[thirdparty/glibc.git] / sysdeps / ieee754 / ldbl-96 / s_fmal.c

/* Compute x * y + z as ternary operation.
   Copyright (C) 2010-2018 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 <libm-alias-ldouble.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_TRUE_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-16445L : 0x1p-16445L;
	  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 * 0x1p65L + tiny;
	  if (TININESS_AFTER_ROUNDING
	      ? v.ieee.exponent < 66
	      : (w.ieee.exponent == 0
		 || (w.ieee.exponent == 1
		     && w.ieee.negative != neg
		     && w.ieee.mantissa1 == 0
		     && w.ieee.mantissa0 == 0x80000000)))
	    {
	      long double force_underflow = x * y;
	      math_force_eval (force_underflow);
	    }
	  return v.d * 0x1p-65L;
	}
      if (u.ieee.exponent + v.ieee.exponent
	  >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
	{
	  /* Compute 1p-64 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 + 2 * 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 *= 0x1p64L;
	}
      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 *= 0x1p64L;
	}
      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 *= 0x1p130L;
	      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 (__glibc_unlikely ((x == 0 || y == 0) && z == 0))
    {
      x = math_opt_barrier (x);
      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;
  /* Ensure the arithmetic is not scheduled after feclearexcept call.  */
  math_force_eval (m2);
  math_force_eval (a2);
  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.  */
      z = math_opt_barrier (z);
      return z + m1;
    }

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

  if (__glibc_likely (adjust == 0))
    {
      if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
	u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
      feupdateenv (&env);
      /* Result is a1 + u.d.  */
      return a1 + u.d;
    }
  else if (__glibc_likely (adjust > 0))
    {
      if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
	u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
      feupdateenv (&env);
      /* Result is a1 + u.d, scaled up.  */
      return (a1 + u.d) * 0x1p64L;
    }
  else
    {
      if ((u.ieee.mantissa1 & 1) == 0)
	u.ieee.mantissa1 |= 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-130L;
      /* If result rounded to zero is not subnormal, no double
	 rounding will occur.  */
      if (v.ieee.exponent > 130)
	return (a1 + u.d) * 0x1p-130L;
      /* If v.d * 0x1p-130L with round to zero is a subnormal above
	 or equal to LDBL_MIN / 2, then v.d * 0x1p-130L shifts mantissa
	 down just by 1 bit, which means v.ieee.mantissa1 |= j would
	 change the round bit, not sticky or guard bit.
	 v.d * 0x1p-130L never normalizes by shifting up,
	 so round bit plus sticky bit should be already enough
	 for proper rounding.  */
      if (v.ieee.exponent == 130)
	{
	  /* 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 == 131)
		return w.d * 0x1p-130L;
	    }
	  /* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
	     v.ieee.mantissa1 & 1 is the round bit and j is our sticky
	     bit.  */
	  w.d = 0.0L;
	  w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) | j;
	  w.ieee.negative = v.ieee.negative;
	  v.ieee.mantissa1 &= ~3U;
	  v.d *= 0x1p-130L;
	  w.d *= 0x1p-2L;
	  return v.d + w.d;
	}
      v.ieee.mantissa1 |= j;
      return v.d * 0x1p-130L;
    }
}
libm_alias_ldouble (__fma, fma)
Commit	Line	Data
3e692e05	1	/* Compute x * y + z as ternary operation.
688903eb	2	Copyright (C) 2010-2018 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>
86f9568a	25	#include <libm-alias-ldouble.h>
ef82f4da	26	#include <tininess.h>
3e692e05 JJ	27
	28	/* This implementation uses rounding to odd to avoid problems with
	29	double rounding. See a paper by Boldo and Melquiond:
	30	http://www.lri.fr/~melquion/doc/08-tc.pdf */
	31
	32	long double
	33	__fmal (long double x, long double y, long double z)
	34	{
	35	union ieee854_long_double u, v, w;
	36	int adjust = 0;
	37	u.d = x;
	38	v.d = y;
	39	w.d = z;
	40	if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
	41	>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS
	42	- LDBL_MANT_DIG, 0)
	43	\|\| __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
	44	\|\| __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
	45	\|\| __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
	46	\|\| __builtin_expect (u.ieee.exponent + v.ieee.exponent
	47	<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0))
	48	{
	49	/* If z is Inf, but x and y are finite, the result should be
	50	z rather than NaN. */
	51	if (w.ieee.exponent == 0x7fff
	52	&& u.ieee.exponent != 0x7fff
	53	&& v.ieee.exponent != 0x7fff)
	54	return (z + x) + y;
bec749fd JM	55	/* If z is zero and x are y are nonzero, compute the result
	56	as x * y to avoid the wrong sign of a zero result if x * y
	57	underflows to 0. */
	58	if (z == 0 && x != 0 && y != 0)
	59	return x * y;
a0c2940d JM	60	/* If x or y or z is Inf/NaN, or if x * y is zero, compute as
a0c2940d JM	61	x * y + z. */
3e692e05 JJ	62	if (u.ieee.exponent == 0x7fff
	63	\|\| v.ieee.exponent == 0x7fff
	64	\|\| w.ieee.exponent == 0x7fff
473611b2 JM	65	\|\| x == 0
473611b2 JM	66	\|\| y == 0)
3e692e05	67	return x * y + z;
a0c2940d JM	68	/* If fma will certainly overflow, compute as x * y. */
	69	if (u.ieee.exponent + v.ieee.exponent
	70	> 0x7fff + IEEE854_LONG_DOUBLE_BIAS)
	71	return x * y;
1f4dafa3	72	/* If x * y is less than 1/4 of LDBL_TRUE_MIN, neither the
473611b2 JM	73	result nor whether there is underflow depends on its exact
	74	value, only on its sign. */
	75	if (u.ieee.exponent + v.ieee.exponent
	76	< IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
	77	{
	78	int neg = u.ieee.negative ^ v.ieee.negative;
	79	long double tiny = neg ? -0x1p-16445L : 0x1p-16445L;
	80	if (w.ieee.exponent >= 3)
	81	return tiny + z;
	82	/* Scaling up, adding TINY and scaling down produces the
	83	correct result, because in round-to-nearest mode adding
	84	TINY has no effect and in other modes double rounding is
	85	harmless. But it may not produce required underflow
	86	exceptions. */
	87	v.d = z * 0x1p65L + tiny;
	88	if (TININESS_AFTER_ROUNDING
	89	? v.ieee.exponent < 66
	90	: (w.ieee.exponent == 0
	91	\|\| (w.ieee.exponent == 1
	92	&& w.ieee.negative != neg
	93	&& w.ieee.mantissa1 == 0
	94	&& w.ieee.mantissa0 == 0x80000000)))
	95	{
d96164c3 JM	96	long double force_underflow = x * y;
d96164c3 JM	97	math_force_eval (force_underflow);
473611b2 JM	98	}
	99	return v.d * 0x1p-65L;
	100	}
3e692e05 JJ	101	if (u.ieee.exponent + v.ieee.exponent
	102	>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
	103	{
	104	/* Compute 1p-64 times smaller result and multiply
	105	at the end. */
	106	if (u.ieee.exponent > v.ieee.exponent)
	107	u.ieee.exponent -= LDBL_MANT_DIG;
	108	else
	109	v.ieee.exponent -= LDBL_MANT_DIG;
	110	/* If x + y exponent is very large and z exponent is very small,
	111	it doesn't matter if we don't adjust it. */
	112	if (w.ieee.exponent > LDBL_MANT_DIG)
	113	w.ieee.exponent -= LDBL_MANT_DIG;
	114	adjust = 1;
	115	}
	116	else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
	117	{
	118	/* Similarly.
	119	If z exponent is very large and x and y exponents are
82477c28 JM	120	very small, adjust them up to avoid spurious underflows,
	121	rather than down. */
	122	if (u.ieee.exponent + v.ieee.exponent
739babd7	123	<= IEEE854_LONG_DOUBLE_BIAS + 2 * LDBL_MANT_DIG)
82477c28 JM	124	{
	125	if (u.ieee.exponent > v.ieee.exponent)
	126	u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
	127	else
	128	v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
	129	}
	130	else if (u.ieee.exponent > v.ieee.exponent)
3e692e05 JJ	131	{
	132	if (u.ieee.exponent > LDBL_MANT_DIG)
	133	u.ieee.exponent -= LDBL_MANT_DIG;
	134	}
	135	else if (v.ieee.exponent > LDBL_MANT_DIG)
	136	v.ieee.exponent -= LDBL_MANT_DIG;
	137	w.ieee.exponent -= LDBL_MANT_DIG;
	138	adjust = 1;
	139	}
	140	else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
	141	{
	142	u.ieee.exponent -= LDBL_MANT_DIG;
	143	if (v.ieee.exponent)
	144	v.ieee.exponent += LDBL_MANT_DIG;
	145	else
	146	v.d *= 0x1p64L;
	147	}
	148	else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
	149	{
	150	v.ieee.exponent -= LDBL_MANT_DIG;
	151	if (u.ieee.exponent)
	152	u.ieee.exponent += LDBL_MANT_DIG;
	153	else
	154	u.d *= 0x1p64L;
	155	}
	156	else /* if (u.ieee.exponent + v.ieee.exponent
	157	<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */
	158	{
	159	if (u.ieee.exponent > v.ieee.exponent)
82477c28	160	u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
3e692e05	161	else
82477c28 JM	162	v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
82477c28 JM	163	if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 6)
3e692e05 JJ	164	{
3e692e05 JJ	165	if (w.ieee.exponent)
82477c28	166	w.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
3e692e05	167	else
82477c28	168	w.d *= 0x1p130L;
3e692e05 JJ	169	adjust = -1;
	170	}
	171	/* Otherwise x * y should just affect inexact
	172	and nothing else. */
	173	}
	174	x = u.d;
	175	y = v.d;
	176	z = w.d;
	177	}
8ec5b013 JM	178
8ec5b013 JM	179	/* Ensure correct sign of exact 0 + 0. */
a1ffb40e	180	if (__glibc_unlikely ((x == 0 \|\| y == 0) && z == 0))
09245377 L	181	{
	182	x = math_opt_barrier (x);
	183	return x * y + z;
	184	}
8ec5b013	185
5b5b04d6 JM	186	fenv_t env;
	187	feholdexcept (&env);
	188	fesetround (FE_TONEAREST);
	189
3e692e05 JJ	190	/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
	191	#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
	192	long double x1 = x * C;
	193	long double y1 = y * C;
	194	long double m1 = x * y;
	195	x1 = (x - x1) + x1;
	196	y1 = (y - y1) + y1;
	197	long double x2 = x - x1;
	198	long double y2 = y - y1;
	199	long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
	200
	201	/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
	202	long double a1 = z + m1;
	203	long double t1 = a1 - z;
	204	long double t2 = a1 - t1;
	205	t1 = m1 - t1;
	206	t2 = z - t2;
	207	long double a2 = t1 + t2;
4896f049 RH	208	/* Ensure the arithmetic is not scheduled after feclearexcept call. */
	209	math_force_eval (m2);
	210	math_force_eval (a2);
5b5b04d6 JM	211	feclearexcept (FE_INEXACT);
5b5b04d6 JM	212
4896f049	213	/* If the result is an exact zero, ensure it has the correct sign. */
5b5b04d6 JM	214	if (a1 == 0 && m2 == 0)
	215	{
	216	feupdateenv (&env);
4896f049 RH	217	/* Ensure that round-to-nearest value of z + m1 is not reused. */
4896f049 RH	218	z = math_opt_barrier (z);
5b5b04d6 JM	219	return z + m1;
5b5b04d6 JM	220	}
3e692e05	221
3e692e05 JJ	222	fesetround (FE_TOWARDZERO);
	223	/* Perform m2 + a2 addition with round to odd. */
	224	u.d = a2 + m2;
	225
a1ffb40e	226	if (__glibc_likely (adjust == 0))
3e692e05 JJ	227	{
	228	if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
	229	u.ieee.mantissa1 \|= fetestexcept (FE_INEXACT) != 0;
	230	feupdateenv (&env);
	231	/* Result is a1 + u.d. */
	232	return a1 + u.d;
	233	}
a1ffb40e	234	else if (__glibc_likely (adjust > 0))
3e692e05 JJ	235	{
	236	if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
	237	u.ieee.mantissa1 \|= fetestexcept (FE_INEXACT) != 0;
	238	feupdateenv (&env);
	239	/* Result is a1 + u.d, scaled up. */
	240	return (a1 + u.d) * 0x1p64L;
	241	}
	242	else
	243	{
	244	if ((u.ieee.mantissa1 & 1) == 0)
	245	u.ieee.mantissa1 \|= fetestexcept (FE_INEXACT) != 0;
	246	v.d = a1 + u.d;
4842e4fe JM	247	/* Ensure the addition is not scheduled after fetestexcept call. */
4842e4fe JM	248	math_force_eval (v.d);
3e692e05 JJ	249	int j = fetestexcept (FE_INEXACT) != 0;
	250	feupdateenv (&env);
	251	/* Ensure the following computations are performed in default rounding
	252	mode instead of just reusing the round to zero computation. */
	253	asm volatile ("" : "=m" (u) : "m" (u));
	254	/* If a1 + u.d is exact, the only rounding happens during
	255	scaling down. */
	256	if (j == 0)
82477c28	257	return v.d * 0x1p-130L;
3e692e05 JJ	258	/* If result rounded to zero is not subnormal, no double
3e692e05 JJ	259	rounding will occur. */
82477c28 JM	260	if (v.ieee.exponent > 130)
	261	return (a1 + u.d) * 0x1p-130L;
	262	/* If v.d * 0x1p-130L with round to zero is a subnormal above
	263	or equal to LDBL_MIN / 2, then v.d * 0x1p-130L shifts mantissa
3e692e05 JJ	264	down just by 1 bit, which means v.ieee.mantissa1 \|= j would
3e692e05 JJ	265	change the round bit, not sticky or guard bit.
82477c28	266	v.d * 0x1p-130L never normalizes by shifting up,
3e692e05 JJ	267	so round bit plus sticky bit should be already enough
3e692e05 JJ	268	for proper rounding. */
82477c28	269	if (v.ieee.exponent == 130)
3e692e05	270	{
ef82f4da JM	271	/* If the exponent would be in the normal range when
	272	rounding to normal precision with unbounded exponent
	273	range, the exact result is known and spurious underflows
	274	must be avoided on systems detecting tininess after
	275	rounding. */
	276	if (TININESS_AFTER_ROUNDING)
	277	{
	278	w.d = a1 + u.d;
82477c28 JM	279	if (w.ieee.exponent == 131)
82477c28 JM	280	return w.d * 0x1p-130L;
ef82f4da	281	}
3e692e05 JJ	282	/* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
3e692e05 JJ	283	v.ieee.mantissa1 & 1 is the round bit and j is our sticky
8627a232 JM	284	bit. */
	285	w.d = 0.0L;
	286	w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) \| j;
	287	w.ieee.negative = v.ieee.negative;
	288	v.ieee.mantissa1 &= ~3U;
82477c28	289	v.d *= 0x1p-130L;
8627a232 JM	290	w.d *= 0x1p-2L;
8627a232 JM	291	return v.d + w.d;
3e692e05 JJ	292	}
3e692e05 JJ	293	v.ieee.mantissa1 \|= j;
82477c28	294	return v.d * 0x1p-130L;
3e692e05 JJ	295	}
3e692e05 JJ	296	}
86f9568a	297	libm_alias_ldouble (__fma, fma)