[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* |
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[a1299c] | 5 | * ABSTRACT: numbers modulo p (<=32749) |
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[35aab3] | 6 | */ |
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| 7 | |
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[22a09d] | 8 | #include <misc/auxiliary.h> |
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[2206753] | 9 | #include <omalloc/omalloc.h> |
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[22a09d] | 10 | |
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| 11 | #include <factory/factory.h> |
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| 12 | |
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[2206753] | 13 | #include <misc/mylimits.h> |
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| 14 | #include <misc/sirandom.h> |
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| 15 | |
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[31213a4] | 16 | #include <reporter/reporter.h> |
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[2206753] | 17 | |
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| 18 | #include <coeffs/coeffs.h> |
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[2d805a] | 19 | #include <coeffs/numbers.h> |
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| 20 | #include <coeffs/mpr_complex.h> |
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[35aab3] | 21 | |
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[2206753] | 22 | #include "longrat.h" |
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| 23 | #include "modulop.h" |
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| 24 | |
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| 25 | #include <string.h> |
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| 26 | |
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| 27 | BOOLEAN npGreaterZero (number k, const coeffs r); |
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| 28 | number npMult (number a, number b, const coeffs r); |
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| 29 | number npInit (long i, const coeffs r); |
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[777f8b] | 30 | long npInt (number &n, const coeffs r); |
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[2206753] | 31 | number npAdd (number a, number b,const coeffs r); |
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| 32 | number npSub (number a, number b,const coeffs r); |
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| 33 | void npPower (number a, int i, number * result,const coeffs r); |
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| 34 | BOOLEAN npIsZero (number a,const coeffs r); |
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| 35 | BOOLEAN npIsOne (number a,const coeffs r); |
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| 36 | BOOLEAN npIsMOne (number a,const coeffs r); |
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| 37 | number npDiv (number a, number b,const coeffs r); |
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| 38 | number npNeg (number c,const coeffs r); |
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| 39 | number npInvers (number c,const coeffs r); |
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| 40 | BOOLEAN npGreater (number a, number b,const coeffs r); |
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| 41 | BOOLEAN npEqual (number a, number b,const coeffs r); |
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[6d92ca] | 42 | void npWrite (number a, const coeffs r); |
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[2206753] | 43 | void npCoeffWrite (const coeffs r, BOOLEAN details); |
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| 44 | const char * npRead (const char *s, number *a,const coeffs r); |
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[fc2acf] | 45 | |
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[2206753] | 46 | #ifdef LDEBUG |
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| 47 | BOOLEAN npDBTest (number a, const char *f, const int l, const coeffs r); |
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| 48 | #endif |
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| 49 | |
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| 50 | //int npGetChar(); |
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| 51 | |
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| 52 | nMapFunc npSetMap(const coeffs src, const coeffs dst); |
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| 53 | number npMapP(number from, const coeffs src, const coeffs r); |
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| 54 | |
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| 55 | // extern int npGen; // obsolete |
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| 56 | |
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| 57 | // int npGen=0; |
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| 58 | |
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| 59 | /*-------specials for spolys, do NOT use otherwise--------------------------*/ |
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| 60 | /* for npMultM, npSubM, npNegM, npEqualM : */ |
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| 61 | #ifdef HAVE_DIV_MOD |
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| 62 | extern unsigned short *npInvTable; |
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| 63 | #else |
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| 64 | #ifndef HAVE_MULT_MOD |
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| 65 | extern long npPminus1M; |
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| 66 | extern unsigned short *npExpTable; |
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| 67 | extern unsigned short *npLogTable; |
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| 68 | #endif |
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| 69 | #endif |
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| 70 | |
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[40e88db] | 71 | #ifdef NV_OPS |
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| 72 | #pragma GCC diagnostic ignored "-Wlong-long" |
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| 73 | static inline number nvMultM(number a, number b, const coeffs r) |
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| 74 | { |
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[6d0515d] | 75 | assume( getCoeffType(r) == n_Zp ); |
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[601105] | 76 | |
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[40e88db] | 77 | #if SIZEOF_LONG == 4 |
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| 78 | #define ULONG64 (unsigned long long)(unsigned long) |
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| 79 | #else |
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| 80 | #define ULONG64 (unsigned long) |
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| 81 | #endif |
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[601105] | 82 | return (number) |
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[40e88db] | 83 | (unsigned long)((ULONG64 a)*(ULONG64 b) % (ULONG64 r->ch)); |
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| 84 | } |
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| 85 | number nvMult (number a, number b, const coeffs r); |
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| 86 | number nvDiv (number a, number b, const coeffs r); |
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| 87 | number nvInvers (number c, const coeffs r); |
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[cc16f0] | 88 | //void nvPower (number a, int i, number * result, const coeffs r); |
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[40e88db] | 89 | #endif |
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| 90 | |
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| 91 | |
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| 92 | |
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| 93 | |
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[7d90aa] | 94 | BOOLEAN npGreaterZero (number k, const coeffs r) |
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[35aab3] | 95 | { |
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[eb55f8a] | 96 | n_Test(k, r); |
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[601105] | 97 | |
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[7447d8] | 98 | int h = (int)((long) k); |
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[e77676] | 99 | return ((int)h !=0) && (h <= (r->ch>>1)); |
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[35aab3] | 100 | } |
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| 101 | |
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[e77676] | 102 | //unsigned long npMultMod(unsigned long a, unsigned long b, int npPrimeM) |
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[35aab3] | 103 | //{ |
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| 104 | // unsigned long c = a*b; |
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| 105 | // c = c % npPrimeM; |
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[e77676] | 106 | // assume(c == (unsigned long) npMultM((number) a, (number) b, npPrimeM)); |
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[35aab3] | 107 | // return c; |
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| 108 | //} |
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| 109 | |
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[7d90aa] | 110 | number npMult (number a,number b, const coeffs r) |
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[35aab3] | 111 | { |
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[eb55f8a] | 112 | n_Test(a, r); |
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| 113 | n_Test(b, r); |
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[0461f0] | 114 | |
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[35aab3] | 115 | if (((long)a == 0) || ((long)b == 0)) |
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| 116 | return (number)0; |
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[0461f0] | 117 | number c = npMultM(a,b, r); |
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[eb55f8a] | 118 | n_Test(c, r); |
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[601105] | 119 | return c; |
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[35aab3] | 120 | } |
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| 121 | |
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| 122 | /*2 |
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| 123 | * create a number from int |
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| 124 | */ |
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[2f3764] | 125 | number npInit (long i, const coeffs r) |
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[35aab3] | 126 | { |
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[d8b0997] | 127 | long ii=i % (long)r->ch; |
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| 128 | if (ii < 0L) ii += (long)r->ch; |
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| 129 | |
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[0461f0] | 130 | number c = (number)ii; |
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[eb55f8a] | 131 | n_Test(c, r); |
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[0461f0] | 132 | return c; |
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[601105] | 133 | |
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[35aab3] | 134 | } |
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| 135 | |
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[0461f0] | 136 | |
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[35aab3] | 137 | /*2 |
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[0461f0] | 138 | * convert a number to an int in (-p/2 .. p/2] |
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| 139 | */ |
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[777f8b] | 140 | long npInt(number &n, const coeffs r) |
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[35aab3] | 141 | { |
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[eb55f8a] | 142 | n_Test(n, r); |
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[601105] | 143 | |
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[777f8b] | 144 | if ((long)n > (((long)r->ch) >>1)) return ((long)n -((long)r->ch)); |
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| 145 | else return ((long)n); |
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[35aab3] | 146 | } |
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| 147 | |
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[7d90aa] | 148 | number npAdd (number a, number b, const coeffs r) |
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[35aab3] | 149 | { |
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[eb55f8a] | 150 | n_Test(a, r); |
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| 151 | n_Test(b, r); |
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[601105] | 152 | |
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[0461f0] | 153 | number c = npAddM(a,b, r); |
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| 154 | |
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[eb55f8a] | 155 | n_Test(c, r); |
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[601105] | 156 | |
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[0461f0] | 157 | return c; |
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[35aab3] | 158 | } |
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| 159 | |
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[7d90aa] | 160 | number npSub (number a, number b, const coeffs r) |
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[35aab3] | 161 | { |
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[eb55f8a] | 162 | n_Test(a, r); |
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| 163 | n_Test(b, r); |
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[601105] | 164 | |
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[0461f0] | 165 | number c = npSubM(a,b,r); |
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| 166 | |
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[eb55f8a] | 167 | n_Test(c, r); |
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[0461f0] | 168 | |
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| 169 | return c; |
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[35aab3] | 170 | } |
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| 171 | |
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[0461f0] | 172 | BOOLEAN npIsZero (number a, const coeffs r) |
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[35aab3] | 173 | { |
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[eb55f8a] | 174 | n_Test(a, r); |
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[601105] | 175 | |
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[35aab3] | 176 | return 0 == (long)a; |
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| 177 | } |
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| 178 | |
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[0461f0] | 179 | BOOLEAN npIsOne (number a, const coeffs r) |
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[35aab3] | 180 | { |
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[eb55f8a] | 181 | n_Test(a, r); |
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[601105] | 182 | |
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[35aab3] | 183 | return 1 == (long)a; |
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| 184 | } |
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| 185 | |
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[7d90aa] | 186 | BOOLEAN npIsMOne (number a, const coeffs r) |
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[35aab3] | 187 | { |
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[eb55f8a] | 188 | n_Test(a, r); |
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[601105] | 189 | |
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[961c76] | 190 | return ((r->npPminus1M == (long)a) &&(1L!=(long)a))/*for char 2*/; |
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[35aab3] | 191 | } |
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| 192 | |
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| 193 | #ifdef HAVE_DIV_MOD |
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[a74143] | 194 | |
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[1fc18b] | 195 | #ifdef USE_NTL_XGCD |
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[a74143] | 196 | |
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[1fc18b] | 197 | //ifdef HAVE_NTL // in ntl.a |
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[35aab3] | 198 | //extern void XGCD(long& d, long& s, long& t, long a, long b); |
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| 199 | #include <NTL/ZZ.h> |
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| 200 | #ifdef NTL_CLIENT |
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| 201 | NTL_CLIENT |
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| 202 | #endif |
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[a74143] | 203 | |
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[1fc18b] | 204 | #endif |
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[35aab3] | 205 | |
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[7d90aa] | 206 | long InvMod(long a, const coeffs R) |
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[1fc18b] | 207 | { |
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| 208 | long d, s, t; |
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[35aab3] | 209 | |
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[1fc18b] | 210 | #ifdef USE_NTL_XGCD |
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[e77676] | 211 | XGCD(d, s, t, a, R->ch); |
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[1fc18b] | 212 | assume (d == 1); |
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| 213 | #else |
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| 214 | long u, v, u0, v0, u1, v1, u2, v2, q, r; |
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[35aab3] | 215 | |
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[1fc18b] | 216 | assume(a>0); |
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| 217 | u1=1; u2=0; |
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[e77676] | 218 | u = a; v = R->ch; |
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[35aab3] | 219 | |
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[1fc18b] | 220 | while (v != 0) |
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| 221 | { |
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[35aab3] | 222 | q = u / v; |
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| 223 | r = u % v; |
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| 224 | u = v; |
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| 225 | v = r; |
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| 226 | u0 = u2; |
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[1fc18b] | 227 | u2 = u1 - q*u2; |
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[35aab3] | 228 | u1 = u0; |
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| 229 | } |
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| 230 | |
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[1fc18b] | 231 | assume(u==1); |
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[35aab3] | 232 | s = u1; |
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| 233 | #endif |
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| 234 | if (s < 0) |
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[e77676] | 235 | return s + R->ch; |
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[35aab3] | 236 | else |
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| 237 | return s; |
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| 238 | } |
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| 239 | #endif |
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| 240 | |
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[7d90aa] | 241 | inline number npInversM (number c, const coeffs r) |
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[35aab3] | 242 | { |
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[eb55f8a] | 243 | n_Test(c, r); |
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[35aab3] | 244 | #ifndef HAVE_DIV_MOD |
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[0461f0] | 245 | number d = (number)(long)r->npExpTable[r->npPminus1M - r->npLogTable[(long)c]]; |
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[35aab3] | 246 | #else |
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[7d90aa] | 247 | long inv=(long)r->npInvTable[(long)c]; |
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[35aab3] | 248 | if (inv==0) |
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| 249 | { |
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[7d90aa] | 250 | inv=InvMod((long)c,r); |
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| 251 | r->npInvTable[(long)c]=inv; |
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[35aab3] | 252 | } |
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[0461f0] | 253 | number d = (number)inv; |
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[35aab3] | 254 | #endif |
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[eb55f8a] | 255 | n_Test(d, r); |
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[0461f0] | 256 | return d; |
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| 257 | |
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[35aab3] | 258 | } |
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| 259 | |
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[7d90aa] | 260 | number npDiv (number a,number b, const coeffs r) |
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[35aab3] | 261 | { |
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[eb55f8a] | 262 | n_Test(a, r); |
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| 263 | n_Test(b, r); |
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[0461f0] | 264 | |
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[6c15ec] | 265 | //#ifdef NV_OPS |
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[e77676] | 266 | // if (r->ch>NV_MAX_PRIME) |
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[6c15ec] | 267 | // return nvDiv(a,b); |
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| 268 | //#endif |
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[9b88e6] | 269 | if ((long)a==0L) |
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| 270 | return (number)0L; |
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[0461f0] | 271 | number d; |
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[601105] | 272 | |
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[35aab3] | 273 | #ifndef HAVE_DIV_MOD |
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[9b88e6] | 274 | if ((long)b==0L) |
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[35aab3] | 275 | { |
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[b7e838] | 276 | WerrorS(nDivBy0); |
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[9b88e6] | 277 | return (number)0L; |
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[35aab3] | 278 | } |
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[601105] | 279 | |
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[0461f0] | 280 | int s = r->npLogTable[(long)a] - r->npLogTable[(long)b]; |
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| 281 | if (s < 0) |
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| 282 | s += r->npPminus1M; |
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| 283 | d = (number)(long)r->npExpTable[s]; |
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[35aab3] | 284 | #else |
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[7d90aa] | 285 | number inv=npInversM(b,r); |
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[0461f0] | 286 | d = npMultM(a,inv,r); |
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[35aab3] | 287 | #endif |
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[0461f0] | 288 | |
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[eb55f8a] | 289 | n_Test(d, r); |
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[0461f0] | 290 | return d; |
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[601105] | 291 | |
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[35aab3] | 292 | } |
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[7d90aa] | 293 | number npInvers (number c, const coeffs r) |
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[35aab3] | 294 | { |
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[eb55f8a] | 295 | n_Test(c, r); |
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[601105] | 296 | |
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[9b88e6] | 297 | if ((long)c==0L) |
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[35aab3] | 298 | { |
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| 299 | WerrorS("1/0"); |
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[9b88e6] | 300 | return (number)0L; |
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[35aab3] | 301 | } |
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[0461f0] | 302 | number d = npInversM(c,r); |
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[601105] | 303 | |
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[eb55f8a] | 304 | n_Test(d, r); |
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[0461f0] | 305 | return d; |
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[601105] | 306 | |
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[35aab3] | 307 | } |
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| 308 | |
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[7d90aa] | 309 | number npNeg (number c, const coeffs r) |
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[35aab3] | 310 | { |
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[eb55f8a] | 311 | n_Test(c, r); |
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[601105] | 312 | |
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[9b88e6] | 313 | if ((long)c==0L) return c; |
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[0461f0] | 314 | |
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[601105] | 315 | #if 0 |
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| 316 | number d = npNegM(c,r); |
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[eb55f8a] | 317 | n_Test(d, r); |
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[0461f0] | 318 | return d; |
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| 319 | #else |
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[601105] | 320 | c = npNegM(c,r); |
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[eb55f8a] | 321 | n_Test(c, r); |
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[0461f0] | 322 | return c; |
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[601105] | 323 | #endif |
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[35aab3] | 324 | } |
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| 325 | |
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[0461f0] | 326 | BOOLEAN npGreater (number a,number b, const coeffs r) |
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[35aab3] | 327 | { |
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[eb55f8a] | 328 | n_Test(a, r); |
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| 329 | n_Test(b, r); |
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[0461f0] | 330 | |
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[35aab3] | 331 | //return (long)a != (long)b; |
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[9b88e6] | 332 | return ((long)a) > ((long)b); |
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[35aab3] | 333 | } |
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| 334 | |
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[7d90aa] | 335 | BOOLEAN npEqual (number a,number b, const coeffs r) |
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[35aab3] | 336 | { |
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[eb55f8a] | 337 | n_Test(a, r); |
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| 338 | n_Test(b, r); |
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[601105] | 339 | |
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[35aab3] | 340 | // return (long)a == (long)b; |
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[601105] | 341 | |
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[7d90aa] | 342 | return npEqualM(a,b,r); |
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[35aab3] | 343 | } |
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| 344 | |
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[6d92ca] | 345 | void npWrite (number a, const coeffs r) |
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[35aab3] | 346 | { |
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[eb55f8a] | 347 | n_Test(a, r); |
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[601105] | 348 | |
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[493225] | 349 | if ((long)a>(((long)r->ch) >>1)) StringAppend("-%d",(int)(((long)r->ch)-((long)a))); |
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| 350 | else StringAppend("%d",(int)((long)a)); |
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[35aab3] | 351 | } |
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| 352 | |
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[cc16f0] | 353 | #if 0 |
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[7d90aa] | 354 | void npPower (number a, int i, number * result, const coeffs r) |
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[35aab3] | 355 | { |
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[eb55f8a] | 356 | n_Test(a, r); |
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[0461f0] | 357 | |
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[35aab3] | 358 | if (i==0) |
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| 359 | { |
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| 360 | //npInit(1,result); |
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| 361 | *(long *)result = 1; |
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| 362 | } |
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| 363 | else if (i==1) |
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| 364 | { |
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| 365 | *result = a; |
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| 366 | } |
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| 367 | else |
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| 368 | { |
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[7d90aa] | 369 | npPower(a,i-1,result,r); |
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| 370 | *result = npMultM(a,*result,r); |
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[35aab3] | 371 | } |
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| 372 | } |
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[cc16f0] | 373 | #endif |
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[35aab3] | 374 | |
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[7d90aa] | 375 | static const char* npEati(const char *s, int *i, const coeffs r) |
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[35aab3] | 376 | { |
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| 377 | |
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| 378 | if (((*s) >= '0') && ((*s) <= '9')) |
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| 379 | { |
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[923b64] | 380 | unsigned long ii=0L; |
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[35aab3] | 381 | do |
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| 382 | { |
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[923b64] | 383 | ii *= 10; |
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| 384 | ii += *s++ - '0'; |
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[e77676] | 385 | if (ii >= (MAX_INT_VAL / 10)) ii = ii % r->ch; |
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[35aab3] | 386 | } |
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| 387 | while (((*s) >= '0') && ((*s) <= '9')); |
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[95eeda] | 388 | if (ii >= (unsigned long)r->ch) ii = ii % r->ch; |
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[923b64] | 389 | *i=(int)ii; |
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[35aab3] | 390 | } |
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| 391 | else (*i) = 1; |
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| 392 | return s; |
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| 393 | } |
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| 394 | |
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[7d90aa] | 395 | const char * npRead (const char *s, number *a, const coeffs r) |
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[35aab3] | 396 | { |
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| 397 | int z; |
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| 398 | int n=1; |
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| 399 | |
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[7d90aa] | 400 | s = npEati(s, &z, r); |
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[35aab3] | 401 | if ((*s) == '/') |
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| 402 | { |
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| 403 | s++; |
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[7d90aa] | 404 | s = npEati(s, &n, r); |
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[35aab3] | 405 | } |
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| 406 | if (n == 1) |
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[e2202ee] | 407 | *a = (number)(long)z; |
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[6c15ec] | 408 | else |
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[100025] | 409 | { |
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| 410 | if ((z==0)&&(n==0)) WerrorS(nDivBy0); |
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[35aab3] | 411 | else |
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[100025] | 412 | { |
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| 413 | #ifdef NV_OPS |
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[e77676] | 414 | if (r->ch>NV_MAX_PRIME) |
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[e2202ee] | 415 | *a = nvDiv((number)(long)z,(number)(long)n,r); |
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[100025] | 416 | else |
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[6c15ec] | 417 | #endif |
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[e2202ee] | 418 | *a = npDiv((number)(long)z,(number)(long)n,r); |
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[100025] | 419 | } |
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| 420 | } |
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[eb55f8a] | 421 | n_Test(*a, r); |
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[35aab3] | 422 | return s; |
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| 423 | } |
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| 424 | |
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| 425 | /*2 |
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| 426 | * set the charcteristic (allocate and init tables) |
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| 427 | */ |
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| 428 | |
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[8c484e] | 429 | void npKillChar(coeffs r) |
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| 430 | { |
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| 431 | #ifdef HAVE_DIV_MOD |
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| 432 | if (r->npInvTable!=NULL) |
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[e77676] | 433 | omFreeSize( (void *)r->npInvTable, r->ch*sizeof(unsigned short) ); |
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[8c484e] | 434 | r->npInvTable=NULL; |
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| 435 | #else |
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| 436 | if (r->npExpTable!=NULL) |
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| 437 | { |
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[e77676] | 438 | omFreeSize( (void *)r->npExpTable, r->ch*sizeof(unsigned short) ); |
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| 439 | omFreeSize( (void *)r->npLogTable, r->ch*sizeof(unsigned short) ); |
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[8c484e] | 440 | r->npExpTable=NULL; r->npLogTable=NULL; |
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| 441 | } |
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| 442 | #endif |
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| 443 | } |
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| 444 | |
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[aff5ae] | 445 | static BOOLEAN npCoeffsEqual(const coeffs r, n_coeffType n, void * parameter) |
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[d2cf18] | 446 | { |
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| 447 | /* test, if r is an instance of nInitCoeffs(n,parameter) */ |
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[aff5ae] | 448 | return (n==n_Zp) && (r->ch==(int)(long)parameter); |
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[d2cf18] | 449 | } |
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[abb4787] | 450 | CanonicalForm npConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs r ) |
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[eca225] | 451 | { |
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[e77676] | 452 | if (setChar) setCharacteristic( r->ch ); |
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[eca225] | 453 | CanonicalForm term(npInt( n,r )); |
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| 454 | return term; |
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| 455 | } |
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| 456 | |
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| 457 | number npConvFactoryNSingN( const CanonicalForm n, const coeffs r) |
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| 458 | { |
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| 459 | if (n.isImm()) |
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| 460 | { |
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[a934fc8] | 461 | return npInit(n.intval(),r); |
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[eca225] | 462 | } |
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| 463 | else |
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| 464 | { |
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| 465 | assume(0); |
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[c262d5] | 466 | return NULL; |
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[eca225] | 467 | } |
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| 468 | } |
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[d2cf18] | 469 | |
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[45cc512] | 470 | static char* npCoeffString(const coeffs r) |
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| 471 | { |
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[f8735a] | 472 | #ifdef SINGULAR_4_1 |
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| 473 | char *s=(char*)omAlloc(14); |
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| 474 | snprintf(s,14,"ZZ/%d",r->ch); |
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| 475 | #else |
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[45cc512] | 476 | char *s=(char*)omAlloc(11); |
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| 477 | snprintf(s,11,"%d",r->ch); |
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[780c1b] | 478 | #endif |
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[45cc512] | 479 | return s; |
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| 480 | } |
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| 481 | |
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[850277] | 482 | static void npWriteFd(number n, FILE* f, const coeffs r) |
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| 483 | { |
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| 484 | fprintf(f,"%d ",(int)(long)n); |
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| 485 | } |
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| 486 | |
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| 487 | static number npReadFd(s_buff f, const coeffs r) |
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| 488 | { |
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| 489 | // read int |
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| 490 | int dd; |
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| 491 | dd=s_readint(f); |
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| 492 | return (number)(long)dd; |
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| 493 | } |
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| 494 | |
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[0d97a85] | 495 | static number npRandom(siRandProc p, number, number, const coeffs cf) |
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[14ace0] | 496 | { |
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[0d97a85] | 497 | return npInit(p(),cf); |
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[14ace0] | 498 | } |
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| 499 | |
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[1cce47] | 500 | BOOLEAN npInitChar(coeffs r, void* p) |
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[35aab3] | 501 | { |
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[6d0515d] | 502 | assume( getCoeffType(r) == n_Zp ); |
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[11206af] | 503 | const int c = (int) (long) p; |
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| 504 | |
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| 505 | assume( c > 0 ); |
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[601105] | 506 | |
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[35aab3] | 507 | int i, w; |
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| 508 | |
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[36a8e9] | 509 | r->is_field=TRUE; |
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| 510 | r->is_domain=TRUE; |
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[6a1aa7] | 511 | r->rep=n_rep_int; |
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[36a8e9] | 512 | |
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[e77676] | 513 | r->ch = c; |
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| 514 | r->npPminus1M = c /*r->ch*/ - 1; |
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[d2cf18] | 515 | |
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| 516 | //r->cfInitChar=npInitChar; |
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| 517 | r->cfKillChar=npKillChar; |
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| 518 | r->nCoeffIsEqual=npCoeffsEqual; |
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[45cc512] | 519 | r->cfCoeffString=npCoeffString; |
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[d2cf18] | 520 | |
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[7bbbef] | 521 | r->cfMult = npMult; |
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| 522 | r->cfSub = npSub; |
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| 523 | r->cfAdd = npAdd; |
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| 524 | r->cfDiv = npDiv; |
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[d2cf18] | 525 | r->cfInit = npInit; |
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[7bbbef] | 526 | //r->cfSize = ndSize; |
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| 527 | r->cfInt = npInt; |
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[d2cf18] | 528 | #ifdef HAVE_RINGS |
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[7bbbef] | 529 | //r->cfDivComp = NULL; // only for ring stuff |
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| 530 | //r->cfIsUnit = NULL; // only for ring stuff |
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| 531 | //r->cfGetUnit = NULL; // only for ring stuff |
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| 532 | //r->cfExtGcd = NULL; // only for ring stuff |
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| 533 | // r->cfDivBy = NULL; // only for ring stuff |
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[d2cf18] | 534 | #endif |
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[ec89bb4] | 535 | r->cfInpNeg = npNeg; |
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[7bbbef] | 536 | r->cfInvers= npInvers; |
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[aff5ae] | 537 | //r->cfCopy = ndCopy; |
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[7bbbef] | 538 | //r->cfRePart = ndCopy; |
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| 539 | //r->cfImPart = ndReturn0; |
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[ce1f78] | 540 | r->cfWriteLong = npWrite; |
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[7bbbef] | 541 | r->cfRead = npRead; |
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| 542 | //r->cfNormalize=ndNormalize; |
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| 543 | r->cfGreater = npGreater; |
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| 544 | r->cfEqual = npEqual; |
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| 545 | r->cfIsZero = npIsZero; |
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| 546 | r->cfIsOne = npIsOne; |
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| 547 | r->cfIsMOne = npIsMOne; |
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| 548 | r->cfGreaterZero = npGreaterZero; |
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[cc16f0] | 549 | //r->cfPower = npPower; |
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[ac000b6] | 550 | //r->cfGetDenom = ndGetDenom; |
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| 551 | //r->cfGetNumerator = ndGetNumerator; |
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[7bbbef] | 552 | //r->cfGcd = ndGcd; |
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| 553 | //r->cfLcm = ndGcd; |
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[aff5ae] | 554 | //r->cfDelete= ndDelete; |
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[d2cf18] | 555 | r->cfSetMap = npSetMap; |
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[7bbbef] | 556 | //r->cfName = ndName; |
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[ac000b6] | 557 | //r->cfInpMult=ndInpMult; |
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[d2cf18] | 558 | #ifdef NV_OPS |
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| 559 | if (c>NV_MAX_PRIME) |
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[35aab3] | 560 | { |
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[7bbbef] | 561 | r->cfMult = nvMult; |
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| 562 | r->cfDiv = nvDiv; |
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| 563 | r->cfExactDiv= nvDiv; |
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| 564 | r->cfInvers= nvInvers; |
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[cc16f0] | 565 | //r->cfPower= nvPower; |
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[d2cf18] | 566 | } |
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| 567 | #endif |
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[c7e3d7] | 568 | r->cfCoeffWrite=npCoeffWrite; |
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[d2cf18] | 569 | #ifdef LDEBUG |
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| 570 | // debug stuff |
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[7bbbef] | 571 | r->cfDBTest=npDBTest; |
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[d2cf18] | 572 | #endif |
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[eca225] | 573 | |
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| 574 | r->convSingNFactoryN=npConvSingNFactoryN; |
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| 575 | r->convFactoryNSingN=npConvFactoryNSingN; |
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[601105] | 576 | |
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[14ace0] | 577 | r->cfRandom=npRandom; |
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| 578 | |
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[850277] | 579 | // io via ssi |
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| 580 | r->cfWriteFd=npWriteFd; |
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| 581 | r->cfReadFd=npReadFd; |
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| 582 | |
---|
[d2cf18] | 583 | // the variables: |
---|
| 584 | r->nNULL = (number)0; |
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[f0797c] | 585 | r->type = n_Zp; |
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[d2cf18] | 586 | r->ch = c; |
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| 587 | r->has_simple_Alloc=TRUE; |
---|
| 588 | r->has_simple_Inverse=TRUE; |
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| 589 | |
---|
| 590 | // the tables |
---|
[35aab3] | 591 | #ifdef NV_OPS |
---|
[e77676] | 592 | if (r->ch <=NV_MAX_PRIME) |
---|
[35aab3] | 593 | #endif |
---|
[aff5ae] | 594 | { |
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[35aab3] | 595 | #if !defined(HAVE_DIV_MOD) || !defined(HAVE_MULT_MOD) |
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[e77676] | 596 | r->npExpTable=(unsigned short *)omAlloc( r->ch*sizeof(unsigned short) ); |
---|
| 597 | r->npLogTable=(unsigned short *)omAlloc( r->ch*sizeof(unsigned short) ); |
---|
[aff5ae] | 598 | r->npExpTable[0] = 1; |
---|
| 599 | r->npLogTable[0] = 0; |
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[e77676] | 600 | if (r->ch > 2) |
---|
[aff5ae] | 601 | { |
---|
| 602 | w = 1; |
---|
| 603 | loop |
---|
[35aab3] | 604 | { |
---|
[aff5ae] | 605 | r->npLogTable[1] = 0; |
---|
| 606 | w++; |
---|
| 607 | i = 0; |
---|
[35aab3] | 608 | loop |
---|
| 609 | { |
---|
[aff5ae] | 610 | i++; |
---|
[2f864f] | 611 | r->npExpTable[i] =(int)(((long)w * (long)r->npExpTable[i-1]) % r->ch); |
---|
[aff5ae] | 612 | r->npLogTable[r->npExpTable[i]] = i; |
---|
[601105] | 613 | if /*(i == r->ch - 1 ) ||*/ (/*(*/ r->npExpTable[i] == 1 /*)*/) |
---|
[35aab3] | 614 | break; |
---|
| 615 | } |
---|
[e77676] | 616 | if (i == r->ch - 1) |
---|
[aff5ae] | 617 | break; |
---|
[35aab3] | 618 | } |
---|
[aff5ae] | 619 | } |
---|
| 620 | else |
---|
| 621 | { |
---|
| 622 | r->npExpTable[1] = 1; |
---|
| 623 | r->npLogTable[1] = 0; |
---|
| 624 | } |
---|
[35aab3] | 625 | #endif |
---|
| 626 | #ifdef HAVE_DIV_MOD |
---|
[e77676] | 627 | r->npInvTable=(unsigned short*)omAlloc0( r->ch*sizeof(unsigned short) ); |
---|
[35aab3] | 628 | #endif |
---|
[aff5ae] | 629 | } |
---|
[5d594a9] | 630 | return FALSE; |
---|
[35aab3] | 631 | } |
---|
| 632 | |
---|
| 633 | #ifdef LDEBUG |
---|
[2b957a] | 634 | BOOLEAN npDBTest (number a, const char *f, const int l, const coeffs r) |
---|
[35aab3] | 635 | { |
---|
[9b88e6] | 636 | if (((long)a<0L) || ((long)a>(long)r->ch)) |
---|
[35aab3] | 637 | { |
---|
[f1e33bb] | 638 | Print("wrong mod p number %ld at %s,%d\n",(long)a,f,l); |
---|
[35aab3] | 639 | return FALSE; |
---|
| 640 | } |
---|
| 641 | return TRUE; |
---|
| 642 | } |
---|
| 643 | #endif |
---|
| 644 | |
---|
[8c484e] | 645 | number npMapP(number from, const coeffs src, const coeffs dst_r) |
---|
[35aab3] | 646 | { |
---|
| 647 | long i = (long)from; |
---|
[e77676] | 648 | if (i>src->ch/2) |
---|
[35aab3] | 649 | { |
---|
[e77676] | 650 | i-=src->ch; |
---|
| 651 | while (i < 0) i+=dst_r->ch; |
---|
[35aab3] | 652 | } |
---|
[e77676] | 653 | i%=dst_r->ch; |
---|
[35aab3] | 654 | return (number)i; |
---|
| 655 | } |
---|
| 656 | |
---|
[c262d5] | 657 | static number npMapLongR(number from, const coeffs /*src*/, const coeffs dst_r) |
---|
[35aab3] | 658 | { |
---|
| 659 | gmp_float *ff=(gmp_float*)from; |
---|
| 660 | mpf_t *f=ff->_mpfp(); |
---|
| 661 | number res; |
---|
[a604c3] | 662 | mpz_ptr dest,ndest; |
---|
[35aab3] | 663 | int size,i; |
---|
[c262d5] | 664 | int e,al,bl; |
---|
[7447d8] | 665 | long iz; |
---|
[35aab3] | 666 | mp_ptr qp,dd,nn; |
---|
| 667 | |
---|
| 668 | size = (*f)[0]._mp_size; |
---|
| 669 | if (size == 0) |
---|
[7d90aa] | 670 | return npInit(0,dst_r); |
---|
[35aab3] | 671 | if(size<0) |
---|
| 672 | size = -size; |
---|
| 673 | |
---|
| 674 | qp = (*f)[0]._mp_d; |
---|
| 675 | while(qp[0]==0) |
---|
| 676 | { |
---|
| 677 | qp++; |
---|
| 678 | size--; |
---|
| 679 | } |
---|
| 680 | |
---|
[e77676] | 681 | if(dst_r->ch>2) |
---|
[35aab3] | 682 | e=(*f)[0]._mp_exp-size; |
---|
| 683 | else |
---|
| 684 | e=0; |
---|
[896561] | 685 | res = ALLOC_RNUMBER(); |
---|
[35aab3] | 686 | #if defined(LDEBUG) |
---|
| 687 | res->debug=123456; |
---|
| 688 | #endif |
---|
[a604c3] | 689 | dest = res->z; |
---|
[35aab3] | 690 | |
---|
[e2202ee] | 691 | long in=0; |
---|
[35aab3] | 692 | if (e<0) |
---|
| 693 | { |
---|
| 694 | al = dest->_mp_size = size; |
---|
| 695 | if (al<2) al = 2; |
---|
| 696 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
---|
| 697 | for (i=0;i<size;i++) dd[i] = qp[i]; |
---|
| 698 | bl = 1-e; |
---|
| 699 | nn = (mp_ptr)omAlloc(sizeof(mp_limb_t)*bl); |
---|
| 700 | nn[bl-1] = 1; |
---|
| 701 | for (i=bl-2;i>=0;i--) nn[i] = 0; |
---|
[a604c3] | 702 | ndest = res->n; |
---|
[35aab3] | 703 | ndest->_mp_d = nn; |
---|
| 704 | ndest->_mp_alloc = ndest->_mp_size = bl; |
---|
| 705 | res->s = 0; |
---|
[e77676] | 706 | in=mpz_fdiv_ui(ndest,dst_r->ch); |
---|
[35aab3] | 707 | mpz_clear(ndest); |
---|
| 708 | } |
---|
| 709 | else |
---|
| 710 | { |
---|
| 711 | al = dest->_mp_size = size+e; |
---|
| 712 | if (al<2) al = 2; |
---|
| 713 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
---|
| 714 | for (i=0;i<size;i++) dd[i+e] = qp[i]; |
---|
| 715 | for (i=0;i<e;i++) dd[i] = 0; |
---|
| 716 | res->s = 3; |
---|
| 717 | } |
---|
| 718 | |
---|
| 719 | dest->_mp_d = dd; |
---|
| 720 | dest->_mp_alloc = al; |
---|
[e77676] | 721 | iz=mpz_fdiv_ui(dest,dst_r->ch); |
---|
[35aab3] | 722 | mpz_clear(dest); |
---|
| 723 | if(res->s==0) |
---|
[8c484e] | 724 | iz=(long)npDiv((number)iz,(number)in,dst_r); |
---|
[d663f2] | 725 | FREE_RNUMBER(res); // Q!? |
---|
[35aab3] | 726 | return (number)iz; |
---|
| 727 | } |
---|
| 728 | |
---|
[894f5b1] | 729 | #ifdef HAVE_RINGS |
---|
| 730 | /*2 |
---|
| 731 | * convert from a GMP integer |
---|
| 732 | */ |
---|
[c262d5] | 733 | number npMapGMP(number from, const coeffs /*src*/, const coeffs dst) |
---|
[894f5b1] | 734 | { |
---|
[6a70f3] | 735 | mpz_ptr erg = (mpz_ptr) omAlloc(sizeof(mpz_t)); // evtl. spaeter mit bin |
---|
[894f5b1] | 736 | mpz_init(erg); |
---|
| 737 | |
---|
[6a70f3] | 738 | mpz_mod_ui(erg, (mpz_ptr) from, dst->ch); |
---|
[894f5b1] | 739 | number r = (number) mpz_get_si(erg); |
---|
| 740 | |
---|
| 741 | mpz_clear(erg); |
---|
[7d90aa] | 742 | omFree((void *) erg); |
---|
[894f5b1] | 743 | return (number) r; |
---|
| 744 | } |
---|
| 745 | |
---|
[6a1aa7] | 746 | number npMapZ(number from, const coeffs src, const coeffs dst) |
---|
| 747 | { |
---|
| 748 | if (SR_HDL(from) & SR_INT) |
---|
| 749 | { |
---|
| 750 | long f_i=SR_TO_INT(from); |
---|
| 751 | return npInit(f_i,dst); |
---|
| 752 | } |
---|
| 753 | return npMapGMP(from,src,dst); |
---|
| 754 | } |
---|
| 755 | |
---|
[894f5b1] | 756 | /*2 |
---|
| 757 | * convert from an machine long |
---|
| 758 | */ |
---|
[c262d5] | 759 | number npMapMachineInt(number from, const coeffs /*src*/,const coeffs dst) |
---|
[894f5b1] | 760 | { |
---|
[e77676] | 761 | long i = (long) (((unsigned long) from) % dst->ch); |
---|
[894f5b1] | 762 | return (number) i; |
---|
| 763 | } |
---|
| 764 | #endif |
---|
| 765 | |
---|
[c262d5] | 766 | number npMapCanonicalForm (number a, const coeffs /*src*/, const coeffs dst) |
---|
[e9d796] | 767 | { |
---|
[e77676] | 768 | setCharacteristic (dst ->ch); |
---|
[e9d796] | 769 | CanonicalForm f= CanonicalForm ((InternalCF*)(a)); |
---|
| 770 | return (number) (f.intval()); |
---|
| 771 | } |
---|
| 772 | |
---|
[7d90aa] | 773 | nMapFunc npSetMap(const coeffs src, const coeffs dst) |
---|
[35aab3] | 774 | { |
---|
[894f5b1] | 775 | #ifdef HAVE_RINGS |
---|
[6a1aa7] | 776 | if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src)) |
---|
[894f5b1] | 777 | { |
---|
| 778 | return npMapMachineInt; |
---|
| 779 | } |
---|
[6a1aa7] | 780 | if (src->rep==n_rep_gmp) //nCoeff_is_Ring_Z(src) || nCoeff_is_Ring_PtoM(src) || nCoeff_is_Ring_ModN(src)) |
---|
[894f5b1] | 781 | { |
---|
| 782 | return npMapGMP; |
---|
| 783 | } |
---|
[6a1aa7] | 784 | if (src->rep==n_rep_gap_gmp) //nCoeff_is_Ring_Z(src) |
---|
| 785 | { |
---|
| 786 | return npMapZ; |
---|
| 787 | } |
---|
[894f5b1] | 788 | #endif |
---|
[6a1aa7] | 789 | if (src->rep==n_rep_gap_rat) /* Q, Z */ |
---|
[75f460] | 790 | { |
---|
[2206753] | 791 | return nlModP; // npMap0; // FIXME? TODO? // extern number nlModP(number q, const coeffs Q, const coeffs Zp); // Map q \in QQ \to Zp // FIXME! |
---|
[35aab3] | 792 | } |
---|
[6a1aa7] | 793 | if ((src->rep==n_rep_int) && nCoeff_is_Zp(src) ) |
---|
[35aab3] | 794 | { |
---|
[7d90aa] | 795 | if (n_GetChar(src) == n_GetChar(dst)) |
---|
[35aab3] | 796 | { |
---|
[8c484e] | 797 | return ndCopyMap; |
---|
[35aab3] | 798 | } |
---|
| 799 | else |
---|
| 800 | { |
---|
| 801 | return npMapP; |
---|
| 802 | } |
---|
| 803 | } |
---|
[6a1aa7] | 804 | if ((src->rep==n_rep_gmp_float) && nCoeff_is_long_R(src)) |
---|
[35aab3] | 805 | { |
---|
| 806 | return npMapLongR; |
---|
| 807 | } |
---|
[1cce47] | 808 | if (nCoeff_is_CF (src)) |
---|
[e9d796] | 809 | { |
---|
| 810 | return npMapCanonicalForm; |
---|
| 811 | } |
---|
[35aab3] | 812 | return NULL; /* default */ |
---|
| 813 | } |
---|
| 814 | |
---|
| 815 | // ----------------------------------------------------------- |
---|
[a1299c] | 816 | // operation for very large primes (32749< p < 2^31-1) |
---|
[35aab3] | 817 | // ---------------------------------------------------------- |
---|
| 818 | #ifdef NV_OPS |
---|
| 819 | |
---|
[7d90aa] | 820 | number nvMult (number a,number b, const coeffs r) |
---|
[35aab3] | 821 | { |
---|
[2e1b74] | 822 | //if (((long)a == 0) || ((long)b == 0)) |
---|
| 823 | // return (number)0; |
---|
| 824 | //else |
---|
[4d92d7] | 825 | return nvMultM(a,b,r); |
---|
[35aab3] | 826 | } |
---|
| 827 | |
---|
[4d92d7] | 828 | void nvInpMult(number &a, number b, const coeffs r) |
---|
[2e1b74] | 829 | { |
---|
[4d92d7] | 830 | number n=nvMultM(a,b,r); |
---|
[2e1b74] | 831 | a=n; |
---|
| 832 | } |
---|
| 833 | |
---|
| 834 | |
---|
[a74143] | 835 | inline long nvInvMod(long a, const coeffs R) |
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[35aab3] | 836 | { |
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[a74143] | 837 | #ifdef HAVE_DIV_MOD |
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| 838 | return InvMod(a, R); |
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| 839 | #else |
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| 840 | /// TODO: use "long InvMod(long a, const coeffs R)"?! |
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[601105] | 841 | |
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[c262d5] | 842 | long s; |
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[35aab3] | 843 | |
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[601105] | 844 | long u, u0, u1, u2, q, r; // v0, v1, v2, |
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[35aab3] | 845 | |
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[a74143] | 846 | u1=1; // v1=0; |
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| 847 | u2=0; // v2=1; |
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| 848 | u = a; |
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| 849 | |
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| 850 | long v = R->ch; |
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[35aab3] | 851 | |
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[9c8927] | 852 | while (v != 0) |
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| 853 | { |
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[35aab3] | 854 | q = u / v; |
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| 855 | r = u % v; |
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| 856 | u = v; |
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| 857 | v = r; |
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| 858 | u0 = u2; |
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[a74143] | 859 | // v0 = v2; |
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| 860 | u2 = u1 - q*u2; |
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| 861 | // v2 = v1 - q*v2; |
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[35aab3] | 862 | u1 = u0; |
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[a74143] | 863 | // v1 = v0; |
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[35aab3] | 864 | } |
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| 865 | |
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| 866 | s = u1; |
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| 867 | //t = v1; |
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| 868 | if (s < 0) |
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[e77676] | 869 | return s + R->ch; |
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[35aab3] | 870 | else |
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[a74143] | 871 | return s; |
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| 872 | #endif |
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[35aab3] | 873 | } |
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| 874 | |
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[7d90aa] | 875 | inline number nvInversM (number c, const coeffs r) |
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[35aab3] | 876 | { |
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[7d90aa] | 877 | long inv=nvInvMod((long)c,r); |
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[35aab3] | 878 | return (number)inv; |
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| 879 | } |
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| 880 | |
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[7d90aa] | 881 | number nvDiv (number a,number b, const coeffs r) |
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[35aab3] | 882 | { |
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[9b88e6] | 883 | if ((long)a==0L) |
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| 884 | return (number)0L; |
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| 885 | else if ((long)b==0L) |
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[35aab3] | 886 | { |
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[b7e838] | 887 | WerrorS(nDivBy0); |
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[9b88e6] | 888 | return (number)0L; |
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[35aab3] | 889 | } |
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| 890 | else |
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| 891 | { |
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[7d90aa] | 892 | number inv=nvInversM(b,r); |
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| 893 | return nvMultM(a,inv,r); |
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[35aab3] | 894 | } |
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| 895 | } |
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[7d90aa] | 896 | number nvInvers (number c, const coeffs r) |
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[35aab3] | 897 | { |
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[9b88e6] | 898 | if ((long)c==0L) |
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[35aab3] | 899 | { |
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[b7e838] | 900 | WerrorS(nDivBy0); |
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[9b88e6] | 901 | return (number)0L; |
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[35aab3] | 902 | } |
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[7d90aa] | 903 | return nvInversM(c,r); |
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[35aab3] | 904 | } |
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[cc16f0] | 905 | #if 0 |
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[7d90aa] | 906 | void nvPower (number a, int i, number * result, const coeffs r) |
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[9c8927] | 907 | { |
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| 908 | if (i==0) |
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| 909 | { |
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| 910 | //npInit(1,result); |
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| 911 | *(long *)result = 1; |
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| 912 | } |
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| 913 | else if (i==1) |
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| 914 | { |
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| 915 | *result = a; |
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| 916 | } |
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| 917 | else |
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| 918 | { |
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[7d90aa] | 919 | nvPower(a,i-1,result,r); |
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| 920 | *result = nvMultM(a,*result,r); |
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[9c8927] | 921 | } |
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| 922 | } |
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[35aab3] | 923 | #endif |
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[cc16f0] | 924 | #endif |
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[c7e3d7] | 925 | |
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[03f7b5] | 926 | void npCoeffWrite (const coeffs r, BOOLEAN /*details*/) |
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[c7e3d7] | 927 | { |
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[e77676] | 928 | Print("// characteristic : %d\n",r->ch); |
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[c7e3d7] | 929 | } |
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| 930 | |
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