diff --git a/Lib/test/test_largefile.py b/Lib/test/test_largefile.py
new file mode 100644
index 0000000000..3c11c59bae
--- /dev/null
+++ b/Lib/test/test_largefile.py
@@ -0,0 +1,292 @@
+"""Test largefile support on system where this makes sense.
+"""
+
+import os
+import stat
+import sys
+import unittest
+import socket
+import shutil
+import threading
+from test.support import requires, bigmemtest
+from test.support import SHORT_TIMEOUT
+from test.support import socket_helper
+from test.support.os_helper import TESTFN, unlink
+import io  # C implementation of io
+import _pyio as pyio # Python implementation of io
+
+# size of file to create (>2 GiB; 2 GiB == 2,147,483,648 bytes)
+size = 2_500_000_000
+TESTFN2 = TESTFN + '2'
+
+
+class LargeFileTest:
+
+    def setUp(self):
+        if os.path.exists(TESTFN):
+            mode = 'r+b'
+        else:
+            mode = 'w+b'
+
+        with self.open(TESTFN, mode) as f:
+            current_size = os.fstat(f.fileno())[stat.ST_SIZE]
+            if current_size == size+1:
+                return
+
+            if current_size == 0:
+                f.write(b'z')
+
+            f.seek(0)
+            f.seek(size)
+            f.write(b'a')
+            f.flush()
+            self.assertEqual(os.fstat(f.fileno())[stat.ST_SIZE], size+1)
+
+    @classmethod
+    def tearDownClass(cls):
+        with cls.open(TESTFN, 'wb'):
+            pass
+        if not os.stat(TESTFN)[stat.ST_SIZE] == 0:
+            raise cls.failureException('File was not truncated by opening '
+                                       'with mode "wb"')
+        unlink(TESTFN2)
+
+
+class TestFileMethods(LargeFileTest):
+    """Test that each file function works as expected for large
+    (i.e. > 2 GiB) files.
+    """
+
+    # _pyio.FileIO.readall() uses a temporary bytearray then casted to bytes,
+    # so memuse=2 is needed
+    @bigmemtest(size=size, memuse=2, dry_run=False)
+    def test_large_read(self, _size):
+        # bpo-24658: Test that a read greater than 2GB does not fail.
+        with self.open(TESTFN, "rb") as f:
+            self.assertEqual(len(f.read()), size + 1)
+            self.assertEqual(f.tell(), size + 1)
+
+    def test_osstat(self):
+        self.assertEqual(os.stat(TESTFN)[stat.ST_SIZE], size+1)
+
+    def test_seek_read(self):
+        with self.open(TESTFN, 'rb') as f:
+            self.assertEqual(f.tell(), 0)
+            self.assertEqual(f.read(1), b'z')
+            self.assertEqual(f.tell(), 1)
+            f.seek(0)
+            self.assertEqual(f.tell(), 0)
+            f.seek(0, 0)
+            self.assertEqual(f.tell(), 0)
+            f.seek(42)
+            self.assertEqual(f.tell(), 42)
+            f.seek(42, 0)
+            self.assertEqual(f.tell(), 42)
+            f.seek(42, 1)
+            self.assertEqual(f.tell(), 84)
+            f.seek(0, 1)
+            self.assertEqual(f.tell(), 84)
+            f.seek(0, 2)  # seek from the end
+            self.assertEqual(f.tell(), size + 1 + 0)
+            f.seek(-10, 2)
+            self.assertEqual(f.tell(), size + 1 - 10)
+            f.seek(-size-1, 2)
+            self.assertEqual(f.tell(), 0)
+            f.seek(size)
+            self.assertEqual(f.tell(), size)
+            # the 'a' that was written at the end of file above
+            self.assertEqual(f.read(1), b'a')
+            f.seek(-size-1, 1)
+            self.assertEqual(f.read(1), b'z')
+            self.assertEqual(f.tell(), 1)
+
+    def test_lseek(self):
+        with self.open(TESTFN, 'rb') as f:
+            self.assertEqual(os.lseek(f.fileno(), 0, 0), 0)
+            self.assertEqual(os.lseek(f.fileno(), 42, 0), 42)
+            self.assertEqual(os.lseek(f.fileno(), 42, 1), 84)
+            self.assertEqual(os.lseek(f.fileno(), 0, 1), 84)
+            self.assertEqual(os.lseek(f.fileno(), 0, 2), size+1+0)
+            self.assertEqual(os.lseek(f.fileno(), -10, 2), size+1-10)
+            self.assertEqual(os.lseek(f.fileno(), -size-1, 2), 0)
+            self.assertEqual(os.lseek(f.fileno(), size, 0), size)
+            # the 'a' that was written at the end of file above
+            self.assertEqual(f.read(1), b'a')
+
+    def test_truncate(self):
+        with self.open(TESTFN, 'r+b') as f:
+            if not hasattr(f, 'truncate'):
+                raise unittest.SkipTest("open().truncate() not available "
+                                        "on this system")
+            f.seek(0, 2)
+            # else we've lost track of the true size
+            self.assertEqual(f.tell(), size+1)
+            # Cut it back via seek + truncate with no argument.
+            newsize = size - 10
+            f.seek(newsize)
+            f.truncate()
+            self.assertEqual(f.tell(), newsize)  # else pointer moved
+            f.seek(0, 2)
+            self.assertEqual(f.tell(), newsize)  # else wasn't truncated
+            # Ensure that truncate(smaller than true size) shrinks
+            # the file.
+            newsize -= 1
+            f.seek(42)
+            f.truncate(newsize)
+            self.assertEqual(f.tell(), 42)
+            f.seek(0, 2)
+            self.assertEqual(f.tell(), newsize)
+            # XXX truncate(larger than true size) is ill-defined
+            # across platform; cut it waaaaay back
+            f.seek(0)
+            f.truncate(1)
+            self.assertEqual(f.tell(), 0)       # else pointer moved
+            f.seek(0)
+            self.assertEqual(len(f.read()), 1)  # else wasn't truncated
+
+    def test_seekable(self):
+        # Issue #5016; seekable() can return False when the current position
+        # is negative when truncated to an int.
+        for pos in (2**31-1, 2**31, 2**31+1):
+            with self.open(TESTFN, 'rb') as f:
+                f.seek(pos)
+                self.assertTrue(f.seekable())
+
+
+def skip_no_disk_space(path, required):
+    def decorator(fun):
+        def wrapper(*args, **kwargs):
+            if not hasattr(shutil, "disk_usage"):
+                raise unittest.SkipTest("requires shutil.disk_usage")
+            if shutil.disk_usage(os.path.realpath(path)).free < required:
+                hsize = int(required / 1024 / 1024)
+                raise unittest.SkipTest(
+                    f"required {hsize} MiB of free disk space")
+            return fun(*args, **kwargs)
+        return wrapper
+    return decorator
+
+
+class TestCopyfile(LargeFileTest, unittest.TestCase):
+    open = staticmethod(io.open)
+
+    # Exact required disk space would be (size * 2), but let's give it a
+    # bit more tolerance.
+    @skip_no_disk_space(TESTFN, size * 2.5)
+    def test_it(self):
+        # Internally shutil.copyfile() can use "fast copy" methods like
+        # os.sendfile().
+        size = os.path.getsize(TESTFN)
+        shutil.copyfile(TESTFN, TESTFN2)
+        self.assertEqual(os.path.getsize(TESTFN2), size)
+        with open(TESTFN2, 'rb') as f:
+            self.assertEqual(f.read(5), b'z\x00\x00\x00\x00')
+            f.seek(size - 5)
+            self.assertEqual(f.read(), b'\x00\x00\x00\x00a')
+
+
+@unittest.skipIf(not hasattr(os, 'sendfile'), 'sendfile not supported')
+class TestSocketSendfile(LargeFileTest, unittest.TestCase):
+    open = staticmethod(io.open)
+    timeout = SHORT_TIMEOUT
+
+    def setUp(self):
+        super().setUp()
+        self.thread = None
+
+    def tearDown(self):
+        super().tearDown()
+        if self.thread is not None:
+            self.thread.join(self.timeout)
+            self.thread = None
+
+    def tcp_server(self, sock):
+        def run(sock):
+            with sock:
+                conn, _ = sock.accept()
+                conn.settimeout(self.timeout)
+                with conn, open(TESTFN2, 'wb') as f:
+                    event.wait(self.timeout)
+                    while True:
+                        chunk = conn.recv(65536)
+                        if not chunk:
+                            return
+                        f.write(chunk)
+
+        event = threading.Event()
+        sock.settimeout(self.timeout)
+        self.thread = threading.Thread(target=run, args=(sock, ))
+        self.thread.start()
+        event.set()
+
+    # Exact required disk space would be (size * 2), but let's give it a
+    # bit more tolerance.
+    @skip_no_disk_space(TESTFN, size * 2.5)
+    def test_it(self):
+        port = socket_helper.find_unused_port()
+        with socket.create_server(("", port)) as sock:
+            self.tcp_server(sock)
+            with socket.create_connection(("127.0.0.1", port)) as client:
+                with open(TESTFN, 'rb') as f:
+                    client.sendfile(f)
+        self.tearDown()
+
+        size = os.path.getsize(TESTFN)
+        self.assertEqual(os.path.getsize(TESTFN2), size)
+        with open(TESTFN2, 'rb') as f:
+            self.assertEqual(f.read(5), b'z\x00\x00\x00\x00')
+            f.seek(size - 5)
+            self.assertEqual(f.read(), b'\x00\x00\x00\x00a')
+
+
+def setUpModule():
+    try:
+        import signal
+        # The default handler for SIGXFSZ is to abort the process.
+        # By ignoring it, system calls exceeding the file size resource
+        # limit will raise OSError instead of crashing the interpreter.
+        signal.signal(signal.SIGXFSZ, signal.SIG_IGN)
+    except (ImportError, AttributeError):
+        pass
+
+    # On Windows and Mac OSX this test consumes large resources; It
+    # takes a long time to build the >2 GiB file and takes >2 GiB of disk
+    # space therefore the resource must be enabled to run this test.
+    # If not, nothing after this line stanza will be executed.
+    if sys.platform[:3] == 'win' or sys.platform == 'darwin':
+        requires('largefile',
+                 'test requires %s bytes and a long time to run' % str(size))
+    else:
+        # Only run if the current filesystem supports large files.
+        # (Skip this test on Windows, since we now always support
+        # large files.)
+        f = open(TESTFN, 'wb', buffering=0)
+        try:
+            # 2**31 == 2147483648
+            f.seek(2147483649)
+            # Seeking is not enough of a test: you must write and flush, too!
+            f.write(b'x')
+            f.flush()
+        except (OSError, OverflowError):
+            raise unittest.SkipTest("filesystem does not have "
+                                    "largefile support")
+        finally:
+            f.close()
+            unlink(TESTFN)
+
+
+class CLargeFileTest(TestFileMethods, unittest.TestCase):
+    open = staticmethod(io.open)
+
+
+class PyLargeFileTest(TestFileMethods, unittest.TestCase):
+    open = staticmethod(pyio.open)
+
+
+def tearDownModule():
+    unlink(TESTFN)
+    unlink(TESTFN2)
+
+
+if __name__ == '__main__':
+    unittest.main()