[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[341696] | 4 | /* $Id$ */ |
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[35aab3] | 5 | /* |
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| 6 | * ABSTRACT: finite fields with a none-prime number of elements (via tables) |
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| 7 | */ |
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| 8 | |
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[18cb65] | 9 | #include <misc/auxiliary.h> |
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[35aab3] | 10 | #include <string.h> |
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[2d805a] | 11 | #include <coeffs/coeffs.h> |
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[18cb65] | 12 | #include <misc/mylimits.h> |
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| 13 | #include <omalloc/omalloc.h> |
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| 14 | #include <reporter/reporter.h> |
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[2d805a] | 15 | #include <coeffs/numbers.h> |
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| 16 | #include <coeffs/ffields.h> |
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[18cb65] | 17 | #include <resources/feFopen.h> |
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[a5cd69] | 18 | #include <math.h> |
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[d0a51ee] | 19 | |
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[5e3046] | 20 | |
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| 21 | //unsigned short *nfPlus1Table=NULL; /* the table i=log(z^i) -> log(z^i+1) */ |
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| 22 | |
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[1b078e] | 23 | const double sixteenlog2= 11.09035489; |
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[35aab3] | 24 | /* the q's from the table 'fftable' */ |
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[6f8225] | 25 | unsigned short fftable[]={ |
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| 26 | 4, 8, 16, 32, 64, 128, 256, 512,1024,2048,4096,8192,16384, 32768, |
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| 27 | /*2^2 2^3 2^4 2^5 2^6 2^7 2^8 2^9 2^10 2^11 2^12 2^13 2^14 2^15*/ |
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| 28 | 9, 27, 81,243,729,2187, 6561,19683,59049, |
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| 29 | /*3^2 3^3 3^4 3^5 3^6 3^7 3^8 3^9 3^10*/ |
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[35aab3] | 30 | 25,125,625,3125,15625, |
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| 31 | /*5^2 5^3 5^4 5^5 5^6*/ |
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| 32 | 49,343,2401,16807, |
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| 33 | /*7^2 7^3 7^4 7^5*/ |
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| 34 | 121,1331, 14641, |
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| 35 | /*11^2 11^3 11^4*/ |
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| 36 | 169, 2197, 28561, |
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| 37 | /*13^2 13^3 13^4*/ |
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| 38 | 289, 4913, |
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| 39 | /*17^2 17^3*/ |
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| 40 | 361, 6859, |
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| 41 | /*19^2 19^3*/ |
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| 42 | 529, 12167, |
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| 43 | /*23^2 23^3*/ |
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| 44 | 841, 24389, |
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| 45 | /*29^2 29^3*/ |
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| 46 | 961, 29791, |
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| 47 | /*31^2 31^3*/ |
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[6f8225] | 48 | 1369, 50653, |
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| 49 | /*37^2 37^3*/ |
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| 50 | 1681, /*41^2*/ |
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| 51 | 1849, /*43^2*/ |
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| 52 | 2209, /*47^2*/ |
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| 53 | 2809, /*53^2*/ |
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| 54 | 3481, /*59^2*/ |
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| 55 | 3721, /*61^2*/ |
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| 56 | 4489, /*67^2*/ |
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| 57 | 5041, /*71^2*/ |
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| 58 | 5329, /*73^2*/ |
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| 59 | 6241, /*79^2*/ |
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| 60 | 6889, /*83^2*/ |
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| 61 | 7921, /*89^2*/ |
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| 62 | 9409, /*97^2*/ |
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| 63 | 10201, /*101^2*/ |
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| 64 | 10609, /*103^2*/ |
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| 65 | 11449, /*107^2*/ |
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| 66 | 11881, /*109^2*/ |
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| 67 | 12769, /*113^2*/ |
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| 68 | 16129, /*127^2*/ |
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| 69 | 17161, /*131^2*/ |
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| 70 | 18769, /*137^2*/ |
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| 71 | 19321, /*139^2*/ |
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| 72 | 22201, /*149^2*/ |
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| 73 | 22801, /*151^2*/ |
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| 74 | 24649, /*157^2*/ |
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| 75 | 26569, /*163^2*/ |
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| 76 | 27889, /*167^2*/ |
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| 77 | 29929, /*173^2*/ |
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| 78 | 32041, /*179^2*/ |
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| 79 | 32761, /*181^2*/ |
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| 80 | 36481, /*191^2*/ |
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| 81 | 37249, /*193^2*/ |
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| 82 | 38809, /*197^2*/ |
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| 83 | 39601, /*199^2*/ |
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| 84 | 49729, /*223^2*/ |
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| 85 | 44521, /*211^2*/ |
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| 86 | 51529, /*227^2*/ |
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| 87 | 52441, /*229^2*/ |
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| 88 | 54289, /*233^2*/ |
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| 89 | 57121, /*239^2*/ |
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| 90 | 58081, /*241^2*/ |
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[85e68dd] | 91 | 63001, /*251^2*/ |
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[35aab3] | 92 | 0 }; |
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| 93 | |
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| 94 | /*1 |
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| 95 | * numbers in GF(p^n): |
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| 96 | * let nfCharQ=q=nfCharP^n=p^n |
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| 97 | * GF(q)\{0} will be generated by powers of an element Z |
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| 98 | * Z^i will be represented by the int i, 1 by the int 0, 0 by the int q=nfChar |
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| 99 | */ |
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| 100 | |
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| 101 | #ifdef LDEBUG |
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| 102 | /*2 |
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| 103 | * debugging: is a a valid representation of a number ? |
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| 104 | */ |
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[5e3046] | 105 | BOOLEAN nfDBTest (number a, const char *f, const int l, const coeffs r) |
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[35aab3] | 106 | { |
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[7f7b2a] | 107 | assume( r->m_nfPlus1Table != NULL ); |
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[5e3046] | 108 | if (((long)a<0L) || ((long)a>(long)r->m_nfCharQ)) |
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[35aab3] | 109 | { |
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[7447d8] | 110 | Print("wrong %d in %s:%d\n",(int)((long)a),f,l); |
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[35aab3] | 111 | return FALSE; |
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| 112 | } |
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| 113 | int i=0; |
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| 114 | do |
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| 115 | { |
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[5e3046] | 116 | if (r->m_nfPlus1Table[i]>r->m_nfCharQ) |
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[35aab3] | 117 | { |
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[5e3046] | 118 | Print("wrong table %d=%d in %s:%d\n",i,r->m_nfPlus1Table[i],f,l); |
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[35aab3] | 119 | return FALSE; |
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| 120 | } |
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| 121 | i++; |
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[5e3046] | 122 | } while (i<r->m_nfCharQ); |
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[35aab3] | 123 | return TRUE; |
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| 124 | } |
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[5e3046] | 125 | #define nfTest(N, R) nfDBTest(N,__FILE__,__LINE__, R) |
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[35aab3] | 126 | #endif |
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| 127 | |
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| 128 | /*2 |
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| 129 | * k >= 0 ? |
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| 130 | */ |
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[3510a6] | 131 | BOOLEAN nfGreaterZero (number k, const coeffs r) |
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[35aab3] | 132 | { |
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| 133 | #ifdef LDEBUG |
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[5e3046] | 134 | nfTest(k, r); |
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[35aab3] | 135 | #endif |
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[3510a6] | 136 | return !nfIsZero(k, r) && !nfIsMOne(k, r); |
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[35aab3] | 137 | } |
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| 138 | |
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| 139 | /*2 |
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| 140 | * a*b |
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| 141 | */ |
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[3510a6] | 142 | number nfMult (number a,number b, const coeffs r) |
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[35aab3] | 143 | { |
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| 144 | #ifdef LDEBUG |
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[5e3046] | 145 | nfTest(a, r); |
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| 146 | nfTest(b, r); |
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[35aab3] | 147 | #endif |
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[5e3046] | 148 | if (((long)a == (long)r->m_nfCharQ) || ((long)b == (long)r->m_nfCharQ)) |
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| 149 | return (number)(long)r->m_nfCharQ; |
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[35aab3] | 150 | /*else*/ |
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[7447d8] | 151 | int i=(int)((long)a+(long)b); |
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[5e3046] | 152 | if (i>=r->m_nfCharQ1) i-=r->m_nfCharQ1; |
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[35aab3] | 153 | #ifdef LDEBUG |
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[5e3046] | 154 | nfTest((number)(long)i, r); |
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[35aab3] | 155 | #endif |
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[1c7953] | 156 | return (number)(long)i; |
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[35aab3] | 157 | } |
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| 158 | |
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| 159 | /*2 |
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| 160 | * int -> number |
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| 161 | */ |
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[3510a6] | 162 | number nfInit (int i, const coeffs r) |
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[35aab3] | 163 | { |
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[7f7b2a] | 164 | assume( r->m_nfPlus1Table != NULL ); |
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[35aab3] | 165 | // Hmm .. this is just to prevent initialization |
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| 166 | // from nfInitChar to go into an infinite loop |
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[5e3046] | 167 | if (i==0) return (number)(long)r->m_nfCharQ; |
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| 168 | while (i < 0) i += r->m_nfCharP; |
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| 169 | while (i >= r->m_nfCharP) i -= r->m_nfCharP; |
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| 170 | if (i==0) return (number)(long)r->m_nfCharQ; |
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[900802] | 171 | unsigned short c=0; |
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[35aab3] | 172 | while (i>1) |
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| 173 | { |
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[5e3046] | 174 | c=r->m_nfPlus1Table[c]; |
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[35aab3] | 175 | i--; |
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| 176 | } |
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| 177 | #ifdef LDEBUG |
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[5e3046] | 178 | nfTest((number)(long)c, r); |
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[35aab3] | 179 | #endif |
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[1c7953] | 180 | return (number)(long)c; |
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[35aab3] | 181 | } |
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| 182 | |
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| 183 | /* |
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| 184 | * the generating element `z` |
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| 185 | */ |
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[3510a6] | 186 | number nfPar (int i, const coeffs r) |
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[35aab3] | 187 | { |
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| 188 | return (number)1; |
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| 189 | } |
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| 190 | |
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| 191 | /*2 |
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| 192 | * the degree of the "alg. number" |
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| 193 | */ |
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[3510a6] | 194 | int nfParDeg(number n, const coeffs r) |
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[35aab3] | 195 | { |
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| 196 | #ifdef LDEBUG |
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[5e3046] | 197 | nfTest(n, r); |
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[35aab3] | 198 | #endif |
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[5e3046] | 199 | if((long)r->m_nfCharQ == (long)n) return -1; |
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[7447d8] | 200 | return (int)((long)n); |
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[35aab3] | 201 | } |
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| 202 | |
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| 203 | /*2 |
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| 204 | * number -> int |
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| 205 | */ |
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[3510a6] | 206 | int nfInt (number &n, const coeffs r) |
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[35aab3] | 207 | { |
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| 208 | return 0; |
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| 209 | } |
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| 210 | |
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| 211 | /*2 |
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| 212 | * a + b |
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| 213 | */ |
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[3510a6] | 214 | number nfAdd (number a, number b, const coeffs R) |
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[35aab3] | 215 | { |
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| 216 | /*4 z^a+z^b=z^b*(z^(a-b)+1), if a>=b; * |
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| 217 | * =z^a*(z^(b-a)+1) if a<b */ |
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| 218 | #ifdef LDEBUG |
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[5e3046] | 219 | nfTest(a, R); |
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| 220 | nfTest(b, R); |
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[35aab3] | 221 | #endif |
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[5e3046] | 222 | if ((long)R->m_nfCharQ == (long)a) return b; |
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| 223 | if ((long)R->m_nfCharQ == (long)b) return a; |
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[7447d8] | 224 | long zb,zab,r; |
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| 225 | if ((long)a >= (long)b) |
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[35aab3] | 226 | { |
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[7447d8] | 227 | zb = (long)b; |
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| 228 | zab = (long)a-(long)b; |
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[35aab3] | 229 | } |
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| 230 | else |
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| 231 | { |
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[7447d8] | 232 | zb = (long)a; |
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| 233 | zab = (long)b-(long)a; |
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[35aab3] | 234 | } |
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| 235 | #ifdef LDEBUG |
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[5e3046] | 236 | nfTest((number)zab, R); |
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[35aab3] | 237 | #endif |
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[5e3046] | 238 | if (R->m_nfPlus1Table[zab]==R->m_nfCharQ) r=(long)R->m_nfCharQ; /*if z^(a-b)+1 =0*/ |
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[35aab3] | 239 | else |
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| 240 | { |
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[5e3046] | 241 | r= zb+(long)R->m_nfPlus1Table[zab]; |
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| 242 | if(r>=(long)R->m_nfCharQ1) r-=(long)R->m_nfCharQ1; |
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[35aab3] | 243 | } |
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| 244 | #ifdef LDEBUG |
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[5e3046] | 245 | nfTest((number)r, R); |
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[35aab3] | 246 | #endif |
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| 247 | return (number)r; |
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| 248 | } |
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| 249 | |
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| 250 | /*2 |
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| 251 | * a - b |
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| 252 | */ |
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[3510a6] | 253 | number nfSub (number a, number b, const coeffs r) |
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[35aab3] | 254 | { |
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[3510a6] | 255 | number mb = nfNeg(b, r); |
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| 256 | return nfAdd(a,mb,r); |
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[35aab3] | 257 | } |
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| 258 | |
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| 259 | /*2 |
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| 260 | * a == 0 ? |
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| 261 | */ |
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[3510a6] | 262 | BOOLEAN nfIsZero (number a, const coeffs r) |
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[35aab3] | 263 | { |
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| 264 | #ifdef LDEBUG |
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[5e3046] | 265 | nfTest(a, r); |
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[35aab3] | 266 | #endif |
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[5e3046] | 267 | return (long)r->m_nfCharQ == (long)a; |
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[35aab3] | 268 | } |
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| 269 | |
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| 270 | /*2 |
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| 271 | * a == 1 ? |
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| 272 | */ |
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[3510a6] | 273 | BOOLEAN nfIsOne (number a, const coeffs r) |
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[35aab3] | 274 | { |
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| 275 | #ifdef LDEBUG |
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[5e3046] | 276 | nfTest(a, r); |
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[35aab3] | 277 | #endif |
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[7447d8] | 278 | return 0L == (long)a; |
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[35aab3] | 279 | } |
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| 280 | |
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| 281 | /*2 |
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| 282 | * a == -1 ? |
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| 283 | */ |
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[3510a6] | 284 | BOOLEAN nfIsMOne (number a, const coeffs r) |
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[35aab3] | 285 | { |
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| 286 | #ifdef LDEBUG |
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[5e3046] | 287 | nfTest(a, r); |
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[35aab3] | 288 | #endif |
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[7447d8] | 289 | if (0L == (long)a) return FALSE; /* special handling of char 2*/ |
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[5e3046] | 290 | return (long)r->m_nfM1 == (long)a; |
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[35aab3] | 291 | } |
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| 292 | |
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| 293 | /*2 |
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| 294 | * a / b |
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| 295 | */ |
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[3510a6] | 296 | number nfDiv (number a,number b, const coeffs r) |
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[35aab3] | 297 | { |
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| 298 | #ifdef LDEBUG |
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[5e3046] | 299 | nfTest(b, r); |
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[35aab3] | 300 | #endif |
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[5e3046] | 301 | if ((long)b==(long)r->m_nfCharQ) |
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[35aab3] | 302 | { |
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[b7e838] | 303 | WerrorS(nDivBy0); |
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[5e3046] | 304 | return (number)((long)r->m_nfCharQ); |
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[35aab3] | 305 | } |
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| 306 | #ifdef LDEBUG |
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[5e3046] | 307 | nfTest(a, r); |
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[35aab3] | 308 | #endif |
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[5e3046] | 309 | if ((long)a==(long)r->m_nfCharQ) |
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| 310 | return (number)((long)r->m_nfCharQ); |
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[35aab3] | 311 | /*else*/ |
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[7447d8] | 312 | long s = (long)a - (long)b; |
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| 313 | if (s < 0L) |
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[5e3046] | 314 | s += (long)r->m_nfCharQ1; |
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[35aab3] | 315 | #ifdef LDEBUG |
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[5e3046] | 316 | nfTest((number)s, r); |
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[35aab3] | 317 | #endif |
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| 318 | return (number)s; |
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| 319 | } |
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| 320 | |
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| 321 | /*2 |
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| 322 | * 1 / c |
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| 323 | */ |
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[3510a6] | 324 | number nfInvers (number c, const coeffs r) |
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[35aab3] | 325 | { |
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| 326 | #ifdef LDEBUG |
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[5e3046] | 327 | nfTest(c, r); |
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[35aab3] | 328 | #endif |
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[5e3046] | 329 | if ((long)c==(long)r->m_nfCharQ) |
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[35aab3] | 330 | { |
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[b7e838] | 331 | WerrorS(nDivBy0); |
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[5e3046] | 332 | return (number)((long)r->m_nfCharQ); |
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[35aab3] | 333 | } |
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| 334 | #ifdef LDEBUG |
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[5e3046] | 335 | nfTest(((number)((long)r->m_nfCharQ1-(long)c)), r); |
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[35aab3] | 336 | #endif |
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[5e3046] | 337 | return (number)((long)r->m_nfCharQ1-(long)c); |
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[35aab3] | 338 | } |
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| 339 | |
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| 340 | /*2 |
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| 341 | * -c |
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| 342 | */ |
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[3510a6] | 343 | number nfNeg (number c, const coeffs r) |
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[35aab3] | 344 | { |
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| 345 | /*4 -z^c=z^c*(-1)=z^c*nfM1*/ |
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| 346 | #ifdef LDEBUG |
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[5e3046] | 347 | nfTest(c, r); |
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[35aab3] | 348 | #endif |
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[5e3046] | 349 | if ((long)r->m_nfCharQ == (long)c) return c; |
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| 350 | long i=(long)c+(long)r->m_nfM1; |
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| 351 | if (i>=(long)r->m_nfCharQ1) i-=(long)r->m_nfCharQ1; |
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[35aab3] | 352 | #ifdef LDEBUG |
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[5e3046] | 353 | nfTest((number)i, r); |
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[35aab3] | 354 | #endif |
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| 355 | return (number)i; |
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| 356 | } |
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| 357 | |
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| 358 | /*2 |
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| 359 | * a > b ? |
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| 360 | */ |
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[3510a6] | 361 | BOOLEAN nfGreater (number a,number b, const coeffs r) |
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[35aab3] | 362 | { |
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| 363 | #ifdef LDEBUG |
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[5e3046] | 364 | nfTest(a, r); |
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| 365 | nfTest(b, r); |
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[35aab3] | 366 | #endif |
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[7447d8] | 367 | return (long)a != (long)b; |
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[35aab3] | 368 | } |
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| 369 | |
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| 370 | /*2 |
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| 371 | * a == b ? |
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| 372 | */ |
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[3510a6] | 373 | BOOLEAN nfEqual (number a,number b, const coeffs r) |
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[35aab3] | 374 | { |
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| 375 | #ifdef LDEBUG |
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[5e3046] | 376 | nfTest(a, r); |
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| 377 | nfTest(b, r); |
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[35aab3] | 378 | #endif |
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[7447d8] | 379 | return (long)a == (long)b; |
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[35aab3] | 380 | } |
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| 381 | |
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| 382 | /*2 |
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| 383 | * write via StringAppend |
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| 384 | */ |
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[3510a6] | 385 | void nfWrite (number &a, const coeffs r) |
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[35aab3] | 386 | { |
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| 387 | #ifdef LDEBUG |
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[5e3046] | 388 | nfTest(a, r); |
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[35aab3] | 389 | #endif |
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[5e3046] | 390 | if ((long)a==(long)r->m_nfCharQ) StringAppendS("0"); |
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[7447d8] | 391 | else if ((long)a==0L) StringAppendS("1"); |
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[3510a6] | 392 | else if (nfIsMOne(a, r)) StringAppendS("-1"); |
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[35aab3] | 393 | else |
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| 394 | { |
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[dc06550] | 395 | StringAppendS(r->m_nfParameter); |
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[7447d8] | 396 | if ((long)a!=1L) |
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[35aab3] | 397 | { |
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[493225] | 398 | if(r->ShortOut==0) StringAppendS("^"); |
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[7447d8] | 399 | StringAppend("%d",(int)((long)a)); |
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[35aab3] | 400 | } |
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| 401 | } |
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| 402 | } |
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| 403 | |
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| 404 | /*2 |
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| 405 | * |
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| 406 | */ |
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[3510a6] | 407 | char * nfName(number a, const coeffs r) |
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[35aab3] | 408 | { |
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| 409 | #ifdef LDEBUG |
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[5e3046] | 410 | nfTest(a, r); |
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[35aab3] | 411 | #endif |
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| 412 | char *s; |
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[dc06550] | 413 | char *nfParameter=r->m_nfParameter; |
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[5e3046] | 414 | if (((long)a==(long)r->m_nfCharQ) || ((long)a==0L)) return NULL; |
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[7447d8] | 415 | else if ((long)a==1L) |
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[35aab3] | 416 | { |
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| 417 | return omStrDup(nfParameter); |
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| 418 | } |
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| 419 | else |
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| 420 | { |
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| 421 | s=(char *)omAlloc(4+strlen(nfParameter)); |
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[7447d8] | 422 | sprintf(s,"%s%d",nfParameter,(int)((long)a)); |
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[35aab3] | 423 | } |
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| 424 | return s; |
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| 425 | } |
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| 426 | /*2 |
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| 427 | * c ^ i with i>=0 |
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| 428 | */ |
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[3510a6] | 429 | void nfPower (number a, int i, number * result, const coeffs r) |
---|
[35aab3] | 430 | { |
---|
| 431 | #ifdef LDEBUG |
---|
[5e3046] | 432 | nfTest(a, r); |
---|
[35aab3] | 433 | #endif |
---|
| 434 | if (i==0) |
---|
| 435 | { |
---|
| 436 | //*result=nfInit(1); |
---|
[7447d8] | 437 | *result = (number)0L; |
---|
[35aab3] | 438 | } |
---|
| 439 | else if (i==1) |
---|
| 440 | { |
---|
| 441 | *result = a; |
---|
| 442 | } |
---|
| 443 | else |
---|
| 444 | { |
---|
[3510a6] | 445 | nfPower(a,i-1,result, r); |
---|
| 446 | *result = nfMult(a,*result, r); |
---|
[35aab3] | 447 | } |
---|
| 448 | #ifdef LDEBUG |
---|
[5e3046] | 449 | nfTest(*result, r); |
---|
[35aab3] | 450 | #endif |
---|
| 451 | } |
---|
| 452 | |
---|
| 453 | /*4 |
---|
| 454 | * read an integer (with reduction mod p) |
---|
| 455 | */ |
---|
[5e3046] | 456 | static const char* nfEati(const char *s, int *i, const coeffs r) |
---|
[35aab3] | 457 | { |
---|
| 458 | if (*s >= '0' && *s <= '9') |
---|
| 459 | { |
---|
| 460 | *i = 0; |
---|
| 461 | do |
---|
| 462 | { |
---|
| 463 | *i *= 10; |
---|
| 464 | *i += *s++ - '0'; |
---|
[5e3046] | 465 | if (*i > (INT_MAX / 10)) *i = *i % r->m_nfCharP; |
---|
[35aab3] | 466 | } |
---|
| 467 | while (*s >= '0' && *s <= '9'); |
---|
[5e3046] | 468 | if (*i >= r->m_nfCharP) *i = *i % r->m_nfCharP; |
---|
[35aab3] | 469 | } |
---|
| 470 | else *i = 1; |
---|
| 471 | return s; |
---|
| 472 | } |
---|
| 473 | |
---|
| 474 | /*2 |
---|
| 475 | * read a number |
---|
| 476 | */ |
---|
[3510a6] | 477 | const char * nfRead (const char *s, number *a, const coeffs r) |
---|
[35aab3] | 478 | { |
---|
| 479 | int i; |
---|
| 480 | number z; |
---|
| 481 | number n; |
---|
| 482 | |
---|
[5e3046] | 483 | s = nfEati(s, &i, r); |
---|
[3510a6] | 484 | z=nfInit(i, r); |
---|
[35aab3] | 485 | *a=z; |
---|
| 486 | if (*s == '/') |
---|
| 487 | { |
---|
| 488 | s++; |
---|
[5e3046] | 489 | s = nfEati(s, &i, r); |
---|
[3510a6] | 490 | n=nfInit(i, r); |
---|
| 491 | *a = nfDiv(z,n,r); |
---|
[35aab3] | 492 | } |
---|
[dc06550] | 493 | char *nfParameter=r->m_nfParameter; |
---|
[35aab3] | 494 | if (strncmp(s,nfParameter,strlen(nfParameter))==0) |
---|
| 495 | { |
---|
| 496 | s+=strlen(nfParameter); |
---|
| 497 | if ((*s >= '0') && (*s <= '9')) |
---|
| 498 | { |
---|
| 499 | s=eati(s,&i); |
---|
[5e3046] | 500 | while (i>=r->m_nfCharQ1) i-=r->m_nfCharQ1; |
---|
[35aab3] | 501 | } |
---|
| 502 | else |
---|
| 503 | i=1; |
---|
[01a57b] | 504 | z=(number)(long)i; |
---|
[3510a6] | 505 | *a=nfMult(*a,z,r); |
---|
[35aab3] | 506 | } |
---|
| 507 | #ifdef LDEBUG |
---|
[5e3046] | 508 | nfTest(*a, r); |
---|
[35aab3] | 509 | #endif |
---|
| 510 | return s; |
---|
| 511 | } |
---|
| 512 | |
---|
| 513 | #ifdef HAVE_FACTORY |
---|
| 514 | int gf_tab_numdigits62 ( int q ); |
---|
| 515 | int convertback62 ( char * p, int n ); |
---|
| 516 | #else |
---|
| 517 | static int gf_tab_numdigits62 ( int q ) |
---|
| 518 | { |
---|
| 519 | if ( q < 62 ) return 1; |
---|
| 520 | else if ( q < 62*62 ) return 2; |
---|
| 521 | /*else*/ return 3; |
---|
| 522 | } |
---|
| 523 | |
---|
| 524 | static int convback62 ( char c ) |
---|
| 525 | { |
---|
| 526 | if ( c >= '0' && c <= '9' ) |
---|
| 527 | return int(c) - int('0'); |
---|
| 528 | else if ( c >= 'A' && c <= 'Z' ) |
---|
| 529 | return int(c) - int('A') + 10; |
---|
| 530 | else |
---|
| 531 | return int(c) - int('a') + 36; |
---|
| 532 | } |
---|
| 533 | |
---|
| 534 | static int convertback62 ( char * p, int n ) |
---|
| 535 | { |
---|
| 536 | int r = 0; |
---|
| 537 | for ( int j = 0; j < n; j++ ) |
---|
| 538 | r = r * 62 + convback62( p[j] ); |
---|
| 539 | return r; |
---|
| 540 | } |
---|
| 541 | #endif |
---|
| 542 | |
---|
| 543 | int nfMinPoly[16]; |
---|
| 544 | |
---|
[d0a51ee] | 545 | void nfShowMipo(const coeffs r) |
---|
[35aab3] | 546 | { |
---|
| 547 | int i=nfMinPoly[0]; |
---|
| 548 | int j=0; |
---|
| 549 | loop |
---|
| 550 | { |
---|
| 551 | j++; |
---|
| 552 | if (nfMinPoly[j]!=0) |
---|
[dc06550] | 553 | StringAppend("%d*%s^%d",nfMinPoly[j],r->m_nfParameter,i); |
---|
[35aab3] | 554 | i--; |
---|
| 555 | if(i<0) break; |
---|
| 556 | if (nfMinPoly[j]!=0) |
---|
| 557 | StringAppendS("+"); |
---|
| 558 | } |
---|
| 559 | } |
---|
| 560 | |
---|
| 561 | static void nfReadMipo(char *s) |
---|
| 562 | { |
---|
| 563 | const char *l=strchr(s,';')+1; |
---|
| 564 | char *n; |
---|
| 565 | int i=strtol(l,&n,10); |
---|
| 566 | l=n; |
---|
| 567 | int j=1; |
---|
| 568 | nfMinPoly[0]=i; |
---|
| 569 | while(i>=0) |
---|
| 570 | { |
---|
| 571 | nfMinPoly[j]=strtol(l,&n,10); |
---|
| 572 | if (l==n) break; |
---|
| 573 | l=n; |
---|
| 574 | j++; |
---|
| 575 | i--; |
---|
| 576 | } |
---|
| 577 | if (i>=0) |
---|
| 578 | { |
---|
| 579 | WerrorS("error in reading minpoly from gftables"); |
---|
| 580 | } |
---|
| 581 | } |
---|
| 582 | |
---|
| 583 | /*2 |
---|
| 584 | * init global variables from files 'gftables/%d' |
---|
| 585 | */ |
---|
[5e3046] | 586 | void nfReadTable(const int c, const coeffs r) |
---|
[35aab3] | 587 | { |
---|
| 588 | //Print("GF(%d)\n",c); |
---|
[5e3046] | 589 | if ((c==r->m_nfCharQ)||(c==-r->m_nfCharQ)) |
---|
[35aab3] | 590 | /*this field is already set*/ return; |
---|
| 591 | int i=0; |
---|
[1b078e] | 592 | |
---|
| 593 | while ((fftable[i]!=c) && (fftable[i]!=0)) |
---|
| 594 | i++; |
---|
| 595 | |
---|
[35aab3] | 596 | if (fftable[i]==0) |
---|
[1b078e] | 597 | { |
---|
| 598 | Werror("illegal GF-table size: %d", c); |
---|
[35aab3] | 599 | return; |
---|
[1b078e] | 600 | } |
---|
| 601 | |
---|
[5e3046] | 602 | if (r->m_nfCharQ > 1) |
---|
[35aab3] | 603 | { |
---|
[5e3046] | 604 | omFreeSize( (ADDRESS)r->m_nfPlus1Table,r->m_nfCharQ*sizeof(unsigned short) ); |
---|
| 605 | r->m_nfPlus1Table=NULL; |
---|
[35aab3] | 606 | } |
---|
| 607 | if ((c>1) || (c<0)) |
---|
| 608 | { |
---|
[5e3046] | 609 | if (c>1) r->m_nfCharQ = c; |
---|
| 610 | else r->m_nfCharQ = -c; |
---|
[35aab3] | 611 | char buf[100]; |
---|
[5e3046] | 612 | sprintf(buf,"gftables/%d",r->m_nfCharQ); |
---|
[35aab3] | 613 | FILE * fp = feFopen(buf,"r",NULL,TRUE); |
---|
| 614 | if (fp==NULL) |
---|
| 615 | { |
---|
| 616 | return; |
---|
| 617 | } |
---|
| 618 | if(!fgets( buf, sizeof(buf), fp)) return; |
---|
| 619 | if(strcmp(buf,"@@ factory GF(q) table @@\n")!=0) |
---|
| 620 | { |
---|
| 621 | goto err; |
---|
| 622 | } |
---|
| 623 | if(!fgets( buf, sizeof(buf), fp)) |
---|
| 624 | { |
---|
| 625 | goto err; |
---|
| 626 | } |
---|
| 627 | int q; |
---|
[5e3046] | 628 | sscanf(buf,"%d %d",&r->m_nfCharP,&q); |
---|
[35aab3] | 629 | nfReadMipo(buf); |
---|
[5e3046] | 630 | r->m_nfCharQ1=r->m_nfCharQ-1; |
---|
[35aab3] | 631 | //Print("nfCharQ=%d,nfCharQ1=%d,mipo=>>%s<<\n",nfCharQ,nfCharQ1,buf); |
---|
[5e3046] | 632 | r->m_nfPlus1Table= (unsigned short *)omAlloc( (r->m_nfCharQ)*sizeof(unsigned short) ); |
---|
| 633 | int digs = gf_tab_numdigits62( r->m_nfCharQ ); |
---|
[35aab3] | 634 | char * bufptr; |
---|
| 635 | int i = 1; |
---|
| 636 | int k; |
---|
[5e3046] | 637 | while ( i < r->m_nfCharQ ) |
---|
[35aab3] | 638 | { |
---|
| 639 | fgets( buf, sizeof(buf), fp); |
---|
| 640 | //( strlen( buffer ) == (size_t)digs * 30, "illegal table" ); |
---|
| 641 | bufptr = buf; |
---|
| 642 | k = 0; |
---|
[5e3046] | 643 | while ( (i < r->m_nfCharQ) && (k < 30) ) |
---|
[35aab3] | 644 | { |
---|
[5e3046] | 645 | r->m_nfPlus1Table[i] = convertback62( bufptr, digs ); |
---|
| 646 | if(r->m_nfPlus1Table[i]>r->m_nfCharQ) |
---|
[35aab3] | 647 | { |
---|
[5e3046] | 648 | Print("wrong entry %d: %d(%c%c%c)\n",i,r->m_nfPlus1Table[i],bufptr[0],bufptr[1],bufptr[2]); |
---|
[35aab3] | 649 | } |
---|
| 650 | bufptr += digs; |
---|
[5e3046] | 651 | if (r->m_nfPlus1Table[i]==r->m_nfCharQ) |
---|
[35aab3] | 652 | { |
---|
[5e3046] | 653 | if(i==r->m_nfCharQ1) |
---|
[35aab3] | 654 | { |
---|
[5e3046] | 655 | r->m_nfM1=0; |
---|
[35aab3] | 656 | } |
---|
| 657 | else |
---|
| 658 | { |
---|
[5e3046] | 659 | r->m_nfM1=i; |
---|
[35aab3] | 660 | } |
---|
| 661 | } |
---|
| 662 | i++; k++; |
---|
| 663 | } |
---|
| 664 | } |
---|
[5e3046] | 665 | r->m_nfPlus1Table[0]=r->m_nfPlus1Table[r->m_nfCharQ1]; |
---|
[35aab3] | 666 | } |
---|
| 667 | else |
---|
[5e3046] | 668 | r->m_nfCharQ=0; |
---|
[35aab3] | 669 | #ifdef LDEBUG |
---|
[5e3046] | 670 | nfTest((number)0, r); |
---|
[35aab3] | 671 | #endif |
---|
| 672 | return; |
---|
| 673 | err: |
---|
[5e3046] | 674 | Werror("illegal GF-table %d",r->m_nfCharQ); |
---|
[35aab3] | 675 | } |
---|
| 676 | |
---|
| 677 | /*2 |
---|
| 678 | * map Z/p -> GF(p,n) |
---|
| 679 | */ |
---|
[49a64cf] | 680 | number nfMapP(number c, const coeffs, const coeffs dst) |
---|
[35aab3] | 681 | { |
---|
[d0a51ee] | 682 | return nfInit((int)((long)c), dst); |
---|
[35aab3] | 683 | } |
---|
| 684 | |
---|
[85e68dd] | 685 | /*2 |
---|
| 686 | * map GF(p,n1) -> GF(p,n2), n1 < n2, n1 | n2 |
---|
| 687 | */ |
---|
| 688 | int nfMapGG_factor; |
---|
[49a64cf] | 689 | number nfMapGG(number c, const coeffs src, const coeffs) |
---|
[85e68dd] | 690 | { |
---|
| 691 | int i=(long)c; |
---|
| 692 | i*= nfMapGG_factor; |
---|
[5e3046] | 693 | while (i >src->m_nfCharQ1) i-=src->m_nfCharQ1; |
---|
[85e68dd] | 694 | return (number)((long)i); |
---|
| 695 | } |
---|
| 696 | /*2 |
---|
| 697 | * map GF(p,n1) -> GF(p,n2), n1 > n2, n2 | n1 |
---|
| 698 | */ |
---|
[49a64cf] | 699 | number nfMapGGrev(number c, const coeffs src, const coeffs) |
---|
[85e68dd] | 700 | { |
---|
| 701 | int ex=(int)((long)c); |
---|
| 702 | if ((ex % nfMapGG_factor)==0) |
---|
| 703 | return (number)(((long)ex) / ((long)nfMapGG_factor)); |
---|
| 704 | else |
---|
[5e3046] | 705 | return (number)(long)src->m_nfCharQ; /* 0 */ |
---|
[85e68dd] | 706 | } |
---|
| 707 | |
---|
[35aab3] | 708 | /*2 |
---|
| 709 | * set map function nMap ... -> GF(p,n) |
---|
| 710 | */ |
---|
[a0ce49] | 711 | nMapFunc nfSetMap(const coeffs src, const coeffs dst) |
---|
[35aab3] | 712 | { |
---|
[1cce47] | 713 | if (nCoeff_is_GF(src,src->m_nfCharQ)) |
---|
[35aab3] | 714 | { |
---|
[d0a51ee] | 715 | return ndCopyMap; /* GF(p,n) -> GF(p,n) */ |
---|
[35aab3] | 716 | } |
---|
[1cce47] | 717 | if (nCoeff_is_GF(src)) |
---|
[85e68dd] | 718 | { |
---|
[a0ce49] | 719 | const coeffs r = dst; |
---|
[85e68dd] | 720 | int q=src->ch; |
---|
[5e3046] | 721 | if ((src->m_nfCharQ % q)==0) /* GF(p,n1) -> GF(p,n2), n2 > n1 */ |
---|
[85e68dd] | 722 | { |
---|
| 723 | // check if n2 is a multiple of n1 |
---|
| 724 | int n1=1; |
---|
[5e3046] | 725 | int qq=r->m_nfCharP; |
---|
| 726 | while(qq!=q) { qq *= r->m_nfCharP; n1++; } |
---|
[85e68dd] | 727 | int n2=1; |
---|
[5e3046] | 728 | qq=r->m_nfCharP; |
---|
| 729 | while(qq!=src->m_nfCharQ) { qq *= r->m_nfCharP; n2++; } |
---|
| 730 | Print("map %d^%d -> %d^%d\n",r->m_nfCharP,n1,r->m_nfCharP,n2); |
---|
[85e68dd] | 731 | if ((n2 % n1)==0) |
---|
| 732 | { |
---|
[d0a51ee] | 733 | int save_ch=r->ch; |
---|
[5e3046] | 734 | nfReadTable(src->ch, r); |
---|
| 735 | int nn=r->m_nfPlus1Table[0]; |
---|
| 736 | nfReadTable(save_ch, r); |
---|
| 737 | nfMapGG_factor= r->m_nfPlus1Table[0] / nn; |
---|
| 738 | Print("nfMapGG_factor=%d (%d / %d)\n",nfMapGG_factor, r->m_nfPlus1Table[0], nn); |
---|
[85e68dd] | 739 | return nfMapGG; |
---|
| 740 | } |
---|
| 741 | else if ((n1 % n2)==0) |
---|
| 742 | { |
---|
| 743 | nfMapGG_factor= (n1/n2); |
---|
| 744 | return nfMapGGrev; |
---|
| 745 | } |
---|
| 746 | else |
---|
| 747 | return NULL; |
---|
| 748 | } |
---|
| 749 | } |
---|
[1cce47] | 750 | if (nCoeff_is_Zp(src,src->m_nfCharP)) |
---|
[35aab3] | 751 | { |
---|
| 752 | return nfMapP; /* Z/p -> GF(p,n) */ |
---|
| 753 | } |
---|
| 754 | return NULL; /* default */ |
---|
| 755 | } |
---|
[5e3046] | 756 | |
---|
[1cce47] | 757 | BOOLEAN nfInitChar(coeffs r, void * parameter) |
---|
[5e3046] | 758 | { |
---|
| 759 | |
---|
| 760 | |
---|
| 761 | //r->cfInitChar=npInitChar; |
---|
| 762 | //r->cfKillChar=nfKillChar; |
---|
| 763 | r->cfSetChar= NULL; |
---|
| 764 | //r->nCoeffIsEqual=nfCoeffsEqual; |
---|
| 765 | |
---|
| 766 | r->cfMult = nfMult; |
---|
| 767 | r->cfSub = nfSub; |
---|
| 768 | r->cfAdd = nfAdd; |
---|
| 769 | r->cfDiv = nfDiv; |
---|
| 770 | r->cfIntDiv= nfDiv; |
---|
| 771 | //r->cfIntMod= ndIntMod; |
---|
| 772 | r->cfExactDiv= nfDiv; |
---|
| 773 | r->cfInit = nfInit; |
---|
| 774 | //r->cfPar = ndPar; |
---|
| 775 | //r->cfParDeg = ndParDeg; |
---|
| 776 | //r->cfSize = ndSize; |
---|
| 777 | r->cfInt = nfInt; |
---|
| 778 | #ifdef HAVE_RINGS |
---|
| 779 | //r->cfDivComp = NULL; // only for ring stuff |
---|
| 780 | //r->cfIsUnit = NULL; // only for ring stuff |
---|
| 781 | //r->cfGetUnit = NULL; // only for ring stuff |
---|
| 782 | //r->cfExtGcd = NULL; // only for ring stuff |
---|
| 783 | // r->cfDivBy = NULL; // only for ring stuff |
---|
| 784 | #endif |
---|
| 785 | r->cfNeg = nfNeg; |
---|
| 786 | r->cfInvers= nfInvers; |
---|
| 787 | //r->cfCopy = ndCopy; |
---|
| 788 | //r->cfRePart = ndCopy; |
---|
| 789 | //r->cfImPart = ndReturn0; |
---|
| 790 | r->cfWrite = nfWrite; |
---|
| 791 | r->cfRead = nfRead; |
---|
| 792 | //r->cfNormalize=ndNormalize; |
---|
| 793 | r->cfGreater = nfGreater; |
---|
| 794 | r->cfEqual = nfEqual; |
---|
| 795 | r->cfIsZero = nfIsZero; |
---|
| 796 | r->cfIsOne = nfIsOne; |
---|
| 797 | r->cfIsMOne = nfIsMOne; |
---|
| 798 | r->cfGreaterZero = nfGreaterZero; |
---|
| 799 | r->cfPower = nfPower; |
---|
| 800 | //r->cfGcd = ndGcd; |
---|
| 801 | //r->cfLcm = ndGcd; |
---|
| 802 | //r->cfDelete= ndDelete; |
---|
| 803 | r->cfSetMap = nfSetMap; |
---|
| 804 | //r->cfName = ndName; |
---|
| 805 | // debug stuff |
---|
[c7e3d7] | 806 | r->cfCoeffWrite=nfCoeffWrite; |
---|
[a0ce49] | 807 | |
---|
| 808 | #ifdef LDEBUG |
---|
[5e3046] | 809 | r->cfDBTest=nfDBTest; |
---|
[a0ce49] | 810 | #endif |
---|
[5e3046] | 811 | |
---|
| 812 | // the variables: |
---|
| 813 | r->nNULL = (number)0; |
---|
[a0ce49] | 814 | assume( r->type == n_GF ); |
---|
[5e3046] | 815 | |
---|
[dc06550] | 816 | GFInfo* p = (GFInfo *)(parameter); |
---|
| 817 | const char * name = p->GFPar_name; |
---|
[5e3046] | 818 | r->m_nfCharQ = 0; |
---|
[dc06550] | 819 | r->m_nfCharP = p->GFChar; |
---|
| 820 | r->m_nfCharQ1 = 0; |
---|
| 821 | r->m_nfParameter= strdup(name); //TODO use omAlloc for allocating memory and use strcpy? |
---|
| 822 | r->m_nfPlus1Table= NULL; |
---|
[5e3046] | 823 | |
---|
| 824 | r->has_simple_Alloc=TRUE; |
---|
| 825 | r->has_simple_Inverse=TRUE; |
---|
[1b078e] | 826 | |
---|
| 827 | assume (p->GFChar > 0); |
---|
| 828 | assume (p->GFDegree > 0); |
---|
| 829 | |
---|
| 830 | if(p->GFChar > (2<<15)) |
---|
| 831 | { |
---|
[a9f584] | 832 | Werror("illegal characteristic"); |
---|
| 833 | return TRUE; |
---|
[1b078e] | 834 | } |
---|
| 835 | |
---|
| 836 | const double check= log ((double) (p->GFChar)); |
---|
| 837 | |
---|
| 838 | if( (p->GFDegree * check) > sixteenlog2 ) |
---|
| 839 | { |
---|
[7f7b2a] | 840 | Werror("Sorry: illegal size: %u ^ %u", p->GFChar, p->GFDegree ); |
---|
[a9f584] | 841 | return TRUE; |
---|
[1b078e] | 842 | } |
---|
| 843 | |
---|
| 844 | int c = pow (p->GFChar, p->GFDegree); |
---|
| 845 | |
---|
[5e3046] | 846 | nfReadTable(c, r); |
---|
[7f7b2a] | 847 | |
---|
| 848 | if( r->m_nfPlus1Table == NULL ) |
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| 849 | { |
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| 850 | Werror("Sorry: cannot init lookup table!"); |
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[a9f584] | 851 | return TRUE; |
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[7f7b2a] | 852 | } |
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| 853 | |
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| 854 | |
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[1b078e] | 855 | assume (r -> m_nfCharQ > 0); |
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| 856 | |
---|
[5e3046] | 857 | r->ch = r->m_nfCharP; |
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[7f7b2a] | 858 | assume( r->m_nfPlus1Table != NULL ); |
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[a9f584] | 859 | |
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| 860 | return FALSE; |
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| 861 | |
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[5e3046] | 862 | } |
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[c7e3d7] | 863 | |
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| 864 | void nfCoeffWrite (const coeffs r) |
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| 865 | { |
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| 866 | Print("// # ground field : %d\n",r->m_nfCharP); |
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| 867 | Print("// primitive element : %s\n", r->m_nfParameter); |
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| 868 | StringSetS("// minpoly : "); |
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| 869 | nfShowMipo(r);PrintS(StringAppendS("\n")); |
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| 870 | } |
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| 871 | |
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