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1/* IEEE754 floating point arithmetic
2 * double precision: common utilities
3 */
4/*
5 * MIPS floating point support
6 * Copyright (C) 1994-2000 Algorithmics Ltd.
7 *
8 * ########################################################################
9 *
10 * This program is free software; you can distribute it and/or modify it
11 * under the terms of the GNU General Public License (Version 2) as
12 * published by the Free Software Foundation.
13 *
14 * This program is distributed in the hope it will be useful, but WITHOUT
15 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
16 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
17 * for more details.
18 *
19 * You should have received a copy of the GNU General Public License along
20 * with this program; if not, write to the Free Software Foundation, Inc.,
21 * 59 Temple Place - Suite 330, Boston MA 02111-1307, USA.
22 *
23 * ########################################################################
24 */
25
26
27#include "ieee754dp.h"
28
29ieee754dp ieee754dp_mul(ieee754dp x, ieee754dp y)
30{
31 COMPXDP;
32 COMPYDP;
33
34 EXPLODEXDP;
35 EXPLODEYDP;
36
37 CLEARCX;
38
39 FLUSHXDP;
40 FLUSHYDP;
41
42 switch (CLPAIR(xc, yc)) {
43 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
44 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
45 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
46 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
47 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
48 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
49 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
50 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
51 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
52 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
53 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
54 SETCX(IEEE754_INVALID_OPERATION);
55 return ieee754dp_nanxcpt(ieee754dp_indef(), "mul", x, y);
56
57 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
58 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
59 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
60 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
61 return y;
62
63 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
64 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
65 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
66 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
67 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
68 return x;
69
70
71 /* Infinity handling */
72
73 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
74 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
75 SETCX(IEEE754_INVALID_OPERATION);
76 return ieee754dp_xcpt(ieee754dp_indef(), "mul", x, y);
77
78 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
79 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
80 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
81 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
82 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
83 return ieee754dp_inf(xs ^ ys);
84
85 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
86 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
87 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
88 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
89 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
90 return ieee754dp_zero(xs ^ ys);
91
92
93 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
94 DPDNORMX;
95
96 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
97 DPDNORMY;
98 break;
99
100 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
101 DPDNORMX;
102 break;
103
104 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
105 break;
106 }
107 /* rm = xm * ym, re = xe+ye basically */
108 assert(xm & DP_HIDDEN_BIT);
109 assert(ym & DP_HIDDEN_BIT);
110 {
111 int re = xe + ye;
112 int rs = xs ^ ys;
113 u64 rm;
114
115 /* shunt to top of word */
116 xm <<= 64 - (DP_MBITS + 1);
117 ym <<= 64 - (DP_MBITS + 1);
118
119 /* multiply 32bits xm,ym to give high 32bits rm with stickness
120 */
121
122 /* 32 * 32 => 64 */
123#define DPXMULT(x, y) ((u64)(x) * (u64)y)
124
125 {
126 unsigned lxm = xm;
127 unsigned hxm = xm >> 32;
128 unsigned lym = ym;
129 unsigned hym = ym >> 32;
130 u64 lrm;
131 u64 hrm;
132
133 lrm = DPXMULT(lxm, lym);
134 hrm = DPXMULT(hxm, hym);
135
136 {
137 u64 t = DPXMULT(lxm, hym);
138 {
139 u64 at =
140 lrm + (t << 32);
141 hrm += at < lrm;
142 lrm = at;
143 }
144 hrm = hrm + (t >> 32);
145 }
146
147 {
148 u64 t = DPXMULT(hxm, lym);
149 {
150 u64 at =
151 lrm + (t << 32);
152 hrm += at < lrm;
153 lrm = at;
154 }
155 hrm = hrm + (t >> 32);
156 }
157 rm = hrm | (lrm != 0);
158 }
159
160 /*
161 * sticky shift down to normal rounding precision
162 */
163 if ((s64) rm < 0) {
164 rm =
165 (rm >> (64 - (DP_MBITS + 1 + 3))) |
166 ((rm << (DP_MBITS + 1 + 3)) != 0);
167 re++;
168 } else {
169 rm =
170 (rm >> (64 - (DP_MBITS + 1 + 3 + 1))) |
171 ((rm << (DP_MBITS + 1 + 3 + 1)) != 0);
172 }
173 assert(rm & (DP_HIDDEN_BIT << 3));
174 DPNORMRET2(rs, re, rm, "mul", x, y);
175 }
176}
1// SPDX-License-Identifier: GPL-2.0-only
2/* IEEE754 floating point arithmetic
3 * double precision: common utilities
4 */
5/*
6 * MIPS floating point support
7 * Copyright (C) 1994-2000 Algorithmics Ltd.
8 */
9
10#include "ieee754dp.h"
11
12union ieee754dp ieee754dp_mul(union ieee754dp x, union ieee754dp y)
13{
14 int re;
15 int rs;
16 u64 rm;
17 unsigned int lxm;
18 unsigned int hxm;
19 unsigned int lym;
20 unsigned int hym;
21 u64 lrm;
22 u64 hrm;
23 u64 t;
24 u64 at;
25
26 COMPXDP;
27 COMPYDP;
28
29 EXPLODEXDP;
30 EXPLODEYDP;
31
32 ieee754_clearcx();
33
34 FLUSHXDP;
35 FLUSHYDP;
36
37 switch (CLPAIR(xc, yc)) {
38 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
39 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
40 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
41 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
42 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
43 return ieee754dp_nanxcpt(y);
44
45 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
46 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
47 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
48 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
49 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
50 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
51 return ieee754dp_nanxcpt(x);
52
53 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
54 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
55 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
56 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
57 return y;
58
59 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
60 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
61 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
62 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
63 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
64 return x;
65
66
67 /*
68 * Infinity handling
69 */
70 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
71 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
72 ieee754_setcx(IEEE754_INVALID_OPERATION);
73 return ieee754dp_indef();
74
75 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
76 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
77 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
78 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
79 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
80 return ieee754dp_inf(xs ^ ys);
81
82 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
83 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
84 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
85 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
86 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
87 return ieee754dp_zero(xs ^ ys);
88
89
90 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
91 DPDNORMX;
92 /* fall through */
93
94 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
95 DPDNORMY;
96 break;
97
98 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
99 DPDNORMX;
100 break;
101
102 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
103 break;
104 }
105 /* rm = xm * ym, re = xe+ye basically */
106 assert(xm & DP_HIDDEN_BIT);
107 assert(ym & DP_HIDDEN_BIT);
108
109 re = xe + ye;
110 rs = xs ^ ys;
111
112 /* shunt to top of word */
113 xm <<= 64 - (DP_FBITS + 1);
114 ym <<= 64 - (DP_FBITS + 1);
115
116 /*
117 * Multiply 64 bits xm, ym to give high 64 bits rm with stickness.
118 */
119
120 lxm = xm;
121 hxm = xm >> 32;
122 lym = ym;
123 hym = ym >> 32;
124
125 lrm = DPXMULT(lxm, lym);
126 hrm = DPXMULT(hxm, hym);
127
128 t = DPXMULT(lxm, hym);
129
130 at = lrm + (t << 32);
131 hrm += at < lrm;
132 lrm = at;
133
134 hrm = hrm + (t >> 32);
135
136 t = DPXMULT(hxm, lym);
137
138 at = lrm + (t << 32);
139 hrm += at < lrm;
140 lrm = at;
141
142 hrm = hrm + (t >> 32);
143
144 rm = hrm | (lrm != 0);
145
146 /*
147 * Sticky shift down to normal rounding precision.
148 */
149 if ((s64) rm < 0) {
150 rm = (rm >> (64 - (DP_FBITS + 1 + 3))) |
151 ((rm << (DP_FBITS + 1 + 3)) != 0);
152 re++;
153 } else {
154 rm = (rm >> (64 - (DP_FBITS + 1 + 3 + 1))) |
155 ((rm << (DP_FBITS + 1 + 3 + 1)) != 0);
156 }
157 assert(rm & (DP_HIDDEN_BIT << 3));
158
159 return ieee754dp_format(rs, re, rm);
160}