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 * http://www.algor.co.uk
8 *
9 * ########################################################################
10 *
11 * This program is free software; you can distribute it and/or modify it
12 * under the terms of the GNU General Public License (Version 2) as
13 * published by the Free Software Foundation.
14 *
15 * This program is distributed in the hope it will be useful, but WITHOUT
16 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
17 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
18 * for more details.
19 *
20 * You should have received a copy of the GNU General Public License along
21 * with this program; if not, write to the Free Software Foundation, Inc.,
22 * 59 Temple Place - Suite 330, Boston MA 02111-1307, USA.
23 *
24 * ########################################################################
25 */
26
27
28 #include "ieee754dp.h"
29
ieee754dp_class(ieee754dp x)30 int ieee754dp_class(ieee754dp x)
31 {
32 COMPXDP;
33 EXPLODEXDP;
34 return xc;
35 }
36
ieee754dp_isnan(ieee754dp x)37 int ieee754dp_isnan(ieee754dp x)
38 {
39 return ieee754dp_class(x) >= IEEE754_CLASS_SNAN;
40 }
41
ieee754dp_issnan(ieee754dp x)42 int ieee754dp_issnan(ieee754dp x)
43 {
44 assert(ieee754dp_isnan(x));
45 return ((DPMANT(x) & DP_MBIT(DP_MBITS-1)) == DP_MBIT(DP_MBITS-1));
46 }
47
48
ieee754dp_xcpt(ieee754dp r,const char * op,...)49 ieee754dp ieee754dp_xcpt(ieee754dp r, const char *op, ...)
50 {
51 struct ieee754xctx ax;
52 if (!TSTX())
53 return r;
54
55 ax.op = op;
56 ax.rt = IEEE754_RT_DP;
57 ax.rv.dp = r;
58 va_start(ax.ap, op);
59 ieee754_xcpt(&ax);
60 va_end(ax.ap);
61 return ax.rv.dp;
62 }
63
ieee754dp_nanxcpt(ieee754dp r,const char * op,...)64 ieee754dp ieee754dp_nanxcpt(ieee754dp r, const char *op, ...)
65 {
66 struct ieee754xctx ax;
67
68 assert(ieee754dp_isnan(r));
69
70 if (!ieee754dp_issnan(r)) /* QNAN does not cause invalid op !! */
71 return r;
72
73 if (!SETANDTESTCX(IEEE754_INVALID_OPERATION)) {
74 /* not enabled convert to a quiet NaN */
75 DPMANT(r) &= (~DP_MBIT(DP_MBITS-1));
76 if (ieee754dp_isnan(r))
77 return r;
78 else
79 return ieee754dp_indef();
80 }
81
82 ax.op = op;
83 ax.rt = 0;
84 ax.rv.dp = r;
85 va_start(ax.ap, op);
86 ieee754_xcpt(&ax);
87 va_end(ax.ap);
88 return ax.rv.dp;
89 }
90
ieee754dp_bestnan(ieee754dp x,ieee754dp y)91 ieee754dp ieee754dp_bestnan(ieee754dp x, ieee754dp y)
92 {
93 assert(ieee754dp_isnan(x));
94 assert(ieee754dp_isnan(y));
95
96 if (DPMANT(x) > DPMANT(y))
97 return x;
98 else
99 return y;
100 }
101
102
get_rounding(int sn,u64 xm)103 static u64 get_rounding(int sn, u64 xm)
104 {
105 /* inexact must round of 3 bits
106 */
107 if (xm & (DP_MBIT(3) - 1)) {
108 switch (ieee754_csr.rm) {
109 case IEEE754_RZ:
110 break;
111 case IEEE754_RN:
112 xm += 0x3 + ((xm >> 3) & 1);
113 /* xm += (xm&0x8)?0x4:0x3 */
114 break;
115 case IEEE754_RU: /* toward +Infinity */
116 if (!sn) /* ?? */
117 xm += 0x8;
118 break;
119 case IEEE754_RD: /* toward -Infinity */
120 if (sn) /* ?? */
121 xm += 0x8;
122 break;
123 }
124 }
125 return xm;
126 }
127
128
129 /* generate a normal/denormal number with over,under handling
130 * sn is sign
131 * xe is an unbiased exponent
132 * xm is 3bit extended precision value.
133 */
ieee754dp_format(int sn,int xe,u64 xm)134 ieee754dp ieee754dp_format(int sn, int xe, u64 xm)
135 {
136 assert(xm); /* we don't gen exact zeros (probably should) */
137
138 assert((xm >> (DP_MBITS + 1 + 3)) == 0); /* no execess */
139 assert(xm & (DP_HIDDEN_BIT << 3));
140
141 if (xe < DP_EMIN) {
142 /* strip lower bits */
143 int es = DP_EMIN - xe;
144
145 if (ieee754_csr.nod) {
146 SETCX(IEEE754_UNDERFLOW);
147 SETCX(IEEE754_INEXACT);
148
149 switch(ieee754_csr.rm) {
150 case IEEE754_RN:
151 return ieee754dp_zero(sn);
152 case IEEE754_RZ:
153 return ieee754dp_zero(sn);
154 case IEEE754_RU: /* toward +Infinity */
155 if(sn == 0)
156 return ieee754dp_min(0);
157 else
158 return ieee754dp_zero(1);
159 case IEEE754_RD: /* toward -Infinity */
160 if(sn == 0)
161 return ieee754dp_zero(0);
162 else
163 return ieee754dp_min(1);
164 }
165 }
166
167 if (xe == DP_EMIN - 1
168 && get_rounding(sn, xm) >> (DP_MBITS + 1 + 3))
169 {
170 /* Not tiny after rounding */
171 SETCX(IEEE754_INEXACT);
172 xm = get_rounding(sn, xm);
173 xm >>= 1;
174 /* Clear grs bits */
175 xm &= ~(DP_MBIT(3) - 1);
176 xe++;
177 }
178 else {
179 /* sticky right shift es bits
180 */
181 xm = XDPSRS(xm, es);
182 xe += es;
183 assert((xm & (DP_HIDDEN_BIT << 3)) == 0);
184 assert(xe == DP_EMIN);
185 }
186 }
187 if (xm & (DP_MBIT(3) - 1)) {
188 SETCX(IEEE754_INEXACT);
189 if ((xm & (DP_HIDDEN_BIT << 3)) == 0) {
190 SETCX(IEEE754_UNDERFLOW);
191 }
192
193 /* inexact must round of 3 bits
194 */
195 xm = get_rounding(sn, xm);
196 /* adjust exponent for rounding add overflowing
197 */
198 if (xm >> (DP_MBITS + 3 + 1)) {
199 /* add causes mantissa overflow */
200 xm >>= 1;
201 xe++;
202 }
203 }
204 /* strip grs bits */
205 xm >>= 3;
206
207 assert((xm >> (DP_MBITS + 1)) == 0); /* no execess */
208 assert(xe >= DP_EMIN);
209
210 if (xe > DP_EMAX) {
211 SETCX(IEEE754_OVERFLOW);
212 SETCX(IEEE754_INEXACT);
213 /* -O can be table indexed by (rm,sn) */
214 switch (ieee754_csr.rm) {
215 case IEEE754_RN:
216 return ieee754dp_inf(sn);
217 case IEEE754_RZ:
218 return ieee754dp_max(sn);
219 case IEEE754_RU: /* toward +Infinity */
220 if (sn == 0)
221 return ieee754dp_inf(0);
222 else
223 return ieee754dp_max(1);
224 case IEEE754_RD: /* toward -Infinity */
225 if (sn == 0)
226 return ieee754dp_max(0);
227 else
228 return ieee754dp_inf(1);
229 }
230 }
231 /* gen norm/denorm/zero */
232
233 if ((xm & DP_HIDDEN_BIT) == 0) {
234 /* we underflow (tiny/zero) */
235 assert(xe == DP_EMIN);
236 if (ieee754_csr.mx & IEEE754_UNDERFLOW)
237 SETCX(IEEE754_UNDERFLOW);
238 return builddp(sn, DP_EMIN - 1 + DP_EBIAS, xm);
239 } else {
240 assert((xm >> (DP_MBITS + 1)) == 0); /* no execess */
241 assert(xm & DP_HIDDEN_BIT);
242
243 return builddp(sn, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
244 }
245 }
246