nataraid(4): Add devstat support.
[dragonfly.git] / sys / libkern / qdivrem.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/qdivrem.c,v 1.8 1999/08/28 00:46:35 peter Exp $
e73e0a5e 38 * $DragonFly: src/sys/libkern/qdivrem.c,v 1.4 2004/01/26 11:09:44 joerg Exp $
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39 */
40
41/*
42 * Multiprecision divide. This algorithm is from Knuth vol. 2 (2nd ed),
43 * section 4.3.1, pp. 257--259.
44 */
45
46#include <libkern/quad.h>
47
48#define B (1 << HALF_BITS) /* digit base */
49
50/* Combine two `digits' to make a single two-digit number. */
51#define COMBINE(a, b) (((u_long)(a) << HALF_BITS) | (b))
52
53/* select a type for digits in base B: use unsigned short if they fit */
54#if ULONG_MAX == 0xffffffff && USHRT_MAX >= 0xffff
55typedef unsigned short digit;
56#else
57typedef u_long digit;
58#endif
59
60/*
61 * Shift p[0]..p[len] left `sh' bits, ignoring any bits that
62 * `fall out' the left (there never will be any such anyway).
63 * We may assume len >= 0. NOTE THAT THIS WRITES len+1 DIGITS.
64 */
65static void
0e99e805 66shl(digit *p, int len, int sh)
984263bc 67{
0e99e805 68 int i;
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69
70 for (i = 0; i < len; i++)
71 p[i] = LHALF(p[i] << sh) | (p[i + 1] >> (HALF_BITS - sh));
72 p[i] = LHALF(p[i] << sh);
73}
74
75/*
76 * __qdivrem(u, v, rem) returns u/v and, optionally, sets *rem to u%v.
77 *
78 * We do this in base 2-sup-HALF_BITS, so that all intermediate products
79 * fit within u_long. As a consequence, the maximum length dividend and
80 * divisor are 4 `digits' in this base (they are shorter if they have
81 * leading zeros).
82 */
83u_quad_t
e73e0a5e 84__qdivrem(u_quad_t uq, u_quad_t vq, u_quad_t *arq)
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85{
86 union uu tmp;
87 digit *u, *v, *q;
0e99e805 88 digit v1, v2;
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89 u_long qhat, rhat, t;
90 int m, n, d, j, i;
91 digit uspace[5], vspace[5], qspace[5];
92
93 /*
94 * Take care of special cases: divide by zero, and u < v.
95 */
96 if (vq == 0) {
97 /* divide by zero. */
98 static volatile const unsigned int zero = 0;
99
100 tmp.ul[H] = tmp.ul[L] = 1 / zero;
101 if (arq)
102 *arq = uq;
103 return (tmp.q);
104 }
105 if (uq < vq) {
106 if (arq)
107 *arq = uq;
108 return (0);
109 }
110 u = &uspace[0];
111 v = &vspace[0];
112 q = &qspace[0];
113
114 /*
115 * Break dividend and divisor into digits in base B, then
116 * count leading zeros to determine m and n. When done, we
117 * will have:
118 * u = (u[1]u[2]...u[m+n]) sub B
119 * v = (v[1]v[2]...v[n]) sub B
120 * v[1] != 0
121 * 1 < n <= 4 (if n = 1, we use a different division algorithm)
122 * m >= 0 (otherwise u < v, which we already checked)
123 * m + n = 4
124 * and thus
125 * m = 4 - n <= 2
126 */
127 tmp.uq = uq;
128 u[0] = 0;
129 u[1] = HHALF(tmp.ul[H]);
130 u[2] = LHALF(tmp.ul[H]);
131 u[3] = HHALF(tmp.ul[L]);
132 u[4] = LHALF(tmp.ul[L]);
133 tmp.uq = vq;
134 v[1] = HHALF(tmp.ul[H]);
135 v[2] = LHALF(tmp.ul[H]);
136 v[3] = HHALF(tmp.ul[L]);
137 v[4] = LHALF(tmp.ul[L]);
138 for (n = 4; v[1] == 0; v++) {
139 if (--n == 1) {
140 u_long rbj; /* r*B+u[j] (not root boy jim) */
141 digit q1, q2, q3, q4;
142
143 /*
144 * Change of plan, per exercise 16.
145 * r = 0;
146 * for j = 1..4:
147 * q[j] = floor((r*B + u[j]) / v),
148 * r = (r*B + u[j]) % v;
149 * We unroll this completely here.
150 */
151 t = v[2]; /* nonzero, by definition */
152 q1 = u[1] / t;
153 rbj = COMBINE(u[1] % t, u[2]);
154 q2 = rbj / t;
155 rbj = COMBINE(rbj % t, u[3]);
156 q3 = rbj / t;
157 rbj = COMBINE(rbj % t, u[4]);
158 q4 = rbj / t;
159 if (arq)
160 *arq = rbj % t;
161 tmp.ul[H] = COMBINE(q1, q2);
162 tmp.ul[L] = COMBINE(q3, q4);
163 return (tmp.q);
164 }
165 }
166
167 /*
168 * By adjusting q once we determine m, we can guarantee that
169 * there is a complete four-digit quotient at &qspace[1] when
170 * we finally stop.
171 */
172 for (m = 4 - n; u[1] == 0; u++)
173 m--;
174 for (i = 4 - m; --i >= 0;)
175 q[i] = 0;
176 q += 4 - m;
177
178 /*
179 * Here we run Program D, translated from MIX to C and acquiring
180 * a few minor changes.
181 *
182 * D1: choose multiplier 1 << d to ensure v[1] >= B/2.
183 */
184 d = 0;
185 for (t = v[1]; t < B / 2; t <<= 1)
186 d++;
187 if (d > 0) {
188 shl(&u[0], m + n, d); /* u <<= d */
189 shl(&v[1], n - 1, d); /* v <<= d */
190 }
191 /*
192 * D2: j = 0.
193 */
194 j = 0;
195 v1 = v[1]; /* for D3 -- note that v[1..n] are constant */
196 v2 = v[2]; /* for D3 */
197 do {
0e99e805 198 digit uj0, uj1, uj2;
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199
200 /*
201 * D3: Calculate qhat (\^q, in TeX notation).
202 * Let qhat = min((u[j]*B + u[j+1])/v[1], B-1), and
203 * let rhat = (u[j]*B + u[j+1]) mod v[1].
204 * While rhat < B and v[2]*qhat > rhat*B+u[j+2],
205 * decrement qhat and increase rhat correspondingly.
206 * Note that if rhat >= B, v[2]*qhat < rhat*B.
207 */
208 uj0 = u[j + 0]; /* for D3 only -- note that u[j+...] change */
209 uj1 = u[j + 1]; /* for D3 only */
210 uj2 = u[j + 2]; /* for D3 only */
211 if (uj0 == v1) {
212 qhat = B;
213 rhat = uj1;
214 goto qhat_too_big;
215 } else {
216 u_long nn = COMBINE(uj0, uj1);
217 qhat = nn / v1;
218 rhat = nn % v1;
219 }
220 while (v2 * qhat > COMBINE(rhat, uj2)) {
221 qhat_too_big:
222 qhat--;
223 if ((rhat += v1) >= B)
224 break;
225 }
226 /*
227 * D4: Multiply and subtract.
228 * The variable `t' holds any borrows across the loop.
229 * We split this up so that we do not require v[0] = 0,
230 * and to eliminate a final special case.
231 */
232 for (t = 0, i = n; i > 0; i--) {
233 t = u[i + j] - v[i] * qhat - t;
234 u[i + j] = LHALF(t);
235 t = (B - HHALF(t)) & (B - 1);
236 }
237 t = u[j] - t;
238 u[j] = LHALF(t);
239 /*
240 * D5: test remainder.
241 * There is a borrow if and only if HHALF(t) is nonzero;
242 * in that (rare) case, qhat was too large (by exactly 1).
243 * Fix it by adding v[1..n] to u[j..j+n].
244 */
245 if (HHALF(t)) {
246 qhat--;
247 for (t = 0, i = n; i > 0; i--) { /* D6: add back. */
248 t += u[i + j] + v[i];
249 u[i + j] = LHALF(t);
250 t = HHALF(t);
251 }
252 u[j] = LHALF(u[j] + t);
253 }
254 q[j] = qhat;
255 } while (++j <= m); /* D7: loop on j. */
256
257 /*
258 * If caller wants the remainder, we have to calculate it as
259 * u[m..m+n] >> d (this is at most n digits and thus fits in
260 * u[m+1..m+n], but we may need more source digits).
261 */
262 if (arq) {
263 if (d) {
264 for (i = m + n; i > m; --i)
265 u[i] = (u[i] >> d) |
266 LHALF(u[i - 1] << (HALF_BITS - d));
267 u[i] = 0;
268 }
269 tmp.ul[H] = COMBINE(uspace[1], uspace[2]);
270 tmp.ul[L] = COMBINE(uspace[3], uspace[4]);
271 *arq = tmp.q;
272 }
273
274 tmp.ul[H] = COMBINE(qspace[1], qspace[2]);
275 tmp.ul[L] = COMBINE(qspace[3], qspace[4]);
276 return (tmp.q);
277}