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1 | /* -*-c-*- |
2 | * |
75263f25 |
3 | * $Id: mpx.h,v 1.15 2002/10/19 17:56:50 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 $ |
75263f25 |
33 | * Revision 1.15 2002/10/19 17:56:50 mdw |
34 | * Fix bit operations. Test them (a bit) better. |
35 | * |
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36 | * Revision 1.14 2002/10/09 00:36:03 mdw |
37 | * Fix bounds on workspace for Karatsuba operations. |
38 | * |
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39 | * Revision 1.13 2002/10/06 22:52:50 mdw |
40 | * Pile of changes for supporting two's complement properly. |
41 | * |
0f32e0f8 |
42 | * Revision 1.12 2001/04/03 19:36:05 mdw |
43 | * Add some simple bitwise operations so that Perl can use them. |
44 | * |
52cdaca9 |
45 | * Revision 1.11 2000/10/08 15:48:35 mdw |
46 | * Rename Karatsuba constants now that we have @gfx_kmul@ too. |
47 | * |
1a05a8ef |
48 | * Revision 1.10 2000/10/08 12:06:12 mdw |
49 | * Provide @mpx_ueq@ for rapidly testing equality of two integers. |
50 | * |
698bd937 |
51 | * Revision 1.9 1999/12/22 15:49:07 mdw |
52 | * New function for division by a small integer. |
53 | * |
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54 | * Revision 1.8 1999/12/11 10:57:43 mdw |
55 | * Karatsuba squaring algorithm. |
56 | * |
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57 | * Revision 1.7 1999/12/11 01:51:28 mdw |
58 | * Change Karatsuba parameters slightly. |
59 | * |
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60 | * Revision 1.6 1999/12/10 23:23:51 mdw |
61 | * Karatsuba-Ofman multiplication algorithm. |
62 | * |
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63 | * Revision 1.5 1999/11/20 22:23:27 mdw |
64 | * Add function versions of some low-level macros with wider use. |
65 | * |
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66 | * Revision 1.4 1999/11/17 18:04:43 mdw |
67 | * Add two's complement support. Fix a bug in MPX_UMLAN. |
68 | * |
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69 | * Revision 1.3 1999/11/13 01:51:29 mdw |
70 | * Minor interface changes. Should be stable now. |
71 | * |
b9b1c853 |
72 | * Revision 1.2 1999/11/11 17:47:55 mdw |
73 | * Minor changes for different `mptypes.h' format. |
74 | * |
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75 | * Revision 1.1 1999/09/03 08:41:12 mdw |
76 | * Initial import. |
77 | * |
78 | */ |
79 | |
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80 | #ifndef CATACOMB_MPX_H |
81 | #define CATACOMB_MPX_H |
d03ab969 |
82 | |
83 | #ifdef __cplusplus |
84 | extern "C" { |
85 | #endif |
86 | |
87 | /*----- The idea ----------------------------------------------------------* |
88 | * |
89 | * This file provides functions and macros which work on vectors of words as |
90 | * unsigned multiprecision integers. The interface works in terms of base |
91 | * and limit pointers (i.e., a pointer to the start of a vector, and a |
92 | * pointer just past its end) rather than base pointer and length, because |
93 | * that requires more arithmetic and state to work on. |
94 | * |
95 | * The interfaces are slightly bizarre in other ways. Try to use the |
96 | * higher-level functions where you can: they're rather better designed to |
97 | * actually be friendly and useful. |
98 | */ |
99 | |
100 | /*----- Header files ------------------------------------------------------*/ |
101 | |
102 | #include <string.h> |
103 | |
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104 | #ifndef CATACOMB_MPW_H |
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105 | # include "mpw.h" |
d03ab969 |
106 | #endif |
107 | |
108 | /*----- General manipulation ----------------------------------------------*/ |
109 | |
110 | /* --- @MPX_SHRINK@ --- * |
111 | * |
112 | * Arguments: @const mpw *v@ = pointer to vector of words |
113 | * @const mpw *vl@ = (updated) current limit of vector |
114 | * |
115 | * Use: Shrinks down the limit of a multiprecision integer vector. |
116 | */ |
117 | |
118 | #define MPX_SHRINK(v, vl) do { \ |
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119 | const mpw *_vv = (v), *_vvl = (vl); \ |
120 | while (_vvl > _vv && !_vvl[-1]) \ |
121 | _vvl--; \ |
122 | (vl) = (mpw *)_vvl; \ |
d03ab969 |
123 | } while (0) |
124 | |
125 | /* --- @MPX_BITS@ --- * |
126 | * |
127 | * Arguments: @unsigned long b@ = result variable |
128 | * @const mpw *v@ = pointer to array of words |
129 | * @const mpw *vl@ = limit of vector (from @MPX_SHRINK@) |
130 | * |
131 | * Use: Calculates the number of bits in a multiprecision value. |
132 | */ |
133 | |
134 | #define MPX_BITS(b, v, vl) do { \ |
135 | const mpw *_v = (v), *_vl = (vl); \ |
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136 | MPX_SHRINK(_v, _vl); \ |
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137 | if (_v == _vl) \ |
138 | (b) = 0; \ |
139 | else { \ |
140 | unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \ |
141 | mpw _w = _vl[-1]; \ |
142 | unsigned _k = MPW_BITS / 2; \ |
143 | while (_k) { \ |
144 | if (_w >> _k) { \ |
145 | _w >>= _k; \ |
146 | _b += _k; \ |
147 | } \ |
148 | _k >>= 1; \ |
149 | } \ |
150 | (b) = _b; \ |
151 | } \ |
152 | } while (0) |
153 | |
154 | /* --- @MPX_OCTETS@ --- * |
155 | * |
156 | * Arguments: @size_t o@ = result variable |
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157 | * @const mpw *v, *vl@ = pointer to array of words |
d03ab969 |
158 | * |
159 | * Use: Calculates the number of octets in a multiprecision value. |
160 | */ |
161 | |
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162 | #define MPX_OCTETS(o, v, vl) do { \ |
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163 | unsigned long _bb; \ |
164 | MPX_BITS(_bb, (v), (vl)); \ |
165 | (o) = (_bb + 7) >> 3; \ |
166 | } while (0) |
167 | |
168 | /* --- @MPX_OCTETS2C@ --- * |
169 | * |
170 | * Arguments: @size_t o@ = result variable |
171 | * @const mpw *v, *vl@ = pointer to array of words |
172 | * |
173 | * Use: Calculates the number of octets in a multiprecision value, if |
174 | * you represent it as two's complement. |
175 | */ |
176 | |
177 | #define MPX_OCTETS2C(o, v, vl) do { \ |
178 | unsigned long _bb; \ |
179 | MPX_BITS(_bb, (v), (vl)); \ |
180 | (o) = (_bb >> 3) + 1; \ |
d03ab969 |
181 | } while (0) |
182 | |
183 | /* --- @MPX_COPY@ --- * |
184 | * |
185 | * Arguments: @dv, dvl@ = destination vector base and limit |
186 | * @av, avl@ = source vector base and limit |
187 | * |
188 | * Use: Copies a multiprecision integer. |
189 | */ |
190 | |
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191 | #define MPX_COPY(dv, dvl, av, avl) do { \ |
192 | mpw *_dv = (dv), *_dvl = (dvl); \ |
193 | size_t _dn = _dvl - _dv; \ |
194 | const mpw *_av = (av), *_avl = (avl); \ |
195 | size_t _an = _avl - _av; \ |
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196 | if (_av == _dv) { \ |
197 | if (_dvl > _avl) \ |
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198 | memset(_dv, 0, MPWS(_dn - _an)); \ |
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199 | } else if (_an >= _dn) \ |
200 | memmove(_dv, _av, MPWS(_dn)); \ |
201 | else { \ |
202 | memmove(_dv, _av, MPWS(_an)); \ |
203 | memset(_dv + _an, 0, MPWS(_dn - _an)); \ |
204 | } \ |
205 | } while (0) |
206 | |
207 | /* --- @MPX_ZERO@ --- * |
208 | * |
209 | * Arguments: @v, vl@ = base and limit of vector to clear |
210 | * |
211 | * Use: Zeroes the area between the two vector pointers. |
212 | */ |
213 | |
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214 | #define MPX_ZERO(v, vl) do { \ |
d03ab969 |
215 | mpw *_v = (v), *_vl = (vl); \ |
3c9ede17 |
216 | if (_v < _vl) \ |
217 | memset(_v, 0, MPWS(_vl - _v)); \ |
d03ab969 |
218 | } while (0) |
219 | |
220 | /*----- Loading and storing -----------------------------------------------*/ |
221 | |
222 | /* --- @mpx_storel@ --- * |
223 | * |
224 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
3c9ede17 |
225 | * @void *p@ = pointer to octet array |
d03ab969 |
226 | * @size_t sz@ = size of octet array |
227 | * |
228 | * Returns: --- |
229 | * |
230 | * Use: Stores an MP in an octet array, least significant octet |
231 | * first. High-end octets are silently discarded if there |
232 | * isn't enough space for them. |
233 | */ |
234 | |
235 | extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
236 | void */*p*/, size_t /*sz*/); |
d03ab969 |
237 | |
238 | /* --- @mpx_loadl@ --- * |
239 | * |
240 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
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241 | * @const void *p@ = pointer to octet array |
d03ab969 |
242 | * @size_t sz@ = size of octet array |
243 | * |
244 | * Returns: --- |
245 | * |
246 | * Use: Loads an MP in an octet array, least significant octet |
247 | * first. High-end octets are ignored if there isn't enough |
248 | * space for them. |
249 | */ |
250 | |
251 | extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
252 | const void */*p*/, size_t /*sz*/); |
d03ab969 |
253 | |
254 | /* --- @mpx_storeb@ --- * |
255 | * |
256 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
3c9ede17 |
257 | * @void *p@ = pointer to octet array |
d03ab969 |
258 | * @size_t sz@ = size of octet array |
259 | * |
260 | * Returns: --- |
261 | * |
262 | * Use: Stores an MP in an octet array, most significant octet |
263 | * first. High-end octets are silently discarded if there |
264 | * isn't enough space for them. |
265 | */ |
266 | |
267 | extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
268 | void */*p*/, size_t /*sz*/); |
d03ab969 |
269 | |
270 | /* --- @mpx_loadb@ --- * |
271 | * |
272 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
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273 | * @const void *p@ = pointer to octet array |
d03ab969 |
274 | * @size_t sz@ = size of octet array |
275 | * |
276 | * Returns: --- |
277 | * |
278 | * Use: Loads an MP in an octet array, most significant octet |
279 | * first. High-end octets are ignored if there isn't enough |
280 | * space for them. |
281 | */ |
282 | |
283 | extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
284 | const void */*p*/, size_t /*sz*/); |
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285 | |
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286 | /* --- @mpx_storel2cn@ --- * |
287 | * |
288 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
289 | * @void *pp@ = pointer to octet array |
290 | * @size_t sz@ = size of octet array |
291 | * |
292 | * Returns: --- |
293 | * |
294 | * Use: Stores a negative MP in an octet array, least significant |
295 | * octet first, as two's complement. High-end octets are |
296 | * silently discarded if there isn't enough space for them. |
297 | * This obviously makes the output bad. |
298 | */ |
299 | |
300 | extern void mpx_storel2cn(const mpw */*v*/, const mpw */*vl*/, |
301 | void */*p*/, size_t /*sz*/); |
302 | |
303 | /* --- @mpx_loadl2cn@ --- * |
304 | * |
305 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
306 | * @const void *pp@ = pointer to octet array |
307 | * @size_t sz@ = size of octet array |
308 | * |
309 | * Returns: --- |
310 | * |
311 | * Use: Loads a negative MP in an octet array, least significant |
312 | * octet first, as two's complement. High-end octets are |
313 | * ignored if there isn't enough space for them. This probably |
314 | * means you made the wrong choice coming here. |
315 | */ |
316 | |
317 | extern void mpx_loadl2cn(mpw */*v*/, mpw */*vl*/, |
318 | const void */*p*/, size_t /*sz*/); |
319 | |
320 | /* --- @mpx_storeb2cn@ --- * |
321 | * |
322 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
323 | * @void *pp@ = pointer to octet array |
324 | * @size_t sz@ = size of octet array |
325 | * |
326 | * Returns: --- |
327 | * |
328 | * Use: Stores a negative MP in an octet array, most significant |
329 | * octet first, as two's complement. High-end octets are |
330 | * silently discarded if there isn't enough space for them, |
331 | * which probably isn't what you meant. |
332 | */ |
333 | |
334 | extern void mpx_storeb2cn(const mpw */*v*/, const mpw */*vl*/, |
335 | void */*p*/, size_t /*sz*/); |
336 | |
337 | /* --- @mpx_loadb2cn@ --- * |
338 | * |
339 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
340 | * @const void *pp@ = pointer to octet array |
341 | * @size_t sz@ = size of octet array |
342 | * |
343 | * Returns: --- |
344 | * |
345 | * Use: Loads a negative MP in an octet array, most significant octet |
346 | * first as two's complement. High-end octets are ignored if |
347 | * there isn't enough space for them. This probably means you |
348 | * chose this function wrongly. |
349 | */ |
350 | |
351 | extern void mpx_loadb2cn(mpw */*v*/, mpw */*vl*/, |
352 | const void */*p*/, size_t /*sz*/); |
353 | |
354 | |
d03ab969 |
355 | /*----- Logical shifting --------------------------------------------------*/ |
356 | |
357 | /* --- @mpx_lsl@ --- * |
358 | * |
359 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
360 | * @const mpw *av, *avl@ = source vector base and limit |
361 | * @size_t n@ = number of bit positions to shift by |
362 | * |
363 | * Returns: --- |
364 | * |
365 | * Use: Performs a logical shift left operation on an integer. |
366 | */ |
367 | |
368 | extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/, |
369 | const mpw */*av*/, const mpw */*avl*/, |
370 | size_t /*n*/); |
371 | |
372 | /* --- @mpx_lsr@ --- * |
373 | * |
374 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
375 | * @const mpw *av, *avl@ = source vector base and limit |
376 | * @size_t n@ = number of bit positions to shift by |
377 | * |
378 | * Returns: --- |
379 | * |
380 | * Use: Performs a logical shift right operation on an integer. |
381 | */ |
382 | |
383 | extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/, |
384 | const mpw */*av*/, const mpw */*avl*/, |
385 | size_t /*n*/); |
386 | |
0f32e0f8 |
387 | /*----- Bitwise operations ------------------------------------------------*/ |
388 | |
f09e814a |
389 | /* --- @mpx_bitop@ --- * |
0f32e0f8 |
390 | * |
391 | * Arguments: @mpw *dv, *dvl@ = destination vector |
392 | * @const mpw *av, *avl@ = first source vector |
393 | * @const mpw *bv, *bvl@ = second source vector |
394 | * |
395 | * Returns: --- |
396 | * |
f09e814a |
397 | * Use: Provide the dyadic boolean functions. The functions are |
398 | * named after the truth table they generate: |
399 | * |
400 | * a: 0011 |
401 | * b: 0101 |
402 | * @mpx_bitXXXX@ |
0f32e0f8 |
403 | */ |
404 | |
f09e814a |
405 | #define MPX_DOBIN(what) \ |
406 | what(0000) what(0001) what(0010) what(0011) \ |
407 | what(0100) what(0101) what(0110) what(0111) \ |
408 | what(1000) what(1001) what(1010) what(1011) \ |
409 | what(1100) what(1101) what(1110) what(1111) |
0f32e0f8 |
410 | |
f09e814a |
411 | #define MPX_BITDECL(string) \ |
412 | extern void mpx_bit##string(mpw */*dv*/, mpw */*dvl*/, \ |
413 | const mpw */*av*/, const mpw */*avl*/, \ |
414 | const mpw */*bv*/, const mpw */*bvl*/); |
415 | MPX_DOBIN(MPX_BITDECL) |
0f32e0f8 |
416 | |
f09e814a |
417 | /* --- @mpx_[n]and@, @mpx_[n]or@, @mpx_xor@ --- * |
418 | * |
419 | * Synonyms for the commonly-used functions above. |
420 | */ |
421 | |
422 | #define mpx_and mpx_bit0001 |
423 | #define mpx_or mpx_bit0111 |
424 | #define mpx_nand mpx_bit1110 |
425 | #define mpx_nor mpx_bit1000 |
426 | #define mpx_xor mpx_bit0110 |
427 | |
428 | /* --- @mpx_not@ --- * |
429 | * |
430 | * Arguments: @mpw *dv, *dvl@ = destination vector |
431 | * @const mpw *av, *avl@ = first source vector |
432 | * |
433 | * Returns: --- |
434 | * |
435 | * Use; Bitwise NOT. |
436 | */ |
0f32e0f8 |
437 | |
438 | extern void mpx_not(mpw */*dv*/, mpw */*dvl*/, |
439 | const mpw */*av*/, const mpw */*avl*/); |
440 | |
d03ab969 |
441 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
442 | |
7c13f461 |
443 | /* --- @mpx_2c@ --- * |
444 | * |
445 | * Arguments: @mpw *dv, *dvl@ = destination vector |
446 | * @const mpw *v, *vl@ = source vector |
447 | * |
448 | * Returns: --- |
449 | * |
450 | * Use: Calculates the two's complement of @v@. |
451 | */ |
452 | |
453 | extern void mpx_2c(mpw */*dv*/, mpw */*dvl*/, |
454 | const mpw */*v*/, const mpw */*vl*/); |
455 | |
1a05a8ef |
456 | /* --- @mpx_ueq@ --- * |
457 | * |
458 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
459 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
460 | * |
461 | * Returns: Nonzero if the two vectors are equal. |
462 | * |
463 | * Use: Performs an unsigned integer test for equality. |
464 | */ |
465 | |
466 | extern int mpx_ueq(const mpw */*av*/, const mpw */*avl*/, |
467 | const mpw */*bv*/, const mpw */*bvl*/); |
468 | |
d03ab969 |
469 | /* --- @mpx_ucmp@ --- * |
470 | * |
471 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
472 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
473 | * |
474 | * Returns: Less than, equal to, or greater than zero depending on |
475 | * whether @a@ is less than, equal to or greater than @b@, |
476 | * respectively. |
477 | * |
478 | * Use: Performs an unsigned integer comparison. |
479 | */ |
480 | |
481 | #define MPX_UCMP(av, avl, op, dv, dvl) \ |
482 | (mpx_ucmp((av), (avl), (dv), (dvl)) op 0) |
483 | |
484 | extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/, |
485 | const mpw */*bv*/, const mpw */*bvl*/); |
486 | |
487 | /* --- @mpx_uadd@ --- * |
488 | * |
489 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
490 | * @const mpw *av, *avl@ = first addend vector base and limit |
491 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
492 | * |
493 | * Returns: --- |
494 | * |
495 | * Use: Performs unsigned integer addition. If the result overflows |
496 | * the destination vector, high-order bits are discarded. This |
497 | * means that two's complement addition happens more or less for |
498 | * free, although that's more a side-effect than anything else. |
499 | * The result vector may be equal to either or both source |
500 | * vectors, but may not otherwise overlap them. |
501 | */ |
502 | |
503 | extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, |
504 | const mpw */*av*/, const mpw */*avl*/, |
505 | const mpw */*bv*/, const mpw */*bvl*/); |
506 | |
dd517851 |
507 | /* --- @mpx_uaddn@ --- * |
508 | * |
509 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
510 | * @mpw n@ = other addend |
3c9ede17 |
511 | * |
dd517851 |
512 | * Returns: --- |
3c9ede17 |
513 | * |
514 | * Use: Adds a small integer to a multiprecision number. |
515 | */ |
516 | |
517 | #define MPX_UADDN(dv, dvl, n) do { \ |
518 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
519 | mpw _c = (n); \ |
520 | \ |
521 | while (_c && _ddv < _ddvl) { \ |
522 | mpd _x = (mpd)*_ddv + (mpd)_c; \ |
523 | *_ddv++ = MPW(_x); \ |
524 | _c = _x >> MPW_BITS; \ |
525 | } \ |
526 | } while (0) |
527 | |
dd517851 |
528 | extern void mpx_uaddn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
529 | |
d03ab969 |
530 | /* --- @mpx_usub@ --- * |
531 | * |
532 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
533 | * @const mpw *av, *avl@ = first argument vector base and limit |
534 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
535 | * |
536 | * Returns: --- |
537 | * |
538 | * Use: Performs unsigned integer subtraction. If the result |
539 | * overflows the destination vector, high-order bits are |
540 | * discarded. This means that two's complement subtraction |
3c9ede17 |
541 | * happens more or less for free, although that's more a side- |
d03ab969 |
542 | * effect than anything else. The result vector may be equal to |
543 | * either or both source vectors, but may not otherwise overlap |
544 | * them. |
545 | */ |
546 | |
547 | extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, |
548 | const mpw */*av*/, const mpw */*avl*/, |
549 | const mpw */*bv*/, const mpw */*bvl*/); |
550 | |
dd517851 |
551 | /* --- @mpx_usubn@ --- * |
3c9ede17 |
552 | * |
dd517851 |
553 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
554 | * @n@ = subtrahend |
555 | * |
556 | * Returns: --- |
3c9ede17 |
557 | * |
558 | * Use: Subtracts a small integer from a multiprecision number. |
559 | */ |
560 | |
561 | #define MPX_USUBN(dv, dvl, n) do { \ |
562 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
563 | mpw _c = (n); \ |
564 | \ |
565 | while (_ddv < _ddvl) { \ |
566 | mpd _x = (mpd)*_ddv - (mpd)_c; \ |
567 | *_ddv++ = MPW(_x); \ |
568 | if (_x >> MPW_BITS) \ |
569 | _c = 1; \ |
570 | else \ |
571 | break; \ |
572 | } \ |
573 | } while (0) |
574 | |
dd517851 |
575 | extern void mpx_usubn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
576 | |
3c9ede17 |
577 | /* --- @mpx_umul@ --- * |
578 | * |
579 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
580 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
581 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
582 | * |
583 | * Returns: --- |
584 | * |
585 | * Use: Performs unsigned integer multiplication. If the result |
586 | * overflows the desination vector, high-order bits are |
587 | * discarded. The result vector may not overlap the argument |
588 | * vectors in any way. |
589 | */ |
590 | |
591 | extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, |
592 | const mpw */*av*/, const mpw */*avl*/, |
593 | const mpw */*bv*/, const mpw */*bvl*/); |
594 | |
dd517851 |
595 | /* --- @mpx_umuln@ --- * |
d03ab969 |
596 | * |
dd517851 |
597 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
598 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
599 | * @mpw m@ = multiplier |
600 | * |
601 | * Returns: --- |
d03ab969 |
602 | * |
603 | * Use: Multiplies a multiprecision integer by a single-word value. |
604 | * The destination and source may be equal. The destination |
605 | * is completely cleared after use. |
606 | */ |
607 | |
608 | #define MPX_UMULN(dv, dvl, av, avl, m) do { \ |
609 | mpw *_dv = (dv), *_dvl = (dvl); \ |
610 | const mpw *_av = (av), *_avl = (avl); \ |
611 | mpw _c = 0; \ |
612 | mpd _m = (m); \ |
613 | \ |
614 | while (_av < _avl) { \ |
615 | mpd _x; \ |
616 | if (_dv >= _dvl) \ |
617 | break; \ |
3c9ede17 |
618 | _x = (mpd)_m * (mpd)*_av++ + _c; \ |
d03ab969 |
619 | *_dv++ = MPW(_x); \ |
620 | _c = _x >> MPW_BITS; \ |
621 | } \ |
622 | if (_dv < _dvl) { \ |
623 | *_dv++ = MPW(_c); \ |
624 | MPX_ZERO(_dv, _dvl); \ |
625 | } \ |
626 | } while (0) |
627 | |
dd517851 |
628 | extern void mpx_umuln(mpw */*dv*/, mpw */*dvl*/, |
629 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
630 | |
631 | /* --- @mpx_umlan@ --- * |
d03ab969 |
632 | * |
dd517851 |
633 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
634 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
635 | * @mpw m@ = multiplier |
636 | * |
637 | * Returns: --- |
d03ab969 |
638 | * |
639 | * Use: Multiplies a multiprecision integer by a single-word value |
640 | * and adds the result to an accumulator. |
641 | */ |
642 | |
643 | #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ |
644 | mpw *_dv = (dv), *_dvl = (dvl); \ |
645 | const mpw *_av = (av), *_avl = (avl); \ |
7c13f461 |
646 | mpw _cc = 0; \ |
d03ab969 |
647 | mpd _m = (m); \ |
648 | \ |
5bf74dea |
649 | while (_dv < _dvl && _av < _avl) { \ |
d03ab969 |
650 | mpd _x; \ |
7c13f461 |
651 | _x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \ |
d03ab969 |
652 | *_dv++ = MPW(_x); \ |
7c13f461 |
653 | _cc = _x >> MPW_BITS; \ |
d03ab969 |
654 | } \ |
7c13f461 |
655 | MPX_UADDN(_dv, _dvl, _cc); \ |
d03ab969 |
656 | } while (0) |
657 | |
dd517851 |
658 | extern void mpx_umlan(mpw */*dv*/, mpw */*dvl*/, |
659 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
660 | |
3c9ede17 |
661 | /* --- @mpx_usqr@ --- * |
d03ab969 |
662 | * |
663 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
3c9ede17 |
664 | * @const mpw *av, *av@ = source vector base and limit |
d03ab969 |
665 | * |
666 | * Returns: --- |
667 | * |
3c9ede17 |
668 | * Use: Performs unsigned integer squaring. The result vector must |
669 | * not overlap the source vector in any way. |
d03ab969 |
670 | */ |
671 | |
3c9ede17 |
672 | extern void mpx_usqr(mpw */*dv*/, mpw */*dvl*/, |
673 | const mpw */*av*/, const mpw */*avl*/); |
d03ab969 |
674 | |
5bf74dea |
675 | /* --- @mpx_udiv@ --- * |
676 | * |
677 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
678 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
679 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
680 | * @mpw *sv, *svl@ = scratch workspace |
681 | * |
682 | * Returns: --- |
683 | * |
684 | * Use: Performs unsigned integer division. If the result overflows |
685 | * the quotient vector, high-order bits are discarded. (Clearly |
686 | * the remainder vector can't overflow.) The various vectors |
687 | * may not overlap in any way. Yes, I know it's a bit odd |
688 | * requiring the dividend to be in the result position but it |
689 | * does make some sense really. The remainder must have |
690 | * headroom for at least two extra words. The scratch space |
691 | * must be at least one word larger than the divisor. |
692 | */ |
693 | |
694 | extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/, |
695 | const mpw */*dv*/, const mpw */*dvl*/, |
696 | mpw */*sv*/, mpw */*svl*/); |
697 | |
698bd937 |
698 | /* --- @mpx_udivn@ --- * |
699 | * |
700 | * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap |
701 | * dividend) |
702 | * @const mpw *rv, *rvl@ = dividend |
703 | * @mpw d@ = single-precision divisor |
704 | * |
705 | * Returns: Remainder after divison. |
706 | * |
707 | * Use: Performs a single-precision division operation. |
708 | */ |
709 | |
710 | extern mpw mpx_udivn(mpw */*qv*/, mpw */*qvl*/, |
711 | const mpw */*rv*/, const mpw */*rvl*/, mpw /*d*/); |
712 | |
5bf74dea |
713 | /*----- Karatsuba multiplication algorithms -------------------------------*/ |
714 | |
52cdaca9 |
715 | /* --- @MPK_THRESH@ --- * |
5bf74dea |
716 | * |
717 | * This is the limiting length for using Karatsuba algorithms. It's best to |
718 | * use the simpler classical multiplication method on numbers smaller than |
dd22938e |
719 | * this. It is unsafe to make this constant less than four (i.e., the |
720 | * algorithms will fail). |
5bf74dea |
721 | */ |
722 | |
52cdaca9 |
723 | #define MPK_THRESH 16 |
5bf74dea |
724 | |
a86e33af |
725 | /* --- @mpx_kmul@ --- * |
726 | * |
727 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
728 | * @const mpw *av, *avl@ = pointer to first argument |
729 | * @const mpw *bv, *bvl@ = pointer to second argument |
730 | * @mpw *sv, *svl@ = pointer to scratch workspace |
731 | * |
732 | * Returns: --- |
733 | * |
734 | * Use: Multiplies two multiprecision integers using Karatsuba's |
735 | * algorithm. This is rather faster than traditional long |
736 | * multiplication (e.g., @mpx_umul@) on large numbers, although |
737 | * more expensive on small ones. |
738 | * |
dd22938e |
739 | * The destination must be three times as large as the larger |
740 | * argument. The scratch space must be five times as large as |
741 | * the larger argument. |
a86e33af |
742 | */ |
743 | |
a86e33af |
744 | extern void mpx_kmul(mpw */*dv*/, mpw */*dvl*/, |
745 | const mpw */*av*/, const mpw */*avl*/, |
746 | const mpw */*bv*/, const mpw */*bvl*/, |
747 | mpw */*sv*/, mpw */*svl*/); |
748 | |
5bf74dea |
749 | /* --- @mpx_ksqr@ --- * |
d03ab969 |
750 | * |
5bf74dea |
751 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
752 | * @const mpw *av, *avl@ = pointer to first argument |
753 | * @mpw *sv, *svl@ = pointer to scratch workspace |
d03ab969 |
754 | * |
755 | * Returns: --- |
756 | * |
5bf74dea |
757 | * Use: Squares a multiprecision integers using something similar to |
758 | * Karatsuba's multiplication algorithm. This is rather faster |
759 | * than traditional long multiplication (e.g., @mpx_umul@) on |
760 | * large numbers, although more expensive on small ones, and |
761 | * rather simpler than full-blown Karatsuba multiplication. |
762 | * |
dd22938e |
763 | * The destination must be three times as large as the larger |
764 | * argument. The scratch space must be five times as large as |
765 | * the larger argument. |
d03ab969 |
766 | */ |
767 | |
5bf74dea |
768 | extern void mpx_ksqr(mpw */*dv*/, mpw */*dvl*/, |
769 | const mpw */*av*/, const mpw */*avl*/, |
3c9ede17 |
770 | mpw */*sv*/, mpw */*svl*/); |
d03ab969 |
771 | |
772 | /*----- That's all, folks -------------------------------------------------*/ |
773 | |
774 | #ifdef __cplusplus |
775 | } |
776 | #endif |
777 | |
778 | #endif |