more zeros work in progress

acb_dirichlet.h

@@ -299,6 +299,8 @@ slong _acb_dirichlet_platt_local_hardy_z_zeros(
     slong Ns_max, const arb_t H, slong sigma_interp, slong prec);
 slong acb_dirichlet_platt_local_hardy_z_zeros(
     arb_ptr res, const fmpz_t n, slong len, slong prec);
+slong acb_dirichlet_platt_hardy_z_zeros(
+    arb_ptr res, const fmpz_t n, slong len, slong prec);
 
 /* Discrete Fourier Transform */
 

acb_dirichlet/platt_hardy_z_zeros.c

@@ -0,0 +1,32 @@
+/*
+    Copyright (C) 2020 D.H.J. Polymath
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_dirichlet.h"
+
+slong
+acb_dirichlet_platt_hardy_z_zeros(
+        arb_ptr res, const fmpz_t n, slong len, slong prec)
+{
+    slong r, s=0;
+    fmpz_t k;
+    fmpz_init(k);
+    fmpz_set(k, n);
+    while (len - s)
+    {
+        r = acb_dirichlet_platt_local_hardy_z_zeros(res + s, k, len - s, prec);
+        flint_printf("r = %ld\n", r);
+        if (!r)
+            break;
+        s += r;
+        fmpz_add_si(k, k, r);
+    }
+    return s;
+}

acb_dirichlet/test/t-platt_hardy_z_zeros.c

@@ -0,0 +1,86 @@
+/*
+    Copyright (C) 2020 D.H.J. Polymath
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_dirichlet.h"
+
+int main()
+{
+    /* Check a specific combination of parameter values that is relatively fast
+     * to evaluate and that has relatively tight bounds. */
+    slong A, B, J, K, sigma_grid, Ns_max, sigma_interp;
+    arb_t h, H;
+    fmpz_t T, n;
+    arb_ptr pa, pb;
+    slong count, i;
+    slong maxcount = 50*5;
+    slong prec = 128;
+
+    flint_printf("platt_hardy_z_zeros....");
+    fflush(stdout);
+
+    arb_init(h);
+    arb_init(H);
+    fmpz_init(T);
+    fmpz_init(n);
+    pa = _arb_vec_init(maxcount);
+    pb = _arb_vec_init(maxcount);
+
+    fmpz_set_si(n, 10142);
+
+    /* parameters related to the location/resolution/width of the grid */
+    fmpz_set_si(T, 10000);
+    A = 8;
+    B = 128;
+
+    /* tuning parameters for the evaluation of grid points */
+    J = 1000;
+    K = 30;
+    sigma_grid = 63;
+    arb_set_d(h, 4.5);
+
+    /* tuning parameters for interpolation on the grid */
+    Ns_max = 200;
+    sigma_interp = 21;
+    arb_one(H);
+
+    count = acb_dirichlet_platt_hardy_z_zeros(pa, n, maxcount, prec);
+    acb_dirichlet_hardy_z_zeros(pb, n, count, prec);
+    if (count != maxcount)
+    {
+        flint_printf("FAIL: not enough zeros were isolated\n\n");
+        flint_printf("count = %wd  maxcount = %wd\n\n", count, maxcount);
+        flint_abort();
+    }
+
+    for (i = 0; i < count; i++)
+    {
+        if (!arb_overlaps(pa+i, pb+i))
+        {
+            flint_printf("FAIL: overlap\n\n");
+            flint_printf("observed[%wd] = ", i);
+            arb_printd(pa+i, 20); flint_printf("\n\n");
+            flint_printf("expected[%wd] = ", i);
+            arb_printd(pb+i, 20); flint_printf("\n\n");
+            flint_abort();
+        }
+    }
+
+    arb_clear(h);
+    arb_clear(H);
+    fmpz_clear(T);
+    fmpz_clear(n);
+    _arb_vec_clear(pa, maxcount);
+    _arb_vec_clear(pb, maxcount);
+
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}

acb_dirichlet/test/t-platt_local_hardy_z_zeros.c

@@ -1,5 +1,5 @@
 /*
-    Copyright (C) 2019 D.H.J. Polymath
+    Copyright (C) 2020 D.H.J. Polymath
 
     This file is part of Arb.
 

doc/source/acb_dirichlet.rst

@@ -785,12 +785,15 @@ and formulas described by David J. Platt in [Pla2017]_.
 
 .. function:: slong _acb_dirichlet_platt_local_hardy_z_zeros(arb_ptr res, const fmpz_t n, slong len, const fmpz_t T, slong A, slong B, const arb_t h, slong J, slong K, slong sigma_grid, slong Ns_max, const arb_t H, slong sigma_interp, slong prec)
 .. function:: slong acb_dirichlet_platt_local_hardy_z_zeros(arb_ptr res, const fmpz_t n, slong len, slong prec)
+.. function:: slong acb_dirichlet_platt_hardy_z_zeros(arb_ptr res, const fmpz_t n, slong len, slong prec)
 
-    Sets the entries of *res* to at most *len* consecutive zeros of the
+    Sets at most the first *len* entries of *res* to consecutive
-    Hardy Z-function, beginning with the *n*-th zero. Requires positive *n*.
+    zeros of the Hardy Z-function starting with the *n*-th zero.
-    The number of isolated zeros is returned. Internally this function uses
+    The number of obtained consecutive zeros is returned. The first two
-    a single call to Platt's grid evaluation of the scaled Lambda function.
+    function variants each make a single call to Platt's grid evaluation
-    The final several parameters of the underscored variant have the same
+    of the scaled Lambda function, whereas the third variant performs as many
+    evluations as necessary to obtain *len* consecutive zeros.
+    The final several parameters of the underscored local variant have the same
     meanings as in the functions :func:`acb_dirichlet_platt_multieval`
     and :func:`acb_dirichlet_platt_ws_interpolation`. The non-underscored
-    variant currently requires `10^4 \leq n \leq 3 \times 10^{17}`.
+    variants currently expect `10^4 \leq n \leq 10^{23}`.