www.pudn.com > QRCodeLib.rar > ReedSolomon.cs, change:2007-07-30,size:9927b

```using System;

namespace ThoughtWorks.QRCode.Codec.Ecc
{
public class ReedSolomon
{
virtual public bool CorrectionSucceeded
{
get
{
return correctionSucceeded;
}

}
virtual public int NumCorrectedErrors
{
get
{
return NErrors;
}

}
//G(x)=a^8+a^4+a^3+a^2+1
internal int[] y;

internal int[] gexp = new int[512];
internal int[] glog = new int[256];
internal int NPAR;
//final int NPAR = 15;
internal int MAXDEG;
internal int[] synBytes;

/* The Error Locator Polynomial, also known as Lambda or Sigma. Lambda[0] == 1 */
internal int[] Lambda;

/* The Error Evaluator Polynomial */
internal int[] Omega;

/* local ANSI declarations */

/* error locations found using Chien's search*/
internal int[] ErrorLocs = new int[256];
internal int NErrors;

/* erasure flags */
internal int[] ErasureLocs = new int[256];
internal int NErasures = 0;

internal bool correctionSucceeded = true;

public ReedSolomon(int[] source, int NPAR)
{
initializeGaloisTables();
y = source;
this.NPAR = NPAR;
MAXDEG = NPAR * 2;
synBytes = new int[MAXDEG];
Lambda = new int[MAXDEG];
Omega = new int[MAXDEG];
}

internal virtual void  initializeGaloisTables()
{
int i, z;
int pinit, p1, p2, p3, p4, p5, p6, p7, p8;

pinit = p2 = p3 = p4 = p5 = p6 = p7 = p8 = 0;
p1 = 1;

gexp[0] = 1;
gexp[255] = gexp[0];
glog[0] = 0; /* shouldn't log[0] be an error? */

for (i = 1; i < 256; i++)
{
pinit = p8;
p8 = p7;
p7 = p6;
p6 = p5;
p5 = p4 ^ pinit;
p4 = p3 ^ pinit;
p3 = p2 ^ pinit;
p2 = p1;
p1 = pinit;
gexp[i] = p1 + p2 * 2 + p3 * 4 + p4 * 8 + p5 * 16 + p6 * 32 + p7 * 64 + p8 * 128;
gexp[i + 255] = gexp[i];
}

for (i = 1; i < 256; i++)
{
for (z = 0; z < 256; z++)
{
if (gexp[z] == i)
{
glog[i] = z;
break;
}
}
}
}

/* multiplication using logarithms */
internal virtual int gmult(int a, int b)
{
int i, j;
if (a == 0 || b == 0)
return (0);
i = glog[a];
j = glog[b];
return (gexp[i + j]);
}

internal virtual int ginv(int elt)
{
return (gexp[255 - glog[elt]]);
}

internal virtual void  decode_data(int[] data)
{
int i, j, sum;
for (j = 0; j < MAXDEG; j++)
{
sum = 0;
for (i = 0; i < data.Length; i++)
{
sum = data[i] ^ gmult(gexp[j + 1], sum);
}
synBytes[j] = sum;
}
}

public virtual void  correct()
{
//
decode_data(y);
correctionSucceeded = true;
bool hasError = false;
for (int i = 0; i < synBytes.Length; i++)
{
//Console.out.println("SyndromeS"+String.valueOf(i) + " = " + synBytes[i]);
if (synBytes[i] != 0)
hasError = true;
}
if (hasError)
correctionSucceeded = correct_errors_erasures(y, y.Length, 0, new int[1]);
}

internal virtual void  Modified_Berlekamp_Massey()
{
int n, L, L2, k, d, i;
int[] psi = new int[MAXDEG];
int[] psi2 = new int[MAXDEG];
int[] D = new int[MAXDEG];
int[] gamma = new int[MAXDEG];

/* initialize Gamma, the erasure locator polynomial */
init_gamma(gamma);

/* initialize to z */
copy_poly(D, gamma);
mul_z_poly(D);

copy_poly(psi, gamma);
k = - 1; L = NErasures;

for (n = NErasures; n < 8; n++)
{

d = compute_discrepancy(psi, synBytes, L, n);

if (d != 0)
{

/* psi2 = psi - d*D */
for (i = 0; i < MAXDEG; i++)
psi2[i] = psi[i] ^ gmult(d, D[i]);

if (L < (n - k))
{
L2 = n - k;
k = n - L;
/* D = scale_poly(ginv(d), psi); */
for (i = 0; i < MAXDEG; i++)
D[i] = gmult(psi[i], ginv(d));
L = L2;
}

/* psi = psi2 */
for (i = 0; i < MAXDEG; i++)
psi[i] = psi2[i];
}

mul_z_poly(D);
}

for (i = 0; i < MAXDEG; i++)
Lambda[i] = psi[i];
compute_modified_omega();
}

/* given Psi (called Lambda in Modified_Berlekamp_Massey) and synBytes,
compute the combined erasure/error evaluator polynomial as
Psi*S mod z^4
*/
internal virtual void  compute_modified_omega()
{
int i;
int[] product = new int[MAXDEG * 2];

mult_polys(product, Lambda, synBytes);
zero_poly(Omega);
for (i = 0; i < NPAR; i++)
Omega[i] = product[i];
}

/* polynomial multiplication */
internal virtual void  mult_polys(int[] dst, int[] p1, int[] p2)
{
int i, j;
int[] tmp1 = new int[MAXDEG * 2];

for (i = 0; i < (MAXDEG * 2); i++)
dst[i] = 0;

for (i = 0; i < MAXDEG; i++)
{
for (j = MAXDEG; j < (MAXDEG * 2); j++)
tmp1[j] = 0;

/* scale tmp1 by p1[i] */
for (j = 0; j < MAXDEG; j++)
tmp1[j] = gmult(p2[j], p1[i]);
/* and mult (shift) tmp1 right by i */
for (j = (MAXDEG * 2) - 1; j >= i; j--)
tmp1[j] = tmp1[j - i];
for (j = 0; j < i; j++)
tmp1[j] = 0;

/* add into partial product */
for (j = 0; j < (MAXDEG * 2); j++)
dst[j] ^= tmp1[j];
}
}

/* gamma = product (1-z*a^Ij) for erasure locs Ij */
internal virtual void  init_gamma(int[] gamma)
{
int e;
int[] tmp = new int[MAXDEG];

zero_poly(gamma);
zero_poly(tmp);
gamma[0] = 1;

for (e = 0; e < NErasures; e++)
{
copy_poly(tmp, gamma);
scale_poly(gexp[ErasureLocs[e]], tmp);
mul_z_poly(tmp);
}
}

internal virtual void  compute_next_omega(int d, int[] A, int[] dst, int[] src)
{
int i;
for (i = 0; i < MAXDEG; i++)
{
dst[i] = src[i] ^ gmult(d, A[i]);
}
}

internal virtual int compute_discrepancy(int[] lambda, int[] S, int L, int n)
{
int i, sum = 0;

for (i = 0; i <= L; i++)
sum ^= gmult(lambda[i], S[n - i]);
return (sum);
}

/// <summary>******* polynomial arithmetic ******************</summary>

internal virtual void  add_polys(int[] dst, int[] src)
{
int i;
for (i = 0; i < MAXDEG; i++)
dst[i] ^= src[i];
}

internal virtual void  copy_poly(int[] dst, int[] src)
{
int i;
for (i = 0; i < MAXDEG; i++)
dst[i] = src[i];
}

internal virtual void  scale_poly(int k, int[] poly)
{
int i;
for (i = 0; i < MAXDEG; i++)
poly[i] = gmult(k, poly[i]);
}

internal virtual void  zero_poly(int[] poly)
{
int i;
for (i = 0; i < MAXDEG; i++)
poly[i] = 0;
}

/* multiply by z, i.e., shift right by 1 */
internal virtual void  mul_z_poly(int[] src)
{
int i;
for (i = MAXDEG - 1; i > 0; i--)
src[i] = src[i - 1];
src[0] = 0;
}

/* Finds all the roots of an error-locator polynomial with coefficients
* Lambda[j] by evaluating Lambda at successive values of alpha.
*
* This can be tested with the decoder's equations case.
*/
internal virtual void  Find_Roots()
{
int sum, r, k;
NErrors = 0;

for (r = 1; r < 256; r++)
{
sum = 0;
/* evaluate lambda at r */
for (k = 0; k < NPAR + 1; k++)
{
sum ^= gmult(gexp[(k * r) % 255], Lambda[k]);
}
if (sum == 0)
{
ErrorLocs[NErrors] = (255 - r); NErrors++;
//if (DEBUG) fprintf(stderr, "Root found at r = %d, (255-r) = %d\n", r, (255-r));
}
}
}

/* Combined Erasure And Error Magnitude Computation
*
* Pass in the codeword, its size in bytes, as well as
* an array of any known erasure locations, along the number
* of these erasures.
*
* Evaluate Omega(actually Psi)/Lambda' at the roots
* alpha^(-i) for error locs i.
*
* Returns 1 if everything ok, or 0 if an out-of-bounds error is found
*
*/

internal virtual bool correct_errors_erasures(int[] codeword, int csize, int nerasures, int[] erasures)
{
int r, i, j, err;

/* If you want to take advantage of erasure correction, be sure to
set NErasures and ErasureLocs[] with the locations of erasures.
*/
NErasures = nerasures;
for (i = 0; i < NErasures; i++)
ErasureLocs[i] = erasures[i];

Modified_Berlekamp_Massey();
Find_Roots();

if ((NErrors <= NPAR) || NErrors > 0)
{

/* first check for illegal error locs */
for (r = 0; r < NErrors; r++)
{
if (ErrorLocs[r] >= csize)
{
//if (DEBUG) fprintf(stderr, "Error loc i=%d outside of codeword length %d\n", i, csize);
//Console.out.println("Error loc i="+ErrorLocs[r]+" outside of codeword length"+csize);
return false;
}
}

for (r = 0; r < NErrors; r++)
{
int num, denom;
i = ErrorLocs[r];
/* evaluate Omega at alpha^(-i) */

num = 0;
for (j = 0; j < MAXDEG; j++)
num ^= gmult(Omega[j], gexp[((255 - i) * j) % 255]);

/* evaluate Lambda' (derivative) at alpha^(-i) ; all odd powers disappear */
denom = 0;
for (j = 1; j < MAXDEG; j += 2)
{
denom ^= gmult(Lambda[j], gexp[((255 - i) * (j - 1)) % 255]);
}

err = gmult(num, ginv(denom));
//if (DEBUG) fprintf(stderr, "Error magnitude %#x at loc %d\n", err, csize-i);

codeword[csize - i - 1] ^= err;
}
//for (int p = 0; p < codeword.length; p++)
//	Console.out.println(codeword[p]);
//Console.out.println("correction succeeded");
return true;
}
else
{
//if (DEBUG && NErrors) fprintf(stderr, "Uncorrectable codeword\n");
//Console.out.println("Uncorrectable codeword");
return false;
}
}
}
}```