diff --git a/faiss/utils/hamming.cpp b/faiss/utils/hamming.cpp
index 402f1f117c..1ebc70dbca 100644
--- a/faiss/utils/hamming.cpp
+++ b/faiss/utils/hamming.cpp
@@ -24,7 +24,6 @@
 #include <faiss/utils/hamming.h>
 
 #include <algorithm>
-#include <cmath>
 #include <cstdio>
 #include <memory>
 #include <vector>
diff --git a/faiss/utils/hamming_distance/neon-inl.h b/faiss/utils/hamming_distance/neon-inl.h
index fa06b2c6b5..d00a402857 100644
--- a/faiss/utils/hamming_distance/neon-inl.h
+++ b/faiss/utils/hamming_distance/neon-inl.h
@@ -98,9 +98,9 @@ inline hamdis_t hamming<256>(const uint64_t* pa, const uint64_t* pb) {
 
 /* Hamming distances for multiple of 64 bits */
 inline hamdis_t hamming(const uint64_t* pa, const uint64_t* pb, size_t nwords) {
-    const size_t nwords256 = nwords / 256;
-    const size_t nwords128 = (nwords - nwords256 * 256) / 128;
-    const size_t nwords64 = (nwords - nwords256 * 256 - nwords128 * 128) / 64;
+    const size_t nwords256 = nwords / 4;
+    const size_t nwords128 = (nwords % 4) / 2;
+    const size_t nwords64 = nwords % 2;
 
     hamdis_t h = 0;
     if (nwords256 > 0) {
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 63c1729d16..2c97118ef8 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -35,6 +35,7 @@ set(FAISS_TEST_SRC
   test_common_ivf_empty_index.cpp
   test_callback.cpp
   test_utils.cpp
+  test_hamming.cpp
 )
 
 add_executable(faiss_test ${FAISS_TEST_SRC})
diff --git a/tests/test_hamming.cpp b/tests/test_hamming.cpp
new file mode 100644
index 0000000000..ff036701da
--- /dev/null
+++ b/tests/test_hamming.cpp
@@ -0,0 +1,295 @@
+/*
+ * Copyright (c) Meta Platforms, Inc. and affiliates.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+#include <gtest/gtest.h>
+
+#include <faiss/impl/FaissAssert.h>
+#include <faiss/utils/hamming.h>
+#include <random>
+
+using namespace ::testing;
+
+template <typename T>
+std::string print_data(
+        std::shared_ptr<std::vector<T>> data,
+        const size_t divider) {
+    std::string ret = "";
+    for (int i = 0; i < data->size(); ++i) {
+        if (i % divider) {
+            ret += " ";
+        } else {
+            ret += "|";
+        }
+        ret += std::to_string((*data)[i]);
+    }
+    ret += "|";
+    return ret;
+}
+
+std::stringstream get_correct_hamming_example(
+        const size_t na, // number of queries
+        const size_t nb, // number of candidates
+        const size_t k,
+        const size_t code_size,
+        std::shared_ptr<std::vector<uint8_t>> a,
+        std::shared_ptr<std::vector<uint8_t>> b,
+        std::shared_ptr<std::vector<long>> true_ids,
+        std::shared_ptr<std::vector<int>> true_distances) {
+    assert(nb > k);
+
+    // Initialization
+    std::default_random_engine rng(123);
+    std::uniform_int_distribution<int32_t> uniform(0, nb - 1);
+
+    const size_t nresults = na * k;
+
+    a->clear();
+    a->resize(na * code_size, 1); // query vectors are all 1
+    b->clear();
+    b->resize(nb * code_size, 2); // database vectors are all 2
+
+    true_ids->clear();
+    true_ids->reserve(nresults);
+    true_distances->clear();
+    true_distances->reserve(nresults);
+
+    // define correct ids (must be unique)
+    std::set<long> correct_ids;
+    do {
+        correct_ids.insert(uniform(rng));
+    } while (correct_ids.size() < k);
+
+    // replace database vector at id with vector more similar to query
+    // ordered, so earlier ids must be more similar
+    for (size_t nmatches = k; nmatches > 0; --nmatches) {
+        // get id and erase it
+        const size_t id = *correct_ids.begin();
+        *correct_ids.erase(correct_ids.begin());
+
+        // assemble true id and distance at locations
+        true_ids->push_back(id);
+        true_distances->push_back(code_size - nmatches); // hamming dist
+        for (size_t i = 0; i < nmatches; ++i) {
+            b->begin()[id * code_size + i] = 1;
+        }
+    }
+
+    // true_ids and true_distances only contain results for the first query
+    // each query is identical, so copy the first query na-1 times
+    for (size_t i = 1; i < na; ++i) {
+        true_ids->insert(
+                true_ids->end(), true_ids->begin(), true_ids->begin() + k);
+        true_distances->insert(
+                true_distances->end(),
+                true_distances->begin(),
+                true_distances->begin() + k);
+    }
+
+    // assemble string for debugging
+    std::stringstream ret;
+    ret << "na: " << na << std::endl
+        << "nb: " << nb << std::endl
+        << "k: " << k << std::endl
+        << "code_size: " << code_size << std::endl
+        << "a: " << print_data(a, code_size) << std::endl
+        << "b: " << print_data(b, code_size) << std::endl
+        << "true_ids: " << print_data(true_ids, k) << std::endl
+        << "true_distances: " << print_data(true_distances, k) << std::endl;
+    return ret;
+}
+
+TEST(TestHamming, test_crosshamming_count_thres) {
+    // Initialize randomizer
+    std::default_random_engine rng(123);
+    std::uniform_int_distribution<int32_t> uniform(0, 255);
+
+    // Initialize inputs
+    const size_t n = 10; // number of codes
+    const hamdis_t hamming_threshold = 20;
+
+    // one for each case - 65 is default
+    for (auto ncodes : {8, 16, 32, 64, 65}) {
+        // initialize inputs
+        const int nbits = ncodes * 8;
+        const size_t nwords = nbits / 64;
+        // 8 to for later conversion to uint64_t, and 2 for buffer
+        std::vector<uint8_t> dbs(nwords * n * 8 * 2);
+        for (int i = 0; i < dbs.size(); ++i) {
+            dbs[i] = uniform(rng);
+        }
+
+        // get true distance
+        size_t true_count = 0;
+        uint64_t* bs1 = (uint64_t*)dbs.data();
+        for (int i = 0; i < n; ++i) {
+            uint64_t* bs2 = bs1 + 2;
+            for (int j = i + 1; j < n; ++j) {
+                if (faiss::hamming(bs1 + i * nwords, bs2 + j * nwords, nwords) <
+                    hamming_threshold) {
+                    ++true_count;
+                }
+            }
+        }
+
+        // run test and check correctness
+        size_t count;
+        if (ncodes == 65) {
+            ASSERT_THROW(
+                    faiss::crosshamming_count_thres(
+                            dbs.data(), n, hamming_threshold, ncodes, &count),
+                    faiss::FaissException);
+            continue;
+        }
+        faiss::crosshamming_count_thres(
+                dbs.data(), n, hamming_threshold, ncodes, &count);
+
+        ASSERT_EQ(count, true_count) << "ncodes = " << ncodes;
+    }
+}
+TEST(TestHamming, test_hamming_thres) {
+    // Initialize randomizer
+    std::default_random_engine rng(123);
+    std::uniform_int_distribution<int32_t> uniform(0, 255);
+
+    // Initialize inputs
+    const size_t n1 = 10;
+    const size_t n2 = 15;
+    const hamdis_t hamming_threshold = 100;
+
+    // one for each case - 65 is default
+    for (auto ncodes : {8, 16, 32, 64, 65}) {
+        // initialize inputs
+        const int nbits = ncodes * 8;
+        const size_t nwords = nbits / 64;
+        std::vector<uint8_t> bs1(nwords * n1 * 8);
+        std::vector<uint8_t> bs2(nwords * n2 * 8);
+        for (int i = 0; i < bs1.size(); ++i) {
+            bs1[i] = uniform(rng);
+        }
+        for (int i = 0; i < bs2.size(); ++i) {
+            bs2[i] = uniform(rng);
+        }
+
+        // get true distance
+        size_t true_count = 0;
+        std::vector<int64_t> true_idx;
+        std::vector<hamdis_t> true_dis;
+
+        uint64_t* bs1_64 = (uint64_t*)bs1.data();
+        uint64_t* bs2_64 = (uint64_t*)bs2.data();
+        for (int i = 0; i < n1; ++i) {
+            for (int j = 0; j < n2; ++j) {
+                hamdis_t ham_dist = faiss::hamming(
+                        bs1_64 + i * nwords, bs2_64 + j * nwords, nwords);
+                if (ham_dist < hamming_threshold) {
+                    ++true_count;
+                    true_idx.push_back(i);
+                    true_idx.push_back(j);
+                    true_dis.push_back(ham_dist);
+                }
+            }
+        }
+
+        // run test and check correctness for both
+        // match_hamming_thres and hamming_count_thres
+        std::vector<int64_t> idx(true_idx.size());
+        std::vector<hamdis_t> dis(true_dis.size());
+        if (ncodes == 65) {
+            ASSERT_THROW(
+                    faiss::match_hamming_thres(
+                            bs1.data(),
+                            bs2.data(),
+                            n1,
+                            n2,
+                            hamming_threshold,
+                            ncodes,
+                            idx.data(),
+                            dis.data()),
+                    faiss::FaissException);
+            ASSERT_THROW(
+                    faiss::hamming_count_thres(
+                            bs1.data(),
+                            bs2.data(),
+                            n1,
+                            n2,
+                            hamming_threshold,
+                            ncodes,
+                            nullptr),
+                    faiss::FaissException);
+            continue;
+        }
+        size_t match_count = faiss::match_hamming_thres(
+                bs1.data(),
+                bs2.data(),
+                n1,
+                n2,
+                hamming_threshold,
+                ncodes,
+                idx.data(),
+                dis.data());
+        size_t count_count;
+        faiss::hamming_count_thres(
+                bs1.data(),
+                bs2.data(),
+                n1,
+                n2,
+                hamming_threshold,
+                ncodes,
+                &count_count);
+
+        ASSERT_EQ(match_count, true_count) << "ncodes = " << ncodes;
+        ASSERT_EQ(count_count, true_count) << "ncodes = " << ncodes;
+        ASSERT_EQ(idx, true_idx) << "ncodes = " << ncodes;
+        ASSERT_EQ(dis, true_dis) << "ncodes = " << ncodes;
+    }
+}
+
+TEST(TestHamming, test_hamming_knn) {
+    // Initialize randomizer
+    std::default_random_engine rng(123);
+    std::uniform_int_distribution<int32_t> uniform(0, 32);
+
+    // Initialize inputs
+    const size_t na = 4;
+    const size_t nb = 12; // number of candidates
+    const size_t k = 6;
+
+    auto a = std::make_shared<std::vector<uint8_t>>();
+    auto b = std::make_shared<std::vector<uint8_t>>();
+    auto true_ids = std::make_shared<std::vector<long>>();
+    auto true_distances = std::make_shared<std::vector<int>>();
+
+    // 8, 16, 32 are cases - 24 will hit default case
+    // all should be multiples of 8
+    for (auto code_size : {8, 16, 24, 32}) {
+        // get example
+        std::stringstream assert_str = get_correct_hamming_example(
+                na, nb, k, code_size, a, b, true_ids, true_distances);
+
+        // run test on generalized_hammings_knn_hc
+        std::vector<long> ids_gen(na * k);
+        std::vector<int> dist_gen(na * k);
+        faiss::int_maxheap_array_t res = {
+                na, k, ids_gen.data(), dist_gen.data()};
+        faiss::generalized_hammings_knn_hc(
+                &res, a->data(), b->data(), nb, code_size, true);
+        ASSERT_EQ(ids_gen, *true_ids) << assert_str.str();
+        ASSERT_EQ(dist_gen, *true_distances) << assert_str.str();
+
+        // run test on hammings_knn
+        std::vector<long> ids_ham_knn(na * k, 0);
+        std::vector<int> dist_ham_knn(na * k, 0);
+        res = {na, k, ids_ham_knn.data(), dist_ham_knn.data()};
+        faiss::hammings_knn(&res, a->data(), b->data(), nb, code_size, true);
+        ASSERT_EQ(ids_ham_knn, *true_ids) << assert_str.str();
+        // hammings_knn results in twice the distance for some reason :/
+        for (int i = 0; i < dist_ham_knn.size(); ++i) {
+            dist_ham_knn[i] /= 2;
+        }
+        ASSERT_EQ(dist_ham_knn, *true_distances) << assert_str.str();
+    }
+}