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Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
381 lines
14 KiB
Plaintext
381 lines
14 KiB
Plaintext
/*
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* lucas_chk - test all primes of the form h*2^n-1, 1<=h<200 and n <= high_n
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*
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* Copyright (C) 1999 Landon Curt Noll
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*
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* Calc is open software; you can redistribute it and/or modify it under
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* the terms of the version 2.1 of the GNU Lesser General Public License
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* as published by the Free Software Foundation.
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*
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* Calc is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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* Public License for more details.
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*
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* A copy of version 2.1 of the GNU Lesser General Public License is
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* distributed with calc under the filename COPYING-LGPL. You should have
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* received a copy with calc; if not, write to Free Software Foundation, Inc.
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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* Under source code control: 1991/01/11 05:41:43
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* File existed as early as: 1991
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*
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* chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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*/
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/*
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* primes of the form h*2^n-1 for 1<=h<200 and 1<=n<1000
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*
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* For all 0 <= i < prime_cnt, h_p[i]*2^n_p[i]-1 is prime.
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*
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* These values were taken from:
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*
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* "Prime numbers and Computer Methods for Factorization", by Hans Riesel,
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* Birkhauser, 1985, pp 384-387.
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*
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* This routine assumes that the file "lucas.cal" has been loaded.
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*
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* NOTE: There are several errors in Riesel's table that have been corrected
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* in this file:
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*
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* 193*2^87-1 is prime
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* 193*2^97-1 is NOT prime
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* 199*2^211-1 is prime
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* 199*2^221-1 is NOT prime
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*/
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static prime_cnt = 1145; /* number of primes in the list */
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/* h = prime parameters */
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static mat h_p[prime_cnt] = {
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, /* element 0 */
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1, 1, 1, 1, 3, 3, 3, 3, 3, 3,
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3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
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3, 3, 3, 3, 3, 3, 3, 3, 3, 5,
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5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
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5, 5, 5, 5, 5, 5, 7, 7, 7, 7,
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7, 7, 7, 7, 9, 9, 9, 9, 9, 9,
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9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
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9, 9, 9, 11, 11, 11, 11, 11, 11, 11,
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11, 11, 11, 13, 13, 13, 13, 13, 13, 15,
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15, 15, 15, 15, 15, 15, 15, 15, 15, 15, /* 100 */
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15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
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15, 15, 17, 17, 17, 17, 17, 17, 17, 17,
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17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
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17, 17, 19, 19, 19, 19, 19, 19, 19, 19,
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19, 19, 19, 19, 19, 19, 19, 19, 19, 19,
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19, 19, 21, 21, 21, 21, 21, 21, 21, 21,
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21, 21, 21, 21, 21, 21, 21, 21, 23, 23,
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23, 23, 23, 23, 23, 23, 23, 25, 25, 25,
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25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
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25, 25, 25, 27, 27, 27, 27, 27, 27, 27, /* 200 */
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27, 27, 27, 27, 27, 27, 27, 27, 27, 27,
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27, 27, 27, 27, 27, 27, 27, 29, 29, 29,
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29, 29, 31, 31, 31, 31, 31, 31, 31, 31,
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31, 31, 31, 31, 31, 31, 31, 31, 31, 31,
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33, 33, 33, 33, 33, 33, 33, 33, 33, 33,
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33, 33, 33, 33, 33, 33, 33, 33, 33, 33,
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33, 33, 33, 33, 35, 35, 35, 35, 35, 35,
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35, 35, 35, 35, 35, 35, 35, 35, 35, 35,
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35, 37, 39, 39, 39, 39, 39, 39, 39, 39,
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39, 41, 41, 41, 41, 41, 41, 41, 41, 41, /* 300 */
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41, 41, 41, 41, 43, 43, 43, 43, 43, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
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45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
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45, 45, 45, 45, 45, 47, 47, 47, 47, 49,
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49, 49, 49, 49, 49, 49, 49, 49, 49, 49,
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49, 49, 49, 49, 49, 49, 51, 51, 51, 51,
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51, 51, 51, 51, 51, 51, 51, 51, 51, 51,
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51, 53, 53, 53, 53, 53, 53, 53, 53, 53,
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53, 55, 55, 55, 55, 55, 55, 55, 55, 55, /* 400 */
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55, 55, 55, 55, 55, 55, 55, 55, 55, 55,
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57, 57, 57, 57, 57, 57, 57, 57, 57, 57,
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57, 57, 57, 57, 57, 57, 57, 57, 59, 59,
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59, 59, 59, 59, 61, 61, 61, 61, 61, 61,
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61, 61, 61, 61, 61, 61, 61, 61, 61, 61,
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61, 63, 63, 63, 63, 63, 63, 63, 63, 63,
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63, 63, 63, 63, 63, 63, 63, 63, 63, 63,
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63, 63, 63, 63, 65, 65, 65, 65, 65, 65,
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65, 65, 65, 65, 65, 65, 65, 65, 65, 65,
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65, 65, 67, 67, 67, 67, 67, 67, 67, 67, /* 500 */
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69, 69, 69, 69, 69, 69, 69, 69, 69, 69,
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69, 69, 69, 69, 69, 69, 69, 69, 69, 69,
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69, 69, 69, 69, 69, 69, 69, 69, 69, 69,
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69, 69, 71, 71, 71, 73, 73, 73, 73, 73,
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73, 75, 75, 75, 75, 75, 75, 75, 75, 75,
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75, 75, 75, 75, 75, 75, 75, 75, 75, 75,
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75, 75, 75, 75, 75, 75, 75, 77, 77, 77,
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77, 77, 77, 77, 77, 77, 77, 77, 77, 79,
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79, 79, 79, 79, 79, 79, 79, 79, 79, 79,
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81, 81, 81, 81, 81, 81, 81, 81, 81, 81, /* 600 */
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81, 81, 81, 83, 83, 83, 83, 83, 83, 83,
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83, 83, 83, 83, 83, 83, 83, 83, 83, 83,
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83, 83, 83, 83, 83, 85, 85, 85, 85, 85,
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85, 85, 85, 85, 87, 87, 87, 87, 87, 87,
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87, 87, 87, 87, 87, 87, 87, 87, 87, 87,
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87, 87, 87, 87, 87, 87, 89, 89, 89, 89,
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89, 89, 89, 89, 89, 91, 91, 91, 91, 91,
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91, 91, 91, 91, 91, 91, 91, 91, 91, 91,
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91, 91, 91, 91, 91, 91, 91, 93, 93, 93,
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93, 93, 93, 93, 93, 93, 93, 93, 93, 93, /* 700 */
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93, 93, 93, 93, 93, 95, 95, 95, 95, 95,
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95, 95, 95, 95, 95, 97, 97, 97, 97, 97,
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99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
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99, 99, 99, 99, 99, 99, 101, 101, 101, 101,
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103, 103, 103, 103, 103, 103, 103, 103, 103, 103,
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103, 103, 103, 105, 105, 105, 105, 105, 105, 105,
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105, 105, 105, 105, 105, 105, 105, 105, 105, 105,
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105, 105, 107, 107, 107, 107, 107, 107, 107, 107,
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107, 107, 107, 107, 107, 107, 109, 109, 109, 109,
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109, 113, 113, 113, 113, 113, 113, 113, 113, 113, /* 800 */
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113, 115, 115, 115, 115, 115, 115, 115, 115, 115,
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115, 115, 115, 115, 115, 115, 115, 119, 119, 119,
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119, 119, 119, 119, 119, 121, 121, 121, 121, 121,
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121, 121, 121, 121, 121, 121, 121, 125, 125, 125,
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125, 125, 125, 127, 127, 131, 131, 131, 131, 131,
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131, 131, 131, 131, 131, 133, 133, 133, 133, 133,
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133, 133, 133, 133, 133, 133, 133, 133, 137, 137,
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137, 137, 139, 139, 139, 139, 139, 139, 139, 139,
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139, 139, 139, 139, 139, 139, 139, 139, 139, 139,
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139, 139, 139, 139, 139, 139, 139, 139, 139, 143, /* 900 */
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143, 143, 143, 143, 143, 143, 143, 143, 143, 143,
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143, 143, 143, 143, 143, 143, 143, 143, 143, 143,
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143, 143, 143, 145, 145, 145, 145, 145, 145, 145,
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145, 145, 145, 145, 149, 149, 149, 149, 149, 149,
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149, 151, 151, 151, 155, 155, 155, 155, 155, 155,
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155, 155, 155, 155, 155, 155, 157, 157, 157, 157,
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157, 157, 157, 157, 157, 161, 161, 161, 161, 161,
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161, 161, 161, 161, 161, 161, 161, 161, 161, 161,
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163, 163, 163, 163, 167, 167, 167, 167, 167, 167,
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167, 167, 167, 167, 167, 167, 169, 169, 169, 169, /* 1000 */
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169, 169, 169, 169, 169, 169, 169, 169, 173, 173,
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173, 173, 173, 173, 173, 173, 173, 173, 173, 173,
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173, 173, 173, 173, 175, 175, 175, 175, 175, 175,
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175, 175, 175, 175, 175, 175, 175, 175, 175, 175,
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179, 179, 179, 181, 181, 181, 181, 181, 181, 181,
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181, 181, 181, 181, 181, 181, 181, 181, 181, 181,
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181, 181, 181, 181, 181, 181, 181, 181, 185, 185,
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185, 185, 185, 185, 185, 185, 185, 185, 187, 187,
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187, 187, 187, 191, 193, 193, 193, 193, 193, 193,
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193, 197, 197, 197, 197, 197, 197, 197, 197, 197, /* 1100 */
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197, 197, 197, 197, 197, 197, 197, 197, 197, 199,
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199, 199, 199, 199, 199, 199, 199, 199, 199, 199,
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199, 199, 199, 199, 199, 199, 199, 199, 199, 199,
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199, 199, 199, 199, 199
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};
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/* n (exponent) prime parameters */
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static mat n_p[prime_cnt] = {
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2, 3, 5, 7, 13, 17, 19, 31, 61, 89, /* element 0 */
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107, 127, 521, 607, 1, 2, 3, 4, 6, 7,
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11, 18, 34, 38, 43, 55, 64, 76, 94, 103,
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143, 206, 216, 306, 324, 391, 458, 470, 827, 2,
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4, 8, 10, 12, 14, 18, 32, 48, 54, 72,
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148, 184, 248, 270, 274, 420, 1, 5, 9, 17,
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21, 29, 45, 177, 1, 3, 7, 13, 15, 21,
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43, 63, 99, 109, 159, 211, 309, 343, 415, 469,
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781, 871, 939, 2, 26, 50, 54, 126, 134, 246,
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354, 362, 950, 3, 7, 23, 287, 291, 795, 1,
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2, 4, 5, 10, 14, 17, 31, 41, 73, 80, /* 100 */
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82, 116, 125, 145, 157, 172, 202, 224, 266, 289,
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293, 463, 2, 4, 6, 16, 20, 36, 54, 60,
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96, 124, 150, 252, 356, 460, 612, 654, 664, 698,
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702, 972, 1, 3, 5, 21, 41, 49, 89, 133,
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141, 165, 189, 293, 305, 395, 651, 665, 771, 801,
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923, 953, 1, 2, 3, 7, 10, 13, 18, 27,
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37, 51, 74, 157, 271, 458, 530, 891, 4, 6,
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12, 46, 72, 244, 264, 544, 888, 3, 9, 11,
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17, 23, 35, 39, 75, 105, 107, 155, 215, 335,
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635, 651, 687, 1, 2, 4, 5, 8, 10, 14, /* 200 */
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28, 37, 38, 70, 121, 122, 160, 170, 253, 329,
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362, 454, 485, 500, 574, 892, 962, 4, 16, 76,
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148, 184, 1, 5, 7, 11, 13, 23, 33, 35,
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37, 47, 115, 205, 235, 271, 409, 739, 837, 887,
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2, 3, 6, 8, 10, 22, 35, 42, 43, 46,
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56, 91, 102, 106, 142, 190, 208, 266, 330, 360,
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382, 462, 503, 815, 2, 6, 10, 20, 44, 114,
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146, 156, 174, 260, 306, 380, 654, 686, 702, 814,
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906, 1, 3, 24, 105, 153, 188, 605, 795, 813,
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839, 2, 10, 14, 18, 50, 114, 122, 294, 362, /* 300 */
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554, 582, 638, 758, 7, 31, 67, 251, 767, 1,
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2, 3, 4, 5, 6, 8, 9, 14, 15, 16,
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22, 28, 29, 36, 37, 54, 59, 85, 93, 117,
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119, 161, 189, 193, 256, 308, 322, 327, 411, 466,
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577, 591, 902, 928, 946, 4, 14, 70, 78, 1,
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5, 7, 9, 13, 15, 29, 33, 39, 55, 81,
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95, 205, 279, 581, 807, 813, 1, 9, 10, 19,
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22, 57, 69, 97, 141, 169, 171, 195, 238, 735,
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885, 2, 6, 8, 42, 50, 62, 362, 488, 642,
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846, 1, 3, 5, 7, 15, 33, 41, 57, 69, /* 400 */
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75, 77, 131, 133, 153, 247, 305, 351, 409, 471,
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1, 2, 4, 5, 8, 10, 20, 22, 25, 26,
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32, 44, 62, 77, 158, 317, 500, 713, 12, 16,
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72, 160, 256, 916, 3, 5, 9, 13, 17, 19,
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25, 39, 63, 67, 75, 119, 147, 225, 419, 715,
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895, 2, 3, 8, 11, 14, 16, 28, 32, 39,
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66, 68, 91, 98, 116, 126, 164, 191, 298, 323,
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443, 714, 758, 759, 4, 6, 12, 22, 28, 52,
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78, 94, 124, 162, 174, 192, 204, 304, 376, 808,
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930, 972, 5, 9, 21, 45, 65, 77, 273, 677, /* 500 */
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1, 4, 5, 7, 9, 11, 13, 17, 19, 23,
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29, 37, 49, 61, 79, 99, 121, 133, 141, 164,
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173, 181, 185, 193, 233, 299, 313, 351, 377, 540,
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569, 909, 2, 14, 410, 7, 11, 19, 71, 79,
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131, 1, 3, 5, 6, 18, 19, 20, 22, 28,
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29, 39, 43, 49, 75, 85, 92, 111, 126, 136,
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159, 162, 237, 349, 381, 767, 969, 2, 4, 14,
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26, 58, 60, 64, 100, 122, 212, 566, 638, 1,
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3, 7, 15, 43, 57, 61, 75, 145, 217, 247,
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3, 5, 11, 17, 21, 27, 81, 101, 107, 327, /* 600 */
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383, 387, 941, 2, 4, 8, 10, 14, 18, 22,
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24, 26, 28, 36, 42, 58, 64, 78, 158, 198,
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206, 424, 550, 676, 904, 5, 11, 71, 113, 115,
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355, 473, 563, 883, 1, 2, 8, 9, 10, 12,
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22, 29, 32, 50, 57, 69, 81, 122, 138, 200,
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296, 514, 656, 682, 778, 881, 4, 8, 12, 24,
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48, 52, 64, 84, 96, 1, 3, 9, 13, 15,
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17, 19, 23, 47, 57, 67, 73, 77, 81, 83,
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191, 301, 321, 435, 867, 869, 917, 3, 4, 7,
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10, 15, 18, 19, 24, 27, 39, 60, 84, 111, /* 700 */
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171, 192, 222, 639, 954, 2, 6, 26, 32, 66,
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128, 170, 288, 320, 470, 1, 9, 45, 177, 585,
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1, 4, 5, 7, 8, 11, 19, 25, 28, 35,
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65, 79, 212, 271, 361, 461, 10, 18, 54, 70,
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3, 7, 11, 19, 63, 75, 95, 127, 155, 163,
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171, 283, 563, 2, 3, 5, 6, 8, 9, 25,
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32, 65, 113, 119, 155, 177, 299, 335, 426, 462,
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617, 896, 10, 12, 18, 24, 28, 40, 90, 132,
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214, 238, 322, 532, 858, 940, 9, 149, 177, 419,
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617, 8, 14, 74, 80, 274, 334, 590, 608, 614, /* 800 */
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650, 1, 3, 11, 13, 19, 21, 31, 49, 59,
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69, 73, 115, 129, 397, 623, 769, 12, 16, 52,
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160, 192, 216, 376, 436, 1, 3, 21, 27, 37,
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43, 91, 117, 141, 163, 373, 421, 2, 4, 44,
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182, 496, 904, 25, 113, 2, 14, 34, 38, 42,
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78, 90, 178, 778, 974, 3, 11, 15, 19, 31,
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59, 75, 103, 163, 235, 375, 615, 767, 2, 18,
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38, 62, 1, 5, 7, 9, 15, 19, 21, 35,
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37, 39, 41, 49, 69, 111, 115, 141, 159, 181,
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201, 217, 487, 567, 677, 765, 811, 841, 917, 2, /* 900 */
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4, 6, 8, 12, 18, 26, 32, 34, 36, 42,
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60, 78, 82, 84, 88, 154, 174, 208, 256, 366,
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448, 478, 746, 5, 13, 15, 31, 77, 151, 181,
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245, 445, 447, 883, 4, 16, 48, 60, 240, 256,
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304, 5, 221, 641, 2, 8, 14, 16, 44, 46,
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82, 172, 196, 254, 556, 806, 1, 5, 33, 121,
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125, 305, 445, 473, 513, 2, 6, 18, 22, 34,
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54, 98, 122, 146, 222, 306, 422, 654, 682, 862,
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3, 31, 63, 303, 4, 6, 8, 10, 16, 32,
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38, 42, 52, 456, 576, 668, 1, 5, 11, 17, /* 1000 */
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67, 137, 157, 203, 209, 227, 263, 917, 2, 4,
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6, 16, 32, 50, 76, 80, 96, 104, 162, 212,
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230, 260, 480, 612, 1, 3, 9, 21, 23, 41,
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47, 57, 69, 83, 193, 249, 291, 421, 433, 997,
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8, 68, 108, 3, 5, 7, 9, 11, 17, 23,
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31, 35, 43, 47, 83, 85, 99, 101, 195, 267,
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281, 363, 391, 519, 623, 653, 673, 701, 2, 6,
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10, 18, 26, 40, 46, 78, 230, 542, 1, 17,
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21, 53, 253, 226, 3, 15, 27, 63, 87, 135,
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543, 2, 16, 20, 22, 40, 82, 112, 178, 230, /* 1100 */
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302, 304, 328, 374, 442, 472, 500, 580, 694, 1,
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5, 7, 15, 19, 23, 25, 27, 43, 65, 99,
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125, 141, 165, 201, 211, 331, 369, 389, 445, 461,
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463, 467, 513, 583, 835
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};
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/* obtain our required libs */
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read -once "lucas.cal";
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/*
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* lucas_chk - check the lucas function on known primes
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*
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* This function tests entries in the above h_p, n_p table
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* when n_p is below a given limit.
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*
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* input:
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* high_n skip tests on n_p[i] > high_n
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* [quiet] if given and != 0, then do not print individual test results
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*
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* returns:
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* 1 all is ok
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* 0 something went wrong
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*/
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define
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lucas_chk(high_n, quiet)
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{
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local i; /* index */
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local result; /* 0 => non-prime, 1 => prime, -1 => bad test */
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local error; /* number of errors and bad tests found */
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/*
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* firewall
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*/
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if (!isint(high_n)) {
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ldebug("test_lucas", "high_n is non-int");
|
|
quit "FATAL: bad args: high_n must be an integer";
|
|
}
|
|
if (param(0) == 1) {
|
|
quiet = 0;
|
|
}
|
|
|
|
/*
|
|
* scan thru the above prime table
|
|
*/
|
|
error = 0;
|
|
for (i=0; i < prime_cnt; ++i) {
|
|
|
|
/* skip primes where h>=2^n */
|
|
if (highbit(h_p[i]) >= n_p[i]) {
|
|
if (config("resource_debug") & 8) {
|
|
print "h>=2^n skip:", h_p[i]:"*2^":n_p[i]:"-1";
|
|
}
|
|
continue;
|
|
}
|
|
|
|
/* test the prime if it is small enough */
|
|
if (n_p[i] <= high_n) {
|
|
|
|
/* test the table value */
|
|
result = lucas(h_p[i], n_p[i]);
|
|
|
|
/* report the test */
|
|
if (result == 0) {
|
|
print "ERROR, bad primality test of",\
|
|
h_p[i]:"*2^":n_p[i]:"-1";
|
|
++error;
|
|
} else if (result == 1) {
|
|
if (quiet == 0) {
|
|
print h_p[i]:"*2^":n_p[i]:"-1 is prime";
|
|
}
|
|
} else if (result == -1) {
|
|
print "ERROR, failed to compute v(1) for",\
|
|
h_p[i]:"*2^":n_p[i]:"-1";
|
|
++error;
|
|
} else {
|
|
print "ERROR, bogus return value:", result;
|
|
++error;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* return the full status */
|
|
if (error == 0) {
|
|
if (quiet == 0) {
|
|
print "lucas_chk(":high_n:") passed";
|
|
}
|
|
return 1;
|
|
} else if (error == 1) {
|
|
print "lucas_chk(":high_n:") failed", error, "test";
|
|
return 0;
|
|
} else {
|
|
print "lucas_chk(":high_n:") failed", error, "tests";
|
|
return 0;
|
|
}
|
|
}
|