void skipjack_dec( iu8* v, iu8* k )
{
iu8 kidx=8, counter=32;
#ifdef INLINE
iu8 tmp;
#endif
#ifdef DEBUG
printf( "skipjack_dec( %.2hX %.2hX %.2hX %.2hX %.2hX %.2hX %.2hX %.2hX, %.2hX %.2hX %.2hX %.2hX %.2hX %.2hX %.2hX %.2hX %.2hX %.2hX )\n",
v[0], v[1], v[2], v[3], v[4], v[5], v[6], v[7],
k[0], k[1], k[2], k[3], k[4], k[4], k[6], k[7],
k[8], k[9]);
#endif
while( counter>24 ) {
ginv( v+2, k, kidx );
rule_binv( v, counter );
#ifndef INLINE
kidx += 6;
if( kidx>=10 ) kidx-=10;
#endif
counter--;
}
while( counter>16 ) {
rule_ainv( v, counter );
ginv( v, k, kidx );
#ifndef INLINE
kidx += 6;
if( kidx>=10 ) kidx-=10;
#endif
counter--;
}
while( counter>8 ) {
ginv( v+2, k, kidx );
rule_binv( v, counter );
#ifndef INLINE
kidx += 6;
if( kidx>=10 ) kidx-=10;
#endif
counter--;
}
while( counter>0 ) {
rule_ainv( v, counter );
ginv( v, k, kidx );
#ifndef INLINE
kidx += 6;
if( kidx>=10 ) kidx-=10;
#endif
counter--;
}
}
static trace_data *
init_trace(trace_data *T, GEN S, nflift_t *L, GEN q)
{
long e = gexpo(S), i,j, l,h;
GEN qgood, S1, invd;
if (e < 0) return NULL; /* S = 0 */
qgood = int2n(e - 32); /* single precision check */
if (cmpii(qgood, q) > 0) q = qgood;
S1 = gdivround(S, q);
if (gcmp0(S1)) return NULL;
invd = ginv(itor(L->den, DEFAULTPREC));
T->dPinvS = gmul(L->iprk, S);
l = lg(S);
h = lg(T->dPinvS[1]);
T->PinvSdbl = (double**)cgetg(l, t_MAT);
init_dalloc();
for (j = 1; j < l; j++)
{
double *t = dalloc(h * sizeof(double));
GEN c = gel(T->dPinvS,j);
pari_sp av = avma;
T->PinvSdbl[j] = t;
for (i=1; i < h; i++) t[i] = rtodbl(mpmul(invd, gel(c,i)));
avma = av;
}
T->d = L->den;
T->P1 = gdivround(L->prk, q);
T->S1 = S1; return T;
}
void skipjack_dec( iu8* v, iu8* k )
{
iu8 kidx=8, counter=32;
#ifdef INLINE
iu8 tmp;
#endif
while( counter>24 ) {
ginv( v+2, k, kidx );
rule_binv( v, counter );
#ifndef INLINE
kidx += 6;
if( kidx>=10 ) kidx-=10;
#endif
counter--;
}
while( counter>16 ) {
rule_ainv( v, counter );
ginv( v, k, kidx );
#ifndef INLINE
kidx += 6;
if( kidx>=10 ) kidx-=10;
#endif
counter--;
}
while( counter>8 ) {
ginv( v+2, k, kidx );
rule_binv( v, counter );
#ifndef INLINE
kidx += 6;
if( kidx>=10 ) kidx-=10;
#endif
counter--;
}
while( counter>0 ) {
rule_ainv( v, counter );
ginv( v, k, kidx );
#ifndef INLINE
kidx += 6;
if( kidx>=10 ) kidx-=10;
#endif
counter--;
}
}
void
debug_check_syndrome (void)
{
int i;
for (i = 0; i < 3; i++) {
fprintf(stderr, " inv log S[%d]/S[%d] = %d\n", i, i+1,
glog[gmult(synBytes[i], ginv(synBytes[i+1]))]);
}
}
int
correct_errors_erasures (unsigned char 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 (RS_DEBUG) fprintf(stderr, "Error loc i=%d outside of codeword length %d\n", i, csize);
return(0);
}
}
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 (RS_DEBUG) fprintf(stderr, "Error magnitude %#x at loc %d\n", err, csize-i);
codeword[csize-i-1] ^= err;
}
return(1);
}
else {
if (RS_DEBUG && NErrors) fprintf(stderr, "Uncorrectable codeword\n");
return(0);
}
}
void
debug_check_syndrome (void)
{
#ifdef NEVER
int i;
for (i = 0; i < 3; i++) {
printf(" inv log S[%d]/S[%d] = %d\n", i, i+1,
glog[gmult(synBytes[i], ginv(synBytes[i+1]))]);
}
#endif
}
static void
bestlift_init(long a, GEN nf, GEN pr, GEN C, nflift_t *L)
{
const long D = 100;
const double alpha = ((double)D-1) / D; /* LLL parameter */
const long d = degpol(nf[1]);
pari_sp av = avma;
GEN prk, PRK, B, GSmin, pk;
pari_timer ti;
TIMERstart(&ti);
if (!a) a = (long)bestlift_bound(C, d, alpha, pr_norm(pr));
for (;; avma = av, a<<=1)
{
if (DEBUGLEVEL>2) fprintferr("exponent: %ld\n",a);
PRK = prk = idealpows(nf, pr, a);
pk = gcoeff(prk,1,1);
/* reduce size first, "scramble" matrix */
PRK = lllintpartial_ip(PRK);
/* now floating point reduction is fast */
PRK = lllint_fp_ip(PRK, 4);
PRK = lllint_i(PRK, D, 0, NULL, NULL, &B);
if (!PRK) { PRK = prk; GSmin = pk; } /* nf = Q */
else
{
pari_sp av2 = avma;
GEN S = invmat( get_R(PRK) ), BB = GS_norms(B, DEFAULTPREC);
GEN smax = gen_0;
long i, j;
for (i=1; i<=d; i++)
{
GEN s = gen_0;
for (j=1; j<=d; j++)
s = gadd(s, gdiv( gsqr(gcoeff(S,i,j)), gel(BB,j)));
if (gcmp(s, smax) > 0) smax = s;
}
GSmin = gerepileupto(av2, ginv(gmul2n(smax, 2)));
}
if (gcmp(GSmin, C) >= 0) break;
}
if (DEBUGLEVEL>2)
fprintferr("for this exponent, GSmin = %Z\nTime reduction: %ld\n",
GSmin, TIMER(&ti));
L->k = a;
L->den = L->pk = pk;
L->prk = PRK;
L->iprk = ZM_inv(PRK, pk);
L->GSmin= GSmin;
L->prkHNF = prk;
init_proj(L, gel(nf,1), gel(pr,1));
}
static real
ginvae(arglist *al) /* like ginv, but enrolling At_reset and At_exit */
{
static int nginv;
AmplExports *ae = al->AE;
if (AEInext < AEIlast) {
AEInext->n = ++nginv;
AEInext->ae = ae;
at_reset(At_reset, AEInext);
at_exit(At_end, AEInext++);
}
return ginv(al);
}
void CReedSolomon::Modified_Berlekamp_Massey (void) {
int L, L2, k, d;
int psi [MAX_LENGTH], psi2 [MAX_LENGTH], D [MAX_LENGTH];
int gamma [MAX_LENGTH];
int iMaxLength = m_iCorrectCodeSize * 2;
/* 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 = m_NErasures;
for (int n = m_NErasures; n < m_iCorrectCodeSize; n ++) {
d = compute_discrepancy (psi, m_synBytes, L, n);
if (d != 0) {
/* psi2 = psi - d*D */
for (int i = 0; i < iMaxLength; 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 (int i = 0; i < iMaxLength; i ++) {
D [i] = gmult (psi [i], ginv (d));
}
L = L2;
}
/* psi = psi2 */
for (int i = 0; i < iMaxLength; i ++) {
psi [i] = psi2 [i];
}
}
mul_z_poly (D);
}
for (int i = 0; i < MAX_LENGTH; i ++) {
m_Lambda [i] = psi [i];
}
compute_modified_omega ();
}
/* From Cain, Clark, "Error-Correction Coding For Digital Communications", pp. 216. */
void
Modified_Berlekamp_Massey (void)
{
int n, L, L2, k, d, i;
int psi[MAXDEG], psi2[MAXDEG], D[MAXDEG];
int gamma[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 < NPAR; 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();
}
int unwhiten(int letter,int row,int column)
{
int highbits; // save the high 3 bits of the letter byte, which indicate whether it's data or check
highbits=letter&-32;
if (debugwhiten)
printf("r%d c%d %c->",row,column,(letter&31)+'@');
letter=bitctunrot[letter&31]-'@';
if (debugwhiten)
printf("%c->",(letter&31)+'@');
letter='_'-bitctrot[oddmul(letter,invoddmul[row&31])];
letter&=31;
if (debugwhiten)
printf("%c->",(letter&31)+'@');
letter=gmult(letter,ginv(column+1))-column-1;
if (debugwhiten)
printf("%c\n",(letter&31)+'@');
return (letter&31)|highbits;
}
int CReedSolomon::correct_errors_erasures (unsigned char codeword [], int csize, int nerasures, int erasures []) {
int i, err;
m_NErasures = nerasures;
for (i = 0; i < m_NErasures; i ++) {
m_ErasureLocs [i] = erasures [i];
}
Modified_Berlekamp_Massey ();
Find_Roots ();
if ((m_NErrors <= m_iCorrectCodeSize) && m_NErrors > 0) {
/* first check for illegal error locs */
for (int r = 0; r < m_NErrors; r ++) {
if (m_ErrorLocs [r] >= csize) {
return(0);
}
}
for (int r = 0; r < m_NErrors; r ++) {
int num, denom;
i = m_ErrorLocs [r];
/* evaluate m_Omega at alpha^(-i) */
num = 0;
for (int j = 0; j < MAX_LENGTH; j ++) {
num ^= gmult (m_Omega [j], byExpToInt [((255 - i) * j) % 255]);
}
/* evaluate m_Lambda' (derivative) at alpha^(-i) ; all odd powers disappear */
denom = 0;
for (int j = 1; j < MAX_LENGTH; j += 2) {
denom ^= gmult (m_Lambda [j], byExpToInt [((255 - i) * (j - 1)) % 255]);
}
err = gmult (num, ginv (denom));
codeword [csize - i - 1] ^= err;
}
return 1;
} else {
return 0;
}
}