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 <omalloc/omalloc.h>
10 
11 #include <misc/mylimits.h>
12 #include <reporter/reporter.h>
13 
14 #include "si_gmp.h"
15 #include "coeffs.h"
16 #include "numbers.h"
17 #include "longrat.h"
18 #include "mpr_complex.h"
19 
20 #include "rmodulo2m.h"
21 #include "rmodulon.h"
22 
23 #include <string.h>
24 
25 #ifdef HAVE_RINGS
26 
27 static inline number nr2mMultM(number a, number b, const coeffs r)
28 {
29  return (number)
30  ((((unsigned long) a) * ((unsigned long) b)) & ((unsigned long)r->mod2mMask));
31 }
32 
33 static inline number nr2mAddM(number a, number b, const coeffs r)
34 {
35  return (number)
36  ((((unsigned long) a) + ((unsigned long) b)) & ((unsigned long)r->mod2mMask));
37 }
38 
39 static inline number nr2mSubM(number a, number b, const coeffs r)
40 {
41  return (number)((unsigned long)a < (unsigned long)b ?
42  r->mod2mMask - (unsigned long)b + (unsigned long)a + 1:
43  (unsigned long)a - (unsigned long)b);
44 }
45 
46 #define nr2mNegM(A,r) (number)((r->mod2mMask - (unsigned long)(A) + 1) & r->mod2mMask)
47 #define nr2mEqualM(A,B) ((A)==(B))
48 
49 extern omBin gmp_nrz_bin; /* init in rintegers*/
50 
51 static char* nr2mCoeffName(const coeffs cf)
52 {
53  static char n2mCoeffName_buf[22];
54  snprintf(n2mCoeffName_buf,21,"ZZ/(2^%lu)",cf->modExponent);
55  return n2mCoeffName_buf;
56 }
57 
58 static void nr2mCoeffWrite (const coeffs r, BOOLEAN /*details*/)
59 {
60  Print("Z/2^%lu", r->modExponent);
61 }
62 
63 static BOOLEAN nr2mCoeffIsEqual(const coeffs r, n_coeffType n, void * p)
64 {
65  if (n==n_Z2m)
66  {
67  int m=(int)(long)(p);
68  unsigned long mm=r->mod2mMask;
69  if (((mm+1)>>m)==1L) return TRUE;
70  }
71  return FALSE;
72 }
73 
74 static char* nr2mCoeffString(const coeffs r)
75 {
76  // r->modExponent <=bitsize(long)
77  char* s = (char*) omAlloc(11+11);
78  sprintf(s,"ZZ/(2^%lu)",r->modExponent);
79  return s;
80 }
81 
82 static coeffs nr2mQuot1(number c, const coeffs r)
83 {
84  coeffs rr;
85  long ch = r->cfInt(c, r);
86  mpz_t a,b;
87  mpz_init_set(a, r->modNumber);
88  mpz_init_set_ui(b, ch);
89  mpz_ptr gcd;
90  gcd = (mpz_ptr) omAlloc(sizeof(mpz_t));
91  mpz_init(gcd);
92  mpz_gcd(gcd, a,b);
93  if(mpz_cmp_ui(gcd, 1) == 0)
94  {
95  WerrorS("constant in q-ideal is coprime to modulus in ground ring");
96  WerrorS("Unable to create qring!");
97  return NULL;
98  }
99  if(mpz_cmp_ui(gcd, 2) == 0)
100  {
101  rr = nInitChar(n_Zp, (void*)2);
102  }
103  else
104  {
105  int kNew = 1;
106  mpz_t baseTokNew;
107  mpz_init(baseTokNew);
108  mpz_set(baseTokNew, r->modBase);
109  while(mpz_cmp(gcd, baseTokNew) > 0)
110  {
111  kNew++;
112  mpz_mul(baseTokNew, baseTokNew, r->modBase);
113  }
114  mpz_clear(baseTokNew);
115  rr = nInitChar(n_Z2m, (void*)(long)kNew);
116  }
117  return(rr);
118 }
119 
120 /* TRUE iff 0 < k <= 2^m / 2 */
121 static BOOLEAN nr2mGreaterZero(number k, const coeffs r)
122 {
123  if ((unsigned long)k == 0) return FALSE;
124  if ((unsigned long)k > ((r->mod2mMask >> 1) + 1)) return FALSE;
125  return TRUE;
126 }
127 
128 /*
129  * Multiply two numbers
130  */
131 static number nr2mMult(number a, number b, const coeffs r)
132 {
133  if (((unsigned long)a == 0) || ((unsigned long)b == 0))
134  return (number)0;
135  else
136  return nr2mMultM(a, b, r);
137 }
138 
139 static number nr2mAnn(number b, const coeffs r);
140 /*
141  * Give the smallest k, such that a * x = k = b * y has a solution
142  */
143 static number nr2mLcm(number a, number b, const coeffs)
144 {
145  unsigned long res = 0;
146  if ((unsigned long)a == 0) a = (number) 1;
147  if ((unsigned long)b == 0) b = (number) 1;
148  while ((unsigned long)a % 2 == 0)
149  {
150  a = (number)((unsigned long)a / 2);
151  if ((unsigned long)b % 2 == 0) b = (number)((unsigned long)b / 2);
152  res++;
153  }
154  while ((unsigned long)b % 2 == 0)
155  {
156  b = (number)((unsigned long)b / 2);
157  res++;
158  }
159  return (number)(1L << res); // (2**res)
160 }
161 
162 /*
163  * Give the largest k, such that a = x * k, b = y * k has
164  * a solution.
165  */
166 static number nr2mGcd(number a, number b, const coeffs)
167 {
168  unsigned long res = 0;
169  if ((unsigned long)a == 0 && (unsigned long)b == 0) return (number)1;
170  while ((unsigned long)a % 2 == 0 && (unsigned long)b % 2 == 0)
171  {
172  a = (number)((unsigned long)a / 2);
173  b = (number)((unsigned long)b / 2);
174  res++;
175  }
176 // if ((unsigned long)b % 2 == 0)
177 // {
178 // return (number)((1L << res)); // * (unsigned long) a); // (2**res)*a a is a unit
179 // }
180 // else
181 // {
182  return (number)((1L << res)); // * (unsigned long) b); // (2**res)*b b is a unit
183 // }
184 }
185 
186 /* assumes that 'a' is odd, i.e., a unit in Z/2^m, and computes
187  the extended gcd of 'a' and 2^m, in order to find some 's'
188  and 't' such that a * s + 2^m * t = gcd(a, 2^m) = 1;
189  this code will always find a positive 's' */
190 static void specialXGCD(unsigned long& s, unsigned long a, const coeffs r)
191 {
192  mpz_ptr u = (mpz_ptr)omAlloc(sizeof(mpz_t));
193  mpz_init_set_ui(u, a);
194  mpz_ptr u0 = (mpz_ptr)omAlloc(sizeof(mpz_t));
195  mpz_init(u0);
196  mpz_ptr u1 = (mpz_ptr)omAlloc(sizeof(mpz_t));
197  mpz_init_set_ui(u1, 1);
198  mpz_ptr u2 = (mpz_ptr)omAlloc(sizeof(mpz_t));
199  mpz_init(u2);
200  mpz_ptr v = (mpz_ptr)omAlloc(sizeof(mpz_t));
201  mpz_init_set_ui(v, r->mod2mMask);
202  mpz_add_ui(v, v, 1); /* now: v = 2^m */
203  mpz_ptr v0 = (mpz_ptr)omAlloc(sizeof(mpz_t));
204  mpz_init(v0);
205  mpz_ptr v1 = (mpz_ptr)omAlloc(sizeof(mpz_t));
206  mpz_init(v1);
207  mpz_ptr v2 = (mpz_ptr)omAlloc(sizeof(mpz_t));
208  mpz_init_set_ui(v2, 1);
209  mpz_ptr q = (mpz_ptr)omAlloc(sizeof(mpz_t));
210  mpz_init(q);
211  mpz_ptr rr = (mpz_ptr)omAlloc(sizeof(mpz_t));
212  mpz_init(rr);
213 
214  while (mpz_cmp_ui(v, 0) != 0) /* i.e., while v != 0 */
215  {
216  mpz_div(q, u, v);
217  mpz_mod(rr, u, v);
218  mpz_set(u, v);
219  mpz_set(v, rr);
220  mpz_set(u0, u2);
221  mpz_set(v0, v2);
222  mpz_mul(u2, u2, q); mpz_sub(u2, u1, u2); /* u2 = u1 - q * u2 */
223  mpz_mul(v2, v2, q); mpz_sub(v2, v1, v2); /* v2 = v1 - q * v2 */
224  mpz_set(u1, u0);
225  mpz_set(v1, v0);
226  }
227 
228  while (mpz_cmp_ui(u1, 0) < 0) /* i.e., while u1 < 0 */
229  {
230  /* we add 2^m = (2^m - 1) + 1 to u1: */
231  mpz_add_ui(u1, u1, r->mod2mMask);
232  mpz_add_ui(u1, u1, 1);
233  }
234  s = mpz_get_ui(u1); /* now: 0 <= s <= 2^m - 1 */
235 
236  mpz_clear(u); omFree((ADDRESS)u);
237  mpz_clear(u0); omFree((ADDRESS)u0);
238  mpz_clear(u1); omFree((ADDRESS)u1);
239  mpz_clear(u2); omFree((ADDRESS)u2);
240  mpz_clear(v); omFree((ADDRESS)v);
241  mpz_clear(v0); omFree((ADDRESS)v0);
242  mpz_clear(v1); omFree((ADDRESS)v1);
243  mpz_clear(v2); omFree((ADDRESS)v2);
244  mpz_clear(q); omFree((ADDRESS)q);
245  mpz_clear(rr); omFree((ADDRESS)rr);
246 }
247 
248 static unsigned long InvMod(unsigned long a, const coeffs r)
249 {
250  assume((unsigned long)a % 2 != 0);
251  unsigned long s;
252  specialXGCD(s, a, r);
253  return s;
254 }
255 
256 static inline number nr2mInversM(number c, const coeffs r)
257 {
258  assume((unsigned long)c % 2 != 0);
259  // Table !!!
260  unsigned long inv;
261  inv = InvMod((unsigned long)c,r);
262  return (number)inv;
263 }
264 
265 static number nr2mInvers(number c, const coeffs r)
266 {
267  if ((unsigned long)c % 2 == 0)
268  {
269  WerrorS("division by zero divisor");
270  return (number)0;
271  }
272  return nr2mInversM(c, r);
273 }
274 
275 /*
276  * Give the largest k, such that a = x * k, b = y * k has
277  * a solution.
278  */
279 static number nr2mExtGcd(number a, number b, number *s, number *t, const coeffs r)
280 {
281  unsigned long res = 0;
282  if ((unsigned long)a == 0 && (unsigned long)b == 0) return (number)1;
283  while ((unsigned long)a % 2 == 0 && (unsigned long)b % 2 == 0)
284  {
285  a = (number)((unsigned long)a / 2);
286  b = (number)((unsigned long)b / 2);
287  res++;
288  }
289  if ((unsigned long)b % 2 == 0)
290  {
291  *t = NULL;
292  *s = nr2mInvers(a,r);
293  return (number)((1L << res)); // * (unsigned long) a); // (2**res)*a a is a unit
294  }
295  else
296  {
297  *s = NULL;
298  *t = nr2mInvers(b,r);
299  return (number)((1L << res)); // * (unsigned long) b); // (2**res)*b b is a unit
300  }
301 }
302 
303 static void nr2mPower(number a, int i, number * result, const coeffs r)
304 {
305  if (i == 0)
306  {
307  *(unsigned long *)result = 1;
308  }
309  else if (i == 1)
310  {
311  *result = a;
312  }
313  else
314  {
315  nr2mPower(a, i-1, result, r);
316  *result = nr2mMultM(a, *result, r);
317  }
318 }
319 
320 /*
321  * create a number from int
322  */
323 static number nr2mInit(long i, const coeffs r)
324 {
325  if (i == 0) return (number)(unsigned long)i;
326 
327  long ii = i;
328  unsigned long j = (unsigned long)1;
329  if (ii < 0) { j = r->mod2mMask; ii = -ii; }
330  unsigned long k = (unsigned long)ii;
331  k = k & r->mod2mMask;
332  /* now we have: i = j * k mod 2^m */
333  return (number)nr2mMult((number)j, (number)k, r);
334 }
335 
336 /*
337  * convert a number to an int in ]-k/2 .. k/2],
338  * where k = 2^m; i.e., an int in ]-2^(m-1) .. 2^(m-1)];
339  */
340 static long nr2mInt(number &n, const coeffs r)
341 {
342  unsigned long nn = (unsigned long)(unsigned long)n & r->mod2mMask;
343  unsigned long l = r->mod2mMask >> 1; l++; /* now: l = 2^(m-1) */
344  if ((unsigned long)nn > l)
345  return (long)((unsigned long)nn - r->mod2mMask - 1);
346  else
347  return (long)((unsigned long)nn);
348 }
349 
350 static number nr2mAdd(number a, number b, const coeffs r)
351 {
352  return nr2mAddM(a, b, r);
353 }
354 
355 static number nr2mSub(number a, number b, const coeffs r)
356 {
357  return nr2mSubM(a, b, r);
358 }
359 
360 static BOOLEAN nr2mIsUnit(number a, const coeffs)
361 {
362  return ((unsigned long)a % 2 == 1);
363 }
364 
365 static number nr2mGetUnit(number k, const coeffs)
366 {
367  if (k == NULL) return (number)1;
368  unsigned long erg = (unsigned long)k;
369  while (erg % 2 == 0) erg = erg / 2;
370  return (number)erg;
371 }
372 
373 static BOOLEAN nr2mIsZero(number a, const coeffs)
374 {
375  return 0 == (unsigned long)a;
376 }
377 
378 static BOOLEAN nr2mIsOne(number a, const coeffs)
379 {
380  return 1 == (unsigned long)a;
381 }
382 
383 static BOOLEAN nr2mIsMOne(number a, const coeffs r)
384 {
385  return ((r->mod2mMask == (unsigned long)a) &&(1L!=(long)a))/*for char 2^1*/;
386 }
387 
388 static BOOLEAN nr2mEqual(number a, number b, const coeffs)
389 {
390  return (a == b);
391 }
392 
393 static number nr2mDiv(number a, number b, const coeffs r)
394 {
395  if ((unsigned long)a == 0) return (number)0;
396  else if ((unsigned long)b % 2 == 0)
397  {
398  if ((unsigned long)b != 0)
399  {
400  while (((unsigned long)b % 2 == 0) && ((unsigned long)a % 2 == 0))
401  {
402  a = (number)((unsigned long)a / 2);
403  b = (number)((unsigned long)b / 2);
404  }
405  }
406  if ((unsigned long)b % 2 == 0)
407  {
408  WerrorS("Division not possible, even by cancelling zero divisors.");
409  WerrorS("Result is integer division without remainder.");
410  return (number) ((unsigned long) a / (unsigned long) b);
411  }
412  }
413  return (number)nr2mMult(a, nr2mInversM(b,r),r);
414 }
415 
416 /* Is 'a' divisible by 'b'? There are two cases:
417  1) a = 0 mod 2^m; then TRUE iff b = 0 or b is a power of 2
418  2) a, b <> 0; then TRUE iff b/gcd(a, b) is a unit mod 2^m */
419 static BOOLEAN nr2mDivBy (number a, number b, const coeffs r)
420 {
421  if (a == NULL)
422  {
423  unsigned long c = r->mod2mMask + 1;
424  if (c != 0) /* i.e., if no overflow */
425  return (c % (unsigned long)b) == 0;
426  else
427  {
428  /* overflow: we need to check whether b
429  is zero or a power of 2: */
430  c = (unsigned long)b;
431  while (c != 0)
432  {
433  if ((c % 2) != 0) return FALSE;
434  c = c >> 1;
435  }
436  return TRUE;
437  }
438  }
439  else
440  {
441  number n = nr2mGcd(a, b, r);
442  n = nr2mDiv(b, n, r);
443  return nr2mIsUnit(n, r);
444  }
445 }
446 
447 static BOOLEAN nr2mGreater(number a, number b, const coeffs r)
448 {
449  return nr2mDivBy(a, b,r);
450 }
451 
452 static int nr2mDivComp(number as, number bs, const coeffs)
453 {
454  unsigned long a = (unsigned long)as;
455  unsigned long b = (unsigned long)bs;
456  assume(a != 0 && b != 0);
457  while (a % 2 == 0 && b % 2 == 0)
458  {
459  a = a / 2;
460  b = b / 2;
461  }
462  if (a % 2 == 0)
463  {
464  return -1;
465  }
466  else
467  {
468  if (b % 2 == 1)
469  {
470  return 2;
471  }
472  else
473  {
474  return 1;
475  }
476  }
477 }
478 
479 static number nr2mMod(number a, number b, const coeffs r)
480 {
481  /*
482  We need to return the number rr which is uniquely determined by the
483  following two properties:
484  (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z)
485  (2) There exists some k in the integers Z such that a = k * b + rr.
486  Consider g := gcd(2^m, |b|). Note that then |b|/g is a unit in Z/2^m.
487  Now, there are three cases:
488  (a) g = 1
489  Then |b| is a unit in Z/2^m, i.e. |b| (and also b) divides a.
490  Thus rr = 0.
491  (b) g <> 1 and g divides a
492  Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0.
493  (c) g <> 1 and g does not divide a
494  Let's denote the division with remainder of a by g as follows:
495  a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b|
496  fulfills (1) and (2), i.e. rr := t is the correct result. Hence
497  in this third case, rr is the remainder of division of a by g in Z.
498  This algorithm is the same as for the case Z/n, except that we may
499  compute the gcd of |b| and 2^m "by hand": We just extract the highest
500  power of 2 (<= 2^m) that is contained in b.
501  */
502  assume((unsigned long) b != 0);
503  unsigned long g = 1;
504  unsigned long b_div = (unsigned long) b;
505 
506  /*
507  * b_div is unsigned, so that (b_div < 0) evaluates false at compile-time
508  *
509  if (b_div < 0) b_div = -b_div; // b_div now represents |b|, BUT b_div is unsigned!
510  */
511 
512  unsigned long rr = 0;
513  while ((g < r->mod2mMask ) && (b_div > 0) && (b_div % 2 == 0))
514  {
515  b_div = b_div >> 1;
516  g = g << 1;
517  } // g is now the gcd of 2^m and |b|
518 
519  if (g != 1) rr = (unsigned long)a % g;
520  return (number)rr;
521 }
522 
523 #if 0
524 // unused
525 static number nr2mIntDiv(number a, number b, const coeffs r)
526 {
527  if ((unsigned long)a == 0)
528  {
529  if ((unsigned long)b == 0)
530  return (number)1;
531  if ((unsigned long)b == 1)
532  return (number)0;
533  unsigned long c = r->mod2mMask + 1;
534  if (c != 0) /* i.e., if no overflow */
535  return (number)(c / (unsigned long)b);
536  else
537  {
538  /* overflow: c = 2^32 resp. 2^64, depending on platform */
539  mpz_ptr cc = (mpz_ptr)omAlloc(sizeof(mpz_t));
540  mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1);
541  mpz_div_ui(cc, cc, (unsigned long)(unsigned long)b);
542  unsigned long s = mpz_get_ui(cc);
543  mpz_clear(cc); omFree((ADDRESS)cc);
544  return (number)(unsigned long)s;
545  }
546  }
547  else
548  {
549  if ((unsigned long)b == 0)
550  return (number)0;
551  return (number)((unsigned long) a / (unsigned long) b);
552  }
553 }
554 #endif
555 
556 static number nr2mAnn(number b, const coeffs r)
557 {
558  if ((unsigned long)b == 0)
559  return NULL;
560  if ((unsigned long)b == 1)
561  return NULL;
562  unsigned long c = r->mod2mMask + 1;
563  if (c != 0) /* i.e., if no overflow */
564  return (number)(c / (unsigned long)b);
565  else
566  {
567  /* overflow: c = 2^32 resp. 2^64, depending on platform */
568  mpz_ptr cc = (mpz_ptr)omAlloc(sizeof(mpz_t));
569  mpz_init_set_ui(cc, r->mod2mMask); mpz_add_ui(cc, cc, 1);
570  mpz_div_ui(cc, cc, (unsigned long)(unsigned long)b);
571  unsigned long s = mpz_get_ui(cc);
572  mpz_clear(cc); omFree((ADDRESS)cc);
573  return (number)(unsigned long)s;
574  }
575 }
576 
577 static number nr2mNeg(number c, const coeffs r)
578 {
579  if ((unsigned long)c == 0) return c;
580  return nr2mNegM(c, r);
581 }
582 
583 static number nr2mMapMachineInt(number from, const coeffs /*src*/, const coeffs dst)
584 {
585  unsigned long i = ((unsigned long)from) % dst->mod2mMask ;
586  return (number)i;
587 }
588 
589 static number nr2mMapProject(number from, const coeffs /*src*/, const coeffs dst)
590 {
591  unsigned long i = ((unsigned long)from) % (dst->mod2mMask + 1);
592  return (number)i;
593 }
594 
595 number nr2mMapZp(number from, const coeffs /*src*/, const coeffs dst)
596 {
597  unsigned long j = (unsigned long)1;
598  long ii = (long)from;
599  if (ii < 0) { j = dst->mod2mMask; ii = -ii; }
600  unsigned long i = (unsigned long)ii;
601  i = i & dst->mod2mMask;
602  /* now we have: from = j * i mod 2^m */
603  return (number)nr2mMult((number)i, (number)j, dst);
604 }
605 
606 static number nr2mMapGMP(number from, const coeffs /*src*/, const coeffs dst)
607 {
608  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
609  mpz_init(erg);
610  mpz_ptr k = (mpz_ptr)omAlloc(sizeof(mpz_t));
611  mpz_init_set_ui(k, dst->mod2mMask);
612 
613  mpz_and(erg, (mpz_ptr)from, k);
614  number res = (number) mpz_get_ui(erg);
615 
616  mpz_clear(erg); omFree((ADDRESS)erg);
617  mpz_clear(k); omFree((ADDRESS)k);
618 
619  return (number)res;
620 }
621 
622 static number nr2mMapQ(number from, const coeffs src, const coeffs dst)
623 {
624  mpz_ptr gmp = (mpz_ptr)omAllocBin(gmp_nrz_bin);
625  mpz_init(gmp);
626  nlGMP(from, (number)gmp, src); // FIXME? TODO? // extern void nlGMP(number &i, number n, const coeffs r); // to be replaced with n_MPZ(erg, from, src); // ?
627  number res=nr2mMapGMP((number)gmp,src,dst);
628  mpz_clear(gmp); omFree((ADDRESS)gmp);
629  return res;
630 }
631 
632 static number nr2mMapZ(number from, const coeffs src, const coeffs dst)
633 {
634  if (SR_HDL(from) & SR_INT)
635  {
636  long f_i=SR_TO_INT(from);
637  return nr2mInit(f_i,dst);
638  }
639  return nr2mMapGMP(from,src,dst);
640 }
641 
642 static nMapFunc nr2mSetMap(const coeffs src, const coeffs dst)
643 {
644  if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src)
645  && (src->mod2mMask == dst->mod2mMask))
646  {
647  return ndCopyMap;
648  }
649  if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src)
650  && (src->mod2mMask < dst->mod2mMask))
651  { /* i.e. map an integer mod 2^s into Z mod 2^t, where t < s */
652  return nr2mMapMachineInt;
653  }
654  if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src)
655  && (src->mod2mMask > dst->mod2mMask))
656  { /* i.e. map an integer mod 2^s into Z mod 2^t, where t > s */
657  // to be done
658  return nr2mMapProject;
659  }
660  if ((src->rep==n_rep_gmp) && nCoeff_is_Ring_Z(src))
661  {
662  return nr2mMapGMP;
663  }
664  if ((src->rep==n_rep_gap_gmp) /*&& nCoeff_is_Ring_Z(src)*/)
665  {
666  return nr2mMapZ;
667  }
668  if ((src->rep==n_rep_gap_rat) && (nCoeff_is_Q(src)||nCoeff_is_Ring_Z(src)))
669  {
670  return nr2mMapQ;
671  }
672  if ((src->rep==n_rep_int) && nCoeff_is_Zp(src) && (src->ch == 2))
673  {
674  return nr2mMapZp;
675  }
676  if ((src->rep==n_rep_gmp) &&
678  {
679  if (mpz_divisible_2exp_p(src->modNumber,dst->modExponent))
680  return nr2mMapGMP;
681  }
682  return NULL; // default
683 }
684 
685 /*
686  * set the exponent
687  */
688 
689 static void nr2mSetExp(int m, coeffs r)
690 {
691  if (m > 1)
692  {
693  /* we want mod2mMask to be the bit pattern
694  '111..1' consisting of m one's: */
695  r->modExponent= m;
696  r->mod2mMask = 1;
697  for (int i = 1; i < m; i++) r->mod2mMask = (r->mod2mMask << 1) + 1;
698  }
699  else
700  {
701  r->modExponent= 2;
702  /* code unexpectedly called with m = 1; we continue with m = 2: */
703  r->mod2mMask = 3; /* i.e., '11' in binary representation */
704  }
705 }
706 
707 static void nr2mInitExp(int m, coeffs r)
708 {
709  nr2mSetExp(m, r);
710  if (m < 2)
711  WarnS("nr2mInitExp unexpectedly called with m = 1 (we continue with Z/2^2");
712 }
713 
714 #ifdef LDEBUG
715 static BOOLEAN nr2mDBTest (number a, const char *, const int, const coeffs r)
716 {
717  //if ((unsigned long)a < 0) return FALSE; // is unsigned!
718  if (((unsigned long)a & r->mod2mMask) != (unsigned long)a) return FALSE;
719  return TRUE;
720 }
721 #endif
722 
723 static void nr2mWrite (number a, const coeffs r)
724 {
725  long i = nr2mInt(a, r);
726  StringAppend("%ld", i);
727 }
728 
729 static const char* nr2mEati(const char *s, int *i, const coeffs r)
730 {
731 
732  if (((*s) >= '0') && ((*s) <= '9'))
733  {
734  (*i) = 0;
735  do
736  {
737  (*i) *= 10;
738  (*i) += *s++ - '0';
739  if ((*i) >= (MAX_INT_VAL / 10)) (*i) = (*i) & r->mod2mMask;
740  }
741  while (((*s) >= '0') && ((*s) <= '9'));
742  (*i) = (*i) & r->mod2mMask;
743  }
744  else (*i) = 1;
745  return s;
746 }
747 
748 static const char * nr2mRead (const char *s, number *a, const coeffs r)
749 {
750  int z;
751  int n=1;
752 
753  s = nr2mEati(s, &z,r);
754  if ((*s) == '/')
755  {
756  s++;
757  s = nr2mEati(s, &n,r);
758  }
759  if (n == 1)
760  *a = (number)(long)z;
761  else
762  *a = nr2mDiv((number)(long)z,(number)(long)n,r);
763  return s;
764 }
765 
766 /* for initializing function pointers */
768 {
769  assume( getCoeffType(r) == n_Z2m );
770  nr2mInitExp((int)(long)(p), r);
771 
772  r->is_field=FALSE;
773  r->is_domain=FALSE;
774  r->rep=n_rep_int;
775 
776  //r->cfKillChar = ndKillChar; /* dummy*/
777  r->nCoeffIsEqual = nr2mCoeffIsEqual;
778  r->cfCoeffString = nr2mCoeffString;
779 
780  r->modBase = (mpz_ptr) omAllocBin (gmp_nrz_bin);
781  mpz_init_set_si (r->modBase, 2L);
782  r->modNumber= (mpz_ptr) omAllocBin (gmp_nrz_bin);
783  mpz_init (r->modNumber);
784  mpz_pow_ui (r->modNumber, r->modBase, r->modExponent);
785 
786  /* next cast may yield an overflow as mod2mMask is an unsigned long */
787  r->ch = (int)r->mod2mMask + 1;
788 
789  r->cfInit = nr2mInit;
790  //r->cfCopy = ndCopy;
791  r->cfInt = nr2mInt;
792  r->cfAdd = nr2mAdd;
793  r->cfSub = nr2mSub;
794  r->cfMult = nr2mMult;
795  r->cfDiv = nr2mDiv;
796  r->cfAnn = nr2mAnn;
797  r->cfIntMod = nr2mMod;
798  r->cfExactDiv = nr2mDiv;
799  r->cfInpNeg = nr2mNeg;
800  r->cfInvers = nr2mInvers;
801  r->cfDivBy = nr2mDivBy;
802  r->cfDivComp = nr2mDivComp;
803  r->cfGreater = nr2mGreater;
804  r->cfEqual = nr2mEqual;
805  r->cfIsZero = nr2mIsZero;
806  r->cfIsOne = nr2mIsOne;
807  r->cfIsMOne = nr2mIsMOne;
808  r->cfGreaterZero = nr2mGreaterZero;
809  r->cfWriteLong = nr2mWrite;
810  r->cfRead = nr2mRead;
811  r->cfPower = nr2mPower;
812  r->cfSetMap = nr2mSetMap;
813 // r->cfNormalize = ndNormalize; // default
814  r->cfLcm = nr2mLcm;
815  r->cfGcd = nr2mGcd;
816  r->cfIsUnit = nr2mIsUnit;
817  r->cfGetUnit = nr2mGetUnit;
818  r->cfExtGcd = nr2mExtGcd;
819  r->cfCoeffWrite = nr2mCoeffWrite;
820  r->cfCoeffName = nr2mCoeffName;
821  r->cfQuot1 = nr2mQuot1;
822 #ifdef LDEBUG
823  r->cfDBTest = nr2mDBTest;
824 #endif
825  r->has_simple_Alloc=TRUE;
826  return FALSE;
827 }
828 
829 #endif
830 /* #ifdef HAVE_RINGS */
mpz_t z
Definition: longrat.h:51
#define omAllocBin(bin)
Definition: omAllocDecl.h:205
static number nr2mMultM(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:27
static void nr2mSetExp(int m, coeffs r)
Definition: rmodulo2m.cc:689
const CanonicalForm int s
Definition: facAbsFact.cc:55
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_ModN(const coeffs r)
Definition: coeffs.h:753
static BOOLEAN nr2mGreater(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:447
const poly a
Definition: syzextra.cc:212
omBin_t * omBin
Definition: omStructs.h:12
#define Print
Definition: emacs.cc:83
static char * nr2mCoeffName(const coeffs cf)
Definition: rmodulo2m.cc:51
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
Definition: coeffs.h:834
static number nr2mLcm(number a, number b, const coeffs)
Definition: rmodulo2m.cc:143
static number nr2mAnn(number b, const coeffs r)
Definition: rmodulo2m.cc:556
static BOOLEAN nr2mDivBy(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:419
static void nr2mWrite(number a, const coeffs r)
Definition: rmodulo2m.cc:723
only used if HAVE_RINGS is defined
Definition: coeffs.h:46
#define FALSE
Definition: auxiliary.h:94
return P p
Definition: myNF.cc:203
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
Definition: numbers.cc:244
static unsigned long InvMod(unsigned long a, const coeffs r)
Definition: rmodulo2m.cc:248
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_Z(const coeffs r)
Definition: coeffs.h:759
static number nr2mMapGMP(number from, const coeffs, const coeffs dst)
Definition: rmodulo2m.cc:606
{p < 2^31}
Definition: coeffs.h:30
#define nr2mNegM(A, r)
Definition: rmodulo2m.cc:46
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_2toM(const coeffs r)
Definition: coeffs.h:750
(), see rinteger.h, new impl.
Definition: coeffs.h:112
static long nr2mInt(number &n, const coeffs r)
Definition: rmodulo2m.cc:340
static number nr2mDiv(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:393
#define TRUE
Definition: auxiliary.h:98
static number nr2mGetUnit(number k, const coeffs)
Definition: rmodulo2m.cc:365
static BOOLEAN nr2mIsZero(number a, const coeffs)
Definition: rmodulo2m.cc:373
number nr2mMapZp(number from, const coeffs, const coeffs dst)
Definition: rmodulo2m.cc:595
static number nr2mMapMachineInt(number from, const coeffs, const coeffs dst)
Definition: rmodulo2m.cc:583
void * ADDRESS
Definition: auxiliary.h:115
g
Definition: cfModGcd.cc:4031
void WerrorS(const char *s)
Definition: feFopen.cc:24
int k
Definition: cfEzgcd.cc:93
BOOLEAN nr2mInitChar(coeffs r, void *p)
Definition: rmodulo2m.cc:767
void nlGMP(number &i, number n, const coeffs r)
Definition: longrat.cc:1482
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
Definition: coeffs.h:840
#define WarnS
Definition: emacs.cc:81
#define omAlloc(size)
Definition: omAllocDecl.h:210
static BOOLEAN nr2mCoeffIsEqual(const coeffs r, n_coeffType n, void *p)
Definition: rmodulo2m.cc:63
static number nr2mNeg(number c, const coeffs r)
Definition: rmodulo2m.cc:577
static BOOLEAN nr2mIsOne(number a, const coeffs)
Definition: rmodulo2m.cc:378
poly res
Definition: myNF.cc:322
static number nr2mMapProject(number from, const coeffs, const coeffs dst)
Definition: rmodulo2m.cc:589
mpz_t n
Definition: longrat.h:52
const ring r
Definition: syzextra.cc:208
#define LDEBUG
Definition: mod2.h:312
Coefficient rings, fields and other domains suitable for Singular polynomials.
static const char * nr2mRead(const char *s, number *a, const coeffs r)
Definition: rmodulo2m.cc:748
int j
Definition: myNF.cc:70
#define omFree(addr)
Definition: omAllocDecl.h:261
#define assume(x)
Definition: mod2.h:394
The main handler for Singular numbers which are suitable for Singular polynomials.
static number nr2mInversM(number c, const coeffs r)
Definition: rmodulo2m.cc:256
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:73
static coeffs nr2mQuot1(number c, const coeffs r)
Definition: rmodulo2m.cc:82
static char * nr2mCoeffString(const coeffs r)
Definition: rmodulo2m.cc:74
const int MAX_INT_VAL
Definition: mylimits.h:12
All the auxiliary stuff.
int m
Definition: cfEzgcd.cc:119
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_PtoM(const coeffs r)
Definition: coeffs.h:756
static int nr2mDivComp(number as, number bs, const coeffs)
Definition: rmodulo2m.cc:452
#define StringAppend
Definition: emacs.cc:82
int i
Definition: cfEzgcd.cc:123
static void nr2mInitExp(int m, coeffs r)
Definition: rmodulo2m.cc:707
static BOOLEAN nr2mGreaterZero(number k, const coeffs r)
Definition: rmodulo2m.cc:121
(mpz_ptr), see rmodulon,h
Definition: coeffs.h:115
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:425
static const char * nr2mEati(const char *s, int *i, const coeffs r)
Definition: rmodulo2m.cc:729
static number nr2mMult(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:131
static BOOLEAN nr2mDBTest(number a, const char *, const int, const coeffs r)
Definition: rmodulo2m.cc:715
#define SR_TO_INT(SR)
Definition: longrat.h:70
(number), see longrat.h
Definition: coeffs.h:111
static number nr2mExtGcd(number a, number b, number *s, number *t, const coeffs r)
Definition: rmodulo2m.cc:279
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:37
static BOOLEAN nr2mIsMOne(number a, const coeffs r)
Definition: rmodulo2m.cc:383
n_coeffType
Definition: coeffs.h:27
CanonicalForm cf
Definition: cfModGcd.cc:4024
#define NULL
Definition: omList.c:10
static BOOLEAN nr2mEqual(number a, number b, const coeffs)
Definition: rmodulo2m.cc:388
static number nr2mInvers(number c, const coeffs r)
Definition: rmodulo2m.cc:265
static number nr2mAddM(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:33
static number nr2mSub(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:355
int gcd(int a, int b)
Definition: walkSupport.cc:839
#define SR_INT
Definition: longrat.h:68
static BOOLEAN nr2mIsUnit(number a, const coeffs)
Definition: rmodulo2m.cc:360
static void nr2mCoeffWrite(const coeffs r, BOOLEAN)
Definition: rmodulo2m.cc:58
static number nr2mMapQ(number from, const coeffs src, const coeffs dst)
Definition: rmodulo2m.cc:622
static number nr2mSubM(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:39
static number nr2mInit(long i, const coeffs r)
Definition: rmodulo2m.cc:323
omBin gmp_nrz_bin
Definition: rintegers.cc:31
(int), see modulop.h
Definition: coeffs.h:110
#define SR_HDL(A)
Definition: tgb.cc:35
static number nr2mGcd(number a, number b, const coeffs)
Definition: rmodulo2m.cc:166
static number nr2mAdd(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:350
static number nr2mMapZ(number from, const coeffs src, const coeffs dst)
Definition: rmodulo2m.cc:632
int BOOLEAN
Definition: auxiliary.h:85
const poly b
Definition: syzextra.cc:213
static void nr2mPower(number a, int i, number *result, const coeffs r)
Definition: rmodulo2m.cc:303
static nMapFunc nr2mSetMap(const coeffs src, const coeffs dst)
Definition: rmodulo2m.cc:642
static number nr2mMod(number a, number b, const coeffs r)
Definition: rmodulo2m.cc:479
int l
Definition: cfEzgcd.cc:94
return result
Definition: facAbsBiFact.cc:76
static void specialXGCD(unsigned long &s, unsigned long a, const coeffs r)
Definition: rmodulo2m.cc:190
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
Definition: numbers.cc:341