matrix.c

Reed-Solomoon 纠错算法C语言的实现

// ==========================================================================
// CVS Version Control:       $RCSfile$ 
//                            $Revision$ 
//                            $Date$
// ==========================================================================
//
//     This confidential and proprietary source code may be used only as
//     authorized by a licensing agreement from SEIKO EPSON CORPORATION.
//
//                (C) COPYRIGHT 2003 SEIKO EPSON CORPORATION.
//            (C) COPYRIGHT 2003 SHANGHAI EPSON ELECTRONIC CO.,LTD.
//                          ALL RIGHTS RESERVED
//
//     The entire notice above must be reproduced on all authorized copies
//     and any such reproduction must be pursuant to a licensing agreement
//     from SEIKO EPSON CORPORATION.
//
// File     : correct.c
// Author   : Handsome Huang
// Abstract : Verification of the Reed-Solomon ECC.
// 
// Modification History:
// Date        By               Change Description
// --------------------------------------------------------------------------
// 2007/06/17  Handsome.Huang   First design.
//
// ==========================================================================

unsigned int DetMA4(unsigned int *Syndrome);
unsigned int DetMB40(unsigned int *Syndrome);
unsigned int DetMB41(unsigned int *Syndrome);
unsigned int DetMB42(unsigned int *Syndrome);
unsigned int DetMB43(unsigned int *Syndrome);

unsigned int DetMA30(unsigned int *Syndrome);
unsigned int DetMB300(unsigned int *Syndrome); 
unsigned int DetMB301(unsigned int *Syndrome); 
unsigned int DetMB302(unsigned int *Syndrome); 

unsigned int DetMA31(unsigned int *Syndrome);
unsigned int DetMB310(unsigned int *Syndrome); 
unsigned int DetMB311(unsigned int *Syndrome); 
unsigned int DetMB312(unsigned int *Syndrome); 

unsigned int DetMA32(unsigned int *Syndrome);
unsigned int DetMB320(unsigned int *Syndrome); 
unsigned int DetMB321(unsigned int *Syndrome); 
unsigned int DetMB322(unsigned int *Syndrome); 

unsigned int DetMA33(unsigned int *Syndrome);

unsigned int DetMA20(unsigned int *Syndrome);
unsigned int DetMB200(unsigned int *Syndrome);
unsigned int DetMB201(unsigned int *Syndrome);

unsigned int DetMA21(unsigned int *Syndrome);
unsigned int DetMB210(unsigned int *Syndrome);
unsigned int DetMB211(unsigned int *Syndrome);

unsigned int DetMA22(unsigned int *Syndrome);
unsigned int DetMB220(unsigned int *Syndrome);
unsigned int DetMB221(unsigned int *Syndrome);

unsigned int DetMA23(unsigned int *Syndrome);
unsigned int DetMB230(unsigned int *Syndrome);
unsigned int DetMB231(unsigned int *Syndrome);

unsigned int DetMA24(unsigned int *Syndrome);
unsigned int DetMA25(unsigned int *Syndrome);

unsigned int DetMA4(unsigned int *Syndrome)
{
  unsigned int mul[10];
  unsigned int add[2];

  mul[0] = gmult4(*(Syndrome+0), *(Syndrome+2), *(Syndrome+4), *(Syndrome+6));
  mul[1] = gmult4(*(Syndrome+0), *(Syndrome+2), *(Syndrome+5), *(Syndrome+5));
  mul[2] = gmult4(*(Syndrome+0), *(Syndrome+3), *(Syndrome+3), *(Syndrome+6));
  mul[3] = gmult4(*(Syndrome+0), *(Syndrome+4), *(Syndrome+4), *(Syndrome+4));
  mul[4] = gmult4(*(Syndrome+1), *(Syndrome+1), *(Syndrome+4), *(Syndrome+6));
  mul[5] = gmult4(*(Syndrome+1), *(Syndrome+1), *(Syndrome+5), *(Syndrome+5));
  mul[6] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+4), *(Syndrome+4));
  mul[7] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+2), *(Syndrome+6));
  mul[8] = gmult4(*(Syndrome+2), *(Syndrome+3), *(Syndrome+3), *(Syndrome+4));
  mul[9] = gmult4(*(Syndrome+3), *(Syndrome+3), *(Syndrome+3), *(Syndrome+3));

  add[0] = gadd6(mul[0], mul[1], mul[2], mul[3], mul[4], mul[5]);
  add[1] = gadd4(mul[6], mul[7], mul[8], mul[9]);

  return (gadd(add[0], add[1]));
}

unsigned int DetMB40(unsigned int *Syndrome)
{
  unsigned int mul[10];
  unsigned int add[2];

  mul[0] = gmult4(*(Syndrome+1), *(Syndrome+3), *(Syndrome+5), *(Syndrome+7));
  mul[1] = gmult4(*(Syndrome+1), *(Syndrome+5), *(Syndrome+5), *(Syndrome+5));
  mul[2] = gmult4(*(Syndrome+1), *(Syndrome+3), *(Syndrome+6), *(Syndrome+6));
  mul[3] = gmult4(*(Syndrome+1), *(Syndrome+4), *(Syndrome+4), *(Syndrome+7));
  mul[4] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+5), *(Syndrome+7));
  mul[5] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+6), *(Syndrome+6));
  mul[6] = gmult4(*(Syndrome+3), *(Syndrome+3), *(Syndrome+5), *(Syndrome+5));
  mul[7] = gmult4(*(Syndrome+3), *(Syndrome+4), *(Syndrome+4), *(Syndrome+5));
  mul[8] = gmult4(*(Syndrome+3), *(Syndrome+3), *(Syndrome+3), *(Syndrome+7));
  mul[9] = gmult4(*(Syndrome+4), *(Syndrome+4), *(Syndrome+4), *(Syndrome+4));

  add[0] = gadd6(mul[0], mul[1], mul[2], mul[3], mul[4], mul[5]);
  add[1] = gadd4(mul[6], mul[7], mul[8], mul[9]);

  return (gadd(add[0], add[1]));
}

unsigned int DetMB41(unsigned int *Syndrome)
{
  unsigned int mul[16];
  unsigned int add[4];

  mul[0]  = gmult4(*(Syndrome+0), *(Syndrome+3), *(Syndrome+5), *(Syndrome+7));
  mul[1]  = gmult4(*(Syndrome+0), *(Syndrome+5), *(Syndrome+5), *(Syndrome+5));
  mul[2]  = gmult4(*(Syndrome+0), *(Syndrome+3), *(Syndrome+6), *(Syndrome+6));
  mul[3]  = gmult4(*(Syndrome+0), *(Syndrome+4), *(Syndrome+4), *(Syndrome+7));

  mul[4]  = gmult4(*(Syndrome+1), *(Syndrome+4), *(Syndrome+4), *(Syndrome+6));
  mul[5]  = gmult4(*(Syndrome+1), *(Syndrome+4), *(Syndrome+5), *(Syndrome+5));
  mul[6]  = gmult4(*(Syndrome+1), *(Syndrome+2), *(Syndrome+6), *(Syndrome+6));
  mul[7]  = gmult4(*(Syndrome+1), *(Syndrome+2), *(Syndrome+5), *(Syndrome+7));
  mul[8]  = gmult4(*(Syndrome+1), *(Syndrome+3), *(Syndrome+5), *(Syndrome+6));
  mul[9]  = gmult4(*(Syndrome+1), *(Syndrome+3), *(Syndrome+4), *(Syndrome+7));

  mul[10] = gmult4(*(Syndrome+2), *(Syndrome+4), *(Syndrome+4), *(Syndrome+5));
  mul[11] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+4), *(Syndrome+7));
  mul[12] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+5), *(Syndrome+6));
  mul[13] = gmult4(*(Syndrome+2), *(Syndrome+3), *(Syndrome+3), *(Syndrome+7));

  mul[14] = gmult4(*(Syndrome+3), *(Syndrome+4), *(Syndrome+4), *(Syndrome+4));
  mul[15] = gmult4(*(Syndrome+3), *(Syndrome+3), *(Syndrome+3), *(Syndrome+6));


  add[0] = gadd4(mul[0], mul[1], mul[2], mul[3]);
  add[1] = gadd6(mul[4], mul[5], mul[6], mul[7], mul[8], mul[9]);
  add[2] = gadd4(mul[10], mul[11], mul[12], mul[13]);
  add[3] = gadd (mul[14], mul[15]);

  return (gadd4(add[0], add[1], add[2], add[3]));
}

unsigned int DetMB42(unsigned int *Syndrome)
{
  unsigned int mul[20];
  unsigned int add[4];

  mul[0]  = gmult4(*(Syndrome+0), *(Syndrome+2), *(Syndrome+6), *(Syndrome+6));
  mul[1]  = gmult4(*(Syndrome+0), *(Syndrome+4), *(Syndrome+5), *(Syndrome+5));
  mul[2]  = gmult4(*(Syndrome+0), *(Syndrome+3), *(Syndrome+4), *(Syndrome+7));
  mul[3]  = gmult4(*(Syndrome+0), *(Syndrome+2), *(Syndrome+5), *(Syndrome+7));
  mul[4]  = gmult4(*(Syndrome+0), *(Syndrome+3), *(Syndrome+5), *(Syndrome+6));
  mul[5]  = gmult4(*(Syndrome+0), *(Syndrome+4), *(Syndrome+4), *(Syndrome+6));

  mul[6]  = gmult4(*(Syndrome+1), *(Syndrome+1), *(Syndrome+6), *(Syndrome+6));
  mul[7]  = gmult4(*(Syndrome+1), *(Syndrome+3), *(Syndrome+5), *(Syndrome+5));
  mul[8]  = gmult4(*(Syndrome+1), *(Syndrome+2), *(Syndrome+4), *(Syndrome+7));
  mul[9]  = gmult4(*(Syndrome+1), *(Syndrome+1), *(Syndrome+5), *(Syndrome+7));
  mul[10] = gmult4(*(Syndrome+1), *(Syndrome+2), *(Syndrome+5), *(Syndrome+6));
  mul[11] = gmult4(*(Syndrome+1), *(Syndrome+4), *(Syndrome+4), *(Syndrome+5));
  mul[12] = gmult4(*(Syndrome+1), *(Syndrome+3), *(Syndrome+3), *(Syndrome+7));
  mul[13] = gmult4(*(Syndrome+1), *(Syndrome+3), *(Syndrome+4), *(Syndrome+6));

  mul[14] = gmult4(*(Syndrome+2), *(Syndrome+4), *(Syndrome+4), *(Syndrome+4));
  mul[15] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+4), *(Syndrome+6));
  mul[16] = gmult4(*(Syndrome+2), *(Syndrome+3), *(Syndrome+3), *(Syndrome+6));
  mul[17] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+3), *(Syndrome+7));

  mul[18] = gmult4(*(Syndrome+3), *(Syndrome+3), *(Syndrome+4), *(Syndrome+4));
  mul[19] = gmult4(*(Syndrome+3), *(Syndrome+3), *(Syndrome+3), *(Syndrome+5));

  add[0] = gadd6(mul[0], mul[1], mul[2], mul[3], mul[4], mul[5]);
  add[1] = gadd6(mul[6], mul[7], mul[8], mul[9], mul[10], mul[11]);
  add[2] = gadd6(mul[12], mul[13], mul[14], mul[15], mul[16], mul[17]);
  add[3] = gadd (mul[18], mul[19]);

  return (gadd4(add[0], add[1], add[2], add[3]));
}

unsigned int DetMB43(unsigned int *Syndrome)
{
  unsigned int mul[18];
  unsigned int add[4];

  mul[0]  = gmult4(*(Syndrome+0), *(Syndrome+2), *(Syndrome+4), *(Syndrome+7));
  mul[1]  = gmult4(*(Syndrome+0), *(Syndrome+3), *(Syndrome+4), *(Syndrome+6));
  mul[2]  = gmult4(*(Syndrome+0), *(Syndrome+3), *(Syndrome+5), *(Syndrome+5));
  mul[3]  = gmult4(*(Syndrome+0), *(Syndrome+2), *(Syndrome+5), *(Syndrome+6));
  mul[4]  = gmult4(*(Syndrome+0), *(Syndrome+3), *(Syndrome+3), *(Syndrome+7));
  mul[5]  = gmult4(*(Syndrome+0), *(Syndrome+4), *(Syndrome+4), *(Syndrome+5));

  mul[6]  = gmult4(*(Syndrome+1), *(Syndrome+1), *(Syndrome+4), *(Syndrome+7));
  mul[7]  = gmult4(*(Syndrome+1), *(Syndrome+3), *(Syndrome+3), *(Syndrome+6));
  mul[8]  = gmult4(*(Syndrome+1), *(Syndrome+2), *(Syndrome+5), *(Syndrome+5));
  mul[9]  = gmult4(*(Syndrome+1), *(Syndrome+1), *(Syndrome+5), *(Syndrome+6));
  mul[10] = gmult4(*(Syndrome+1), *(Syndrome+2), *(Syndrome+4), *(Syndrome+6));
  mul[11] = gmult4(*(Syndrome+1), *(Syndrome+4), *(Syndrome+4), *(Syndrome+4));

  mul[12] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+3), *(Syndrome+6));
  mul[13] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+4), *(Syndrome+5));
  mul[14] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+2), *(Syndrome+7));
  mul[15] = gmult4(*(Syndrome+2), *(Syndrome+3), *(Syndrome+3), *(Syndrome+5));
  mul[16] = gmult4(*(Syndrome+2), *(Syndrome+2), *(Syndrome+4), *(Syndrome+5));

  mul[17] = gmult4(*(Syndrome+3), *(Syndrome+3), *(Syndrome+3), *(Syndrome+4));

  add[0] = gadd6(mul[0], mul[1], mul[2], mul[3], mul[4], mul[5]);
  add[1] = gadd6(mul[6], mul[7], mul[8], mul[9], mul[10], mul[11]);
  add[2] = gadd4(mul[12], mul[13], mul[14], mul[15]);
  add[3] = gadd (mul[16], mul[17]);

  return (gadd4(add[0], add[1], add[2], add[3]));
}


unsigned int DetMA30(unsigned int *Syndrome)
{
  unsigned int mul[4];

  mul[0] = gmult3(*(Syndrome+1), *(Syndrome+3), *(Syndrome+5));
  mul[1] = gmult3(*(Syndrome+1), *(Syndrome+4), *(Syndrome+4));
  mul[2] = gmult3(*(Syndrome+2), *(Syndrome+2), *(Syndrome+5));
  mul[3] = gmult3(*(Syndrome+3), *(Syndrome+3), *(Syndrome+3));

  return(gadd4(mul[0], mul[1], mul[2], mul[3]));
}

unsigned int DetMB300(unsigned int *Syndrome)
{
  unsigned int mul[4];

  mul[0] = gmult3(*(Syndrome+2), *(Syndrome+4), *(Syndrome+6));
  mul[1] = gmult3(*(Syndrome+4), *(Syndrome+4), *(Syndrome+4));
  mul[2] = gmult3(*(Syndrome+2), *(Syndrome+5), *(Syndrome+5));
  mul[3] = gmult3(*(Syndrome+3), *(Syndrome+3), *(Syndrome+6));

  return(gadd4(mul[0], mul[1], mul[2], mul[3]));
}

unsigned int DetMB301(unsigned int *Syndrome)
{
  unsigned int mul[6];

  mul[0] = gmult3(*(Syndrome+1), *(Syndrome+5), *(Syndrome+5));
  mul[1] = gmult3(*(Syndrome+3), *(Syndrome+4), *(Syndrome+4));
  mul[2] = gmult3(*(Syndrome+2), *(Syndrome+3), *(Syndrome+6));
  mul[3] = gmult3(*(Syndrome+1), *(Syndrome+4), *(Syndrome+6));
  mul[4] = gmult3(*(Syndrome+2), *(Syndrome+4), *(Syndrome+5));
  mul[5] = gmult3(*(Syndrome+3), *(Syndrome+3), *(Syndrome+5));

  return(gadd6(mul[0], mul[1], mul[2], mul[3], mul[4], mul[5]));
}

unsigned int DetMB302(unsigned int *Syndrome)
{
  unsigned int mul[6];

  mul[0] = gmult3(*(Syndrome+1), *(Syndrome+3), *(Syndrome+6));
  mul[1] = gmult3(*(Syndrome+2), *(Syndrome+3), *(Syndrome+5));
  mul[2] = gmult3(*(Syndrome+2), *(Syndrome+4), *(Syndrome+4));
  mul[3] = gmult3(*(Syndrome+1), *(Syndrome+4), *(Syndrome+5));
  mul[4] = gmult3(*(Syndrome+2), *(Syndrome+2), *(Syndrome+6));
  mul[5] = gmult3(*(Syndrome+3), *(Syndrome+3), *(Syndrome+4));

  return(gadd6(mul[0], mul[1], mul[2], mul[3], mul[4], mul[5]));
}

unsigned int DetMA31(unsigned int *Syndrome)
{
  unsigned int mul[6];

  mul[0] = gmult3(*(Syndrome+1), *(Syndrome+3), *(Syndrome+6));
  mul[1] = gmult3(*(Syndrome+2), *(Syndrome+4), *(Syndrome+4));
  mul[2] = gmult3(*(Syndrome+2), *(Syndrome+3), *(Syndrome+5));
  mul[3] = gmult3(*(Syndrome+1), *(Syndrome+4), *(Syndrome+5));
  mul[4] = gmult3(*(Syndrome+2), *(Syndrome+2), *(Syndrome+6));
  mul[5] = gmult3(*(Syndrome+3), *(Syndrome+3), *(Syndrome+4));

  return(gadd6(mul[0], mul[1], mul[2], mul[3], mul[4], mul[5]));
}

unsigned int DetMB310(unsigned int *Syndrome)
{
  unsigned int mul[6];

  mul[0] = gmult3(*(Syndrome+3), *(Syndrome+4), *(Syndrome+6));
  mul[1] = gmult3(*(Syndrome+2), *(Syndrome+4), *(Syndrome+7));
  mul[2] = gmult3(*(Syndrome+3), *(Syndrome+5), *(Syndrome+5));
  mul[3] = gmult3(*(Syndrome+4), *(Syndrome+4), *(Syndrome+5));
  mul[4] = gmult3(*(Syndrome+2), *(Syndrome+5), *(Syndrome+6));
  mul[5] = gmult3(*(Syndrome+3), *(Syndrome+3), *(Syndrome+7));

  return(gadd6(mul[0], mul[1], mul[2], mul[3], mul[4], mul[5]));
}

unsigned int DetMB311(unsigned int *Syndrome)
{
  unsigned int mul[6];