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3d4837df | 1 | /* Compute x * y + z as ternary operation. |
d614a753 | 2 | Copyright (C) 2011-2020 Free Software Foundation, Inc. |
3d4837df UD |
3 | This file is part of the GNU C Library. |
4 | Contributed by David Flaherty <flaherty@linux.vnet.ibm.com>. | |
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/>. */ |
3d4837df | 19 | |
ffe9aaf2 JM |
20 | #include <fenv.h> |
21 | #include <float.h> | |
3d4837df | 22 | #include <math.h> |
b4d5b8b0 | 23 | #include <math-barriers.h> |
ffe9aaf2 | 24 | #include <math_private.h> |
70e2ba33 | 25 | #include <fenv_private.h> |
8f5b00d3 | 26 | #include <math-underflow.h> |
3d4837df | 27 | #include <math_ldbl_opt.h> |
4482ff22 | 28 | #include <mul_split.h> |
ffe9aaf2 JM |
29 | #include <stdlib.h> |
30 | ||
31 | /* Calculate X + Y exactly and store the result in *HI + *LO. It is | |
32 | given that |X| >= |Y| and the values are small enough that no | |
33 | overflow occurs. */ | |
34 | ||
35 | static void | |
36 | add_split (double *hi, double *lo, double x, double y) | |
37 | { | |
38 | /* Apply Dekker's algorithm. */ | |
39 | *hi = x + y; | |
40 | *lo = (x - *hi) + y; | |
41 | } | |
42 | ||
ffe9aaf2 JM |
43 | /* Value with extended range, used in intermediate computations. */ |
44 | typedef struct | |
45 | { | |
46 | /* Value in [0.5, 1), as from frexp, or 0. */ | |
47 | double val; | |
48 | /* Exponent of power of 2 it is multiplied by, or 0 for zero. */ | |
49 | int exp; | |
50 | } ext_val; | |
51 | ||
52 | /* Store D as an ext_val value. */ | |
53 | ||
54 | static void | |
55 | store_ext_val (ext_val *v, double d) | |
56 | { | |
57 | v->val = __frexp (d, &v->exp); | |
58 | } | |
59 | ||
60 | /* Store X * Y as ext_val values *V0 and *V1. */ | |
61 | ||
62 | static void | |
63 | mul_ext_val (ext_val *v0, ext_val *v1, double x, double y) | |
64 | { | |
65 | int xexp, yexp; | |
66 | x = __frexp (x, &xexp); | |
67 | y = __frexp (y, &yexp); | |
68 | double hi, lo; | |
69 | mul_split (&hi, &lo, x, y); | |
70 | store_ext_val (v0, hi); | |
71 | if (hi != 0) | |
72 | v0->exp += xexp + yexp; | |
73 | store_ext_val (v1, lo); | |
74 | if (lo != 0) | |
75 | v1->exp += xexp + yexp; | |
76 | } | |
77 | ||
78 | /* Compare absolute values of ext_val values pointed to by P and Q for | |
79 | qsort. */ | |
80 | ||
81 | static int | |
82 | compare (const void *p, const void *q) | |
83 | { | |
84 | const ext_val *pe = p; | |
85 | const ext_val *qe = q; | |
86 | if (pe->val == 0) | |
87 | return qe->val == 0 ? 0 : -1; | |
88 | else if (qe->val == 0) | |
89 | return 1; | |
90 | else if (pe->exp < qe->exp) | |
91 | return -1; | |
92 | else if (pe->exp > qe->exp) | |
93 | return 1; | |
94 | else | |
95 | { | |
96 | double pd = fabs (pe->val); | |
97 | double qd = fabs (qe->val); | |
98 | if (pd < qd) | |
99 | return -1; | |
100 | else if (pd == qd) | |
101 | return 0; | |
102 | else | |
103 | return 1; | |
104 | } | |
105 | } | |
106 | ||
107 | /* Calculate *X + *Y exactly, storing the high part in *X (rounded to | |
108 | nearest) and the low part in *Y. It is given that |X| >= |Y|. */ | |
109 | ||
110 | static void | |
111 | add_split_ext (ext_val *x, ext_val *y) | |
112 | { | |
113 | int xexp = x->exp, yexp = y->exp; | |
114 | if (y->val == 0 || xexp - yexp > 53) | |
115 | return; | |
116 | double hi = x->val; | |
117 | double lo = __scalbn (y->val, yexp - xexp); | |
118 | add_split (&hi, &lo, hi, lo); | |
119 | store_ext_val (x, hi); | |
120 | if (hi != 0) | |
121 | x->exp += xexp; | |
122 | store_ext_val (y, lo); | |
123 | if (lo != 0) | |
124 | y->exp += xexp; | |
125 | } | |
3d4837df UD |
126 | |
127 | long double | |
128 | __fmal (long double x, long double y, long double z) | |
129 | { | |
ffe9aaf2 JM |
130 | double xhi, xlo, yhi, ylo, zhi, zlo; |
131 | int64_t hx, hy, hz; | |
132 | int xexp, yexp, zexp; | |
133 | double scale_val; | |
134 | int scale_exp; | |
135 | ldbl_unpack (x, &xhi, &xlo); | |
136 | EXTRACT_WORDS64 (hx, xhi); | |
137 | xexp = (hx & 0x7ff0000000000000LL) >> 52; | |
138 | ldbl_unpack (y, &yhi, &ylo); | |
139 | EXTRACT_WORDS64 (hy, yhi); | |
140 | yexp = (hy & 0x7ff0000000000000LL) >> 52; | |
141 | ldbl_unpack (z, &zhi, &zlo); | |
142 | EXTRACT_WORDS64 (hz, zhi); | |
143 | zexp = (hz & 0x7ff0000000000000LL) >> 52; | |
144 | ||
145 | /* If z is Inf or NaN, but x and y are finite, avoid any exceptions | |
146 | from computing x * y. */ | |
147 | if (zexp == 0x7ff && xexp != 0x7ff && yexp != 0x7ff) | |
148 | return (z + x) + y; | |
149 | ||
150 | /* If z is zero and x are y are nonzero, compute the result as x * y | |
151 | to avoid the wrong sign of a zero result if x * y underflows to | |
152 | 0. */ | |
153 | if (z == 0 && x != 0 && y != 0) | |
154 | return x * y; | |
155 | ||
156 | /* If x or y or z is Inf/NaN, or if x * y is zero, compute as x * y | |
157 | + z. */ | |
158 | if (xexp == 0x7ff || yexp == 0x7ff || zexp == 0x7ff | |
159 | || x == 0 || y == 0) | |
160 | return (x * y) + z; | |
161 | ||
162 | { | |
163 | SET_RESTORE_ROUND (FE_TONEAREST); | |
164 | ||
165 | ext_val vals[10]; | |
166 | store_ext_val (&vals[0], zhi); | |
167 | store_ext_val (&vals[1], zlo); | |
168 | mul_ext_val (&vals[2], &vals[3], xhi, yhi); | |
169 | mul_ext_val (&vals[4], &vals[5], xhi, ylo); | |
170 | mul_ext_val (&vals[6], &vals[7], xlo, yhi); | |
171 | mul_ext_val (&vals[8], &vals[9], xlo, ylo); | |
172 | qsort (vals, 10, sizeof (ext_val), compare); | |
173 | /* Add up the values so that each element of VALS has absolute | |
174 | value at most equal to the last set bit of the next nonzero | |
175 | element. */ | |
176 | for (size_t i = 0; i <= 8; i++) | |
177 | { | |
178 | add_split_ext (&vals[i + 1], &vals[i]); | |
179 | qsort (vals + i + 1, 9 - i, sizeof (ext_val), compare); | |
180 | } | |
181 | /* Add up the values in the other direction, so that each element | |
182 | of VALS has absolute value less than 5ulp of the next | |
183 | value. */ | |
184 | size_t dstpos = 9; | |
185 | for (size_t i = 1; i <= 9; i++) | |
186 | { | |
187 | if (vals[dstpos].val == 0) | |
188 | { | |
189 | vals[dstpos] = vals[9 - i]; | |
190 | vals[9 - i].val = 0; | |
191 | vals[9 - i].exp = 0; | |
192 | } | |
193 | else | |
194 | { | |
195 | add_split_ext (&vals[dstpos], &vals[9 - i]); | |
196 | if (vals[9 - i].val != 0) | |
197 | { | |
198 | if (9 - i < dstpos - 1) | |
199 | { | |
200 | vals[dstpos - 1] = vals[9 - i]; | |
201 | vals[9 - i].val = 0; | |
202 | vals[9 - i].exp = 0; | |
203 | } | |
204 | dstpos--; | |
205 | } | |
206 | } | |
207 | } | |
208 | /* If the result is an exact zero, it results from adding two | |
209 | values with opposite signs; recompute in the original rounding | |
210 | mode. */ | |
211 | if (vals[9].val == 0) | |
212 | goto zero_out; | |
213 | /* Adding the top three values will now give a result as accurate | |
214 | as the underlying long double arithmetic. */ | |
215 | add_split_ext (&vals[9], &vals[8]); | |
216 | if (compare (&vals[8], &vals[7]) < 0) | |
217 | { | |
218 | ext_val tmp = vals[7]; | |
219 | vals[7] = vals[8]; | |
220 | vals[8] = tmp; | |
221 | } | |
222 | add_split_ext (&vals[8], &vals[7]); | |
223 | add_split_ext (&vals[9], &vals[8]); | |
224 | if (vals[9].exp > DBL_MAX_EXP || vals[9].exp < DBL_MIN_EXP) | |
225 | { | |
226 | /* Overflow or underflow, with the result depending on the | |
227 | original rounding mode, but not on the low part computed | |
228 | here. */ | |
229 | scale_val = vals[9].val; | |
230 | scale_exp = vals[9].exp; | |
231 | goto scale_out; | |
232 | } | |
233 | double hi = __scalbn (vals[9].val, vals[9].exp); | |
234 | double lo = __scalbn (vals[8].val, vals[8].exp); | |
235 | /* It is possible that the low part became subnormal and was | |
236 | rounded so that the result is no longer canonical. */ | |
237 | ldbl_canonicalize (&hi, &lo); | |
238 | long double ret = ldbl_pack (hi, lo); | |
239 | math_check_force_underflow (ret); | |
240 | return ret; | |
241 | } | |
3d4837df | 242 | |
ffe9aaf2 JM |
243 | scale_out: |
244 | scale_val = math_opt_barrier (scale_val); | |
245 | scale_val = __scalbn (scale_val, scale_exp); | |
246 | if (fabs (scale_val) == DBL_MAX) | |
81dca813 | 247 | return copysignl (LDBL_MAX, scale_val); |
ffe9aaf2 JM |
248 | math_check_force_underflow (scale_val); |
249 | return scale_val; | |
c60d3bf2 | 250 | |
ffe9aaf2 JM |
251 | zero_out:; |
252 | double zero = 0.0; | |
253 | zero = math_opt_barrier (zero); | |
254 | return zero - zero; | |
3d4837df | 255 | } |
a109996e | 256 | #if IS_IN (libm) |
3d4837df UD |
257 | long_double_symbol (libm, __fmal, fmal); |
258 | #else | |
259 | long_double_symbol (libc, __fmal, fmal); | |
260 | #endif |