diff --git a/arch/alpha/include/asm/sfp-machine.h b/arch/alpha/include/asm/sfp-machine.h
index 5fe63afbd474..bff1ad963c68 100644
--- a/arch/alpha/include/asm/sfp-machine.h
+++ b/arch/alpha/include/asm/sfp-machine.h
@@ -59,6 +59,10 @@
     R##_c = FP_CLS_NAN;						\
   } while (0)
 
+/* Alpha determines tininess after rounding, so the emulation must do the
+   same as the hardware does for the results it produces itself.  */
+#define _FP_TININESS_AFTER_ROUNDING	1
+
 /* Obtain the current rounding mode. */
 #define FP_ROUNDMODE	mode
 #define FP_RND_NEAREST	(FPCR_DYN_NORMAL >> FPCR_DYN_SHIFT)
diff --git a/include/math-emu/op-common.h b/include/math-emu/op-common.h
index 8ce066c035cf..1d1ce5c08efc 100644
--- a/include/math-emu/op-common.h
+++ b/include/math-emu/op-common.h
@@ -135,6 +135,24 @@ do {								\
     else							\
       {								\
 	/* we've got a denormalized number */			\
+	int _FP_PACK_CANONICAL_is_tiny = 1;			\
+	if (_FP_TININESS_AFTER_ROUNDING && X##_e == 0)		\
+	  {							\
+	    /* Architectures that detect tininess after rounding	\
+	       only signal underflow if the result is still		\
+	       subnormal once rounded as if the exponent range	\
+	       were unbounded.  Round a copy to find out.  */	\
+	    FP_DECL_##fs(_FP_PACK_CANONICAL_T);			\
+	    /* The class field is not used by the rounding below,	\
+	       and is unused entirely where this block is dead.  */	\
+	    (void)_FP_PACK_CANONICAL_T##_c;			\
+	    _FP_FRAC_COPY_##wc(_FP_PACK_CANONICAL_T, X);	\
+	    _FP_PACK_CANONICAL_T##_s = X##_s;			\
+	    _FP_PACK_CANONICAL_T##_e = X##_e;			\
+	    _FP_ROUND(wc, _FP_PACK_CANONICAL_T);		\
+	    if (_FP_FRAC_OVERP_##wc(fs, _FP_PACK_CANONICAL_T))	\
+	      _FP_PACK_CANONICAL_is_tiny = 0;			\
+	  }							\
 	X##_e = -X##_e + 1;					\
 	if (X##_e <= _FP_WFRACBITS_##fs)			\
 	  {							\
@@ -161,8 +179,9 @@ do {								\
 		    _FP_FRAC_SRL_##wc(X, _FP_WORKBITS);		\
 		  }						\
 	      }							\
-	    if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) ||		\
-		(FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW))	\
+	    if (_FP_PACK_CANONICAL_is_tiny			\
+		&& ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) ||	\
+		    (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)))	\
 		FP_SET_EXCEPTION(FP_EX_UNDERFLOW);		\
 	  }							\
 	else							\
diff --git a/include/math-emu/soft-fp.h b/include/math-emu/soft-fp.h
index 5650c1628383..02ada0a9fca1 100644
--- a/include/math-emu/soft-fp.h
+++ b/include/math-emu/soft-fp.h
@@ -31,6 +31,14 @@
 #include <endian.h>
 #endif
 
+/* Whether the architecture determines tininess of a floating-point
+   result after rounding rather than before it.  IEEE 754 permits either
+   but requires the same choice for every operation, so this has to agree
+   with what the hardware does for the results it produces itself.  */
+#ifndef _FP_TININESS_AFTER_ROUNDING
+#define _FP_TININESS_AFTER_ROUNDING	0
+#endif
+
 #define _FP_WORKBITS		3
 #define _FP_WORK_LSB		((_FP_W_TYPE)1 << 3)
 #define _FP_WORK_ROUND		((_FP_W_TYPE)1 << 2)