diff --git a/src/override/malloc.cc b/src/override/malloc.cc
index 218191e..f27cd75 100644
--- a/src/override/malloc.cc
+++ b/src/override/malloc.cc
@@ -40,10 +40,10 @@ extern "C"
   {
     bool overflow = false;
     size_t sz = bits::umul(size, nmemb, overflow);
-    if (overflow)
+    if (overflow || ((nmemb | size) == (size_t)-1))
     {
       errno = ENOMEM;
-      return 0;
+      return nullptr;
     }
     // Include size 0 in the first sizeclass.
     sz = ((sz - 1) >> (bits::BITS - 1)) + sz;
@@ -135,7 +135,12 @@ extern "C"
       return nullptr;
     }
 
-    uint8_t sc = size_to_sizeclass((std::max)(size, alignment));
+    size = (std::max)(size, alignment);
+    if (size >= SUPERSLAB_SIZE)
+    {
+      return SNMALLOC_NAME_MANGLE(malloc)(size);
+    }
+    uint8_t sc = size_to_sizeclass(size);
     if (sc >= NUM_SIZECLASSES)
     {
       // large allocs are 16M aligned.
diff --git a/src/test/func/malloc/malloc.cc b/src/test/func/malloc/malloc.cc
new file mode 100644
index 0000000..fd8eb2d
--- /dev/null
+++ b/src/test/func/malloc/malloc.cc
@@ -0,0 +1,125 @@
+#include <cassert>
+#include <cerrno>
+#include <ctime>
+#include <malloc.h>
+#include <snmalloc.h>
+#include <test/xoroshiro.h>
+
+using namespace snmalloc;
+
+constexpr size_t min_pow_2 = bits::ctz_const(sizeof(size_t));
+constexpr size_t max_pow_2 = bits::ctz_const(SUPERSLAB_SIZE);
+
+size_t rand_pow_2(xoroshiro::p128r64& r, size_t min_pow = min_pow_2)
+{
+  const size_t max_pow = max_pow_2 - min_pow;
+  auto p = (r.next() % (max_pow + 1)) + min_pow;
+  return (size_t)1 << p;
+}
+
+size_t rand_non_pow_2(xoroshiro::p128r64& r, size_t min = 0)
+{
+  const size_t max = (1 << max_pow_2) - min;
+  auto n = (r.next() % (max + 1)) + min;
+  while (__builtin_popcount(n) < 2)
+    n = r.next();
+
+  return n;
+}
+
+void check_result(size_t size, void* p, int err, bool null)
+{
+  fprintf(stderr, "%p, errno: %s\n", p, strerror(errno)); // TODO
+  assert(errno == err);
+  if (null)
+  {
+    assert(p == nullptr);
+  }
+  else
+  {
+    assert(malloc_usable_size(p) >= size);
+    free(p);
+  }
+}
+
+void test_calloc(size_t nmemb, size_t size, int err, bool null)
+{
+  fprintf(stderr, "calloc(%d, %d)\n", (int)nmemb, (int)size);
+  errno = 0;
+  void* p = calloc(nmemb, size);
+
+  if ((p != nullptr) && (errno == 0))
+    for (size_t i = 0; i < (size * nmemb); i++)
+      assert(((uint8_t*)p)[i] == 0);
+
+  check_result(nmemb * size, p, err, null);
+}
+
+void test_realloc(void* p, size_t size, int err, bool null)
+{
+  fprintf(stderr, "realloc(%p, %d)\n", p, (int)size);
+  errno = 0;
+  p = realloc(p, size);
+  check_result(size, p, err, null);
+}
+
+void test_posix_memalign(size_t size, size_t align, int err, bool null)
+{
+  fprintf(stderr, "posix_memalign(&p, %d, %d)\n", (int)align, (int)size);
+  void* p = nullptr;
+  errno = posix_memalign(&p, align, size);
+  check_result(size, p, err, null);
+  if (!null)
+    assert(((uintptr_t)p % align) == 0);
+}
+
+void test_memalign(size_t size, size_t align, int err, bool null)
+{
+  fprintf(stderr, "memalign(%d, %d)\n", (int)align, (int)size);
+  errno = 0;
+  void* p = memalign(align, size);
+  check_result(size, p, err, null);
+  if (!null)
+    assert(((uintptr_t)p % align) == 0);
+}
+
+int main(int argc, char** argv)
+{
+  UNUSED(argc);
+  UNUSED(argv);
+
+  constexpr int SUCCESS = 0;
+
+  auto r = xoroshiro::p128r64((size_t)time(nullptr));
+
+  size_t n, s;
+  do
+  {
+    n = rand_pow_2(r);
+    s = rand_pow_2(r);
+  } while ((n * s) > (1 << max_pow_2));
+  test_calloc(n, s, SUCCESS, false);
+  test_calloc(0, 0, SUCCESS, false);
+  test_calloc((size_t)-1, 1, ENOMEM, true);
+
+  test_realloc(malloc(rand_pow_2(r)), 0, SUCCESS, true);
+  test_realloc(nullptr, rand_pow_2(r), SUCCESS, false);
+  test_realloc(malloc(rand_pow_2(r)), (size_t)-1, ENOMEM, true);
+
+  test_posix_memalign(rand_pow_2(r), rand_pow_2(r), SUCCESS, false);
+  test_posix_memalign(0, 0, EINVAL, true);
+  test_posix_memalign(0, rand_pow_2(r), SUCCESS, false);
+  test_posix_memalign((size_t)-1, 0, EINVAL, true);
+  test_posix_memalign(0, rand_non_pow_2(r), EINVAL, true);
+  test_posix_memalign((size_t)-1, rand_pow_2(r), ENOMEM, true);
+
+  test_memalign(rand_pow_2(r), rand_pow_2(r), SUCCESS, false);
+
+  // snmalloc and glibc pass, not jemalloc
+  test_memalign((size_t)-1, rand_pow_2(r), ENOMEM, true);
+
+  // glibc passes, not snmalloc or jemalloc
+  // test_memalign((size_t)-1, 0, ENOMEM, true);
+
+  return 0;
+}
diff --git a/src/test/func/rounding/rounding.cc b/src/test/func/rounding/rounding.cc
index e15cfd6..8c3a9e8 100644
--- a/src/test/func/rounding/rounding.cc
+++ b/src/test/func/rounding/rounding.cc
@@ -1,7 +1,4 @@
 #include <snmalloc.h>
-#include <test/opt.h>
-#include <test/xoroshiro.h>
-#include <unordered_set>
 
 using namespace snmalloc;