diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/poly.c | 2236 |
1 files changed, 2227 insertions, 9 deletions
@@ -4,6 +4,869 @@ */ #include "poly.h" +// HP range [2, 159] + [2001, 10000] +/** + * Table of Low-Weight Binary Irreducible Polynomials + * Gadiel Seroussi + * Computer Systems Laboratory + * HPL-98-135 + * August, 1998 + * + * http://www.hpl.hp.com/techreports/98/HPL-98-135.pdf + */ +static polynomial_t hp_trinomials[] = { + {2, 1}, {3, 1}, {4, 1}, {5, 2}, {6, 1}, + {7, 1}, {9, 1}, {10, 3}, {11, 2}, {12, 3}, + {14, 5}, {15, 1}, {17, 3}, {18, 3}, {20, 3}, + {21, 2}, {22, 1}, {23, 5}, {25, 3}, {28, 1}, + {29, 2}, {30, 1}, {31, 3}, {33, 10}, {34, 7}, + {35, 2}, {36, 9}, {39, 4}, {41, 3}, {42, 7}, + {44, 5}, {46, 1}, {47, 5}, {49, 9}, {52, 3}, + {54, 9}, {55, 7}, {57, 4}, {58, 19}, {60, 1}, + {62, 29}, {63, 1}, {65, 18}, {66, 3}, {68, 9}, + {71, 6}, {73, 25}, {74, 35}, {76, 21}, {79, 9}, + {81, 4}, {84, 5}, {86, 21}, {87, 13}, {89, 38}, + {90, 27}, {92, 21}, {93, 2}, {94, 21}, {95, 11}, + {97, 6}, {98, 11}, {100, 15}, {102, 29}, {103, 9}, + {105, 4}, {106, 15}, {108, 17}, {110, 33}, {111, 10}, + {113, 9}, {118, 33}, {119, 8}, {121, 18}, {123, 2}, + {124, 19}, {126, 21}, {127, 1}, {129, 5}, {130, 3}, + {132, 17}, {134, 57}, {135, 11}, {137, 21}, {140, 15}, + {142, 21}, {145, 52}, {146, 71}, {147, 14}, {148, 27}, + {150, 53}, {151, 3}, {153, 1}, {154, 15}, {155, 62}, + {156, 9}, {159, 31}, {2001, 169}, {2004, 441}, {2006, 917}, + {2007, 205}, {2009, 54}, {2010, 459}, {2015, 42}, {2017, 330}, + {2020, 81}, {2022, 349}, {2023, 165}, {2025, 274}, {2026, 475}, + {2028, 93}, {2031, 386}, {2033, 881}, {2034, 143}, {2036, 71}, + {2039, 155}, {2041, 735}, {2044, 45}, {2047, 3}, {2049, 124}, + {2052, 323}, {2054, 201}, {2055, 11}, {2057, 245}, {2058, 343}, + {2060, 387}, {2063, 48}, {2065, 97}, {2066, 71}, {2070, 237}, + {2073, 253}, {2074, 231}, {2076, 851}, {2079, 35}, {2081, 467}, + {2082, 523}, {2086, 261}, {2087, 141}, {2089, 150}, {2094, 645}, + {2095, 256}, {2097, 119}, {2098, 19}, {2100, 35}, {2102, 33}, + {2103, 98}, {2105, 153}, {2106, 111}, {2111, 249}, {2113, 385}, + {2114, 155}, {2116, 25}, {2118, 385}, {2119, 84}, {2121, 304}, + {2122, 91}, {2124, 45}, {2126, 881}, {2127, 539}, {2129, 21}, + {2130, 239}, {2132, 213}, {2135, 47}, {2137, 331}, {2140, 283}, + {2142, 69}, {2143, 345}, {2145, 19}, {2146, 595}, {2148, 549}, + {2150, 569}, {2151, 224}, {2153, 582}, {2156, 405}, {2158, 93}, + {2159, 6}, {2161, 766}, {2162, 47}, {2164, 561}, {2166, 693}, + {2167, 840}, {2169, 55}, {2170, 411}, {2174, 225}, {2175, 128}, + {2177, 554}, {2178, 15}, {2180, 111}, {2182, 93}, {2183, 162}, + {2185, 51}, {2186, 51}, {2188, 99}, {2190, 441}, {2191, 111}, + {2193, 71}, {2196, 539}, {2198, 893}, {2199, 49}, {2201, 143}, + {2206, 793}, {2207, 438}, {2209, 142}, {2210, 539}, {2212, 423}, + {2214, 1041}, {2215, 39}, {2217, 455}, {2218, 603}, {2220, 7}, + {2222, 333}, {2225, 47}, {2228, 425}, {2230, 637}, {2231, 654}, + {2233, 249}, {2236, 63}, {2238, 1053}, {2239, 120}, {2241, 20}, + {2242, 7}, {2244, 399}, {2247, 217}, {2249, 126}, {2250, 927}, + {2252, 75}, {2255, 729}, {2257, 829}, {2258, 983}, {2262, 57}, + {2263, 273}, {2265, 151}, {2266, 343}, {2268, 115}, {2270, 369}, + {2271, 560}, {2273, 630}, {2274, 239}, {2276, 21}, {2279, 276}, + {2281, 715}, {2282, 975}, {2284, 889}, {2286, 249}, {2287, 651}, + {2289, 136}, {2292, 89}, {2295, 259}, {2297, 405}, {2300, 95}, + {2303, 80}, {2305, 424}, {2306, 551}, {2308, 31}, {2310, 233}, + {2311, 148}, {2313, 221}, {2314, 879}, {2316, 21}, {2318, 245}, + {2319, 161}, {2321, 543}, {2322, 83}, {2324, 717}, {2327, 32}, + {2329, 105}, {2331, 14}, {2332, 349}, {2334, 1125}, {2335, 553}, + {2337, 523}, {2338, 211}, {2340, 39}, {2342, 65}, {2343, 415}, + {2345, 29}, {2346, 987}, {2348, 731}, {2351, 950}, {2353, 328}, + {2356, 183}, {2358, 161}, {2359, 172}, {2361, 646}, {2364, 643}, + {2367, 610}, {2369, 77}, {2372, 1139}, {2375, 198}, {2377, 381}, + {2378, 243}, {2380, 1}, {2382, 429}, {2383, 49}, {2385, 607}, + {2388, 11}, {2390, 629}, {2391, 956}, {2393, 59}, {2394, 423}, + {2396, 173}, {2399, 107}, {2401, 61}, {2402, 251}, {2404, 67}, + {2407, 91}, {2409, 1198}, {2410, 807}, {2412, 25}, {2414, 29}, + {2415, 154}, {2417, 225}, {2418, 311}, {2420, 77}, {2422, 1117}, + {2423, 102}, {2425, 678}, {2428, 301}, {2430, 477}, {2431, 303}, + {2433, 305}, {2434, 507}, {2436, 145}, {2438, 929}, {2439, 404}, + {2441, 339}, {2442, 127}, {2444, 1115}, {2447, 786}, {2449, 621}, + {2450, 191}, {2452, 331}, {2454, 357}, {2455, 313}, {2457, 238}, + {2460, 35}, {2463, 1172}, {2465, 531}, {2466, 599}, {2468, 99}, + {2470, 217}, {2473, 225}, {2474, 899}, {2478, 765}, {2479, 72}, + {2481, 710}, {2484, 523}, {2485, 142}, {2487, 155}, {2489, 315}, + {2492, 141}, {2495, 497}, {2497, 1171}, {2500, 135}, {2502, 45}, + {2503, 316}, {2505, 131}, {2508, 25}, {2510, 1113}, {2511, 110}, + {2513, 99}, {2514, 183}, {2516, 563}, {2519, 579}, {2521, 426}, + {2526, 141}, {2527, 640}, {2529, 49}, {2534, 185}, {2537, 77}, + {2538, 315}, {2540, 209}, {2542, 97}, {2543, 240}, {2545, 982}, + {2546, 891}, {2548, 373}, {2550, 333}, {2551, 103}, {2553, 28}, + {2554, 1123}, {2556, 349}, {2559, 23}, {2561, 201}, {2562, 203}, + {2564, 561}, {2566, 37}, {2567, 122}, {2569, 69}, {2572, 535}, + {2574, 5}, {2575, 867}, {2577, 674}, {2580, 105}, {2583, 31}, + {2585, 263}, {2586, 1047}, {2590, 1017}, {2591, 219}, {2593, 297}, + {2594, 863}, {2596, 145}, {2598, 225}, {2599, 289}, {2601, 406}, + {2604, 435}, {2606, 1181}, {2607, 34}, {2609, 425}, {2610, 427}, + {2614, 553}, {2615, 518}, {2617, 462}, {2618, 71}, {2620, 835}, + {2623, 409}, {2625, 112}, {2626, 43}, {2628, 47}, {2630, 177}, + {2631, 139}, {2633, 1241}, {2639, 144}, {2641, 736}, {2642, 551}, + {2644, 597}, {2646, 297}, {2647, 513}, {2649, 689}, {2652, 519}, + {2655, 53}, {2657, 242}, {2660, 5}, {2663, 458}, {2665, 772}, + {2666, 663}, {2667, 254}, {2668, 819}, {2670, 229}, {2671, 46}, + {2673, 530}, {2674, 967}, {2676, 93}, {2679, 286}, {2681, 635}, + {2682, 463}, {2686, 789}, {2687, 225}, {2689, 36}, {2692, 577}, + {2694, 621}, {2695, 123}, {2697, 170}, {2698, 963}, {2700, 3}, + {2702, 257}, {2703, 67}, {2706, 515}, {2708, 423}, {2711, 690}, + {2713, 840}, {2716, 255}, {2718, 369}, {2719, 102}, {2721, 826}, + {2722, 127}, {2724, 121}, {2727, 430}, {2729, 96}, {2730, 343}, + {2732, 845}, {2735, 933}, {2737, 226}, {2738, 923}, {2740, 109}, + {2742, 149}, {2743, 447}, {2745, 484}, {2748, 25}, {2750, 629}, + {2751, 49}, {2753, 716}, {2754, 231}, {2756, 159}, {2759, 842}, + {2761, 108}, {2762, 1319}, {2764, 687}, {2766, 1285}, {2767, 102}, + {2769, 269}, {2770, 567}, {2772, 135}, {2775, 802}, {2778, 1095}, + {2780, 51}, {2783, 168}, {2785, 349}, {2786, 339}, {2790, 837}, + {2791, 490}, {2793, 343}, {2796, 769}, {2799, 880}, {2801, 279}, + {2804, 609}, {2806, 729}, {2807, 270}, {2809, 1342}, {2812, 453}, + {2814, 621}, {2815, 84}, {2817, 109}, {2820, 815}, {2823, 592}, + {2825, 288}, {2826, 135}, {2828, 1103}, {2831, 186}, {2833, 409}, + {2836, 1113}, {2839, 1033}, {2841, 370}, {2842, 1231}, {2844, 25}, + {2847, 329}, {2849, 114}, {2850, 1411}, {2852, 1145}, {2854, 313}, + {2855, 41}, {2857, 756}, {2860, 603}, {2862, 405}, {2863, 139}, + {2865, 212}, {2868, 915}, {2871, 272}, {2873, 75}, {2876, 605}, + {2878, 781}, {2879, 149}, {2881, 1201}, {2882, 1431}, {2884, 529}, + {2887, 469}, {2889, 76}, {2890, 31}, {2892, 309}, {2895, 358}, + {2897, 15}, {2898, 91}, {2900, 303}, {2903, 279}, {2905, 321}, + {2906, 1155}, {2910, 1301}, {2911, 685}, {2913, 238}, {2914, 351}, + {2916, 21}, {2918, 237}, {2919, 149}, {2921, 480}, {2922, 559}, + {2927, 974}, {2929, 651}, {2934, 713}, {2937, 172}, {2938, 499}, + {2940, 49}, {2942, 1425}, {2943, 320}, {2945, 146}, {2946, 551}, + {2950, 397}, {2951, 872}, {2953, 33}, {2956, 823}, {2959, 69}, + {2961, 86}, {2962, 319}, {2964, 83}, {2966, 861}, {2967, 1028}, + {2969, 561}, {2970, 583}, {2972, 693}, {2975, 192}, {2977, 126}, + {2978, 375}, {2980, 381}, {2982, 669}, {2983, 330}, {2985, 166}, + {2986, 343}, {2988, 313}, {2991, 292}, {2993, 569}, {2994, 303}, + {2996, 345}, {2998, 669}, {2999, 1011}, {3001, 975}, {3004, 351}, + {3007, 963}, {3009, 1349}, {3012, 1327}, {3015, 308}, {3017, 108}, + {3018, 203}, {3020, 413}, {3023, 734}, {3025, 757}, {3028, 135}, + {3031, 55}, {3033, 238}, {3034, 399}, {3036, 391}, {3038, 633}, + {3039, 436}, {3041, 776}, {3042, 415}, {3044, 69}, {3046, 1021}, + {3049, 765}, {3050, 651}, {3052, 363}, {3057, 110}, {3058, 811}, + {3060, 405}, {3062, 1053}, {3063, 32}, {3065, 432}, {3066, 455}, + {3068, 215}, {3071, 65}, {3073, 184}, {3076, 475}, {3078, 105}, + {3079, 174}, {3081, 64}, {3084, 109}, {3086, 1281}, {3087, 49}, + {3089, 261}, {3090, 279}, {3092, 45}, {3094, 769}, {3095, 419}, + {3097, 1162}, {3100, 45}, {3102, 225}, {3103, 124}, {3105, 833}, + {3108, 61}, {3110, 1421}, {3111, 199}, {3113, 191}, {3116, 461}, + {3118, 525}, {3119, 315}, {3121, 493}, {3124, 861}, {3126, 449}, + {3127, 139}, {3129, 23}, {3130, 867}, {3132, 123}, {3134, 89}, + {3135, 356}, {3137, 587}, {3140, 1115}, {3142, 981}, {3143, 8}, + {3145, 112}, {3148, 1171}, {3150, 253}, {3151, 1254}, {3153, 98}, + {3156, 565}, {3159, 103}, {3161, 858}, {3162, 315}, {3164, 113}, + {3167, 672}, {3169, 1123}, {3170, 783}, {3172, 301}, {3174, 81}, + {3175, 646}, {3177, 484}, {3178, 915}, {3180, 1085}, {3182, 1205}, + {3183, 1225}, {3185, 204}, {3186, 891}, {3188, 129}, {3191, 495}, + {3193, 211}, {3194, 1059}, {3196, 175}, {3198, 841}, {3199, 54}, + {3201, 674}, {3204, 31}, {3207, 704}, {3209, 81}, {3210, 1303}, + {3212, 1559}, {3214, 1197}, {3215, 614}, {3217, 67}, {3220, 19}, + {3222, 145}, {3223, 784}, {3225, 101}, {3228, 1225}, {3230, 501}, + {3233, 575}, {3234, 511}, {3236, 887}, {3238, 409}, {3239, 98}, + {3241, 127}, {3244, 1249}, {3246, 1221}, {3247, 426}, {3249, 149}, + {3252, 567}, {3254, 1485}, {3255, 124}, {3257, 806}, {3258, 203}, + {3260, 237}, {3263, 939}, {3268, 73}, {3270, 237}, {3271, 333}, + {3273, 1408}, {3274, 775}, {3276, 69}, {3279, 446}, {3281, 47}, + {3282, 783}, {3286, 397}, {3287, 717}, {3289, 43}, {3292, 61}, + {3294, 249}, {3295, 594}, {3297, 7}, {3298, 639}, {3300, 55}, + {3302, 605}, {3303, 1336}, {3305, 806}, {3306, 127}, {3308, 717}, + {3310, 1}, {3311, 618}, {3313, 436}, {3314, 1019}, {3316, 1641}, + {3318, 585}, {3319, 58}, {3321, 20}, {3322, 567}, {3324, 173}, + {3326, 1145}, {3327, 875}, {3329, 525}, {3330, 191}, {3332, 587}, + {3335, 636}, {3337, 370}, {3338, 1155}, {3343, 73}, {3345, 796}, + {3348, 177}, {3350, 1401}, {3351, 731}, {3353, 389}, {3356, 339}, + {3359, 99}, {3364, 85}, {3366, 257}, {3367, 136}, {3369, 1541}, + {3372, 47}, {3374, 417}, {3375, 49}, {3377, 236}, {3378, 623}, + {3380, 659}, {3382, 217}, {3383, 956}, {3385, 603}, {3388, 169}, + {3390, 1381}, {3391, 465}, {3393, 1615}, {3398, 245}, {3399, 416}, + {3401, 531}, {3402, 387}, {3404, 173}, {3407, 507}, {3409, 244}, + {3410, 1023}, {3412, 325}, {3414, 93}, {3415, 1272}, {3417, 32}, + {3418, 15}, {3420, 423}, {3422, 1121}, {3423, 11}, {3425, 189}, + {3426, 1071}, {3430, 153}, {3431, 153}, {3436, 159}, {3438, 393}, + {3439, 147}, {3441, 394}, {3444, 69}, {3447, 404}, {3449, 917}, + {3452, 1145}, {3455, 21}, {3457, 120}, {3458, 519}, {3460, 1495}, + {3462, 225}, {3463, 289}, {3465, 304}, {3466, 43}, {3468, 921}, + {3470, 917}, {3471, 314}, {3473, 720}, {3474, 735}, {3476, 525}, + {3478, 465}, {3479, 155}, {3481, 546}, {3484, 1329}, {3486, 1085}, + {3487, 120}, {3489, 518}, {3492, 57}, {3495, 254}, {3497, 1025}, + {3498, 567}, {3500, 375}, {3503, 993}, {3505, 103}, {3510, 81}, + {3511, 1141}, {3513, 41}, {3516, 667}, {3519, 569}, {3521, 129}, + {3522, 399}, {3524, 1439}, {3527, 476}, {3529, 270}, {3532, 1561}, + {3534, 973}, {3535, 162}, {3537, 218}, {3540, 75}, {3542, 345}, + {3543, 377}, {3545, 998}, {3546, 151}, {3548, 255}, {3550, 1269}, + {3551, 183}, {3556, 127}, {3558, 397}, {3559, 69}, {3561, 257}, + {3562, 927}, {3564, 225}, {3569, 1028}, {3570, 699}, {3572, 1143}, + {3574, 889}, {3575, 339}, {3577, 348}, {3580, 915}, {3582, 713}, + {3583, 747}, {3585, 7}, {3588, 843}, {3590, 1713}, {3591, 509}, + {3593, 72}, {3594, 59}, {3596, 383}, {3599, 114}, {3601, 669}, + {3604, 637}, {3606, 861}, {3607, 142}, {3609, 1016}, {3612, 215}, + {3614, 29}, {3615, 47}, {3617, 377}, {3618, 1539}, {3620, 231}, + {3622, 481}, {3625, 279}, {3628, 957}, {3630, 729}, {3631, 90}, + {3633, 553}, {3634, 651}, {3636, 391}, {3639, 76}, {3641, 1626}, + {3642, 771}, {3644, 1365}, {3647, 45}, {3649, 394}, {3650, 1691}, + {3652, 721}, {3654, 273}, {3655, 112}, {3657, 928}, {3658, 1471}, + {3660, 61}, {3662, 1365}, {3663, 130}, {3665, 189}, {3668, 269}, + {3671, 101}, {3673, 544}, {3676, 609}, {3678, 501}, {3679, 21}, + {3681, 115}, {3682, 471}, {3684, 81}, {3686, 81}, {3687, 889}, + {3689, 759}, {3690, 839}, {3694, 1129}, {3695, 62}, {3697, 91}, + {3698, 1719}, {3700, 675}, {3702, 1281}, {3703, 429}, {3705, 148}, + {3706, 1195}, {3708, 147}, {3710, 797}, {3711, 1735}, {3713, 413}, + {3714, 459}, {3719, 488}, {3721, 31}, {3726, 609}, {3727, 42}, + {3729, 184}, {3730, 1191}, {3732, 1327}, {3734, 1305}, {3735, 46}, + {3737, 287}, {3738, 75}, {3740, 95}, {3743, 279}, {3745, 684}, + {3750, 1013}, {3751, 435}, {3753, 407}, {3754, 1611}, {3756, 291}, + {3759, 208}, {3761, 30}, {3762, 383}, {3764, 1307}, {3767, 672}, + {3769, 300}, {3770, 107}, {3772, 61}, {3775, 1416}, {3777, 1414}, + {3780, 63}, {3782, 1785}, {3783, 272}, {3785, 87}, {3786, 1027}, + {3788, 1173}, {3791, 45}, {3793, 481}, {3796, 127}, {3798, 1337}, + {3799, 202}, {3801, 112}, {3804, 349}, {3807, 68}, {3809, 938}, + {3810, 323}, {3812, 1799}, {3815, 143}, {3817, 252}, {3822, 29}, + {3823, 609}, {3825, 437}, {3828, 1217}, {3830, 713}, {3831, 310}, + {3833, 35}, {3834, 567}, {3836, 681}, {3838, 273}, {3839, 503}, + {3841, 840}, {3842, 1331}, {3844, 1063}, {3846, 693}, {3847, 108}, + {3849, 71}, {3850, 583}, {3852, 169}, {3854, 765}, {3855, 1399}, + {3857, 50}, {3858, 459}, {3860, 35}, {3863, 834}, {3865, 289}, + {3866, 315}, {3870, 913}, {3871, 264}, {3873, 32}, {3876, 157}, + {3879, 121}, {3881, 810}, {3882, 1775}, {3884, 45}, 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2333}, + {8105, 1611}, {8106, 771}, {8108, 627}, {8110, 217}, {8111, 1130}, + {8113, 3058}, {8114, 1667}, {8116, 1057}, {8119, 10}, {8121, 3494}, + {8124, 269}, {8127, 218}, {8129, 548}, {8130, 719}, {8134, 25}, + {8135, 468}, {8137, 739}, {8138, 1043}, {8140, 1683}, {8143, 1890}, + {8145, 728}, {8146, 1911}, {8148, 133}, {8150, 89}, {8151, 3841}, + {8153, 1020}, {8154, 995}, {8156, 3641}, {8159, 1026}, {8161, 292}, + {8162, 1391}, {8164, 471}, {8166, 381}, {8167, 2553}, {8169, 481}, + {8172, 539}, {8175, 661}, {8177, 905}, {8178, 2611}, {8180, 185}, + {8182, 1477}, {8183, 1139}, {8185, 777}, {8188, 1155}, {8190, 1869}, + {8191, 714}, {8193, 1055}, {8194, 3847}, {8196, 2477}, {8198, 657}, + {8199, 2758}, {8201, 365}, {8204, 1727}, {8207, 5}, {8209, 943}, + {8210, 3507}, {8212, 1773}, {8215, 469}, {8217, 94}, {8218, 1443}, + {8220, 327}, {8222, 2345}, {8223, 308}, {8225, 2588}, {8226, 447}, + {8230, 2149}, {8231, 3564}, {8233, 1407}, {8234, 215}, {8236, 351}, + {8239, 1462}, {8241, 1694}, {8244, 343}, {8246, 173}, {8247, 2050}, + {8250, 3399}, {8252, 2861}, {8254, 3157}, {8255, 1496}, {8257, 1530}, + {8258, 1407}, {8260, 225}, {8262, 693}, {8263, 2232}, {8265, 161}, + {8268, 477}, {8271, 44}, {8273, 3500}, {8274, 419}, {8276, 915}, + {8278, 193}, {8279, 2439}, {8281, 226}, {8282, 351}, {8284, 2197}, + {8286, 3957}, {8287, 1755}, {8289, 98}, {8292, 637}, {8295, 938}, + {8297, 2846}, {8300, 185}, {8302, 1305}, {8303, 3789}, {8305, 417}, + {8310, 3333}, {8311, 1470}, {8313, 4117}, {8316, 405}, {8319, 458}, + {8321, 2985}, {8324, 1149}, {8327, 596}, {8329, 775}, {8330, 1107}, + {8332, 651}, {8334, 3285}, {8335, 129}, {8337, 643}, {8340, 553}, + {8342, 2921}, {8343, 1667}, {8345, 777}, {8348, 1737}, {8350, 3177}, + {8351, 170}, {8353, 2548}, {8354, 1515}, {8358, 677}, {8359, 1905}, + {8362, 655}, {8364, 2443}, {8366, 2381}, {8367, 154}, {8370, 1643}, + {8372, 17}, {8374, 4125}, {8375, 2316}, {8377, 2035}, {8378, 3851}, + {8380, 1815}, {8385, 2369}, {8386, 907}, {8388, 691}, {8390, 3797}, + {8391, 1336}, {8393, 312}, {8398, 3481}, {8399, 4191}, {8401, 1105}, + {8402, 287}, {8404, 805}, {8407, 1557}, {8409, 2506}, {8412, 1049}, + {8414, 3197}, {8415, 1061}, {8417, 2240}, {8418, 2187}, {8420, 2751}, + {8423, 168}, {8425, 3}, {8426, 1539}, {8428, 129}, {8430, 361}, + {8431, 97}, {8433, 1255}, {8434, 1459}, {8436, 401}, {8439, 43}, + {8441, 992}, {8442, 1863}, {8444, 905}, {8446, 3201}, {8447, 213}, + {8449, 25}, {8455, 412}, {8457, 230}, {8460, 127}, {8463, 397}, + {8465, 936}, {8466, 451}, {8470, 1713}, {8471, 827}, {8473, 2398}, + {8476, 85}, {8478, 405}, {8479, 1425}, {8481, 641}, {8482, 331}, + {8484, 1421}, {8487, 4112}, {8489, 3096}, {8492, 497}, {8495, 122}, + {8497, 540}, {8500, 753}, {8502, 3157}, {8503, 91}, {8505, 109}, + {8506, 3555}, {8508, 1207}, {8510, 2709}, {8511, 4177}, {8513, 3044}, + {8516, 1221}, {8518, 721}, {8519, 36}, {8521, 2646}, {8522, 3603}, + {8524, 1575}, {8526, 637}, {8527, 435}, {8529, 2296}, {8530, 2019}, + {8532, 787}, {8535, 2996}, {8537, 242}, {8540, 465}, {8543, 969}, + {8545, 1944}, {8548, 519}, {8550, 893}, {8551, 639}, {8553, 4171}, + {8556, 2011}, {8558, 4193}, {8559, 2161}, {8562, 939}, {8564, 801}, + {8566, 2581}, {8569, 1429}, {8572, 1081}, {8575, 457}, {8577, 439}, + {8580, 143}, {8582, 1817}, {8583, 3448}, {8585, 137}, {8586, 407}, + {8588, 29}, {8591, 431}, {8593, 94}, {8599, 2385}, {8601, 734}, + {8602, 1431}, {8604, 1381}, {8607, 203}, {8609, 434}, {8612, 287}, + {8614, 1585}, {8615, 3713}, {8617, 1150}, {8618, 1947}, {8620, 1197}, + {8623, 1483}, {8625, 256}, {8626, 103}, {8631, 857}, {8633, 3234}, + {8636, 2345}, {8638, 3961}, {8639, 441}, {8641, 81}, {8644, 103}, + {8646, 4293}, {8647, 145}, {8649, 280}, {8650, 783}, {8652, 833}, + {8654, 2529}, {8655, 2863}, {8657, 884}, {8658, 3323}, {8660, 1157}, + {8663, 2306}, {8665, 2416}, {8666, 2111}, {8668, 1839}, {8670, 1061}, + {8671, 1329}, {8673, 28}, {8674, 3403}, {8676, 927}, {8679, 1370}, + {8681, 1175}, {8682, 947}, {8684, 3815}, {8686, 2653}, {8689, 855}, + {8692, 1095}, {8694, 1809}, {8695, 2283}, {8697, 164}, {8698, 2583}, + {8700, 1295}, {8703, 281}, {8705, 59}, {8708, 417}, {8711, 360}, + {8713, 1785}, {8714, 231}, {8718, 3465}, {8719, 7}, {8721, 467}, + {8722, 1551}, {8724, 2279}, {8727, 748}, {8729, 68}, {8730, 959}, + {8732, 525}, {8734, 2817}, {8735, 1326}, {8737, 3235}, {8740, 2835}, + {8742, 1053}, {8743, 90}, {8745, 79}, {8746, 4183}, {8748, 63}, + {8750, 53}, {8751, 1922}, {8753, 693}, {8754, 2871}, {8756, 1181}, + {8759, 3675}, {8762, 2159}, {8766, 1677}, {8767, 70}, {8769, 188}, + {8770, 603}, {8772, 37}, {8775, 508}, {8777, 257}, {8780, 495}, + {8783, 860}, {8785, 1597}, {8791, 463}, {8793, 272}, {8796, 1585}, + {8798, 1301}, {8799, 656}, {8801, 309}, {8802, 2139}, {8804, 549}, + {8806, 1773}, {8807, 3569}, {8809, 1089}, {8812, 2295}, {8814, 1497}, + {8815, 1174}, {8817, 1654}, {8820, 147}, {8823, 1028}, {8825, 303}, + {8826, 4275}, {8828, 1133}, {8830, 3889}, {8831, 891}, {8833, 328}, + {8834, 683}, {8836, 1171}, {8838, 1653}, {8839, 285}, {8841, 539}, + {8842, 4143}, {8844, 355}, {8847, 1100}, {8849, 2324}, {8850, 1191}, + {8852, 1697}, {8855, 138}, {8857, 2493}, {8860, 3577}, {8862, 49}, + {8863, 1099}, {8865, 2713}, {8868, 623}, {8870, 1029}, {8871, 2422}, + {8873, 689}, {8874, 2239}, {8876, 381}, {8878, 3949}, {8879, 2369}, + {8881, 990}, {8884, 2121}, {8886, 469}, {8887, 1107}, {8889, 1216}, + {8890, 2007}, {8892, 249}, {8895, 958}, {8897, 1439}, {8898, 287}, + {8900, 2285}, {8903, 222}, {8905, 433}, {8908, 3031}, {8910, 1749}, + {8911, 963}, {8913, 158}, {8916, 2259}, {8919, 2479}, {8921, 6}, + {8922, 787}, {8924, 797}, {8926, 853}, {8927, 1425}, {8929, 358}, + {8930, 83}, {8932, 507}, {8934, 1125}, {8935, 861}, {8937, 3733}, + {8938, 2295}, {8940, 529}, {8943, 3635}, {8945, 563}, {8946, 967}, + {8948, 2637}, {8951, 506}, {8953, 25}, {8956, 4231}, {8958, 1029}, + {8959, 225}, {8961, 176}, {8962, 691}, {8964, 939}, {8966, 1233}, + {8967, 2744}, {8969, 435}, {8970, 2191}, {8972, 1619}, {8974, 981}, + {8975, 1128}, {8977, 966}, {8980, 3093}, {8982, 169}, {8983, 345}, + {8985, 2674}, {8986, 495}, {8988, 1513}, {8990, 333}, {8991, 2020}, + {8993, 2079}, {8994, 1051}, {8999, 1386}, {9001, 1599}, {9002, 3995}, + {9004, 649}, {9006, 1477}, {9007, 222}, {9009, 29}, {9012, 1053}, + {9014, 1217}, {9017, 155}, {9018, 1327}, {9020, 287}, {9022, 861}, + {9023, 4350}, {9025, 744}, {9026, 35}, {9028, 2935}, {9031, 714}, + {9033, 1615}, {9034, 2095}, {9036, 449}, {9039, 1741}, {9041, 813}, + {9042, 103}, {9044, 2819}, {9047, 287}, {9049, 2490}, {9050, 1319}, + {9052, 2725}, {9054, 609}, {9055, 946}, {9057, 2345}, {9058, 235}, + {9060, 151}, {9062, 3929}, {9063, 2320}, {9065, 2022}, {9068, 2565}, + {9071, 2276}, {9074, 207}, {9076, 2395}, {9078, 2681}, {9079, 2179}, + {9081, 190}, {9084, 1699}, {9086, 2445}, {9089, 440}, {9092, 29}, + {9094, 2769}, {9095, 2546}, {9097, 1260}, {9100, 55}, {9103, 4200}, + {9105, 1493}, {9106, 1723}, {9108, 575}, {9111, 487}, {9113, 3563}, + {9114, 539}, {9116, 1841}, {9119, 917}, {9121, 249}, {9126, 181}, + {9127, 1120}, {9129, 23}, {9130, 2991}, {9132, 207}, {9134, 1545}, + {9135, 944}, {9137, 2163}, {9138, 2671}, {9140, 1365}, {9142, 4545}, + {9143, 1268}, {9145, 546}, {9148, 1921}, {9150, 469}, {9151, 1330}, + {9153, 682}, {9154, 3087}, {9156, 281}, {9158, 809}, {9159, 3470}, + {9161, 1046}, {9162, 2807}, {9164, 1913}, {9169, 229}, {9170, 1103}, + {9175, 2806}, {9177, 884}, {9180, 1153}, {9182, 1769}, {9185, 207}, + {9186, 3159}, {9188, 4305}, {9190, 2217}, {9191, 3936}, {9193, 1216}, + {9198, 1365}, {9199, 109}, {9201, 146}, {9202, 211}, {9204, 645}, + {9206, 4085}, {9207, 397}, {9209, 2181}, {9210, 2603}, {9212, 3839}, + {9214, 397}, {9215, 1217}, {9217, 1956}, {9218, 2919}, {9220, 1875}, + {9223, 1023}, {9225, 181}, {9226, 4315}, {9228, 145}, {9231, 3899}, + {9233, 545}, {9234, 315}, {9238, 49}, {9239, 1629}, {9241, 909}, + {9242, 239}, {9244, 441}, {9247, 48}, {9249, 1663}, {9250, 531}, + {9252, 327}, {9255, 298}, {9257, 1364}, {9258, 3843}, {9260, 2729}, + {9262, 1549}, {9263, 3173}, {9265, 1123}, {9268, 3183}, {9270, 837}, + {9271, 1488}, {9273, 502}, {9274, 1219}, {9276, 135}, {9278, 2145}, + {9279, 1526}, {9281, 2049}, {9282, 2307}, {9284, 1883}, {9287, 2520}, + {9289, 358}, {9290, 1731}, {9292, 3087}, {9294, 3373}, {9295, 2149}, + {9297, 1838}, {9298, 2139}, {9300, 135}, {9302, 605}, {9303, 208}, + {9305, 3344}, {9306, 675}, {9308, 1559}, {9310, 3141}, {9311, 2657}, + {9313, 924}, {9316, 1233}, {9319, 477}, {9321, 2627}, {9322, 4027}, + {9324, 665}, {9327, 4165}, {9329, 2910}, {9330, 4263}, {9332, 2081}, + {9334, 3141}, {9335, 1176}, {9337, 546}, {9340, 1339}, {9343, 2700}, + {9345, 353}, {9350, 1221}, {9351, 56}, {9353, 3221}, {9356, 1773}, + {9358, 453}, {9359, 1227}, {9361, 369}, {9364, 3297}, {9366, 2245}, + {9367, 3172}, {9369, 116}, {9370, 2311}, {9372, 269}, {9375, 4459}, + {9377, 914}, {9378, 1347}, {9380, 561}, {9382, 3297}, {9383, 1124}, + {9385, 523}, {9386, 3863}, {9390, 2601}, {9391, 1239}, {9393, 623}, + {9394, 3471}, {9396, 369}, {9398, 2769}, {9399, 1295}, {9401, 429}, + {9402, 267}, {9404, 2009}, {9407, 260}, {9409, 405}, {9414, 673}, + {9415, 1678}, {9417, 218}, {9418, 823}, {9420, 2701}, {9423, 1280}, + {9425, 699}, {9431, 3113}, {9433, 42}, {9436, 225}, {9439, 105}, + {9441, 479}, {9442, 4611}, {9444, 3513}, {9447, 458}, {9449, 584}, + {9450, 1431}, {9454, 4189}, {9455, 2807}, {9457, 4}, {9463, 327}, + {9465, 197}, {9468, 1695}, {9470, 2289}, {9471, 1459}, {9473, 656}, + {9476, 2583}, {9478, 909}, {9479, 200}, {9481, 4060}, {9484, 853}, + {9486, 945}, {9487, 211}, {9489, 2089}, {9490, 999}, {9492, 373}, + {9494, 477}, {9497, 2301}, {9500, 1175}, {9502, 621}, {9503, 99}, + {9508, 1141}, {9510, 2349}, {9511, 399}, {9513, 686}, {9516, 903}, + {9518, 1797}, {9519, 1573}, {9521, 116}, {9522, 243}, {9524, 3207}, + {9527, 1650}, {9529, 43}, {9530, 1623}, {9532, 2103}, {9534, 1193}, + {9535, 1119}, {9537, 565}, {9540, 3059}, {9542, 1185}, {9543, 533}, + {9545, 539}, {9546, 47}, {9548, 335}, {9551, 126}, {9553, 1498}, + {9558, 2041}, {9559, 702}, {9561, 3059}, {9562, 687}, {9564, 387}, + {9566, 1901}, {9567, 1883}, {9569, 60}, {9570, 487}, {9575, 888}, + {9577, 1668}, {9578, 1503}, {9580, 1771}, {9582, 3177}, {9583, 790}, + {9585, 2524}, {9586, 1867}, {9588, 525}, {9590, 2061}, {9591, 841}, + {9593, 284}, {9594, 499}, {9598, 4309}, {9599, 14}, {9601, 963}, + {9607, 262}, {9609, 1526}, {9610, 2883}, {9612, 93}, {9614, 4577}, + {9615, 361}, {9617, 1385}, {9620, 557}, {9622, 2145}, {9623, 2429}, + {9625, 508}, {9628, 31}, {9630, 37}, {9631, 295}, {9633, 2333}, + {9634, 3075}, {9636, 515}, {9639, 700}, {9641, 3287}, {9642, 3591}, + {9644, 1671}, {9647, 1227}, {9649, 657}, {9652, 2733}, {9654, 1969}, + {9655, 3558}, {9657, 1192}, {9658, 3691}, {9660, 57}, {9663, 446}, + {9665, 2763}, {9666, 435}, {9668, 225}, {9671, 1086}, {9673, 3538}, + {9674, 759}, {9676, 3367}, {9678, 4277}, {9679, 864}, {9681, 910}, + {9682, 3175}, {9684, 2405}, {9686, 2333}, {9687, 2054}, {9689, 84}, + {9690, 1503}, {9692, 3381}, {9695, 207}, {9697, 1201}, {9700, 565}, + {9702, 1533}, {9705, 1802}, {9708, 1753}, {9711, 917}, {9713, 2933}, + {9714, 1227}, {9716, 263}, {9719, 3492}, {9721, 171}, {9727, 760}, + {9729, 938}, {9730, 663}, {9732, 3747}, {9734, 4125}, {9735, 2086}, + {9737, 275}, {9738, 3663}, {9740, 3015}, {9743, 869}, {9745, 2361}, + {9746, 2559}, {9748, 889}, {9750, 833}, {9751, 1093}, {9753, 1078}, + {9754, 3891}, {9756, 1701}, {9758, 1557}, {9759, 706}, {9761, 2588}, + {9762, 4455}, {9766, 585}, {9767, 1668}, {9769, 1390}, {9770, 1091}, + {9772, 741}, {9774, 401}, {9775, 537}, {9777, 773}, {9780, 711}, + {9782, 161}, {9783, 88}, {9785, 2036}, {9786, 4147}, {9788, 2007}, + {9790, 177}, {9791, 390}, {9793, 339}, {9796, 321}, {9798, 2677}, + {9799, 139}, {9801, 284}, {9804, 1165}, {9807, 337}, {9810, 711}, + {9814, 1545}, {9817, 4420}, {9820, 105}, {9822, 305}, {9823, 144}, + {9825, 2563}, {9828, 207}, {9830, 1541}, {9831, 1159}, {9833, 104}, + {9839, 389}, {9841, 1788}, {9844, 565}, {9846, 2349}, {9847, 3537}, + {9849, 329}, {9852, 3379}, {9854, 317}, {9855, 803}, {9857, 4386}, + {9858, 4235}, {9860, 2997}, {9863, 1809}, {9865, 2604}, {9868, 339}, + {9870, 2681}, {9871, 903}, {9873, 3842}, {9874, 4279}, {9876, 183}, + {9878, 573}, {9879, 1181}, {9882, 747}, {9884, 389}, {9886, 3673}, + {9887, 710}, {9889, 2019}, {9890, 2583}, {9895, 787}, {9897, 430}, + {9900, 11}, {9903, 40}, {9905, 219}, {9906, 2027}, {9908, 2699}, + {9911, 483}, {9913, 1899}, {9914, 95}, {9916, 4483}, {9918, 381}, + {9919, 1185}, {9921, 901}, {9922, 2691}, {9926, 1445}, {9927, 1987}, + {9929, 1382}, {9930, 331}, {9932, 2397}, {9935, 2216}, {9937, 451}, + {9940, 2059}, {9942, 133}, {9943, 3069}, {9945, 1882}, {9946, 2355}, + {9948, 1535}, {9950, 2453}, {9951, 1334}, {9953, 539}, {9954, 343}, + {9956, 851}, {9959, 381}, {9961, 2707}, {9964, 2691}, {9966, 1701}, + {9967, 4399}, {9969, 295}, {9970, 2587}, {9972, 519}, {9974, 2045}, + {9975, 124}, {9977, 2954}, {9978, 1483}, {9980, 707}, {9982, 993}, + {9983, 785}, {9985, 1974}, {9986, 1143}, {9988, 3129}, {9990, 573}, + {9991, 495}, {9993, 121}, {9996, 1447}, {9998, 4013}, {9999, 2951}}; + +// ANSI range [160, 2000] +/** + * ANSI X9.62 irreducible trinomials + * + * Accredited Standards Committee X9: + * Harold Deal, Chairman + * Alice Droogan, Vice Chairman + * Cynthia Fuller, Secretariat + * The X9F subcommittee on Data and Information Security: + * Glenda Barnes, Chairman + * The X9F1 working group: + * M. Blake Greenlee, Chairman + */ static polynomial_t ansi_trinomials[] = { {161, 18}, {162, 27}, {166, 37}, {167, 6}, {169, 34}, {170, 11}, {172, 1}, {174, 13}, {175, 6}, {177, 8}, @@ -198,6 +1061,1354 @@ static polynomial_t ansi_trinomials[] = { {1988, 555}, {1990, 133}, {1991, 546}, {1993, 103}, {1994, 15}, {1996, 307}, {1999, 367}}; +// HP range [2, 159] + [2001, 10000] +/** + * Table of Low-Weight Binary Irreducible Polynomials + * Gadiel Seroussi + * Computer Systems Laboratory + * HPL-98-135 + * August, 1998 + * + * http://www.hpl.hp.com/techreports/98/HPL-98-135.pdf + */ +static polynomial_t hp_pentanomials[] = { + {8, 4, 3, 1}, {13, 4, 3, 1}, {16, 5, 3, 1}, + {19, 5, 2, 1}, {24, 4, 3, 1}, {26, 4, 3, 1}, + {27, 5, 2, 1}, {32, 7, 3, 2}, {37, 6, 4, 1}, + {38, 6, 5, 1}, {40, 5, 4, 3}, {43, 6, 4, 3}, + {45, 4, 3, 1}, {48, 5, 3, 2}, {50, 4, 3, 2}, + {51, 6, 3, 1}, {53, 6, 2, 1}, {56, 7, 4, 2}, + {59, 7, 4, 2}, {61, 5, 2, 1}, {64, 4, 3, 1}, + {67, 5, 2, 1}, {69, 6, 5, 2}, {70, 5, 3, 1}, + {72, 10, 9, 3}, {75, 6, 3, 1}, {77, 6, 5, 2}, + {78, 6, 5, 3}, {80, 9, 4, 2}, {82, 8, 3, 1}, + {83, 7, 4, 2}, {85, 8, 2, 1}, {88, 7, 6, 2}, + {91, 8, 5, 1}, {96, 10, 9, 6}, {99, 6, 3, 1}, + {101, 7, 6, 1}, {104, 4, 3, 1}, {107, 9, 7, 4}, + {109, 5, 4, 2}, {112, 5, 4, 3}, {114, 5, 3, 2}, + {115, 8, 7, 5}, {116, 4, 2, 1}, {117, 5, 2, 1}, + {120, 4, 3, 1}, {122, 6, 2, 1}, {125, 7, 6, 5}, + {128, 7, 2, 1}, {131, 8, 3, 2}, {133, 9, 8, 2}, + {136, 5, 3, 2}, {138, 8, 7, 1}, {139, 8, 5, 3}, + {141, 10, 4, 1}, {143, 5, 3, 2}, {144, 7, 4, 2}, + {149, 10, 9, 7}, {152, 6, 3, 2}, {157, 6, 5, 2}, + {158, 8, 6, 5}, {2002, 22, 21, 11}, {2003, 12, 10, 8}, + {2005, 17, 12, 7}, {2008, 26, 23, 13}, {2011, 17, 15, 4}, + {2012, 19, 15, 4}, {2013, 5, 4, 2}, {2014, 9, 7, 6}, + {2016, 21, 15, 7}, {2018, 20, 7, 3}, {2019, 20, 7, 2}, + {2021, 19, 14, 1}, {2024, 40, 35, 9}, {2027, 11, 10, 3}, + {2029, 12, 7, 4}, {2030, 13, 12, 2}, {2032, 7, 6, 2}, + {2035, 9, 8, 4}, {2037, 19, 18, 3}, {2038, 16, 11, 6}, + {2040, 7, 2, 1}, {2042, 16, 8, 7}, {2043, 9, 7, 4}, + {2045, 7, 6, 4}, {2046, 12, 11, 3}, {2048, 19, 14, 13}, + {2050, 15, 13, 8}, {2051, 13, 6, 5}, {2053, 21, 13, 6}, + {2056, 13, 12, 3}, {2059, 14, 12, 10}, {2061, 19, 4, 1}, + {2062, 16, 3, 2}, {2064, 17, 9, 2}, {2067, 17, 13, 8}, + {2068, 18, 10, 7}, {2069, 18, 9, 8}, {2071, 11, 5, 3}, + {2072, 13, 10, 3}, {2075, 9, 7, 4}, {2077, 15, 14, 4}, + {2078, 16, 6, 5}, {2080, 4, 3, 1}, {2083, 21, 11, 10}, + {2084, 4, 2, 1}, {2085, 9, 8, 3}, {2088, 18, 11, 5}, + {2090, 9, 4, 1}, {2091, 12, 9, 5}, {2092, 17, 15, 7}, + {2093, 16, 15, 7}, {2096, 19, 4, 2}, {2099, 15, 12, 9}, + {2101, 25, 22, 9}, {2104, 19, 15, 9}, {2107, 17, 10, 2}, + {2108, 21, 5, 3}, {2109, 10, 5, 1}, {2110, 12, 9, 6}, + {2112, 16, 13, 7}, {2115, 11, 10, 1}, {2117, 24, 16, 11}, + {2120, 17, 14, 6}, {2123, 14, 11, 3}, {2125, 24, 17, 14}, + {2128, 23, 9, 1}, {2131, 13, 6, 5}, {2133, 24, 22, 4}, + {2134, 23, 13, 2}, {2136, 15, 12, 9}, {2138, 13, 9, 2}, + {2139, 14, 4, 1}, {2141, 16, 3, 1}, {2144, 13, 7, 3}, + {2147, 8, 3, 2}, {2149, 17, 9, 2}, {2152, 24, 13, 7}, + {2154, 10, 7, 5}, {2155, 10, 9, 8}, {2157, 14, 4, 1}, + {2160, 31, 25, 14}, {2163, 12, 9, 7}, {2165, 10, 4, 2}, + {2168, 11, 9, 3}, {2171, 7, 6, 4}, {2172, 6, 4, 1}, + {2173, 15, 8, 4}, {2176, 15, 8, 1}, {2179, 8, 7, 2}, + {2181, 18, 12, 7}, {2184, 11, 10, 5}, {2187, 22, 11, 1}, + {2189, 19, 8, 7}, {2192, 8, 5, 3}, {2194, 15, 13, 9}, + {2195, 23, 22, 16}, {2197, 6, 5, 2}, {2200, 20, 15, 5}, + {2202, 15, 3, 2}, {2203, 14, 6, 5}, {2204, 11, 7, 1}, + {2205, 14, 7, 4}, {2208, 21, 16, 6}, {2211, 20, 14, 3}, + {2213, 20, 19, 4}, {2216, 24, 7, 2}, {2219, 22, 12, 11}, + {2221, 17, 16, 6}, {2223, 17, 6, 2}, {2224, 21, 19, 5}, + {2226, 19, 16, 7}, {2227, 14, 9, 8}, {2229, 17, 8, 7}, + {2232, 19, 17, 4}, {2234, 7, 6, 1}, {2235, 20, 17, 11}, + {2237, 7, 4, 2}, {2240, 23, 7, 1}, {2243, 27, 15, 2}, + {2245, 22, 12, 11}, {2246, 23, 15, 6}, {2248, 9, 4, 3}, + {2251, 19, 16, 13}, {2253, 19, 14, 2}, {2254, 10, 9, 2}, + {2256, 14, 9, 6}, {2259, 16, 10, 6}, {2260, 12, 4, 1}, + {2261, 14, 12, 7}, {2264, 15, 7, 2}, {2267, 18, 17, 8}, + {2269, 15, 10, 7}, {2272, 21, 10, 9}, {2275, 15, 12, 1}, + {2277, 10, 4, 2}, {2278, 17, 14, 7}, {2280, 13, 4, 2}, + {2283, 20, 13, 4}, {2285, 8, 6, 2}, {2288, 17, 16, 7}, + {2290, 23, 6, 5}, {2291, 13, 10, 2}, {2293, 10, 8, 3}, + {2294, 21, 17, 10}, {2296, 15, 10, 1}, {2298, 15, 13, 3}, + {2299, 16, 6, 1}, {2301, 15, 9, 8}, {2302, 15, 8, 1}, + {2304, 8, 7, 5}, {2307, 11, 7, 2}, {2309, 12, 10, 8}, + {2312, 19, 6, 4}, {2315, 17, 15, 4}, {2317, 17, 4, 2}, + {2320, 13, 11, 5}, {2323, 16, 3, 2}, {2325, 14, 8, 5}, + {2326, 13, 10, 7}, {2328, 15, 9, 2}, {2330, 15, 5, 1}, + {2333, 18, 15, 8}, {2336, 15, 10, 8}, {2339, 10, 3, 2}, + {2341, 24, 18, 16}, {2344, 27, 26, 14}, {2347, 11, 10, 2}, + {2349, 31, 16, 9}, {2350, 21, 19, 4}, {2352, 23, 20, 2}, + {2354, 14, 11, 6}, {2355, 12, 11, 6}, {2357, 10, 9, 8}, + {2360, 19, 10, 8}, {2362, 13, 10, 6}, {2363, 9, 7, 4}, + {2365, 21, 14, 5}, {2366, 16, 13, 6}, {2368, 13, 11, 8}, + {2370, 12, 11, 6}, {2371, 20, 18, 17}, {2373, 17, 14, 5}, + {2374, 24, 16, 13}, {2376, 7, 5, 4}, {2379, 22, 9, 3}, + {2381, 18, 12, 2}, {2384, 21, 19, 1}, {2386, 11, 9, 1}, + {2387, 8, 7, 6}, {2389, 31, 12, 10}, {2392, 31, 13, 3}, + {2395, 17, 8, 7}, {2397, 22, 17, 4}, {2398, 15, 13, 11}, + {2400, 20, 19, 17}, {2403, 11, 8, 2}, {2405, 17, 14, 5}, + {2406, 14, 12, 5}, {2408, 23, 6, 4}, {2411, 12, 2, 1}, + {2413, 11, 6, 1}, {2416, 23, 6, 5}, {2419, 22, 16, 6}, + {2421, 11, 8, 4}, {2424, 21, 16, 6}, {2426, 20, 4, 3}, + {2427, 8, 6, 5}, {2429, 22, 14, 7}, {2432, 29, 22, 19}, + {2435, 18, 6, 2}, {2437, 9, 4, 3}, {2440, 12, 7, 5}, + {2443, 15, 13, 4}, {2445, 23, 20, 10}, {2446, 18, 13, 6}, + {2448, 21, 10, 4}, {2451, 10, 4, 3}, {2453, 21, 14, 11}, + {2456, 12, 5, 3}, {2458, 23, 20, 18}, {2459, 17, 7, 4}, + {2461, 19, 18, 10}, {2462, 22, 13, 8}, {2464, 5, 4, 3}, + {2467, 18, 14, 2}, {2469, 26, 16, 11}, {2471, 15, 6, 3}, + {2472, 12, 3, 1}, {2475, 12, 11, 9}, {2476, 17, 3, 2}, + {2477, 19, 17, 6}, {2480, 20, 5, 2}, {2482, 11, 7, 6}, + {2483, 12, 11, 2}, {2486, 19, 14, 9}, {2488, 23, 13, 9}, + {2490, 8, 7, 5}, {2491, 25, 16, 12}, {2493, 18, 15, 7}, + {2494, 13, 8, 2}, {2496, 12, 3, 1}, {2498, 8, 7, 4}, + {2499, 13, 12, 9}, {2501, 22, 21, 5}, {2504, 19, 8, 6}, + {2506, 17, 11, 3}, {2507, 13, 8, 1}, {2509, 14, 13, 3}, + {2512, 29, 21, 7}, {2515, 8, 7, 5}, {2517, 14, 4, 1}, + {2518, 18, 13, 2}, {2520, 31, 15, 13}, {2522, 16, 10, 5}, + {2523, 23, 17, 14}, {2524, 15, 6, 4}, {2525, 7, 6, 5}, + {2528, 19, 9, 4}, {2530, 14, 5, 3}, {2531, 6, 2, 1}, + {2532, 26, 22, 13}, {2533, 10, 3, 1}, {2535, 24, 19, 16}, + {2536, 21, 10, 9}, {2539, 10, 9, 3}, {2541, 11, 8, 7}, + {2544, 21, 20, 6}, {2547, 22, 10, 3}, {2549, 10, 9, 5}, + {2552, 28, 3, 2}, {2555, 9, 6, 2}, {2557, 18, 17, 7}, + {2558, 18, 8, 1}, {2560, 9, 3, 1}, {2563, 12, 11, 10}, + {2565, 25, 16, 14}, {2568, 8, 5, 2}, {2570, 18, 15, 14}, + {2571, 18, 16, 9}, {2573, 12, 11, 3}, {2576, 7, 2, 1}, + {2578, 15, 7, 3}, {2579, 23, 6, 1}, {2581, 26, 14, 12}, + {2582, 22, 19, 15}, {2584, 25, 19, 12}, {2587, 23, 12, 10}, + {2588, 13, 8, 1}, {2589, 29, 11, 10}, {2592, 15, 12, 5}, + {2595, 24, 17, 2}, {2597, 16, 8, 7}, {2600, 14, 13, 7}, + {2602, 11, 6, 1}, {2603, 18, 8, 7}, {2605, 19, 14, 5}, + {2608, 15, 11, 2}, {2611, 27, 17, 10}, {2612, 21, 14, 6}, + {2613, 14, 12, 9}, {2616, 17, 8, 7}, {2619, 17, 10, 1}, + {2621, 8, 7, 1}, {2622, 11, 5, 3}, {2624, 15, 10, 4}, + {2627, 20, 17, 11}, {2629, 13, 9, 6}, {2632, 19, 5, 3}, + {2634, 20, 11, 5}, {2635, 25, 21, 14}, {2636, 18, 11, 10}, + {2637, 9, 6, 4}, {2638, 10, 3, 1}, {2640, 23, 11, 9}, + {2643, 16, 13, 10}, {2645, 18, 11, 10}, {2648, 15, 8, 1}, + {2650, 17, 13, 5}, {2651, 7, 5, 4}, {2653, 17, 4, 2}, + {2654, 20, 16, 13}, {2656, 19, 11, 5}, {2658, 6, 3, 2}, + {2659, 20, 18, 16}, {2661, 17, 14, 2}, {2662, 14, 12, 7}, + {2664, 27, 21, 19}, {2669, 18, 4, 2}, {2672, 18, 7, 1}, + {2675, 13, 10, 9}, {2677, 17, 8, 6}, {2678, 15, 6, 5}, + {2680, 15, 9, 4}, {2683, 11, 6, 1}, {2684, 14, 12, 3}, + {2685, 8, 2, 1}, {2688, 21, 10, 6}, {2690, 12, 9, 3}, + {2691, 14, 10, 8}, {2693, 10, 5, 3}, {2696, 17, 15, 12}, + {2699, 32, 30, 29}, {2701, 12, 10, 5}, {2704, 12, 9, 7}, + {2705, 12, 10, 5}, {2707, 9, 6, 4}, {2709, 10, 9, 3}, + {2710, 7, 3, 1}, {2712, 21, 12, 7}, {2714, 12, 8, 7}, + {2715, 30, 26, 15}, {2717, 14, 8, 3}, {2720, 25, 18, 1}, + {2723, 9, 6, 5}, {2725, 21, 17, 2}, {2726, 10, 6, 1}, + {2728, 21, 7, 5}, {2731, 15, 11, 2}, {2733, 19, 8, 7}, + {2734, 9, 5, 4}, {2736, 16, 3, 1}, {2739, 12, 9, 5}, + {2741, 6, 5, 4}, {2744, 19, 18, 10}, {2746, 9, 7, 2}, + {2747, 15, 11, 6}, {2749, 22, 18, 17}, {2752, 15, 4, 2}, + {2755, 13, 7, 6}, {2757, 24, 23, 12}, {2758, 17, 5, 4}, + {2760, 29, 26, 7}, {2763, 12, 10, 6}, {2765, 16, 10, 3}, + {2768, 25, 19, 15}, {2771, 13, 12, 5}, {2773, 30, 25, 20}, + {2774, 28, 3, 2}, {2776, 7, 3, 2}, {2777, 22, 21, 17}, + {2779, 20, 17, 9}, {2781, 28, 27, 10}, {2782, 22, 10, 9}, + {2784, 29, 21, 15}, {2787, 19, 18, 3}, {2788, 21, 16, 2}, + {2789, 14, 12, 8}, {2792, 12, 7, 2}, {2794, 11, 9, 4}, + {2795, 10, 8, 4}, {2797, 19, 6, 1}, {2798, 20, 14, 5}, + {2800, 17, 14, 6}, {2802, 18, 14, 3}, {2803, 18, 16, 13}, + {2805, 24, 8, 2}, {2808, 15, 13, 1}, {2810, 23, 10, 9}, + {2811, 10, 9, 7}, {2813, 13, 7, 6}, {2816, 21, 19, 8}, + {2818, 15, 9, 1}, {2819, 10, 6, 5}, {2821, 16, 6, 4}, + {2822, 18, 17, 3}, {2824, 15, 14, 10}, {2827, 19, 10, 6}, + {2829, 9, 6, 4}, {2830, 17, 15, 13}, {2832, 27, 18, 1}, + {2834, 15, 13, 7}, {2835, 20, 13, 5}, {2837, 17, 8, 3}, + {2838, 20, 4, 1}, {2840, 20, 15, 9}, {2843, 7, 3, 2}, + {2845, 10, 9, 1}, {2846, 23, 15, 4}, {2848, 15, 8, 1}, + {2851, 10, 7, 1}, {2853, 14, 8, 1}, {2856, 15, 13, 3}, + {2858, 17, 9, 7}, {2859, 29, 20, 11}, {2861, 20, 16, 10}, + {2864, 21, 17, 15}, {2866, 9, 7, 2}, {2867, 15, 13, 10}, + {2869, 8, 6, 1}, {2870, 12, 11, 1}, {2872, 21, 5, 2}, + {2874, 13, 6, 3}, {2875, 20, 16, 2}, {2877, 10, 7, 4}, + {2880, 13, 10, 6}, {2883, 16, 13, 12}, {2885, 13, 11, 6}, + {2886, 20, 14, 9}, {2888, 11, 4, 1}, {2891, 16, 15, 10}, + {2893, 27, 7, 2}, {2894, 16, 14, 9}, {2896, 29, 6, 1}, + {2899, 19, 10, 1}, {2901, 11, 3, 2}, {2902, 14, 10, 9}, + {2904, 27, 15, 6}, {2907, 17, 14, 1}, {2908, 19, 13, 10}, + {2909, 23, 22, 4}, {2912, 16, 9, 2}, {2915, 18, 7, 5}, + {2917, 16, 15, 4}, {2920, 19, 9, 5}, {2923, 11, 6, 5}, + {2924, 12, 4, 1}, {2925, 12, 4, 3}, {2926, 20, 14, 1}, + {2928, 24, 21, 11}, {2930, 9, 4, 1}, {2931, 13, 8, 1}, + {2932, 14, 7, 6}, {2933, 15, 14, 13}, {2935, 13, 12, 7}, + {2936, 5, 3, 2}, {2939, 30, 17, 5}, {2941, 23, 18, 17}, + {2944, 5, 3, 2}, {2947, 22, 20, 11}, {2948, 17, 3, 2}, + {2949, 17, 7, 4}, {2952, 17, 13, 2}, {2954, 9, 6, 5}, + {2955, 12, 10, 6}, {2957, 19, 14, 3}, {2958, 23, 13, 5}, + {2960, 12, 3, 2}, {2963, 21, 14, 5}, {2965, 25, 22, 15}, + {2968, 29, 27, 4}, {2971, 18, 13, 2}, {2973, 18, 10, 4}, + {2974, 11, 3, 1}, {2976, 21, 10, 3}, {2979, 12, 11, 6}, + {2981, 13, 2, 1}, {2984, 17, 9, 6}, {2987, 8, 3, 2}, + {2989, 18, 9, 7}, {2990, 26, 22, 9}, {2992, 23, 3, 1}, + {2995, 9, 6, 4}, {2997, 12, 6, 5}, {3000, 15, 12, 9}, + {3002, 22, 21, 10}, {3003, 12, 11, 5}, {3005, 14, 12, 5}, + {3006, 15, 9, 6}, {3008, 15, 13, 1}, {3010, 25, 12, 10}, + {3011, 22, 8, 6}, {3013, 23, 6, 2}, {3014, 17, 15, 5}, + {3016, 38, 25, 9}, {3019, 16, 6, 1}, {3021, 22, 10, 1}, + {3022, 14, 12, 1}, {3024, 32, 3, 2}, {3026, 19, 18, 13}, + {3027, 17, 16, 4}, {3029, 11, 6, 4}, {3030, 12, 9, 4}, + {3032, 17, 15, 4}, {3035, 21, 20, 2}, {3037, 7, 6, 3}, + {3040, 27, 21, 3}, {3043, 18, 16, 15}, {3045, 17, 14, 11}, + {3047, 19, 15, 4}, {3048, 18, 3, 2}, {3051, 19, 17, 16}, + {3053, 22, 20, 15}, {3054, 21, 4, 3}, {3055, 13, 7, 1}, + {3056, 5, 4, 3}, {3059, 15, 10, 1}, {3061, 22, 15, 1}, + {3064, 25, 11, 9}, {3067, 18, 16, 13}, {3069, 34, 26, 19}, + {3070, 20, 13, 8}, {3072, 11, 10, 5}, {3074, 17, 9, 3}, + {3075, 16, 14, 10}, {3077, 12, 10, 8}, {3080, 21, 19, 16}, + {3082, 9, 6, 1}, {3083, 23, 20, 18}, {3085, 25, 14, 12}, + {3088, 20, 13, 11}, {3091, 12, 7, 5}, {3093, 14, 11, 8}, + {3096, 33, 29, 14}, {3098, 18, 17, 11}, {3099, 14, 13, 11}, + {3101, 10, 7, 3}, {3104, 23, 9, 5}, {3106, 6, 2, 1}, + {3107, 14, 12, 11}, {3109, 26, 20, 19}, {3112, 17, 15, 1}, + {3114, 19, 15, 4}, {3115, 25, 18, 16}, {3117, 19, 8, 4}, + {3120, 18, 17, 11}, {3122, 22, 7, 6}, {3123, 15, 10, 4}, + {3125, 24, 21, 18}, {3128, 30, 19, 11}, {3131, 22, 8, 7}, + {3133, 6, 4, 3}, {3136, 15, 12, 10}, {3138, 29, 19, 13}, + {3139, 14, 11, 10}, {3141, 23, 18, 12}, {3144, 23, 21, 8}, + {3146, 18, 11, 6}, {3147, 17, 10, 7}, {3149, 22, 3, 2}, + {3152, 21, 17, 6}, {3154, 19, 17, 6}, {3155, 15, 12, 2}, + {3157, 24, 14, 10}, {3158, 19, 9, 5}, {3160, 7, 6, 2}, + {3163, 18, 13, 10}, {3165, 17, 13, 10}, {3166, 18, 10, 1}, + {3168, 33, 31, 18}, {3171, 19, 14, 13}, {3173, 20, 17, 14}, + {3176, 13, 10, 5}, {3179, 22, 12, 2}, {3181, 12, 10, 3}, + {3184, 11, 10, 2}, {3187, 9, 8, 2}, {3189, 19, 18, 12}, + {3190, 12, 4, 1}, {3192, 25, 8, 7}, {3195, 19, 14, 1}, + {3197, 22, 16, 14}, {3200, 11, 6, 4}, {3202, 24, 12, 3}, + {3203, 14, 7, 3}, {3205, 17, 9, 2}, {3206, 15, 8, 6}, + {3208, 16, 13, 3}, {3211, 12, 10, 5}, {3213, 30, 16, 1}, + {3216, 21, 11, 3}, {3218, 10, 9, 8}, {3219, 24, 10, 3}, + {3221, 11, 6, 5}, {3224, 23, 19, 1}, {3226, 9, 7, 5}, + {3227, 8, 7, 6}, {3229, 12, 9, 7}, {3231, 15, 9, 8}, + {3232, 12, 9, 7}, {3235, 21, 11, 8}, {3237, 19, 8, 4}, + {3240, 12, 3, 2}, {3242, 27, 13, 7}, {3243, 22, 13, 5}, + {3245, 11, 10, 4}, {3248, 15, 8, 1}, {3250, 15, 11, 8}, + {3251, 9, 6, 5}, {3253, 10, 5, 3}, {3256, 31, 26, 2}, + {3259, 22, 4, 1}, {3261, 18, 12, 10}, {3262, 15, 13, 7}, + {3264, 17, 5, 2}, {3265, 18, 16, 7}, {3266, 19, 2, 1}, + {3267, 20, 19, 10}, {3269, 22, 3, 2}, {3272, 23, 10, 1}, + {3275, 24, 13, 10}, {3277, 25, 22, 1}, {3278, 22, 12, 1}, + {3280, 16, 15, 6}, {3283, 30, 28, 21}, {3284, 24, 17, 13}, + {3285, 18, 4, 1}, {3288, 21, 18, 11}, {3290, 11, 7, 3}, + {3291, 18, 7, 1}, {3293, 20, 18, 15}, {3296, 19, 14, 13}, + {3299, 18, 17, 14}, {3301, 24, 10, 4}, {3304, 19, 17, 3}, + {3307, 15, 10, 2}, {3309, 23, 20, 6}, {3312, 14, 9, 3}, + {3315, 12, 8, 2}, {3317, 22, 17, 7}, {3320, 17, 10, 4}, + {3323, 28, 14, 10}, {3325, 25, 19, 10}, {3328, 17, 9, 2}, + {3331, 18, 17, 11}, {3333, 16, 8, 7}, {3334, 6, 4, 1}, + {3336, 11, 10, 5}, {3339, 22, 16, 12}, {3340, 11, 7, 5}, + {3341, 25, 19, 12}, {3342, 9, 6, 5}, {3344, 30, 27, 15}, + {3346, 15, 6, 1}, {3347, 23, 18, 16}, {3349, 20, 19, 17}, + {3352, 21, 20, 19}, {3354, 10, 9, 3}, {3355, 10, 6, 4}, + {3357, 24, 17, 15}, {3358, 19, 8, 6}, {3360, 18, 15, 5}, + {3361, 12, 10, 4}, {3362, 11, 7, 4}, {3363, 14, 10, 2}, + {3365, 24, 15, 2}, {3368, 7, 5, 1}, {3370, 15, 10, 1}, + {3371, 30, 29, 18}, {3373, 14, 6, 4}, {3376, 11, 9, 1}, + {3379, 25, 20, 9}, {3381, 7, 4, 1}, {3384, 21, 9, 3}, + {3386, 19, 9, 2}, {3387, 26, 25, 16}, {3389, 17, 15, 4}, + {3392, 23, 13, 6}, {3394, 13, 12, 3}, {3395, 22, 10, 6}, + {3396, 13, 6, 1}, {3397, 19, 4, 1}, {3400, 14, 13, 6}, + {3403, 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29, 23, 17}, {8859, 35, 30, 27}, {8861, 18, 16, 10}, + {8864, 37, 12, 7}, {8866, 29, 16, 5}, {8867, 32, 9, 5}, + {8869, 34, 19, 7}, {8872, 51, 4, 2}, {8875, 19, 18, 1}, + {8877, 21, 13, 10}, {8880, 36, 9, 6}, {8882, 17, 11, 6}, + {8883, 28, 27, 10}, {8885, 30, 26, 20}, {8888, 43, 13, 9}, + {8891, 10, 9, 4}, {8893, 27, 7, 6}, {8894, 17, 6, 5}, + {8896, 41, 10, 6}, {8899, 29, 2, 1}, {8901, 17, 12, 2}, + {8902, 10, 9, 2}, {8904, 40, 25, 10}, {8906, 35, 16, 13}, + {8907, 22, 21, 16}, {8909, 22, 17, 9}, {8912, 18, 17, 1}, + {8914, 16, 4, 3}, {8915, 11, 6, 5}, {8917, 28, 21, 3}, + {8918, 16, 10, 9}, {8920, 33, 32, 31}, {8923, 11, 8, 6}, + {8925, 22, 11, 7}, {8928, 35, 29, 2}, {8931, 17, 6, 5}, + {8933, 24, 10, 4}, {8936, 17, 3, 1}, {8939, 22, 21, 14}, + {8941, 36, 35, 31}, {8942, 21, 16, 13}, {8944, 39, 34, 1}, + {8947, 28, 20, 6}, {8949, 29, 22, 13}, {8950, 9, 5, 1}, + {8952, 27, 14, 2}, {8954, 25, 23, 1}, {8955, 18, 13, 1}, + {8957, 16, 10, 3}, {8960, 12, 7, 5}, {8963, 30, 26, 10}, + {8965, 30, 7, 5}, {8968, 29, 11, 10}, {8971, 23, 5, 4}, + {8973, 24, 19, 12}, {8976, 23, 8, 2}, {8978, 18, 17, 5}, + {8979, 29, 22, 16}, {8981, 22, 2, 1}, {8984, 9, 8, 6}, + {8987, 16, 12, 10}, {8989, 15, 7, 2}, {8992, 35, 6, 2}, + {8995, 19, 16, 13}, {8996, 25, 16, 12}, {8997, 33, 22, 1}, + {8998, 23, 10, 2}, {9000, 28, 19, 17}, {9003, 37, 20, 10}, + {9005, 19, 14, 4}, {9008, 31, 17, 7}, {9010, 17, 12, 1}, + {9011, 31, 14, 10}, {9013, 32, 9, 7}, {9015, 12, 3, 1}, + {9016, 23, 21, 8}, {9019, 26, 22, 15}, {9021, 28, 22, 10}, + {9024, 32, 29, 11}, {9027, 23, 14, 3}, {9029, 36, 26, 1}, + {9030, 32, 8, 1}, {9032, 45, 19, 1}, {9035, 30, 22, 5}, + {9037, 28, 14, 5}, {9038, 21, 9, 8}, {9040, 9, 6, 4}, + {9043, 27, 26, 23}, {9045, 33, 8, 6}, {9046, 36, 30, 15}, + {9048, 23, 16, 10}, {9051, 17, 10, 7}, {9053, 21, 15, 12}, + {9056, 11, 3, 2}, {9059, 24, 15, 6}, {9061, 26, 18, 7}, + {9064, 33, 4, 2}, {9066, 15, 6, 1}, {9067, 9, 2, 1}, + {9069, 36, 31, 12}, {9070, 23, 13, 3}, {9072, 45, 38, 6}, + {9073, 20, 16, 5}, {9075, 30, 17, 15}, {9077, 16, 6, 4}, + {9080, 17, 10, 7}, {9082, 19, 17, 14}, {9083, 31, 18, 5}, + {9085, 26, 13, 5}, {9087, 23, 19, 7}, {9088, 33, 31, 1}, + {9090, 18, 7, 3}, {9091, 20, 9, 7}, {9093, 11, 8, 4}, + {9096, 27, 26, 11}, {9098, 25, 15, 14}, {9099, 16, 9, 1}, + {9101, 14, 8, 6}, {9102, 15, 14, 2}, {9104, 47, 33, 24}, + {9107, 28, 13, 6}, {9109, 9, 5, 2}, {9110, 32, 17, 8}, + {9112, 9, 7, 5}, {9115, 30, 9, 7}, {9117, 18, 16, 7}, + {9118, 21, 11, 10}, {9120, 35, 25, 5}, {9122, 47, 29, 23}, + {9123, 15, 13, 10}, {9124, 23, 17, 12}, {9125, 26, 12, 10}, + {9128, 39, 25, 22}, {9131, 7, 5, 4}, {9133, 26, 9, 4}, + {9136, 21, 14, 1}, {9139, 10, 3, 1}, {9141, 36, 7, 1}, + {9144, 35, 25, 4}, {9146, 12, 2, 1}, {9147, 31, 16, 2}, + {9149, 30, 28, 7}, {9152, 33, 29, 7}, {9155, 25, 11, 6}, + {9157, 30, 10, 7}, {9160, 22, 15, 3}, {9163, 20, 7, 6}, + {9165, 13, 12, 3}, {9166, 19, 10, 3}, {9167, 12, 3, 2}, + {9168, 15, 10, 4}, {9171, 38, 5, 4}, {9172, 33, 26, 8}, + {9173, 31, 17, 12}, {9174, 29, 23, 8}, {9176, 43, 37, 30}, + {9178, 19, 17, 8}, {9179, 10, 6, 5}, {9181, 23, 13, 6}, + {9183, 30, 13, 1}, {9184, 33, 26, 14}, {9187, 20, 18, 4}, + {9189, 26, 14, 8}, {9192, 21, 18, 13}, {9194, 16, 10, 5}, + {9195, 14, 13, 1}, {9196, 31, 12, 5}, {9197, 14, 12, 5}, + {9200, 31, 24, 2}, {9203, 28, 20, 6}, {9205, 14, 11, 3}, + {9208, 35, 10, 9}, {9211, 36, 19, 17}, {9213, 38, 7, 5}, + {9216, 21, 14, 8}, {9219, 30, 6, 4}, {9221, 33, 26, 5}, + {9222, 33, 23, 11}, {9224, 35, 21, 7}, {9227, 38, 29, 3}, + {9229, 20, 19, 17}, {9230, 17, 12, 8}, {9232, 49, 18, 8}, + {9235, 23, 22, 2}, {9236, 22, 14, 9}, {9237, 18, 16, 12}, + {9240, 17, 11, 7}, {9243, 5, 2, 1}, {9245, 43, 35, 18}, + {9246, 27, 18, 3}, {9248, 37, 18, 13}, {9251, 8, 3, 2}, + {9253, 42, 28, 10}, {9254, 24, 17, 13}, {9256, 19, 6, 4}, + {9259, 22, 16, 6}, {9261, 30, 18, 10}, {9264, 39, 17, 14}, + {9266, 23, 14, 6}, {9267, 23, 8, 5}, {9269, 42, 18, 14}, + {9272, 13, 4, 3}, {9275, 10, 6, 2}, {9277, 11, 3, 2}, + {9280, 23, 7, 2}, {9283, 20, 7, 6}, {9285, 29, 6, 5}, + {9286, 25, 20, 14}, {9288, 49, 43, 18}, {9291, 8, 5, 1}, + {9293, 20, 18, 3}, {9296, 29, 17, 15}, {9299, 22, 21, 1}, + {9301, 35, 25, 18}, {9304, 27, 13, 9}, {9307, 31, 25, 4}, + {9309, 19, 16, 10}, {9312, 21, 19, 16}, {9314, 27, 23, 12}, + {9315, 26, 21, 8}, {9317, 23, 20, 2}, {9318, 18, 6, 3}, + {9320, 55, 22, 8}, {9323, 18, 4, 1}, {9325, 18, 16, 1}, + {9326, 35, 23, 20}, {9328, 21, 14, 8}, {9331, 31, 30, 2}, + {9333, 26, 14, 8}, {9336, 17, 5, 3}, {9338, 23, 8, 5}, + {9339, 23, 14, 1}, {9341, 19, 18, 14}, {9342, 19, 10, 8}, + {9344, 51, 44, 5}, {9346, 18, 10, 3}, {9347, 16, 14, 7}, + {9348, 19, 9, 3}, {9349, 25, 18, 2}, {9352, 31, 26, 15}, + {9354, 16, 7, 4}, {9355, 22, 16, 4}, {9357, 35, 34, 2}, + {9360, 28, 23, 1}, {9362, 23, 13, 1}, {9363, 26, 21, 17}, + {9365, 21, 20, 7}, {9368, 38, 7, 1}, {9371, 28, 21, 17}, + {9373, 28, 10, 4}, {9374, 18, 9, 2}, {9376, 23, 5, 1}, + {9379, 14, 9, 5}, {9381, 19, 9, 6}, {9384, 17, 11, 6}, + {9387, 31, 30, 9}, {9388, 24, 7, 3}, {9389, 20, 7, 3}, + {9392, 29, 24, 11}, {9395, 17, 15, 4}, {9397, 32, 14, 7}, + {9400, 18, 13, 1}, {9403, 30, 8, 1}, {9405, 18, 4, 1}, + {9406, 28, 27, 7}, {9408, 28, 15, 6}, {9410, 32, 11, 8}, + {9411, 24, 22, 1}, {9412, 11, 9, 2}, {9413, 11, 10, 9}, + {9416, 19, 11, 6}, {9419, 30, 19, 13}, {9421, 14, 9, 5}, + {9422, 22, 10, 9}, {9424, 22, 9, 6}, {9426, 21, 6, 5}, + {9427, 23, 18, 8}, {9428, 21, 17, 7}, {9429, 21, 9, 2}, + {9430, 37, 18, 5}, {9432, 52, 43, 25}, {9434, 19, 14, 12}, + {9435, 7, 5, 4}, {9437, 14, 12, 1}, {9438, 15, 13, 6}, + {9440, 25, 22, 14}, {9443, 30, 19, 2}, {9445, 34, 14, 12}, + {9446, 12, 5, 3}, {9448, 23, 21, 20}, {9451, 13, 12, 3}, + {9452, 18, 14, 13}, {9453, 32, 29, 23}, {9456, 35, 19, 5}, + {9458, 25, 16, 6}, {9459, 36, 18, 13}, {9460, 20, 17, 1}, + {9461, 32, 28, 6}, {9462, 34, 14, 5}, {9464, 37, 18, 13}, + {9466, 23, 14, 1}, {9467, 27, 14, 7}, {9469, 28, 22, 18}, + {9472, 45, 40, 15}, {9474, 23, 20, 7}, {9475, 29, 25, 2}, + {9477, 26, 11, 7}, {9480, 18, 9, 2}, {9482, 19, 12, 4}, + {9483, 20, 10, 5}, {9485, 23, 22, 9}, {9488, 25, 12, 7}, + {9491, 19, 6, 5}, {9493, 38, 22, 3}, {9495, 23, 20, 18}, + {9496, 29, 17, 15}, {9498, 41, 17, 10}, {9499, 29, 20, 10}, + {9501, 29, 26, 4}, {9504, 19, 15, 6}, {9505, 15, 10, 1}, + {9506, 12, 7, 5}, {9507, 29, 28, 14}, {9509, 13, 9, 2}, + {9512, 39, 17, 16}, {9514, 28, 21, 9}, {9515, 18, 9, 2}, + {9517, 32, 18, 11}, {9520, 13, 5, 2}, {9523, 8, 4, 2}, + {9525, 30, 27, 2}, {9526, 16, 10, 1}, {9528, 37, 33, 22}, + {9531, 32, 14, 2}, {9533, 36, 31, 5}, {9536, 31, 26, 6}, + {9538, 24, 9, 3}, {9539, 38, 27, 13}, {9541, 31, 21, 14}, + {9544, 43, 32, 9}, {9547, 12, 8, 2}, {9549, 37, 34, 32}, + {9550, 19, 15, 11}, {9552, 11, 4, 1}, {9554, 29, 28, 15}, + {9555, 24, 22, 10}, {9556, 21, 9, 1}, {9557, 27, 20, 1}, + {9560, 27, 13, 2}, {9563, 25, 9, 2}, {9565, 6, 5, 4}, + {9568, 49, 26, 14}, {9571, 24, 16, 5}, {9572, 31, 19, 9}, + {9573, 8, 6, 5}, {9574, 38, 37, 8}, {9576, 29, 25, 7}, + {9579, 34, 33, 6}, {9581, 12, 7, 4}, {9584, 36, 29, 27}, + {9587, 36, 29, 22}, {9589, 28, 22, 15}, {9592, 15, 8, 1}, + {9595, 28, 18, 15}, {9596, 18, 11, 5}, {9597, 28, 25, 22}, + {9600, 19, 6, 4}, {9602, 21, 5, 2}, {9603, 19, 10, 4}, + {9604, 13, 11, 9}, {9605, 37, 26, 12}, {9606, 15, 12, 1}, + {9608, 14, 13, 1}, {9611, 14, 6, 5}, {9613, 32, 16, 3}, + {9616, 25, 8, 2}, {9618, 16, 3, 1}, {9619, 29, 14, 10}, + {9621, 29, 20, 11}, {9624, 31, 17, 7}, {9626, 7, 6, 1}, + {9627, 25, 19, 18}, {9629, 16, 15, 10}, {9632, 30, 23, 5}, + {9635, 26, 21, 10}, {9637, 21, 18, 6}, {9638, 21, 19, 13}, + {9640, 33, 7, 3}, {9643, 18, 14, 11}, {9645, 9, 7, 6}, + {9646, 31, 30, 17}, {9648, 31, 24, 21}, {9650, 32, 18, 11}, + {9651, 22, 14, 4}, {9653, 22, 15, 2}, {9656, 19, 16, 2}, + {9659, 15, 14, 8}, {9661, 22, 14, 6}, {9662, 22, 9, 8}, + {9664, 35, 21, 1}, {9667, 34, 22, 6}, {9669, 29, 27, 24}, + {9670, 35, 34, 3}, {9672, 17, 9, 3}, {9675, 44, 25, 23}, + {9677, 30, 27, 12}, {9680, 25, 6, 2}, {9683, 46, 37, 21}, + {9685, 17, 14, 4}, {9688, 20, 9, 2}, {9691, 17, 14, 1}, + {9693, 10, 6, 3}, {9694, 50, 18, 17}, {9696, 36, 27, 21}, + {9698, 38, 27, 24}, {9699, 30, 6, 1}, {9701, 23, 12, 3}, + {9703, 13, 7, 1}, {9704, 7, 3, 2}, {9706, 22, 15, 11}, + {9707, 26, 15, 1}, {9709, 16, 13, 10}, {9710, 30, 15, 9}, + {9712, 27, 19, 17}, {9715, 27, 10, 6}, {9717, 9, 6, 2}, + {9718, 46, 29, 11}, {9720, 37, 4, 2}, {9722, 12, 11, 8}, + {9723, 32, 29, 25}, {9724, 30, 28, 15}, {9725, 14, 8, 5}, + {9726, 29, 28, 23}, {9728, 30, 5, 2}, {9731, 16, 12, 10}, + {9733, 22, 21, 8}, {9736, 15, 7, 6}, {9739, 15, 14, 2}, + {9741, 11, 8, 1}, {9742, 30, 18, 15}, {9744, 36, 9, 2}, + {9747, 26, 8, 1}, {9749, 20, 7, 6}, {9752, 42, 17, 3}, + {9755, 6, 5, 1}, {9757, 22, 14, 6}, {9760, 56, 49, 47}, + {9763, 30, 18, 1}, {9764, 25, 13, 9}, {9765, 28, 17, 11}, + {9768, 41, 23, 22}, {9771, 29, 8, 1}, {9773, 32, 10, 6}, + {9776, 24, 19, 1}, {9778, 24, 18, 15}, {9779, 40, 21, 20}, + {9781, 40, 28, 15}, {9784, 38, 37, 9}, {9787, 20, 13, 9}, + {9789, 17, 8, 2}, {9792, 27, 26, 21}, {9794, 24, 15, 6}, + {9795, 26, 5, 4}, {9797, 35, 32, 2}, {9800, 42, 41, 10}, + {9802, 12, 10, 3}, {9803, 18, 10, 2}, {9805, 22, 21, 18}, + {9806, 30, 9, 8}, {9808, 43, 32, 21}, {9809, 19, 15, 10}, + {9811, 41, 28, 27}, {9812, 31, 30, 22}, {9813, 26, 17, 12}, + {9815, 27, 26, 8}, {9816, 46, 33, 22}, {9818, 30, 19, 10}, + {9819, 18, 4, 3}, {9821, 34, 23, 18}, {9824, 13, 10, 3}, + {9826, 22, 10, 7}, {9827, 13, 12, 5}, {9829, 4, 3, 1}, + {9832, 39, 37, 25}, {9834, 32, 25, 7}, {9835, 32, 29, 1}, + {9836, 18, 13, 10}, {9837, 35, 16, 2}, {9838, 25, 19, 12}, + {9840, 49, 47, 13}, {9842, 35, 28, 24}, {9843, 18, 12, 2}, + {9845, 38, 18, 11}, {9848, 25, 23, 10}, {9850, 19, 16, 4}, + {9851, 11, 6, 5}, {9853, 18, 11, 10}, {9856, 36, 15, 1}, + {9859, 34, 28, 1}, {9861, 33, 18, 16}, {9862, 13, 10, 3}, + {9864, 35, 32, 21}, {9866, 34, 27, 14}, {9867, 26, 8, 2}, + {9869, 23, 8, 6}, {9872, 13, 11, 3}, {9875, 19, 18, 2}, + {9877, 19, 16, 15}, {9880, 35, 28, 5}, {9881, 27, 7, 5}, + {9883, 35, 34, 11}, {9885, 38, 15, 3}, {9888, 33, 6, 4}, + {9891, 46, 38, 7}, {9892, 31, 4, 1}, {9893, 32, 28, 18}, + {9894, 27, 7, 1}, {9896, 39, 38, 26}, {9898, 23, 13, 5}, + {9899, 34, 21, 13}, {9901, 10, 4, 3}, {9902, 27, 19, 10}, + {9904, 21, 10, 2}, {9907, 10, 7, 1}, {9909, 11, 10, 7}, + {9910, 27, 16, 15}, {9912, 42, 35, 15}, {9915, 29, 17, 8}, + {9917, 32, 9, 6}, {9920, 49, 18, 14}, {9923, 37, 33, 26}, + {9924, 30, 29, 26}, {9925, 12, 9, 7}, {9928, 39, 38, 31}, + {9931, 34, 10, 3}, {9933, 23, 6, 2}, {9934, 34, 7, 3}, + {9936, 22, 21, 1}, {9938, 25, 19, 9}, {9939, 32, 26, 17}, + {9941, 29, 12, 10}, {9944, 15, 14, 6}, {9947, 23, 17, 8}, + {9949, 32, 24, 10}, {9952, 31, 30, 11}, {9955, 9, 8, 5}, + {9957, 25, 11, 4}, {9958, 17, 14, 4}, {9960, 30, 15, 10}, + {9962, 20, 14, 3}, {9963, 34, 29, 20}, {9965, 34, 24, 23}, + {9968, 36, 3, 2}, {9971, 11, 8, 5}, {9973, 27, 24, 12}, + {9976, 21, 19, 5}, {9979, 26, 10, 2}, {9981, 30, 27, 22}, + {9984, 27, 10, 7}, {9987, 14, 11, 10}, {9989, 21, 20, 6}, + {9992, 7, 4, 2}, {9994, 29, 22, 3}, {9995, 41, 40, 31}, + {9997, 26, 10, 6}, {10000, 19, 13, 9}}; + +// ANSI range [160, 2000] +/** + * ANSI X9.62 irreducible pentanomials + * + * Accredited Standards Committee X9: + * Harold Deal, Chairman + * Alice Droogan, Vice Chairman + * Cynthia Fuller, Secretariat + * The X9F subcommittee on Data and Information Security: + * Glenda Barnes, Chairman + * The X9F1 working group: + * M. Blake Greenlee, Chairman + */ static polynomial_t ansi_pentanomials[] = { {160, 1, 2, 117}, {163, 1, 2, 8}, {164, 1, 2, 49}, {165, 1, 2, 25}, {168, 1, 2, 65}, {171, 1, 3, 42}, @@ -501,24 +2712,31 @@ int compare_poly(const void *a, const void *b) { return (one->m - other->m); } -bool poly_exists(long m) { return m >= 160 && m <= 2000; } +bool poly_exists(long m) { return m >= 2 && m <= 10000; } polynomial_t *poly_find(long m) { if (!poly_exists(m)) { return NULL; } + polynomial_t *search_tri = ansi_trinomials; + polynomial_t *search_penta = ansi_trinomials; + size_t len_tri = sizeof(ansi_trinomials) / sizeof(polynomial_t); + size_t len_penta = sizeof(ansi_pentanomials) / sizeof(polynomial_t); + if (m < 160 || m > 2000) { + search_tri = hp_trinomials; + search_penta = hp_pentanomials; + len_tri = sizeof(hp_trinomials) / sizeof(polynomial_t); + len_penta = sizeof(hp_pentanomials) / sizeof(polynomial_t); + } + polynomial_t searched = {(int)m}; - polynomial_t *tri = - (polynomial_t *)bsearch(&searched, ansi_trinomials, - sizeof(ansi_trinomials) / sizeof(polynomial_t), - sizeof(polynomial_t), &compare_poly); + polynomial_t *tri = (polynomial_t *)bsearch( + &searched, search_tri, len_tri, sizeof(polynomial_t), &compare_poly); if (tri) { return tri; } else { - return (polynomial_t *)bsearch( - &searched, ansi_pentanomials, - sizeof(ansi_pentanomials) / sizeof(polynomial_t), - sizeof(polynomial_t), &compare_poly); + return (polynomial_t *)bsearch(&searched, search_penta, len_penta, + sizeof(polynomial_t), &compare_poly); } } |