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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
29int ieee754dp_class(ieee754dp x)
30{
31 COMPXDP;
32 EXPLODEXDP;
33 return xc;
34}
35
36int ieee754dp_isnan(ieee754dp x)
37{
38 return ieee754dp_class(x) >= IEEE754_CLASS_SNAN;
39}
40
41int ieee754dp_issnan(ieee754dp x)
42{
43 assert(ieee754dp_isnan(x));
44 return ((DPMANT(x) & DP_MBIT(DP_MBITS-1)) == DP_MBIT(DP_MBITS-1));
45}
46
47
48ieee754dp ieee754dp_xcpt(ieee754dp r, const char *op, ...)
49{
50 struct ieee754xctx ax;
51 if (!TSTX())
52 return r;
53
54 ax.op = op;
55 ax.rt = IEEE754_RT_DP;
56 ax.rv.dp = r;
57 va_start(ax.ap, op);
58 ieee754_xcpt(&ax);
59 va_end(ax.ap);
60 return ax.rv.dp;
61}
62
63ieee754dp ieee754dp_nanxcpt(ieee754dp r, const char *op, ...)
64{
65 struct ieee754xctx ax;
66
67 assert(ieee754dp_isnan(r));
68
69 if (!ieee754dp_issnan(r)) /* QNAN does not cause invalid op !! */
70 return r;
71
72 if (!SETANDTESTCX(IEEE754_INVALID_OPERATION)) {
73 /* not enabled convert to a quiet NaN */
74 DPMANT(r) &= (~DP_MBIT(DP_MBITS-1));
75 if (ieee754dp_isnan(r))
76 return r;
77 else
78 return ieee754dp_indef();
79 }
80
81 ax.op = op;
82 ax.rt = 0;
83 ax.rv.dp = r;
84 va_start(ax.ap, op);
85 ieee754_xcpt(&ax);
86 va_end(ax.ap);
87 return ax.rv.dp;
88}
89
90ieee754dp ieee754dp_bestnan(ieee754dp x, ieee754dp y)
91{
92 assert(ieee754dp_isnan(x));
93 assert(ieee754dp_isnan(y));
94
95 if (DPMANT(x) > DPMANT(y))
96 return x;
97 else
98 return y;
99}
100
101
102static u64 get_rounding(int sn, u64 xm)
103{
104 /* inexact must round of 3 bits
105 */
106 if (xm & (DP_MBIT(3) - 1)) {
107 switch (ieee754_csr.rm) {
108 case IEEE754_RZ:
109 break;
110 case IEEE754_RN:
111 xm += 0x3 + ((xm >> 3) & 1);
112 /* xm += (xm&0x8)?0x4:0x3 */
113 break;
114 case IEEE754_RU: /* toward +Infinity */
115 if (!sn) /* ?? */
116 xm += 0x8;
117 break;
118 case IEEE754_RD: /* toward -Infinity */
119 if (sn) /* ?? */
120 xm += 0x8;
121 break;
122 }
123 }
124 return xm;
125}
126
127
128/* generate a normal/denormal number with over,under handling
129 * sn is sign
130 * xe is an unbiased exponent
131 * xm is 3bit extended precision value.
132 */
133ieee754dp ieee754dp_format(int sn, int xe, u64 xm)
134{
135 assert(xm); /* we don't gen exact zeros (probably should) */
136
137 assert((xm >> (DP_MBITS + 1 + 3)) == 0); /* no execess */
138 assert(xm & (DP_HIDDEN_BIT << 3));
139
140 if (xe < DP_EMIN) {
141 /* strip lower bits */
142 int es = DP_EMIN - xe;
143
144 if (ieee754_csr.nod) {
145 SETCX(IEEE754_UNDERFLOW);
146 SETCX(IEEE754_INEXACT);
147
148 switch(ieee754_csr.rm) {
149 case IEEE754_RN:
150 case IEEE754_RZ:
151 return ieee754dp_zero(sn);
152 case IEEE754_RU: /* toward +Infinity */
153 if(sn == 0)
154 return ieee754dp_min(0);
155 else
156 return ieee754dp_zero(1);
157 case IEEE754_RD: /* toward -Infinity */
158 if(sn == 0)
159 return ieee754dp_zero(0);
160 else
161 return ieee754dp_min(1);
162 }
163 }
164
165 if (xe == DP_EMIN - 1
166 && get_rounding(sn, xm) >> (DP_MBITS + 1 + 3))
167 {
168 /* Not tiny after rounding */
169 SETCX(IEEE754_INEXACT);
170 xm = get_rounding(sn, xm);
171 xm >>= 1;
172 /* Clear grs bits */
173 xm &= ~(DP_MBIT(3) - 1);
174 xe++;
175 }
176 else {
177 /* sticky right shift es bits
178 */
179 xm = XDPSRS(xm, es);
180 xe += es;
181 assert((xm & (DP_HIDDEN_BIT << 3)) == 0);
182 assert(xe == DP_EMIN);
183 }
184 }
185 if (xm & (DP_MBIT(3) - 1)) {
186 SETCX(IEEE754_INEXACT);
187 if ((xm & (DP_HIDDEN_BIT << 3)) == 0) {
188 SETCX(IEEE754_UNDERFLOW);
189 }
190
191 /* inexact must round of 3 bits
192 */
193 xm = get_rounding(sn, xm);
194 /* adjust exponent for rounding add overflowing
195 */
196 if (xm >> (DP_MBITS + 3 + 1)) {
197 /* add causes mantissa overflow */
198 xm >>= 1;
199 xe++;
200 }
201 }
202 /* strip grs bits */
203 xm >>= 3;
204
205 assert((xm >> (DP_MBITS + 1)) == 0); /* no execess */
206 assert(xe >= DP_EMIN);
207
208 if (xe > DP_EMAX) {
209 SETCX(IEEE754_OVERFLOW);
210 SETCX(IEEE754_INEXACT);
211 /* -O can be table indexed by (rm,sn) */
212 switch (ieee754_csr.rm) {
213 case IEEE754_RN:
214 return ieee754dp_inf(sn);
215 case IEEE754_RZ:
216 return ieee754dp_max(sn);
217 case IEEE754_RU: /* toward +Infinity */
218 if (sn == 0)
219 return ieee754dp_inf(0);
220 else
221 return ieee754dp_max(1);
222 case IEEE754_RD: /* toward -Infinity */
223 if (sn == 0)
224 return ieee754dp_max(0);
225 else
226 return ieee754dp_inf(1);
227 }
228 }
229 /* gen norm/denorm/zero */
230
231 if ((xm & DP_HIDDEN_BIT) == 0) {
232 /* we underflow (tiny/zero) */
233 assert(xe == DP_EMIN);
234 if (ieee754_csr.mx & IEEE754_UNDERFLOW)
235 SETCX(IEEE754_UNDERFLOW);
236 return builddp(sn, DP_EMIN - 1 + DP_EBIAS, xm);
237 } else {
238 assert((xm >> (DP_MBITS + 1)) == 0); /* no execess */
239 assert(xm & DP_HIDDEN_BIT);
240
241 return builddp(sn, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
242 }
243}
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
29int ieee754dp_class(ieee754dp x)
30{
31 COMPXDP;
32 EXPLODEXDP;
33 return xc;
34}
35
36int ieee754dp_isnan(ieee754dp x)
37{
38 return ieee754dp_class(x) >= IEEE754_CLASS_SNAN;
39}
40
41int ieee754dp_issnan(ieee754dp x)
42{
43 assert(ieee754dp_isnan(x));
44 return ((DPMANT(x) & DP_MBIT(DP_MBITS-1)) == DP_MBIT(DP_MBITS-1));
45}
46
47
48ieee754dp ieee754dp_xcpt(ieee754dp r, const char *op, ...)
49{
50 struct ieee754xctx ax;
51 if (!TSTX())
52 return r;
53
54 ax.op = op;
55 ax.rt = IEEE754_RT_DP;
56 ax.rv.dp = r;
57 va_start(ax.ap, op);
58 ieee754_xcpt(&ax);
59 va_end(ax.ap);
60 return ax.rv.dp;
61}
62
63ieee754dp ieee754dp_nanxcpt(ieee754dp r, const char *op, ...)
64{
65 struct ieee754xctx ax;
66
67 assert(ieee754dp_isnan(r));
68
69 if (!ieee754dp_issnan(r)) /* QNAN does not cause invalid op !! */
70 return r;
71
72 if (!SETANDTESTCX(IEEE754_INVALID_OPERATION)) {
73 /* not enabled convert to a quiet NaN */
74 DPMANT(r) &= (~DP_MBIT(DP_MBITS-1));
75 if (ieee754dp_isnan(r))
76 return r;
77 else
78 return ieee754dp_indef();
79 }
80
81 ax.op = op;
82 ax.rt = 0;
83 ax.rv.dp = r;
84 va_start(ax.ap, op);
85 ieee754_xcpt(&ax);
86 va_end(ax.ap);
87 return ax.rv.dp;
88}
89
90ieee754dp ieee754dp_bestnan(ieee754dp x, ieee754dp y)
91{
92 assert(ieee754dp_isnan(x));
93 assert(ieee754dp_isnan(y));
94
95 if (DPMANT(x) > DPMANT(y))
96 return x;
97 else
98 return y;
99}
100
101
102static u64 get_rounding(int sn, u64 xm)
103{
104 /* inexact must round of 3 bits
105 */
106 if (xm & (DP_MBIT(3) - 1)) {
107 switch (ieee754_csr.rm) {
108 case IEEE754_RZ:
109 break;
110 case IEEE754_RN:
111 xm += 0x3 + ((xm >> 3) & 1);
112 /* xm += (xm&0x8)?0x4:0x3 */
113 break;
114 case IEEE754_RU: /* toward +Infinity */
115 if (!sn) /* ?? */
116 xm += 0x8;
117 break;
118 case IEEE754_RD: /* toward -Infinity */
119 if (sn) /* ?? */
120 xm += 0x8;
121 break;
122 }
123 }
124 return xm;
125}
126
127
128/* generate a normal/denormal number with over,under handling
129 * sn is sign
130 * xe is an unbiased exponent
131 * xm is 3bit extended precision value.
132 */
133ieee754dp ieee754dp_format(int sn, int xe, u64 xm)
134{
135 assert(xm); /* we don't gen exact zeros (probably should) */
136
137 assert((xm >> (DP_MBITS + 1 + 3)) == 0); /* no execess */
138 assert(xm & (DP_HIDDEN_BIT << 3));
139
140 if (xe < DP_EMIN) {
141 /* strip lower bits */
142 int es = DP_EMIN - xe;
143
144 if (ieee754_csr.nod) {
145 SETCX(IEEE754_UNDERFLOW);
146 SETCX(IEEE754_INEXACT);
147
148 switch(ieee754_csr.rm) {
149 case IEEE754_RN:
150 case IEEE754_RZ:
151 return ieee754dp_zero(sn);
152 case IEEE754_RU: /* toward +Infinity */
153 if(sn == 0)
154 return ieee754dp_min(0);
155 else
156 return ieee754dp_zero(1);
157 case IEEE754_RD: /* toward -Infinity */
158 if(sn == 0)
159 return ieee754dp_zero(0);
160 else
161 return ieee754dp_min(1);
162 }
163 }
164
165 if (xe == DP_EMIN - 1
166 && get_rounding(sn, xm) >> (DP_MBITS + 1 + 3))
167 {
168 /* Not tiny after rounding */
169 SETCX(IEEE754_INEXACT);
170 xm = get_rounding(sn, xm);
171 xm >>= 1;
172 /* Clear grs bits */
173 xm &= ~(DP_MBIT(3) - 1);
174 xe++;
175 }
176 else {
177 /* sticky right shift es bits
178 */
179 xm = XDPSRS(xm, es);
180 xe += es;
181 assert((xm & (DP_HIDDEN_BIT << 3)) == 0);
182 assert(xe == DP_EMIN);
183 }
184 }
185 if (xm & (DP_MBIT(3) - 1)) {
186 SETCX(IEEE754_INEXACT);
187 if ((xm & (DP_HIDDEN_BIT << 3)) == 0) {
188 SETCX(IEEE754_UNDERFLOW);
189 }
190
191 /* inexact must round of 3 bits
192 */
193 xm = get_rounding(sn, xm);
194 /* adjust exponent for rounding add overflowing
195 */
196 if (xm >> (DP_MBITS + 3 + 1)) {
197 /* add causes mantissa overflow */
198 xm >>= 1;
199 xe++;
200 }
201 }
202 /* strip grs bits */
203 xm >>= 3;
204
205 assert((xm >> (DP_MBITS + 1)) == 0); /* no execess */
206 assert(xe >= DP_EMIN);
207
208 if (xe > DP_EMAX) {
209 SETCX(IEEE754_OVERFLOW);
210 SETCX(IEEE754_INEXACT);
211 /* -O can be table indexed by (rm,sn) */
212 switch (ieee754_csr.rm) {
213 case IEEE754_RN:
214 return ieee754dp_inf(sn);
215 case IEEE754_RZ:
216 return ieee754dp_max(sn);
217 case IEEE754_RU: /* toward +Infinity */
218 if (sn == 0)
219 return ieee754dp_inf(0);
220 else
221 return ieee754dp_max(1);
222 case IEEE754_RD: /* toward -Infinity */
223 if (sn == 0)
224 return ieee754dp_max(0);
225 else
226 return ieee754dp_inf(1);
227 }
228 }
229 /* gen norm/denorm/zero */
230
231 if ((xm & DP_HIDDEN_BIT) == 0) {
232 /* we underflow (tiny/zero) */
233 assert(xe == DP_EMIN);
234 if (ieee754_csr.mx & IEEE754_UNDERFLOW)
235 SETCX(IEEE754_UNDERFLOW);
236 return builddp(sn, DP_EMIN - 1 + DP_EBIAS, xm);
237 } else {
238 assert((xm >> (DP_MBITS + 1)) == 0); /* no execess */
239 assert(xm & DP_HIDDEN_BIT);
240
241 return builddp(sn, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
242 }
243}