diff --git a/float.cpp b/float.cpp
index a49da312..691cfa1f 100644
--- a/float.cpp
+++ b/float.cpp
@@ -126,6 +126,12 @@ ieee_float<E, S>::almost_equal (floating_t _a,
     if (a.s == b.s)
         return true;
 
+    // Order as twos complement to avoid negative zero/zero comparison issues
+    if (a.s < 0)
+        a.s = (1L << (TOTAL_BITS - 1)) - a.s;
+    if (b.s < 0)
+        b.s = (1L << (TOTAL_BITS - 1)) - b.s;
+
     uint_t diff = std::abs (a.s - b.s);
     return diff <= ulps;
 }
diff --git a/test/maths/maths.cpp b/test/maths/maths.cpp
index 3df7a8b4..b43e38a9 100644
--- a/test/maths/maths.cpp
+++ b/test/maths/maths.cpp
@@ -23,6 +23,8 @@ main (int, char **) {
     CHECK (!almost_equal (numeric_limits<double>::quiet_NaN (),
                           numeric_limits<double>::quiet_NaN ()));
 
+    CHECK (almost_equal (0.f, -0.f));
+    CHECK (almost_equal (0.,  -0.));
 
     CHECK_EQ (min (-2, 0, 2), -2);
     CHECK_EQ (max (-2, 0, 2),  2);