diff --git a/src/dilithium_py/utilities/utils.py b/src/dilithium_py/utilities/utils.py
index 28b384b..5486c85 100644
--- a/src/dilithium_py/utilities/utils.py
+++ b/src/dilithium_py/utilities/utils.py
@@ -1,19 +1,17 @@
-def reduce_mod_pm(x, n):
+def reduce_mod_pm(r, n):
     """
-    Takes an integer 0 < x < n and represents
-    it as an integer in the range
+    Takes an integer 0 < r < n and computes the value
+    r' = r mod^± n, defined to be integer in the range
 
-    r = x % n
-
-    for n odd:
-        -(n-1)/2 < r <= (n-1)/2
     for n even:
-        - n / 2  <= r <= n / 2
+        -(n / 2) < r' <= (n / 2)
+    for n odd:
+        -(n - 1) / 2 <= r' <= (n - 1) / 2
     """
-    x = x % n
-    if x > (n >> 1):
-        x -= n
-    return x
+    r = r % n
+    if r > (n >> 1):
+        r -= n
+    return r
 
 
 def decompose(r, a, q):
diff --git a/tests/test_utils.py b/tests/test_utils.py
index ef596d3..0c5d71a 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -5,17 +5,25 @@
 
 class TestUtils(unittest.TestCase):
     def test_reduce_mod_pm_even(self):
+        """
+        For odd modulus the reduced value should be bounded by
+        -(n-1)/2 <= x <= (n-1)/2
+        """
         for _ in range(100):
             modulus = 2 * randint(0, 100)
             for i in range(modulus):
                 x = reduce_mod_pm(i, modulus)
                 self.assertTrue(x <= modulus // 2)
-                self.assertTrue(x > -modulus // 2)
+                self.assertTrue(-modulus // 2 < x)
 
     def test_reduce_mod_pm_odd(self):
+        """
+        For even modulus the reduced value should be bounded by
+        -n/2 < x <= n/2
+        """
         for _ in range(100):
             modulus = 2 * randint(0, 100) + 1
             for i in range(modulus):
                 x = reduce_mod_pm(i, modulus)
                 self.assertTrue(x <= (modulus - 1) // 2)
-                self.assertTrue(x >= -(modulus - 1) // 2)
+                self.assertTrue(-(modulus - 1) // 2 <= x)