diff --git a/src/util/half_float.c b/src/util/half_float.c
index 05aeac14abb..606e4b9522e 100644
--- a/src/util/half_float.c
+++ b/src/util/half_float.c
@@ -83,8 +83,12 @@ _mesa_float_to_half_slow(float val)
       e = 31;
    }
    else if ((flt_e == 0xff) && (flt_m != 0)) {
-      /* NaN */
-      m = 1;
+      /* Retain the top bits of a NaN to make sure that the quiet/signaling
+       * status stays the same.
+       */
+      m = flt_m >> 13;
+      if (!m)
+         m = 1;
       e = 31;
    }
    else {
diff --git a/src/util/softfloat.c b/src/util/softfloat.c
index cc386aa46fb..2ff835f7452 100644
--- a/src/util/softfloat.c
+++ b/src/util/softfloat.c
@@ -1452,7 +1452,12 @@ _mesa_float_to_half_rtz_slow(float val)
         if (flt_m != 0) {
             /* 'val' is a NaN, return NaN */
             e = 0x1f;
-            m = 0x1;
+            /* Retain the top bits of a NaN to make sure that the quiet/signaling
+            * status stays the same.
+            */
+            m = flt_m >> 13;
+            if (!m)
+               m = 1;
             return (s << 15) + (e << 10) + m;
         }