/* Author: G. Jungman
*/
/* Implement Niederreiter base 2 generator.
* See:
* Bratley, Fox, Niederreiter, ACM Trans. Model. Comp. Sim. 2, 195 (1992)
*/
#include <config.h>
#include <gsl/gsl_qrng.h>
#define NIED2_CHARACTERISTIC 2
#define NIED2_BASE 2
#define NIED2_MAX_DIMENSION 12
#define NIED2_MAX_PRIM_DEGREE 5
#define NIED2_MAX_DEGREE 50
#define NIED2_BIT_COUNT 30
#define NIED2_NBITS (NIED2_BIT_COUNT+1)
#define MAXV (NIED2_NBITS + NIED2_MAX_DEGREE)
/* Z_2 field operations */
#define NIED2_ADD(x,y) (((x)+(y))%2)
#define NIED2_MUL(x,y) (((x)*(y))%2)
#define NIED2_SUB(x,y) NIED2_ADD((x),(y))
static size_t nied2_state_size(unsigned int dimension);
static int nied2_init(void * state, unsigned int dimension);
static int nied2_get(void * state, unsigned int dimension, double * v);
static const gsl_qrng_type nied2_type =
{
"niederreiter-base-2",
NIED2_MAX_DIMENSION,
nied2_state_size,
nied2_init,
nied2_get
};
const gsl_qrng_type * gsl_qrng_niederreiter_2 = &nied2_type;
/* primitive polynomials in binary encoding */
static const int primitive_poly[NIED2_MAX_DIMENSION+1][NIED2_MAX_PRIM_DEGREE+1] =
{
{ 1, 0, 0, 0, 0, 0 }, /* 1 */
{ 0, 1, 0, 0, 0, 0 }, /* x */
{ 1, 1, 0, 0, 0, 0 }, /* 1 + x */
{ 1, 1, 1, 0, 0, 0 }, /* 1 + x + x^2 */
{ 1, 1, 0, 1, 0, 0 }, /* 1 + x + x^3 */
{ 1, 0, 1, 1, 0, 0 }, /* 1 + x^2 + x^3 */
{ 1, 1, 0, 0, 1, 0 }, /* 1 + x + x^4 */
{ 1, 0, 0, 1, 1, 0 }, /* 1 + x^3 + x^4 */
{ 1, 1, 1, 1, 1, 0 }, /* 1 + x + x^2 + x^3 + x^4 */
{ 1, 0, 1, 0, 0, 1 }, /* 1 + x^2 + x^5 */
{ 1, 0, 0, 1, 0, 1 }, /* 1 + x^3 + x^5 */
{ 1, 1, 1, 1, 0, 1 }, /* 1 + x + x^2 + x^3 + x^5 */
{ 1, 1, 1, 0, 1, 1 } /* 1 + x + x^2 + x^4 + x^5 */
};
/* degrees of primitive polynomials */
static const int poly_degree[NIED2_MAX_DIMENSION+1] =
{
0, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5
};
typedef struct
{
unsigned int sequence_count;
int cj[NIED2_NBITS][NIED2_MAX_DIMENSION];
int nextq[NIED2_MAX_DIMENSION];
} nied2_state_t;
static size_t nied2_state_size(unsigned int dimension)
{
return sizeof(nied2_state_t);
}
/* Multiply polynomials over Z_2.
* Notice use of a temporary vector,
* side-stepping aliasing issues when
* one of inputs is the same as the output
* [especially important in the original fortran version, I guess].
*/
static void poly_multiply(
const int pa[], int pa_degree,
const int pb[], int pb_degree,
int pc[], int * pc_degree
)
{
int j, k;
int pt[NIED2_MAX_DEGREE+1];
int pt_degree = pa_degree + pb_degree;
for(k=0; k<=pt_degree; k++) {
int term = 0;
for(j=0; j<=k; j++) {
const int conv_term = NIED2_MUL(pa[k-j], pb[j]);
term = NIED2_ADD(term, conv_term);
}
pt[k] = term;
}
for(k=0; k<=pt_degree; k++) {
pc[k] = pt[k];
}
for(k=pt_degree+1; k<=NIED2_MAX_DEGREE; k++) {
pc[k] = 0;
}
*pc_degree = pt_degree;
}
/* Calculate the values of the constants V(J,R) as
* described in BFN section 3.3.
*
* px = appropriate irreducible polynomial for current dimension
* pb = polynomial defined in section 2.3 of BFN.
* pb is modified
*/
static void calculate_v(
const int px[], int px_degree,
int pb[], int * pb_degree,
int v[], int maxv
)
{
const int nonzero_element = 1; /* nonzero element of Z_2 */
const int arbitrary_element = 1; /* arbitray element of Z_2 */
/* The polynomial ph is px**(J-1), which is the value of B on arrival.
* In section 3.3, the values of Hi are defined with a minus sign:
* don't forget this if you use them later !
*/
int ph[NIED2_MAX_DEGREE+1];
/* int ph_degree = *pb_degree; */
int bigm = *pb_degree; /* m from section 3.3 */
int m; /* m from section 2.3 */
int r, k, kj;
for(k=0; k<=NIED2_MAX_DEGREE; k++) {
ph[k] = pb[k];
}
/* Now multiply B by PX so B becomes PX**J.
* In section 2.3, the values of Bi are defined with a minus sign :
* don't forget this if you use them later !
*/
poly_multiply(px, px_degree, pb, *pb_degree, pb, pb_degree);
m = *pb_degree;
/* Now choose a value of Kj as defined in section 3.3.
* We must have 0 <= Kj < E*J = M.
* The limit condition on Kj does not seem very relevant
* in this program.
*/
/* Quoting from BFN: "Our program currently sets each K_q
* equal to eq. This has the effect of setting all unrestricted
* values of v to 1."
* Actually, it sets them to the arbitrary chosen value.
* Whatever.
*/
kj = bigm;
/* Now choose values of V in accordance with
* the conditions in section 3.3.
*/
for(r=0; r<kj; r++) {
v[r] = 0;
}
v[kj] = 1;
if(kj >= bigm) {
for(r=kj+1; r<m; r++) {
v[r] = arbitrary_element;
}
}
else {
/* This block is never reached. */
int term = NIED2_SUB(0, ph[kj]);
for(r=kj+1; r<bigm; r++) {
v[r] = arbitrary_element;
/* Check the condition of section 3.3,
* remembering that the H's have the opposite sign. [????????]
*/
term = NIED2_SUB(term, NIED2_MUL(ph[r], v[r]));
}
/* Now v[bigm] != term. */
v[bigm] = NIED2_ADD(nonzero_element, term);
for(r=bigm+1; r<m; r++) {
v[r] = arbitrary_element;
}
}
/* Calculate the remaining V's using the recursion of section 2.3,
* remembering that the B's have the opposite sign.
*/
for(r=0; r<=maxv-m; r++) {
int term = 0;
for(k=0; k<m; k++) {
term = NIED2_SUB(term, NIED2_MUL(pb[k], v[r+k]));
}
v[r+m] = term;
}
}
static void calculate_cj(nied2_state_t * ns, unsigned int dimension)
{
int ci[NIED2_NBITS][NIED2_NBITS];
int v[MAXV+1];
int r;
unsigned int i_dim;
for(i_dim=0; i_dim<dimension; i_dim++) {
const int poly_index = i_dim + 1;
int j, k;
/* Niederreiter (page 56, after equation (7), defines two
* variables Q and U. We do not need Q explicitly, but we
* do need U.
*/
int u = 0;
/* For each dimension, we need to calculate powers of an
* appropriate irreducible polynomial, see Niederreiter
* page 65, just below equation (19).
* Copy the appropriate irreducible polynomial into PX,
* and its degree into E. Set polynomial B = PX ** 0 = 1.
* M is the degree of B. Subsequently B will hold higher
* powers of PX.
*/
int pb[NIED2_MAX_DEGREE+1];
int px[NIED2_MAX_DEGREE+1];
int px_degree = poly_degree[poly_index];
int pb_degree = 0;
for(k=0; k<=px_degree; k++) {
px[k] = primitive_poly[poly_index][k];
pb[k] = 0;
}
for (;k<NIED2_MAX_DEGREE+1;k++) {
px[k] = 0;
pb[k] = 0;
}
pb[0] = 1;
for(j=0; j<NIED2_NBITS; j++) {
/* If U = 0, we need to set B to the next power of PX
* and recalculate V.
*/
if(u == 0) calculate_v(px, px_degree, pb, &pb_degree, v, MAXV);
/* Now C is obtained from V. Niederreiter
* obtains A from V (page 65, near the bottom), and then gets
* C from A (page 56, equation (7)). However this can be done
* in one step. Here CI(J,R) corresponds to
* Niederreiter's C(I,J,R).
*/
for(r=0; r<NIED2_NBITS; r++) {
ci[r][j] = v[r+u];
}
/* Advance Niederreiter's state variables. */
++u;
if(u == px_degree) u = 0;
}
/* The array CI now holds the values of C(I,J,R) for this value
* of I. We pack them into array CJ so that CJ(I,R) holds all
* the values of C(I,J,R) for J from 1 to NBITS.
*/
for(r=0; r<NIED2_NBITS; r++) {
int term = 0;
for(j=0; j<NIED2_NBITS; j++) {
term = 2*term + ci[r][j];
}
ns->cj[r][i_dim] = term;
}
}
}
static int nied2_init(void * state, unsigned int dimension)
{
nied2_state_t * n_state = (nied2_state_t *) state;
unsigned int i_dim;
if(dimension < 1 || dimension > NIED2_MAX_DIMENSION) return GSL_EINVAL;
calculate_cj(n_state, dimension);
for(i_dim=0; i_dim<dimension; i_dim++) n_state->nextq[i_dim] = 0;
n_state->sequence_count = 0;
return GSL_SUCCESS;
}
static int nied2_get(void * state, unsigned int dimension, double * v)
{
static const double recip = 1.0/(double)(1U << NIED2_NBITS); /* 2^(-nbits) */
nied2_state_t * n_state = (nied2_state_t *) state;
int r;
int c;
unsigned int i_dim;
/* Load the result from the saved state. */
for(i_dim=0; i_dim<dimension; i_dim++) {
v[i_dim] = n_state->nextq[i_dim] * recip;
}
/* Find the position of the least-significant zero in sequence_count.
* This is the bit that changes in the Gray-code representation as
* the count is advanced.
*/
r = 0;
c = n_state->sequence_count;
while(1) {
if((c % 2) == 1) {
++r;
c /= 2;
}
else break;
}
if(r >= NIED2_NBITS) return GSL_EFAILED; /* FIXME: better error code here */
/* Calculate the next state. */
for(i_dim=0; i_dim<dimension; i_dim++) {
n_state->nextq[i_dim] ^= n_state->cj[r][i_dim];
}
n_state->sequence_count++;
return GSL_SUCCESS;
}