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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mpx.h,v 1.2 1999/11/11 17:47:55 mdw Exp $ |
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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 $ |
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33 | * Revision 1.2 1999/11/11 17:47:55 mdw |
34 | * Minor changes for different `mptypes.h' format. |
35 | * |
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36 | * Revision 1.1 1999/09/03 08:41:12 mdw |
37 | * Initial import. |
38 | * |
39 | */ |
40 | |
41 | #ifndef MPX_H |
42 | #define MPX_H |
43 | |
44 | #ifdef __cplusplus |
45 | extern "C" { |
46 | #endif |
47 | |
48 | /*----- The idea ----------------------------------------------------------* |
49 | * |
50 | * This file provides functions and macros which work on vectors of words as |
51 | * unsigned multiprecision integers. The interface works in terms of base |
52 | * and limit pointers (i.e., a pointer to the start of a vector, and a |
53 | * pointer just past its end) rather than base pointer and length, because |
54 | * that requires more arithmetic and state to work on. |
55 | * |
56 | * The interfaces are slightly bizarre in other ways. Try to use the |
57 | * higher-level functions where you can: they're rather better designed to |
58 | * actually be friendly and useful. |
59 | */ |
60 | |
61 | /*----- Header files ------------------------------------------------------*/ |
62 | |
63 | #include <string.h> |
64 | |
65 | #ifndef MPTYPES_H |
66 | # include "mptypes.h" |
67 | #endif |
68 | |
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69 | /*----- Basic macros ------------------------------------------------------*/ |
70 | |
71 | /* --- @MPW@ --- * |
72 | * |
73 | * Arguments: @x@ = an unsigned value |
74 | * |
75 | * Use: Expands to the value of @x@ masked and typecast to a |
76 | * multiprecision integer word. |
77 | */ |
78 | |
79 | #define MPW(x) ((mpw)((x) & MPW_MAX)) |
80 | |
81 | /* --- @MPWS@ --- * |
82 | * |
83 | * Arguments: @n@ = number of words |
84 | * |
85 | * Use: Expands to the number of bytes occupied by a given number of |
86 | * words. |
87 | */ |
88 | |
89 | #define MPWS(n) ((n) * sizeof(mpw)) |
90 | |
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91 | /*----- General manipulation ----------------------------------------------*/ |
92 | |
93 | /* --- @MPX_SHRINK@ --- * |
94 | * |
95 | * Arguments: @const mpw *v@ = pointer to vector of words |
96 | * @const mpw *vl@ = (updated) current limit of vector |
97 | * |
98 | * Use: Shrinks down the limit of a multiprecision integer vector. |
99 | */ |
100 | |
101 | #define MPX_SHRINK(v, vl) do { \ |
102 | const mpw *_v = (v), *_vl = (vl); \ |
103 | while (_vl > _v && *--_vl) \ |
104 | ; \ |
105 | (vl) = _vl; \ |
106 | } while (0) |
107 | |
108 | /* --- @MPX_BITS@ --- * |
109 | * |
110 | * Arguments: @unsigned long b@ = result variable |
111 | * @const mpw *v@ = pointer to array of words |
112 | * @const mpw *vl@ = limit of vector (from @MPX_SHRINK@) |
113 | * |
114 | * Use: Calculates the number of bits in a multiprecision value. |
115 | */ |
116 | |
117 | #define MPX_BITS(b, v, vl) do { \ |
118 | const mpw *_v = (v), *_vl = (vl); \ |
119 | if (_v == _vl) \ |
120 | (b) = 0; \ |
121 | else { \ |
122 | unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \ |
123 | mpw _w = _vl[-1]; \ |
124 | unsigned _k = MPW_BITS / 2; \ |
125 | while (_k) { \ |
126 | if (_w >> _k) { \ |
127 | _w >>= _k; \ |
128 | _b += _k; \ |
129 | } \ |
130 | _k >>= 1; \ |
131 | } \ |
132 | (b) = _b; \ |
133 | } \ |
134 | } while (0) |
135 | |
136 | /* --- @MPX_OCTETS@ --- * |
137 | * |
138 | * Arguments: @size_t o@ = result variable |
139 | * @const mpw *v@ = pointer to array of words |
140 | * @size_t len@ = length of the array (from @MPX_LEN@) |
141 | * |
142 | * Use: Calculates the number of octets in a multiprecision value. |
143 | */ |
144 | |
145 | #define MPX_OCTETS(o, v, len) do { \ |
146 | const mpw *_v = (v), *_vl = (vl); \ |
147 | if (_v == _vl) \ |
148 | (o) = 0; \ |
149 | else { \ |
150 | _size_t _o = (MPW_BITS / 8) * (_vl - _v - 1); \ |
151 | mpw _w = _vl[-1]; \ |
152 | unsigned _k = MPW_BITS / 2; \ |
153 | while (_k > 3) { \ |
154 | if (_w >> _k) { \ |
155 | _w >>= _k; \ |
156 | _o += _k - 3; \ |
157 | } \ |
158 | _k >>= 1; \ |
159 | } \ |
160 | if (_w) \ |
161 | _o++; \ |
162 | (o) = _o; \ |
163 | } \ |
164 | } while (0) |
165 | |
166 | /* --- @MPX_COPY@ --- * |
167 | * |
168 | * Arguments: @dv, dvl@ = destination vector base and limit |
169 | * @av, avl@ = source vector base and limit |
170 | * |
171 | * Use: Copies a multiprecision integer. |
172 | */ |
173 | |
174 | #define MPX_COPY(dv, dvl, av, dvl) do { \ |
175 | mpw *_dv = (dv); \ |
176 | size_t _dn = (dvl) - _dv; \ |
177 | const mpw *_av = (av); \ |
178 | size_t _an = (avl) - _av; \ |
179 | if (_av == _dv) { \ |
180 | if (_dvl > _avl) \ |
181 | memset(_avl, 0, MPWS(_dn - _an)); \ |
182 | } else if (_an >= _dn) \ |
183 | memmove(_dv, _av, MPWS(_dn)); \ |
184 | else { \ |
185 | memmove(_dv, _av, MPWS(_an)); \ |
186 | memset(_dv + _an, 0, MPWS(_dn - _an)); \ |
187 | } \ |
188 | } while (0) |
189 | |
190 | /* --- @MPX_ZERO@ --- * |
191 | * |
192 | * Arguments: @v, vl@ = base and limit of vector to clear |
193 | * |
194 | * Use: Zeroes the area between the two vector pointers. |
195 | */ |
196 | |
197 | #define MPX_ZERO(v, vl) { \ |
198 | mpw *_v = (v), *_vl = (vl); \ |
199 | memset(_v, 0, MPWS(_vl - _v)); \ |
200 | } while (0) |
201 | |
202 | /*----- Loading and storing -----------------------------------------------*/ |
203 | |
204 | /* --- @mpx_storel@ --- * |
205 | * |
206 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
207 | * @octet *p@ = pointer to octet array |
208 | * @size_t sz@ = size of octet array |
209 | * |
210 | * Returns: --- |
211 | * |
212 | * Use: Stores an MP in an octet array, least significant octet |
213 | * first. High-end octets are silently discarded if there |
214 | * isn't enough space for them. |
215 | */ |
216 | |
217 | extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, |
218 | octet */*p*/, size_t /*sz*/); |
219 | |
220 | /* --- @mpx_loadl@ --- * |
221 | * |
222 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
223 | * @const octet *p@ = pointer to octet array |
224 | * @size_t sz@ = size of octet array |
225 | * |
226 | * Returns: --- |
227 | * |
228 | * Use: Loads an MP in an octet array, least significant octet |
229 | * first. High-end octets are ignored if there isn't enough |
230 | * space for them. |
231 | */ |
232 | |
233 | extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, |
234 | const octet */*p*/, size_t /*sz*/); |
235 | |
236 | /* --- @mpx_storeb@ --- * |
237 | * |
238 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
239 | * @octet *p@ = pointer to octet array |
240 | * @size_t sz@ = size of octet array |
241 | * |
242 | * Returns: --- |
243 | * |
244 | * Use: Stores an MP in an octet array, most significant octet |
245 | * first. High-end octets are silently discarded if there |
246 | * isn't enough space for them. |
247 | */ |
248 | |
249 | extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, |
250 | octet */*p*/, size_t /*sz*/); |
251 | |
252 | /* --- @mpx_loadb@ --- * |
253 | * |
254 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
255 | * @const octet *p@ = pointer to octet array |
256 | * @size_t sz@ = size of octet array |
257 | * |
258 | * Returns: --- |
259 | * |
260 | * Use: Loads an MP in an octet array, most significant octet |
261 | * first. High-end octets are ignored if there isn't enough |
262 | * space for them. |
263 | */ |
264 | |
265 | extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, |
266 | const octet */*p*/, size_t /*sz*/); |
267 | |
268 | /*----- Logical shifting --------------------------------------------------*/ |
269 | |
270 | /* --- @mpx_lsl@ --- * |
271 | * |
272 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
273 | * @const mpw *av, *avl@ = source vector base and limit |
274 | * @size_t n@ = number of bit positions to shift by |
275 | * |
276 | * Returns: --- |
277 | * |
278 | * Use: Performs a logical shift left operation on an integer. |
279 | */ |
280 | |
281 | extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/, |
282 | const mpw */*av*/, const mpw */*avl*/, |
283 | size_t /*n*/); |
284 | |
285 | /* --- @mpx_lsr@ --- * |
286 | * |
287 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
288 | * @const mpw *av, *avl@ = source vector base and limit |
289 | * @size_t n@ = number of bit positions to shift by |
290 | * |
291 | * Returns: --- |
292 | * |
293 | * Use: Performs a logical shift right operation on an integer. |
294 | */ |
295 | |
296 | extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/, |
297 | const mpw */*av*/, const mpw */*avl*/, |
298 | size_t /*n*/); |
299 | |
300 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
301 | |
302 | /* --- @mpx_ucmp@ --- * |
303 | * |
304 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
305 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
306 | * |
307 | * Returns: Less than, equal to, or greater than zero depending on |
308 | * whether @a@ is less than, equal to or greater than @b@, |
309 | * respectively. |
310 | * |
311 | * Use: Performs an unsigned integer comparison. |
312 | */ |
313 | |
314 | #define MPX_UCMP(av, avl, op, dv, dvl) \ |
315 | (mpx_ucmp((av), (avl), (dv), (dvl)) op 0) |
316 | |
317 | extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/, |
318 | const mpw */*bv*/, const mpw */*bvl*/); |
319 | |
320 | /* --- @mpx_uadd@ --- * |
321 | * |
322 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
323 | * @const mpw *av, *avl@ = first addend vector base and limit |
324 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
325 | * |
326 | * Returns: --- |
327 | * |
328 | * Use: Performs unsigned integer addition. If the result overflows |
329 | * the destination vector, high-order bits are discarded. This |
330 | * means that two's complement addition happens more or less for |
331 | * free, although that's more a side-effect than anything else. |
332 | * The result vector may be equal to either or both source |
333 | * vectors, but may not otherwise overlap them. |
334 | */ |
335 | |
336 | extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, |
337 | const mpw */*av*/, const mpw */*avl*/, |
338 | const mpw */*bv*/, const mpw */*bvl*/); |
339 | |
340 | /* --- @mpx_usub@ --- * |
341 | * |
342 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
343 | * @const mpw *av, *avl@ = first argument vector base and limit |
344 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
345 | * |
346 | * Returns: --- |
347 | * |
348 | * Use: Performs unsigned integer subtraction. If the result |
349 | * overflows the destination vector, high-order bits are |
350 | * discarded. This means that two's complement subtraction |
351 | * happens more or less for free, althuogh that's more a side- |
352 | * effect than anything else. The result vector may be equal to |
353 | * either or both source vectors, but may not otherwise overlap |
354 | * them. |
355 | */ |
356 | |
357 | extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, |
358 | const mpw */*av*/, const mpw */*avl*/, |
359 | const mpw */*bv*/, const mpw */*bvl*/); |
360 | |
361 | /* --- @MPX_UMULN@ --- * |
362 | * |
363 | * Arguments: @dv, dvl@ = destination vector base and limit |
364 | * @av, avl@ = multiplicand vector base and limit |
365 | * @m@ = multiplier |
366 | * |
367 | * Use: Multiplies a multiprecision integer by a single-word value. |
368 | * The destination and source may be equal. The destination |
369 | * is completely cleared after use. |
370 | */ |
371 | |
372 | #define MPX_UMULN(dv, dvl, av, avl, m) do { \ |
373 | mpw *_dv = (dv), *_dvl = (dvl); \ |
374 | const mpw *_av = (av), *_avl = (avl); \ |
375 | mpw _c = 0; \ |
376 | mpd _m = (m); \ |
377 | \ |
378 | while (_av < _avl) { \ |
379 | mpd _x; \ |
380 | if (_dv >= _dvl) \ |
381 | break; \ |
382 | _x = _m * *_av++ + c; \ |
383 | *_dv++ = MPW(_x); \ |
384 | _c = _x >> MPW_BITS; \ |
385 | } \ |
386 | if (_dv < _dvl) { \ |
387 | *_dv++ = MPW(_c); \ |
388 | MPX_ZERO(_dv, _dvl); \ |
389 | } \ |
390 | } while (0) |
391 | |
392 | /* --- @MPX_UMLAN@ --- * |
393 | * |
394 | * Arguments: @dv, dvl@ = destination/accumulator vector base and limit |
395 | * @av, avl@ = multiplicand vector base and limit |
396 | * @m@ = multiplier |
397 | * |
398 | * Use: Multiplies a multiprecision integer by a single-word value |
399 | * and adds the result to an accumulator. |
400 | */ |
401 | |
402 | #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ |
403 | mpw *_dv = (dv), *_dvl = (dvl); \ |
404 | const mpw *_av = (av), *_avl = (avl); \ |
405 | mpw _c = 0; \ |
406 | mpd _m = (m); \ |
407 | \ |
408 | while (_av < _avl) { \ |
409 | mpd _x; \ |
410 | if (_dv >= _dvl) \ |
411 | break; \ |
412 | _x = *_dv + _m * *_av++ + _c; \ |
413 | *_dv++ = MPW(_x); \ |
414 | _c = _x >> MPW_BITS; \ |
415 | } \ |
416 | if (_dv < _dvl) { \ |
417 | *_dv++ = MPW(_c); \ |
418 | MPX_ZERO(_dv, _dvl); \ |
419 | } \ |
420 | } while (0) |
421 | |
422 | /* --- @mpx_umul@ --- * |
423 | * |
424 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
425 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
426 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
427 | * |
428 | * Returns: --- |
429 | * |
430 | * Use: Performs unsigned integer multiplication. If the result |
431 | * overflows the desination vector, high-order bits are |
432 | * discarded. The result vector may not overlap the argument |
433 | * vectors in any way. |
434 | */ |
435 | |
436 | extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, |
437 | const mpw */*av*/, const mpw */*avl*/, |
438 | const mpw */*bv*/, const mpw */*bvl*/); |
439 | |
440 | /* --- @mpx_udiv@ --- * |
441 | * |
442 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
443 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
444 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
445 | * |
446 | * Returns: --- |
447 | * |
448 | * Use: Performs unsigned integer division. If the result overflows |
449 | * the quotient vector, high-order bits are discarded. (Clearly |
450 | * the remainder vector can't overflow.) The various vectors |
451 | * may not overlap in any way. Yes, I know it's a bit odd |
452 | * requiring the dividend to be in the result position but it |
453 | * does make some sense really. |
454 | */ |
455 | |
456 | extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/, |
457 | const mpw */*dv*/, const mpw */*dvl*/); |
458 | |
459 | /*----- That's all, folks -------------------------------------------------*/ |
460 | |
461 | #ifdef __cplusplus |
462 | } |
463 | #endif |
464 | |
465 | #endif |