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rmodulo2m.cc
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1/****************************************
2* Computer Algebra System SINGULAR *
3****************************************/
4/*
5* ABSTRACT: numbers modulo 2^m
6*/
7#include "misc/auxiliary.h"
8
9#include "misc/mylimits.h"
10#include "reporter/reporter.h"
11
12#include "coeffs/si_gmp.h"
13#include "coeffs/coeffs.h"
14#include "coeffs/numbers.h"
15#include "coeffs/longrat.h"
16#include "coeffs/mpr_complex.h"
17
18#include "coeffs/rmodulo2m.h"
19#include "coeffs/rmodulon.h"
20
21#include <string.h>
22
23#ifdef HAVE_RINGS
24
25#ifdef LDEBUG
26static BOOLEAN nr2mDBTest(number a, const char *f, const int l, const coeffs r)
27{
28 if ((((long)a<0L) || ((long)a>(long)r->mod2mMask))
29 && (r->mod2mMask!= ~0UL))
30 {
31 Print("wrong mod 2^n number %ld (m:%ld) at %s,%d\n",(long)a,(long)r->mod2mMask,f,l);
32 return FALSE;
33 }
34 return TRUE;
35}
36#endif
37
38
39static inline number nr2mMultM(number a, number b, const coeffs r)
40{
41 return (number)
42 ((((unsigned long) a) * ((unsigned long) b)) & r->mod2mMask);
43}
44
45static inline void nr2mInpMultM(number &a, number b, const coeffs r)
46{
47 a= (number)
48 ((((unsigned long) a) * ((unsigned long) b)) & r->mod2mMask);
49}
50
51static inline number nr2mAddM(number a, number b, const coeffs r)
52{
53 return (number)
54 ((((unsigned long) a) + ((unsigned long) b)) & r->mod2mMask);
55}
56
57static inline void nr2mInpAddM(number &a, number b, const coeffs r)
58{
59 a= (number)
60 ((((unsigned long) a) + ((unsigned long) b)) & r->mod2mMask);
61}
62
63static inline number nr2mSubM(number a, number b, const coeffs r)
64{
65 return (number)((unsigned long)a < (unsigned long)b ?
66 r->mod2mMask+1 - (unsigned long)b + (unsigned long)a:
67 (unsigned long)a - (unsigned long)b);
68}
69
70#define nr2mNegM(A,r) (number)((r->mod2mMask+1 - (unsigned long)(A)) & r->mod2mMask)
71#define nr2mEqualM(A,B) ((A)==(B))
72
73EXTERN_VAR omBin gmp_nrz_bin; /* init in rintegers*/
74
75static char* nr2mCoeffName(const coeffs cf)
76{
77 STATIC_VAR char n2mCoeffName_buf[37];
78 if (cf->modExponent>32) /* for 32/64bit arch.*/
79 snprintf(n2mCoeffName_buf,36,"ZZ/(bigint(2)^%lu)",cf->modExponent);
80 else
81 snprintf(n2mCoeffName_buf,36,"ZZ/(2^%lu)",cf->modExponent);
82 return n2mCoeffName_buf;
83}
84
85static BOOLEAN nr2mCoeffIsEqual(const coeffs r, n_coeffType n, void * p)
86{
87 if (n==n_Z2m)
88 {
89 int m=(int)(long)(p);
90 unsigned long mm=r->mod2mMask;
91 if (((mm+1)>>m)==1L) return TRUE;
92 }
93 return FALSE;
94}
95
96static coeffs nr2mQuot1(number c, const coeffs r)
97{
98 coeffs rr;
99 long ch = r->cfInt(c, r);
100 mpz_t a,b;
101 mpz_init_set(a, r->modNumber);
102 mpz_init_set_ui(b, ch);
103 mpz_ptr gcd;
104 gcd = (mpz_ptr) omAlloc(sizeof(mpz_t));
105 mpz_init(gcd);
106 mpz_gcd(gcd, a,b);
107 if(mpz_cmp_ui(gcd, 1) == 0)
108 {
109 WerrorS("constant in q-ideal is coprime to modulus in ground ring");
110 WerrorS("Unable to create qring!");
111 return NULL;
112 }
113 if(mpz_cmp_ui(gcd, 2) == 0)
114 {
115 rr = nInitChar(n_Zp, (void*)2);
116 }
117 else
118 {
119 int kNew = 1;
120 mpz_t baseTokNew;
121 mpz_init(baseTokNew);
122 mpz_set(baseTokNew, r->modBase);
123 while(mpz_cmp(gcd, baseTokNew) > 0)
124 {
125 kNew++;
126 mpz_mul(baseTokNew, baseTokNew, r->modBase);
127 }
128 mpz_clear(baseTokNew);
129 rr = nInitChar(n_Z2m, (void*)(long)kNew);
130 }
131 return(rr);
132}
133
134/* TRUE iff 0 < k <= 2^m / 2 */
135static BOOLEAN nr2mGreaterZero(number k, const coeffs r)
136{
137 if ((unsigned long)k == 0) return FALSE;
138 if ((unsigned long)k > ((r->mod2mMask >> 1) + 1)) return FALSE;
139 return TRUE;
140}
141
142/*
143 * Multiply two numbers
144 */
145static number nr2mMult(number a, number b, const coeffs r)
146{
147 number n;
148 if (((unsigned long)a == 0) || ((unsigned long)b == 0))
149 return (number)0;
150 else
151 n=nr2mMultM(a, b, r);
152 n_Test(n,r);
153 return n;
154}
155
156static void nr2mInpMult(number &a, number b, const coeffs r)
157{
158 if (((unsigned long)a == 0) || ((unsigned long)b == 0))
159 { a=(number)0; return; }
160 else
161 nr2mInpMultM(a, b, r);
162 n_Test(a,r);
163}
164
165static number nr2mAnn(number b, const coeffs r);
166/*
167 * Give the smallest k, such that a * x = k = b * y has a solution
168 */
169static number nr2mLcm(number a, number b, const coeffs)
170{
171 unsigned long res = 0;
172 if ((unsigned long)a == 0) a = (number) 1;
173 if ((unsigned long)b == 0) b = (number) 1;
174 while ((unsigned long)a % 2 == 0)
175 {
176 a = (number)((unsigned long)a / 2);
177 if ((unsigned long)b % 2 == 0) b = (number)((unsigned long)b / 2);
178 res++;
179 }
180 while ((unsigned long)b % 2 == 0)
181 {
182 b = (number)((unsigned long)b / 2);
183 res++;
184 }
185 return (number)(1L << res); // (2**res)
186}
187
188/*
189 * Give the largest k, such that a = x * k, b = y * k has
190 * a solution.
191 */
192static number nr2mGcd(number a, number b, const coeffs)
193{
194 unsigned long res = 0;
195 if ((unsigned long)a == 0 && (unsigned long)b == 0) return (number)1;
196 while ((unsigned long)a % 2 == 0 && (unsigned long)b % 2 == 0)
197 {
198 a = (number)((unsigned long)a / 2);
199 b = (number)((unsigned long)b / 2);
200 res++;
201 }
202// if ((unsigned long)b % 2 == 0)
203// {
204// return (number)((1L << res)); // * (unsigned long) a); // (2**res)*a a is a unit
205// }
206// else
207// {
208 return (number)((1L << res)); // * (unsigned long) b); // (2**res)*b b is a unit
209// }
210}
211
212/* assumes that 'a' is odd, i.e., a unit in Z/2^m, and computes
213 the extended gcd of 'a' and 2^m, in order to find some 's'
214 and 't' such that a * s + 2^m * t = gcd(a, 2^m) = 1;
215 this code will always find a positive 's' */
216static void specialXGCD(unsigned long& s, unsigned long a, const coeffs r)
217{
218 mpz_ptr u = (mpz_ptr)omAlloc(sizeof(mpz_t));
219 mpz_init_set_ui(u, a);
220 mpz_ptr u0 = (mpz_ptr)omAlloc(sizeof(mpz_t));
221 mpz_init(u0);
222 mpz_ptr u1 = (mpz_ptr)omAlloc(sizeof(mpz_t));
223 mpz_init_set_ui(u1, 1);
224 mpz_ptr u2 = (mpz_ptr)omAlloc(sizeof(mpz_t));
225 mpz_init(u2);
226 mpz_ptr v = (mpz_ptr)omAlloc(sizeof(mpz_t));
227 mpz_init_set_ui(v, r->mod2mMask);
228 mpz_add_ui(v, v, 1); /* now: v = 2^m */
229 mpz_ptr v0 = (mpz_ptr)omAlloc(sizeof(mpz_t));
230 mpz_init(v0);
231 mpz_ptr v1 = (mpz_ptr)omAlloc(sizeof(mpz_t));
232 mpz_init(v1);
233 mpz_ptr v2 = (mpz_ptr)omAlloc(sizeof(mpz_t));
234 mpz_init_set_ui(v2, 1);
235 mpz_ptr q = (mpz_ptr)omAlloc(sizeof(mpz_t));
236 mpz_init(q);
237 mpz_ptr rr = (mpz_ptr)omAlloc(sizeof(mpz_t));
238 mpz_init(rr);
239
240 while (mpz_sgn1(v) != 0) /* i.e., while v != 0 */
241 {
242 mpz_div(q, u, v);
243 mpz_mod(rr, u, v);
244 mpz_set(u, v);
245 mpz_set(v, rr);
246 mpz_set(u0, u2);
247 mpz_set(v0, v2);
248 mpz_mul(u2, u2, q); mpz_sub(u2, u1, u2); /* u2 = u1 - q * u2 */
249 mpz_mul(v2, v2, q); mpz_sub(v2, v1, v2); /* v2 = v1 - q * v2 */
250 mpz_set(u1, u0);
251 mpz_set(v1, v0);
252 }
253
254 while (mpz_sgn1(u1) < 0) /* i.e., while u1 < 0 */
255 {
256 /* we add 2^m = (2^m - 1) + 1 to u1: */
257 mpz_add_ui(u1, u1, r->mod2mMask);
258 mpz_add_ui(u1, u1, 1);
259 }
260 s = mpz_get_ui(u1); /* now: 0 <= s <= 2^m - 1 */
261
262 mpz_clear(u); omFreeBinAddr((ADDRESS)u);
263 mpz_clear(u0); omFreeBinAddr((ADDRESS)u0);
264 mpz_clear(u1); omFreeBinAddr((ADDRESS)u1);
265 mpz_clear(u2); omFreeBinAddr((ADDRESS)u2);
266 mpz_clear(v); omFreeBinAddr((ADDRESS)v);
267 mpz_clear(v0); omFreeBinAddr((ADDRESS)v0);
268 mpz_clear(v1); omFreeBinAddr((ADDRESS)v1);
269 mpz_clear(v2); omFreeBinAddr((ADDRESS)v2);
270 mpz_clear(q); omFreeBinAddr((ADDRESS)q);
271 mpz_clear(rr); omFreeBinAddr((ADDRESS)rr);
272}
273
274static unsigned long InvMod(unsigned long a, const coeffs r)
275{
276 assume((unsigned long)a % 2 != 0);
277 unsigned long s;
278 specialXGCD(s, a, r);
279 return s;
280}
281
282static inline number nr2mInversM(number c, const coeffs r)
283{
284 assume((unsigned long)c % 2 != 0);
285 // Table !!!
286 unsigned long inv;
287 inv = InvMod((unsigned long)c,r);
288 return (number)inv;
289}
290
291static number nr2mInvers(number c, const coeffs r)
292{
293 if ((unsigned long)c % 2 == 0)
294 {
295 WerrorS("division by zero divisor");
296 return (number)0;
297 }
298 return nr2mInversM(c, r);
299}
300
301/*
302 * Give the largest k, such that a = x * k, b = y * k has
303 * a solution.
304 */
305static number nr2mExtGcd(number a, number b, number *s, number *t, const coeffs r)
306{
307 unsigned long res = 0;
308 if ((unsigned long)a == 0 && (unsigned long)b == 0) return (number)1;
309 while ((unsigned long)a % 2 == 0 && (unsigned long)b % 2 == 0)
310 {
311 a = (number)((unsigned long)a / 2);
312 b = (number)((unsigned long)b / 2);
313 res++;
314 }
315 if ((unsigned long)b % 2 == 0)
316 {
317 *t = NULL;
318 *s = nr2mInvers(a,r);
319 return (number)((1L << res)); // * (unsigned long) a); // (2**res)*a a is a unit
320 }
321 else
322 {
323 *s = NULL;
324 *t = nr2mInvers(b,r);
325 return (number)((1L << res)); // * (unsigned long) b); // (2**res)*b b is a unit
326 }
327}
328
329static void nr2mPower(number a, int i, number * result, const coeffs r)
330{
331 if (i == 0)
332 {
333 *(unsigned long *)result = 1;
334 }
335 else if (i == 1)
336 {
337 *result = a;
338 }
339 else
340 {
341 nr2mPower(a, i-1, result, r);
342 *result = nr2mMultM(a, *result, r);
343 }
344}
345
346/*
347 * create a number from int
348 */
349static number nr2mInit(long i, const coeffs r)
350{
351 if (i == 0) return (number)(unsigned long)0;
352
353 long ii = i;
354 unsigned long j = (unsigned long)1;
355 if (ii < 0) { j = r->mod2mMask; ii = -ii; }
356 unsigned long k = (unsigned long)ii;
357 k = k & r->mod2mMask;
358 /* now we have: i = j * k mod 2^m */
359 return nr2mMult((number)j, (number)k, r);
360}
361
362/*
363 * convert a number to an int in ]-k/2 .. k/2],
364 * where k = 2^m; i.e., an int in ]-2^(m-1) .. 2^(m-1)];
365 */
366static long nr2mInt(number &n, const coeffs r)
367{
368 unsigned long nn = (unsigned long)n;
369 unsigned long l = r->mod2mMask >> 1; l++; /* now: l = 2^(m-1) */
370 if ((unsigned long)nn > l)
371 return (long)((unsigned long)nn - r->mod2mMask - 1);
372 else
373 return (long)((unsigned long)nn);
374}
375
376static number nr2mAdd(number a, number b, const coeffs r)
377{
378 number n=nr2mAddM(a, b, r);
379 n_Test(n,r);
380 return n;
381}
382
383static void nr2mInpAdd(number &a, number b, const coeffs r)
384{
385 nr2mInpAddM(a, b, r);
386 n_Test(a,r);
387}
388
389static number nr2mSub(number a, number b, const coeffs r)
390{
391 number n=nr2mSubM(a, b, r);
392 n_Test(n,r);
393 return n;
394}
395
396static BOOLEAN nr2mIsUnit(number a, const coeffs)
397{
398 return ((unsigned long)a % 2 == 1);
399}
400
401static number nr2mGetUnit(number k, const coeffs)
402{
403 if (k == NULL) return (number)1;
404 unsigned long erg = (unsigned long)k;
405 while (erg % 2 == 0) erg = erg / 2;
406 return (number)erg;
407}
408
409static BOOLEAN nr2mIsZero(number a, const coeffs)
410{
411 return 0 == (unsigned long)a;
412}
413
414static BOOLEAN nr2mIsOne(number a, const coeffs)
415{
416 return 1 == (unsigned long)a;
417}
418
419static BOOLEAN nr2mIsMOne(number a, const coeffs r)
420{
421 return ((r->mod2mMask == (unsigned long)a) &&(1L!=(long)a))/*for char 2^1*/;
422}
423
424static BOOLEAN nr2mEqual(number a, number b, const coeffs)
425{
426 return (a == b);
427}
428
429static number nr2mDiv(number a, number b, const coeffs r)
430{
431 if ((unsigned long)a == 0) return (number)0;
432 else if ((unsigned long)b % 2 == 0)
433 {
434 if ((unsigned long)b != 0)
435 {
436 while (((unsigned long)b % 2 == 0) && ((unsigned long)a % 2 == 0))
437 {
438 a = (number)((unsigned long)a / 2);
439 b = (number)((unsigned long)b / 2);
440 }
441 }
442 if ((long)b==0L)
443 {
445 return (number)0L;
446 }
447 else if ((unsigned long)b % 2 == 0)
448 {
449 WerrorS("Division not possible, even by cancelling zero divisors.");
450 WerrorS("Result is integer division without remainder.");
451 return (number) ((unsigned long) a / (unsigned long) b);
452 }
453 }
454 number n=nr2mMult(a, nr2mInversM(b,r),r);
455 n_Test(n,r);
456 return n;
457}
458
459/* Is 'a' divisible by 'b'? There are two cases:
460 1) a = 0 mod 2^m; then TRUE iff b = 0 or b is a power of 2
461 2) a, b <> 0; then TRUE iff b/gcd(a, b) is a unit mod 2^m */
462static BOOLEAN nr2mDivBy (number a, number b, const coeffs r)
463{
464 if (a == NULL)
465 {
466 unsigned long c = r->mod2mMask + 1;
467 if (c != 0) /* i.e., if no overflow */
468 return (c % (unsigned long)b) == 0;
469 else
470 {
471 /* overflow: we need to check whether b
472 is zero or a power of 2: */
473 c = (unsigned long)b;
474 while (c != 0)
475 {
476 if ((c % 2) != 0) return FALSE;
477 c = c >> 1;
478 }
479 return TRUE;
480 }
481 }
482 else
483 {
484 number n = nr2mGcd(a, b, r);
485 n = nr2mDiv(b, n, r);
486 return nr2mIsUnit(n, r);
487 }
488}
489
490static BOOLEAN nr2mGreater(number a, number b, const coeffs r)
491{
492 return nr2mDivBy(a, b,r);
493}
494
495static int nr2mDivComp(number as, number bs, const coeffs)
496{
497 unsigned long a = (unsigned long)as;
498 unsigned long b = (unsigned long)bs;
499 assume(a != 0 && b != 0);
500 while (a % 2 == 0 && b % 2 == 0)
501 {
502 a = a / 2;
503 b = b / 2;
504 }
505 if (a % 2 == 0)
506 {
507 return -1;
508 }
509 else
510 {
511 if (b % 2 == 1)
512 {
513 return 2;
514 }
515 else
516 {
517 return 1;
518 }
519 }
520}
521
522static number nr2mMod(number a, number b, const coeffs r)
523{
524 /*
525 We need to return the number rr which is uniquely determined by the
526 following two properties:
527 (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z)
528 (2) There exists some k in the integers Z such that a = k * b + rr.
529 Consider g := gcd(2^m, |b|). Note that then |b|/g is a unit in Z/2^m.
530 Now, there are three cases:
531 (a) g = 1
532 Then |b| is a unit in Z/2^m, i.e. |b| (and also b) divides a.
533 Thus rr = 0.
534 (b) g <> 1 and g divides a
535 Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0.
536 (c) g <> 1 and g does not divide a
537 Let's denote the division with remainder of a by g as follows:
538 a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b|
539 fulfills (1) and (2), i.e. rr := t is the correct result. Hence
540 in this third case, rr is the remainder of division of a by g in Z.
541 This algorithm is the same as for the case Z/n, except that we may
542 compute the gcd of |b| and 2^m "by hand": We just extract the highest
543 power of 2 (<= 2^m) that is contained in b.
544 */
545 assume((unsigned long) b != 0);
546 unsigned long g = 1;
547 unsigned long b_div = (unsigned long) b;
548
549 /*
550 * b_div is unsigned, so that (b_div < 0) evaluates false at compile-time
551 *
552 if (b_div < 0) b_div = -b_div; // b_div now represents |b|, BUT b_div is unsigned!
553 */
554
555 unsigned long rr = 0;
556 while ((g < r->mod2mMask ) && (b_div > 0) && (b_div % 2 == 0))
557 {
558 b_div = b_div >> 1;
559 g = g << 1;
560 } // g is now the gcd of 2^m and |b|
561
562 if (g != 1) rr = (unsigned long)a % g;
563 return (number)rr;
564}
565
566#if 0
567// unused
568static number nr2mIntDiv(number a, number b, const coeffs r)
569{
570 if ((unsigned long)a == 0)
571 {
572 if ((unsigned long)b == 0)
573 return (number)1;
574 if ((unsigned long)b == 1)
575 return (number)0;
576 unsigned long c = r->mod2mMask + 1;
577 if (c != 0) /* i.e., if no overflow */
578 return (number)(c / (unsigned long)b);
579 else
580 {
581 /* overflow: c = 2^32 resp. 2^64, depending on platform */
582 mpz_ptr cc = (mpz_ptr)omAlloc(sizeof(mpz_t));
583 mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1);
584 mpz_div_ui(cc, cc, (unsigned long)(unsigned long)b);
585 unsigned long s = mpz_get_ui(cc);
586 mpz_clear(cc); omFree((ADDRESS)cc);
587 return (number)(unsigned long)s;
588 }
589 }
590 else
591 {
592 if ((unsigned long)b == 0)
593 return (number)0;
594 return (number)((unsigned long) a / (unsigned long) b);
595 }
596}
597#endif
598
599static number nr2mAnn(number b, const coeffs r)
600{
601 if ((unsigned long)b == 0)
602 return NULL;
603 if ((unsigned long)b == 1)
604 return NULL;
605 unsigned long c = r->mod2mMask + 1;
606 if (c != 0) /* i.e., if no overflow */
607 return (number)(c / (unsigned long)b);
608 else
609 {
610 /* overflow: c = 2^32 resp. 2^64, depending on platform */
611 mpz_ptr cc = (mpz_ptr)omAlloc(sizeof(mpz_t));
612 mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1);
613 mpz_div_ui(cc, cc, (unsigned long)(unsigned long)b);
614 unsigned long s = mpz_get_ui(cc);
615 mpz_clear(cc); omFreeBinAddr((ADDRESS)cc);
616 return (number)(unsigned long)s;
617 }
618}
619
620static number nr2mNeg(number c, const coeffs r)
621{
622 if ((unsigned long)c == 0) return c;
623 number n=nr2mNegM(c, r);
624 n_Test(n,r);
625 return n;
626}
627
628static number nr2mMapMachineInt(number from, const coeffs /*src*/, const coeffs dst)
629{
630 unsigned long i = ((unsigned long)from) % (dst->mod2mMask + 1) ;
631 return (number)i;
632}
633
634static number nr2mMapProject(number from, const coeffs /*src*/, const coeffs dst)
635{
636 unsigned long i = ((unsigned long)from) % (dst->mod2mMask + 1);
637 return (number)i;
638}
639
640number nr2mMapZp(number from, const coeffs /*src*/, const coeffs dst)
641{
642 unsigned long j = (unsigned long)1;
643 long ii = (long)from;
644 if (ii < 0) { j = dst->mod2mMask; ii = -ii; }
645 unsigned long i = (unsigned long)ii;
646 i = i & dst->mod2mMask;
647 /* now we have: from = j * i mod 2^m */
648 return nr2mMult((number)i, (number)j, dst);
649}
650
651static number nr2mMapGMP(number from, const coeffs /*src*/, const coeffs dst)
652{
653 mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
654 mpz_init(erg);
655 mpz_ptr k = (mpz_ptr)omAlloc(sizeof(mpz_t));
656 mpz_init_set_ui(k, dst->mod2mMask);
657
658 mpz_and(erg, (mpz_ptr)from, k);
659 number res = (number) mpz_get_ui(erg);
660
661 mpz_clear(erg); omFreeBinAddr((ADDRESS)erg);
662 mpz_clear(k); omFreeBinAddr((ADDRESS)k);
663
664 return (number)res;
665}
666
667static number nr2mMapQ(number from, const coeffs src, const coeffs dst)
668{
669 mpz_ptr gmp = (mpz_ptr)omAllocBin(gmp_nrz_bin);
670 nlMPZ(gmp, from, src);
671 number res=nr2mMapGMP((number)gmp,src,dst);
672 mpz_clear(gmp); omFreeBinAddr((ADDRESS)gmp);
673 return res;
674}
675
676static number nr2mMapZ(number from, const coeffs src, const coeffs dst)
677{
678 if (SR_HDL(from) & SR_INT)
679 {
680 long f_i=SR_TO_INT(from);
681 return nr2mInit(f_i,dst);
682 }
683 return nr2mMapGMP(from,src,dst);
684}
685
686static nMapFunc nr2mSetMap(const coeffs src, const coeffs dst)
687{
688 if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src)
689 && (src->mod2mMask < dst->mod2mMask))
690 { /* i.e. map an integer mod 2^s into Z mod 2^t, where t < s */
691 return nr2mMapMachineInt;
692 }
693 if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src)
694 && (src->mod2mMask > dst->mod2mMask))
695 { /* i.e. map an integer mod 2^s into Z mod 2^t, where t > s */
696 // to be done
697 return nr2mMapProject;
698 }
699 if ((src->rep==n_rep_gmp) && nCoeff_is_Z(src))
700 {
701 return nr2mMapGMP;
702 }
703 if ((src->rep==n_rep_gap_gmp) /*&& nCoeff_is_Z(src)*/)
704 {
705 return nr2mMapZ;
706 }
707 if ((src->rep==n_rep_gap_rat) && (nCoeff_is_Q(src)||nCoeff_is_Z(src)))
708 {
709 return nr2mMapQ;
710 }
711 if ((src->rep==n_rep_int) && nCoeff_is_Zp(src) && (src->ch == 2))
712 {
713 return nr2mMapZp;
714 }
715 if ((src->rep==n_rep_gmp) &&
716 (nCoeff_is_Ring_PtoM(src) || nCoeff_is_Zn(src)))
717 {
718 if (mpz_divisible_2exp_p(src->modNumber,dst->modExponent))
719 return nr2mMapGMP;
720 }
721 return NULL; // default
722}
723
724/*
725 * set the exponent
726 */
727
728static void nr2mSetExp(int m, coeffs r)
729{
730 if (m > 1)
731 {
732 /* we want mod2mMask to be the bit pattern
733 '111..1' consisting of m one's: */
734 r->modExponent= m;
735 r->mod2mMask = 1;
736 for (int i = 1; i < m; i++) r->mod2mMask = (r->mod2mMask << 1) + 1;
737 }
738 else
739 {
740 r->modExponent= 2;
741 /* code unexpectedly called with m = 1; we continue with m = 2: */
742 r->mod2mMask = 3; /* i.e., '11' in binary representation */
743 }
744}
745
746static void nr2mInitExp(int m, coeffs r)
747{
748 nr2mSetExp(m, r);
749 if (m < 2)
750 WarnS("nr2mInitExp unexpectedly called with m = 1 (we continue with Z/2^2");
751}
752
753static void nr2mWrite (number a, const coeffs r)
754{
755 long i = nr2mInt(a, r);
756 StringAppend("%ld", i);
757}
758
759static const char* nr2mEati(const char *s, int *i, const coeffs r)
760{
761
762 if (((*s) >= '0') && ((*s) <= '9'))
763 {
764 (*i) = 0;
765 do
766 {
767 (*i) *= 10;
768 (*i) += *s++ - '0';
769 if ((*i) >= (MAX_INT_VAL / 10)) (*i) = (*i) & r->mod2mMask;
770 }
771 while (((*s) >= '0') && ((*s) <= '9'));
772 (*i) = (*i) & r->mod2mMask;
773 }
774 else (*i) = 1;
775 return s;
776}
777
778static const char * nr2mRead (const char *s, number *a, const coeffs r)
779{
780 int z;
781 int n=1;
782
783 s = nr2mEati(s, &z,r);
784 if ((*s) == '/')
785 {
786 s++;
787 s = nr2mEati(s, &n,r);
788 }
789 if (n == 1)
790 *a = (number)(long)z;
791 else
792 *a = nr2mDiv((number)(long)z,(number)(long)n,r);
793 return s;
794}
795
796/* for initializing function pointers */
798{
799 assume( getCoeffType(r) == n_Z2m );
800 nr2mInitExp((int)(long)(p), r);
801
802 r->is_field=FALSE;
803 r->is_domain=FALSE;
804 r->rep=n_rep_int;
805
806 //r->cfKillChar = ndKillChar; /* dummy*/
807 r->nCoeffIsEqual = nr2mCoeffIsEqual;
808
809 r->modBase = (mpz_ptr) omAllocBin (gmp_nrz_bin);
810 mpz_init_set_si (r->modBase, 2L);
811 r->modNumber= (mpz_ptr) omAllocBin (gmp_nrz_bin);
812 mpz_init (r->modNumber);
813 mpz_pow_ui (r->modNumber, r->modBase, r->modExponent);
814
815 /* next cast may yield an overflow as mod2mMask is an unsigned long */
816 r->ch = (int)r->mod2mMask + 1;
817
818 r->cfInit = nr2mInit;
819 //r->cfCopy = ndCopy;
820 r->cfInt = nr2mInt;
821 r->cfAdd = nr2mAdd;
822 r->cfInpAdd = nr2mInpAdd;
823 r->cfSub = nr2mSub;
824 r->cfMult = nr2mMult;
825 r->cfInpMult = nr2mInpMult;
826 r->cfDiv = nr2mDiv;
827 r->cfAnn = nr2mAnn;
828 r->cfIntMod = nr2mMod;
829 r->cfExactDiv = nr2mDiv;
830 r->cfInpNeg = nr2mNeg;
831 r->cfInvers = nr2mInvers;
832 r->cfDivBy = nr2mDivBy;
833 r->cfDivComp = nr2mDivComp;
834 r->cfGreater = nr2mGreater;
835 r->cfEqual = nr2mEqual;
836 r->cfIsZero = nr2mIsZero;
837 r->cfIsOne = nr2mIsOne;
838 r->cfIsMOne = nr2mIsMOne;
839 r->cfGreaterZero = nr2mGreaterZero;
840 r->cfWriteLong = nr2mWrite;
841 r->cfRead = nr2mRead;
842 r->cfPower = nr2mPower;
843 r->cfSetMap = nr2mSetMap;
844// r->cfNormalize = ndNormalize; // default
845 r->cfLcm = nr2mLcm;
846 r->cfGcd = nr2mGcd;
847 r->cfIsUnit = nr2mIsUnit;
848 r->cfGetUnit = nr2mGetUnit;
849 r->cfExtGcd = nr2mExtGcd;
850 r->cfCoeffName = nr2mCoeffName;
851 r->cfQuot1 = nr2mQuot1;
852#ifdef LDEBUG
853 r->cfDBTest = nr2mDBTest;
854#endif
855 r->has_simple_Alloc=TRUE;
856 return FALSE;
857}
858
859#endif
860/* #ifdef HAVE_RINGS */
All the auxiliary stuff.
int BOOLEAN
Definition: auxiliary.h:87
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
void * ADDRESS
Definition: auxiliary.h:119
int l
Definition: cfEzgcd.cc:100
int m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
int k
Definition: cfEzgcd.cc:99
int p
Definition: cfModGcd.cc:4078
g
Definition: cfModGcd.cc:4090
CanonicalForm cf
Definition: cfModGcd.cc:4083
CanonicalForm b
Definition: cfModGcd.cc:4103
FILE * f
Definition: checklibs.c:9
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE BOOLEAN nCoeff_is_Z(const coeffs r)
Definition: coeffs.h:813
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
Definition: coeffs.h:709
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_PtoM(const coeffs r)
Definition: coeffs.h:724
n_coeffType
Definition: coeffs.h:27
@ n_Z2m
only used if HAVE_RINGS is defined
Definition: coeffs.h:46
@ n_Zp
\F{p < 2^31}
Definition: coeffs.h:29
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
Definition: coeffs.h:803
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
Definition: numbers.cc:413
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:422
static FORCE_INLINE BOOLEAN nCoeff_is_Zn(const coeffs r)
Definition: coeffs.h:823
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
Definition: coeffs.h:797
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_2toM(const coeffs r)
Definition: coeffs.h:721
@ n_rep_gap_rat
(number), see longrat.h
Definition: coeffs.h:111
@ n_rep_gap_gmp
(), see rinteger.h, new impl.
Definition: coeffs.h:112
@ n_rep_int
(int), see modulop.h
Definition: coeffs.h:110
@ n_rep_gmp
(mpz_ptr), see rmodulon,h
Definition: coeffs.h:115
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:73
#define Print
Definition: emacs.cc:80
#define WarnS
Definition: emacs.cc:78
#define StringAppend
Definition: emacs.cc:79
return result
Definition: facAbsBiFact.cc:75
const CanonicalForm int s
Definition: facAbsFact.cc:51
CanonicalForm res
Definition: facAbsFact.cc:60
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
int j
Definition: facHensel.cc:110
void WerrorS(const char *s)
Definition: feFopen.cc:24
#define STATIC_VAR
Definition: globaldefs.h:7
#define EXTERN_VAR
Definition: globaldefs.h:6
void nlMPZ(mpz_t m, number &n, const coeffs r)
Definition: longrat.cc:2819
#define SR_INT
Definition: longrat.h:67
#define SR_TO_INT(SR)
Definition: longrat.h:69
#define assume(x)
Definition: mod2.h:389
#define LDEBUG
Definition: mod2.h:307
const int MAX_INT_VAL
Definition: mylimits.h:12
The main handler for Singular numbers which are suitable for Singular polynomials.
const char *const nDivBy0
Definition: numbers.h:89
#define omAlloc(size)
Definition: omAllocDecl.h:210
#define omAllocBin(bin)
Definition: omAllocDecl.h:205
#define omFree(addr)
Definition: omAllocDecl.h:261
#define omFreeBinAddr(addr)
Definition: omAllocDecl.h:258
#define NULL
Definition: omList.c:12
omBin_t * omBin
Definition: omStructs.h:12
#define nr2mNegM(A, r)
Definition: rmodulo2m.cc:70
static number nr2mInversM(number c, const coeffs r)
Definition: rmodulo2m.cc:282
static number nr2mGcd(number a, number b, const coeffs)
Definition: rmodulo2m.cc:192
static nMapFunc nr2mSetMap(const coeffs src, const coeffs dst)
Definition: rmodulo2m.cc:686
static unsigned long InvMod(unsigned long a, const coeffs r)
Definition: rmodulo2m.cc:274
static const char * nr2mEati(const char *s, int *i, const coeffs r)
Definition: rmodulo2m.cc:759
static void nr2mWrite(number a, const coeffs r)
Definition: rmodulo2m.cc:753
static void nr2mSetExp(int m, coeffs r)
Definition: rmodulo2m.cc:728
static void specialXGCD(unsigned long &s, unsigned long a, const coeffs r)
Definition: rmodulo2m.cc:216
static number nr2mMapProject(number from, const coeffs, const coeffs dst)
Definition: rmodulo2m.cc:634
static BOOLEAN nr2mIsUnit(number a, const coeffs)
Definition: rmodulo2m.cc:396
static void nr2mInpAdd(number &a, number b, const coeffs r)
Definition: rmodulo2m.cc:383
static number nr2mMapQ(number from, const coeffs src, const coeffs dst)
Definition: rmodulo2m.cc:667
static number nr2mSub(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:389
static number nr2mLcm(number a, number b, const coeffs)
Definition: rmodulo2m.cc:169
static BOOLEAN nr2mIsOne(number a, const coeffs)
Definition: rmodulo2m.cc:414
BOOLEAN nr2mInitChar(coeffs r, void *p)
Definition: rmodulo2m.cc:797
static number nr2mAnn(number b, const coeffs r)
Definition: rmodulo2m.cc:599
static number nr2mInit(long i, const coeffs r)
Definition: rmodulo2m.cc:349
static number nr2mExtGcd(number a, number b, number *s, number *t, const coeffs r)
Definition: rmodulo2m.cc:305
static number nr2mGetUnit(number k, const coeffs)
Definition: rmodulo2m.cc:401
static void nr2mInitExp(int m, coeffs r)
Definition: rmodulo2m.cc:746
static void nr2mPower(number a, int i, number *result, const coeffs r)
Definition: rmodulo2m.cc:329
static number nr2mInvers(number c, const coeffs r)
Definition: rmodulo2m.cc:291
static number nr2mMultM(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:39
static number nr2mMapGMP(number from, const coeffs, const coeffs dst)
Definition: rmodulo2m.cc:651
number nr2mMapZp(number from, const coeffs, const coeffs dst)
Definition: rmodulo2m.cc:640
static int nr2mDivComp(number as, number bs, const coeffs)
Definition: rmodulo2m.cc:495
static number nr2mMult(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:145
static long nr2mInt(number &n, const coeffs r)
Definition: rmodulo2m.cc:366
static BOOLEAN nr2mDivBy(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:462
static BOOLEAN nr2mGreaterZero(number k, const coeffs r)
Definition: rmodulo2m.cc:135
static number nr2mMapMachineInt(number from, const coeffs, const coeffs dst)
Definition: rmodulo2m.cc:628
static number nr2mNeg(number c, const coeffs r)
Definition: rmodulo2m.cc:620
EXTERN_VAR omBin gmp_nrz_bin
Definition: rmodulo2m.cc:73
static BOOLEAN nr2mDBTest(number a, const char *f, const int l, const coeffs r)
Definition: rmodulo2m.cc:26
static number nr2mMod(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:522
static BOOLEAN nr2mCoeffIsEqual(const coeffs r, n_coeffType n, void *p)
Definition: rmodulo2m.cc:85
static number nr2mAdd(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:376
static void nr2mInpMult(number &a, number b, const coeffs r)
Definition: rmodulo2m.cc:156
static char * nr2mCoeffName(const coeffs cf)
Definition: rmodulo2m.cc:75
static number nr2mMapZ(number from, const coeffs src, const coeffs dst)
Definition: rmodulo2m.cc:676
static BOOLEAN nr2mEqual(number a, number b, const coeffs)
Definition: rmodulo2m.cc:424
static void nr2mInpMultM(number &a, number b, const coeffs r)
Definition: rmodulo2m.cc:45
static BOOLEAN nr2mGreater(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:490
static void nr2mInpAddM(number &a, number b, const coeffs r)
Definition: rmodulo2m.cc:57
static BOOLEAN nr2mIsZero(number a, const coeffs)
Definition: rmodulo2m.cc:409
static number nr2mAddM(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:51
static const char * nr2mRead(const char *s, number *a, const coeffs r)
Definition: rmodulo2m.cc:778
static BOOLEAN nr2mIsMOne(number a, const coeffs r)
Definition: rmodulo2m.cc:419
static number nr2mSubM(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:63
static number nr2mDiv(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:429
static coeffs nr2mQuot1(number c, const coeffs r)
Definition: rmodulo2m.cc:96
#define mpz_sgn1(A)
Definition: si_gmp.h:18
#define SR_HDL(A)
Definition: tgb.cc:35
int gcd(int a, int b)
Definition: walkSupport.cc:836