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
npMultM(number a,number b,const coeffs r)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 }
npInpMultM(number & a,number b,const coeffs r)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
npMultM(number a,number b,const coeffs r)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 }
npInpMultM(number & a,number b,const coeffs r)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
npAddM(number a,number b,const coeffs r)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 }
npInpAddM(number & a,number b,const coeffs r)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 }
npSubM(number a,number b,const coeffs r)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
npAddM(number a,number b,const coeffs r)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 }
npInpAddM(number & a,number b,const coeffs r)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 }
npSubM(number a,number b,const coeffs r)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
npNegM(number a,const coeffs r)166 static inline number npNegM(number a, const coeffs r)
167 {
168 return (number)((long)(r->ch)-(long)(a));
169 }
170
npIsOne(number a,const coeffs)171 static inline BOOLEAN npIsOne (number a, const coeffs)
172 {
173 return 1 == (long)a;
174 }
175
npInvMod(long a,const coeffs R)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
npInversM(number c,const coeffs r)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
254