[thirdparty/glibc.git] / sysdeps / ieee754 / dbl-64 / s_fma.c

/* Compute x * y + z as ternary operation.
   Copyright (C) 2010-2021 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
   <https://www.gnu.org/licenses/>.  */

#include <float.h>
#include <math.h>
#include <fenv.h>
#include <ieee754.h>
#include <math-barriers.h>
#include <fenv_private.h>
#include <libm-alias-double.h>
#include <tininess.h>
#include <math-use-builtins.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  */

double
__fma (double x, double y, double z)
{
#if USE_FMA_BUILTIN
  return __builtin_fma (x, y, z);
#else
  /* Use generic implementation.  */
  union ieee754_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
			>= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG, 0)
      || __builtin_expect (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
      || __builtin_expect (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
      || __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
      || __builtin_expect (u.ieee.exponent + v.ieee.exponent
			   <= IEEE754_DOUBLE_BIAS + DBL_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 == 0x7ff
	  && u.ieee.exponent != 0x7ff
	  && v.ieee.exponent != 0x7ff)
	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 == 0x7ff
	  || v.ieee.exponent == 0x7ff
	  || w.ieee.exponent == 0x7ff
	  || x == 0
	  || y == 0)
	return x * y + z;
      /* If fma will certainly overflow, compute as x * y.  */
      if (u.ieee.exponent + v.ieee.exponent > 0x7ff + IEEE754_DOUBLE_BIAS)
	return x * y;
      /* If x * y is less than 1/4 of DBL_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
	  < IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2)
	{
	  int neg = u.ieee.negative ^ v.ieee.negative;
	  double tiny = neg ? -0x1p-1074 : 0x1p-1074;
	  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 * 0x1p54 + tiny;
	  if (TININESS_AFTER_ROUNDING
	      ? v.ieee.exponent < 55
	      : (w.ieee.exponent == 0
		 || (w.ieee.exponent == 1
		     && w.ieee.negative != neg
		     && w.ieee.mantissa1 == 0
		     && w.ieee.mantissa0 == 0)))
	    {
	      double force_underflow = x * y;
	      math_force_eval (force_underflow);
	    }
	  return v.d * 0x1p-54;
	}
      if (u.ieee.exponent + v.ieee.exponent
	  >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG)
	{
	  /* Compute 1p-53 times smaller result and multiply
	     at the end.  */
	  if (u.ieee.exponent > v.ieee.exponent)
	    u.ieee.exponent -= DBL_MANT_DIG;
	  else
	    v.ieee.exponent -= DBL_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 > DBL_MANT_DIG)
	    w.ieee.exponent -= DBL_MANT_DIG;
	  adjust = 1;
	}
      else if (w.ieee.exponent >= 0x7ff - DBL_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
	      <= IEEE754_DOUBLE_BIAS + 2 * DBL_MANT_DIG)
	    {
	      if (u.ieee.exponent > v.ieee.exponent)
		u.ieee.exponent += 2 * DBL_MANT_DIG + 2;
	      else
		v.ieee.exponent += 2 * DBL_MANT_DIG + 2;
	    }
	  else if (u.ieee.exponent > v.ieee.exponent)
	    {
	      if (u.ieee.exponent > DBL_MANT_DIG)
		u.ieee.exponent -= DBL_MANT_DIG;
	    }
	  else if (v.ieee.exponent > DBL_MANT_DIG)
	    v.ieee.exponent -= DBL_MANT_DIG;
	  w.ieee.exponent -= DBL_MANT_DIG;
	  adjust = 1;
	}
      else if (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
	{
	  u.ieee.exponent -= DBL_MANT_DIG;
	  if (v.ieee.exponent)
	    v.ieee.exponent += DBL_MANT_DIG;
	  else
	    v.d *= 0x1p53;
	}
      else if (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
	{
	  v.ieee.exponent -= DBL_MANT_DIG;
	  if (u.ieee.exponent)
	    u.ieee.exponent += DBL_MANT_DIG;
	  else
	    u.d *= 0x1p53;
	}
      else /* if (u.ieee.exponent + v.ieee.exponent
		  <= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG) */
	{
	  if (u.ieee.exponent > v.ieee.exponent)
	    u.ieee.exponent += 2 * DBL_MANT_DIG + 2;
	  else
	    v.ieee.exponent += 2 * DBL_MANT_DIG + 2;
	  if (w.ieee.exponent <= 4 * DBL_MANT_DIG + 6)
	    {
	      if (w.ieee.exponent)
		w.ieee.exponent += 2 * DBL_MANT_DIG + 2;
	      else
		w.d *= 0x1p108;
	      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;
  libc_feholdexcept_setround (&env, FE_TONEAREST);

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

  /* Addition a1 + a2 = z + m1 using Knuth's algorithm.  */
  double a1 = z + m1;
  double t1 = a1 - z;
  double t2 = a1 - t1;
  t1 = m1 - t1;
  t2 = z - t2;
  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)
    {
      libc_feupdateenv (&env);
      /* Ensure that round-to-nearest value of z + m1 is not reused.  */
      z = math_opt_barrier (z);
      return z + m1;
    }

  libc_fesetround (FE_TOWARDZERO);

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

  if (__glibc_unlikely (adjust < 0))
    {
      if ((u.ieee.mantissa1 & 1) == 0)
	u.ieee.mantissa1 |= libc_fetestexcept (FE_INEXACT) != 0;
      v.d = a1 + u.d;
      /* Ensure the addition is not scheduled after fetestexcept call.  */
      math_force_eval (v.d);
    }

  /* Reset rounding mode and test for inexact simultaneously.  */
  int j = libc_feupdateenv_test (&env, FE_INEXACT) != 0;

  if (__glibc_likely (adjust == 0))
    {
      if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
	u.ieee.mantissa1 |= j;
      /* Result is a1 + u.d.  */
      return a1 + u.d;
    }
  else if (__glibc_likely (adjust > 0))
    {
      if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
	u.ieee.mantissa1 |= j;
      /* Result is a1 + u.d, scaled up.  */
      return (a1 + u.d) * 0x1p53;
    }
  else
    {
      /* If a1 + u.d is exact, the only rounding happens during
	 scaling down.  */
      if (j == 0)
	return v.d * 0x1p-108;
      /* If result rounded to zero is not subnormal, no double
	 rounding will occur.  */
      if (v.ieee.exponent > 108)
	return (a1 + u.d) * 0x1p-108;
      /* If v.d * 0x1p-108 with round to zero is a subnormal above
	 or equal to DBL_MIN / 2, then v.d * 0x1p-108 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-108 never normalizes by shifting up,
	 so round bit plus sticky bit should be already enough
	 for proper rounding.  */
      if (v.ieee.exponent == 108)
	{
	  /* 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 == 109)
		return w.d * 0x1p-108;
	    }
	  /* 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 = 0.0;
	  w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) | j;
	  w.ieee.negative = v.ieee.negative;
	  v.ieee.mantissa1 &= ~3U;
	  v.d *= 0x1p-108;
	  w.d *= 0x1p-2;
	  return v.d + w.d;
	}
      v.ieee.mantissa1 |= j;
      return v.d * 0x1p-108;
    }
#endif /* ! USE_FMA_BUILTIN  */
}
#ifndef __fma
libm_alias_double (__fma, fma)
#endif
Commit	Line	Data
5e908464	1	/* Compute x * y + z as ternary operation.
2b778ceb	2	Copyright (C) 2010-2021 Free Software Foundation, Inc.
5e908464 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	17	License along with the GNU C Library; if not, see
5a82c748	18	<https://www.gnu.org/licenses/>. */
5e908464 JJ	19
	20	#include <float.h>
	21	#include <math.h>
	22	#include <fenv.h>
	23	#include <ieee754.h>
b4d5b8b0	24	#include <math-barriers.h>
70e2ba33	25	#include <fenv_private.h>
7e16a5d1	26	#include <libm-alias-double.h>
ef82f4da	27	#include <tininess.h>
628d90c5	28	#include <math-use-builtins.h>
5e908464 JJ	29
	30	/* This implementation uses rounding to odd to avoid problems with
	31	double rounding. See a paper by Boldo and Melquiond:
	32	http://www.lri.fr/~melquion/doc/08-tc.pdf */
	33
	34	double
	35	__fma (double x, double y, double z)
	36	{
628d90c5 VG	37	#if USE_FMA_BUILTIN
	38	return __builtin_fma (x, y, z);
	39	#else
	40	/* Use generic implementation. */
5e908464 JJ	41	union ieee754_double u, v, w;
	42	int adjust = 0;
	43	u.d = x;
	44	v.d = y;
	45	w.d = z;
	46	if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
	47	>= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG, 0)
	48	\|\| __builtin_expect (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
	49	\|\| __builtin_expect (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
f3f7372d JJ	50	\|\| __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
	51	\|\| __builtin_expect (u.ieee.exponent + v.ieee.exponent
	52	<= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG, 0))
5e908464	53	{
3e692e05 JJ	54	/* If z is Inf, but x and y are finite, the result should be
	55	z rather than NaN. */
	56	if (w.ieee.exponent == 0x7ff
	57	&& u.ieee.exponent != 0x7ff
d9a8d0ab	58	&& v.ieee.exponent != 0x7ff)
3e692e05	59	return (z + x) + y;
bec749fd JM	60	/* If z is zero and x are y are nonzero, compute the result
	61	as x * y to avoid the wrong sign of a zero result if x * y
	62	underflows to 0. */
	63	if (z == 0 && x != 0 && y != 0)
	64	return x * y;
a0c2940d JM	65	/* If x or y or z is Inf/NaN, or if x * y is zero, compute as
a0c2940d JM	66	x * y + z. */
5e908464 JJ	67	if (u.ieee.exponent == 0x7ff
	68	\|\| v.ieee.exponent == 0x7ff
	69	\|\| w.ieee.exponent == 0x7ff
473611b2 JM	70	\|\| x == 0
473611b2 JM	71	\|\| y == 0)
5e908464	72	return x * y + z;
a0c2940d JM	73	/* If fma will certainly overflow, compute as x * y. */
	74	if (u.ieee.exponent + v.ieee.exponent > 0x7ff + IEEE754_DOUBLE_BIAS)
	75	return x * y;
1f4dafa3	76	/* If x * y is less than 1/4 of DBL_TRUE_MIN, neither the
473611b2 JM	77	result nor whether there is underflow depends on its exact
	78	value, only on its sign. */
	79	if (u.ieee.exponent + v.ieee.exponent
	80	< IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2)
	81	{
	82	int neg = u.ieee.negative ^ v.ieee.negative;
	83	double tiny = neg ? -0x1p-1074 : 0x1p-1074;
	84	if (w.ieee.exponent >= 3)
	85	return tiny + z;
	86	/* Scaling up, adding TINY and scaling down produces the
	87	correct result, because in round-to-nearest mode adding
	88	TINY has no effect and in other modes double rounding is
	89	harmless. But it may not produce required underflow
	90	exceptions. */
	91	v.d = z * 0x1p54 + tiny;
	92	if (TININESS_AFTER_ROUNDING
	93	? v.ieee.exponent < 55
	94	: (w.ieee.exponent == 0
	95	\|\| (w.ieee.exponent == 1
	96	&& w.ieee.negative != neg
	97	&& w.ieee.mantissa1 == 0
	98	&& w.ieee.mantissa0 == 0)))
	99	{
d96164c3 JM	100	double force_underflow = x * y;
d96164c3 JM	101	math_force_eval (force_underflow);
473611b2 JM	102	}
	103	return v.d * 0x1p-54;
	104	}
5e908464 JJ	105	if (u.ieee.exponent + v.ieee.exponent
	106	>= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG)
	107	{
	108	/* Compute 1p-53 times smaller result and multiply
	109	at the end. */
	110	if (u.ieee.exponent > v.ieee.exponent)
	111	u.ieee.exponent -= DBL_MANT_DIG;
	112	else
	113	v.ieee.exponent -= DBL_MANT_DIG;
	114	/* If x + y exponent is very large and z exponent is very small,
	115	it doesn't matter if we don't adjust it. */
	116	if (w.ieee.exponent > DBL_MANT_DIG)
	117	w.ieee.exponent -= DBL_MANT_DIG;
	118	adjust = 1;
	119	}
	120	else if (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
	121	{
	122	/* Similarly.
	123	If z exponent is very large and x and y exponents are
82477c28 JM	124	very small, adjust them up to avoid spurious underflows,
	125	rather than down. */
	126	if (u.ieee.exponent + v.ieee.exponent
739babd7	127	<= IEEE754_DOUBLE_BIAS + 2 * DBL_MANT_DIG)
82477c28 JM	128	{
	129	if (u.ieee.exponent > v.ieee.exponent)
	130	u.ieee.exponent += 2 * DBL_MANT_DIG + 2;
	131	else
	132	v.ieee.exponent += 2 * DBL_MANT_DIG + 2;
	133	}
	134	else if (u.ieee.exponent > v.ieee.exponent)
5e908464 JJ	135	{
	136	if (u.ieee.exponent > DBL_MANT_DIG)
	137	u.ieee.exponent -= DBL_MANT_DIG;
	138	}
	139	else if (v.ieee.exponent > DBL_MANT_DIG)
	140	v.ieee.exponent -= DBL_MANT_DIG;
	141	w.ieee.exponent -= DBL_MANT_DIG;
	142	adjust = 1;
	143	}
	144	else if (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
	145	{
	146	u.ieee.exponent -= DBL_MANT_DIG;
	147	if (v.ieee.exponent)
	148	v.ieee.exponent += DBL_MANT_DIG;
	149	else
	150	v.d *= 0x1p53;
	151	}
f3f7372d	152	else if (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
5e908464 JJ	153	{
	154	v.ieee.exponent -= DBL_MANT_DIG;
	155	if (u.ieee.exponent)
	156	u.ieee.exponent += DBL_MANT_DIG;
	157	else
	158	u.d *= 0x1p53;
	159	}
f3f7372d JJ	160	else /* if (u.ieee.exponent + v.ieee.exponent
	161	<= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG) */
	162	{
	163	if (u.ieee.exponent > v.ieee.exponent)
82477c28	164	u.ieee.exponent += 2 * DBL_MANT_DIG + 2;
f3f7372d	165	else
82477c28 JM	166	v.ieee.exponent += 2 * DBL_MANT_DIG + 2;
82477c28 JM	167	if (w.ieee.exponent <= 4 * DBL_MANT_DIG + 6)
f3f7372d JJ	168	{
f3f7372d JJ	169	if (w.ieee.exponent)
82477c28	170	w.ieee.exponent += 2 * DBL_MANT_DIG + 2;
f3f7372d	171	else
82477c28	172	w.d *= 0x1p108;
f3f7372d JJ	173	adjust = -1;
	174	}
	175	/* Otherwise x * y should just affect inexact
	176	and nothing else. */
	177	}
5e908464 JJ	178	x = u.d;
	179	y = v.d;
	180	z = w.d;
	181	}
8ec5b013 JM	182
8ec5b013 JM	183	/* Ensure correct sign of exact 0 + 0. */
a1ffb40e	184	if (__glibc_unlikely ((x == 0 \|\| y == 0) && z == 0))
09245377 L	185	{
	186	x = math_opt_barrier (x);
	187	return x * y + z;
	188	}
8ec5b013	189
5b5b04d6 JM	190	fenv_t env;
	191	libc_feholdexcept_setround (&env, FE_TONEAREST);
	192
5e908464 JJ	193	/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
	194	#define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
	195	double x1 = x * C;
	196	double y1 = y * C;
	197	double m1 = x * y;
	198	x1 = (x - x1) + x1;
	199	y1 = (y - y1) + y1;
	200	double x2 = x - x1;
	201	double y2 = y - y1;
	202	double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
	203
	204	/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
	205	double a1 = z + m1;
	206	double t1 = a1 - z;
	207	double t2 = a1 - t1;
	208	t1 = m1 - t1;
	209	t2 = z - t2;
	210	double a2 = t1 + t2;
4896f049 RH	211	/* Ensure the arithmetic is not scheduled after feclearexcept call. */
	212	math_force_eval (m2);
	213	math_force_eval (a2);
5b5b04d6	214	feclearexcept (FE_INEXACT);
5e908464	215
4896f049	216	/* If the result is an exact zero, ensure it has the correct sign. */
5b5b04d6 JM	217	if (a1 == 0 && m2 == 0)
	218	{
	219	libc_feupdateenv (&env);
4896f049 RH	220	/* Ensure that round-to-nearest value of z + m1 is not reused. */
4896f049 RH	221	z = math_opt_barrier (z);
5b5b04d6 JM	222	return z + m1;
	223	}
	224
	225	libc_fesetround (FE_TOWARDZERO);
0fe0f1f8	226
5e908464 JJ	227	/* Perform m2 + a2 addition with round to odd. */
5e908464 JJ	228	u.d = a2 + m2;
5e908464	229
a1ffb40e	230	if (__glibc_unlikely (adjust < 0))
0fe0f1f8 RH	231	{
	232	if ((u.ieee.mantissa1 & 1) == 0)
	233	u.ieee.mantissa1 \|= libc_fetestexcept (FE_INEXACT) != 0;
	234	v.d = a1 + u.d;
efb73488 AJ	235	/* Ensure the addition is not scheduled after fetestexcept call. */
efb73488 AJ	236	math_force_eval (v.d);
0fe0f1f8 RH	237	}
	238
	239	/* Reset rounding mode and test for inexact simultaneously. */
	240	int j = libc_feupdateenv_test (&env, FE_INEXACT) != 0;
	241
a1ffb40e	242	if (__glibc_likely (adjust == 0))
f3f7372d JJ	243	{
f3f7372d JJ	244	if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
0fe0f1f8	245	u.ieee.mantissa1 \|= j;
f3f7372d JJ	246	/* Result is a1 + u.d. */
	247	return a1 + u.d;
	248	}
a1ffb40e	249	else if (__glibc_likely (adjust > 0))
f3f7372d JJ	250	{
f3f7372d JJ	251	if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
0fe0f1f8	252	u.ieee.mantissa1 \|= j;
f3f7372d JJ	253	/* Result is a1 + u.d, scaled up. */
	254	return (a1 + u.d) * 0x1p53;
	255	}
	256	else
	257	{
f3f7372d JJ	258	/* If a1 + u.d is exact, the only rounding happens during
	259	scaling down. */
	260	if (j == 0)
82477c28	261	return v.d * 0x1p-108;
f3f7372d JJ	262	/* If result rounded to zero is not subnormal, no double
f3f7372d JJ	263	rounding will occur. */
82477c28 JM	264	if (v.ieee.exponent > 108)
	265	return (a1 + u.d) * 0x1p-108;
	266	/* If v.d * 0x1p-108 with round to zero is a subnormal above
	267	or equal to DBL_MIN / 2, then v.d * 0x1p-108 shifts mantissa
f3f7372d JJ	268	down just by 1 bit, which means v.ieee.mantissa1 \|= j would
f3f7372d JJ	269	change the round bit, not sticky or guard bit.
82477c28	270	v.d * 0x1p-108 never normalizes by shifting up,
f3f7372d JJ	271	so round bit plus sticky bit should be already enough
f3f7372d JJ	272	for proper rounding. */
82477c28	273	if (v.ieee.exponent == 108)
f3f7372d	274	{
ef82f4da JM	275	/* If the exponent would be in the normal range when
	276	rounding to normal precision with unbounded exponent
	277	range, the exact result is known and spurious underflows
	278	must be avoided on systems detecting tininess after
	279	rounding. */
	280	if (TININESS_AFTER_ROUNDING)
	281	{
	282	w.d = a1 + u.d;
82477c28 JM	283	if (w.ieee.exponent == 109)
82477c28 JM	284	return w.d * 0x1p-108;
ef82f4da	285	}
f3f7372d JJ	286	/* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
f3f7372d JJ	287	v.ieee.mantissa1 & 1 is the round bit and j is our sticky
8627a232 JM	288	bit. */
	289	w.d = 0.0;
	290	w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) \| j;
	291	w.ieee.negative = v.ieee.negative;
	292	v.ieee.mantissa1 &= ~3U;
82477c28	293	v.d *= 0x1p-108;
8627a232 JM	294	w.d *= 0x1p-2;
8627a232 JM	295	return v.d + w.d;
f3f7372d JJ	296	}
f3f7372d JJ	297	v.ieee.mantissa1 \|= j;
82477c28	298	return v.d * 0x1p-108;
f3f7372d	299	}
628d90c5	300	#endif /* ! USE_FMA_BUILTIN */
5e908464 JJ	301	}
5e908464 JJ	302	#ifndef __fma
7e16a5d1	303	libm_alias_double (__fma, fma)
5e908464	304	#endif