Learn how easy it is to sync an existing GitHub or Google Code repo to a SourceForge project! See Demo

Close

[08b5c0]: src / gmp / mpz / kronuz.c Maximize Restore History

Download this file

kronuz.c    122 lines (101 with data), 3.6 kB

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
/* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol.
Copyright 1999, 2000, 2001, 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 the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
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 Lesser General Public
License for more details.
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
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include "gmp.h"
#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);
}