diff --git a/string/test-memcpy.c b/string/test-memcpy.c
index c9dfc88fed..705d79ba13 100644
--- a/string/test-memcpy.c
+++ b/string/test-memcpy.c
@@ -79,7 +79,7 @@ do_one_test (impl_t *impl, char *dst, const char *src,
 static void
 do_test (size_t align1, size_t align2, size_t len)
 {
-  size_t i, j;
+  size_t i, j, repeats;
   char *s1, *s2;
 
   align1 &= 4095;
@@ -92,12 +92,14 @@ do_test (size_t align1, size_t align2, size_t len)
 
   s1 = (char *) (buf1 + align1);
   s2 = (char *) (buf2 + align2);
+  for (repeats = 0; repeats < 2; ++repeats)
+    {
+      for (i = 0, j = 1; i < len; i++, j += 23)
+        s1[i] = j;
 
-  for (i = 0, j = 1; i < len; i++, j += 23)
-    s1[i] = j;
-
-  FOR_EACH_IMPL (impl, 0)
-    do_one_test (impl, s2, s1, len);
+      FOR_EACH_IMPL (impl, 0)
+        do_one_test (impl, s2, s1, len);
+    }
 }
 
 static void
@@ -213,56 +215,88 @@ do_random_tests (void)
 }
 
 static void
-do_test1 (size_t size)
+do_test1 (size_t align1, size_t align2, size_t size)
 {
   void *large_buf;
-  large_buf = mmap (NULL, size * 2 + page_size, PROT_READ | PROT_WRITE,
-		    MAP_PRIVATE | MAP_ANON, -1, 0);
+  size_t mmap_size, region_size;
+
+  align1 &= (page_size - 1);
+  if (align1 == 0)
+    align1 = page_size;
+
+  align2 &= (page_size - 1);
+  if (align2 == 0)
+    align2 = page_size;
+
+  region_size = (size + page_size - 1) & (~(page_size - 1));
+
+  mmap_size = region_size * 2 + 3 * page_size;
+  large_buf = mmap(NULL, mmap_size, PROT_READ | PROT_WRITE,
+                   MAP_PRIVATE | MAP_ANON, -1, 0);
   if (large_buf == MAP_FAILED)
     {
-      puts ("Failed to allocat large_buf, skipping do_test1");
+      puts ("Failed to allocate large_buf, skipping do_test1");
       return;
     }
-
-  if (mprotect (large_buf + size, page_size, PROT_NONE))
+  if (mprotect (large_buf + region_size + page_size, page_size, PROT_NONE))
     error (EXIT_FAILURE, errno, "mprotect failed");
 
-  size_t arrary_size = size / sizeof (uint32_t);
-  uint32_t *dest = large_buf;
-  uint32_t *src = large_buf + size + page_size;
+  size_t array_size = size / sizeof (uint32_t);
+  uint32_t *dest = large_buf + align1;
+  uint32_t *src = large_buf + region_size + 2 * page_size + align2;
   size_t i;
   size_t repeats;
   for(repeats = 0; repeats < 2; repeats++)
     {
-      for (i = 0; i < arrary_size; i++)
+      for (i = 0; i < array_size; i++)
         src[i] = (uint32_t) i;
-
       FOR_EACH_IMPL (impl, 0)
         {
-            printf ("\t\tRunning: %s\n", impl->name);
+            //            printf ("\t\tRunning: %s\n", impl->name);
           memset (dest, -1, size);
           CALL (impl, (char *) dest, (char *) src, size);
-          for (i = 0; i < arrary_size; i++)
+          for (i = 0; i < array_size; i++)
         if (dest[i] != src[i])
           {
             error (0, 0,
                "Wrong result in function %s dst \"%p\" src \"%p\" offset \"%zd\"",
                impl->name, dest, src, i);
             ret = 1;
-            munmap ((void *) large_buf, size * 2 + page_size);
+            munmap ((void *) large_buf, mmap_size);
             return;
           }
         }
-      dest = src;
-      src = large_buf;
+      dest = large_buf + region_size + 2 * page_size + align1;
+      src = large_buf + align2;
+    }
+  munmap ((void *) large_buf, mmap_size);
+}
+
+static void
+do_random_large_tests (void)
+{
+  size_t i, align1, align2, size;
+  for (i = 0; i < 32; ++i)
+    {
+      align1 = random ();
+      align2 = random ();
+      size = (random() % 0x1000000) + 0x200000;
+      do_test1 (align1, align2, size);
+    }
+
+  for (i = 0; i < 128; ++i)
+    {
+      align1 = random ();
+      align2 = random ();
+      size = (random() % 32768) + 4096;
+      do_test1 (align1, align2, size);
     }
-  munmap ((void *) large_buf, size * 2 + page_size);
 }
 
 int
 test_main (void)
 {
-  size_t i;
+  size_t i, j;
 
   test_init ();
 
@@ -299,6 +333,7 @@ test_main (void)
   for (i = 19; i <= 25; ++i)
     {
       do_test (255, 0, 1 << i);
+      do_test (0, 4000, 1 << i);
       do_test (0, 255, i);
       do_test (0, 4000, i);
     }
@@ -307,8 +342,46 @@ test_main (void)
 
   do_random_tests ();
 
-  do_test1 (0x100000);
-  do_test1 (0x2000000);
+  do_test1 (0, 0, 0x100000);
+  do_test1 (0, 0, 0x2000000);
+
+  for (i = 4096; i < 32768; i += 4096)
+    {
+      for (j = 1; j <= 1024; j <<= 1)
+        {
+          do_test1 (0, j, i);
+          do_test1 (4095, j, i);
+          do_test1 (4096 - j, 0, i);
+
+          do_test1 (0, j - 1, i);
+          do_test1 (4095, j - 1, i);
+          do_test1 (4096 - j - 1, 0, i);
+
+          do_test1 (0, j + 1, i);
+          do_test1 (4095, j + 1, i);
+          do_test1 (4096 - j, 1, i);
+        }
+    }
+
+  for (i = 0x300000; i < 0x2000000; i += 0x235689)
+    {
+      for (j = 64; j <= 1024; j <<= 1)
+        {
+          do_test1 (0, j, i);
+          do_test1 (4095, j, i);
+          do_test1 (4096 - j, 0, i);
+
+          do_test1 (0, j - 1, i);
+          do_test1 (4095, j - 1, i);
+          do_test1 (4096 - j - 1, 0, i);
+
+          do_test1 (0, j + 1, i);
+          do_test1 (4095, j + 1, i);
+          do_test1 (4096 - j, 1, i);
+        }
+    }
+
+  do_random_large_tests ();
   return ret;
 }
 
diff --git a/string/test-memmove.c b/string/test-memmove.c
index 670094c9dc..5ba79acf61 100644
--- a/string/test-memmove.c
+++ b/string/test-memmove.c
@@ -101,11 +101,11 @@ do_test (size_t align1, size_t align2, size_t len)
   size_t i, j;
   char *s1, *s2;
 
-  align1 &= 63;
+  align1 &= (getpagesize() - 1);
   if (align1 + len >= page_size)
     return;
 
-  align2 &= 63;
+  align2 &= (getpagesize() - 1);
   if (align2 + len >= page_size)
     return;
 
@@ -356,6 +356,51 @@ do_test3 (size_t bytes_move, size_t offset)
   munmap ((void *) buf, size);
 }
 
+static void
+do_test4 (size_t bytes_move, size_t offset1, size_t offset2)
+{
+  size_t size, repeats, i;
+  uint8_t *buf, *dst, *src;
+
+  size = bytes_move + MAX(offset1, offset2);
+  buf  = mmap(NULL, size, PROT_READ | PROT_WRITE,
+             MAP_PRIVATE | MAP_ANON, -1, 0);
+
+  if (buf == MAP_FAILED)
+    error (EXIT_UNSUPPORTED, errno, "mmap failed");
+
+  dst = &buf[offset1];
+  src = &buf[offset2];
+  for (repeats = 0; repeats < 2; ++repeats)
+    {
+      FOR_EACH_IMPL (impl, 0)
+        {
+          for (i = 0; i < bytes_move; i++)
+              src[i] = (uint8_t) i;
+#ifdef TEST_BCOPY
+          CALL (impl, (char *) src, (char *) dst, bytes_move);
+#else
+          CALL (impl, (char *) dst, (char *) src, bytes_move);
+#endif
+          for (i = 0; i < bytes_move; i++)
+            {
+              if (dst[i] != (uint8_t) i)
+                {
+                  error (0, 0,
+                         "Wrong result in function %s dst \"%p\" src \"%p\" offset \"%zd\"",
+                         impl->name, dst, buf, i);
+                  ret = 1;
+                  break;
+                }
+            }
+        }
+      dst = &buf[offset2];
+      src = &buf[offset1];
+    }
+  munmap ((void *) buf, size);
+}
+
+
 int
 test_main (void)
 {
@@ -396,13 +441,37 @@ test_main (void)
 
   do_random_tests ();
 
+  do_test2 (0);
   do_test2 (33);
   do_test2 (0x200000);
+  do_test2 (0x200000 - 1);
+  do_test2 (0x200000 + 1);
+  do_test2 (0x1000000 + 1);
   do_test2 (0x4000000 - 1);
   do_test2 (0x4000000);
 
+
   /* Copy 16KB data.  */
   do_test3 (16384, 3);
+  for (i = 4096; i <= 16384; i <<= 1)
+    {
+      do_test4 (i, 0, i);
+      do_test4 (i, 0, i - 1);
+      do_test4 (i, 0, i + 1);      
+      do_test4 (i, 63, i + 63);
+      do_test4 (i, 63, i + 64);
+      do_test4 (i, 63, i);
+
+      do_test4 (i, 0, 1);
+      do_test4 (i, 0, 15);
+      do_test4 (i, 0, 31);
+      do_test4 (i, 0, 63);
+      do_test4 (i, 0, 64);
+      do_test4 (i, 0, 65);
+      do_test4 (i, 0, 127);
+      do_test4 (i, 0, 129);
+    }
+
 
   return ret;
 }
