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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mpx.h,v 1.13 2002/10/06 22:52:50 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 $ |
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33 | * Revision 1.13 2002/10/06 22:52:50 mdw |
34 | * Pile of changes for supporting two's complement properly. |
35 | * |
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36 | * Revision 1.12 2001/04/03 19:36:05 mdw |
37 | * Add some simple bitwise operations so that Perl can use them. |
38 | * |
52cdaca9 |
39 | * Revision 1.11 2000/10/08 15:48:35 mdw |
40 | * Rename Karatsuba constants now that we have @gfx_kmul@ too. |
41 | * |
1a05a8ef |
42 | * Revision 1.10 2000/10/08 12:06:12 mdw |
43 | * Provide @mpx_ueq@ for rapidly testing equality of two integers. |
44 | * |
698bd937 |
45 | * Revision 1.9 1999/12/22 15:49:07 mdw |
46 | * New function for division by a small integer. |
47 | * |
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48 | * Revision 1.8 1999/12/11 10:57:43 mdw |
49 | * Karatsuba squaring algorithm. |
50 | * |
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51 | * Revision 1.7 1999/12/11 01:51:28 mdw |
52 | * Change Karatsuba parameters slightly. |
53 | * |
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54 | * Revision 1.6 1999/12/10 23:23:51 mdw |
55 | * Karatsuba-Ofman multiplication algorithm. |
56 | * |
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57 | * Revision 1.5 1999/11/20 22:23:27 mdw |
58 | * Add function versions of some low-level macros with wider use. |
59 | * |
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60 | * Revision 1.4 1999/11/17 18:04:43 mdw |
61 | * Add two's complement support. Fix a bug in MPX_UMLAN. |
62 | * |
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63 | * Revision 1.3 1999/11/13 01:51:29 mdw |
64 | * Minor interface changes. Should be stable now. |
65 | * |
b9b1c853 |
66 | * Revision 1.2 1999/11/11 17:47:55 mdw |
67 | * Minor changes for different `mptypes.h' format. |
68 | * |
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69 | * Revision 1.1 1999/09/03 08:41:12 mdw |
70 | * Initial import. |
71 | * |
72 | */ |
73 | |
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74 | #ifndef CATACOMB_MPX_H |
75 | #define CATACOMB_MPX_H |
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76 | |
77 | #ifdef __cplusplus |
78 | extern "C" { |
79 | #endif |
80 | |
81 | /*----- The idea ----------------------------------------------------------* |
82 | * |
83 | * This file provides functions and macros which work on vectors of words as |
84 | * unsigned multiprecision integers. The interface works in terms of base |
85 | * and limit pointers (i.e., a pointer to the start of a vector, and a |
86 | * pointer just past its end) rather than base pointer and length, because |
87 | * that requires more arithmetic and state to work on. |
88 | * |
89 | * The interfaces are slightly bizarre in other ways. Try to use the |
90 | * higher-level functions where you can: they're rather better designed to |
91 | * actually be friendly and useful. |
92 | */ |
93 | |
94 | /*----- Header files ------------------------------------------------------*/ |
95 | |
96 | #include <string.h> |
97 | |
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98 | #ifndef CATACOMB_MPW_H |
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99 | # include "mpw.h" |
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100 | #endif |
101 | |
102 | /*----- General manipulation ----------------------------------------------*/ |
103 | |
104 | /* --- @MPX_SHRINK@ --- * |
105 | * |
106 | * Arguments: @const mpw *v@ = pointer to vector of words |
107 | * @const mpw *vl@ = (updated) current limit of vector |
108 | * |
109 | * Use: Shrinks down the limit of a multiprecision integer vector. |
110 | */ |
111 | |
112 | #define MPX_SHRINK(v, vl) do { \ |
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113 | const mpw *_vv = (v), *_vvl = (vl); \ |
114 | while (_vvl > _vv && !_vvl[-1]) \ |
115 | _vvl--; \ |
116 | (vl) = (mpw *)_vvl; \ |
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117 | } while (0) |
118 | |
119 | /* --- @MPX_BITS@ --- * |
120 | * |
121 | * Arguments: @unsigned long b@ = result variable |
122 | * @const mpw *v@ = pointer to array of words |
123 | * @const mpw *vl@ = limit of vector (from @MPX_SHRINK@) |
124 | * |
125 | * Use: Calculates the number of bits in a multiprecision value. |
126 | */ |
127 | |
128 | #define MPX_BITS(b, v, vl) do { \ |
129 | const mpw *_v = (v), *_vl = (vl); \ |
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130 | MPX_SHRINK(_v, _vl); \ |
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131 | if (_v == _vl) \ |
132 | (b) = 0; \ |
133 | else { \ |
134 | unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \ |
135 | mpw _w = _vl[-1]; \ |
136 | unsigned _k = MPW_BITS / 2; \ |
137 | while (_k) { \ |
138 | if (_w >> _k) { \ |
139 | _w >>= _k; \ |
140 | _b += _k; \ |
141 | } \ |
142 | _k >>= 1; \ |
143 | } \ |
144 | (b) = _b; \ |
145 | } \ |
146 | } while (0) |
147 | |
148 | /* --- @MPX_OCTETS@ --- * |
149 | * |
150 | * Arguments: @size_t o@ = result variable |
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151 | * @const mpw *v, *vl@ = pointer to array of words |
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152 | * |
153 | * Use: Calculates the number of octets in a multiprecision value. |
154 | */ |
155 | |
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156 | #define MPX_OCTETS(o, v, vl) do { \ |
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157 | unsigned long _bb; \ |
158 | MPX_BITS(_bb, (v), (vl)); \ |
159 | (o) = (_bb + 7) >> 3; \ |
160 | } while (0) |
161 | |
162 | /* --- @MPX_OCTETS2C@ --- * |
163 | * |
164 | * Arguments: @size_t o@ = result variable |
165 | * @const mpw *v, *vl@ = pointer to array of words |
166 | * |
167 | * Use: Calculates the number of octets in a multiprecision value, if |
168 | * you represent it as two's complement. |
169 | */ |
170 | |
171 | #define MPX_OCTETS2C(o, v, vl) do { \ |
172 | unsigned long _bb; \ |
173 | MPX_BITS(_bb, (v), (vl)); \ |
174 | (o) = (_bb >> 3) + 1; \ |
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175 | } while (0) |
176 | |
177 | /* --- @MPX_COPY@ --- * |
178 | * |
179 | * Arguments: @dv, dvl@ = destination vector base and limit |
180 | * @av, avl@ = source vector base and limit |
181 | * |
182 | * Use: Copies a multiprecision integer. |
183 | */ |
184 | |
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185 | #define MPX_COPY(dv, dvl, av, avl) do { \ |
186 | mpw *_dv = (dv), *_dvl = (dvl); \ |
187 | size_t _dn = _dvl - _dv; \ |
188 | const mpw *_av = (av), *_avl = (avl); \ |
189 | size_t _an = _avl - _av; \ |
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190 | if (_av == _dv) { \ |
191 | if (_dvl > _avl) \ |
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192 | memset(_dv, 0, MPWS(_dn - _an)); \ |
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193 | } else if (_an >= _dn) \ |
194 | memmove(_dv, _av, MPWS(_dn)); \ |
195 | else { \ |
196 | memmove(_dv, _av, MPWS(_an)); \ |
197 | memset(_dv + _an, 0, MPWS(_dn - _an)); \ |
198 | } \ |
199 | } while (0) |
200 | |
201 | /* --- @MPX_ZERO@ --- * |
202 | * |
203 | * Arguments: @v, vl@ = base and limit of vector to clear |
204 | * |
205 | * Use: Zeroes the area between the two vector pointers. |
206 | */ |
207 | |
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208 | #define MPX_ZERO(v, vl) do { \ |
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209 | mpw *_v = (v), *_vl = (vl); \ |
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210 | if (_v < _vl) \ |
211 | memset(_v, 0, MPWS(_vl - _v)); \ |
d03ab969 |
212 | } while (0) |
213 | |
214 | /*----- Loading and storing -----------------------------------------------*/ |
215 | |
216 | /* --- @mpx_storel@ --- * |
217 | * |
218 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
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219 | * @void *p@ = pointer to octet array |
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220 | * @size_t sz@ = size of octet array |
221 | * |
222 | * Returns: --- |
223 | * |
224 | * Use: Stores an MP in an octet array, least significant octet |
225 | * first. High-end octets are silently discarded if there |
226 | * isn't enough space for them. |
227 | */ |
228 | |
229 | extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
230 | void */*p*/, size_t /*sz*/); |
d03ab969 |
231 | |
232 | /* --- @mpx_loadl@ --- * |
233 | * |
234 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
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235 | * @const void *p@ = pointer to octet array |
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236 | * @size_t sz@ = size of octet array |
237 | * |
238 | * Returns: --- |
239 | * |
240 | * Use: Loads an MP in an octet array, least significant octet |
241 | * first. High-end octets are ignored if there isn't enough |
242 | * space for them. |
243 | */ |
244 | |
245 | extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
246 | const void */*p*/, size_t /*sz*/); |
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247 | |
248 | /* --- @mpx_storeb@ --- * |
249 | * |
250 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
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251 | * @void *p@ = pointer to octet array |
d03ab969 |
252 | * @size_t sz@ = size of octet array |
253 | * |
254 | * Returns: --- |
255 | * |
256 | * Use: Stores an MP in an octet array, most significant octet |
257 | * first. High-end octets are silently discarded if there |
258 | * isn't enough space for them. |
259 | */ |
260 | |
261 | extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, |
3c9ede17 |
262 | void */*p*/, size_t /*sz*/); |
d03ab969 |
263 | |
264 | /* --- @mpx_loadb@ --- * |
265 | * |
266 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
3c9ede17 |
267 | * @const void *p@ = pointer to octet array |
d03ab969 |
268 | * @size_t sz@ = size of octet array |
269 | * |
270 | * Returns: --- |
271 | * |
272 | * Use: Loads an MP in an octet array, most significant octet |
273 | * first. High-end octets are ignored if there isn't enough |
274 | * space for them. |
275 | */ |
276 | |
277 | extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, |
3c9ede17 |
278 | const void */*p*/, size_t /*sz*/); |
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279 | |
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280 | /* --- @mpx_storel2cn@ --- * |
281 | * |
282 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
283 | * @void *pp@ = pointer to octet array |
284 | * @size_t sz@ = size of octet array |
285 | * |
286 | * Returns: --- |
287 | * |
288 | * Use: Stores a negative MP in an octet array, least significant |
289 | * octet first, as two's complement. High-end octets are |
290 | * silently discarded if there isn't enough space for them. |
291 | * This obviously makes the output bad. |
292 | */ |
293 | |
294 | extern void mpx_storel2cn(const mpw */*v*/, const mpw */*vl*/, |
295 | void */*p*/, size_t /*sz*/); |
296 | |
297 | /* --- @mpx_loadl2cn@ --- * |
298 | * |
299 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
300 | * @const void *pp@ = pointer to octet array |
301 | * @size_t sz@ = size of octet array |
302 | * |
303 | * Returns: --- |
304 | * |
305 | * Use: Loads a negative MP in an octet array, least significant |
306 | * octet first, as two's complement. High-end octets are |
307 | * ignored if there isn't enough space for them. This probably |
308 | * means you made the wrong choice coming here. |
309 | */ |
310 | |
311 | extern void mpx_loadl2cn(mpw */*v*/, mpw */*vl*/, |
312 | const void */*p*/, size_t /*sz*/); |
313 | |
314 | /* --- @mpx_storeb2cn@ --- * |
315 | * |
316 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
317 | * @void *pp@ = pointer to octet array |
318 | * @size_t sz@ = size of octet array |
319 | * |
320 | * Returns: --- |
321 | * |
322 | * Use: Stores a negative MP in an octet array, most significant |
323 | * octet first, as two's complement. High-end octets are |
324 | * silently discarded if there isn't enough space for them, |
325 | * which probably isn't what you meant. |
326 | */ |
327 | |
328 | extern void mpx_storeb2cn(const mpw */*v*/, const mpw */*vl*/, |
329 | void */*p*/, size_t /*sz*/); |
330 | |
331 | /* --- @mpx_loadb2cn@ --- * |
332 | * |
333 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
334 | * @const void *pp@ = pointer to octet array |
335 | * @size_t sz@ = size of octet array |
336 | * |
337 | * Returns: --- |
338 | * |
339 | * Use: Loads a negative MP in an octet array, most significant octet |
340 | * first as two's complement. High-end octets are ignored if |
341 | * there isn't enough space for them. This probably means you |
342 | * chose this function wrongly. |
343 | */ |
344 | |
345 | extern void mpx_loadb2cn(mpw */*v*/, mpw */*vl*/, |
346 | const void */*p*/, size_t /*sz*/); |
347 | |
348 | |
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349 | /*----- Logical shifting --------------------------------------------------*/ |
350 | |
351 | /* --- @mpx_lsl@ --- * |
352 | * |
353 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
354 | * @const mpw *av, *avl@ = source vector base and limit |
355 | * @size_t n@ = number of bit positions to shift by |
356 | * |
357 | * Returns: --- |
358 | * |
359 | * Use: Performs a logical shift left operation on an integer. |
360 | */ |
361 | |
362 | extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/, |
363 | const mpw */*av*/, const mpw */*avl*/, |
364 | size_t /*n*/); |
365 | |
366 | /* --- @mpx_lsr@ --- * |
367 | * |
368 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
369 | * @const mpw *av, *avl@ = source vector base and limit |
370 | * @size_t n@ = number of bit positions to shift by |
371 | * |
372 | * Returns: --- |
373 | * |
374 | * Use: Performs a logical shift right operation on an integer. |
375 | */ |
376 | |
377 | extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/, |
378 | const mpw */*av*/, const mpw */*avl*/, |
379 | size_t /*n*/); |
380 | |
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381 | /*----- Bitwise operations ------------------------------------------------*/ |
382 | |
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383 | /* --- How to implement them --- * |
384 | * |
385 | * x: 0011 |
386 | * y: 0101 |
387 | */ |
388 | |
389 | #define MPX_B0000(x, y) (0u) |
390 | #define MPX_B0001(x, y) ((x) & (y)) |
391 | #define MPX_B0010(x, y) ((x) & ~(y)) |
392 | #define MPX_B0011(x, y) (x) |
393 | #define MPX_B0100(x, y) (~(x) & ~(y)) |
394 | #define MPX_B0101(x, y) (y) |
395 | #define MPX_B0110(x, y) ((x) ^ (y)) |
396 | #define MPX_B0111(x, y) ((x) | (y)) |
397 | #define MPX_B1000(x, y) (~((x) | (y))) |
398 | #define MPX_B1001(x, y) (~((x) ^ (y))) |
399 | #define MPX_B1010(x, y) (~(y)) |
400 | #define MPX_B1011(x, y) ((x) | ~(y)) |
401 | #define MPX_B1100(x, y) (~(x)) |
402 | #define MPX_B1101(x, y) (~(x) | (y)) |
403 | #define MPX_B1110(x, y) (~((x) & (y))) |
404 | #define MPX_B1111(x, y) (~0u) |
405 | |
406 | /* --- @mpx_bitop@ --- * |
0f32e0f8 |
407 | * |
408 | * Arguments: @mpw *dv, *dvl@ = destination vector |
409 | * @const mpw *av, *avl@ = first source vector |
410 | * @const mpw *bv, *bvl@ = second source vector |
411 | * |
412 | * Returns: --- |
413 | * |
f09e814a |
414 | * Use: Provide the dyadic boolean functions. The functions are |
415 | * named after the truth table they generate: |
416 | * |
417 | * a: 0011 |
418 | * b: 0101 |
419 | * @mpx_bitXXXX@ |
0f32e0f8 |
420 | */ |
421 | |
f09e814a |
422 | #define MPX_DOBIN(what) \ |
423 | what(0000) what(0001) what(0010) what(0011) \ |
424 | what(0100) what(0101) what(0110) what(0111) \ |
425 | what(1000) what(1001) what(1010) what(1011) \ |
426 | what(1100) what(1101) what(1110) what(1111) |
0f32e0f8 |
427 | |
f09e814a |
428 | #define MPX_BITDECL(string) \ |
429 | extern void mpx_bit##string(mpw */*dv*/, mpw */*dvl*/, \ |
430 | const mpw */*av*/, const mpw */*avl*/, \ |
431 | const mpw */*bv*/, const mpw */*bvl*/); |
432 | MPX_DOBIN(MPX_BITDECL) |
0f32e0f8 |
433 | |
f09e814a |
434 | /* --- @mpx_[n]and@, @mpx_[n]or@, @mpx_xor@ --- * |
435 | * |
436 | * Synonyms for the commonly-used functions above. |
437 | */ |
438 | |
439 | #define mpx_and mpx_bit0001 |
440 | #define mpx_or mpx_bit0111 |
441 | #define mpx_nand mpx_bit1110 |
442 | #define mpx_nor mpx_bit1000 |
443 | #define mpx_xor mpx_bit0110 |
444 | |
445 | /* --- @mpx_not@ --- * |
446 | * |
447 | * Arguments: @mpw *dv, *dvl@ = destination vector |
448 | * @const mpw *av, *avl@ = first source vector |
449 | * |
450 | * Returns: --- |
451 | * |
452 | * Use; Bitwise NOT. |
453 | */ |
0f32e0f8 |
454 | |
455 | extern void mpx_not(mpw */*dv*/, mpw */*dvl*/, |
456 | const mpw */*av*/, const mpw */*avl*/); |
457 | |
d03ab969 |
458 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
459 | |
7c13f461 |
460 | /* --- @mpx_2c@ --- * |
461 | * |
462 | * Arguments: @mpw *dv, *dvl@ = destination vector |
463 | * @const mpw *v, *vl@ = source vector |
464 | * |
465 | * Returns: --- |
466 | * |
467 | * Use: Calculates the two's complement of @v@. |
468 | */ |
469 | |
470 | extern void mpx_2c(mpw */*dv*/, mpw */*dvl*/, |
471 | const mpw */*v*/, const mpw */*vl*/); |
472 | |
1a05a8ef |
473 | /* --- @mpx_ueq@ --- * |
474 | * |
475 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
476 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
477 | * |
478 | * Returns: Nonzero if the two vectors are equal. |
479 | * |
480 | * Use: Performs an unsigned integer test for equality. |
481 | */ |
482 | |
483 | extern int mpx_ueq(const mpw */*av*/, const mpw */*avl*/, |
484 | const mpw */*bv*/, const mpw */*bvl*/); |
485 | |
d03ab969 |
486 | /* --- @mpx_ucmp@ --- * |
487 | * |
488 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
489 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
490 | * |
491 | * Returns: Less than, equal to, or greater than zero depending on |
492 | * whether @a@ is less than, equal to or greater than @b@, |
493 | * respectively. |
494 | * |
495 | * Use: Performs an unsigned integer comparison. |
496 | */ |
497 | |
498 | #define MPX_UCMP(av, avl, op, dv, dvl) \ |
499 | (mpx_ucmp((av), (avl), (dv), (dvl)) op 0) |
500 | |
501 | extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/, |
502 | const mpw */*bv*/, const mpw */*bvl*/); |
503 | |
504 | /* --- @mpx_uadd@ --- * |
505 | * |
506 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
507 | * @const mpw *av, *avl@ = first addend vector base and limit |
508 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
509 | * |
510 | * Returns: --- |
511 | * |
512 | * Use: Performs unsigned integer addition. If the result overflows |
513 | * the destination vector, high-order bits are discarded. This |
514 | * means that two's complement addition happens more or less for |
515 | * free, although that's more a side-effect than anything else. |
516 | * The result vector may be equal to either or both source |
517 | * vectors, but may not otherwise overlap them. |
518 | */ |
519 | |
520 | extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, |
521 | const mpw */*av*/, const mpw */*avl*/, |
522 | const mpw */*bv*/, const mpw */*bvl*/); |
523 | |
dd517851 |
524 | /* --- @mpx_uaddn@ --- * |
525 | * |
526 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
527 | * @mpw n@ = other addend |
3c9ede17 |
528 | * |
dd517851 |
529 | * Returns: --- |
3c9ede17 |
530 | * |
531 | * Use: Adds a small integer to a multiprecision number. |
532 | */ |
533 | |
534 | #define MPX_UADDN(dv, dvl, n) do { \ |
535 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
536 | mpw _c = (n); \ |
537 | \ |
538 | while (_c && _ddv < _ddvl) { \ |
539 | mpd _x = (mpd)*_ddv + (mpd)_c; \ |
540 | *_ddv++ = MPW(_x); \ |
541 | _c = _x >> MPW_BITS; \ |
542 | } \ |
543 | } while (0) |
544 | |
dd517851 |
545 | extern void mpx_uaddn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
546 | |
d03ab969 |
547 | /* --- @mpx_usub@ --- * |
548 | * |
549 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
550 | * @const mpw *av, *avl@ = first argument vector base and limit |
551 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
552 | * |
553 | * Returns: --- |
554 | * |
555 | * Use: Performs unsigned integer subtraction. If the result |
556 | * overflows the destination vector, high-order bits are |
557 | * discarded. This means that two's complement subtraction |
3c9ede17 |
558 | * happens more or less for free, although that's more a side- |
d03ab969 |
559 | * effect than anything else. The result vector may be equal to |
560 | * either or both source vectors, but may not otherwise overlap |
561 | * them. |
562 | */ |
563 | |
564 | extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, |
565 | const mpw */*av*/, const mpw */*avl*/, |
566 | const mpw */*bv*/, const mpw */*bvl*/); |
567 | |
dd517851 |
568 | /* --- @mpx_usubn@ --- * |
3c9ede17 |
569 | * |
dd517851 |
570 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
571 | * @n@ = subtrahend |
572 | * |
573 | * Returns: --- |
3c9ede17 |
574 | * |
575 | * Use: Subtracts a small integer from a multiprecision number. |
576 | */ |
577 | |
578 | #define MPX_USUBN(dv, dvl, n) do { \ |
579 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
580 | mpw _c = (n); \ |
581 | \ |
582 | while (_ddv < _ddvl) { \ |
583 | mpd _x = (mpd)*_ddv - (mpd)_c; \ |
584 | *_ddv++ = MPW(_x); \ |
585 | if (_x >> MPW_BITS) \ |
586 | _c = 1; \ |
587 | else \ |
588 | break; \ |
589 | } \ |
590 | } while (0) |
591 | |
dd517851 |
592 | extern void mpx_usubn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
593 | |
3c9ede17 |
594 | /* --- @mpx_umul@ --- * |
595 | * |
596 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
597 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
598 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
599 | * |
600 | * Returns: --- |
601 | * |
602 | * Use: Performs unsigned integer multiplication. If the result |
603 | * overflows the desination vector, high-order bits are |
604 | * discarded. The result vector may not overlap the argument |
605 | * vectors in any way. |
606 | */ |
607 | |
608 | extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, |
609 | const mpw */*av*/, const mpw */*avl*/, |
610 | const mpw */*bv*/, const mpw */*bvl*/); |
611 | |
dd517851 |
612 | /* --- @mpx_umuln@ --- * |
d03ab969 |
613 | * |
dd517851 |
614 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
615 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
616 | * @mpw m@ = multiplier |
617 | * |
618 | * Returns: --- |
d03ab969 |
619 | * |
620 | * Use: Multiplies a multiprecision integer by a single-word value. |
621 | * The destination and source may be equal. The destination |
622 | * is completely cleared after use. |
623 | */ |
624 | |
625 | #define MPX_UMULN(dv, dvl, av, avl, m) do { \ |
626 | mpw *_dv = (dv), *_dvl = (dvl); \ |
627 | const mpw *_av = (av), *_avl = (avl); \ |
628 | mpw _c = 0; \ |
629 | mpd _m = (m); \ |
630 | \ |
631 | while (_av < _avl) { \ |
632 | mpd _x; \ |
633 | if (_dv >= _dvl) \ |
634 | break; \ |
3c9ede17 |
635 | _x = (mpd)_m * (mpd)*_av++ + _c; \ |
d03ab969 |
636 | *_dv++ = MPW(_x); \ |
637 | _c = _x >> MPW_BITS; \ |
638 | } \ |
639 | if (_dv < _dvl) { \ |
640 | *_dv++ = MPW(_c); \ |
641 | MPX_ZERO(_dv, _dvl); \ |
642 | } \ |
643 | } while (0) |
644 | |
dd517851 |
645 | extern void mpx_umuln(mpw */*dv*/, mpw */*dvl*/, |
646 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
647 | |
648 | /* --- @mpx_umlan@ --- * |
d03ab969 |
649 | * |
dd517851 |
650 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
651 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
652 | * @mpw m@ = multiplier |
653 | * |
654 | * Returns: --- |
d03ab969 |
655 | * |
656 | * Use: Multiplies a multiprecision integer by a single-word value |
657 | * and adds the result to an accumulator. |
658 | */ |
659 | |
660 | #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ |
661 | mpw *_dv = (dv), *_dvl = (dvl); \ |
662 | const mpw *_av = (av), *_avl = (avl); \ |
7c13f461 |
663 | mpw _cc = 0; \ |
d03ab969 |
664 | mpd _m = (m); \ |
665 | \ |
5bf74dea |
666 | while (_dv < _dvl && _av < _avl) { \ |
d03ab969 |
667 | mpd _x; \ |
7c13f461 |
668 | _x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \ |
d03ab969 |
669 | *_dv++ = MPW(_x); \ |
7c13f461 |
670 | _cc = _x >> MPW_BITS; \ |
d03ab969 |
671 | } \ |
7c13f461 |
672 | MPX_UADDN(_dv, _dvl, _cc); \ |
d03ab969 |
673 | } while (0) |
674 | |
dd517851 |
675 | extern void mpx_umlan(mpw */*dv*/, mpw */*dvl*/, |
676 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
677 | |
3c9ede17 |
678 | /* --- @mpx_usqr@ --- * |
d03ab969 |
679 | * |
680 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
3c9ede17 |
681 | * @const mpw *av, *av@ = source vector base and limit |
d03ab969 |
682 | * |
683 | * Returns: --- |
684 | * |
3c9ede17 |
685 | * Use: Performs unsigned integer squaring. The result vector must |
686 | * not overlap the source vector in any way. |
d03ab969 |
687 | */ |
688 | |
3c9ede17 |
689 | extern void mpx_usqr(mpw */*dv*/, mpw */*dvl*/, |
690 | const mpw */*av*/, const mpw */*avl*/); |
d03ab969 |
691 | |
5bf74dea |
692 | /* --- @mpx_udiv@ --- * |
693 | * |
694 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
695 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
696 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
697 | * @mpw *sv, *svl@ = scratch workspace |
698 | * |
699 | * Returns: --- |
700 | * |
701 | * Use: Performs unsigned integer division. If the result overflows |
702 | * the quotient vector, high-order bits are discarded. (Clearly |
703 | * the remainder vector can't overflow.) The various vectors |
704 | * may not overlap in any way. Yes, I know it's a bit odd |
705 | * requiring the dividend to be in the result position but it |
706 | * does make some sense really. The remainder must have |
707 | * headroom for at least two extra words. The scratch space |
708 | * must be at least one word larger than the divisor. |
709 | */ |
710 | |
711 | extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/, |
712 | const mpw */*dv*/, const mpw */*dvl*/, |
713 | mpw */*sv*/, mpw */*svl*/); |
714 | |
698bd937 |
715 | /* --- @mpx_udivn@ --- * |
716 | * |
717 | * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap |
718 | * dividend) |
719 | * @const mpw *rv, *rvl@ = dividend |
720 | * @mpw d@ = single-precision divisor |
721 | * |
722 | * Returns: Remainder after divison. |
723 | * |
724 | * Use: Performs a single-precision division operation. |
725 | */ |
726 | |
727 | extern mpw mpx_udivn(mpw */*qv*/, mpw */*qvl*/, |
728 | const mpw */*rv*/, const mpw */*rvl*/, mpw /*d*/); |
729 | |
5bf74dea |
730 | /*----- Karatsuba multiplication algorithms -------------------------------*/ |
731 | |
52cdaca9 |
732 | /* --- @MPK_THRESH@ --- * |
5bf74dea |
733 | * |
734 | * This is the limiting length for using Karatsuba algorithms. It's best to |
735 | * use the simpler classical multiplication method on numbers smaller than |
736 | * this. |
737 | */ |
738 | |
52cdaca9 |
739 | #define MPK_THRESH 16 |
5bf74dea |
740 | |
52cdaca9 |
741 | /* --- @MPK_SLOP@ --- * |
5bf74dea |
742 | * |
743 | * The extra number of words required as scratch space by the Karatsuba |
744 | * routines. This is a (generous) guess, since the actual amount of space |
745 | * required is proportional to the recursion depth. |
746 | */ |
747 | |
52cdaca9 |
748 | #define MPK_SLOP 64 |
5bf74dea |
749 | |
a86e33af |
750 | /* --- @mpx_kmul@ --- * |
751 | * |
752 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
753 | * @const mpw *av, *avl@ = pointer to first argument |
754 | * @const mpw *bv, *bvl@ = pointer to second argument |
755 | * @mpw *sv, *svl@ = pointer to scratch workspace |
756 | * |
757 | * Returns: --- |
758 | * |
759 | * Use: Multiplies two multiprecision integers using Karatsuba's |
760 | * algorithm. This is rather faster than traditional long |
761 | * multiplication (e.g., @mpx_umul@) on large numbers, although |
762 | * more expensive on small ones. |
763 | * |
764 | * The destination and scratch buffers must be twice as large as |
5bf74dea |
765 | * the larger argument. The scratch space must be twice as |
766 | * large as the larger argument, plus the magic number |
52cdaca9 |
767 | * @MPK_SLOP@. |
a86e33af |
768 | */ |
769 | |
a86e33af |
770 | extern void mpx_kmul(mpw */*dv*/, mpw */*dvl*/, |
771 | const mpw */*av*/, const mpw */*avl*/, |
772 | const mpw */*bv*/, const mpw */*bvl*/, |
773 | mpw */*sv*/, mpw */*svl*/); |
774 | |
5bf74dea |
775 | /* --- @mpx_ksqr@ --- * |
d03ab969 |
776 | * |
5bf74dea |
777 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
778 | * @const mpw *av, *avl@ = pointer to first argument |
779 | * @mpw *sv, *svl@ = pointer to scratch workspace |
d03ab969 |
780 | * |
781 | * Returns: --- |
782 | * |
5bf74dea |
783 | * Use: Squares a multiprecision integers using something similar to |
784 | * Karatsuba's multiplication algorithm. This is rather faster |
785 | * than traditional long multiplication (e.g., @mpx_umul@) on |
786 | * large numbers, although more expensive on small ones, and |
787 | * rather simpler than full-blown Karatsuba multiplication. |
788 | * |
789 | * The destination must be twice as large as the argument. The |
790 | * scratch space must be twice as large as the argument, plus |
52cdaca9 |
791 | * the magic number @MPK_SLOP@. |
d03ab969 |
792 | */ |
793 | |
5bf74dea |
794 | extern void mpx_ksqr(mpw */*dv*/, mpw */*dvl*/, |
795 | const mpw */*av*/, const mpw */*avl*/, |
3c9ede17 |
796 | mpw */*sv*/, mpw */*svl*/); |
d03ab969 |
797 | |
798 | /*----- That's all, folks -------------------------------------------------*/ |
799 | |
800 | #ifdef __cplusplus |
801 | } |
802 | #endif |
803 | |
804 | #endif |