Loading...
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 fallthrough;
93 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
94 DPDNORMY;
95 break;
96
97 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
98 DPDNORMX;
99 break;
100
101 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
102 break;
103 }
104 /* rm = xm * ym, re = xe+ye basically */
105 assert(xm & DP_HIDDEN_BIT);
106 assert(ym & DP_HIDDEN_BIT);
107
108 re = xe + ye;
109 rs = xs ^ ys;
110
111 /* shunt to top of word */
112 xm <<= 64 - (DP_FBITS + 1);
113 ym <<= 64 - (DP_FBITS + 1);
114
115 /*
116 * Multiply 64 bits xm, ym to give high 64 bits rm with stickness.
117 */
118
119 lxm = xm;
120 hxm = xm >> 32;
121 lym = ym;
122 hym = ym >> 32;
123
124 lrm = DPXMULT(lxm, lym);
125 hrm = DPXMULT(hxm, hym);
126
127 t = DPXMULT(lxm, hym);
128
129 at = lrm + (t << 32);
130 hrm += at < lrm;
131 lrm = at;
132
133 hrm = hrm + (t >> 32);
134
135 t = DPXMULT(hxm, lym);
136
137 at = lrm + (t << 32);
138 hrm += at < lrm;
139 lrm = at;
140
141 hrm = hrm + (t >> 32);
142
143 rm = hrm | (lrm != 0);
144
145 /*
146 * Sticky shift down to normal rounding precision.
147 */
148 if ((s64) rm < 0) {
149 rm = (rm >> (64 - (DP_FBITS + 1 + 3))) |
150 ((rm << (DP_FBITS + 1 + 3)) != 0);
151 re++;
152 } else {
153 rm = (rm >> (64 - (DP_FBITS + 1 + 3 + 1))) |
154 ((rm << (DP_FBITS + 1 + 3 + 1)) != 0);
155 }
156 assert(rm & (DP_HIDDEN_BIT << 3));
157
158 return ieee754dp_format(rs, re, rm);
159}
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 fallthrough;
93 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
94 DPDNORMY;
95 break;
96
97 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
98 DPDNORMX;
99 break;
100
101 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
102 break;
103 }
104 /* rm = xm * ym, re = xe+ye basically */
105 assert(xm & DP_HIDDEN_BIT);
106 assert(ym & DP_HIDDEN_BIT);
107
108 re = xe + ye;
109 rs = xs ^ ys;
110
111 /* shunt to top of word */
112 xm <<= 64 - (DP_FBITS + 1);
113 ym <<= 64 - (DP_FBITS + 1);
114
115 /*
116 * Multiply 64 bits xm, ym to give high 64 bits rm with stickness.
117 */
118
119 lxm = xm;
120 hxm = xm >> 32;
121 lym = ym;
122 hym = ym >> 32;
123
124 lrm = DPXMULT(lxm, lym);
125 hrm = DPXMULT(hxm, hym);
126
127 t = DPXMULT(lxm, hym);
128
129 at = lrm + (t << 32);
130 hrm += at < lrm;
131 lrm = at;
132
133 hrm = hrm + (t >> 32);
134
135 t = DPXMULT(hxm, lym);
136
137 at = lrm + (t << 32);
138 hrm += at < lrm;
139 lrm = at;
140
141 hrm = hrm + (t >> 32);
142
143 rm = hrm | (lrm != 0);
144
145 /*
146 * Sticky shift down to normal rounding precision.
147 */
148 if ((s64) rm < 0) {
149 rm = (rm >> (64 - (DP_FBITS + 1 + 3))) |
150 ((rm << (DP_FBITS + 1 + 3)) != 0);
151 re++;
152 } else {
153 rm = (rm >> (64 - (DP_FBITS + 1 + 3 + 1))) |
154 ((rm << (DP_FBITS + 1 + 3 + 1)) != 0);
155 }
156 assert(rm & (DP_HIDDEN_BIT << 3));
157
158 return ieee754dp_format(rs, re, rm);
159}