version 1.1.1.1, 2000/09/09 14:12:54 |
version 1.1.1.2, 2003/08/25 16:06:33 |
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/* mpz_kronecker_ui -- Kronecker/Jacobi symbol. */ |
/* mpz_kronecker_ui -- mpz+ulong Kronecker/Jacobi symbol. |
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/* |
Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc. |
Copyright (C) 1999, 2000 Free Software Foundation, Inc. |
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This file is part of the GNU MP Library. |
This file is part of the GNU MP Library. |
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Line 18 License for more details. |
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Line 17 License for more details. |
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You should have received a copy of the GNU Lesser General Public License |
You should have received a copy of the GNU Lesser General Public License |
along with the GNU MP Library; see the file COPYING.LIB. If not, write to |
along with the GNU MP Library; see the file COPYING.LIB. If not, write to |
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
MA 02111-1307, USA. |
MA 02111-1307, USA. */ |
*/ |
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#include "gmp.h" |
#include "gmp.h" |
#include "gmp-impl.h" |
#include "gmp-impl.h" |
#include "longlong.h" |
#include "longlong.h" |
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/* This function is expected to be often used with b an odd prime, so the |
/* This implementation depends on BITS_PER_MP_LIMB being even, so that |
code for odd b is nice and short. */ |
(a/2)^BITS_PER_MP_LIMB = 1 and so there's no need to pay attention to how |
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many low zero limbs are stripped. */ |
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#if BITS_PER_MP_LIMB % 2 != 0 |
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Error, error, unsupported BITS_PER_MP_LIMB |
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#endif |
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int |
int |
#if __STDC__ |
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mpz_kronecker_ui (mpz_srcptr a, unsigned long b) |
mpz_kronecker_ui (mpz_srcptr a, unsigned long b) |
#else |
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mpz_kronecker_ui (a, b) |
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mpz_srcptr a; |
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unsigned long b; |
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#endif |
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{ |
{ |
int twos; |
mp_srcptr a_ptr = PTR(a); |
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mp_size_t a_size; |
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mp_limb_t a_rem; |
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int result_bit1; |
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if (b & 1) |
a_size = SIZ(a); |
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if (a_size == 0) |
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return JACOBI_0U (b); |
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if (b > GMP_NUMB_MAX) |
{ |
{ |
if (b != 1) |
mp_limb_t blimbs[2]; |
return mpn_jacobi_base (mpz_fdiv_ui (a, b), b, 0); |
mpz_t bz; |
else |
ALLOC(bz) = numberof (blimbs); |
return 1; /* (a/1)=1 for any a */ |
PTR(bz) = blimbs; |
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mpz_set_ui (bz, b); |
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return mpz_kronecker (a, bz); |
} |
} |
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if (b == 0) |
if ((b & 1) != 0) |
return JACOBI_Z0 (a); |
{ |
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result_bit1 = JACOBI_ASGN_SU_BIT1 (a_size, b); |
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} |
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else |
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{ |
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mp_limb_t a_low = a_ptr[0]; |
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int twos; |
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/* (a/2)=0 if a even */ |
if (b == 0) |
if (mpz_even_p (a)) |
return JACOBI_LS0 (a_low, a_size); /* (a/0) */ |
return 0; |
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/* (a/2)=(2/a) when a odd */ |
if (! (a_low & 1)) |
count_trailing_zeros (twos, b); |
return 0; /* (even/even)=0 */ |
b >>= twos; |
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/* (a/2)=(2/a) for a odd */ |
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count_trailing_zeros (twos, b); |
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b >>= twos; |
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result_bit1 = (JACOBI_TWOS_U_BIT1 (twos, a_low) |
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^ JACOBI_ASGN_SU_BIT1 (a_size, b)); |
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} |
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if (b == 1) |
if (b == 1) |
return JACOBI_TWOS_U (twos, PTR(a)[0]); |
return JACOBI_BIT1_TO_PN (result_bit1); /* (a/1)=1 for any a */ |
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return mpn_jacobi_base (mpz_fdiv_ui (a, b), b, |
a_size = ABS(a_size); |
JACOBI_TWOS_U_BIT1(twos, PTR(a)[0])); |
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/* (a/b) = (a mod b / b) */ |
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JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, a_rem, a_ptr, a_size, b); |
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return mpn_jacobi_base (a_rem, (mp_limb_t) b, result_bit1); |
} |
} |