1 /* mpn_perfect_square_p(u,usize) -- Return non-zero if U is a perfect square,
4 Copyright (C) 1991, 1993, 1994, 1996 Free Software Foundation, Inc.
6 This file is part of the GNU MP Library.
8 The GNU MP Library is free software; you can redistribute it and/or modify
9 it under the terms of the GNU Library General Public License as published by
10 the Free Software Foundation; either version 2 of the License, or (at your
11 option) any later version.
13 The GNU MP Library is distributed in the hope that it will be useful, but
14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
16 License for more details.
18 You should have received a copy of the GNU Library General Public License
19 along with the GNU MP Library; see the file COPYING.LIB. If not, write to
20 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
21 MA 02111-1307, USA. */
32 #define UDIV_TIME UMUL_TIME
35 #if BITS_PER_MP_LIMB == 32
36 #define PP 0xC0CFD797L /* 3 x 5 x 7 x 11 x 13 x ... x 29 */
37 #define PP_INVERTED 0x53E5645CL
40 #if BITS_PER_MP_LIMB == 64
41 #define PP 0xE221F97C30E94E1DL /* 3 x 5 x 7 x 11 x 13 x ... x 53 */
42 #define PP_INVERTED 0x21CFE6CFC938B36BL
45 /* sq_res_0x100[x mod 0x100] == 1 iff x mod 0x100 is a quadratic residue
47 static unsigned char const sq_res_0x100[0x100] =
49 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,
50 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,
51 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,
52 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,
53 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,
54 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,
55 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,
56 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,
61 mpn_perfect_square_p (mp_srcptr up, mp_size_t usize)
63 mpn_perfect_square_p (up, usize)
73 /* The first test excludes 55/64 (85.9%) of the perfect square candidates
75 if ((sq_res_0x100[(unsigned int) up[0] % 0x100] & 1) == 0)
79 /* The second test excludes 30652543/30808063 (99.5%) of the remaining
80 perfect square candidates in O(n) time. */
82 /* Firstly, compute REM = A mod PP. */
83 if (UDIV_TIME > (2 * UMUL_TIME + 6))
84 rem = mpn_preinv_mod_1 (up, usize, (mp_limb_t) PP, (mp_limb_t) PP_INVERTED);
86 rem = mpn_mod_1 (up, usize, (mp_limb_t) PP);
88 /* Now decide if REM is a quadratic residue modulo the factors in PP. */
90 /* If A is just a few limbs, computing the square root does not take long
91 time, so things might run faster if we limit this loop according to the
94 #if BITS_PER_MP_LIMB == 64
95 if (((0x12DD703303AED3L >> rem % 53) & 1) == 0)
97 if (((0x4351B2753DFL >> rem % 47) & 1) == 0)
99 if (((0x35883A3EE53L >> rem % 43) & 1) == 0)
101 if (((0x1B382B50737L >> rem % 41) & 1) == 0)
103 if (((0x165E211E9BL >> rem % 37) & 1) == 0)
105 if (((0x121D47B7L >> rem % 31) & 1) == 0)
108 if (((0x13D122F3L >> rem % 29) & 1) == 0)
110 if (((0x5335FL >> rem % 23) & 1) == 0)
112 if (((0x30AF3L >> rem % 19) & 1) == 0)
114 if (((0x1A317L >> rem % 17) & 1) == 0)
116 if (((0x161BL >> rem % 13) & 1) == 0)
118 if (((0x23BL >> rem % 11) & 1) == 0)
120 if (((0x017L >> rem % 7) & 1) == 0)
122 if (((0x13L >> rem % 5) & 1) == 0)
124 if (((0x3L >> rem % 3) & 1) == 0)
130 /* For the third and last test, we finally compute the square root,
131 to make sure we've really got a perfect square. */
132 root_ptr = (mp_ptr) TMP_ALLOC ((usize + 1) / 2 * BYTES_PER_MP_LIMB);
134 /* Iff mpn_sqrtrem returns zero, the square is perfect. */
135 res = ! mpn_sqrtrem (root_ptr, NULL, up, usize);