1 /* mpn_perfect_square_p(u,usize) -- Return non-zero if U is a perfect square,
4 Copyright (C) 1991, 1993, 1994, 1996, 1997, 2000 Free Software Foundation,
7 This file is part of the GNU MP Library.
9 The GNU MP Library is free software; you can redistribute it and/or modify
10 it under the terms of the GNU Lesser General Public License as published by
11 the Free Software Foundation; either version 2.1 of the License, or (at your
12 option) any later version.
14 The GNU MP Library is distributed in the hope that it will be useful, but
15 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
16 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
17 License for more details.
19 You should have received a copy of the GNU Lesser General Public License
20 along with the GNU MP Library; see the file COPYING.LIB. If not, write to
21 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 MA 02111-1307, USA. */
24 #include <stdio.h> /* for NULL */
30 /* sq_res_0x100[x mod 0x100] == 1 iff x mod 0x100 is a quadratic residue
32 static unsigned char const sq_res_0x100[0x100] =
34 1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
35 0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
36 1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
37 0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
38 0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
39 0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
40 0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
41 0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
46 mpn_perfect_square_p (mp_srcptr up, mp_size_t usize)
48 mpn_perfect_square_p (up, usize)
58 /* The first test excludes 55/64 (85.9%) of the perfect square candidates
60 if ((sq_res_0x100[(unsigned int) up[0] % 0x100] & 1) == 0)
64 /* The second test excludes 30652543/30808063 (99.5%) of the remaining
65 perfect square candidates in O(n) time. */
67 /* Firstly, compute REM = A mod PP. */
68 if (UDIV_TIME > (2 * UMUL_TIME + 6))
69 rem = mpn_preinv_mod_1 (up, usize, (mp_limb_t) PP, (mp_limb_t) PP_INVERTED);
71 rem = mpn_mod_1 (up, usize, (mp_limb_t) PP);
73 /* Now decide if REM is a quadratic residue modulo the factors in PP. */
75 /* If A is just a few limbs, computing the square root does not take long
76 time, so things might run faster if we limit this loop according to the
79 #if BITS_PER_MP_LIMB == 64
80 if (((CNST_LIMB(0x12DD703303AED3) >> rem % 53) & 1) == 0)
82 if (((CNST_LIMB(0x4351B2753DF) >> rem % 47) & 1) == 0)
84 if (((CNST_LIMB(0x35883A3EE53) >> rem % 43) & 1) == 0)
86 if (((CNST_LIMB(0x1B382B50737) >> rem % 41) & 1) == 0)
88 if (((CNST_LIMB(0x165E211E9B) >> rem % 37) & 1) == 0)
90 if (((CNST_LIMB(0x121D47B7) >> rem % 31) & 1) == 0)
93 if (((0x13D122F3L >> rem % 29) & 1) == 0)
95 if (((0x5335FL >> rem % 23) & 1) == 0)
97 if (((0x30AF3L >> rem % 19) & 1) == 0)
99 if (((0x1A317L >> rem % 17) & 1) == 0)
101 if (((0x161BL >> rem % 13) & 1) == 0)
103 if (((0x23BL >> rem % 11) & 1) == 0)
105 if (((0x017L >> rem % 7) & 1) == 0)
107 if (((0x13L >> rem % 5) & 1) == 0)
109 if (((0x3L >> rem % 3) & 1) == 0)
115 /* For the third and last test, we finally compute the square root,
116 to make sure we've really got a perfect square. */
117 root_ptr = (mp_ptr) TMP_ALLOC ((usize + 1) / 2 * BYTES_PER_MP_LIMB);
119 /* Iff mpn_sqrtrem returns zero, the square is perfect. */
120 res = ! mpn_sqrtrem (root_ptr, NULL, up, usize);