[543931] | 1 | /*--------------------------------------------------------------------------- |
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| 2 | / Integral LLL Algorithm | |
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| 3 | / | |
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| 4 | / Implemented by | |
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| 5 | / Alberto Vigneron-Tenorio and Alfredo Sánchez-Navarro | |
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| 6 | / alberto.vigneron@uca.es, alfredo.sanchez@uca.es | |
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| 7 | / E.U.E.Empresariales de Jerez. | |
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| 8 | / Universidad de Cádiz | |
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| 9 | / Porvera 54. | |
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| 10 | / Jerez de la Frontera (Cádiz, Spain) | |
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| 11 | / | |
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| 12 | / | |
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| 13 | / This application computes the LLL-reduced basis of a Z-lattice using | |
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| 14 | / the algorithm 2.6.7 appeared in: | |
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| 15 | / Cohen, H. A course in computational algebraic number theory. | |
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| 16 | / GTM 138, Springer 1996. | |
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| 17 | / | |
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| 18 | / The Input is a file with the structure: | |
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| 19 | / Number of vectors, Number of coordinates | |
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| 20 | / b11 b12 b13 ... b1C | |
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| 21 | / b21 b22 b23 ... b2C | |
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| 22 | / ... | |
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| 23 | / bF1 bF2 bF3 ... bFC | |
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| 24 | / | |
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| 25 | / All these inputs are integer numbers. | |
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| 26 | / | |
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| 27 | / The Output is a LLL-reduced basis of the Z-lattice generated by | |
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| 28 | / (b11,b12,...,b1C),...,(bF1,...,bFC) | |
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| 29 | / | |
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| 30 | / All these outputs are integer numbers. | |
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| 31 | ---------------------------------------------------------------------------*/ |
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| 32 | |
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| 33 | |
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| 34 | /*--------------------------------------------------------------------------- |
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| 35 | | EXAMPLE: | |
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| 36 | | | |
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| 37 | | Let prf be the file: | |
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| 38 | | 2,3 | |
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| 39 | | 1 -2 4 | |
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| 40 | | 2 1 -7 | |
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| 41 | | then: | |
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| 42 | | | |
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| 43 | | ./LLL_lattice <prf | |
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| 44 | | Output: | |
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| 45 | | 1 -2 4 | |
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| 46 | | 3 -1 -3 | |
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| 47 | | | |
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| 48 | | The output is a LLL-reduced basis of the lattice of ZxZxZ generated by | |
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| 49 | | (1,-2,4),(2,1,-7) | |
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| 50 | | | |
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| 51 | ---------------------------------------------------------------------------*/ |
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| 52 | |
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| 53 | |
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| 54 | #include <stdio.h> |
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| 55 | #include <stdlib.h> |
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| 56 | #include <string.h> |
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| 57 | #include <ctype.h> |
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| 58 | #include <new> |
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| 59 | #include <cstring> |
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[76f3a18] | 60 | #include <gmp.h> |
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[543931] | 61 | |
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| 62 | #define LLL_MAX(a,b) (a > b ? a : b) |
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| 63 | |
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| 64 | /* Global variables */ |
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| 65 | mpz_t * lll_d; |
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| 66 | mpz_t ** lll_lambda; |
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| 67 | mpz_t ** lll_b; |
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| 68 | |
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| 69 | mpz_t **proc_entrada (int *F, int *C); |
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| 70 | void lll_swapi (int k, int kmax, int C); |
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| 71 | void lll_redi (int k, int l, int C); |
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| 72 | void lll_test (int *k, int kma, int C); |
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| 73 | void lll_product (mpz_t * a, mpz_t * f, int n, mpz_t * prod); |
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| 74 | |
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| 75 | int main (void) |
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| 76 | { |
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| 77 | int i, j, k, kmax; |
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| 78 | int F, C; |
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| 79 | mpz_t prod; |
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| 80 | mpz_t u; |
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| 81 | mpz_t auxi1; |
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| 82 | mpz_t auxi2; |
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| 83 | mpz_init (prod); |
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| 84 | mpz_init (u); |
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| 85 | mpz_init (auxi1); |
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| 86 | mpz_init (auxi2); |
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| 87 | |
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| 88 | k = 2; /* Initialize */ |
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| 89 | kmax = 1; /* Initialize */ |
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| 90 | |
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| 91 | lll_b = proc_entrada (&F, &C); |
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| 92 | |
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| 93 | lll_d = new mpz_t[F + 1]; |
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| 94 | lll_lambda = new mpz_t *[F + 1]; |
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| 95 | mpz_init (lll_d[0]); |
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| 96 | for (i = 1; i <= F; i++) { |
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| 97 | mpz_init (lll_d[i]); |
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| 98 | lll_lambda[i] = new mpz_t[F + 1]; |
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| 99 | for (j = 1; j <= F; j++) |
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| 100 | mpz_init (lll_lambda[i][j]); |
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| 101 | } |
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| 102 | mpz_set_ui (lll_d[0], 1); /* Initialize */ |
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| 103 | lll_product (lll_b[1], lll_b[1], C, &prod); |
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| 104 | mpz_set (lll_d[1], prod); /* Initialize */ |
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| 105 | |
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| 106 | |
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| 107 | /* Incremental Gram-Schmidt */ |
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| 108 | while (k <= F) |
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| 109 | { |
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| 110 | if (k > kmax) |
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| 111 | { |
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| 112 | kmax = k; |
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| 113 | for (j = 1; j < k + 1; j++) |
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| 114 | { |
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| 115 | lll_product (lll_b[k], lll_b[j], C, &prod); |
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| 116 | mpz_set (u, prod); |
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| 117 | for (i = 1; i < j - 1 + 1; i++) |
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| 118 | { |
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| 119 | mpz_mul (auxi1, lll_d[i], u); |
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| 120 | mpz_mul (auxi2, lll_lambda[k][i], lll_lambda[j][i]); |
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| 121 | mpz_sub (u, auxi1, auxi2); |
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| 122 | mpz_tdiv_q (u, u, lll_d[i - 1]); |
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| 123 | } |
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| 124 | if (j < k) |
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| 125 | { |
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| 126 | mpz_set (lll_lambda[k][j], u); |
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| 127 | } |
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| 128 | else |
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| 129 | { |
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| 130 | mpz_set (lll_d[k], u); |
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| 131 | if (mpz_cmp_ui (lll_d[k], 0) == 0) |
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| 132 | { /* The input is not a basis */ |
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| 133 | fprintf (stderr, "\n INPUT NOT BASIS !!!! \n"); |
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| 134 | exit (1); |
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| 135 | } |
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| 136 | } |
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| 137 | } |
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| 138 | } |
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| 139 | lll_test (&k, kmax, C); |
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| 140 | for (i = k - 2; i > 0; i--) |
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| 141 | lll_redi (k, i, C); |
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| 142 | k = k + 1; |
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| 143 | } |
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| 144 | fprintf (stdout, "list res="); |
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| 145 | for (i = 1; i < F + 1; i++) |
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| 146 | { |
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| 147 | printf ("\nlist("); |
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| 148 | for (j = 1; j < C + 1; j++) |
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| 149 | { |
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| 150 | fprintf (stdout, " "); |
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| 151 | mpz_out_str (stdout, 0, lll_b[i][j]); |
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| 152 | if (j!=C) fprintf (stdout, ","); |
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| 153 | } |
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| 154 | if (i!=F) printf("),\n"); |
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| 155 | else printf(");\n"); |
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| 156 | } |
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| 157 | mpz_clear (auxi1); |
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| 158 | mpz_clear (auxi2); |
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| 159 | mpz_clear (u); |
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| 160 | mpz_clear (prod); |
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| 161 | mpz_clear (lll_d[0]); |
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| 162 | for (i = 1; i <= F; i++) |
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| 163 | { |
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| 164 | mpz_clear (lll_d[i]); |
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| 165 | for (j = 1; j <= F; j++) |
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| 166 | mpz_clear (lll_lambda[i][j]); |
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| 167 | delete[]lll_lambda[i]; |
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| 168 | } |
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| 169 | delete[]lll_lambda; |
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| 170 | delete[]lll_d; |
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| 171 | for (i = 1; i < F + 1; i++) |
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| 172 | { |
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| 173 | for (j = 1; j < C + 1; j++) |
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| 174 | mpz_clear (lll_b[i][j]); |
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| 175 | delete[]lll_b[i]; |
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| 176 | } |
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| 177 | delete[]lll_b; |
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| 178 | return 0; |
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| 179 | } |
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| 180 | |
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| 181 | /*--------------------------------------------------------------------------- |
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| 182 | | proc_entrada {}: | |
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| 183 | | Read the input file. | |
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| 184 | |___________________________________________________________________________|*/ |
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| 185 | |
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| 186 | mpz_t **proc_entrada (int *F, int *C) /* Inputs */ |
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| 187 | { |
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| 188 | int numF, numC; |
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| 189 | int i, j, c; |
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| 190 | mpz_t **base; |
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| 191 | mpz_t valor; |
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| 192 | char *aux, caux; |
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| 193 | int tamano=100; |
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| 194 | |
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| 195 | aux=new char[tamano]; |
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| 196 | fscanf (stdin, "%i, %i\n", &numF, &numC); |
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| 197 | base = new mpz_t *[numF+1]; |
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| 198 | for (i = 1; i <= numF; i++) { |
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| 199 | base[i] = new mpz_t[numC+1]; |
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| 200 | for (j = 1; j <= numC; j++) |
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| 201 | { |
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| 202 | do { caux=getc (stdin); } |
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| 203 | while (!feof(stdin) && !(caux=='-' || isdigit(caux))); |
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| 204 | mpz_init (base[i][j]); |
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| 205 | c=0; |
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| 206 | if (!feof(stdin)) |
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| 207 | { |
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| 208 | do |
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| 209 | { |
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| 210 | aux[c++]=caux; |
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| 211 | if (c==tamano) |
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| 212 | { |
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| 213 | char *nuevo=new char[3*tamano/2]; |
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| 214 | memcpy (nuevo, aux, tamano); |
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| 215 | delete[] aux; |
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| 216 | aux=nuevo; |
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| 217 | tamano=3*tamano/2; |
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| 218 | } |
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| 219 | caux=getc(stdin); |
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| 220 | } |
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| 221 | while (!feof(stdin) && caux!=' ' && caux!='\n' && caux!='\t'); |
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| 222 | aux[c]='\0'; |
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| 223 | mpz_set_str (base[i][j], aux, 0); |
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| 224 | } |
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| 225 | else |
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| 226 | { |
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| 227 | fprintf(stderr,"Empty file.\n"); |
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| 228 | mpz_set_ui (base[i][j],0); |
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| 229 | } |
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| 230 | } |
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| 231 | } |
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| 232 | *F = numF; |
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| 233 | *C = numC; |
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| 234 | delete[] aux; |
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| 235 | return (base); |
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| 236 | } |
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| 237 | |
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| 238 | /*--------------------------------------------------------------------------- |
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| 239 | | lll_product {}: | |
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| 240 | | Multiply the integer vectors a and f with n coordinates. | |
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| 241 | |___________________________________________________________________________|*/ |
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| 242 | |
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| 243 | void lll_product (mpz_t * a, mpz_t * f, int n, mpz_t * prod) |
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| 244 | { |
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| 245 | int i; |
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| 246 | mpz_t auxi; |
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| 247 | |
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| 248 | mpz_init (auxi); |
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| 249 | mpz_set_ui (*prod, 0); |
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| 250 | for (i = 1; i < n + 1; i++) |
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| 251 | { |
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| 252 | mpz_mul (auxi, a[i], f[i]); |
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| 253 | mpz_add (*prod, *prod, auxi); |
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| 254 | } |
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| 255 | mpz_clear (auxi); |
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| 256 | } |
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| 257 | |
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| 258 | void lll_test (int *k, int kma, int C) /* Test LLL condition */ |
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| 259 | { |
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| 260 | int i; |
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| 261 | mpz_t auxi1; |
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| 262 | mpz_t auxi2; |
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| 263 | mpz_t auxi3; |
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| 264 | mpz_t auxi4; |
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| 265 | |
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| 266 | mpz_init (auxi1); |
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| 267 | mpz_init (auxi2); |
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| 268 | mpz_init (auxi3); |
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| 269 | |
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| 270 | lll_redi (*k, *k - 1, C); |
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| 271 | mpz_mul (auxi1, lll_d[*k], lll_d[*k - 2]); |
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| 272 | mpz_mul_ui (auxi1, auxi1, 4); |
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| 273 | mpz_mul (auxi2, lll_d[*k - 1], lll_d[*k - 1]); |
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| 274 | mpz_mul_ui (auxi2, auxi2, 3); |
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| 275 | mpz_mul (auxi3, lll_lambda[*k][*k - 1], lll_lambda[*k][*k - 1]); |
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| 276 | mpz_mul_ui (auxi3, auxi3, 4); |
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| 277 | mpz_sub (auxi3, auxi2, auxi3); |
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| 278 | if (mpz_cmp (auxi1, auxi3) < 0) |
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| 279 | { |
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| 280 | lll_swapi (*k, kma, C); |
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| 281 | *k = LLL_MAX (2, *k - 1); |
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| 282 | lll_test (&*k, kma, C); |
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| 283 | } |
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| 284 | |
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| 285 | mpz_clear (auxi1); |
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| 286 | mpz_clear (auxi2); |
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| 287 | mpz_clear (auxi3); |
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| 288 | } |
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| 289 | |
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| 290 | /*--------------------------------------------------------------------------- |
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| 291 | | lll_redi {}: | |
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| 292 | | Make some changes in global variables. | |
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| 293 | |___________________________________________________________________________|*/ |
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| 294 | |
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| 295 | |
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| 296 | void lll_redi (int k, int l, int C) |
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| 297 | { |
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| 298 | int i; |
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| 299 | mpz_t q; |
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| 300 | mpz_t auxi1; |
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| 301 | |
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| 302 | mpz_init (q); |
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| 303 | mpz_init (auxi1); |
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| 304 | |
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| 305 | mpz_mul_ui (auxi1, lll_lambda[k][l], 2); |
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| 306 | mpz_abs (auxi1, auxi1); |
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| 307 | |
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| 308 | if (mpz_cmp (auxi1, lll_d[l]) > 0) |
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| 309 | { |
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| 310 | mpz_mul_ui (auxi1, lll_lambda[k][l], 2); |
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| 311 | mpz_add (auxi1, auxi1, lll_d[l]); |
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| 312 | mpz_mul_ui (q, lll_d[l], 2); |
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| 313 | mpz_fdiv_q (q, auxi1, q); |
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| 314 | for (i = 1; i < C + 1; i++) |
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| 315 | { |
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| 316 | mpz_mul (auxi1, q, lll_b[l][i]); |
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| 317 | mpz_sub (lll_b[k][i], lll_b[k][i], auxi1); |
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| 318 | } |
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| 319 | mpz_mul (auxi1, q, lll_d[l]); |
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| 320 | mpz_sub (lll_lambda[k][l], lll_lambda[k][l], auxi1); |
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| 321 | for (i = 1; i <= l - 1; i++) |
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| 322 | { |
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| 323 | mpz_mul (auxi1, q, lll_lambda[l][i]); |
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| 324 | mpz_sub (lll_lambda[k][i], lll_lambda[k][i], auxi1); |
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| 325 | } |
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| 326 | } |
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| 327 | mpz_clear (q); |
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| 328 | mpz_clear (auxi1); |
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| 329 | } |
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| 330 | |
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| 331 | /*--------------------------------------------------------------------------- |
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| 332 | | lll_swapi {}: | |
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| 333 | | Exchange some global variables | |
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| 334 | |___________________________________________________________________________|*/ |
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| 335 | |
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| 336 | void lll_swapi (int k, int kmax, int C) |
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| 337 | { |
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| 338 | int j; |
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| 339 | mpz_t lamb; |
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| 340 | mpz_t B; |
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| 341 | mpz_t auxi1; |
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| 342 | mpz_t auxi2; |
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| 343 | mpz_t t; |
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| 344 | mpz_t swap; |
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| 345 | |
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| 346 | mpz_init (lamb); |
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| 347 | mpz_init (B); |
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| 348 | mpz_init (auxi1); |
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| 349 | mpz_init (auxi2); |
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| 350 | mpz_init (t); |
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| 351 | mpz_init (swap); |
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| 352 | |
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| 353 | for (j = 1; j < C + 1; j++) |
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| 354 | { |
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| 355 | mpz_set (swap, lll_b[k][j]); |
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| 356 | mpz_set (lll_b[k][j], lll_b[k - 1][j]); |
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| 357 | mpz_set (lll_b[k - 1][j], swap); |
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| 358 | } |
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| 359 | if (k > 2) |
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| 360 | { |
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| 361 | for (j = 1; j <= k - 2; j++) |
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| 362 | { |
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| 363 | mpz_set (swap, lll_lambda[k][j]); |
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| 364 | mpz_set (lll_lambda[k][j], lll_lambda[k - 1][j]); |
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| 365 | mpz_set (lll_lambda[k - 1][j], swap); |
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| 366 | } |
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| 367 | } |
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| 368 | |
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| 369 | mpz_set (lamb, lll_lambda[k][k - 1]); |
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| 370 | mpz_mul (auxi1, lll_d[k - 2], lll_d[k]); |
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| 371 | mpz_mul (auxi2, lamb, lamb); |
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| 372 | mpz_add (B, auxi1, auxi2); |
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| 373 | mpz_tdiv_q (B, B, lll_d[k - 1]); |
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| 374 | for (j = k + 1; j <= kmax; j++) |
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| 375 | { |
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| 376 | mpz_set (t, lll_lambda[j][k]); |
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| 377 | mpz_mul (auxi1, lll_d[k], lll_lambda[j][k - 1]); |
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| 378 | mpz_mul (auxi2, lamb, t); |
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| 379 | mpz_sub (auxi1, auxi1, auxi2); |
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| 380 | mpz_tdiv_q (lll_lambda[j][k], auxi1, lll_d[k - 1]); |
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| 381 | mpz_mul (auxi2, lamb, lll_lambda[j][k]); |
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| 382 | mpz_mul (auxi1, B, t); |
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| 383 | mpz_add (auxi1, auxi1, auxi2); |
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| 384 | mpz_tdiv_q (lll_lambda[j][k - 1], auxi1, lll_d[k]); |
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| 385 | } |
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| 386 | mpz_set (lll_d[k - 1], B); |
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| 387 | |
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| 388 | mpz_clear (auxi1); |
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| 389 | mpz_clear (auxi2); |
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| 390 | mpz_clear (lamb); |
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| 391 | mpz_clear (B); |
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| 392 | mpz_clear (t); |
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| 393 | mpz_clear (swap); |
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| 394 | } |
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