1  /* gen-jacobi.c
       2  
       3     Contributed to the GNU project by Niels Möller.
       4  
       5  Copyright 2010 Free Software Foundation, Inc.
       6  
       7  This file is part of the GNU MP Library.
       8  
       9  The GNU MP Library is free software; you can redistribute it and/or modify
      10  it 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  
      16  or
      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  
      22  or both in parallel, as here.
      23  
      24  The GNU MP Library is distributed in the hope that it will be useful, but
      25  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
      26  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
      27  for more details.
      28  
      29  You should have received copies of the GNU General Public License and the
      30  GNU Lesser General Public License along with the GNU MP Library.  If not,
      31  see 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  
      40  static 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  
      66  static unsigned
      67  encode (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  
      87  int
      88  main (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  }