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1/*
2 * IEEE754 floating point arithmetic
3 * double precision: MIN{,A}.f
4 * MIN : Scalar Floating-Point Minimum
5 * MINA: Scalar Floating-Point argument with Minimum Absolute Value
6 *
7 * MIN.D : FPR[fd] = minNum(FPR[fs],FPR[ft])
8 * MINA.D: FPR[fd] = maxNumMag(FPR[fs],FPR[ft])
9 *
10 * MIPS floating point support
11 * Copyright (C) 2015 Imagination Technologies, Ltd.
12 * Author: Markos Chandras <markos.chandras@imgtec.com>
13 *
14 * This program is free software; you can distribute it and/or modify it
15 * under the terms of the GNU General Public License as published by the
16 * Free Software Foundation; version 2 of the License.
17 */
18
19#include "ieee754dp.h"
20
21union ieee754dp ieee754dp_fmax(union ieee754dp x, union ieee754dp y)
22{
23 COMPXDP;
24 COMPYDP;
25
26 EXPLODEXDP;
27 EXPLODEYDP;
28
29 FLUSHXDP;
30 FLUSHYDP;
31
32 ieee754_clearcx();
33
34 switch (CLPAIR(xc, yc)) {
35 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
36 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
37 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
38 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
39 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
40 return ieee754dp_nanxcpt(y);
41
42 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
43 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
44 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
45 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
46 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
47 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
48 return ieee754dp_nanxcpt(x);
49
50 /* numbers are preferred to NaNs */
51 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
52 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
53 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
54 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
55 return x;
56
57 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
58 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
59 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
60 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
61 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
62 return y;
63
64 /*
65 * Infinity and zero handling
66 */
67 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
68 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
69 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
70 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
71 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
72 return xs ? y : x;
73
74 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
75 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
76 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
77 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
78 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
79 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
80 return ys ? x : y;
81
82 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
83 if (xs == ys)
84 return x;
85 return ieee754dp_zero(1);
86
87 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
88 DPDNORMX;
89
90 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
91 DPDNORMY;
92 break;
93
94 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
95 DPDNORMX;
96 }
97
98 /* Finally get to do some computation */
99
100 assert(xm & DP_HIDDEN_BIT);
101 assert(ym & DP_HIDDEN_BIT);
102
103 /* Compare signs */
104 if (xs > ys)
105 return y;
106 else if (xs < ys)
107 return x;
108
109 /* Compare exponent */
110 if (xe > ye)
111 return x;
112 else if (xe < ye)
113 return y;
114
115 /* Compare mantissa */
116 if (xm <= ym)
117 return y;
118 return x;
119}
120
121union ieee754dp ieee754dp_fmaxa(union ieee754dp x, union ieee754dp y)
122{
123 COMPXDP;
124 COMPYDP;
125
126 EXPLODEXDP;
127 EXPLODEYDP;
128
129 FLUSHXDP;
130 FLUSHYDP;
131
132 ieee754_clearcx();
133
134 switch (CLPAIR(xc, yc)) {
135 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
136 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
137 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
138 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
139 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
140 return ieee754dp_nanxcpt(y);
141
142 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
143 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
144 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
145 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
146 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
147 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
148 return ieee754dp_nanxcpt(x);
149
150 /* numbers are preferred to NaNs */
151 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
152 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
153 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
154 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
155 return x;
156
157 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
158 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
159 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
160 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
161 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
162 return y;
163
164 /*
165 * Infinity and zero handling
166 */
167 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
168 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
169 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
170 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
171 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
172 return x;
173
174 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
175 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
176 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
177 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
178 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
179 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
180 return y;
181
182 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
183 if (xs == ys)
184 return x;
185 return ieee754dp_zero(1);
186
187 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
188 DPDNORMX;
189
190 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
191 DPDNORMY;
192 break;
193
194 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
195 DPDNORMX;
196 }
197
198 /* Finally get to do some computation */
199
200 assert(xm & DP_HIDDEN_BIT);
201 assert(ym & DP_HIDDEN_BIT);
202
203 /* Compare exponent */
204 if (xe > ye)
205 return x;
206 else if (xe < ye)
207 return y;
208
209 /* Compare mantissa */
210 if (xm <= ym)
211 return y;
212 return x;
213}
1/*
2 * IEEE754 floating point arithmetic
3 * double precision: MIN{,A}.f
4 * MIN : Scalar Floating-Point Minimum
5 * MINA: Scalar Floating-Point argument with Minimum Absolute Value
6 *
7 * MIN.D : FPR[fd] = minNum(FPR[fs],FPR[ft])
8 * MINA.D: FPR[fd] = maxNumMag(FPR[fs],FPR[ft])
9 *
10 * MIPS floating point support
11 * Copyright (C) 2015 Imagination Technologies, Ltd.
12 * Author: Markos Chandras <markos.chandras@imgtec.com>
13 *
14 * This program is free software; you can distribute it and/or modify it
15 * under the terms of the GNU General Public License as published by the
16 * Free Software Foundation; version 2 of the License.
17 */
18
19#include "ieee754dp.h"
20
21union ieee754dp ieee754dp_fmax(union ieee754dp x, union ieee754dp y)
22{
23 COMPXDP;
24 COMPYDP;
25
26 EXPLODEXDP;
27 EXPLODEYDP;
28
29 FLUSHXDP;
30 FLUSHYDP;
31
32 ieee754_clearcx();
33
34 switch (CLPAIR(xc, yc)) {
35 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
36 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
37 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
38 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
39 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
40 return ieee754dp_nanxcpt(y);
41
42 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
43 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
44 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
45 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
46 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
47 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
48 return ieee754dp_nanxcpt(x);
49
50 /*
51 * Quiet NaN handling
52 */
53
54 /*
55 * The case of both inputs quiet NaNs
56 */
57 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
58 return x;
59
60 /*
61 * The cases of exactly one input quiet NaN (numbers
62 * are here preferred as returned values to NaNs)
63 */
64 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
65 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
66 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
67 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
68 return x;
69
70 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
71 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
72 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
73 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
74 return y;
75
76 /*
77 * Infinity and zero handling
78 */
79 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
80 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
81 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
82 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
83 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
84 return xs ? y : x;
85
86 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
87 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
88 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
89 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
90 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
91 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
92 return ys ? x : y;
93
94 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
95 return ieee754dp_zero(xs & ys);
96
97 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
98 DPDNORMX;
99 /* fall through */
100
101 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
102 DPDNORMY;
103 break;
104
105 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
106 DPDNORMX;
107 }
108
109 /* Finally get to do some computation */
110
111 assert(xm & DP_HIDDEN_BIT);
112 assert(ym & DP_HIDDEN_BIT);
113
114 /* Compare signs */
115 if (xs > ys)
116 return y;
117 else if (xs < ys)
118 return x;
119
120 /* Signs of inputs are equal, let's compare exponents */
121 if (xs == 0) {
122 /* Inputs are both positive */
123 if (xe > ye)
124 return x;
125 else if (xe < ye)
126 return y;
127 } else {
128 /* Inputs are both negative */
129 if (xe > ye)
130 return y;
131 else if (xe < ye)
132 return x;
133 }
134
135 /* Signs and exponents of inputs are equal, let's compare mantissas */
136 if (xs == 0) {
137 /* Inputs are both positive, with equal signs and exponents */
138 if (xm <= ym)
139 return y;
140 return x;
141 }
142 /* Inputs are both negative, with equal signs and exponents */
143 if (xm <= ym)
144 return x;
145 return y;
146}
147
148union ieee754dp ieee754dp_fmaxa(union ieee754dp x, union ieee754dp y)
149{
150 COMPXDP;
151 COMPYDP;
152
153 EXPLODEXDP;
154 EXPLODEYDP;
155
156 FLUSHXDP;
157 FLUSHYDP;
158
159 ieee754_clearcx();
160
161 switch (CLPAIR(xc, yc)) {
162 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
163 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
164 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
165 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
166 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
167 return ieee754dp_nanxcpt(y);
168
169 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
170 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
171 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
172 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
173 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
174 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
175 return ieee754dp_nanxcpt(x);
176
177 /*
178 * Quiet NaN handling
179 */
180
181 /*
182 * The case of both inputs quiet NaNs
183 */
184 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
185 return x;
186
187 /*
188 * The cases of exactly one input quiet NaN (numbers
189 * are here preferred as returned values to NaNs)
190 */
191 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
192 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
193 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
194 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
195 return x;
196
197 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
198 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
199 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
200 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
201 return y;
202
203 /*
204 * Infinity and zero handling
205 */
206 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
207 return ieee754dp_inf(xs & ys);
208
209 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
210 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
211 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
212 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
213 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
214 return x;
215
216 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
217 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
218 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
219 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
220 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
221 return y;
222
223 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
224 return ieee754dp_zero(xs & ys);
225
226 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
227 DPDNORMX;
228 /* fall through */
229
230 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
231 DPDNORMY;
232 break;
233
234 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
235 DPDNORMX;
236 }
237
238 /* Finally get to do some computation */
239
240 assert(xm & DP_HIDDEN_BIT);
241 assert(ym & DP_HIDDEN_BIT);
242
243 /* Compare exponent */
244 if (xe > ye)
245 return x;
246 else if (xe < ye)
247 return y;
248
249 /* Compare mantissa */
250 if (xm < ym)
251 return y;
252 else if (xm > ym)
253 return x;
254 else if (xs == 0)
255 return x;
256 return y;
257}