1 /* IEEE754 floating point arithmetic
2 * single precision
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 "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 va_end(ax.ap);
62 return ax.rv.sp;
63 }
64
ieee754sp_nanxcpt(ieee754sp r,const char * op,...)65 ieee754sp ieee754sp_nanxcpt(ieee754sp r, const char *op, ...)
66 {
67 struct ieee754xctx ax;
68
69 assert(ieee754sp_isnan(r));
70
71 if (!ieee754sp_issnan(r)) /* QNAN does not cause invalid op !! */
72 return r;
73
74 if (!SETANDTESTCX(IEEE754_INVALID_OPERATION)) {
75 /* not enabled convert to a quiet NaN */
76 SPMANT(r) &= (~SP_MBIT(SP_MBITS-1));
77 if (ieee754sp_isnan(r))
78 return r;
79 else
80 return ieee754sp_indef();
81 }
82
83 ax.op = op;
84 ax.rt = 0;
85 ax.rv.sp = r;
86 va_start(ax.ap, op);
87 ieee754_xcpt(&ax);
88 va_end(ax.ap);
89 return ax.rv.sp;
90 }
91
ieee754sp_bestnan(ieee754sp x,ieee754sp y)92 ieee754sp ieee754sp_bestnan(ieee754sp x, ieee754sp y)
93 {
94 assert(ieee754sp_isnan(x));
95 assert(ieee754sp_isnan(y));
96
97 if (SPMANT(x) > SPMANT(y))
98 return x;
99 else
100 return y;
101 }
102
103
get_rounding(int sn,unsigned xm)104 static unsigned get_rounding(int sn, unsigned xm)
105 {
106 /* inexact must round of 3 bits
107 */
108 if (xm & (SP_MBIT(3) - 1)) {
109 switch (ieee754_csr.rm) {
110 case IEEE754_RZ:
111 break;
112 case IEEE754_RN:
113 xm += 0x3 + ((xm >> 3) & 1);
114 /* xm += (xm&0x8)?0x4:0x3 */
115 break;
116 case IEEE754_RU: /* toward +Infinity */
117 if (!sn) /* ?? */
118 xm += 0x8;
119 break;
120 case IEEE754_RD: /* toward -Infinity */
121 if (sn) /* ?? */
122 xm += 0x8;
123 break;
124 }
125 }
126 return xm;
127 }
128
129
130 /* generate a normal/denormal number with over,under handling
131 * sn is sign
132 * xe is an unbiased exponent
133 * xm is 3bit extended precision value.
134 */
ieee754sp_format(int sn,int xe,unsigned xm)135 ieee754sp ieee754sp_format(int sn, int xe, unsigned xm)
136 {
137 assert(xm); /* we don't gen exact zeros (probably should) */
138
139 assert((xm >> (SP_MBITS + 1 + 3)) == 0); /* no execess */
140 assert(xm & (SP_HIDDEN_BIT << 3));
141
142 if (xe < SP_EMIN) {
143 /* strip lower bits */
144 int es = SP_EMIN - xe;
145
146 if (ieee754_csr.nod) {
147 SETCX(IEEE754_UNDERFLOW);
148 SETCX(IEEE754_INEXACT);
149
150 switch(ieee754_csr.rm) {
151 case IEEE754_RN:
152 return ieee754sp_zero(sn);
153 case IEEE754_RZ:
154 return ieee754sp_zero(sn);
155 case IEEE754_RU: /* toward +Infinity */
156 if(sn == 0)
157 return ieee754sp_min(0);
158 else
159 return ieee754sp_zero(1);
160 case IEEE754_RD: /* toward -Infinity */
161 if(sn == 0)
162 return ieee754sp_zero(0);
163 else
164 return ieee754sp_min(1);
165 }
166 }
167
168 if (xe == SP_EMIN - 1
169 && get_rounding(sn, xm) >> (SP_MBITS + 1 + 3))
170 {
171 /* Not tiny after rounding */
172 SETCX(IEEE754_INEXACT);
173 xm = get_rounding(sn, xm);
174 xm >>= 1;
175 /* Clear grs bits */
176 xm &= ~(SP_MBIT(3) - 1);
177 xe++;
178 }
179 else {
180 /* sticky right shift es bits
181 */
182 SPXSRSXn(es);
183 assert((xm & (SP_HIDDEN_BIT << 3)) == 0);
184 assert(xe == SP_EMIN);
185 }
186 }
187 if (xm & (SP_MBIT(3) - 1)) {
188 SETCX(IEEE754_INEXACT);
189 if ((xm & (SP_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 >> (SP_MBITS + 1 + 3)) {
199 /* add causes mantissa overflow */
200 xm >>= 1;
201 xe++;
202 }
203 }
204 /* strip grs bits */
205 xm >>= 3;
206
207 assert((xm >> (SP_MBITS + 1)) == 0); /* no execess */
208 assert(xe >= SP_EMIN);
209
210 if (xe > SP_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 ieee754sp_inf(sn);
217 case IEEE754_RZ:
218 return ieee754sp_max(sn);
219 case IEEE754_RU: /* toward +Infinity */
220 if (sn == 0)
221 return ieee754sp_inf(0);
222 else
223 return ieee754sp_max(1);
224 case IEEE754_RD: /* toward -Infinity */
225 if (sn == 0)
226 return ieee754sp_max(0);
227 else
228 return ieee754sp_inf(1);
229 }
230 }
231 /* gen norm/denorm/zero */
232
233 if ((xm & SP_HIDDEN_BIT) == 0) {
234 /* we underflow (tiny/zero) */
235 assert(xe == SP_EMIN);
236 if (ieee754_csr.mx & IEEE754_UNDERFLOW)
237 SETCX(IEEE754_UNDERFLOW);
238 return buildsp(sn, SP_EMIN - 1 + SP_EBIAS, xm);
239 } else {
240 assert((xm >> (SP_MBITS + 1)) == 0); /* no execess */
241 assert(xm & SP_HIDDEN_BIT);
242
243 return buildsp(sn, xe + SP_EBIAS, xm & ~SP_HIDDEN_BIT);
244 }
245 }
246