[thirdparty/glibc.git] / sysdeps / ieee754 / ldbl-128 / s_fmal.c

/* Compute x * y + z as ternary operation.
   Copyright (C) 2010-2014 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <http://www.gnu.org/licenses/>.  */

#include <float.h>
#include <math.h>
#include <fenv.h>
#include <ieee754.h>
#include <math_private.h>
#include <tininess.h>

/* This implementation uses rounding to odd to avoid problems with
   double rounding.  See a paper by Boldo and Melquiond:
   http://www.lri.fr/~melquion/doc/08-tc.pdf  */

long double
__fmal (long double x, long double y, long double z)
{
  union ieee854_long_double u, v, w;
  int adjust = 0;
  u.d = x;
  v.d = y;
  w.d = z;
  if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
			>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS
			   - LDBL_MANT_DIG, 0)
      || __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
      || __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
      || __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
      || __builtin_expect (u.ieee.exponent + v.ieee.exponent
			   <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0))
    {
      /* If z is Inf, but x and y are finite, the result should be
	 z rather than NaN.  */
      if (w.ieee.exponent == 0x7fff
	  && u.ieee.exponent != 0x7fff
          && v.ieee.exponent != 0x7fff)
	return (z + x) + y;
      /* If z is zero and x are y are nonzero, compute the result
	 as x * y to avoid the wrong sign of a zero result if x * y
	 underflows to 0.  */
      if (z == 0 && x != 0 && y != 0)
	return x * y;
      /* If x or y or z is Inf/NaN, or if x * y is zero, compute as
	 x * y + z.  */
      if (u.ieee.exponent == 0x7fff
	  || v.ieee.exponent == 0x7fff
	  || w.ieee.exponent == 0x7fff
	  || x == 0
	  || y == 0)
	return x * y + z;
      /* If fma will certainly overflow, compute as x * y.  */
      if (u.ieee.exponent + v.ieee.exponent
	  > 0x7fff + IEEE854_LONG_DOUBLE_BIAS)
	return x * y;
      /* If x * y is less than 1/4 of LDBL_DENORM_MIN, neither the
	 result nor whether there is underflow depends on its exact
	 value, only on its sign.  */
      if (u.ieee.exponent + v.ieee.exponent
	  < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
	{
	  int neg = u.ieee.negative ^ v.ieee.negative;
	  long double tiny = neg ? -0x1p-16494L : 0x1p-16494L;
	  if (w.ieee.exponent >= 3)
	    return tiny + z;
	  /* Scaling up, adding TINY and scaling down produces the
	     correct result, because in round-to-nearest mode adding
	     TINY has no effect and in other modes double rounding is
	     harmless.  But it may not produce required underflow
	     exceptions.  */
	  v.d = z * 0x1p114L + tiny;
	  if (TININESS_AFTER_ROUNDING
	      ? v.ieee.exponent < 115
	      : (w.ieee.exponent == 0
		 || (w.ieee.exponent == 1
		     && w.ieee.negative != neg
		     && w.ieee.mantissa3 == 0
		     && w.ieee.mantissa2 == 0
		     && w.ieee.mantissa1 == 0
		     && w.ieee.mantissa0 == 0)))
	    {
	      volatile long double force_underflow = x * y;
	      (void) force_underflow;
	    }
	  return v.d * 0x1p-114L;
	}
      if (u.ieee.exponent + v.ieee.exponent
	  >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
	{
	  /* Compute 1p-113 times smaller result and multiply
	     at the end.  */
	  if (u.ieee.exponent > v.ieee.exponent)
	    u.ieee.exponent -= LDBL_MANT_DIG;
	  else
	    v.ieee.exponent -= LDBL_MANT_DIG;
	  /* If x + y exponent is very large and z exponent is very small,
	     it doesn't matter if we don't adjust it.  */
	  if (w.ieee.exponent > LDBL_MANT_DIG)
	    w.ieee.exponent -= LDBL_MANT_DIG;
	  adjust = 1;
	}
      else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
	{
	  /* Similarly.
	     If z exponent is very large and x and y exponents are
	     very small, adjust them up to avoid spurious underflows,
	     rather than down.  */
	  if (u.ieee.exponent + v.ieee.exponent
	      <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG)
	    {
	      if (u.ieee.exponent > v.ieee.exponent)
		u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
	      else
		v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
	    }
	  else if (u.ieee.exponent > v.ieee.exponent)
	    {
	      if (u.ieee.exponent > LDBL_MANT_DIG)
		u.ieee.exponent -= LDBL_MANT_DIG;
	    }
	  else if (v.ieee.exponent > LDBL_MANT_DIG)
	    v.ieee.exponent -= LDBL_MANT_DIG;
	  w.ieee.exponent -= LDBL_MANT_DIG;
	  adjust = 1;
	}
      else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
	{
	  u.ieee.exponent -= LDBL_MANT_DIG;
	  if (v.ieee.exponent)
	    v.ieee.exponent += LDBL_MANT_DIG;
	  else
	    v.d *= 0x1p113L;
	}
      else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
	{
	  v.ieee.exponent -= LDBL_MANT_DIG;
	  if (u.ieee.exponent)
	    u.ieee.exponent += LDBL_MANT_DIG;
	  else
	    u.d *= 0x1p113L;
	}
      else /* if (u.ieee.exponent + v.ieee.exponent
		  <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */
	{
	  if (u.ieee.exponent > v.ieee.exponent)
	    u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
	  else
	    v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
	  if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 6)
	    {
	      if (w.ieee.exponent)
		w.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
	      else
		w.d *= 0x1p228L;
	      adjust = -1;
	    }
	  /* Otherwise x * y should just affect inexact
	     and nothing else.  */
	}
      x = u.d;
      y = v.d;
      z = w.d;
    }

  /* Ensure correct sign of exact 0 + 0.  */
  if (__builtin_expect ((x == 0 || y == 0) && z == 0, 0))
    return x * y + z;

  fenv_t env;
  feholdexcept (&env);
  fesetround (FE_TONEAREST);

  /* Multiplication m1 + m2 = x * y using Dekker's algorithm.  */
#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
  long double x1 = x * C;
  long double y1 = y * C;
  long double m1 = x * y;
  x1 = (x - x1) + x1;
  y1 = (y - y1) + y1;
  long double x2 = x - x1;
  long double y2 = y - y1;
  long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;

  /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
  long double a1 = z + m1;
  long double t1 = a1 - z;
  long double t2 = a1 - t1;
  t1 = m1 - t1;
  t2 = z - t2;
  long double a2 = t1 + t2;
  feclearexcept (FE_INEXACT);

  /* If the result is an exact zero, ensure it has the correct
     sign.  */
  if (a1 == 0 && m2 == 0)
    {
      feupdateenv (&env);
      /* Ensure that round-to-nearest value of z + m1 is not
	 reused.  */
      asm volatile ("" : "=m" (z) : "m" (z));
      return z + m1;
    }

  fesetround (FE_TOWARDZERO);
  /* Perform m2 + a2 addition with round to odd.  */
  u.d = a2 + m2;

  if (__builtin_expect (adjust == 0, 1))
    {
      if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff)
	u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0;
      feupdateenv (&env);
      /* Result is a1 + u.d.  */
      return a1 + u.d;
    }
  else if (__builtin_expect (adjust > 0, 1))
    {
      if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff)
	u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0;
      feupdateenv (&env);
      /* Result is a1 + u.d, scaled up.  */
      return (a1 + u.d) * 0x1p113L;
    }
  else
    {
      if ((u.ieee.mantissa3 & 1) == 0)
	u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0;
      v.d = a1 + u.d;
      /* Ensure the addition is not scheduled after fetestexcept call.  */
      math_force_eval (v.d);
      int j = fetestexcept (FE_INEXACT) != 0;
      feupdateenv (&env);
      /* Ensure the following computations are performed in default rounding
	 mode instead of just reusing the round to zero computation.  */
      asm volatile ("" : "=m" (u) : "m" (u));
      /* If a1 + u.d is exact, the only rounding happens during
	 scaling down.  */
      if (j == 0)
	return v.d * 0x1p-228L;
      /* If result rounded to zero is not subnormal, no double
	 rounding will occur.  */
      if (v.ieee.exponent > 228)
	return (a1 + u.d) * 0x1p-228L;
      /* If v.d * 0x1p-228L with round to zero is a subnormal above
	 or equal to LDBL_MIN / 2, then v.d * 0x1p-228L shifts mantissa
	 down just by 1 bit, which means v.ieee.mantissa3 |= j would
	 change the round bit, not sticky or guard bit.
	 v.d * 0x1p-228L never normalizes by shifting up,
	 so round bit plus sticky bit should be already enough
	 for proper rounding.  */
      if (v.ieee.exponent == 228)
	{
	  /* If the exponent would be in the normal range when
	     rounding to normal precision with unbounded exponent
	     range, the exact result is known and spurious underflows
	     must be avoided on systems detecting tininess after
	     rounding.  */
	  if (TININESS_AFTER_ROUNDING)
	    {
	      w.d = a1 + u.d;
	      if (w.ieee.exponent == 229)
		return w.d * 0x1p-228L;
	    }
	  /* v.ieee.mantissa3 & 2 is LSB bit of the result before rounding,
	     v.ieee.mantissa3 & 1 is the round bit and j is our sticky
	     bit.  */
	  w.d = 0.0L;
	  w.ieee.mantissa3 = ((v.ieee.mantissa3 & 3) << 1) | j;
	  w.ieee.negative = v.ieee.negative;
	  v.ieee.mantissa3 &= ~3U;
	  v.d *= 0x1p-228L;
	  w.d *= 0x1p-2L;
	  return v.d + w.d;
	}
      v.ieee.mantissa3 |= j;
      return v.d * 0x1p-228L;
    }
}
weak_alias (__fmal, fmal)
Commit	Line	Data
3e692e05	1	/* Compute x * y + z as ternary operation.
d4697bc9	2	Copyright (C) 2010-2014 Free Software Foundation, Inc.
3e692e05 JJ	3	This file is part of the GNU C Library.
	4	Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
	5
	6	The GNU C Library is free software; you can redistribute it and/or
	7	modify it under the terms of the GNU Lesser General Public
	8	License as published by the Free Software Foundation; either
	9	version 2.1 of the License, or (at your option) any later version.
	10
	11	The GNU C Library is distributed in the hope that it will be useful,
	12	but WITHOUT ANY WARRANTY; without even the implied warranty of
	13	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
	14	Lesser General Public License for more details.
	15
	16	You should have received a copy of the GNU Lesser General Public
59ba27a6 PE	17	License along with the GNU C Library; if not, see
59ba27a6 PE	18	<http://www.gnu.org/licenses/>. */
3e692e05 JJ	19
	20	#include <float.h>
	21	#include <math.h>
	22	#include <fenv.h>
	23	#include <ieee754.h>
4842e4fe	24	#include <math_private.h>
ef82f4da	25	#include <tininess.h>
3e692e05 JJ	26
	27	/* This implementation uses rounding to odd to avoid problems with
	28	double rounding. See a paper by Boldo and Melquiond:
	29	http://www.lri.fr/~melquion/doc/08-tc.pdf */
	30
	31	long double
	32	__fmal (long double x, long double y, long double z)
	33	{
	34	union ieee854_long_double u, v, w;
	35	int adjust = 0;
	36	u.d = x;
	37	v.d = y;
	38	w.d = z;
	39	if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
	40	>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS
	41	- LDBL_MANT_DIG, 0)
	42	\|\| __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
	43	\|\| __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
	44	\|\| __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
	45	\|\| __builtin_expect (u.ieee.exponent + v.ieee.exponent
	46	<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0))
	47	{
	48	/* If z is Inf, but x and y are finite, the result should be
	49	z rather than NaN. */
	50	if (w.ieee.exponent == 0x7fff
	51	&& u.ieee.exponent != 0x7fff
	52	&& v.ieee.exponent != 0x7fff)
	53	return (z + x) + y;
bec749fd JM	54	/* If z is zero and x are y are nonzero, compute the result
	55	as x * y to avoid the wrong sign of a zero result if x * y
	56	underflows to 0. */
	57	if (z == 0 && x != 0 && y != 0)
	58	return x * y;
a0c2940d JM	59	/* If x or y or z is Inf/NaN, or if x * y is zero, compute as
a0c2940d JM	60	x * y + z. */
3e692e05 JJ	61	if (u.ieee.exponent == 0x7fff
	62	\|\| v.ieee.exponent == 0x7fff
	63	\|\| w.ieee.exponent == 0x7fff
473611b2 JM	64	\|\| x == 0
473611b2 JM	65	\|\| y == 0)
3e692e05	66	return x * y + z;
a0c2940d JM	67	/* If fma will certainly overflow, compute as x * y. */
	68	if (u.ieee.exponent + v.ieee.exponent
	69	> 0x7fff + IEEE854_LONG_DOUBLE_BIAS)
	70	return x * y;
473611b2 JM	71	/* If x * y is less than 1/4 of LDBL_DENORM_MIN, neither the
	72	result nor whether there is underflow depends on its exact
	73	value, only on its sign. */
	74	if (u.ieee.exponent + v.ieee.exponent
	75	< IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
	76	{
	77	int neg = u.ieee.negative ^ v.ieee.negative;
	78	long double tiny = neg ? -0x1p-16494L : 0x1p-16494L;
	79	if (w.ieee.exponent >= 3)
	80	return tiny + z;
	81	/* Scaling up, adding TINY and scaling down produces the
	82	correct result, because in round-to-nearest mode adding
	83	TINY has no effect and in other modes double rounding is
	84	harmless. But it may not produce required underflow
	85	exceptions. */
	86	v.d = z * 0x1p114L + tiny;
	87	if (TININESS_AFTER_ROUNDING
	88	? v.ieee.exponent < 115
	89	: (w.ieee.exponent == 0
	90	\|\| (w.ieee.exponent == 1
	91	&& w.ieee.negative != neg
	92	&& w.ieee.mantissa3 == 0
	93	&& w.ieee.mantissa2 == 0
	94	&& w.ieee.mantissa1 == 0
	95	&& w.ieee.mantissa0 == 0)))
	96	{
	97	volatile long double force_underflow = x * y;
	98	(void) force_underflow;
	99	}
	100	return v.d * 0x1p-114L;
	101	}
3e692e05 JJ	102	if (u.ieee.exponent + v.ieee.exponent
	103	>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
	104	{
	105	/* Compute 1p-113 times smaller result and multiply
	106	at the end. */
	107	if (u.ieee.exponent > v.ieee.exponent)
	108	u.ieee.exponent -= LDBL_MANT_DIG;
	109	else
	110	v.ieee.exponent -= LDBL_MANT_DIG;
	111	/* If x + y exponent is very large and z exponent is very small,
	112	it doesn't matter if we don't adjust it. */
	113	if (w.ieee.exponent > LDBL_MANT_DIG)
	114	w.ieee.exponent -= LDBL_MANT_DIG;
	115	adjust = 1;
	116	}
	117	else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
	118	{
	119	/* Similarly.
	120	If z exponent is very large and x and y exponents are
82477c28 JM	121	very small, adjust them up to avoid spurious underflows,
	122	rather than down. */
	123	if (u.ieee.exponent + v.ieee.exponent
	124	<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG)
	125	{
	126	if (u.ieee.exponent > v.ieee.exponent)
	127	u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
	128	else
	129	v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
	130	}
	131	else if (u.ieee.exponent > v.ieee.exponent)
3e692e05 JJ	132	{
	133	if (u.ieee.exponent > LDBL_MANT_DIG)
	134	u.ieee.exponent -= LDBL_MANT_DIG;
	135	}
	136	else if (v.ieee.exponent > LDBL_MANT_DIG)
	137	v.ieee.exponent -= LDBL_MANT_DIG;
	138	w.ieee.exponent -= LDBL_MANT_DIG;
	139	adjust = 1;
	140	}
	141	else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
	142	{
	143	u.ieee.exponent -= LDBL_MANT_DIG;
	144	if (v.ieee.exponent)
	145	v.ieee.exponent += LDBL_MANT_DIG;
	146	else
	147	v.d *= 0x1p113L;
	148	}
	149	else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
	150	{
	151	v.ieee.exponent -= LDBL_MANT_DIG;
	152	if (u.ieee.exponent)
	153	u.ieee.exponent += LDBL_MANT_DIG;
	154	else
	155	u.d *= 0x1p113L;
	156	}
	157	else /* if (u.ieee.exponent + v.ieee.exponent
	158	<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */
	159	{
	160	if (u.ieee.exponent > v.ieee.exponent)
82477c28	161	u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
3e692e05	162	else
82477c28 JM	163	v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
82477c28 JM	164	if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 6)
3e692e05 JJ	165	{
3e692e05 JJ	166	if (w.ieee.exponent)
82477c28	167	w.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
3e692e05	168	else
82477c28	169	w.d *= 0x1p228L;
3e692e05 JJ	170	adjust = -1;
	171	}
	172	/* Otherwise x * y should just affect inexact
	173	and nothing else. */
	174	}
	175	x = u.d;
	176	y = v.d;
	177	z = w.d;
	178	}
8ec5b013 JM	179
	180	/* Ensure correct sign of exact 0 + 0. */
	181	if (__builtin_expect ((x == 0 \|\| y == 0) && z == 0, 0))
	182	return x * y + z;
	183
5b5b04d6 JM	184	fenv_t env;
	185	feholdexcept (&env);
	186	fesetround (FE_TONEAREST);
	187
3e692e05 JJ	188	/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
	189	#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
	190	long double x1 = x * C;
	191	long double y1 = y * C;
	192	long double m1 = x * y;
	193	x1 = (x - x1) + x1;
	194	y1 = (y - y1) + y1;
	195	long double x2 = x - x1;
	196	long double y2 = y - y1;
	197	long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
	198
	199	/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
	200	long double a1 = z + m1;
	201	long double t1 = a1 - z;
	202	long double t2 = a1 - t1;
	203	t1 = m1 - t1;
	204	t2 = z - t2;
	205	long double a2 = t1 + t2;
5b5b04d6 JM	206	feclearexcept (FE_INEXACT);
	207
	208	/* If the result is an exact zero, ensure it has the correct
	209	sign. */
	210	if (a1 == 0 && m2 == 0)
	211	{
	212	feupdateenv (&env);
	213	/* Ensure that round-to-nearest value of z + m1 is not
	214	reused. */
	215	asm volatile ("" : "=m" (z) : "m" (z));
	216	return z + m1;
	217	}
3e692e05	218
3e692e05 JJ	219	fesetround (FE_TOWARDZERO);
	220	/* Perform m2 + a2 addition with round to odd. */
	221	u.d = a2 + m2;
	222
	223	if (__builtin_expect (adjust == 0, 1))
	224	{
	225	if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff)
	226	u.ieee.mantissa3 \|= fetestexcept (FE_INEXACT) != 0;
	227	feupdateenv (&env);
	228	/* Result is a1 + u.d. */
	229	return a1 + u.d;
	230	}
	231	else if (__builtin_expect (adjust > 0, 1))
	232	{
	233	if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff)
	234	u.ieee.mantissa3 \|= fetestexcept (FE_INEXACT) != 0;
	235	feupdateenv (&env);
	236	/* Result is a1 + u.d, scaled up. */
	237	return (a1 + u.d) * 0x1p113L;
	238	}
	239	else
	240	{
	241	if ((u.ieee.mantissa3 & 1) == 0)
	242	u.ieee.mantissa3 \|= fetestexcept (FE_INEXACT) != 0;
	243	v.d = a1 + u.d;
7c08a05c	244	/* Ensure the addition is not scheduled after fetestexcept call. */
4842e4fe	245	math_force_eval (v.d);
3e692e05 JJ	246	int j = fetestexcept (FE_INEXACT) != 0;
	247	feupdateenv (&env);
	248	/* Ensure the following computations are performed in default rounding
	249	mode instead of just reusing the round to zero computation. */
	250	asm volatile ("" : "=m" (u) : "m" (u));
	251	/* If a1 + u.d is exact, the only rounding happens during
	252	scaling down. */
	253	if (j == 0)
82477c28	254	return v.d * 0x1p-228L;
3e692e05 JJ	255	/* If result rounded to zero is not subnormal, no double
3e692e05 JJ	256	rounding will occur. */
82477c28 JM	257	if (v.ieee.exponent > 228)
	258	return (a1 + u.d) * 0x1p-228L;
	259	/* If v.d * 0x1p-228L with round to zero is a subnormal above
	260	or equal to LDBL_MIN / 2, then v.d * 0x1p-228L shifts mantissa
3e692e05 JJ	261	down just by 1 bit, which means v.ieee.mantissa3 \|= j would
3e692e05 JJ	262	change the round bit, not sticky or guard bit.
82477c28	263	v.d * 0x1p-228L never normalizes by shifting up,
3e692e05 JJ	264	so round bit plus sticky bit should be already enough
3e692e05 JJ	265	for proper rounding. */
82477c28	266	if (v.ieee.exponent == 228)
3e692e05	267	{
ef82f4da JM	268	/* If the exponent would be in the normal range when
	269	rounding to normal precision with unbounded exponent
	270	range, the exact result is known and spurious underflows
	271	must be avoided on systems detecting tininess after
	272	rounding. */
	273	if (TININESS_AFTER_ROUNDING)
	274	{
	275	w.d = a1 + u.d;
82477c28 JM	276	if (w.ieee.exponent == 229)
82477c28 JM	277	return w.d * 0x1p-228L;
ef82f4da	278	}
3e692e05 JJ	279	/* v.ieee.mantissa3 & 2 is LSB bit of the result before rounding,
3e692e05 JJ	280	v.ieee.mantissa3 & 1 is the round bit and j is our sticky
8627a232 JM	281	bit. */
	282	w.d = 0.0L;
	283	w.ieee.mantissa3 = ((v.ieee.mantissa3 & 3) << 1) \| j;
	284	w.ieee.negative = v.ieee.negative;
	285	v.ieee.mantissa3 &= ~3U;
82477c28	286	v.d *= 0x1p-228L;
8627a232 JM	287	w.d *= 0x1p-2L;
8627a232 JM	288	return v.d + w.d;
3e692e05 JJ	289	}
3e692e05 JJ	290	v.ieee.mantissa3 \|= j;
82477c28	291	return v.d * 0x1p-228L;
3e692e05 JJ	292	}
	293	}
	294	weak_alias (__fmal, fmal)