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/* mpn_perfect_square_p(u,usize) -- Return non-zero if U is a perfect square,
zero otherwise.
Copyright (C) 1991, 1993, 1994, 1996 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Library General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at your
option) any later version.
The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
License for more details.
You should have received a copy of the GNU Library General Public License
along with the GNU MP Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#ifndef UMUL_TIME
#define UMUL_TIME 1
#endif
#ifndef UDIV_TIME
#define UDIV_TIME UMUL_TIME
#endif
#if BITS_PER_MP_LIMB == 32
#define PP 0xC0CFD797L /* 3 x 5 x 7 x 11 x 13 x ... x 29 */
#define PP_INVERTED 0x53E5645CL
#endif
#if BITS_PER_MP_LIMB == 64
#define PP 0xE221F97C30E94E1DL /* 3 x 5 x 7 x 11 x 13 x ... x 53 */
#define PP_INVERTED 0x21CFE6CFC938B36BL
#endif
/* sq_res_0x100[x mod 0x100] == 1 iff x mod 0x100 is a quadratic residue
modulo 0x100. */
static unsigned char const sq_res_0x100[0x100] =
{
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,
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,
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,
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,
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,
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,
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,
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,
};
int
#if __STDC__
mpn_perfect_square_p (mp_srcptr up, mp_size_t usize)
#else
mpn_perfect_square_p (up, usize)
mp_srcptr up;
mp_size_t usize;
#endif
{
mp_limb_t rem;
mp_ptr root_ptr;
int res;
TMP_DECL (marker);
/* The first test excludes 55/64 (85.9%) of the perfect square candidates
in O(1) time. */
if ((sq_res_0x100[(unsigned int) up[0] % 0x100] & 1) == 0)
return 0;
#if defined (PP)
/* The second test excludes 30652543/30808063 (99.5%) of the remaining
perfect square candidates in O(n) time. */
/* Firstly, compute REM = A mod PP. */
if (UDIV_TIME > (2 * UMUL_TIME + 6))
rem = mpn_preinv_mod_1 (up, usize, (mp_limb_t) PP, (mp_limb_t) PP_INVERTED);
else
rem = mpn_mod_1 (up, usize, (mp_limb_t) PP);
/* Now decide if REM is a quadratic residue modulo the factors in PP. */
/* If A is just a few limbs, computing the square root does not take long
time, so things might run faster if we limit this loop according to the
size of A. */
#if BITS_PER_MP_LIMB == 64
if (((0x12DD703303AED3L >> rem % 53) & 1) == 0)
return 0;
if (((0x4351B2753DFL >> rem % 47) & 1) == 0)
return 0;
if (((0x35883A3EE53L >> rem % 43) & 1) == 0)
return 0;
if (((0x1B382B50737L >> rem % 41) & 1) == 0)
return 0;
if (((0x165E211E9BL >> rem % 37) & 1) == 0)
return 0;
if (((0x121D47B7L >> rem % 31) & 1) == 0)
return 0;
#endif
if (((0x13D122F3L >> rem % 29) & 1) == 0)
return 0;
if (((0x5335FL >> rem % 23) & 1) == 0)
return 0;
if (((0x30AF3L >> rem % 19) & 1) == 0)
return 0;
if (((0x1A317L >> rem % 17) & 1) == 0)
return 0;
if (((0x161BL >> rem % 13) & 1) == 0)
return 0;
if (((0x23BL >> rem % 11) & 1) == 0)
return 0;
if (((0x017L >> rem % 7) & 1) == 0)
return 0;
if (((0x13L >> rem % 5) & 1) == 0)
return 0;
if (((0x3L >> rem % 3) & 1) == 0)
return 0;
#endif
TMP_MARK (marker);
/* For the third and last test, we finally compute the square root,
to make sure we've really got a perfect square. */
root_ptr = (mp_ptr) TMP_ALLOC ((usize + 1) / 2 * BYTES_PER_MP_LIMB);
/* Iff mpn_sqrtrem returns zero, the square is perfect. */
res = ! mpn_sqrtrem (root_ptr, NULL, up, usize);
TMP_FREE (marker);
return res;
}
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