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/* mpz_perfect_square_p(arg) -- Return non-zero if ARG is a pefect square,
zero otherwise.
Copyright (C) 1991 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 General Public License as published by
the Free Software Foundation; either version 2, 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with the GNU MP Library; see the file COPYING. If not, write to
the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#if BITS_PER_MP_LIMB == 32
static unsigned int primes[] = {3, 5, 7, 11, 13, 17, 19, 23, 29};
static unsigned long int residue_map[] =
{0x3, 0x13, 0x17, 0x23b, 0x161b, 0x1a317, 0x30af3, 0x5335f, 0x13d122f3};
#define PP 0xC0CFD797L /* 3 x 5 x 7 x 11 x 13 x ... x 29 */
#endif
/* sq_res_0x100[x mod 0x100] == 1 iff x mod 0x100 is a quadratic residue
modulo 0x100. */
static char 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
#ifdef __STDC__
mpz_perfect_square_p (const MP_INT *a)
#else
mpz_perfect_square_p (a)
const MP_INT *a;
#endif
{
mp_limb n1, n0;
mp_size i;
mp_size asize = a->size;
mp_srcptr aptr = a->d;
mp_limb rem;
mp_ptr root_ptr;
/* No negative numbers are perfect squares. */
if (asize < 0)
return 0;
/* The first test excludes 55/64 (85.9%) of the perfect square candidates
in O(1) time. */
if (sq_res_0x100[aptr[0] % 0x100] == 0)
return 0;
#if BITS_PER_MP_LIMB == 32
/* The second test excludes 30652543/30808063 (99.5%) of the remaining
perfect square candidates in O(n) time. */
/* Firstly, compute REM = A mod PP. */
n1 = aptr[asize - 1];
if (n1 >= PP)
{
n1 = 0;
i = asize - 1;
}
else
i = asize - 2;
for (; i >= 0; i--)
{
mp_limb dummy;
n0 = aptr[i];
udiv_qrnnd (dummy, n1, n1, n0, PP);
}
rem = n1;
/* We have A mod PP in REM. Now decide if REM is a quadratic residue
modulo the factors in PP. */
for (i = 0; i < (sizeof primes) / sizeof (int); i++)
{
unsigned int p;
p = primes[i];
rem %= p;
if ((residue_map[i] & (1L << rem)) == 0)
return 0;
}
#endif
/* 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) alloca ((asize + 1) / 2 * BYTES_PER_MP_LIMB);
/* Iff mpn_sqrt returns zero, the square is perfect. */
{
int retval = !mpn_sqrt (root_ptr, NULL, aptr, asize);
alloca (0);
return retval;
}
}
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