1 /* IEEE754 floating point arithmetic
2 * single precision
3 */
4 /*
5 * MIPS floating point support
6 * Copyright (C) 1994-2000 Algorithmics Ltd. All rights reserved.
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 "ieee754sp.h"
29
ieee754sp_class(ieee754sp x)30 int ieee754sp_class(ieee754sp x)
31 {
32 COMPXSP;
33 EXPLODEXSP;
34 return xc;
35 }
36
ieee754sp_isnan(ieee754sp x)37 int ieee754sp_isnan(ieee754sp x)
38 {
39 return ieee754sp_class(x) >= IEEE754_CLASS_SNAN;
40 }
41
ieee754sp_issnan(ieee754sp x)42 int ieee754sp_issnan(ieee754sp x)
43 {
44 assert(ieee754sp_isnan(x));
45 return (SPMANT(x) & SP_MBIT(SP_MBITS-1));
46 }
47
48
ieee754sp_xcpt(ieee754sp r,const char * op,...)49 ieee754sp ieee754sp_xcpt(ieee754sp r, const char *op, ...)
50 {
51 struct ieee754xctx ax;
52
53 if (!TSTX())
54 return r;
55
56 ax.op = op;
57 ax.rt = IEEE754_RT_SP;
58 ax.rv.sp = r;
59 va_start(ax.ap, op);
60 ieee754_xcpt(&ax);
61 return ax.rv.sp;
62 }
63
ieee754sp_nanxcpt(ieee754sp r,const char * op,...)64 ieee754sp ieee754sp_nanxcpt(ieee754sp r, const char *op, ...)
65 {
66 struct ieee754xctx ax;
67
68 assert(ieee754sp_isnan(r));
69
70 if (!ieee754sp_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 SPMANT(r) &= (~SP_MBIT(SP_MBITS-1));
76 if (ieee754sp_isnan(r))
77 return r;
78 else
79 return ieee754sp_indef();
80 }
81
82 ax.op = op;
83 ax.rt = 0;
84 ax.rv.sp = r;
85 va_start(ax.ap, op);
86 ieee754_xcpt(&ax);
87 return ax.rv.sp;
88 }
89
ieee754sp_bestnan(ieee754sp x,ieee754sp y)90 ieee754sp ieee754sp_bestnan(ieee754sp x, ieee754sp y)
91 {
92 assert(ieee754sp_isnan(x));
93 assert(ieee754sp_isnan(y));
94
95 if (SPMANT(x) > SPMANT(y))
96 return x;
97 else
98 return y;
99 }
100
101
get_rounding(int sn,unsigned xm)102 static unsigned get_rounding(int sn, unsigned xm)
103 {
104 /* inexact must round of 3 bits
105 */
106 if (xm & (SP_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 handeling
129 * sn is sign
130 * xe is an unbiased exponent
131 * xm is 3bit extended precision value.
132 */
ieee754sp_format(int sn,int xe,unsigned xm)133 ieee754sp ieee754sp_format(int sn, int xe, unsigned xm)
134 {
135 assert(xm); /* we dont gen exact zeros (probably should) */
136
137 assert((xm >> (SP_MBITS + 1 + 3)) == 0); /* no execess */
138 assert(xm & (SP_HIDDEN_BIT << 3));
139
140 if (xe < SP_EMIN) {
141 /* strip lower bits */
142 int es = SP_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 return ieee754sp_zero(sn);
151 case IEEE754_RZ:
152 return ieee754sp_zero(sn);
153 case IEEE754_RU: /* toward +Infinity */
154 if(sn == 0)
155 return ieee754sp_min(0);
156 else
157 return ieee754sp_zero(1);
158 case IEEE754_RD: /* toward -Infinity */
159 if(sn == 0)
160 return ieee754sp_zero(0);
161 else
162 return ieee754sp_min(1);
163 }
164 }
165
166 if (xe == SP_EMIN - 1
167 && get_rounding(sn, xm) >> (SP_MBITS + 1 + 3))
168 {
169 /* Not tiny after rounding */
170 SETCX(IEEE754_INEXACT);
171 xm = get_rounding(sn, xm);
172 xm >>= 1;
173 /* Clear grs bits */
174 xm &= ~(SP_MBIT(3) - 1);
175 xe++;
176 }
177 else {
178 /* sticky right shift es bits
179 */
180 SPXSRSXn(es);
181 assert((xm & (SP_HIDDEN_BIT << 3)) == 0);
182 assert(xe == SP_EMIN);
183 }
184 }
185 if (xm & (SP_MBIT(3) - 1)) {
186 SETCX(IEEE754_INEXACT);
187 if ((xm & (SP_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 >> (SP_MBITS + 1 + 3)) {
197 /* add causes mantissa overflow */
198 xm >>= 1;
199 xe++;
200 }
201 }
202 /* strip grs bits */
203 xm >>= 3;
204
205 assert((xm >> (SP_MBITS + 1)) == 0); /* no execess */
206 assert(xe >= SP_EMIN);
207
208 if (xe > SP_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 ieee754sp_inf(sn);
215 case IEEE754_RZ:
216 return ieee754sp_max(sn);
217 case IEEE754_RU: /* toward +Infinity */
218 if (sn == 0)
219 return ieee754sp_inf(0);
220 else
221 return ieee754sp_max(1);
222 case IEEE754_RD: /* toward -Infinity */
223 if (sn == 0)
224 return ieee754sp_max(0);
225 else
226 return ieee754sp_inf(1);
227 }
228 }
229 /* gen norm/denorm/zero */
230
231 if ((xm & SP_HIDDEN_BIT) == 0) {
232 /* we underflow (tiny/zero) */
233 assert(xe == SP_EMIN);
234 if (ieee754_csr.mx & IEEE754_UNDERFLOW)
235 SETCX(IEEE754_UNDERFLOW);
236 return buildsp(sn, SP_EMIN - 1 + SP_EBIAS, xm);
237 } else {
238 assert((xm >> (SP_MBITS + 1)) == 0); /* no execess */
239 assert(xm & SP_HIDDEN_BIT);
240
241 return buildsp(sn, xe + SP_EBIAS, xm & ~SP_HIDDEN_BIT);
242 }
243 }
244