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dp_mul.c
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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  *
8  * ########################################################################
9  *
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.
13  *
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
17  * for more details.
18  *
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.
22  *
23  * ########################################################################
24  */
25 
26 
27 #include "ieee754dp.h"
28 
29 ieee754dp ieee754dp_mul(ieee754dp x, ieee754dp y)
30 {
31  COMPXDP;
32  COMPYDP;
33 
34  EXPLODEXDP;
35  EXPLODEYDP;
36 
37  CLEARCX;
38 
39  FLUSHXDP;
40  FLUSHYDP;
41 
42  switch (CLPAIR(xc, yc)) {
43  case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
44  case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
45  case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
46  case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
47  case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
48  case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
49  case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
50  case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
51  case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
52  case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
53  case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
54  SETCX(IEEE754_INVALID_OPERATION);
55  return ieee754dp_nanxcpt(ieee754dp_indef(), "mul", x, y);
56 
57  case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
58  case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
59  case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
60  case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
61  return y;
62 
63  case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
64  case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
65  case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
66  case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
67  case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
68  return x;
69 
70 
71  /* Infinity handling */
72 
73  case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
74  case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
75  SETCX(IEEE754_INVALID_OPERATION);
76  return ieee754dp_xcpt(ieee754dp_indef(), "mul", x, y);
77 
78  case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
79  case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
80  case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
81  case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
82  case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
83  return ieee754dp_inf(xs ^ ys);
84 
85  case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
86  case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
87  case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
88  case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
89  case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
90  return ieee754dp_zero(xs ^ ys);
91 
92 
93  case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
94  DPDNORMX;
95 
96  case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
97  DPDNORMY;
98  break;
99 
100  case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
101  DPDNORMX;
102  break;
103 
104  case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
105  break;
106  }
107  /* rm = xm * ym, re = xe+ye basically */
108  assert(xm & DP_HIDDEN_BIT);
109  assert(ym & DP_HIDDEN_BIT);
110  {
111  int re = xe + ye;
112  int rs = xs ^ ys;
113  u64 rm;
114 
115  /* shunt to top of word */
116  xm <<= 64 - (DP_MBITS + 1);
117  ym <<= 64 - (DP_MBITS + 1);
118 
119  /* multiply 32bits xm,ym to give high 32bits rm with stickness
120  */
121 
122  /* 32 * 32 => 64 */
123 #define DPXMULT(x, y) ((u64)(x) * (u64)y)
124 
125  {
126  unsigned lxm = xm;
127  unsigned hxm = xm >> 32;
128  unsigned lym = ym;
129  unsigned hym = ym >> 32;
130  u64 lrm;
131  u64 hrm;
132 
133  lrm = DPXMULT(lxm, lym);
134  hrm = DPXMULT(hxm, hym);
135 
136  {
137  u64 t = DPXMULT(lxm, hym);
138  {
139  u64 at =
140  lrm + (t << 32);
141  hrm += at < lrm;
142  lrm = at;
143  }
144  hrm = hrm + (t >> 32);
145  }
146 
147  {
148  u64 t = DPXMULT(hxm, lym);
149  {
150  u64 at =
151  lrm + (t << 32);
152  hrm += at < lrm;
153  lrm = at;
154  }
155  hrm = hrm + (t >> 32);
156  }
157  rm = hrm | (lrm != 0);
158  }
159 
160  /*
161  * sticky shift down to normal rounding precision
162  */
163  if ((s64) rm < 0) {
164  rm =
165  (rm >> (64 - (DP_MBITS + 1 + 3))) |
166  ((rm << (DP_MBITS + 1 + 3)) != 0);
167  re++;
168  } else {
169  rm =
170  (rm >> (64 - (DP_MBITS + 1 + 3 + 1))) |
171  ((rm << (DP_MBITS + 1 + 3 + 1)) != 0);
172  }
173  assert(rm & (DP_HIDDEN_BIT << 3));
174  DPNORMRET2(rs, re, rm, "mul", x, y);
175  }
176 }
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