aa9bc17601
BMakefiles and other bits will follow. Requested by: Andrey Chernov Made world by: Chuck Robey
139 lines
4.2 KiB
C
139 lines
4.2 KiB
C
/* mpn_perfect_square_p(u,usize) -- Return non-zero if U is a perfect square,
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zero otherwise.
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Copyright (C) 1991, 1993, 1994, 1996 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 Library General Public License as published by
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the Free Software Foundation; either version 2 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
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License for more details.
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You should have received a copy of the GNU Library General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
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MA 02111-1307, 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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#ifndef UMUL_TIME
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#define UMUL_TIME 1
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#endif
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#ifndef UDIV_TIME
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#define UDIV_TIME UMUL_TIME
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#endif
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#if BITS_PER_MP_LIMB == 32
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#define PP 0xC0CFD797L /* 3 x 5 x 7 x 11 x 13 x ... x 29 */
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#define PP_INVERTED 0x53E5645CL
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#endif
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#if BITS_PER_MP_LIMB == 64
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#define PP 0xE221F97C30E94E1DL /* 3 x 5 x 7 x 11 x 13 x ... x 53 */
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#define PP_INVERTED 0x21CFE6CFC938B36BL
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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 unsigned char const 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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#if __STDC__
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mpn_perfect_square_p (mp_srcptr up, mp_size_t usize)
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#else
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mpn_perfect_square_p (up, usize)
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mp_srcptr up;
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mp_size_t usize;
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#endif
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{
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mp_limb_t rem;
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mp_ptr root_ptr;
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int res;
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TMP_DECL (marker);
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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[(unsigned int) up[0] % 0x100] & 1) == 0)
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return 0;
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#if defined (PP)
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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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if (UDIV_TIME > (2 * UMUL_TIME + 6))
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rem = mpn_preinv_mod_1 (up, usize, (mp_limb_t) PP, (mp_limb_t) PP_INVERTED);
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else
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rem = mpn_mod_1 (up, usize, (mp_limb_t) PP);
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/* Now decide if REM is a quadratic residue modulo the factors in PP. */
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/* If A is just a few limbs, computing the square root does not take long
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time, so things might run faster if we limit this loop according to the
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size of A. */
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#if BITS_PER_MP_LIMB == 64
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if (((0x12DD703303AED3L >> rem % 53) & 1) == 0)
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return 0;
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if (((0x4351B2753DFL >> rem % 47) & 1) == 0)
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return 0;
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if (((0x35883A3EE53L >> rem % 43) & 1) == 0)
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return 0;
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if (((0x1B382B50737L >> rem % 41) & 1) == 0)
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return 0;
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if (((0x165E211E9BL >> rem % 37) & 1) == 0)
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return 0;
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if (((0x121D47B7L >> rem % 31) & 1) == 0)
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return 0;
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#endif
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if (((0x13D122F3L >> rem % 29) & 1) == 0)
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return 0;
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if (((0x5335FL >> rem % 23) & 1) == 0)
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return 0;
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if (((0x30AF3L >> rem % 19) & 1) == 0)
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return 0;
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if (((0x1A317L >> rem % 17) & 1) == 0)
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return 0;
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if (((0x161BL >> rem % 13) & 1) == 0)
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return 0;
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if (((0x23BL >> rem % 11) & 1) == 0)
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return 0;
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if (((0x017L >> rem % 7) & 1) == 0)
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return 0;
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if (((0x13L >> rem % 5) & 1) == 0)
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return 0;
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if (((0x3L >> rem % 3) & 1) == 0)
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return 0;
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#endif
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TMP_MARK (marker);
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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) TMP_ALLOC ((usize + 1) / 2 * BYTES_PER_MP_LIMB);
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/* Iff mpn_sqrtrem returns zero, the square is perfect. */
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res = ! mpn_sqrtrem (root_ptr, NULL, up, usize);
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TMP_FREE (marker);
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return res;
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}
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