119 lines
3.4 KiB
C
119 lines
3.4 KiB
C
/* mpz_perfect_square_p(arg) -- Return non-zero if ARG is a pefect square,
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zero otherwise.
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Copyright (C) 1991 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2, or (at your option)
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any later version.
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The GNU MP Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with the GNU MP Library; see the file COPYING. If not, write to
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the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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#if BITS_PER_MP_LIMB == 32
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static unsigned int primes[] = {3, 5, 7, 11, 13, 17, 19, 23, 29};
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static unsigned long int residue_map[] =
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{0x3, 0x13, 0x17, 0x23b, 0x161b, 0x1a317, 0x30af3, 0x5335f, 0x13d122f3};
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#define PP 0xC0CFD797L /* 3 x 5 x 7 x 11 x 13 x ... x 29 */
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#endif
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/* sq_res_0x100[x mod 0x100] == 1 iff x mod 0x100 is a quadratic residue
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modulo 0x100. */
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static char sq_res_0x100[0x100] =
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{
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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};
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int
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#ifdef __STDC__
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mpz_perfect_square_p (const MP_INT *a)
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#else
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mpz_perfect_square_p (a)
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const MP_INT *a;
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#endif
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{
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mp_limb n1, n0;
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mp_size i;
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mp_size asize = a->size;
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mp_srcptr aptr = a->d;
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mp_limb rem;
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mp_ptr root_ptr;
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/* No negative numbers are perfect squares. */
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if (asize < 0)
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return 0;
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/* The first test excludes 55/64 (85.9%) of the perfect square candidates
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in O(1) time. */
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if (sq_res_0x100[aptr[0] % 0x100] == 0)
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return 0;
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#if BITS_PER_MP_LIMB == 32
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/* The second test excludes 30652543/30808063 (99.5%) of the remaining
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perfect square candidates in O(n) time. */
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/* Firstly, compute REM = A mod PP. */
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n1 = aptr[asize - 1];
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if (n1 >= PP)
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{
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n1 = 0;
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i = asize - 1;
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}
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else
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i = asize - 2;
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for (; i >= 0; i--)
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{
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mp_limb dummy;
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n0 = aptr[i];
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udiv_qrnnd (dummy, n1, n1, n0, PP);
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}
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rem = n1;
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/* We have A mod PP in REM. Now decide if REM is a quadratic residue
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modulo the factors in PP. */
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for (i = 0; i < (sizeof primes) / sizeof (int); i++)
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{
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unsigned int p;
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p = primes[i];
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rem %= p;
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if ((residue_map[i] & (1L << rem)) == 0)
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return 0;
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}
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#endif
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/* For the third and last test, we finally compute the square root,
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to make sure we've really got a perfect square. */
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root_ptr = (mp_ptr) alloca ((asize + 1) / 2 * BYTES_PER_MP_LIMB);
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/* Iff mpn_sqrt returns zero, the square is perfect. */
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{
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int retval = !mpn_sqrt (root_ptr, NULL, aptr, asize);
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alloca (0);
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return retval;
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}
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}
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