nataraid(4): Add devstat support.
[dragonfly.git] / sys / libkern / muldi3.c
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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 * $FreeBSD: src/sys/libkern/muldi3.c,v 1.6 1999/08/28 00:46:34 peter Exp $
e73e0a5e 38 * $DragonFly: src/sys/libkern/muldi3.c,v 1.4 2004/01/26 11:09:44 joerg Exp $
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39 */
40
41#include "quad.h"
42
43/*
44 * Multiply two quads.
45 *
46 * Our algorithm is based on the following. Split incoming quad values
47 * u and v (where u,v >= 0) into
48 *
49 * u = 2^n u1 * u0 (n = number of bits in `u_long', usu. 32)
50 *
51 * and
52 *
53 * v = 2^n v1 * v0
54 *
55 * Then
56 *
57 * uv = 2^2n u1 v1 + 2^n u1 v0 + 2^n v1 u0 + u0 v0
58 * = 2^2n u1 v1 + 2^n (u1 v0 + v1 u0) + u0 v0
59 *
60 * Now add 2^n u1 v1 to the first term and subtract it from the middle,
61 * and add 2^n u0 v0 to the last term and subtract it from the middle.
62 * This gives:
63 *
64 * uv = (2^2n + 2^n) (u1 v1) +
65 * (2^n) (u1 v0 - u1 v1 + u0 v1 - u0 v0) +
66 * (2^n + 1) (u0 v0)
67 *
68 * Factoring the middle a bit gives us:
69 *
70 * uv = (2^2n + 2^n) (u1 v1) + [u1v1 = high]
71 * (2^n) (u1 - u0) (v0 - v1) + [(u1-u0)... = mid]
72 * (2^n + 1) (u0 v0) [u0v0 = low]
73 *
74 * The terms (u1 v1), (u1 - u0) (v0 - v1), and (u0 v0) can all be done
75 * in just half the precision of the original. (Note that either or both
76 * of (u1 - u0) or (v0 - v1) may be negative.)
77 *
78 * This algorithm is from Knuth vol. 2 (2nd ed), section 4.3.3, p. 278.
79 *
80 * Since C does not give us a `long * long = quad' operator, we split
81 * our input quads into two longs, then split the two longs into two
82 * shorts. We can then calculate `short * short = long' in native
83 * arithmetic.
84 *
85 * Our product should, strictly speaking, be a `long quad', with 128
86 * bits, but we are going to discard the upper 64. In other words,
87 * we are not interested in uv, but rather in (uv mod 2^2n). This
88 * makes some of the terms above vanish, and we get:
89 *
90 * (2^n)(high) + (2^n)(mid) + (2^n + 1)(low)
91 *
92 * or
93 *
94 * (2^n)(high + mid + low) + low
95 *
96 * Furthermore, `high' and `mid' can be computed mod 2^n, as any factor
97 * of 2^n in either one will also vanish. Only `low' need be computed
98 * mod 2^2n, and only because of the final term above.
99 */
e73e0a5e 100static quad_t __lmulq(u_long u, u_long v);
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101
102quad_t
e73e0a5e 103__muldi3(quad_t a, quad_t b)
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104{
105 union uu u, v, low, prod;
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106 u_long high, mid, udiff, vdiff;
107 int negall, negmid;
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108#define u1 u.ul[H]
109#define u0 u.ul[L]
110#define v1 v.ul[H]
111#define v0 v.ul[L]
112
113 /*
114 * Get u and v such that u, v >= 0. When this is finished,
115 * u1, u0, v1, and v0 will be directly accessible through the
116 * longword fields.
117 */
118 if (a >= 0)
119 u.q = a, negall = 0;
120 else
121 u.q = -a, negall = 1;
122 if (b >= 0)
123 v.q = b;
124 else
125 v.q = -b, negall ^= 1;
126
127 if (u1 == 0 && v1 == 0) {
128 /*
129 * An (I hope) important optimization occurs when u1 and v1
130 * are both 0. This should be common since most numbers
131 * are small. Here the product is just u0*v0.
132 */
133 prod.q = __lmulq(u0, v0);
134 } else {
135 /*
136 * Compute the three intermediate products, remembering
137 * whether the middle term is negative. We can discard
138 * any upper bits in high and mid, so we can use native
139 * u_long * u_long => u_long arithmetic.
140 */
141 low.q = __lmulq(u0, v0);
142
143 if (u1 >= u0)
144 negmid = 0, udiff = u1 - u0;
145 else
146 negmid = 1, udiff = u0 - u1;
147 if (v0 >= v1)
148 vdiff = v0 - v1;
149 else
150 vdiff = v1 - v0, negmid ^= 1;
151 mid = udiff * vdiff;
152
153 high = u1 * v1;
154
155 /*
156 * Assemble the final product.
157 */
158 prod.ul[H] = high + (negmid ? -mid : mid) + low.ul[L] +
159 low.ul[H];
160 prod.ul[L] = low.ul[L];
161 }
162 return (negall ? -prod.q : prod.q);
163#undef u1
164#undef u0
165#undef v1
166#undef v0
167}
168
169/*
170 * Multiply two 2N-bit longs to produce a 4N-bit quad, where N is half
171 * the number of bits in a long (whatever that is---the code below
172 * does not care as long as quad.h does its part of the bargain---but
173 * typically N==16).
174 *
175 * We use the same algorithm from Knuth, but this time the modulo refinement
176 * does not apply. On the other hand, since N is half the size of a long,
177 * we can get away with native multiplication---none of our input terms
178 * exceeds (ULONG_MAX >> 1).
179 *
180 * Note that, for u_long l, the quad-precision result
181 *
182 * l << N
183 *
184 * splits into high and low longs as HHALF(l) and LHUP(l) respectively.
185 */
186static quad_t
187__lmulq(u_long u, u_long v)
188{
189 u_long u1, u0, v1, v0, udiff, vdiff, high, mid, low;
190 u_long prodh, prodl, was;
191 union uu prod;
192 int neg;
193
194 u1 = HHALF(u);
195 u0 = LHALF(u);
196 v1 = HHALF(v);
197 v0 = LHALF(v);
198
199 low = u0 * v0;
200
201 /* This is the same small-number optimization as before. */
202 if (u1 == 0 && v1 == 0)
203 return (low);
204
205 if (u1 >= u0)
206 udiff = u1 - u0, neg = 0;
207 else
208 udiff = u0 - u1, neg = 1;
209 if (v0 >= v1)
210 vdiff = v0 - v1;
211 else
212 vdiff = v1 - v0, neg ^= 1;
213 mid = udiff * vdiff;
214
215 high = u1 * v1;
216
217 /* prod = (high << 2N) + (high << N); */
218 prodh = high + HHALF(high);
219 prodl = LHUP(high);
220
221 /* if (neg) prod -= mid << N; else prod += mid << N; */
222 if (neg) {
223 was = prodl;
224 prodl -= LHUP(mid);
225 prodh -= HHALF(mid) + (prodl > was);
226 } else {
227 was = prodl;
228 prodl += LHUP(mid);
229 prodh += HHALF(mid) + (prodl < was);
230 }
231
232 /* prod += low << N */
233 was = prodl;
234 prodl += LHUP(low);
235 prodh += HHALF(low) + (prodl < was);
236 /* ... + low; */
237 if ((prodl += low) < low)
238 prodh++;
239
240 /* return 4N-bit product */
241 prod.ul[H] = prodh;
242 prod.ul[L] = prodl;
243 return (prod.q);
244}