diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index ac116c70b8..6094d267b5 100644
--- a/fpu/softfloat.c
+++ b/fpu/softfloat.c
@@ -5866,6 +5866,12 @@ static floatx80 addFloatx80Sigs(floatx80 a, floatx80 b, flag zSign,
         zSig1 = 0;
         zSig0 = aSig + bSig;
         if ( aExp == 0 ) {
+            if ((aSig | bSig) & UINT64_C(0x8000000000000000) && zSig0 < aSig) {
+                /* At least one of the values is a pseudo-denormal,
+                 * and there is a carry out of the result.  */
+                zExp = 1;
+                goto shiftRight1;
+            }
             if (zSig0 == 0) {
                 return packFloatx80(zSign, 0, 0);
             }
diff --git a/tests/tcg/i386/test-i386-pseudo-denormal.c b/tests/tcg/i386/test-i386-pseudo-denormal.c
new file mode 100644
index 0000000000..cfa2a500b0
--- /dev/null
+++ b/tests/tcg/i386/test-i386-pseudo-denormal.c
@@ -0,0 +1,24 @@
+/* Test pseudo-denormal operations.  */
+
+#include <stdint.h>
+#include <stdio.h>
+
+union u {
+    struct { uint64_t sig; uint16_t sign_exp; } s;
+    long double ld;
+};
+
+volatile union u ld_pseudo_m16382 = { .s = { UINT64_C(1) << 63, 0 } };
+
+volatile long double ld_res;
+
+int main(void)
+{
+    int ret = 0;
+    ld_res = ld_pseudo_m16382.ld + ld_pseudo_m16382.ld;
+    if (ld_res != 0x1p-16381L) {
+        printf("FAIL: pseudo-denormal add\n");
+        ret = 1;
+    }
+    return ret;
+}