d03ab969 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: mpx.h,v 1.1 1999/09/03 08:41:12 mdw Exp $ |
4 | * |
5 | * Low level multiprecision arithmetic |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: mpx.h,v $ |
33 | * Revision 1.1 1999/09/03 08:41:12 mdw |
34 | * Initial import. |
35 | * |
36 | */ |
37 | |
38 | #ifndef MPX_H |
39 | #define MPX_H |
40 | |
41 | #ifdef __cplusplus |
42 | extern "C" { |
43 | #endif |
44 | |
45 | /*----- The idea ----------------------------------------------------------* |
46 | * |
47 | * This file provides functions and macros which work on vectors of words as |
48 | * unsigned multiprecision integers. The interface works in terms of base |
49 | * and limit pointers (i.e., a pointer to the start of a vector, and a |
50 | * pointer just past its end) rather than base pointer and length, because |
51 | * that requires more arithmetic and state to work on. |
52 | * |
53 | * The interfaces are slightly bizarre in other ways. Try to use the |
54 | * higher-level functions where you can: they're rather better designed to |
55 | * actually be friendly and useful. |
56 | */ |
57 | |
58 | /*----- Header files ------------------------------------------------------*/ |
59 | |
60 | #include <string.h> |
61 | |
62 | #ifndef MPTYPES_H |
63 | # include "mptypes.h" |
64 | #endif |
65 | |
66 | /*----- General manipulation ----------------------------------------------*/ |
67 | |
68 | /* --- @MPX_SHRINK@ --- * |
69 | * |
70 | * Arguments: @const mpw *v@ = pointer to vector of words |
71 | * @const mpw *vl@ = (updated) current limit of vector |
72 | * |
73 | * Use: Shrinks down the limit of a multiprecision integer vector. |
74 | */ |
75 | |
76 | #define MPX_SHRINK(v, vl) do { \ |
77 | const mpw *_v = (v), *_vl = (vl); \ |
78 | while (_vl > _v && *--_vl) \ |
79 | ; \ |
80 | (vl) = _vl; \ |
81 | } while (0) |
82 | |
83 | /* --- @MPX_BITS@ --- * |
84 | * |
85 | * Arguments: @unsigned long b@ = result variable |
86 | * @const mpw *v@ = pointer to array of words |
87 | * @const mpw *vl@ = limit of vector (from @MPX_SHRINK@) |
88 | * |
89 | * Use: Calculates the number of bits in a multiprecision value. |
90 | */ |
91 | |
92 | #define MPX_BITS(b, v, vl) do { \ |
93 | const mpw *_v = (v), *_vl = (vl); \ |
94 | if (_v == _vl) \ |
95 | (b) = 0; \ |
96 | else { \ |
97 | unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \ |
98 | mpw _w = _vl[-1]; \ |
99 | unsigned _k = MPW_BITS / 2; \ |
100 | while (_k) { \ |
101 | if (_w >> _k) { \ |
102 | _w >>= _k; \ |
103 | _b += _k; \ |
104 | } \ |
105 | _k >>= 1; \ |
106 | } \ |
107 | (b) = _b; \ |
108 | } \ |
109 | } while (0) |
110 | |
111 | /* --- @MPX_OCTETS@ --- * |
112 | * |
113 | * Arguments: @size_t o@ = result variable |
114 | * @const mpw *v@ = pointer to array of words |
115 | * @size_t len@ = length of the array (from @MPX_LEN@) |
116 | * |
117 | * Use: Calculates the number of octets in a multiprecision value. |
118 | */ |
119 | |
120 | #define MPX_OCTETS(o, v, len) do { \ |
121 | const mpw *_v = (v), *_vl = (vl); \ |
122 | if (_v == _vl) \ |
123 | (o) = 0; \ |
124 | else { \ |
125 | _size_t _o = (MPW_BITS / 8) * (_vl - _v - 1); \ |
126 | mpw _w = _vl[-1]; \ |
127 | unsigned _k = MPW_BITS / 2; \ |
128 | while (_k > 3) { \ |
129 | if (_w >> _k) { \ |
130 | _w >>= _k; \ |
131 | _o += _k - 3; \ |
132 | } \ |
133 | _k >>= 1; \ |
134 | } \ |
135 | if (_w) \ |
136 | _o++; \ |
137 | (o) = _o; \ |
138 | } \ |
139 | } while (0) |
140 | |
141 | /* --- @MPX_COPY@ --- * |
142 | * |
143 | * Arguments: @dv, dvl@ = destination vector base and limit |
144 | * @av, avl@ = source vector base and limit |
145 | * |
146 | * Use: Copies a multiprecision integer. |
147 | */ |
148 | |
149 | #define MPX_COPY(dv, dvl, av, dvl) do { \ |
150 | mpw *_dv = (dv); \ |
151 | size_t _dn = (dvl) - _dv; \ |
152 | const mpw *_av = (av); \ |
153 | size_t _an = (avl) - _av; \ |
154 | if (_av == _dv) { \ |
155 | if (_dvl > _avl) \ |
156 | memset(_avl, 0, MPWS(_dn - _an)); \ |
157 | } else if (_an >= _dn) \ |
158 | memmove(_dv, _av, MPWS(_dn)); \ |
159 | else { \ |
160 | memmove(_dv, _av, MPWS(_an)); \ |
161 | memset(_dv + _an, 0, MPWS(_dn - _an)); \ |
162 | } \ |
163 | } while (0) |
164 | |
165 | /* --- @MPX_ZERO@ --- * |
166 | * |
167 | * Arguments: @v, vl@ = base and limit of vector to clear |
168 | * |
169 | * Use: Zeroes the area between the two vector pointers. |
170 | */ |
171 | |
172 | #define MPX_ZERO(v, vl) { \ |
173 | mpw *_v = (v), *_vl = (vl); \ |
174 | memset(_v, 0, MPWS(_vl - _v)); \ |
175 | } while (0) |
176 | |
177 | /*----- Loading and storing -----------------------------------------------*/ |
178 | |
179 | /* --- @mpx_storel@ --- * |
180 | * |
181 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
182 | * @octet *p@ = pointer to octet array |
183 | * @size_t sz@ = size of octet array |
184 | * |
185 | * Returns: --- |
186 | * |
187 | * Use: Stores an MP in an octet array, least significant octet |
188 | * first. High-end octets are silently discarded if there |
189 | * isn't enough space for them. |
190 | */ |
191 | |
192 | extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, |
193 | octet */*p*/, size_t /*sz*/); |
194 | |
195 | /* --- @mpx_loadl@ --- * |
196 | * |
197 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
198 | * @const octet *p@ = pointer to octet array |
199 | * @size_t sz@ = size of octet array |
200 | * |
201 | * Returns: --- |
202 | * |
203 | * Use: Loads an MP in an octet array, least significant octet |
204 | * first. High-end octets are ignored if there isn't enough |
205 | * space for them. |
206 | */ |
207 | |
208 | extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, |
209 | const octet */*p*/, size_t /*sz*/); |
210 | |
211 | /* --- @mpx_storeb@ --- * |
212 | * |
213 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
214 | * @octet *p@ = pointer to octet array |
215 | * @size_t sz@ = size of octet array |
216 | * |
217 | * Returns: --- |
218 | * |
219 | * Use: Stores an MP in an octet array, most significant octet |
220 | * first. High-end octets are silently discarded if there |
221 | * isn't enough space for them. |
222 | */ |
223 | |
224 | extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, |
225 | octet */*p*/, size_t /*sz*/); |
226 | |
227 | /* --- @mpx_loadb@ --- * |
228 | * |
229 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
230 | * @const octet *p@ = pointer to octet array |
231 | * @size_t sz@ = size of octet array |
232 | * |
233 | * Returns: --- |
234 | * |
235 | * Use: Loads an MP in an octet array, most significant octet |
236 | * first. High-end octets are ignored if there isn't enough |
237 | * space for them. |
238 | */ |
239 | |
240 | extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, |
241 | const octet */*p*/, size_t /*sz*/); |
242 | |
243 | /*----- Logical shifting --------------------------------------------------*/ |
244 | |
245 | /* --- @mpx_lsl@ --- * |
246 | * |
247 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
248 | * @const mpw *av, *avl@ = source vector base and limit |
249 | * @size_t n@ = number of bit positions to shift by |
250 | * |
251 | * Returns: --- |
252 | * |
253 | * Use: Performs a logical shift left operation on an integer. |
254 | */ |
255 | |
256 | extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/, |
257 | const mpw */*av*/, const mpw */*avl*/, |
258 | size_t /*n*/); |
259 | |
260 | /* --- @mpx_lsr@ --- * |
261 | * |
262 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
263 | * @const mpw *av, *avl@ = source vector base and limit |
264 | * @size_t n@ = number of bit positions to shift by |
265 | * |
266 | * Returns: --- |
267 | * |
268 | * Use: Performs a logical shift right operation on an integer. |
269 | */ |
270 | |
271 | extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/, |
272 | const mpw */*av*/, const mpw */*avl*/, |
273 | size_t /*n*/); |
274 | |
275 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
276 | |
277 | /* --- @mpx_ucmp@ --- * |
278 | * |
279 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
280 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
281 | * |
282 | * Returns: Less than, equal to, or greater than zero depending on |
283 | * whether @a@ is less than, equal to or greater than @b@, |
284 | * respectively. |
285 | * |
286 | * Use: Performs an unsigned integer comparison. |
287 | */ |
288 | |
289 | #define MPX_UCMP(av, avl, op, dv, dvl) \ |
290 | (mpx_ucmp((av), (avl), (dv), (dvl)) op 0) |
291 | |
292 | extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/, |
293 | const mpw */*bv*/, const mpw */*bvl*/); |
294 | |
295 | /* --- @mpx_uadd@ --- * |
296 | * |
297 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
298 | * @const mpw *av, *avl@ = first addend vector base and limit |
299 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
300 | * |
301 | * Returns: --- |
302 | * |
303 | * Use: Performs unsigned integer addition. If the result overflows |
304 | * the destination vector, high-order bits are discarded. This |
305 | * means that two's complement addition happens more or less for |
306 | * free, although that's more a side-effect than anything else. |
307 | * The result vector may be equal to either or both source |
308 | * vectors, but may not otherwise overlap them. |
309 | */ |
310 | |
311 | extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, |
312 | const mpw */*av*/, const mpw */*avl*/, |
313 | const mpw */*bv*/, const mpw */*bvl*/); |
314 | |
315 | /* --- @mpx_usub@ --- * |
316 | * |
317 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
318 | * @const mpw *av, *avl@ = first argument vector base and limit |
319 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
320 | * |
321 | * Returns: --- |
322 | * |
323 | * Use: Performs unsigned integer subtraction. If the result |
324 | * overflows the destination vector, high-order bits are |
325 | * discarded. This means that two's complement subtraction |
326 | * happens more or less for free, althuogh that's more a side- |
327 | * effect than anything else. The result vector may be equal to |
328 | * either or both source vectors, but may not otherwise overlap |
329 | * them. |
330 | */ |
331 | |
332 | extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, |
333 | const mpw */*av*/, const mpw */*avl*/, |
334 | const mpw */*bv*/, const mpw */*bvl*/); |
335 | |
336 | /* --- @MPX_UMULN@ --- * |
337 | * |
338 | * Arguments: @dv, dvl@ = destination vector base and limit |
339 | * @av, avl@ = multiplicand vector base and limit |
340 | * @m@ = multiplier |
341 | * |
342 | * Use: Multiplies a multiprecision integer by a single-word value. |
343 | * The destination and source may be equal. The destination |
344 | * is completely cleared after use. |
345 | */ |
346 | |
347 | #define MPX_UMULN(dv, dvl, av, avl, m) do { \ |
348 | mpw *_dv = (dv), *_dvl = (dvl); \ |
349 | const mpw *_av = (av), *_avl = (avl); \ |
350 | mpw _c = 0; \ |
351 | mpd _m = (m); \ |
352 | \ |
353 | while (_av < _avl) { \ |
354 | mpd _x; \ |
355 | if (_dv >= _dvl) \ |
356 | break; \ |
357 | _x = _m * *_av++ + c; \ |
358 | *_dv++ = MPW(_x); \ |
359 | _c = _x >> MPW_BITS; \ |
360 | } \ |
361 | if (_dv < _dvl) { \ |
362 | *_dv++ = MPW(_c); \ |
363 | MPX_ZERO(_dv, _dvl); \ |
364 | } \ |
365 | } while (0) |
366 | |
367 | /* --- @MPX_UMLAN@ --- * |
368 | * |
369 | * Arguments: @dv, dvl@ = destination/accumulator vector base and limit |
370 | * @av, avl@ = multiplicand vector base and limit |
371 | * @m@ = multiplier |
372 | * |
373 | * Use: Multiplies a multiprecision integer by a single-word value |
374 | * and adds the result to an accumulator. |
375 | */ |
376 | |
377 | #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ |
378 | mpw *_dv = (dv), *_dvl = (dvl); \ |
379 | const mpw *_av = (av), *_avl = (avl); \ |
380 | mpw _c = 0; \ |
381 | mpd _m = (m); \ |
382 | \ |
383 | while (_av < _avl) { \ |
384 | mpd _x; \ |
385 | if (_dv >= _dvl) \ |
386 | break; \ |
387 | _x = *_dv + _m * *_av++ + _c; \ |
388 | *_dv++ = MPW(_x); \ |
389 | _c = _x >> MPW_BITS; \ |
390 | } \ |
391 | if (_dv < _dvl) { \ |
392 | *_dv++ = MPW(_c); \ |
393 | MPX_ZERO(_dv, _dvl); \ |
394 | } \ |
395 | } while (0) |
396 | |
397 | /* --- @mpx_umul@ --- * |
398 | * |
399 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
400 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
401 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
402 | * |
403 | * Returns: --- |
404 | * |
405 | * Use: Performs unsigned integer multiplication. If the result |
406 | * overflows the desination vector, high-order bits are |
407 | * discarded. The result vector may not overlap the argument |
408 | * vectors in any way. |
409 | */ |
410 | |
411 | extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, |
412 | const mpw */*av*/, const mpw */*avl*/, |
413 | const mpw */*bv*/, const mpw */*bvl*/); |
414 | |
415 | /* --- @mpx_udiv@ --- * |
416 | * |
417 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
418 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
419 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
420 | * |
421 | * Returns: --- |
422 | * |
423 | * Use: Performs unsigned integer division. If the result overflows |
424 | * the quotient vector, high-order bits are discarded. (Clearly |
425 | * the remainder vector can't overflow.) The various vectors |
426 | * may not overlap in any way. Yes, I know it's a bit odd |
427 | * requiring the dividend to be in the result position but it |
428 | * does make some sense really. |
429 | */ |
430 | |
431 | extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/, |
432 | const mpw */*dv*/, const mpw */*dvl*/); |
433 | |
434 | /*----- That's all, folks -------------------------------------------------*/ |
435 | |
436 | #ifdef __cplusplus |
437 | } |
438 | #endif |
439 | |
440 | #endif |