Use CSTD and remove local CSTD settings which are no longer needed.
[dragonfly.git] / lib / libstand / 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/lib/libstand/qdivrem.c,v 1.2 1999/08/28 00:05:33 peter Exp $
ff2aef30 38 * $DragonFly: src/lib/libstand/qdivrem.c,v 1.4 2005/12/11 02:27:26 swildner Exp $
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39 * From: Id: qdivrem.c,v 1.7 1997/11/07 09:20:40 phk Exp
40 */
41
42/*
43 * Multiprecision divide. This algorithm is from Knuth vol. 2 (2nd ed),
44 * section 4.3.1, pp. 257--259.
45 */
46
47#include "quad.h"
48
49#define B (1 << HALF_BITS) /* digit base */
50
51/* Combine two `digits' to make a single two-digit number. */
52#define COMBINE(a, b) (((u_long)(a) << HALF_BITS) | (b))
53
54/* select a type for digits in base B: use unsigned short if they fit */
55#if ULONG_MAX == 0xffffffff && USHRT_MAX >= 0xffff
56typedef unsigned short digit;
57#else
58typedef u_long digit;
59#endif
60
61/*
62 * Shift p[0]..p[len] left `sh' bits, ignoring any bits that
63 * `fall out' the left (there never will be any such anyway).
64 * We may assume len >= 0. NOTE THAT THIS WRITES len+1 DIGITS.
65 */
66static void
660c873b 67shl(digit *p, int len, int sh)
984263bc 68{
660c873b 69 int i;
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70
71 for (i = 0; i < len; i++)
72 p[i] = LHALF(p[i] << sh) | (p[i + 1] >> (HALF_BITS - sh));
73 p[i] = LHALF(p[i] << sh);
74}
75
76/*
77 * __qdivrem(u, v, rem) returns u/v and, optionally, sets *rem to u%v.
78 *
79 * We do this in base 2-sup-HALF_BITS, so that all intermediate products
80 * fit within u_long. As a consequence, the maximum length dividend and
81 * divisor are 4 `digits' in this base (they are shorter if they have
82 * leading zeros).
83 */
84u_quad_t
ff2aef30 85__qdivrem(u_quad_t uq, u_quad_t vq, u_quad_t *arq)
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86{
87 union uu tmp;
88 digit *u, *v, *q;
660c873b 89 digit v1, v2;
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90 u_long qhat, rhat, t;
91 int m, n, d, j, i;
92 digit uspace[5], vspace[5], qspace[5];
93
94 /*
95 * Take care of special cases: divide by zero, and u < v.
96 */
97 if (vq == 0) {
98 /* divide by zero. */
99 static volatile const unsigned int zero = 0;
100
101 tmp.ul[H] = tmp.ul[L] = 1 / zero;
102 if (arq)
103 *arq = uq;
104 return (tmp.q);
105 }
106 if (uq < vq) {
107 if (arq)
108 *arq = uq;
109 return (0);
110 }
111 u = &uspace[0];
112 v = &vspace[0];
113 q = &qspace[0];
114
115 /*
116 * Break dividend and divisor into digits in base B, then
117 * count leading zeros to determine m and n. When done, we
118 * will have:
119 * u = (u[1]u[2]...u[m+n]) sub B
120 * v = (v[1]v[2]...v[n]) sub B
121 * v[1] != 0
122 * 1 < n <= 4 (if n = 1, we use a different division algorithm)
123 * m >= 0 (otherwise u < v, which we already checked)
124 * m + n = 4
125 * and thus
126 * m = 4 - n <= 2
127 */
128 tmp.uq = uq;
129 u[0] = 0;
130 u[1] = HHALF(tmp.ul[H]);
131 u[2] = LHALF(tmp.ul[H]);
132 u[3] = HHALF(tmp.ul[L]);
133 u[4] = LHALF(tmp.ul[L]);
134 tmp.uq = vq;
135 v[1] = HHALF(tmp.ul[H]);
136 v[2] = LHALF(tmp.ul[H]);
137 v[3] = HHALF(tmp.ul[L]);
138 v[4] = LHALF(tmp.ul[L]);
139 for (n = 4; v[1] == 0; v++) {
140 if (--n == 1) {
141 u_long rbj; /* r*B+u[j] (not root boy jim) */
142 digit q1, q2, q3, q4;
143
144 /*
145 * Change of plan, per exercise 16.
146 * r = 0;
147 * for j = 1..4:
148 * q[j] = floor((r*B + u[j]) / v),
149 * r = (r*B + u[j]) % v;
150 * We unroll this completely here.
151 */
152 t = v[2]; /* nonzero, by definition */
153 q1 = u[1] / t;
154 rbj = COMBINE(u[1] % t, u[2]);
155 q2 = rbj / t;
156 rbj = COMBINE(rbj % t, u[3]);
157 q3 = rbj / t;
158 rbj = COMBINE(rbj % t, u[4]);
159 q4 = rbj / t;
160 if (arq)
161 *arq = rbj % t;
162 tmp.ul[H] = COMBINE(q1, q2);
163 tmp.ul[L] = COMBINE(q3, q4);
164 return (tmp.q);
165 }
166 }
167
168 /*
169 * By adjusting q once we determine m, we can guarantee that
170 * there is a complete four-digit quotient at &qspace[1] when
171 * we finally stop.
172 */
173 for (m = 4 - n; u[1] == 0; u++)
174 m--;
175 for (i = 4 - m; --i >= 0;)
176 q[i] = 0;
177 q += 4 - m;
178
179 /*
180 * Here we run Program D, translated from MIX to C and acquiring
181 * a few minor changes.
182 *
183 * D1: choose multiplier 1 << d to ensure v[1] >= B/2.
184 */
185 d = 0;
186 for (t = v[1]; t < B / 2; t <<= 1)
187 d++;
188 if (d > 0) {
189 shl(&u[0], m + n, d); /* u <<= d */
190 shl(&v[1], n - 1, d); /* v <<= d */
191 }
192 /*
193 * D2: j = 0.
194 */
195 j = 0;
196 v1 = v[1]; /* for D3 -- note that v[1..n] are constant */
197 v2 = v[2]; /* for D3 */
198 do {
660c873b 199 digit uj0, uj1, uj2;
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200
201 /*
202 * D3: Calculate qhat (\^q, in TeX notation).
203 * Let qhat = min((u[j]*B + u[j+1])/v[1], B-1), and
204 * let rhat = (u[j]*B + u[j+1]) mod v[1].
205 * While rhat < B and v[2]*qhat > rhat*B+u[j+2],
206 * decrement qhat and increase rhat correspondingly.
207 * Note that if rhat >= B, v[2]*qhat < rhat*B.
208 */
209 uj0 = u[j + 0]; /* for D3 only -- note that u[j+...] change */
210 uj1 = u[j + 1]; /* for D3 only */
211 uj2 = u[j + 2]; /* for D3 only */
212 if (uj0 == v1) {
213 qhat = B;
214 rhat = uj1;
215 goto qhat_too_big;
216 } else {
217 u_long nn = COMBINE(uj0, uj1);
218 qhat = nn / v1;
219 rhat = nn % v1;
220 }
221 while (v2 * qhat > COMBINE(rhat, uj2)) {
222 qhat_too_big:
223 qhat--;
224 if ((rhat += v1) >= B)
225 break;
226 }
227 /*
228 * D4: Multiply and subtract.
229 * The variable `t' holds any borrows across the loop.
230 * We split this up so that we do not require v[0] = 0,
231 * and to eliminate a final special case.
232 */
233 for (t = 0, i = n; i > 0; i--) {
234 t = u[i + j] - v[i] * qhat - t;
235 u[i + j] = LHALF(t);
236 t = (B - HHALF(t)) & (B - 1);
237 }
238 t = u[j] - t;
239 u[j] = LHALF(t);
240 /*
241 * D5: test remainder.
242 * There is a borrow if and only if HHALF(t) is nonzero;
243 * in that (rare) case, qhat was too large (by exactly 1).
244 * Fix it by adding v[1..n] to u[j..j+n].
245 */
246 if (HHALF(t)) {
247 qhat--;
248 for (t = 0, i = n; i > 0; i--) { /* D6: add back. */
249 t += u[i + j] + v[i];
250 u[i + j] = LHALF(t);
251 t = HHALF(t);
252 }
253 u[j] = LHALF(u[j] + t);
254 }
255 q[j] = qhat;
256 } while (++j <= m); /* D7: loop on j. */
257
258 /*
259 * If caller wants the remainder, we have to calculate it as
260 * u[m..m+n] >> d (this is at most n digits and thus fits in
261 * u[m+1..m+n], but we may need more source digits).
262 */
263 if (arq) {
264 if (d) {
265 for (i = m + n; i > m; --i)
266 u[i] = (u[i] >> d) |
267 LHALF(u[i - 1] << (HALF_BITS - d));
268 u[i] = 0;
269 }
270 tmp.ul[H] = COMBINE(uspace[1], uspace[2]);
271 tmp.ul[L] = COMBINE(uspace[3], uspace[4]);
272 *arq = tmp.q;
273 }
274
275 tmp.ul[H] = COMBINE(qspace[1], qspace[2]);
276 tmp.ul[L] = COMBINE(qspace[3], qspace[4]);
277 return (tmp.q);
278}
279
280/*
281 * Divide two unsigned quads.
282 */
283
284u_quad_t
ff2aef30 285__udivdi3(u_quad_t a, u_quad_t b)
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286{
287
288 return (__qdivrem(a, b, (u_quad_t *)0));
289}
290
291/*
292 * Return remainder after dividing two unsigned quads.
293 */
294u_quad_t
ff2aef30 295__umoddi3(u_quad_t a, u_quad_t b)
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296{
297 u_quad_t r;
298
299 (void)__qdivrem(a, b, &r);
300 return (r);
301}