summary refs log tree commit diff
path: root/sysdeps/ieee754/ldbl-128ibm/s_fmal.c
blob: bc61e9049c17e690bf91d765a6d6b4b5dc724a94 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
/* Compute x * y + z as ternary operation.
   Copyright (C) 2011-2018 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by David Flaherty <flaherty@linux.vnet.ibm.com>.

   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 <fenv.h>
#include <float.h>
#include <math.h>
#include <math-barriers.h>
#include <math_private.h>
#include <fenv_private.h>
#include <math-underflow.h>
#include <math_ldbl_opt.h>
#include <mul_split.h>
#include <stdlib.h>

/* Calculate X + Y exactly and store the result in *HI + *LO.  It is
   given that |X| >= |Y| and the values are small enough that no
   overflow occurs.  */

static void
add_split (double *hi, double *lo, double x, double y)
{
  /* Apply Dekker's algorithm.  */
  *hi = x + y;
  *lo = (x - *hi) + y;
}

/* Value with extended range, used in intermediate computations.  */
typedef struct
{
  /* Value in [0.5, 1), as from frexp, or 0.  */
  double val;
  /* Exponent of power of 2 it is multiplied by, or 0 for zero.  */
  int exp;
} ext_val;

/* Store D as an ext_val value.  */

static void
store_ext_val (ext_val *v, double d)
{
  v->val = __frexp (d, &v->exp);
}

/* Store X * Y as ext_val values *V0 and *V1.  */

static void
mul_ext_val (ext_val *v0, ext_val *v1, double x, double y)
{
  int xexp, yexp;
  x = __frexp (x, &xexp);
  y = __frexp (y, &yexp);
  double hi, lo;
  mul_split (&hi, &lo, x, y);
  store_ext_val (v0, hi);
  if (hi != 0)
    v0->exp += xexp + yexp;
  store_ext_val (v1, lo);
  if (lo != 0)
    v1->exp += xexp + yexp;
}

/* Compare absolute values of ext_val values pointed to by P and Q for
   qsort.  */

static int
compare (const void *p, const void *q)
{
  const ext_val *pe = p;
  const ext_val *qe = q;
  if (pe->val == 0)
    return qe->val == 0 ? 0 : -1;
  else if (qe->val == 0)
    return 1;
  else if (pe->exp < qe->exp)
    return -1;
  else if (pe->exp > qe->exp)
    return 1;
  else
    {
      double pd = fabs (pe->val);
      double qd = fabs (qe->val);
      if (pd < qd)
	return -1;
      else if (pd == qd)
	return 0;
      else
	return 1;
    }
}

/* Calculate *X + *Y exactly, storing the high part in *X (rounded to
   nearest) and the low part in *Y.  It is given that |X| >= |Y|.  */

static void
add_split_ext (ext_val *x, ext_val *y)
{
  int xexp = x->exp, yexp = y->exp;
  if (y->val == 0 || xexp - yexp > 53)
    return;
  double hi = x->val;
  double lo = __scalbn (y->val, yexp - xexp);
  add_split (&hi, &lo, hi, lo);
  store_ext_val (x, hi);
  if (hi != 0)
    x->exp += xexp;
  store_ext_val (y, lo);
  if (lo != 0)
    y->exp += xexp;
}

long double
__fmal (long double x, long double y, long double z)
{
  double xhi, xlo, yhi, ylo, zhi, zlo;
  int64_t hx, hy, hz;
  int xexp, yexp, zexp;
  double scale_val;
  int scale_exp;
  ldbl_unpack (x, &xhi, &xlo);
  EXTRACT_WORDS64 (hx, xhi);
  xexp = (hx & 0x7ff0000000000000LL) >> 52;
  ldbl_unpack (y, &yhi, &ylo);
  EXTRACT_WORDS64 (hy, yhi);
  yexp = (hy & 0x7ff0000000000000LL) >> 52;
  ldbl_unpack (z, &zhi, &zlo);
  EXTRACT_WORDS64 (hz, zhi);
  zexp = (hz & 0x7ff0000000000000LL) >> 52;

  /* If z is Inf or NaN, but x and y are finite, avoid any exceptions
     from computing x * y.  */
  if (zexp == 0x7ff && xexp != 0x7ff && yexp != 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 (xexp == 0x7ff || yexp == 0x7ff || zexp == 0x7ff
      || x == 0 || y == 0)
    return (x * y) + z;

  {
    SET_RESTORE_ROUND (FE_TONEAREST);

    ext_val vals[10];
    store_ext_val (&vals[0], zhi);
    store_ext_val (&vals[1], zlo);
    mul_ext_val (&vals[2], &vals[3], xhi, yhi);
    mul_ext_val (&vals[4], &vals[5], xhi, ylo);
    mul_ext_val (&vals[6], &vals[7], xlo, yhi);
    mul_ext_val (&vals[8], &vals[9], xlo, ylo);
    qsort (vals, 10, sizeof (ext_val), compare);
    /* Add up the values so that each element of VALS has absolute
       value at most equal to the last set bit of the next nonzero
       element.  */
    for (size_t i = 0; i <= 8; i++)
      {
	add_split_ext (&vals[i + 1], &vals[i]);
	qsort (vals + i + 1, 9 - i, sizeof (ext_val), compare);
      }
    /* Add up the values in the other direction, so that each element
       of VALS has absolute value less than 5ulp of the next
       value.  */
    size_t dstpos = 9;
    for (size_t i = 1; i <= 9; i++)
      {
	if (vals[dstpos].val == 0)
	  {
	    vals[dstpos] = vals[9 - i];
	    vals[9 - i].val = 0;
	    vals[9 - i].exp = 0;
	  }
	else
	  {
	    add_split_ext (&vals[dstpos], &vals[9 - i]);
	    if (vals[9 - i].val != 0)
	      {
		if (9 - i < dstpos - 1)
		  {
		    vals[dstpos - 1] = vals[9 - i];
		    vals[9 - i].val = 0;
		    vals[9 - i].exp = 0;
		  }
		dstpos--;
	      }
	  }
      }
    /* If the result is an exact zero, it results from adding two
       values with opposite signs; recompute in the original rounding
       mode.  */
    if (vals[9].val == 0)
      goto zero_out;
    /* Adding the top three values will now give a result as accurate
       as the underlying long double arithmetic.  */
    add_split_ext (&vals[9], &vals[8]);
    if (compare (&vals[8], &vals[7]) < 0)
      {
	ext_val tmp = vals[7];
	vals[7] = vals[8];
	vals[8] = tmp;
      }
    add_split_ext (&vals[8], &vals[7]);
    add_split_ext (&vals[9], &vals[8]);
    if (vals[9].exp > DBL_MAX_EXP || vals[9].exp < DBL_MIN_EXP)
      {
	/* Overflow or underflow, with the result depending on the
	   original rounding mode, but not on the low part computed
	   here.  */
	scale_val = vals[9].val;
	scale_exp = vals[9].exp;
	goto scale_out;
      }
    double hi = __scalbn (vals[9].val, vals[9].exp);
    double lo = __scalbn (vals[8].val, vals[8].exp);
    /* It is possible that the low part became subnormal and was
       rounded so that the result is no longer canonical.  */
    ldbl_canonicalize (&hi, &lo);
    long double ret = ldbl_pack (hi, lo);
    math_check_force_underflow (ret);
    return ret;
  }

 scale_out:
  scale_val = math_opt_barrier (scale_val);
  scale_val = __scalbn (scale_val, scale_exp);
  if (fabs (scale_val) == DBL_MAX)
    return __copysignl (LDBL_MAX, scale_val);
  math_check_force_underflow (scale_val);
  return scale_val;

 zero_out:;
  double zero = 0.0;
  zero = math_opt_barrier (zero);
  return zero - zero;
}
#if IS_IN (libm)
long_double_symbol (libm, __fmal, fmal);
#else
long_double_symbol (libc, __fmal, fmal);
#endif