version 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_si -- Kronecker/Jacobi symbol. */ |
/* mpz_kronecker_si -- mpz+long 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 odd, so there's a test |
/* This implementation depends on BITS_PER_MP_LIMB being even, so that |
for this before invoking count_trailing_zeros(). |
(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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After the absolute value of b is established it's treated as an unsigned |
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/* After the absolute value of b is established it's treated as an unsigned |
long, because 0x80..00 doesn't fit in a signed long. */ |
long, because 0x80..00 doesn't fit in a signed long. */ |
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int |
int |
#if __STDC__ |
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mpz_kronecker_si (mpz_srcptr a, long b) |
mpz_kronecker_si (mpz_srcptr a, long b) |
#else |
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mpz_kronecker_si (a, b) |
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mpz_srcptr a; |
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long b; |
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#endif |
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{ |
{ |
int result_bit1; |
mp_srcptr a_ptr = PTR(a); |
int twos; |
mp_size_t a_size; |
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mp_limb_t a_rem, b_limb; |
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int result_bit1; |
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if (b == 0) |
a_size = SIZ(a); |
return JACOBI_Z0 (a); |
if (a_size == 0) |
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return JACOBI_0S (b); |
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result_bit1 = JACOBI_BSGN_ZS_BIT1(a, b); |
#if GMP_NUMB_BITS < BITS_PER_ULONG |
b = ABS (b); |
if (b > GMP_NUMB_MAX || b < -GMP_NUMB_MAX) |
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{ |
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mp_limb_t blimbs[2]; |
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mpz_t bz; |
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ALLOC(bz) = numberof (blimbs); |
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PTR(bz) = blimbs; |
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mpz_set_si (bz, b); |
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return mpz_kronecker (a, bz); |
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} |
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#endif |
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if (b == 1) |
result_bit1 = JACOBI_BSGN_SS_BIT1 (a_size, b); |
return JACOBI_BIT1_TO_PN (result_bit1); /* (a/1) = 1 for any a */ |
b_limb = (unsigned long) ABS (b); |
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if (b & 1) |
if ((b_limb & 1) == 0) |
return mpn_jacobi_base (mpz_fdiv_ui (a, b), b, result_bit1); |
{ |
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mp_limb_t a_low = a_ptr[0]; |
/* result 0 if both a,b even */ |
int twos; |
if (mpz_even_p (a)) |
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return 0; |
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/* (a/2)=(2/a) when a odd */ |
if (b_limb == 0) |
count_trailing_zeros (twos, b); |
return JACOBI_LS0 (a_low, a_size); /* (a/0) */ |
result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(a)[0]); |
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b = ((unsigned long) b) >> twos; |
if (! (a_low & 1)) |
if (b == 1) |
return 0; /* (even/even)=0 */ |
return JACOBI_BIT1_TO_PN (result_bit1); |
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else |
/* (a/2)=(2/a) for a odd */ |
return mpn_jacobi_base (mpz_fdiv_ui (a, b), b, result_bit1); |
count_trailing_zeros (twos, b_limb); |
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b_limb >>= twos; |
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result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, a_low); |
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} |
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if (b_limb == 1) |
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return JACOBI_BIT1_TO_PN (result_bit1); /* (a/1)=1 for any a */ |
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result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a_size, b_limb); |
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a_size = ABS(a_size); |
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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_limb); |
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return mpn_jacobi_base (a_rem, b_limb, result_bit1); |
} |
} |
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