[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 | nMapFunc npSetMap(const coeffs src, const coeffs dst); |
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| 51 | |
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[40e88db] | 52 | #ifdef NV_OPS |
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| 53 | #pragma GCC diagnostic ignored "-Wlong-long" |
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| 54 | static inline number nvMultM(number a, number b, const coeffs r) |
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| 55 | { |
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[6d0515d] | 56 | assume( getCoeffType(r) == n_Zp ); |
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[601105] | 57 | |
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[40e88db] | 58 | #if SIZEOF_LONG == 4 |
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| 59 | #define ULONG64 (unsigned long long)(unsigned long) |
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| 60 | #else |
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| 61 | #define ULONG64 (unsigned long) |
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| 62 | #endif |
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[601105] | 63 | return (number) |
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[40e88db] | 64 | (unsigned long)((ULONG64 a)*(ULONG64 b) % (ULONG64 r->ch)); |
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| 65 | } |
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| 66 | number nvMult (number a, number b, const coeffs r); |
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| 67 | number nvDiv (number a, number b, const coeffs r); |
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| 68 | number nvInvers (number c, const coeffs r); |
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[cc16f0] | 69 | //void nvPower (number a, int i, number * result, const coeffs r); |
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[40e88db] | 70 | #endif |
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| 71 | |
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[7d90aa] | 72 | BOOLEAN npGreaterZero (number k, const coeffs r) |
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[35aab3] | 73 | { |
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[eb55f8a] | 74 | n_Test(k, r); |
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[601105] | 75 | |
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[7447d8] | 76 | int h = (int)((long) k); |
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[e77676] | 77 | return ((int)h !=0) && (h <= (r->ch>>1)); |
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[35aab3] | 78 | } |
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| 79 | |
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[e77676] | 80 | //unsigned long npMultMod(unsigned long a, unsigned long b, int npPrimeM) |
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[35aab3] | 81 | //{ |
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| 82 | // unsigned long c = a*b; |
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| 83 | // c = c % npPrimeM; |
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[e77676] | 84 | // assume(c == (unsigned long) npMultM((number) a, (number) b, npPrimeM)); |
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[35aab3] | 85 | // return c; |
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| 86 | //} |
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| 87 | |
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[7d90aa] | 88 | number npMult (number a,number b, const coeffs r) |
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[35aab3] | 89 | { |
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[eb55f8a] | 90 | n_Test(a, r); |
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| 91 | n_Test(b, r); |
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[0461f0] | 92 | |
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[35aab3] | 93 | if (((long)a == 0) || ((long)b == 0)) |
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| 94 | return (number)0; |
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[0461f0] | 95 | number c = npMultM(a,b, r); |
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[eb55f8a] | 96 | n_Test(c, r); |
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[601105] | 97 | return c; |
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[35aab3] | 98 | } |
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| 99 | |
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| 100 | /*2 |
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| 101 | * create a number from int |
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| 102 | */ |
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[2f3764] | 103 | number npInit (long i, const coeffs r) |
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[35aab3] | 104 | { |
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[d8b0997] | 105 | long ii=i % (long)r->ch; |
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| 106 | if (ii < 0L) ii += (long)r->ch; |
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| 107 | |
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[0461f0] | 108 | number c = (number)ii; |
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[eb55f8a] | 109 | n_Test(c, r); |
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[0461f0] | 110 | return c; |
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[35aab3] | 111 | } |
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| 112 | |
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[0461f0] | 113 | |
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[35aab3] | 114 | /*2 |
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[0461f0] | 115 | * convert a number to an int in (-p/2 .. p/2] |
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| 116 | */ |
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[777f8b] | 117 | long npInt(number &n, const coeffs r) |
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[35aab3] | 118 | { |
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[eb55f8a] | 119 | n_Test(n, r); |
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[601105] | 120 | |
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[777f8b] | 121 | if ((long)n > (((long)r->ch) >>1)) return ((long)n -((long)r->ch)); |
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| 122 | else return ((long)n); |
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[35aab3] | 123 | } |
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| 124 | |
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[7d90aa] | 125 | number npAdd (number a, number b, const coeffs r) |
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[35aab3] | 126 | { |
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[eb55f8a] | 127 | n_Test(a, r); |
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| 128 | n_Test(b, r); |
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[601105] | 129 | |
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[0461f0] | 130 | number c = npAddM(a,b, r); |
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| 131 | |
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[eb55f8a] | 132 | n_Test(c, r); |
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[601105] | 133 | |
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[0461f0] | 134 | return c; |
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[35aab3] | 135 | } |
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| 136 | |
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[7d90aa] | 137 | number npSub (number a, number b, const coeffs r) |
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[35aab3] | 138 | { |
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[eb55f8a] | 139 | n_Test(a, r); |
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| 140 | n_Test(b, r); |
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[601105] | 141 | |
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[0461f0] | 142 | number c = npSubM(a,b,r); |
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| 143 | |
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[eb55f8a] | 144 | n_Test(c, r); |
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[0461f0] | 145 | |
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| 146 | return c; |
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[35aab3] | 147 | } |
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| 148 | |
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[0461f0] | 149 | BOOLEAN npIsZero (number a, const coeffs r) |
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[35aab3] | 150 | { |
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[eb55f8a] | 151 | n_Test(a, r); |
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[601105] | 152 | |
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[35aab3] | 153 | return 0 == (long)a; |
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| 154 | } |
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| 155 | |
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[0461f0] | 156 | BOOLEAN npIsOne (number a, const coeffs r) |
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[35aab3] | 157 | { |
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[eb55f8a] | 158 | n_Test(a, r); |
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[601105] | 159 | |
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[35aab3] | 160 | return 1 == (long)a; |
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| 161 | } |
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| 162 | |
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[7d90aa] | 163 | BOOLEAN npIsMOne (number a, const coeffs r) |
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[35aab3] | 164 | { |
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[eb55f8a] | 165 | n_Test(a, r); |
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[601105] | 166 | |
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[961c76] | 167 | return ((r->npPminus1M == (long)a) &&(1L!=(long)a))/*for char 2*/; |
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[35aab3] | 168 | } |
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| 169 | |
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| 170 | #ifdef HAVE_DIV_MOD |
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[a74143] | 171 | |
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[1fc18b] | 172 | #ifdef USE_NTL_XGCD |
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[a74143] | 173 | |
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[1fc18b] | 174 | //ifdef HAVE_NTL // in ntl.a |
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[35aab3] | 175 | //extern void XGCD(long& d, long& s, long& t, long a, long b); |
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| 176 | #include <NTL/ZZ.h> |
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| 177 | #ifdef NTL_CLIENT |
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| 178 | NTL_CLIENT |
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| 179 | #endif |
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[a74143] | 180 | |
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[1fc18b] | 181 | #endif |
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[35aab3] | 182 | |
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[7d90aa] | 183 | long InvMod(long a, const coeffs R) |
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[1fc18b] | 184 | { |
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| 185 | long d, s, t; |
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[35aab3] | 186 | |
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[1fc18b] | 187 | #ifdef USE_NTL_XGCD |
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[e77676] | 188 | XGCD(d, s, t, a, R->ch); |
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[1fc18b] | 189 | assume (d == 1); |
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| 190 | #else |
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| 191 | long u, v, u0, v0, u1, v1, u2, v2, q, r; |
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[35aab3] | 192 | |
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[1fc18b] | 193 | assume(a>0); |
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| 194 | u1=1; u2=0; |
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[e77676] | 195 | u = a; v = R->ch; |
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[35aab3] | 196 | |
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[1fc18b] | 197 | while (v != 0) |
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| 198 | { |
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[35aab3] | 199 | q = u / v; |
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| 200 | r = u % v; |
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| 201 | u = v; |
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| 202 | v = r; |
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| 203 | u0 = u2; |
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[1fc18b] | 204 | u2 = u1 - q*u2; |
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[35aab3] | 205 | u1 = u0; |
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| 206 | } |
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| 207 | |
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[1fc18b] | 208 | assume(u==1); |
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[35aab3] | 209 | s = u1; |
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| 210 | #endif |
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| 211 | if (s < 0) |
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[e77676] | 212 | return s + R->ch; |
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[35aab3] | 213 | else |
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| 214 | return s; |
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| 215 | } |
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| 216 | #endif |
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| 217 | |
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[7d90aa] | 218 | inline number npInversM (number c, const coeffs r) |
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[35aab3] | 219 | { |
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[eb55f8a] | 220 | n_Test(c, r); |
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[35aab3] | 221 | #ifndef HAVE_DIV_MOD |
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[0461f0] | 222 | number d = (number)(long)r->npExpTable[r->npPminus1M - r->npLogTable[(long)c]]; |
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[35aab3] | 223 | #else |
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[7d90aa] | 224 | long inv=(long)r->npInvTable[(long)c]; |
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[35aab3] | 225 | if (inv==0) |
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| 226 | { |
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[7d90aa] | 227 | inv=InvMod((long)c,r); |
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| 228 | r->npInvTable[(long)c]=inv; |
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[35aab3] | 229 | } |
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[0461f0] | 230 | number d = (number)inv; |
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[35aab3] | 231 | #endif |
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[eb55f8a] | 232 | n_Test(d, r); |
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[0461f0] | 233 | return d; |
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| 234 | |
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[35aab3] | 235 | } |
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| 236 | |
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[7d90aa] | 237 | number npDiv (number a,number b, const coeffs r) |
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[35aab3] | 238 | { |
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[eb55f8a] | 239 | n_Test(a, r); |
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| 240 | n_Test(b, r); |
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[0461f0] | 241 | |
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[6c15ec] | 242 | //#ifdef NV_OPS |
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[e77676] | 243 | // if (r->ch>NV_MAX_PRIME) |
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[6c15ec] | 244 | // return nvDiv(a,b); |
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| 245 | //#endif |
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[9b88e6] | 246 | if ((long)a==0L) |
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| 247 | return (number)0L; |
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[0461f0] | 248 | number d; |
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[601105] | 249 | |
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[35aab3] | 250 | #ifndef HAVE_DIV_MOD |
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[9b88e6] | 251 | if ((long)b==0L) |
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[35aab3] | 252 | { |
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[b7e838] | 253 | WerrorS(nDivBy0); |
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[9b88e6] | 254 | return (number)0L; |
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[35aab3] | 255 | } |
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[601105] | 256 | |
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[0461f0] | 257 | int s = r->npLogTable[(long)a] - r->npLogTable[(long)b]; |
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| 258 | if (s < 0) |
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| 259 | s += r->npPminus1M; |
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| 260 | d = (number)(long)r->npExpTable[s]; |
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[35aab3] | 261 | #else |
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[7d90aa] | 262 | number inv=npInversM(b,r); |
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[0461f0] | 263 | d = npMultM(a,inv,r); |
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[35aab3] | 264 | #endif |
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[0461f0] | 265 | |
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[eb55f8a] | 266 | n_Test(d, r); |
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[0461f0] | 267 | return d; |
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[601105] | 268 | |
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[35aab3] | 269 | } |
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[7d90aa] | 270 | number npInvers (number c, const coeffs r) |
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[35aab3] | 271 | { |
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[eb55f8a] | 272 | n_Test(c, r); |
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[601105] | 273 | |
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[9b88e6] | 274 | if ((long)c==0L) |
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[35aab3] | 275 | { |
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| 276 | WerrorS("1/0"); |
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[9b88e6] | 277 | return (number)0L; |
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[35aab3] | 278 | } |
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[0461f0] | 279 | number d = npInversM(c,r); |
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[601105] | 280 | |
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[eb55f8a] | 281 | n_Test(d, r); |
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[0461f0] | 282 | return d; |
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[35aab3] | 283 | } |
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| 284 | |
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[7d90aa] | 285 | number npNeg (number c, const coeffs r) |
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[35aab3] | 286 | { |
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[eb55f8a] | 287 | n_Test(c, r); |
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[601105] | 288 | |
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[9b88e6] | 289 | if ((long)c==0L) return c; |
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[0461f0] | 290 | |
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[601105] | 291 | #if 0 |
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| 292 | number d = npNegM(c,r); |
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[eb55f8a] | 293 | n_Test(d, r); |
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[0461f0] | 294 | return d; |
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| 295 | #else |
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[601105] | 296 | c = npNegM(c,r); |
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[eb55f8a] | 297 | n_Test(c, r); |
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[0461f0] | 298 | return c; |
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[601105] | 299 | #endif |
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[35aab3] | 300 | } |
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| 301 | |
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[0461f0] | 302 | BOOLEAN npGreater (number a,number b, const coeffs r) |
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[35aab3] | 303 | { |
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[eb55f8a] | 304 | n_Test(a, r); |
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| 305 | n_Test(b, r); |
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[0461f0] | 306 | |
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[35aab3] | 307 | //return (long)a != (long)b; |
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[9b88e6] | 308 | return ((long)a) > ((long)b); |
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[35aab3] | 309 | } |
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| 310 | |
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[7d90aa] | 311 | BOOLEAN npEqual (number a,number b, const coeffs r) |
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[35aab3] | 312 | { |
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[eb55f8a] | 313 | n_Test(a, r); |
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| 314 | n_Test(b, r); |
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[601105] | 315 | |
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[35aab3] | 316 | // return (long)a == (long)b; |
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[601105] | 317 | |
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[7d90aa] | 318 | return npEqualM(a,b,r); |
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[35aab3] | 319 | } |
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| 320 | |
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[6d92ca] | 321 | void npWrite (number a, const coeffs r) |
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[35aab3] | 322 | { |
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[eb55f8a] | 323 | n_Test(a, r); |
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[601105] | 324 | |
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[493225] | 325 | if ((long)a>(((long)r->ch) >>1)) StringAppend("-%d",(int)(((long)r->ch)-((long)a))); |
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| 326 | else StringAppend("%d",(int)((long)a)); |
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[35aab3] | 327 | } |
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| 328 | |
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[cc16f0] | 329 | #if 0 |
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[7d90aa] | 330 | void npPower (number a, int i, number * result, const coeffs r) |
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[35aab3] | 331 | { |
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[eb55f8a] | 332 | n_Test(a, r); |
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[0461f0] | 333 | |
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[35aab3] | 334 | if (i==0) |
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| 335 | { |
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| 336 | //npInit(1,result); |
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| 337 | *(long *)result = 1; |
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| 338 | } |
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| 339 | else if (i==1) |
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| 340 | { |
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| 341 | *result = a; |
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| 342 | } |
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| 343 | else |
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| 344 | { |
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[7d90aa] | 345 | npPower(a,i-1,result,r); |
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| 346 | *result = npMultM(a,*result,r); |
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[35aab3] | 347 | } |
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| 348 | } |
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[cc16f0] | 349 | #endif |
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[35aab3] | 350 | |
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[7d90aa] | 351 | static const char* npEati(const char *s, int *i, const coeffs r) |
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[35aab3] | 352 | { |
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| 353 | if (((*s) >= '0') && ((*s) <= '9')) |
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| 354 | { |
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[923b64] | 355 | unsigned long ii=0L; |
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[35aab3] | 356 | do |
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| 357 | { |
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[923b64] | 358 | ii *= 10; |
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| 359 | ii += *s++ - '0'; |
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[e77676] | 360 | if (ii >= (MAX_INT_VAL / 10)) ii = ii % r->ch; |
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[35aab3] | 361 | } |
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| 362 | while (((*s) >= '0') && ((*s) <= '9')); |
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[95eeda] | 363 | if (ii >= (unsigned long)r->ch) ii = ii % r->ch; |
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[923b64] | 364 | *i=(int)ii; |
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[35aab3] | 365 | } |
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| 366 | else (*i) = 1; |
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| 367 | return s; |
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| 368 | } |
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| 369 | |
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[7d90aa] | 370 | const char * npRead (const char *s, number *a, const coeffs r) |
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[35aab3] | 371 | { |
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| 372 | int z; |
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| 373 | int n=1; |
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| 374 | |
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[7d90aa] | 375 | s = npEati(s, &z, r); |
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[35aab3] | 376 | if ((*s) == '/') |
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| 377 | { |
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| 378 | s++; |
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[7d90aa] | 379 | s = npEati(s, &n, r); |
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[35aab3] | 380 | } |
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| 381 | if (n == 1) |
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[e2202ee] | 382 | *a = (number)(long)z; |
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[6c15ec] | 383 | else |
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[100025] | 384 | { |
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| 385 | if ((z==0)&&(n==0)) WerrorS(nDivBy0); |
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[35aab3] | 386 | else |
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[100025] | 387 | { |
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| 388 | #ifdef NV_OPS |
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[e77676] | 389 | if (r->ch>NV_MAX_PRIME) |
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[e2202ee] | 390 | *a = nvDiv((number)(long)z,(number)(long)n,r); |
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[100025] | 391 | else |
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[6c15ec] | 392 | #endif |
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[e2202ee] | 393 | *a = npDiv((number)(long)z,(number)(long)n,r); |
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[100025] | 394 | } |
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| 395 | } |
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[eb55f8a] | 396 | n_Test(*a, r); |
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[35aab3] | 397 | return s; |
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| 398 | } |
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| 399 | |
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| 400 | /*2 |
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| 401 | * set the charcteristic (allocate and init tables) |
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| 402 | */ |
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| 403 | |
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[8c484e] | 404 | void npKillChar(coeffs r) |
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| 405 | { |
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| 406 | #ifdef HAVE_DIV_MOD |
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| 407 | if (r->npInvTable!=NULL) |
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[e77676] | 408 | omFreeSize( (void *)r->npInvTable, r->ch*sizeof(unsigned short) ); |
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[8c484e] | 409 | r->npInvTable=NULL; |
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| 410 | #else |
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| 411 | if (r->npExpTable!=NULL) |
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| 412 | { |
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[e77676] | 413 | omFreeSize( (void *)r->npExpTable, r->ch*sizeof(unsigned short) ); |
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| 414 | omFreeSize( (void *)r->npLogTable, r->ch*sizeof(unsigned short) ); |
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[8c484e] | 415 | r->npExpTable=NULL; r->npLogTable=NULL; |
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| 416 | } |
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| 417 | #endif |
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| 418 | } |
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| 419 | |
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[aff5ae] | 420 | static BOOLEAN npCoeffsEqual(const coeffs r, n_coeffType n, void * parameter) |
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[d2cf18] | 421 | { |
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| 422 | /* test, if r is an instance of nInitCoeffs(n,parameter) */ |
---|
[aff5ae] | 423 | return (n==n_Zp) && (r->ch==(int)(long)parameter); |
---|
[d2cf18] | 424 | } |
---|
[abb4787] | 425 | CanonicalForm npConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs r ) |
---|
[eca225] | 426 | { |
---|
[e77676] | 427 | if (setChar) setCharacteristic( r->ch ); |
---|
[eca225] | 428 | CanonicalForm term(npInt( n,r )); |
---|
| 429 | return term; |
---|
| 430 | } |
---|
| 431 | |
---|
| 432 | number npConvFactoryNSingN( const CanonicalForm n, const coeffs r) |
---|
| 433 | { |
---|
| 434 | if (n.isImm()) |
---|
| 435 | { |
---|
[a934fc8] | 436 | return npInit(n.intval(),r); |
---|
[eca225] | 437 | } |
---|
| 438 | else |
---|
| 439 | { |
---|
| 440 | assume(0); |
---|
[c262d5] | 441 | return NULL; |
---|
[eca225] | 442 | } |
---|
| 443 | } |
---|
[d2cf18] | 444 | |
---|
[9a1960] | 445 | static char* npCoeffName(const coeffs cf) |
---|
[45cc512] | 446 | { |
---|
[9a1960] | 447 | static char npCoeffName_buf[15]; |
---|
| 448 | snprintf(npCoeffName_buf,14,"ZZ/%d",cf->ch); |
---|
| 449 | return npCoeffName_buf; |
---|
| 450 | } |
---|
| 451 | |
---|
| 452 | static char* npCoeffString(const coeffs cf) |
---|
| 453 | { |
---|
| 454 | return omStrDup(npCoeffName(cf)); |
---|
[45cc512] | 455 | } |
---|
| 456 | |
---|
[f5e732] | 457 | static void npWriteFd(number n, FILE* f, const coeffs) |
---|
[850277] | 458 | { |
---|
| 459 | fprintf(f,"%d ",(int)(long)n); |
---|
| 460 | } |
---|
| 461 | |
---|
[f5e732] | 462 | static number npReadFd(s_buff f, const coeffs) |
---|
[850277] | 463 | { |
---|
| 464 | // read int |
---|
| 465 | int dd; |
---|
| 466 | dd=s_readint(f); |
---|
| 467 | return (number)(long)dd; |
---|
| 468 | } |
---|
| 469 | |
---|
[0d97a85] | 470 | static number npRandom(siRandProc p, number, number, const coeffs cf) |
---|
[14ace0] | 471 | { |
---|
[0d97a85] | 472 | return npInit(p(),cf); |
---|
[14ace0] | 473 | } |
---|
| 474 | |
---|
[1cce47] | 475 | BOOLEAN npInitChar(coeffs r, void* p) |
---|
[35aab3] | 476 | { |
---|
[6d0515d] | 477 | assume( getCoeffType(r) == n_Zp ); |
---|
[11206af] | 478 | const int c = (int) (long) p; |
---|
| 479 | |
---|
| 480 | assume( c > 0 ); |
---|
[601105] | 481 | |
---|
[35aab3] | 482 | int i, w; |
---|
| 483 | |
---|
[36a8e9] | 484 | r->is_field=TRUE; |
---|
| 485 | r->is_domain=TRUE; |
---|
[6a1aa7] | 486 | r->rep=n_rep_int; |
---|
[36a8e9] | 487 | |
---|
[e77676] | 488 | r->ch = c; |
---|
| 489 | r->npPminus1M = c /*r->ch*/ - 1; |
---|
[d2cf18] | 490 | |
---|
| 491 | //r->cfInitChar=npInitChar; |
---|
| 492 | r->cfKillChar=npKillChar; |
---|
| 493 | r->nCoeffIsEqual=npCoeffsEqual; |
---|
[45cc512] | 494 | r->cfCoeffString=npCoeffString; |
---|
[9a1960] | 495 | r->cfCoeffName=npCoeffName; |
---|
| 496 | r->cfCoeffWrite=npCoeffWrite; |
---|
[d2cf18] | 497 | |
---|
[7bbbef] | 498 | r->cfMult = npMult; |
---|
| 499 | r->cfSub = npSub; |
---|
| 500 | r->cfAdd = npAdd; |
---|
| 501 | r->cfDiv = npDiv; |
---|
[d2cf18] | 502 | r->cfInit = npInit; |
---|
[7bbbef] | 503 | //r->cfSize = ndSize; |
---|
| 504 | r->cfInt = npInt; |
---|
[d2cf18] | 505 | #ifdef HAVE_RINGS |
---|
[7bbbef] | 506 | //r->cfDivComp = NULL; // only for ring stuff |
---|
| 507 | //r->cfIsUnit = NULL; // only for ring stuff |
---|
| 508 | //r->cfGetUnit = NULL; // only for ring stuff |
---|
| 509 | //r->cfExtGcd = NULL; // only for ring stuff |
---|
| 510 | // r->cfDivBy = NULL; // only for ring stuff |
---|
[d2cf18] | 511 | #endif |
---|
[ec89bb4] | 512 | r->cfInpNeg = npNeg; |
---|
[7bbbef] | 513 | r->cfInvers= npInvers; |
---|
[aff5ae] | 514 | //r->cfCopy = ndCopy; |
---|
[7bbbef] | 515 | //r->cfRePart = ndCopy; |
---|
| 516 | //r->cfImPart = ndReturn0; |
---|
[ce1f78] | 517 | r->cfWriteLong = npWrite; |
---|
[7bbbef] | 518 | r->cfRead = npRead; |
---|
| 519 | //r->cfNormalize=ndNormalize; |
---|
| 520 | r->cfGreater = npGreater; |
---|
| 521 | r->cfEqual = npEqual; |
---|
| 522 | r->cfIsZero = npIsZero; |
---|
| 523 | r->cfIsOne = npIsOne; |
---|
| 524 | r->cfIsMOne = npIsMOne; |
---|
| 525 | r->cfGreaterZero = npGreaterZero; |
---|
[cc16f0] | 526 | //r->cfPower = npPower; |
---|
[ac000b6] | 527 | //r->cfGetDenom = ndGetDenom; |
---|
| 528 | //r->cfGetNumerator = ndGetNumerator; |
---|
[7bbbef] | 529 | //r->cfGcd = ndGcd; |
---|
| 530 | //r->cfLcm = ndGcd; |
---|
[aff5ae] | 531 | //r->cfDelete= ndDelete; |
---|
[d2cf18] | 532 | r->cfSetMap = npSetMap; |
---|
[7bbbef] | 533 | //r->cfName = ndName; |
---|
[ac000b6] | 534 | //r->cfInpMult=ndInpMult; |
---|
[d2cf18] | 535 | #ifdef NV_OPS |
---|
| 536 | if (c>NV_MAX_PRIME) |
---|
[35aab3] | 537 | { |
---|
[7bbbef] | 538 | r->cfMult = nvMult; |
---|
| 539 | r->cfDiv = nvDiv; |
---|
| 540 | r->cfExactDiv= nvDiv; |
---|
| 541 | r->cfInvers= nvInvers; |
---|
[cc16f0] | 542 | //r->cfPower= nvPower; |
---|
[d2cf18] | 543 | } |
---|
| 544 | #endif |
---|
| 545 | #ifdef LDEBUG |
---|
| 546 | // debug stuff |
---|
[7bbbef] | 547 | r->cfDBTest=npDBTest; |
---|
[d2cf18] | 548 | #endif |
---|
[eca225] | 549 | |
---|
| 550 | r->convSingNFactoryN=npConvSingNFactoryN; |
---|
| 551 | r->convFactoryNSingN=npConvFactoryNSingN; |
---|
[601105] | 552 | |
---|
[14ace0] | 553 | r->cfRandom=npRandom; |
---|
| 554 | |
---|
[850277] | 555 | // io via ssi |
---|
| 556 | r->cfWriteFd=npWriteFd; |
---|
| 557 | r->cfReadFd=npReadFd; |
---|
| 558 | |
---|
[d2cf18] | 559 | // the variables: |
---|
| 560 | r->nNULL = (number)0; |
---|
[f0797c] | 561 | r->type = n_Zp; |
---|
[d2cf18] | 562 | r->ch = c; |
---|
| 563 | r->has_simple_Alloc=TRUE; |
---|
| 564 | r->has_simple_Inverse=TRUE; |
---|
| 565 | |
---|
| 566 | // the tables |
---|
[35aab3] | 567 | #ifdef NV_OPS |
---|
[e77676] | 568 | if (r->ch <=NV_MAX_PRIME) |
---|
[35aab3] | 569 | #endif |
---|
[aff5ae] | 570 | { |
---|
[35aab3] | 571 | #if !defined(HAVE_DIV_MOD) || !defined(HAVE_MULT_MOD) |
---|
[e77676] | 572 | r->npExpTable=(unsigned short *)omAlloc( r->ch*sizeof(unsigned short) ); |
---|
| 573 | r->npLogTable=(unsigned short *)omAlloc( r->ch*sizeof(unsigned short) ); |
---|
[aff5ae] | 574 | r->npExpTable[0] = 1; |
---|
| 575 | r->npLogTable[0] = 0; |
---|
[e77676] | 576 | if (r->ch > 2) |
---|
[aff5ae] | 577 | { |
---|
| 578 | w = 1; |
---|
| 579 | loop |
---|
[35aab3] | 580 | { |
---|
[aff5ae] | 581 | r->npLogTable[1] = 0; |
---|
| 582 | w++; |
---|
| 583 | i = 0; |
---|
[35aab3] | 584 | loop |
---|
| 585 | { |
---|
[aff5ae] | 586 | i++; |
---|
[2f864f] | 587 | r->npExpTable[i] =(int)(((long)w * (long)r->npExpTable[i-1]) % r->ch); |
---|
[aff5ae] | 588 | r->npLogTable[r->npExpTable[i]] = i; |
---|
[601105] | 589 | if /*(i == r->ch - 1 ) ||*/ (/*(*/ r->npExpTable[i] == 1 /*)*/) |
---|
[35aab3] | 590 | break; |
---|
| 591 | } |
---|
[e77676] | 592 | if (i == r->ch - 1) |
---|
[aff5ae] | 593 | break; |
---|
[35aab3] | 594 | } |
---|
[aff5ae] | 595 | } |
---|
| 596 | else |
---|
| 597 | { |
---|
| 598 | r->npExpTable[1] = 1; |
---|
| 599 | r->npLogTable[1] = 0; |
---|
| 600 | } |
---|
[35aab3] | 601 | #endif |
---|
| 602 | #ifdef HAVE_DIV_MOD |
---|
[e77676] | 603 | r->npInvTable=(unsigned short*)omAlloc0( r->ch*sizeof(unsigned short) ); |
---|
[35aab3] | 604 | #endif |
---|
[aff5ae] | 605 | } |
---|
[5d594a9] | 606 | return FALSE; |
---|
[35aab3] | 607 | } |
---|
| 608 | |
---|
| 609 | #ifdef LDEBUG |
---|
[2b957a] | 610 | BOOLEAN npDBTest (number a, const char *f, const int l, const coeffs r) |
---|
[35aab3] | 611 | { |
---|
[9b88e6] | 612 | if (((long)a<0L) || ((long)a>(long)r->ch)) |
---|
[35aab3] | 613 | { |
---|
[f1e33bb] | 614 | Print("wrong mod p number %ld at %s,%d\n",(long)a,f,l); |
---|
[35aab3] | 615 | return FALSE; |
---|
| 616 | } |
---|
| 617 | return TRUE; |
---|
| 618 | } |
---|
| 619 | #endif |
---|
| 620 | |
---|
[29fc71e] | 621 | static number npMapP(number from, const coeffs src, const coeffs dst_r) |
---|
[35aab3] | 622 | { |
---|
| 623 | long i = (long)from; |
---|
[e77676] | 624 | if (i>src->ch/2) |
---|
[35aab3] | 625 | { |
---|
[e77676] | 626 | i-=src->ch; |
---|
| 627 | while (i < 0) i+=dst_r->ch; |
---|
[35aab3] | 628 | } |
---|
[e77676] | 629 | i%=dst_r->ch; |
---|
[35aab3] | 630 | return (number)i; |
---|
| 631 | } |
---|
| 632 | |
---|
[c262d5] | 633 | static number npMapLongR(number from, const coeffs /*src*/, const coeffs dst_r) |
---|
[35aab3] | 634 | { |
---|
| 635 | gmp_float *ff=(gmp_float*)from; |
---|
| 636 | mpf_t *f=ff->_mpfp(); |
---|
| 637 | number res; |
---|
[a604c3] | 638 | mpz_ptr dest,ndest; |
---|
[35aab3] | 639 | int size,i; |
---|
[c262d5] | 640 | int e,al,bl; |
---|
[7447d8] | 641 | long iz; |
---|
[35aab3] | 642 | mp_ptr qp,dd,nn; |
---|
| 643 | |
---|
| 644 | size = (*f)[0]._mp_size; |
---|
| 645 | if (size == 0) |
---|
[7d90aa] | 646 | return npInit(0,dst_r); |
---|
[35aab3] | 647 | if(size<0) |
---|
| 648 | size = -size; |
---|
| 649 | |
---|
| 650 | qp = (*f)[0]._mp_d; |
---|
| 651 | while(qp[0]==0) |
---|
| 652 | { |
---|
| 653 | qp++; |
---|
| 654 | size--; |
---|
| 655 | } |
---|
| 656 | |
---|
[e77676] | 657 | if(dst_r->ch>2) |
---|
[35aab3] | 658 | e=(*f)[0]._mp_exp-size; |
---|
| 659 | else |
---|
| 660 | e=0; |
---|
[896561] | 661 | res = ALLOC_RNUMBER(); |
---|
[35aab3] | 662 | #if defined(LDEBUG) |
---|
| 663 | res->debug=123456; |
---|
| 664 | #endif |
---|
[a604c3] | 665 | dest = res->z; |
---|
[35aab3] | 666 | |
---|
[e2202ee] | 667 | long in=0; |
---|
[35aab3] | 668 | if (e<0) |
---|
| 669 | { |
---|
| 670 | al = dest->_mp_size = size; |
---|
| 671 | if (al<2) al = 2; |
---|
| 672 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
---|
| 673 | for (i=0;i<size;i++) dd[i] = qp[i]; |
---|
| 674 | bl = 1-e; |
---|
| 675 | nn = (mp_ptr)omAlloc(sizeof(mp_limb_t)*bl); |
---|
| 676 | nn[bl-1] = 1; |
---|
| 677 | for (i=bl-2;i>=0;i--) nn[i] = 0; |
---|
[a604c3] | 678 | ndest = res->n; |
---|
[35aab3] | 679 | ndest->_mp_d = nn; |
---|
| 680 | ndest->_mp_alloc = ndest->_mp_size = bl; |
---|
| 681 | res->s = 0; |
---|
[e77676] | 682 | in=mpz_fdiv_ui(ndest,dst_r->ch); |
---|
[35aab3] | 683 | mpz_clear(ndest); |
---|
| 684 | } |
---|
| 685 | else |
---|
| 686 | { |
---|
| 687 | al = dest->_mp_size = size+e; |
---|
| 688 | if (al<2) al = 2; |
---|
| 689 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
---|
| 690 | for (i=0;i<size;i++) dd[i+e] = qp[i]; |
---|
| 691 | for (i=0;i<e;i++) dd[i] = 0; |
---|
| 692 | res->s = 3; |
---|
| 693 | } |
---|
| 694 | |
---|
| 695 | dest->_mp_d = dd; |
---|
| 696 | dest->_mp_alloc = al; |
---|
[e77676] | 697 | iz=mpz_fdiv_ui(dest,dst_r->ch); |
---|
[35aab3] | 698 | mpz_clear(dest); |
---|
| 699 | if(res->s==0) |
---|
[8c484e] | 700 | iz=(long)npDiv((number)iz,(number)in,dst_r); |
---|
[d663f2] | 701 | FREE_RNUMBER(res); // Q!? |
---|
[35aab3] | 702 | return (number)iz; |
---|
| 703 | } |
---|
| 704 | |
---|
[894f5b1] | 705 | #ifdef HAVE_RINGS |
---|
| 706 | /*2 |
---|
| 707 | * convert from a GMP integer |
---|
| 708 | */ |
---|
[29fc71e] | 709 | static number npMapGMP(number from, const coeffs /*src*/, const coeffs dst) |
---|
[894f5b1] | 710 | { |
---|
[6a70f3] | 711 | mpz_ptr erg = (mpz_ptr) omAlloc(sizeof(mpz_t)); // evtl. spaeter mit bin |
---|
[894f5b1] | 712 | mpz_init(erg); |
---|
| 713 | |
---|
[6a70f3] | 714 | mpz_mod_ui(erg, (mpz_ptr) from, dst->ch); |
---|
[894f5b1] | 715 | number r = (number) mpz_get_si(erg); |
---|
| 716 | |
---|
| 717 | mpz_clear(erg); |
---|
[7d90aa] | 718 | omFree((void *) erg); |
---|
[894f5b1] | 719 | return (number) r; |
---|
| 720 | } |
---|
| 721 | |
---|
[29fc71e] | 722 | static number npMapZ(number from, const coeffs src, const coeffs dst) |
---|
[6a1aa7] | 723 | { |
---|
| 724 | if (SR_HDL(from) & SR_INT) |
---|
| 725 | { |
---|
| 726 | long f_i=SR_TO_INT(from); |
---|
| 727 | return npInit(f_i,dst); |
---|
| 728 | } |
---|
| 729 | return npMapGMP(from,src,dst); |
---|
| 730 | } |
---|
| 731 | |
---|
[894f5b1] | 732 | /*2 |
---|
| 733 | * convert from an machine long |
---|
| 734 | */ |
---|
[29fc71e] | 735 | static number npMapMachineInt(number from, const coeffs /*src*/,const coeffs dst) |
---|
[894f5b1] | 736 | { |
---|
[e77676] | 737 | long i = (long) (((unsigned long) from) % dst->ch); |
---|
[894f5b1] | 738 | return (number) i; |
---|
| 739 | } |
---|
| 740 | #endif |
---|
| 741 | |
---|
[29fc71e] | 742 | static number npMapCanonicalForm (number a, const coeffs /*src*/, const coeffs dst) |
---|
[e9d796] | 743 | { |
---|
[e77676] | 744 | setCharacteristic (dst ->ch); |
---|
[e9d796] | 745 | CanonicalForm f= CanonicalForm ((InternalCF*)(a)); |
---|
| 746 | return (number) (f.intval()); |
---|
| 747 | } |
---|
| 748 | |
---|
[7d90aa] | 749 | nMapFunc npSetMap(const coeffs src, const coeffs dst) |
---|
[35aab3] | 750 | { |
---|
[894f5b1] | 751 | #ifdef HAVE_RINGS |
---|
[6a1aa7] | 752 | if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src)) |
---|
[894f5b1] | 753 | { |
---|
| 754 | return npMapMachineInt; |
---|
| 755 | } |
---|
[6a1aa7] | 756 | if (src->rep==n_rep_gmp) //nCoeff_is_Ring_Z(src) || nCoeff_is_Ring_PtoM(src) || nCoeff_is_Ring_ModN(src)) |
---|
[894f5b1] | 757 | { |
---|
| 758 | return npMapGMP; |
---|
| 759 | } |
---|
[6a1aa7] | 760 | if (src->rep==n_rep_gap_gmp) //nCoeff_is_Ring_Z(src) |
---|
| 761 | { |
---|
| 762 | return npMapZ; |
---|
| 763 | } |
---|
[894f5b1] | 764 | #endif |
---|
[6a1aa7] | 765 | if (src->rep==n_rep_gap_rat) /* Q, Z */ |
---|
[75f460] | 766 | { |
---|
[2206753] | 767 | return nlModP; // npMap0; // FIXME? TODO? // extern number nlModP(number q, const coeffs Q, const coeffs Zp); // Map q \in QQ \to Zp // FIXME! |
---|
[35aab3] | 768 | } |
---|
[6a1aa7] | 769 | if ((src->rep==n_rep_int) && nCoeff_is_Zp(src) ) |
---|
[35aab3] | 770 | { |
---|
[7d90aa] | 771 | if (n_GetChar(src) == n_GetChar(dst)) |
---|
[35aab3] | 772 | { |
---|
[8c484e] | 773 | return ndCopyMap; |
---|
[35aab3] | 774 | } |
---|
| 775 | else |
---|
| 776 | { |
---|
| 777 | return npMapP; |
---|
| 778 | } |
---|
| 779 | } |
---|
[6a1aa7] | 780 | if ((src->rep==n_rep_gmp_float) && nCoeff_is_long_R(src)) |
---|
[35aab3] | 781 | { |
---|
| 782 | return npMapLongR; |
---|
| 783 | } |
---|
[1cce47] | 784 | if (nCoeff_is_CF (src)) |
---|
[e9d796] | 785 | { |
---|
| 786 | return npMapCanonicalForm; |
---|
| 787 | } |
---|
[35aab3] | 788 | return NULL; /* default */ |
---|
| 789 | } |
---|
| 790 | |
---|
| 791 | // ----------------------------------------------------------- |
---|
[a1299c] | 792 | // operation for very large primes (32749< p < 2^31-1) |
---|
[35aab3] | 793 | // ---------------------------------------------------------- |
---|
| 794 | #ifdef NV_OPS |
---|
| 795 | |
---|
[7d90aa] | 796 | number nvMult (number a,number b, const coeffs r) |
---|
[35aab3] | 797 | { |
---|
[2e1b74] | 798 | //if (((long)a == 0) || ((long)b == 0)) |
---|
| 799 | // return (number)0; |
---|
| 800 | //else |
---|
[4d92d7] | 801 | return nvMultM(a,b,r); |
---|
[35aab3] | 802 | } |
---|
| 803 | |
---|
[4d92d7] | 804 | void nvInpMult(number &a, number b, const coeffs r) |
---|
[2e1b74] | 805 | { |
---|
[4d92d7] | 806 | number n=nvMultM(a,b,r); |
---|
[2e1b74] | 807 | a=n; |
---|
| 808 | } |
---|
| 809 | |
---|
| 810 | |
---|
[a74143] | 811 | inline long nvInvMod(long a, const coeffs R) |
---|
[35aab3] | 812 | { |
---|
[a74143] | 813 | #ifdef HAVE_DIV_MOD |
---|
| 814 | return InvMod(a, R); |
---|
| 815 | #else |
---|
| 816 | /// TODO: use "long InvMod(long a, const coeffs R)"?! |
---|
[601105] | 817 | |
---|
[c262d5] | 818 | long s; |
---|
[35aab3] | 819 | |
---|
[601105] | 820 | long u, u0, u1, u2, q, r; // v0, v1, v2, |
---|
[35aab3] | 821 | |
---|
[a74143] | 822 | u1=1; // v1=0; |
---|
| 823 | u2=0; // v2=1; |
---|
| 824 | u = a; |
---|
| 825 | |
---|
| 826 | long v = R->ch; |
---|
[35aab3] | 827 | |
---|
[9c8927] | 828 | while (v != 0) |
---|
| 829 | { |
---|
[35aab3] | 830 | q = u / v; |
---|
| 831 | r = u % v; |
---|
| 832 | u = v; |
---|
| 833 | v = r; |
---|
| 834 | u0 = u2; |
---|
[a74143] | 835 | // v0 = v2; |
---|
| 836 | u2 = u1 - q*u2; |
---|
| 837 | // v2 = v1 - q*v2; |
---|
[35aab3] | 838 | u1 = u0; |
---|
[a74143] | 839 | // v1 = v0; |
---|
[35aab3] | 840 | } |
---|
| 841 | |
---|
| 842 | s = u1; |
---|
| 843 | //t = v1; |
---|
| 844 | if (s < 0) |
---|
[e77676] | 845 | return s + R->ch; |
---|
[35aab3] | 846 | else |
---|
[a74143] | 847 | return s; |
---|
| 848 | #endif |
---|
[35aab3] | 849 | } |
---|
| 850 | |
---|
[7d90aa] | 851 | inline number nvInversM (number c, const coeffs r) |
---|
[35aab3] | 852 | { |
---|
[7d90aa] | 853 | long inv=nvInvMod((long)c,r); |
---|
[35aab3] | 854 | return (number)inv; |
---|
| 855 | } |
---|
| 856 | |
---|
[7d90aa] | 857 | number nvDiv (number a,number b, const coeffs r) |
---|
[35aab3] | 858 | { |
---|
[9b88e6] | 859 | if ((long)a==0L) |
---|
| 860 | return (number)0L; |
---|
| 861 | else if ((long)b==0L) |
---|
[35aab3] | 862 | { |
---|
[b7e838] | 863 | WerrorS(nDivBy0); |
---|
[9b88e6] | 864 | return (number)0L; |
---|
[35aab3] | 865 | } |
---|
| 866 | else |
---|
| 867 | { |
---|
[7d90aa] | 868 | number inv=nvInversM(b,r); |
---|
| 869 | return nvMultM(a,inv,r); |
---|
[35aab3] | 870 | } |
---|
| 871 | } |
---|
[7d90aa] | 872 | number nvInvers (number c, const coeffs r) |
---|
[35aab3] | 873 | { |
---|
[9b88e6] | 874 | if ((long)c==0L) |
---|
[35aab3] | 875 | { |
---|
[b7e838] | 876 | WerrorS(nDivBy0); |
---|
[9b88e6] | 877 | return (number)0L; |
---|
[35aab3] | 878 | } |
---|
[7d90aa] | 879 | return nvInversM(c,r); |
---|
[35aab3] | 880 | } |
---|
[cc16f0] | 881 | #if 0 |
---|
[7d90aa] | 882 | void nvPower (number a, int i, number * result, const coeffs r) |
---|
[9c8927] | 883 | { |
---|
| 884 | if (i==0) |
---|
| 885 | { |
---|
| 886 | //npInit(1,result); |
---|
| 887 | *(long *)result = 1; |
---|
| 888 | } |
---|
| 889 | else if (i==1) |
---|
| 890 | { |
---|
| 891 | *result = a; |
---|
| 892 | } |
---|
| 893 | else |
---|
| 894 | { |
---|
[7d90aa] | 895 | nvPower(a,i-1,result,r); |
---|
| 896 | *result = nvMultM(a,*result,r); |
---|
[9c8927] | 897 | } |
---|
| 898 | } |
---|
[35aab3] | 899 | #endif |
---|
[cc16f0] | 900 | #endif |
---|
[c7e3d7] | 901 | |
---|
[03f7b5] | 902 | void npCoeffWrite (const coeffs r, BOOLEAN /*details*/) |
---|
[c7e3d7] | 903 | { |
---|
[8d1432e] | 904 | Print("ZZ/%d",r->ch); |
---|
[c7e3d7] | 905 | } |
---|
| 906 | |
---|