Subversion Repositories shark

Rev

Rev 3 | Details | Compare with Previous | Last modification | View Log | RSS feed

Rev Author Line No. Line
2 pj 1
/*-
2
 * Copyright (c) 1992, 1993
3
 *      The Regents of the University of California.  All rights reserved.
4
 *
5
 * This software was developed by the Computer Systems Engineering group
6
 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
7
 * contributed to Berkeley.
8
 *
9
 * Redistribution and use in source and binary forms, with or without
10
 * modification, are permitted provided that the following conditions
11
 * are met:
12
 * 1. Redistributions of source code must retain the above copyright
13
 *    notice, this list of conditions and the following disclaimer.
14
 * 2. Redistributions in binary form must reproduce the above copyright
15
 *    notice, this list of conditions and the following disclaimer in the
16
 *    documentation and/or other materials provided with the distribution.
17
 * 3. All advertising materials mentioning features or use of this software
18
 *    must display the following acknowledgement:
19
 *      This product includes software developed by the University of
20
 *      California, Berkeley and its contributors.
21
 * 4. Neither the name of the University nor the names of its contributors
22
 *    may be used to endorse or promote products derived from this software
23
 *    without specific prior written permission.
24
 *
25
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35
 * SUCH DAMAGE.
36
 */
37
 
38
#if defined(LIBC_SCCS) && !defined(lint)
39
static char sccsid[] = "@(#)muldi3.c    8.1 (Berkeley) 6/4/93";
40
#endif /* LIBC_SCCS and not lint */
41
 
42
#include "quad.h"
43
 
44
/*
45
 * Multiply two quads.
46
 *
47
 * Our algorithm is based on the following.  Split incoming quad values
48
 * u and v (where u,v >= 0) into
49
 *
50
 *      u = 2^n u1  *  u0       (n = number of bits in `u_long', usu. 32)
51
 *
52
 * and
53
 *
54
 *      v = 2^n v1  *  v0
55
 *
56
 * Then
57
 *
58
 *      uv = 2^2n u1 v1  +  2^n u1 v0  +  2^n v1 u0  +  u0 v0
59
 *         = 2^2n u1 v1  +     2^n (u1 v0 + v1 u0)   +  u0 v0
60
 *
61
 * Now add 2^n u1 v1 to the first term and subtract it from the middle,
62
 * and add 2^n u0 v0 to the last term and subtract it from the middle.
63
 * This gives:
64
 *
65
 *      uv = (2^2n + 2^n) (u1 v1)  +
66
 *               (2^n)    (u1 v0 - u1 v1 + u0 v1 - u0 v0)  +
67
 *             (2^n + 1)  (u0 v0)
68
 *
69
 * Factoring the middle a bit gives us:
70
 *
71
 *      uv = (2^2n + 2^n) (u1 v1)  +                    [u1v1 = high]
72
 *               (2^n)    (u1 - u0) (v0 - v1)  +        [(u1-u0)... = mid]
73
 *             (2^n + 1)  (u0 v0)                       [u0v0 = low]
74
 *
75
 * The terms (u1 v1), (u1 - u0) (v0 - v1), and (u0 v0) can all be done
76
 * in just half the precision of the original.  (Note that either or both
77
 * of (u1 - u0) or (v0 - v1) may be negative.)
78
 *
79
 * This algorithm is from Knuth vol. 2 (2nd ed), section 4.3.3, p. 278.
80
 *
81
 * Since C does not give us a `long * long = quad' operator, we split
82
 * our input quads into two longs, then split the two longs into two
83
 * shorts.  We can then calculate `short * short = long' in native
84
 * arithmetic.
85
 *
86
 * Our product should, strictly speaking, be a `long quad', with 128
87
 * bits, but we are going to discard the upper 64.  In other words,
88
 * we are not interested in uv, but rather in (uv mod 2^2n).  This
89
 * makes some of the terms above vanish, and we get:
90
 *
91
 *      (2^n)(high) + (2^n)(mid) + (2^n + 1)(low)
92
 *
93
 * or
94
 *
95
 *      (2^n)(high + mid + low) + low
96
 *
97
 * Furthermore, `high' and `mid' can be computed mod 2^n, as any factor
98
 * of 2^n in either one will also vanish.  Only `low' need be computed
99
 * mod 2^2n, and only because of the final term above.
100
 */
101
static quad_t __lmulq(u_long, u_long);
102
 
103
quad_t
104
__muldi3(a, b)
105
        quad_t a, b;
106
{
107
        union uu u, v, low, prod;
108
        register u_long high, mid, udiff, vdiff;
109
        register int negall, negmid;
110
#define u1      u.ul[H]
111
#define u0      u.ul[L]
112
#define v1      v.ul[H]
113
#define v0      v.ul[L]
114
 
115
        /*
116
         * Get u and v such that u, v >= 0.  When this is finished,
117
         * u1, u0, v1, and v0 will be directly accessible through the
118
         * longword fields.
119
         */
120
        if (a >= 0)
121
                u.q = a, negall = 0;
122
        else
123
                u.q = -a, negall = 1;
124
        if (b >= 0)
125
                v.q = b;
126
        else
127
                v.q = -b, negall ^= 1;
128
 
129
        if (u1 == 0 && v1 == 0) {
130
                /*
131
                 * An (I hope) important optimization occurs when u1 and v1
132
                 * are both 0.  This should be common since most numbers
133
                 * are small.  Here the product is just u0*v0.
134
                 */
135
                prod.q = __lmulq(u0, v0);
136
        } else {
137
                /*
138
                 * Compute the three intermediate products, remembering
139
                 * whether the middle term is negative.  We can discard
140
                 * any upper bits in high and mid, so we can use native
141
                 * u_long * u_long => u_long arithmetic.
142
                 */
143
                low.q = __lmulq(u0, v0);
144
 
145
                if (u1 >= u0)
146
                        negmid = 0, udiff = u1 - u0;
147
                else
148
                        negmid = 1, udiff = u0 - u1;
149
                if (v0 >= v1)
150
                        vdiff = v0 - v1;
151
                else
152
                        vdiff = v1 - v0, negmid ^= 1;
153
                mid = udiff * vdiff;
154
 
155
                high = u1 * v1;
156
 
157
                /*
158
                 * Assemble the final product.
159
                 */
160
                prod.ul[H] = high + (negmid ? -mid : mid) + low.ul[L] +
161
                    low.ul[H];
162
                prod.ul[L] = low.ul[L];
163
        }
164
        return (negall ? -prod.q : prod.q);
165
#undef u1
166
#undef u0
167
#undef v1
168
#undef v0
169
}
170
 
171
/*
172
 * Multiply two 2N-bit longs to produce a 4N-bit quad, where N is half
173
 * the number of bits in a long (whatever that is---the code below
174
 * does not care as long as quad.h does its part of the bargain---but
175
 * typically N==16).
176
 *
177
 * We use the same algorithm from Knuth, but this time the modulo refinement
178
 * does not apply.  On the other hand, since N is half the size of a long,
179
 * we can get away with native multiplication---none of our input terms
180
 * exceeds (ULONG_MAX >> 1).
181
 *
182
 * Note that, for u_long l, the quad-precision result
183
 *
184
 *      l << N
185
 *
186
 * splits into high and low longs as HHALF(l) and LHUP(l) respectively.
187
 */
188
static quad_t
189
__lmulq(u_long u, u_long v)
190
{
191
        u_long u1, u0, v1, v0, udiff, vdiff, high, mid, low;
192
        u_long prodh, prodl, was;
193
        union uu prod;
194
        int neg;
195
 
196
        u1 = HHALF(u);
197
        u0 = LHALF(u);
198
        v1 = HHALF(v);
199
        v0 = LHALF(v);
200
 
201
        low = u0 * v0;
202
 
203
        /* This is the same small-number optimization as before. */
204
        if (u1 == 0 && v1 == 0)
205
                return (low);
206
 
207
        if (u1 >= u0)
208
                udiff = u1 - u0, neg = 0;
209
        else
210
                udiff = u0 - u1, neg = 1;
211
        if (v0 >= v1)
212
                vdiff = v0 - v1;
213
        else
214
                vdiff = v1 - v0, neg ^= 1;
215
        mid = udiff * vdiff;
216
 
217
        high = u1 * v1;
218
 
219
        /* prod = (high << 2N) + (high << N); */
220
        prodh = high + HHALF(high);
221
        prodl = LHUP(high);
222
 
223
        /* if (neg) prod -= mid << N; else prod += mid << N; */
224
        if (neg) {
225
                was = prodl;
226
                prodl -= LHUP(mid);
227
                prodh -= HHALF(mid) + (prodl > was);
228
        } else {
229
                was = prodl;
230
                prodl += LHUP(mid);
231
                prodh += HHALF(mid) + (prodl < was);
232
        }
233
 
234
        /* prod += low << N */
235
        was = prodl;
236
        prodl += LHUP(low);
237
        prodh += HHALF(low) + (prodl < was);
238
        /* ... + low; */
239
        if ((prodl += low) < low)
240
                prodh++;
241
 
242
        /* return 4N-bit product */
243
        prod.ul[H] = prodh;
244
        prod.ul[L] = prodl;
245
        return (prod.q);
246
}