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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// 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 /* fall through */
97
98 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
99 DPDNORMY;
100 break;
101
102 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
103 DPDNORMX;
104 }
105
106 /* Finally get to do some computation */
107
108 assert(xm & DP_HIDDEN_BIT);
109 assert(ym & DP_HIDDEN_BIT);
110
111 /* Compare signs */
112 if (xs > ys)
113 return y;
114 else if (xs < ys)
115 return x;
116
117 /* Signs of inputs are equal, let's compare exponents */
118 if (xs == 0) {
119 /* Inputs are both positive */
120 if (xe > ye)
121 return x;
122 else if (xe < ye)
123 return y;
124 } else {
125 /* Inputs are both negative */
126 if (xe > ye)
127 return y;
128 else if (xe < ye)
129 return x;
130 }
131
132 /* Signs and exponents of inputs are equal, let's compare mantissas */
133 if (xs == 0) {
134 /* Inputs are both positive, with equal signs and exponents */
135 if (xm <= ym)
136 return y;
137 return x;
138 }
139 /* Inputs are both negative, with equal signs and exponents */
140 if (xm <= ym)
141 return x;
142 return y;
143}
144
145union ieee754dp ieee754dp_fmaxa(union ieee754dp x, union ieee754dp y)
146{
147 COMPXDP;
148 COMPYDP;
149
150 EXPLODEXDP;
151 EXPLODEYDP;
152
153 FLUSHXDP;
154 FLUSHYDP;
155
156 ieee754_clearcx();
157
158 switch (CLPAIR(xc, yc)) {
159 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
160 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
161 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
162 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
163 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
164 return ieee754dp_nanxcpt(y);
165
166 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
167 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
168 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
169 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
170 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
171 case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
172 return ieee754dp_nanxcpt(x);
173
174 /*
175 * Quiet NaN handling
176 */
177
178 /*
179 * The case of both inputs quiet NaNs
180 */
181 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
182 return x;
183
184 /*
185 * The cases of exactly one input quiet NaN (numbers
186 * are here preferred as returned values to NaNs)
187 */
188 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
189 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
190 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
191 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
192 return x;
193
194 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
195 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
196 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
197 case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
198 return y;
199
200 /*
201 * Infinity and zero handling
202 */
203 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
204 return ieee754dp_inf(xs & ys);
205
206 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
207 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
208 case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
209 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
210 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
211 return x;
212
213 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
214 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
215 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
216 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
217 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
218 return y;
219
220 case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
221 return ieee754dp_zero(xs & ys);
222
223 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
224 DPDNORMX;
225 /* fall through */
226
227 case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
228 DPDNORMY;
229 break;
230
231 case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
232 DPDNORMX;
233 }
234
235 /* Finally get to do some computation */
236
237 assert(xm & DP_HIDDEN_BIT);
238 assert(ym & DP_HIDDEN_BIT);
239
240 /* Compare exponent */
241 if (xe > ye)
242 return x;
243 else if (xe < ye)
244 return y;
245
246 /* Compare mantissa */
247 if (xm < ym)
248 return y;
249 else if (xm > ym)
250 return x;
251 else if (xs == 0)
252 return x;
253 return y;
254}