ia64/xen-unstable

view extras/mini-os/lib/math.c @ 13878:9d103e5fd471

[XEN] Fix typos in comment describing 32on64 memory layout

Signed-off-by: Ian Campbell <ian.campbell@xensource.com>
author Ian Campbell <ian.campbell@xensource.com>
date Thu Feb 08 12:33:32 2007 +0000 (2007-02-08)
parents e9e327c3e81b
children 945820bfedb6
line source
1 /* -*- Mode:C; c-basic-offset:4; tab-width:4 -*-
2 ****************************************************************************
3 * (C) 2003 - Rolf Neugebauer - Intel Research Cambridge
4 ****************************************************************************
5 *
6 * File: math.c
7 * Author: Rolf Neugebauer (neugebar@dcs.gla.ac.uk)
8 * Changes:
9 *
10 * Date: Aug 2003
11 *
12 * Environment: Xen Minimal OS
13 * Description: Library functions for 64bit arith and other
14 * from freebsd, files in sys/libkern/ (qdivrem.c, etc)
15 *
16 ****************************************************************************
17 * $Id: c-insert.c,v 1.7 2002/11/08 16:04:34 rn Exp $
18 ****************************************************************************
19 *-
20 * Copyright (c) 1992, 1993
21 * The Regents of the University of California. All rights reserved.
22 *
23 * This software was developed by the Computer Systems Engineering group
24 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
25 * contributed to Berkeley.
26 *
27 * Redistribution and use in source and binary forms, with or without
28 * modification, are permitted provided that the following conditions
29 * are met:
30 * 1. Redistributions of source code must retain the above copyright
31 * notice, this list of conditions and the following disclaimer.
32 * 2. Redistributions in binary form must reproduce the above copyright
33 * notice, this list of conditions and the following disclaimer in the
34 * documentation and/or other materials provided with the distribution.
35 * 3. All advertising materials mentioning features or use of this software
36 * must display the following acknowledgement:
37 * This product includes software developed by the University of
38 * California, Berkeley and its contributors.
39 * 4. Neither the name of the University nor the names of its contributors
40 * may be used to endorse or promote products derived from this software
41 * without specific prior written permission.
42 *
43 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
44 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
45 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
46 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
47 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
48 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
49 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
50 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
51 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
52 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * SUCH DAMAGE.
54 *
55 * $FreeBSD: src/sys/libkern/divdi3.c,v 1.6 1999/08/28 00:46:31 peter Exp $
56 */
58 #include <types.h>
60 /* On ia64 these functions lead to crashes. These are replaced by
61 * assembler functions. */
62 #if !defined(__ia64__)
64 /*
65 * Depending on the desired operation, we view a `long long' (aka quad_t) in
66 * one or more of the following formats.
67 */
68 union uu {
69 s64 q; /* as a (signed) quad */
70 s64 uq; /* as an unsigned quad */
71 long sl[2]; /* as two signed longs */
72 unsigned long ul[2]; /* as two unsigned longs */
73 };
74 /* XXX RN: Yuck hardcoded endianess :) */
75 #define _QUAD_HIGHWORD 1
76 #define _QUAD_LOWWORD 0
77 /*
78 * Define high and low longwords.
79 */
80 #define H _QUAD_HIGHWORD
81 #define L _QUAD_LOWWORD
83 /*
84 * Total number of bits in a quad_t and in the pieces that make it up.
85 * These are used for shifting, and also below for halfword extraction
86 * and assembly.
87 */
88 #define CHAR_BIT 8 /* number of bits in a char */
89 #define QUAD_BITS (sizeof(s64) * CHAR_BIT)
90 #define LONG_BITS (sizeof(long) * CHAR_BIT)
91 #define HALF_BITS (sizeof(long) * CHAR_BIT / 2)
93 /*
94 * Extract high and low shortwords from longword, and move low shortword of
95 * longword to upper half of long, i.e., produce the upper longword of
96 * ((quad_t)(x) << (number_of_bits_in_long/2)). (`x' must actually be u_long.)
97 *
98 * These are used in the multiply code, to split a longword into upper
99 * and lower halves, and to reassemble a product as a quad_t, shifted left
100 * (sizeof(long)*CHAR_BIT/2).
101 */
102 #define HHALF(x) ((x) >> HALF_BITS)
103 #define LHALF(x) ((x) & ((1UL << HALF_BITS) - 1))
104 #define LHUP(x) ((x) << HALF_BITS)
106 /*
107 * Multiprecision divide. This algorithm is from Knuth vol. 2 (2nd ed),
108 * section 4.3.1, pp. 257--259.
109 */
110 #define B (1UL << HALF_BITS) /* digit base */
112 /* Combine two `digits' to make a single two-digit number. */
113 #define COMBINE(a, b) (((u_long)(a) << HALF_BITS) | (b))
115 /* select a type for digits in base B: use unsigned short if they fit */
116 #if ULONG_MAX == 0xffffffff && USHRT_MAX >= 0xffff
117 typedef unsigned short digit;
118 #else
119 typedef u_long digit;
120 #endif
123 /*
124 * Shift p[0]..p[len] left `sh' bits, ignoring any bits that
125 * `fall out' the left (there never will be any such anyway).
126 * We may assume len >= 0. NOTE THAT THIS WRITES len+1 DIGITS.
127 */
128 static void
129 shl(register digit *p, register int len, register int sh)
130 {
131 register int i;
133 for (i = 0; i < len; i++)
134 p[i] = LHALF(p[i] << sh) | (p[i + 1] >> (HALF_BITS - sh));
135 p[i] = LHALF(p[i] << sh);
136 }
138 /*
139 * __qdivrem(u, v, rem) returns u/v and, optionally, sets *rem to u%v.
140 *
141 * We do this in base 2-sup-HALF_BITS, so that all intermediate products
142 * fit within u_long. As a consequence, the maximum length dividend and
143 * divisor are 4 `digits' in this base (they are shorter if they have
144 * leading zeros).
145 */
146 u64
147 __qdivrem(u64 uq, u64 vq, u64 *arq)
148 {
149 union uu tmp;
150 digit *u, *v, *q;
151 register digit v1, v2;
152 u_long qhat, rhat, t;
153 int m, n, d, j, i;
154 digit uspace[5], vspace[5], qspace[5];
156 /*
157 * Take care of special cases: divide by zero, and u < v.
158 */
159 if (vq == 0) {
160 /* divide by zero. */
161 static volatile const unsigned int zero = 0;
163 tmp.ul[H] = tmp.ul[L] = 1 / zero;
164 if (arq)
165 *arq = uq;
166 return (tmp.q);
167 }
168 if (uq < vq) {
169 if (arq)
170 *arq = uq;
171 return (0);
172 }
173 u = &uspace[0];
174 v = &vspace[0];
175 q = &qspace[0];
177 /*
178 * Break dividend and divisor into digits in base B, then
179 * count leading zeros to determine m and n. When done, we
180 * will have:
181 * u = (u[1]u[2]...u[m+n]) sub B
182 * v = (v[1]v[2]...v[n]) sub B
183 * v[1] != 0
184 * 1 < n <= 4 (if n = 1, we use a different division algorithm)
185 * m >= 0 (otherwise u < v, which we already checked)
186 * m + n = 4
187 * and thus
188 * m = 4 - n <= 2
189 */
190 tmp.uq = uq;
191 u[0] = 0;
192 u[1] = HHALF(tmp.ul[H]);
193 u[2] = LHALF(tmp.ul[H]);
194 u[3] = HHALF(tmp.ul[L]);
195 u[4] = LHALF(tmp.ul[L]);
196 tmp.uq = vq;
197 v[1] = HHALF(tmp.ul[H]);
198 v[2] = LHALF(tmp.ul[H]);
199 v[3] = HHALF(tmp.ul[L]);
200 v[4] = LHALF(tmp.ul[L]);
201 for (n = 4; v[1] == 0; v++) {
202 if (--n == 1) {
203 u_long rbj; /* r*B+u[j] (not root boy jim) */
204 digit q1, q2, q3, q4;
206 /*
207 * Change of plan, per exercise 16.
208 * r = 0;
209 * for j = 1..4:
210 * q[j] = floor((r*B + u[j]) / v),
211 * r = (r*B + u[j]) % v;
212 * We unroll this completely here.
213 */
214 t = v[2]; /* nonzero, by definition */
215 q1 = u[1] / t;
216 rbj = COMBINE(u[1] % t, u[2]);
217 q2 = rbj / t;
218 rbj = COMBINE(rbj % t, u[3]);
219 q3 = rbj / t;
220 rbj = COMBINE(rbj % t, u[4]);
221 q4 = rbj / t;
222 if (arq)
223 *arq = rbj % t;
224 tmp.ul[H] = COMBINE(q1, q2);
225 tmp.ul[L] = COMBINE(q3, q4);
226 return (tmp.q);
227 }
228 }
230 /*
231 * By adjusting q once we determine m, we can guarantee that
232 * there is a complete four-digit quotient at &qspace[1] when
233 * we finally stop.
234 */
235 for (m = 4 - n; u[1] == 0; u++)
236 m--;
237 for (i = 4 - m; --i >= 0;)
238 q[i] = 0;
239 q += 4 - m;
241 /*
242 * Here we run Program D, translated from MIX to C and acquiring
243 * a few minor changes.
244 *
245 * D1: choose multiplier 1 << d to ensure v[1] >= B/2.
246 */
247 d = 0;
248 for (t = v[1]; t < B / 2; t <<= 1)
249 d++;
250 if (d > 0) {
251 shl(&u[0], m + n, d); /* u <<= d */
252 shl(&v[1], n - 1, d); /* v <<= d */
253 }
254 /*
255 * D2: j = 0.
256 */
257 j = 0;
258 v1 = v[1]; /* for D3 -- note that v[1..n] are constant */
259 v2 = v[2]; /* for D3 */
260 do {
261 register digit uj0, uj1, uj2;
263 /*
264 * D3: Calculate qhat (\^q, in TeX notation).
265 * Let qhat = min((u[j]*B + u[j+1])/v[1], B-1), and
266 * let rhat = (u[j]*B + u[j+1]) mod v[1].
267 * While rhat < B and v[2]*qhat > rhat*B+u[j+2],
268 * decrement qhat and increase rhat correspondingly.
269 * Note that if rhat >= B, v[2]*qhat < rhat*B.
270 */
271 uj0 = u[j + 0]; /* for D3 only -- note that u[j+...] change */
272 uj1 = u[j + 1]; /* for D3 only */
273 uj2 = u[j + 2]; /* for D3 only */
274 if (uj0 == v1) {
275 qhat = B;
276 rhat = uj1;
277 goto qhat_too_big;
278 } else {
279 u_long nn = COMBINE(uj0, uj1);
280 qhat = nn / v1;
281 rhat = nn % v1;
282 }
283 while (v2 * qhat > COMBINE(rhat, uj2)) {
284 qhat_too_big:
285 qhat--;
286 if ((rhat += v1) >= B)
287 break;
288 }
289 /*
290 * D4: Multiply and subtract.
291 * The variable `t' holds any borrows across the loop.
292 * We split this up so that we do not require v[0] = 0,
293 * and to eliminate a final special case.
294 */
295 for (t = 0, i = n; i > 0; i--) {
296 t = u[i + j] - v[i] * qhat - t;
297 u[i + j] = LHALF(t);
298 t = (B - HHALF(t)) & (B - 1);
299 }
300 t = u[j] - t;
301 u[j] = LHALF(t);
302 /*
303 * D5: test remainder.
304 * There is a borrow if and only if HHALF(t) is nonzero;
305 * in that (rare) case, qhat was too large (by exactly 1).
306 * Fix it by adding v[1..n] to u[j..j+n].
307 */
308 if (HHALF(t)) {
309 qhat--;
310 for (t = 0, i = n; i > 0; i--) { /* D6: add back. */
311 t += u[i + j] + v[i];
312 u[i + j] = LHALF(t);
313 t = HHALF(t);
314 }
315 u[j] = LHALF(u[j] + t);
316 }
317 q[j] = qhat;
318 } while (++j <= m); /* D7: loop on j. */
320 /*
321 * If caller wants the remainder, we have to calculate it as
322 * u[m..m+n] >> d (this is at most n digits and thus fits in
323 * u[m+1..m+n], but we may need more source digits).
324 */
325 if (arq) {
326 if (d) {
327 for (i = m + n; i > m; --i)
328 u[i] = (u[i] >> d) |
329 LHALF(u[i - 1] << (HALF_BITS - d));
330 u[i] = 0;
331 }
332 tmp.ul[H] = COMBINE(uspace[1], uspace[2]);
333 tmp.ul[L] = COMBINE(uspace[3], uspace[4]);
334 *arq = tmp.q;
335 }
337 tmp.ul[H] = COMBINE(qspace[1], qspace[2]);
338 tmp.ul[L] = COMBINE(qspace[3], qspace[4]);
339 return (tmp.q);
340 }
343 /*
344 * Divide two signed quads.
345 * ??? if -1/2 should produce -1 on this machine, this code is wrong
346 */
347 s64
348 __divdi3(s64 a, s64 b)
349 {
350 u64 ua, ub, uq;
351 int neg;
353 if (a < 0)
354 ua = -(u64)a, neg = 1;
355 else
356 ua = a, neg = 0;
357 if (b < 0)
358 ub = -(u64)b, neg ^= 1;
359 else
360 ub = b;
361 uq = __qdivrem(ua, ub, (u64 *)0);
362 return (neg ? -uq : uq);
363 }
365 /*
366 * Divide two unsigned quads.
367 */
368 u64
369 __udivdi3(u64 a, u64 b)
370 {
371 return (__qdivrem(a, b, (u64 *)0));
372 }
375 /*
376 * Return remainder after dividing two unsigned quads.
377 */
378 u_quad_t
379 __umoddi3(u_quad_t a, u_quad_t b)
380 {
381 u_quad_t r;
383 (void)__qdivrem(a, b, &r);
384 return (r);
385 }
387 #endif /* !defined(__ia64__) */