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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_sub(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(), "sub", 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
74 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
75 if (xs != ys)
76 return x;
77 SETCX(IEEE754_INVALID_OPERATION);
78 return ieee754dp_xcpt(ieee754dp_indef(), "sub", x, y);
79
80 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
81 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
82 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
83 return ieee754dp_inf(ys ^ 1);
84
85 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
86 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
87 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
88 return x;
89
90 /* Zero handling
91 */
92
93 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
94 if (xs != ys)
95 return x;
96 else
97 return ieee754dp_zero(ieee754_csr.rm ==
98 IEEE754_RD);
99
100 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
101 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
102 return x;
103
104 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
105 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
106 /* quick fix up */
107 DPSIGN(y) ^= 1;
108 return y;
109
110 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
111 DPDNORMX;
112 /* FALL THROUGH */
113
114 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
115 /* normalize ym,ye */
116 DPDNORMY;
117 break;
118
119 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
120 /* normalize xm,xe */
121 DPDNORMX;
122 break;
123
124 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
125 break;
126 }
127 /* flip sign of y and handle as add */
128 ys ^= 1;
129
130 assert(xm & DP_HIDDEN_BIT);
131 assert(ym & DP_HIDDEN_BIT);
132
133
134 /* provide guard,round and stick bit dpace */
135 xm <<= 3;
136 ym <<= 3;
137
138 if (xe > ye) {
139 /* have to shift y fraction right to align
140 */
141 int s = xe - ye;
142 ym = XDPSRS(ym, s);
143 ye += s;
144 } else if (ye > xe) {
145 /* have to shift x fraction right to align
146 */
147 int s = ye - xe;
148 xm = XDPSRS(xm, s);
149 xe += s;
150 }
151 assert(xe == ye);
152 assert(xe <= DP_EMAX);
153
154 if (xs == ys) {
155 /* generate 28 bit result of adding two 27 bit numbers
156 */
157 xm = xm + ym;
158 xe = xe;
159 xs = xs;
160
161 if (xm >> (DP_MBITS + 1 + 3)) { /* carry out */
162 xm = XDPSRS1(xm); /* shift preserving sticky */
163 xe++;
164 }
165 } else {
166 if (xm >= ym) {
167 xm = xm - ym;
168 xe = xe;
169 xs = xs;
170 } else {
171 xm = ym - xm;
172 xe = xe;
173 xs = ys;
174 }
175 if (xm == 0) {
176 if (ieee754_csr.rm == IEEE754_RD)
177 return ieee754dp_zero(1); /* round negative inf. => sign = -1 */
178 else
179 return ieee754dp_zero(0); /* other round modes => sign = 1 */
180 }
181
182 /* normalize to rounding precision
183 */
184 while ((xm >> (DP_MBITS + 3)) == 0) {
185 xm <<= 1;
186 xe--;
187 }
188 }
189 DPNORMRET2(xs, xe, xm, "sub", x, y);
190}
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 * This program is free software; you can distribute it and/or modify it
9 * under the terms of the GNU General Public License (Version 2) as
10 * published by the Free Software Foundation.
11 *
12 * This program is distributed in the hope it will be useful, but WITHOUT
13 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
15 * for more details.
16 *
17 * You should have received a copy of the GNU General Public License along
18 * with this program; if not, write to the Free Software Foundation, Inc.,
19 * 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 */
21
22#include "ieee754dp.h"
23
24union ieee754dp ieee754dp_sub(union ieee754dp x, union ieee754dp y)
25{
26 int s;
27
28 COMPXDP;
29 COMPYDP;
30
31 EXPLODEXDP;
32 EXPLODEYDP;
33
34 ieee754_clearcx();
35
36 FLUSHXDP;
37 FLUSHYDP;
38
39 switch (CLPAIR(xc, yc)) {
40 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
41 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
42 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
43 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
44 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
45 return ieee754dp_nanxcpt(y);
46
47 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
48 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
49 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
50 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
51 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
52 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
53 return ieee754dp_nanxcpt(x);
54
55 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
56 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
57 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
58 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
59 return y;
60
61 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
62 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
63 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
64 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
65 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
66 return x;
67
68
69 /*
70 * Infinity handling
71 */
72 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
73 if (xs != ys)
74 return x;
75 ieee754_setcx(IEEE754_INVALID_OPERATION);
76 return ieee754dp_indef();
77
78 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
79 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
80 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
81 return ieee754dp_inf(ys ^ 1);
82
83 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
84 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
85 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
86 return x;
87
88 /*
89 * Zero handling
90 */
91 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
92 if (xs != ys)
93 return x;
94 else
95 return ieee754dp_zero(ieee754_csr.rm == FPU_CSR_RD);
96
97 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
98 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
99 return x;
100
101 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
102 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
103 /* quick fix up */
104 DPSIGN(y) ^= 1;
105 return y;
106
107 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
108 DPDNORMX;
109 /* FALL THROUGH */
110
111 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
112 /* normalize ym,ye */
113 DPDNORMY;
114 break;
115
116 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
117 /* normalize xm,xe */
118 DPDNORMX;
119 break;
120
121 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
122 break;
123 }
124 /* flip sign of y and handle as add */
125 ys ^= 1;
126
127 assert(xm & DP_HIDDEN_BIT);
128 assert(ym & DP_HIDDEN_BIT);
129
130
131 /* provide guard,round and stick bit dpace */
132 xm <<= 3;
133 ym <<= 3;
134
135 if (xe > ye) {
136 /*
137 * Have to shift y fraction right to align
138 */
139 s = xe - ye;
140 ym = XDPSRS(ym, s);
141 ye += s;
142 } else if (ye > xe) {
143 /*
144 * Have to shift x fraction right to align
145 */
146 s = ye - xe;
147 xm = XDPSRS(xm, s);
148 xe += s;
149 }
150 assert(xe == ye);
151 assert(xe <= DP_EMAX);
152
153 if (xs == ys) {
154 /* generate 28 bit result of adding two 27 bit numbers
155 */
156 xm = xm + ym;
157
158 if (xm >> (DP_FBITS + 1 + 3)) { /* carry out */
159 xm = XDPSRS1(xm); /* shift preserving sticky */
160 xe++;
161 }
162 } else {
163 if (xm >= ym) {
164 xm = xm - ym;
165 } else {
166 xm = ym - xm;
167 xs = ys;
168 }
169 if (xm == 0) {
170 if (ieee754_csr.rm == FPU_CSR_RD)
171 return ieee754dp_zero(1); /* round negative inf. => sign = -1 */
172 else
173 return ieee754dp_zero(0); /* other round modes => sign = 1 */
174 }
175
176 /* normalize to rounding precision
177 */
178 while ((xm >> (DP_FBITS + 3)) == 0) {
179 xm <<= 1;
180 xe--;
181 }
182 }
183
184 return ieee754dp_format(xs, xe, xm);
185}