuit_and_gate_count(builder, 2837);
}
 
TYPED_TEST(CycleGroupTest, TestMul)
{
    STDLIB_TYPE_ALIASES
    auto builder = Builder();
 
    const size_t num_muls = 5;
 
    // case 1, general MSM with inputs that are combinations of constant and witnesses
    {
        cycle_group_ct point;
        typename cycle_group_ct::cycle_scalar scalar;
        cycle_group_ct result;
        for (size_t i = 0; i < num_muls; ++i) {
            auto element = TestFixture::generators[i];
            typename Group::Fr native_scalar = Group::Fr::random_element(&engine);
            auto expected_result = element * native_scalar;
 
            // 1: perform mul where point, scalar are witnesses
            point = (cycle_group_ct::from_witness(&builder, element));
            scalar = (cycle_group_ct::cycle_scalar::from_witness(&builder, native_scalar));
            point.set_origin_tag(submitted_value_origin_tag);
            scalar.set_origin_tag(challenge_origin_tag);
            result = point * scalar;
            EXPECT_EQ((result).get_value(), (expected_result));
 
            // 2: perform mul where point is constant, scalar is witness
            point = (cycle_group_ct(element));
            scalar = (cycle_group_ct::cycle_scalar::from_witness(&builder, native_scalar));
            result = point * scalar;
            EXPECT_EQ((result).get_value(), (expected_result));
 
            // 3: perform mul where point is witness, scalar is constant
            point = (cycle_group_ct::from_witness(&builder, element));
            scalar = (typename cycle_group_ct::cycle_scalar(native_scalar));
            result = point * scalar;
            EXPECT_EQ((result).get_value(), (expected_result));
 
            // 4: perform mul where point is constant, scalar is constant
            point = (cycle_group_ct(element));
            scalar = (typename cycle_group_ct::cycle_scalar(native_scalar));
            result = point * scalar;
            EXPECT_EQ((result).get_value(), (expected_result));
        }
    }
 
    // Gate count difference due to additional constants added by default in Mega builder
    if constexpr (std::is_same_v<TypeParam, bb::MegaCircuitBuilder>) {
        check_circuit_and_gate_count(builder, 12973); // Mega
    } else {
        check_circuit_and_gate_count(builder, 12976); // Ultra
    }
}
 
TYPED_TEST(CycleGroupTest, TestOne)
{
    STDLIB_TYPE_ALIASES
    Builder builder;
    cycle_group_ct one = cycle_group_ct::one(&builder);
    auto expected_one_native = Group::one;
    auto one_native = one.get_value();
    EXPECT_EQ(one_native.x, expected_one_native.x);
    EXPECT_EQ(one_native.y, expected_one_native.y);
}
 
TYPED_TEST(CycleGroupTest, TestConversionFromBigfield)
{
    STDLIB_TYPE_ALIASES
    using FF = typename Curve::ScalarField;
    using FF_ct = stdlib::bigfield<Builder, typename FF::Params>;
 
    const auto run_test = [](bool construct_witnesses) {
        Builder builder;
        auto elt = FF::random_element(&engine);
        FF_ct big_elt;
        if (construct_witnesses) {
            big_elt = FF_ct::from_witness(&builder, elt);
        } else {
            big_elt = FF_ct(elt);
        }
        big_elt.set_origin_tag(submitted_value_origin_tag);
        cycle_scalar_ct scalar_from_big_elt(big_elt);
        EXPECT_EQ(elt, scalar_from_big_elt.get_value());
        EXPECT_EQ(scalar_from_big_elt.get_origin_tag(), big_elt.get_origin_tag());
        if (construct_witnesses) {
            EXPECT_FALSE(big_elt.is_constant());
            EXPECT_FALSE(scalar_from_big_elt.is_constant());
            check_circuit_and_gate_count(builder, 3523);
        }
    };
    run_test(/*construct_witnesses=*/true);
    run_test(/*construct_witnesses=*/false);
}
 
TYPED_TEST(CycleGroupTest, TestBatchMulIsConsistent)
{
    STDLIB_TYPE_ALIASES
    using FF = typename Curve::ScalarField;
    using FF_ct = stdlib::bigfield<Builder, typename FF::Params>;
 
    const auto run_test = [](bool construct_witnesses) {
        Builder builder;
        auto scalar1 = FF::random_element(&engine);
        auto scalar2 = FF::random_element(&engine);
 
        FF_ct big_scalar1;
        FF_ct big_scalar2;
        if (construct_witnesses) {
            big_scalar1 = FF_ct::from_witness(&builder, scalar1);
            big_scalar2 = FF_ct::from_witness(&builder, scalar2);
        } else {
            big_scalar1 = FF_ct(scalar1);
            big_scalar2 = FF_ct(scalar2);
        }
        cycle_group_ct result1 = cycle_group_ct::batch_mul({ TestFixture::generators[0], TestFixture::generators[1] },
                                                           { big_scalar1, big_scalar2 });
 
        cycle_group_ct result2 =
            cycle_group_ct::batch_mul({ TestFixture::generators[0], TestFixture::generators[1] },
                                      { cycle_scalar_ct(big_scalar1), cycle_scalar_ct(big_scalar2) });
 
        AffineElement result1_native = result1.get_value();
        AffineElement result2_native = result2.get_value();
        EXPECT_EQ(result1_native.x, result2_native.x);
        EXPECT_EQ(result1_native.y, result2_native.y);
        if (construct_witnesses) {
            EXPECT_FALSE(result1.is_constant());
            EXPECT_FALSE(result2.is_constant());
            // Gate count difference due to additional constants added by default in Mega builder
            if constexpr (std::is_same_v<TypeParam, bb::MegaCircuitBuilder>) {
                check_circuit_and_gate_count(builder, 5285); // Mega
            } else {
                check_circuit_and_gate_count(builder, 5288); // Ultra
            }
        }
    };
    run_test(/*construct_witnesses=*/true);
    run_test(/*construct_witnesses=*/false);
}
 
TYPED_TEST(CycleGroupTest, TestFixedBaseBatchMul)
{
    STDLIB_TYPE_ALIASES
    Builder builder;
 
    // Get the fixed base points that have lookup tables
    auto lhs_generator = plookup::fixed_base::table::lhs_generator_point();
    auto rhs_generator = plookup::fixed_base::table::rhs_generator_point();
 
    // Test with two scalars and both generators
    std::vector<cycle_scalar_ct> scalars;
    std::vector<cycle_group_ct> points;
 
    auto scalar1_val = Group::Fr::random_element(&engine);
    auto scalar2_val = Group::Fr::random_element(&engine);
 
    scalars.push_back(cycle_scalar_ct::from_witness(&builder, scalar1_val));
    scalars.push_back(cycle_scalar_ct::from_witness(&builder, scalar2_val));
    points.push_back(cycle_group_ct(lhs_generator)); // constant point
    points.push_back(cycle_group_ct(rhs_generator)); // constant point
 
    auto result = cycle_group_ct::batch_mul(points, scalars);
 
    // Compute expected result natively
    AffineElement expected = lhs_generator * scalar1_val + rhs_generator * scalar2_val;
 
    EXPECT_EQ(result.get_value(), expected);
 
    check_circuit_and_gate_count(builder, 2908);
}
 
TYPED_TEST(CycleGroupTest, TestInfinityChainedOperations)
{
    STDLIB_TYPE_ALIASES
    Builder builder;
 
    // Case 1: (a + infinity) - a = infinity
    {
        auto input = TestFixture::generators[0];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, input);
        cycle_group_ct inf = cycle_group_ct::constant_infinity(&builder);
 
        cycle_group_ct temp = a + inf;
        cycle_group_ct result = temp - a;
 
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        // Note: raw coordinates may not be (0,0) for non-canonical intermediates.
        // Canonicalization happens at observation boundaries (serialize, set_public, ==).
        EXPECT_TRUE(result.get_value().is_point_at_infinity());
    }
 
    // Case 2: a + (b - b) = a
    {
        auto input_a = TestFixture::generators[0];
        auto input_b = TestFixture::generators[1];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, input_a);
        cycle_group_ct b = cycle_group_ct::from_witness(&builder, input_b);
 
        cycle_group_ct zero = b - b; // Should be infinity
        cycle_group_ct result = a + zero;
 
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
        EXPECT_EQ(result.get_value().x, input_a.x);
        EXPECT_EQ(result.get_value().y, input_a.y);
    }
 
    // Case 3: (infinity - infinity) + a = a
    {
        auto input = TestFixture::generators[0];
        cycle_group_ct a = cycle_group_ct::from_witness(&builder, input);
        cycle_group_ct inf1 = cycle_group_ct::constant_infinity(&builder);
        cycle_group_ct inf2 = cycle_group_ct::constant_infinity(&builder);
 
        cycle_group_ct zero = inf1 - inf2;
        cycle_group_ct result = zero + a;
 
        EXPECT_EQ(result.get_value().x, input.x);
        EXPECT_EQ(result.get_value().y, input.y);
    }
 
    EXPECT_FALSE(builder.failed());
    EXPECT_TRUE(CircuitChecker::check(builder));
}
 
TYPED_TEST(CycleGroupTest, TestConditionalAssignWithInfinity)
{
    STDLIB_TYPE_ALIASES
    Builder builder;
 
    auto input = TestFixture::generators[0];
    cycle_group_ct a = cycle_group_ct::from_witness(&builder, input);
    cycle_group_ct inf = cycle_group_ct::constant_infinity(&builder);
 
    // Case 1: Select finite point when predicate is false (returns rhs = a)
    // conditional_assign(pred, lhs, rhs) returns lhs if pred is true, rhs otherwise
    {
        bool_ct pred(witness_ct(&builder, false));
        cycle_group_ct result = cycle_group_ct::conditional_assign(pred, inf, a);
 
        EXPECT_FALSE(result.is_point_at_infinity().get_value());
        EXPECT_EQ(result.get_value().x, input.x);
        EXPECT_EQ(result.get_value().y, input.y);
    }
 
    // Case 2: Select infinity when predicate is true (returns lhs = inf)
    {
        bool_ct pred(witness_ct(&builder, true));
        cycle_group_ct result = cycle_group_ct::conditional_assign(pred, inf, a);
 
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        EXPECT_TRUE(result.x().get_value() == 0);
        EXPECT_TRUE(result.y().get_value() == 0);
    }
 
    // Case 3: Select between two infinity points
    {
        cycle_group_ct inf2 = cycle_group_ct::constant_infinity(&builder);
        bool_ct pred(witness_ct(&builder, true));
        cycle_group_ct result = cycle_group_ct::conditional_assign(pred, inf, inf2);
 
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        EXPECT_TRUE(result.x().get_value() == 0);
        EXPECT_TRUE(result.y().get_value() == 0);
    }
 
    EXPECT_FALSE(builder.failed());
    EXPECT_TRUE(CircuitChecker::check(builder));
}
 
TYPED_TEST(CycleGroupTest, TestWitnessInfinityFromOperations)
{
    STDLIB_TYPE_ALIASES
    Builder builder;
 
    // Create infinity as P - P (witness-based infinity)
    auto input = TestFixture::generators[0];
    cycle_group_ct P = cycle_group_ct::from_witness(&builder, input);
    cycle_group_ct witness_inf = P - P;
 
    EXPECT_TRUE(witness_inf.is_point_at_infinity().get_value());
 
    // Use this witness infinity in operations
    auto input2 = TestFixture::generators[1];
    cycle_group_ct Q = cycle_group_ct::from_witness(&builder, input2);
 
    // Q + witness_inf = Q
    cycle_group_ct result = Q + witness_inf;
    EXPECT_EQ(result.get_value().x, input2.x);
    EXPECT_EQ(result.get_value().y, input2.y);
 
    // witness_inf + Q = Q
    cycle_group_ct result2 = witness_inf + Q;
    EXPECT_EQ(result2.get_value().x, input2.x);
    EXPECT_EQ(result2.get_value().y, input2.y);
 
    EXPECT_FALSE(builder.failed());
    EXPECT_TRUE(CircuitChecker::check(builder));
}
 
TYPED_TEST(CycleGroupTest, TestBatchMulCompleteCancellation)
{
    STDLIB_TYPE_ALIASES
    Builder builder;
 
    // P*a + Q*b + P*(-a) + Q*(-b) = infinity
    auto P_val = TestFixture::generators[0];
    auto Q_val = TestFixture::generators[1];
    auto a = Group::Fr::random_element(&engine);
    auto b = Group::Fr::random_element(&engine);
 
    std::vector<cycle_group_ct> points = {
        cycle_group_ct::from_witness(&builder, P_val),
        cycle_group_ct::from_witness(&builder, Q_val),
        cycle_group_ct::from_witness(&builder, P_val),
        cycle_group_ct::from_witness(&builder, Q_val),
    };
 
    std::vector<cycle_scalar_ct> scalars = {
        cycle_scalar_ct::from_witness(&builder, a),
        cycle_scalar_ct::from_witness(&builder, b),
        cycle_scalar_ct::from_witness(&builder, -a),
        cycle_scalar_ct::from_witness(&builder, -b),
    };
 
    cycle_group_ct result = cycle_group_ct::batch_mul(points, scalars);
 
    EXPECT_TRUE(result.is_point_at_infinity().get_value());
    // Note: raw coordinates may not be (0,0) for non-canonical intermediates.
    EXPECT_TRUE(result.get_value().is_point_at_infinity());
 
    EXPECT_FALSE(builder.failed());
    EXPECT_TRUE(CircuitChecker::check(builder));
}
 
TYPED_TEST(CycleGroupTest, TestInfinityCanonicalRepresentation)
{
    STDLIB_TYPE_ALIASES
    Builder builder;
 
    // Note: For grumpkin, native AffineElement uses x=modulus for infinity, not (0,0)
    // The circuit representation uses (0,0) but get_value() returns native format
 
    // Case 1: constant_infinity is correctly identified
    {
        cycle_group_ct inf = cycle_group_ct::constant_infinity(&builder);
        EXPECT_TRUE(inf.is_point_at_infinity().get_value());
        EXPECT_TRUE(inf.get_value().is_point_at_infinity());
        // Circuit coordinates should be (0, 0)
        EXPECT_EQ(inf.x().get_value(), 0);
        EXPECT_EQ(inf.y().get_value(), 0);
    }
 
    // Case 2: P + (-P) returns infinity
    {
        auto input = TestFixture::generators[0];
        cycle_group_ct P = cycle_group_ct::from_witness(&builder, input);
        cycle_group_ct neg_P = -P;
        cycle_group_ct result = P + neg_P;
 
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        // Note: raw coordinates may not be (0,0) for non-canonical intermediates.
        // Canonicalization happens at observation boundaries (serialize, set_public, ==).
        EXPECT_TRUE(result.get_value().is_point_at_infinity());
    }
 
    // Case 3: 2 * infinity returns infinity
    {
        cycle_group_ct inf = cycle_group_ct::constant_infinity(&builder);
        cycle_group_ct result = inf.dbl();
 
        EXPECT_TRUE(result.is_point_at_infinity().get_value());
        // Note: raw coordinates may not be (0,0) for non-canonical intermediates.
        EXPECT_TRUE(result.get_value().is_point_at_infinity());
    }
 
    EXPECT_FALSE(builder.failed());
    EXPECT_TRUE(CircuitChecker::check(builder));
}
 
TYPED_TEST(CycleGroupTest, TestInfinityAutoDetectionInConstructor)
{
    STDLIB_TYPE_ALIASES
    Builder builder;
 
    // Create element with (0, 0) coordinates - should auto-detect as infinity
    using field_t = stdlib::field_t<Builder>;
    auto x_zero = field_t::from_witness(&builder, typename field_t::native(0));
    auto y_zero = field_t::from_witness(&builder, typename field_t::native(0));
 
    // Use 3-arg constructor which should auto-detect infinity
    cycle_group_ct point(x_zero, y_zero, /*assert_on_curve=*/false);
 
    EXPECT_TRUE(point.is_point_at_infinity().get_value());
 
    EXPECT_FALSE(builder.failed());
    EXPECT_TRUE(CircuitChecker::check(builder));
}
#pragma GCC diagnostic pop