1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
|
/* IEEE754 floating point arithmetic
* double precision: common utilities
*/
/*
* MIPS floating point support
* Copyright (C) 1994-2000 Algorithmics Ltd.
*
* ########################################################################
*
* This program is free software; you can distribute it and/or modify it
* under the terms of the GNU General Public License (Version 2) as
* published by the Free Software Foundation.
*
* This program is distributed in the hope it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place - Suite 330, Boston MA 02111-1307, USA.
*
* ########################################################################
*/
#include "ieee754dp.h"
int ieee754dp_class(ieee754dp x)
{
COMPXDP;
EXPLODEXDP;
return xc;
}
int ieee754dp_isnan(ieee754dp x)
{
return ieee754dp_class(x) >= IEEE754_CLASS_SNAN;
}
int ieee754dp_issnan(ieee754dp x)
{
assert(ieee754dp_isnan(x));
return ((DPMANT(x) & DP_MBIT(DP_MBITS-1)) == DP_MBIT(DP_MBITS-1));
}
ieee754dp ieee754dp_xcpt(ieee754dp r, const char *op, ...)
{
struct ieee754xctx ax;
if (!TSTX())
return r;
ax.op = op;
ax.rt = IEEE754_RT_DP;
ax.rv.dp = r;
va_start(ax.ap, op);
ieee754_xcpt(&ax);
va_end(ax.ap);
return ax.rv.dp;
}
ieee754dp ieee754dp_nanxcpt(ieee754dp r, const char *op, ...)
{
struct ieee754xctx ax;
assert(ieee754dp_isnan(r));
if (!ieee754dp_issnan(r)) /* QNAN does not cause invalid op !! */
return r;
if (!SETANDTESTCX(IEEE754_INVALID_OPERATION)) {
/* not enabled convert to a quiet NaN */
DPMANT(r) &= (~DP_MBIT(DP_MBITS-1));
if (ieee754dp_isnan(r))
return r;
else
return ieee754dp_indef();
}
ax.op = op;
ax.rt = 0;
ax.rv.dp = r;
va_start(ax.ap, op);
ieee754_xcpt(&ax);
va_end(ax.ap);
return ax.rv.dp;
}
ieee754dp ieee754dp_bestnan(ieee754dp x, ieee754dp y)
{
assert(ieee754dp_isnan(x));
assert(ieee754dp_isnan(y));
if (DPMANT(x) > DPMANT(y))
return x;
else
return y;
}
static u64 get_rounding(int sn, u64 xm)
{
/* inexact must round of 3 bits
*/
if (xm & (DP_MBIT(3) - 1)) {
switch (ieee754_csr.rm) {
case IEEE754_RZ:
break;
case IEEE754_RN:
xm += 0x3 + ((xm >> 3) & 1);
/* xm += (xm&0x8)?0x4:0x3 */
break;
case IEEE754_RU: /* toward +Infinity */
if (!sn) /* ?? */
xm += 0x8;
break;
case IEEE754_RD: /* toward -Infinity */
if (sn) /* ?? */
xm += 0x8;
break;
}
}
return xm;
}
/* generate a normal/denormal number with over,under handling
* sn is sign
* xe is an unbiased exponent
* xm is 3bit extended precision value.
*/
ieee754dp ieee754dp_format(int sn, int xe, u64 xm)
{
assert(xm); /* we don't gen exact zeros (probably should) */
assert((xm >> (DP_MBITS + 1 + 3)) == 0); /* no execess */
assert(xm & (DP_HIDDEN_BIT << 3));
if (xe < DP_EMIN) {
/* strip lower bits */
int es = DP_EMIN - xe;
if (ieee754_csr.nod) {
SETCX(IEEE754_UNDERFLOW);
SETCX(IEEE754_INEXACT);
switch(ieee754_csr.rm) {
case IEEE754_RN:
case IEEE754_RZ:
return ieee754dp_zero(sn);
case IEEE754_RU: /* toward +Infinity */
if(sn == 0)
return ieee754dp_min(0);
else
return ieee754dp_zero(1);
case IEEE754_RD: /* toward -Infinity */
if(sn == 0)
return ieee754dp_zero(0);
else
return ieee754dp_min(1);
}
}
if (xe == DP_EMIN - 1
&& get_rounding(sn, xm) >> (DP_MBITS + 1 + 3))
{
/* Not tiny after rounding */
SETCX(IEEE754_INEXACT);
xm = get_rounding(sn, xm);
xm >>= 1;
/* Clear grs bits */
xm &= ~(DP_MBIT(3) - 1);
xe++;
}
else {
/* sticky right shift es bits
*/
xm = XDPSRS(xm, es);
xe += es;
assert((xm & (DP_HIDDEN_BIT << 3)) == 0);
assert(xe == DP_EMIN);
}
}
if (xm & (DP_MBIT(3) - 1)) {
SETCX(IEEE754_INEXACT);
if ((xm & (DP_HIDDEN_BIT << 3)) == 0) {
SETCX(IEEE754_UNDERFLOW);
}
/* inexact must round of 3 bits
*/
xm = get_rounding(sn, xm);
/* adjust exponent for rounding add overflowing
*/
if (xm >> (DP_MBITS + 3 + 1)) {
/* add causes mantissa overflow */
xm >>= 1;
xe++;
}
}
/* strip grs bits */
xm >>= 3;
assert((xm >> (DP_MBITS + 1)) == 0); /* no execess */
assert(xe >= DP_EMIN);
if (xe > DP_EMAX) {
SETCX(IEEE754_OVERFLOW);
SETCX(IEEE754_INEXACT);
/* -O can be table indexed by (rm,sn) */
switch (ieee754_csr.rm) {
case IEEE754_RN:
return ieee754dp_inf(sn);
case IEEE754_RZ:
return ieee754dp_max(sn);
case IEEE754_RU: /* toward +Infinity */
if (sn == 0)
return ieee754dp_inf(0);
else
return ieee754dp_max(1);
case IEEE754_RD: /* toward -Infinity */
if (sn == 0)
return ieee754dp_max(0);
else
return ieee754dp_inf(1);
}
}
/* gen norm/denorm/zero */
if ((xm & DP_HIDDEN_BIT) == 0) {
/* we underflow (tiny/zero) */
assert(xe == DP_EMIN);
if (ieee754_csr.mx & IEEE754_UNDERFLOW)
SETCX(IEEE754_UNDERFLOW);
return builddp(sn, DP_EMIN - 1 + DP_EBIAS, xm);
} else {
assert((xm >> (DP_MBITS + 1)) == 0); /* no execess */
assert(xm & DP_HIDDEN_BIT);
return builddp(sn, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
}
}
|
