/************************************************************************* * recline.c - tools for recursive filtering of 1D lines * * \$Id\$ * * LICENSE: * GPL v3.0 (see gpl-3.0.txt for details) * * DESCRIPTION: * * Recursive filtering of a line (a 1D array) * Filter coefficient are static variables. * * * AUTHOR: * Gregoire Malandain (gregoire.malandain@inria.fr) * * CREATION DATE: * June, 9 1998 * * ADDITIONS, CHANGES * */ #include #include #include #include static int _VERBOSE_ = 0; #define EXIT_ON_FAILURE 0 #define EXIT_ON_SUCCESS 1 void printRecursiveCoefficients( RFcoefficientType *RFC ) { printf( "denominator:\n" ); printf( "%f %f %f %f\n", RFC->sd1, RFC->sd2, RFC->sd3, RFC->sd4 ); printf( "positive numerator:\n" ); printf( "%f %f %f %f\n", RFC->sp0, RFC->sp1, RFC->sp2, RFC->sp3 ); printf( "negative numerator:\n" ); printf( "%f %f %f %f %f\n", RFC->sn0, RFC->sn1, RFC->sn2, RFC->sn3, RFC->sn4 ); printf( "\n" ); } RFcoefficientType * InitRecursiveCoefficients( double x, recursiveFilterType type_filter, derivativeOrder derivative ) { char *proc="InitRecursiveCoefficients"; double ex, k1, k2; double a0, a1, c0, c1, omega0, omega1, b0, b1; double cos0, sin0, cos1, sin1; double sumA=0.0, sumC=0.0, aux; RFcoefficientType *RFC = NULL; RFC = (RFcoefficientType *)malloc( sizeof(RFcoefficientType) ); if ( RFC == NULL ) { if ( _VERBOSE_ != 0 ) fprintf( stderr, "%s: allocation failed\n", proc ); return( NULL ); } RFC->sd1 = RFC->sd2 = RFC->sd3 = RFC->sd4 = 0.0; RFC->sp0 = RFC->sp1 = RFC->sp2 = RFC->sp3 = 0.0; RFC->sn0 = RFC->sn1 = RFC->sn2 = RFC->sn3 = RFC->sn4 = 0.0; RFC->type_filter = UNKNOWN_FILTER; RFC->derivative = NODERIVATIVE; ex = k1 = k2 = 0.0; a0 = a1 = c0 = c1 = 0.0; b0 = b1 = omega0 = omega1 = 0.0; /*--- Selon le type de filtrage (filtres de Deriche, ou approximation de la gaussienne), x designe soit alpha, soit sigma ---*/ switch ( type_filter ) { case GAUSSIAN_FIDRICH : if ( x < 0.1 ) { if ( _VERBOSE_ != 0 ) { fprintf( stderr, "%s: improper value of coefficient (should be >= 0.1).\n", proc ); } free( RFC ); return( NULL ); } switch ( derivative ) { default : if ( _VERBOSE_ != 0 ) { fprintf( stderr, "%s: improper value of derivative order.\n", proc ); } free( RFC ); return( NULL ); case DERIVATIVE_0 : a0 = 0.6570033214 / x; a1 = 1.978946687 / x; c0 = -0.2580640608 / x; c1 = -0.2391206463 / x; omega0 = 0.6512453378; omega1 = 2.05339943; b0 = 1.906154352; b1 = 1.881305409; break; case DERIVATIVE_1 : case DERIVATIVE_1_CONTOURS : a0 = -0.1726729496 / x; a1 = -2.003565572 / x; c0 = 0.1726730777 / x; c1 = 0.4440126835 / x; b0 = 1.560644213; b1 = 1.594202256; omega0 = 0.6995461735; omega1 = 2.144671764; break; case DERIVATIVE_2 : a0 = -0.7241334169 / x; a1 = 1.688628765 / x; c0 = 0.3251949838 / x; c1 = -0.7211796018 / x; b0 = 1.294951143; b1 = 1.427007123; omega0 = 0.7789803775; omega1 = 2.233566862; break; case DERIVATIVE_3 : a0 = 1.285774106 / x; a1 = -0.2896378408 / x; c0 = -1.28577129 / x; c1 = 0.26249833 / x; b0 = 1.01162886; b1 = 1.273344739; omega0 = 0.9474270928; omega1 = 2.337607006; break; } omega0 /= x; sin0 = sin( omega0 ); cos0 = cos( omega0 ); omega1 /= x; sin1 = sin( omega1 ); cos1 = cos( omega1 ); b0 /= x; b1 /= x; RFC->sp0 = a0 + c0; RFC->sp1 = exp( -b1 ) * (c1 * sin1 - (c0 + 2 * a0) * cos1); RFC->sp1 += exp( -b0 ) * (a1 * sin0 - (2 * c0 + a0) * cos0); RFC->sp2 = 2.0 * exp( -b0 - b1 ) * ((a0 + c0) * cos1 * cos0 - cos1 * a1 * sin0 - cos0 * c1 * sin1); RFC->sp2 += c0 * exp( -2.0 * b0 ) + a0 * exp( -2.0 * b1 ); RFC->sp3 = exp( -b1 - 2.0 * b0 ) * (c1 * sin1 - c0 * cos1); RFC->sp3 += exp( -b0 - 2.0 * b1 ) * (a1 * sin0 - a0 * cos0); RFC->sd1 = -2.0 * exp( -b1 ) * cos1 - 2.0 * exp( -b0 ) * cos0; RFC->sd2 = 4.0 * cos1 * cos0 * exp( -b0 - b1 ) + exp( -2.0 * b1 ) + exp( -2.0 * b0 ); RFC->sd3 = -2.0 * cos0 * exp( -b0 - 2.0 * b1 ) - 2.0 * cos1 * exp( -b1 - 2.0 * b0 ); RFC->sd4 = exp( -2.0 * b0 - 2.0 * b1 ); switch ( derivative ) { default : if ( _VERBOSE_ != 0 ) { fprintf( stderr, "%s: improper value of derivative order.\n", proc ); } free( RFC ); return( NULL ); case DERIVATIVE_0 : case DERIVATIVE_2 : RFC->sn1 = RFC->sp1 - RFC->sd1 * RFC->sp0; RFC->sn2 = RFC->sp2 - RFC->sd2 * RFC->sp0; RFC->sn3 = RFC->sp3 - RFC->sd3 * RFC->sp0; RFC->sn4 = - RFC->sd4 * RFC->sp0; break; case DERIVATIVE_1 : case DERIVATIVE_1_CONTOURS : case DERIVATIVE_3 : RFC->sn1 = - RFC->sp1 + RFC->sd1 * RFC->sp0; RFC->sn2 = - RFC->sp2 + RFC->sd2 * RFC->sp0; RFC->sn3 = - RFC->sp3 + RFC->sd3 * RFC->sp0; RFC->sn4 = RFC->sd4 * RFC->sp0; } RFC->type_filter = type_filter; RFC->derivative = derivative; break; case GAUSSIAN_DERICHE : if ( x < 0.1 ) { if ( _VERBOSE_ != 0 ) { fprintf( stderr, "%s: improper value of coefficient (should be >= 0.1).\n", proc ); } free( RFC ); return( NULL ); } switch ( derivative ) { default : if ( _VERBOSE_ != 0 ) { fprintf( stderr, "%s: switch to default coefficients (smoothing).\n", proc ); } derivative = DERIVATIVE_0; case DERIVATIVE_0 : a0 = 1.68; omega0 = 0.6318; a1 = 3.735; b0 = 1.783; c0 = -0.6803; omega1 = 1.997; c1 = -0.2598; b1 = 1.723; break; case DERIVATIVE_1 : case DERIVATIVE_1_CONTOURS : a0 = -0.6472; omega0 = 0.6719; a1 = -4.531; b0 = 1.527; c0 = 0.6494; omega1 = 2.072; c1 = 0.9557; b1 = 1.516; break; case DERIVATIVE_2 : a0 = -1.331; omega0 = 0.748; a1 = 3.661; b0 = 1.24; c0 = 0.3225; omega1 = 2.166; c1 = -1.738; b1 = 1.314; } omega0 /= x; sin0 = sin( omega0 ); cos0 = cos( omega0 ); omega1 /= x; sin1 = sin( omega1 ); cos1 = cos( omega1 ); b0 /= x; b1 /= x; /*--- normalisation ---*/ switch ( derivative ) { default : case DERIVATIVE_0 : sumA = 2.0 * a1 * exp( b0 ) * cos0 * cos0 - a0 * sin0 * exp( 2.0 * b0 ); sumA += a0 * sin0 - 2.0 * a1 * exp( b0 ); sumA /= ( 2.0 * cos0 * exp( b0 ) - exp( 2.0 * b0 ) - 1 ) * sin0; sumC = 2.0 * c1 * exp( b1 ) * cos1 * cos1 - c0 * sin1 * exp( 2.0 * b1 ); sumC += c0 * sin1 - 2.0 * c1 * exp( b1 ); sumC /= ( 2.0 * cos1 * exp( b1 ) - exp( 2.0 * b1 ) - 1 ) * sin1; break; case DERIVATIVE_1 : aux = exp( 4.0 * b0 ) - 4.0 * cos0 * exp( 3.0 * b0 ); aux += 2.0 * exp( 2.0 * b0 ) + 4.0 * cos0 * cos0 * exp( 2.0 * b0 ); aux += 1.0 - 4.0 * cos0 * exp( b0 ); sumA = a0 * cos0 - a1 * sin0 + a1 * sin0 * exp( 2.0 * b0 ); sumA += a0 * cos0 * exp( 2.0 * b0 ) - 2.0 * a0 * exp( b0 ); sumA *= exp( b0 ) / aux; aux = exp( 4.0 * b1 ) - 4.0 * cos1 * exp( 3.0 * b1 ); aux += 2.0 * exp( 2.0 * b1 ) + 4.0 * cos1 * cos1 * exp( 2.0 * b1 ); aux += 1.0 - 4.0 * cos1 * exp( b1 ); sumC = c0 * cos1 - c1 * sin1 + c1 * sin1 * exp( 2.0 * b1 ); sumC += c0 * cos1 * exp( 2.0 * b1 ) - 2.0 * c0 * exp( b1 ); sumC *= exp( b1 ) / aux; /*--- on multiplie les sommes par 2 car on n'a calcule que des demi-sommes et on change le signe car la somme doit etre egale a -1 ---*/ sumA *= (-2.0); sumC *= (-2.0); break; case DERIVATIVE_1_CONTOURS : /*--- la somme de 1 a l'infini est egale a 1 : cela introduit un petit biais (reponse un rien superieur a la hauteur du step). Avec une somme de 0 a l'infini, c'est pire ---*/ sumA = a1 * exp( b0 ) - a1 * cos0 * cos0 * exp( b0 ); sumA += a0 * cos0 * sin0 * exp( b0 ) - a0 * sin0; sumA /= sin0 * ( 2.0 * cos0 * exp( b0 ) - exp( 2.0 * b0 ) - 1 ); sumC = c1 * exp( b1 ) - c1 * cos1 * cos1 * exp( b1 ); sumC += c0 * cos1 * sin1 * exp( b1 ) - c0 * sin1; sumC /= sin1 * ( 2.0 * cos1 * exp( b1 ) - exp( 2.0 * b1 ) - 1 ); break; case DERIVATIVE_2 : aux = 12.0 * cos0 * exp( 3.0 * b0 ) - 3.0 * exp( 2.0 * b0 ); aux += 8.0 * cos0 * cos0 * cos0 * exp( 3.0 * b0 ) - 12.0 * cos0 * cos0 * exp( 4.0 * b0 ); aux -= 3.0 * exp( 4.0 * b0 ); aux += 6.0 * cos0 * exp( 5.0 * b0 ) - exp( 6.0 * b0 ) + 6.0 * cos0 * exp( b0 ); aux -= ( 1.0 + 12.0 * cos0 * cos0 * exp( 2.0 * b0 ) ); sumA = 4.0 * a0 * sin0 * exp( 3.0 * b0 ) + a1 * cos0 * cos0 * exp( 4.0 * b0 ); sumA -= ( 4.0 * a0 * sin0 * exp( b0 ) + 6.0 * a1 * cos0 * cos0 * exp( 2.0 * b0 ) ); sumA += 2.0 * a1 * cos0 * cos0 * cos0 * exp( b0 ) - 2.0 * a1 * cos0 * exp( b0 ); sumA += 2.0 * a1 * cos0 * cos0 * cos0 * exp( 3.0 * b0 ) - 2.0 * a1 * cos0 * exp( 3.0 * b0 ); sumA += a1 * cos0 * cos0 - a1 * exp( 4.0 * b0 ); sumA += 2.0 * a0 * sin0 * cos0 * cos0 * exp( b0 ) - 2.0 * a0 * sin0 * cos0 * cos0 * exp( 3.0 * b0 ); sumA -= ( a0 * sin0 * cos0 * exp( 4.0 * b0 ) + a1 ); sumA += 6.0 * a1 * exp( 2.0 * b0 ) + a0 * cos0 * sin0; sumA *= 2.0 * exp( b0 ) / ( aux * sin0 ); aux = 12.0 * cos1 * exp( 3.0 * b1 ) - 3.0 * exp( 2.0 * b1 ); aux += 8.0 * cos1 * cos1 * cos1 * exp( 3.0 * b1 ) - 12.0 * cos1 * cos1 * exp( 4.0 * b1 ); aux -= 3.0 * exp( 4.0 * b1 ); aux += 6.0 * cos1 * exp( 5.0 * b1 ) - exp( 6.0 * b1 ) + 6.0 * cos1 * exp( b1 ); aux -= ( 1.0 + 12.0 * cos1 * cos1 * exp( 2.0 * b1 ) ); sumC = 4.0 * c0 * sin1 * exp( 3.0 * b1 ) + c1 * cos1 * cos1 * exp( 4.0 * b1 ); sumC -= ( 4.0 * c0 * sin1 * exp( b1 ) + 6.0 * c1 * cos1 * cos1 * exp( 2.0 * b1 ) ); sumC += 2.0 * c1 * cos1 * cos1 * cos1 * exp( b1 ) - 2.0 * c1 * cos1 * exp( b1 ); sumC += 2.0 * c1 * cos1 * cos1 * cos1 * exp( 3.0 * b1 ) - 2.0 * c1 * cos1 * exp( 3.0 * b1 ); sumC += c1 * cos1 * cos1 - c1 * exp( 4.0 * b1 ); sumC += 2.0 * c0 * sin1 * cos1 * cos1 * exp( b1 ) - 2.0 * c0 * sin1 * cos1 * cos1 * exp( 3.0 * b1 ); sumC -= ( c0 * sin1 * cos1 * exp( 4.0 * b1 ) + c1 ); sumC += 6.0 * c1 * exp( 2.0 * b1 ) + c0 * cos1 * sin1; sumC *= 2.0 * exp( b1 ) / ( aux * sin1 ); /*--- on divise les sommes par 2 (la somme doit etre egale a 2) ---*/ sumA /= 2; sumC /= 2; } a0 /= ( sumA + sumC ); a1 /= ( sumA + sumC ); c0 /= ( sumA + sumC ); c1 /= ( sumA + sumC ); /*--- coefficients du calcul recursif ---*/ RFC->sp0 = a0 + c0; RFC->sp1 = exp( -b1 ) * (c1 * sin1 - (c0 + 2 * a0) * cos1); RFC->sp1 += exp( -b0 ) * (a1 * sin0 - (2 * c0 + a0) * cos0); RFC->sp2 = 2.0 * exp( -b0 - b1 ) * ((a0 + c0) * cos1 * cos0 - cos1 * a1 * sin0 - cos0 * c1 * sin1); RFC->sp2 += c0 * exp( -2.0 * b0 ) + a0 * exp( -2.0 * b1 ); RFC->sp3 = exp( -b1 - 2.0 * b0 ) * (c1 * sin1 - c0 * cos1); RFC->sp3 += exp( -b0 - 2.0 * b1 ) * (a1 * sin0 - a0 * cos0); RFC->sd1 = -2.0 * exp( -b1 ) * cos1 - 2.0 * exp( -b0 ) * cos0; RFC->sd2 = 4.0 * cos1 * cos0 * exp( -b0 - b1 ) + exp( -2.0 * b1 ) + exp( -2.0 * b0 ); RFC->sd3 = -2.0 * cos0 * exp( -b0 - 2.0 * b1 ) - 2.0 * cos1 * exp( -b1 - 2.0 * b0 ); RFC->sd4 = exp( -2.0 * b0 - 2.0 * b1 ); switch ( derivative ) { default : case DERIVATIVE_0 : case DERIVATIVE_2 : RFC->sn1 = RFC->sp1 - RFC->sd1 * RFC->sp0; RFC->sn2 = RFC->sp2 - RFC->sd2 * RFC->sp0; RFC->sn3 = RFC->sp3 - RFC->sd3 * RFC->sp0; RFC->sn4 = - RFC->sd4 * RFC->sp0; break; case DERIVATIVE_1 : case DERIVATIVE_1_CONTOURS : case DERIVATIVE_3 : RFC->sn1 = - RFC->sp1 + RFC->sd1 * RFC->sp0; RFC->sn2 = - RFC->sp2 + RFC->sd2 * RFC->sp0; RFC->sn3 = - RFC->sp3 + RFC->sd3 * RFC->sp0; RFC->sn4 = RFC->sd4 * RFC->sp0; } RFC->type_filter = type_filter; RFC->derivative = derivative; break; default : if ( _VERBOSE_ != 0 ) { fprintf( stderr, "%s: switch to default recursive filter (Deriche's filters).\n", proc ); } type_filter = ALPHA_DERICHE; case ALPHA_DERICHE : if ( (x < 0.1) || (x > 1.9) ) { if ( _VERBOSE_ != 0 ) { fprintf( stderr, "%s: improper value of coefficient (should be >= 0.1 and <= 1.9).\n", proc ); } free( RFC ); return( NULL ); } ex = exp( (-x) ); switch ( derivative ) { default : if ( _VERBOSE_ != 0 ) { fprintf( stderr, "%s: switch to default coefficients (smoothing).\n", proc ); } derivative = DERIVATIVE_0; case DERIVATIVE_0 : RFC->sp0 = (1.0 - ex) * (1.0 - ex) / (1.0 + 2.0 * x * ex - ex * ex); RFC->sp1 = RFC->sp0 * (x - 1.0) * ex; RFC->sn1 = RFC->sp0 * (x + 1.0) * ex; RFC->sn2 = (- RFC->sp0) * ex * ex; RFC->sd1 = (- 2.0) * ex; RFC->sd2 = ex * ex; break; case DERIVATIVE_1 : RFC->sp1 = - (1.0 - ex) * (1.0 - ex) * (1.0 - ex) / (2.0 * (1.0 + ex)); RFC->sn1 = (- RFC->sp1); RFC->sd1 = (- 2.0) * ex; RFC->sd2 = ex * ex; break; case DERIVATIVE_1_CONTOURS : RFC->sp1 = - (1.0 - ex) * (1.0 - ex); RFC->sn1 = (- RFC->sp1); RFC->sd1 = (- 2.0) * ex; RFC->sd2 = ex * ex; break; case DERIVATIVE_2 : k1 = (- 2.0) * (1.0 - ex) * (1.0 - ex) * (1.0 - ex); k1 /= (1.0 + ex) * (1.0 + ex) * (1.0 + ex); k2 = (1.0 - ex * ex) / (2.0 * ex); RFC->sp0 = k1; RFC->sp1 = (- k1) * (1.0 + k2) * ex; RFC->sn1 = k1 * (1.0 - k2) * ex; RFC->sn2 = (- k1) * ex * ex; RFC->sd1 = (- 2.0) * ex; RFC->sd2 = ex * ex; break; case DERIVATIVE_3 : k1 = (1.0 + x) * ex + (x - 1.0); k2 = (1.0 - ex) / k1; k1 *= (1.0 - ex) * (1.0 - ex) * (1.0 - ex) * (1.0 - ex); k1 /= 2.0 * x * x * ex * ex; k1 /= ex + 1.0; RFC->sp0 = k1 * x * (k2 + 1.0); RFC->sp1 = (- k1) * x * (1.0 + k2 + k2*x) * ex; RFC->sn0 = (- RFC->sp0); RFC->sn1 = (- RFC->sp1); RFC->sd1 = (- 2.0) * ex; RFC->sd2 = ex * ex; } RFC->type_filter = type_filter; RFC->derivative = derivative; } return( RFC ); } int RecursiveFilter1D( RFcoefficientType *RFC, double *in, double *out, double *work1, double *work2, int dim ) { char *proc="RecursiveFilter1D"; register double rp0, rp1, rp2, rp3; register double rd1, rd2, rd3, rd4; register double rn0, rn1, rn2, rn3, rn4; register int i; register double *w0, *w1, *w2, *w3, *w4; register double *d0, *d1, *d2, *d3, *d4; if ( RFC->type_filter == UNKNOWN_FILTER ) { if ( _VERBOSE_ != 0 ) fprintf( stderr, "%s: unknown type of recursive filter.\n", proc ); return( EXIT_ON_FAILURE ); } if ( RFC->derivative == NODERIVATIVE ) { if ( _VERBOSE_ != 0 ) fprintf( stderr, "%s: unknown type of derivative.\n", proc ); return( EXIT_ON_FAILURE ); } rd1 = rd2 = rd3 = rd4 = 0.0; rp0 = rp1 = rp2 = rp3 = 0.0; rn0 = rn1 = rn2 = rn3 = rn4 = 0.0; switch( RFC->type_filter ) { default : if ( _VERBOSE_ != 0 ) fprintf( stderr, "%s: unknown type of recursive filter.\n", proc ); return( EXIT_ON_FAILURE ); case GAUSSIAN_FIDRICH : case GAUSSIAN_DERICHE : /*--- filtrage generique d'ordre 4 ---*/ rp0 = RFC->sp0; rp1 = RFC->sp1; rp2 = RFC->sp2; rp3 = RFC->sp3; rd1 = RFC->sd1; rd2 = RFC->sd2; rd3 = RFC->sd3; rd4 = RFC->sd4; rn1 = RFC->sn1; rn2 = RFC->sn2; rn3 = RFC->sn3; rn4 = RFC->sn4; /* on positionne les pointeurs */ w4 = work1; w3 = w4+1; w2 = w3+1; w1 = w2+1; w0 = w1+1; d3 = in+1; d2 = d3+1; d1 = d2+1; d0 = d1+1; /*--- calcul de y+ ---*/ *(w4) = rp0 * *(in); *(w3) = rp0 * *(d3) + rp1 * *(in) - rd1 * *(w4); *(w2) = rp0 * *(d2) + rp1 * *(d3) + rp2 * *(in) - rd1 * *(w3) - rd2 * *(w4); *(w1) = rp0 * *(d1) + rp1 * *(d2) + rp2 * *(d3) + rp3 * *(in) - rd1 * *(w2) - rd2 * *(w3) - rd3 * *(w4); for (i=4; i=0; i--,w0--,w1--,w2--,w3--,w4--,d1--,d2--,d3--,d4--) *(w0) = rn1 * *(d1) + rn2 * *(d2) + rn3 * *(d3) + rn4 * *(d4) - rd1 * *(w1) - rd2 * *(w2) - rd3 * *(w3) - rd4 * *(w4); /*--- calcul final ---*/ w1 = work1; w2 = work2; d0 = out; for (i=0 ; iderivative ) { default : case DERIVATIVE_0 : case DERIVATIVE_2 : rp0 = RFC->sp0; rp1 = RFC->sp1; rd1 = RFC->sd1; rd2 = RFC->sd2; rn1 = RFC->sn1; rn2 = RFC->sn2; /* on positionne les pointeurs */ w2 = work1; w1 = w2+1; w0 = w1+1; d1 = in+1; d0 = d1+1; /*--- calcul de y+ ---*/ *(w2) = rp0 * *(in); *(w1) = rp0 * *(d1) + rp1 * *(in) - rd1 * *(w2); for (i=2; i=0; i--,w0--,w1--,w2--,d1--,d2--) *(w0) = rn1 * *(d1) + rn2 * *(d2) - rd1 * *(w1) - rd2 * *(w2); /*--- calcul final ---*/ w1 = work1; w2 = work2; d0 = out; for (i=0 ; isp1; rn1 = RFC->sn1; rd1 = RFC->sd1; rd2 = RFC->sd2; /* on positionne les pointeurs */ w2 = work1; w1 = w2+1; w0 = w1+1; d1 = in+1; /*--- calcul de y+ ---*/ *(w2) = 0.0; *(w1) = rp1 * *(in); for (i=2; i=0; i--,w0--,w1--,w2--,d1--) *(w0) = rn1 * *(d1) - rd1 * *(w1) - rd2 * *(w2); /*--- calcul final ---*/ w1 = work1; w2 = work2; d0 = out; for (i=0 ; isp0; rp1 = RFC->sp1; rd1 = RFC->sd1; rd2 = RFC->sd2; rn0 = RFC->sn0; rn1 = RFC->sn1; w2 = work1; w1 = w2+1; w0 = w1+1; d1 = in+1; d0 = d1+1; /*--- calcul de y+ ---*/ *(w2) = rp0 * *(in); *(w1) = rp0 * *(d1) + rp1 * *(in) - rd1 * *(w2); for (i=2; i=0; i--,w0--,w1--,w2--,d0--,d1--) *(w0) = rn0 * *(d0) + rn1 * *(d1) - rd1 * *(w1) - rd2 * *(w2); /*--- calcul final ---*/ w1 = work1; w2 = work2; d0 = out; for (i=0 ; i