/* Author: G. Jungman *//* Implementation for Sobol generator. * See *   [Bratley+Fox, TOMS 14, 88 (1988)] *   [Antonov+Saleev, USSR Comput. Maths. Math. Phys. 19, 252 (1980)] */#include <config.h>#include <gsl/gsl_qrng.h>/* maximum allowed space dimension */#define SOBOL_MAX_DIMENSION 40/* bit count; assumes sizeof(int) >= 32-bit */#define SOBOL_BIT_COUNT 30/* prototypes for generator type functions */static size_t sobol_state_size(unsigned int dimension);static int sobol_init(void * state, unsigned int dimension);static int sobol_get(void * state, unsigned int dimension, double * v);/* global Sobol generator type object */static const gsl_qrng_type sobol_type = {  "sobol",  SOBOL_MAX_DIMENSION,  sobol_state_size,  sobol_init,  sobol_get};const gsl_qrng_type * gsl_qrng_sobol = &sobol_type;/* primitive polynomials in binary encoding */static const int primitive_polynomials[SOBOL_MAX_DIMENSION] = {  1,     3,   7,  11,  13,  19,  25,  37,  59,  47,  61,   55,  41,  67,  97,  91, 109, 103, 115, 131,  193, 137, 145, 143, 241, 157, 185, 167, 229, 171,  213, 191, 253, 203, 211, 239, 247, 285, 369, 299};/* degrees of the primitive polynomials */static const int degree_table[SOBOL_MAX_DIMENSION] = {  0, 1, 2, 3, 3, 4, 4, 5, 5, 5,  5, 5, 5, 6, 6, 6, 6, 6, 6, 7,  7, 7, 7, 7, 7, 7, 7, 7, 7, 7,   7, 7, 7, 7, 7, 7, 7, 8, 8, 8};/* initial values for direction tables, following * Bratley+Fox, taken from [Sobol+Levitan, preprint 1976] */static const int v_init[8][SOBOL_MAX_DIMENSION] ={  {    0, 1, 1, 1, 1, 1, 1, 1, 1, 1,    1, 1, 1, 1, 1, 1, 1, 1, 1, 1,    1, 1, 1, 1, 1, 1, 1, 1, 1, 1,    1, 1, 1, 1, 1, 1, 1, 1, 1, 1  },  {    0, 0, 1, 3, 1, 3, 1, 3, 3, 1,    3, 1, 3, 1, 3, 1, 1, 3, 1, 3,    1, 3, 1, 3, 3, 1, 3, 1, 3, 1,    3, 1, 1, 3, 1, 3, 1, 3, 1, 3  },   {    0, 0, 0, 7, 5, 1, 3, 3, 7, 5,    5, 7, 7, 1, 3, 3, 7, 5, 1, 1,    5, 3, 3, 1, 7, 5, 1, 3, 3, 7,    5, 1, 1, 5, 7, 7, 5, 1, 3, 3  },   {    0,  0,  0,  0,  0,  1,  7,  9, 13, 11,    1,  3,  7,  9,  5, 13, 13, 11,  3, 15,    5,  3, 15,  7,  9, 13,  9,  1, 11,  7,    5, 15,  1, 15, 11,  5,  3,  1,  7,  9  },   {     0,  0,  0,  0,  0,  0,  0,  9,  3, 27,    15, 29, 21, 23, 19, 11, 25,  7, 13, 17,     1, 25, 29,  3, 31, 11,  5, 23, 27, 19,    21,  5,  1, 17, 13,  7, 15,  9, 31,  9  },   {     0,  0,  0,  0,  0,  0,  0,  0,  0,  0,     0,  0,  0, 37, 33,  7,  5, 11, 39, 63,    27, 17, 15, 23, 29,  3, 21, 13, 31, 25,     9, 49, 33, 19, 29, 11, 19, 27, 15, 25  },   {     0,   0,  0,  0,  0,  0,    0,  0,  0,   0,     0,   0,  0,  0,  0,  0,    0,  0,  0,  13,    33, 115, 41, 79, 17,  29, 119, 75, 73, 105,     7,  59, 65, 21,  3, 113,  61, 89, 45, 107  },   {    0, 0, 0, 0, 0, 0, 0, 0,  0,  0,    0, 0, 0, 0, 0, 0, 0, 0,  0,  0,    0, 0, 0, 0, 0, 0, 0, 0,  0,  0,    0, 0, 0, 0, 0, 0, 0, 7, 23, 39  }};/* Sobol generator state. *   sequence_count       = number of calls with this generator *   last_numerator_vec   = last generated numerator vector *   last_denominator_inv = 1/denominator for last numerator vector *   v_direction          = direction number table */typedef struct{  unsigned int  sequence_count;  double        last_denominator_inv;  int           last_numerator_vec[SOBOL_MAX_DIMENSION];  int           v_direction[SOBOL_BIT_COUNT][SOBOL_MAX_DIMENSION];} sobol_state_t;/* NOTE: I fixed the size for the preliminary implementation.   This could/should be relaxed, as an optimization. */static size_t sobol_state_size(unsigned int dimension){  return sizeof(sobol_state_t);}static int sobol_init(void * state, unsigned int dimension){  sobol_state_t * s_state = (sobol_state_t *) state;  unsigned int i_dim;  int j, k;  int ell;  if(dimension < 1 || dimension > SOBOL_MAX_DIMENSION) {    return GSL_EINVAL;  }  /* Initialize direction table in dimension 0. */  for(k=0; k<SOBOL_BIT_COUNT; k++) s_state->v_direction[k][0] = 1;  /* Initialize in remaining dimensions. */  for(i_dim=1; i_dim<dimension; i_dim++) {    const int poly_index = i_dim;    const int degree_i = degree_table[poly_index];    int includ[8];    /* Expand the polynomial bit pattern to separate     * components of the logical array includ[].     */    int p_i = primitive_polynomials[poly_index];    for(k = degree_i-1; k >= 0; k--) {      includ[k] = ((p_i % 2) == 1);      p_i /= 2;    }    /* Leading elements for dimension i come from v_init[][]. */    for(j=0; j<degree_i; j++) s_state->v_direction[j][i_dim] = v_init[j][i_dim];    /* Calculate remaining elements for this dimension,     * as explained in Bratley+Fox, section 2.     */    for(j=degree_i; j<SOBOL_BIT_COUNT; j++) {      int newv = s_state->v_direction[j-degree_i][i_dim];      ell = 1;      for(k=0; k<degree_i; k++) {        ell *= 2;        if(includ[k]) newv ^= (ell * s_state->v_direction[j-k-1][i_dim]);      }      s_state->v_direction[j][i_dim] = newv;    }  }  /* Multiply columns of v by appropriate power of 2. */  ell = 1;  for(j=SOBOL_BIT_COUNT-1-1; j>=0; j--) {    ell *= 2;    for(i_dim=0; i_dim<dimension; i_dim++) {      s_state->v_direction[j][i_dim] *= ell;    }  }  /* 1/(common denominator of the elements in v_direction) */  s_state->last_denominator_inv = 1.0 /(2.0 * ell);  /* final setup */  s_state->sequence_count = 0;  for(i_dim=0; i_dim<dimension; i_dim++) s_state->last_numerator_vec[i_dim] = 0;  return GSL_SUCCESS;}static int sobol_get(void * state, unsigned int dimension, double * v){  sobol_state_t * s_state = (sobol_state_t *) state;  unsigned int i_dimension;  /* Find the position of the least-significant zero in count. */  int ell = 0;  int c = s_state->sequence_count;  while(1) {    ++ell;    if((c % 2) == 1) c /= 2;    else break;  }  /* Check for exhaustion. */  if(ell > SOBOL_BIT_COUNT) return GSL_EFAILED; /* FIXME: good return code here */  for(i_dimension=0; i_dimension<dimension; i_dimension++) {    const int direction_i     = s_state->v_direction[ell-1][i_dimension];    const int old_numerator_i = s_state->last_numerator_vec[i_dimension];    const int new_numerator_i = old_numerator_i ^ direction_i;    s_state->last_numerator_vec[i_dimension] = new_numerator_i;    v[i_dimension] = new_numerator_i * s_state->last_denominator_inv;  }  s_state->sequence_count++;  return GSL_SUCCESS;}