* sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c

	(__mpn_construct_long_double): Fix conversion where result ought
	to be smaller than __LDBL_MIN__, or the low double should be
	denormal.  Fix decision where to negate low double - honor round
	to even rules.
	* stdio-common/tst-sprintf2.c: Include string.h.
	(COMPARE_LDBL): Define.
	(TEST): Also test whether a string hexadecimal float representation
	can be parsed back to the number.
	(main): Add a couple of further tests.

	* sysdeps/ieee754/ldbl-128ibm/printf_fphex.c
	(PRINT_FPHEX_LONG_DOUBLE): Fix printing numbers where lower double
	is non-zero, but smaller than 2 * __DBL_MIN__.
	* stdio-common/tst-sprintf2.c: New test.
	* stdio-common/Makefile (tests): Add tst-sprintf2.

2 files changed, 79 insertions, 27 deletions

diff --git a/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c b/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c
index 8a2d45e2d8..90f2ded03f 100644
--- a/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c
@@ -31,19 +31,20 @@ long double
 __mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign)
 {
   union ibm_extended_long_double u;
-  unsigned long hidden2, lzcount;
+  unsigned long lzcount;
   unsigned long long hi, lo;
+  int exponent2;
 
   u.ieee.negative = sign;
   u.ieee.negative2 = sign;
   u.ieee.exponent = expt + IBM_EXTENDED_LONG_DOUBLE_BIAS;
-  u.ieee.exponent2 = expt - 53 + IBM_EXTENDED_LONG_DOUBLE_BIAS;
+  u.ieee.exponent2 = 0;
+  exponent2 = expt - 53 + IBM_EXTENDED_LONG_DOUBLE_BIAS;
 
 #if BITS_PER_MP_LIMB == 32
   /* The low order 53 bits (52 + hidden) go into the lower double */
   lo = frac_ptr[0];
   lo |= (frac_ptr[1] & ((1LL << (53 - 32)) - 1)) << 32;
-  hidden2 = (frac_ptr[1] >> (52 - 32)) & ((mp_limb_t) 1);
   /* The high order 53 bits (52 + hidden) go into the upper double */
   hi = (frac_ptr[1] >> (53 - 32)) & ((1 << 11) - 1);
   hi |= ((unsigned long long) frac_ptr[2]) << 11;
@@ -51,7 +52,6 @@ __mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign)
 #elif BITS_PER_MP_LIMB == 64
   /* The low order 53 bits (52 + hidden) go into the lower double */
   lo = frac_ptr[0] & (((mp_limb_t) 1 << 53) - 1);
-  hidden2 = (frac_ptr[0] >> 52) & ((mp_limb_t) 1);
   /* The high order 53 bits (52 + hidden) go into the upper double */
   hi = (frac_ptr[0] >> 53) & (((mp_limb_t) 1 << 11) - 1);
   hi |= (frac_ptr[1] << 11);
@@ -59,14 +59,62 @@ __mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign)
   #error "mp_limb size " BITS_PER_MP_LIMB "not accounted for"
 #endif
 
+  if ((hi & (1LL << 52)) == 0 && (hi | lo) != 0)
+    {
+      /* denormal number  */
+      unsigned long long val = hi ? hi : lo;
+
+      if (sizeof (val) == sizeof (long))
+	lzcount = __builtin_clzl (val);
+      else if ((val >> 32) != 0)
+	lzcount = __builtin_clzl ((long) (val >> 32));
+      else
+	lzcount = __builtin_clzl ((long) val) + 32;
+      if (hi)
+	lzcount = lzcount - 11;
+      else
+	lzcount = lzcount + 42;
+
+      if (lzcount > u.ieee.exponent)
+	{
+	  lzcount = u.ieee.exponent;
+	  u.ieee.exponent = 0;
+	  exponent2 -= lzcount;
+	}
+      else
+	{
+	  u.ieee.exponent -= (lzcount - 1);
+	  exponent2 -= (lzcount - 1);
+	}
+
+      if (lzcount <= 53)
+	{
+	  hi = (hi << lzcount) | (lo >> (53 - lzcount));
+	  lo = (lo << lzcount) & ((1LL << 53) - 1);
+	}
+      else
+	{
+	  hi = lo << (lzcount - 53);
+	  lo = 0;
+	}
+    }
+
   if (lo != 0L)
     {
       /* hidden2 bit of low double controls rounding of the high double.
-	 If hidden2 is '1' then round up hi and adjust lo (2nd mantissa)
+	 If hidden2 is '1' and either the explicit mantissa is non-zero
+	 or hi is odd, then round up hi and adjust lo (2nd mantissa)
 	 plus change the sign of the low double to compensate.  */
-      if (hidden2)
+      if ((lo & (1LL << 52)) != 0
+	  && ((hi & 1) != 0 || (lo & ((1LL << 52) - 1))))
 	{
 	  hi++;
+	  if ((hi & ((1LL << 52) - 1)) == 0)
+	    {
+	      if ((hi & (1LL << 53)) != 0)
+		hi -= 1LL << 52;
+	      u.ieee.exponent++;
+	    }
 	  u.ieee.negative2 = !sign;
 	  lo = (1LL << 53) - lo;
 	}
@@ -85,17 +133,18 @@ __mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign)
       if (lzcount > 0)
 	{
 	  lo = lo << lzcount;
-	  u.ieee.exponent2 = u.ieee.exponent2 - lzcount;
+	  exponent2 = exponent2 - lzcount;
 	}
+      if (exponent2 > 0)
+	u.ieee.exponent2 = exponent2;
+      else
+	lo >>= 1 - exponent2;
     }
   else
-    {
-      u.ieee.negative2 = 0;
-      u.ieee.exponent2 = 0;
-    }
+    u.ieee.negative2 = 0;
 
   u.ieee.mantissa3 = lo & 0xffffffffLL;
-  u.ieee.mantissa2 = (lo >> 32) & 0xffffff;
+  u.ieee.mantissa2 = (lo >> 32) & 0xfffff;
   u.ieee.mantissa1 = hi & 0xffffffffLL;
   u.ieee.mantissa0 = (hi >> 32) & ((1LL << (LDBL_MANT_DIG - 86)) - 1);
 
diff --git a/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c b/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c
index 2a7b70fabf..a8317938f7 100644
--- a/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c
+++ b/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c
@@ -35,21 +35,24 @@ do {									      \
 									      \
       lo = ((long long)eldbl.ieee.mantissa2 << 32) | eldbl.ieee.mantissa3;    \
       hi = ((long long)eldbl.ieee.mantissa0 << 32) | eldbl.ieee.mantissa1;    \
-   /* If the lower double is not a denomal or zero then set the hidden	      \
-      53rd bit.  */							      \
-      if (eldbl.ieee.exponent2 > 0x001)					      \
-	{								      \
-	  lo |= (1ULL << 52);						      \
-	  lo = lo << 7; /* pre-shift lo to match ieee854.  */		      \
-	  /* The lower double is normalized separately from the upper.  We    \
-	     may need to adjust the lower manitissa to reflect this.  */      \
-	  ediff = eldbl.ieee.exponent - eldbl.ieee.exponent2;		      \
-	  if (ediff > 53)						      \
-	    lo = lo >> (ediff-53);					      \
-	}								      \
-  									      \
-      if ((eldbl.ieee.negative != eldbl.ieee.negative2)			      \
-	  && ((eldbl.ieee.exponent2 != 0) && (lo != 0L)))		      \
+      lo <<= 7; /* pre-shift lo to match ieee854.  */			      \
+      /* If the lower double is not a denomal or zero then set the hidden     \
+	 53rd bit.  */							      \
+      if (eldbl.ieee.exponent2 != 0)					      \
+	lo |= (1ULL << (52 + 7));					      \
+      else								      \
+	lo <<= 1;							      \
+      /* The lower double is normalized separately from the upper.  We	      \
+	 may need to adjust the lower manitissa to reflect this.  */	      \
+      ediff = eldbl.ieee.exponent - eldbl.ieee.exponent2;		      \
+      if (ediff > 53 + 63)						      \
+	lo = 0;								      \
+      else if (ediff > 53)						      \
+	lo = lo >> (ediff - 53);					      \
+      else if (eldbl.ieee.exponent2 == 0 && ediff < 53)			      \
+	lo = lo << (53 - ediff);					      \
+      if (eldbl.ieee.negative != eldbl.ieee.negative2			      \
+	  && (eldbl.ieee.exponent2 != 0 || lo != 0L))			      \
 	{								      \
 	  lo = (1ULL << 60) - lo;					      \
 	  if (hi == 0L)							      \