mirror of https://github.com/macssh/macssh.git
127 lines
3.6 KiB
C
Executable File
127 lines
3.6 KiB
C
Executable File
/* mpz_si_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_si_kronecker (long a, mpz_srcptr b)
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#else
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mpz_si_kronecker (a, b)
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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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b_abs_size = ABSIZ (b);
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if (b_abs_size == 0)
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return JACOBI_S0 (a); /* (a/0) */
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b_ptr = PTR(b);
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b_low = b_ptr[0];
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/* (0/b) = 1 if b=+/-1, 0 otherwise */
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if (a == 0)
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return (b_abs_size == 1) & (b_low == 1);
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/* account for the effect of the sign of b, so can then ignore it */
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result_bit1 = JACOBI_BSGN_SZ_BIT1 (a, b);
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if ((b_low & 1) == 0)
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{
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/* b even */
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if ((a & 1) == 0)
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return 0; /* (a/b)=0 if both a,b even */
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/* Require MP_BITS_PER_LIMB even, so that (a/2)^MP_BITS_PER_LIMB = 1,
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and so that therefore there's no need to account for how many zero
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limbs are 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) == 0)
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{
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/* odd a, even b */
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mp_limb_t b_shl_bit1;
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count_trailing_zeros (twos, b_low);
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/* b_shl_bit1 is b>>twos, but with only bit 1 guaranteed */
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if (twos == BITS_PER_MP_LIMB-1)
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b_shl_bit1 = (b_abs_size == 1) ? 0 : (b_ptr[1] << 1);
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else
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b_shl_bit1 = (b_low >> twos);
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result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_shl_bit1);
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a = ABS(a);
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if (a == 1)
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return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */
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/* twos (a/2), reciprocity to (b/a), and (b/a) = (b mod a / b) */
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return mpn_jacobi_base (mpn_mod_1_rshift (b_ptr, b_abs_size,
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twos, a),
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a,
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result_bit1
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^ JACOBI_TWOS_U_BIT1 (twos, a)
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^ JACOBI_RECIP_UU_BIT1 (a, b_shl_bit1));
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}
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}
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/* b odd */
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result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
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a = ABS(a);
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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 JACOBI_BIT1_TO_PN (result_bit1);
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/* Note a is cast to unsigned because 0x80..00 doesn't fit in a signed. */
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if ((a & 1) == 0)
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{
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count_trailing_zeros (twos, a);
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a = ((unsigned long) a) >> twos;
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result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
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}
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if (a == 1)
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return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */
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/* reciprocity to (b/a), and (b/a) == (b mod a / a) */
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return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a), a,
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result_bit1 ^ JACOBI_RECIP_UU_BIT1 (a, b_low));
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}
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