diff --git a/Lib/test/test_xrange.py b/Lib/test/test_xrange.py
index a0b94fa..8e65477 100644
--- a/Lib/test/test_xrange.py
+++ b/Lib/test/test_xrange.py
@@ -3,12 +3,49 @@
 import test.test_support, unittest
 import sys
 import pickle
+import itertools
 
 import warnings
 warnings.filterwarnings("ignore", "integer argument expected",
                         DeprecationWarning, "unittest")
 
+# pure Python implementations (3 args only), for comparison
+def pyrange(start, stop, step):
+    if (start - stop) // step < 0:
+        # replace stop with next element in the sequence of integers
+        # that are congruent to start modulo step.
+        stop += (start - stop) % step
+        while start != stop:
+            yield start
+            start += step
+
+def pyrange_reversed(start, stop, step):
+    stop += (start - stop) % step
+    return pyrange(stop - step, start - step, -step)
+
+
 class XrangeTest(unittest.TestCase):
+    def assert_iterators_equal(self, xs, ys, test_id, limit=None):
+        # check that an iterator xs matches the expected results ys,
+        # up to a given limit.
+        if limit is not None:
+            xs = itertools.islice(xs, limit)
+            ys = itertools.islice(ys, limit)
+        sentinel = object()
+        pairs = itertools.izip_longest(xs, ys, fillvalue=sentinel)
+        for i, (x, y) in enumerate(pairs):
+            if x == y:
+                continue
+            elif x == sentinel:
+                self.fail('{}: iterator ended unexpectedly '
+                          'at position {}; expected {}'.format(test_id, i, y))
+            elif y == sentinel:
+                self.fail('{}: unexpected excess element {} at '
+                          'position {}'.format(test_id, x, i))
+            else:
+                self.fail('{}: wrong element at position {};'
+                          'expected {}, got {}'.format(test_id, i, y, x))
+
     def test_xrange(self):
         self.assertEqual(list(xrange(3)), [0, 1, 2])
         self.assertEqual(list(xrange(1, 5)), [1, 2, 3, 4])
@@ -67,6 +104,37 @@
                 self.assertEquals(list(pickle.loads(pickle.dumps(r, proto))),
                                   list(r))
 
+    def test_range_iterators(self):
+        # see issue 7298
+        limits = [base + jiggle
+                  for M in (2**32, 2**64)
+                  for base in (-M, -M//2, 0, M//2, M)
+                  for jiggle in (-2, -1, 0, 1, 2)]
+        test_ranges = [(start, end, step)
+                       for start in limits
+                       for end in limits
+                       for step in (-2**63, -2**31, -2, -1, 1, 2)]
+
+        for start, end, step in test_ranges:
+            try:
+                iter1 = xrange(start, end, step)
+            except OverflowError:
+                pass
+            else:
+                iter2 = pyrange(start, end, step)
+                test_id = "xrange({}, {}, {})".format(start, end, step)
+                # check first 100 entries
+                self.assert_iterators_equal(iter1, iter2, test_id, limit=100)
+
+            try:
+                iter1 = reversed(xrange(start, end, step))
+            except OverflowError:
+                pass
+            else:
+                iter2 = pyrange_reversed(start, end, step)
+                test_id = "reversed(xrange({}, {}, {}))".format(start, end, step)
+                self.assert_iterators_equal(iter1, iter2, test_id, limit=100)
+
 
 def test_main():
     test.test_support.run_unittest(XrangeTest)
diff --git a/Objects/rangeobject.c b/Objects/rangeobject.c
index 76d3849..0fee40f 100644
--- a/Objects/rangeobject.c
+++ b/Objects/rangeobject.c
@@ -9,33 +9,32 @@
 	long	len;
 } rangeobject;
 
-/* Return number of items in range/xrange (lo, hi, step).  step > 0
- * required.  Return a value < 0 if & only if the true value is too
- * large to fit in a signed long.
+/* Return number of items in range (lo, hi, step).  step != 0
+ * required.  The result always fits in an unsigned long.
  */
-static long
+static unsigned long
 get_len_of_range(long lo, long hi, long step)
 {
-	/* -------------------------------------------------------------
-	If lo >= hi, the range is empty.
-	Else if n values are in the range, the last one is
-	lo + (n-1)*step, which must be <= hi-1.  Rearranging,
-	n <= (hi - lo - 1)/step + 1, so taking the floor of the RHS gives
-	the proper value.  Since lo < hi in this case, hi-lo-1 >= 0, so
-	the RHS is non-negative and so truncation is the same as the
-	floor.  Letting M be the largest positive long, the worst case
-	for the RHS numerator is hi=M, lo=-M-1, and then
-	hi-lo-1 = M-(-M-1)-1 = 2*M.  Therefore unsigned long has enough
-	precision to compute the RHS exactly.
-	---------------------------------------------------------------*/
-	long n = 0;
-	if (lo < hi) {
-		unsigned long uhi = (unsigned long)hi;
-		unsigned long ulo = (unsigned long)lo;
-		unsigned long diff = uhi - ulo - 1;
-		n = (long)(diff / (unsigned long)step + 1);
-	}
-	return n;
+    /* -------------------------------------------------------------
+    If step > 0 and lo >= hi, or step < 0 and lo <= hi, the range is empty.
+    Else for step > 0, if n values are in the range, the last one is
+    lo + (n-1)*step, which must be <= hi-1.  Rearranging,
+    n <= (hi - lo - 1)/step + 1, so taking the floor of the RHS gives
+    the proper value.  Since lo < hi in this case, hi-lo-1 >= 0, so
+    the RHS is non-negative and so truncation is the same as the
+    floor.  Letting M be the largest positive long, the worst case
+    for the RHS numerator is hi=M, lo=-M-1, and then
+    hi-lo-1 = M-(-M-1)-1 = 2*M.  Therefore unsigned long has enough
+    precision to compute the RHS exactly.  The analysis for step < 0
+    is similar.
+    ---------------------------------------------------------------*/
+    assert(step != 0);
+    if (step > 0 && lo < hi)
+        return 1UL + (hi - 1UL - lo) / step;
+    else if (step < 0 && lo > hi)
+        return 1UL + (lo - 1UL - hi) / (0UL - step);
+    else
+        return 0UL;
 }
 
 static PyObject *
@@ -43,7 +42,7 @@
 {
 	rangeobject *obj;
 	long ilow = 0, ihigh = 0, istep = 1;
-	long n;
+	unsigned long n;
 
 	if (!_PyArg_NoKeywords("xrange()", kw))
 		return NULL;
@@ -64,11 +63,8 @@
 		PyErr_SetString(PyExc_ValueError, "xrange() arg 3 must not be zero");
 		return NULL;
 	}
-	if (istep > 0)
-		n = get_len_of_range(ilow, ihigh, istep);
-	else
-		n = get_len_of_range(ihigh, ilow, -istep);
-	if (n < 0) {
+	n = get_len_of_range(ilow, ihigh, istep);
+	if (n > (unsigned long)LONG_MAX || (long)n > PY_SSIZE_T_MAX) {
 		PyErr_SetString(PyExc_OverflowError,
 				"xrange() result has too many items");
 		return NULL;
@@ -78,7 +74,7 @@
 	if (obj == NULL)
 		return NULL;
 	obj->start = ilow;
-	obj->len   = n;
+	obj->len   = (long)n;
 	obj->step  = istep;
 	return (PyObject *) obj;
 }
@@ -98,7 +94,9 @@
 				"xrange object index out of range");
 		return NULL;
 	}
-	return PyInt_FromSsize_t(r->start + i * r->step);
+	/* do calculation entirely using unsigned longs, to avoid
+	   undefined behaviour due to signed overflow. */
+	return PyInt_FromLong((long)(r->start + (unsigned long)i * r->step));
 }
 
 static Py_ssize_t
@@ -304,9 +302,21 @@
 	len = ((rangeobject *)seq)->len;
 
 	it->index = 0;
-	it->start = start + (len-1) * step;
-	it->step = -step;
 	it->len = len;
+	/* the casts below guard against signed overflow by turning it
+	   into unsigned overflow instead.  The correctness of this
+	   code still depends on conversion from unsigned long to long
+	   wrapping modulo ULONG_MAX+1, which isn't guaranteed (see
+	   C99 6.3.1.3p3) but seems to hold in practice for all
+	   platforms we're likely to meet.
+
+	   If step == LONG_MIN then we still end up with LONG_MIN
+	   after negation; but this works out, since we've still got
+	   the correct value modulo ULONG_MAX+1, and the range_item
+	   calculation is also done modulo ULONG_MAX+1.
+	*/
+	it->start = (long)(start + (unsigned long)(len-1) * step);
+	it->step = (long)(-(unsigned long)step);
 
 	return (PyObject *)it;
 }