1/* gen-jacobi.c
2
3   Contributed to the GNU project by Niels M��ller.
4
5Copyright 2010 Free Software Foundation, Inc.
6
7This file is part of the GNU MP Library.
8
9The GNU MP Library is free software; you can redistribute it and/or modify
10it under the terms of either:
11
12  * the GNU Lesser General Public License as published by the Free
13    Software Foundation; either version 3 of the License, or (at your
14    option) any later version.
15
16or
17
18  * the GNU General Public License as published by the Free Software
19    Foundation; either version 2 of the License, or (at your option) any
20    later version.
21
22or both in parallel, as here.
23
24The GNU MP Library is distributed in the hope that it will be useful, but
25WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
26or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
27for more details.
28
29You should have received copies of the GNU General Public License and the
30GNU Lesser General Public License along with the GNU MP Library.  If not,
31see https://www.gnu.org/licenses/.  */
32
33/* Generate the lookup table needed for fast left-to-right computation
34   of the Jacobi symbol. */
35
36#include <assert.h>
37#include <stdio.h>
38#include <stdlib.h>
39
40static const struct
41{
42  unsigned char a;
43  unsigned char b;
44} decode_table[13] = {
45  /*  0 */ { 0, 1 },
46  /*  1 */ { 0, 3 },
47  /*  2 */ { 1, 1 },
48  /*  3 */ { 1, 3 },
49  /*  4 */ { 2, 1 },
50  /*  5 */ { 2, 3 },
51  /*  6 */ { 3, 1 },
52  /*  7 */ { 3, 3 }, /* d = 1 */
53  /*  8 */ { 1, 0 },
54  /*  9 */ { 1, 2 },
55  /* 10 */ { 3, 0 },
56  /* 11 */ { 3, 2 },
57  /* 12 */ { 3, 3 }, /* d = 0 */
58
59};
60#define JACOBI_A(bits) (decode_table[(bits)>>1].a)
61#define JACOBI_B(bits) (decode_table[(bits)>>1].b)
62
63#define JACOBI_E(bits) ((bits) & 1)
64#define JACOBI_D(bits) (((bits)>>1) == 7) /* Gives 0 for don't care states. */
65
66static unsigned
67encode (unsigned a, unsigned b, unsigned d)
68{
69  unsigned i;
70
71  assert (d < 2);
72  assert (a < 4);
73  assert (b < 4);
74  assert ( (a | b ) & 1);
75
76  if (a == 3 && b == 3)
77    return d ? 7 : 12;
78
79  for (i = 0; i < 12; i++)
80    if (decode_table[i].a == a
81	&& decode_table[i].b == b)
82      return i;
83
84  abort ();
85}
86
87int
88main (int argc, char **argv)
89{
90  unsigned bits;
91
92  for (bits = 0; bits < 208; bits++)
93    {
94      unsigned e, a, b, d_old, d, q;
95
96      if (bits && !(bits & 0xf))
97	printf("\n");
98
99      q = bits & 3;
100      d = (bits >> 2) & 1;
101
102      e = JACOBI_E (bits >> 3);
103      a = JACOBI_A (bits >> 3);
104      b = JACOBI_B (bits >> 3);
105      d_old = JACOBI_D (bits >> 3);
106
107      if (d != d_old && a == 3 && b == 3)
108	e ^= 1;
109
110      if (d == 1)
111	{
112	  if (b == 2)
113	    e ^= (q & (a >> 1)) ^ (q >> 1);
114	  a = (a - q * b) & 3;
115	}
116      else
117	{
118	  if (a == 2)
119	    e ^= (q & (b >> 1)) ^ (q >> 1);
120	  b = (b - q * a) & 3;
121	}
122
123      printf("%2d,", (encode (a, b, d) << 1) | e);
124    }
125  printf("\n");
126
127  return 0;
128}
129