diff --git a/cpp/roaring/roaring64map.hh b/cpp/roaring/roaring64map.hh
index fd82b99b..60de8377 100644
--- a/cpp/roaring/roaring64map.hh
+++ b/cpp/roaring/roaring64map.hh
@@ -879,6 +879,138 @@ class Roaring64Map {
 #endif
     }
 
+    /**
+     * Computes the size of the intersection between two bitmaps.
+     * Throws std::length_error in the special case where the result is 2^64.
+     */
+    uint64_t and_cardinality(const Roaring64Map &r) const {
+        uint64_t card = 0;
+        auto lhs = roarings.cbegin();
+        auto rhs = r.roarings.cbegin();
+        while (lhs != roarings.cend() && rhs != r.roarings.cend()) {
+            if (lhs->first < rhs->first) {
+                ++lhs;
+            } else if (lhs->first > rhs->first) {
+                ++rhs;
+            } else {
+                card = addCardinalities(
+                    card, lhs->second.and_cardinality(rhs->second));
+                ++lhs;
+                ++rhs;
+            }
+        }
+        return card;
+    }
+
+    /**
+     * Check whether the two bitmaps intersect. Stops at the first shared
+     * value rather than computing the whole intersection.
+     */
+    bool intersect(const Roaring64Map &r) const {
+        auto lhs = roarings.cbegin();
+        auto rhs = r.roarings.cbegin();
+        while (lhs != roarings.cend() && rhs != r.roarings.cend()) {
+            if (lhs->first < rhs->first) {
+                ++lhs;
+            } else if (lhs->first > rhs->first) {
+                ++rhs;
+            } else {
+                if (lhs->second.intersect(rhs->second)) {
+                    return true;
+                }
+                ++lhs;
+                ++rhs;
+            }
+        }
+        return false;
+    }
+
+    /**
+     * Computes the size of the union between two bitmaps.
+     * Throws std::length_error in the special case where the result is 2^64.
+     */
+    uint64_t or_cardinality(const Roaring64Map &r) const {
+        uint64_t card = 0;
+        auto lhs = roarings.cbegin();
+        auto rhs = r.roarings.cbegin();
+        while (lhs != roarings.cend() && rhs != r.roarings.cend()) {
+            if (lhs->first < rhs->first) {
+                card = addCardinalities(card, lhs->second.cardinality());
+                ++lhs;
+            } else if (lhs->first > rhs->first) {
+                card = addCardinalities(card, rhs->second.cardinality());
+                ++rhs;
+            } else {
+                card = addCardinalities(
+                    card, lhs->second.or_cardinality(rhs->second));
+                ++lhs;
+                ++rhs;
+            }
+        }
+        for (; lhs != roarings.cend(); ++lhs) {
+            card = addCardinalities(card, lhs->second.cardinality());
+        }
+        for (; rhs != r.roarings.cend(); ++rhs) {
+            card = addCardinalities(card, rhs->second.cardinality());
+        }
+        return card;
+    }
+
+    /**
+     * Computes the size of the symmetric difference between two bitmaps.
+     * Throws std::length_error in the special case where the result is 2^64.
+     */
+    uint64_t xor_cardinality(const Roaring64Map &r) const {
+        uint64_t card = 0;
+        auto lhs = roarings.cbegin();
+        auto rhs = r.roarings.cbegin();
+        while (lhs != roarings.cend() && rhs != r.roarings.cend()) {
+            if (lhs->first < rhs->first) {
+                card = addCardinalities(card, lhs->second.cardinality());
+                ++lhs;
+            } else if (lhs->first > rhs->first) {
+                card = addCardinalities(card, rhs->second.cardinality());
+                ++rhs;
+            } else {
+                card = addCardinalities(
+                    card, lhs->second.xor_cardinality(rhs->second));
+                ++lhs;
+                ++rhs;
+            }
+        }
+        for (; lhs != roarings.cend(); ++lhs) {
+            card = addCardinalities(card, lhs->second.cardinality());
+        }
+        for (; rhs != r.roarings.cend(); ++rhs) {
+            card = addCardinalities(card, rhs->second.cardinality());
+        }
+        return card;
+    }
+
+    /**
+     * Computes the size of the difference (andnot) between two bitmaps.
+     * Throws std::length_error in the special case where the result is 2^64.
+     */
+    uint64_t andnot_cardinality(const Roaring64Map &r) const {
+        uint64_t card = 0;
+        auto lhs = roarings.cbegin();
+        auto rhs = r.roarings.cbegin();
+        while (lhs != roarings.cend()) {
+            if (rhs == r.roarings.cend() || lhs->first < rhs->first) {
+                card = addCardinalities(card, lhs->second.cardinality());
+                ++lhs;
+            } else if (lhs->first > rhs->first) {
+                ++rhs;
+            } else {
+                card = addCardinalities(
+                    card, lhs->second.andnot_cardinality(rhs->second));
+                ++lhs;
+                ++rhs;
+            }
+        }
+        return card;
+    }
+
     /**
      * Returns true if the bitmap is subset of the other.
      */
@@ -1702,6 +1834,28 @@ class Roaring64Map {
     static constexpr uint32_t lowBytes(const uint64_t in) {
         return uint32_t(in);
     }
+    /**
+     * Adds two cardinalities. A 64-bit bitmap can hold 2^64 values, which is
+     * not representable in a uint64_t, so this mirrors what cardinality()
+     * does in that case. Each addend is at most 2^32 and there are at most
+     * 2^32 keys, so the true sum never exceeds 2^64 and a wraparound check is
+     * exact.
+     */
+    static uint64_t addCardinalities(uint64_t lhs, uint64_t rhs) {
+        uint64_t sum = lhs + rhs;
+        if (sum < lhs) {
+#if ROARING_EXCEPTIONS
+            throw std::length_error(
+                "cardinality is 2^64, "
+                "unable to represent in a 64-bit integer");
+#else
+            ROARING_TERMINATE(
+                "cardinality is 2^64, "
+                "unable to represent in a 64-bit integer");
+#endif
+        }
+        return sum;
+    }
     static constexpr uint64_t uniteBytes(const uint32_t highBytes,
                                          const uint32_t lowBytes) {
         return (uint64_t(highBytes) << 32) | uint64_t(lowBytes);
diff --git a/tests/cpp_unit.cpp b/tests/cpp_unit.cpp
index a9592d1a..bb185f3d 100644
--- a/tests/cpp_unit.cpp
+++ b/tests/cpp_unit.cpp
@@ -2110,6 +2110,137 @@ DEFINE_TEST(test_combinatoric_flip_many_64) {
     }
 }
 
+DEFINE_TEST(test_cpp_and_cardinality_64_basic) {
+    Roaring64Map r1, r2;
+    for (uint64_t i = 0; i < 100; ++i) {
+        r1.add(i);
+        r1.add((uint64_t(1) << 32) + i);
+    }
+    for (uint64_t i = 50; i < 150; ++i) {
+        r2.add(i);
+        r2.add((uint64_t(1) << 32) + i);
+    }
+    assert_true(r1.and_cardinality(r2) == 100);
+}
+
+DEFINE_TEST(test_cpp_and_cardinality_64_disjoint_keys) {
+    Roaring64Map r1, r2;
+    r1.add(uint64_t(1));
+    r1.add((uint64_t(2) << 32) + 5);
+    r2.add((uint64_t(7) << 32) + 1);
+    r2.add((uint64_t(9) << 32) + 5);
+    assert_true(r1.and_cardinality(r2) == 0);
+    assert_false(r1.intersect(r2));
+}
+
+DEFINE_TEST(test_cpp_intersect_predicate_64) {
+    Roaring64Map r1, r2, empty;
+    r1.add(uint64_t(1));
+    r1.add((uint64_t(3) << 32) + 8);
+    r2.add((uint64_t(3) << 32) + 8);
+    assert_true(r1.intersect(r2));
+    assert_true(r2.intersect(r1));
+    assert_false(r1.intersect(empty));
+    assert_false(empty.intersect(r1));
+    assert_false(empty.intersect(empty));
+    assert_true(r1.intersect(r1));
+}
+
+DEFINE_TEST(test_cpp_and_cardinality_64_matches_materialized) {
+    Roaring64Map r1, r2;
+    for (uint64_t k = 0; k < 4; ++k) {
+        for (uint64_t i = 0; i < 200; i += 3) {
+            r1.add((k << 32) + i);
+        }
+        for (uint64_t i = 0; i < 200; i += 2) {
+            r2.add(((k + 1) << 32) + i);
+        }
+    }
+    assert_true(r1.and_cardinality(r2) == (r1 & r2).cardinality());
+    assert_true(r1.intersect(r2) == ((r1 & r2).cardinality() > 0));
+}
+
+DEFINE_TEST(test_cpp_or_cardinality_64) {
+    Roaring64Map r1, r2, empty;
+    for (uint64_t i = 0; i < 100; ++i) {
+        r1.add(i);
+        r1.add((uint64_t(2) << 32) + i);
+    }
+    for (uint64_t i = 50; i < 150; ++i) {
+        r2.add(i);
+        r2.add((uint64_t(8) << 32) + i);
+    }
+    assert_true(r1.or_cardinality(r2) == (r1 | r2).cardinality());
+    assert_true(r2.or_cardinality(r1) == (r1 | r2).cardinality());
+    assert_true(r1.or_cardinality(empty) == r1.cardinality());
+    assert_true(empty.or_cardinality(r1) == r1.cardinality());
+    assert_true(r1.or_cardinality(r1) == r1.cardinality());
+}
+
+DEFINE_TEST(test_cpp_xor_cardinality_64) {
+    Roaring64Map r1, r2, empty;
+    for (uint64_t i = 0; i < 100; ++i) {
+        r1.add(i);
+        r1.add((uint64_t(4) << 32) + i);
+    }
+    for (uint64_t i = 50; i < 150; ++i) {
+        r2.add(i);
+        r2.add((uint64_t(6) << 32) + i);
+    }
+    assert_true(r1.xor_cardinality(r2) == (r1 ^ r2).cardinality());
+    assert_true(r2.xor_cardinality(r1) == (r1 ^ r2).cardinality());
+    assert_true(r1.xor_cardinality(empty) == r1.cardinality());
+    assert_true(r1.xor_cardinality(r1) == 0);
+}
+
+DEFINE_TEST(test_cpp_andnot_cardinality_64) {
+    Roaring64Map r1, r2, empty;
+    for (uint64_t i = 0; i < 100; ++i) {
+        r1.add(i);
+        r1.add((uint64_t(3) << 32) + i);
+    }
+    for (uint64_t i = 50; i < 150; ++i) {
+        r2.add(i);
+        r2.add((uint64_t(5) << 32) + i);
+    }
+    // A key held only by r1, so the two differences have distinct sizes and
+    // the asymmetry check below is meaningful.
+    r1.add((uint64_t(9) << 32) + 1);
+    assert_true(r1.andnot_cardinality(r2) == (r1 - r2).cardinality());
+    assert_true(r2.andnot_cardinality(r1) == (r2 - r1).cardinality());
+    assert_true(r1.andnot_cardinality(r2) != r2.andnot_cardinality(r1));
+    assert_true(r1.andnot_cardinality(empty) == r1.cardinality());
+    assert_true(empty.andnot_cardinality(r1) == 0);
+    assert_true(r1.andnot_cardinality(r1) == 0);
+}
+
+DEFINE_TEST(test_cpp_set_cardinality_64_checked) {
+    // The checked wrappers assert against std::set, so simply calling each
+    // method on operands with shared, disjoint and one-sided keys is the test.
+    doublechecked::Roaring64Map r1, r2, empty;
+    for (uint64_t k = 0; k < 3; ++k) {
+        for (uint64_t i = 0; i < 300; i += 7) {
+            r1.add((k << 32) + i);
+        }
+        for (uint64_t i = 0; i < 300; i += 5) {
+            r2.add(((k + 1) << 32) + i);
+        }
+    }
+    r1.add((uint64_t(90) << 32) + 3);
+    r2.add((uint64_t(91) << 32) + 4);
+
+    const doublechecked::Roaring64Map *operands[3] = {&r1, &r2, &empty};
+    for (auto *a : operands) {
+        for (auto *b : operands) {
+            a->and_cardinality(*b);
+            a->intersect(*b);
+            a->or_cardinality(*b);
+            a->xor_cardinality(*b);
+            a->andnot_cardinality(*b);
+        }
+    }
+}
+
 DEFINE_TEST(test_cpp_is_subset_64) {
     Roaring64Map r1 = Roaring64Map::bitmapOf(1, uint64_t(1));
     Roaring64Map r2 = Roaring64Map::bitmapOf(1, uint64_t(1) << 32);
@@ -2398,6 +2529,14 @@ int main() {
         cmocka_unit_test(test_issue304),
         cmocka_unit_test(issue_336),
         cmocka_unit_test(issue_372),
+        cmocka_unit_test(test_cpp_and_cardinality_64_basic),
+        cmocka_unit_test(test_cpp_and_cardinality_64_disjoint_keys),
+        cmocka_unit_test(test_cpp_intersect_predicate_64),
+        cmocka_unit_test(test_cpp_and_cardinality_64_matches_materialized),
+        cmocka_unit_test(test_cpp_or_cardinality_64),
+        cmocka_unit_test(test_cpp_xor_cardinality_64),
+        cmocka_unit_test(test_cpp_andnot_cardinality_64),
+        cmocka_unit_test(test_cpp_set_cardinality_64_checked),
         cmocka_unit_test(test_cpp_is_subset_64),
         cmocka_unit_test(test_cpp_fast_union_64),
         cmocka_unit_test(test_cpp_to_string),
diff --git a/tests/roaring64map_checked.hh b/tests/roaring64map_checked.hh
index 0f7e0bb4..4dfd0c16 100644
--- a/tests/roaring64map_checked.hh
+++ b/tests/roaring64map_checked.hh
@@ -29,11 +29,13 @@
 #define INCLUDE_ROARING_64_MAP_CHECKED_HH_
 
 #include <algorithm>
+#include <iterator>
 #include <new>
 #include <set>  // sorted set, typically a red-black tree implementation
 #include <stdarg.h>
 #include <stdexcept>
 #include <string>
+#include <vector>
 
 #include "test.h"
 
@@ -415,6 +417,52 @@ class Roaring64Map {
         return ans;
     }
 
+    uint64_t and_cardinality(const Roaring64Map &r) const {
+        uint64_t ans = plain.and_cardinality(r.plain);
+        std::vector<uint64_t> expected;
+        std::set_intersection(check.begin(), check.end(), r.check.begin(),
+                              r.check.end(), std::back_inserter(expected));
+        assert_true(ans == expected.size());
+        return ans;
+    }
+
+    bool intersect(const Roaring64Map &r) const {
+        bool ans = plain.intersect(r.plain);
+        std::vector<uint64_t> expected;
+        std::set_intersection(check.begin(), check.end(), r.check.begin(),
+                              r.check.end(), std::back_inserter(expected));
+        assert_true(ans == !expected.empty());
+        return ans;
+    }
+
+    uint64_t or_cardinality(const Roaring64Map &r) const {
+        uint64_t ans = plain.or_cardinality(r.plain);
+        std::vector<uint64_t> expected;
+        std::set_union(check.begin(), check.end(), r.check.begin(),
+                       r.check.end(), std::back_inserter(expected));
+        assert_true(ans == expected.size());
+        return ans;
+    }
+
+    uint64_t xor_cardinality(const Roaring64Map &r) const {
+        uint64_t ans = plain.xor_cardinality(r.plain);
+        std::vector<uint64_t> expected;
+        std::set_symmetric_difference(check.begin(), check.end(),
+                                      r.check.begin(), r.check.end(),
+                                      std::back_inserter(expected));
+        assert_true(ans == expected.size());
+        return ans;
+    }
+
+    uint64_t andnot_cardinality(const Roaring64Map &r) const {
+        uint64_t ans = plain.andnot_cardinality(r.plain);
+        std::vector<uint64_t> expected;
+        std::set_difference(check.begin(), check.end(), r.check.begin(),
+                            r.check.end(), std::back_inserter(expected));
+        assert_true(ans == expected.size());
+        return ans;
+    }
+
     bool isStrictSubset(
         const Roaring64Map &r) const {  // is `this` subset of `r`?
         bool ans = plain.isStrictSubset(r.plain);