1 /* IEEE754 floating point arithmetic
2 * double precision: common utilities
5 * MIPS floating point support
6 * Copyright (C) 1994-2000 Algorithmics Ltd.
8 * ########################################################################
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.
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
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.
23 * ########################################################################
27 #include "ieee754dp.h"
29 int ieee754dp_class(ieee754dp x
)
36 int ieee754dp_isnan(ieee754dp x
)
38 return ieee754dp_class(x
) >= IEEE754_CLASS_SNAN
;
41 int ieee754dp_issnan(ieee754dp x
)
43 assert(ieee754dp_isnan(x
));
44 return ((DPMANT(x
) & DP_MBIT(DP_MBITS
-1)) == DP_MBIT(DP_MBITS
-1));
48 ieee754dp
ieee754dp_xcpt(ieee754dp r
, const char *op
, ...)
50 struct ieee754xctx ax
;
55 ax
.rt
= IEEE754_RT_DP
;
63 ieee754dp
ieee754dp_nanxcpt(ieee754dp r
, const char *op
, ...)
65 struct ieee754xctx ax
;
67 assert(ieee754dp_isnan(r
));
69 if (!ieee754dp_issnan(r
)) /* QNAN does not cause invalid op !! */
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
))
78 return ieee754dp_indef();
90 ieee754dp
ieee754dp_bestnan(ieee754dp x
, ieee754dp y
)
92 assert(ieee754dp_isnan(x
));
93 assert(ieee754dp_isnan(y
));
95 if (DPMANT(x
) > DPMANT(y
))
102 static u64
get_rounding(int sn
, u64 xm
)
104 /* inexact must round of 3 bits
106 if (xm
& (DP_MBIT(3) - 1)) {
107 switch (ieee754_csr
.rm
) {
111 xm
+= 0x3 + ((xm
>> 3) & 1);
112 /* xm += (xm&0x8)?0x4:0x3 */
114 case IEEE754_RU
: /* toward +Infinity */
118 case IEEE754_RD
: /* toward -Infinity */
128 /* generate a normal/denormal number with over,under handling
130 * xe is an unbiased exponent
131 * xm is 3bit extended precision value.
133 ieee754dp
ieee754dp_format(int sn
, int xe
, u64 xm
)
135 assert(xm
); /* we don't gen exact zeros (probably should) */
137 assert((xm
>> (DP_MBITS
+ 1 + 3)) == 0); /* no execess */
138 assert(xm
& (DP_HIDDEN_BIT
<< 3));
141 /* strip lower bits */
142 int es
= DP_EMIN
- xe
;
144 if (ieee754_csr
.nod
) {
145 SETCX(IEEE754_UNDERFLOW
);
146 SETCX(IEEE754_INEXACT
);
148 switch(ieee754_csr
.rm
) {
151 return ieee754dp_zero(sn
);
152 case IEEE754_RU
: /* toward +Infinity */
154 return ieee754dp_min(0);
156 return ieee754dp_zero(1);
157 case IEEE754_RD
: /* toward -Infinity */
159 return ieee754dp_zero(0);
161 return ieee754dp_min(1);
165 if (xe
== DP_EMIN
- 1
166 && get_rounding(sn
, xm
) >> (DP_MBITS
+ 1 + 3))
168 /* Not tiny after rounding */
169 SETCX(IEEE754_INEXACT
);
170 xm
= get_rounding(sn
, xm
);
173 xm
&= ~(DP_MBIT(3) - 1);
177 /* sticky right shift es bits
181 assert((xm
& (DP_HIDDEN_BIT
<< 3)) == 0);
182 assert(xe
== DP_EMIN
);
185 if (xm
& (DP_MBIT(3) - 1)) {
186 SETCX(IEEE754_INEXACT
);
187 if ((xm
& (DP_HIDDEN_BIT
<< 3)) == 0) {
188 SETCX(IEEE754_UNDERFLOW
);
191 /* inexact must round of 3 bits
193 xm
= get_rounding(sn
, xm
);
194 /* adjust exponent for rounding add overflowing
196 if (xm
>> (DP_MBITS
+ 3 + 1)) {
197 /* add causes mantissa overflow */
205 assert((xm
>> (DP_MBITS
+ 1)) == 0); /* no execess */
206 assert(xe
>= DP_EMIN
);
209 SETCX(IEEE754_OVERFLOW
);
210 SETCX(IEEE754_INEXACT
);
211 /* -O can be table indexed by (rm,sn) */
212 switch (ieee754_csr
.rm
) {
214 return ieee754dp_inf(sn
);
216 return ieee754dp_max(sn
);
217 case IEEE754_RU
: /* toward +Infinity */
219 return ieee754dp_inf(0);
221 return ieee754dp_max(1);
222 case IEEE754_RD
: /* toward -Infinity */
224 return ieee754dp_max(0);
226 return ieee754dp_inf(1);
229 /* gen norm/denorm/zero */
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
);
238 assert((xm
>> (DP_MBITS
+ 1)) == 0); /* no execess */
239 assert(xm
& DP_HIDDEN_BIT
);
241 return builddp(sn
, xe
+ DP_EBIAS
, xm
& ~DP_HIDDEN_BIT
);