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1// SPDX-License-Identifier: GPL-2.0-only
2/*
3 * IEEE754 floating point arithmetic
4 * double precision: MIN{,A}.f
5 * MIN : Scalar Floating-Point Minimum
6 * MINA: Scalar Floating-Point argument with Minimum Absolute Value
7 *
8 * MIN.D : FPR[fd] = minNum(FPR[fs],FPR[ft])
9 * MINA.D: FPR[fd] = maxNumMag(FPR[fs],FPR[ft])
10 *
11 * MIPS floating point support
12 * Copyright (C) 2015 Imagination Technologies, Ltd.
13 * Author: Markos Chandras <markos.chandras@imgtec.com>
14 */
15
16#include "ieee754dp.h"
17
18union ieee754dp ieee754dp_fmax(union ieee754dp x, union ieee754dp y)
19{
20 COMPXDP;
21 COMPYDP;
22
23 EXPLODEXDP;
24 EXPLODEYDP;
25
26 FLUSHXDP;
27 FLUSHYDP;
28
29 ieee754_clearcx();
30
31 switch (CLPAIR(xc, yc)) {
32 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
33 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
34 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
35 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
36 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
37 return ieee754dp_nanxcpt(y);
38
39 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
40 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
41 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
42 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
43 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
44 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
45 return ieee754dp_nanxcpt(x);
46
47 /*
48 * Quiet NaN handling
49 */
50
51 /*
52 * The case of both inputs quiet NaNs
53 */
54 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
55 return x;
56
57 /*
58 * The cases of exactly one input quiet NaN (numbers
59 * are here preferred as returned values to NaNs)
60 */
61 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
62 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
63 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
64 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
65 return x;
66
67 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
68 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
69 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
70 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
71 return y;
72
73 /*
74 * Infinity and zero handling
75 */
76 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
77 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
78 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
79 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
80 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
81 return xs ? y : x;
82
83 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
84 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
85 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
86 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
87 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
88 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
89 return ys ? x : y;
90
91 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
92 return ieee754dp_zero(xs & ys);
93
94 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
95 DPDNORMX;
96 fallthrough;
97 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
98 DPDNORMY;
99 break;
100
101 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
102 DPDNORMX;
103 }
104
105 /* Finally get to do some computation */
106
107 assert(xm & DP_HIDDEN_BIT);
108 assert(ym & DP_HIDDEN_BIT);
109
110 /* Compare signs */
111 if (xs > ys)
112 return y;
113 else if (xs < ys)
114 return x;
115
116 /* Signs of inputs are equal, let's compare exponents */
117 if (xs == 0) {
118 /* Inputs are both positive */
119 if (xe > ye)
120 return x;
121 else if (xe < ye)
122 return y;
123 } else {
124 /* Inputs are both negative */
125 if (xe > ye)
126 return y;
127 else if (xe < ye)
128 return x;
129 }
130
131 /* Signs and exponents of inputs are equal, let's compare mantissas */
132 if (xs == 0) {
133 /* Inputs are both positive, with equal signs and exponents */
134 if (xm <= ym)
135 return y;
136 return x;
137 }
138 /* Inputs are both negative, with equal signs and exponents */
139 if (xm <= ym)
140 return x;
141 return y;
142}
143
144union ieee754dp ieee754dp_fmaxa(union ieee754dp x, union ieee754dp y)
145{
146 COMPXDP;
147 COMPYDP;
148
149 EXPLODEXDP;
150 EXPLODEYDP;
151
152 FLUSHXDP;
153 FLUSHYDP;
154
155 ieee754_clearcx();
156
157 switch (CLPAIR(xc, yc)) {
158 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
159 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
160 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
161 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
162 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
163 return ieee754dp_nanxcpt(y);
164
165 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
166 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
167 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
168 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
169 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
170 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
171 return ieee754dp_nanxcpt(x);
172
173 /*
174 * Quiet NaN handling
175 */
176
177 /*
178 * The case of both inputs quiet NaNs
179 */
180 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
181 return x;
182
183 /*
184 * The cases of exactly one input quiet NaN (numbers
185 * are here preferred as returned values to NaNs)
186 */
187 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
188 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
189 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
190 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
191 return x;
192
193 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
194 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
195 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
196 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
197 return y;
198
199 /*
200 * Infinity and zero handling
201 */
202 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
203 return ieee754dp_inf(xs & ys);
204
205 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
206 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
207 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
208 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
209 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
210 return x;
211
212 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
213 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
214 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
215 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
216 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
217 return y;
218
219 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
220 return ieee754dp_zero(xs & ys);
221
222 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
223 DPDNORMX;
224 fallthrough;
225 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
226 DPDNORMY;
227 break;
228
229 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
230 DPDNORMX;
231 }
232
233 /* Finally get to do some computation */
234
235 assert(xm & DP_HIDDEN_BIT);
236 assert(ym & DP_HIDDEN_BIT);
237
238 /* Compare exponent */
239 if (xe > ye)
240 return x;
241 else if (xe < ye)
242 return y;
243
244 /* Compare mantissa */
245 if (xm < ym)
246 return y;
247 else if (xm > ym)
248 return x;
249 else if (xs == 0)
250 return x;
251 return y;
252}
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}