1 | |
---|
2 | #include <NTL/lip.h> |
---|
3 | |
---|
4 | #include <NTL/ctools.h> |
---|
5 | |
---|
6 | |
---|
7 | #include <stdlib.h> |
---|
8 | #include <stdio.h> |
---|
9 | #include <math.h> |
---|
10 | |
---|
11 | |
---|
12 | |
---|
13 | |
---|
14 | |
---|
15 | |
---|
16 | #define MustAlloc(c, len) (!(c) || ((c)[-1] >> 1) < (len)) |
---|
17 | /* Fast test to determine if allocation is necessary */ |
---|
18 | |
---|
19 | |
---|
20 | static |
---|
21 | void zhalt(char *c) |
---|
22 | { |
---|
23 | fprintf(stderr,"fatal error:\n %s\nexit...\n",c); |
---|
24 | fflush(stderr); |
---|
25 | abort(); |
---|
26 | } |
---|
27 | |
---|
28 | |
---|
29 | |
---|
30 | #define NTL_GMP_MUL_CROSS (4) |
---|
31 | #define NTL_GMP_SQR_CROSS (4) |
---|
32 | #define NTL_GMP_DIV_CROSS (4) |
---|
33 | #define NTL_GMP_REM_CROSS (4) |
---|
34 | #define NTL_GMP_QREM_CROSS (4) |
---|
35 | #define NTL_GMP_SQRT_CROSS (2) |
---|
36 | #define NTL_GMP_GCD_CROSS (1) |
---|
37 | #define NTL_GMP_XGCD_CROSS (1) |
---|
38 | #define NTL_GMP_INVMOD_CROSS (1) |
---|
39 | |
---|
40 | #ifdef NTL_GMP_HACK |
---|
41 | |
---|
42 | /* using GMP */ |
---|
43 | |
---|
44 | #ifdef NTL_SINGLE_MUL |
---|
45 | #error "sorry...not implemented" |
---|
46 | #endif |
---|
47 | |
---|
48 | #if (NTL_NBITS != NTL_NBITS_MAX) |
---|
49 | #error "sorry...not implemented" |
---|
50 | #endif |
---|
51 | |
---|
52 | int _ntl_gmp_hack = 1; |
---|
53 | |
---|
54 | |
---|
55 | #include <gmp.h> |
---|
56 | |
---|
57 | |
---|
58 | static mp_limb_t *gspace_data = 0; |
---|
59 | static long gspace_size = 0; |
---|
60 | |
---|
61 | |
---|
62 | static void alloc_gspace(long n) |
---|
63 | { |
---|
64 | if (n <= gspace_size) return; |
---|
65 | |
---|
66 | if (n <= gspace_size*1.1) |
---|
67 | n = ((long) (gspace_size*1.1)) + 10; |
---|
68 | |
---|
69 | if (gspace_data) |
---|
70 | gspace_data = |
---|
71 | (mp_limb_t *) NTL_REALLOC(gspace_data, n, sizeof(mp_limb_t), 0); |
---|
72 | else |
---|
73 | gspace_data = (mp_limb_t *) NTL_MALLOC(n, sizeof(mp_limb_t), 0); |
---|
74 | |
---|
75 | if (!gspace_data) zhalt("alloc_gspace: out of memory"); |
---|
76 | |
---|
77 | gspace_size = n; |
---|
78 | } |
---|
79 | |
---|
80 | |
---|
81 | #define NTL_GSPACE(n) \ |
---|
82 | { long _n = (n); if (_n > gspace_size) alloc_gspace(_n); } |
---|
83 | |
---|
84 | |
---|
85 | static mpz_t gt_1, gt_2, gt_3, gt_4, gt_5; |
---|
86 | static long gt_init = 0; |
---|
87 | |
---|
88 | static |
---|
89 | void do_gt_init() |
---|
90 | { |
---|
91 | gt_init = 1; |
---|
92 | mpz_init(gt_1); |
---|
93 | mpz_init(gt_2); |
---|
94 | mpz_init(gt_3); |
---|
95 | mpz_init(gt_4); |
---|
96 | mpz_init(gt_5); |
---|
97 | } |
---|
98 | |
---|
99 | #define GT_INIT { if (!gt_init) do_gt_init(); } |
---|
100 | |
---|
101 | #include "lip_gmp_aux_impl.h" |
---|
102 | |
---|
103 | |
---|
104 | /* Check that we really have it...otherwise, some compilers |
---|
105 | * only issue warnings for missing functions. |
---|
106 | */ |
---|
107 | |
---|
108 | |
---|
109 | #ifndef HAVE_LIP_GMP_AUX |
---|
110 | |
---|
111 | #error "do not have lip_gmp_aux.h" |
---|
112 | |
---|
113 | #endif |
---|
114 | |
---|
115 | static |
---|
116 | void lip_to_mpz(const long *x, mpz_t y) |
---|
117 | { |
---|
118 | long sx; |
---|
119 | long neg; |
---|
120 | long gsx; |
---|
121 | |
---|
122 | if (!x || (x[0] == 1 && x[1] == 0)) { |
---|
123 | mpz_set_ui(y, 0); |
---|
124 | return; |
---|
125 | } |
---|
126 | |
---|
127 | sx = x[0]; |
---|
128 | if (sx < 0) { |
---|
129 | neg = 1; |
---|
130 | sx = -sx; |
---|
131 | } |
---|
132 | else |
---|
133 | neg = 0; |
---|
134 | |
---|
135 | gsx = L_TO_G(sx); |
---|
136 | |
---|
137 | if (gsx > y->_mp_alloc) _mpz_realloc(y, gsx); |
---|
138 | lip_to_gmp(x+1, y->_mp_d, sx); |
---|
139 | while (y->_mp_d[gsx-1] == 0) gsx--; |
---|
140 | if (neg) gsx = -gsx; |
---|
141 | y->_mp_size = gsx; |
---|
142 | } |
---|
143 | |
---|
144 | static |
---|
145 | void mpz_to_lip(long **x, mpz_t y) |
---|
146 | { |
---|
147 | long gsy; |
---|
148 | long neg; |
---|
149 | long sx; |
---|
150 | long *xp; |
---|
151 | |
---|
152 | gsy = y->_mp_size; |
---|
153 | |
---|
154 | if (gsy == 0) { |
---|
155 | _ntl_zzero(x); |
---|
156 | return; |
---|
157 | } |
---|
158 | |
---|
159 | if (gsy < 0) { |
---|
160 | neg = 1; |
---|
161 | gsy = -gsy; |
---|
162 | } |
---|
163 | else |
---|
164 | neg = 0; |
---|
165 | |
---|
166 | sx = G_TO_L(gsy); |
---|
167 | |
---|
168 | xp = *x; |
---|
169 | if (MustAlloc(xp, sx)) { |
---|
170 | _ntl_zsetlength(x, sx); |
---|
171 | xp = *x; |
---|
172 | } |
---|
173 | |
---|
174 | gmp_to_lip1(xp+1, y->_mp_d, sx); |
---|
175 | |
---|
176 | while (xp[sx] == 0) sx--; |
---|
177 | if (neg) sx = -sx; |
---|
178 | xp[0] = sx; |
---|
179 | } |
---|
180 | |
---|
181 | |
---|
182 | void _ntl_gmp_powermod(long **x, long *a, long *e, long *n) |
---|
183 | { |
---|
184 | long neg = 0; |
---|
185 | |
---|
186 | GT_INIT |
---|
187 | |
---|
188 | |
---|
189 | lip_to_mpz(a, gt_2); |
---|
190 | lip_to_mpz(e, gt_3); |
---|
191 | lip_to_mpz(n, gt_4); |
---|
192 | |
---|
193 | if (mpz_sgn(gt_3) < 0) { |
---|
194 | mpz_neg(gt_3, gt_3); |
---|
195 | neg = 1; |
---|
196 | } |
---|
197 | |
---|
198 | mpz_powm(gt_1, gt_2, gt_3, gt_4); |
---|
199 | |
---|
200 | /* This fixes a bug in GMP 3.0.1 */ |
---|
201 | if (mpz_cmp(gt_1, gt_4) >= 0) |
---|
202 | mpz_sub(gt_1, gt_1, gt_4); |
---|
203 | |
---|
204 | if (neg) { |
---|
205 | if (!mpz_invert(gt_1, gt_1, gt_4)) |
---|
206 | zhalt("Modular inverse not defined"); |
---|
207 | } |
---|
208 | |
---|
209 | mpz_to_lip(x, gt_1); |
---|
210 | } |
---|
211 | |
---|
212 | |
---|
213 | #else |
---|
214 | |
---|
215 | /* not using GMP */ |
---|
216 | |
---|
217 | int _ntl_gmp_hack = 0; |
---|
218 | |
---|
219 | |
---|
220 | #endif |
---|
221 | |
---|
222 | |
---|
223 | |
---|
224 | #define DENORMALIZE NTL_FDOUBLE_PRECISION |
---|
225 | |
---|
226 | |
---|
227 | #define MIN_SETL (4) |
---|
228 | /* _ntl_zsetlength allocates a multiple of MIN_SETL digits */ |
---|
229 | |
---|
230 | |
---|
231 | |
---|
232 | #if (defined(NTL_SINGLE_MUL) && !defined(NTL_FAST_INT_MUL)) |
---|
233 | #define MulLo(rres,a,b) \ |
---|
234 | { \ |
---|
235 | double _x = ((double) a) * ((double) b) + (DENORMALIZE); \ |
---|
236 | unsigned long _x_lo; \ |
---|
237 | NTL_FetchLo(_x_lo, _x); \ |
---|
238 | rres = _x_lo; \ |
---|
239 | } |
---|
240 | #else |
---|
241 | #define MulLo(rres,a,b) rres = (a)*(b) |
---|
242 | #endif |
---|
243 | |
---|
244 | |
---|
245 | |
---|
246 | |
---|
247 | |
---|
248 | |
---|
249 | /* |
---|
250 | * definitions of zaddmulp, zxmulp, zaddmulpsq for the various |
---|
251 | * long integer arithmentic implementation options. |
---|
252 | */ |
---|
253 | |
---|
254 | |
---|
255 | #if (defined(NTL_SINGLE_MUL)) |
---|
256 | |
---|
257 | #define zaddmulp(a,b,d,t) \ |
---|
258 | { \ |
---|
259 | long _a = (a), _b = (b), _d = (d), _t = (t); \ |
---|
260 | unsigned long __lhi, __llo;\ |
---|
261 | double __lx = ((double) ((_a) + (_t))) + ((double) _b)*((double) _d); \ |
---|
262 | __lx += (DENORMALIZE); \ |
---|
263 | NTL_FetchHiLo(__lhi,__llo,__lx);\ |
---|
264 | __lhi = ((__lhi<<6)|(__llo>>26)) & 0x3FFFFFF; \ |
---|
265 | __llo &= 0x3FFFFFF; \ |
---|
266 | (a) = __llo;\ |
---|
267 | (t) = __lhi;\ |
---|
268 | } |
---|
269 | |
---|
270 | #define zxmulp(a,b,d,t) \ |
---|
271 | { \ |
---|
272 | long _b = (b), _d = (d), _t = (t); \ |
---|
273 | unsigned long __lhi, __llo;\ |
---|
274 | double __lx = ((double) ((_t))) + ((double) _b)*((double) _d); \ |
---|
275 | __lx += (DENORMALIZE); \ |
---|
276 | NTL_FetchHiLo(__lhi,__llo,__lx);\ |
---|
277 | __lhi = ((__lhi<<6)|(__llo>>26)) & 0x3FFFFFF; \ |
---|
278 | __llo &= 0x3FFFFFF; \ |
---|
279 | (a) = __llo;\ |
---|
280 | (t) = __lhi;\ |
---|
281 | } |
---|
282 | |
---|
283 | #define zaddmulpsq(a,b,t) \ |
---|
284 | { \ |
---|
285 | long _a = (a), _b = (b); \ |
---|
286 | unsigned long __lhi, __llo; \ |
---|
287 | double __lx = ((double) (_a)) + ((double) _b)*((double) _b); \ |
---|
288 | __lx += (DENORMALIZE); \ |
---|
289 | NTL_FetchHiLo(__lhi,__llo,__lx);\ |
---|
290 | __lhi = ((__lhi<<6)|(__llo>>26)) & 0x3FFFFFF; \ |
---|
291 | __llo &= 0x3FFFFFF; \ |
---|
292 | (a) = __llo;\ |
---|
293 | (t) = __lhi;\ |
---|
294 | } |
---|
295 | |
---|
296 | #elif (defined(NTL_LONG_LONG)) |
---|
297 | |
---|
298 | #ifndef NTL_LONG_LONG_TYPE |
---|
299 | #define NTL_LONG_LONG_TYPE long long |
---|
300 | #endif |
---|
301 | |
---|
302 | #if (!defined(NTL_CLEAN_INT)) |
---|
303 | |
---|
304 | /* |
---|
305 | * One might get slightly better code with this version. |
---|
306 | */ |
---|
307 | |
---|
308 | #define zaddmulp(a, b, d, t) { \ |
---|
309 | NTL_LONG_LONG_TYPE _pp = ((NTL_LONG_LONG_TYPE) (b)) * ((NTL_LONG_LONG_TYPE) (d)) + ((t)+(a)); \ |
---|
310 | (a) = ((long)(_pp)) & NTL_RADIXM; \ |
---|
311 | (t) = (long) (_pp >> NTL_NBITS); \ |
---|
312 | } |
---|
313 | |
---|
314 | |
---|
315 | #define zxmulp(a, b, d, t) { \ |
---|
316 | NTL_LONG_LONG_TYPE _pp = ((NTL_LONG_LONG_TYPE) (b)) * ((NTL_LONG_LONG_TYPE) (d)) + (t); \ |
---|
317 | (a) = ((long)(_pp)) & NTL_RADIXM; \ |
---|
318 | (t) = (long) (_pp >> NTL_NBITS); \ |
---|
319 | } |
---|
320 | |
---|
321 | #define zaddmulpsq(a,b,t) { \ |
---|
322 | NTL_LONG_LONG_TYPE _pp = ((NTL_LONG_LONG_TYPE) (b)) * ((NTL_LONG_LONG_TYPE) (b)) + (a); \ |
---|
323 | (a) = ((long)(_pp)) & NTL_RADIXM; \ |
---|
324 | (t) = (long) (_pp >> NTL_NBITS); \ |
---|
325 | } |
---|
326 | |
---|
327 | #else |
---|
328 | |
---|
329 | /* |
---|
330 | * This version conforms to the language standard when d is non-negative. |
---|
331 | * Some compilers may emit sub-optimal code, though. |
---|
332 | */ |
---|
333 | |
---|
334 | |
---|
335 | |
---|
336 | #define zaddmulp(a, b, d, t) { \ |
---|
337 | NTL_LONG_LONG_TYPE _pp = ((NTL_LONG_LONG_TYPE) (b)) * ((NTL_LONG_LONG_TYPE) (d)) + ((t)+(a)); \ |
---|
338 | (a) = (long) (_pp & NTL_RADIXM); \ |
---|
339 | (t) = (long) (_pp >> NTL_NBITS); \ |
---|
340 | } |
---|
341 | |
---|
342 | |
---|
343 | #define zxmulp(a, b, d, t) { \ |
---|
344 | NTL_LONG_LONG_TYPE _pp = ((NTL_LONG_LONG_TYPE) (b)) * ((NTL_LONG_LONG_TYPE) (d)) + (t); \ |
---|
345 | (a) = (long) (_pp & NTL_RADIXM); \ |
---|
346 | (t) = (long) (_pp >> NTL_NBITS); \ |
---|
347 | } |
---|
348 | |
---|
349 | #define zaddmulpsq(a,b,t) { \ |
---|
350 | NTL_LONG_LONG_TYPE _pp = ((NTL_LONG_LONG_TYPE) (b)) * ((NTL_LONG_LONG_TYPE) (b)) + (a); \ |
---|
351 | (a) = (long) (_pp & NTL_RADIXM); \ |
---|
352 | (t) = (long) (_pp >> NTL_NBITS); \ |
---|
353 | } |
---|
354 | |
---|
355 | |
---|
356 | #endif |
---|
357 | |
---|
358 | |
---|
359 | #elif (defined(NTL_AVOID_FLOAT)) |
---|
360 | |
---|
361 | |
---|
362 | #define zaddmulp( a, b, d, t) { \ |
---|
363 | unsigned long _b1 = b & NTL_RADIXROOTM; \ |
---|
364 | unsigned long _d1 = d & NTL_RADIXROOTM; \ |
---|
365 | unsigned long _bd,_b1d1,_m,_aa= (a) + (t); \ |
---|
366 | unsigned long _ld = (d>>NTL_NBITSH); \ |
---|
367 | unsigned long _lb = (b>>NTL_NBITSH); \ |
---|
368 | \ |
---|
369 | _bd=_lb*_ld; \ |
---|
370 | _b1d1=_b1*_d1; \ |
---|
371 | _m=(_lb+_b1)*(_ld+_d1) - _bd - _b1d1; \ |
---|
372 | _aa += ( _b1d1+ ((_m&NTL_RADIXROOTM)<<NTL_NBITSH)); \ |
---|
373 | (t) = (_aa >> NTL_NBITS) + _bd + (_m>>NTL_NBITSH); \ |
---|
374 | (a) = _aa & NTL_RADIXM; \ |
---|
375 | } |
---|
376 | |
---|
377 | |
---|
378 | |
---|
379 | |
---|
380 | |
---|
381 | #define zxmulp( a, b, d, t) { \ |
---|
382 | unsigned long _b1 = b & NTL_RADIXROOTM; \ |
---|
383 | unsigned long _d1 = d & NTL_RADIXROOTM; \ |
---|
384 | unsigned long _bd,_b1d1,_m,_aa= (t); \ |
---|
385 | unsigned long _ld = (d>>NTL_NBITSH); \ |
---|
386 | unsigned long _lb = (b>>NTL_NBITSH); \ |
---|
387 | \ |
---|
388 | _bd=_lb*_ld; \ |
---|
389 | _b1d1=_b1*_d1; \ |
---|
390 | _m=(_lb+_b1)*(_ld+_d1) - _bd - _b1d1; \ |
---|
391 | _aa += ( _b1d1+ ((_m&NTL_RADIXROOTM)<<NTL_NBITSH)); \ |
---|
392 | (t) = (_aa >> NTL_NBITS) + _bd + (_m>>NTL_NBITSH); \ |
---|
393 | (a) = _aa & NTL_RADIXM; \ |
---|
394 | } |
---|
395 | |
---|
396 | |
---|
397 | #define zaddmulpsq(_a, _b, _t) \ |
---|
398 | { \ |
---|
399 | long _lb = (_b); \ |
---|
400 | long _b1 = (_b) & NTL_RADIXROOTM; \ |
---|
401 | long _aa = (_a) + _b1 * _b1; \ |
---|
402 | \ |
---|
403 | _b1 = (_b1 * (_lb >>= NTL_NBITSH) << 1) + (_aa >> NTL_NBITSH); \ |
---|
404 | _aa = (_aa & NTL_RADIXROOTM) + ((_b1 & NTL_RADIXROOTM) << NTL_NBITSH); \ |
---|
405 | (_t) = _lb * _lb + (_b1 >> NTL_NBITSH) + (_aa >> NTL_NBITS); \ |
---|
406 | (_a) = (_aa & NTL_RADIXM); \ |
---|
407 | } |
---|
408 | |
---|
409 | |
---|
410 | |
---|
411 | #else |
---|
412 | |
---|
413 | /* default long integer arithemtic */ |
---|
414 | /* various "software pipelining" routines are also defined */ |
---|
415 | |
---|
416 | |
---|
417 | /* |
---|
418 | * The macros CARRY_TYPE and CARRY_CONV are only used in the submul |
---|
419 | * logic. |
---|
420 | */ |
---|
421 | |
---|
422 | |
---|
423 | #if (defined(NTL_CLEAN_INT)) |
---|
424 | |
---|
425 | #define CARRY_TYPE unsigned long |
---|
426 | #define CARRY_CONV(x) (-((long)(-x))) |
---|
427 | |
---|
428 | #else |
---|
429 | |
---|
430 | #define CARRY_TYPE long |
---|
431 | #define CARRY_CONV(x) (x) |
---|
432 | |
---|
433 | #endif |
---|
434 | |
---|
435 | |
---|
436 | #if (NTL_BITS_PER_LONG <= NTL_NBITS + 2) |
---|
437 | |
---|
438 | #if (NTL_ARITH_RIGHT_SHIFT && !defined(NTL_CLEAN_INT)) |
---|
439 | /* value right-shifted is -1..1 */ |
---|
440 | #define zaddmulp(a, b, d, t) \ |
---|
441 | { \ |
---|
442 | long _a = (a), _b = (b), _d = (d), _t = (t); \ |
---|
443 | long _t1 = _b*_d; \ |
---|
444 | long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ); \ |
---|
445 | _t2 = _t2 + ((_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS); \ |
---|
446 | _t1 = (_t1 & NTL_RADIXM) + _a +_t; \ |
---|
447 | (t) = _t2 + (((unsigned long)_t1) >> NTL_NBITS); \ |
---|
448 | (a) = _t1 & NTL_RADIXM; \ |
---|
449 | } |
---|
450 | |
---|
451 | |
---|
452 | #define zxmulp(a, b, d, t) \ |
---|
453 | { \ |
---|
454 | long _b = (b), _d = (d), _t = (t); \ |
---|
455 | long _t1 = _b*_d + _t; \ |
---|
456 | long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ) - 1; \ |
---|
457 | (t) = _t2 + (((unsigned long)(_t1 - (_t2 << NTL_NBITS))) >> NTL_NBITS); \ |
---|
458 | (a) = _t1 & NTL_RADIXM; \ |
---|
459 | } |
---|
460 | |
---|
461 | /* value shifted is -1..1 */ |
---|
462 | #define zaddmulpsq(a, b, t) \ |
---|
463 | { \ |
---|
464 | long _a = (a), _b = (b); \ |
---|
465 | long _t1 = _b*_b; \ |
---|
466 | long _t2 = (long) ( ((double) _b)*(((double) _b)*NTL_FRADIX_INV) ); \ |
---|
467 | _t2 = _t2 + ((_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS); \ |
---|
468 | _t1 = (_t1 & NTL_RADIXM) + _a; \ |
---|
469 | (t) = _t2 + (((unsigned long)_t1) >> NTL_NBITS); \ |
---|
470 | (a) = _t1 & NTL_RADIXM; \ |
---|
471 | } |
---|
472 | |
---|
473 | /* |
---|
474 | * In the following definition of zam_init, the value _ds is computed so that |
---|
475 | * it is slightly bigger than s*NTL_RADIX_INV. This has the consequence that |
---|
476 | * the value _hi is equal to floor(_b*_s/NTL_RADIX) or |
---|
477 | * floor(_b*_s/NTL_RADIX) + 1, assuming only that (1) conversion of "small" |
---|
478 | * integer to doubles is exact, (2) multiplication by powers of 2 is exact, and |
---|
479 | * (3) multiplication of two general doubles yields a result with relative |
---|
480 | * error 1/2^{NTL_DOUBLE_PRECISION-1}. These assumptions are very |
---|
481 | * conservative, and in fact, the IEEE floating point standard would guarantee |
---|
482 | * this result *without* making _ds slightly bigger. |
---|
483 | */ |
---|
484 | |
---|
485 | #define zam_decl double _ds; long _hi, _lo, _s; |
---|
486 | |
---|
487 | #define zam_init(b,s) \ |
---|
488 | { \ |
---|
489 | long _b = (b); \ |
---|
490 | _s = (s); \ |
---|
491 | _ds = ((_s << 1)+1)*(NTL_FRADIX_INV/2.0); \ |
---|
492 | _lo = _b*_s; \ |
---|
493 | _hi = (long) (((double) _b)*_ds); \ |
---|
494 | } |
---|
495 | |
---|
496 | /* value shifted is 0..3 */ |
---|
497 | #define zam_loop(a,t,nb) \ |
---|
498 | { \ |
---|
499 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
500 | long _vv; \ |
---|
501 | double _yy; \ |
---|
502 | _vv = _nb*_s; \ |
---|
503 | _yy = ((double) _nb)*_ds; \ |
---|
504 | _lo = _lo + _a + _t; \ |
---|
505 | _hi--; \ |
---|
506 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
507 | (a) = _lo & NTL_RADIXM; \ |
---|
508 | _lo = _vv; \ |
---|
509 | _hi = (long) _yy; \ |
---|
510 | } |
---|
511 | |
---|
512 | /* shift is -1..+1 */ |
---|
513 | #define zsx_loop(a,t,nb) \ |
---|
514 | { \ |
---|
515 | long _t = (t), _nb = (nb); \ |
---|
516 | long _vv; \ |
---|
517 | double _yy; \ |
---|
518 | _vv = _nb*_s; \ |
---|
519 | _yy = ((double) _nb)*_ds; \ |
---|
520 | _lo = _lo + _t; \ |
---|
521 | (t) = _hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS); \ |
---|
522 | (a) = _lo & NTL_RADIXM; \ |
---|
523 | _lo = _vv; \ |
---|
524 | _hi = (long) _yy; \ |
---|
525 | } |
---|
526 | |
---|
527 | |
---|
528 | /* value shifted is -2..+1 */ |
---|
529 | #define zam_subloop(a,t,nb) \ |
---|
530 | { \ |
---|
531 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
532 | long _vv; \ |
---|
533 | double _yy; \ |
---|
534 | _vv = _nb*_s; \ |
---|
535 | _yy = ((double) _nb)*_ds; \ |
---|
536 | _lo = _a + _t - _lo; \ |
---|
537 | (t) = ((_lo + (_hi<<NTL_NBITS)) >> NTL_NBITS) - _hi; \ |
---|
538 | (a) = _lo & NTL_RADIXM; \ |
---|
539 | _lo = _vv; \ |
---|
540 | _hi = (long) _yy; \ |
---|
541 | } |
---|
542 | |
---|
543 | /* value shifted is 0..3 */ |
---|
544 | #define zam_finish(a,t) \ |
---|
545 | { \ |
---|
546 | long _a = (a), _t = (t); \ |
---|
547 | _lo = _lo + _a + _t; \ |
---|
548 | _hi--; \ |
---|
549 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
550 | (a) = _lo & NTL_RADIXM; \ |
---|
551 | } |
---|
552 | |
---|
553 | /* value shifted is -1..+1 */ |
---|
554 | #define zsx_finish(a,t) \ |
---|
555 | { \ |
---|
556 | long _t = (t); \ |
---|
557 | _lo = _lo + _t; \ |
---|
558 | (t) = _hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS); \ |
---|
559 | (a) = _lo & NTL_RADIXM; \ |
---|
560 | } |
---|
561 | |
---|
562 | /* value shifted is -2..+1 */ |
---|
563 | #define zam_subfinish(a,t) \ |
---|
564 | { \ |
---|
565 | long _a = (a), _t = (t); \ |
---|
566 | _lo = _a + _t - _lo; \ |
---|
567 | (t) = ((_lo + (_hi<<NTL_NBITS)) >> NTL_NBITS) - _hi; \ |
---|
568 | (a) = _lo & NTL_RADIXM; \ |
---|
569 | } |
---|
570 | |
---|
571 | #elif (!defined(NTL_CLEAN_INT)) |
---|
572 | |
---|
573 | /* right shift is not arithmetic */ |
---|
574 | |
---|
575 | /* value right-shifted is 0..2 */ |
---|
576 | #define zaddmulp(a, b, d, t) \ |
---|
577 | { \ |
---|
578 | long _a = (a), _b = (b), _d = (d), _t = (t); \ |
---|
579 | long _t1 = _b*_d; \ |
---|
580 | long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ) - 1; \ |
---|
581 | _t2 = _t2 + ( ((unsigned long) (_t1 - (_t2 << NTL_NBITS))) >> NTL_NBITS ); \ |
---|
582 | _t1 = (_t1 & NTL_RADIXM) + _a +_t; \ |
---|
583 | (t) = _t2 + (((unsigned long)_t1) >> NTL_NBITS); \ |
---|
584 | (a) = _t1 & NTL_RADIXM; \ |
---|
585 | } |
---|
586 | |
---|
587 | |
---|
588 | #define zxmulp(a, b, d, t) \ |
---|
589 | { \ |
---|
590 | long _b = (b), _d = (d), _t = (t); \ |
---|
591 | long _t1 = _b*_d + _t; \ |
---|
592 | long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ) - 1; \ |
---|
593 | (t) = _t2 + (((unsigned long)(_t1 - (_t2 << NTL_NBITS))) >> NTL_NBITS); \ |
---|
594 | (a) = _t1 & NTL_RADIXM; \ |
---|
595 | } |
---|
596 | |
---|
597 | /* value shifted is 0..2 */ |
---|
598 | #define zaddmulpsq(a, b, t) \ |
---|
599 | { \ |
---|
600 | long _a = (a), _b = (b); \ |
---|
601 | long _t1 = _b*_b; \ |
---|
602 | long _t2 = (long) ( ((double) _b)*(((double) _b)*NTL_FRADIX_INV) ) - 1; \ |
---|
603 | _t2 = _t2 + ( ((unsigned long) (_t1 - (_t2 << NTL_NBITS))) >> NTL_NBITS ); \ |
---|
604 | _t1 = (_t1 & NTL_RADIXM) + _a; \ |
---|
605 | (t) = _t2 + (((unsigned long)_t1) >> NTL_NBITS); \ |
---|
606 | (a) = _t1 & NTL_RADIXM; \ |
---|
607 | } |
---|
608 | |
---|
609 | #define zam_decl double _ds; long _hi, _lo, _s; |
---|
610 | |
---|
611 | #define zam_init(b,s) \ |
---|
612 | { \ |
---|
613 | long _b = (b); \ |
---|
614 | _s = (s); \ |
---|
615 | _ds = ((_s << 1)+1)*(NTL_FRADIX_INV/2.0); \ |
---|
616 | _lo = _b*_s; \ |
---|
617 | _hi = (long) (((double) _b)*_ds); \ |
---|
618 | } |
---|
619 | |
---|
620 | /* value shifted is 0..3 */ |
---|
621 | #define zam_loop(a,t,nb) \ |
---|
622 | { \ |
---|
623 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
624 | long _vv; \ |
---|
625 | double _yy; \ |
---|
626 | _vv = _nb*_s; \ |
---|
627 | _yy = ((double) _nb)*_ds; \ |
---|
628 | _lo = _lo + _a + _t; \ |
---|
629 | _hi--; \ |
---|
630 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
631 | (a) = _lo & NTL_RADIXM; \ |
---|
632 | _lo = _vv; \ |
---|
633 | _hi = (long) _yy; \ |
---|
634 | } |
---|
635 | |
---|
636 | /* value shifted is 0..2 */ |
---|
637 | #define zsx_loop(a,t,nb) \ |
---|
638 | { \ |
---|
639 | long _t = (t), _nb = (nb); \ |
---|
640 | long _vv; \ |
---|
641 | double _yy; \ |
---|
642 | _vv = _nb*_s; \ |
---|
643 | _yy = ((double) _nb)*_ds; \ |
---|
644 | _lo = _lo + _t; \ |
---|
645 | _hi--; \ |
---|
646 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
647 | (a) = _lo & NTL_RADIXM; \ |
---|
648 | _lo = _vv; \ |
---|
649 | _hi = (long) _yy; \ |
---|
650 | } |
---|
651 | |
---|
652 | /* value shifted is 0..3 */ |
---|
653 | #define zam_subloop(a,t,nb) \ |
---|
654 | { \ |
---|
655 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
656 | long _vv; \ |
---|
657 | double _yy; \ |
---|
658 | _vv = _nb*_s; \ |
---|
659 | _yy = ((double) _nb)*_ds; \ |
---|
660 | _hi += 2; \ |
---|
661 | _lo = _a + _t - _lo; \ |
---|
662 | (t) = (((unsigned long)(_lo + (_hi<<NTL_NBITS))) >> NTL_NBITS) - _hi; \ |
---|
663 | (a) = _lo & NTL_RADIXM; \ |
---|
664 | _lo = _vv; \ |
---|
665 | _hi = (long) _yy; \ |
---|
666 | } |
---|
667 | |
---|
668 | /* value shifted is 0..3 */ |
---|
669 | #define zam_finish(a,t) \ |
---|
670 | { \ |
---|
671 | long _a = (a), _t = (t); \ |
---|
672 | _lo = _lo + _a + _t; \ |
---|
673 | _hi--; \ |
---|
674 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
675 | (a) = _lo & NTL_RADIXM; \ |
---|
676 | } |
---|
677 | |
---|
678 | /* value shifted is 0..2 */ |
---|
679 | #define zsx_finish(a,t) \ |
---|
680 | { \ |
---|
681 | long _a = (a), _t = (t); \ |
---|
682 | _lo = _lo + _t; \ |
---|
683 | _hi--; \ |
---|
684 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
685 | (a) = _lo & NTL_RADIXM; \ |
---|
686 | } |
---|
687 | |
---|
688 | /* value shifted is 0..3 */ |
---|
689 | #define zam_subfinish(a,t) \ |
---|
690 | { \ |
---|
691 | long _a = (a), _t = (t); \ |
---|
692 | _hi += 2; \ |
---|
693 | _lo = _a + _t - _lo; \ |
---|
694 | (t) = (((unsigned long)(_lo + (_hi<<NTL_NBITS))) >> NTL_NBITS) - _hi; \ |
---|
695 | (a) = _lo & NTL_RADIXM; \ |
---|
696 | } |
---|
697 | |
---|
698 | #else |
---|
699 | /* clean int version */ |
---|
700 | |
---|
701 | /* value right-shifted is 0..2 */ |
---|
702 | #define zaddmulp(a, b, d, t) \ |
---|
703 | { \ |
---|
704 | long _a = (a), _b = (b), _d = (d), _t = (t); \ |
---|
705 | unsigned long _t1 = ((unsigned long) _b)*((unsigned long) _d); \ |
---|
706 | unsigned long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ) - 1; \ |
---|
707 | _t2 = _t2 + ( (_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS ); \ |
---|
708 | _t1 = (_t1 & NTL_RADIXM) + ((unsigned long) _a) + ((unsigned long) _t); \ |
---|
709 | (t) = (long) (_t2 + (_t1 >> NTL_NBITS)); \ |
---|
710 | (a) = (long) (_t1 & NTL_RADIXM); \ |
---|
711 | } |
---|
712 | |
---|
713 | |
---|
714 | #define zxmulp(a, b, d, t) \ |
---|
715 | { \ |
---|
716 | long _b = (b), _d = (d), _t = (t); \ |
---|
717 | unsigned long _t1 = ((unsigned long) _b)*((unsigned long) _d) + ((unsigned long) _t); \ |
---|
718 | unsigned long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ) - 1; \ |
---|
719 | (t) = (long) (_t2 + ((_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS)); \ |
---|
720 | (a) = (long) (_t1 & NTL_RADIXM); \ |
---|
721 | } |
---|
722 | |
---|
723 | /* value shifted is 0..2 */ |
---|
724 | #define zaddmulpsq(a, b, t) \ |
---|
725 | { \ |
---|
726 | long _a = (a), _b = (b); \ |
---|
727 | unsigned long _t1 = ((unsigned long) _b)*((unsigned long) _b); \ |
---|
728 | unsigned long _t2 = (long) ( ((double) _b)*(((double) _b)*NTL_FRADIX_INV) ) - 1; \ |
---|
729 | _t2 = _t2 + ( (_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS ); \ |
---|
730 | _t1 = (_t1 & NTL_RADIXM) + ((unsigned long) _a); \ |
---|
731 | (t) = (long) (_t2 + (_t1 >> NTL_NBITS)); \ |
---|
732 | (a) = (long) (_t1 & NTL_RADIXM); \ |
---|
733 | } |
---|
734 | |
---|
735 | #define zam_decl double _ds; long _s; unsigned long _hi, _lo; |
---|
736 | |
---|
737 | #define zam_init(b,s) \ |
---|
738 | { \ |
---|
739 | long _b = (b); \ |
---|
740 | _s = (s); \ |
---|
741 | _ds = ((_s << 1)+1)*(NTL_FRADIX_INV/2.0); \ |
---|
742 | _lo = ((unsigned long) _b)*((unsigned long) _s); \ |
---|
743 | _hi = (long) (((double) _b)*_ds); \ |
---|
744 | } |
---|
745 | |
---|
746 | /* value shifted is 0..3 */ |
---|
747 | #define zam_loop(a,t,nb) \ |
---|
748 | { \ |
---|
749 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
750 | unsigned long _vv; \ |
---|
751 | double _yy; \ |
---|
752 | _vv = ((unsigned long) _nb)*((unsigned long)_s); \ |
---|
753 | _yy = ((double) _nb)*_ds; \ |
---|
754 | _lo = _lo + ((unsigned long) _a) + ((unsigned long) _t); \ |
---|
755 | _hi--; \ |
---|
756 | (t) = (long) (_hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS)); \ |
---|
757 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
758 | _lo = _vv; \ |
---|
759 | _hi = (long) _yy; \ |
---|
760 | } |
---|
761 | |
---|
762 | /* value shifted is 0..2 */ |
---|
763 | #define zsx_loop(a,t,nb) \ |
---|
764 | { \ |
---|
765 | long _t = (t), _nb = (nb); \ |
---|
766 | unsigned long _vv; \ |
---|
767 | double _yy; \ |
---|
768 | _vv = ((unsigned long) _nb)*((unsigned long) _s); \ |
---|
769 | _yy = ((double) _nb)*_ds; \ |
---|
770 | _lo = _lo + ((unsigned long) _t); \ |
---|
771 | _hi--; \ |
---|
772 | (t) = (long) (_hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS)); \ |
---|
773 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
774 | _lo = _vv; \ |
---|
775 | _hi = (long) _yy; \ |
---|
776 | } |
---|
777 | |
---|
778 | /* value shifted is 0..3 */ |
---|
779 | #define zam_subloop(a,t,nb) \ |
---|
780 | { \ |
---|
781 | long _a = (a); unsigned long _t = (t); long _nb = (nb); \ |
---|
782 | unsigned long _vv; \ |
---|
783 | double _yy; \ |
---|
784 | _vv = ((unsigned long) _nb)*((unsigned long) _s); \ |
---|
785 | _yy = ((double) _nb)*_ds; \ |
---|
786 | _hi += 2; \ |
---|
787 | _lo = ((unsigned long) _a) + _t - _lo; \ |
---|
788 | (t) = ((_lo + (_hi<<NTL_NBITS)) >> NTL_NBITS) - _hi; \ |
---|
789 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
790 | _lo = _vv; \ |
---|
791 | _hi = (long) _yy; \ |
---|
792 | } |
---|
793 | |
---|
794 | /* value shifted is 0..3 */ |
---|
795 | #define zam_finish(a,t) \ |
---|
796 | { \ |
---|
797 | long _a = (a), _t = (t); \ |
---|
798 | _lo = _lo + ((unsigned long) _a) + ((unsigned long) _t); \ |
---|
799 | _hi--; \ |
---|
800 | (t) = (long) (_hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS)); \ |
---|
801 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
802 | } |
---|
803 | |
---|
804 | /* value shifted is 0..2 */ |
---|
805 | #define zsx_finish(a,t) \ |
---|
806 | { \ |
---|
807 | long _a = (a), _t = (t); \ |
---|
808 | _lo = _lo + ((unsigned long) _t); \ |
---|
809 | _hi--; \ |
---|
810 | (t) = (long) (_hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS)); \ |
---|
811 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
812 | } |
---|
813 | |
---|
814 | /* value shifted is 0..3 */ |
---|
815 | #define zam_subfinish(a,t) \ |
---|
816 | { \ |
---|
817 | long _a = (a); unsigned long _t = (t); \ |
---|
818 | _hi += 2; \ |
---|
819 | _lo = ((unsigned long) _a) + _t - _lo; \ |
---|
820 | (t) = ((_lo + (_hi<<NTL_NBITS)) >> NTL_NBITS) - _hi; \ |
---|
821 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
822 | } |
---|
823 | |
---|
824 | #endif |
---|
825 | /* end of arithmemtic-right-shift if-then else */ |
---|
826 | |
---|
827 | #else |
---|
828 | /* NTL_BITS_PER_LONG > NTL_NBITS + 2, and certain optimizations can be |
---|
829 | made. Useful on 64-bit machines. */ |
---|
830 | |
---|
831 | #if (NTL_ARITH_RIGHT_SHIFT && !defined(NTL_CLEAN_INT)) |
---|
832 | /* shift is -1..+3 */ |
---|
833 | #define zaddmulp(a, b, d, t) \ |
---|
834 | { \ |
---|
835 | long _a = (a), _b = (b), _d = (d), _t = (t); \ |
---|
836 | long _t1 = _b*_d + _a + _t; \ |
---|
837 | long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ); \ |
---|
838 | (t) = _t2 + ((_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS); \ |
---|
839 | (a) = _t1 & NTL_RADIXM; \ |
---|
840 | } |
---|
841 | |
---|
842 | #define zxmulp(a, b, d, t) \ |
---|
843 | { \ |
---|
844 | long _b = (b), _d = (d), _t = (t); \ |
---|
845 | long _t1 = _b*_d + _t; \ |
---|
846 | long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ); \ |
---|
847 | (t) = _t2 + ((_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS); \ |
---|
848 | (a) = _t1 & NTL_RADIXM; \ |
---|
849 | } |
---|
850 | |
---|
851 | /* shift is -1..+2 */ |
---|
852 | #define zaddmulpsq(a, b, t) \ |
---|
853 | { \ |
---|
854 | long _a = (a), _b = (b), _t = (t); \ |
---|
855 | long _t1 = _b*_b + _a; \ |
---|
856 | long _t2 = (long) ( ((double) _b)*(((double) _b)*NTL_FRADIX_INV) ); \ |
---|
857 | (t) = _t2 + ((_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS); \ |
---|
858 | (a) = _t1 & NTL_RADIXM; \ |
---|
859 | } |
---|
860 | |
---|
861 | #define zam_decl double _ds; long _hi, _lo, _s; |
---|
862 | |
---|
863 | #define zam_init(b,s) \ |
---|
864 | { \ |
---|
865 | long _b = (b); \ |
---|
866 | _s = (s); \ |
---|
867 | _ds = _s*NTL_FRADIX_INV; \ |
---|
868 | _lo = _b*_s; \ |
---|
869 | _hi = (long) (((double) _b)*_ds); \ |
---|
870 | } |
---|
871 | |
---|
872 | /* shift is -1..+3 */ |
---|
873 | #define zam_loop(a,t,nb) \ |
---|
874 | { \ |
---|
875 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
876 | long _vv; \ |
---|
877 | double _yy; \ |
---|
878 | _vv = _nb*_s; \ |
---|
879 | _yy = ((double) _nb)*_ds; \ |
---|
880 | _lo = _lo + _a + _t; \ |
---|
881 | (t) = _hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS); \ |
---|
882 | (a) = _lo & NTL_RADIXM; \ |
---|
883 | _lo = _vv; \ |
---|
884 | _hi = (long) _yy; \ |
---|
885 | } |
---|
886 | |
---|
887 | /* shift is -1..+2 */ |
---|
888 | #define zsx_loop(a,t,nb) \ |
---|
889 | { \ |
---|
890 | long _t = (t), _nb = (nb); \ |
---|
891 | long _vv; \ |
---|
892 | double _yy; \ |
---|
893 | _vv = _nb*_s; \ |
---|
894 | _yy = ((double) _nb)*_ds; \ |
---|
895 | _lo = _lo + _t; \ |
---|
896 | (t) = _hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS); \ |
---|
897 | (a) = _lo & NTL_RADIXM; \ |
---|
898 | _lo = _vv; \ |
---|
899 | _hi = (long) _yy; \ |
---|
900 | } |
---|
901 | |
---|
902 | /* shift is -3..+1 */ |
---|
903 | #define zam_subloop(a,t,nb) \ |
---|
904 | { \ |
---|
905 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
906 | long _vv; \ |
---|
907 | double _yy; \ |
---|
908 | _vv = _nb*_s; \ |
---|
909 | _yy = ((double) _nb)*_ds; \ |
---|
910 | _lo = _a + _t - _lo; \ |
---|
911 | (t) = ((_lo + (_hi<<NTL_NBITS)) >> NTL_NBITS) - _hi; \ |
---|
912 | (a) = _lo & NTL_RADIXM; \ |
---|
913 | _lo = _vv; \ |
---|
914 | _hi = (long) _yy; \ |
---|
915 | } |
---|
916 | |
---|
917 | /* shift is -1..+3 */ |
---|
918 | #define zam_finish(a,t) \ |
---|
919 | { \ |
---|
920 | long _a = (a), _t = (t); \ |
---|
921 | _lo = _lo + _a + _t; \ |
---|
922 | (t) = _hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS); \ |
---|
923 | (a) = _lo & NTL_RADIXM; \ |
---|
924 | } |
---|
925 | |
---|
926 | /* shift is -1..+2 */ |
---|
927 | #define zsx_finish(a,t) \ |
---|
928 | { \ |
---|
929 | long _t = (t); \ |
---|
930 | _lo = _lo + _t; \ |
---|
931 | (t) = _hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS); \ |
---|
932 | (a) = _lo & NTL_RADIXM; \ |
---|
933 | } |
---|
934 | |
---|
935 | /* shift is -3..+1 */ |
---|
936 | #define zam_subfinish(a,t) \ |
---|
937 | { \ |
---|
938 | long _a = (a), _t = (t); \ |
---|
939 | _lo = _a + _t - _lo; \ |
---|
940 | (t) = ((_lo + (_hi<<NTL_NBITS)) >> NTL_NBITS) - _hi; \ |
---|
941 | (a) = _lo & NTL_RADIXM; \ |
---|
942 | } |
---|
943 | |
---|
944 | #elif (!defined(NTL_CLEAN_INT)) |
---|
945 | /* right shift is not arithmetic */ |
---|
946 | |
---|
947 | /* shift is 0..4 */ |
---|
948 | #define zaddmulp(a, b, d, t) \ |
---|
949 | { \ |
---|
950 | long _a = (a), _b = (b), _d = (d), _t = (t); \ |
---|
951 | long _t1 = _b*_d + _a + _t; \ |
---|
952 | long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ) - 1; \ |
---|
953 | (t) = _t2 + (((unsigned long)(_t1 - (_t2 << NTL_NBITS))) >> NTL_NBITS); \ |
---|
954 | (a) = _t1 & NTL_RADIXM; \ |
---|
955 | } |
---|
956 | |
---|
957 | #define zxmulp(a, b, d, t) \ |
---|
958 | { \ |
---|
959 | long _b = (b), _d = (d), _t = (t); \ |
---|
960 | long _t1 = _b*_d + _t; \ |
---|
961 | long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ) - 1; \ |
---|
962 | (t) = _t2 + (((unsigned long)(_t1 - (_t2 << NTL_NBITS))) >> NTL_NBITS); \ |
---|
963 | (a) = _t1 & NTL_RADIXM; \ |
---|
964 | } |
---|
965 | |
---|
966 | /* shift is 0..3 */ |
---|
967 | #define zaddmulpsq(a, b, t) \ |
---|
968 | { \ |
---|
969 | long _a = (a), _b = (b), _t = (t); \ |
---|
970 | long _t1 = _b*_b + _a; \ |
---|
971 | long _t2 = (long) ( ((double) _b)*(((double) _b)*NTL_FRADIX_INV) ) - 1; \ |
---|
972 | (t) = _t2 + (((unsigned long)(_t1 - (_t2 << NTL_NBITS))) >> NTL_NBITS); \ |
---|
973 | (a) = _t1 & NTL_RADIXM; \ |
---|
974 | } |
---|
975 | |
---|
976 | #define zam_decl double _ds; long _hi, _lo, _s; |
---|
977 | |
---|
978 | #define zam_init(b,s) \ |
---|
979 | { \ |
---|
980 | long _b = (b); \ |
---|
981 | _s = (s); \ |
---|
982 | _ds = _s*NTL_FRADIX_INV; \ |
---|
983 | _lo = _b*_s; \ |
---|
984 | _hi = (long) (((double) _b)*_ds); \ |
---|
985 | } |
---|
986 | |
---|
987 | /* shift is 0..4 */ |
---|
988 | #define zam_loop(a,t,nb) \ |
---|
989 | { \ |
---|
990 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
991 | long _vv; \ |
---|
992 | double _yy; \ |
---|
993 | _vv = _nb*_s; \ |
---|
994 | _yy = ((double) _nb)*_ds; \ |
---|
995 | _hi--; \ |
---|
996 | _lo = _lo + _a + _t; \ |
---|
997 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
998 | (a) = _lo & NTL_RADIXM; \ |
---|
999 | _lo = _vv; \ |
---|
1000 | _hi = (long) _yy; \ |
---|
1001 | } |
---|
1002 | |
---|
1003 | /* shift is 0..3 */ |
---|
1004 | #define zsx_loop(a,t,nb) \ |
---|
1005 | { \ |
---|
1006 | long _t = (t), _nb = (nb); \ |
---|
1007 | long _vv; \ |
---|
1008 | double _yy; \ |
---|
1009 | _vv = _nb*_s; \ |
---|
1010 | _yy = ((double) _nb)*_ds; \ |
---|
1011 | _hi--; \ |
---|
1012 | _lo = _lo + _t; \ |
---|
1013 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
1014 | (a) = _lo & NTL_RADIXM; \ |
---|
1015 | _lo = _vv; \ |
---|
1016 | _hi = (long) _yy; \ |
---|
1017 | } |
---|
1018 | |
---|
1019 | /* shift is 0..4 */ |
---|
1020 | #define zam_subloop(a,t,nb) \ |
---|
1021 | { \ |
---|
1022 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
1023 | long _vv; \ |
---|
1024 | double _yy; \ |
---|
1025 | _vv = _nb*_s; \ |
---|
1026 | _yy = ((double) _nb)*_ds; \ |
---|
1027 | _hi += 3; \ |
---|
1028 | _lo = _a + _t - _lo; \ |
---|
1029 | (t) = (((unsigned long)(_lo + (_hi<<NTL_NBITS))) >> NTL_NBITS) - _hi; \ |
---|
1030 | (a) = _lo & NTL_RADIXM; \ |
---|
1031 | _lo = _vv; \ |
---|
1032 | _hi = (long) _yy; \ |
---|
1033 | } |
---|
1034 | |
---|
1035 | /* shift is 0..4 */ |
---|
1036 | #define zam_finish(a,t) \ |
---|
1037 | { \ |
---|
1038 | long _a = (a), _t = (t); \ |
---|
1039 | _lo = _lo + _a + _t; \ |
---|
1040 | _hi--; \ |
---|
1041 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
1042 | (a) = _lo & NTL_RADIXM; \ |
---|
1043 | } |
---|
1044 | |
---|
1045 | /* shift is 0..3 */ |
---|
1046 | #define zsx_finish(a,t) \ |
---|
1047 | { \ |
---|
1048 | long _t = (t); \ |
---|
1049 | _lo = _lo + _t; \ |
---|
1050 | _hi--; \ |
---|
1051 | (t) = _hi + (((unsigned long)(_lo - (_hi<<NTL_NBITS))) >> NTL_NBITS); \ |
---|
1052 | (a) = _lo & NTL_RADIXM; \ |
---|
1053 | } |
---|
1054 | |
---|
1055 | /* shift is 0..4 */ |
---|
1056 | #define zam_subfinish(a,t) \ |
---|
1057 | { \ |
---|
1058 | long _a = (a), _t = (t); \ |
---|
1059 | _hi += 3; \ |
---|
1060 | _lo = _a + _t - _lo; \ |
---|
1061 | (t) = (((unsigned long)(_lo + (_hi<<NTL_NBITS))) >> NTL_NBITS) - _hi; \ |
---|
1062 | (a) = _lo & NTL_RADIXM; \ |
---|
1063 | } |
---|
1064 | #else |
---|
1065 | |
---|
1066 | /* clean int version */ |
---|
1067 | |
---|
1068 | /* shift is 0..4 */ |
---|
1069 | #define zaddmulp(a, b, d, t) \ |
---|
1070 | { \ |
---|
1071 | long _a = (a), _b = (b), _d = (d), _t = (t); \ |
---|
1072 | unsigned long _t1 = ((unsigned long) _b)*((unsigned long) _d) + ((unsigned long) _a) + ((unsigned long) _t); \ |
---|
1073 | unsigned long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ) - 1; \ |
---|
1074 | (t) = (long) (_t2 + ((_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS)); \ |
---|
1075 | (a) = (long) (_t1 & NTL_RADIXM); \ |
---|
1076 | } |
---|
1077 | |
---|
1078 | #define zxmulp(a, b, d, t) \ |
---|
1079 | { \ |
---|
1080 | long _b = (b), _d = (d), _t = (t); \ |
---|
1081 | unsigned long _t1 = ((unsigned long) _b)*((unsigned long) _d) + ((unsigned long) _t); \ |
---|
1082 | unsigned long _t2 = (long) ( ((double) _b)*(((double) _d)*NTL_FRADIX_INV) ) - 1; \ |
---|
1083 | (t) = (long) (_t2 + ((_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS)); \ |
---|
1084 | (a) = (long) (_t1 & NTL_RADIXM); \ |
---|
1085 | } |
---|
1086 | |
---|
1087 | /* shift is 0..3 */ |
---|
1088 | #define zaddmulpsq(a, b, t) \ |
---|
1089 | { \ |
---|
1090 | long _a = (a), _b = (b), _t = (t); \ |
---|
1091 | unsigned long _t1 = ((unsigned long) _b)*((unsigned long) _b) + ((unsigned long) _a); \ |
---|
1092 | unsigned long _t2 = (long) ( ((double) _b)*(((double) _b)*NTL_FRADIX_INV) ) - 1; \ |
---|
1093 | (t) = (long) (_t2 + ((_t1 - (_t2 << NTL_NBITS)) >> NTL_NBITS)); \ |
---|
1094 | (a) = (long) (_t1 & NTL_RADIXM); \ |
---|
1095 | } |
---|
1096 | |
---|
1097 | #define zam_decl double _ds; long _s; unsigned long _hi, _lo; |
---|
1098 | |
---|
1099 | #define zam_init(b,s) \ |
---|
1100 | { \ |
---|
1101 | long _b = (b); \ |
---|
1102 | _s = (s); \ |
---|
1103 | _ds = _s*NTL_FRADIX_INV; \ |
---|
1104 | _lo = ((unsigned long) _b)*((unsigned long) _s); \ |
---|
1105 | _hi = (long) (((double) _b)*_ds); \ |
---|
1106 | } |
---|
1107 | |
---|
1108 | /* shift is 0..4 */ |
---|
1109 | #define zam_loop(a,t,nb) \ |
---|
1110 | { \ |
---|
1111 | long _a = (a), _t = (t), _nb = (nb); \ |
---|
1112 | unsigned long _vv; \ |
---|
1113 | double _yy; \ |
---|
1114 | _vv = ((unsigned long) _nb)*((unsigned long) _s); \ |
---|
1115 | _yy = ((double) _nb)*_ds; \ |
---|
1116 | _hi--; \ |
---|
1117 | _lo = _lo + ((unsigned long) _a) + ((unsigned long) _t); \ |
---|
1118 | (t) = (long) (_hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS)); \ |
---|
1119 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
1120 | _lo = _vv; \ |
---|
1121 | _hi = (long) _yy; \ |
---|
1122 | } |
---|
1123 | |
---|
1124 | /* shift is 0..3 */ |
---|
1125 | #define zsx_loop(a,t,nb) \ |
---|
1126 | { \ |
---|
1127 | long _t = (t), _nb = (nb); \ |
---|
1128 | unsigned long _vv; \ |
---|
1129 | double _yy; \ |
---|
1130 | _vv = ((unsigned long) _nb)*((unsigned long) _s); \ |
---|
1131 | _yy = ((double) _nb)*_ds; \ |
---|
1132 | _hi--; \ |
---|
1133 | _lo = _lo + ((unsigned long) _t); \ |
---|
1134 | (t) = (long) (_hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS)); \ |
---|
1135 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
1136 | _lo = _vv; \ |
---|
1137 | _hi = (long) _yy; \ |
---|
1138 | } |
---|
1139 | |
---|
1140 | /* shift is 0..4 */ |
---|
1141 | #define zam_subloop(a,t,nb) \ |
---|
1142 | { \ |
---|
1143 | long _a = (a); unsigned long _t = (t); long _nb = (nb); \ |
---|
1144 | unsigned long _vv; \ |
---|
1145 | double _yy; \ |
---|
1146 | _vv = ((unsigned long) _nb)*((unsigned long) _s); \ |
---|
1147 | _yy = ((double) _nb)*_ds; \ |
---|
1148 | _hi += 3; \ |
---|
1149 | _lo = ((unsigned long) _a) + _t - _lo; \ |
---|
1150 | (t) = ((_lo + (_hi<<NTL_NBITS)) >> NTL_NBITS) - _hi; \ |
---|
1151 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
1152 | _lo = _vv; \ |
---|
1153 | _hi = (long) _yy; \ |
---|
1154 | } |
---|
1155 | |
---|
1156 | /* shift is 0..4 */ |
---|
1157 | #define zam_finish(a,t) \ |
---|
1158 | { \ |
---|
1159 | long _a = (a), _t = (t); \ |
---|
1160 | _lo = _lo + ((unsigned long) _a) + ((unsigned long) _t); \ |
---|
1161 | _hi--; \ |
---|
1162 | (t) = (long) (_hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS)); \ |
---|
1163 | (a) = _lo & NTL_RADIXM; \ |
---|
1164 | } |
---|
1165 | |
---|
1166 | /* shift is 0..3 */ |
---|
1167 | #define zsx_finish(a,t) \ |
---|
1168 | { \ |
---|
1169 | long _t = (t); \ |
---|
1170 | _lo = _lo + ((unsigned long) _t); \ |
---|
1171 | _hi--; \ |
---|
1172 | (t) = (long) (_hi + ((_lo - (_hi<<NTL_NBITS)) >> NTL_NBITS)); \ |
---|
1173 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
1174 | } |
---|
1175 | |
---|
1176 | /* shift is 0..4 */ |
---|
1177 | #define zam_subfinish(a,t) \ |
---|
1178 | { \ |
---|
1179 | long _a = (a); unsigned long _t = (t); \ |
---|
1180 | _hi += 3; \ |
---|
1181 | _lo = ((unsigned long) _a) + _t - _lo; \ |
---|
1182 | (t) = ((_lo + (_hi<<NTL_NBITS)) >> NTL_NBITS) - _hi; \ |
---|
1183 | (a) = (long) (_lo & NTL_RADIXM); \ |
---|
1184 | } |
---|
1185 | |
---|
1186 | #endif |
---|
1187 | /* end of arithmetic-right-shift if-then-else */ |
---|
1188 | |
---|
1189 | #endif |
---|
1190 | /* end of "NTL_BITS_PER_LONG <= NTL_NBITS + 2" if-then-else */ |
---|
1191 | |
---|
1192 | #endif |
---|
1193 | /* end of long-integer-implementation if-then-else */ |
---|
1194 | |
---|
1195 | |
---|
1196 | |
---|
1197 | |
---|
1198 | |
---|
1199 | |
---|
1200 | static |
---|
1201 | void zaddmulone(long *lama, long *lamb) |
---|
1202 | { |
---|
1203 | long lami; |
---|
1204 | long lams = 0; |
---|
1205 | |
---|
1206 | lams = 0; |
---|
1207 | for (lami = (*lamb++); lami > 0; lami--) { |
---|
1208 | lams += (*lama + *lamb++); |
---|
1209 | *lama++ = lams & NTL_RADIXM; |
---|
1210 | lams >>= NTL_NBITS; |
---|
1211 | } |
---|
1212 | *lama += lams; |
---|
1213 | } |
---|
1214 | |
---|
1215 | #if (NTL_ARITH_RIGHT_SHIFT && !defined(NTL_CLEAN_INT)) |
---|
1216 | |
---|
1217 | static |
---|
1218 | void zsubmulone(long *lama, long *lamb) |
---|
1219 | { |
---|
1220 | long lami; |
---|
1221 | long lams = 0; |
---|
1222 | |
---|
1223 | lams = 0; |
---|
1224 | for (lami = (*lamb++); lami > 0; lami--) { |
---|
1225 | lams += (*lama - *lamb++); |
---|
1226 | *lama++ = lams & NTL_RADIXM; |
---|
1227 | lams >>= NTL_NBITS; |
---|
1228 | } |
---|
1229 | *lama += lams; |
---|
1230 | } |
---|
1231 | |
---|
1232 | |
---|
1233 | #else |
---|
1234 | |
---|
1235 | |
---|
1236 | static |
---|
1237 | void zsubmulone(long *lama, long *lamb) |
---|
1238 | { |
---|
1239 | long lami; |
---|
1240 | long lams = 0; |
---|
1241 | |
---|
1242 | lams = 0; |
---|
1243 | for (lami = (*lamb++); lami > 0; lami--) { |
---|
1244 | lams = *lama - *lamb++ - lams; |
---|
1245 | *lama++ = lams & NTL_RADIXM; |
---|
1246 | lams = (lams < 0); |
---|
1247 | } |
---|
1248 | *lama -= lams; |
---|
1249 | } |
---|
1250 | |
---|
1251 | #endif |
---|
1252 | |
---|
1253 | |
---|
1254 | /* |
---|
1255 | * definitions of zaddmul, zsxmul, zaddmulsq for the various |
---|
1256 | * long integer implementation options. |
---|
1257 | */ |
---|
1258 | |
---|
1259 | |
---|
1260 | #if (defined(NTL_SINGLE_MUL)) |
---|
1261 | |
---|
1262 | static |
---|
1263 | void zaddmul(long ams, long *ama, long *amb) |
---|
1264 | { |
---|
1265 | long carry = 0; |
---|
1266 | long i = (*amb++); |
---|
1267 | double dams = (double) ams; |
---|
1268 | double xx; |
---|
1269 | double yy; |
---|
1270 | unsigned long lo_wd, lo; |
---|
1271 | unsigned long hi_wd, hi; |
---|
1272 | |
---|
1273 | xx = ((double) (*amb++))*dams + DENORMALIZE; |
---|
1274 | for (; i > 1; i--) { |
---|
1275 | yy = ((double) (*amb++))*dams +DENORMALIZE; |
---|
1276 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1277 | lo = lo_wd & 0x3FFFFFF; |
---|
1278 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1279 | lo = lo + (*ama) + carry; |
---|
1280 | *ama = lo & 0x3FFFFFF; |
---|
1281 | carry = hi + (lo >> 26); |
---|
1282 | ama++; |
---|
1283 | xx = yy; |
---|
1284 | } |
---|
1285 | |
---|
1286 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1287 | lo = lo_wd & 0x3FFFFFF; |
---|
1288 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1289 | lo = lo + (*ama) + carry; |
---|
1290 | *ama = lo & 0x3FFFFFF; |
---|
1291 | carry = hi + (lo >> 26); |
---|
1292 | ama++; |
---|
1293 | *ama += carry; |
---|
1294 | } |
---|
1295 | |
---|
1296 | static |
---|
1297 | void zsxmul(long ams, long *ama, long *amb) |
---|
1298 | { |
---|
1299 | long carry = 0; |
---|
1300 | long i = (*amb++); |
---|
1301 | double dams = (double) ams; |
---|
1302 | double xx; |
---|
1303 | double yy; |
---|
1304 | unsigned long lo_wd, lo; |
---|
1305 | unsigned long hi_wd, hi; |
---|
1306 | |
---|
1307 | xx = ((double) (*amb++))*dams + DENORMALIZE; |
---|
1308 | for (; i > 1; i--) { |
---|
1309 | yy = ((double) (*amb++))*dams +DENORMALIZE; |
---|
1310 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1311 | lo = lo_wd & 0x3FFFFFF; |
---|
1312 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1313 | lo = lo + carry; |
---|
1314 | *ama = lo & 0x3FFFFFF; |
---|
1315 | carry = hi + (lo >> 26); |
---|
1316 | ama++; |
---|
1317 | xx = yy; |
---|
1318 | } |
---|
1319 | |
---|
1320 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1321 | lo = lo_wd & 0x3FFFFFF; |
---|
1322 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1323 | lo = lo + carry; |
---|
1324 | *ama = lo & 0x3FFFFFF; |
---|
1325 | carry = hi + (lo >> 26); |
---|
1326 | ama++; |
---|
1327 | *ama = carry; |
---|
1328 | } |
---|
1329 | |
---|
1330 | static |
---|
1331 | void zaddmulsq(long ams, long *ama, long *amb) |
---|
1332 | { |
---|
1333 | long carry = 0; |
---|
1334 | long i = ams; |
---|
1335 | double dams = (double) (*amb++); |
---|
1336 | double xx; |
---|
1337 | double yy; |
---|
1338 | unsigned long lo, lo_wd; |
---|
1339 | unsigned long hi, hi_wd; |
---|
1340 | |
---|
1341 | xx = ((double) (*amb++))*dams + DENORMALIZE; |
---|
1342 | for (; i > 1; i--) { |
---|
1343 | yy = ((double) (*amb++))*dams + DENORMALIZE; |
---|
1344 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1345 | lo = lo_wd & 0x3FFFFFF; |
---|
1346 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1347 | lo = lo + (*ama) + carry; |
---|
1348 | *ama = lo & 0x3FFFFFF; |
---|
1349 | carry = hi + (lo >> 26); |
---|
1350 | ama++; |
---|
1351 | xx = yy; |
---|
1352 | } |
---|
1353 | if (i==1) { |
---|
1354 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1355 | lo = lo_wd & 0x3FFFFFF; |
---|
1356 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1357 | lo = lo + (*ama) + carry; |
---|
1358 | *ama = lo & 0x3FFFFFF; |
---|
1359 | carry = hi + (lo >> 26); |
---|
1360 | ama++; |
---|
1361 | } |
---|
1362 | *ama += carry; |
---|
1363 | } |
---|
1364 | |
---|
1365 | #elif (defined(NTL_AVOID_FLOAT) || defined(NTL_LONG_LONG)) |
---|
1366 | |
---|
1367 | static |
---|
1368 | void zaddmul(long lams, long *lama, long *lamb) |
---|
1369 | { |
---|
1370 | long lami; |
---|
1371 | long lamcarry = 0; |
---|
1372 | |
---|
1373 | for (lami = (*lamb++); lami > 0; lami--) |
---|
1374 | { |
---|
1375 | zaddmulp(*lama, *lamb, lams, lamcarry); |
---|
1376 | lama++; |
---|
1377 | lamb++; |
---|
1378 | } |
---|
1379 | *lama += lamcarry; |
---|
1380 | } |
---|
1381 | |
---|
1382 | static |
---|
1383 | void zsxmul(long lams, long *lama, long *lamb) |
---|
1384 | { |
---|
1385 | long lami; |
---|
1386 | long lamcarry = 0; |
---|
1387 | |
---|
1388 | for (lami = (*lamb++); lami > 0; lami--) |
---|
1389 | { |
---|
1390 | zxmulp(*lama, *lamb, lams, lamcarry); |
---|
1391 | lama++; |
---|
1392 | lamb++; |
---|
1393 | } |
---|
1394 | *lama = lamcarry; |
---|
1395 | } |
---|
1396 | |
---|
1397 | static |
---|
1398 | void zaddmulsq(long lsqi, long *lsqa, long *lsqb) |
---|
1399 | { |
---|
1400 | long lsqs = *(lsqb); |
---|
1401 | long lsqcarry = 0; |
---|
1402 | |
---|
1403 | lsqb++; |
---|
1404 | for (; lsqi > 0; lsqi--) |
---|
1405 | { |
---|
1406 | zaddmulp(*lsqa, *lsqb, lsqs, lsqcarry); |
---|
1407 | lsqa++; |
---|
1408 | lsqb++; |
---|
1409 | } |
---|
1410 | *lsqa += lsqcarry; |
---|
1411 | } |
---|
1412 | |
---|
1413 | |
---|
1414 | #else |
---|
1415 | /* default long integer arithmetic */ |
---|
1416 | |
---|
1417 | static |
---|
1418 | void zaddmul(long lams, long *lama, long *lamb) |
---|
1419 | { |
---|
1420 | long lami = (*lamb++)-1; |
---|
1421 | long lamcarry = 0; |
---|
1422 | zam_decl; |
---|
1423 | |
---|
1424 | zam_init(*lamb, lams); |
---|
1425 | lamb++; |
---|
1426 | |
---|
1427 | |
---|
1428 | for (; lami > 0; lami--) { |
---|
1429 | zam_loop(*lama, lamcarry, *lamb); |
---|
1430 | lama++; |
---|
1431 | lamb++; |
---|
1432 | } |
---|
1433 | zam_finish(*lama, lamcarry); |
---|
1434 | lama++; |
---|
1435 | *lama += lamcarry; |
---|
1436 | } |
---|
1437 | |
---|
1438 | |
---|
1439 | |
---|
1440 | static |
---|
1441 | void zsxmul(long lams, long *lama, long *lamb) |
---|
1442 | { |
---|
1443 | long lami = (*lamb++)-1; |
---|
1444 | long lamcarry = 0; |
---|
1445 | zam_decl; |
---|
1446 | |
---|
1447 | zam_init(*lamb, lams); |
---|
1448 | lamb++; |
---|
1449 | |
---|
1450 | |
---|
1451 | for (; lami > 0; lami--) { |
---|
1452 | zsx_loop(*lama, lamcarry, *lamb); |
---|
1453 | lama++; |
---|
1454 | lamb++; |
---|
1455 | } |
---|
1456 | zsx_finish(*lama, lamcarry); |
---|
1457 | lama++; |
---|
1458 | *lama = lamcarry; |
---|
1459 | } |
---|
1460 | |
---|
1461 | |
---|
1462 | |
---|
1463 | static |
---|
1464 | void zaddmulsq(long lsqi, long *lsqa, long *lsqb) |
---|
1465 | { |
---|
1466 | long lsqs; |
---|
1467 | long lsqcarry; |
---|
1468 | zam_decl |
---|
1469 | |
---|
1470 | if (lsqi <= 0) return; |
---|
1471 | |
---|
1472 | lsqs = *lsqb; |
---|
1473 | lsqcarry = 0; |
---|
1474 | |
---|
1475 | lsqb++; |
---|
1476 | zam_init(*lsqb, lsqs); |
---|
1477 | lsqb++; |
---|
1478 | lsqi--; |
---|
1479 | for (; lsqi > 0; lsqi--) { |
---|
1480 | zam_loop(*lsqa, lsqcarry, *lsqb); |
---|
1481 | lsqa++; |
---|
1482 | lsqb++; |
---|
1483 | } |
---|
1484 | zam_finish(*lsqa, lsqcarry); |
---|
1485 | lsqa++; |
---|
1486 | *lsqa += lsqcarry; |
---|
1487 | } |
---|
1488 | |
---|
1489 | |
---|
1490 | #endif |
---|
1491 | |
---|
1492 | |
---|
1493 | |
---|
1494 | |
---|
1495 | |
---|
1496 | |
---|
1497 | |
---|
1498 | /* |
---|
1499 | * definition of zsubmul for the various long integer implementation options. |
---|
1500 | * Note that zsubmul is only called with a positive first argument. |
---|
1501 | */ |
---|
1502 | |
---|
1503 | |
---|
1504 | |
---|
1505 | #if (defined(NTL_SINGLE_MUL)) |
---|
1506 | |
---|
1507 | #if (NTL_ARITH_RIGHT_SHIFT) |
---|
1508 | |
---|
1509 | static |
---|
1510 | void zsubmul(long ams, long *ama, long *amb) |
---|
1511 | { |
---|
1512 | long carry = 0; |
---|
1513 | long i = (*amb++); |
---|
1514 | double dams = (double) ams; |
---|
1515 | double xx; |
---|
1516 | double yy; |
---|
1517 | unsigned long lo_wd, lo; |
---|
1518 | unsigned long hi_wd, hi; |
---|
1519 | |
---|
1520 | xx = ((double) (*amb++))*dams + DENORMALIZE; |
---|
1521 | for (; i > 1; i--) { |
---|
1522 | yy = ((double) (*amb++))*dams +DENORMALIZE; |
---|
1523 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1524 | lo = lo_wd & 0x3FFFFFF; |
---|
1525 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1526 | lo = (*ama) + carry - lo; |
---|
1527 | *ama = lo & 0x3FFFFFF; |
---|
1528 | carry = (((long)lo) >> 26) - hi; |
---|
1529 | ama++; |
---|
1530 | xx = yy; |
---|
1531 | } |
---|
1532 | |
---|
1533 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1534 | lo = lo_wd & 0x3FFFFFF; |
---|
1535 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1536 | lo = (*ama) + carry - lo; |
---|
1537 | *ama = lo & 0x3FFFFFF; |
---|
1538 | carry = (((long)lo) >> 26) - hi; |
---|
1539 | ama++; |
---|
1540 | *ama += carry; |
---|
1541 | } |
---|
1542 | |
---|
1543 | #else |
---|
1544 | |
---|
1545 | static |
---|
1546 | void zsubmul(long ams, long *ama, long *amb) |
---|
1547 | { |
---|
1548 | long carry = 0; |
---|
1549 | long i = (*amb++); |
---|
1550 | double dams = (double) ams; |
---|
1551 | double xx; |
---|
1552 | double yy; |
---|
1553 | unsigned long lo_wd, lo; |
---|
1554 | unsigned long hi_wd, hi; |
---|
1555 | |
---|
1556 | xx = ((double) (*amb++))*dams + DENORMALIZE; |
---|
1557 | for (; i > 1; i--) { |
---|
1558 | yy = ((double) (*amb++))*dams +DENORMALIZE; |
---|
1559 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1560 | lo = lo_wd & 0x3FFFFFF; |
---|
1561 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1562 | lo = (*ama) + carry - lo; |
---|
1563 | *ama = lo & 0x3FFFFFF; |
---|
1564 | carry = ((lo + (1L << 27)) >> 26) - hi - 2; |
---|
1565 | ama++; |
---|
1566 | xx = yy; |
---|
1567 | } |
---|
1568 | |
---|
1569 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
1570 | lo = lo_wd & 0x3FFFFFF; |
---|
1571 | hi = ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
1572 | lo = (*ama) + carry - lo; |
---|
1573 | *ama = lo & 0x3FFFFFF; |
---|
1574 | carry = ((lo + (1L << 27)) >> 26) - hi - 2; |
---|
1575 | ama++; |
---|
1576 | *ama += carry; |
---|
1577 | } |
---|
1578 | |
---|
1579 | #endif |
---|
1580 | |
---|
1581 | |
---|
1582 | |
---|
1583 | #elif (defined(NTL_AVOID_FLOAT) || (defined(NTL_LONG_LONG) && defined(NTL_CLEAN_INT))) |
---|
1584 | |
---|
1585 | static void |
---|
1586 | zsubmul( |
---|
1587 | long r, |
---|
1588 | _ntl_verylong a, |
---|
1589 | _ntl_verylong b |
---|
1590 | ) |
---|
1591 | { |
---|
1592 | long rd = NTL_RADIX - r; |
---|
1593 | long i; |
---|
1594 | long carry = NTL_RADIX; |
---|
1595 | |
---|
1596 | for (i = (*b++); i > 0; i--) |
---|
1597 | { |
---|
1598 | zaddmulp(*a, *b, rd, carry); |
---|
1599 | a++; |
---|
1600 | carry += NTL_RADIXM - (*b++); |
---|
1601 | } |
---|
1602 | *a += carry - NTL_RADIX; /* unnormalized */ |
---|
1603 | } |
---|
1604 | |
---|
1605 | #elif (defined(NTL_LONG_LONG)) |
---|
1606 | |
---|
1607 | /* |
---|
1608 | * NOTE: the implementation of zaddmulp for the NTL_LONG_LONG option |
---|
1609 | * will work on most machines even when the single-precision |
---|
1610 | * multiplicand is negative; however, the C language standard does |
---|
1611 | * not guarantee correct behaviour in this case, which is why the above |
---|
1612 | * implementation is used when NTL_CLEAN_INT is set. |
---|
1613 | */ |
---|
1614 | |
---|
1615 | static |
---|
1616 | void zsubmul(long lams, long *lama, long *lamb) |
---|
1617 | { |
---|
1618 | long lami; |
---|
1619 | long lamcarry = 0; |
---|
1620 | |
---|
1621 | lams = -lams; |
---|
1622 | |
---|
1623 | for (lami = (*lamb++); lami > 0; lami--) |
---|
1624 | { |
---|
1625 | zaddmulp(*lama, *lamb, lams, lamcarry); |
---|
1626 | lama++; |
---|
1627 | lamb++; |
---|
1628 | } |
---|
1629 | *lama += lamcarry; |
---|
1630 | } |
---|
1631 | |
---|
1632 | |
---|
1633 | #else |
---|
1634 | /* default long integer arithmetic */ |
---|
1635 | |
---|
1636 | static |
---|
1637 | void zsubmul(long lams, long *lama, long *lamb) |
---|
1638 | { |
---|
1639 | long lami = (*lamb++)-1; |
---|
1640 | CARRY_TYPE lamcarry = 0; |
---|
1641 | zam_decl; |
---|
1642 | |
---|
1643 | zam_init(*lamb, lams); |
---|
1644 | lamb++; |
---|
1645 | |
---|
1646 | |
---|
1647 | for (; lami > 0; lami--) { |
---|
1648 | zam_subloop(*lama, lamcarry, *lamb); |
---|
1649 | lama++; |
---|
1650 | lamb++; |
---|
1651 | } |
---|
1652 | zam_subfinish(*lama, lamcarry); |
---|
1653 | lama++; |
---|
1654 | *lama += CARRY_CONV(lamcarry); |
---|
1655 | } |
---|
1656 | |
---|
1657 | #endif |
---|
1658 | |
---|
1659 | |
---|
1660 | |
---|
1661 | |
---|
1662 | |
---|
1663 | /* |
---|
1664 | * |
---|
1665 | * zdiv21 returns quot, numhigh so |
---|
1666 | * |
---|
1667 | * quot = (numhigh*NTL_RADIX + numlow)/denom; |
---|
1668 | * numhigh = (numhigh*NTL_RADIX + numlow)%denom; |
---|
1669 | * Assumes 0 <= numhigh < denom < NTL_RADIX and 0 <= numlow < NTL_RADIX. |
---|
1670 | */ |
---|
1671 | |
---|
1672 | |
---|
1673 | #if (defined(NTL_CLEAN_INT)) |
---|
1674 | |
---|
1675 | /* |
---|
1676 | * This "clean" version relies on the guaranteed semantics of |
---|
1677 | * unsigned integer arithmetic. |
---|
1678 | */ |
---|
1679 | |
---|
1680 | #define zdiv21(numhigh, numlow, denom, deninv, quot) \ |
---|
1681 | { \ |
---|
1682 | unsigned long udenom = denom; \ |
---|
1683 | unsigned long lq21 = (long) (((NTL_FRADIX * (double) (numhigh)) + \ |
---|
1684 | (double) (numlow)) * (deninv)); \ |
---|
1685 | unsigned long lr21 = (((unsigned long) numhigh) << NTL_NBITS) + \ |
---|
1686 | ((unsigned long) numlow) - udenom*lq21 ; \ |
---|
1687 | \ |
---|
1688 | if (lr21 >> (NTL_BITS_PER_LONG-1)) { \ |
---|
1689 | lq21--; \ |
---|
1690 | lr21 += udenom; \ |
---|
1691 | } \ |
---|
1692 | else if (lr21 >= udenom) { \ |
---|
1693 | lr21 -= udenom; \ |
---|
1694 | lq21++; \ |
---|
1695 | } \ |
---|
1696 | quot = (long) lq21; \ |
---|
1697 | numhigh = (long) lr21; \ |
---|
1698 | } |
---|
1699 | |
---|
1700 | |
---|
1701 | #else |
---|
1702 | |
---|
1703 | /* |
---|
1704 | * This "less clean" version relies on wrap-around semantics for |
---|
1705 | * signed integer arithmetic. |
---|
1706 | */ |
---|
1707 | |
---|
1708 | #define zdiv21(numhigh, numlow, denom, deninv, quot) \ |
---|
1709 | { \ |
---|
1710 | long lr21; \ |
---|
1711 | long lq21 = (long) (((NTL_FRADIX * (double) (numhigh)) \ |
---|
1712 | + (double) (numlow)) * (deninv)); \ |
---|
1713 | long lp21; \ |
---|
1714 | MulLo(lp21, lq21, denom); \ |
---|
1715 | lr21 = (numhigh << NTL_NBITS) + numlow - lp21; \ |
---|
1716 | if (lr21 < 0) { \ |
---|
1717 | lq21--; \ |
---|
1718 | lr21 += denom; \ |
---|
1719 | } \ |
---|
1720 | else if (lr21 >= denom) { \ |
---|
1721 | lr21 -= denom; \ |
---|
1722 | lq21++; \ |
---|
1723 | } \ |
---|
1724 | quot = lq21; \ |
---|
1725 | numhigh = lr21; \ |
---|
1726 | } |
---|
1727 | |
---|
1728 | #endif |
---|
1729 | |
---|
1730 | |
---|
1731 | |
---|
1732 | |
---|
1733 | /* |
---|
1734 | * zrem21 behaves just like zdiv21, except the only the remainder is computed. |
---|
1735 | */ |
---|
1736 | |
---|
1737 | |
---|
1738 | #if (defined(NTL_CLEAN_INT)) |
---|
1739 | |
---|
1740 | #define zrem21(numhigh, numlow, denom, deninv) \ |
---|
1741 | { \ |
---|
1742 | unsigned long udenom = denom; \ |
---|
1743 | unsigned long lq21 = (long) (((NTL_FRADIX * (double) (numhigh)) + \ |
---|
1744 | (double) (numlow)) * (deninv)); \ |
---|
1745 | unsigned long lr21 = (((unsigned long) numhigh) << NTL_NBITS) + \ |
---|
1746 | ((unsigned long) numlow) - udenom*lq21 ; \ |
---|
1747 | \ |
---|
1748 | if (lr21 >> (NTL_BITS_PER_LONG-1)) { \ |
---|
1749 | lr21 += udenom; \ |
---|
1750 | } \ |
---|
1751 | else if (lr21 >= udenom) { \ |
---|
1752 | lr21 -= udenom; \ |
---|
1753 | } \ |
---|
1754 | numhigh = (long) lr21; \ |
---|
1755 | } |
---|
1756 | |
---|
1757 | |
---|
1758 | #elif (NTL_ARITH_RIGHT_SHIFT && defined(NTL_AVOID_BRANCHING)) |
---|
1759 | |
---|
1760 | #define zrem21(numhigh, numlow, denom, deninv) \ |
---|
1761 | { \ |
---|
1762 | long lr21; \ |
---|
1763 | long lq21 = (long) (((NTL_FRADIX * (double) (numhigh)) \ |
---|
1764 | + (double) (numlow)) * (deninv)); \ |
---|
1765 | long lp21; \ |
---|
1766 | MulLo(lp21, lq21, denom); \ |
---|
1767 | lr21 = (numhigh << NTL_NBITS) + numlow - lp21; \ |
---|
1768 | lr21 += (lr21 >> (NTL_BITS_PER_LONG-1)) & denom; \ |
---|
1769 | lr21 -= denom; \ |
---|
1770 | lr21 += (lr21 >> (NTL_BITS_PER_LONG-1)) & denom; \ |
---|
1771 | numhigh = lr21; \ |
---|
1772 | } |
---|
1773 | |
---|
1774 | #else |
---|
1775 | |
---|
1776 | #define zrem21(numhigh, numlow, denom, deninv) \ |
---|
1777 | { \ |
---|
1778 | long lr21; \ |
---|
1779 | long lq21 = (long) (((NTL_FRADIX * (double) (numhigh)) \ |
---|
1780 | + (double) (numlow)) * (deninv)); \ |
---|
1781 | long lp21; \ |
---|
1782 | MulLo(lp21, lq21, denom); \ |
---|
1783 | lr21 = (numhigh << NTL_NBITS) + numlow - lp21; \ |
---|
1784 | if (lr21 < 0) lr21 += denom; \ |
---|
1785 | else if (lr21 >= denom) lr21 -= denom; \ |
---|
1786 | numhigh = lr21; \ |
---|
1787 | } |
---|
1788 | |
---|
1789 | #endif |
---|
1790 | |
---|
1791 | |
---|
1792 | |
---|
1793 | void _ntl_zsetlength(_ntl_verylong *v, long len) |
---|
1794 | { |
---|
1795 | _ntl_verylong x = *v; |
---|
1796 | |
---|
1797 | if (len < 0) |
---|
1798 | zhalt("negative size allocation in _ntl_zsetlength"); |
---|
1799 | |
---|
1800 | if (NTL_OVERFLOW(len, NTL_NBITS, 0)) |
---|
1801 | zhalt("size too big in _ntl_zsetlength"); |
---|
1802 | |
---|
1803 | #ifdef L_TO_G_CHECK_LEN |
---|
1804 | /* this makes sure that numbers don't get too big for GMP */ |
---|
1805 | if (len >= (1L << (NTL_BITS_PER_INT-4))) |
---|
1806 | zhalt("size too big for GMP"); |
---|
1807 | #endif |
---|
1808 | |
---|
1809 | if (x) { |
---|
1810 | long oldlen = x[-1]; |
---|
1811 | long fixed = oldlen & 1; |
---|
1812 | |
---|
1813 | oldlen = oldlen >> 1; |
---|
1814 | |
---|
1815 | if (fixed) { |
---|
1816 | if (len > oldlen) |
---|
1817 | zhalt("internal error: can't grow this _ntl_verylong"); |
---|
1818 | else |
---|
1819 | return; |
---|
1820 | } |
---|
1821 | |
---|
1822 | if (len <= oldlen) return; |
---|
1823 | |
---|
1824 | len++; /* always allocate at least one more than requested */ |
---|
1825 | |
---|
1826 | oldlen = (long) (oldlen * 1.2); /* always increase by at least 20% */ |
---|
1827 | if (len < oldlen) |
---|
1828 | len = oldlen; |
---|
1829 | |
---|
1830 | /* round up to multiple of MIN_SETL */ |
---|
1831 | len = ((len+(MIN_SETL-1))/MIN_SETL)*MIN_SETL; |
---|
1832 | |
---|
1833 | /* test len again */ |
---|
1834 | if (NTL_OVERFLOW(len, NTL_NBITS, 0)) |
---|
1835 | zhalt("size too big in _ntl_zsetlength"); |
---|
1836 | |
---|
1837 | x[-1] = len << 1; |
---|
1838 | if (!(x = (_ntl_verylong)NTL_REALLOC(&(x[-1]), |
---|
1839 | len, sizeof(long), 2*sizeof(long)))) { |
---|
1840 | zhalt("reallocation failed in _ntl_zsetlength"); |
---|
1841 | } |
---|
1842 | } |
---|
1843 | else { |
---|
1844 | len++; |
---|
1845 | len = ((len+(MIN_SETL-1))/MIN_SETL)*MIN_SETL; |
---|
1846 | |
---|
1847 | /* test len again */ |
---|
1848 | if (NTL_OVERFLOW(len, NTL_NBITS, 0)) |
---|
1849 | zhalt("size too big in _ntl_zsetlength"); |
---|
1850 | |
---|
1851 | |
---|
1852 | if (!(x = (_ntl_verylong)NTL_MALLOC(len, |
---|
1853 | sizeof(long), 2*sizeof(long)))) { |
---|
1854 | zhalt("allocation failed in _ntl_zsetlength"); |
---|
1855 | } |
---|
1856 | x[0] = len << 1; |
---|
1857 | x[1] = 1; |
---|
1858 | x[2] = 0; |
---|
1859 | } |
---|
1860 | |
---|
1861 | *v = x+1; |
---|
1862 | } |
---|
1863 | |
---|
1864 | void _ntl_zfree(_ntl_verylong *x) |
---|
1865 | { |
---|
1866 | _ntl_verylong y; |
---|
1867 | |
---|
1868 | if (!(*x)) |
---|
1869 | return; |
---|
1870 | |
---|
1871 | if ((*x)[-1] & 1) |
---|
1872 | zhalt("Internal error: can't free this _ntl_verylong"); |
---|
1873 | |
---|
1874 | y = (*x - 1); |
---|
1875 | free((void*)y); |
---|
1876 | *x = 0; |
---|
1877 | } |
---|
1878 | |
---|
1879 | |
---|
1880 | |
---|
1881 | |
---|
1882 | |
---|
1883 | |
---|
1884 | long _ntl_zround_correction(_ntl_verylong a, long k, long residual) |
---|
1885 | { |
---|
1886 | long direction; |
---|
1887 | long p; |
---|
1888 | long sgn; |
---|
1889 | long bl; |
---|
1890 | long wh; |
---|
1891 | long i; |
---|
1892 | |
---|
1893 | if (a[0] > 0) |
---|
1894 | sgn = 1; |
---|
1895 | else |
---|
1896 | sgn = -1; |
---|
1897 | |
---|
1898 | p = k - 1; |
---|
1899 | bl = (p/NTL_NBITS); |
---|
1900 | wh = 1L << (p - NTL_NBITS*bl); |
---|
1901 | bl++; |
---|
1902 | |
---|
1903 | if (a[bl] & wh) { |
---|
1904 | /* bit is 1...we have to see if lower bits are all 0 |
---|
1905 | in order to implement "round to even" */ |
---|
1906 | |
---|
1907 | if (a[bl] & (wh - 1)) |
---|
1908 | direction = 1; |
---|
1909 | else { |
---|
1910 | i = bl - 1; |
---|
1911 | while (i > 0 && a[i] == 0) i--; |
---|
1912 | if (i > 0) |
---|
1913 | direction = 1; |
---|
1914 | else |
---|
1915 | direction = 0; |
---|
1916 | } |
---|
1917 | |
---|
1918 | /* use residual to break ties */ |
---|
1919 | |
---|
1920 | if (direction == 0 && residual != 0) { |
---|
1921 | if (residual == sgn) |
---|
1922 | direction = 1; |
---|
1923 | else |
---|
1924 | direction = -1; |
---|
1925 | } |
---|
1926 | |
---|
1927 | if (direction == 0) { |
---|
1928 | /* round to even */ |
---|
1929 | |
---|
1930 | wh = wh << 1; |
---|
1931 | if (wh == NTL_RADIX) { |
---|
1932 | wh = 1; |
---|
1933 | bl++; |
---|
1934 | } |
---|
1935 | |
---|
1936 | if (a[bl] & wh) |
---|
1937 | direction = 1; |
---|
1938 | else |
---|
1939 | direction = -1; |
---|
1940 | } |
---|
1941 | } |
---|
1942 | else |
---|
1943 | direction = -1; |
---|
1944 | |
---|
1945 | if (direction == 1) |
---|
1946 | return sgn; |
---|
1947 | |
---|
1948 | return 0; |
---|
1949 | } |
---|
1950 | |
---|
1951 | |
---|
1952 | |
---|
1953 | double _ntl_zdoub_aux(_ntl_verylong n) |
---|
1954 | { |
---|
1955 | double res; |
---|
1956 | long i; |
---|
1957 | |
---|
1958 | if (!n) |
---|
1959 | return ((double) 0); |
---|
1960 | if ((i = n[0]) < 0) |
---|
1961 | i = -i; |
---|
1962 | res = (double) (n[i--]); |
---|
1963 | for (; i; i--) |
---|
1964 | res = res * NTL_FRADIX + (double) (n[i]); |
---|
1965 | if (n[0] > 0) |
---|
1966 | return (res); |
---|
1967 | return (-res); |
---|
1968 | } |
---|
1969 | |
---|
1970 | |
---|
1971 | |
---|
1972 | double _ntl_zdoub(_ntl_verylong n) |
---|
1973 | { |
---|
1974 | static _ntl_verylong tmp = 0; |
---|
1975 | |
---|
1976 | long s; |
---|
1977 | long shamt; |
---|
1978 | long correction; |
---|
1979 | double x; |
---|
1980 | |
---|
1981 | s = _ntl_z2log(n); |
---|
1982 | shamt = s - NTL_DOUBLE_PRECISION; |
---|
1983 | |
---|
1984 | if (shamt <= 0) |
---|
1985 | return _ntl_zdoub_aux(n); |
---|
1986 | |
---|
1987 | _ntl_zrshift(n, shamt, &tmp); |
---|
1988 | |
---|
1989 | correction = _ntl_zround_correction(n, shamt, 0); |
---|
1990 | |
---|
1991 | if (correction) _ntl_zsadd(tmp, correction, &tmp); |
---|
1992 | |
---|
1993 | x = _ntl_zdoub_aux(tmp); |
---|
1994 | |
---|
1995 | x = _ntl_ldexp(x, shamt); |
---|
1996 | |
---|
1997 | return x; |
---|
1998 | } |
---|
1999 | |
---|
2000 | |
---|
2001 | double _ntl_zlog(_ntl_verylong n) |
---|
2002 | { |
---|
2003 | static _ntl_verylong tmp = 0; |
---|
2004 | |
---|
2005 | static double log_2; |
---|
2006 | static long init = 0; |
---|
2007 | |
---|
2008 | long s; |
---|
2009 | long shamt; |
---|
2010 | long correction; |
---|
2011 | double x; |
---|
2012 | |
---|
2013 | if (!init) { |
---|
2014 | log_2 = log(2.0); |
---|
2015 | init = 1; |
---|
2016 | } |
---|
2017 | |
---|
2018 | if (_ntl_zsign(n) <= 0) |
---|
2019 | zhalt("log argument <= 0"); |
---|
2020 | |
---|
2021 | s = _ntl_z2log(n); |
---|
2022 | shamt = s - NTL_DOUBLE_PRECISION; |
---|
2023 | |
---|
2024 | if (shamt <= 0) |
---|
2025 | return log(_ntl_zdoub_aux(n)); |
---|
2026 | |
---|
2027 | _ntl_zrshift(n, shamt, &tmp); |
---|
2028 | |
---|
2029 | correction = _ntl_zround_correction(n, shamt, 0); |
---|
2030 | |
---|
2031 | if (correction) _ntl_zsadd(tmp, correction, &tmp); |
---|
2032 | |
---|
2033 | x = _ntl_zdoub_aux(tmp); |
---|
2034 | |
---|
2035 | return log(x) + shamt*log_2; |
---|
2036 | } |
---|
2037 | |
---|
2038 | |
---|
2039 | |
---|
2040 | void _ntl_zdoubtoz(double a, _ntl_verylong *xx) |
---|
2041 | { |
---|
2042 | _ntl_verylong x; |
---|
2043 | long neg, i, t, sz; |
---|
2044 | |
---|
2045 | |
---|
2046 | a = floor(a); |
---|
2047 | |
---|
2048 | if (!_ntl_IsFinite(&a)) |
---|
2049 | zhalt("_ntl_zdoubtoz: attempt to convert non-finite value"); |
---|
2050 | |
---|
2051 | |
---|
2052 | if (a < 0) { |
---|
2053 | a = -a; |
---|
2054 | neg = 1; |
---|
2055 | } |
---|
2056 | else |
---|
2057 | neg = 0; |
---|
2058 | |
---|
2059 | if (a == 0) { |
---|
2060 | _ntl_zzero(xx); |
---|
2061 | return; |
---|
2062 | } |
---|
2063 | |
---|
2064 | sz = 1; |
---|
2065 | a = a*NTL_FRADIX_INV; |
---|
2066 | |
---|
2067 | while (a >= 1) { |
---|
2068 | a = a*NTL_FRADIX_INV; |
---|
2069 | sz++; |
---|
2070 | } |
---|
2071 | |
---|
2072 | x = *xx; |
---|
2073 | if (MustAlloc(x, sz)) { |
---|
2074 | _ntl_zsetlength(&x, sz); |
---|
2075 | *xx = x; |
---|
2076 | } |
---|
2077 | |
---|
2078 | for (i = sz; i > 0; i--) { |
---|
2079 | a = a*NTL_FRADIX; |
---|
2080 | t = (long) a; |
---|
2081 | x[i] = t; |
---|
2082 | a = a - t; |
---|
2083 | } |
---|
2084 | |
---|
2085 | x[0] = (neg ? -sz : sz); |
---|
2086 | } |
---|
2087 | |
---|
2088 | void _ntl_zzero(_ntl_verylong *aa) |
---|
2089 | { |
---|
2090 | if (!(*aa)) _ntl_zsetlength(aa, 1); |
---|
2091 | (*aa)[0] = 1; |
---|
2092 | (*aa)[1] = 0; |
---|
2093 | } |
---|
2094 | |
---|
2095 | /* same as _ntl_zzero, except does not unnecessarily allocate space */ |
---|
2096 | |
---|
2097 | void _ntl_zzero1(_ntl_verylong *aa) |
---|
2098 | { |
---|
2099 | if (!(*aa)) return; |
---|
2100 | (*aa)[0] = 1; |
---|
2101 | (*aa)[1] = 0; |
---|
2102 | } |
---|
2103 | |
---|
2104 | void _ntl_zone(_ntl_verylong *aa) |
---|
2105 | { |
---|
2106 | if (!(*aa)) _ntl_zsetlength(aa, 1); |
---|
2107 | (*aa)[0] = 1; |
---|
2108 | (*aa)[1] = 1; |
---|
2109 | } |
---|
2110 | |
---|
2111 | void _ntl_zcopy(_ntl_verylong a, _ntl_verylong *bb) |
---|
2112 | { |
---|
2113 | long i; |
---|
2114 | _ntl_verylong b = *bb; |
---|
2115 | |
---|
2116 | if (!a) { |
---|
2117 | _ntl_zzero(bb); |
---|
2118 | return; |
---|
2119 | } |
---|
2120 | if (a != b) { |
---|
2121 | if ((i = *a) < 0) |
---|
2122 | i = (-i); |
---|
2123 | if (MustAlloc(b, i)) { |
---|
2124 | _ntl_zsetlength(&b, i); |
---|
2125 | *bb = b; |
---|
2126 | } |
---|
2127 | for (; i >= 0; i--) |
---|
2128 | *b++ = *a++; |
---|
2129 | } |
---|
2130 | } |
---|
2131 | |
---|
2132 | /* same as _ntl_zcopy, but does not unnecessarily allocate space */ |
---|
2133 | |
---|
2134 | void _ntl_zcopy1(_ntl_verylong a, _ntl_verylong *bb) |
---|
2135 | { |
---|
2136 | long i; |
---|
2137 | _ntl_verylong b = *bb; |
---|
2138 | |
---|
2139 | if (!a) { |
---|
2140 | _ntl_zzero1(bb); |
---|
2141 | return; |
---|
2142 | } |
---|
2143 | if (a != b) { |
---|
2144 | if ((i = *a) < 0) |
---|
2145 | i = (-i); |
---|
2146 | if (MustAlloc(b, i)) { |
---|
2147 | _ntl_zsetlength(&b, i); |
---|
2148 | *bb = b; |
---|
2149 | } |
---|
2150 | for (; i >= 0; i--) |
---|
2151 | *b++ = *a++; |
---|
2152 | } |
---|
2153 | } |
---|
2154 | |
---|
2155 | void _ntl_zintoz(long d, _ntl_verylong *aa) |
---|
2156 | { |
---|
2157 | long i; |
---|
2158 | long anegative; |
---|
2159 | unsigned long d1, d2; |
---|
2160 | _ntl_verylong a = *aa; |
---|
2161 | |
---|
2162 | anegative = 0; |
---|
2163 | if (d < 0) { |
---|
2164 | anegative = 1; |
---|
2165 | d1 = - ((unsigned long) d); /* careful: avoid overflow */ |
---|
2166 | } |
---|
2167 | else |
---|
2168 | d1 = d; |
---|
2169 | |
---|
2170 | i = 0; |
---|
2171 | d2 = d1; |
---|
2172 | do { |
---|
2173 | d2 >>= NTL_NBITS; |
---|
2174 | i++; |
---|
2175 | } |
---|
2176 | while (d2 > 0); |
---|
2177 | |
---|
2178 | if (MustAlloc(a, i)) { |
---|
2179 | _ntl_zsetlength(&a, i); |
---|
2180 | *aa = a; |
---|
2181 | } |
---|
2182 | |
---|
2183 | i = 0; |
---|
2184 | a[1] = 0; |
---|
2185 | while (d1 > 0) { |
---|
2186 | a[++i] = d1 & NTL_RADIXM; |
---|
2187 | d1 >>= NTL_NBITS; |
---|
2188 | } |
---|
2189 | if (i > 0) |
---|
2190 | a[0] = i; |
---|
2191 | else |
---|
2192 | a[0] = 1; |
---|
2193 | |
---|
2194 | if (anegative) |
---|
2195 | a[0] = (-a[0]); |
---|
2196 | } |
---|
2197 | |
---|
2198 | |
---|
2199 | /* same as _ntl_zintoz, but does not unnecessarily allocate space */ |
---|
2200 | |
---|
2201 | void _ntl_zintoz1(long d, _ntl_verylong *aa) |
---|
2202 | { |
---|
2203 | long i; |
---|
2204 | long anegative; |
---|
2205 | unsigned long d1, d2; |
---|
2206 | _ntl_verylong a = *aa; |
---|
2207 | |
---|
2208 | if (!d && !a) return; |
---|
2209 | |
---|
2210 | anegative = 0; |
---|
2211 | if (d < 0) { |
---|
2212 | anegative = 1; |
---|
2213 | d1 = - ((unsigned long) d); /* careful: avoid overlow */ |
---|
2214 | } |
---|
2215 | else |
---|
2216 | d1 = d; |
---|
2217 | |
---|
2218 | i = 0; |
---|
2219 | d2 = d1; |
---|
2220 | do { |
---|
2221 | d2 >>= NTL_NBITS; |
---|
2222 | i++; |
---|
2223 | } |
---|
2224 | while (d2 > 0); |
---|
2225 | |
---|
2226 | if (MustAlloc(a, i)) { |
---|
2227 | _ntl_zsetlength(&a, i); |
---|
2228 | *aa = a; |
---|
2229 | } |
---|
2230 | |
---|
2231 | i = 0; |
---|
2232 | a[1] = 0; |
---|
2233 | while (d1 > 0) { |
---|
2234 | a[++i] = d1 & NTL_RADIXM; |
---|
2235 | d1 >>= NTL_NBITS; |
---|
2236 | } |
---|
2237 | if (i > 0) |
---|
2238 | a[0] = i; |
---|
2239 | else |
---|
2240 | a[0] = 1; |
---|
2241 | |
---|
2242 | if (anegative) |
---|
2243 | a[0] = (-a[0]); |
---|
2244 | } |
---|
2245 | |
---|
2246 | |
---|
2247 | void _ntl_zuintoz(unsigned long d, _ntl_verylong *aa) |
---|
2248 | { |
---|
2249 | long i; |
---|
2250 | unsigned long d1, d2; |
---|
2251 | _ntl_verylong a = *aa; |
---|
2252 | |
---|
2253 | d1 = d; |
---|
2254 | i = 0; |
---|
2255 | d2 = d1; |
---|
2256 | do { |
---|
2257 | d2 >>= NTL_NBITS; |
---|
2258 | i++; |
---|
2259 | } |
---|
2260 | while (d2 > 0); |
---|
2261 | |
---|
2262 | if (MustAlloc(a, i)) { |
---|
2263 | _ntl_zsetlength(&a, i); |
---|
2264 | *aa = a; |
---|
2265 | } |
---|
2266 | |
---|
2267 | i = 0; |
---|
2268 | a[1] = 0; |
---|
2269 | while (d1 > 0) { |
---|
2270 | a[++i] = d1 & NTL_RADIXM; |
---|
2271 | d1 >>= NTL_NBITS; |
---|
2272 | } |
---|
2273 | if (i > 0) |
---|
2274 | a[0] = i; |
---|
2275 | else |
---|
2276 | a[0] = 1; |
---|
2277 | } |
---|
2278 | |
---|
2279 | |
---|
2280 | unsigned long _ntl_ztouint(_ntl_verylong a) |
---|
2281 | { |
---|
2282 | unsigned long d; |
---|
2283 | long sa; |
---|
2284 | |
---|
2285 | if (!a) |
---|
2286 | return (0); |
---|
2287 | |
---|
2288 | if ((sa = *a) < 0) |
---|
2289 | sa = -sa; |
---|
2290 | |
---|
2291 | d = (unsigned long) (*(a += sa)); |
---|
2292 | while (--sa) { |
---|
2293 | d <<= NTL_NBITS; |
---|
2294 | d += (unsigned long) (*(--a)); |
---|
2295 | } |
---|
2296 | |
---|
2297 | if ((*(--a)) < 0) |
---|
2298 | return (-d); |
---|
2299 | return (d); |
---|
2300 | } |
---|
2301 | |
---|
2302 | |
---|
2303 | long _ntl_ztoint(_ntl_verylong a) |
---|
2304 | { |
---|
2305 | unsigned long res = _ntl_ztouint(a); |
---|
2306 | return NTL_ULONG_TO_LONG(res); |
---|
2307 | } |
---|
2308 | |
---|
2309 | |
---|
2310 | |
---|
2311 | long _ntl_zcompare(_ntl_verylong a, _ntl_verylong b) |
---|
2312 | { |
---|
2313 | long sa; |
---|
2314 | long sb; |
---|
2315 | |
---|
2316 | if (!a) { |
---|
2317 | if (!b) |
---|
2318 | return (0); |
---|
2319 | if (b[0] < 0) |
---|
2320 | return (1); |
---|
2321 | if (b[0] > 1) |
---|
2322 | return (-1); |
---|
2323 | if (b[1]) |
---|
2324 | return (-1); |
---|
2325 | return (0); |
---|
2326 | } |
---|
2327 | if (!b) { |
---|
2328 | if (a[0] < 0) |
---|
2329 | return (-1); |
---|
2330 | if (a[0] > 1) |
---|
2331 | return (1); |
---|
2332 | if (a[1]) |
---|
2333 | return (1); |
---|
2334 | return (0); |
---|
2335 | } |
---|
2336 | |
---|
2337 | if ((sa = *a) > (sb = *b)) |
---|
2338 | return (1); |
---|
2339 | if (sa < sb) |
---|
2340 | return (-1); |
---|
2341 | if (sa < 0) |
---|
2342 | sa = (-sa); |
---|
2343 | a += sa; |
---|
2344 | b += sa; |
---|
2345 | for (; sa; sa--) { |
---|
2346 | long diff = *a - *b; |
---|
2347 | |
---|
2348 | if (diff > 0) { |
---|
2349 | if (sb < 0) |
---|
2350 | return (-1); |
---|
2351 | return (1); |
---|
2352 | } |
---|
2353 | if (diff < 0) { |
---|
2354 | if (sb < 0) |
---|
2355 | return (1); |
---|
2356 | return (-1); |
---|
2357 | } |
---|
2358 | |
---|
2359 | a--; |
---|
2360 | b--; |
---|
2361 | } |
---|
2362 | return (0); |
---|
2363 | } |
---|
2364 | |
---|
2365 | void _ntl_znegate(_ntl_verylong *aa) |
---|
2366 | { |
---|
2367 | _ntl_verylong a = *aa; |
---|
2368 | |
---|
2369 | if (!a) |
---|
2370 | return; |
---|
2371 | if (a[1] || a[0] != 1) |
---|
2372 | a[0] = (-a[0]); |
---|
2373 | } |
---|
2374 | |
---|
2375 | void _ntl_zsadd(_ntl_verylong a, long d, _ntl_verylong *b) |
---|
2376 | { |
---|
2377 | static _ntl_verylong x = 0; |
---|
2378 | |
---|
2379 | _ntl_zintoz(d, &x); |
---|
2380 | _ntl_zadd(a, x, b); |
---|
2381 | } |
---|
2382 | |
---|
2383 | |
---|
2384 | void |
---|
2385 | _ntl_zadd(_ntl_verylong a, _ntl_verylong b, _ntl_verylong *cc) |
---|
2386 | { |
---|
2387 | long sa; |
---|
2388 | long sb; |
---|
2389 | long anegative; |
---|
2390 | _ntl_verylong c; |
---|
2391 | long a_alias, b_alias; |
---|
2392 | |
---|
2393 | if (!a) { |
---|
2394 | if (b) |
---|
2395 | _ntl_zcopy(b, cc); |
---|
2396 | else |
---|
2397 | _ntl_zzero(cc); |
---|
2398 | return; |
---|
2399 | } |
---|
2400 | |
---|
2401 | if (!b) { |
---|
2402 | _ntl_zcopy(a, cc); |
---|
2403 | return; |
---|
2404 | } |
---|
2405 | |
---|
2406 | c = *cc; |
---|
2407 | a_alias = (a == c); |
---|
2408 | b_alias = (b == c); |
---|
2409 | |
---|
2410 | if ((anegative = ((sa = a[0]) < 0)) == ((sb = b[0]) < 0)) { |
---|
2411 | /* signs a and b are the same */ |
---|
2412 | _ntl_verylong pc; |
---|
2413 | long carry; |
---|
2414 | long i; |
---|
2415 | long maxab; |
---|
2416 | |
---|
2417 | if (anegative) { |
---|
2418 | sa = -sa; |
---|
2419 | sb = -sb; |
---|
2420 | } |
---|
2421 | |
---|
2422 | if (sa < sb) { |
---|
2423 | i = sa; |
---|
2424 | maxab = sb; |
---|
2425 | } |
---|
2426 | else { |
---|
2427 | i = sb; |
---|
2428 | maxab = sa; |
---|
2429 | } |
---|
2430 | |
---|
2431 | if (MustAlloc(c, maxab+1)) { |
---|
2432 | _ntl_zsetlength(&c, maxab + 1); |
---|
2433 | if (a_alias) a = c; |
---|
2434 | if (b_alias) b = c; |
---|
2435 | *cc = c; |
---|
2436 | } |
---|
2437 | |
---|
2438 | pc = c; |
---|
2439 | carry = 0; |
---|
2440 | |
---|
2441 | do { |
---|
2442 | long t = (*(++a)) + (*(++b)) + carry; |
---|
2443 | carry = t >> NTL_NBITS; |
---|
2444 | *(++pc) = t & NTL_RADIXM; |
---|
2445 | i--; |
---|
2446 | } while (i); |
---|
2447 | |
---|
2448 | i = sa-sb; |
---|
2449 | if (!i) goto i_exit; |
---|
2450 | |
---|
2451 | if (i < 0) { |
---|
2452 | i = -i; |
---|
2453 | a = b; |
---|
2454 | } |
---|
2455 | |
---|
2456 | if (!carry) goto carry_exit; |
---|
2457 | |
---|
2458 | for (;;) { |
---|
2459 | long t = (*(++a)) + 1; |
---|
2460 | carry = t >> NTL_NBITS; |
---|
2461 | *(++pc) = t & NTL_RADIXM; |
---|
2462 | i--; |
---|
2463 | if (!i) goto i_exit; |
---|
2464 | if (!carry) goto carry_exit; |
---|
2465 | } |
---|
2466 | |
---|
2467 | i_exit: |
---|
2468 | if (carry) { |
---|
2469 | *(++pc) = 1; |
---|
2470 | maxab++; |
---|
2471 | } |
---|
2472 | *c = anegative ? -maxab : maxab; |
---|
2473 | return; |
---|
2474 | |
---|
2475 | carry_exit: |
---|
2476 | if (pc != a) { |
---|
2477 | do { |
---|
2478 | *(++pc) = *(++a); |
---|
2479 | i--; |
---|
2480 | } while (i); |
---|
2481 | } |
---|
2482 | *c = anegative ? -maxab : maxab; |
---|
2483 | } |
---|
2484 | else { |
---|
2485 | /* signs a and b are different...use _ntl_zsub */ |
---|
2486 | |
---|
2487 | if (anegative) { |
---|
2488 | a[0] = -sa; |
---|
2489 | _ntl_zsub(b, a, cc); |
---|
2490 | if (!a_alias) a[0] = sa; |
---|
2491 | } |
---|
2492 | else { |
---|
2493 | b[0] = -sb; |
---|
2494 | _ntl_zsub(a, b, cc); |
---|
2495 | if (!b_alias) b[0] = sb; |
---|
2496 | } |
---|
2497 | } |
---|
2498 | } |
---|
2499 | |
---|
2500 | void |
---|
2501 | _ntl_zsub(_ntl_verylong a, _ntl_verylong b, _ntl_verylong *cc) |
---|
2502 | { |
---|
2503 | long sa; |
---|
2504 | long sb; |
---|
2505 | long anegative; |
---|
2506 | long a_alias, b_alias; |
---|
2507 | _ntl_verylong c; |
---|
2508 | |
---|
2509 | if (!b) { |
---|
2510 | if (a) |
---|
2511 | _ntl_zcopy(a, cc); |
---|
2512 | else |
---|
2513 | _ntl_zzero(cc); |
---|
2514 | return; |
---|
2515 | } |
---|
2516 | |
---|
2517 | if (!a) { |
---|
2518 | _ntl_zcopy(b, cc); |
---|
2519 | _ntl_znegate(cc); |
---|
2520 | return; |
---|
2521 | } |
---|
2522 | |
---|
2523 | c = *cc; |
---|
2524 | a_alias = (a == c); |
---|
2525 | b_alias = (b == c); |
---|
2526 | |
---|
2527 | if ((anegative = ((sa = a[0]) < 0)) == ((sb = b[0]) < 0)) { |
---|
2528 | /* signs agree */ |
---|
2529 | |
---|
2530 | long i, carry, *pc; |
---|
2531 | |
---|
2532 | if (anegative) { |
---|
2533 | sa = -sa; |
---|
2534 | sb = -sb; |
---|
2535 | } |
---|
2536 | |
---|
2537 | carry = sa - sb; |
---|
2538 | if (!carry) { |
---|
2539 | long *aa = a + sa; |
---|
2540 | long *bb = b + sa; |
---|
2541 | |
---|
2542 | i = sa; |
---|
2543 | while (i && !(carry = (*aa - *bb))) { |
---|
2544 | aa--; bb--; i--; |
---|
2545 | } |
---|
2546 | } |
---|
2547 | |
---|
2548 | if (!carry) { |
---|
2549 | _ntl_zzero(cc); |
---|
2550 | return; |
---|
2551 | } |
---|
2552 | |
---|
2553 | if (carry < 0) { |
---|
2554 | { long t = sa; sa = sb; sb = t; } |
---|
2555 | { long t = a_alias; a_alias = b_alias; b_alias = t; } |
---|
2556 | { long *t = a; a = b; b = t; } |
---|
2557 | anegative = !anegative; |
---|
2558 | } |
---|
2559 | |
---|
2560 | if (MustAlloc(c, sa)) { |
---|
2561 | _ntl_zsetlength(&c, sa); |
---|
2562 | /* must have !a_alias */ |
---|
2563 | if (b_alias) b = c; |
---|
2564 | *cc = c; |
---|
2565 | } |
---|
2566 | |
---|
2567 | i = sb; |
---|
2568 | carry = 0; |
---|
2569 | pc = c; |
---|
2570 | |
---|
2571 | do { |
---|
2572 | #if (!NTL_ARITH_RIGHT_SHIFT || defined(NTL_CLEAN_INT)) |
---|
2573 | long t = (*(++a)) - (*(++b)) - carry; |
---|
2574 | carry = (t < 0); |
---|
2575 | #else |
---|
2576 | long t = (*(++a)) - (*(++b)) + carry; |
---|
2577 | carry = t >> NTL_NBITS; |
---|
2578 | #endif |
---|
2579 | *(++pc) = t & NTL_RADIXM; |
---|
2580 | i--; |
---|
2581 | } while (i); |
---|
2582 | |
---|
2583 | i = sa-sb; |
---|
2584 | while (carry) { |
---|
2585 | long t = (*(++a)) - 1; |
---|
2586 | #if (!NTL_ARITH_RIGHT_SHIFT || defined(NTL_CLEAN_INT)) |
---|
2587 | carry = (t < 0); |
---|
2588 | #else |
---|
2589 | carry = t >> NTL_NBITS; |
---|
2590 | #endif |
---|
2591 | *(++pc) = t & NTL_RADIXM; |
---|
2592 | i--; |
---|
2593 | } |
---|
2594 | |
---|
2595 | if (i) { |
---|
2596 | if (pc != a) { |
---|
2597 | do { |
---|
2598 | *(++pc) = *(++a); |
---|
2599 | i--; |
---|
2600 | } while (i); |
---|
2601 | } |
---|
2602 | } |
---|
2603 | else { |
---|
2604 | while (sa > 1 && *pc == 0) { sa--; pc--; } |
---|
2605 | } |
---|
2606 | |
---|
2607 | if (anegative) sa = -sa; |
---|
2608 | *c = sa; |
---|
2609 | } |
---|
2610 | else { |
---|
2611 | /* signs of a and b are different...use _ntl_zadd */ |
---|
2612 | |
---|
2613 | if (anegative) { |
---|
2614 | a[0] = -sa; |
---|
2615 | _ntl_zadd(a, b, cc); |
---|
2616 | if (!a_alias) a[0] = sa; |
---|
2617 | c = *cc; |
---|
2618 | c[0] = -c[0]; |
---|
2619 | } |
---|
2620 | else { |
---|
2621 | b[0] = -sb; |
---|
2622 | _ntl_zadd(a, b, cc); |
---|
2623 | if (!b_alias) b[0] = sb; |
---|
2624 | } |
---|
2625 | } |
---|
2626 | } |
---|
2627 | |
---|
2628 | |
---|
2629 | void |
---|
2630 | _ntl_zsmul(_ntl_verylong a, long d, _ntl_verylong *bb) |
---|
2631 | { |
---|
2632 | long sa; |
---|
2633 | long anegative, bnegative; |
---|
2634 | _ntl_verylong b; |
---|
2635 | long a_alias; |
---|
2636 | |
---|
2637 | |
---|
2638 | if (d == 2) { |
---|
2639 | _ntl_z2mul(a, bb); |
---|
2640 | return; |
---|
2641 | } |
---|
2642 | |
---|
2643 | |
---|
2644 | if ((d >= NTL_RADIX) || (d <= -NTL_RADIX)) { |
---|
2645 | static _ntl_verylong x = 0; |
---|
2646 | _ntl_zintoz(d,&x); |
---|
2647 | _ntl_zmul(a, x, bb); |
---|
2648 | return; |
---|
2649 | } |
---|
2650 | |
---|
2651 | if (!a || (a[0] == 1 && a[1] == 0)) { |
---|
2652 | _ntl_zzero(bb); |
---|
2653 | return; |
---|
2654 | } |
---|
2655 | |
---|
2656 | if (!d) { |
---|
2657 | _ntl_zzero(bb); |
---|
2658 | return; |
---|
2659 | } |
---|
2660 | |
---|
2661 | /* both inputs non-zero */ |
---|
2662 | |
---|
2663 | anegative = 0; |
---|
2664 | bnegative = 0; |
---|
2665 | |
---|
2666 | if ((sa = a[0]) < 0) { |
---|
2667 | anegative = 1; |
---|
2668 | a[0] = sa = (-sa); |
---|
2669 | if (d < 0) |
---|
2670 | d = (-d); |
---|
2671 | else |
---|
2672 | bnegative = 1; |
---|
2673 | } |
---|
2674 | else if (bnegative = (d < 0)) |
---|
2675 | d = (-d); |
---|
2676 | |
---|
2677 | b = *bb; |
---|
2678 | a_alias = (a == b); |
---|
2679 | |
---|
2680 | if (MustAlloc(b, sa + 1)) { |
---|
2681 | _ntl_zsetlength(&b, sa + 1); |
---|
2682 | if (a_alias) a = b; |
---|
2683 | *bb = b; |
---|
2684 | } |
---|
2685 | |
---|
2686 | zsxmul(d, b+1, a); |
---|
2687 | |
---|
2688 | sa++; |
---|
2689 | while ((sa > 1) && (!(b[sa]))) |
---|
2690 | sa--; |
---|
2691 | b[0] = sa; |
---|
2692 | |
---|
2693 | if (bnegative) |
---|
2694 | b[0] = (-b[0]); |
---|
2695 | |
---|
2696 | if (anegative && !a_alias) |
---|
2697 | a[0] = -a[0]; |
---|
2698 | } |
---|
2699 | |
---|
2700 | void _ntl_zsubpos(_ntl_verylong a, _ntl_verylong b, _ntl_verylong *cc) |
---|
2701 | { |
---|
2702 | long sa; |
---|
2703 | long sb; |
---|
2704 | |
---|
2705 | long *c, *pc; |
---|
2706 | long i, carry; |
---|
2707 | |
---|
2708 | long b_alias; |
---|
2709 | |
---|
2710 | if (!b) { |
---|
2711 | if (a) |
---|
2712 | _ntl_zcopy(a, cc); |
---|
2713 | else |
---|
2714 | _ntl_zzero(cc); |
---|
2715 | return; |
---|
2716 | } |
---|
2717 | |
---|
2718 | if (!a) { |
---|
2719 | _ntl_zzero(cc); |
---|
2720 | return; |
---|
2721 | } |
---|
2722 | |
---|
2723 | sa = a[0]; |
---|
2724 | sb = b[0]; |
---|
2725 | |
---|
2726 | c = *cc; |
---|
2727 | b_alias = (b == c); |
---|
2728 | |
---|
2729 | if (MustAlloc(c, sa)) { |
---|
2730 | _ntl_zsetlength(&c, sa); |
---|
2731 | if (b_alias) b = c; |
---|
2732 | *cc = c; |
---|
2733 | } |
---|
2734 | |
---|
2735 | i = sb; |
---|
2736 | carry = 0; |
---|
2737 | pc = c; |
---|
2738 | |
---|
2739 | while (i) { |
---|
2740 | #if (!NTL_ARITH_RIGHT_SHIFT || defined(NTL_CLEAN_INT)) |
---|
2741 | long t = (*(++a)) - (*(++b)) - carry; |
---|
2742 | carry = (t < 0); |
---|
2743 | #else |
---|
2744 | long t = (*(++a)) - (*(++b)) + carry; |
---|
2745 | carry = t >> NTL_NBITS; |
---|
2746 | #endif |
---|
2747 | *(++pc) = t & NTL_RADIXM; |
---|
2748 | i--; |
---|
2749 | } |
---|
2750 | |
---|
2751 | i = sa-sb; |
---|
2752 | while (carry) { |
---|
2753 | long t = (*(++a)) - 1; |
---|
2754 | #if (!NTL_ARITH_RIGHT_SHIFT || defined(NTL_CLEAN_INT)) |
---|
2755 | carry = (t < 0); |
---|
2756 | #else |
---|
2757 | carry = t >> NTL_NBITS; |
---|
2758 | #endif |
---|
2759 | *(++pc) = t & NTL_RADIXM; |
---|
2760 | i--; |
---|
2761 | } |
---|
2762 | |
---|
2763 | if (i) { |
---|
2764 | if (pc != a) { |
---|
2765 | do { |
---|
2766 | *(++pc) = *(++a); |
---|
2767 | i--; |
---|
2768 | } while (i); |
---|
2769 | } |
---|
2770 | } |
---|
2771 | else { |
---|
2772 | while (sa > 1 && *pc == 0) { sa--; pc--; } |
---|
2773 | } |
---|
2774 | |
---|
2775 | *c = sa; |
---|
2776 | } |
---|
2777 | |
---|
2778 | |
---|
2779 | |
---|
2780 | |
---|
2781 | |
---|
2782 | static long *kmem = 0; /* globals for Karatsuba */ |
---|
2783 | static long max_kmem = 0; |
---|
2784 | |
---|
2785 | |
---|
2786 | /* These cross-over points were estimated using |
---|
2787 | a Sparc-10, a Sparc-20, and a Pentium-90. */ |
---|
2788 | |
---|
2789 | #if (defined(NTL_SINGLE_MUL)) |
---|
2790 | #define KARX (18) |
---|
2791 | #else |
---|
2792 | #define KARX (16) |
---|
2793 | #endif |
---|
2794 | |
---|
2795 | /* Auxilliary routines for Karatsuba */ |
---|
2796 | |
---|
2797 | |
---|
2798 | static |
---|
2799 | void kar_fold(long *T, long *b, long hsa) |
---|
2800 | { |
---|
2801 | long sb, *p2, *p3, i, carry; |
---|
2802 | |
---|
2803 | sb = *b; |
---|
2804 | p2 = b + hsa; |
---|
2805 | p3 = T; |
---|
2806 | carry = 0; |
---|
2807 | |
---|
2808 | for (i = sb-hsa; i>0; i--) { |
---|
2809 | long t = (*(++b)) + (*(++p2)) + carry; |
---|
2810 | carry = t >> NTL_NBITS; |
---|
2811 | *(++p3) = t & NTL_RADIXM; |
---|
2812 | } |
---|
2813 | |
---|
2814 | for (i = (hsa << 1) - sb; i>0; i--) { |
---|
2815 | long t = (*(++b)) + carry; |
---|
2816 | carry = t >> NTL_NBITS; |
---|
2817 | *(++p3) = t & NTL_RADIXM; |
---|
2818 | } |
---|
2819 | |
---|
2820 | if (carry) { |
---|
2821 | *(++p3) = carry; |
---|
2822 | *T = hsa + 1; |
---|
2823 | } |
---|
2824 | else |
---|
2825 | *T = hsa; |
---|
2826 | } |
---|
2827 | |
---|
2828 | static |
---|
2829 | void kar_sub(long *T, long *c) |
---|
2830 | { |
---|
2831 | long i, carry; |
---|
2832 | |
---|
2833 | i = *c; |
---|
2834 | carry = 0; |
---|
2835 | |
---|
2836 | while (i>0) { |
---|
2837 | #if (!NTL_ARITH_RIGHT_SHIFT || defined(NTL_CLEAN_INT)) |
---|
2838 | long t = (*(++T)) - (*(++c)) - carry; |
---|
2839 | carry = (t < 0); |
---|
2840 | #else |
---|
2841 | long t = (*(++T)) - (*(++c)) + carry; |
---|
2842 | carry = t >> NTL_NBITS; |
---|
2843 | #endif |
---|
2844 | *T = t & NTL_RADIXM; |
---|
2845 | i--; |
---|
2846 | } |
---|
2847 | |
---|
2848 | while (carry) { |
---|
2849 | long t = (*(++T)) - 1; |
---|
2850 | #if (!NTL_ARITH_RIGHT_SHIFT || defined(NTL_CLEAN_INT)) |
---|
2851 | carry = (t < 0); |
---|
2852 | #else |
---|
2853 | carry = t >> NTL_NBITS; |
---|
2854 | #endif |
---|
2855 | *T = t & NTL_RADIXM; |
---|
2856 | } |
---|
2857 | } |
---|
2858 | |
---|
2859 | |
---|
2860 | static |
---|
2861 | void kar_add(long *c, long *T, long hsa) |
---|
2862 | { |
---|
2863 | long i, carry; |
---|
2864 | |
---|
2865 | c += hsa; |
---|
2866 | i = *T; |
---|
2867 | while (T[i] == 0 && i > 0) i--; |
---|
2868 | carry = 0; |
---|
2869 | |
---|
2870 | while (i>0) { |
---|
2871 | long t = (*(++c)) + (*(++T)) + carry; |
---|
2872 | carry = t >> NTL_NBITS; |
---|
2873 | *c = t & NTL_RADIXM; |
---|
2874 | i--; |
---|
2875 | } |
---|
2876 | |
---|
2877 | while (carry) { |
---|
2878 | long t = (*(++c)) + 1; |
---|
2879 | carry = t >> NTL_NBITS; |
---|
2880 | *c = t & NTL_RADIXM; |
---|
2881 | } |
---|
2882 | } |
---|
2883 | |
---|
2884 | static |
---|
2885 | void kar_fix(long *c, long *T, long hsa) |
---|
2886 | { |
---|
2887 | long i, carry, s; |
---|
2888 | |
---|
2889 | s = *T; |
---|
2890 | |
---|
2891 | i = hsa; |
---|
2892 | while (i>0) { |
---|
2893 | *(++c) = *(++T); |
---|
2894 | i--; |
---|
2895 | } |
---|
2896 | |
---|
2897 | |
---|
2898 | i = s - hsa; |
---|
2899 | carry = 0; |
---|
2900 | |
---|
2901 | while (i > 0) { |
---|
2902 | long t = (*(++c)) + (*(++T)) + carry; |
---|
2903 | carry = t >> NTL_NBITS; |
---|
2904 | *c = t & NTL_RADIXM; |
---|
2905 | i--; |
---|
2906 | } |
---|
2907 | |
---|
2908 | while (carry) { |
---|
2909 | long t = (*(++c)) + 1; |
---|
2910 | carry = t >> NTL_NBITS; |
---|
2911 | *c = t & NTL_RADIXM; |
---|
2912 | } |
---|
2913 | } |
---|
2914 | |
---|
2915 | |
---|
2916 | |
---|
2917 | static |
---|
2918 | void kar_mul(long *c, long *a, long *b, long *stk) |
---|
2919 | { |
---|
2920 | long sa, sb, sc; |
---|
2921 | |
---|
2922 | if (*a < *b) { long *t = a; a = b; b = t; } |
---|
2923 | |
---|
2924 | sa = *a; |
---|
2925 | sb = *b; |
---|
2926 | sc = sa + sb; |
---|
2927 | |
---|
2928 | if (sb < KARX) { |
---|
2929 | /* classic algorithm */ |
---|
2930 | |
---|
2931 | long *pc, i, *pb; |
---|
2932 | |
---|
2933 | pc = c; |
---|
2934 | for (i = sc; i; i--) { |
---|
2935 | pc++; |
---|
2936 | *pc = 0; |
---|
2937 | } |
---|
2938 | |
---|
2939 | pc = c; |
---|
2940 | pb = b; |
---|
2941 | for (i = sb; i; i--) { |
---|
2942 | pb++; |
---|
2943 | pc++; |
---|
2944 | zaddmul(*pb, pc, a); |
---|
2945 | } |
---|
2946 | } |
---|
2947 | else { |
---|
2948 | long hsa = (sa + 1) >> 1; |
---|
2949 | |
---|
2950 | if (hsa < sb) { |
---|
2951 | /* normal case */ |
---|
2952 | |
---|
2953 | long *T1, *T2, *T3; |
---|
2954 | |
---|
2955 | /* allocate space */ |
---|
2956 | |
---|
2957 | T1 = stk; stk += hsa + 2; |
---|
2958 | T2 = stk; stk += hsa + 2; |
---|
2959 | T3 = stk; stk += (hsa << 1) + 3; |
---|
2960 | |
---|
2961 | if (stk-kmem > max_kmem) zhalt("internal error: kmem overflow"); |
---|
2962 | |
---|
2963 | /* compute T1 = a_lo + a_hi */ |
---|
2964 | |
---|
2965 | kar_fold(T1, a, hsa); |
---|
2966 | |
---|
2967 | /* compute T2 = b_lo + b_hi */ |
---|
2968 | |
---|
2969 | kar_fold(T2, b, hsa); |
---|
2970 | |
---|
2971 | /* recursively compute T3 = T1 * T2 */ |
---|
2972 | |
---|
2973 | kar_mul(T3, T1, T2, stk); |
---|
2974 | |
---|
2975 | /* recursively compute a_hi * b_hi into high part of c */ |
---|
2976 | /* and subtract from T3 */ |
---|
2977 | |
---|
2978 | { |
---|
2979 | long olda, oldb; |
---|
2980 | |
---|
2981 | olda = a[hsa]; a[hsa] = sa-hsa; |
---|
2982 | oldb = b[hsa]; b[hsa] = sb-hsa; |
---|
2983 | |
---|
2984 | kar_mul(c + (hsa << 1), a + hsa, b + hsa, stk); |
---|
2985 | kar_sub(T3, c + (hsa << 1)); |
---|
2986 | |
---|
2987 | a[hsa] = olda; |
---|
2988 | b[hsa] = oldb; |
---|
2989 | } |
---|
2990 | |
---|
2991 | /* recursively compute a_lo*b_lo into low part of c */ |
---|
2992 | /* and subtract from T3 */ |
---|
2993 | |
---|
2994 | *a = hsa; |
---|
2995 | *b = hsa; |
---|
2996 | |
---|
2997 | kar_mul(c, a, b, stk); |
---|
2998 | kar_sub(T3, c); |
---|
2999 | |
---|
3000 | *a = sa; |
---|
3001 | *b = sb; |
---|
3002 | |
---|
3003 | /* finally, add T3 * NTL_RADIX^{hsa} to c */ |
---|
3004 | |
---|
3005 | kar_add(c, T3, hsa); |
---|
3006 | } |
---|
3007 | else { |
---|
3008 | /* degenerate case */ |
---|
3009 | |
---|
3010 | long *T; |
---|
3011 | |
---|
3012 | T = stk; stk += sb + hsa + 1; |
---|
3013 | |
---|
3014 | if (stk-kmem > max_kmem) zhalt("internal error: kmem overflow"); |
---|
3015 | |
---|
3016 | /* recursively compute b*a_hi into high part of c */ |
---|
3017 | { |
---|
3018 | long olda; |
---|
3019 | |
---|
3020 | olda = a[hsa]; a[hsa] = sa-hsa; |
---|
3021 | kar_mul(c + hsa, a + hsa, b, stk); |
---|
3022 | a[hsa] = olda; |
---|
3023 | } |
---|
3024 | |
---|
3025 | /* recursively compute b*a_lo into T */ |
---|
3026 | |
---|
3027 | *a = hsa; |
---|
3028 | kar_mul(T, a, b, stk); |
---|
3029 | *a = sa; |
---|
3030 | |
---|
3031 | /* fix-up result */ |
---|
3032 | |
---|
3033 | kar_fix(c, T, hsa); |
---|
3034 | } |
---|
3035 | } |
---|
3036 | |
---|
3037 | /* normalize result */ |
---|
3038 | |
---|
3039 | while (c[sc] == 0 && sc > 1) sc--; |
---|
3040 | *c = sc; |
---|
3041 | } |
---|
3042 | |
---|
3043 | |
---|
3044 | |
---|
3045 | #if (defined(NTL_SINGLE_MUL)) |
---|
3046 | #define KARSX (36) |
---|
3047 | #else |
---|
3048 | #define KARSX (32) |
---|
3049 | #endif |
---|
3050 | |
---|
3051 | static |
---|
3052 | void kar_sq(long *c, long *a, long *stk) |
---|
3053 | { |
---|
3054 | long sa, sc; |
---|
3055 | |
---|
3056 | sa = *a; |
---|
3057 | sc = sa << 1; |
---|
3058 | |
---|
3059 | if (sa < KARSX) { |
---|
3060 | /* classic algorithm */ |
---|
3061 | |
---|
3062 | long carry, i, j, *pc; |
---|
3063 | |
---|
3064 | pc = c; |
---|
3065 | for (i = sc; i; i--) { |
---|
3066 | pc++; |
---|
3067 | *pc = 0; |
---|
3068 | } |
---|
3069 | |
---|
3070 | carry = 0; |
---|
3071 | i = 0; |
---|
3072 | for (j = 1; j <= sa; j++) { |
---|
3073 | unsigned long uncar; |
---|
3074 | long t; |
---|
3075 | |
---|
3076 | i += 2; |
---|
3077 | uncar = ((unsigned long) carry) + (((unsigned long) c[i-1]) << 1); |
---|
3078 | t = uncar & NTL_RADIXM; |
---|
3079 | zaddmulpsq(t, a[j], carry); |
---|
3080 | c[i-1] = t; |
---|
3081 | zaddmulsq(sa-j, c+i, a+j); |
---|
3082 | uncar = (uncar >> NTL_NBITS) + (((unsigned long) c[i]) << 1); |
---|
3083 | uncar += ((unsigned long) carry); |
---|
3084 | carry = uncar >> NTL_NBITS; |
---|
3085 | c[i] = uncar & NTL_RADIXM; |
---|
3086 | } |
---|
3087 | } |
---|
3088 | else { |
---|
3089 | long hsa = (sa + 1) >> 1; |
---|
3090 | long *T1, *T2, olda; |
---|
3091 | |
---|
3092 | T1 = stk; stk += hsa + 2; |
---|
3093 | T2 = stk; stk += (hsa << 1) + 3; |
---|
3094 | |
---|
3095 | if (stk-kmem > max_kmem) zhalt("internal error: kmem overflow"); |
---|
3096 | |
---|
3097 | kar_fold(T1, a, hsa); |
---|
3098 | kar_sq(T2, T1, stk); |
---|
3099 | |
---|
3100 | olda = a[hsa]; a[hsa] = sa - hsa; |
---|
3101 | kar_sq(c + (hsa << 1), a + hsa, stk); |
---|
3102 | kar_sub(T2, c + (hsa << 1)); |
---|
3103 | a[hsa] = olda; |
---|
3104 | |
---|
3105 | *a = hsa; |
---|
3106 | kar_sq(c, a, stk); |
---|
3107 | kar_sub(T2, c); |
---|
3108 | *a = sa; |
---|
3109 | |
---|
3110 | kar_add(c, T2, hsa); |
---|
3111 | } |
---|
3112 | |
---|
3113 | while (c[sc] == 0 && sc > 1) sc--; |
---|
3114 | *c = sc; |
---|
3115 | } |
---|
3116 | |
---|
3117 | |
---|
3118 | void _ntl_zmul(_ntl_verylong a, _ntl_verylong b, _ntl_verylong *cc) |
---|
3119 | { |
---|
3120 | static _ntl_verylong mem = 0; |
---|
3121 | _ntl_verylong c = *cc; |
---|
3122 | |
---|
3123 | if (!a || (a[0] == 1 && a[1] == 0) || !b || (b[0] == 1 && b[1] == 0)) { |
---|
3124 | _ntl_zzero(cc); |
---|
3125 | return; |
---|
3126 | } |
---|
3127 | |
---|
3128 | if (a == b) { |
---|
3129 | if (a == c) { |
---|
3130 | _ntl_zcopy(a, &mem); |
---|
3131 | a = mem; |
---|
3132 | } |
---|
3133 | |
---|
3134 | _ntl_zsq(a, cc); |
---|
3135 | } |
---|
3136 | else { |
---|
3137 | long aneg, bneg, sa, sb, sc; |
---|
3138 | |
---|
3139 | if (a == c) { |
---|
3140 | _ntl_zcopy(a, &mem); |
---|
3141 | a = mem; |
---|
3142 | } |
---|
3143 | else if (b == c) { |
---|
3144 | _ntl_zcopy(b, &mem); |
---|
3145 | b = mem; |
---|
3146 | } |
---|
3147 | |
---|
3148 | sa = *a; |
---|
3149 | if (sa < 0) { |
---|
3150 | *a = sa = -sa; |
---|
3151 | aneg = 1; |
---|
3152 | } |
---|
3153 | else |
---|
3154 | aneg = 0; |
---|
3155 | |
---|
3156 | sb = *b; |
---|
3157 | if (*b < 0) { |
---|
3158 | *b = sb = -sb; |
---|
3159 | bneg = 1; |
---|
3160 | } |
---|
3161 | else |
---|
3162 | bneg = 0; |
---|
3163 | |
---|
3164 | sc = sa + sb; |
---|
3165 | if (MustAlloc(c, sc)) { |
---|
3166 | _ntl_zsetlength(&c, sc); |
---|
3167 | *cc = c; |
---|
3168 | } |
---|
3169 | |
---|
3170 | /* we optimize for *very* small numbers, |
---|
3171 | * avoiding all function calls and loops */ |
---|
3172 | |
---|
3173 | if (sa <= 3 && sb <= 3) { |
---|
3174 | long carry, d; |
---|
3175 | |
---|
3176 | switch (sa) { |
---|
3177 | case 1: |
---|
3178 | switch (sb) { |
---|
3179 | case 1: |
---|
3180 | carry = 0; |
---|
3181 | zxmulp(c[1], a[1], b[1], carry); |
---|
3182 | c[2] = carry; |
---|
3183 | break; |
---|
3184 | case 2: |
---|
3185 | carry = 0; |
---|
3186 | d = a[1]; |
---|
3187 | zxmulp(c[1], b[1], d, carry); |
---|
3188 | zxmulp(c[2], b[2], d, carry); |
---|
3189 | c[3] = carry; |
---|
3190 | break; |
---|
3191 | case 3: |
---|
3192 | carry = 0; |
---|
3193 | d = a[1]; |
---|
3194 | zxmulp(c[1], b[1], d, carry); |
---|
3195 | zxmulp(c[2], b[2], d, carry); |
---|
3196 | zxmulp(c[3], b[3], d, carry); |
---|
3197 | c[4] = carry; |
---|
3198 | break; |
---|
3199 | } |
---|
3200 | break; |
---|
3201 | |
---|
3202 | case 2: |
---|
3203 | switch (sb) { |
---|
3204 | case 1: |
---|
3205 | carry = 0; |
---|
3206 | d = b[1]; |
---|
3207 | zxmulp(c[1], a[1], d, carry); |
---|
3208 | zxmulp(c[2], a[2], d, carry); |
---|
3209 | c[3] = carry; |
---|
3210 | break; |
---|
3211 | case 2: |
---|
3212 | carry = 0; |
---|
3213 | d = b[1]; |
---|
3214 | zxmulp(c[1], a[1], d, carry); |
---|
3215 | zxmulp(c[2], a[2], d, carry); |
---|
3216 | c[3] = carry; |
---|
3217 | carry = 0; |
---|
3218 | d = b[2]; |
---|
3219 | zaddmulp(c[2], a[1], d, carry); |
---|
3220 | zaddmulp(c[3], a[2], d, carry); |
---|
3221 | c[4] = carry; |
---|
3222 | break; |
---|
3223 | case 3: |
---|
3224 | carry = 0; |
---|
3225 | d = a[1]; |
---|
3226 | zxmulp(c[1], b[1], d, carry); |
---|
3227 | zxmulp(c[2], b[2], d, carry); |
---|
3228 | zxmulp(c[3], b[3], d, carry); |
---|
3229 | c[4] = carry; |
---|
3230 | carry = 0; |
---|
3231 | d = a[2]; |
---|
3232 | zaddmulp(c[2], b[1], d, carry); |
---|
3233 | zaddmulp(c[3], b[2], d, carry); |
---|
3234 | zaddmulp(c[4], b[3], d, carry); |
---|
3235 | c[5] = carry; |
---|
3236 | break; |
---|
3237 | } |
---|
3238 | break; |
---|
3239 | |
---|
3240 | case 3: |
---|
3241 | switch (sb) { |
---|
3242 | case 1: |
---|
3243 | carry = 0; |
---|
3244 | d = b[1]; |
---|
3245 | zxmulp(c[1], a[1], d, carry); |
---|
3246 | zxmulp(c[2], a[2], d, carry); |
---|
3247 | zxmulp(c[3], a[3], d, carry); |
---|
3248 | c[4] = carry; |
---|
3249 | break; |
---|
3250 | case 2: |
---|
3251 | carry = 0; |
---|
3252 | d = b[1]; |
---|
3253 | zxmulp(c[1], a[1], d, carry); |
---|
3254 | zxmulp(c[2], a[2], d, carry); |
---|
3255 | zxmulp(c[3], a[3], d, carry); |
---|
3256 | c[4] = carry; |
---|
3257 | carry = 0; |
---|
3258 | d = b[2]; |
---|
3259 | zaddmulp(c[2], a[1], d, carry); |
---|
3260 | zaddmulp(c[3], a[2], d, carry); |
---|
3261 | zaddmulp(c[4], a[3], d, carry); |
---|
3262 | c[5] = carry; |
---|
3263 | break; |
---|
3264 | case 3: |
---|
3265 | carry = 0; |
---|
3266 | d = b[1]; |
---|
3267 | zxmulp(c[1], a[1], d, carry); |
---|
3268 | zxmulp(c[2], a[2], d, carry); |
---|
3269 | zxmulp(c[3], a[3], d, carry); |
---|
3270 | c[4] = carry; |
---|
3271 | carry = 0; |
---|
3272 | d = b[2]; |
---|
3273 | zaddmulp(c[2], a[1], d, carry); |
---|
3274 | zaddmulp(c[3], a[2], d, carry); |
---|
3275 | zaddmulp(c[4], a[3], d, carry); |
---|
3276 | c[5] = carry; |
---|
3277 | carry = 0; |
---|
3278 | d = b[3]; |
---|
3279 | zaddmulp(c[3], a[1], d, carry); |
---|
3280 | zaddmulp(c[4], a[2], d, carry); |
---|
3281 | zaddmulp(c[5], a[3], d, carry); |
---|
3282 | c[6] = carry; |
---|
3283 | break; |
---|
3284 | } |
---|
3285 | } |
---|
3286 | |
---|
3287 | if (c[sc] == 0) sc--; |
---|
3288 | if (aneg != bneg) sc = -sc; |
---|
3289 | *c = sc; |
---|
3290 | if (aneg) *a = -sa; |
---|
3291 | if (bneg) *b = -sb; |
---|
3292 | |
---|
3293 | return; |
---|
3294 | |
---|
3295 | } |
---|
3296 | |
---|
3297 | |
---|
3298 | #ifdef NTL_GMP_HACK |
---|
3299 | |
---|
3300 | if (_ntl_gmp_hack && sa >= NTL_GMP_MUL_CROSS && sb >= NTL_GMP_MUL_CROSS) { |
---|
3301 | long gsa = L_TO_G(sa); |
---|
3302 | long gsb = L_TO_G(sb); |
---|
3303 | |
---|
3304 | mp_limb_t *a_p, *b_p, *c_p, *end_p; |
---|
3305 | |
---|
3306 | NTL_GSPACE((gsa + gsb) << 1); |
---|
3307 | a_p = gspace_data; |
---|
3308 | b_p = a_p + gsa; |
---|
3309 | c_p = b_p + gsb; |
---|
3310 | end_p = c_p + (gsa + gsb); |
---|
3311 | |
---|
3312 | lip_to_gmp(a+1, a_p, sa); |
---|
3313 | lip_to_gmp(b+1, b_p, sb); |
---|
3314 | |
---|
3315 | if (!a_p[gsa-1]) gsa--; |
---|
3316 | if (!b_p[gsb-1]) gsb--; |
---|
3317 | end_p[-1] = 0; |
---|
3318 | end_p[-2] = 0; |
---|
3319 | |
---|
3320 | if (gsa >= gsb) |
---|
3321 | mpn_mul(c_p, a_p, gsa, b_p, gsb); |
---|
3322 | else |
---|
3323 | mpn_mul(c_p, b_p, gsb, a_p, gsa); |
---|
3324 | |
---|
3325 | gmp_to_lip(c+1, c_p, sc); |
---|
3326 | |
---|
3327 | if (!c[sc]) sc--; |
---|
3328 | if (aneg != bneg) sc = -sc; |
---|
3329 | c[0] = sc; |
---|
3330 | if (aneg) *a = - *a; |
---|
3331 | if (bneg) *b = - *b; |
---|
3332 | return; |
---|
3333 | } |
---|
3334 | |
---|
3335 | |
---|
3336 | |
---|
3337 | #endif |
---|
3338 | |
---|
3339 | if (*a < KARX || *b < KARX) { |
---|
3340 | /* classic algorithm */ |
---|
3341 | |
---|
3342 | long i, *pc; |
---|
3343 | |
---|
3344 | pc = c; |
---|
3345 | for (i = sc; i; i--) { |
---|
3346 | pc++; |
---|
3347 | *pc = 0; |
---|
3348 | } |
---|
3349 | |
---|
3350 | pc = c; |
---|
3351 | |
---|
3352 | if (*a >= *b) { |
---|
3353 | long *pb = b; |
---|
3354 | for (i = *pb; i; i--) { |
---|
3355 | pb++; |
---|
3356 | pc++; |
---|
3357 | zaddmul(*pb, pc, a); |
---|
3358 | } |
---|
3359 | } |
---|
3360 | else { |
---|
3361 | long *pa = a; |
---|
3362 | for (i = *pa; i; i--) { |
---|
3363 | pa++; |
---|
3364 | pc++; |
---|
3365 | zaddmul(*pa, pc, b); |
---|
3366 | } |
---|
3367 | } |
---|
3368 | |
---|
3369 | while (c[sc] == 0 && sc > 1) sc--; |
---|
3370 | if (aneg != bneg) sc = -sc; |
---|
3371 | c[0] = sc; |
---|
3372 | if (aneg) *a = - *a; |
---|
3373 | if (bneg) *b = - *b; |
---|
3374 | } |
---|
3375 | else { |
---|
3376 | /* karatsuba */ |
---|
3377 | |
---|
3378 | long n, hn, sp; |
---|
3379 | |
---|
3380 | if (*a < *b) |
---|
3381 | n = *b; |
---|
3382 | else |
---|
3383 | n = *a; |
---|
3384 | |
---|
3385 | sp = 0; |
---|
3386 | do { |
---|
3387 | hn = (n + 1) >> 1; |
---|
3388 | sp += (hn << 2) + 7; |
---|
3389 | n = hn+1; |
---|
3390 | } while (n >= KARX); |
---|
3391 | |
---|
3392 | if (sp > max_kmem) { |
---|
3393 | if (max_kmem == 0) |
---|
3394 | kmem = (long *) NTL_MALLOC(sp, sizeof(long), 0); |
---|
3395 | else |
---|
3396 | kmem = (long *) NTL_REALLOC(kmem, sp, sizeof(long), 0); |
---|
3397 | |
---|
3398 | max_kmem = sp; |
---|
3399 | if (!kmem) zhalt("out of memory in karatsuba"); |
---|
3400 | } |
---|
3401 | |
---|
3402 | kar_mul(c, a, b, kmem); |
---|
3403 | if (aneg != bneg) *c = - *c; |
---|
3404 | if (aneg) *a = - *a; |
---|
3405 | if (bneg) *b = - *b; |
---|
3406 | } |
---|
3407 | } |
---|
3408 | } |
---|
3409 | |
---|
3410 | |
---|
3411 | void _ntl_zsq(_ntl_verylong a, _ntl_verylong *cc) |
---|
3412 | { |
---|
3413 | static _ntl_verylong mem = 0; |
---|
3414 | _ntl_verylong c = *cc; |
---|
3415 | long sa, aneg, sc; |
---|
3416 | |
---|
3417 | if (!a || (a[0] == 1 && a[1] == 0)) { |
---|
3418 | _ntl_zzero(cc); |
---|
3419 | return; |
---|
3420 | } |
---|
3421 | |
---|
3422 | if (a == c) { |
---|
3423 | _ntl_zcopy(a, &mem); |
---|
3424 | a = mem; |
---|
3425 | } |
---|
3426 | |
---|
3427 | sa = *a; |
---|
3428 | |
---|
3429 | if (*a < 0) { |
---|
3430 | *a = sa = -sa; |
---|
3431 | aneg = 1; |
---|
3432 | } |
---|
3433 | else |
---|
3434 | aneg = 0; |
---|
3435 | |
---|
3436 | sc = (sa) << 1; |
---|
3437 | if (MustAlloc(c, sc)) { |
---|
3438 | _ntl_zsetlength(&c, sc); |
---|
3439 | *cc = c; |
---|
3440 | } |
---|
3441 | |
---|
3442 | if (sa <= 3) { |
---|
3443 | long carry, d; |
---|
3444 | |
---|
3445 | switch (sa) { |
---|
3446 | case 1: |
---|
3447 | carry = 0; |
---|
3448 | zxmulp(c[1], a[1], a[1], carry); |
---|
3449 | c[2] = carry; |
---|
3450 | break; |
---|
3451 | |
---|
3452 | case 2: |
---|
3453 | carry = 0; |
---|
3454 | d = a[1]; |
---|
3455 | zxmulp(c[1], a[1], d, carry); |
---|
3456 | zxmulp(c[2], a[2], d, carry); |
---|
3457 | c[3] = carry; |
---|
3458 | carry = 0; |
---|
3459 | d = a[2]; |
---|
3460 | zaddmulp(c[2], a[1], d, carry); |
---|
3461 | zaddmulp(c[3], a[2], d, carry); |
---|
3462 | c[4] = carry; |
---|
3463 | break; |
---|
3464 | |
---|
3465 | case 3: |
---|
3466 | carry = 0; |
---|
3467 | d = a[1]; |
---|
3468 | zxmulp(c[1], a[1], d, carry); |
---|
3469 | zxmulp(c[2], a[2], d, carry); |
---|
3470 | zxmulp(c[3], a[3], d, carry); |
---|
3471 | c[4] = carry; |
---|
3472 | carry = 0; |
---|
3473 | d = a[2]; |
---|
3474 | zaddmulp(c[2], a[1], d, carry); |
---|
3475 | zaddmulp(c[3], a[2], d, carry); |
---|
3476 | zaddmulp(c[4], a[3], d, carry); |
---|
3477 | c[5] = carry; |
---|
3478 | carry = 0; |
---|
3479 | d = a[3]; |
---|
3480 | zaddmulp(c[3], a[1], d, carry); |
---|
3481 | zaddmulp(c[4], a[2], d, carry); |
---|
3482 | zaddmulp(c[5], a[3], d, carry); |
---|
3483 | c[6] = carry; |
---|
3484 | break; |
---|
3485 | } |
---|
3486 | |
---|
3487 | if (c[sc] == 0) sc--; |
---|
3488 | *c = sc; |
---|
3489 | if (aneg) *a = -sa; |
---|
3490 | |
---|
3491 | return; |
---|
3492 | } |
---|
3493 | |
---|
3494 | #ifdef NTL_GMP_HACK |
---|
3495 | |
---|
3496 | if (_ntl_gmp_hack && sa >= NTL_GMP_SQR_CROSS) { |
---|
3497 | long gsa = L_TO_G(sa); |
---|
3498 | |
---|
3499 | mp_limb_t *a_p, *c_p, *end_p;; |
---|
3500 | |
---|
3501 | NTL_GSPACE(gsa + gsa + gsa); |
---|
3502 | a_p = gspace_data; |
---|
3503 | c_p = a_p + gsa; |
---|
3504 | end_p = c_p + (gsa + gsa); |
---|
3505 | |
---|
3506 | lip_to_gmp(a+1, a_p, sa); |
---|
3507 | |
---|
3508 | if (!a_p[gsa-1]) gsa--; |
---|
3509 | end_p[-1] = 0; |
---|
3510 | end_p[-2] = 0; |
---|
3511 | |
---|
3512 | mpn_mul(c_p, a_p, gsa, a_p, gsa); |
---|
3513 | |
---|
3514 | gmp_to_lip(c+1, c_p, sc); |
---|
3515 | |
---|
3516 | if (!c[sc]) sc--; |
---|
3517 | c[0] = sc; |
---|
3518 | if (aneg) *a = - *a; |
---|
3519 | return; |
---|
3520 | } |
---|
3521 | |
---|
3522 | |
---|
3523 | #endif |
---|
3524 | |
---|
3525 | if (sa < KARSX) { |
---|
3526 | /* classic algorithm */ |
---|
3527 | |
---|
3528 | long carry, i, j, *pc; |
---|
3529 | |
---|
3530 | pc = c; |
---|
3531 | for (i = sc; i; i--) { |
---|
3532 | pc++; |
---|
3533 | *pc = 0; |
---|
3534 | } |
---|
3535 | |
---|
3536 | carry = 0; |
---|
3537 | i = 0; |
---|
3538 | for (j = 1; j <= sa; j++) { |
---|
3539 | unsigned long uncar; |
---|
3540 | long t; |
---|
3541 | |
---|
3542 | i += 2; |
---|
3543 | uncar = ((unsigned long) carry) + (((unsigned long) c[i-1]) << 1); |
---|
3544 | t = uncar & NTL_RADIXM; |
---|
3545 | zaddmulpsq(t, a[j], carry); |
---|
3546 | c[i-1] = t; |
---|
3547 | zaddmulsq(sa-j, c+i, a+j); |
---|
3548 | uncar = (uncar >> NTL_NBITS) + (((unsigned long) c[i]) << 1); |
---|
3549 | uncar += ((unsigned long) carry); |
---|
3550 | carry = uncar >> NTL_NBITS; |
---|
3551 | c[i] = uncar & NTL_RADIXM; |
---|
3552 | } |
---|
3553 | |
---|
3554 | |
---|
3555 | while (c[sc] == 0 && sc > 1) sc--; |
---|
3556 | c[0] = sc; |
---|
3557 | if (aneg) *a = - *a; |
---|
3558 | } |
---|
3559 | else { |
---|
3560 | /* karatsuba */ |
---|
3561 | |
---|
3562 | long n, hn, sp; |
---|
3563 | |
---|
3564 | n = *a; |
---|
3565 | |
---|
3566 | sp = 0; |
---|
3567 | do { |
---|
3568 | hn = (n + 1) >> 1; |
---|
3569 | sp += hn + hn + hn + 5; |
---|
3570 | n = hn+1; |
---|
3571 | } while (n >= KARSX); |
---|
3572 | |
---|
3573 | if (sp > max_kmem) { |
---|
3574 | if (max_kmem == 0) |
---|
3575 | kmem = (long *) NTL_MALLOC(sp, sizeof(long), 0); |
---|
3576 | else |
---|
3577 | kmem = (long *) NTL_REALLOC(kmem, sp, sizeof(long), 0); |
---|
3578 | |
---|
3579 | max_kmem = sp; |
---|
3580 | if (!kmem) zhalt("out of memory in karatsuba"); |
---|
3581 | } |
---|
3582 | |
---|
3583 | kar_sq(c, a, kmem); |
---|
3584 | if (aneg) *a = - *a; |
---|
3585 | } |
---|
3586 | } |
---|
3587 | |
---|
3588 | |
---|
3589 | |
---|
3590 | |
---|
3591 | long _ntl_zsdiv(_ntl_verylong a, long d, _ntl_verylong *bb) |
---|
3592 | { |
---|
3593 | long sa; |
---|
3594 | _ntl_verylong b = *bb; |
---|
3595 | |
---|
3596 | if (!d) { |
---|
3597 | zhalt("division by zero in _ntl_zsdiv"); |
---|
3598 | } |
---|
3599 | |
---|
3600 | if (!a) { |
---|
3601 | _ntl_zzero(bb); |
---|
3602 | return (0); |
---|
3603 | } |
---|
3604 | |
---|
3605 | |
---|
3606 | if (d == 2) { |
---|
3607 | long is_odd = a[1] & 1; |
---|
3608 | long fix = (a[0] < 0) & is_odd; |
---|
3609 | _ntl_zrshift(a, 1, bb); |
---|
3610 | if (fix) _ntl_zsadd(*bb, -1, bb); |
---|
3611 | return is_odd; |
---|
3612 | } |
---|
3613 | |
---|
3614 | |
---|
3615 | if ((sa = a[0]) < 0) |
---|
3616 | sa = (-sa); |
---|
3617 | |
---|
3618 | /* if b aliases a, then b won't move */ |
---|
3619 | _ntl_zsetlength(&b, sa); |
---|
3620 | *bb = b; |
---|
3621 | |
---|
3622 | if ((d >= NTL_RADIX) || (d <= -NTL_RADIX)) { |
---|
3623 | static _ntl_verylong zd = 0; |
---|
3624 | static _ntl_verylong zb = 0; |
---|
3625 | |
---|
3626 | _ntl_zintoz(d, &zb); |
---|
3627 | _ntl_zdiv(a, zb, &b, &zd); |
---|
3628 | *bb = b; |
---|
3629 | return (_ntl_ztoint(zd)); |
---|
3630 | } |
---|
3631 | else { |
---|
3632 | long den = d; |
---|
3633 | double deninv; |
---|
3634 | long carry = 0; |
---|
3635 | long i; |
---|
3636 | long flag = (*a < 0 ? 2 : 0) | (den < 0 ? 1 : 0); |
---|
3637 | |
---|
3638 | if (den < 0) |
---|
3639 | den = -den; |
---|
3640 | deninv = 1.0 / ((double) den); |
---|
3641 | |
---|
3642 | if (a[sa] < den && sa > 1) |
---|
3643 | carry = a[sa--]; |
---|
3644 | |
---|
3645 | for (i = sa; i; i--) { |
---|
3646 | zdiv21(carry, a[i], den, deninv, b[i]); |
---|
3647 | } |
---|
3648 | |
---|
3649 | while ((sa > 1) && (!(b[sa]))) |
---|
3650 | sa--; |
---|
3651 | b[0] = sa; |
---|
3652 | |
---|
3653 | if (flag) { |
---|
3654 | if (flag <= 2) { |
---|
3655 | if (!carry) |
---|
3656 | _ntl_znegate(&b); |
---|
3657 | else { |
---|
3658 | _ntl_zsadd(b, 1, &b); |
---|
3659 | b[0] = -b[0]; |
---|
3660 | if (flag == 1) |
---|
3661 | carry = carry - den; |
---|
3662 | else |
---|
3663 | carry = den - carry; |
---|
3664 | *bb = b; |
---|
3665 | } |
---|
3666 | } |
---|
3667 | else |
---|
3668 | carry = -carry; |
---|
3669 | } |
---|
3670 | |
---|
3671 | return (carry); |
---|
3672 | } |
---|
3673 | } |
---|
3674 | |
---|
3675 | long _ntl_zsmod(_ntl_verylong a, long d) |
---|
3676 | { |
---|
3677 | long sa; |
---|
3678 | |
---|
3679 | if (!a) { |
---|
3680 | return (0); |
---|
3681 | } |
---|
3682 | |
---|
3683 | if (d == 2) return (a[1] & 1); |
---|
3684 | |
---|
3685 | if (!d) { |
---|
3686 | zhalt("division by zero in _ntl_zsdiv"); |
---|
3687 | } |
---|
3688 | |
---|
3689 | if ((sa = a[0]) < 0) |
---|
3690 | sa = (-sa); |
---|
3691 | |
---|
3692 | if ((d >= NTL_RADIX) || (d <= -NTL_RADIX)) { |
---|
3693 | static _ntl_verylong zd = 0; |
---|
3694 | static _ntl_verylong zb = 0; |
---|
3695 | |
---|
3696 | _ntl_zintoz(d, &zb); |
---|
3697 | _ntl_zmod(a, zb, &zd); |
---|
3698 | return (_ntl_ztoint(zd)); |
---|
3699 | } |
---|
3700 | else { |
---|
3701 | long den = d; |
---|
3702 | double deninv; |
---|
3703 | long carry = 0; |
---|
3704 | long i; |
---|
3705 | long flag = (*a < 0 ? 2 : 0) | (den < 0 ? 1 : 0); |
---|
3706 | |
---|
3707 | if (den < 0) |
---|
3708 | den = -den; |
---|
3709 | deninv = 1.0 / ((double) den); |
---|
3710 | |
---|
3711 | if (a[sa] < den && sa > 1) |
---|
3712 | carry = a[sa--]; |
---|
3713 | |
---|
3714 | for (i = sa; i; i--) { |
---|
3715 | zrem21(carry, a[i], den, deninv); |
---|
3716 | } |
---|
3717 | |
---|
3718 | if (flag) { |
---|
3719 | if (flag <= 2) { |
---|
3720 | if (carry) { |
---|
3721 | if (flag == 1) |
---|
3722 | carry = carry - den; |
---|
3723 | else |
---|
3724 | carry = den - carry; |
---|
3725 | } |
---|
3726 | } |
---|
3727 | else |
---|
3728 | carry = -carry; |
---|
3729 | } |
---|
3730 | |
---|
3731 | return (carry); |
---|
3732 | } |
---|
3733 | } |
---|
3734 | |
---|
3735 | void _ntl_zmultirem(_ntl_verylong a, long n, long* dd, long *rr) |
---|
3736 | { |
---|
3737 | long j; |
---|
3738 | long sa; |
---|
3739 | |
---|
3740 | if (!a || (a[0] == 1 && a[1] == 0)) { |
---|
3741 | for (j = 0; j < n; j++) rr[j] = 0; |
---|
3742 | return; |
---|
3743 | } |
---|
3744 | |
---|
3745 | sa = a[0]; |
---|
3746 | |
---|
3747 | for (j = 0; j < n; j++) { |
---|
3748 | long den = dd[j]; |
---|
3749 | double deninv; |
---|
3750 | long carry = 0; |
---|
3751 | long i; |
---|
3752 | long lsa = sa; |
---|
3753 | |
---|
3754 | deninv = 1.0 / ((double) den); |
---|
3755 | |
---|
3756 | if (a[lsa] < den && lsa > 1) |
---|
3757 | carry = a[lsa--]; |
---|
3758 | |
---|
3759 | for (i = lsa; i; i--) { |
---|
3760 | zrem21(carry, a[i], den, deninv); |
---|
3761 | } |
---|
3762 | |
---|
3763 | rr[j] = carry; |
---|
3764 | } |
---|
3765 | } |
---|
3766 | |
---|
3767 | |
---|
3768 | |
---|
3769 | |
---|
3770 | #if (defined(NTL_SINGLE_MUL)) |
---|
3771 | |
---|
3772 | #define REDUCE_CROSS 8 |
---|
3773 | |
---|
3774 | void _ntl_zmultirem2(_ntl_verylong a, long n, long* dd, double **ttbl, long *rr) |
---|
3775 | |
---|
3776 | { |
---|
3777 | long d; |
---|
3778 | double *tbl; |
---|
3779 | long ac0, ac1, ac2; |
---|
3780 | long *ap; |
---|
3781 | double *tp; |
---|
3782 | long sa, i, j, k; |
---|
3783 | unsigned long pc0, pc1, lo_wd, hi_wd; |
---|
3784 | long carry; |
---|
3785 | double xx, yy, dinv; |
---|
3786 | |
---|
3787 | if (!a || a[0] < REDUCE_CROSS || a[0] >= NTL_RADIX) { |
---|
3788 | _ntl_zmultirem(a, n, dd, rr); |
---|
3789 | return; |
---|
3790 | } |
---|
3791 | |
---|
3792 | sa = a[0]; |
---|
3793 | |
---|
3794 | for (i = 0; i < n; i++) { |
---|
3795 | d = dd[i]; |
---|
3796 | tbl = ttbl[i]; |
---|
3797 | |
---|
3798 | ac0 = a[1]; |
---|
3799 | ac1 = 0; |
---|
3800 | ac2 = 0; |
---|
3801 | |
---|
3802 | ap = &a[2]; |
---|
3803 | tp = &tbl[1]; |
---|
3804 | |
---|
3805 | k = sa-1; |
---|
3806 | while (k) { |
---|
3807 | j = k; |
---|
3808 | if (j > 64) j = 64; |
---|
3809 | k -= j; |
---|
3810 | |
---|
3811 | pc0 = 0; |
---|
3812 | pc1 = 0; |
---|
3813 | |
---|
3814 | xx = ((double) (*ap++))* (*tp++) + DENORMALIZE; |
---|
3815 | for (; j > 1; j--) { |
---|
3816 | yy = ((double) (*ap++))*(*tp++) |
---|
3817 | + DENORMALIZE; |
---|
3818 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
3819 | pc0 += lo_wd & 0x3FFFFFF; |
---|
3820 | pc1 += ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
3821 | xx = yy; |
---|
3822 | } |
---|
3823 | NTL_FetchHiLo(hi_wd, lo_wd, xx); |
---|
3824 | pc0 += lo_wd & 0x3FFFFFF; |
---|
3825 | pc1 += ((hi_wd<<6)|(lo_wd>>26)) & 0x3FFFFFF; |
---|
3826 | pc1 += (pc0 >> 26); |
---|
3827 | |
---|
3828 | ac0 += (pc0 & 0x3FFFFFF); |
---|
3829 | if (ac0 > NTL_RADIX) { |
---|
3830 | ac0 -= NTL_RADIX; |
---|
3831 | carry = 1; |
---|
3832 | } |
---|
3833 | else |
---|
3834 | carry = 0; |
---|
3835 | |
---|
3836 | ac1 += carry + (pc1 & 0x3FFFFFF); |
---|
3837 | if (ac1 > NTL_RADIX) { |
---|
3838 | ac1 -= NTL_RADIX; |
---|
3839 | carry = 1; |
---|
3840 | } |
---|
3841 | else |
---|
3842 | carry = 0; |
---|
3843 | |
---|
3844 | ac2 += carry + (pc1 >> 26); |
---|
3845 | } |
---|
3846 | |
---|
3847 | carry = 0; |
---|
3848 | dinv = ((double) 1)/((double) d); |
---|
3849 | if (ac2 >= d) { |
---|
3850 | zrem21(carry, ac2, d, dinv); |
---|
3851 | } |
---|
3852 | else |
---|
3853 | carry = ac2; |
---|
3854 | |
---|
3855 | zrem21(carry, ac1, d, dinv); |
---|
3856 | zrem21(carry, ac0, d, dinv); |
---|
3857 | |
---|
3858 | rr[i] = carry; |
---|
3859 | } |
---|
3860 | } |
---|
3861 | |
---|
3862 | |
---|
3863 | #elif (defined(NTL_TBL_REM)) |
---|
3864 | |
---|
3865 | void _ntl_zmultirem3(_ntl_verylong a, long n, long* dd, long **ttbl, long *rr) |
---|
3866 | { |
---|
3867 | long sa, i, d, *tbl, ac0, ac1, ac2, *ap, *tp, k, t, carry; |
---|
3868 | double dinv; |
---|
3869 | |
---|
3870 | if (!a || a[0] < 8 || a[0] >= NTL_RADIX) { |
---|
3871 | _ntl_zmultirem(a, n, dd, rr); |
---|
3872 | return; |
---|
3873 | } |
---|
3874 | |
---|
3875 | sa = a[0]; |
---|
3876 | |
---|
3877 | for (i = 0; i < n; i++) { |
---|
3878 | d = dd[i]; |
---|
3879 | tbl = ttbl[i]; |
---|
3880 | ac0 = a[1]; |
---|
3881 | ac1 = 0; |
---|
3882 | ac2 = 0; |
---|
3883 | ap = &a[2]; |
---|
3884 | tp = &tbl[1]; |
---|
3885 | k = sa-1; |
---|
3886 | |
---|
3887 | while (k) { |
---|
3888 | zxmulp(t, *ap, *tp, ac0); |
---|
3889 | ac1 += ac0; |
---|
3890 | ac2 += ac1 >> NTL_NBITS; |
---|
3891 | ac1 &= NTL_RADIXM; |
---|
3892 | ac0 = t; |
---|
3893 | k--; |
---|
3894 | ap++; |
---|
3895 | tp++; |
---|
3896 | } |
---|
3897 | |
---|
3898 | carry = 0; |
---|
3899 | dinv = ((double) 1)/((double) d); |
---|
3900 | if (ac2 >= d) { |
---|
3901 | zrem21(carry, ac2, d, dinv); |
---|
3902 | } |
---|
3903 | else |
---|
3904 | carry = ac2; |
---|
3905 | |
---|
3906 | zrem21(carry, ac1, d, dinv); |
---|
3907 | zrem21(carry, ac0, d, dinv); |
---|
3908 | |
---|
3909 | rr[i] = carry; |
---|
3910 | } |
---|
3911 | } |
---|
3912 | |
---|
3913 | #endif |
---|
3914 | |
---|
3915 | |
---|
3916 | |
---|
3917 | |
---|
3918 | long _ntl_zsfastrem(_ntl_verylong a, long d) |
---|
3919 | /* assumes a >= 0, and 0 < d < NTL_RADIX */ |
---|
3920 | /* computes a % d */ |
---|
3921 | |
---|
3922 | { |
---|
3923 | long sa; |
---|
3924 | |
---|
3925 | if (!a || (a[0] == 1 && a[1] == 0)) { |
---|
3926 | return 0; |
---|
3927 | } |
---|
3928 | |
---|
3929 | sa = a[0]; |
---|
3930 | |
---|
3931 | { |
---|
3932 | long den = d; |
---|
3933 | double deninv = ((double)1)/((double)den); |
---|
3934 | long carry = 0; |
---|
3935 | long i; |
---|
3936 | long lsa = sa; |
---|
3937 | |
---|
3938 | if (a[lsa] < den && lsa > 1) |
---|
3939 | carry = a[lsa--]; |
---|
3940 | for (i = lsa; i; i--) { |
---|
3941 | zrem21(carry, a[i], den, deninv); |
---|
3942 | } |
---|
3943 | return carry; |
---|
3944 | } |
---|
3945 | } |
---|
3946 | |
---|
3947 | |
---|
3948 | |
---|
3949 | void _ntl_zdiv(_ntl_verylong a, _ntl_verylong b, _ntl_verylong *qq, _ntl_verylong *rr) |
---|
3950 | { |
---|
3951 | long sa, sb, sq, i; |
---|
3952 | long sign; |
---|
3953 | long q1; |
---|
3954 | long *rp; |
---|
3955 | double btopinv, aux; |
---|
3956 | static _ntl_verylong q=0, r=0; |
---|
3957 | |
---|
3958 | if (!b || (((sb=b[0]) == 1) && (!b[1]))) { |
---|
3959 | zhalt("division by zero in _ntl_zdiv"); |
---|
3960 | } |
---|
3961 | |
---|
3962 | if (!a || (((sa=a[0]) == 1) && (!a[1]))) { |
---|
3963 | _ntl_zzero(qq); |
---|
3964 | if (rr) _ntl_zzero(rr); |
---|
3965 | return; |
---|
3966 | } |
---|
3967 | |
---|
3968 | |
---|
3969 | if (sb == 1) { |
---|
3970 | long t1 = _ntl_zsdiv(a, b[1], qq); |
---|
3971 | if (rr) _ntl_zintoz(t1, rr); |
---|
3972 | return; |
---|
3973 | } |
---|
3974 | |
---|
3975 | if (sb == -1) { |
---|
3976 | long t1 = _ntl_zsdiv(a, -b[1], qq); |
---|
3977 | if (rr) _ntl_zintoz(t1, rr); |
---|
3978 | return; |
---|
3979 | } |
---|
3980 | |
---|
3981 | sign = 0; |
---|
3982 | if (sa < 0) { |
---|
3983 | a[0] = sa = -sa; |
---|
3984 | sign = 2; |
---|
3985 | } |
---|
3986 | |
---|
3987 | if (sb < 0) { |
---|
3988 | b[0] = sb = -sb; |
---|
3989 | sign |= 1; |
---|
3990 | } |
---|
3991 | |
---|
3992 | |
---|
3993 | sq = sa-sb+1; |
---|
3994 | |
---|
3995 | if (sq <= 0) { |
---|
3996 | _ntl_zcopy(a, &r); |
---|
3997 | _ntl_zzero(&q); |
---|
3998 | goto done; |
---|
3999 | } |
---|
4000 | |
---|
4001 | #ifdef NTL_GMP_HACK |
---|
4002 | if (_ntl_gmp_hack && sb >= NTL_GMP_DIV_CROSS && sq >= NTL_GMP_DIV_CROSS) { |
---|
4003 | GT_INIT |
---|
4004 | |
---|
4005 | lip_to_mpz(a, gt_1); |
---|
4006 | lip_to_mpz(b, gt_2); |
---|
4007 | mpz_fdiv_qr(gt_3, gt_4, gt_1, gt_2); |
---|
4008 | mpz_to_lip(&q, gt_3); |
---|
4009 | mpz_to_lip(&r, gt_4); |
---|
4010 | |
---|
4011 | goto done; |
---|
4012 | } |
---|
4013 | #endif |
---|
4014 | |
---|
4015 | _ntl_zsetlength(&q, sq); |
---|
4016 | _ntl_zsetlength(&r, sa+1); |
---|
4017 | |
---|
4018 | _ntl_zcopy(a, &r); |
---|
4019 | rp = &r[sa+1]; |
---|
4020 | *rp = 0; |
---|
4021 | |
---|
4022 | r[0] = 0; /* this streamlines the last evaluation of aux */ |
---|
4023 | |
---|
4024 | btopinv = b[sb]*NTL_FRADIX + b[sb-1]; |
---|
4025 | if (sb > 2) |
---|
4026 | btopinv = NTL_FRADIX / (btopinv*NTL_FRADIX + b[sb-2]); |
---|
4027 | else |
---|
4028 | btopinv = 1.0 / btopinv; |
---|
4029 | |
---|
4030 | |
---|
4031 | aux = btopinv*(rp[-1]*NTL_FRADIX + rp[-2]); |
---|
4032 | if (aux >= NTL_FRADIX) |
---|
4033 | aux = NTL_FRADIX-1; |
---|
4034 | |
---|
4035 | for (i = sq; i >= 1; i--, rp--) { |
---|
4036 | q1 = (long) aux; |
---|
4037 | if (q1) { |
---|
4038 | zsubmul(q1, &r[i], b); |
---|
4039 | } |
---|
4040 | |
---|
4041 | while (rp[0] < 0) { |
---|
4042 | zaddmulone(&r[i], b); |
---|
4043 | q1--; |
---|
4044 | } |
---|
4045 | |
---|
4046 | while (rp[0] > 0) { |
---|
4047 | zsubmulone(&r[i], b); |
---|
4048 | q1++; |
---|
4049 | } |
---|
4050 | |
---|
4051 | aux = btopinv*((rp[-1]*NTL_FRADIX + rp[-2])*NTL_FRADIX + rp[-3]); |
---|
4052 | while (aux > NTL_FRADIX - 16) { |
---|
4053 | /* q1 might be too small */ |
---|
4054 | if (aux >= NTL_FRADIX) |
---|
4055 | aux = NTL_FRADIX-1; |
---|
4056 | |
---|
4057 | |
---|
4058 | zsubmulone(&r[i], b); |
---|
4059 | if (rp[0] < 0) { |
---|
4060 | /* oops...false alarm! */ |
---|
4061 | zaddmulone(&r[i], b); |
---|
4062 | break; |
---|
4063 | } |
---|
4064 | else { |
---|
4065 | q1++; |
---|
4066 | aux = btopinv*((rp[-1]*NTL_FRADIX + rp[-2])*NTL_FRADIX + rp[-3]); |
---|
4067 | } |
---|
4068 | } |
---|
4069 | |
---|
4070 | q[i] = q1; |
---|
4071 | } |
---|
4072 | |
---|
4073 | while (sq > 1 && q[sq] == 0) sq--; |
---|
4074 | q[0] = sq; |
---|
4075 | |
---|
4076 | i = sb; |
---|
4077 | while (i > 1 && r[i] == 0) i--; |
---|
4078 | r[0] = i; |
---|
4079 | |
---|
4080 | done: |
---|
4081 | if (sign) |
---|
4082 | { |
---|
4083 | if (sign <= 2) |
---|
4084 | { |
---|
4085 | if (!(r[1]) && (r[0] == 1)) |
---|
4086 | _ntl_znegate(&q); |
---|
4087 | else |
---|
4088 | { |
---|
4089 | _ntl_zsadd(q, 1, &q); |
---|
4090 | _ntl_znegate(&q); |
---|
4091 | if (sign == 1) |
---|
4092 | _ntl_zsub(r, b, &r); |
---|
4093 | else |
---|
4094 | _ntl_zsub(b, r, &r); |
---|
4095 | } |
---|
4096 | } |
---|
4097 | else |
---|
4098 | _ntl_znegate(&r); |
---|
4099 | |
---|
4100 | if (sign & 2) |
---|
4101 | a[0] = -sa; |
---|
4102 | |
---|
4103 | if (sign & 1) |
---|
4104 | b[0] = -sb; |
---|
4105 | } |
---|
4106 | |
---|
4107 | _ntl_zcopy(q, qq); |
---|
4108 | if (rr) _ntl_zcopy(r, rr); |
---|
4109 | } |
---|
4110 | |
---|
4111 | void |
---|
4112 | _ntl_zmod(_ntl_verylong a, _ntl_verylong b, _ntl_verylong *rr) |
---|
4113 | { |
---|
4114 | long sa, sb, sq, i; |
---|
4115 | long sign; |
---|
4116 | long q1; |
---|
4117 | long *rp; |
---|
4118 | double btopinv, aux; |
---|
4119 | static _ntl_verylong r=0; |
---|
4120 | |
---|
4121 | if (!b || (((sb=b[0]) == 1) && (!b[1]))) { |
---|
4122 | zhalt("division by zero in _ntl_zdiv"); |
---|
4123 | } |
---|
4124 | |
---|
4125 | if (!a || (((sa=a[0]) == 1) && (!a[1]))) { |
---|
4126 | _ntl_zzero(rr); |
---|
4127 | return; |
---|
4128 | } |
---|
4129 | |
---|
4130 | |
---|
4131 | if (sb == 1) { |
---|
4132 | _ntl_zintoz(_ntl_zsmod(a, b[1]), rr); |
---|
4133 | return; |
---|
4134 | } |
---|
4135 | |
---|
4136 | if (sb == -1) { |
---|
4137 | _ntl_zintoz(_ntl_zsmod(a, -b[1]), rr); |
---|
4138 | return; |
---|
4139 | } |
---|
4140 | |
---|
4141 | sign = 0; |
---|
4142 | if (sa < 0) { |
---|
4143 | a[0] = sa = -sa; |
---|
4144 | sign = 2; |
---|
4145 | } |
---|
4146 | |
---|
4147 | if (sb < 0) { |
---|
4148 | b[0] = sb = -sb; |
---|
4149 | sign |= 1; |
---|
4150 | } |
---|
4151 | |
---|
4152 | |
---|
4153 | sq = sa-sb+1; |
---|
4154 | |
---|
4155 | if (sq <= 0) { |
---|
4156 | _ntl_zcopy(a, &r); |
---|
4157 | goto done; |
---|
4158 | } |
---|
4159 | |
---|
4160 | #ifdef NTL_GMP_HACK |
---|
4161 | if (_ntl_gmp_hack && sb >= NTL_GMP_REM_CROSS && sq >= NTL_GMP_REM_CROSS) { |
---|
4162 | GT_INIT |
---|
4163 | |
---|
4164 | lip_to_mpz(a, gt_1); |
---|
4165 | lip_to_mpz(b, gt_2); |
---|
4166 | mpz_fdiv_r(gt_4, gt_1, gt_2); |
---|
4167 | mpz_to_lip(&r, gt_4); |
---|
4168 | |
---|
4169 | goto done; |
---|
4170 | } |
---|
4171 | #endif |
---|
4172 | |
---|
4173 | _ntl_zsetlength(&r, sa+1); |
---|
4174 | |
---|
4175 | _ntl_zcopy(a, &r); |
---|
4176 | rp = &r[sa+1]; |
---|
4177 | *rp = 0; |
---|
4178 | |
---|
4179 | r[0] = 0; /* this streamlines the last evaluation of aux */ |
---|
4180 | |
---|
4181 | btopinv = b[sb]*NTL_FRADIX + b[sb-1]; |
---|
4182 | if (sb > 2) |
---|
4183 | btopinv = NTL_FRADIX / (btopinv*NTL_FRADIX + b[sb-2]); |
---|
4184 | else |
---|
4185 | btopinv = 1.0 / btopinv; |
---|
4186 | |
---|
4187 | |
---|
4188 | aux = btopinv*(rp[-1]*NTL_FRADIX + rp[-2]); |
---|
4189 | if (aux >= NTL_FRADIX) |
---|
4190 | aux = NTL_FRADIX-1; |
---|
4191 | |
---|
4192 | for (i = sq; i >= 1; i--, rp--) { |
---|
4193 | q1 = (long) aux; |
---|
4194 | if (q1) { |
---|
4195 | zsubmul(q1, &r[i], b); |
---|
4196 | } |
---|
4197 | |
---|
4198 | while (rp[0] < 0) { |
---|
4199 | zaddmulone(&r[i], b); |
---|
4200 | } |
---|
4201 | |
---|
4202 | while (rp[0] > 0) { |
---|
4203 | zsubmulone(&r[i], b); |
---|
4204 | } |
---|
4205 | |
---|
4206 | aux = btopinv*((rp[-1]*NTL_FRADIX + rp[-2])*NTL_FRADIX + rp[-3]); |
---|
4207 | while (aux > NTL_FRADIX - 16) { |
---|
4208 | /* q1 might be too small */ |
---|
4209 | if (aux >= NTL_FRADIX) |
---|
4210 | aux = NTL_FRADIX-1; |
---|
4211 | |
---|
4212 | |
---|
4213 | zsubmulone(&r[i], b); |
---|
4214 | if (rp[0] < 0) { |
---|
4215 | /* oops...false alarm! */ |
---|
4216 | zaddmulone(&r[i], b); |
---|
4217 | break; |
---|
4218 | } |
---|
4219 | else { |
---|
4220 | aux = btopinv*((rp[-1]*NTL_FRADIX + rp[-2])*NTL_FRADIX + rp[-3]); |
---|
4221 | } |
---|
4222 | } |
---|
4223 | } |
---|
4224 | |
---|
4225 | i = sb; |
---|
4226 | while (i > 1 && r[i] == 0) i--; |
---|
4227 | r[0] = i; |
---|
4228 | |
---|
4229 | done: |
---|
4230 | if (sign) |
---|
4231 | { |
---|
4232 | if (sign <= 2) |
---|
4233 | { |
---|
4234 | if (!(r[1]) && (r[0] == 1)) |
---|
4235 | /* no op */; |
---|
4236 | else |
---|
4237 | { |
---|
4238 | if (sign == 1) |
---|
4239 | _ntl_zsub(r, b, &r); |
---|
4240 | else |
---|
4241 | _ntl_zsub(b, r, &r); |
---|
4242 | } |
---|
4243 | } |
---|
4244 | else |
---|
4245 | _ntl_znegate(&r); |
---|
4246 | |
---|
4247 | if (sign & 2) |
---|
4248 | a[0] = -sa; |
---|
4249 | |
---|
4250 | if (sign & 1) |
---|
4251 | b[0] = -sb; |
---|
4252 | } |
---|
4253 | |
---|
4254 | _ntl_zcopy(r, rr); |
---|
4255 | } |
---|
4256 | |
---|
4257 | void |
---|
4258 | _ntl_zquickmod(_ntl_verylong *rr, _ntl_verylong b) |
---|
4259 | { |
---|
4260 | long sa, sb, sq, i; |
---|
4261 | long q1; |
---|
4262 | long *rp; |
---|
4263 | double btopinv, aux; |
---|
4264 | _ntl_verylong r; |
---|
4265 | |
---|
4266 | sb = b[0]; |
---|
4267 | |
---|
4268 | r = *rr; |
---|
4269 | |
---|
4270 | if (!r || (((sa=r[0]) == 1) && (!r[1]))) { |
---|
4271 | _ntl_zzero(rr); |
---|
4272 | return; |
---|
4273 | } |
---|
4274 | |
---|
4275 | |
---|
4276 | if (sb == 1) { |
---|
4277 | _ntl_zintoz(_ntl_zsmod(r, b[1]), rr); |
---|
4278 | return; |
---|
4279 | } |
---|
4280 | |
---|
4281 | sq = sa-sb+1; |
---|
4282 | |
---|
4283 | if (sq <= 0) { |
---|
4284 | return; |
---|
4285 | } |
---|
4286 | |
---|
4287 | #ifdef NTL_GMP_HACK |
---|
4288 | if (_ntl_gmp_hack && sb >= NTL_GMP_QREM_CROSS && sq >= NTL_GMP_QREM_CROSS) { |
---|
4289 | GT_INIT |
---|
4290 | |
---|
4291 | lip_to_mpz(r, gt_1); |
---|
4292 | lip_to_mpz(b, gt_2); |
---|
4293 | mpz_fdiv_r(gt_4, gt_1, gt_2); |
---|
4294 | mpz_to_lip(rr, gt_4); |
---|
4295 | return; |
---|
4296 | } |
---|
4297 | #endif |
---|
4298 | |
---|
4299 | _ntl_zsetlength(rr, sa+1); |
---|
4300 | r = *rr; |
---|
4301 | |
---|
4302 | rp = &r[sa+1]; |
---|
4303 | *rp = 0; |
---|
4304 | |
---|
4305 | r[0] = 0; /* this streamlines the last evaluation of aux */ |
---|
4306 | |
---|
4307 | btopinv = b[sb]*NTL_FRADIX + b[sb-1]; |
---|
4308 | if (sb > 2) |
---|
4309 | btopinv = NTL_FRADIX / (btopinv*NTL_FRADIX + b[sb-2]); |
---|
4310 | else |
---|
4311 | btopinv = 1.0 / btopinv; |
---|
4312 | |
---|
4313 | |
---|
4314 | aux = btopinv*(rp[-1]*NTL_FRADIX + rp[-2]); |
---|
4315 | if (aux >= NTL_FRADIX) |
---|
4316 | aux = NTL_FRADIX-1; |
---|
4317 | |
---|
4318 | for (i = sq; i >= 1; i--, rp--) { |
---|
4319 | q1 = (long) aux; |
---|
4320 | if (q1) { |
---|
4321 | zsubmul(q1, &r[i], b); |
---|
4322 | } |
---|
4323 | |
---|
4324 | while (rp[0] < 0) { |
---|
4325 | zaddmulone(&r[i], b); |
---|
4326 | } |
---|
4327 | |
---|
4328 | while (rp[0] > 0) { |
---|
4329 | zsubmulone(&r[i], b); |
---|
4330 | } |
---|
4331 | |
---|
4332 | aux = btopinv*((rp[-1]*NTL_FRADIX + rp[-2])*NTL_FRADIX + rp[-3]); |
---|
4333 | while (aux > NTL_FRADIX - 16) { |
---|
4334 | /* q1 might be too small */ |
---|
4335 | if (aux >= NTL_FRADIX) |
---|
4336 | aux = NTL_FRADIX-1; |
---|
4337 | |
---|
4338 | |
---|
4339 | zsubmulone(&r[i], b); |
---|
4340 | if (rp[0] < 0) { |
---|
4341 | /* oops...false alarm! */ |
---|
4342 | zaddmulone(&r[i], b); |
---|
4343 | break; |
---|
4344 | } |
---|
4345 | else { |
---|
4346 | aux = btopinv*((rp[-1]*NTL_FRADIX + rp[-2])*NTL_FRADIX + rp[-3]); |
---|
4347 | } |
---|
4348 | } |
---|
4349 | } |
---|
4350 | |
---|
4351 | i = sb; |
---|
4352 | while (i > 1 && r[i] == 0) i--; |
---|
4353 | r[0] = i; |
---|
4354 | } |
---|
4355 | |
---|
4356 | |
---|
4357 | void |
---|
4358 | _ntl_zaddmod( |
---|
4359 | _ntl_verylong a, |
---|
4360 | _ntl_verylong b, |
---|
4361 | _ntl_verylong n, |
---|
4362 | _ntl_verylong *c |
---|
4363 | ) |
---|
4364 | { |
---|
4365 | if (*c != n) { |
---|
4366 | _ntl_zadd(a, b, c); |
---|
4367 | if (_ntl_zcompare(*c, n) >= 0) |
---|
4368 | _ntl_zsubpos(*c, n, c); |
---|
4369 | } |
---|
4370 | else { |
---|
4371 | static _ntl_verylong mem = 0; |
---|
4372 | |
---|
4373 | _ntl_zadd(a, b, &mem); |
---|
4374 | if (_ntl_zcompare(mem, n) >= 0) |
---|
4375 | _ntl_zsubpos(mem, n, c); |
---|
4376 | else |
---|
4377 | _ntl_zcopy(mem, c); |
---|
4378 | } |
---|
4379 | } |
---|
4380 | |
---|
4381 | void |
---|
4382 | _ntl_zsubmod( |
---|
4383 | _ntl_verylong a, |
---|
4384 | _ntl_verylong b, |
---|
4385 | _ntl_verylong n, |
---|
4386 | _ntl_verylong *c |
---|
4387 | ) |
---|
4388 | { |
---|
4389 | static _ntl_verylong mem = 0; |
---|
4390 | long cmp; |
---|
4391 | |
---|
4392 | if ((cmp=_ntl_zcompare(a, b)) < 0) { |
---|
4393 | _ntl_zadd(n, a, &mem); |
---|
4394 | _ntl_zsubpos(mem, b, c); |
---|
4395 | } else if (!cmp) |
---|
4396 | _ntl_zzero(c); |
---|
4397 | else |
---|
4398 | _ntl_zsubpos(a, b, c); |
---|
4399 | } |
---|
4400 | |
---|
4401 | void |
---|
4402 | _ntl_zsmulmod( |
---|
4403 | _ntl_verylong a, |
---|
4404 | long d, |
---|
4405 | _ntl_verylong n, |
---|
4406 | _ntl_verylong *c |
---|
4407 | ) |
---|
4408 | { |
---|
4409 | static _ntl_verylong mem = 0; |
---|
4410 | |
---|
4411 | _ntl_zsmul(a, d, &mem); |
---|
4412 | _ntl_zquickmod(&mem, n); |
---|
4413 | _ntl_zcopy(mem, c); |
---|
4414 | } |
---|
4415 | |
---|
4416 | |
---|
4417 | |
---|
4418 | |
---|
4419 | void |
---|
4420 | _ntl_zmulmod( |
---|
4421 | _ntl_verylong a, |
---|
4422 | _ntl_verylong b, |
---|
4423 | _ntl_verylong n, |
---|
4424 | _ntl_verylong *c |
---|
4425 | ) |
---|
4426 | { |
---|
4427 | static _ntl_verylong mem = 0; |
---|
4428 | |
---|
4429 | _ntl_zmul(a, b, &mem); |
---|
4430 | _ntl_zquickmod(&mem, n); |
---|
4431 | _ntl_zcopy(mem, c); |
---|
4432 | } |
---|
4433 | |
---|
4434 | void |
---|
4435 | _ntl_zsqmod( |
---|
4436 | _ntl_verylong a, |
---|
4437 | _ntl_verylong n, |
---|
4438 | _ntl_verylong *c |
---|
4439 | ) |
---|
4440 | { |
---|
4441 | static _ntl_verylong mem = 0; |
---|
4442 | |
---|
4443 | _ntl_zsq(a, &mem); |
---|
4444 | _ntl_zquickmod(&mem, n); |
---|
4445 | _ntl_zcopy(mem, c); |
---|
4446 | } |
---|
4447 | |
---|
4448 | |
---|
4449 | void |
---|
4450 | _ntl_zinvmod( |
---|
4451 | _ntl_verylong a, |
---|
4452 | _ntl_verylong n, |
---|
4453 | _ntl_verylong *c |
---|
4454 | ) |
---|
4455 | { |
---|
4456 | if (_ntl_zinv(a, n, c)) |
---|
4457 | zhalt("undefined inverse in _ntl_zinvmod"); |
---|
4458 | } |
---|
4459 | |
---|
4460 | |
---|
4461 | static long |
---|
4462 | zxxeucl( |
---|
4463 | _ntl_verylong ain, |
---|
4464 | _ntl_verylong nin, |
---|
4465 | _ntl_verylong *invv, |
---|
4466 | _ntl_verylong *uu |
---|
4467 | ) |
---|
4468 | { |
---|
4469 | static _ntl_verylong a = 0; |
---|
4470 | static _ntl_verylong n = 0; |
---|
4471 | static _ntl_verylong q = 0; |
---|
4472 | static _ntl_verylong w = 0; |
---|
4473 | static _ntl_verylong x = 0; |
---|
4474 | static _ntl_verylong y = 0; |
---|
4475 | static _ntl_verylong z = 0; |
---|
4476 | _ntl_verylong inv = *invv; |
---|
4477 | _ntl_verylong u = *uu; |
---|
4478 | long diff; |
---|
4479 | long ilo; |
---|
4480 | long sa; |
---|
4481 | long sn; |
---|
4482 | long temp; |
---|
4483 | long e; |
---|
4484 | long fast; |
---|
4485 | long parity; |
---|
4486 | long gotthem; |
---|
4487 | _ntl_verylong pin; |
---|
4488 | _ntl_verylong p; |
---|
4489 | long i; |
---|
4490 | long try11; |
---|
4491 | long try12; |
---|
4492 | long try21; |
---|
4493 | long try22; |
---|
4494 | long got11; |
---|
4495 | long got12; |
---|
4496 | long got21; |
---|
4497 | long got22; |
---|
4498 | double hi; |
---|
4499 | double lo; |
---|
4500 | double dt; |
---|
4501 | double fhi, fhi1; |
---|
4502 | double flo, flo1; |
---|
4503 | double num; |
---|
4504 | double den; |
---|
4505 | double dirt; |
---|
4506 | |
---|
4507 | |
---|
4508 | _ntl_zsetlength(&a, (e = (ain[0] > nin[0] ? ain[0] : nin[0]))); |
---|
4509 | _ntl_zsetlength(&n, e); |
---|
4510 | _ntl_zsetlength(&q, e); |
---|
4511 | _ntl_zsetlength(&w, e); |
---|
4512 | _ntl_zsetlength(&x, e); |
---|
4513 | _ntl_zsetlength(&y, e); |
---|
4514 | _ntl_zsetlength(&z, e); |
---|
4515 | _ntl_zsetlength(&inv, e); |
---|
4516 | *invv = inv; |
---|
4517 | _ntl_zsetlength(&u, e); |
---|
4518 | *uu = u; |
---|
4519 | |
---|
4520 | fhi1 = 1.0 + ((double) 32.0)/NTL_FDOUBLE_PRECISION; |
---|
4521 | flo1 = 1.0 - ((double) 32.0)/NTL_FDOUBLE_PRECISION; |
---|
4522 | |
---|
4523 | fhi = 1.0 + ((double) 8.0)/NTL_FDOUBLE_PRECISION; |
---|
4524 | flo = 1.0 - ((double) 8.0)/NTL_FDOUBLE_PRECISION; |
---|
4525 | |
---|
4526 | pin = &ain[0]; |
---|
4527 | p = &a[0]; |
---|
4528 | for (i = (*pin); i >= 0; i--) |
---|
4529 | *p++ = *pin++; |
---|
4530 | pin = &nin[0]; |
---|
4531 | p = &n[0]; |
---|
4532 | for (i = (*pin); i >= 0; i--) |
---|
4533 | *p++ = *pin++; |
---|
4534 | inv[0] = 1; |
---|
4535 | inv[1] = 1; |
---|
4536 | w[0] = 1; |
---|
4537 | w[1] = 0; |
---|
4538 | while (n[0] > 1 || n[1] > 0) |
---|
4539 | { |
---|
4540 | gotthem = 0; |
---|
4541 | sa = a[0]; |
---|
4542 | sn = n[0]; |
---|
4543 | diff = sa - sn; |
---|
4544 | if (!diff || diff == 1) |
---|
4545 | { |
---|
4546 | sa = a[0]; |
---|
4547 | p = &a[sa]; |
---|
4548 | num = ((double) (*p)) * NTL_FRADIX; |
---|
4549 | if (sa > 1) |
---|
4550 | num += (*(--p)); |
---|
4551 | num *= NTL_FRADIX; |
---|
4552 | if (sa > 2) |
---|
4553 | num += (*(p - 1)); |
---|
4554 | sn = n[0]; |
---|
4555 | p = &n[sn]; |
---|
4556 | den = (double) (*p) * NTL_FRADIX; |
---|
4557 | if (sn > 1) |
---|
4558 | den += (*(--p)); |
---|
4559 | den *= NTL_FRADIX; |
---|
4560 | if (sn > 2) |
---|
4561 | den += (*(p - 1)); |
---|
4562 | hi = fhi1 * (num + 1.0) / den; |
---|
4563 | lo = flo1 * num / (den + 1.0); |
---|
4564 | if (diff > 0) |
---|
4565 | { |
---|
4566 | hi *= NTL_FRADIX; |
---|
4567 | lo *= NTL_FRADIX; |
---|
4568 | } |
---|
4569 | try11 = 1; |
---|
4570 | try12 = 0; |
---|
4571 | try21 = 0; |
---|
4572 | try22 = 1; |
---|
4573 | parity = 1; |
---|
4574 | fast = 1; |
---|
4575 | while (fast > 0) |
---|
4576 | { |
---|
4577 | parity = 1 - parity; |
---|
4578 | if (hi >= NTL_FRADIX) |
---|
4579 | fast = 0; |
---|
4580 | else |
---|
4581 | { |
---|
4582 | ilo = (long)lo; |
---|
4583 | dirt = hi - ilo; |
---|
4584 | if (dirt < 1.0/NTL_FDOUBLE_PRECISION || !ilo || ilo < (long)hi) |
---|
4585 | fast = 0; |
---|
4586 | else |
---|
4587 | { |
---|
4588 | dt = lo-ilo; |
---|
4589 | lo = flo / dirt; |
---|
4590 | if (dt > 1.0/NTL_FDOUBLE_PRECISION) |
---|
4591 | hi = fhi / dt; |
---|
4592 | else |
---|
4593 | hi = NTL_FRADIX; |
---|
4594 | temp = try11; |
---|
4595 | try11 = try21; |
---|
4596 | if ((NTL_RADIX - temp) / ilo < try21) |
---|
4597 | fast = 0; |
---|
4598 | else |
---|
4599 | try21 = temp + ilo * try21; |
---|
4600 | temp = try12; |
---|
4601 | try12 = try22; |
---|
4602 | if ((NTL_RADIX - temp) / ilo < try22) |
---|
4603 | fast = 0; |
---|
4604 | else |
---|
4605 | try22 = temp + ilo * try22; |
---|
4606 | if ((fast > 0) && (parity > 0)) |
---|
4607 | { |
---|
4608 | gotthem = 1; |
---|
4609 | got11 = try11; |
---|
4610 | got12 = try12; |
---|
4611 | got21 = try21; |
---|
4612 | got22 = try22; |
---|
4613 | } |
---|
4614 | } |
---|
4615 | } |
---|
4616 | } |
---|
4617 | } |
---|
4618 | if (gotthem) |
---|
4619 | { |
---|
4620 | _ntl_zsmul(inv, got11, &x); |
---|
4621 | _ntl_zsmul(w, got12, &y); |
---|
4622 | _ntl_zsmul(inv, got21, &z); |
---|
4623 | _ntl_zsmul(w, got22, &w); |
---|
4624 | _ntl_zadd(x, y, &inv); |
---|
4625 | _ntl_zadd(z, w, &w); |
---|
4626 | _ntl_zsmul(a, got11, &x); |
---|
4627 | _ntl_zsmul(n, got12, &y); |
---|
4628 | _ntl_zsmul(a, got21, &z); |
---|
4629 | _ntl_zsmul(n, got22, &n); |
---|
4630 | _ntl_zsub(x, y, &a); |
---|
4631 | _ntl_zsub(n, z, &n); |
---|
4632 | } |
---|
4633 | else |
---|
4634 | { |
---|
4635 | _ntl_zdiv(a, n, &q, &a); |
---|
4636 | _ntl_zmul(q, w, &x); |
---|
4637 | _ntl_zadd(inv, x, &inv); |
---|
4638 | if (a[0] > 1 || a[1] > 0) |
---|
4639 | { |
---|
4640 | _ntl_zdiv(n, a, &q, &n); |
---|
4641 | _ntl_zmul(q, inv, &x); |
---|
4642 | _ntl_zadd(w, x, &w); |
---|
4643 | } |
---|
4644 | else |
---|
4645 | { |
---|
4646 | p = &a[0]; |
---|
4647 | pin = &n[0]; |
---|
4648 | for (i = (*pin); i >= 0; i--) |
---|
4649 | *p++ = *pin++; |
---|
4650 | n[0] = 1; |
---|
4651 | n[1] = 0; |
---|
4652 | _ntl_zcopy(w, &inv); |
---|
4653 | _ntl_znegate(&inv); |
---|
4654 | } |
---|
4655 | } |
---|
4656 | } |
---|
4657 | |
---|
4658 | if ((a[0] == 1) && (a[1] == 1)) |
---|
4659 | e = 0; |
---|
4660 | else |
---|
4661 | e = 1; |
---|
4662 | |
---|
4663 | p = &u[0]; |
---|
4664 | pin = &a[0]; |
---|
4665 | for (i = (*pin); i >= 0; i--) |
---|
4666 | *p++ = *pin++; |
---|
4667 | *invv = inv; |
---|
4668 | *uu = u; |
---|
4669 | |
---|
4670 | return (e); |
---|
4671 | } |
---|
4672 | |
---|
4673 | long |
---|
4674 | _ntl_zinv( |
---|
4675 | _ntl_verylong ain, |
---|
4676 | _ntl_verylong nin, |
---|
4677 | _ntl_verylong *invv |
---|
4678 | ) |
---|
4679 | { |
---|
4680 | static _ntl_verylong u = 0; |
---|
4681 | static _ntl_verylong v = 0; |
---|
4682 | long sgn; |
---|
4683 | |
---|
4684 | |
---|
4685 | if (_ntl_zscompare(nin, 1) <= 0) { |
---|
4686 | zhalt("InvMod: second input <= 1"); |
---|
4687 | } |
---|
4688 | |
---|
4689 | sgn = _ntl_zsign(ain); |
---|
4690 | if (sgn < 0) { |
---|
4691 | zhalt("InvMod: first input negative"); |
---|
4692 | } |
---|
4693 | |
---|
4694 | if (_ntl_zcompare(ain, nin) >= 0) { |
---|
4695 | zhalt("InvMod: first input too big"); |
---|
4696 | } |
---|
4697 | |
---|
4698 | |
---|
4699 | if (sgn == 0) { |
---|
4700 | _ntl_zcopy(nin, invv); |
---|
4701 | return 1; |
---|
4702 | } |
---|
4703 | |
---|
4704 | #ifdef NTL_GMP_HACK |
---|
4705 | #if (__GNU_MP_VERSION >= 3) |
---|
4706 | /* versions of gmp prior to version 3 have really bad xgcd */ |
---|
4707 | if (_ntl_gmp_hack && nin[0] >= NTL_GMP_INVMOD_CROSS) { |
---|
4708 | GT_INIT |
---|
4709 | |
---|
4710 | lip_to_mpz(ain, gt_1); |
---|
4711 | lip_to_mpz(nin, gt_2); |
---|
4712 | mpz_gcdext(gt_3, gt_4, 0, gt_1, gt_2); |
---|
4713 | mpz_to_lip(&u, gt_3); |
---|
4714 | mpz_to_lip(&v, gt_4); |
---|
4715 | |
---|
4716 | if (u && u[0] == 1 && u[1] == 1) { |
---|
4717 | |
---|
4718 | /* |
---|
4719 | * We make sure v is in range 0..n-1, |
---|
4720 | * just in case GMP is sloppy. |
---|
4721 | */ |
---|
4722 | |
---|
4723 | while (_ntl_zsign(v) < 0) |
---|
4724 | _ntl_zadd(v, nin, &v); |
---|
4725 | |
---|
4726 | while (_ntl_zcompare(v, nin) >= 0) |
---|
4727 | _ntl_zsub(v, nin, &v); |
---|
4728 | |
---|
4729 | _ntl_zcopy(v, invv); |
---|
4730 | return 0; |
---|
4731 | } |
---|
4732 | else { |
---|
4733 | _ntl_zcopy(u, invv); |
---|
4734 | return 1; |
---|
4735 | } |
---|
4736 | } |
---|
4737 | #endif |
---|
4738 | #endif |
---|
4739 | |
---|
4740 | if (!(zxxeucl(ain, nin, &v, &u))) { |
---|
4741 | if (_ntl_zsign(v) < 0) _ntl_zadd(v, nin, &v); |
---|
4742 | _ntl_zcopy(v, invv); |
---|
4743 | return 0; |
---|
4744 | } |
---|
4745 | |
---|
4746 | _ntl_zcopy(u, invv); |
---|
4747 | return 1; |
---|
4748 | } |
---|
4749 | |
---|
4750 | void |
---|
4751 | _ntl_zexteucl( |
---|
4752 | _ntl_verylong aa, |
---|
4753 | _ntl_verylong *xa, |
---|
4754 | _ntl_verylong bb, |
---|
4755 | _ntl_verylong *xb, |
---|
4756 | _ntl_verylong *d |
---|
4757 | ) |
---|
4758 | { |
---|
4759 | static _ntl_verylong modcon = 0; |
---|
4760 | static _ntl_verylong a=0, b=0; |
---|
4761 | long anegative = 0; |
---|
4762 | long bnegative = 0; |
---|
4763 | |
---|
4764 | _ntl_zcopy(aa, &a); |
---|
4765 | _ntl_zcopy(bb, &b); |
---|
4766 | |
---|
4767 | if (anegative = (a[0] < 0)) |
---|
4768 | a[0] = -a[0]; |
---|
4769 | if (bnegative = (b[0] < 0)) |
---|
4770 | b[0] = -b[0]; |
---|
4771 | |
---|
4772 | if (!b[1] && (b[0] == 1)) |
---|
4773 | { |
---|
4774 | _ntl_zone(xa); |
---|
4775 | _ntl_zzero(xb); |
---|
4776 | _ntl_zcopy(a, d); |
---|
4777 | goto done; |
---|
4778 | } |
---|
4779 | |
---|
4780 | if (!a[1] && (a[0] == 1)) |
---|
4781 | { |
---|
4782 | _ntl_zzero(xa); |
---|
4783 | _ntl_zone(xb); |
---|
4784 | _ntl_zcopy(b, d); |
---|
4785 | goto done; |
---|
4786 | } |
---|
4787 | |
---|
4788 | #ifdef NTL_GMP_HACK |
---|
4789 | #if (__GNU_MP_VERSION >= 3) |
---|
4790 | /* versions of gmp prior to version 3 have really bad xgcd */ |
---|
4791 | if (_ntl_gmp_hack && |
---|
4792 | a[0] >= NTL_GMP_XGCD_CROSS && b[0] >= NTL_GMP_XGCD_CROSS) { |
---|
4793 | GT_INIT |
---|
4794 | |
---|
4795 | lip_to_mpz(aa, gt_1); |
---|
4796 | lip_to_mpz(bb, gt_2); |
---|
4797 | mpz_gcdext(gt_3, gt_4, gt_5, gt_1, gt_2); |
---|
4798 | mpz_to_lip(&a, gt_3); |
---|
4799 | mpz_to_lip(&b, gt_4); |
---|
4800 | mpz_to_lip(&modcon, gt_5); |
---|
4801 | _ntl_zcopy(a, d); |
---|
4802 | _ntl_zcopy(b, xa); |
---|
4803 | _ntl_zcopy(modcon, xb); |
---|
4804 | return; |
---|
4805 | } |
---|
4806 | #endif |
---|
4807 | #endif |
---|
4808 | |
---|
4809 | |
---|
4810 | zxxeucl(a, b, xa, d); |
---|
4811 | _ntl_zmul(a, *xa, xb); |
---|
4812 | _ntl_zsub(*d, *xb, xb); |
---|
4813 | _ntl_zdiv(*xb, b, xb, &modcon); |
---|
4814 | |
---|
4815 | if ((modcon[1]) || (modcon[0] != 1)) |
---|
4816 | { |
---|
4817 | zhalt("non-zero remainder in _ntl_zexteucl BUG"); |
---|
4818 | } |
---|
4819 | done: |
---|
4820 | if (anegative) |
---|
4821 | { |
---|
4822 | _ntl_znegate(xa); |
---|
4823 | } |
---|
4824 | if (bnegative) |
---|
4825 | { |
---|
4826 | _ntl_znegate(xb); |
---|
4827 | } |
---|
4828 | } |
---|
4829 | |
---|
4830 | |
---|
4831 | |
---|
4832 | /* I've adapted LIP's extended euclidean algorithm to |
---|
4833 | * do rational reconstruction. -- VJS. |
---|
4834 | */ |
---|
4835 | |
---|
4836 | |
---|
4837 | long |
---|
4838 | _ntl_zxxratrecon( |
---|
4839 | _ntl_verylong ain, |
---|
4840 | _ntl_verylong nin, |
---|
4841 | _ntl_verylong num_bound, |
---|
4842 | _ntl_verylong den_bound, |
---|
4843 | _ntl_verylong *num_out, |
---|
4844 | _ntl_verylong *den_out |
---|
4845 | ) |
---|
4846 | { |
---|
4847 | static _ntl_verylong a = 0; |
---|
4848 | static _ntl_verylong n = 0; |
---|
4849 | static _ntl_verylong q = 0; |
---|
4850 | static _ntl_verylong w = 0; |
---|
4851 | static _ntl_verylong x = 0; |
---|
4852 | static _ntl_verylong y = 0; |
---|
4853 | static _ntl_verylong z = 0; |
---|
4854 | static _ntl_verylong inv = 0; |
---|
4855 | static _ntl_verylong u = 0; |
---|
4856 | static _ntl_verylong a_bak = 0; |
---|
4857 | static _ntl_verylong n_bak = 0; |
---|
4858 | static _ntl_verylong inv_bak = 0; |
---|
4859 | static _ntl_verylong w_bak = 0; |
---|
4860 | |
---|
4861 | _ntl_verylong p; |
---|
4862 | |
---|
4863 | long diff; |
---|
4864 | long ilo; |
---|
4865 | long sa; |
---|
4866 | long sn; |
---|
4867 | long snum; |
---|
4868 | long sden; |
---|
4869 | long e; |
---|
4870 | long fast; |
---|
4871 | long temp; |
---|
4872 | long parity; |
---|
4873 | long gotthem; |
---|
4874 | long try11; |
---|
4875 | long try12; |
---|
4876 | long try21; |
---|
4877 | long try22; |
---|
4878 | long got11; |
---|
4879 | long got12; |
---|
4880 | long got21; |
---|
4881 | long got22; |
---|
4882 | |
---|
4883 | double hi; |
---|
4884 | double lo; |
---|
4885 | double dt; |
---|
4886 | double fhi, fhi1; |
---|
4887 | double flo, flo1; |
---|
4888 | double num; |
---|
4889 | double den; |
---|
4890 | double dirt; |
---|
4891 | |
---|
4892 | if (_ntl_zsign(num_bound) < 0) |
---|
4893 | zhalt("rational reconstruction: bad numerator bound"); |
---|
4894 | |
---|
4895 | if (!num_bound) |
---|
4896 | snum = 1; |
---|
4897 | else |
---|
4898 | snum = num_bound[0]; |
---|
4899 | |
---|
4900 | if (_ntl_zsign(den_bound) <= 0) |
---|
4901 | zhalt("rational reconstruction: bad denominator bound"); |
---|
4902 | |
---|
4903 | sden = den_bound[0]; |
---|
4904 | |
---|
4905 | if (_ntl_zsign(nin) <= 0) |
---|
4906 | zhalt("rational reconstruction: bad modulus"); |
---|
4907 | |
---|
4908 | if (_ntl_zsign(ain) < 0 || _ntl_zcompare(ain, nin) >= 0) |
---|
4909 | zhalt("rational reconstruction: bad residue"); |
---|
4910 | |
---|
4911 | |
---|
4912 | e = nin[0]; |
---|
4913 | _ntl_zsetlength(&a, e); |
---|
4914 | _ntl_zsetlength(&n, e); |
---|
4915 | _ntl_zsetlength(&q, e); |
---|
4916 | _ntl_zsetlength(&w, e); |
---|
4917 | _ntl_zsetlength(&x, e); |
---|
4918 | _ntl_zsetlength(&y, e); |
---|
4919 | _ntl_zsetlength(&z, e); |
---|
4920 | _ntl_zsetlength(&inv, e); |
---|
4921 | _ntl_zsetlength(&u, e); |
---|
4922 | _ntl_zsetlength(&a_bak, e); |
---|
4923 | _ntl_zsetlength(&n_bak, e); |
---|
4924 | _ntl_zsetlength(&inv_bak, e); |
---|
4925 | _ntl_zsetlength(&w_bak, e); |
---|
4926 | |
---|
4927 | fhi1 = 1.0 + ((double) 32.0)/NTL_FDOUBLE_PRECISION; |
---|
4928 | flo1 = 1.0 - ((double) 32.0)/NTL_FDOUBLE_PRECISION; |
---|
4929 | |
---|
4930 | fhi = 1.0 + ((double) 8.0)/NTL_FDOUBLE_PRECISION; |
---|
4931 | flo = 1.0 - ((double) 8.0)/NTL_FDOUBLE_PRECISION; |
---|
4932 | |
---|
4933 | _ntl_zcopy(ain, &a); |
---|
4934 | _ntl_zcopy(nin, &n); |
---|
4935 | |
---|
4936 | _ntl_zone(&inv); |
---|
4937 | _ntl_zzero(&w); |
---|
4938 | |
---|
4939 | while (1) |
---|
4940 | { |
---|
4941 | if (w[0] >= sden && _ntl_zcompare(w, den_bound) > 0) break; |
---|
4942 | if (n[0] <= snum && _ntl_zcompare(n, num_bound) <= 0) break; |
---|
4943 | |
---|
4944 | _ntl_zcopy(a, &a_bak); |
---|
4945 | _ntl_zcopy(n, &n_bak); |
---|
4946 | _ntl_zcopy(w, &w_bak); |
---|
4947 | _ntl_zcopy(inv, &inv_bak); |
---|
4948 | |
---|
4949 | gotthem = 0; |
---|
4950 | sa = a[0]; |
---|
4951 | sn = n[0]; |
---|
4952 | diff = sa - sn; |
---|
4953 | if (!diff || diff == 1) |
---|
4954 | { |
---|
4955 | sa = a[0]; |
---|
4956 | p = &a[sa]; |
---|
4957 | num = (double) (*p) * NTL_FRADIX; |
---|
4958 | if (sa > 1) |
---|
4959 | num += (*(--p)); |
---|
4960 | num *= NTL_FRADIX; |
---|
4961 | if (sa > 2) |
---|
4962 | num += (*(p - 1)); |
---|
4963 | sn = n[0]; |
---|
4964 | p = &n[sn]; |
---|
4965 | den = (double) (*p) * NTL_FRADIX; |
---|
4966 | if (sn > 1) |
---|
4967 | den += (*(--p)); |
---|
4968 | den *= NTL_FRADIX; |
---|
4969 | if (sn > 2) |
---|
4970 | den += (*(p - 1)); |
---|
4971 | hi = fhi1 * (num + 1.0) / den; |
---|
4972 | lo = flo1 * num / (den + 1.0); |
---|
4973 | if (diff > 0) |
---|
4974 | { |
---|
4975 | hi *= NTL_FRADIX; |
---|
4976 | lo *= NTL_FRADIX; |
---|
4977 | } |
---|
4978 | try11 = 1; |
---|
4979 | try12 = 0; |
---|
4980 | try21 = 0; |
---|
4981 | try22 = 1; |
---|
4982 | parity = 1; |
---|
4983 | fast = 1; |
---|
4984 | while (fast > 0) |
---|
4985 | { |
---|
4986 | parity = 1 - parity; |
---|
4987 | if (hi >= NTL_FRADIX) |
---|
4988 | fast = 0; |
---|
4989 | else |
---|
4990 | { |
---|
4991 | ilo = (long)lo; |
---|
4992 | dirt = hi - ilo; |
---|
4993 | if (dirt < 1.0/NTL_FDOUBLE_PRECISION || !ilo || ilo < (long)hi) |
---|
4994 | fast = 0; |
---|
4995 | else |
---|
4996 | { |
---|
4997 | dt = lo-ilo; |
---|
4998 | lo = flo / dirt; |
---|
4999 | if (dt > 1.0/NTL_FDOUBLE_PRECISION) |
---|
5000 | hi = fhi / dt; |
---|
5001 | else |
---|
5002 | hi = NTL_FRADIX; |
---|
5003 | temp = try11; |
---|
5004 | try11 = try21; |
---|
5005 | if ((NTL_RADIX - temp) / ilo < try21) |
---|
5006 | fast = 0; |
---|
5007 | else |
---|
5008 | try21 = temp + ilo * try21; |
---|
5009 | temp = try12; |
---|
5010 | try12 = try22; |
---|
5011 | if ((NTL_RADIX - temp) / ilo < try22) |
---|
5012 | fast = 0; |
---|
5013 | else |
---|
5014 | try22 = temp + ilo * try22; |
---|
5015 | if ((fast > 0) && (parity > 0)) |
---|
5016 | { |
---|
5017 | gotthem = 1; |
---|
5018 | got11 = try11; |
---|
5019 | got12 = try12; |
---|
5020 | got21 = try21; |
---|
5021 | got22 = try22; |
---|
5022 | } |
---|
5023 | } |
---|
5024 | } |
---|
5025 | } |
---|
5026 | } |
---|
5027 | if (gotthem) |
---|
5028 | { |
---|
5029 | _ntl_zsmul(inv, got11, &x); |
---|
5030 | _ntl_zsmul(w, got12, &y); |
---|
5031 | _ntl_zsmul(inv, got21, &z); |
---|
5032 | _ntl_zsmul(w, got22, &w); |
---|
5033 | _ntl_zadd(x, y, &inv); |
---|
5034 | _ntl_zadd(z, w, &w); |
---|
5035 | _ntl_zsmul(a, got11, &x); |
---|
5036 | _ntl_zsmul(n, got12, &y); |
---|
5037 | _ntl_zsmul(a, got21, &z); |
---|
5038 | _ntl_zsmul(n, got22, &n); |
---|
5039 | _ntl_zsub(x, y, &a); |
---|
5040 | _ntl_zsub(n, z, &n); |
---|
5041 | } |
---|
5042 | else |
---|
5043 | { |
---|
5044 | _ntl_zdiv(a, n, &q, &a); |
---|
5045 | _ntl_zmul(q, w, &x); |
---|
5046 | _ntl_zadd(inv, x, &inv); |
---|
5047 | if (a[0] > 1 || a[1] > 0) |
---|
5048 | { |
---|
5049 | _ntl_zdiv(n, a, &q, &n); |
---|
5050 | _ntl_zmul(q, inv, &x); |
---|
5051 | _ntl_zadd(w, x, &w); |
---|
5052 | } |
---|
5053 | else |
---|
5054 | { |
---|
5055 | break; |
---|
5056 | } |
---|
5057 | } |
---|
5058 | } |
---|
5059 | |
---|
5060 | _ntl_zcopy(a_bak, &a); |
---|
5061 | _ntl_zcopy(n_bak, &n); |
---|
5062 | _ntl_zcopy(w_bak, &w); |
---|
5063 | _ntl_zcopy(inv_bak, &inv); |
---|
5064 | |
---|
5065 | _ntl_znegate(&w); |
---|
5066 | |
---|
5067 | while (1) |
---|
5068 | { |
---|
5069 | sa = w[0]; |
---|
5070 | if (sa < 0) w[0] = -sa; |
---|
5071 | if (w[0] >= sden && _ntl_zcompare(w, den_bound) > 0) return 0; |
---|
5072 | w[0] = sa; |
---|
5073 | |
---|
5074 | if (n[0] <= snum && _ntl_zcompare(n, num_bound) <= 0) break; |
---|
5075 | |
---|
5076 | fast = 0; |
---|
5077 | sa = a[0]; |
---|
5078 | sn = n[0]; |
---|
5079 | diff = sa - sn; |
---|
5080 | if (!diff || diff == 1) |
---|
5081 | { |
---|
5082 | sa = a[0]; |
---|
5083 | p = &a[sa]; |
---|
5084 | num = (double) (*p) * NTL_FRADIX; |
---|
5085 | if (sa > 1) |
---|
5086 | num += (*(--p)); |
---|
5087 | num *= NTL_FRADIX; |
---|
5088 | if (sa > 2) |
---|
5089 | num += (*(p - 1)); |
---|
5090 | sn = n[0]; |
---|
5091 | p = &n[sn]; |
---|
5092 | den = (double) (*p) * NTL_FRADIX; |
---|
5093 | if (sn > 1) |
---|
5094 | den += (*(--p)); |
---|
5095 | den *= NTL_FRADIX; |
---|
5096 | if (sn > 2) |
---|
5097 | den += (*(p - 1)); |
---|
5098 | hi = fhi1 * (num + 1.0) / den; |
---|
5099 | lo = flo1 * num / (den + 1.0); |
---|
5100 | if (diff > 0) |
---|
5101 | { |
---|
5102 | hi *= NTL_FRADIX; |
---|
5103 | lo *= NTL_FRADIX; |
---|
5104 | } |
---|
5105 | if (hi < NTL_FRADIX) |
---|
5106 | { |
---|
5107 | ilo = (long)lo; |
---|
5108 | if (ilo == (long)hi) |
---|
5109 | fast = 1; |
---|
5110 | } |
---|
5111 | } |
---|
5112 | |
---|
5113 | if (fast) |
---|
5114 | { |
---|
5115 | if (ilo != 0) { |
---|
5116 | if (ilo == 1) { |
---|
5117 | _ntl_zsub(inv, w, &inv); |
---|
5118 | _ntl_zsubpos(a, n, &a); |
---|
5119 | } |
---|
5120 | else if (ilo == 2) { |
---|
5121 | _ntl_z2mul(w, &x); |
---|
5122 | _ntl_zsub(inv, x, &inv); |
---|
5123 | _ntl_z2mul(n, &x); |
---|
5124 | _ntl_zsubpos(a, x, &a); |
---|
5125 | } |
---|
5126 | else if (ilo ==3) { |
---|
5127 | _ntl_z2mul(w, &x); |
---|
5128 | _ntl_zadd(w, x, &x); |
---|
5129 | _ntl_zsub(inv, x, &inv); |
---|
5130 | _ntl_z2mul(n, &x); |
---|
5131 | _ntl_zadd(n, x, &x); |
---|
5132 | _ntl_zsubpos(a, x, &a); |
---|
5133 | } |
---|
5134 | else if (ilo == 4) { |
---|
5135 | _ntl_zlshift(w, 2, &x); |
---|
5136 | _ntl_zsub(inv, x, &inv); |
---|
5137 | _ntl_zlshift(n, 2, &x); |
---|
5138 | _ntl_zsubpos(a, x, &a); |
---|
5139 | } |
---|
5140 | else { |
---|
5141 | _ntl_zsmul(w, ilo, &x); |
---|
5142 | _ntl_zsub(inv, x, &inv); |
---|
5143 | _ntl_zsmul(n, ilo, &x); |
---|
5144 | _ntl_zsubpos(a, x, &a); |
---|
5145 | } |
---|
5146 | } |
---|
5147 | } |
---|
5148 | else { |
---|
5149 | _ntl_zdiv(a, n, &q, &a); |
---|
5150 | _ntl_zmul(q, w, &x); |
---|
5151 | _ntl_zsub(inv, x, &inv); |
---|
5152 | } |
---|
5153 | |
---|
5154 | _ntl_zswap(&a, &n); |
---|
5155 | _ntl_zswap(&inv, &w); |
---|
5156 | } |
---|
5157 | |
---|
5158 | if (_ntl_zsign(w) < 0) { |
---|
5159 | _ntl_znegate(&w); |
---|
5160 | _ntl_znegate(&n); |
---|
5161 | } |
---|
5162 | |
---|
5163 | _ntl_zcopy(n, num_out); |
---|
5164 | _ntl_zcopy(w, den_out); |
---|
5165 | |
---|
5166 | return 1; |
---|
5167 | } |
---|
5168 | |
---|
5169 | |
---|
5170 | |
---|
5171 | static |
---|
5172 | long OptWinSize(long n) |
---|
5173 | /* finds k that minimizes n/(k+1) + 2^{k-1} */ |
---|
5174 | |
---|
5175 | { |
---|
5176 | long k; |
---|
5177 | double v, v_new; |
---|
5178 | |
---|
5179 | |
---|
5180 | v = n/2.0 + 1.0; |
---|
5181 | k = 1; |
---|
5182 | |
---|
5183 | for (;;) { |
---|
5184 | v_new = n/((double)(k+2)) + ((double)(1L << k)); |
---|
5185 | if (v_new >= v) break; |
---|
5186 | v = v_new; |
---|
5187 | k++; |
---|
5188 | } |
---|
5189 | |
---|
5190 | return k; |
---|
5191 | } |
---|
5192 | |
---|
5193 | |
---|
5194 | |
---|
5195 | static |
---|
5196 | void _ntl_zsppowermod(long a, _ntl_verylong e, _ntl_verylong n, |
---|
5197 | _ntl_verylong *x) |
---|
5198 | { |
---|
5199 | _ntl_verylong res; |
---|
5200 | long i, k; |
---|
5201 | |
---|
5202 | if (_ntl_ziszero(e)) { |
---|
5203 | _ntl_zone(x); |
---|
5204 | return; |
---|
5205 | } |
---|
5206 | |
---|
5207 | res = 0; |
---|
5208 | _ntl_zsetlength(&res, n[0]); |
---|
5209 | _ntl_zone(&res); |
---|
5210 | |
---|
5211 | k = _ntl_z2log(e); |
---|
5212 | |
---|
5213 | for (i = k - 1; i >= 0; i--) { |
---|
5214 | _ntl_zsqmod(res, n, &res); |
---|
5215 | if (_ntl_zbit(e, i)) |
---|
5216 | _ntl_zsmulmod(res, a, n, &res); |
---|
5217 | } |
---|
5218 | |
---|
5219 | if (_ntl_zsign(e) < 0) _ntl_zinvmod(res, n, &res); |
---|
5220 | |
---|
5221 | _ntl_zcopy(res, x); |
---|
5222 | _ntl_zfree(&res); |
---|
5223 | } |
---|
5224 | |
---|
5225 | |
---|
5226 | |
---|
5227 | static |
---|
5228 | void _ntl_ztwopowermod( _ntl_verylong e, _ntl_verylong n, |
---|
5229 | _ntl_verylong *x) |
---|
5230 | { |
---|
5231 | _ntl_verylong res; |
---|
5232 | long i, k; |
---|
5233 | |
---|
5234 | if (_ntl_ziszero(e)) { |
---|
5235 | _ntl_zone(x); |
---|
5236 | return; |
---|
5237 | } |
---|
5238 | |
---|
5239 | res = 0; |
---|
5240 | _ntl_zsetlength(&res, n[0]); |
---|
5241 | _ntl_zone(&res); |
---|
5242 | |
---|
5243 | k = _ntl_z2log(e); |
---|
5244 | |
---|
5245 | for (i = k - 1; i >= 0; i--) { |
---|
5246 | _ntl_zsqmod(res, n, &res); |
---|
5247 | if (_ntl_zbit(e, i)) |
---|
5248 | _ntl_zaddmod(res, res, n, &res); |
---|
5249 | } |
---|
5250 | |
---|
5251 | if (_ntl_zsign(e) < 0) _ntl_zinvmod(res, n, &res); |
---|
5252 | |
---|
5253 | _ntl_zcopy(res, x); |
---|
5254 | _ntl_zfree(&res); |
---|
5255 | } |
---|
5256 | |
---|
5257 | |
---|
5258 | void _ntl_zpowermod(_ntl_verylong g, _ntl_verylong e, _ntl_verylong F, |
---|
5259 | _ntl_verylong *h) |
---|
5260 | |
---|
5261 | /* h = g^e mod f using "sliding window" algorithm |
---|
5262 | |
---|
5263 | remark: the notation (h, g, e, F) is strange, because I |
---|
5264 | copied the code from BB.c. |
---|
5265 | */ |
---|
5266 | |
---|
5267 | { |
---|
5268 | _ntl_verylong res, *v, t; |
---|
5269 | long n, i, k, val, cnt, m; |
---|
5270 | |
---|
5271 | if (_ntl_zsign(g) < 0 || _ntl_zcompare(g, F) >= 0 || |
---|
5272 | _ntl_zscompare(F, 1) <= 0) |
---|
5273 | zhalt("PowerMod: bad args"); |
---|
5274 | |
---|
5275 | #ifdef NTL_GMP_HACK |
---|
5276 | |
---|
5277 | if (_ntl_gmp_hack) { |
---|
5278 | res = 0; |
---|
5279 | _ntl_gmp_powermod(&res, g, e, F); |
---|
5280 | |
---|
5281 | /* careful...don't compute directly into h, as it could lead |
---|
5282 | * to an allocation error in some cases. |
---|
5283 | */ |
---|
5284 | |
---|
5285 | _ntl_zcopy(res, h); |
---|
5286 | _ntl_zfree(&res); |
---|
5287 | return; |
---|
5288 | } |
---|
5289 | |
---|
5290 | #endif |
---|
5291 | |
---|
5292 | if (!g || g[0] == 1 || g[0] == -1) { |
---|
5293 | long gg = _ntl_ztoint(g); |
---|
5294 | if (gg == 2) |
---|
5295 | _ntl_ztwopowermod(e, F, h); |
---|
5296 | else |
---|
5297 | _ntl_zsppowermod(gg, e, F, h); |
---|
5298 | return; |
---|
5299 | } |
---|
5300 | |
---|
5301 | if (_ntl_zscompare(e, 0) == 0) { |
---|
5302 | _ntl_zone(h); |
---|
5303 | return; |
---|
5304 | } |
---|
5305 | |
---|
5306 | if (_ntl_zscompare(e, 1) == 0) { |
---|
5307 | _ntl_zcopy(g, h); |
---|
5308 | return; |
---|
5309 | } |
---|
5310 | |
---|
5311 | if (_ntl_zscompare(e, -1) == 0) { |
---|
5312 | _ntl_zinvmod(g, F, h); |
---|
5313 | return; |
---|
5314 | } |
---|
5315 | |
---|
5316 | if (_ntl_zscompare(e, 2) == 0) { |
---|
5317 | _ntl_zsqmod(g, F, h); |
---|
5318 | return; |
---|
5319 | } |
---|
5320 | |
---|
5321 | if (_ntl_zscompare(e, -2) == 0) { |
---|
5322 | res = 0; |
---|
5323 | _ntl_zsqmod(g, F, &res); |
---|
5324 | _ntl_zinvmod(res, F, h); |
---|
5325 | _ntl_zfree(&res); |
---|
5326 | return; |
---|
5327 | } |
---|
5328 | |
---|
5329 | n = _ntl_z2log(e); |
---|
5330 | |
---|
5331 | res = 0; |
---|
5332 | _ntl_zone(&res); |
---|
5333 | |
---|
5334 | if (n < 16) { |
---|
5335 | /* plain square-and-multiply algorithm */ |
---|
5336 | |
---|
5337 | for (i = n - 1; i >= 0; i--) { |
---|
5338 | _ntl_zsqmod(res, F, &res); |
---|
5339 | if (_ntl_zbit(e, i)) |
---|
5340 | _ntl_zmulmod(res, g, F, &res); |
---|
5341 | } |
---|
5342 | |
---|
5343 | if (_ntl_zsign(e) < 0) _ntl_zinvmod(res, F, &res); |
---|
5344 | |
---|
5345 | _ntl_zcopy(res, h); |
---|
5346 | _ntl_zfree(&res); |
---|
5347 | return; |
---|
5348 | } |
---|
5349 | |
---|
5350 | k = OptWinSize(n); |
---|
5351 | |
---|
5352 | if (k > 5) k = 5; |
---|
5353 | |
---|
5354 | v = (_ntl_verylong *) NTL_MALLOC(1L << (k-1), sizeof(_ntl_verylong), 0); |
---|
5355 | if (!v) zhalt("out of memory"); |
---|
5356 | for (i = 0; i < (1L << (k-1)); i++) |
---|
5357 | v[i] = 0; |
---|
5358 | |
---|
5359 | _ntl_zcopy(g, &v[0]); |
---|
5360 | |
---|
5361 | if (k > 1) { |
---|
5362 | t = 0; |
---|
5363 | _ntl_zsqmod(g, F, &t); |
---|
5364 | |
---|
5365 | for (i = 1; i < (1L << (k-1)); i++) |
---|
5366 | _ntl_zmulmod(v[i-1], t, F, &v[i]); |
---|
5367 | |
---|
5368 | _ntl_zfree(&t); |
---|
5369 | } |
---|
5370 | |
---|
5371 | |
---|
5372 | val = 0; |
---|
5373 | for (i = n-1; i >= 0; i--) { |
---|
5374 | val = (val << 1) | _ntl_zbit(e, i); |
---|
5375 | if (val == 0) |
---|
5376 | _ntl_zsqmod(res, F, &res); |
---|
5377 | else if (val >= (1L << (k-1)) || i == 0) { |
---|
5378 | cnt = 0; |
---|
5379 | while ((val & 1) == 0) { |
---|
5380 | val = val >> 1; |
---|
5381 | cnt++; |
---|
5382 | } |
---|
5383 | |
---|
5384 | m = val; |
---|
5385 | while (m > 0) { |
---|
5386 | _ntl_zsqmod(res, F, &res); |
---|
5387 | m = m >> 1; |
---|
5388 | } |
---|
5389 | |
---|
5390 | _ntl_zmulmod(res, v[val >> 1], F, &res); |
---|
5391 | |
---|
5392 | while (cnt > 0) { |
---|
5393 | _ntl_zsqmod(res, F, &res); |
---|
5394 | cnt--; |
---|
5395 | } |
---|
5396 | |
---|
5397 | val = 0; |
---|
5398 | } |
---|
5399 | } |
---|
5400 | |
---|
5401 | if (_ntl_zsign(e) < 0) _ntl_zinvmod(res, F, &res); |
---|
5402 | |
---|
5403 | _ntl_zcopy(res, h); |
---|
5404 | |
---|
5405 | _ntl_zfree(&res); |
---|
5406 | for (i = 0; i < (1L << (k-1)); i++) |
---|
5407 | _ntl_zfree(&v[i]); |
---|
5408 | free(v); |
---|
5409 | } |
---|
5410 | |
---|
5411 | |
---|
5412 | |
---|
5413 | |
---|
5414 | |
---|
5415 | |
---|
5416 | void |
---|
5417 | _ntl_zexp( |
---|
5418 | _ntl_verylong a, |
---|
5419 | long e, |
---|
5420 | _ntl_verylong *bb |
---|
5421 | ) |
---|
5422 | { |
---|
5423 | long k; |
---|
5424 | long len_a; |
---|
5425 | long sa; |
---|
5426 | static _ntl_verylong res = 0; |
---|
5427 | |
---|
5428 | if (!a) |
---|
5429 | sa = 0; |
---|
5430 | else { |
---|
5431 | sa = a[0]; |
---|
5432 | if (sa < 0) sa = -sa; |
---|
5433 | } |
---|
5434 | |
---|
5435 | if (sa <= 1) { |
---|
5436 | _ntl_zexps(_ntl_ztoint(a), e, bb); |
---|
5437 | return; |
---|
5438 | } |
---|
5439 | |
---|
5440 | |
---|
5441 | if (!e) |
---|
5442 | { |
---|
5443 | _ntl_zone(bb); |
---|
5444 | return; |
---|
5445 | } |
---|
5446 | |
---|
5447 | if (e < 0) |
---|
5448 | zhalt("negative exponent in _ntl_zexp"); |
---|
5449 | |
---|
5450 | if (_ntl_ziszero(a)) |
---|
5451 | { |
---|
5452 | _ntl_zzero(bb); |
---|
5453 | return; |
---|
5454 | } |
---|
5455 | |
---|
5456 | len_a = _ntl_z2log(a); |
---|
5457 | if (len_a > (NTL_MAX_LONG-(NTL_NBITS-1))/e) |
---|
5458 | zhalt("overflow in _ntl_zexp"); |
---|
5459 | |
---|
5460 | _ntl_zsetlength(&res, (len_a*e+NTL_NBITS-1)/NTL_NBITS); |
---|
5461 | |
---|
5462 | _ntl_zcopy(a, &res); |
---|
5463 | k = 1; |
---|
5464 | while ((k << 1) <= e) |
---|
5465 | k <<= 1; |
---|
5466 | while (k >>= 1) { |
---|
5467 | _ntl_zsq(res, &res); |
---|
5468 | if (e & k) |
---|
5469 | _ntl_zmul(a, res, &res); |
---|
5470 | } |
---|
5471 | |
---|
5472 | _ntl_zcopy(res, bb); |
---|
5473 | } |
---|
5474 | |
---|
5475 | void |
---|
5476 | _ntl_zexps( |
---|
5477 | long a, |
---|
5478 | long e, |
---|
5479 | _ntl_verylong *bb |
---|
5480 | ) |
---|
5481 | { |
---|
5482 | long k; |
---|
5483 | long len_a; |
---|
5484 | static _ntl_verylong res = 0; |
---|
5485 | |
---|
5486 | if (!e) |
---|
5487 | { |
---|
5488 | _ntl_zone(bb); |
---|
5489 | return; |
---|
5490 | } |
---|
5491 | |
---|
5492 | if (e < 0) |
---|
5493 | zhalt("negative exponent in _ntl_zexps"); |
---|
5494 | |
---|
5495 | if (!a) |
---|
5496 | { |
---|
5497 | _ntl_zzero(bb); |
---|
5498 | return; |
---|
5499 | } |
---|
5500 | |
---|
5501 | if (a >= NTL_RADIX || a <= -NTL_RADIX) { |
---|
5502 | _ntl_zintoz(a, &res); |
---|
5503 | _ntl_zexp(res, e, &res); |
---|
5504 | return; |
---|
5505 | } |
---|
5506 | |
---|
5507 | len_a = _ntl_z2logs(a); |
---|
5508 | if (len_a > (NTL_MAX_LONG-(NTL_NBITS-1))/e) |
---|
5509 | zhalt("overflow in _ntl_zexps"); |
---|
5510 | |
---|
5511 | _ntl_zsetlength(&res, (len_a*e+NTL_NBITS-1)/NTL_NBITS); |
---|
5512 | |
---|
5513 | _ntl_zintoz(a, &res); |
---|
5514 | k = 1; |
---|
5515 | while ((k << 1) <= e) |
---|
5516 | k <<= 1; |
---|
5517 | while (k >>= 1) { |
---|
5518 | _ntl_zsq(res, &res); |
---|
5519 | if (e & k) |
---|
5520 | _ntl_zsmul(res, a, &res); |
---|
5521 | } |
---|
5522 | |
---|
5523 | _ntl_zcopy(res, bb); |
---|
5524 | } |
---|
5525 | |
---|
5526 | |
---|
5527 | void |
---|
5528 | _ntl_z2mul( |
---|
5529 | _ntl_verylong n, |
---|
5530 | _ntl_verylong *rres |
---|
5531 | ) |
---|
5532 | { |
---|
5533 | long sn; |
---|
5534 | long i; |
---|
5535 | long n_alias; |
---|
5536 | long carry; |
---|
5537 | _ntl_verylong res; |
---|
5538 | |
---|
5539 | if (!n) |
---|
5540 | { |
---|
5541 | _ntl_zzero(rres); |
---|
5542 | return; |
---|
5543 | } |
---|
5544 | |
---|
5545 | |
---|
5546 | if ((!n[1]) && (n[0] == 1)) |
---|
5547 | { |
---|
5548 | _ntl_zzero(rres); |
---|
5549 | return; |
---|
5550 | } |
---|
5551 | |
---|
5552 | if ((sn = n[0]) < 0) |
---|
5553 | sn = -sn; |
---|
5554 | |
---|
5555 | res = *rres; |
---|
5556 | n_alias = (n == res); |
---|
5557 | |
---|
5558 | _ntl_zsetlength(&res, sn + 1); |
---|
5559 | if (n_alias) n = res; |
---|
5560 | *rres = res; |
---|
5561 | |
---|
5562 | carry = 0; |
---|
5563 | |
---|
5564 | for (i = 1; i <= sn; i++) |
---|
5565 | { |
---|
5566 | if ((res[i] = (n[i] << 1) + carry) >= NTL_RADIX) |
---|
5567 | { |
---|
5568 | res[i] -= NTL_RADIX; |
---|
5569 | carry = 1; |
---|
5570 | } |
---|
5571 | else |
---|
5572 | carry = 0; |
---|
5573 | } |
---|
5574 | |
---|
5575 | if (carry) |
---|
5576 | res[++sn] = 1; |
---|
5577 | |
---|
5578 | if (n[0] < 0) |
---|
5579 | res[0] = -sn; |
---|
5580 | else |
---|
5581 | res[0] = sn; |
---|
5582 | } |
---|
5583 | |
---|
5584 | |
---|
5585 | long |
---|
5586 | _ntl_z2div( |
---|
5587 | _ntl_verylong n, |
---|
5588 | _ntl_verylong *rres |
---|
5589 | ) |
---|
5590 | { |
---|
5591 | long sn; |
---|
5592 | long i; |
---|
5593 | long result; |
---|
5594 | _ntl_verylong res = *rres; |
---|
5595 | |
---|
5596 | if ((!n) || ((!n[1]) && (n[0] == 1))) |
---|
5597 | { |
---|
5598 | _ntl_zzero(rres); |
---|
5599 | return (0); |
---|
5600 | } |
---|
5601 | |
---|
5602 | if ((sn = n[0]) < 0) |
---|
5603 | sn = -sn; |
---|
5604 | |
---|
5605 | /* n won't move if res aliases n */ |
---|
5606 | _ntl_zsetlength(&res, sn); |
---|
5607 | *rres = res; |
---|
5608 | |
---|
5609 | result = n[1] & 1; |
---|
5610 | for (i = 1; i < sn; i++) |
---|
5611 | { |
---|
5612 | res[i] = (n[i] >> 1); |
---|
5613 | if (n[i + 1] & 1) |
---|
5614 | res[i] += (NTL_RADIX >> 1); |
---|
5615 | } |
---|
5616 | |
---|
5617 | if (res[sn] = (n[sn] >> 1)) |
---|
5618 | res[0] = n[0]; |
---|
5619 | else if (sn == 1) |
---|
5620 | { |
---|
5621 | res[0] = 1; |
---|
5622 | } |
---|
5623 | else if (n[0] < 0) |
---|
5624 | res[0] = -sn + 1; |
---|
5625 | else |
---|
5626 | res[0] = sn - 1; |
---|
5627 | |
---|
5628 | return (result); |
---|
5629 | } |
---|
5630 | |
---|
5631 | |
---|
5632 | void |
---|
5633 | _ntl_zlshift( |
---|
5634 | _ntl_verylong n, |
---|
5635 | long k, |
---|
5636 | _ntl_verylong *rres |
---|
5637 | ) |
---|
5638 | { |
---|
5639 | long big; |
---|
5640 | long small; |
---|
5641 | long sn; |
---|
5642 | long i; |
---|
5643 | long cosmall; |
---|
5644 | long n_alias; |
---|
5645 | _ntl_verylong res; |
---|
5646 | |
---|
5647 | |
---|
5648 | if (!n) |
---|
5649 | { |
---|
5650 | _ntl_zzero(rres); |
---|
5651 | return; |
---|
5652 | } |
---|
5653 | |
---|
5654 | if ((!n[1]) && (n[0] == 1)) |
---|
5655 | { |
---|
5656 | _ntl_zzero(rres); |
---|
5657 | return; |
---|
5658 | } |
---|
5659 | |
---|
5660 | res = *rres; |
---|
5661 | n_alias = (n == res); |
---|
5662 | |
---|
5663 | |
---|
5664 | if (!k) |
---|
5665 | { |
---|
5666 | if (!n_alias) |
---|
5667 | _ntl_zcopy(n, rres); |
---|
5668 | return; |
---|
5669 | } |
---|
5670 | |
---|
5671 | if (k < 0) |
---|
5672 | { |
---|
5673 | if (k < -NTL_MAX_LONG) |
---|
5674 | _ntl_zzero(rres); |
---|
5675 | else |
---|
5676 | _ntl_zrshift(n, -k, rres); |
---|
5677 | return; |
---|
5678 | } |
---|
5679 | if (k == 1) |
---|
5680 | { |
---|
5681 | _ntl_z2mul(n, rres); |
---|
5682 | return; |
---|
5683 | } |
---|
5684 | |
---|
5685 | if ((sn = n[0]) < 0) |
---|
5686 | sn = -sn; |
---|
5687 | |
---|
5688 | i = sn + (big = k / NTL_NBITS); |
---|
5689 | if (small = k - big * NTL_NBITS) |
---|
5690 | { |
---|
5691 | _ntl_zsetlength(&res, i + 1); |
---|
5692 | if (n_alias) n = res; |
---|
5693 | *rres = res; |
---|
5694 | |
---|
5695 | res[i + 1] = n[sn] >> (cosmall = NTL_NBITS - small); |
---|
5696 | for (i = sn; i > 1; i--) |
---|
5697 | res[i + big] = ((((unsigned long) n[i]) << small) & NTL_RADIXM) + (n[i - 1] >> cosmall); |
---|
5698 | res[big + 1] = (((unsigned long) n[1]) << small) & NTL_RADIXM; |
---|
5699 | for (i = big; i; i--) |
---|
5700 | res[i] = 0; |
---|
5701 | if (res[sn + big + 1]) |
---|
5702 | big++; |
---|
5703 | } |
---|
5704 | else |
---|
5705 | { |
---|
5706 | _ntl_zsetlength(&res, i); |
---|
5707 | if (n_alias) n = res; |
---|
5708 | *rres = res; |
---|
5709 | |
---|
5710 | for (i = sn; i; i--) |
---|
5711 | res[i + big] = n[i]; |
---|
5712 | for (i = big; i; i--) |
---|
5713 | res[i] = 0; |
---|
5714 | } |
---|
5715 | if (n[0] > 0) |
---|
5716 | res[0] = n[0] + big; |
---|
5717 | else |
---|
5718 | res[0] = n[0] - big; |
---|
5719 | } |
---|
5720 | |
---|
5721 | |
---|
5722 | void |
---|
5723 | _ntl_zrshift( |
---|
5724 | _ntl_verylong n, |
---|
5725 | long k, |
---|
5726 | _ntl_verylong *rres |
---|
5727 | ) |
---|
5728 | { |
---|
5729 | long big; |
---|
5730 | long small; |
---|
5731 | long sn; |
---|
5732 | long i; |
---|
5733 | long cosmall; |
---|
5734 | _ntl_verylong res; |
---|
5735 | |
---|
5736 | if (!n) |
---|
5737 | { |
---|
5738 | _ntl_zzero(rres); |
---|
5739 | return; |
---|
5740 | } |
---|
5741 | |
---|
5742 | if ((!n[1]) && (n[0] == 1)) |
---|
5743 | { |
---|
5744 | _ntl_zzero(rres); |
---|
5745 | return; |
---|
5746 | } |
---|
5747 | |
---|
5748 | res = *rres; |
---|
5749 | |
---|
5750 | if (!k) |
---|
5751 | { |
---|
5752 | if (n != res) |
---|
5753 | _ntl_zcopy(n, rres); |
---|
5754 | return; |
---|
5755 | } |
---|
5756 | |
---|
5757 | if (k < 0) |
---|
5758 | { |
---|
5759 | if (k < -NTL_MAX_LONG) zhalt("overflow in _ntl_zrshift"); |
---|
5760 | _ntl_zlshift(n, -k, rres); |
---|
5761 | return; |
---|
5762 | } |
---|
5763 | |
---|
5764 | if (k == 1) |
---|
5765 | { |
---|
5766 | _ntl_z2div(n, rres); |
---|
5767 | return; |
---|
5768 | } |
---|
5769 | |
---|
5770 | big = k / NTL_NBITS; |
---|
5771 | small = k - big * NTL_NBITS; |
---|
5772 | |
---|
5773 | if ((sn = n[0]) < 0) |
---|
5774 | sn = -sn; |
---|
5775 | |
---|
5776 | if ((big >= sn) || |
---|
5777 | ((big == sn - 1) && small && (!(n[sn] >> small)))) |
---|
5778 | /* The microsoft optimizer generates bad code without |
---|
5779 | the above test for small != 0 */ |
---|
5780 | { |
---|
5781 | _ntl_zzero(rres); |
---|
5782 | return; |
---|
5783 | } |
---|
5784 | |
---|
5785 | sn -= big; |
---|
5786 | |
---|
5787 | /* n won't move if res aliases n */ |
---|
5788 | _ntl_zsetlength(&res, sn); |
---|
5789 | *rres = res; |
---|
5790 | |
---|
5791 | if (small) |
---|
5792 | { |
---|
5793 | cosmall = NTL_NBITS - small; |
---|
5794 | for (i = 1; i < sn; i++) |
---|
5795 | res[i] = (n[i + big] >> small) + |
---|
5796 | ((((unsigned long) n[i + big + 1]) << cosmall) & NTL_RADIXM); |
---|
5797 | if (!(res[sn] = (n[sn + big] >> small))) |
---|
5798 | sn--; |
---|
5799 | } |
---|
5800 | else |
---|
5801 | for (i = 1; i <= sn; i++) |
---|
5802 | res[i] = n[i + big]; |
---|
5803 | if (n[0] > 0) |
---|
5804 | res[0] = sn; |
---|
5805 | else |
---|
5806 | res[0] = -sn; |
---|
5807 | } |
---|
5808 | |
---|
5809 | |
---|
5810 | long |
---|
5811 | _ntl_zmakeodd( |
---|
5812 | _ntl_verylong *nn |
---|
5813 | ) |
---|
5814 | { |
---|
5815 | _ntl_verylong n = *nn; |
---|
5816 | long i; |
---|
5817 | long shift = 1; |
---|
5818 | |
---|
5819 | if (!n || (!n[1] && (n[0] == 1))) |
---|
5820 | return (0); |
---|
5821 | while (!(n[shift])) |
---|
5822 | shift++; |
---|
5823 | i = n[shift]; |
---|
5824 | shift = NTL_NBITS * (shift - 1); |
---|
5825 | while (!(i & 1)) |
---|
5826 | { |
---|
5827 | shift++; |
---|
5828 | i >>= 1; |
---|
5829 | } |
---|
5830 | _ntl_zrshift(n, shift, &n); |
---|
5831 | return (shift); |
---|
5832 | } |
---|
5833 | |
---|
5834 | |
---|
5835 | long |
---|
5836 | _ntl_znumtwos( |
---|
5837 | _ntl_verylong n |
---|
5838 | ) |
---|
5839 | { |
---|
5840 | long i; |
---|
5841 | long shift = 1; |
---|
5842 | |
---|
5843 | if (!n || (!n[1] && (n[0] == 1))) |
---|
5844 | return (0); |
---|
5845 | while (!(n[shift])) |
---|
5846 | shift++; |
---|
5847 | i = n[shift]; |
---|
5848 | shift = NTL_NBITS * (shift - 1); |
---|
5849 | while (!(i & 1)) |
---|
5850 | { |
---|
5851 | shift++; |
---|
5852 | i >>= 1; |
---|
5853 | } |
---|
5854 | return (shift); |
---|
5855 | } |
---|
5856 | |
---|
5857 | |
---|
5858 | long |
---|
5859 | _ntl_zsqrts( |
---|
5860 | long n |
---|
5861 | ) |
---|
5862 | { |
---|
5863 | long a; |
---|
5864 | long ndiva; |
---|
5865 | long newa; |
---|
5866 | static _ntl_verylong ln=0; |
---|
5867 | static _ntl_verylong rr=0; |
---|
5868 | |
---|
5869 | if (n < 0) |
---|
5870 | zhalt("_ntl_zsqrts: negative argument"); |
---|
5871 | |
---|
5872 | if (n <= 0) |
---|
5873 | return (0); |
---|
5874 | if (n <= 3) |
---|
5875 | return (1); |
---|
5876 | if (n <= 8) |
---|
5877 | return (2); |
---|
5878 | if (n >= NTL_RADIX) |
---|
5879 | { |
---|
5880 | _ntl_zintoz(n,&ln); |
---|
5881 | _ntl_zsqrt(ln,&rr); |
---|
5882 | return(_ntl_ztoint(rr)); |
---|
5883 | } |
---|
5884 | newa = 3L << (2 * (NTL_NBITSH - 1)); |
---|
5885 | a = 1L << NTL_NBITSH; |
---|
5886 | while (!(n & newa)) |
---|
5887 | { |
---|
5888 | newa >>= 2; |
---|
5889 | a >>= 1; |
---|
5890 | } |
---|
5891 | while (1) |
---|
5892 | { |
---|
5893 | newa = ((ndiva = n / a) + a) / 2; |
---|
5894 | if (newa - ndiva <= 1) |
---|
5895 | { |
---|
5896 | if (newa * newa <= n) |
---|
5897 | return (newa); |
---|
5898 | else |
---|
5899 | return (ndiva); |
---|
5900 | } |
---|
5901 | a = newa; |
---|
5902 | } |
---|
5903 | } |
---|
5904 | |
---|
5905 | |
---|
5906 | void _ntl_zsqrt(_ntl_verylong n, _ntl_verylong *rr) |
---|
5907 | { |
---|
5908 | static _ntl_verylong a = 0; |
---|
5909 | static _ntl_verylong ndiva = 0; |
---|
5910 | static _ntl_verylong diff = 0; |
---|
5911 | static _ntl_verylong r = 0; |
---|
5912 | long i; |
---|
5913 | |
---|
5914 | if (!n) { |
---|
5915 | _ntl_zzero(rr); |
---|
5916 | return; |
---|
5917 | } |
---|
5918 | |
---|
5919 | if ((i = n[0]) < 0) |
---|
5920 | zhalt("negative argument in _ntl_zsqrt"); |
---|
5921 | |
---|
5922 | if (i == 1) { |
---|
5923 | _ntl_zintoz(_ntl_zsqrts(n[1]), rr); |
---|
5924 | return; |
---|
5925 | } |
---|
5926 | |
---|
5927 | #ifdef NTL_GMP_HACK |
---|
5928 | if (_ntl_gmp_hack && i >= NTL_GMP_SQRT_CROSS) { |
---|
5929 | GT_INIT |
---|
5930 | |
---|
5931 | lip_to_mpz(n, gt_1); |
---|
5932 | mpz_sqrt(gt_2, gt_1); |
---|
5933 | mpz_to_lip(&r, gt_2); |
---|
5934 | _ntl_zcopy(r, rr); |
---|
5935 | return; |
---|
5936 | } |
---|
5937 | #endif |
---|
5938 | |
---|
5939 | _ntl_zsetlength(&a, i); |
---|
5940 | _ntl_zsetlength(&ndiva, i); |
---|
5941 | _ntl_zsetlength(&diff, i); |
---|
5942 | |
---|
5943 | a[(a[0] = (i + 1) / 2)] = _ntl_zsqrts(n[i]) + 1; |
---|
5944 | if (!(i & 1)) |
---|
5945 | a[a[0]] <<= NTL_NBITSH; |
---|
5946 | |
---|
5947 | if (a[a[0]] & NTL_RADIX) { |
---|
5948 | a[a[0]] = 0; |
---|
5949 | a[0]++; |
---|
5950 | a[a[0]] = 1; |
---|
5951 | } |
---|
5952 | |
---|
5953 | for (i = a[0] - 1; i; i--) |
---|
5954 | a[i] = 0; |
---|
5955 | |
---|
5956 | while (1) { |
---|
5957 | _ntl_zdiv(n, a, &ndiva, &r); |
---|
5958 | _ntl_zadd(a, ndiva, &r); |
---|
5959 | _ntl_zrshift(r, 1, &r); |
---|
5960 | if (_ntl_zcompare(r, ndiva) <= 0) |
---|
5961 | goto done; |
---|
5962 | |
---|
5963 | _ntl_zsubpos(r, ndiva, &diff); |
---|
5964 | if ((diff[0] == 1) && (diff[1] <= 1)) { |
---|
5965 | _ntl_zsq(r, &diff); |
---|
5966 | if (_ntl_zcompare(diff, n) > 0) |
---|
5967 | _ntl_zcopy(ndiva, &r); |
---|
5968 | |
---|
5969 | goto done; |
---|
5970 | } |
---|
5971 | _ntl_zcopy(r, &a); |
---|
5972 | } |
---|
5973 | done: |
---|
5974 | _ntl_zcopy(r, rr); |
---|
5975 | } |
---|
5976 | |
---|
5977 | |
---|
5978 | |
---|
5979 | void |
---|
5980 | _ntl_zgcd( |
---|
5981 | _ntl_verylong mm1, |
---|
5982 | _ntl_verylong mm2, |
---|
5983 | _ntl_verylong *rres |
---|
5984 | ) |
---|
5985 | { |
---|
5986 | long agrb; |
---|
5987 | long shibl; |
---|
5988 | static _ntl_verylong aa = 0; |
---|
5989 | static _ntl_verylong bb = 0; |
---|
5990 | static _ntl_verylong cc = 0; |
---|
5991 | _ntl_verylong a; |
---|
5992 | _ntl_verylong b; |
---|
5993 | _ntl_verylong c; |
---|
5994 | _ntl_verylong d; |
---|
5995 | long m1negative; |
---|
5996 | long m2negative; |
---|
5997 | |
---|
5998 | /* _ntl_ziszero is necessary here and below to fix an |
---|
5999 | an aliasing bug in LIP */ |
---|
6000 | |
---|
6001 | if (_ntl_ziszero(mm1)) |
---|
6002 | { |
---|
6003 | if (mm2 != *rres) |
---|
6004 | _ntl_zcopy(mm2,rres); |
---|
6005 | _ntl_zabs(rres); |
---|
6006 | return; |
---|
6007 | } |
---|
6008 | |
---|
6009 | if (_ntl_ziszero(mm2)) |
---|
6010 | { |
---|
6011 | if (mm1 != *rres) |
---|
6012 | _ntl_zcopy(mm1,rres); |
---|
6013 | _ntl_zabs(rres); |
---|
6014 | return; |
---|
6015 | } |
---|
6016 | |
---|
6017 | if (mm1 == mm2) |
---|
6018 | { |
---|
6019 | if (mm1 != *rres) |
---|
6020 | _ntl_zcopy(mm1, rres); |
---|
6021 | _ntl_zabs(rres); |
---|
6022 | return; |
---|
6023 | } |
---|
6024 | |
---|
6025 | #ifdef NTL_GMP_HACK |
---|
6026 | { |
---|
6027 | long s1 = mm1[0]; |
---|
6028 | long s2 = mm2[0]; |
---|
6029 | |
---|
6030 | if (s1 < 0) s1 = -s1; |
---|
6031 | if (s2 < 0) s2 = -s2; |
---|
6032 | |
---|
6033 | if (_ntl_gmp_hack && s1 >= NTL_GMP_GCD_CROSS && s2 >= NTL_GMP_GCD_CROSS) { |
---|
6034 | GT_INIT |
---|
6035 | |
---|
6036 | lip_to_mpz(mm1, gt_1); |
---|
6037 | lip_to_mpz(mm2, gt_2); |
---|
6038 | mpz_gcd(gt_3, gt_1, gt_2); |
---|
6039 | mpz_to_lip(&aa, gt_3); |
---|
6040 | _ntl_zcopy(aa, rres); |
---|
6041 | return; |
---|
6042 | } |
---|
6043 | } |
---|
6044 | #endif |
---|
6045 | |
---|
6046 | if (m1negative = (mm1[0] < 0)) |
---|
6047 | mm1[0] = -mm1[0]; |
---|
6048 | if (m2negative = (mm2[0] < 0)) |
---|
6049 | mm2[0] = -mm2[0]; |
---|
6050 | |
---|
6051 | if ((agrb = mm1[0]) < mm2[0]) |
---|
6052 | agrb = mm2[0]; |
---|
6053 | |
---|
6054 | _ntl_zsetlength(&aa, agrb+1); |
---|
6055 | _ntl_zsetlength(&bb, agrb+1); |
---|
6056 | _ntl_zsetlength(&cc, agrb+1); |
---|
6057 | |
---|
6058 | if (mm1[0] != mm2[0]) |
---|
6059 | { |
---|
6060 | if (mm1[0] > mm2[0]) |
---|
6061 | { |
---|
6062 | _ntl_zcopy(mm2, &aa); |
---|
6063 | _ntl_zmod(mm1, aa, &bb); |
---|
6064 | } |
---|
6065 | else |
---|
6066 | { |
---|
6067 | _ntl_zcopy(mm1, &aa); |
---|
6068 | _ntl_zmod(mm2, aa, &bb); |
---|
6069 | } |
---|
6070 | if (!(bb[1]) && (bb[0] == 1)) |
---|
6071 | { |
---|
6072 | a = aa; |
---|
6073 | goto done; |
---|
6074 | } |
---|
6075 | } |
---|
6076 | else |
---|
6077 | { |
---|
6078 | _ntl_zcopy(mm1, &aa); |
---|
6079 | _ntl_zcopy(mm2, &bb); |
---|
6080 | } |
---|
6081 | if ((agrb = _ntl_zmakeodd(&aa)) < (shibl = _ntl_zmakeodd(&bb))) |
---|
6082 | shibl = agrb; |
---|
6083 | if (!(agrb = _ntl_zcompare(aa, bb))) |
---|
6084 | { |
---|
6085 | a = aa; |
---|
6086 | goto endshift; |
---|
6087 | } |
---|
6088 | else if (agrb < 0) |
---|
6089 | { |
---|
6090 | a = bb; |
---|
6091 | b = aa; |
---|
6092 | } |
---|
6093 | else |
---|
6094 | { |
---|
6095 | a = aa; |
---|
6096 | b = bb; |
---|
6097 | } |
---|
6098 | c = cc; |
---|
6099 | _ntl_zsubpos(a, b, &c); |
---|
6100 | do |
---|
6101 | { |
---|
6102 | _ntl_zmakeodd(&c); |
---|
6103 | if (!(agrb = _ntl_zcompare(b, c))) |
---|
6104 | { |
---|
6105 | a = b; |
---|
6106 | goto endshift; |
---|
6107 | } |
---|
6108 | else if (agrb > 0) |
---|
6109 | { |
---|
6110 | a = b; |
---|
6111 | b = c; |
---|
6112 | c = a; |
---|
6113 | } |
---|
6114 | else |
---|
6115 | { |
---|
6116 | d = a; |
---|
6117 | a = c; |
---|
6118 | c = d; |
---|
6119 | } |
---|
6120 | _ntl_zsubpos(a, b, &c); |
---|
6121 | } while (c[1] || c[0] != 1); |
---|
6122 | endshift: |
---|
6123 | _ntl_zlshift(a, shibl, &a); |
---|
6124 | done: |
---|
6125 | if (m1negative) |
---|
6126 | mm1[0] = -mm1[0]; |
---|
6127 | if (m2negative) |
---|
6128 | mm2[0] = -mm2[0]; |
---|
6129 | _ntl_zcopy(a, rres); |
---|
6130 | } |
---|
6131 | |
---|
6132 | |
---|
6133 | long _ntl_zsign(_ntl_verylong a) |
---|
6134 | { |
---|
6135 | if (!a) |
---|
6136 | { |
---|
6137 | return (0); |
---|
6138 | } |
---|
6139 | if (a[0] < 0) |
---|
6140 | return (-1); |
---|
6141 | if (a[0] > 1) |
---|
6142 | return (1); |
---|
6143 | if (a[1]) |
---|
6144 | return (1); |
---|
6145 | return (0); |
---|
6146 | } |
---|
6147 | |
---|
6148 | void _ntl_zabs(_ntl_verylong *pa) |
---|
6149 | { |
---|
6150 | _ntl_verylong a = *pa; |
---|
6151 | |
---|
6152 | if (!a) |
---|
6153 | return; |
---|
6154 | if (a[0] < 0) |
---|
6155 | a[0] = (-a[0]); |
---|
6156 | } |
---|
6157 | |
---|
6158 | long |
---|
6159 | _ntl_z2logs( |
---|
6160 | long aa |
---|
6161 | ) |
---|
6162 | { |
---|
6163 | long i = 0; |
---|
6164 | unsigned long a; |
---|
6165 | |
---|
6166 | if (aa < 0) |
---|
6167 | a = - ((unsigned long) aa); |
---|
6168 | else |
---|
6169 | a = aa; |
---|
6170 | |
---|
6171 | while (a>=256) |
---|
6172 | i += 8, a >>= 8; |
---|
6173 | if (a >=16) |
---|
6174 | i += 4, a >>= 4; |
---|
6175 | if (a >= 4) |
---|
6176 | i += 2, a >>= 2; |
---|
6177 | if (a >= 2) |
---|
6178 | i += 2; |
---|
6179 | else if (a >= 1) |
---|
6180 | i++; |
---|
6181 | return (i); |
---|
6182 | } |
---|
6183 | |
---|
6184 | long |
---|
6185 | _ntl_z2log( |
---|
6186 | _ntl_verylong a |
---|
6187 | ) |
---|
6188 | { |
---|
6189 | long la; |
---|
6190 | |
---|
6191 | if (!a) |
---|
6192 | return (0); |
---|
6193 | la = (a[0] > 0 ? a[0] : -a[0]); |
---|
6194 | return ( NTL_NBITS * (la - 1) + _ntl_z2logs(a[la]) ); |
---|
6195 | } |
---|
6196 | |
---|
6197 | |
---|
6198 | |
---|
6199 | long |
---|
6200 | _ntl_zscompare( |
---|
6201 | _ntl_verylong a, |
---|
6202 | long b |
---|
6203 | ) |
---|
6204 | { |
---|
6205 | if (!b) |
---|
6206 | return _ntl_zsign(a); |
---|
6207 | else { |
---|
6208 | static _ntl_verylong c = 0; |
---|
6209 | _ntl_zintoz(b, &c); |
---|
6210 | return (_ntl_zcompare(a, c)); |
---|
6211 | } |
---|
6212 | } |
---|
6213 | |
---|
6214 | void |
---|
6215 | _ntl_zswap( |
---|
6216 | _ntl_verylong *a, |
---|
6217 | _ntl_verylong *b |
---|
6218 | ) |
---|
6219 | { |
---|
6220 | _ntl_verylong c; |
---|
6221 | |
---|
6222 | if ((*a && ((*a)[-1] & 1)) || (*b && ((*b)[-1] & 1))) { |
---|
6223 | static _ntl_verylong t = 0; |
---|
6224 | _ntl_zcopy(*a, &t); |
---|
6225 | _ntl_zcopy(*b, a); |
---|
6226 | _ntl_zcopy(t, b); |
---|
6227 | return; |
---|
6228 | } |
---|
6229 | |
---|
6230 | c = *a; |
---|
6231 | *a = *b; |
---|
6232 | *b = c; |
---|
6233 | } |
---|
6234 | |
---|
6235 | long |
---|
6236 | _ntl_ziszero( |
---|
6237 | _ntl_verylong a |
---|
6238 | ) |
---|
6239 | { |
---|
6240 | if (!a) return (1); |
---|
6241 | if (a[1]) return (0); |
---|
6242 | if (a[0]==1) return (1); |
---|
6243 | return (0); |
---|
6244 | } |
---|
6245 | |
---|
6246 | long |
---|
6247 | _ntl_zodd( |
---|
6248 | _ntl_verylong a |
---|
6249 | ) |
---|
6250 | { |
---|
6251 | if (!a) return (0); |
---|
6252 | return (a[1]&1); |
---|
6253 | } |
---|
6254 | |
---|
6255 | |
---|
6256 | long |
---|
6257 | _ntl_zbit( |
---|
6258 | _ntl_verylong a, |
---|
6259 | long p |
---|
6260 | ) |
---|
6261 | { |
---|
6262 | long bl; |
---|
6263 | long wh; |
---|
6264 | long sa; |
---|
6265 | |
---|
6266 | if (p < 0 || !a) return 0; |
---|
6267 | bl = (p/NTL_NBITS); |
---|
6268 | wh = 1L << (p - NTL_NBITS*bl); |
---|
6269 | bl ++; |
---|
6270 | sa = a[0]; |
---|
6271 | if (sa < 0) sa = -sa; |
---|
6272 | if (sa < bl) return (0); |
---|
6273 | if (a[bl] & wh) return (1); |
---|
6274 | return (0); |
---|
6275 | } |
---|
6276 | |
---|
6277 | |
---|
6278 | void |
---|
6279 | _ntl_zlowbits( |
---|
6280 | _ntl_verylong a, |
---|
6281 | long b, |
---|
6282 | _ntl_verylong *cc |
---|
6283 | ) |
---|
6284 | { |
---|
6285 | _ntl_verylong c; |
---|
6286 | long bl; |
---|
6287 | long wh; |
---|
6288 | long sa; |
---|
6289 | |
---|
6290 | if (_ntl_ziszero(a) || (b<=0)) { |
---|
6291 | _ntl_zzero(cc); |
---|
6292 | return; |
---|
6293 | } |
---|
6294 | |
---|
6295 | |
---|
6296 | bl = b/NTL_NBITS; |
---|
6297 | wh = b - NTL_NBITS*bl; |
---|
6298 | if (wh != 0) |
---|
6299 | bl++; |
---|
6300 | else |
---|
6301 | wh = NTL_NBITS; |
---|
6302 | |
---|
6303 | sa = a[0]; |
---|
6304 | if (sa < 0) sa = -sa; |
---|
6305 | |
---|
6306 | if (sa < bl) { |
---|
6307 | _ntl_zcopy(a,cc); |
---|
6308 | _ntl_zabs(cc); |
---|
6309 | return; |
---|
6310 | } |
---|
6311 | |
---|
6312 | c = *cc; |
---|
6313 | |
---|
6314 | /* a won't move if c aliases a */ |
---|
6315 | _ntl_zsetlength(&c, bl); |
---|
6316 | *cc = c; |
---|
6317 | |
---|
6318 | for (sa=1; sa<bl; sa++) |
---|
6319 | c[sa] = a[sa]; |
---|
6320 | c[bl] = a[bl]&((1L<<wh)-1); |
---|
6321 | while ((bl>1) && (!c[bl])) |
---|
6322 | bl --; |
---|
6323 | c[0] = bl; |
---|
6324 | } |
---|
6325 | |
---|
6326 | |
---|
6327 | long _ntl_zslowbits(_ntl_verylong a, long p) |
---|
6328 | { |
---|
6329 | static _ntl_verylong x = 0; |
---|
6330 | |
---|
6331 | if (p > NTL_BITS_PER_LONG) |
---|
6332 | p = NTL_BITS_PER_LONG; |
---|
6333 | |
---|
6334 | _ntl_zlowbits(a, p, &x); |
---|
6335 | |
---|
6336 | return _ntl_ztoint(x); |
---|
6337 | } |
---|
6338 | |
---|
6339 | |
---|
6340 | |
---|
6341 | |
---|
6342 | long |
---|
6343 | _ntl_zweights( |
---|
6344 | long aa |
---|
6345 | ) |
---|
6346 | { |
---|
6347 | unsigned long a; |
---|
6348 | long res = 0; |
---|
6349 | |
---|
6350 | if (aa < 0) |
---|
6351 | a = - ((unsigned long) aa); |
---|
6352 | else |
---|
6353 | a = aa; |
---|
6354 | |
---|
6355 | while (a) { |
---|
6356 | if (a & 1) res ++; |
---|
6357 | a >>= 1; |
---|
6358 | } |
---|
6359 | return (res); |
---|
6360 | } |
---|
6361 | |
---|
6362 | long |
---|
6363 | _ntl_zweight( |
---|
6364 | _ntl_verylong a |
---|
6365 | ) |
---|
6366 | { |
---|
6367 | long i; |
---|
6368 | long res = 0; |
---|
6369 | |
---|
6370 | if (!a) return (0); |
---|
6371 | i = a[0]; |
---|
6372 | if (i<0) i = -i; |
---|
6373 | for (;i;i--) |
---|
6374 | res += _ntl_zweights(a[i]); |
---|
6375 | return (res); |
---|
6376 | } |
---|
6377 | |
---|
6378 | |
---|
6379 | |
---|
6380 | void |
---|
6381 | _ntl_zand( |
---|
6382 | _ntl_verylong a, |
---|
6383 | _ntl_verylong b, |
---|
6384 | _ntl_verylong *cc |
---|
6385 | ) |
---|
6386 | |
---|
6387 | { |
---|
6388 | _ntl_verylong c; |
---|
6389 | long sa; |
---|
6390 | long sb; |
---|
6391 | long sm; |
---|
6392 | long a_alias; |
---|
6393 | long b_alias; |
---|
6394 | |
---|
6395 | if (_ntl_ziszero(a) || _ntl_ziszero(b)) { |
---|
6396 | _ntl_zzero(cc); |
---|
6397 | return; |
---|
6398 | } |
---|
6399 | |
---|
6400 | c = *cc; |
---|
6401 | a_alias = (a == c); |
---|
6402 | b_alias = (b == c); |
---|
6403 | |
---|
6404 | sa = a[0]; |
---|
6405 | if (sa < 0) sa = -sa; |
---|
6406 | |
---|
6407 | sb = b[0]; |
---|
6408 | if (sb < 0) sb = -sb; |
---|
6409 | |
---|
6410 | sm = (sa > sb ? sb : sa ); |
---|
6411 | |
---|
6412 | _ntl_zsetlength(&c, sm); |
---|
6413 | if (a_alias) a = c; |
---|
6414 | if (b_alias) b = c; |
---|
6415 | *cc = c; |
---|
6416 | |
---|
6417 | for (sa = 1; sa <= sm; sa ++) |
---|
6418 | c[sa] = a[sa] & b[sa]; |
---|
6419 | |
---|
6420 | while ((sm > 1) && (!(c[sm]))) |
---|
6421 | sm --; |
---|
6422 | c[0] = sm; |
---|
6423 | } |
---|
6424 | |
---|
6425 | void |
---|
6426 | _ntl_zxor( |
---|
6427 | _ntl_verylong a, |
---|
6428 | _ntl_verylong b, |
---|
6429 | _ntl_verylong *cc |
---|
6430 | ) |
---|
6431 | { |
---|
6432 | _ntl_verylong c; |
---|
6433 | long sa; |
---|
6434 | long sb; |
---|
6435 | long sm; |
---|
6436 | long la; |
---|
6437 | long i; |
---|
6438 | long a_alias; |
---|
6439 | long b_alias; |
---|
6440 | |
---|
6441 | if (_ntl_ziszero(a)) { |
---|
6442 | _ntl_zcopy(b,cc); |
---|
6443 | _ntl_zabs(cc); |
---|
6444 | return; |
---|
6445 | } |
---|
6446 | |
---|
6447 | if (_ntl_ziszero(b)) { |
---|
6448 | _ntl_zcopy(a,cc); |
---|
6449 | _ntl_zabs(cc); |
---|
6450 | return; |
---|
6451 | } |
---|
6452 | |
---|
6453 | c = *cc; |
---|
6454 | a_alias = (a == c); |
---|
6455 | b_alias = (b == c); |
---|
6456 | |
---|
6457 | sa = a[0]; |
---|
6458 | if (sa < 0) sa = -sa; |
---|
6459 | |
---|
6460 | sb = b[0]; |
---|
6461 | if (sb < 0) sb = -sb; |
---|
6462 | |
---|
6463 | if (sa > sb) { |
---|
6464 | la = sa; |
---|
6465 | sm = sb; |
---|
6466 | } else { |
---|
6467 | la = sb; |
---|
6468 | sm = sa; |
---|
6469 | } |
---|
6470 | |
---|
6471 | _ntl_zsetlength(&c, la); |
---|
6472 | if (a_alias) a = c; |
---|
6473 | if (b_alias) b = c; |
---|
6474 | *cc = c; |
---|
6475 | |
---|
6476 | for (i = 1; i <= sm; i ++) |
---|
6477 | c[i] = a[i] ^ b[i]; |
---|
6478 | |
---|
6479 | if (sa > sb) |
---|
6480 | for (;i <= la; i++) c[i] = a[i]; |
---|
6481 | else |
---|
6482 | for (;i <= la; i++) c[i] = b[i]; |
---|
6483 | |
---|
6484 | while ((la > 1) && (!(c[la]))) |
---|
6485 | la --; |
---|
6486 | c[0] = la; |
---|
6487 | } |
---|
6488 | |
---|
6489 | void |
---|
6490 | _ntl_zor( |
---|
6491 | _ntl_verylong a, |
---|
6492 | _ntl_verylong b, |
---|
6493 | _ntl_verylong *cc |
---|
6494 | ) |
---|
6495 | { |
---|
6496 | _ntl_verylong c; |
---|
6497 | long sa; |
---|
6498 | long sb; |
---|
6499 | long sm; |
---|
6500 | long la; |
---|
6501 | long i; |
---|
6502 | long a_alias; |
---|
6503 | long b_alias; |
---|
6504 | |
---|
6505 | if (_ntl_ziszero(a)) { |
---|
6506 | _ntl_zcopy(b,cc); |
---|
6507 | _ntl_zabs(cc); |
---|
6508 | return; |
---|
6509 | } |
---|
6510 | |
---|
6511 | if (_ntl_ziszero(b)) { |
---|
6512 | _ntl_zcopy(a,cc); |
---|
6513 | _ntl_zabs(cc); |
---|
6514 | return; |
---|
6515 | } |
---|
6516 | |
---|
6517 | c = *cc; |
---|
6518 | a_alias = (a == c); |
---|
6519 | b_alias = (b == c); |
---|
6520 | |
---|
6521 | sa = a[0]; |
---|
6522 | if (sa < 0) sa = -sa; |
---|
6523 | |
---|
6524 | sb = b[0]; |
---|
6525 | if (sb < 0) sb = -sb; |
---|
6526 | |
---|
6527 | if (sa > sb) { |
---|
6528 | la = sa; |
---|
6529 | sm = sb; |
---|
6530 | } else { |
---|
6531 | la = sb; |
---|
6532 | sm = sa; |
---|
6533 | } |
---|
6534 | |
---|
6535 | _ntl_zsetlength(&c, la); |
---|
6536 | if (a_alias) a = c; |
---|
6537 | if (b_alias) b = c; |
---|
6538 | *cc = c; |
---|
6539 | |
---|
6540 | for (i = 1; i <= sm; i ++) |
---|
6541 | c[i] = a[i] | b[i]; |
---|
6542 | |
---|
6543 | if (sa > sb) |
---|
6544 | for (;i <= la; i++) c[i] = a[i]; |
---|
6545 | else |
---|
6546 | for (;i <= la; i++) c[i] = b[i]; |
---|
6547 | |
---|
6548 | c[0] = la; |
---|
6549 | } |
---|
6550 | |
---|
6551 | long |
---|
6552 | _ntl_zsetbit( |
---|
6553 | _ntl_verylong *a, |
---|
6554 | long b |
---|
6555 | ) |
---|
6556 | { |
---|
6557 | long bl; |
---|
6558 | long wh; |
---|
6559 | long sa; |
---|
6560 | |
---|
6561 | if (b<0) zhalt("_ntl_zsetbit: negative index"); |
---|
6562 | |
---|
6563 | if (_ntl_ziszero(*a)) { |
---|
6564 | _ntl_zintoz(1,a); |
---|
6565 | _ntl_zlshift(*a,b,a); |
---|
6566 | return (0); |
---|
6567 | } |
---|
6568 | |
---|
6569 | bl = (b/NTL_NBITS); |
---|
6570 | wh = 1L << (b - NTL_NBITS*bl); |
---|
6571 | bl ++; |
---|
6572 | sa = (*a)[0]; |
---|
6573 | if (sa<0) sa = -sa; |
---|
6574 | if (sa >= bl) { |
---|
6575 | sa = (*a)[bl] & wh; |
---|
6576 | (*a)[bl] |= wh; |
---|
6577 | if (sa) return (1); |
---|
6578 | return (0); |
---|
6579 | } else { |
---|
6580 | _ntl_zsetlength(a,bl); |
---|
6581 | sa ++; |
---|
6582 | for (;sa<=bl;sa++) (*a)[sa]=0; |
---|
6583 | if ((*a)[0] < 0) |
---|
6584 | (*a)[0] = -bl; |
---|
6585 | else (*a)[0] = bl; |
---|
6586 | (*a)[bl] |= wh; |
---|
6587 | return (0); |
---|
6588 | } |
---|
6589 | } |
---|
6590 | |
---|
6591 | long |
---|
6592 | _ntl_zswitchbit( |
---|
6593 | _ntl_verylong *a, |
---|
6594 | long p |
---|
6595 | ) |
---|
6596 | { |
---|
6597 | long bl; |
---|
6598 | long wh; |
---|
6599 | long sa; |
---|
6600 | |
---|
6601 | if (p < 0) zhalt("_ntl_zswitchbit: negative index"); |
---|
6602 | |
---|
6603 | if (_ntl_ziszero(*a)) { |
---|
6604 | _ntl_zintoz(1,a); |
---|
6605 | _ntl_zlshift(*a,p,a); |
---|
6606 | return (0); |
---|
6607 | } |
---|
6608 | |
---|
6609 | bl = (p/NTL_NBITS); |
---|
6610 | wh = 1L << (p - NTL_NBITS*bl); |
---|
6611 | bl ++; |
---|
6612 | sa = (*a)[0]; |
---|
6613 | if (sa < 0) sa = -sa; |
---|
6614 | if ((sa < bl) || (!((*a)[bl] & wh))) { |
---|
6615 | _ntl_zsetbit(a,p); |
---|
6616 | return (0); |
---|
6617 | } |
---|
6618 | (*a)[bl] ^= wh; |
---|
6619 | while ((sa>1) && (!(*a)[sa])) |
---|
6620 | sa --; |
---|
6621 | if ((*a)[0] > 0) (*a)[0] = sa; |
---|
6622 | else (*a)[0] = -sa; |
---|
6623 | return (1); |
---|
6624 | } |
---|
6625 | |
---|
6626 | |
---|
6627 | long _ntl_zsize(_ntl_verylong rep) |
---|
6628 | { |
---|
6629 | if (!rep || (rep[0] == 1 && rep[1] == 0)) |
---|
6630 | return 0; |
---|
6631 | else if (rep[0] < 0) |
---|
6632 | return -rep[0]; |
---|
6633 | else |
---|
6634 | return rep[0]; |
---|
6635 | } |
---|
6636 | |
---|
6637 | |
---|
6638 | long _ntl_zdigit(_ntl_verylong rep, long i) |
---|
6639 | { |
---|
6640 | long sa; |
---|
6641 | if (i < 0 || !rep) return 0; |
---|
6642 | |
---|
6643 | sa = rep[0]; |
---|
6644 | if (sa < 0) sa = -sa; |
---|
6645 | if (i >= sa) return 0; |
---|
6646 | return rep[i+1]; |
---|
6647 | } |
---|
6648 | |
---|
6649 | long _ntl_zisone(_ntl_verylong rep) |
---|
6650 | { |
---|
6651 | return rep != 0 && rep[0] == 1 && rep[1] == 1; |
---|
6652 | } |
---|
6653 | |
---|
6654 | long _ntl_zsptest(_ntl_verylong rep) |
---|
6655 | { |
---|
6656 | return !rep || rep[0] == 1 || rep[0] == -1; |
---|
6657 | } |
---|
6658 | |
---|
6659 | long _ntl_zwsptest(_ntl_verylong rep) |
---|
6660 | { |
---|
6661 | return !rep || rep[0] == 1 || rep[0] == -1; |
---|
6662 | } |
---|
6663 | |
---|
6664 | long _ntl_zcrtinrange(_ntl_verylong g, _ntl_verylong a) |
---|
6665 | { |
---|
6666 | long sa, sg, carry, i, diff; |
---|
6667 | |
---|
6668 | if (!a || a[0] < 0 || (a[0] == 1 && a[1] == 0)) return 0; |
---|
6669 | |
---|
6670 | sa = a[0]; |
---|
6671 | |
---|
6672 | if (!g) return 1; |
---|
6673 | |
---|
6674 | sg = g[0]; |
---|
6675 | |
---|
6676 | if (sg == 1 && g[1] == 0) return 1; |
---|
6677 | |
---|
6678 | if (sg < 0) sg = -sg; |
---|
6679 | |
---|
6680 | if (sa-sg > 1) return 1; |
---|
6681 | |
---|
6682 | if (sa-sg < 0) return 0; |
---|
6683 | |
---|
6684 | carry=0; |
---|
6685 | |
---|
6686 | if (sa-sg == 1) { |
---|
6687 | if (a[sa] > 1) return 1; |
---|
6688 | carry = 1; |
---|
6689 | } |
---|
6690 | |
---|
6691 | i = sg; |
---|
6692 | diff = 0; |
---|
6693 | while (i > 0 && diff == 0) { |
---|
6694 | diff = (carry << (NTL_NBITS-1)) + (a[i] >> 1) - g[i]; |
---|
6695 | carry = (a[i] & 1); |
---|
6696 | i--; |
---|
6697 | } |
---|
6698 | |
---|
6699 | if (diff == 0) { |
---|
6700 | if (carry) return 1; |
---|
6701 | return (g[0] > 0); |
---|
6702 | } |
---|
6703 | else |
---|
6704 | return (diff > 0); |
---|
6705 | } |
---|
6706 | |
---|
6707 | |
---|
6708 | |
---|
6709 | void _ntl_zfrombytes(_ntl_verylong *x, const unsigned char *p, long n) |
---|
6710 | { |
---|
6711 | long sz; |
---|
6712 | long i; |
---|
6713 | _ntl_verylong a; |
---|
6714 | long bitpos, wordpos, bitoffset, diff; |
---|
6715 | |
---|
6716 | if (n <= 0) { |
---|
6717 | _ntl_zzero(x); |
---|
6718 | return; |
---|
6719 | } |
---|
6720 | |
---|
6721 | if (n > (NTL_MAX_LONG-(NTL_NBITS-1))/8) |
---|
6722 | zhalt("ZZFromBytes: excessive length"); |
---|
6723 | |
---|
6724 | sz = (n*8 + NTL_NBITS-1)/NTL_NBITS; |
---|
6725 | |
---|
6726 | _ntl_zsetlength(x, sz); |
---|
6727 | |
---|
6728 | a = *x; |
---|
6729 | |
---|
6730 | for (i = 1; i <= sz; i++) |
---|
6731 | a[i] = 0; |
---|
6732 | |
---|
6733 | for (i = 0; i < n; i++) { |
---|
6734 | bitpos = i*8; |
---|
6735 | wordpos = bitpos/NTL_NBITS; |
---|
6736 | bitoffset = bitpos - wordpos*NTL_NBITS; |
---|
6737 | diff = NTL_NBITS-bitoffset; |
---|
6738 | |
---|
6739 | if (diff < 8) { |
---|
6740 | a[wordpos+1] |= |
---|
6741 | ((( ((unsigned long)(p[i])) & 255UL ) << bitoffset) & NTL_RADIXM); |
---|
6742 | a[wordpos+2] = ( ((long)(p[i])) & 255 ) >> diff; |
---|
6743 | } |
---|
6744 | else { |
---|
6745 | a[wordpos+1] |= (( ((long)(p[i])) & 255 ) << bitoffset); |
---|
6746 | } |
---|
6747 | } |
---|
6748 | |
---|
6749 | while (sz > 1 && a[sz] == 0) sz--; |
---|
6750 | a[0] = sz; |
---|
6751 | } |
---|
6752 | |
---|
6753 | |
---|
6754 | void _ntl_zbytesfromz(unsigned char *p, _ntl_verylong a, long nn) |
---|
6755 | { |
---|
6756 | long k = _ntl_z2log(a); |
---|
6757 | long n = (k+7)/8; |
---|
6758 | long sz = _ntl_zsize(a); |
---|
6759 | long min_n = ((n < nn) ? n : nn); |
---|
6760 | |
---|
6761 | long i; |
---|
6762 | |
---|
6763 | for (i = 0; i < min_n; i++) { |
---|
6764 | long bitpos = i*8; |
---|
6765 | long wordpos = bitpos/NTL_NBITS; |
---|
6766 | long bitoffset = bitpos - wordpos*NTL_NBITS; |
---|
6767 | long diff; |
---|
6768 | |
---|
6769 | p[i] = (a[wordpos+1] >> bitoffset) & 255; |
---|
6770 | |
---|
6771 | diff = NTL_NBITS - bitoffset; |
---|
6772 | |
---|
6773 | if (diff < 8 && wordpos < sz-1) { |
---|
6774 | long msk = (1L << (8-diff))-1; |
---|
6775 | p[i] |= ((a[wordpos+2] & msk) << diff); |
---|
6776 | } |
---|
6777 | } |
---|
6778 | |
---|
6779 | for (i = min_n; i < nn; i++) |
---|
6780 | p[i] = 0; |
---|
6781 | } |
---|
6782 | |
---|
6783 | |
---|
6784 | |
---|
6785 | long _ntl_zblock_construct_alloc(_ntl_verylong *x, long d, long n) |
---|
6786 | { |
---|
6787 | long nwords, nbytes, AllocAmt, m, *p, *q, j; |
---|
6788 | |
---|
6789 | |
---|
6790 | /* check n value */ |
---|
6791 | |
---|
6792 | if (n <= 0) |
---|
6793 | zhalt("block construct: n must be positive"); |
---|
6794 | |
---|
6795 | /* check d value */ |
---|
6796 | |
---|
6797 | if (d <= 0) |
---|
6798 | zhalt("block construct: d must be positive"); |
---|
6799 | |
---|
6800 | if (NTL_OVERFLOW(d, NTL_NBITS, NTL_NBITS) || |
---|
6801 | NTL_OVERFLOW(d, sizeof(long), 3*sizeof(long))) |
---|
6802 | zhalt("block construct: d too large"); |
---|
6803 | |
---|
6804 | #ifdef L_TO_G_CHECK_LEN |
---|
6805 | /* this makes sure that numbers don't get too big for GMP */ |
---|
6806 | if (d >= (1L << (NTL_BITS_PER_INT-4))) |
---|
6807 | zhalt("size too big for GMP"); |
---|
6808 | #endif |
---|
6809 | |
---|
6810 | nwords = d + 3; |
---|
6811 | nbytes = nwords*sizeof(long); |
---|
6812 | |
---|
6813 | AllocAmt = (NTL_MAX_ALLOC_BLOCK - sizeof(long)) / nbytes; |
---|
6814 | if (AllocAmt == 0) AllocAmt = 1; |
---|
6815 | |
---|
6816 | if (AllocAmt < n) |
---|
6817 | m = AllocAmt; |
---|
6818 | else |
---|
6819 | m = n; |
---|
6820 | |
---|
6821 | p = (long *) NTL_MALLOC(m, nbytes, sizeof(long)); |
---|
6822 | if (!p) zhalt("out of memory in block construct"); |
---|
6823 | |
---|
6824 | *p = m; |
---|
6825 | |
---|
6826 | q = p+2; |
---|
6827 | *x = q; |
---|
6828 | |
---|
6829 | for (j = 0; j < m; j++) { |
---|
6830 | q[-1] = ((d+1) << 1) | 1; |
---|
6831 | q[0] = 1; |
---|
6832 | q[1] = 0; |
---|
6833 | q += nwords; |
---|
6834 | } |
---|
6835 | |
---|
6836 | return m; |
---|
6837 | } |
---|
6838 | |
---|
6839 | void _ntl_zblock_construct_set(_ntl_verylong x, _ntl_verylong *y, long i) |
---|
6840 | { |
---|
6841 | long d, size; |
---|
6842 | |
---|
6843 | d = (x[-1] >> 1) - 1; |
---|
6844 | size = d + 3; |
---|
6845 | |
---|
6846 | *y = x + i*size; |
---|
6847 | } |
---|
6848 | |
---|
6849 | |
---|
6850 | long _ntl_zblock_destroy(_ntl_verylong x) |
---|
6851 | { |
---|
6852 | long m, *p; |
---|
6853 | |
---|
6854 | p = x - 2; |
---|
6855 | m = *p; |
---|
6856 | free(p); |
---|
6857 | return m; |
---|
6858 | } |
---|
6859 | |
---|
6860 | |
---|
6861 | long _ntl_zblock_storage(long d) |
---|
6862 | { |
---|
6863 | long size = d+3; |
---|
6864 | return size * (sizeof (long)) + sizeof(_ntl_verylong); |
---|
6865 | } |
---|
6866 | |
---|
6867 | |
---|
6868 | |
---|
6869 | |
---|
6870 | /* The following routines provide special support for ZZ_pX |
---|
6871 | * arithmetic. */ |
---|
6872 | |
---|
6873 | |
---|
6874 | |
---|
6875 | /* this is a generic single-precision mul mod that will work |
---|
6876 | * on any platform */ |
---|
6877 | |
---|
6878 | |
---|
6879 | #define SP_MUL_MOD(r, a, b, n) \ |
---|
6880 | { \ |
---|
6881 | long l__a = (a); \ |
---|
6882 | long l__b = (b); \ |
---|
6883 | long l__n = (n); \ |
---|
6884 | long l__q; \ |
---|
6885 | unsigned long l__res; \ |
---|
6886 | \ |
---|
6887 | l__q = (long) ((((double) l__a) * ((double) l__b)) / ((double) l__n)); \ |
---|
6888 | l__res = ((unsigned long) l__a)*((unsigned long) l__b) - \ |
---|
6889 | ((unsigned long) l__q)*((unsigned long) l__n); \ |
---|
6890 | if (l__res >> (NTL_BITS_PER_LONG-1)) \ |
---|
6891 | l__res += l__n; \ |
---|
6892 | else if (((long) l__res) >= l__n) \ |
---|
6893 | l__res -= l__n; \ |
---|
6894 | \ |
---|
6895 | r = (long) l__res; \ |
---|
6896 | } |
---|
6897 | |
---|
6898 | |
---|
6899 | |
---|
6900 | |
---|
6901 | static |
---|
6902 | void sp_ext_eucl(long *dd, long *ss, long *tt, long a, long b) |
---|
6903 | { |
---|
6904 | long u, v, u0, v0, u1, v1, u2, v2, q, r; |
---|
6905 | |
---|
6906 | long aneg = 0, bneg = 0; |
---|
6907 | |
---|
6908 | if (a < 0) { |
---|
6909 | if (a < -NTL_MAX_LONG) zhalt("integer overflow"); |
---|
6910 | a = -a; |
---|
6911 | aneg = 1; |
---|
6912 | } |
---|
6913 | |
---|
6914 | if (b < 0) { |
---|
6915 | if (b < -NTL_MAX_LONG) zhalt("integer overflow"); |
---|
6916 | b = -b; |
---|
6917 | bneg = 1; |
---|
6918 | } |
---|
6919 | |
---|
6920 | u1=1; v1=0; |
---|
6921 | u2=0; v2=1; |
---|
6922 | u = a; v = b; |
---|
6923 | |
---|
6924 | while (v != 0) { |
---|
6925 | q = u / v; |
---|
6926 | r = u % v; |
---|
6927 | u = v; |
---|
6928 | v = r; |
---|
6929 | u0 = u2; |
---|
6930 | v0 = v2; |
---|
6931 | u2 = u1 - q*u2; |
---|
6932 | v2 = v1- q*v2; |
---|
6933 | u1 = u0; |
---|
6934 | v1 = v0; |
---|
6935 | } |
---|
6936 | |
---|
6937 | if (aneg) |
---|
6938 | u1 = -u1; |
---|
6939 | |
---|
6940 | if (bneg) |
---|
6941 | v1 = -v1; |
---|
6942 | |
---|
6943 | *dd = u; |
---|
6944 | *ss = u1; |
---|
6945 | *tt = v1; |
---|
6946 | } |
---|
6947 | |
---|
6948 | |
---|
6949 | static |
---|
6950 | long sp_inv_mod(long a, long n) |
---|
6951 | { |
---|
6952 | long d, s, t; |
---|
6953 | |
---|
6954 | sp_ext_eucl(&d, &s, &t, a, n); |
---|
6955 | if (d != 1) zhalt("inverse undefined"); |
---|
6956 | if (s < 0) |
---|
6957 | return s + n; |
---|
6958 | else |
---|
6959 | return s; |
---|
6960 | } |
---|
6961 | |
---|
6962 | |
---|
6963 | /* Data structures and algorithms for fast Chinese Remaindering */ |
---|
6964 | |
---|
6965 | |
---|
6966 | struct crt_body_lip { |
---|
6967 | _ntl_verylong *v; |
---|
6968 | long sbuf; |
---|
6969 | long n; |
---|
6970 | }; |
---|
6971 | |
---|
6972 | #ifdef NTL_GMP_HACK |
---|
6973 | |
---|
6974 | struct crt_body_gmp { |
---|
6975 | MP_INT *v; |
---|
6976 | long sbuf; |
---|
6977 | long n; |
---|
6978 | mpz_t buf; |
---|
6979 | }; |
---|
6980 | |
---|
6981 | struct crt_body_gmp1 { |
---|
6982 | long n; |
---|
6983 | long levels; |
---|
6984 | long *primes; |
---|
6985 | long *inv_vec; |
---|
6986 | long *val_vec; |
---|
6987 | long *index_vec; |
---|
6988 | MP_INT *prod_vec; |
---|
6989 | MP_INT *rem_vec; |
---|
6990 | MP_INT *coeff_vec; |
---|
6991 | MP_INT temps[2]; |
---|
6992 | mpz_t modulus; |
---|
6993 | }; |
---|
6994 | |
---|
6995 | #endif |
---|
6996 | |
---|
6997 | |
---|
6998 | struct crt_body { |
---|
6999 | long strategy; |
---|
7000 | |
---|
7001 | union { |
---|
7002 | struct crt_body_lip L; |
---|
7003 | |
---|
7004 | #ifdef NTL_GMP_HACK |
---|
7005 | struct crt_body_gmp G; |
---|
7006 | struct crt_body_gmp1 G1; |
---|
7007 | #endif |
---|
7008 | } U; |
---|
7009 | }; |
---|
7010 | |
---|
7011 | |
---|
7012 | long _ntl_crt_struct_special(void *crt_struct) |
---|
7013 | { |
---|
7014 | struct crt_body *c = (struct crt_body *) crt_struct; |
---|
7015 | return (c->strategy == 2); |
---|
7016 | } |
---|
7017 | |
---|
7018 | |
---|
7019 | void _ntl_crt_struct_init(void **crt_struct, long n, _ntl_verylong p, |
---|
7020 | const long *primes) |
---|
7021 | { |
---|
7022 | struct crt_body *c; |
---|
7023 | |
---|
7024 | c = (struct crt_body *) NTL_MALLOC(1, sizeof(struct crt_body), 0); |
---|
7025 | if (!c) zhalt("out of memory"); |
---|
7026 | |
---|
7027 | |
---|
7028 | #ifdef NTL_GMP_HACK |
---|
7029 | if (_ntl_gmp_hack && n >= 600) { |
---|
7030 | struct crt_body_gmp1 *C = &c->U.G1; |
---|
7031 | long *q; |
---|
7032 | long i, j; |
---|
7033 | long levels, vec_len; |
---|
7034 | long *val_vec, *inv_vec; |
---|
7035 | long *index_vec; |
---|
7036 | MP_INT *prod_vec, *rem_vec, *coeff_vec; |
---|
7037 | MP_INT *temps; |
---|
7038 | |
---|
7039 | mpz_init(C->modulus); |
---|
7040 | lip_to_mpz(p, C->modulus); |
---|
7041 | |
---|
7042 | temps = &C->temps[0]; |
---|
7043 | |
---|
7044 | mpz_init(&temps[0]); |
---|
7045 | mpz_init(&temps[1]); |
---|
7046 | |
---|
7047 | q = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
7048 | if (!q) zhalt("out of memory"); |
---|
7049 | |
---|
7050 | val_vec = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
7051 | if (!val_vec) zhalt("out of memory"); |
---|
7052 | |
---|
7053 | inv_vec = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
7054 | if (!inv_vec) zhalt("out of memory"); |
---|
7055 | |
---|
7056 | for (i = 0; i < n; i++) |
---|
7057 | q[i] = primes[i]; |
---|
7058 | |
---|
7059 | levels = 0; |
---|
7060 | while ((n >> levels) >= 16) levels++; |
---|
7061 | |
---|
7062 | vec_len = (1L << levels) - 1; |
---|
7063 | |
---|
7064 | index_vec = (long *) NTL_MALLOC((vec_len+1), sizeof(long), 0); |
---|
7065 | if (!index_vec) zhalt("out of memory"); |
---|
7066 | |
---|
7067 | prod_vec = (MP_INT *) NTL_MALLOC(vec_len, sizeof(MP_INT), 0); |
---|
7068 | if (!prod_vec) zhalt("out of memory"); |
---|
7069 | |
---|
7070 | rem_vec = (MP_INT *) NTL_MALLOC(vec_len, sizeof(MP_INT), 0); |
---|
7071 | if (!rem_vec) zhalt("out of memory"); |
---|
7072 | |
---|
7073 | coeff_vec = (MP_INT *) NTL_MALLOC(n, sizeof(MP_INT), 0); |
---|
7074 | if (!coeff_vec) zhalt("out of memory"); |
---|
7075 | |
---|
7076 | for (i = 0; i < vec_len; i++) |
---|
7077 | mpz_init(&prod_vec[i]); |
---|
7078 | |
---|
7079 | for (i = 0; i < vec_len; i++) |
---|
7080 | mpz_init(&rem_vec[i]); |
---|
7081 | |
---|
7082 | for (i = 0; i < n; i++) |
---|
7083 | mpz_init(&coeff_vec[i]); |
---|
7084 | |
---|
7085 | index_vec[0] = 0; |
---|
7086 | index_vec[1] = n; |
---|
7087 | |
---|
7088 | for (i = 0; i <= levels-2; i++) { |
---|
7089 | long start = (1L << i) - 1; |
---|
7090 | long finish = (1L << (i+1)) - 2; |
---|
7091 | for (j = finish; j >= start; j--) { |
---|
7092 | index_vec[2*j+2] = index_vec[j] + (index_vec[j+1] - index_vec[j])/2; |
---|
7093 | index_vec[2*j+1] = index_vec[j]; |
---|
7094 | } |
---|
7095 | index_vec[2*finish+3] = n; |
---|
7096 | } |
---|
7097 | |
---|
7098 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
7099 | /* multiply primes index_vec[i]..index_vec[i+1]-1 into |
---|
7100 | * prod_vec[i] |
---|
7101 | */ |
---|
7102 | |
---|
7103 | mpz_set_ui(&prod_vec[i], 1); |
---|
7104 | for (j = index_vec[i]; j < index_vec[i+1]; j++) |
---|
7105 | mpz_mul_ui(&prod_vec[i], &prod_vec[i], q[j]); |
---|
7106 | } |
---|
7107 | |
---|
7108 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
7109 | for (j = index_vec[i]; j < index_vec[i+1]; j++) |
---|
7110 | mpz_fdiv_q_ui(&coeff_vec[j], &prod_vec[i], q[j]); |
---|
7111 | } |
---|
7112 | |
---|
7113 | for (i = (1L << (levels-1)) - 2; i >= 0; i--) |
---|
7114 | mpz_mul(&prod_vec[i], &prod_vec[2*i+1], &prod_vec[2*i+2]); |
---|
7115 | |
---|
7116 | |
---|
7117 | /* the following is asymptotically the bottleneck...but it |
---|
7118 | * it probably doesn't matter. */ |
---|
7119 | |
---|
7120 | for (i = 0; i < n; i++) { |
---|
7121 | long tt; |
---|
7122 | mpz_fdiv_q_ui(&temps[0], &prod_vec[0], q[i]); |
---|
7123 | tt = mpn_mod_1(temps[0]._mp_d, temps[0]._mp_size, q[i]); |
---|
7124 | inv_vec[i] = sp_inv_mod(tt, q[i]); |
---|
7125 | } |
---|
7126 | |
---|
7127 | c->strategy = 2; |
---|
7128 | C->n = n; |
---|
7129 | C->primes = q; |
---|
7130 | C->val_vec = val_vec; |
---|
7131 | C->inv_vec = inv_vec; |
---|
7132 | C->levels = levels; |
---|
7133 | C->index_vec = index_vec; |
---|
7134 | C->prod_vec = prod_vec; |
---|
7135 | C->rem_vec = rem_vec; |
---|
7136 | C->coeff_vec = coeff_vec; |
---|
7137 | |
---|
7138 | *crt_struct = (void *) c; |
---|
7139 | return; |
---|
7140 | } |
---|
7141 | |
---|
7142 | if (_ntl_gmp_hack) { |
---|
7143 | struct crt_body_gmp *C = &c->U.G; |
---|
7144 | long i; |
---|
7145 | c->strategy = 1; |
---|
7146 | |
---|
7147 | C->n = n; |
---|
7148 | C->v = (MP_INT *) NTL_MALLOC(n, sizeof(MP_INT), 0); |
---|
7149 | if (!C->v) zhalt("out of memory"); |
---|
7150 | |
---|
7151 | for (i = 0; i < n; i++) |
---|
7152 | mpz_init(&C->v[i]); |
---|
7153 | |
---|
7154 | C->sbuf = L_TO_G(p[0])+2; |
---|
7155 | |
---|
7156 | mpz_init(C->buf); |
---|
7157 | _mpz_realloc(C->buf, C->sbuf); |
---|
7158 | |
---|
7159 | *crt_struct = (void *) c; |
---|
7160 | return; |
---|
7161 | } |
---|
7162 | |
---|
7163 | #endif |
---|
7164 | |
---|
7165 | { |
---|
7166 | struct crt_body_lip *C = &c->U.L; |
---|
7167 | long i; |
---|
7168 | c->strategy = 0; |
---|
7169 | |
---|
7170 | C->n = n; |
---|
7171 | |
---|
7172 | C->v = (_ntl_verylong *) NTL_MALLOC(n, sizeof(_ntl_verylong), 0); |
---|
7173 | if (!C->v) zhalt("out of memory"); |
---|
7174 | |
---|
7175 | for (i = 0; i < n; i++) |
---|
7176 | C->v[i] = 0; |
---|
7177 | |
---|
7178 | C->sbuf = p[0]+3; |
---|
7179 | |
---|
7180 | *crt_struct = (void *) c; |
---|
7181 | } |
---|
7182 | } |
---|
7183 | |
---|
7184 | void _ntl_crt_struct_insert(void *crt_struct, long i, _ntl_verylong m) |
---|
7185 | { |
---|
7186 | struct crt_body *c = (struct crt_body *) crt_struct; |
---|
7187 | |
---|
7188 | switch (c->strategy) { |
---|
7189 | |
---|
7190 | case 0: { |
---|
7191 | _ntl_zcopy(m, &c->U.L.v[i]); |
---|
7192 | break; |
---|
7193 | } |
---|
7194 | |
---|
7195 | #ifdef NTL_GMP_HACK |
---|
7196 | case 1: { |
---|
7197 | lip_to_mpz(m, &c->U.G.v[i]); |
---|
7198 | break; |
---|
7199 | } |
---|
7200 | #endif |
---|
7201 | |
---|
7202 | default: |
---|
7203 | zhalt("_ntl_crt_struct_insert: inconsistent strategy"); |
---|
7204 | |
---|
7205 | } /* end switch */ |
---|
7206 | } |
---|
7207 | |
---|
7208 | void _ntl_crt_struct_free(void *crt_struct) |
---|
7209 | { |
---|
7210 | struct crt_body *c = (struct crt_body *) crt_struct; |
---|
7211 | |
---|
7212 | switch (c->strategy) { |
---|
7213 | |
---|
7214 | case 0: { |
---|
7215 | struct crt_body_lip *C = &c->U.L; |
---|
7216 | long i, n; |
---|
7217 | |
---|
7218 | n = C->n; |
---|
7219 | |
---|
7220 | for (i = 0; i < n; i++) |
---|
7221 | _ntl_zfree(&C->v[i]); |
---|
7222 | |
---|
7223 | free(C->v); |
---|
7224 | |
---|
7225 | free(c); |
---|
7226 | |
---|
7227 | break; |
---|
7228 | } |
---|
7229 | |
---|
7230 | #ifdef NTL_GMP_HACK |
---|
7231 | |
---|
7232 | case 1: { |
---|
7233 | struct crt_body_gmp *C = &c->U.G; |
---|
7234 | long i, n; |
---|
7235 | |
---|
7236 | n = C->n; |
---|
7237 | |
---|
7238 | for (i = 0; i < n; i++) |
---|
7239 | mpz_clear(&C->v[i]); |
---|
7240 | |
---|
7241 | mpz_clear(C->buf); |
---|
7242 | |
---|
7243 | free(C->v); |
---|
7244 | |
---|
7245 | free(c); |
---|
7246 | break; |
---|
7247 | } |
---|
7248 | |
---|
7249 | case 2: { |
---|
7250 | struct crt_body_gmp1 *C = &c->U.G1; |
---|
7251 | long n = C->n; |
---|
7252 | long levels = C->levels; |
---|
7253 | long *primes = C->primes; |
---|
7254 | long *inv_vec = C->inv_vec; |
---|
7255 | long *val_vec = C->val_vec; |
---|
7256 | long *index_vec = C->index_vec; |
---|
7257 | MP_INT *prod_vec = C->prod_vec; |
---|
7258 | MP_INT *rem_vec = C->rem_vec; |
---|
7259 | MP_INT *coeff_vec = C->coeff_vec; |
---|
7260 | MP_INT *temps = C->temps; |
---|
7261 | MP_INT *modulus = C->modulus; |
---|
7262 | long vec_len = (1L << levels) - 1; |
---|
7263 | |
---|
7264 | long i; |
---|
7265 | |
---|
7266 | for (i = 0; i < vec_len; i++) |
---|
7267 | mpz_clear(&prod_vec[i]); |
---|
7268 | |
---|
7269 | for (i = 0; i < vec_len; i++) |
---|
7270 | mpz_clear(&rem_vec[i]); |
---|
7271 | |
---|
7272 | for (i = 0; i < n; i++) |
---|
7273 | mpz_clear(&coeff_vec[i]); |
---|
7274 | |
---|
7275 | mpz_clear(&temps[0]); |
---|
7276 | mpz_clear(&temps[1]); |
---|
7277 | |
---|
7278 | mpz_clear(modulus); |
---|
7279 | |
---|
7280 | free(primes); |
---|
7281 | free(inv_vec); |
---|
7282 | free(val_vec); |
---|
7283 | free(index_vec); |
---|
7284 | free(prod_vec); |
---|
7285 | free(rem_vec); |
---|
7286 | free(coeff_vec); |
---|
7287 | |
---|
7288 | free(c); |
---|
7289 | break; |
---|
7290 | } |
---|
7291 | |
---|
7292 | #endif |
---|
7293 | |
---|
7294 | default: |
---|
7295 | |
---|
7296 | zhalt("_ntl_crt_struct_free: inconsistent strategy"); |
---|
7297 | |
---|
7298 | } /* end case */ |
---|
7299 | } |
---|
7300 | |
---|
7301 | |
---|
7302 | |
---|
7303 | #ifdef NTL_GMP_HACK |
---|
7304 | |
---|
7305 | |
---|
7306 | static |
---|
7307 | void mpz_add_mul_many(MP_INT *res, MP_INT *a, long *b, |
---|
7308 | long n, long sz) |
---|
7309 | |
---|
7310 | { |
---|
7311 | mp_limb_t *xx, *yy; |
---|
7312 | long i, sx; |
---|
7313 | long sy; |
---|
7314 | mp_limb_t carry; |
---|
7315 | |
---|
7316 | sx = sz + 2; |
---|
7317 | if (sx > res->_mp_alloc) |
---|
7318 | _mpz_realloc(res, sx); |
---|
7319 | |
---|
7320 | xx = res->_mp_d; |
---|
7321 | |
---|
7322 | for (i = 0; i < sx; i++) |
---|
7323 | xx[i] = 0; |
---|
7324 | |
---|
7325 | for (i = 0; i < n; i++) { |
---|
7326 | yy = a[i]._mp_d; |
---|
7327 | sy = a[i]._mp_size; |
---|
7328 | |
---|
7329 | if (!sy || !b[i]) continue; |
---|
7330 | |
---|
7331 | carry = mpn_addmul_1(xx, yy, sy, b[i]); |
---|
7332 | yy = xx + sy; |
---|
7333 | *yy += carry; |
---|
7334 | |
---|
7335 | if (*yy < carry) { /* unsigned comparison! */ |
---|
7336 | do { |
---|
7337 | yy++; |
---|
7338 | *yy += 1; |
---|
7339 | } while (*yy == 0); |
---|
7340 | } |
---|
7341 | } |
---|
7342 | |
---|
7343 | while (sx > 0 && xx[sx-1] == 0) sx--; |
---|
7344 | res->_mp_size = sx; |
---|
7345 | } |
---|
7346 | |
---|
7347 | #endif |
---|
7348 | |
---|
7349 | void _ntl_crt_struct_eval(void *crt_struct, _ntl_verylong *x, const long *b) |
---|
7350 | { |
---|
7351 | struct crt_body *c = (struct crt_body *) crt_struct; |
---|
7352 | |
---|
7353 | switch (c->strategy) { |
---|
7354 | |
---|
7355 | case 0: { |
---|
7356 | struct crt_body_lip *C = &c->U.L; |
---|
7357 | |
---|
7358 | _ntl_verylong xx, yy, *a; |
---|
7359 | long i, sx, n; |
---|
7360 | |
---|
7361 | n = C->n; |
---|
7362 | sx = C->sbuf; |
---|
7363 | |
---|
7364 | _ntl_zsetlength(x, sx); |
---|
7365 | xx = *x; |
---|
7366 | |
---|
7367 | a = C->v; |
---|
7368 | |
---|
7369 | |
---|
7370 | for (i = 1; i <= sx; i++) |
---|
7371 | xx[i] = 0; |
---|
7372 | |
---|
7373 | xx++; |
---|
7374 | |
---|
7375 | for (i = 0; i < n; i++) { |
---|
7376 | yy = a[i]; |
---|
7377 | |
---|
7378 | if (!yy || !b[i]) continue; |
---|
7379 | |
---|
7380 | zaddmul(b[i], xx, yy); |
---|
7381 | yy = xx + yy[0]; |
---|
7382 | |
---|
7383 | if ((*yy) >= NTL_RADIX) { |
---|
7384 | (*yy) -= NTL_RADIX; |
---|
7385 | yy++; |
---|
7386 | while ((*yy) == NTL_RADIX-1) { |
---|
7387 | *yy = 0; |
---|
7388 | yy++; |
---|
7389 | } |
---|
7390 | (*yy)++; |
---|
7391 | } |
---|
7392 | } |
---|
7393 | |
---|
7394 | xx--; |
---|
7395 | while (sx > 1 && xx[sx] == 0) sx--; |
---|
7396 | xx[0] = sx; |
---|
7397 | |
---|
7398 | break; |
---|
7399 | } |
---|
7400 | |
---|
7401 | #ifdef NTL_GMP_HACK |
---|
7402 | |
---|
7403 | case 1: { |
---|
7404 | struct crt_body_gmp *C = &c->U.G; |
---|
7405 | |
---|
7406 | mp_limb_t *xx, *yy; |
---|
7407 | MP_INT *a; |
---|
7408 | long i, sx, n; |
---|
7409 | long sy; |
---|
7410 | mp_limb_t carry; |
---|
7411 | |
---|
7412 | n = C->n; |
---|
7413 | sx = C->sbuf; |
---|
7414 | |
---|
7415 | xx = C->buf->_mp_d; |
---|
7416 | |
---|
7417 | for (i = 0; i < sx; i++) |
---|
7418 | xx[i] = 0; |
---|
7419 | |
---|
7420 | a = C->v; |
---|
7421 | |
---|
7422 | for (i = 0; i < n; i++) { |
---|
7423 | yy = a[i]._mp_d; |
---|
7424 | sy = a[i]._mp_size; |
---|
7425 | |
---|
7426 | if (!sy || !b[i]) continue; |
---|
7427 | |
---|
7428 | carry = mpn_addmul_1(xx, yy, sy, b[i]); |
---|
7429 | yy = xx + sy; |
---|
7430 | *yy += carry; |
---|
7431 | |
---|
7432 | if (*yy < carry) { /* unsigned comparison! */ |
---|
7433 | do { |
---|
7434 | yy++; |
---|
7435 | *yy += 1; |
---|
7436 | } while (*yy == 0); |
---|
7437 | } |
---|
7438 | } |
---|
7439 | |
---|
7440 | while (sx > 0 && xx[sx-1] == 0) sx--; |
---|
7441 | C->buf->_mp_size = sx; |
---|
7442 | mpz_to_lip(x, C->buf); |
---|
7443 | break; |
---|
7444 | } |
---|
7445 | |
---|
7446 | case 2: { |
---|
7447 | struct crt_body_gmp1 *C = &c->U.G1; |
---|
7448 | |
---|
7449 | long n = C->n; |
---|
7450 | long levels = C->levels; |
---|
7451 | long *primes = C->primes; |
---|
7452 | long *inv_vec = C->inv_vec; |
---|
7453 | long *val_vec = C->val_vec; |
---|
7454 | long *index_vec = C->index_vec; |
---|
7455 | MP_INT *prod_vec = C->prod_vec; |
---|
7456 | MP_INT *rem_vec = C->rem_vec; |
---|
7457 | MP_INT *coeff_vec = C->coeff_vec; |
---|
7458 | MP_INT *temps = C->temps; |
---|
7459 | long vec_len = (1L << levels) - 1; |
---|
7460 | |
---|
7461 | long i, j; |
---|
7462 | |
---|
7463 | for (i = 0; i < n; i++) { |
---|
7464 | SP_MUL_MOD(val_vec[i], b[i], inv_vec[i], primes[i]); |
---|
7465 | } |
---|
7466 | |
---|
7467 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
7468 | long j1 = index_vec[i]; |
---|
7469 | long j2 = index_vec[i+1]; |
---|
7470 | mpz_add_mul_many(&rem_vec[i], &coeff_vec[j1], &val_vec[j1], j2-j1, |
---|
7471 | prod_vec[i]._mp_size); |
---|
7472 | } |
---|
7473 | |
---|
7474 | for (i = (1L << (levels-1)) - 2; i >= 0; i--) { |
---|
7475 | mpz_mul(&temps[0], &prod_vec[2*i+1], &rem_vec[2*i+2]); |
---|
7476 | mpz_mul(&temps[1], &rem_vec[2*i+1], &prod_vec[2*i+2]); |
---|
7477 | mpz_add(&rem_vec[i], &temps[0], &temps[1]); |
---|
7478 | } |
---|
7479 | |
---|
7480 | /* temps[0] = rem_vec[0] mod prod_vec[0] (least absolute residue) */ |
---|
7481 | mpz_fdiv_r(&temps[0], &rem_vec[0], &prod_vec[0]); |
---|
7482 | mpz_sub(&temps[1], &temps[0], &prod_vec[0]); |
---|
7483 | if (mpz_cmpabs(&temps[0], &temps[1]) > 0) |
---|
7484 | mpz_set(&temps[0], &temps[1]); |
---|
7485 | |
---|
7486 | mpz_fdiv_r(&temps[1], &temps[0], C->modulus); |
---|
7487 | mpz_to_lip(x, &temps[1]); |
---|
7488 | |
---|
7489 | break; |
---|
7490 | } |
---|
7491 | #endif |
---|
7492 | |
---|
7493 | default: |
---|
7494 | |
---|
7495 | zhalt("_crt_struct_eval: inconsistent strategy"); |
---|
7496 | |
---|
7497 | } /* end case */ |
---|
7498 | } |
---|
7499 | |
---|
7500 | |
---|
7501 | |
---|
7502 | |
---|
7503 | |
---|
7504 | |
---|
7505 | /* Data structures and algorithms for multi-modulus remaindering */ |
---|
7506 | |
---|
7507 | |
---|
7508 | struct rem_body_lip { |
---|
7509 | long n; |
---|
7510 | long *primes; |
---|
7511 | }; |
---|
7512 | |
---|
7513 | #ifdef NTL_GMP_HACK |
---|
7514 | |
---|
7515 | struct rem_body_gmp { |
---|
7516 | long n; |
---|
7517 | long levels; |
---|
7518 | long *primes; |
---|
7519 | long *index_vec; |
---|
7520 | MP_INT *prod_vec; |
---|
7521 | MP_INT *rem_vec; |
---|
7522 | }; |
---|
7523 | |
---|
7524 | #endif |
---|
7525 | |
---|
7526 | |
---|
7527 | |
---|
7528 | #ifdef NTL_SINGLE_MUL |
---|
7529 | |
---|
7530 | struct rem_body_sm { |
---|
7531 | long n; |
---|
7532 | long *primes; |
---|
7533 | double **tbl; |
---|
7534 | }; |
---|
7535 | |
---|
7536 | #endif |
---|
7537 | |
---|
7538 | |
---|
7539 | #if (defined(NTL_TBL_REM) && !defined(NTL_SINGLE_MUL)) |
---|
7540 | |
---|
7541 | struct rem_body_tbl { |
---|
7542 | long n; |
---|
7543 | long *primes; |
---|
7544 | long **tbl; |
---|
7545 | }; |
---|
7546 | |
---|
7547 | #endif |
---|
7548 | |
---|
7549 | struct rem_body { |
---|
7550 | long strategy; |
---|
7551 | |
---|
7552 | union { |
---|
7553 | struct rem_body_lip L; |
---|
7554 | #ifdef NTL_GMP_HACK |
---|
7555 | struct rem_body_gmp G; |
---|
7556 | #endif |
---|
7557 | #ifdef NTL_SINGLE_MUL |
---|
7558 | struct rem_body_sm S; |
---|
7559 | #endif |
---|
7560 | #if (defined(NTL_TBL_REM) && !defined(NTL_SINGLE_MUL)) |
---|
7561 | struct rem_body_tbl T; |
---|
7562 | #endif |
---|
7563 | } U; |
---|
7564 | }; |
---|
7565 | |
---|
7566 | |
---|
7567 | |
---|
7568 | void _ntl_rem_struct_init(void **rem_struct, long n, _ntl_verylong modulus, |
---|
7569 | const long *p) |
---|
7570 | { |
---|
7571 | struct rem_body *r; |
---|
7572 | |
---|
7573 | r = (struct rem_body *) NTL_MALLOC(1, sizeof(struct rem_body), 0); |
---|
7574 | if (!r) zhalt("out of memory"); |
---|
7575 | |
---|
7576 | #ifdef NTL_GMP_HACK |
---|
7577 | if (_ntl_gmp_hack && n >= 32) { |
---|
7578 | struct rem_body_gmp *R = &r->U.G; |
---|
7579 | |
---|
7580 | long *q; |
---|
7581 | long i, j; |
---|
7582 | long levels, vec_len; |
---|
7583 | long *index_vec; |
---|
7584 | MP_INT *prod_vec, *rem_vec; |
---|
7585 | |
---|
7586 | q = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
7587 | if (!q) zhalt("out of memory"); |
---|
7588 | |
---|
7589 | for (i = 0; i < n; i++) |
---|
7590 | q[i] = p[i]; |
---|
7591 | |
---|
7592 | levels = 0; |
---|
7593 | while ((n >> levels) >= 4) levels++; |
---|
7594 | |
---|
7595 | vec_len = (1L << levels) - 1; |
---|
7596 | |
---|
7597 | index_vec = (long *) NTL_MALLOC((vec_len+1), sizeof(long), 0); |
---|
7598 | if (!index_vec) zhalt("out of memory"); |
---|
7599 | |
---|
7600 | prod_vec = (MP_INT *) NTL_MALLOC(vec_len, sizeof(MP_INT), 0); |
---|
7601 | if (!prod_vec) zhalt("out of memory"); |
---|
7602 | |
---|
7603 | rem_vec = (MP_INT *) NTL_MALLOC(vec_len, sizeof(MP_INT), 0); |
---|
7604 | if (!rem_vec) zhalt("out of memory"); |
---|
7605 | |
---|
7606 | for (i = 0; i < vec_len; i++) |
---|
7607 | mpz_init(&prod_vec[i]); |
---|
7608 | |
---|
7609 | for (i = 0; i < vec_len; i++) |
---|
7610 | mpz_init(&rem_vec[i]); |
---|
7611 | |
---|
7612 | index_vec[0] = 0; |
---|
7613 | index_vec[1] = n; |
---|
7614 | |
---|
7615 | for (i = 0; i <= levels-2; i++) { |
---|
7616 | long start = (1L << i) - 1; |
---|
7617 | long finish = (1L << (i+1)) - 2; |
---|
7618 | for (j = finish; j >= start; j--) { |
---|
7619 | index_vec[2*j+2] = index_vec[j] + (index_vec[j+1] - index_vec[j])/2; |
---|
7620 | index_vec[2*j+1] = index_vec[j]; |
---|
7621 | } |
---|
7622 | index_vec[2*finish+3] = n; |
---|
7623 | } |
---|
7624 | |
---|
7625 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
7626 | /* multiply primes index_vec[i]..index_vec[i+1]-1 into |
---|
7627 | * prod_vec[i] |
---|
7628 | */ |
---|
7629 | |
---|
7630 | mpz_set_ui(&prod_vec[i], 1); |
---|
7631 | for (j = index_vec[i]; j < index_vec[i+1]; j++) |
---|
7632 | mpz_mul_ui(&prod_vec[i], &prod_vec[i], q[j]); |
---|
7633 | } |
---|
7634 | |
---|
7635 | for (i = (1L << (levels-1)) - 2; i >= 3; i--) |
---|
7636 | mpz_mul(&prod_vec[i], &prod_vec[2*i+1], &prod_vec[2*i+2]); |
---|
7637 | |
---|
7638 | r->strategy = 1; |
---|
7639 | R->n = n; |
---|
7640 | R->primes = q; |
---|
7641 | R->levels = levels; |
---|
7642 | R->index_vec = index_vec; |
---|
7643 | R->prod_vec = prod_vec; |
---|
7644 | R->rem_vec = rem_vec; |
---|
7645 | |
---|
7646 | *rem_struct = (void *) r; |
---|
7647 | |
---|
7648 | return; |
---|
7649 | } |
---|
7650 | #endif |
---|
7651 | |
---|
7652 | #ifdef NTL_SINGLE_MUL |
---|
7653 | { |
---|
7654 | struct rem_body_sm *R = &r->U.S; |
---|
7655 | |
---|
7656 | long *qq; |
---|
7657 | long i; |
---|
7658 | double **tbl; |
---|
7659 | long t, t1, j, q; |
---|
7660 | long sz = modulus[0]; |
---|
7661 | |
---|
7662 | r->strategy = 2; |
---|
7663 | R->n = n; |
---|
7664 | qq = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
7665 | if (!qq) zhalt("out of memory"); |
---|
7666 | R->primes = qq; |
---|
7667 | |
---|
7668 | for (i = 0; i < n; i++) |
---|
7669 | qq[i] = p[i]; |
---|
7670 | |
---|
7671 | tbl = (double **) NTL_MALLOC(n, sizeof(double *), 0); |
---|
7672 | if (!tbl) zhalt("out of space"); |
---|
7673 | |
---|
7674 | for (i = 0; i < n; i++) { |
---|
7675 | tbl[i] = (double *) NTL_MALLOC(sz, sizeof(double), 0); |
---|
7676 | if (!tbl[i]) zhalt("out of space"); |
---|
7677 | } |
---|
7678 | R->tbl = tbl; |
---|
7679 | |
---|
7680 | |
---|
7681 | for (i = 0; i < n; i++) { |
---|
7682 | q = qq[i]; |
---|
7683 | t = (((long)1) << NTL_NBITS) % q; |
---|
7684 | t1 = 1; |
---|
7685 | tbl[i][0] = (double) 1; |
---|
7686 | for (j = 1; j < sz; j++) { |
---|
7687 | SP_MUL_MOD(t1, t1, t, q); |
---|
7688 | tbl[i][j] = (double) t1; |
---|
7689 | } |
---|
7690 | } |
---|
7691 | |
---|
7692 | *rem_struct = (void *) r; |
---|
7693 | return; |
---|
7694 | } |
---|
7695 | |
---|
7696 | #endif |
---|
7697 | |
---|
7698 | #if (defined(NTL_TBL_REM) && !defined(NTL_SINGLE_MUL)) |
---|
7699 | |
---|
7700 | { |
---|
7701 | struct rem_body_tbl *R = &r->U.T; |
---|
7702 | |
---|
7703 | long *qq; |
---|
7704 | long i; |
---|
7705 | long **tbl; |
---|
7706 | long t, t1, j, q; |
---|
7707 | long sz = modulus[0]; |
---|
7708 | |
---|
7709 | r->strategy = 3; |
---|
7710 | R->n = n; |
---|
7711 | qq = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
7712 | if (!qq) zhalt("out of memory"); |
---|
7713 | R->primes = qq; |
---|
7714 | |
---|
7715 | for (i = 0; i < n; i++) |
---|
7716 | qq[i] = p[i]; |
---|
7717 | |
---|
7718 | tbl = (long **) NTL_MALLOC(n, sizeof(long *), 0); |
---|
7719 | if (!tbl) zhalt("out of space"); |
---|
7720 | |
---|
7721 | for (i = 0; i < n; i++) { |
---|
7722 | tbl[i] = (long *) NTL_MALLOC(sz, sizeof(long), 0); |
---|
7723 | if (!tbl[i]) zhalt("out of space"); |
---|
7724 | } |
---|
7725 | R->tbl = tbl; |
---|
7726 | |
---|
7727 | |
---|
7728 | for (i = 0; i < n; i++) { |
---|
7729 | q = qq[i]; |
---|
7730 | t = (((long)1) << NTL_NBITS) % q; |
---|
7731 | t1 = 1; |
---|
7732 | tbl[i][0] = 1; |
---|
7733 | for (j = 1; j < sz; j++) { |
---|
7734 | SP_MUL_MOD(t1, t1, t, q); |
---|
7735 | tbl[i][j] = t1; |
---|
7736 | } |
---|
7737 | } |
---|
7738 | |
---|
7739 | *rem_struct = (void *) r; |
---|
7740 | return; |
---|
7741 | } |
---|
7742 | |
---|
7743 | #endif |
---|
7744 | |
---|
7745 | |
---|
7746 | { |
---|
7747 | struct rem_body_lip *R = &r->U.L; |
---|
7748 | |
---|
7749 | long *q; |
---|
7750 | long i; |
---|
7751 | |
---|
7752 | r->strategy = 0; |
---|
7753 | R->n = n; |
---|
7754 | q = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
7755 | if (!q) zhalt("out of memory"); |
---|
7756 | R->primes = q; |
---|
7757 | |
---|
7758 | for (i = 0; i < n; i++) |
---|
7759 | q[i] = p[i]; |
---|
7760 | |
---|
7761 | *rem_struct = (void *) r; |
---|
7762 | } |
---|
7763 | } |
---|
7764 | |
---|
7765 | void _ntl_rem_struct_free(void *rem_struct) |
---|
7766 | { |
---|
7767 | struct rem_body *r = (struct rem_body *) rem_struct; |
---|
7768 | |
---|
7769 | switch (r->strategy) { |
---|
7770 | |
---|
7771 | case 0: { |
---|
7772 | free(r->U.L.primes); |
---|
7773 | free(r); |
---|
7774 | break; |
---|
7775 | } |
---|
7776 | |
---|
7777 | #ifdef NTL_GMP_HACK |
---|
7778 | |
---|
7779 | case 1: { |
---|
7780 | struct rem_body_gmp *R = &r->U.G; |
---|
7781 | |
---|
7782 | long levels = R->levels; |
---|
7783 | long vec_len = (1L << levels) - 1; |
---|
7784 | long i; |
---|
7785 | |
---|
7786 | for (i = 0; i < vec_len; i++) |
---|
7787 | mpz_clear(&R->prod_vec[i]); |
---|
7788 | |
---|
7789 | for (i = 0; i < vec_len; i++) |
---|
7790 | mpz_clear(&R->rem_vec[i]); |
---|
7791 | |
---|
7792 | free(R->primes); |
---|
7793 | free(R->index_vec); |
---|
7794 | free(R->prod_vec); |
---|
7795 | free(R->rem_vec); |
---|
7796 | free(r); |
---|
7797 | break; |
---|
7798 | } |
---|
7799 | |
---|
7800 | #endif |
---|
7801 | |
---|
7802 | |
---|
7803 | #ifdef NTL_SINGLE_MUL |
---|
7804 | |
---|
7805 | case 2: { |
---|
7806 | struct rem_body_sm *R = &r->U.S; |
---|
7807 | |
---|
7808 | long n = R->n; |
---|
7809 | double **tbl = R->tbl; |
---|
7810 | long i; |
---|
7811 | |
---|
7812 | for (i = 0; i < n; i++) |
---|
7813 | free(tbl[i]); |
---|
7814 | |
---|
7815 | free(tbl); |
---|
7816 | |
---|
7817 | free(R->primes); |
---|
7818 | free(r); |
---|
7819 | break; |
---|
7820 | } |
---|
7821 | |
---|
7822 | #endif |
---|
7823 | |
---|
7824 | |
---|
7825 | #if (defined(NTL_TBL_REM) && !defined(NTL_SINGLE_MUL)) |
---|
7826 | |
---|
7827 | case 3: { |
---|
7828 | struct rem_body_tbl *R = &r->U.T; |
---|
7829 | |
---|
7830 | long n = R->n; |
---|
7831 | long **tbl = R->tbl; |
---|
7832 | long i; |
---|
7833 | |
---|
7834 | for (i = 0; i < n; i++) |
---|
7835 | free(tbl[i]); |
---|
7836 | |
---|
7837 | free(tbl); |
---|
7838 | |
---|
7839 | free(R->primes); |
---|
7840 | free(r); |
---|
7841 | break; |
---|
7842 | } |
---|
7843 | |
---|
7844 | |
---|
7845 | #endif |
---|
7846 | |
---|
7847 | default: |
---|
7848 | zhalt("_ntl_rem_struct_free: inconsistent strategy"); |
---|
7849 | |
---|
7850 | } /* end switch */ |
---|
7851 | |
---|
7852 | } |
---|
7853 | |
---|
7854 | |
---|
7855 | void _ntl_rem_struct_eval(void *rem_struct, long *x, _ntl_verylong a) |
---|
7856 | { |
---|
7857 | struct rem_body *r = (struct rem_body *) rem_struct; |
---|
7858 | |
---|
7859 | switch (r->strategy) { |
---|
7860 | |
---|
7861 | case 0: { |
---|
7862 | struct rem_body_lip *R = &r->U.L; |
---|
7863 | |
---|
7864 | _ntl_zmultirem(a, R->n, R->primes, x); |
---|
7865 | return; |
---|
7866 | } |
---|
7867 | |
---|
7868 | #ifdef NTL_GMP_HACK |
---|
7869 | |
---|
7870 | case 1: { |
---|
7871 | struct rem_body_gmp *R = &r->U.G; |
---|
7872 | |
---|
7873 | long n = R->n; |
---|
7874 | long levels = R->levels; |
---|
7875 | long *q = R->primes; |
---|
7876 | long *index_vec = R->index_vec; |
---|
7877 | MP_INT *prod_vec = R->prod_vec; |
---|
7878 | MP_INT *rem_vec = R->rem_vec; |
---|
7879 | long vec_len = (1L << levels) - 1; |
---|
7880 | |
---|
7881 | long i, j; |
---|
7882 | |
---|
7883 | lip_to_mpz(a, &rem_vec[1]); |
---|
7884 | mpz_set(&rem_vec[2], &rem_vec[1]); |
---|
7885 | |
---|
7886 | for (i = 1; i < (1L << (levels-1)) - 1; i++) { |
---|
7887 | mpz_mod(&rem_vec[2*i+1], &rem_vec[i], &prod_vec[2*i+1]); |
---|
7888 | mpz_mod(&rem_vec[2*i+2], &rem_vec[i], &prod_vec[2*i+2]); |
---|
7889 | } |
---|
7890 | |
---|
7891 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
7892 | long lo = index_vec[i]; |
---|
7893 | long hi = index_vec[i+1]; |
---|
7894 | mp_limb_t *s1p = rem_vec[i]._mp_d; |
---|
7895 | long s1size = rem_vec[i]._mp_size; |
---|
7896 | if (s1size == 0) { |
---|
7897 | for (j = lo; j <hi; j++) |
---|
7898 | x[j] = 0; |
---|
7899 | } |
---|
7900 | else { |
---|
7901 | for (j = lo; j < hi; j++) |
---|
7902 | x[j] = mpn_mod_1(s1p, s1size, q[j]); |
---|
7903 | } |
---|
7904 | } |
---|
7905 | |
---|
7906 | break; |
---|
7907 | } |
---|
7908 | |
---|
7909 | #endif |
---|
7910 | |
---|
7911 | |
---|
7912 | #ifdef NTL_SINGLE_MUL |
---|
7913 | |
---|
7914 | case 2: { |
---|
7915 | struct rem_body_sm *R = &r->U.S; |
---|
7916 | |
---|
7917 | _ntl_zmultirem2(a, R->n, R->primes, R->tbl, x); |
---|
7918 | break; |
---|
7919 | } |
---|
7920 | |
---|
7921 | #endif |
---|
7922 | |
---|
7923 | #if (defined(NTL_TBL_REM) && !defined(NTL_SINGLE_MUL)) |
---|
7924 | |
---|
7925 | case 3: { |
---|
7926 | struct rem_body_tbl *R = &r->U.T; |
---|
7927 | |
---|
7928 | _ntl_zmultirem3(a, R->n, R->primes, R->tbl, x); |
---|
7929 | break; |
---|
7930 | } |
---|
7931 | |
---|
7932 | #endif |
---|
7933 | |
---|
7934 | default: |
---|
7935 | zhalt("_ntl_rem_struct_eval: inconsistent strategy"); |
---|
7936 | |
---|
7937 | |
---|
7938 | } /* end switch */ |
---|
7939 | } |
---|
7940 | |
---|