cvc_linalg.h

/* cvc_linalg.h */

#ifndef _CVC_LINALG_H
#define _CVC_LINALG_H

#include <math.h>
#include "cvc_complex.h"
#include "types.h"

/*
 ********************

 The gamma matrices.

 Standard choice (as in gwc):

 gamma_0:

 |  0  0 -1  0 |
 |  0  0  0 -1 |
 | -1  0  0  0 |
 |  0 -1  0  0 |

 gamma_1:

 |  0  0  0 -i |
 |  0  0 -i  0 |
 |  0 +i  0  0 |
 | +i  0  0  0 |

 gamma_2:

 |  0  0  0 -1 |
 |  0  0 +1  0 |
 |  0 +1  0  0 |
 | -1  0  0  0 |

 gamma_3:

 |  0  0 -i  0 |
 |  0  0  0 +i |
 | +i  0  0  0 |
 |  0 -i  0  0 |

 Permutation of the eight elements of a spinor (re0, im0, re1, im1, ...).
*/

/********************/

/* A = 0. */

#define _cm_eq_zero(A) {\
  (A)[ 0] = 0.0; \
  (A)[ 1] = 0.0; \
  (A)[ 2] = 0.0; \
  (A)[ 3] = 0.0; \
  (A)[ 4] = 0.0; \
  (A)[ 5] = 0.0; \
  (A)[ 6] = 0.0; \
  (A)[ 7] = 0.0; \
  (A)[ 8] = 0.0; \
  (A)[ 9] = 0.0; \
  (A)[10] = 0.0; \
  (A)[11] = 0.0; \
  (A)[12] = 0.0; \
  (A)[13] = 0.0; \
  (A)[14] = 0.0; \
  (A)[15] = 0.0; \
  (A)[16] = 0.0; \
  (A)[17] = 0.0;}

/********************/

/* A = 1. */

#define _cm_eq_id(A) {\
  (A)[ 0] = 1.0; \
  (A)[ 1] = 0.0; \
  (A)[ 2] = 0.0; \
  (A)[ 3] = 0.0; \
  (A)[ 4] = 0.0; \
  (A)[ 5] = 0.0; \
  (A)[ 6] = 0.0; \
  (A)[ 7] = 0.0; \
  (A)[ 8] = 1.0; \
  (A)[ 9] = 0.0; \
  (A)[10] = 0.0; \
  (A)[11] = 0.0; \
  (A)[12] = 0.0; \
  (A)[13] = 0.0; \
  (A)[14] = 0.0; \
  (A)[15] = 0.0; \
  (A)[16] = 1.0; \
  (A)[17] = 0.0;}


/********************/

/* A = B. */

#define _cm_eq_cm(A,B) {\
  (A)[ 0] = (B)[ 0];\
  (A)[ 1] = (B)[ 1];\
  (A)[ 2] = (B)[ 2];\
  (A)[ 3] = (B)[ 3];\
  (A)[ 4] = (B)[ 4];\
  (A)[ 5] = (B)[ 5];\
  (A)[ 6] = (B)[ 6];\
  (A)[ 7] = (B)[ 7];\
  (A)[ 8] = (B)[ 8];\
  (A)[ 9] = (B)[ 9];\
  (A)[10] = (B)[10];\
  (A)[11] = (B)[11];\
  (A)[12] = (B)[12];\
  (A)[13] = (B)[13];\
  (A)[14] = (B)[14];\
  (A)[15] = (B)[15];\
  (A)[16] = (B)[16];\
  (A)[17] = (B)[17];}

/********************/

/* A = A + B. */

#define _cm_pl_eq_cm(A,B) {\
  (A)[ 0] += (B)[ 0];\
  (A)[ 1] += (B)[ 1];\
  (A)[ 2] += (B)[ 2];\
  (A)[ 3] += (B)[ 3];\
  (A)[ 4] += (B)[ 4];\
  (A)[ 5] += (B)[ 5];\
  (A)[ 6] += (B)[ 6];\
  (A)[ 7] += (B)[ 7];\
  (A)[ 8] += (B)[ 8];\
  (A)[ 9] += (B)[ 9];\
  (A)[10] += (B)[10];\
  (A)[11] += (B)[11];\
  (A)[12] += (B)[12];\
  (A)[13] += (B)[13];\
  (A)[14] += (B)[14];\
  (A)[15] += (B)[15];\
  (A)[16] += (B)[16];\
  (A)[17] += (B)[17];}

/*********************/



/* A = B^\dagger. */

#define _cm_eq_cm_dag(A,B) {\
  (A)[ 0] =  (B)[ 0];\
  (A)[ 1] = -(B)[ 1];\
  (A)[ 2] =  (B)[ 6];\
  (A)[ 3] = -(B)[ 7];\
  (A)[ 4] =  (B)[12];\
  (A)[ 5] = -(B)[13];\
  (A)[ 6] =  (B)[ 2];\
  (A)[ 7] = -(B)[ 3];\
  (A)[ 8] =  (B)[ 8];\
  (A)[ 9] = -(B)[ 9];\
  (A)[10] =  (B)[14];\
  (A)[11] = -(B)[15];\
  (A)[12] =  (B)[ 4];\
  (A)[13] = -(B)[ 5];\
  (A)[14] =  (B)[10];\
  (A)[15] = -(B)[11];\
  (A)[16] =  (B)[16];\
  (A)[17] = -(B)[17];}

/********************/

/* c = det(A). */

#define _co_eq_det_cm(c,A) {\
  (c)->re = \
    ((A)[ 0]*(A)[ 8]*(A)[16] - (A)[ 0]*(A)[ 9]*(A)[17] - (A)[ 1]*(A)[ 8]*(A)[17] - (A)[ 1]*(A)[ 9]*(A)[16]) +\
    ((A)[ 2]*(A)[10]*(A)[12] - (A)[ 2]*(A)[11]*(A)[13] - (A)[ 3]*(A)[10]*(A)[13] - (A)[ 3]*(A)[11]*(A)[12]) +\
    ((A)[ 4]*(A)[ 6]*(A)[14] - (A)[ 4]*(A)[ 7]*(A)[15] - (A)[ 5]*(A)[ 6]*(A)[15] - (A)[ 5]*(A)[ 7]*(A)[14]) -\
    ((A)[12]*(A)[ 8]*(A)[ 4] - (A)[12]*(A)[ 9]*(A)[ 5] - (A)[13]*(A)[ 8]*(A)[ 5] - (A)[13]*(A)[ 9]*(A)[ 4]) -\
    ((A)[14]*(A)[10]*(A)[ 0] - (A)[14]*(A)[11]*(A)[ 1] - (A)[15]*(A)[10]*(A)[ 1] - (A)[15]*(A)[11]*(A)[ 0]) -\
    ((A)[16]*(A)[ 6]*(A)[ 2] - (A)[16]*(A)[ 7]*(A)[ 3] - (A)[17]*(A)[ 6]*(A)[ 3] - (A)[17]*(A)[ 7]*(A)[ 2]);\
  (c)->im =\
    ((A)[ 1]*(A)[ 8]*(A)[16] + (A)[ 0]*(A)[ 9]*(A)[16] + (A)[ 0]*(A)[ 8]*(A)[17] - (A)[ 1]*(A)[ 9]*(A)[17]) +\
    ((A)[ 3]*(A)[10]*(A)[12] + (A)[ 2]*(A)[11]*(A)[12] + (A)[ 2]*(A)[10]*(A)[13] - (A)[ 3]*(A)[11]*(A)[13]) +\
    ((A)[ 5]*(A)[ 6]*(A)[14] + (A)[ 4]*(A)[ 7]*(A)[14] + (A)[ 4]*(A)[ 6]*(A)[15] - (A)[ 5]*(A)[ 7]*(A)[15]) -\
    ((A)[13]*(A)[ 8]*(A)[ 4] + (A)[12]*(A)[ 9]*(A)[ 4] + (A)[12]*(A)[ 8]*(A)[ 5] - (A)[13]*(A)[ 9]*(A)[ 5]) -\
    ((A)[15]*(A)[10]*(A)[ 0] + (A)[14]*(A)[11]*(A)[ 0] + (A)[14]*(A)[10]*(A)[ 1] - (A)[15]*(A)[11]*(A)[ 1]) -\
    ((A)[17]*(A)[ 6]*(A)[ 2] + (A)[16]*(A)[ 7]*(A)[ 2] + (A)[16]*(A)[ 6]*(A)[ 3] - (A)[17]*(A)[ 7]*(A)[ 3]);}

/********************/

/* c = tr(A). */

#define _co_eq_tr_cm(c,A) {\
  (c)->re = (A)[ 0] + (A)[ 8] + (A)[16];\
  (c)->im = (A)[ 1] + (A)[ 9] + (A)[17];}

/********************/

/* Prints A. */

#define _cm_fprintf(A,file) {\
  fprintf(file, "%+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I\n", \
	  (A)[ 0], (A)[ 1], (A)[ 2], (A)[ 3], (A)[ 4], (A)[ 5]);\
  fprintf(file, "%+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I\n",\
	  (A)[ 6], (A)[ 7], (A)[ 8], (A)[ 9], (A)[10], (A)[11]);\
  fprintf(file, "%+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I\n",\
	  (A)[12], (A)[13], (A)[14], (A)[15], (A)[16], (A)[17]);}

/********************/

/* A = B * d. */

#define _cm_eq_cm_ti_re(A,B,d) {\
  (A)[ 0] = (B)[ 0] * (d);\
  (A)[ 1] = (B)[ 1] * (d);\
  (A)[ 2] = (B)[ 2] * (d);\
  (A)[ 3] = (B)[ 3] * (d);\
  (A)[ 4] = (B)[ 4] * (d);\
  (A)[ 5] = (B)[ 5] * (d);\
  (A)[ 6] = (B)[ 6] * (d);\
  (A)[ 7] = (B)[ 7] * (d);\
  (A)[ 8] = (B)[ 8] * (d);\
  (A)[ 9] = (B)[ 9] * (d);\
  (A)[10] = (B)[10] * (d);\
  (A)[11] = (B)[11] * (d);\
  (A)[12] = (B)[12] * (d);\
  (A)[13] = (B)[13] * (d);\
  (A)[14] = (B)[14] * (d);\
  (A)[15] = (B)[15] * (d);\
  (A)[16] = (B)[16] * (d);\
  (A)[17] = (B)[17] * (d);}

/********************/

/* A = A * d. */

#define _cm_ti_eq_re(A,d) {\
  (A)[ 0] *= (d);\
  (A)[ 1] *= (d);\
  (A)[ 2] *= (d);\
  (A)[ 3] *= (d);\
  (A)[ 4] *= (d);\
  (A)[ 5] *= (d);\
  (A)[ 6] *= (d);\
  (A)[ 7] *= (d);\
  (A)[ 8] *= (d);\
  (A)[ 9] *= (d);\
  (A)[10] *= (d);\
  (A)[11] *= (d);\
  (A)[12] *= (d);\
  (A)[13] *= (d);\
  (A)[14] *= (d);\
  (A)[15] *= (d);\
  (A)[16] *= (d);\
  (A)[17] *= (d);}

/********************/

/* A = B * c. */

#define _cm_eq_cm_ti_co(A,B,c) {\
  (A)[ 0] = (B)[ 0] * (c)->re - (B)[ 1] * (c)->im;\
  (A)[ 1] = (B)[ 1] * (c)->re + (B)[ 0] * (c)->im;\
  (A)[ 2] = (B)[ 2] * (c)->re - (B)[ 3] * (c)->im;\
  (A)[ 3] = (B)[ 3] * (c)->re + (B)[ 2] * (c)->im;\
  (A)[ 4] = (B)[ 4] * (c)->re - (B)[ 5] * (c)->im;\
  (A)[ 5] = (B)[ 5] * (c)->re + (B)[ 4] * (c)->im;\
  (A)[ 6] = (B)[ 6] * (c)->re - (B)[ 7] * (c)->im;\
  (A)[ 7] = (B)[ 7] * (c)->re + (B)[ 6] * (c)->im;\
  (A)[ 8] = (B)[ 8] * (c)->re - (B)[ 9] * (c)->im;\
  (A)[ 9] = (B)[ 9] * (c)->re + (B)[ 8] * (c)->im;\
  (A)[10] = (B)[10] * (c)->re - (B)[11] * (c)->im;\
  (A)[11] = (B)[11] * (c)->re + (B)[10] * (c)->im;\
  (A)[12] = (B)[12] * (c)->re - (B)[13] * (c)->im;\
  (A)[13] = (B)[13] * (c)->re + (B)[12] * (c)->im;\
  (A)[14] = (B)[14] * (c)->re - (B)[15] * (c)->im;\
  (A)[15] = (B)[15] * (c)->re + (B)[14] * (c)->im;\
  (A)[16] = (B)[16] * (c)->re - (B)[17] * (c)->im;\
  (A)[17] = (B)[17] * (c)->re + (B)[16] * (c)->im;}


/********************/

/* A = B * C^\dagger. */

#define _cm_eq_cm_ti_cm_dag(A,B,C) {\
  /* A00 = B00*C00 + B01*C10 + B02*C20 */ \
  (A)[ 0] =\
    (B)[ 0]*(C)[ 0] + (B)[ 1]*(C)[ 1] +\
    (B)[ 2]*(C)[ 2] + (B)[ 3]*(C)[ 3] +\
    (B)[ 4]*(C)[ 4] + (B)[ 5]*(C)[ 5];\
  (A)[ 1] =\
    -(B)[ 0]*(C)[ 1] + (B)[ 1]*(C)[ 0] +\
    -(B)[ 2]*(C)[ 3] + (B)[ 3]*(C)[ 2] +\
    -(B)[ 4]*(C)[ 5] + (B)[ 5]*(C)[ 4];\
/* A01 = B00*C01 + B01*C11 + B02*C21 */\
  (A)[ 2] =\
    (B)[ 0]*(C)[ 6] + (B)[ 1]*(C)[ 7] +\
    (B)[ 2]*(C)[ 8] + (B)[ 3]*(C)[ 9] +\
    (B)[ 4]*(C)[10] + (B)[ 5]*(C)[11];\
  (A)[ 3] =\
    -(B)[ 0]*(C)[ 7] + (B)[ 1]*(C)[ 6] +\
    -(B)[ 2]*(C)[ 9] + (B)[ 3]*(C)[ 8] +\
    -(B)[ 4]*(C)[11] + (B)[ 5]*(C)[10];\
/* A02 = B00*C02 + B01*C12 + B02*C22 */\
  (A)[ 4] =\
    (B)[ 0]*(C)[12] + (B)[ 1]*(C)[13] +\
    (B)[ 2]*(C)[14] + (B)[ 3]*(C)[15] +\
    (B)[ 4]*(C)[16] + (B)[ 5]*(C)[17];\
  (A)[ 5] =\
    -(B)[ 0]*(C)[13] + (B)[ 1]*(C)[12] +\
    -(B)[ 2]*(C)[15] + (B)[ 3]*(C)[14] +\
    -(B)[ 4]*(C)[17] + (B)[ 5]*(C)[16];\
/* A10 = B10*C00 + B11*C10 + B12*C20 */\
  (A)[ 6] =\
    (B)[ 6]*(C)[ 0] + (B)[ 7]*(C)[ 1] +\
    (B)[ 8]*(C)[ 2] + (B)[ 9]*(C)[ 3] +\
    (B)[10]*(C)[ 4] + (B)[11]*(C)[ 5];\
  (A)[ 7] =\
    -(B)[ 6]*(C)[ 1] + (B)[ 7]*(C)[ 0] +\
    -(B)[ 8]*(C)[ 3] + (B)[ 9]*(C)[ 2] +\
    -(B)[10]*(C)[ 5] + (B)[11]*(C)[ 4];\
/* A11 = B10*C01 + B11*C11 + B12*C21 */\
  (A)[ 8] =\
    (B)[ 6]*(C)[ 6] + (B)[ 7]*(C)[ 7] +\
    (B)[ 8]*(C)[ 8] + (B)[ 9]*(C)[ 9] +\
    (B)[10]*(C)[10] + (B)[11]*(C)[11];\
  (A)[ 9] =\
    -(B)[ 6]*(C)[ 7] + (B)[ 7]*(C)[ 6] +\
    -(B)[ 8]*(C)[ 9] + (B)[ 9]*(C)[ 8] +\
    -(B)[10]*(C)[11] + (B)[11]*(C)[10];\
/* A12 = B10*C02 + B11*C12 + B12*C22 */\
  (A)[10] =\
    (B)[ 6]*(C)[12] + (B)[ 7]*(C)[13] +\
    (B)[ 8]*(C)[14] + (B)[ 9]*(C)[15] +\
    (B)[10]*(C)[16] + (B)[11]*(C)[17];\
  (A)[11] =\
    -(B)[ 6]*(C)[13] + (B)[ 7]*(C)[12] +\
    -(B)[ 8]*(C)[15] + (B)[ 9]*(C)[14] +\
    -(B)[10]*(C)[17] + (B)[11]*(C)[16];\
/* A20 = B20*C00 + B21*C10 + B22*C20 */\
  (A)[12] =\
    (B)[12]*(C)[ 0] + (B)[13]*(C)[ 1] +\
    (B)[14]*(C)[ 2] + (B)[15]*(C)[ 3] +\
    (B)[16]*(C)[ 4] + (B)[17]*(C)[ 5];\
  (A)[13] =\
    -(B)[12]*(C)[ 1] + (B)[13]*(C)[ 0] +\
    -(B)[14]*(C)[ 3] + (B)[15]*(C)[ 2] +\
    -(B)[16]*(C)[ 5] + (B)[17]*(C)[ 4];\
/* A21 = B20*C01 + B21*C11 + B22*C21 */\
  (A)[14] =\
    (B)[12]*(C)[ 6] + (B)[13]*(C)[ 7] +\
    (B)[14]*(C)[ 8] + (B)[15]*(C)[ 9] +\
    (B)[16]*(C)[10] + (B)[17]*(C)[11];\
  (A)[15] =\
    -(B)[12]*(C)[ 7] + (B)[13]*(C)[ 6] +\
    -(B)[14]*(C)[ 9] + (B)[15]*(C)[ 8] +\
    -(B)[16]*(C)[11] + (B)[17]*(C)[10];\
/* A22 = B20*C02 + B21*C12 + B22*C22 */\
  (A)[16] =\
    (B)[12]*(C)[12] + (B)[13]*(C)[13] +\
    (B)[14]*(C)[14] + (B)[15]*(C)[15] +\
    (B)[16]*(C)[16] + (B)[17]*(C)[17];\
  (A)[17] =\
    -(B)[12]*(C)[13] + (B)[13]*(C)[12] +\
    -(B)[14]*(C)[15] + (B)[15]*(C)[14] +\
    -(B)[16]*(C)[17] + (B)[17]*(C)[16];}


/********************/

#define _cm_eq_cm_ti_cm(A,B,C) {\
  /* A00 = B00*C00 + B01*C10 + B02*C20 */\
  (A)[ 0] =\
    (B)[ 0]*(C)[ 0] - (B)[ 1]*(C)[ 1] +\
    (B)[ 2]*(C)[ 6] - (B)[ 3]*(C)[ 7] +\
    (B)[ 4]*(C)[12] - (B)[ 5]*(C)[13];\
  (A)[ 1] =\
    (B)[ 0]*(C)[ 1] + (B)[ 1]*(C)[ 0] +\
    (B)[ 2]*(C)[ 7] + (B)[ 3]*(C)[ 6] +\
    (B)[ 4]*(C)[13] + (B)[ 5]*(C)[12];\
  /* A01 = B00*C01 + B01*C11 + B02*C21 */\
  (A)[ 2] =\
    (B)[ 0]*(C)[ 2] - (B)[ 1]*(C)[ 3] +\
    (B)[ 2]*(C)[ 8] - (B)[ 3]*(C)[ 9] +\
    (B)[ 4]*(C)[14] - (B)[ 5]*(C)[15];\
  (A)[ 3] =\
    (B)[ 0]*(C)[ 3] + (B)[ 1]*(C)[ 2] +\
    (B)[ 2]*(C)[ 9] + (B)[ 3]*(C)[ 8] +\
    (B)[ 4]*(C)[15] + (B)[ 5]*(C)[14];\
  /* A02 = B00*C02 + B01*C12 + B02*C22 */\
  (A)[ 4] =\
    (B)[ 0]*(C)[ 4] - (B)[ 1]*(C)[ 5] +\
    (B)[ 2]*(C)[10] - (B)[ 3]*(C)[11] +\
    (B)[ 4]*(C)[16] - (B)[ 5]*(C)[17];\
  (A)[ 5] =\
    (B)[ 0]*(C)[ 5] + (B)[ 1]*(C)[ 4] +\
    (B)[ 2]*(C)[11] + (B)[ 3]*(C)[10] +\
    (B)[ 4]*(C)[17] + (B)[ 5]*(C)[16];\
  /* A10 = B10*C00 + B11*C10 + B12*C20 */\
  (A)[ 6] =\
    (B)[ 6]*(C)[ 0] - (B)[ 7]*(C)[ 1] +\
    (B)[ 8]*(C)[ 6] - (B)[ 9]*(C)[ 7] +\
    (B)[10]*(C)[12] - (B)[11]*(C)[13];\
  (A)[ 7] =\
    (B)[ 6]*(C)[ 1] + (B)[ 7]*(C)[ 0] +\
    (B)[ 8]*(C)[ 7] + (B)[ 9]*(C)[ 6] +\
    (B)[10]*(C)[13] + (B)[11]*(C)[12];\
  /* A11 = B10*C01 + B11*C11 + B12*C21 */\
  (A)[ 8] =\
    (B)[ 6]*(C)[ 2] - (B)[ 7]*(C)[ 3] +\
    (B)[ 8]*(C)[ 8] - (B)[ 9]*(C)[ 9] +\
    (B)[10]*(C)[14] - (B)[11]*(C)[15];\
  (A)[ 9] =\
    (B)[ 6]*(C)[ 3] + (B)[ 7]*(C)[ 2] +\
    (B)[ 8]*(C)[ 9] + (B)[ 9]*(C)[ 8] +\
    (B)[10]*(C)[15] + (B)[11]*(C)[14];\
  /* A12 = B10*C02 + B11*C12 + B12*C22 */\
  (A)[10] =\
    (B)[ 6]*(C)[ 4] - (B)[ 7]*(C)[ 5] +\
    (B)[ 8]*(C)[10] - (B)[ 9]*(C)[11] +\
    (B)[10]*(C)[16] - (B)[11]*(C)[17];\
  (A)[11] =\
    (B)[ 6]*(C)[ 5] + (B)[ 7]*(C)[ 4] +\
    (B)[ 8]*(C)[11] + (B)[ 9]*(C)[10] +\
    (B)[10]*(C)[17] + (B)[11]*(C)[16];\
  /* A20 = B20*C00 + B21*C10 + B22*C20 */\
  (A)[12] =\
    (B)[12]*(C)[ 0] - (B)[13]*(C)[ 1] +\
    (B)[14]*(C)[ 6] - (B)[15]*(C)[ 7] +\
    (B)[16]*(C)[12] - (B)[17]*(C)[13];\
  (A)[13] =\
    (B)[12]*(C)[ 1] + (B)[13]*(C)[ 0] +\
    (B)[14]*(C)[ 7] + (B)[15]*(C)[ 6] +\
    (B)[16]*(C)[13] + (B)[17]*(C)[12];\
  /* A21 = B20*C01 + B21*C11 + B22*C21 */\
  (A)[14] =\
    (B)[12]*(C)[ 2] - (B)[13]*(C)[ 3] +\
    (B)[14]*(C)[ 8] - (B)[15]*(C)[ 9] +\
    (B)[16]*(C)[14] - (B)[17]*(C)[15];\
  (A)[15] =\
    (B)[12]*(C)[ 3] + (B)[13]*(C)[ 2] +\
    (B)[14]*(C)[ 9] + (B)[15]*(C)[ 8] +\
    (B)[16]*(C)[15] + (B)[17]*(C)[14];\
  /* A22 = B20*C02 + B21*C12 + B22*C22 */\
  (A)[16] =\
    (B)[12]*(C)[ 4] - (B)[13]*(C)[ 5] +\
    (B)[14]*(C)[10] - (B)[15]*(C)[11] +\
    (B)[16]*(C)[16] - (B)[17]*(C)[17];\
  (A)[17] =\
    (B)[12]*(C)[ 5] + (B)[13]*(C)[ 4] +\
    (B)[14]*(C)[11] + (B)[15]*(C)[10] +\
    (B)[16]*(C)[17] + (B)[17]*(C)[16];}


/********************/

/* A = B^\dagger * C. */

#define _cm_eq_cm_dag_ti_cm(A,B,C) {\
  /* A00 = B00*C00 + B01*C10 + B02*C20 */ \
  (A)[ 0] =\
    (B)[ 0]*(C)[ 0] + (B)[ 1]*(C)[ 1] +\
    (B)[ 6]*(C)[ 6] + (B)[ 7]*(C)[ 7] +\
    (B)[12]*(C)[12] + (B)[13]*(C)[13];\
  (A)[ 1] =\
    -(B)[ 1]*(C)[ 0] + (B)[ 0]*(C)[ 1] +\
    -(B)[ 7]*(C)[ 6] + (B)[ 6]*(C)[ 7] +\
    -(B)[13]*(C)[12] + (B)[12]*(C)[13];\
/* A01 = B00*C01 + B01*C11 + B02*C21 */\
  (A)[ 2] =\
    (B)[ 0]*(C)[ 2] + (B)[ 1]*(C)[ 3] +\
    (B)[ 6]*(C)[ 8] + (B)[ 7]*(C)[ 9] +\
    (B)[12]*(C)[14] + (B)[13]*(C)[15];\
  (A)[ 3] =\
    -(B)[ 1]*(C)[ 2] + (B)[ 0]*(C)[ 3] +\
    -(B)[ 7]*(C)[ 8] + (B)[ 6]*(C)[ 9] +\
    -(B)[13]*(C)[14] + (B)[12]*(C)[15];\
/* A02 = B00*C02 + B01*C12 + B02*C22 */\
  (A)[ 4] =\
    (B)[ 0]*(C)[ 4] + (B)[ 1]*(C)[ 5] +\
    (B)[ 6]*(C)[10] + (B)[ 7]*(C)[11] +\
    (B)[12]*(C)[16] + (B)[13]*(C)[17];\
  (A)[ 5] =\
    -(B)[ 1]*(C)[ 4] + (B)[ 0]*(C)[ 5] +\
    -(B)[ 7]*(C)[10] + (B)[ 6]*(C)[11] +\
    -(B)[13]*(C)[16] + (B)[12]*(C)[17];\
/* A10 = B10*C00 + B11*C10 + B12*C20 */\
  (A)[ 6] =\
    (B)[ 2]*(C)[ 0] + (B)[ 3]*(C)[ 1] +\
    (B)[ 8]*(C)[ 6] + (B)[ 9]*(C)[ 7] +\
    (B)[14]*(C)[12] + (B)[15]*(C)[13];\
  (A)[ 7] =\
    -(B)[ 3]*(C)[ 0] + (B)[ 2]*(C)[ 1] +\
    -(B)[ 9]*(C)[ 6] + (B)[ 8]*(C)[ 7] +\
    -(B)[15]*(C)[12] + (B)[14]*(C)[13];\
/* A11 = B10*C01 + B11*C11 + B12*C21 */\
  (A)[ 8] =\
    (B)[ 2]*(C)[ 2] + (B)[ 3]*(C)[ 3] +\
    (B)[ 8]*(C)[ 8] + (B)[ 9]*(C)[ 9] +\
    (B)[14]*(C)[14] + (B)[15]*(C)[15];\
  (A)[ 9] =\
    -(B)[ 3]*(C)[ 2] + (B)[ 2]*(C)[ 3] +\
    -(B)[ 9]*(C)[ 8] + (B)[ 8]*(C)[ 9] +\
    -(B)[15]*(C)[14] + (B)[14]*(C)[15];\
/* A12 = B10*C02 + B11*C12 + B12*C22 */\
  (A)[10] =\
    (B)[ 2]*(C)[ 4] + (B)[ 3]*(C)[ 5] +\
    (B)[ 8]*(C)[10] + (B)[ 9]*(C)[11] +\
    (B)[14]*(C)[16] + (B)[15]*(C)[17];\
  (A)[11] =\
    -(B)[ 3]*(C)[ 4] + (B)[ 2]*(C)[ 5] +\
    -(B)[ 9]*(C)[10] + (B)[ 8]*(C)[11] +\
    -(B)[15]*(C)[16] + (B)[14]*(C)[17];\
/* A20 = B20*C00 + B21*C10 + B22*C20 */\
  (A)[12] =\
    (B)[ 4]*(C)[ 0] + (B)[ 5]*(C)[ 1] +\
    (B)[10]*(C)[ 6] + (B)[11]*(C)[ 7] +\
    (B)[16]*(C)[12] + (B)[17]*(C)[13];\
  (A)[13] =\
    -(B)[ 5]*(C)[ 0] + (B)[ 4]*(C)[ 1] +\
    -(B)[11]*(C)[ 6] + (B)[10]*(C)[ 7] +\
    -(B)[17]*(C)[12] + (B)[16]*(C)[13];\
/* A21 = B20*C01 + B21*C11 + B22*C21 */\
  (A)[14] =\
    (B)[ 4]*(C)[ 2] + (B)[ 5]*(C)[ 3] +\
    (B)[10]*(C)[ 8] + (B)[11]*(C)[ 9] +\
    (B)[16]*(C)[14] + (B)[17]*(C)[15];\
  (A)[15] =\
    -(B)[ 5]*(C)[ 2] + (B)[ 4]*(C)[ 3] +\
    -(B)[11]*(C)[ 8] + (B)[10]*(C)[ 9] +\
    -(B)[17]*(C)[14] + (B)[16]*(C)[15];\
/* A22 = B20*C02 + B21*C12 + B22*C22 */\
  (A)[16] =\
    (B)[ 4]*(C)[ 4] + (B)[ 5]*(C)[ 5] +\
    (B)[10]*(C)[10] + (B)[11]*(C)[11] +\
    (B)[16]*(C)[16] + (B)[17]*(C)[17];\
  (A)[17] =\
    -(B)[ 5]*(C)[ 4] + (B)[ 4]*(C)[ 5] +\
    -(B)[11]*(C)[10] + (B)[10]*(C)[11] +\
    -(B)[17]*(C)[16] + (B)[16]*(C)[17];}

/*******************************/
/* methods for fermion vectors */
/*******************************/



/* s = 0. */

#define _fv_eq_zero(s) {\
  (s)[ 0] = 0.0;\
  (s)[ 1] = 0.0;\
  (s)[ 2] = 0.0;\
  (s)[ 3] = 0.0;\
  (s)[ 4] = 0.0;\
  (s)[ 5] = 0.0;\
  (s)[ 6] = 0.0;\
  (s)[ 7] = 0.0;\
  (s)[ 8] = 0.0;\
  (s)[ 9] = 0.0;\
  (s)[10] = 0.0;\
  (s)[11] = 0.0;\
  (s)[12] = 0.0;\
  (s)[13] = 0.0;\
  (s)[14] = 0.0;\
  (s)[15] = 0.0;\
  (s)[16] = 0.0;\
  (s)[17] = 0.0;\
  (s)[18] = 0.0;\
  (s)[19] = 0.0;\
  (s)[20] = 0.0;\
  (s)[21] = 0.0;\
  (s)[22] = 0.0;\
  (s)[23] = 0.0;}

/********************/



/* s = -s. */

#define _fv_mi(s) {\
  (s)[ 0] = -(s)[ 0];\
  (s)[ 1] = -(s)[ 1];\
  (s)[ 2] = -(s)[ 2];\
  (s)[ 3] = -(s)[ 3];\
  (s)[ 4] = -(s)[ 4];\
  (s)[ 5] = -(s)[ 5];\
  (s)[ 6] = -(s)[ 6];\
  (s)[ 7] = -(s)[ 7];\
  (s)[ 8] = -(s)[ 8];\
  (s)[ 9] = -(s)[ 9];\
  (s)[10] = -(s)[10];\
  (s)[11] = -(s)[11];\
  (s)[12] = -(s)[12];\
  (s)[13] = -(s)[13];\
  (s)[14] = -(s)[14];\
  (s)[15] = -(s)[15];\
  (s)[16] = -(s)[16];\
  (s)[17] = -(s)[17];\
  (s)[18] = -(s)[18];\
  (s)[19] = -(s)[19];\
  (s)[20] = -(s)[20];\
  (s)[21] = -(s)[21];\
  (s)[22] = -(s)[22];\
  (s)[23] = -(s)[23];}

/********************/

/* s = t. */

#define _fv_eq_fv(s,t) {\
  (s)[ 0] = (t)[ 0];\
  (s)[ 1] = (t)[ 1];\
  (s)[ 2] = (t)[ 2];\
  (s)[ 3] = (t)[ 3];\
  (s)[ 4] = (t)[ 4];\
  (s)[ 5] = (t)[ 5];\
  (s)[ 6] = (t)[ 6];\
  (s)[ 7] = (t)[ 7];\
  (s)[ 8] = (t)[ 8];\
  (s)[ 9] = (t)[ 9];\
  (s)[10] = (t)[10];\
  (s)[11] = (t)[11];\
  (s)[12] = (t)[12];\
  (s)[13] = (t)[13];\
  (s)[14] = (t)[14];\
  (s)[15] = (t)[15];\
  (s)[16] = (t)[16];\
  (s)[17] = (t)[17];\
  (s)[18] = (t)[18];\
  (s)[19] = (t)[19];\
  (s)[20] = (t)[20];\
  (s)[21] = (t)[21];\
  (s)[22] = (t)[22];\
  (s)[23] = (t)[23];}

/********************/



/* Prints s. */

#define _fv_fprintf(s,file) {\
  fprintf((file), "%+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I\n",\
	  (s)[ 0], (s)[ 1], (s)[ 2], (s)[ 3], (s)[ 4], (s)[ 5]);\
  fprintf((file), "%+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I\n",\
	  (s)[ 6], (s)[ 7], (s)[ 8], (s)[ 9], (s)[10], (s)[11]);\
  fprintf((file), "%+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I\n",\
	  (s)[12], (s)[13], (s)[14], (s)[15], (s)[16], (s)[17]);\
  fprintf((file), "%+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I   %+9.6lf %+9.6lf I\n",\
	  (s)[18], (s)[19], (s)[20], (s)[21], (s)[22], (s)[23]);}

/********************/

/* s^dagger * t. */

#define _co_eq_fv_dag_ti_fv(c,s,t) {\
  (c)->re = \
    (s)[ 0]*(t)[ 0] + (s)[ 1]*(t)[ 1] +\
    (s)[ 2]*(t)[ 2] + (s)[ 3]*(t)[ 3] +\
    (s)[ 4]*(t)[ 4] + (s)[ 5]*(t)[ 5] +\
    (s)[ 6]*(t)[ 6] + (s)[ 7]*(t)[ 7] +\
    (s)[ 8]*(t)[ 8] + (s)[ 9]*(t)[ 9] +\
    (s)[10]*(t)[10] + (s)[11]*(t)[11] +\
    (s)[12]*(t)[12] + (s)[13]*(t)[13] +\
    (s)[14]*(t)[14] + (s)[15]*(t)[15] +\
    (s)[16]*(t)[16] + (s)[17]*(t)[17] +\
    (s)[18]*(t)[18] + (s)[19]*(t)[19] +\
    (s)[20]*(t)[20] + (s)[21]*(t)[21] +\
    (s)[22]*(t)[22] + (s)[23]*(t)[23];\
  (c)->im =\
    (s)[ 0]*(t)[ 1] - (s)[ 1]*(t)[ 0] +\
    (s)[ 2]*(t)[ 3] - (s)[ 3]*(t)[ 2] +\
    (s)[ 4]*(t)[ 5] - (s)[ 5]*(t)[ 4] +\
    (s)[ 6]*(t)[ 7] - (s)[ 7]*(t)[ 6] +\
    (s)[ 8]*(t)[ 9] - (s)[ 9]*(t)[ 8] +\
    (s)[10]*(t)[11] - (s)[11]*(t)[10] +\
    (s)[12]*(t)[13] - (s)[13]*(t)[12] +\
    (s)[14]*(t)[15] - (s)[15]*(t)[14] +\
    (s)[16]*(t)[17] - (s)[17]*(t)[16] +\
    (s)[18]*(t)[19] - (s)[19]*(t)[18] +\
    (s)[20]*(t)[21] - (s)[21]*(t)[20] +\
    (s)[22]*(t)[23] - (s)[23]*(t)[22];}

  /********************/

#define _cm_eq_fv_trans_ti_fv(c,s,t) {\
  /* 0 0 */\
  (c)[ 0] = \
    (s)[ 0]*(t)[ 0] - (s)[ 1]*(t)[ 1] +\
    (s)[ 6]*(t)[ 6] - (s)[ 7]*(t)[ 7] +\
    (s)[12]*(t)[12] - (s)[13]*(t)[13] +\
    (s)[18]*(t)[18] - (s)[19]*(t)[19]; \
  (c)[ 1] = \
    (s)[ 0]*(t)[ 1] + (s)[ 1]*(t)[ 0] +\
    (s)[ 6]*(t)[ 7] + (s)[ 7]*(t)[ 6] +\
    (s)[12]*(t)[13] + (s)[13]*(t)[12] +\
    (s)[18]*(t)[19] + (s)[19]*(t)[18]; \
  /* 0 1 */\
  (c)[ 2] = \
    (s)[ 0]*(t)[ 2] - (s)[ 1]*(t)[ 3] +\
    (s)[ 6]*(t)[ 8] - (s)[ 7]*(t)[ 9] +\
    (s)[12]*(t)[14] - (s)[13]*(t)[15] +\
    (s)[18]*(t)[20] - (s)[19]*(t)[21]; \
  (c)[ 3] = \
    (s)[ 0]*(t)[ 3] + (s)[ 1]*(t)[ 2] +\
    (s)[ 6]*(t)[ 9] + (s)[ 7]*(t)[ 8] +\
    (s)[12]*(t)[15] + (s)[13]*(t)[14] +\
    (s)[18]*(t)[21] + (s)[19]*(t)[20]; \
  /* 0 2 */\
  (c)[ 4] = \
    (s)[ 0]*(t)[ 4] - (s)[ 1]*(t)[ 5] +\
    (s)[ 6]*(t)[10] - (s)[ 7]*(t)[11] +\
    (s)[12]*(t)[16] - (s)[13]*(t)[17] +\
    (s)[18]*(t)[22] - (s)[19]*(t)[23]; \
  (c)[ 5] = \
    (s)[ 0]*(t)[ 5] + (s)[ 1]*(t)[ 4] +\
    (s)[ 6]*(t)[11] + (s)[ 7]*(t)[10] +\
    (s)[12]*(t)[17] + (s)[13]*(t)[16] +\
    (s)[18]*(t)[23] + (s)[19]*(t)[22]; \
  /* 1 0 */\
  (c)[ 6] = \
    (s)[ 2]*(t)[ 0] - (s)[ 3]*(t)[ 1] +\
    (s)[ 8]*(t)[ 6] - (s)[ 9]*(t)[ 7] +\
    (s)[14]*(t)[12] - (s)[15]*(t)[13] +\
    (s)[20]*(t)[18] - (s)[21]*(t)[19]; \
  (c)[ 7] = \
    (s)[ 2]*(t)[ 1] + (s)[ 3]*(t)[ 0] +\
    (s)[ 8]*(t)[ 7] + (s)[ 9]*(t)[ 6] +\
    (s)[14]*(t)[13] + (s)[15]*(t)[12] +\
    (s)[20]*(t)[19] + (s)[21]*(t)[18]; \
  /* 1 1 */\
  (c)[ 8] =\
    (s)[ 2]*(t)[ 2] - (s)[ 3]*(t)[ 3] +\
    (s)[ 8]*(t)[ 8] - (s)[ 9]*(t)[ 9] +\
    (s)[14]*(t)[14] - (s)[15]*(t)[15] +\
    (s)[20]*(t)[20] - (s)[21]*(t)[21]; \
  (c)[ 9] =\
    (s)[ 2]*(t)[ 3] + (s)[ 3]*(t)[ 2] +\
    (s)[ 8]*(t)[ 9] + (s)[ 9]*(t)[ 8] +\
    (s)[14]*(t)[15] + (s)[15]*(t)[14] +\
    (s)[20]*(t)[21] + (s)[21]*(t)[20]; \
  /* 1 2 */\
  (c)[10] =\
    (s)[ 2]*(t)[ 4] - (s)[ 3]*(t)[ 5] +\
    (s)[ 8]*(t)[10] - (s)[ 9]*(t)[11] +\
    (s)[14]*(t)[16] - (s)[15]*(t)[17] +\
    (s)[20]*(t)[22] - (s)[21]*(t)[23]; \
  (c)[11] =\
    (s)[ 2]*(t)[ 5] + (s)[ 3]*(t)[ 4] +\
    (s)[ 8]*(t)[11] + (s)[ 9]*(t)[10] +\
    (s)[14]*(t)[17] + (s)[15]*(t)[16] +\
    (s)[20]*(t)[23] + (s)[21]*(t)[22]; \
  /* 2 0 */\
  (c)[12] = \
    (s)[ 4]*(t)[ 0] - (s)[ 5]*(t)[ 1] +\
    (s)[10]*(t)[ 6] - (s)[11]*(t)[ 7] +\
    (s)[16]*(t)[12] - (s)[17]*(t)[13] +\
    (s)[22]*(t)[18] - (s)[23]*(t)[19]; \
  (c)[13] = \
    (s)[ 4]*(t)[ 1] + (s)[ 5]*(t)[ 0] +\
    (s)[10]*(t)[ 7] + (s)[11]*(t)[ 6] +\
    (s)[16]*(t)[13] + (s)[17]*(t)[12] +\
    (s)[22]*(t)[19] + (s)[23]*(t)[18]; \
  /* 2 1 */\
  (c)[14] = \
    (s)[ 4]*(t)[ 2] - (s)[ 5]*(t)[ 3] +\
    (s)[10]*(t)[ 8] - (s)[11]*(t)[ 9] +\
    (s)[16]*(t)[14] - (s)[17]*(t)[15] +\
    (s)[22]*(t)[20] - (s)[23]*(t)[21]; \
  (c)[15] = \
    (s)[ 4]*(t)[ 3] + (s)[ 5]*(t)[ 2] +\
    (s)[10]*(t)[ 9] + (s)[11]*(t)[ 8] +\
    (s)[16]*(t)[15] + (s)[17]*(t)[14] +\
    (s)[22]*(t)[21] + (s)[23]*(t)[20]; \
  /* 2 2 */ \
  (c)[16] =\
    (s)[ 4]*(t)[ 4] - (s)[ 5]*(t)[ 5] +\
    (s)[10]*(t)[10] - (s)[11]*(t)[11] +\
    (s)[16]*(t)[16] - (s)[17]*(t)[17] +\
    (s)[22]*(t)[22] - (s)[23]*(t)[23]; \
  (c)[17] =\
    (s)[ 4]*(t)[ 5] + (s)[ 5]*(t)[ 4] +\
    (s)[10]*(t)[11] + (s)[11]*(t)[10] +\
    (s)[16]*(t)[17] + (s)[17]*(t)[16] +\
    (s)[22]*(t)[23] + (s)[23]*(t)[22]; }

  /********************/


/* s = t + u. */

#define _fv_eq_fv_pl_fv(s,t,u) {\
  (s)[ 0] = (t)[ 0] + (u)[ 0];\
  (s)[ 1] = (t)[ 1] + (u)[ 1];\
  (s)[ 2] = (t)[ 2] + (u)[ 2];\
  (s)[ 3] = (t)[ 3] + (u)[ 3];\
  (s)[ 4] = (t)[ 4] + (u)[ 4];\
  (s)[ 5] = (t)[ 5] + (u)[ 5];\
  (s)[ 6] = (t)[ 6] + (u)[ 6];\
  (s)[ 7] = (t)[ 7] + (u)[ 7];\
  (s)[ 8] = (t)[ 8] + (u)[ 8];\
  (s)[ 9] = (t)[ 9] + (u)[ 9];\
  (s)[10] = (t)[10] + (u)[10];\
  (s)[11] = (t)[11] + (u)[11];\
  (s)[12] = (t)[12] + (u)[12];\
  (s)[13] = (t)[13] + (u)[13];\
  (s)[14] = (t)[14] + (u)[14];\
  (s)[15] = (t)[15] + (u)[15];\
  (s)[16] = (t)[16] + (u)[16];\
  (s)[17] = (t)[17] + (u)[17];\
  (s)[18] = (t)[18] + (u)[18];\
  (s)[19] = (t)[19] + (u)[19];\
  (s)[20] = (t)[20] + (u)[20];\
  (s)[21] = (t)[21] + (u)[21];\
  (s)[22] = (t)[22] + (u)[22];\
  (s)[23] = (t)[23] + (u)[23];}

/********************/



/* s = t - u. */

#define _fv_eq_fv_mi_fv(s,t,u) {\
  (s)[ 0] = (t)[ 0] - (u)[ 0];\
  (s)[ 1] = (t)[ 1] - (u)[ 1];\
  (s)[ 2] = (t)[ 2] - (u)[ 2];\
  (s)[ 3] = (t)[ 3] - (u)[ 3];\
  (s)[ 4] = (t)[ 4] - (u)[ 4];\
  (s)[ 5] = (t)[ 5] - (u)[ 5];\
  (s)[ 6] = (t)[ 6] - (u)[ 6];\
  (s)[ 7] = (t)[ 7] - (u)[ 7];\
  (s)[ 8] = (t)[ 8] - (u)[ 8];\
  (s)[ 9] = (t)[ 9] - (u)[ 9];\
  (s)[10] = (t)[10] - (u)[10];\
  (s)[11] = (t)[11] - (u)[11];\
  (s)[12] = (t)[12] - (u)[12];\
  (s)[13] = (t)[13] - (u)[13];\
  (s)[14] = (t)[14] - (u)[14];\
  (s)[15] = (t)[15] - (u)[15];\
  (s)[16] = (t)[16] - (u)[16];\
  (s)[17] = (t)[17] - (u)[17];\
  (s)[18] = (t)[18] - (u)[18];\
  (s)[19] = (t)[19] - (u)[19];\
  (s)[20] = (t)[20] - (u)[20];\
  (s)[21] = (t)[21] - (u)[21];\
  (s)[22] = (t)[22] - (u)[22];\
  (s)[23] = (t)[23] - (u)[23];}

/********************/

/* s = s + t. */

#define _fv_pl_eq_fv(s,t) {\
  (s)[ 0] += (t)[ 0];\
  (s)[ 1] += (t)[ 1];\
  (s)[ 2] += (t)[ 2];\
  (s)[ 3] += (t)[ 3];\
  (s)[ 4] += (t)[ 4];\
  (s)[ 5] += (t)[ 5];\
  (s)[ 6] += (t)[ 6];\
  (s)[ 7] += (t)[ 7];\
  (s)[ 8] += (t)[ 8];\
  (s)[ 9] += (t)[ 9];\
  (s)[10] += (t)[10];\
  (s)[11] += (t)[11];\
  (s)[12] += (t)[12];\
  (s)[13] += (t)[13];\
  (s)[14] += (t)[14];\
  (s)[15] += (t)[15];\
  (s)[16] += (t)[16];\
  (s)[17] += (t)[17];\
  (s)[18] += (t)[18];\
  (s)[19] += (t)[19];\
  (s)[20] += (t)[20];\
  (s)[21] += (t)[21];\
  (s)[22] += (t)[22];\
  (s)[23] += (t)[23];}

  /********************/



/* s = s - t. */

#define _fv_mi_eq_fv(s,t) {\
  (s)[ 0] -= (t)[ 0];\
  (s)[ 1] -= (t)[ 1];\
  (s)[ 2] -= (t)[ 2];\
  (s)[ 3] -= (t)[ 3];\
  (s)[ 4] -= (t)[ 4];\
  (s)[ 5] -= (t)[ 5];\
  (s)[ 6] -= (t)[ 6];\
  (s)[ 7] -= (t)[ 7];\
  (s)[ 8] -= (t)[ 8];\
  (s)[ 9] -= (t)[ 9];\
  (s)[10] -= (t)[10];\
  (s)[11] -= (t)[11];\
  (s)[12] -= (t)[12];\
  (s)[13] -= (t)[13];\
  (s)[14] -= (t)[14];\
  (s)[15] -= (t)[15];\
  (s)[16] -= (t)[16];\
  (s)[17] -= (t)[17];\
  (s)[18] -= (t)[18];\
  (s)[19] -= (t)[19];\
  (s)[20] -= (t)[20];\
  (s)[21] -= (t)[21];\
  (s)[22] -= (t)[22];\
  (s)[23] -= (t)[23];}

  /********************/



/* s = t * d. */

#define _fv_eq_fv_ti_re(s,t,d) {\
  (s)[ 0] = (t)[ 0] * (d);\
  (s)[ 1] = (t)[ 1] * (d);\
  (s)[ 2] = (t)[ 2] * (d);\
  (s)[ 3] = (t)[ 3] * (d);\
  (s)[ 4] = (t)[ 4] * (d);\
  (s)[ 5] = (t)[ 5] * (d);\
  (s)[ 6] = (t)[ 6] * (d);\
  (s)[ 7] = (t)[ 7] * (d);\
  (s)[ 8] = (t)[ 8] * (d);\
  (s)[ 9] = (t)[ 9] * (d);\
  (s)[10] = (t)[10] * (d);\
  (s)[11] = (t)[11] * (d);\
  (s)[12] = (t)[12] * (d);\
  (s)[13] = (t)[13] * (d);\
  (s)[14] = (t)[14] * (d);\
  (s)[15] = (t)[15] * (d);\
  (s)[16] = (t)[16] * (d);\
  (s)[17] = (t)[17] * (d);\
  (s)[18] = (t)[18] * (d);\
  (s)[19] = (t)[19] * (d);\
  (s)[20] = (t)[20] * (d);\
  (s)[21] = (t)[21] * (d);\
  (s)[22] = (t)[22] * (d);\
  (s)[23] = (t)[23] * (d);}

/********************/

/* s = s * d. */

#define _fv_ti_eq_re(s,d) {\
  (s)[ 0] *= (d);\
  (s)[ 1] *= (d);\
  (s)[ 2] *= (d);\
  (s)[ 3] *= (d);\
  (s)[ 4] *= (d);\
  (s)[ 5] *= (d);\
  (s)[ 6] *= (d);\
  (s)[ 7] *= (d);\
  (s)[ 8] *= (d);\
  (s)[ 9] *= (d);\
  (s)[10] *= (d);\
  (s)[11] *= (d);\
  (s)[12] *= (d);\
  (s)[13] *= (d);\
  (s)[14] *= (d);\
  (s)[15] *= (d);\
  (s)[16] *= (d);\
  (s)[17] *= (d);\
  (s)[18] *= (d);\
  (s)[19] *= (d);\
  (s)[20] *= (d);\
  (s)[21] *= (d);\
  (s)[22] *= (d);\
  (s)[23] *= (d);}

/********************/

/* s = t * I*d */

#define _fv_eq_fv_ti_im(s,t,d) {\
  (s)[ 0] = -(t)[ 1] * (d);\
  (s)[ 1] =  (t)[ 0] * (d);\
  (s)[ 2] = -(t)[ 3] * (d);\
  (s)[ 3] =  (t)[ 2] * (d);\
  (s)[ 4] = -(t)[ 5] * (d);\
  (s)[ 5] =  (t)[ 4] * (d);\
  (s)[ 6] = -(t)[ 7] * (d);\
  (s)[ 7] =  (t)[ 6] * (d);\
  (s)[ 8] = -(t)[ 9] * (d);\
  (s)[ 9] =  (t)[ 8] * (d);\
  (s)[10] = -(t)[11] * (d);\
  (s)[11] =  (t)[10] * (d);\
  (s)[12] = -(t)[13] * (d);\
  (s)[13] =  (t)[12] * (d);\
  (s)[14] = -(t)[15] * (d);\
  (s)[15] =  (t)[14] * (d);\
  (s)[16] = -(t)[17] * (d);\
  (s)[17] =  (t)[16] * (d);\
  (s)[18] = -(t)[19] * (d);\
  (s)[19] =  (t)[18] * (d);\
  (s)[20] = -(t)[21] * (d);\
  (s)[21] =  (t)[20] * (d);\
  (s)[22] = -(t)[23] * (d);\
  (s)[23] =  (t)[22] * (d);}

/********************/

/* s = t * c. */

#define _fv_eq_fv_ti_co(s,t,c) {\
  (s)[ 0] = (t)[ 0] * (c)->re - (t)[ 1] * (c)->im;\
  (s)[ 1] = (t)[ 1] * (c)->re + (t)[ 0] * (c)->im;\
  (s)[ 2] = (t)[ 2] * (c)->re - (t)[ 3] * (c)->im;\
  (s)[ 3] = (t)[ 3] * (c)->re + (t)[ 2] * (c)->im;\
  (s)[ 4] = (t)[ 4] * (c)->re - (t)[ 5] * (c)->im;\
  (s)[ 5] = (t)[ 5] * (c)->re + (t)[ 4] * (c)->im;\
  (s)[ 6] = (t)[ 6] * (c)->re - (t)[ 7] * (c)->im;\
  (s)[ 7] = (t)[ 7] * (c)->re + (t)[ 6] * (c)->im;\
  (s)[ 8] = (t)[ 8] * (c)->re - (t)[ 9] * (c)->im;\
  (s)[ 9] = (t)[ 9] * (c)->re + (t)[ 8] * (c)->im;\
  (s)[10] = (t)[10] * (c)->re - (t)[11] * (c)->im;\
  (s)[11] = (t)[11] * (c)->re + (t)[10] * (c)->im;\
  (s)[12] = (t)[12] * (c)->re - (t)[13] * (c)->im;\
  (s)[13] = (t)[13] * (c)->re + (t)[12] * (c)->im;\
  (s)[14] = (t)[14] * (c)->re - (t)[15] * (c)->im;\
  (s)[15] = (t)[15] * (c)->re + (t)[14] * (c)->im;\
  (s)[16] = (t)[16] * (c)->re - (t)[17] * (c)->im;\
  (s)[17] = (t)[17] * (c)->re + (t)[16] * (c)->im;\
  (s)[18] = (t)[18] * (c)->re - (t)[19] * (c)->im;\
  (s)[19] = (t)[19] * (c)->re + (t)[18] * (c)->im;\
  (s)[20] = (t)[20] * (c)->re - (t)[21] * (c)->im;\
  (s)[21] = (t)[21] * (c)->re + (t)[20] * (c)->im;\
  (s)[22] = (t)[22] * (c)->re - (t)[23] * (c)->im;\
  (s)[23] = (t)[23] * (c)->re + (t)[22] * (c)->im;}

  /********************/

#define _fv_eq_fv_ti_co_conj(s,t,c) {\
  (s)[ 0] = (t)[ 0] * (c)->re + (t)[ 1] * (c)->im;\
  (s)[ 1] = (t)[ 1] * (c)->re - (t)[ 0] * (c)->im;\
  (s)[ 2] = (t)[ 2] * (c)->re + (t)[ 3] * (c)->im;\
  (s)[ 3] = (t)[ 3] * (c)->re - (t)[ 2] * (c)->im;\
  (s)[ 4] = (t)[ 4] * (c)->re + (t)[ 5] * (c)->im;\
  (s)[ 5] = (t)[ 5] * (c)->re - (t)[ 4] * (c)->im;\
  (s)[ 6] = (t)[ 6] * (c)->re + (t)[ 7] * (c)->im;\
  (s)[ 7] = (t)[ 7] * (c)->re - (t)[ 6] * (c)->im;\
  (s)[ 8] = (t)[ 8] * (c)->re + (t)[ 9] * (c)->im;\
  (s)[ 9] = (t)[ 9] * (c)->re - (t)[ 8] * (c)->im;\
  (s)[10] = (t)[10] * (c)->re + (t)[11] * (c)->im;\
  (s)[11] = (t)[11] * (c)->re - (t)[10] * (c)->im;\
  (s)[12] = (t)[12] * (c)->re + (t)[13] * (c)->im;\
  (s)[13] = (t)[13] * (c)->re - (t)[12] * (c)->im;\
  (s)[14] = (t)[14] * (c)->re + (t)[15] * (c)->im;\
  (s)[15] = (t)[15] * (c)->re - (t)[14] * (c)->im;\
  (s)[16] = (t)[16] * (c)->re + (t)[17] * (c)->im;\
  (s)[17] = (t)[17] * (c)->re - (t)[16] * (c)->im;\
  (s)[18] = (t)[18] * (c)->re + (t)[19] * (c)->im;\
  (s)[19] = (t)[19] * (c)->re - (t)[18] * (c)->im;\
  (s)[20] = (t)[20] * (c)->re + (t)[21] * (c)->im;\
  (s)[21] = (t)[21] * (c)->re - (t)[20] * (c)->im;\
  (s)[22] = (t)[22] * (c)->re + (t)[23] * (c)->im;\
  (s)[23] = (t)[23] * (c)->re - (t)[22] * (c)->im;}

  /********************/

/* s = A * t. */

#define _fv_eq_cm_ti_fv(s,A,t) {\
  /* s0 = U00*t0 + U01*t1 + U02*t2 */\
  (s)[ 0] =\
    (A)[ 0]*(t)[ 0] - (A)[ 1]*(t)[ 1] +\
    (A)[ 2]*(t)[ 2] - (A)[ 3]*(t)[ 3] +\
    (A)[ 4]*(t)[ 4] - (A)[ 5]*(t)[ 5];\
  (s)[ 1] =\
    (A)[ 0]*(t)[ 1] + (A)[ 1]*(t)[ 0] +\
    (A)[ 2]*(t)[ 3] + (A)[ 3]*(t)[ 2] +\
    (A)[ 4]*(t)[ 5] + (A)[ 5]*(t)[ 4];\
  /* s1 = U10*t0 + U11*t1 + U12*t2 */\
  (s)[ 2] =\
    (A)[ 6]*(t)[ 0] - (A)[ 7]*(t)[ 1] +\
    (A)[ 8]*(t)[ 2] - (A)[ 9]*(t)[ 3] +\
    (A)[10]*(t)[ 4] - (A)[11]*(t)[ 5];\
  (s)[ 3] =\
    (A)[ 6]*(t)[ 1] + (A)[ 7]*(t)[ 0] +\
    (A)[ 8]*(t)[ 3] + (A)[ 9]*(t)[ 2] +\
    (A)[10]*(t)[ 5] + (A)[11]*(t)[ 4];\
  /* s2 = U20*t0 + U21*t1 + U22*t2 */\
  (s)[ 4] =\
    (A)[12]*(t)[ 0] - (A)[13]*(t)[ 1] +\
    (A)[14]*(t)[ 2] - (A)[15]*(t)[ 3] +\
    (A)[16]*(t)[ 4] - (A)[17]*(t)[ 5];\
  (s)[ 5] =\
    (A)[12]*(t)[ 1] + (A)[13]*(t)[ 0] +\
    (A)[14]*(t)[ 3] + (A)[15]*(t)[ 2] +\
    (A)[16]*(t)[ 5] + (A)[17]*(t)[ 4];\
  /* s3 = U00*t3 + U01*t4 + U02*t5 */\
  (s)[ 6] =\
    (A)[ 0]*(t)[ 6] - (A)[ 1]*(t)[ 7] +\
    (A)[ 2]*(t)[ 8] - (A)[ 3]*(t)[ 9] +\
    (A)[ 4]*(t)[10] - (A)[ 5]*(t)[11];\
  (s)[ 7] =\
    (A)[ 0]*(t)[ 7] + (A)[ 1]*(t)[ 6] +\
    (A)[ 2]*(t)[ 9] + (A)[ 3]*(t)[ 8] +\
    (A)[ 4]*(t)[11] + (A)[ 5]*(t)[10];\
  /* s4 = U10*t3 + U11*t4 + U12*t5 */\
  (s)[ 8] =\
    (A)[ 6]*(t)[ 6] - (A)[ 7]*(t)[ 7] +\
    (A)[ 8]*(t)[ 8] - (A)[ 9]*(t)[ 9] +\
    (A)[10]*(t)[10] - (A)[11]*(t)[11];\
  (s)[ 9] =\
    (A)[ 6]*(t)[ 7] + (A)[ 7]*(t)[ 6] +\
    (A)[ 8]*(t)[ 9] + (A)[ 9]*(t)[ 8] +\
    (A)[10]*(t)[11] + (A)[11]*(t)[10];\
  /* s5 = U20*t3 + U21*t4 + U22*t5 */\
  (s)[10] =\
    (A)[12]*(t)[ 6] - (A)[13]*(t)[ 7] +\
    (A)[14]*(t)[ 8] - (A)[15]*(t)[ 9] +\
    (A)[16]*(t)[10] - (A)[17]*(t)[11];\
  (s)[11] =\
    (A)[12]*(t)[ 7] + (A)[13]*(t)[ 6] +\
    (A)[14]*(t)[ 9] + (A)[15]*(t)[ 8] +\
    (A)[16]*(t)[11] + (A)[17]*(t)[10];\
  /* s6 = U00*t6 + U01*t7 + U02*t8 */\
  (s)[12] =\
    (A)[ 0]*(t)[12] - (A)[ 1]*(t)[13] +\
    (A)[ 2]*(t)[14] - (A)[ 3]*(t)[15] +\
    (A)[ 4]*(t)[16] - (A)[ 5]*(t)[17];\
  (s)[13] =\
    (A)[ 0]*(t)[13] + (A)[ 1]*(t)[12] +\
    (A)[ 2]*(t)[15] + (A)[ 3]*(t)[14] +\
    (A)[ 4]*(t)[17] + (A)[ 5]*(t)[16];\
  /* s7 = U10*t6 + U11*t7 + U12*t8 */\
  (s)[14] =\
    (A)[ 6]*(t)[12] - (A)[ 7]*(t)[13] +\
    (A)[ 8]*(t)[14] - (A)[ 9]*(t)[15] +\
    (A)[10]*(t)[16] - (A)[11]*(t)[17];\
  (s)[15] =\
    (A)[ 6]*(t)[13] + (A)[ 7]*(t)[12] +\
    (A)[ 8]*(t)[15] + (A)[ 9]*(t)[14] +\
    (A)[10]*(t)[17] + (A)[11]*(t)[16];\
  /* s8 = U20*t6 + U21*t7 + U22*t8 */\
  (s)[16] =\
    (A)[12]*(t)[12] - (A)[13]*(t)[13] +\
    (A)[14]*(t)[14] - (A)[15]*(t)[15] +\
    (A)[16]*(t)[16] - (A)[17]*(t)[17];\
  (s)[17] =\
    (A)[12]*(t)[13] + (A)[13]*(t)[12] +\
    (A)[14]*(t)[15] + (A)[15]*(t)[14] +\
    (A)[16]*(t)[17] + (A)[17]*(t)[16];\
  /* s9 = U00*t9 + U01*t10 + U02*t11 */\
  (s)[18] =\
    (A)[ 0]*(t)[18] - (A)[ 1]*(t)[19] +\
    (A)[ 2]*(t)[20] - (A)[ 3]*(t)[21] +\
    (A)[ 4]*(t)[22] - (A)[ 5]*(t)[23];\
  (s)[19] =\
    (A)[ 0]*(t)[19] + (A)[ 1]*(t)[18] +\
    (A)[ 2]*(t)[21] + (A)[ 3]*(t)[20] +\
    (A)[ 4]*(t)[23] + (A)[ 5]*(t)[22];\
  /* s10 = U10*t9 + U11*t10 + U12*t11 */\
  (s)[20] =\
    (A)[ 6]*(t)[18] - (A)[ 7]*(t)[19] +\
    (A)[ 8]*(t)[20] - (A)[ 9]*(t)[21] +\
    (A)[10]*(t)[22] - (A)[11]*(t)[23];\
  (s)[21] =\
    (A)[ 6]*(t)[19] + (A)[ 7]*(t)[18] +\
    (A)[ 8]*(t)[21] + (A)[ 9]*(t)[20] +\
    (A)[10]*(t)[23] + (A)[11]*(t)[22];\
  /* s11 = U20*t9 + U21*t10 + U22*t11 */\
  (s)[22] =\
    (A)[12]*(t)[18] - (A)[13]*(t)[19] +\
    (A)[14]*(t)[20] - (A)[15]*(t)[21] +\
    (A)[16]*(t)[22] - (A)[17]*(t)[23];\
  (s)[23] =\
    (A)[12]*(t)[19] + (A)[13]*(t)[18] +\
    (A)[14]*(t)[21] + (A)[15]*(t)[20] +\
    (A)[16]*(t)[23] + (A)[17]*(t)[22];}

/********************/



/* s = A^\dagger * t. */

#define _fv_eq_cm_dag_ti_fv(s,A,t) {\
/* s0 = U00*t0 + U01*t1 + U02*t2 */\
  (s)[ 0] =\
    (A)[ 0]*(t)[ 0] + (A)[ 1]*(t)[ 1] +\
    (A)[ 6]*(t)[ 2] + (A)[ 7]*(t)[ 3] +\
    (A)[12]*(t)[ 4] + (A)[13]*(t)[ 5];\
  (s)[ 1] =\
    (A)[ 0]*(t)[ 1] - (A)[ 1]*(t)[ 0] +\
    (A)[ 6]*(t)[ 3] - (A)[ 7]*(t)[ 2] +\
    (A)[12]*(t)[ 5] - (A)[13]*(t)[ 4];\
/* s1 = U10*t0 + U11*t1 + U12*t2 */\
  (s)[ 2] =\
    (A)[ 2]*(t)[ 0] + (A)[ 3]*(t)[ 1] +\
    (A)[ 8]*(t)[ 2] + (A)[ 9]*(t)[ 3] +\
    (A)[14]*(t)[ 4] + (A)[15]*(t)[ 5];\
  (s)[ 3] =\
    (A)[ 2]*(t)[ 1] - (A)[ 3]*(t)[ 0] +\
    (A)[ 8]*(t)[ 3] - (A)[ 9]*(t)[ 2] +\
    (A)[14]*(t)[ 5] - (A)[15]*(t)[ 4];\
/* s2 = U20*t0 + U21*t1 + U22*t2 */\
  (s)[ 4] =\
    (A)[ 4]*(t)[ 0] + (A)[ 5]*(t)[ 1] +\
    (A)[10]*(t)[ 2] + (A)[11]*(t)[ 3] +\
    (A)[16]*(t)[ 4] + (A)[17]*(t)[ 5];\
  (s)[ 5] =\
    (A)[ 4]*(t)[ 1] - (A)[ 5]*(t)[ 0] +\
    (A)[10]*(t)[ 3] - (A)[11]*(t)[ 2] +\
    (A)[16]*(t)[ 5] - (A)[17]*(t)[ 4];\
/* s3 = U00*t3 + U01*t4 + U02*t5 */\
  (s)[ 6] =\
    (A)[ 0]*(t)[ 6] + (A)[ 1]*(t)[ 7] +\
    (A)[ 6]*(t)[ 8] + (A)[ 7]*(t)[ 9] +\
    (A)[12]*(t)[10] + (A)[13]*(t)[11];\
  (s)[ 7] =\
    (A)[ 0]*(t)[ 7] - (A)[ 1]*(t)[ 6] +\
    (A)[ 6]*(t)[ 9] - (A)[ 7]*(t)[ 8] +\
    (A)[12]*(t)[11] - (A)[13]*(t)[10];\
/* s4 = U10*t3 + U11*t4 + U12*t5 */\
  (s)[ 8] =\
    (A)[ 2]*(t)[ 6] + (A)[ 3]*(t)[ 7] +\
    (A)[ 8]*(t)[ 8] + (A)[ 9]*(t)[ 9] +\
    (A)[14]*(t)[10] + (A)[15]*(t)[11];\
  (s)[ 9] =\
    (A)[ 2]*(t)[ 7] - (A)[ 3]*(t)[ 6] +\
    (A)[ 8]*(t)[ 9] - (A)[ 9]*(t)[ 8] +\
    (A)[14]*(t)[11] - (A)[15]*(t)[10];\
/* s5 = U20*t3 + U21*t4 + U22*t5 */\
  (s)[10] =\
    (A)[ 4]*(t)[ 6] + (A)[ 5]*(t)[ 7] +\
    (A)[10]*(t)[ 8] + (A)[11]*(t)[ 9] +\
    (A)[16]*(t)[10] + (A)[17]*(t)[11];\
  (s)[11] =\
    (A)[ 4]*(t)[ 7] - (A)[ 5]*(t)[ 6] +\
    (A)[10]*(t)[ 9] - (A)[11]*(t)[ 8] +\
    (A)[16]*(t)[11] - (A)[17]*(t)[10];\
/* s6 = U00*t6 + U01*t7 + U02*t8 */\
  (s)[12] =\
    (A)[ 0]*(t)[12] + (A)[ 1]*(t)[13] +\
    (A)[ 6]*(t)[14] + (A)[ 7]*(t)[15] +\
    (A)[12]*(t)[16] + (A)[13]*(t)[17];\
  (s)[13] =\
    (A)[ 0]*(t)[13] - (A)[ 1]*(t)[12] +\
    (A)[ 6]*(t)[15] - (A)[ 7]*(t)[14] +\
    (A)[12]*(t)[17] - (A)[13]*(t)[16];\
/* s7 = U10*t6 + U11*t7 + U12*t8 */\
  (s)[14] =\
    (A)[ 2]*(t)[12] + (A)[ 3]*(t)[13] +\
    (A)[ 8]*(t)[14] + (A)[ 9]*(t)[15] +\
    (A)[14]*(t)[16] + (A)[15]*(t)[17];\
  (s)[15] =\
    (A)[ 2]*(t)[13] - (A)[ 3]*(t)[12] +\
    (A)[ 8]*(t)[15] - (A)[ 9]*(t)[14] +\
    (A)[14]*(t)[17] - (A)[15]*(t)[16];\
/* s8 = U20*t6 + U21*t7 + U22*t8 */\
  (s)[16] =\
    (A)[ 4]*(t)[12] + (A)[ 5]*(t)[13] +\
    (A)[10]*(t)[14] + (A)[11]*(t)[15] +\
    (A)[16]*(t)[16] + (A)[17]*(t)[17];\
  (s)[17] =\
    (A)[ 4]*(t)[13] - (A)[ 5]*(t)[12] +\
    (A)[10]*(t)[15] - (A)[11]*(t)[14] +\
    (A)[16]*(t)[17] - (A)[17]*(t)[16];\
/* s9 = U00*t9 + U01*t10 + U02*t11 */\
  (s)[18] =\
    (A)[ 0]*(t)[18] + (A)[ 1]*(t)[19] +\
    (A)[ 6]*(t)[20] + (A)[ 7]*(t)[21] +\
    (A)[12]*(t)[22] + (A)[13]*(t)[23];\
  (s)[19] =\
    (A)[ 0]*(t)[19] - (A)[ 1]*(t)[18] +\
    (A)[ 6]*(t)[21] - (A)[ 7]*(t)[20] +\
    (A)[12]*(t)[23] - (A)[13]*(t)[22];\
/* s10 = U10*t9 + U11*t10 + U12*t11 */\
  (s)[20] =\
    (A)[ 2]*(t)[18] + (A)[ 3]*(t)[19] +\
    (A)[ 8]*(t)[20] + (A)[ 9]*(t)[21] +\
    (A)[14]*(t)[22] + (A)[15]*(t)[23];\
  (s)[21] =\
    (A)[ 2]*(t)[19] - (A)[ 3]*(t)[18] +\
    (A)[ 8]*(t)[21] - (A)[ 9]*(t)[20] +\
    (A)[14]*(t)[23] - (A)[15]*(t)[22];\
/* s11 = U20*t9 + U21*t10 + U22*t11 */\
  (s)[22] =\
    (A)[ 4]*(t)[18] + (A)[ 5]*(t)[19] +\
    (A)[10]*(t)[20] + (A)[11]*(t)[21] +\
    (A)[16]*(t)[22] + (A)[17]*(t)[23];\
  (s)[23] =\
    (A)[ 4]*(t)[19] - (A)[ 5]*(t)[18] +\
    (A)[10]*(t)[21] - (A)[11]*(t)[20] +\
    (A)[16]*(t)[23] - (A)[17]*(t)[22];}




/********************/

/* s = gamma * t. */

#define _fv_eq_gamma_ti_fv(s,gamma_index,t) {\
  (s)[ 0] = (t)[gamma_permutation[(gamma_index)][ 0]] * gamma_sign[(gamma_index)][ 0];\
  (s)[ 1] = (t)[gamma_permutation[(gamma_index)][ 1]] * gamma_sign[(gamma_index)][ 1];\
  (s)[ 2] = (t)[gamma_permutation[(gamma_index)][ 2]] * gamma_sign[(gamma_index)][ 2];\
  (s)[ 3] = (t)[gamma_permutation[(gamma_index)][ 3]] * gamma_sign[(gamma_index)][ 3];\
  (s)[ 4] = (t)[gamma_permutation[(gamma_index)][ 4]] * gamma_sign[(gamma_index)][ 4];\
  (s)[ 5] = (t)[gamma_permutation[(gamma_index)][ 5]] * gamma_sign[(gamma_index)][ 5];\
  (s)[ 6] = (t)[gamma_permutation[(gamma_index)][ 6]] * gamma_sign[(gamma_index)][ 6];\
  (s)[ 7] = (t)[gamma_permutation[(gamma_index)][ 7]] * gamma_sign[(gamma_index)][ 7];\
  (s)[ 8] = (t)[gamma_permutation[(gamma_index)][ 8]] * gamma_sign[(gamma_index)][ 8];\
  (s)[ 9] = (t)[gamma_permutation[(gamma_index)][ 9]] * gamma_sign[(gamma_index)][ 9];\
  (s)[10] = (t)[gamma_permutation[(gamma_index)][10]] * gamma_sign[(gamma_index)][10];\
  (s)[11] = (t)[gamma_permutation[(gamma_index)][11]] * gamma_sign[(gamma_index)][11];\
  (s)[12] = (t)[gamma_permutation[(gamma_index)][12]] * gamma_sign[(gamma_index)][12];\
  (s)[13] = (t)[gamma_permutation[(gamma_index)][13]] * gamma_sign[(gamma_index)][13];\
  (s)[14] = (t)[gamma_permutation[(gamma_index)][14]] * gamma_sign[(gamma_index)][14];\
  (s)[15] = (t)[gamma_permutation[(gamma_index)][15]] * gamma_sign[(gamma_index)][15];\
  (s)[16] = (t)[gamma_permutation[(gamma_index)][16]] * gamma_sign[(gamma_index)][16];\
  (s)[17] = (t)[gamma_permutation[(gamma_index)][17]] * gamma_sign[(gamma_index)][17];\
  (s)[18] = (t)[gamma_permutation[(gamma_index)][18]] * gamma_sign[(gamma_index)][18];\
  (s)[19] = (t)[gamma_permutation[(gamma_index)][19]] * gamma_sign[(gamma_index)][19];\
  (s)[20] = (t)[gamma_permutation[(gamma_index)][20]] * gamma_sign[(gamma_index)][20];\
  (s)[21] = (t)[gamma_permutation[(gamma_index)][21]] * gamma_sign[(gamma_index)][21];\
  (s)[22] = (t)[gamma_permutation[(gamma_index)][22]] * gamma_sign[(gamma_index)][22];\
  (s)[23] = (t)[gamma_permutation[(gamma_index)][23]] * gamma_sign[(gamma_index)][23];}

/*************************************************/

#define _fv_PRe_eq_fv(s) {\
  (s)[12] = 0.;\
  (s)[13] = 0.;\
  (s)[14] = 0.;\
  (s)[15] = 0.;\
  (s)[16] = 0.;\
  (s)[17] = 0.;\
  (s)[18] = 0.;\
  (s)[19] = 0.;\
  (s)[20] = 0.;\
  (s)[21] = 0.;\
  (s)[22] = 0.;\
  (s)[23] = 0.;}

/****************************************/

#define _fv_pl_eq_PRe_fv(s, t) {\
  (s)[ 0] += (t)[ 0];\
  (s)[ 1] += (t)[ 1];\
  (s)[ 2] += (t)[ 2];\
  (s)[ 3] += (t)[ 3];\
  (s)[ 4] += (t)[ 4];\
  (s)[ 5] += (t)[ 5];\
  (s)[ 6] += (t)[ 6];\
  (s)[ 7] += (t)[ 7];\
  (s)[ 8] += (t)[ 8];\
  (s)[ 9] += (t)[ 9];\
  (s)[10] += (t)[10];\
  (s)[11] += (t)[11];}

/****************************************/

#define _fv_mi_eq_PRe_fv(s, t) {\
  (s)[ 0] -= (t)[ 0];\
  (s)[ 1] -= (t)[ 1];\
  (s)[ 2] -= (t)[ 2];\
  (s)[ 3] -= (t)[ 3];\
  (s)[ 4] -= (t)[ 4];\
  (s)[ 5] -= (t)[ 5];\
  (s)[ 6] -= (t)[ 6];\
  (s)[ 7] -= (t)[ 7];\
  (s)[ 8] -= (t)[ 8];\
  (s)[ 9] -= (t)[ 9];\
  (s)[10] -= (t)[10];\
  (s)[11] -= (t)[11];}

/****************************************/

#define _fv_pl_eq_PRe_fv_ti_re(s, t, r) {\
  (s)[ 0] += (r)*(t)[ 0];\
  (s)[ 1] += (r)*(t)[ 1];\
  (s)[ 2] += (r)*(t)[ 2];\
  (s)[ 3] += (r)*(t)[ 3];\
  (s)[ 4] += (r)*(t)[ 4];\
  (s)[ 5] += (r)*(t)[ 5];\
  (s)[ 6] += (r)*(t)[ 6];\
  (s)[ 7] += (r)*(t)[ 7];\
  (s)[ 8] += (r)*(t)[ 8];\
  (s)[ 9] += (r)*(t)[ 9];\
  (s)[10] += (r)*(t)[10];\
  (s)[11] += (r)*(t)[11];}

/****************************************/

#define _fv_eq_PRe_fv(s, t) {\
  (s)[ 0] = (t)[ 0];\
  (s)[ 1] = (t)[ 1];\
  (s)[ 2] = (t)[ 2];\
  (s)[ 3] = (t)[ 3];\
  (s)[ 4] = (t)[ 4];\
  (s)[ 5] = (t)[ 5];\
  (s)[ 6] = (t)[ 6];\
  (s)[ 7] = (t)[ 7];\
  (s)[ 8] = (t)[ 8];\
  (s)[ 9] = (t)[ 9];\
  (s)[10] = (t)[10];\
  (s)[11] = (t)[11];\
  (s)[12] = 0.;\
  (s)[13] = 0.;\
  (s)[14] = 0.;\
  (s)[15] = 0.;\
  (s)[16] = 0.;\
  (s)[17] = 0.;\
  (s)[18] = 0.;\
  (s)[19] = 0.;\
  (s)[20] = 0.;\
  (s)[21] = 0.;\
  (s)[22] = 0.;\
  (s)[23] = 0.;}

/****************************************/

#define _fv_PLi_eq_fv(s) {\
  (s)[ 0] = 0.;\
  (s)[ 1] = 0.;\
  (s)[ 2] = 0.;\
  (s)[ 3] = 0.;\
  (s)[ 4] = 0.;\
  (s)[ 5] = 0.;\
  (s)[ 6] = 0.;\
  (s)[ 7] = 0.;\
  (s)[ 8] = 0.;\
  (s)[ 9] = 0.;\
  (s)[10] = 0.;\
  (s)[11] = 0.;}

/****************************************/

#define _fv_pl_eq_PLi_fv(s, t) {\
  (s)[12] += (t)[12];\
  (s)[13] += (t)[13];\
  (s)[14] += (t)[14];\
  (s)[15] += (t)[15];\
  (s)[16] += (t)[16];\
  (s)[17] += (t)[17];\
  (s)[18] += (t)[18];\
  (s)[19] += (t)[19];\
  (s)[20] += (t)[20];\
  (s)[21] += (t)[21];\
  (s)[22] += (t)[22];\
  (s)[23] += (t)[23];}

/****************************************/

#define _fv_mi_eq_PLi_fv(s, t) {\
  (s)[12] -= (t)[12];\
  (s)[13] -= (t)[13];\
  (s)[14] -= (t)[14];\
  (s)[15] -= (t)[15];\
  (s)[16] -= (t)[16];\
  (s)[17] -= (t)[17];\
  (s)[18] -= (t)[18];\
  (s)[19] -= (t)[19];\
  (s)[20] -= (t)[20];\
  (s)[21] -= (t)[21];\
  (s)[22] -= (t)[22];\
  (s)[23] -= (t)[23];}

/****************************************/

#define _fv_pl_eq_PLi_fv_ti_re(s, t, r) {\
  (s)[12] += (r)*(t)[12];\
  (s)[13] += (r)*(t)[13];\
  (s)[14] += (r)*(t)[14];\
  (s)[15] += (r)*(t)[15];\
  (s)[16] += (r)*(t)[16];\
  (s)[17] += (r)*(t)[17];\
  (s)[18] += (r)*(t)[18];\
  (s)[19] += (r)*(t)[19];\
  (s)[20] += (r)*(t)[20];\
  (s)[21] += (r)*(t)[21];\
  (s)[22] += (r)*(t)[22];\
  (s)[23] += (r)*(t)[23];}

/****************************************/

#define _fv_eq_PLi_fv(s, t) {\
  (s)[ 0] = 0.;\
  (s)[ 1] = 0.;\
  (s)[ 2] = 0.;\
  (s)[ 3] = 0.;\
  (s)[ 4] = 0.;\
  (s)[ 5] = 0.;\
  (s)[ 6] = 0.;\
  (s)[ 7] = 0.;\
  (s)[ 8] = 0.;\
  (s)[ 9] = 0.;\
  (s)[10] = 0.;\
  (s)[11] = 0.;\
  (s)[12] = (t)[12];\
  (s)[13] = (t)[13];\
  (s)[14] = (t)[14];\
  (s)[15] = (t)[15];\
  (s)[16] = (t)[16];\
  (s)[17] = (t)[17];\
  (s)[18] = (t)[18];\
  (s)[19] = (t)[19];\
  (s)[20] = (t)[20];\
  (s)[21] = (t)[21];\
  (s)[22] = (t)[22];\
  (s)[23] = (t)[23];}

/****************************************/

/* s = gamma^T * t (transposed of gamma) */

#define _fv_eq_gamma_transposed_ti_fv(_s ,_gamma_index,_t) {\
  (_s)[ 0] = (_t)[gamma_permutation[(_gamma_index)][ 0]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 1]];\
  (_s)[ 1] = (_t)[gamma_permutation[(_gamma_index)][ 1]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 0]];\
  (_s)[ 2] = (_t)[gamma_permutation[(_gamma_index)][ 2]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 3]];\
  (_s)[ 3] = (_t)[gamma_permutation[(_gamma_index)][ 3]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 2]];\
  (_s)[ 4] = (_t)[gamma_permutation[(_gamma_index)][ 4]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 5]];\
  (_s)[ 5] = (_t)[gamma_permutation[(_gamma_index)][ 5]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 4]];\
  (_s)[ 6] = (_t)[gamma_permutation[(_gamma_index)][ 6]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 7]];\
  (_s)[ 7] = (_t)[gamma_permutation[(_gamma_index)][ 7]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 6]];\
  (_s)[ 8] = (_t)[gamma_permutation[(_gamma_index)][ 8]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 9]];\
  (_s)[ 9] = (_t)[gamma_permutation[(_gamma_index)][ 9]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][ 8]];\
  (_s)[10] = (_t)[gamma_permutation[(_gamma_index)][10]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][11]];\
  (_s)[11] = (_t)[gamma_permutation[(_gamma_index)][11]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][10]];\
  (_s)[12] = (_t)[gamma_permutation[(_gamma_index)][12]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][13]];\
  (_s)[13] = (_t)[gamma_permutation[(_gamma_index)][13]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][12]];\
  (_s)[14] = (_t)[gamma_permutation[(_gamma_index)][14]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][15]];\
  (_s)[15] = (_t)[gamma_permutation[(_gamma_index)][15]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][14]];\
  (_s)[16] = (_t)[gamma_permutation[(_gamma_index)][16]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][17]];\
  (_s)[17] = (_t)[gamma_permutation[(_gamma_index)][17]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][16]];\
  (_s)[18] = (_t)[gamma_permutation[(_gamma_index)][18]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][19]];\
  (_s)[19] = (_t)[gamma_permutation[(_gamma_index)][19]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][18]];\
  (_s)[20] = (_t)[gamma_permutation[(_gamma_index)][20]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][21]];\
  (_s)[21] = (_t)[gamma_permutation[(_gamma_index)][21]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][20]];\
  (_s)[22] = (_t)[gamma_permutation[(_gamma_index)][22]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][23]];\
  (_s)[23] = (_t)[gamma_permutation[(_gamma_index)][23]] * gamma_sign[(_gamma_index)][gamma_permutation[(_gamma_index)][22]];\
}

/********************/

#define _co_eq_tr_gammaU_sm(_w, _mu, _g, _C) {\
  (_w)->re =\
       /* first spinor component */\
         gamma_sign[(_mu)][ 0] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 0]/2)%3)  ] * (_C)[0][gamma_permutation[(_mu)][ 0]]\
       - gamma_sign[(_mu)][ 1] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 1]/2)%3)+1] * (_C)[0][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 2] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 2]/2)%3)  ] * (_C)[0][gamma_permutation[(_mu)][ 2]]\
       - gamma_sign[(_mu)][ 3] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 3]/2)%3)+1] * (_C)[0][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 4] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 4]/2)%3)  ] * (_C)[0][gamma_permutation[(_mu)][ 4]]\
       - gamma_sign[(_mu)][ 5] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 5]/2)%3)+1] * (_C)[0][gamma_permutation[(_mu)][ 5]]\
       + gamma_sign[(_mu)][ 0] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 0]/2)%3)  ] * (_C)[1][gamma_permutation[(_mu)][ 0]]\
       - gamma_sign[(_mu)][ 1] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 1]/2)%3)+1] * (_C)[1][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 2] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 2]/2)%3)  ] * (_C)[1][gamma_permutation[(_mu)][ 2]]\
       - gamma_sign[(_mu)][ 3] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 3]/2)%3)+1] * (_C)[1][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 4] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 4]/2)%3)  ] * (_C)[1][gamma_permutation[(_mu)][ 4]]\
       - gamma_sign[(_mu)][ 5] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 5]/2)%3)+1] * (_C)[1][gamma_permutation[(_mu)][ 5]]\
       + gamma_sign[(_mu)][ 0] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 0]/2)%3)  ] * (_C)[2][gamma_permutation[(_mu)][ 0]]\
       - gamma_sign[(_mu)][ 1] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 1]/2)%3)+1] * (_C)[2][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 2] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 2]/2)%3)  ] * (_C)[2][gamma_permutation[(_mu)][ 2]]\
       - gamma_sign[(_mu)][ 3] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 3]/2)%3)+1] * (_C)[2][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 4] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 4]/2)%3)  ] * (_C)[2][gamma_permutation[(_mu)][ 4]]\
       - gamma_sign[(_mu)][ 5] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 5]/2)%3)+1] * (_C)[2][gamma_permutation[(_mu)][ 5]]\
       /* second spinor component */\
       + gamma_sign[(_mu)][ 6] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 6]/2)%3)  ] * (_C)[3][gamma_permutation[(_mu)][ 6]]\
       - gamma_sign[(_mu)][ 7] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 7]/2)%3)+1] * (_C)[3][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 8] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 8]/2)%3)  ] * (_C)[3][gamma_permutation[(_mu)][ 8]]\
       - gamma_sign[(_mu)][ 9] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 9]/2)%3)+1] * (_C)[3][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][10] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][10]/2)%3)  ] * (_C)[3][gamma_permutation[(_mu)][10]]\
       - gamma_sign[(_mu)][11] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][11]/2)%3)+1] * (_C)[3][gamma_permutation[(_mu)][11]]\
       + gamma_sign[(_mu)][ 6] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 6]/2)%3)  ] * (_C)[4][gamma_permutation[(_mu)][ 6]]\
       - gamma_sign[(_mu)][ 7] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 7]/2)%3)+1] * (_C)[4][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 8] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 8]/2)%3)  ] * (_C)[4][gamma_permutation[(_mu)][ 8]]\
       - gamma_sign[(_mu)][ 9] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 9]/2)%3)+1] * (_C)[4][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][10] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][10]/2)%3)  ] * (_C)[4][gamma_permutation[(_mu)][10]]\
       - gamma_sign[(_mu)][11] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][11]/2)%3)+1] * (_C)[4][gamma_permutation[(_mu)][11]]\
       + gamma_sign[(_mu)][ 6] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 6]/2)%3)  ] * (_C)[5][gamma_permutation[(_mu)][ 6]]\
       - gamma_sign[(_mu)][ 7] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 7]/2)%3)+1] * (_C)[5][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 8] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 8]/2)%3)  ] * (_C)[5][gamma_permutation[(_mu)][ 8]]\
       - gamma_sign[(_mu)][ 9] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 9]/2)%3)+1] * (_C)[5][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][10] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][10]/2)%3)  ] * (_C)[5][gamma_permutation[(_mu)][10]]\
       - gamma_sign[(_mu)][11] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][11]/2)%3)+1] * (_C)[5][gamma_permutation[(_mu)][11]]\
       /* third spinor component */\
       + gamma_sign[(_mu)][12] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][12]/2)%3)  ] * (_C)[6][gamma_permutation[(_mu)][12]]\
       - gamma_sign[(_mu)][13] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][13]/2)%3)+1] * (_C)[6][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][14] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][14]/2)%3)  ] * (_C)[6][gamma_permutation[(_mu)][14]]\
       - gamma_sign[(_mu)][15] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][15]/2)%3)+1] * (_C)[6][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][16] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][16]/2)%3)  ] * (_C)[6][gamma_permutation[(_mu)][16]]\
       - gamma_sign[(_mu)][17] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][17]/2)%3)+1] * (_C)[6][gamma_permutation[(_mu)][17]]\
       + gamma_sign[(_mu)][12] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][12]/2)%3)  ] * (_C)[7][gamma_permutation[(_mu)][12]]\
       - gamma_sign[(_mu)][13] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][13]/2)%3)+1] * (_C)[7][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][14] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][14]/2)%3)  ] * (_C)[7][gamma_permutation[(_mu)][14]]\
       - gamma_sign[(_mu)][15] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][15]/2)%3)+1] * (_C)[7][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][16] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][16]/2)%3)  ] * (_C)[7][gamma_permutation[(_mu)][16]]\
       - gamma_sign[(_mu)][17] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][17]/2)%3)+1] * (_C)[7][gamma_permutation[(_mu)][17]]\
       + gamma_sign[(_mu)][12] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][12]/2)%3)  ] * (_C)[8][gamma_permutation[(_mu)][12]]\
       - gamma_sign[(_mu)][13] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][13]/2)%3)+1] * (_C)[8][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][14] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][14]/2)%3)  ] * (_C)[8][gamma_permutation[(_mu)][14]]\
       - gamma_sign[(_mu)][15] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][15]/2)%3)+1] * (_C)[8][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][16] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][16]/2)%3)  ] * (_C)[8][gamma_permutation[(_mu)][16]]\
       - gamma_sign[(_mu)][17] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][17]/2)%3)+1] * (_C)[8][gamma_permutation[(_mu)][17]]\
       /* third spinor component */\
       + gamma_sign[(_mu)][18] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][18]/2)%3)  ] * (_C)[9][gamma_permutation[(_mu)][18]]\
       - gamma_sign[(_mu)][19] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][19]/2)%3)+1] * (_C)[9][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][20] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][20]/2)%3)  ] * (_C)[9][gamma_permutation[(_mu)][20]]\
       - gamma_sign[(_mu)][21] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][21]/2)%3)+1] * (_C)[9][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][22] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][22]/2)%3)  ] * (_C)[9][gamma_permutation[(_mu)][22]]\
       - gamma_sign[(_mu)][23] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][23]/2)%3)+1] * (_C)[9][gamma_permutation[(_mu)][23]]\
       + gamma_sign[(_mu)][18] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][18]/2)%3)  ] * (_C)[10][gamma_permutation[(_mu)][18]]\
       - gamma_sign[(_mu)][19] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][19]/2)%3)+1] * (_C)[10][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][20] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][20]/2)%3)  ] * (_C)[10][gamma_permutation[(_mu)][20]]\
       - gamma_sign[(_mu)][21] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][21]/2)%3)+1] * (_C)[10][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][22] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][22]/2)%3)  ] * (_C)[10][gamma_permutation[(_mu)][22]]\
       - gamma_sign[(_mu)][23] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][23]/2)%3)+1] * (_C)[10][gamma_permutation[(_mu)][23]]\
       + gamma_sign[(_mu)][18] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][18]/2)%3)  ] * (_C)[11][gamma_permutation[(_mu)][18]]\
       - gamma_sign[(_mu)][19] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][19]/2)%3)+1] * (_C)[11][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][20] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][20]/2)%3)  ] * (_C)[11][gamma_permutation[(_mu)][20]]\
       - gamma_sign[(_mu)][21] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][21]/2)%3)+1] * (_C)[11][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][22] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][22]/2)%3)  ] * (_C)[11][gamma_permutation[(_mu)][22]]\
       - gamma_sign[(_mu)][23] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][23]/2)%3)+1] * (_C)[11][gamma_permutation[(_mu)][23]];\
\
  (_w)->im = \
       /* first spinor component */\
         gamma_sign[(_mu)][ 0] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 1]/2)%3)+1] * (_C)[0][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 1] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 0]/2)%3)  ] * (_C)[0][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 2] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 3]/2)%3)+1] * (_C)[0][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 3] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 2]/2)%3)  ] * (_C)[0][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 4] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 5]/2)%3)+1] * (_C)[0][gamma_permutation[(_mu)][ 4]]\
       + gamma_sign[(_mu)][ 5] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 4]/2)%3)  ] * (_C)[0][gamma_permutation[(_mu)][ 5]]\
       + gamma_sign[(_mu)][ 0] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 1]/2)%3)+1] * (_C)[1][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 1] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 0]/2)%3)  ] * (_C)[1][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 2] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 3]/2)%3)+1] * (_C)[1][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 3] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 2]/2)%3)  ] * (_C)[1][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 4] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 5]/2)%3)+1] * (_C)[1][gamma_permutation[(_mu)][ 4]]\
       + gamma_sign[(_mu)][ 5] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 4]/2)%3)  ] * (_C)[1][gamma_permutation[(_mu)][ 5]]\
       + gamma_sign[(_mu)][ 0] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 1]/2)%3)+1] * (_C)[2][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 1] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 0]/2)%3)  ] * (_C)[2][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 2] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 3]/2)%3)+1] * (_C)[2][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 3] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 2]/2)%3)  ] * (_C)[2][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 4] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 5]/2)%3)+1] * (_C)[2][gamma_permutation[(_mu)][ 4]]\
       + gamma_sign[(_mu)][ 5] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 4]/2)%3)  ] * (_C)[2][gamma_permutation[(_mu)][ 5]]\
       /* second spinor component */\
       + gamma_sign[(_mu)][ 6] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 7]/2)%3)+1] * (_C)[3][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 7] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 6]/2)%3)  ] * (_C)[3][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 8] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 9]/2)%3)+1] * (_C)[3][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][ 9] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][ 8]/2)%3)  ] * (_C)[3][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][10] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][11]/2)%3)+1] * (_C)[3][gamma_permutation[(_mu)][10]]\
       + gamma_sign[(_mu)][11] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][10]/2)%3)  ] * (_C)[3][gamma_permutation[(_mu)][11]]\
       + gamma_sign[(_mu)][ 6] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 7]/2)%3)+1] * (_C)[4][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 7] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 6]/2)%3)  ] * (_C)[4][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 8] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 9]/2)%3)+1] * (_C)[4][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][ 9] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][ 8]/2)%3)  ] * (_C)[4][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][10] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][11]/2)%3)+1] * (_C)[4][gamma_permutation[(_mu)][10]]\
       + gamma_sign[(_mu)][11] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][10]/2)%3)  ] * (_C)[4][gamma_permutation[(_mu)][11]]\
       + gamma_sign[(_mu)][ 6] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 7]/2)%3)+1] * (_C)[5][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 7] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 6]/2)%3)  ] * (_C)[5][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 8] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 9]/2)%3)+1] * (_C)[5][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][ 9] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][ 8]/2)%3)  ] * (_C)[5][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][10] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][11]/2)%3)+1] * (_C)[5][gamma_permutation[(_mu)][10]]\
       + gamma_sign[(_mu)][11] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][10]/2)%3)  ] * (_C)[5][gamma_permutation[(_mu)][11]]\
       /* third spinor component */\
       + gamma_sign[(_mu)][12] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][13]/2)%3)+1] * (_C)[6][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][13] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][12]/2)%3)  ] * (_C)[6][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][14] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][15]/2)%3)+1] * (_C)[6][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][15] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][14]/2)%3)  ] * (_C)[6][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][16] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][17]/2)%3)+1] * (_C)[6][gamma_permutation[(_mu)][16]]\
       + gamma_sign[(_mu)][17] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][16]/2)%3)  ] * (_C)[6][gamma_permutation[(_mu)][17]]\
       + gamma_sign[(_mu)][12] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][13]/2)%3)+1] * (_C)[7][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][13] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][12]/2)%3)  ] * (_C)[7][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][14] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][15]/2)%3)+1] * (_C)[7][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][15] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][14]/2)%3)  ] * (_C)[7][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][16] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][17]/2)%3)+1] * (_C)[7][gamma_permutation[(_mu)][16]]\
       + gamma_sign[(_mu)][17] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][16]/2)%3)  ] * (_C)[7][gamma_permutation[(_mu)][17]]\
       + gamma_sign[(_mu)][12] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][13]/2)%3)+1] * (_C)[8][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][13] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][12]/2)%3)  ] * (_C)[8][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][14] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][15]/2)%3)+1] * (_C)[8][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][15] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][14]/2)%3)  ] * (_C)[8][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][16] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][17]/2)%3)+1] * (_C)[8][gamma_permutation[(_mu)][16]]\
       + gamma_sign[(_mu)][17] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][16]/2)%3)  ] * (_C)[8][gamma_permutation[(_mu)][17]]\
       /* fourth spinor component */\
       + gamma_sign[(_mu)][18] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][19]/2)%3)+1] * (_C)[ 9][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][19] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][18]/2)%3)  ] * (_C)[ 9][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][20] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][21]/2)%3)+1] * (_C)[ 9][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][21] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][20]/2)%3)  ] * (_C)[ 9][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][22] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][23]/2)%3)+1] * (_C)[ 9][gamma_permutation[(_mu)][22]]\
       + gamma_sign[(_mu)][23] * (_g)[2*(3* 0+(gamma_permutation[(_mu)][22]/2)%3)  ] * (_C)[ 9][gamma_permutation[(_mu)][23]]\
       + gamma_sign[(_mu)][18] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][19]/2)%3)+1] * (_C)[10][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][19] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][18]/2)%3)  ] * (_C)[10][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][20] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][21]/2)%3)+1] * (_C)[10][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][21] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][20]/2)%3)  ] * (_C)[10][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][22] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][23]/2)%3)+1] * (_C)[10][gamma_permutation[(_mu)][22]]\
       + gamma_sign[(_mu)][23] * (_g)[2*(3* 1+(gamma_permutation[(_mu)][22]/2)%3)  ] * (_C)[10][gamma_permutation[(_mu)][23]]\
       + gamma_sign[(_mu)][18] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][19]/2)%3)+1] * (_C)[11][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][19] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][18]/2)%3)  ] * (_C)[11][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][20] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][21]/2)%3)+1] * (_C)[11][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][21] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][20]/2)%3)  ] * (_C)[11][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][22] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][23]/2)%3)+1] * (_C)[11][gamma_permutation[(_mu)][22]]\
       + gamma_sign[(_mu)][23] * (_g)[2*(3* 2+(gamma_permutation[(_mu)][22]/2)%3)  ] * (_C)[11][gamma_permutation[(_mu)][23]];}

/********************/

#define _co_eq_tr_gammaUdag_sm(_w, _mu, _g, _C) {\
  (_w)->re =\
       /* first spinor component */\
         gamma_sign[(_mu)][ 0] * (_g)[2*(3*((gamma_permutation[(_mu)][ 0]/2)%3)+0)  ] * (_C)[0][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 1] * (_g)[2*(3*((gamma_permutation[(_mu)][ 1]/2)%3)+0)+1] * (_C)[0][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 2] * (_g)[2*(3*((gamma_permutation[(_mu)][ 2]/2)%3)+0)  ] * (_C)[0][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 3] * (_g)[2*(3*((gamma_permutation[(_mu)][ 3]/2)%3)+0)+1] * (_C)[0][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 4] * (_g)[2*(3*((gamma_permutation[(_mu)][ 4]/2)%3)+0)  ] * (_C)[0][gamma_permutation[(_mu)][ 4]]\
       + gamma_sign[(_mu)][ 5] * (_g)[2*(3*((gamma_permutation[(_mu)][ 5]/2)%3)+0)+1] * (_C)[0][gamma_permutation[(_mu)][ 5]]\
       + gamma_sign[(_mu)][ 0] * (_g)[2*(3*((gamma_permutation[(_mu)][ 0]/2)%3)+1)  ] * (_C)[1][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 1] * (_g)[2*(3*((gamma_permutation[(_mu)][ 1]/2)%3)+1)+1] * (_C)[1][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 2] * (_g)[2*(3*((gamma_permutation[(_mu)][ 2]/2)%3)+1)  ] * (_C)[1][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 3] * (_g)[2*(3*((gamma_permutation[(_mu)][ 3]/2)%3)+1)+1] * (_C)[1][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 4] * (_g)[2*(3*((gamma_permutation[(_mu)][ 4]/2)%3)+1)  ] * (_C)[1][gamma_permutation[(_mu)][ 4]]\
       + gamma_sign[(_mu)][ 5] * (_g)[2*(3*((gamma_permutation[(_mu)][ 5]/2)%3)+1)+1] * (_C)[1][gamma_permutation[(_mu)][ 5]]\
       + gamma_sign[(_mu)][ 0] * (_g)[2*(3*((gamma_permutation[(_mu)][ 0]/2)%3)+2)  ] * (_C)[2][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 1] * (_g)[2*(3*((gamma_permutation[(_mu)][ 1]/2)%3)+2)+1] * (_C)[2][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 2] * (_g)[2*(3*((gamma_permutation[(_mu)][ 2]/2)%3)+2)  ] * (_C)[2][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 3] * (_g)[2*(3*((gamma_permutation[(_mu)][ 3]/2)%3)+2)+1] * (_C)[2][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 4] * (_g)[2*(3*((gamma_permutation[(_mu)][ 4]/2)%3)+2)  ] * (_C)[2][gamma_permutation[(_mu)][ 4]]\
       + gamma_sign[(_mu)][ 5] * (_g)[2*(3*((gamma_permutation[(_mu)][ 5]/2)%3)+2)+1] * (_C)[2][gamma_permutation[(_mu)][ 5]]\
       /* second spinor component */\
       + gamma_sign[(_mu)][ 6] * (_g)[2*(3*((gamma_permutation[(_mu)][ 6]/2)%3)+0)  ] * (_C)[3][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 7] * (_g)[2*(3*((gamma_permutation[(_mu)][ 7]/2)%3)+0)+1] * (_C)[3][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 8] * (_g)[2*(3*((gamma_permutation[(_mu)][ 8]/2)%3)+0)  ] * (_C)[3][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][ 9] * (_g)[2*(3*((gamma_permutation[(_mu)][ 9]/2)%3)+0)+1] * (_C)[3][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][10] * (_g)[2*(3*((gamma_permutation[(_mu)][10]/2)%3)+0)  ] * (_C)[3][gamma_permutation[(_mu)][10]]\
       + gamma_sign[(_mu)][11] * (_g)[2*(3*((gamma_permutation[(_mu)][11]/2)%3)+0)+1] * (_C)[3][gamma_permutation[(_mu)][11]]\
       + gamma_sign[(_mu)][ 6] * (_g)[2*(3*((gamma_permutation[(_mu)][ 6]/2)%3)+1)  ] * (_C)[4][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 7] * (_g)[2*(3*((gamma_permutation[(_mu)][ 7]/2)%3)+1)+1] * (_C)[4][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 8] * (_g)[2*(3*((gamma_permutation[(_mu)][ 8]/2)%3)+1)  ] * (_C)[4][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][ 9] * (_g)[2*(3*((gamma_permutation[(_mu)][ 9]/2)%3)+1)+1] * (_C)[4][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][10] * (_g)[2*(3*((gamma_permutation[(_mu)][10]/2)%3)+1)  ] * (_C)[4][gamma_permutation[(_mu)][10]]\
       + gamma_sign[(_mu)][11] * (_g)[2*(3*((gamma_permutation[(_mu)][11]/2)%3)+1)+1] * (_C)[4][gamma_permutation[(_mu)][11]]\
       + gamma_sign[(_mu)][ 6] * (_g)[2*(3*((gamma_permutation[(_mu)][ 6]/2)%3)+2)  ] * (_C)[5][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 7] * (_g)[2*(3*((gamma_permutation[(_mu)][ 7]/2)%3)+2)+1] * (_C)[5][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 8] * (_g)[2*(3*((gamma_permutation[(_mu)][ 8]/2)%3)+2)  ] * (_C)[5][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][ 9] * (_g)[2*(3*((gamma_permutation[(_mu)][ 9]/2)%3)+2)+1] * (_C)[5][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][10] * (_g)[2*(3*((gamma_permutation[(_mu)][10]/2)%3)+2)  ] * (_C)[5][gamma_permutation[(_mu)][10]]\
       + gamma_sign[(_mu)][11] * (_g)[2*(3*((gamma_permutation[(_mu)][11]/2)%3)+2)+1] * (_C)[5][gamma_permutation[(_mu)][11]]\
       /* third spinor component */\
       + gamma_sign[(_mu)][12] * (_g)[2*(3*((gamma_permutation[(_mu)][12]/2)%3)+0)  ] * (_C)[6][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][13] * (_g)[2*(3*((gamma_permutation[(_mu)][13]/2)%3)+0)+1] * (_C)[6][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][14] * (_g)[2*(3*((gamma_permutation[(_mu)][14]/2)%3)+0)  ] * (_C)[6][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][15] * (_g)[2*(3*((gamma_permutation[(_mu)][15]/2)%3)+0)+1] * (_C)[6][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][16] * (_g)[2*(3*((gamma_permutation[(_mu)][16]/2)%3)+0)  ] * (_C)[6][gamma_permutation[(_mu)][16]]\
       + gamma_sign[(_mu)][17] * (_g)[2*(3*((gamma_permutation[(_mu)][17]/2)%3)+0)+1] * (_C)[6][gamma_permutation[(_mu)][17]]\
       + gamma_sign[(_mu)][12] * (_g)[2*(3*((gamma_permutation[(_mu)][12]/2)%3)+1)  ] * (_C)[7][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][13] * (_g)[2*(3*((gamma_permutation[(_mu)][13]/2)%3)+1)+1] * (_C)[7][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][14] * (_g)[2*(3*((gamma_permutation[(_mu)][14]/2)%3)+1)  ] * (_C)[7][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][15] * (_g)[2*(3*((gamma_permutation[(_mu)][15]/2)%3)+1)+1] * (_C)[7][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][16] * (_g)[2*(3*((gamma_permutation[(_mu)][16]/2)%3)+1)  ] * (_C)[7][gamma_permutation[(_mu)][16]]\
       + gamma_sign[(_mu)][17] * (_g)[2*(3*((gamma_permutation[(_mu)][17]/2)%3)+1)+1] * (_C)[7][gamma_permutation[(_mu)][17]]\
       + gamma_sign[(_mu)][12] * (_g)[2*(3*((gamma_permutation[(_mu)][12]/2)%3)+2)  ] * (_C)[8][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][13] * (_g)[2*(3*((gamma_permutation[(_mu)][13]/2)%3)+2)+1] * (_C)[8][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][14] * (_g)[2*(3*((gamma_permutation[(_mu)][14]/2)%3)+2)  ] * (_C)[8][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][15] * (_g)[2*(3*((gamma_permutation[(_mu)][15]/2)%3)+2)+1] * (_C)[8][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][16] * (_g)[2*(3*((gamma_permutation[(_mu)][16]/2)%3)+2)  ] * (_C)[8][gamma_permutation[(_mu)][16]]\
       + gamma_sign[(_mu)][17] * (_g)[2*(3*((gamma_permutation[(_mu)][17]/2)%3)+2)+1] * (_C)[8][gamma_permutation[(_mu)][17]]\
       /* fourth spinor component */\
       + gamma_sign[(_mu)][18] * (_g)[2*(3*((gamma_permutation[(_mu)][18]/2)%3)+0)  ] * (_C)[9][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][19] * (_g)[2*(3*((gamma_permutation[(_mu)][19]/2)%3)+0)+1] * (_C)[9][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][20] * (_g)[2*(3*((gamma_permutation[(_mu)][20]/2)%3)+0)  ] * (_C)[9][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][21] * (_g)[2*(3*((gamma_permutation[(_mu)][21]/2)%3)+0)+1] * (_C)[9][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][22] * (_g)[2*(3*((gamma_permutation[(_mu)][22]/2)%3)+0)  ] * (_C)[9][gamma_permutation[(_mu)][22]]\
       + gamma_sign[(_mu)][23] * (_g)[2*(3*((gamma_permutation[(_mu)][23]/2)%3)+0)+1] * (_C)[9][gamma_permutation[(_mu)][23]]\
       + gamma_sign[(_mu)][18] * (_g)[2*(3*((gamma_permutation[(_mu)][18]/2)%3)+1)  ] * (_C)[10][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][19] * (_g)[2*(3*((gamma_permutation[(_mu)][19]/2)%3)+1)+1] * (_C)[10][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][20] * (_g)[2*(3*((gamma_permutation[(_mu)][20]/2)%3)+1)  ] * (_C)[10][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][21] * (_g)[2*(3*((gamma_permutation[(_mu)][21]/2)%3)+1)+1] * (_C)[10][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][22] * (_g)[2*(3*((gamma_permutation[(_mu)][22]/2)%3)+1)  ] * (_C)[10][gamma_permutation[(_mu)][22]]\
       + gamma_sign[(_mu)][23] * (_g)[2*(3*((gamma_permutation[(_mu)][23]/2)%3)+1)+1] * (_C)[10][gamma_permutation[(_mu)][23]]\
       + gamma_sign[(_mu)][18] * (_g)[2*(3*((gamma_permutation[(_mu)][18]/2)%3)+2)  ] * (_C)[11][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][19] * (_g)[2*(3*((gamma_permutation[(_mu)][19]/2)%3)+2)+1] * (_C)[11][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][20] * (_g)[2*(3*((gamma_permutation[(_mu)][20]/2)%3)+2)  ] * (_C)[11][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][21] * (_g)[2*(3*((gamma_permutation[(_mu)][21]/2)%3)+2)+1] * (_C)[11][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][22] * (_g)[2*(3*((gamma_permutation[(_mu)][22]/2)%3)+2)  ] * (_C)[11][gamma_permutation[(_mu)][22]]\
       + gamma_sign[(_mu)][23] * (_g)[2*(3*((gamma_permutation[(_mu)][23]/2)%3)+2)+1] * (_C)[11][gamma_permutation[(_mu)][23]];\
\
  (_w)->im = \
       /* first spinor component */\
       - gamma_sign[(_mu)][ 0] * (_g)[2*(3*((gamma_permutation[(_mu)][ 1]/2)%3)+0)+1] * (_C)[0][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 1] * (_g)[2*(3*((gamma_permutation[(_mu)][ 0]/2)%3)+0)  ] * (_C)[0][gamma_permutation[(_mu)][ 1]]\
       - gamma_sign[(_mu)][ 2] * (_g)[2*(3*((gamma_permutation[(_mu)][ 3]/2)%3)+0)+1] * (_C)[0][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 3] * (_g)[2*(3*((gamma_permutation[(_mu)][ 2]/2)%3)+0)  ] * (_C)[0][gamma_permutation[(_mu)][ 3]]\
       - gamma_sign[(_mu)][ 4] * (_g)[2*(3*((gamma_permutation[(_mu)][ 5]/2)%3)+0)+1] * (_C)[0][gamma_permutation[(_mu)][ 4]]\
       + gamma_sign[(_mu)][ 5] * (_g)[2*(3*((gamma_permutation[(_mu)][ 4]/2)%3)+0)  ] * (_C)[0][gamma_permutation[(_mu)][ 5]]\
       - gamma_sign[(_mu)][ 0] * (_g)[2*(3*((gamma_permutation[(_mu)][ 1]/2)%3)+1)+1] * (_C)[1][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 1] * (_g)[2*(3*((gamma_permutation[(_mu)][ 0]/2)%3)+1)  ] * (_C)[1][gamma_permutation[(_mu)][ 1]]\
       - gamma_sign[(_mu)][ 2] * (_g)[2*(3*((gamma_permutation[(_mu)][ 3]/2)%3)+1)+1] * (_C)[1][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 3] * (_g)[2*(3*((gamma_permutation[(_mu)][ 2]/2)%3)+1)  ] * (_C)[1][gamma_permutation[(_mu)][ 3]]\
       - gamma_sign[(_mu)][ 4] * (_g)[2*(3*((gamma_permutation[(_mu)][ 5]/2)%3)+1)+1] * (_C)[1][gamma_permutation[(_mu)][ 4]]\
       + gamma_sign[(_mu)][ 5] * (_g)[2*(3*((gamma_permutation[(_mu)][ 4]/2)%3)+1)  ] * (_C)[1][gamma_permutation[(_mu)][ 5]]\
       - gamma_sign[(_mu)][ 0] * (_g)[2*(3*((gamma_permutation[(_mu)][ 1]/2)%3)+2)+1] * (_C)[2][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 1] * (_g)[2*(3*((gamma_permutation[(_mu)][ 0]/2)%3)+2)  ] * (_C)[2][gamma_permutation[(_mu)][ 1]]\
       - gamma_sign[(_mu)][ 2] * (_g)[2*(3*((gamma_permutation[(_mu)][ 3]/2)%3)+2)+1] * (_C)[2][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 3] * (_g)[2*(3*((gamma_permutation[(_mu)][ 2]/2)%3)+2)  ] * (_C)[2][gamma_permutation[(_mu)][ 3]]\
       - gamma_sign[(_mu)][ 4] * (_g)[2*(3*((gamma_permutation[(_mu)][ 5]/2)%3)+2)+1] * (_C)[2][gamma_permutation[(_mu)][ 4]]\
       + gamma_sign[(_mu)][ 5] * (_g)[2*(3*((gamma_permutation[(_mu)][ 4]/2)%3)+2)  ] * (_C)[2][gamma_permutation[(_mu)][ 5]]\
       /* second spinor component */\
       - gamma_sign[(_mu)][ 6] * (_g)[2*(3*((gamma_permutation[(_mu)][ 7]/2)%3)+0)+1] * (_C)[3][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 7] * (_g)[2*(3*((gamma_permutation[(_mu)][ 6]/2)%3)+0)  ] * (_C)[3][gamma_permutation[(_mu)][ 7]]\
       - gamma_sign[(_mu)][ 8] * (_g)[2*(3*((gamma_permutation[(_mu)][ 9]/2)%3)+0)+1] * (_C)[3][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][ 9] * (_g)[2*(3*((gamma_permutation[(_mu)][ 8]/2)%3)+0)  ] * (_C)[3][gamma_permutation[(_mu)][ 9]]\
       - gamma_sign[(_mu)][10] * (_g)[2*(3*((gamma_permutation[(_mu)][11]/2)%3)+0)+1] * (_C)[3][gamma_permutation[(_mu)][10]]\
       + gamma_sign[(_mu)][11] * (_g)[2*(3*((gamma_permutation[(_mu)][10]/2)%3)+0)  ] * (_C)[3][gamma_permutation[(_mu)][11]]\
       - gamma_sign[(_mu)][ 6] * (_g)[2*(3*((gamma_permutation[(_mu)][ 7]/2)%3)+1)+1] * (_C)[4][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 7] * (_g)[2*(3*((gamma_permutation[(_mu)][ 6]/2)%3)+1)  ] * (_C)[4][gamma_permutation[(_mu)][ 7]]\
       - gamma_sign[(_mu)][ 8] * (_g)[2*(3*((gamma_permutation[(_mu)][ 9]/2)%3)+1)+1] * (_C)[4][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][ 9] * (_g)[2*(3*((gamma_permutation[(_mu)][ 8]/2)%3)+1)  ] * (_C)[4][gamma_permutation[(_mu)][ 9]]\
       - gamma_sign[(_mu)][10] * (_g)[2*(3*((gamma_permutation[(_mu)][11]/2)%3)+1)+1] * (_C)[4][gamma_permutation[(_mu)][10]]\
       + gamma_sign[(_mu)][11] * (_g)[2*(3*((gamma_permutation[(_mu)][10]/2)%3)+1)  ] * (_C)[4][gamma_permutation[(_mu)][11]]\
       - gamma_sign[(_mu)][ 6] * (_g)[2*(3*((gamma_permutation[(_mu)][ 7]/2)%3)+2)+1] * (_C)[5][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 7] * (_g)[2*(3*((gamma_permutation[(_mu)][ 6]/2)%3)+2)  ] * (_C)[5][gamma_permutation[(_mu)][ 7]]\
       - gamma_sign[(_mu)][ 8] * (_g)[2*(3*((gamma_permutation[(_mu)][ 9]/2)%3)+2)+1] * (_C)[5][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][ 9] * (_g)[2*(3*((gamma_permutation[(_mu)][ 8]/2)%3)+2)  ] * (_C)[5][gamma_permutation[(_mu)][ 9]]\
       - gamma_sign[(_mu)][10] * (_g)[2*(3*((gamma_permutation[(_mu)][11]/2)%3)+2)+1] * (_C)[5][gamma_permutation[(_mu)][10]]\
       + gamma_sign[(_mu)][11] * (_g)[2*(3*((gamma_permutation[(_mu)][10]/2)%3)+2)  ] * (_C)[5][gamma_permutation[(_mu)][11]]\
       /* third spinor component */\
       - gamma_sign[(_mu)][12] * (_g)[2*(3*((gamma_permutation[(_mu)][13]/2)%3)+0)+1] * (_C)[6][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][13] * (_g)[2*(3*((gamma_permutation[(_mu)][12]/2)%3)+0)  ] * (_C)[6][gamma_permutation[(_mu)][13]]\
       - gamma_sign[(_mu)][14] * (_g)[2*(3*((gamma_permutation[(_mu)][15]/2)%3)+0)+1] * (_C)[6][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][15] * (_g)[2*(3*((gamma_permutation[(_mu)][14]/2)%3)+0)  ] * (_C)[6][gamma_permutation[(_mu)][15]]\
       - gamma_sign[(_mu)][16] * (_g)[2*(3*((gamma_permutation[(_mu)][17]/2)%3)+0)+1] * (_C)[6][gamma_permutation[(_mu)][16]]\
       + gamma_sign[(_mu)][17] * (_g)[2*(3*((gamma_permutation[(_mu)][16]/2)%3)+0)  ] * (_C)[6][gamma_permutation[(_mu)][17]]\
       - gamma_sign[(_mu)][12] * (_g)[2*(3*((gamma_permutation[(_mu)][13]/2)%3)+1)+1] * (_C)[7][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][13] * (_g)[2*(3*((gamma_permutation[(_mu)][12]/2)%3)+1)  ] * (_C)[7][gamma_permutation[(_mu)][13]]\
       - gamma_sign[(_mu)][14] * (_g)[2*(3*((gamma_permutation[(_mu)][15]/2)%3)+1)+1] * (_C)[7][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][15] * (_g)[2*(3*((gamma_permutation[(_mu)][14]/2)%3)+1)  ] * (_C)[7][gamma_permutation[(_mu)][15]]\
       - gamma_sign[(_mu)][16] * (_g)[2*(3*((gamma_permutation[(_mu)][17]/2)%3)+1)+1] * (_C)[7][gamma_permutation[(_mu)][16]]\
       + gamma_sign[(_mu)][17] * (_g)[2*(3*((gamma_permutation[(_mu)][16]/2)%3)+1)  ] * (_C)[7][gamma_permutation[(_mu)][17]]\
       - gamma_sign[(_mu)][12] * (_g)[2*(3*((gamma_permutation[(_mu)][13]/2)%3)+2)+1] * (_C)[8][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][13] * (_g)[2*(3*((gamma_permutation[(_mu)][12]/2)%3)+2)  ] * (_C)[8][gamma_permutation[(_mu)][13]]\
       - gamma_sign[(_mu)][14] * (_g)[2*(3*((gamma_permutation[(_mu)][15]/2)%3)+2)+1] * (_C)[8][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][15] * (_g)[2*(3*((gamma_permutation[(_mu)][14]/2)%3)+2)  ] * (_C)[8][gamma_permutation[(_mu)][15]]\
       - gamma_sign[(_mu)][16] * (_g)[2*(3*((gamma_permutation[(_mu)][17]/2)%3)+2)+1] * (_C)[8][gamma_permutation[(_mu)][16]]\
       + gamma_sign[(_mu)][17] * (_g)[2*(3*((gamma_permutation[(_mu)][16]/2)%3)+2)  ] * (_C)[8][gamma_permutation[(_mu)][17]]\
       /* fourth spinor component */\
       - gamma_sign[(_mu)][18] * (_g)[2*(3*((gamma_permutation[(_mu)][19]/2)%3)+0)+1] * (_C)[ 9][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][19] * (_g)[2*(3*((gamma_permutation[(_mu)][18]/2)%3)+0)  ] * (_C)[ 9][gamma_permutation[(_mu)][19]]\
       - gamma_sign[(_mu)][20] * (_g)[2*(3*((gamma_permutation[(_mu)][21]/2)%3)+0)+1] * (_C)[ 9][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][21] * (_g)[2*(3*((gamma_permutation[(_mu)][20]/2)%3)+0)  ] * (_C)[ 9][gamma_permutation[(_mu)][21]]\
       - gamma_sign[(_mu)][22] * (_g)[2*(3*((gamma_permutation[(_mu)][23]/2)%3)+0)+1] * (_C)[ 9][gamma_permutation[(_mu)][22]]\
       + gamma_sign[(_mu)][23] * (_g)[2*(3*((gamma_permutation[(_mu)][22]/2)%3)+0)  ] * (_C)[ 9][gamma_permutation[(_mu)][23]]\
       - gamma_sign[(_mu)][18] * (_g)[2*(3*((gamma_permutation[(_mu)][19]/2)%3)+1)+1] * (_C)[10][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][19] * (_g)[2*(3*((gamma_permutation[(_mu)][18]/2)%3)+1)  ] * (_C)[10][gamma_permutation[(_mu)][19]]\
       - gamma_sign[(_mu)][20] * (_g)[2*(3*((gamma_permutation[(_mu)][21]/2)%3)+1)+1] * (_C)[10][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][21] * (_g)[2*(3*((gamma_permutation[(_mu)][20]/2)%3)+1)  ] * (_C)[10][gamma_permutation[(_mu)][21]]\
       - gamma_sign[(_mu)][22] * (_g)[2*(3*((gamma_permutation[(_mu)][23]/2)%3)+1)+1] * (_C)[10][gamma_permutation[(_mu)][22]]\
       + gamma_sign[(_mu)][23] * (_g)[2*(3*((gamma_permutation[(_mu)][22]/2)%3)+1)  ] * (_C)[10][gamma_permutation[(_mu)][23]]\
       - gamma_sign[(_mu)][18] * (_g)[2*(3*((gamma_permutation[(_mu)][19]/2)%3)+2)+1] * (_C)[11][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][19] * (_g)[2*(3*((gamma_permutation[(_mu)][18]/2)%3)+2)  ] * (_C)[11][gamma_permutation[(_mu)][19]]\
       - gamma_sign[(_mu)][20] * (_g)[2*(3*((gamma_permutation[(_mu)][21]/2)%3)+2)+1] * (_C)[11][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][21] * (_g)[2*(3*((gamma_permutation[(_mu)][20]/2)%3)+2)  ] * (_C)[11][gamma_permutation[(_mu)][21]]\
       - gamma_sign[(_mu)][22] * (_g)[2*(3*((gamma_permutation[(_mu)][23]/2)%3)+2)+1] * (_C)[11][gamma_permutation[(_mu)][22]]\
       + gamma_sign[(_mu)][23] * (_g)[2*(3*((gamma_permutation[(_mu)][22]/2)%3)+2)  ] * (_C)[11][gamma_permutation[(_mu)][23]];}

/********************/

#define _co_eq_tr_gamma_sm(_w, _mu, _C) {\
  (_w)->re =\
       /* first spinor component */\
         gamma_sign[(_mu)][ 0] * (_C)[ 0][gamma_permutation[(_mu)][ 0]]\
       + gamma_sign[(_mu)][ 2] * (_C)[ 1][gamma_permutation[(_mu)][ 2]]\
       + gamma_sign[(_mu)][ 4] * (_C)[ 2][gamma_permutation[(_mu)][ 4]]\
       /* second spinor component */\
       + gamma_sign[(_mu)][ 6] * (_C)[ 3][gamma_permutation[(_mu)][ 6]]\
       + gamma_sign[(_mu)][ 8] * (_C)[ 4][gamma_permutation[(_mu)][ 8]]\
       + gamma_sign[(_mu)][10] * (_C)[ 5][gamma_permutation[(_mu)][10]]\
       /* third spinor component */\
       + gamma_sign[(_mu)][12] * (_C)[ 6][gamma_permutation[(_mu)][12]]\
       + gamma_sign[(_mu)][14] * (_C)[ 7][gamma_permutation[(_mu)][14]]\
       + gamma_sign[(_mu)][16] * (_C)[ 8][gamma_permutation[(_mu)][16]]\
       /* fourth spinor component */\
       + gamma_sign[(_mu)][18] * (_C)[ 9][gamma_permutation[(_mu)][18]]\
       + gamma_sign[(_mu)][20] * (_C)[10][gamma_permutation[(_mu)][20]]\
       + gamma_sign[(_mu)][22] * (_C)[11][gamma_permutation[(_mu)][22]];\
\
  (_w)->im = \
       /* first spinor component */\
         gamma_sign[(_mu)][ 1] * (_C)[ 0][gamma_permutation[(_mu)][ 1]]\
       + gamma_sign[(_mu)][ 3] * (_C)[ 1][gamma_permutation[(_mu)][ 3]]\
       + gamma_sign[(_mu)][ 5] * (_C)[ 2][gamma_permutation[(_mu)][ 5]]\
       /* second spinor component */\
       + gamma_sign[(_mu)][ 7] * (_C)[ 3][gamma_permutation[(_mu)][ 7]]\
       + gamma_sign[(_mu)][ 9] * (_C)[ 4][gamma_permutation[(_mu)][ 9]]\
       + gamma_sign[(_mu)][11] * (_C)[ 5][gamma_permutation[(_mu)][11]]\
       /* third spinor component */\
       + gamma_sign[(_mu)][13] * (_C)[ 6][gamma_permutation[(_mu)][13]]\
       + gamma_sign[(_mu)][15] * (_C)[ 7][gamma_permutation[(_mu)][15]]\
       + gamma_sign[(_mu)][17] * (_C)[ 8][gamma_permutation[(_mu)][17]]\
       /* fourth spinor component */\
       + gamma_sign[(_mu)][19] * (_C)[ 9][gamma_permutation[(_mu)][19]]\
       + gamma_sign[(_mu)][21] * (_C)[10][gamma_permutation[(_mu)][21]]\
       + gamma_sign[(_mu)][23] * (_C)[11][gamma_permutation[(_mu)][23]];}

/********************/

#define _fv_eq_hpem_ti_fv(_s, _t, _gindex, _sigma, _mut, _fact) {\
  (_s)[ 0] = (_t)[ 0] + ( (_t)[gamma_permutation[(_gindex)][ 0]] * gamma_sign[(_gindex)][ 0]            \
           + (_t)[gamma_permutation[6+(_gindex)][ 1]] * gamma_sign[6+(_gindex)][ 1] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][ 1]] * gamma_sign[5][ 1] * (_mut);                               \
\
  (_s)[ 1] = (_t)[ 1] + ( (_t)[gamma_permutation[(_gindex)][ 1]] * gamma_sign[(_gindex)][ 1]            \
           - (_t)[gamma_permutation[6+(_gindex)][ 0]] * gamma_sign[6+(_gindex)][ 0] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][ 0]] * gamma_sign[5][ 0] * (_mut);                               \
\
  (_s)[ 2] = (_t)[ 2] + ( (_t)[gamma_permutation[(_gindex)][ 2]] * gamma_sign[(_gindex)][ 2]            \
           + (_t)[gamma_permutation[6+(_gindex)][ 3]] * gamma_sign[6+(_gindex)][ 3] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][ 3]] * gamma_sign[5][ 3] * (_mut);                               \
\
  (_s)[ 3] = (_t)[ 3] + ( (_t)[gamma_permutation[(_gindex)][ 3]] * gamma_sign[(_gindex)][ 3]            \
           - (_t)[gamma_permutation[6+(_gindex)][ 2]] * gamma_sign[6+(_gindex)][ 2] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][ 2]] * gamma_sign[5][ 2] * (_mut);                               \
\
  (_s)[ 4] = (_t)[ 4] + ( (_t)[gamma_permutation[(_gindex)][ 4]] * gamma_sign[(_gindex)][ 4]            \
           + (_t)[gamma_permutation[6+(_gindex)][ 5]] * gamma_sign[6+(_gindex)][ 5] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][ 5]] * gamma_sign[5][ 5] * (_mut);                               \
\
  (_s)[ 5] = (_t)[ 5] + ( (_t)[gamma_permutation[(_gindex)][ 5]] * gamma_sign[(_gindex)][ 5]            \
           - (_t)[gamma_permutation[6+(_gindex)][ 4]] * gamma_sign[6+(_gindex)][ 4] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][ 4]] * gamma_sign[5][ 4] * (_mut);                               \
\
  (_s)[ 6] = (_t)[ 6] + ( (_t)[gamma_permutation[(_gindex)][ 6]] * gamma_sign[(_gindex)][ 6]            \
           + (_t)[gamma_permutation[6+(_gindex)][ 7]] * gamma_sign[6+(_gindex)][ 7] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][ 7]] * gamma_sign[5][ 7] * (_mut);                               \
\
  (_s)[ 7] = (_t)[ 7] + ( (_t)[gamma_permutation[(_gindex)][ 7]] * gamma_sign[(_gindex)][ 7]            \
           - (_t)[gamma_permutation[6+(_gindex)][ 6]] * gamma_sign[6+(_gindex)][ 6] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][ 6]] * gamma_sign[5][ 6] * (_mut);                               \
\
  (_s)[ 8] = (_t)[ 8] + ( (_t)[gamma_permutation[(_gindex)][ 8]] * gamma_sign[(_gindex)][ 8]            \
           + (_t)[gamma_permutation[6+(_gindex)][ 9]] * gamma_sign[6+(_gindex)][ 9] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][ 9]] * gamma_sign[5][ 9] * (_mut);                               \
\
  (_s)[ 9] = (_t)[ 9] + ( (_t)[gamma_permutation[(_gindex)][ 9]] * gamma_sign[(_gindex)][ 9]            \
           - (_t)[gamma_permutation[6+(_gindex)][ 8]] * gamma_sign[6+(_gindex)][ 8] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][ 8]] * gamma_sign[5][ 8] * (_mut);                               \
\
  (_s)[10] = (_t)[10] + ( (_t)[gamma_permutation[(_gindex)][10]] * gamma_sign[(_gindex)][10]            \
           + (_t)[gamma_permutation[6+(_gindex)][11]] * gamma_sign[6+(_gindex)][11] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][11]] * gamma_sign[5][11] * (_mut);                               \
\
  (_s)[11] = (_t)[11] + ( (_t)[gamma_permutation[(_gindex)][11]] * gamma_sign[(_gindex)][11]            \
           - (_t)[gamma_permutation[6+(_gindex)][10]] * gamma_sign[6+(_gindex)][10] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][10]] * gamma_sign[5][10] * (_mut);                               \
\
  (_s)[12] = (_t)[12] + ( (_t)[gamma_permutation[(_gindex)][12]] * gamma_sign[(_gindex)][12]            \
           + (_t)[gamma_permutation[6+(_gindex)][13]] * gamma_sign[6+(_gindex)][13] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][13]] * gamma_sign[5][13] * (_mut);                               \
\
  (_s)[13] = (_t)[13] + ( (_t)[gamma_permutation[(_gindex)][13]] * gamma_sign[(_gindex)][13]            \
           - (_t)[gamma_permutation[6+(_gindex)][12]] * gamma_sign[6+(_gindex)][12] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][12]] * gamma_sign[5][12] * (_mut);                               \
\
  (_s)[14] = (_t)[14] + ( (_t)[gamma_permutation[(_gindex)][14]] * gamma_sign[(_gindex)][14]            \
           + (_t)[gamma_permutation[6+(_gindex)][15]] * gamma_sign[6+(_gindex)][15] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][15]] * gamma_sign[5][15] * (_mut);                               \
\
  (_s)[15] = (_t)[15] + ( (_t)[gamma_permutation[(_gindex)][15]] * gamma_sign[(_gindex)][15]            \
           - (_t)[gamma_permutation[6+(_gindex)][14]] * gamma_sign[6+(_gindex)][14] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][14]] * gamma_sign[5][14] * (_mut);                               \
\
  (_s)[16] = (_t)[16] + ( (_t)[gamma_permutation[(_gindex)][16]] * gamma_sign[(_gindex)][16]            \
           + (_t)[gamma_permutation[6+(_gindex)][17]] * gamma_sign[6+(_gindex)][17] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][17]] * gamma_sign[5][17] * (_mut);                               \
\
  (_s)[17] = (_t)[17] + ( (_t)[gamma_permutation[(_gindex)][17]] * gamma_sign[(_gindex)][17]            \
           - (_t)[gamma_permutation[6+(_gindex)][16]] * gamma_sign[6+(_gindex)][16] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][16]] * gamma_sign[5][16] * (_mut);                               \
\
  (_s)[18] = (_t)[18] + ( (_t)[gamma_permutation[(_gindex)][18]] * gamma_sign[(_gindex)][18]            \
           + (_t)[gamma_permutation[6+(_gindex)][19]] * gamma_sign[6+(_gindex)][19] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][19]] * gamma_sign[5][19] * (_mut);                               \
\
  (_s)[19] = (_t)[19] + ( (_t)[gamma_permutation[(_gindex)][19]] * gamma_sign[(_gindex)][19]            \
           - (_t)[gamma_permutation[6+(_gindex)][18]] * gamma_sign[6+(_gindex)][18] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][18]] * gamma_sign[5][18] * (_mut);                               \
\
  (_s)[20] = (_t)[20] + ( (_t)[gamma_permutation[(_gindex)][20]] * gamma_sign[(_gindex)][20]            \
           + (_t)[gamma_permutation[6+(_gindex)][21]] * gamma_sign[6+(_gindex)][21] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][21]] * gamma_sign[5][21] * (_mut);                               \
\
  (_s)[21] = (_t)[21] + ( (_t)[gamma_permutation[(_gindex)][21]] * gamma_sign[(_gindex)][21]            \
           - (_t)[gamma_permutation[6+(_gindex)][20]] * gamma_sign[6+(_gindex)][20] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][20]] * gamma_sign[5][20] * (_mut);                               \
\
  (_s)[22] = (_t)[22] + ( (_t)[gamma_permutation[(_gindex)][22]] * gamma_sign[(_gindex)][22]            \
           + (_t)[gamma_permutation[6+(_gindex)][23]] * gamma_sign[6+(_gindex)][23] *(_mut)) * (_sigma) \
           + (_t)[gamma_permutation[5][23]] * gamma_sign[5][23] * (_mut);                               \
\
  (_s)[23] = (_t)[23] + ( (_t)[gamma_permutation[(_gindex)][23]] * gamma_sign[(_gindex)][23]            \
           - (_t)[gamma_permutation[6+(_gindex)][22]] * gamma_sign[6+(_gindex)][22] *(_mut)) * (_sigma) \
           - (_t)[gamma_permutation[5][22]] * gamma_sign[5][22] * (_mut);                               \
\
  (_s)[ 0] *= (_fact); (_s)[ 1] *= (_fact); (_s)[ 2] *= (_fact); (_s)[ 3] *= (_fact); \
  (_s)[ 4] *= (_fact); (_s)[ 5] *= (_fact); (_s)[ 6] *= (_fact); (_s)[ 7] *= (_fact); \
  (_s)[ 8] *= (_fact); (_s)[ 9] *= (_fact); (_s)[10] *= (_fact); (_s)[11] *= (_fact); \
  (_s)[12] *= (_fact); (_s)[13] *= (_fact); (_s)[14] *= (_fact); (_s)[15] *= (_fact); \
  (_s)[16] *= (_fact); (_s)[17] *= (_fact); (_s)[18] *= (_fact); (_s)[19] *= (_fact); \
  (_s)[20] *= (_fact); (_s)[21] *= (_fact); (_s)[22] *= (_fact); (_s)[23] *= (_fact); }



/*
// s = t * c
#define _fv_eq_fv_ti_co(s,t,c) {\
  (s)[ 0] = (t)[ 0] * (c->re) - (t)[ 1] * (c->im);\
  (s)[ 1] = (t)[ 0] * (c->im) + (t)[ 1] * (c->re);\
  (s)[ 2] = (t)[ 2] * (c->re) - (t)[ 3] * (c->im);\
  (s)[ 3] = (t)[ 2] * (c->im) + (t)[ 3] * (c->re);\
  (s)[ 4] = (t)[ 4] * (c->re) - (t)[ 5] * (c->im);\
  (s)[ 5] = (t)[ 4] * (c->im) + (t)[ 5] * (c->re);\
  (s)[ 6] = (t)[ 6] * (c->re) - (t)[ 7] * (c->im);\
  (s)[ 7] = (t)[ 6] * (c->im) + (t)[ 7] * (c->re);\
  (s)[ 8] = (t)[ 8] * (c->re) - (t)[ 9] * (c->im);\
  (s)[ 9] = (t)[ 8] * (c->im) + (t)[ 9] * (c->re);\
  (s)[10] = (t)[10] * (c->re) - (t)[11] * (c->im);\
  (s)[11] = (t)[10] * (c->im) + (t)[11] * (c->re);\
  (s)[12] = (t)[12] * (c->re) - (t)[13] * (c->im);\
  (s)[13] = (t)[12] * (c->im) + (t)[13] * (c->re);\
  (s)[14] = (t)[14] * (c->re) - (t)[15] * (c->im);\
  (s)[15] = (t)[14] * (c->im) + (t)[15] * (c->re);\
  (s)[16] = (t)[16] * (c->re) - (t)[17] * (c->im);\
  (s)[17] = (t)[16] * (c->im) + (t)[17] * (c->re);\
  (s)[18] = (t)[18] * (c->re) - (t)[19] * (c->im);\
  (s)[19] = (t)[18] * (c->im) + (t)[19] * (c->re);\
  (s)[20] = (t)[20] * (c->re) - (t)[21] * (c->im);\
  (s)[21] = (t)[20] * (c->im) + (t)[21] * (c->re);\
  (s)[22] = (t)[22] * (c->re) - (t)[23] * (c->im);\
  (s)[23] = (t)[22] * (c->im) + (t)[23] * (c->re);\
}

// s = t * c^*
#define _fv_eq_fv_ti_co_conj(s,t,c) {\
  (s)[ 0] = (t)[ 0] * (c->re) + (t)[ 1] * (c->im);\
  (s)[ 1] =-(t)[ 0] * (c->im) + (t)[ 1] * (c->re);\
  (s)[ 2] = (t)[ 2] * (c->re) + (t)[ 3] * (c->im);\
  (s)[ 3] =-(t)[ 2] * (c->im) + (t)[ 3] * (c->re);\
  (s)[ 4] = (t)[ 4] * (c->re) + (t)[ 5] * (c->im);\
  (s)[ 5] =-(t)[ 4] * (c->im) + (t)[ 5] * (c->re);\
  (s)[ 6] = (t)[ 6] * (c->re) + (t)[ 7] * (c->im);\
  (s)[ 7] =-(t)[ 6] * (c->im) + (t)[ 7] * (c->re);\
  (s)[ 8] = (t)[ 8] * (c->re) + (t)[ 9] * (c->im);\
  (s)[ 9] =-(t)[ 8] * (c->im) + (t)[ 9] * (c->re);\
  (s)[10] = (t)[10] * (c->re) + (t)[11] * (c->im);\
  (s)[11] =-(t)[10] * (c->im) + (t)[11] * (c->re);\
  (s)[12] = (t)[12] * (c->re) + (t)[13] * (c->im);\
  (s)[13] =-(t)[12] * (c->im) + (t)[13] * (c->re);\
  (s)[14] = (t)[14] * (c->re) + (t)[15] * (c->im);\
  (s)[15] =-(t)[14] * (c->im) + (t)[15] * (c->re);\
  (s)[16] = (t)[16] * (c->re) + (t)[17] * (c->im);\
  (s)[17] =-(t)[16] * (c->im) + (t)[17] * (c->re);\
  (s)[18] = (t)[18] * (c->re) + (t)[19] * (c->im);\
  (s)[19] =-(t)[18] * (c->im) + (t)[19] * (c->re);\
  (s)[20] = (t)[20] * (c->re) + (t)[21] * (c->im);\
  (s)[21] =-(t)[20] * (c->im) + (t)[21] * (c->re);\
  (s)[22] = (t)[22] * (c->re) + (t)[23] * (c->im);\
  (s)[23] =-(t)[22] * (c->im) + (t)[23] * (c->re);\
}
*/
#endif