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modulop.h
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1 #ifndef MODULOP_H
2 #define MODULOP_H
3 /****************************************
4 * Computer Algebra System SINGULAR *
5 ****************************************/
6 /*
7 * ABSTRACT: numbers modulo p (<=32749)
8 */
9 #include "misc/auxiliary.h"
10 
11 
12 // define if a*b is with mod instead of tables
13 //#define HAVE_GENERIC_MULT
14 // define if 1/b is from tables
15 //#define HAVE_INVTABLE
16 // define if an if should be used
17 //#define HAVE_GENERIC_ADD
18 
19 //#undef HAVE_GENERIC_ADD
20 //#undef HAVE_GENERIC_MULT
21 //#undef HAVE_INVTABLE
22 
23 //#define HAVE_GENERIC_ADD 1
24 //#define HAVE_GENERIC_MULT 1
25 //#define HAVE_INVTABLE 1
26 
27 // enable large primes (32749 < p < 2^31-)
28 #define NV_OPS
29 #define NV_MAX_PRIME 32749
30 #define FACTORY_MAX_PRIME 536870909
31 
32 struct n_Procs_s; typedef struct n_Procs_s *coeffs;
33 struct snumber; typedef struct snumber * number;
34 
35 BOOLEAN npInitChar(coeffs r, void* p);
36 
37 // inline number npMultM(number a, number b, int npPrimeM)
38 // // return (a*b)%n
39 // {
40 // double ab;
41 // long q, res;
42 //
43 // ab = ((double) ((int)a)) * ((double) ((int)b));
44 // q = (long) (ab/((double) npPrimeM)); // q could be off by (+/-) 1
45 // res = (long) (ab - ((double) q)*((double) npPrimeM));
46 // res += (res >> 31) & npPrimeM;
47 // res -= npPrimeM;
48 // res += (res >> 31) & npPrimeM;
49 // return (number)res;
50 // }
51 #ifdef HAVE_GENERIC_MULT
52 static inline number npMultM(number a, number b, const coeffs r)
53 {
54  return (number)
55  ((((unsigned long) a)*((unsigned long) b)) % ((unsigned long) r->ch));
56 }
57 static inline void npInpMultM(number &a, number b, const coeffs r)
58 {
59  a=(number)
60  ((((unsigned long) a)*((unsigned long) b)) % ((unsigned long) r->ch));
61 }
62 #else
63 static inline number npMultM(number a, number b, const coeffs r)
64 {
65  long x = (long)r->npLogTable[(long)a]+ r->npLogTable[(long)b];
66  #ifdef HAVE_GENERIC_ADD
67  if (x>=r->npPminus1M) x-=r->npPminus1M;
68  #else
69  x-=r->npPminus1M;
70  #if SIZEOF_LONG == 8
71  x += (x >> 63) & r->npPminus1M;
72  #else
73  x += (x >> 31) & r->npPminus1M;
74  #endif
75  #endif
76  return (number)(long)r->npExpTable[x];
77 }
78 static inline void npInpMultM(number &a, number b, const coeffs r)
79 {
80  long x = (long)r->npLogTable[(long)a]+ r->npLogTable[(long)b];
81  #ifdef HAVE_GENERIC_ADD
82  if (x>=r->npPminus1M) x-=r->npPminus1M;
83  #else
84  x-=r->npPminus1M;
85  #if SIZEOF_LONG == 8
86  x += (x >> 63) & r->npPminus1M;
87  #else
88  x += (x >> 31) & r->npPminus1M;
89  #endif
90  #endif
91  a=(number)(long)r->npExpTable[x];
92 }
93 #endif
94 
95 #if 0
96 inline number npAddAsm(number a, number b, int m)
97 {
98  number r;
99  asm ("addl %2, %1; cmpl %3, %1; jb 0f; subl %3, %1; 0:"
100  : "=&r" (r)
101  : "%0" (a), "g" (b), "g" (m)
102  : "cc");
103  return r;
104 }
105 inline number npSubAsm(number a, number b, int m)
106 {
107  number r;
108  asm ("subl %2, %1; jnc 0f; addl %3, %1; 0:"
109  : "=&r" (r)
110  : "%0" (a), "g" (b), "g" (m)
111  : "cc");
112  return r;
113 }
114 #endif
115 #ifdef HAVE_GENERIC_ADD
116 static inline number npAddM(number a, number b, const coeffs r)
117 {
118  unsigned long R = (unsigned long)a + (unsigned long)b;
119  return (number)(R >= (unsigned long)r->ch ? R - (unsigned long)r->ch : R);
120 }
121 static inline void npInpAddM(number &a, number b, const coeffs r)
122 {
123  unsigned long R = (unsigned long)a + (unsigned long)b;
124  a=(number)(R >= (unsigned long)r->ch ? R - (unsigned long)r->ch : R);
125 }
126 static inline number npSubM(number a, number b, const coeffs r)
127 {
128  return (number)((long)a<(long)b ?
129  r->ch-(long)b+(long)a : (long)a-(long)b);
130 }
131 #else
132 static inline number npAddM(number a, number b, const coeffs r)
133 {
134  unsigned long res = ((unsigned long)a + (unsigned long)b);
135  res -= r->ch;
136 #if SIZEOF_LONG == 8
137  res += ((long)res >> 63) & r->ch;
138 #else
139  res += ((long)res >> 31) & r->ch;
140 #endif
141  return (number)res;
142 }
143 static inline void npInpAddM(number &a, number b, const coeffs r)
144 {
145  unsigned long res = ((unsigned long)a + (unsigned long)b);
146  res -= r->ch;
147 #if SIZEOF_LONG == 8
148  res += ((long)res >> 63) & r->ch;
149 #else
150  res += ((long)res >> 31) & r->ch;
151 #endif
152  a=(number)res;
153 }
154 static inline number npSubM(number a, number b, const coeffs r)
155 {
156  long res = ((long)a - (long)b);
157 #if SIZEOF_LONG == 8
158  res += (res >> 63) & r->ch;
159 #else
160  res += (res >> 31) & r->ch;
161 #endif
162  return (number)res;
163 }
164 #endif
165 
166 static inline number npNegM(number a, const coeffs r)
167 {
168  return (number)((long)(r->ch)-(long)(a));
169 }
170 
171 static inline BOOLEAN npIsOne (number a, const coeffs)
172 {
173  return 1 == (long)a;
174 }
175 
176 static inline long npInvMod(long a, const coeffs R)
177 {
178  long s;
179 
180  long u, v, u0, u1, u2, q, r;
181 
182  assume(a>0);
183  u1=1; u2=0;
184  u = a; v = R->ch;
185 
186  do
187  {
188  q = u / v;
189  //r = u % v;
190  r = u - q*v;
191  u = v;
192  v = r;
193  u0 = u2;
194  u2 = u1 - q*u2;
195  u1 = u0;
196  } while (v != 0);
197 
198  assume(u==1);
199  s = u1;
200 #ifdef HAVE_GENERIC_ADD
201  if (s < 0)
202  return s + R->ch;
203  else
204  return s;
205 #else
206  #if SIZEOF_LONG == 8
207  s += (s >> 63) & R->ch;
208  #else
209  s += (s >> 31) & R->ch;
210  #endif
211  return s;
212 #endif
213 }
214 
215 static inline number npInversM (number c, const coeffs r)
216 {
217  n_Test(c, r);
218 #ifndef HAVE_GENERIC_MULT
219  #ifndef HAVE_INVTABLE
220  number d = (number)(long)r->npExpTable[r->npPminus1M - r->npLogTable[(long)c]];
221  #else
222  long inv=(long)r->npInvTable[(long)c];
223  if (inv==0)
224  {
225  inv = (long)r->npExpTable[r->npPminus1M - r->npLogTable[(long)c]];
226  r->npInvTable[(long)c]=inv;
227  }
228  number d = (number)inv;
229  #endif
230 #else
231  #ifdef HAVE_INVTABLE
232  long inv=(long)r->npInvTable[(long)c];
233  if (inv==0)
234  {
235  inv=npInvMod((long)c,r);
236  r->npInvTable[(long)c]=inv;
237  }
238  #else
239  long inv=npInvMod((long)c,r);
240  #endif
241  number d = (number)inv;
242 #endif
243  n_Test(d, r);
244  return d;
245 }
246 
247 
248 // The folloing is reused inside gnumpc.cc, gnumpfl.cc and longrat.cc
249 long npInt (number &n, const coeffs r);
250 
251 #define npEqualM(A,B,r) ((A)==(B))
252 
253 #endif
All the auxiliary stuff.
int BOOLEAN
Definition: auxiliary.h:87
int m
Definition: cfEzgcd.cc:128
Variable x
Definition: cfModGcd.cc:4084
int p
Definition: cfModGcd.cc:4080
CanonicalForm b
Definition: cfModGcd.cc:4105
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
Definition: coeffs.h:736
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
mpz_t n
Definition: longrat.h:51
'SR_INT' is the type of those integers small enough to fit into 29 bits.
Definition: longrat.h:49
#define assume(x)
Definition: mod2.h:387
static BOOLEAN npIsOne(number a, const coeffs)
Definition: modulop.h:171
static number npAddM(number a, number b, const coeffs r)
Definition: modulop.h:116
static number npMultM(number a, number b, const coeffs r)
Definition: modulop.h:63
BOOLEAN npInitChar(coeffs r, void *p)
Definition: modulop.cc:340
static number npNegM(number a, const coeffs r)
Definition: modulop.h:166
static void npInpMultM(number &a, number b, const coeffs r)
Definition: modulop.h:78
static long npInvMod(long a, const coeffs R)
Definition: modulop.h:176
static number npInversM(number c, const coeffs r)
Definition: modulop.h:215
long npInt(number &n, const coeffs r)
Definition: modulop.cc:85
static void npInpAddM(number &a, number b, const coeffs r)
Definition: modulop.h:121
static number npSubM(number a, number b, const coeffs r)
Definition: modulop.h:126
The main handler for Singular numbers which are suitable for Singular polynomials.
#define R
Definition: sirandom.c:27