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1 /* Finds Mersenne primes using the Lucas-Lehmer test |
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2 * |
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3 * Tom St Denis, [email protected] |
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4 */ |
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5 #include <time.h> |
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6 #include <tommath.h> |
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7 |
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8 int |
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9 is_mersenne (long s, int *pp) |
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10 { |
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11 mp_int n, u; |
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12 int res, k; |
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13 |
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14 *pp = 0; |
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15 |
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16 if ((res = mp_init (&n)) != MP_OKAY) { |
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17 return res; |
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18 } |
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19 |
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20 if ((res = mp_init (&u)) != MP_OKAY) { |
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21 goto __N; |
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22 } |
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23 |
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24 /* n = 2^s - 1 */ |
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25 if ((res = mp_2expt(&n, s)) != MP_OKAY) { |
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26 goto __MU; |
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27 } |
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28 if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) { |
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29 goto __MU; |
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30 } |
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31 |
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32 /* set u=4 */ |
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33 mp_set (&u, 4); |
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34 |
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35 /* for k=1 to s-2 do */ |
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36 for (k = 1; k <= s - 2; k++) { |
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37 /* u = u^2 - 2 mod n */ |
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38 if ((res = mp_sqr (&u, &u)) != MP_OKAY) { |
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39 goto __MU; |
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40 } |
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41 if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) { |
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42 goto __MU; |
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43 } |
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44 |
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45 /* make sure u is positive */ |
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46 while (u.sign == MP_NEG) { |
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47 if ((res = mp_add (&u, &n, &u)) != MP_OKAY) { |
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48 goto __MU; |
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49 } |
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50 } |
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51 |
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52 /* reduce */ |
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53 if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) { |
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54 goto __MU; |
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55 } |
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56 } |
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57 |
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58 /* if u == 0 then its prime */ |
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59 if (mp_iszero (&u) == 1) { |
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60 mp_prime_is_prime(&n, 8, pp); |
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61 if (*pp != 1) printf("FAILURE\n"); |
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62 } |
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63 |
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64 res = MP_OKAY; |
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65 __MU:mp_clear (&u); |
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66 __N:mp_clear (&n); |
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67 return res; |
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68 } |
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69 |
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70 /* square root of a long < 65536 */ |
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71 long |
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72 i_sqrt (long x) |
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73 { |
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74 long x1, x2; |
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75 |
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76 x2 = 16; |
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77 do { |
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78 x1 = x2; |
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79 x2 = x1 - ((x1 * x1) - x) / (2 * x1); |
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80 } while (x1 != x2); |
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81 |
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82 if (x1 * x1 > x) { |
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83 --x1; |
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84 } |
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85 |
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86 return x1; |
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87 } |
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88 |
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89 /* is the long prime by brute force */ |
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90 int |
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91 isprime (long k) |
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92 { |
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93 long y, z; |
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94 |
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95 y = i_sqrt (k); |
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96 for (z = 2; z <= y; z++) { |
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97 if ((k % z) == 0) |
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98 return 0; |
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99 } |
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100 return 1; |
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101 } |
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102 |
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103 |
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104 int |
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105 main (void) |
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106 { |
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107 int pp; |
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108 long k; |
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109 clock_t tt; |
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110 |
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111 k = 3; |
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112 |
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113 for (;;) { |
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114 /* start time */ |
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115 tt = clock (); |
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116 |
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117 /* test if 2^k - 1 is prime */ |
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118 if (is_mersenne (k, &pp) != MP_OKAY) { |
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119 printf ("Whoa error\n"); |
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120 return -1; |
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121 } |
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122 |
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123 if (pp == 1) { |
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124 /* count time */ |
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125 tt = clock () - tt; |
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126 |
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127 /* display if prime */ |
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128 printf ("2^%-5ld - 1 is prime, test took %ld ticks\n", k, tt); |
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129 } |
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130 |
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131 /* goto next odd exponent */ |
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132 k += 2; |
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133 |
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134 /* but make sure its prime */ |
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135 while (isprime (k) == 0) { |
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136 k += 2; |
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137 } |
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138 } |
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139 return 0; |
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140 } |
