mirror of https://github.com/macssh/macssh.git
116 lines
3.3 KiB
C
116 lines
3.3 KiB
C
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/* mpz_ui_kronecker -- Kronecker/Jacobi symbol. */
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/*
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Copyright (C) 1999, 2000 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 Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 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 Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser 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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*/
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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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int
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#if __STDC__
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mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
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#else
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mpz_ui_kronecker (a, b)
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unsigned long a;
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mpz_srcptr b;
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#endif
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{
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int b_abs_size;
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mp_srcptr b_ptr;
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mp_limb_t b_low;
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int twos;
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int result_bit1;
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/* (a/0) */
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b_abs_size = ABSIZ (b);
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if (b_abs_size == 0)
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return JACOBI_U0 (a);
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/* (a/-1)=1 when a>=0, so the sign of b is ignored */
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b_ptr = PTR(b);
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b_low = b_ptr[0];
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/* (0/1)=1; (0/-1)=1; (0/b)=0 for b!=+/-1
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(1/b)=1, for any b */
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if (a <= 1)
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return (a == 1) | ((b_abs_size == 1) & (b_low == 1));
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if (b_low & 1)
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{
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/* (a/1) = 1 for any a */
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if (b_abs_size == 1 && b_low == 1)
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return 1;
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count_trailing_zeros (twos, a);
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a >>= twos;
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if (a == 1)
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return JACOBI_TWOS_U (twos, b_low); /* powers of (2/b) only */
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/* powers of (2/b); reciprocity to (b/a); (b/a) == (b mod a / a) */
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return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a),
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a,
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JACOBI_TWOS_U_BIT1 (twos, b_low)
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^ JACOBI_RECIP_UU_BIT1 (b_low, a));
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}
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/* b is even; (a/2)=0 if a is even */
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if ((a & 1) == 0)
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return 0;
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/* Require MP_BITS_PER_LIMB even, so (a/2)^MP_BITS_PER_LIMB = 1, and so we
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don't have to pay attention to how many trailing zero limbs are
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stripped. */
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ASSERT ((BITS_PER_MP_LIMB & 1) == 0);
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MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size);
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b_low = b_ptr[0];
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if (b_low & 1)
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/* reciprocity to (b/a); (b/a) == (b mod a / a) */
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return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a),
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a,
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JACOBI_RECIP_UU_BIT1 (b_low, a));
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count_trailing_zeros (twos, b_low);
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/* reciprocity to get (b/a) */
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if (twos == BITS_PER_MP_LIMB-1)
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{
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if (b_abs_size == 1)
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{
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/* b==0x800...00, one limb high bit only, so (a/2)^(BPML-1) */
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return JACOBI_TWOS_U (BITS_PER_MP_LIMB-1, a);
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}
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/* b_abs_size > 1 */
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result_bit1 = JACOBI_RECIP_UU_BIT1 (a, b_ptr[1] << 1);
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}
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else
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result_bit1 = JACOBI_RECIP_UU_BIT1 (a, b_low >> twos);
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/* powers of (a/2); reciprocity to (b/a); (b/a) == (b mod a / a) */
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return mpn_jacobi_base (mpn_mod_1_rshift (b_ptr, b_abs_size, twos, a),
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a,
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JACOBI_TWOS_U_BIT1 (twos, a) ^ result_bit1);
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}
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