#if GMP_LIMB_BITS == 32 && GMP_NAIL_BITS == 0 /* Non-zero bit indicates a quadratic residue mod 0x100. This test identifies 82.81% as non-squares (212/256). */ static const mp_limb_t sq_res_0x100[8] = { CNST_LIMB(0x2030213), CNST_LIMB(0x2020212), CNST_LIMB(0x2020213), CNST_LIMB(0x2020212), CNST_LIMB(0x2030212), CNST_LIMB(0x2020212), CNST_LIMB(0x2020212), CNST_LIMB(0x2020212), }; /* 2^24-1 = 3^2 * 5 * 7 * 13 * 17 ... */ #define PERFSQR_MOD_BITS 25 /* This test identifies 95.66% as non-squares. */ #define PERFSQR_MOD_TEST(up, usize) \ do { \ mp_limb_t r; \ PERFSQR_MOD_34 (r, up, usize); \ \ /* 73.33% */ \ PERFSQR_MOD_2 (r, CNST_LIMB(45), CNST_LIMB(0xfa4fa5), \ CNST_LIMB(0x920), CNST_LIMB(0x1a442481)); \ \ /* 47.06% */ \ PERFSQR_MOD_1 (r, CNST_LIMB(17), CNST_LIMB(0xf0f0f1), \ CNST_LIMB(0x1a317)); \ \ /* 46.15% */ \ PERFSQR_MOD_1 (r, CNST_LIMB(13), CNST_LIMB(0xec4ec5), \ CNST_LIMB(0x9e5)); \ \ /* 42.86% */ \ PERFSQR_MOD_1 (r, CNST_LIMB( 7), CNST_LIMB(0xdb6db7), \ CNST_LIMB(0x69)); \ } while (0) /* Grand total sq_res_0x100 and PERFSQR_MOD_TEST, 99.25% non-squares. */ /* helper for tests/mpz/t-perfsqr.c */ #define PERFSQR_DIVISORS { 256, 45, 17, 13, 7, } #elif GMP_LIMB_BITS == 64 && GMP_NAIL_BITS == 0 /* Non-zero bit indicates a quadratic residue mod 0x100. This test identifies 82.81% as non-squares (212/256). */ static const mp_limb_t sq_res_0x100[4] = { CNST_LIMB(0x202021202030213), CNST_LIMB(0x202021202020213), CNST_LIMB(0x202021202030212), CNST_LIMB(0x202021202020212), }; /* 2^48-1 = 3^2 * 5 * 7 * 13 * 17 * 97 ... */ #define PERFSQR_MOD_BITS 49 /* This test identifies 97.81% as non-squares. */ #define PERFSQR_MOD_TEST(up, usize) \ do { \ mp_limb_t r; \ PERFSQR_MOD_34 (r, up, usize); \ \ /* 69.23% */ \ PERFSQR_MOD_2 (r, CNST_LIMB(91), CNST_LIMB(0xfd2fd2fd2fd3), \ CNST_LIMB(0x2191240), CNST_LIMB(0x8850a206953820e1)); \ \ /* 68.24% */ \ PERFSQR_MOD_2 (r, CNST_LIMB(85), CNST_LIMB(0xfcfcfcfcfcfd), \ CNST_LIMB(0x82158), CNST_LIMB(0x10b48c4b4206a105)); \ \ /* 55.56% */ \ PERFSQR_MOD_1 (r, CNST_LIMB( 9), CNST_LIMB(0xe38e38e38e39), \ CNST_LIMB(0x93)); \ \ /* 49.48% */ \ PERFSQR_MOD_2 (r, CNST_LIMB(97), CNST_LIMB(0xfd5c5f02a3a1), \ CNST_LIMB(0x1eb628b47), CNST_LIMB(0x6067981b8b451b5f)); \ } while (0) /* Grand total sq_res_0x100 and PERFSQR_MOD_TEST, 99.62% non-squares. */ /* helper for tests/mpz/t-perfsqr.c */ #define PERFSQR_DIVISORS { 256, 91, 85, 9, 97, } #else #error no data available for this limb size in perfsqr.h #endif