[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* $Id: modulop.cc,v 1.1.1.1 2003-10-06 12:15:55 Singular Exp $ */ |
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| 5 | /* |
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| 6 | * ABSTRACT: numbers modulo p (<=32003) |
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| 7 | */ |
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| 8 | |
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| 9 | #include <string.h> |
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| 10 | #include "mod2.h" |
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| 11 | #include <mylimits.h> |
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| 12 | #include "structs.h" |
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| 13 | #include "febase.h" |
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| 14 | #include "omalloc.h" |
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| 15 | #include "numbers.h" |
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| 16 | #include "longrat.h" |
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| 17 | #include "mpr_complex.h" |
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| 18 | #include "ring.h" |
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| 19 | #include "modulop.h" |
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| 20 | |
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| 21 | long npPrimeM=0; |
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| 22 | int npGen=0; |
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| 23 | long npPminus1M=0; |
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| 24 | long npMapPrime; |
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| 25 | |
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| 26 | #ifdef HAVE_DIV_MOD |
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| 27 | CARDINAL *npInvTable=NULL; |
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| 28 | #endif |
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| 29 | |
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| 30 | #if !defined(HAVE_DIV_MOD) || !defined(HAVE_MULT_MOD) |
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| 31 | CARDINAL *npExpTable=NULL; |
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| 32 | CARDINAL *npLogTable=NULL; |
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| 33 | #endif |
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| 34 | |
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| 35 | |
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| 36 | BOOLEAN npGreaterZero (number k) |
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| 37 | { |
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| 38 | int h = (int) k; |
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| 39 | return ((int)h !=0) && (h <= (npPrimeM>>1)); |
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| 40 | } |
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| 41 | |
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| 42 | //unsigned long npMultMod(unsigned long a, unsigned long b) |
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| 43 | //{ |
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| 44 | // unsigned long c = a*b; |
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| 45 | // c = c % npPrimeM; |
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| 46 | // assume(c == (unsigned long) npMultM((number) a, (number) b)); |
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| 47 | // return c; |
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| 48 | //} |
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| 49 | |
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| 50 | number npMult (number a,number b) |
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| 51 | { |
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| 52 | if (((long)a == 0) || ((long)b == 0)) |
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| 53 | return (number)0; |
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| 54 | else |
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| 55 | return npMultM(a,b); |
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| 56 | } |
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| 57 | |
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| 58 | /*2 |
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| 59 | * create a number from int |
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| 60 | */ |
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| 61 | number npInit (int i) |
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| 62 | { |
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| 63 | long ii=i; |
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| 64 | while (ii < 0) ii += npPrimeM; |
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| 65 | while ((ii>1) && (ii >= npPrimeM)) ii -= npPrimeM; |
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| 66 | return (number)ii; |
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| 67 | } |
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| 68 | |
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| 69 | /*2 |
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| 70 | * convert a number to int (-p/2 .. p/2) |
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| 71 | */ |
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| 72 | int npInt(number &n) |
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| 73 | { |
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| 74 | if ((long)n > (npPrimeM >>1)) return (int)((long)n -npPrimeM); |
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| 75 | else return (int)n; |
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| 76 | } |
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| 77 | |
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| 78 | number npAdd (number a, number b) |
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| 79 | { |
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| 80 | return npAddM(a,b); |
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| 81 | } |
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| 82 | |
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| 83 | number npSub (number a, number b) |
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| 84 | { |
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| 85 | return npSubM(a,b); |
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| 86 | } |
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| 87 | |
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| 88 | BOOLEAN npIsZero (number a) |
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| 89 | { |
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| 90 | return 0 == (long)a; |
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| 91 | } |
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| 92 | |
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| 93 | BOOLEAN npIsOne (number a) |
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| 94 | { |
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| 95 | return 1 == (long)a; |
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| 96 | } |
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| 97 | |
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| 98 | BOOLEAN npIsMOne (number a) |
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| 99 | { |
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| 100 | return ((npPminus1M == (long)a)&&((long)1!=(long)a)); |
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| 101 | } |
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| 102 | |
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| 103 | #ifdef HAVE_DIV_MOD |
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| 104 | #if 1 //ifdef HAVE_NTL // in ntl.a |
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| 105 | //extern void XGCD(long& d, long& s, long& t, long a, long b); |
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| 106 | #include <NTL/ZZ.h> |
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| 107 | #ifdef NTL_CLIENT |
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| 108 | NTL_CLIENT |
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| 109 | #endif |
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| 110 | #else |
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| 111 | void XGCD(long& d, long& s, long& t, long a, long b) |
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| 112 | { |
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| 113 | long u, v, u0, v0, u1, v1, u2, v2, q, r; |
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| 114 | |
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| 115 | long aneg = 0, bneg = 0; |
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| 116 | |
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| 117 | if (a < 0) { |
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| 118 | a = -a; |
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| 119 | aneg = 1; |
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| 120 | } |
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| 121 | |
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| 122 | if (b < 0) { |
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| 123 | b = -b; |
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| 124 | bneg = 1; |
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| 125 | } |
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| 126 | |
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| 127 | u1=1; v1=0; |
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| 128 | u2=0; v2=1; |
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| 129 | u = a; v = b; |
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| 130 | |
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| 131 | while (v != 0) { |
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| 132 | q = u / v; |
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| 133 | r = u % v; |
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| 134 | u = v; |
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| 135 | v = r; |
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| 136 | u0 = u2; |
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| 137 | v0 = v2; |
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| 138 | u2 = u1 - q*u2; |
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| 139 | v2 = v1- q*v2; |
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| 140 | u1 = u0; |
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| 141 | v1 = v0; |
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| 142 | } |
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| 143 | |
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| 144 | if (aneg) |
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| 145 | u1 = -u1; |
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| 146 | |
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| 147 | if (bneg) |
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| 148 | v1 = -v1; |
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| 149 | |
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| 150 | d = u; |
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| 151 | s = u1; |
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| 152 | t = v1; |
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| 153 | } |
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| 154 | #endif |
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| 155 | |
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| 156 | long InvMod(long a) |
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| 157 | { |
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| 158 | long d, s, t; |
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| 159 | |
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| 160 | XGCD(d, s, t, a, npPrimeM); |
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| 161 | assume (d == 1); |
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| 162 | if (s < 0) |
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| 163 | return s + npPrimeM; |
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| 164 | else |
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| 165 | return s; |
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| 166 | } |
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| 167 | #endif |
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| 168 | |
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| 169 | inline number npInversM (number c) |
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| 170 | { |
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| 171 | #ifndef HAVE_DIV_MOD |
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| 172 | return (number)npExpTable[npPminus1M - npLogTable[(long)c]]; |
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| 173 | #else |
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| 174 | long inv=npInvTable[(long)c]; |
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| 175 | if (inv==0) |
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| 176 | { |
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| 177 | inv=InvMod((long)c); |
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| 178 | npInvTable[(long)c]=inv; |
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| 179 | } |
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| 180 | return (number)inv; |
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| 181 | #endif |
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| 182 | } |
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| 183 | |
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| 184 | number npDiv (number a,number b) |
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| 185 | { |
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| 186 | if ((long)a==0) |
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| 187 | return (number)0; |
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| 188 | #ifndef HAVE_DIV_MOD |
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| 189 | else if ((long)b==0) |
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| 190 | { |
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| 191 | WerrorS("div by 0"); |
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| 192 | return (number)0; |
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| 193 | } |
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| 194 | else |
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| 195 | { |
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| 196 | int s = npLogTable[(long)a] - npLogTable[(long)b]; |
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| 197 | if (s < 0) |
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| 198 | s += npPminus1M; |
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| 199 | return (number)npExpTable[s]; |
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| 200 | } |
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| 201 | #else |
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| 202 | number inv=npInversM(b); |
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| 203 | return npMultM(a,inv); |
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| 204 | #endif |
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| 205 | } |
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| 206 | number npInvers (number c) |
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| 207 | { |
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| 208 | if ((long)c==0) |
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| 209 | { |
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| 210 | WerrorS("1/0"); |
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| 211 | return (number)0; |
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| 212 | } |
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| 213 | return npInversM(c); |
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| 214 | } |
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| 215 | |
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| 216 | number npNeg (number c) |
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| 217 | { |
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| 218 | if ((long)c==0) return c; |
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| 219 | return npNegM(c); |
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| 220 | } |
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| 221 | |
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| 222 | BOOLEAN npGreater (number a,number b) |
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| 223 | { |
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| 224 | //return (long)a != (long)b; |
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| 225 | return (long)a > (long)b; |
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| 226 | } |
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| 227 | |
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| 228 | BOOLEAN npEqual (number a,number b) |
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| 229 | { |
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| 230 | // return (long)a == (long)b; |
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| 231 | return npEqualM(a,b); |
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| 232 | } |
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| 233 | |
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| 234 | void npWrite (number &a) |
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| 235 | { |
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| 236 | if ((long)a > (npPrimeM >>1)) StringAppend("-%d",(int)(npPrimeM-((long)a))); |
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| 237 | else StringAppend("%d",(int)a); |
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| 238 | } |
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| 239 | |
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| 240 | void npPower (number a, int i, number * result) |
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| 241 | { |
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| 242 | if (i==0) |
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| 243 | { |
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| 244 | //npInit(1,result); |
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| 245 | *(long *)result = 1; |
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| 246 | } |
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| 247 | else if (i==1) |
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| 248 | { |
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| 249 | *result = a; |
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| 250 | } |
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| 251 | else |
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| 252 | { |
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| 253 | npPower(a,i-1,result); |
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| 254 | *result = npMultM(a,*result); |
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| 255 | } |
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| 256 | } |
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| 257 | |
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| 258 | char* npEati(char *s, int *i) |
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| 259 | { |
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| 260 | |
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| 261 | if (((*s) >= '0') && ((*s) <= '9')) |
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| 262 | { |
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| 263 | (*i) = 0; |
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| 264 | do |
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| 265 | { |
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| 266 | (*i) *= 10; |
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| 267 | (*i) += *s++ - '0'; |
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| 268 | if ((*i) >= (MAX_INT_VAL / 10)) (*i) = (*i) % npPrimeM; |
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| 269 | } |
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| 270 | while (((*s) >= '0') && ((*s) <= '9')); |
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| 271 | if ((*i) >= npPrimeM) (*i) = (*i) % npPrimeM; |
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| 272 | } |
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| 273 | else (*i) = 1; |
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| 274 | return s; |
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| 275 | } |
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| 276 | |
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| 277 | char * npRead (char *s, number *a) |
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| 278 | { |
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| 279 | int z; |
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| 280 | int n=1; |
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| 281 | |
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| 282 | s = npEati(s, &z); |
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| 283 | if ((*s) == '/') |
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| 284 | { |
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| 285 | s++; |
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| 286 | s = npEati(s, &n); |
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| 287 | } |
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| 288 | if (n == 1) |
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| 289 | *a = (number)z; |
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| 290 | else |
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| 291 | #ifdef NV_OPS |
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| 292 | if (npPrimeM>NV_MAX_PRIME) |
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| 293 | *a = nvDiv((number)z,(number)n); |
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| 294 | else |
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| 295 | #endif |
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| 296 | *a = npDiv((number)z,(number)n); |
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| 297 | return s; |
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| 298 | } |
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| 299 | |
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| 300 | /*2 |
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| 301 | * the last used charcteristic |
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| 302 | */ |
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| 303 | //int npGetChar() |
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| 304 | //{ |
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| 305 | // return npPrimeM; |
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| 306 | //} |
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| 307 | |
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| 308 | /*2 |
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| 309 | * set the charcteristic (allocate and init tables) |
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| 310 | */ |
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| 311 | |
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| 312 | void npSetChar(int c, ring r) |
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| 313 | { |
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| 314 | // int i, w; |
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| 315 | |
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| 316 | // if (c==npPrimeM) return; |
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| 317 | if ((c>1) || (c<(-1))) |
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| 318 | { |
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| 319 | if (c>1) npPrimeM = c; |
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| 320 | else npPrimeM = -c; |
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| 321 | npPminus1M = npPrimeM - 1; |
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| 322 | #ifdef HAVE_DIV_MOD |
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| 323 | npInvTable=r->cf->npInvTable; |
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| 324 | #endif |
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| 325 | #if !defined(HAVE_DIV_MOD) || !defined(HAVE_MULT_MOD) |
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| 326 | npExpTable=r->cf->npExpTable; |
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| 327 | npLogTable=r->cf->npLogTable; |
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| 328 | npGen = npExpTable[1]; |
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| 329 | #endif |
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| 330 | } |
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| 331 | else |
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| 332 | { |
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| 333 | npPrimeM=0; |
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| 334 | #ifdef HAVE_DIV_MOD |
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| 335 | npInvTable=NULL; |
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| 336 | #endif |
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| 337 | #if !defined(HAVE_DIV_MOD) || !defined(HAVE_MULT_MOD) |
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| 338 | npExpTable=NULL; |
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| 339 | npLogTable=NULL; |
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| 340 | #endif |
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| 341 | } |
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| 342 | } |
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| 343 | |
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| 344 | void npInitChar(int c, ring r) |
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| 345 | { |
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| 346 | int i, w; |
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| 347 | |
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| 348 | if ((c>1) || (c<(-1))) |
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| 349 | { |
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| 350 | if (c>1) r->cf->npPrimeM = c; |
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| 351 | else r->cf->npPrimeM = -c; |
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| 352 | r->cf->npPminus1M = r->cf->npPrimeM - 1; |
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| 353 | #ifdef NV_OPS |
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| 354 | if (r->cf->npPrimeM <=NV_MAX_PRIME) |
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| 355 | #endif |
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| 356 | { |
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| 357 | #if !defined(HAVE_DIV_MOD) || !defined(HAVE_MULT_MOD) |
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| 358 | r->cf->npExpTable=(CARDINAL *)omAlloc( r->cf->npPrimeM*sizeof(CARDINAL) ); |
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| 359 | r->cf->npLogTable=(CARDINAL *)omAlloc( r->cf->npPrimeM*sizeof(CARDINAL) ); |
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| 360 | r->cf->npExpTable[0] = 1; |
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| 361 | r->cf->npLogTable[0] = 0; |
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| 362 | if (r->cf->npPrimeM > 2) |
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| 363 | { |
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| 364 | w = 1; |
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| 365 | loop |
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| 366 | { |
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| 367 | r->cf->npLogTable[1] = 0; |
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| 368 | w++; |
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| 369 | i = 0; |
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| 370 | loop |
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| 371 | { |
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| 372 | i++; |
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| 373 | r->cf->npExpTable[i] =(int)(((long)w * (long)r->cf->npExpTable[i-1]) |
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| 374 | % r->cf->npPrimeM); |
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| 375 | r->cf->npLogTable[r->cf->npExpTable[i]] = i; |
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| 376 | if (/*(i == npPrimeM - 1 ) ||*/ (r->cf->npExpTable[i] == 1)) |
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| 377 | break; |
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| 378 | } |
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| 379 | if (i == r->cf->npPrimeM - 1) |
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| 380 | break; |
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| 381 | } |
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| 382 | } |
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| 383 | else |
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| 384 | { |
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| 385 | r->cf->npExpTable[1] = 1; |
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| 386 | r->cf->npLogTable[1] = 0; |
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| 387 | } |
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| 388 | #endif |
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| 389 | #ifdef HAVE_DIV_MOD |
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| 390 | r->cf->npInvTable=(CARDINAL*)omAlloc0( r->cf->npPrimeM*sizeof(CARDINAL) ); |
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| 391 | #endif |
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| 392 | } |
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| 393 | } |
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| 394 | else |
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| 395 | { |
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| 396 | WarnS("nInitChar failed"); |
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| 397 | } |
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| 398 | } |
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| 399 | |
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| 400 | #ifdef LDEBUG |
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| 401 | BOOLEAN npDBTest (number a, char *f, int l) |
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| 402 | { |
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| 403 | if (((long)a<0) || ((long)a>npPrimeM)) |
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| 404 | { |
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| 405 | return FALSE; |
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| 406 | } |
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| 407 | return TRUE; |
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| 408 | } |
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| 409 | #endif |
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| 410 | |
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| 411 | number npMap0(number from) |
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| 412 | { |
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| 413 | return npInit(nlModP(from,npPrimeM)); |
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| 414 | } |
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| 415 | |
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| 416 | number npMapP(number from) |
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| 417 | { |
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| 418 | long i = (long)from; |
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| 419 | if (i>npMapPrime/2) |
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| 420 | { |
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| 421 | i-=npMapPrime; |
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| 422 | while (i < 0) i+=npPrimeM; |
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| 423 | } |
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| 424 | i%=npPrimeM; |
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| 425 | return (number)i; |
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| 426 | } |
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| 427 | |
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| 428 | static number npMapLongR(number from) |
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| 429 | { |
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| 430 | gmp_float *ff=(gmp_float*)from; |
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| 431 | mpf_t *f=ff->_mpfp(); |
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| 432 | number res; |
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| 433 | lint *dest,*ndest; |
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| 434 | int size,i; |
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| 435 | int e,al,bl,iz,in; |
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| 436 | mp_ptr qp,dd,nn; |
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| 437 | |
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| 438 | size = (*f)[0]._mp_size; |
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| 439 | if (size == 0) |
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| 440 | return npInit(0); |
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| 441 | if(size<0) |
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| 442 | size = -size; |
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| 443 | |
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| 444 | qp = (*f)[0]._mp_d; |
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| 445 | while(qp[0]==0) |
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| 446 | { |
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| 447 | qp++; |
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| 448 | size--; |
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| 449 | } |
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| 450 | |
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| 451 | if(npPrimeM>2) |
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| 452 | e=(*f)[0]._mp_exp-size; |
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| 453 | else |
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| 454 | e=0; |
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| 455 | res = (number)omAllocBin(rnumber_bin); |
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| 456 | #if defined(LDEBUG) |
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| 457 | res->debug=123456; |
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| 458 | #endif |
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| 459 | dest = &(res->z); |
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| 460 | |
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| 461 | if (e<0) |
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| 462 | { |
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| 463 | al = dest->_mp_size = size; |
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| 464 | if (al<2) al = 2; |
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| 465 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
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| 466 | for (i=0;i<size;i++) dd[i] = qp[i]; |
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| 467 | bl = 1-e; |
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| 468 | nn = (mp_ptr)omAlloc(sizeof(mp_limb_t)*bl); |
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| 469 | nn[bl-1] = 1; |
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| 470 | for (i=bl-2;i>=0;i--) nn[i] = 0; |
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| 471 | ndest = &(res->n); |
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| 472 | ndest->_mp_d = nn; |
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| 473 | ndest->_mp_alloc = ndest->_mp_size = bl; |
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| 474 | res->s = 0; |
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| 475 | in=mpz_mmod_ui(NULL,ndest,npPrimeM); |
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| 476 | mpz_clear(ndest); |
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| 477 | } |
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| 478 | else |
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| 479 | { |
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| 480 | al = dest->_mp_size = size+e; |
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| 481 | if (al<2) al = 2; |
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| 482 | dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al); |
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| 483 | for (i=0;i<size;i++) dd[i+e] = qp[i]; |
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| 484 | for (i=0;i<e;i++) dd[i] = 0; |
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| 485 | res->s = 3; |
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| 486 | } |
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| 487 | |
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| 488 | dest->_mp_d = dd; |
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| 489 | dest->_mp_alloc = al; |
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| 490 | iz=mpz_mmod_ui(NULL,dest,npPrimeM); |
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| 491 | mpz_clear(dest); |
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| 492 | omFreeBin((ADDRESS)res, rnumber_bin); |
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| 493 | if(res->s==0) |
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| 494 | iz=(int)npDiv((number)iz,(number)in); |
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| 495 | return (number)iz; |
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| 496 | } |
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| 497 | |
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| 498 | nMapFunc npSetMap(ring src, ring dst) |
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| 499 | { |
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| 500 | if (rField_is_Q(src)) |
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| 501 | { |
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| 502 | return npMap0; |
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| 503 | } |
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| 504 | if ( rField_is_Zp(src) ) |
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| 505 | { |
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| 506 | if (rChar(src) == rChar(dst)) |
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| 507 | { |
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| 508 | return ndCopy; |
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| 509 | } |
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| 510 | else |
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| 511 | { |
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| 512 | npMapPrime=rChar(src); |
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| 513 | return npMapP; |
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| 514 | } |
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| 515 | } |
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| 516 | if (rField_is_long_R(src)) |
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| 517 | { |
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| 518 | return npMapLongR; |
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| 519 | } |
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| 520 | return NULL; /* default */ |
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| 521 | } |
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| 522 | |
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| 523 | // ----------------------------------------------------------- |
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| 524 | // operation for very large primes (32003< p < 2^31-1) |
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| 525 | // ---------------------------------------------------------- |
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| 526 | #ifdef NV_OPS |
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| 527 | |
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| 528 | number nvMult (number a,number b) |
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| 529 | { |
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| 530 | if (((long)a == 0) || ((long)b == 0)) |
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| 531 | return (number)0; |
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| 532 | else |
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| 533 | return nvMultM(a,b); |
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| 534 | } |
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| 535 | |
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| 536 | long nvInvMod(long a) |
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| 537 | { |
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| 538 | long s, t; |
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| 539 | |
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| 540 | long u, v, u0, v0, u1, v1, u2, v2, q, r; |
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| 541 | |
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| 542 | u1=1; v1=0; |
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| 543 | u2=0; v2=1; |
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| 544 | u = a; v = npPrimeM; |
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| 545 | |
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| 546 | while (v != 0) { |
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| 547 | q = u / v; |
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| 548 | r = u % v; |
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| 549 | u = v; |
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| 550 | v = r; |
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| 551 | u0 = u2; |
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| 552 | v0 = v2; |
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| 553 | u2 = u1 - q*u2; |
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| 554 | v2 = v1- q*v2; |
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| 555 | u1 = u0; |
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| 556 | v1 = v0; |
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| 557 | } |
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| 558 | |
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| 559 | s = u1; |
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| 560 | //t = v1; |
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| 561 | if (s < 0) |
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| 562 | return s + npPrimeM; |
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| 563 | else |
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| 564 | return s; |
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| 565 | } |
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| 566 | |
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| 567 | inline number nvInversM (number c) |
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| 568 | { |
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| 569 | long inv=nvInvMod((long)c); |
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| 570 | return (number)inv; |
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| 571 | } |
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| 572 | |
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| 573 | number nvDiv (number a,number b) |
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| 574 | { |
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| 575 | if ((long)a==0) |
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| 576 | return (number)0; |
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| 577 | else if ((long)b==0) |
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| 578 | { |
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| 579 | WerrorS("div by 0"); |
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| 580 | return (number)0; |
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| 581 | } |
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| 582 | else |
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| 583 | { |
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| 584 | number inv=nvInversM(b); |
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| 585 | return nvMultM(a,inv); |
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| 586 | } |
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| 587 | } |
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| 588 | number nvInvers (number c) |
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| 589 | { |
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| 590 | if ((long)c==0) |
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| 591 | { |
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| 592 | WerrorS("1/0"); |
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| 593 | return (number)0; |
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| 594 | } |
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| 595 | return nvInversM(c); |
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| 596 | } |
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| 597 | #endif |
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