1 #include <xen/byteorder.h>
2 #include <xen/macros.h>
3 #include <xen/types.h>
4
5 /*
6 * A couple of 64 bit operations ported from FreeBSD.
7 * The code within the '#if BITS_PER_LONG == 32' block below, and no other
8 * code in this file, is distributed under the following licensing terms
9 * This is the modified '3-clause' BSD license with the obnoxious
10 * advertising clause removed, as permitted by University of California.
11 *
12 * Copyright (c) 1992, 1993
13 * The Regents of the University of California. All rights reserved.
14 *
15 * This software was developed by the Computer Systems Engineering group
16 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
17 * contributed to Berkeley.
18 *
19 * Redistribution and use in source and binary forms, with or without
20 * modification, are permitted provided that the following conditions
21 * are met:
22 * 1. Redistributions of source code must retain the above copyright
23 * notice, this list of conditions and the following disclaimer.
24 * 2. Redistributions in binary form must reproduce the above copyright
25 * notice, this list of conditions and the following disclaimer in the
26 * documentation and/or other materials provided with the distribution.
27 * 3. Neither the name of the University nor the names of its contributors
28 * may be used to endorse or promote products derived from this software
29 * without specific prior written permission.
30 *
31 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
32 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
33 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
34 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
35 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
36 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
37 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
38 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
39 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
40 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
41 * SUCH DAMAGE.
42 */
43
44 /*
45 * Depending on the desired operation, we view a `long long' (aka quad_t) in
46 * one or more of the following formats.
47 */
48 union uu {
49 int64_t q; /* as a (signed) quad */
50 uint64_t uq; /* as an unsigned quad */
51 long sl[2]; /* as two signed longs */
52 unsigned long ul[2]; /* as two unsigned longs */
53 };
54
55 #ifdef __BIG_ENDIAN
56 #define _QUAD_HIGHWORD 0
57 #define _QUAD_LOWWORD 1
58 #else /* __LITTLE_ENDIAN */
59 #define _QUAD_HIGHWORD 1
60 #define _QUAD_LOWWORD 0
61 #endif
62
63 /*
64 * Define high and low longwords.
65 */
66 #define H _QUAD_HIGHWORD
67 #define L _QUAD_LOWWORD
68
69 /*
70 * Total number of bits in a quad_t and in the pieces that make it up.
71 * These are used for shifting, and also below for halfword extraction
72 * and assembly.
73 */
74 #define CHAR_BIT 8 /* number of bits in a char */
75 #define QUAD_BITS (sizeof(int64_t) * CHAR_BIT)
76 #define LONG_BITS (sizeof(long) * CHAR_BIT)
77 #define HALF_BITS (sizeof(long) * CHAR_BIT / 2)
78
79 /*
80 * Extract high and low shortwords from longword, and move low shortword of
81 * longword to upper half of long, i.e., produce the upper longword of
82 * ((quad_t)(x) << (number_of_bits_in_long/2)). (`x' must actually be
83 * unsigned long.)
84 *
85 * These are used in the multiply code, to split a longword into upper
86 * and lower halves, and to reassemble a product as a quad_t, shifted left
87 * (sizeof(long)*CHAR_BIT/2).
88 */
89 #define HHALF(x) ((x) >> HALF_BITS)
90 #define LHALF(x) ((x) & ((1 << HALF_BITS) - 1))
91 #define LHUP(x) ((x) << HALF_BITS)
92
93 /*
94 * Multiprecision divide. This algorithm is from Knuth vol. 2 (2nd ed),
95 * section 4.3.1, pp. 257--259.
96 */
97 #define B (1 << HALF_BITS) /* digit base */
98
99 /* Combine two `digits' to make a single two-digit number. */
100 #define COMBINE(a, b) (((unsigned long)(a) << HALF_BITS) | (b))
101
102 /* select a type for digits in base B */
103 typedef unsigned long digit;
104
105 /*
106 * Shift p[0]..p[len] left `sh' bits, ignoring any bits that
107 * `fall out' the left (there never will be any such anyway).
108 * We may assume len >= 0. NOTE THAT THIS WRITES len+1 DIGITS.
109 */
shl(register digit * p,register int len,register int sh)110 static void shl(register digit *p, register int len, register int sh)
111 {
112 register int i;
113
114 for (i = 0; i < len; i++)
115 p[i] = LHALF(p[i] << sh) | (p[i + 1] >> (HALF_BITS - sh));
116 p[i] = LHALF(p[i] << sh);
117 }
118
119 /*
120 * __qdivrem(u, v, rem) returns u/v and, optionally, sets *rem to u%v.
121 *
122 * We do this in base 2-sup-HALF_BITS, so that all intermediate products
123 * fit within unsigned long. As a consequence, the maximum length dividend
124 * and divisor are 4 `digits' in this base (they are shorter if they have
125 * leading zeros).
126 */
__qdivrem(u64 uq,u64 vq,u64 * arq)127 u64 __qdivrem(u64 uq, u64 vq, u64 *arq)
128 {
129 union uu tmp;
130 digit *u, *v, *q;
131 register digit v1, v2;
132 unsigned long qhat, rhat, t;
133 int m, n, d, j, i;
134 digit uspace[5], vspace[5], qspace[5];
135
136 /*
137 * Take care of special cases: divide by zero, and u < v.
138 */
139 if (vq == 0) {
140 /* divide by zero. */
141 static volatile const unsigned int zero = 0;
142
143 tmp.ul[H] = tmp.ul[L] = 1 / zero;
144 if (arq)
145 *arq = uq;
146 return (tmp.q);
147 }
148 if (uq < vq) {
149 if (arq)
150 *arq = uq;
151 return (0);
152 }
153 u = &uspace[0];
154 v = &vspace[0];
155 q = &qspace[0];
156
157 /*
158 * Break dividend and divisor into digits in base B, then
159 * count leading zeros to determine m and n. When done, we
160 * will have:
161 * u = (u[1]u[2]...u[m+n]) sub B
162 * v = (v[1]v[2]...v[n]) sub B
163 * v[1] != 0
164 * 1 < n <= 4 (if n = 1, we use a different division algorithm)
165 * m >= 0 (otherwise u < v, which we already checked)
166 * m + n = 4
167 * and thus
168 * m = 4 - n <= 2
169 */
170 tmp.uq = uq;
171 u[0] = 0;
172 u[1] = HHALF(tmp.ul[H]);
173 u[2] = LHALF(tmp.ul[H]);
174 u[3] = HHALF(tmp.ul[L]);
175 u[4] = LHALF(tmp.ul[L]);
176 tmp.uq = vq;
177 v[1] = HHALF(tmp.ul[H]);
178 v[2] = LHALF(tmp.ul[H]);
179 v[3] = HHALF(tmp.ul[L]);
180 v[4] = LHALF(tmp.ul[L]);
181 for (n = 4; v[1] == 0; v++) {
182 if (--n == 1) {
183 unsigned long rbj; /* r*B+u[j] (not root boy jim) */
184 digit q1, q2, q3, q4;
185
186 /*
187 * Change of plan, per exercise 16.
188 * r = 0;
189 * for j = 1..4:
190 * q[j] = floor((r*B + u[j]) / v),
191 * r = (r*B + u[j]) % v;
192 * We unroll this completely here.
193 */
194 t = v[2]; /* nonzero, by definition */
195 q1 = u[1] / t;
196 rbj = COMBINE(u[1] % t, u[2]);
197 q2 = rbj / t;
198 rbj = COMBINE(rbj % t, u[3]);
199 q3 = rbj / t;
200 rbj = COMBINE(rbj % t, u[4]);
201 q4 = rbj / t;
202 if (arq)
203 *arq = rbj % t;
204 tmp.ul[H] = COMBINE(q1, q2);
205 tmp.ul[L] = COMBINE(q3, q4);
206 return (tmp.q);
207 }
208 }
209
210 /*
211 * By adjusting q once we determine m, we can guarantee that
212 * there is a complete four-digit quotient at &qspace[1] when
213 * we finally stop.
214 */
215 for (m = 4 - n; u[1] == 0; u++)
216 m--;
217 for (i = 4 - m; --i >= 0;)
218 q[i] = 0;
219 q += 4 - m;
220
221 /*
222 * Here we run Program D, translated from MIX to C and acquiring
223 * a few minor changes.
224 *
225 * D1: choose multiplier 1 << d to ensure v[1] >= B/2.
226 */
227 d = 0;
228 for (t = v[1]; t < B / 2; t <<= 1)
229 d++;
230 if (d > 0) {
231 shl(&u[0], m + n, d); /* u <<= d */
232 shl(&v[1], n - 1, d); /* v <<= d */
233 }
234 /*
235 * D2: j = 0.
236 */
237 j = 0;
238 v1 = v[1]; /* for D3 -- note that v[1..n] are constant */
239 v2 = v[2]; /* for D3 */
240 do {
241 register digit uj0, uj1, uj2;
242
243 /*
244 * D3: Calculate qhat (\^q, in TeX notation).
245 * Let qhat = min((u[j]*B + u[j+1])/v[1], B-1), and
246 * let rhat = (u[j]*B + u[j+1]) mod v[1].
247 * While rhat < B and v[2]*qhat > rhat*B+u[j+2],
248 * decrement qhat and increase rhat correspondingly.
249 * Note that if rhat >= B, v[2]*qhat < rhat*B.
250 */
251 uj0 = u[j + 0]; /* for D3 only -- note that u[j+...] change */
252 uj1 = u[j + 1]; /* for D3 only */
253 uj2 = u[j + 2]; /* for D3 only */
254 if (uj0 == v1) {
255 qhat = B;
256 rhat = uj1;
257 goto qhat_too_big;
258 } else {
259 unsigned long nn = COMBINE(uj0, uj1);
260
261 qhat = nn / v1;
262 rhat = nn % v1;
263 }
264 while (v2 * qhat > COMBINE(rhat, uj2)) {
265 qhat_too_big:
266 qhat--;
267 if ((rhat += v1) >= B)
268 break;
269 }
270 /*
271 * D4: Multiply and subtract.
272 * The variable `t' holds any borrows across the loop.
273 * We split this up so that we do not require v[0] = 0,
274 * and to eliminate a final special case.
275 */
276 for (t = 0, i = n; i > 0; i--) {
277 t = u[i + j] - v[i] * qhat - t;
278 u[i + j] = LHALF(t);
279 t = (B - HHALF(t)) & (B - 1);
280 }
281 t = u[j] - t;
282 u[j] = LHALF(t);
283 /*
284 * D5: test remainder.
285 * There is a borrow if and only if HHALF(t) is nonzero;
286 * in that (rare) case, qhat was too large (by exactly 1).
287 * Fix it by adding v[1..n] to u[j..j+n].
288 */
289 if (HHALF(t)) {
290 qhat--;
291 for (t = 0, i = n; i > 0; i--) { /* D6: add back. */
292 t += u[i + j] + v[i];
293 u[i + j] = LHALF(t);
294 t = HHALF(t);
295 }
296 u[j] = LHALF(u[j] + t);
297 }
298 q[j] = qhat;
299 } while (++j <= m); /* D7: loop on j. */
300
301 /*
302 * If caller wants the remainder, we have to calculate it as
303 * u[m..m+n] >> d (this is at most n digits and thus fits in
304 * u[m+1..m+n], but we may need more source digits).
305 */
306 if (arq) {
307 if (d) {
308 for (i = m + n; i > m; --i)
309 u[i] = (u[i] >> d) |
310 LHALF(u[i - 1] << (HALF_BITS - d));
311 u[i] = 0;
312 }
313 tmp.ul[H] = COMBINE(uspace[1], uspace[2]);
314 tmp.ul[L] = COMBINE(uspace[3], uspace[4]);
315 *arq = tmp.q;
316 }
317
318 tmp.ul[H] = COMBINE(qspace[1], qspace[2]);
319 tmp.ul[L] = COMBINE(qspace[3], qspace[4]);
320 return (tmp.q);
321 }
322
323 /*
324 * Divide two signed quads.
325 * Truncates towards zero, as required by C99.
326 */
__divdi3(int64_t a,int64_t b)327 int64_t __divdi3(int64_t a, int64_t b)
328 {
329 u64 ua, ub, uq;
330 int neg = (a < 0) ^ (b < 0);
331 ua = (a < 0) ? -(u64)a : a;
332 ub = (b < 0) ? -(u64)b : b;
333 uq = __qdivrem(ua, ub, (u64 *)0);
334 return (neg ? -uq : uq);
335 }
336
337
338 /*
339 * Divide two unsigned quads.
340 */
__udivdi3(u64 a,u64 b)341 u64 __udivdi3(u64 a, u64 b)
342 {
343 return __qdivrem(a, b, (u64 *)0);
344 }
345
346 /*
347 * Remainder of unsigned quad division
348 */
__umoddi3(u64 a,u64 b)349 u64 __umoddi3(u64 a, u64 b)
350 {
351 u64 rem;
352 __qdivrem(a, b, &rem);
353 return rem;
354 }
355
356 /*
357 * Remainder of signed quad division.
358 * Truncates towards zero, as required by C99:
359 * 11 % 5 = 1
360 * -11 % 5 = -1
361 * 11 % -5 = 1
362 * -11 % -5 = -1
363 */
__moddi3(int64_t a,int64_t b)364 int64_t __moddi3(int64_t a, int64_t b)
365 {
366 u64 ua, ub, urem;
367 int neg = (a < 0);
368 ua = neg ? -(u64)a : a;
369 ub = (b < 0) ? -(u64)b : b;
370 __qdivrem(ua, ub, &urem);
371 return (neg ? -urem : urem);
372 }
373
374 /*
375 * Quotient and remainder of unsigned long long division
376 */
__ldivmod_helper(int64_t a,int64_t b,int64_t * r)377 int64_t __ldivmod_helper(int64_t a, int64_t b, int64_t *r)
378 {
379 u64 ua, ub, rem, quot;
380
381 ua = ABS(a);
382 ub = ABS(b);
383 quot = __qdivrem(ua, ub, &rem);
384 if ( a < 0 )
385 *r = -rem;
386 else
387 *r = rem;
388 if ( (a < 0) ^ (b < 0) )
389 return -quot;
390 else
391 return quot;
392 }
393
394 /*
395 * Local variables:
396 * mode: C
397 * c-file-style: "BSD"
398 * c-basic-offset: 4
399 * tab-width: 4
400 * indent-tabs-mode: nil
401 * End:
402 */
403