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more tuning of pfq_choose_n

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Fredrik Johansson 2015-02-19 15:22:07 +01:00
parent a6d6a70f51
commit 2dd056d726
1 changed files with 91 additions and 68 deletions
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159
acb_hypgeom/pfq_choose_n.c
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@ -27,24 +27,86 @@
double mag_get_log2_d_approx(const mag_t x); double mag_get_log2_d_approx(const mag_t x);
int
acb_hypgeom_pfq_choose_n_double(long * nn,
const double * are, const double * aim, long p,
const double * bre, const double * bim, long q,
double log2_z,
long n_skip, long n_min, long n_max, long prec)
{
double increase, term, term_max, accuracy, accuracy_best, t, u;
double required_decrease;
long k, n, n_best;
int success;
if (p < q)
required_decrease = 0.01;
else if (p == q)
required_decrease = 0.0001;
else
required_decrease = 0.01;
term = term_max = accuracy = accuracy_best = 0.0;
success = 0;
for (n = n_best = n_skip; n < n_max; n++)
{
t = 1.0;
for (k = 0; k < FLINT_MAX(p, q); k++)
{
if (k < p)
{
u = (are[k]+n-1)*(are[k]+n-1) + (aim[k]*aim[k]);
t *= FLINT_ABS(u);
}
if (k < q)
{
u = (bre[k]+n-1)*(bre[k]+n-1) + (bim[k]*bim[k]);
u = FLINT_ABS(u);
if (u > 1e-100)
t /= u;
}
}
increase = 0.5 * log(t) * 1.4426950408889634074 + log2_z;
term += increase;
term_max = FLINT_MAX(term_max, term);
accuracy = term_max - term;
if (accuracy > accuracy_best && n >= n_min && increase < -required_decrease)
{
n_best = n;
accuracy_best = accuracy;
}
if (accuracy_best > prec + 4)
{
success = 1;
break;
}
}
*nn = n_best;
return success;
}
long long
acb_hypgeom_pfq_choose_n(acb_srcptr a, long p, acb_hypgeom_pfq_choose_n(acb_srcptr a, long p,
acb_srcptr b, long q, const acb_t z, long prec) acb_srcptr b, long q, const acb_t z, long prec)
{ {
long k, n, minimum_n, maximum_n, nint; long n_skip, n_min, n_max, n_terminating, nint;
long k, n;
double t, u;
double log2_z; double log2_z;
double log2_term;
double log2_factor;
double log2_term_max;
double * are; double * are;
double * aim; double * aim;
double * bre; double * bre;
double * bim; double * bim;
mag_t zmag; mag_t zmag;
int success;
if (acb_is_zero(z) || !acb_is_finite(z)) if (acb_is_zero(z) || !acb_is_finite(z))
return 1; return 1;
@ -59,10 +121,10 @@ acb_hypgeom_pfq_choose_n(acb_srcptr a, long p,
acb_get_mag(zmag, z); acb_get_mag(zmag, z);
log2_z = mag_get_log2_d_approx(zmag); log2_z = mag_get_log2_d_approx(zmag);
minimum_n = 1; n_skip = 1;
maximum_n = 50 + 2 * prec; n_min = 1;
n_max = FLINT_MIN(LONG_MAX / 2, 50 + 10.0 * prec);
n = 1; n_terminating = LONG_MAX;
for (k = 0; k < p; k++) for (k = 0; k < p; k++)
{ {
@ -72,8 +134,8 @@ acb_hypgeom_pfq_choose_n(acb_srcptr a, long p,
/* If the series is terminating, stop at this n. */ /* If the series is terminating, stop at this n. */
if (acb_is_int(a + k) && are[k] <= 0.0) if (acb_is_int(a + k) && are[k] <= 0.0)
{ {
maximum_n = FLINT_MIN(maximum_n, (long) (-are[k] + 1)); n_terminating = FLINT_MIN(n_terminating, (long) (-are[k] + 1));
maximum_n = FLINT_MAX(maximum_n, 1); n_terminating = FLINT_MAX(n_terminating, 1);
} }
else if (are[k] <= 0.01 && FLINT_ABS(aim[k]) < 0.01) else if (are[k] <= 0.01 && FLINT_ABS(aim[k]) < 0.01)
{ {
@ -82,10 +144,12 @@ acb_hypgeom_pfq_choose_n(acb_srcptr a, long p,
log2 of the difference instead when this happens). */ log2 of the difference instead when this happens). */
nint = floor(are[k] + 0.5); nint = floor(are[k] + 0.5);
if (FLINT_ABS(nint - are[k]) < 0.01) if (FLINT_ABS(nint - are[k]) < 0.01)
n = FLINT_MAX(n, 2 - nint); n_skip = FLINT_MAX(n_skip, 2 - nint);
} }
} }
n_max = FLINT_MIN(n_max, n_terminating);
for (k = 0; k < q; k++) for (k = 0; k < q; k++)
{ {
bre[k] = arf_get_d(arb_midref(acb_realref(b + k)), ARF_RND_DOWN); bre[k] = arf_get_d(arb_midref(acb_realref(b + k)), ARF_RND_DOWN);
@ -93,7 +157,7 @@ acb_hypgeom_pfq_choose_n(acb_srcptr a, long p,
if (bre[k] <= 0.25) if (bre[k] <= 0.25)
{ {
minimum_n = FLINT_MAX(minimum_n, 2 - bre[k]); n_min = FLINT_MAX(n_min, 2 - bre[k]);
/* Also avoid near-integers here (can even allow exact /* Also avoid near-integers here (can even allow exact
integers when computing regularized hypergeometric functions). */ integers when computing regularized hypergeometric functions). */
@ -101,68 +165,27 @@ acb_hypgeom_pfq_choose_n(acb_srcptr a, long p,
{ {
nint = floor(bre[k] + 0.5); nint = floor(bre[k] + 0.5);
if (FLINT_ABS(nint - bre[k]) < 0.01) if (FLINT_ABS(nint - bre[k]) < 0.01)
n = FLINT_MAX(n, 2 - nint); n_skip = FLINT_MAX(n_skip, 2 - nint);
} }
} }
} }
log2_term = 0.0; success = acb_hypgeom_pfq_choose_n_double(&n, are, aim, p, bre, bim, q,
log2_term_max = log2_term; log2_z, n_skip, n_min, n_max, prec);
n = FLINT_MIN(n, maximum_n); if (!success)
while (n < maximum_n && minimum_n < maximum_n)
{ {
if (log2_term < log2_term_max - prec - 4 && n >= minimum_n) if (n_terminating <= n_max)
break;
t = 1.0;
for (k = 0; k < FLINT_MAX(p, q); k++)
{ {
if (k < p) n = n_terminating;
{ }
u = (are[k] + n) * (are[k] + n) + (aim[k] * aim[k]); else
u = FLINT_ABS(u); {
n = FLINT_MAX(n_min, n);
if (u < 1e-8 || u > 1e100 || t > 1e100) n = FLINT_MIN(n_max, n);
{
n++;
goto somethingstrange;
}
t *= u;
}
if (k < q)
{
u = (bre[k] + n) * (bre[k] + n) + (bim[k] * bim[k]);
u = FLINT_ABS(u);
if (u < 1e-8 || u > 1e100 || t > 1e100)
{
n++;
goto somethingstrange;
}
t /= u;
}
} }
log2_factor = 0.5 * log(t) * 1.4426950408889634074 + log2_z;
/* For asymptotic series, require rapid decay */
if (p > q && n >= minimum_n && log2_factor > -0.2)
break;
log2_term += log2_factor;
log2_term_max = FLINT_MAX(log2_term_max, log2_term);
n++;
} }
somethingstrange:
n = FLINT_MIN(n, maximum_n);
flint_free(are); flint_free(are);
mag_clear(zmag); mag_clear(zmag);