diff --git a/Lib/test/test_struct.py b/Lib/test/test_struct.py
index a03438f16..a1e1a5c48 100644
--- a/Lib/test/test_struct.py
+++ b/Lib/test/test_struct.py
@@ -5,7 +5,6 @@ import gc
 import math
 import operator
 import unittest
-import platform
 import struct
 import sys
 import weakref
@@ -435,41 +434,11 @@ class StructTest(ComplexesAreIdenticalMixin, unittest.TestCase):
         self.assertEqual(s.unpack_from(buffer=test_string, offset=2),
                          (b'cd01',))
 
-    def test_pack_into(self):
+    def _test_pack_into(self, pack_into):
         test_string = b'Reykjavik rocks, eow!'
-        writable_buf = array.array('b', b' '*100)
-        fmt = '21s'
-        s = struct.Struct(fmt)
+        writable_buf = memoryview(array.array('b', b' '*100))
 
         # Test without offset
-        s.pack_into(writable_buf, 0, test_string)
-        from_buf = writable_buf.tobytes()[:len(test_string)]
-        self.assertEqual(from_buf, test_string)
-
-        # Test with offset.
-        s.pack_into(writable_buf, 10, test_string)
-        from_buf = writable_buf.tobytes()[:len(test_string)+10]
-        self.assertEqual(from_buf, test_string[:10] + test_string)
-
-        # Go beyond boundaries.
-        small_buf = array.array('b', b' '*10)
-        self.assertRaises((ValueError, struct.error), s.pack_into, small_buf, 0,
-                          test_string)
-        self.assertRaises((ValueError, struct.error), s.pack_into, small_buf, 2,
-                          test_string)
-
-        # Test bogus offset (issue 3694)
-        sb = small_buf
-        self.assertRaises((TypeError, struct.error), struct.pack_into, b'', sb,
-                          None)
-
-    def test_pack_into_fn(self):
-        test_string = b'Reykjavik rocks, eow!'
-        writable_buf = array.array('b', b' '*100)
-        fmt = '21s'
-        pack_into = lambda *args: struct.pack_into(fmt, *args)
-
-        # Test without offset.
         pack_into(writable_buf, 0, test_string)
         from_buf = writable_buf.tobytes()[:len(test_string)]
         self.assertEqual(from_buf, test_string)
@@ -479,12 +448,49 @@ class StructTest(ComplexesAreIdenticalMixin, unittest.TestCase):
         from_buf = writable_buf.tobytes()[:len(test_string)+10]
         self.assertEqual(from_buf, test_string[:10] + test_string)
 
+        # Test with negative offset.
+        pack_into(writable_buf, -30, test_string)
+        from_buf = writable_buf.tobytes()[-30:-30+len(test_string)]
+        self.assertEqual(from_buf, test_string)
+
         # Go beyond boundaries.
         small_buf = array.array('b', b' '*10)
-        self.assertRaises((ValueError, struct.error), pack_into, small_buf, 0,
-                          test_string)
-        self.assertRaises((ValueError, struct.error), pack_into, small_buf, 2,
-                          test_string)
+        with self.assertRaises((ValueError, struct.error)):
+            pack_into(small_buf, 0, test_string)
+        with self.assertRaises((ValueError, struct.error)):
+            pack_into(writable_buf, 90, test_string)
+        with self.assertRaises((ValueError, struct.error)):
+            pack_into(writable_buf, -10, test_string)
+        with self.assertRaises((ValueError, struct.error)):
+            pack_into(writable_buf, 150, test_string)
+        with self.assertRaises((ValueError, struct.error)):
+            pack_into(writable_buf, -150, test_string)
+
+        # Test invalid buffer.
+        self.assertRaises(TypeError, pack_into, b' '*100, 0, test_string)
+        self.assertRaises(TypeError, pack_into, ' '*100, 0, test_string)
+        self.assertRaises(TypeError, pack_into, [0]*100, 0, test_string)
+        self.assertRaises(TypeError, pack_into, None, 0, test_string)
+        self.assertRaises(TypeError, pack_into, writable_buf[::2], 0, test_string)
+        self.assertRaises(TypeError, pack_into, writable_buf[::-1], 0, test_string)
+
+        # Test bogus offset (issue bpo-3694)
+        with self.assertRaises(TypeError):
+            pack_into(writable_buf, None, test_string)
+        with self.assertRaises(TypeError):
+            pack_into(writable_buf, 0.0, test_string)
+        with self.assertRaises((IndexError, OverflowError)):
+            pack_into(writable_buf, 2**1000, test_string)
+        with self.assertRaises((IndexError, OverflowError)):
+            pack_into(writable_buf, -2**1000, test_string)
+
+    def test_pack_into(self):
+        s = struct.Struct('21s')
+        self._test_pack_into(s.pack_into)
+
+    def test_pack_into_fn(self):
+        pack_into = lambda *args: struct.pack_into('21s', *args)
+        self._test_pack_into(pack_into)
 
     def test_unpack_with_buffer(self):
         # SF bug 1563759: struct.unpack doesn't support buffer protocol objects
@@ -821,6 +827,18 @@ class StructTest(ComplexesAreIdenticalMixin, unittest.TestCase):
             results = executor.map(exec, [code] * 5)
             self.assertListEqual(list(results), [None] * 5)
 
+    def test_operations_on_half_initialized_Struct(self):
+        S = struct.Struct.__new__(struct.Struct)
+
+        spam = array.array('b', b' ')
+        self.assertRaises(RuntimeError, S.iter_unpack, spam)
+        self.assertRaises(RuntimeError, S.pack, 1)
+        self.assertRaises(RuntimeError, S.pack_into, spam, 1)
+        self.assertRaises(RuntimeError, S.unpack, spam)
+        self.assertRaises(RuntimeError, S.unpack_from, spam)
+        self.assertRaises(RuntimeError, getattr, S, 'format')
+        self.assertEqual(S.size, -1)
+
 
 class UnpackIteratorTest(unittest.TestCase):
     """
@@ -895,6 +913,7 @@ class UnpackIteratorTest(unittest.TestCase):
         self.assertRaises(StopIteration, next, it)
 
     def test_half_float(self):
+        _testcapi = import_helper.import_module('_testcapi')
         # Little-endian examples from:
         # http://en.wikipedia.org/wiki/Half_precision_floating-point_format
         format_bits_float__cleanRoundtrip_list = [
@@ -939,8 +958,8 @@ class UnpackIteratorTest(unittest.TestCase):
 
         # Check that packing produces a bit pattern representing a quiet NaN:
         # all exponent bits and the msb of the fraction should all be 1.
-        if platform.machine().startswith('parisc'):
-            # HP PA RISC uses 0 for quiet, see:
+        if _testcapi.nan_msb_is_signaling:
+            # HP PA RISC and some MIPS CPUs use 0 for quiet, see:
             # https://en.wikipedia.org/wiki/NaN#Encoding
             expected = 0x7c
         else: