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_si_kronecker -- Kronecker/Jacobi symbol. */ |
/* mpz_si_kronecker -- long+mpz 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 implementation depends on BITS_PER_MP_LIMB being even, so that |
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(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_si_kronecker (long a, mpz_srcptr b) |
mpz_si_kronecker (long a, mpz_srcptr b) |
#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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{ |
{ |
int b_abs_size; |
mp_srcptr b_ptr = PTR(b); |
mp_srcptr b_ptr; |
mp_limb_t b_low = b_ptr[0]; |
mp_limb_t b_low; |
mp_size_t b_size = SIZ (b); |
int twos; |
mp_size_t b_abs_size = ABS (b_size); |
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mp_limb_t a_limb, b_rem; |
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unsigned twos; |
int result_bit1; |
int result_bit1; |
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b_abs_size = ABSIZ (b); |
#if GMP_NUMB_BITS < BITS_PER_ULONG |
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if (a > GMP_NUMB_MAX || a < -GMP_NUMB_MAX) |
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{ |
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mp_limb_t alimbs[2]; |
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mpz_t az; |
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ALLOC(az) = numberof (alimbs); |
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PTR(az) = alimbs; |
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mpz_set_si (az, a); |
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return mpz_kronecker (az, b); |
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} |
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#endif |
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if (b_abs_size == 0) |
if (b_abs_size == 0) |
return JACOBI_S0 (a); /* (a/0) */ |
return JACOBI_S0 (a); /* (a/0) */ |
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b_ptr = PTR(b); |
/* account for the effect of the sign of b, then ignore it */ |
b_low = b_ptr[0]; |
result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size); |
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/* (0/b) = 1 if b=+/-1, 0 otherwise */ |
if ((b_low & 1) != 0) |
if (a == 0) |
{ |
return (b_abs_size == 1) & (b_low == 1); |
/* b odd */ |
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/* account for the effect of the sign of b, so can then ignore it */ |
result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low); |
result_bit1 = JACOBI_BSGN_SZ_BIT1 (a, b); |
a_limb = (unsigned long) ABS(a); |
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if ((b_low & 1) == 0) |
if ((a_limb & 1) == 0) |
{ |
{ |
/* b even */ |
/* (0/b)=1 for b=+/-1, 0 otherwise */ |
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if (a_limb == 0) |
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return (b_abs_size == 1 && b_low == 1); |
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/* a even, b odd */ |
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count_trailing_zeros (twos, a_limb); |
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a_limb >>= twos; |
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/* (a*2^n/b) = (a/b) * twos(n,a) */ |
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result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low); |
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} |
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} |
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else |
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{ |
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/* (even/even)=0, and (0/b)=0 for b!=+/-1 */ |
if ((a & 1) == 0) |
if ((a & 1) == 0) |
return 0; /* (a/b)=0 if both a,b even */ |
return 0; |
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/* Require MP_BITS_PER_LIMB even, so that (a/2)^MP_BITS_PER_LIMB = 1, |
/* a odd, b even */ |
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); |
/* establish shifted b_low with valid bit1 for use with ASGN and RECIP */ |
b_low = b_ptr[0]; |
MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size, b_low); |
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if ((b_low & 1) == 0) |
if ((b_low & 1) == 0) |
{ |
{ |
/* odd a, even b */ |
if (b_low == GMP_NUMB_HIGHBIT) |
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{ |
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if (b_abs_size == 1) |
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{ |
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/* (a/0x80000000) = (a/2)^(BPML-1) */ |
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result_bit1 ^= JACOBI_TWOS_U_BIT1 (GMP_NUMB_BITS - 1, a); |
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return JACOBI_BIT1_TO_PN (result_bit1); |
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} |
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mp_limb_t b_shl_bit1; |
/* b_abs_size > 1 */ |
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b_low = b_ptr[1] << 1; |
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 |
else |
b_shl_bit1 = (b_low >> twos); |
{ |
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count_trailing_zeros (twos, b_low); |
result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_shl_bit1); |
b_low >>= twos; |
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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/* b odd */ |
result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low); |
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a_limb = (unsigned long) ABS(a); |
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) |
if (a_limb == 1) |
return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */ |
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) */ |
/* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */ |
return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a), a, |
JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a_limb); |
result_bit1 ^ JACOBI_RECIP_UU_BIT1 (a, b_low)); |
result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a_limb, b_low); |
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return mpn_jacobi_base (b_rem, a_limb, result_bit1); |
} |
} |