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upper incomplete gamma workaround

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This commit is contained in:
p15-git-acc 2019-06-10 16:13:14 -05:00
parent f258c0477f
commit 90ac72b841
4 changed files with 114 additions and 6 deletions
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29
acb_dirichlet/platt_c_bound.c
View file

@ -12,6 +12,33 @@
#include "acb_dirichlet.h"
#include "arb_hypgeom.h"
/* Increase precision adaptively. */
static void
_gamma_upper_workaround(arb_t res, const arb_t s, const arb_t z,
int regularized, slong prec)
{
if (!arb_is_finite(s) || !arb_is_finite(z))
{
arb_indeterminate(res);
}
else
{
arb_t x;
slong i;
arb_init(x);
for (i = 0; i < 5; i++)
{
arb_hypgeom_gamma_upper(x, s, z, regularized, prec * (1 << i));
if (arb_rel_accuracy_bits(x) > 1)
{
break;
}
}
arb_swap(res, x);
arb_clear(x);
}
}
static void
_arb_pow_si(arb_t res, const arb_t x, slong y, slong prec)
{
@ -148,7 +175,7 @@ _pre_c_p(arb_ptr res, slong sigma, const arb_t h, ulong k, slong prec)
arb_set_si(x, k + l + 1);
arb_mul_2exp_si(x, x, -1);
arb_hypgeom_gamma_upper(x, x, u, 0, prec);
_gamma_upper_workaround(x, x, u, 0, prec);
arb_mul(res + l, res + l, x, prec);
}

31
acb_dirichlet/platt_lemma_A11.c
View file

@ -12,6 +12,33 @@
#include "acb_dirichlet.h"
#include "arb_hypgeom.h"
/* Increase precision adaptively. */
static void
_gamma_upper_workaround(arb_t res, const arb_t s, const arb_t z,
int regularized, slong prec)
{
if (!arb_is_finite(s) || !arb_is_finite(z))
{
arb_indeterminate(res);
}
else
{
arb_t x;
slong i;
arb_init(x);
for (i = 0; i < 5; i++)
{
arb_hypgeom_gamma_upper(x, s, z, regularized, prec * (1 << i));
if (arb_rel_accuracy_bits(x) > 1)
{
break;
}
}
arb_swap(res, x);
arb_clear(x);
}
}
static void
_platt_lemma_A11_X(arb_t out,
const arb_t t0, const arb_t h, slong B, const arb_t beta, slong prec)
@ -63,7 +90,7 @@ _platt_lemma_A11_Y(arb_t out,
arb_sqr(x4, x4, prec);
arb_mul_2exp_si(x4, x4, -3);
arb_hypgeom_gamma_upper(x5, x3, x4, 0, prec);
_gamma_upper_workaround(x5, x3, x4, 0, prec);
arb_mul(out, x1, x2, prec);
arb_mul(out, out, x5, prec);
@ -104,7 +131,7 @@ _platt_lemma_A11_Z(arb_t out,
arb_sqr(x4, x4, prec);
arb_mul_2exp_si(x4, x4, -1);
arb_hypgeom_gamma_upper(x5, x3, x4, 0, prec);
_gamma_upper_workaround(x5, x3, x4, 0, prec);
arb_mul(out, x1, x2, prec);
arb_mul(out, out, x5, prec);

29
acb_dirichlet/platt_lemma_A5.c
View file

@ -13,6 +13,33 @@
#include "arb_hypgeom.h"
/* Increase precision adaptively. */
static void
_gamma_upper_workaround(arb_t res, const arb_t s, const arb_t z,
int regularized, slong prec)
{
if (!arb_is_finite(s) || !arb_is_finite(z))
{
arb_indeterminate(res);
}
else
{
arb_t x;
slong i;
arb_init(x);
for (i = 0; i < 5; i++)
{
arb_hypgeom_gamma_upper(x, s, z, regularized, prec * (1 << i));
if (arb_rel_accuracy_bits(x) > 1)
{
break;
}
}
arb_swap(res, x);
arb_clear(x);
}
}
/* Lemma A5 requires B > h*sqrt(k) */
static int
_platt_lemma_A5_constraint(slong B, const arb_t h, slong k, slong prec)
@ -79,7 +106,7 @@ acb_dirichlet_platt_lemma_A5(arb_t out, slong B, const arb_t h,
arb_mul_2exp_si(x6, b, -1);
arb_hypgeom_gamma_upper(x6, x6, a, 0, prec);
_gamma_upper_workaround(x6, x6, a, 0, prec);
arb_mul(out, x4, x5, prec);
arb_mul(out, out, x6, prec);

31
acb_dirichlet/platt_ws_interpolation.c
View file

@ -12,6 +12,33 @@
#include "acb_dirichlet.h"
#include "arb_hypgeom.h"
/* Increase precision adaptively. */
static void
_gamma_upper_workaround(arb_t res, const arb_t s, const arb_t z,
int regularized, slong prec)
{
if (!arb_is_finite(s) || !arb_is_finite(z))
{
arb_indeterminate(res);
}
else
{
arb_t x;
slong i;
arb_init(x);
for (i = 0; i < 5; i++)
{
arb_hypgeom_gamma_upper(x, s, z, regularized, prec * (1 << i));
if (arb_rel_accuracy_bits(x) > 1)
{
break;
}
}
arb_swap(res, x);
arb_clear(x);
}
}
static void
_arb_div_si_si(arb_t res, slong x, slong y, slong prec)
{
@ -188,7 +215,7 @@ _platt_bound_C3_Y(arb_t res, const arb_t t0, slong A, const arb_t H,
arb_div(g2, g2, H, prec);
arb_sqr(g2, g2, prec);
arb_mul_2exp_si(g2, g2, -1);
arb_hypgeom_gamma_upper(g, g1, g2, 0, prec);
_gamma_upper_workaround(g, g1, g2, 0, prec);
/* res = a*b*A*H*g */
arb_mul_si(res, H, A, prec);
@ -231,7 +258,7 @@ _platt_bound_C3_Z(arb_t res, const arb_t t0, slong A, const arb_t H,
arb_div(g2, t0, H, prec);
arb_sqr(g2, g2, prec);
arb_mul_2exp_si(g2, g2, -1);
arb_hypgeom_gamma_upper(g, g1, g2, 0, prec);
_gamma_upper_workaround(g, g1, g2, 0, prec);
/* res = a*b*A*g */
arb_mul_si(res, g, A, prec);