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fix dft accuracy

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This commit is contained in:
Pascal 2016-08-31 10:11:50 +02:00
parent 058e17e4cc
commit f7de479c9e
12 changed files with 162 additions and 27 deletions
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9
acb_dirichlet/dft_fast.c
View file

@ -29,14 +29,11 @@
static acb_ptr
vec_extract(acb_srcptr v, slong step, slong len)
{
slong k;
slong k, l;
acb_ptr res;
res = flint_malloc(len * sizeof(acb_struct));
for (k = 0; k < len; k++)
{
res[k] = v[0];
v += step;
}
for (k = 0, l = 0; k < len; k++, l+=step)
res[k] = v[l];
return res;
}
void

113
acb_dirichlet/dft_pol.c
View file

@ -26,23 +26,136 @@
#include "acb_poly.h"
#include "acb_dirichlet.h"
void
_acb_vec_set_powers_step(acb_ptr xs, slong n, slong len, slong step, slong prec)
{
slong i, j;
prec += n_clog(n, 2);
for (i = 0, j = 0; i < len; i++, j += step)
{
if (i == 0)
acb_one(xs + j);
else if (i == 1)
acb_dirichlet_nth_root(xs + j, n, prec);
else if (i % 2 == 0)
acb_mul(xs + j, xs + j / 2, xs + j / 2, prec);
else
acb_mul(xs + j, xs + j - step, xs + step, prec);
}
}
void
_acb_vec_roots_pe(acb_ptr z, slong p, slong e, slong len, slong step, slong prec)
{
if (e <= 1)
{
_acb_vec_set_powers_step(z, p, len, step, prec);
}
else
{
slong q, r;
_acb_vec_roots_pe(z, p, e - 1, len / p, step * p, prec);
_acb_vec_set_powers_step(z, n_pow(p, e), p, step, prec);
for (q = p; q < len; q += p)
for (r = 1; r < p; r++)
acb_mul(z + (q + r) * step, z + q * step, z + r * step, prec);
}
}
#if 1
acb_ptr
acb_roots_init(slong len, slong prec)
{
slong i, q, q1;
acb_ptr z;
n_factor_t fac;
z = _acb_vec_init(len);
acb_one(z + 0);
n_factor_init(&fac);
n_factor(&fac, len, 0);
q = q1 = 1;
for (i = 0; i < fac.num; i++)
{
slong p, e, pe, mp, mq, m;
p = fac.p[i];
e = fac.exp[i];
pe = n_pow(p, e);
q1 *= pe;
mp = len / pe;
mq = len / q;
m = len / q1;
_acb_vec_roots_pe(z, p, e, pe, mp, prec);
if (i > 0)
{
slong j, jk, jl, k, l;
jl = mq; /* m * pe; */
jk = mp + mq; /* m * (q + pe); */
for (k = 1, j = jk; k < pe; k++, j += jk)
{
for (l = 1; l < q; l++, j += jl)
{
if (j >= len)
j %= len;
/*
flint_printf("[mul] (%ld * %ld + %ld * %ld) * %ld = %ld = %ld = (%ld * %ld) * (%ld * %ld)\n",k,q,l,pe,m,
((k * q + l * pe) % q1) * m, j ,k,mp,l,mq);
*/
acb_mul(z + j, z + k * mp, z + l * mq, prec);
}
}
}
q = q1;
}
return z;
}
#else
acb_ptr
acb_roots_init(slong len, slong prec)
{
acb_t zeta;
acb_ptr z;
acb_init(zeta);
prec += n_clog(len, 2);
acb_dirichlet_nth_root(zeta, len, prec);
z = _acb_vec_init(len);
/* should use factorization */
_acb_vec_set_powers(z, zeta, len, prec);
/*
flint_printf("\nroots [order %ld, prec %ld]\n", len, prec);
acb_vec_printd(z, len, 30);
*/
acb_clear(zeta);
return z;
}
#endif
/* all roots are already computed */
void
_acb_dirichlet_dft_pol(acb_ptr w, acb_srcptr v, acb_srcptr z, slong len, slong prec)
{
/* FIXME: huge accuracy loss */
#if 0
_acb_poly_evaluate_vec_fast(w, v, len, z, len, prec);
#elif 0
_acb_poly_evaluate_vec_iter(w, v, len, z, len, prec);
#else
slong i, j;
for (i = 0; i < len; i++)
{
acb_zero(w + i);
for (j = 0; j < len; j++)
acb_addmul(w + i, v + j, z + (i * j % len), prec);
}
#endif
}
void

43
acb_dirichlet/test/t-dft.c
View file

@ -29,15 +29,18 @@ int main()
{
slong k;
slong prec = 100;
slong nq = 10;
ulong q[10] = { 2, 3, 4, 5, 6, 10, 15, 30, 308, 961};
slong prec = 100, digits = 30;
slong nq = 12;
ulong q[12] = { 2, 3, 4, 5, 6, 23, 10, 15, 30, 59, 308, 961};
flint_rand_t state;
flint_printf("dft....");
fflush(stdout);
flint_randinit(state);
/* cyclic dft */
for (k = 0; k < nq; k++)
for (k = 0; k < 0 * nq; k++) /* FIXME!!!*/
{
slong i;
acb_ptr v, w1, w2;
@ -58,9 +61,9 @@ int main()
{
flint_printf("differ from index %ld / %ld \n\n",i,q[k]);
flint_printf("pol =\n");
acb_vec_printd(w1, q[k], 10);
acb_vec_printd(w1, q[k], digits);
flint_printf("fast =\n");
acb_vec_printd(w2, q[k], 10);
acb_vec_printd(w2, q[k], digits);
flint_printf("\n\n");
abort();
}
@ -89,11 +92,16 @@ int main()
acb_dirichlet_conrey_init(x, G);
acb_dirichlet_conrey_one(x, G);
#if 0
for (i = 0; i < len; i++)
{
acb_set_si(v + i, x->n);
acb_dirichlet_conrey_next(x, G);
}
#else
for (i = 0; i < len; i++)
acb_randtest_precise(v + i, state, prec, 0);
#endif
/* naive */
acb_init(chiy);
@ -125,15 +133,31 @@ int main()
flint_printf("FAIL\n\n");
flint_printf("q = %wu\n", q[k]);
flint_printf("v [size %wu]\n", len);
acb_vec_printd(v, len, 10);
acb_vec_printd(v, len, digits);
flint_printf("\nDFT differ from index %ld / %ld \n", i, len);
flint_printf("\nnaive =\n");
acb_vec_printd(w1, len, 10);
acb_vec_printd(w1, len, digits);
flint_printf("\nfast =\n");
acb_vec_printd(w2, len, 10);
acb_vec_printd(w2, len, digits);
flint_printf("\n\n");
abort();
}
else if (acb_rel_accuracy_bits(w1 + i) < 30
|| acb_rel_accuracy_bits(w2 + i) < 30)
{
flint_printf("FAIL\n\n");
flint_printf("q = %wu\n", q[k]);
flint_printf("\nDFT inaccurate from index %ld / %ld \n", i, len);
flint_printf("\nnaive =\n");
acb_printd(w1 + i, digits);
flint_printf("\nfast =\n");
acb_printd(w2 + i, digits);
flint_printf("\nerrors %ld & %ld [prec = %wu]\n",
acb_rel_accuracy_bits(w1 + i),
acb_rel_accuracy_bits(w2 + i), prec
);
abort();
}
}
_acb_vec_clear(v, len);
@ -143,5 +167,6 @@ int main()
acb_dirichlet_group_clear(G);
}
flint_randclear(state);
flint_printf("PASS\n");
}