mirror of
https://review.haiku-os.org/buildtools
synced 2025-01-19 04:48:37 +01:00
4c74403188
Change-Id: Iae65e95cfa0d92091b8b0a424ae36d88efa76aa9 Reviewed-on: https://review.haiku-os.org/c/buildtools/+/3020 Reviewed-by: Adrien Destugues <pulkomandy@gmail.com>
130 lines
3.3 KiB
C
130 lines
3.3 KiB
C
/* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol.
|
|
|
|
Copyright 1999-2002 Free Software Foundation, Inc.
|
|
|
|
This file is part of the GNU MP Library.
|
|
|
|
The GNU MP Library is free software; you can redistribute it and/or modify
|
|
it under the terms of either:
|
|
|
|
* the GNU Lesser General Public License as published by the Free
|
|
Software Foundation; either version 3 of the License, or (at your
|
|
option) any later version.
|
|
|
|
or
|
|
|
|
* the GNU General Public License as published by the Free Software
|
|
Foundation; either version 2 of the License, or (at your option) any
|
|
later version.
|
|
|
|
or both in parallel, as here.
|
|
|
|
The GNU MP Library is distributed in the hope that it will be useful, but
|
|
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
|
for more details.
|
|
|
|
You should have received copies of the GNU General Public License and the
|
|
GNU Lesser General Public License along with the GNU MP Library. If not,
|
|
see https://www.gnu.org/licenses/. */
|
|
|
|
#include "gmp-impl.h"
|
|
#include "longlong.h"
|
|
|
|
|
|
int
|
|
mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
|
|
{
|
|
mp_srcptr b_ptr;
|
|
mp_limb_t b_low;
|
|
int b_abs_size;
|
|
mp_limb_t b_rem;
|
|
int twos;
|
|
int result_bit1;
|
|
|
|
/* (a/-1)=1 when a>=0, so the sign of b is ignored */
|
|
b_abs_size = ABSIZ (b);
|
|
|
|
if (b_abs_size == 0)
|
|
return JACOBI_U0 (a); /* (a/0) */
|
|
|
|
if (a > GMP_NUMB_MAX)
|
|
{
|
|
mp_limb_t alimbs[2];
|
|
mpz_t az;
|
|
ALLOC(az) = numberof (alimbs);
|
|
PTR(az) = alimbs;
|
|
mpz_set_ui (az, a);
|
|
return mpz_kronecker (az, b);
|
|
}
|
|
|
|
b_ptr = PTR(b);
|
|
b_low = b_ptr[0];
|
|
result_bit1 = 0;
|
|
|
|
if (! (b_low & 1))
|
|
{
|
|
/* (0/b)=0 for b!=+/-1; and (even/even)=0 */
|
|
if (! (a & 1))
|
|
return 0;
|
|
|
|
/* a odd, b even
|
|
|
|
Establish shifted b_low with valid bit1 for the RECIP below. Zero
|
|
limbs stripped are accounted for, but zero bits on b_low are not
|
|
because they remain in {b_ptr,b_abs_size} for
|
|
JACOBI_MOD_OR_MODEXACT_1_ODD. */
|
|
|
|
JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
|
|
if (! (b_low & 1))
|
|
{
|
|
if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
|
|
{
|
|
/* need b_ptr[1] to get bit1 in b_low */
|
|
if (b_abs_size == 1)
|
|
{
|
|
/* (a/0x80...00) == (a/2)^(NUMB-1) */
|
|
if ((GMP_NUMB_BITS % 2) == 0)
|
|
{
|
|
/* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
|
|
when GMP_NUMB_BITS is even, so it's still 0. */
|
|
ASSERT (result_bit1 == 0);
|
|
result_bit1 = JACOBI_TWO_U_BIT1 (a);
|
|
}
|
|
return JACOBI_BIT1_TO_PN (result_bit1);
|
|
}
|
|
|
|
/* b_abs_size > 1 */
|
|
b_low = b_ptr[1] << 1;
|
|
}
|
|
else
|
|
{
|
|
count_trailing_zeros (twos, b_low);
|
|
b_low >>= twos;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if (a == 0) /* (0/b)=1 for b=+/-1, 0 otherwise */
|
|
return (b_abs_size == 1 && b_low == 1);
|
|
|
|
if (! (a & 1))
|
|
{
|
|
/* a even, b odd */
|
|
count_trailing_zeros (twos, a);
|
|
a >>= twos;
|
|
/* (a*2^n/b) = (a/b) * (2/a)^n */
|
|
result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
|
|
}
|
|
}
|
|
|
|
if (a == 1)
|
|
return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */
|
|
|
|
/* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */
|
|
JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a);
|
|
result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
|
|
return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
|
|
}
|