int main(void)
{
fmpz_t p;
long d, i;
fq_ctx_t ctx;
clock_t c0, c1;
double c;
fq_poly_t f, g, h;
FLINT_TEST_INIT(state);
fq_poly_init(f, ctx);
fq_poly_init(g, ctx);
fq_poly_init(h, ctx);
printf("Polynomial multiplication over GF(q)\n");
printf("------------------------------------\n");
{
printf("1) Two length-10,000 polynomials over GF(3^2)\n");
fmpz_init_set_ui(p, 3);
d = 2;
fq_ctx_init_conway(ctx, p, d, "X");
fq_poly_randtest(g, state, 10000, ctx);
fq_poly_randtest(h, state, 10000, ctx);
c0 = clock();
fq_poly_mul_classical(f, g, h, ctx);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
printf("Classical: %fs\n", c);
c0 = clock();
for (i = 0; i < 100; i++)
fq_poly_mul_reorder(f, g, h, ctx);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
printf("Reorder: %fms\n", 10 * c);
c0 = clock();
for (i = 0; i < 100; i++)
fq_poly_mul_KS(f, g, h, ctx);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
printf("KS: %fms\n", 10 * c);
fq_ctx_clear(ctx);
fmpz_clear(p);
}
{
printf("2) Two length-500 polynomials over GF(3^263)\n");
fmpz_init_set_ui(p, 3);
d = 263;
fq_ctx_init_conway(ctx, p, d, "X");
fq_poly_randtest(g, state, 500, ctx);
fq_poly_randtest(h, state, 500, ctx);
c0 = clock();
fq_poly_mul_classical(f, g, h, ctx);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
printf("Classical: %fs\n", c);
c0 = clock();
fq_poly_mul_reorder(f, g, h, ctx);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
printf("Reorder: %fs\n", c);
c0 = clock();
for (i = 0; i < 100; i++)
fq_poly_mul_KS(f, g, h, ctx);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
printf("KS: %fms\n", 10 * c);
fq_ctx_clear(ctx);
fmpz_clear(p);
}
{
printf("3) Two length-5 polynomials over GF(109987^4)\n");
fmpz_init_set_ui(p, 109987);
d = 4;
fq_ctx_init_conway(ctx, p, d, "X");
fq_poly_randtest(g, state, 4, ctx);
fq_poly_randtest(h, state, 4, ctx);
c0 = clock();
for (i = 0; i < 1000 * 100; i++)
fq_poly_mul_classical(f, g, h, ctx);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
printf("Classical: %f\xb5s\n", 10 * c);
c0 = clock();
for (i = 0; i < 1000 * 100; i++)
fq_poly_mul_reorder(f, g, h, ctx);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
printf("Reorder: %f\xb5s\n", 10 * c);
c0 = clock();
for (i = 0; i < 1000 * 100; i++)
fq_poly_mul_KS(f, g, h, ctx);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
printf("KS: %f\xb5s\n", 10 * c);
fq_ctx_clear(ctx);
fmpz_clear(p);
}
fq_poly_clear(f, ctx);
fq_poly_clear(g, ctx);
fq_poly_clear(h, ctx);
FLINT_TEST_CLEANUP(state);
return EXIT_SUCCESS;
}
// Version Fq
void fq_poly_compose_mod_kedlaya_umans(fq_poly_t fg, const fq_poly_t f, const fq_poly_t g, const fq_poly_t h, slong d, fq_ctx_t ctx) {
slong n, i, j, m, dm, N, Nm, degree;
fmpz* p;
fmpz_t q;
fq_multi_poly_t f_prime;
fq_struct *vect_beta, *vect_alpha, *vect_alpha2, *vect_eval;
fq_poly_t gi;
// Vérification des paramètres
n = FLINT_MAX(fq_poly_length(f,ctx),fq_poly_length(g,ctx));
i = fq_poly_length(h,ctx);
if(n >= i) {
printf("Erreur, f ou g n'a pas été modulé par h.\n");
exit(1);
}
// Les polynômes f et g étant réduits modulo h, n vaut le nombre de coefficients de h
n = i;
if(d < 2) {
printf("d < 2\n");
exit(1);
}
if(d >= n) {
printf("d >= n\n");
exit(1);
}
p = fq_ctx_prime(ctx);
degree = fq_ctx_degree(ctx);
m = n_clog(n,d);
dm = n_pow(d,m);
N = n_pow(d,m)*m*d;
Nm = N*m;
if(fmpz_cmp_ui(p,N) < 0) {
flint_printf("\nErreur, pas assez de points d'interpolation !\n");
flint_printf("\np tient sur un mot machine, utilisez donc la version fq_nmod !\n");
exit(1);
}
// Étape 1 //////////////////////////////
fq_multi_poly_init(f_prime, dm, d, m, ctx);
_fq_vec_zero(f_prime->poly, dm, ctx);
for(i = 0 ; i < n ; i++) {
fq_poly_get_coeff(&(f_prime->poly[i]),f,i,ctx);
}
// Étape 3 //////////////////////////////
vect_beta = _fq_vec_init(N,ctx);
for(i = 0 ; i < N ; i++) {
fmpz_poly_set_coeff_ui(vect_beta + i, 0, i);
}
vect_alpha = _fq_vec_init(N*m, ctx);
fq_poly_init(gi,ctx);
fq_poly_set(gi,g,ctx);
fq_poly_evaluate_fq_vec(vect_alpha, gi, vect_beta, N, ctx);
for(i = 1 ; i < m ; i++) {
// Étape 2 //////////////////////////////
// Calcul du g^(d^i) avec g^(d^i) = [ (g^(d^(i-1))) ^ d ] mod h
fq_poly_powmod_ui_binexp(gi,gi,d,h,ctx);
fq_poly_evaluate_fq_vec(vect_alpha+i*N, gi, vect_beta, N, ctx);
}
fq_poly_clear(gi, ctx);
// Transposition
// Passe de m lignes N colonnes
// à N lignes m colonnes ==> nécessaire pour EMM dans Fp
vect_alpha2 = _fq_vec_init(Nm,ctx);
for(i = 0 ; i < m ; i++) {
for(j = 0 ; j < N ; j++) {
fq_set(vect_alpha2 + j*m + i,vect_alpha + i*N + j,ctx);
}
}
vect_alpha = vect_alpha2;
// Étape 4 //////////////////////////////
// EMM
vect_eval = _fq_vec_init(N,ctx);
fq_multi_poly_multimodular(vect_eval, N, f_prime, vect_alpha, ctx);
_fq_vec_clear(vect_alpha,Nm,ctx);
fq_multi_poly_clear(f_prime,ctx);
// Étape 5 //////////////////////////////
fq_poly_interpolate_fq_vec_fast(fg, vect_beta, vect_eval, N, ctx);
_fq_vec_clear(vect_beta,N,ctx);
_fq_vec_clear(vect_eval,N,ctx);
// Étape 6 //////////////////////////////
fq_poly_rem(fg,fg,h,ctx);
}