add test code for acb_dirichlet_hurwitz; more special case handling

acb_dirichlet/hurwitz.c

@@ -29,6 +29,22 @@ acb_dirichlet_hurwitz(acb_t res, const acb_t s, const acb_t a, slong prec)
         return;
     }
 
+    if (acb_is_int(s) && arf_sgn(arb_midref(acb_realref(s))) < 0 &&
+        arf_cmpabs_ui(arb_midref(acb_realref(s)), prec / 2) < 0)
+    {
+        slong n = arf_get_si(arb_midref(acb_realref(s)), ARF_RND_FLOOR);
+
+        acb_bernoulli_poly_ui(res, 1 - n, a, prec);
+        acb_div_si(res, res, n - 1, prec);
+        return;
+    }
+
+    if (arb_contains_zero(acb_imagref(s)) && arb_contains_si(acb_realref(s), 1))
+    {
+        acb_indeterminate(res);
+        return;
+    }
+
     _acb_poly_zeta_cpx_series(res, s, a, 0, 1, prec);
 }
 

acb_dirichlet/test/t-hurwitz.c

@@ -0,0 +1,84 @@
+/*
+    Copyright (C) 2017 Fredrik Johansson
+
+    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()
+{
+    slong iter;
+    flint_rand_t state;
+
+    flint_printf("hurwitz....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 3000 * arb_test_multiplier(); iter++)
+    {
+        acb_t s, a, b, z1, z2;
+        slong prec1, prec2;
+
+        acb_init(s);
+        acb_init(a);
+        acb_init(b);
+        acb_init(z1);
+        acb_init(z2);
+
+        prec1 = 2 + n_randint(state, 200);
+        prec2 = 2 + n_randint(state, 200);
+
+        acb_randtest(s, state, 1 + n_randint(state, 500), 3);
+        acb_randtest(a, state, 1 + n_randint(state, 500), 3);
+        acb_randtest(b, state, 1 + n_randint(state, 500), 10);
+        acb_randtest(z1, state, 1 + n_randint(state, 500), 10);
+        acb_randtest(z2, state, 1 + n_randint(state, 500), 10);
+
+        if (n_randint(state, 2))
+            acb_set_si(a, n_randint(state, 100) - 50);
+        if (n_randint(state, 2))
+            acb_set_si(s, n_randint(state, 100) - 50);
+
+        /* test zeta(s,a) = 2^(-s) (zeta(s,a/2) + zeta(s,(a+1)/2)) */
+        acb_mul_2exp_si(b, a, -1);
+        acb_dirichlet_hurwitz(z2, s, b, prec2);
+        acb_add_ui(b, a, 1, prec2);
+        acb_mul_2exp_si(b, b, -1);
+        acb_dirichlet_hurwitz(b, s, b, prec2);
+        acb_add(z2, z2, b, prec2);
+        acb_neg(b, s);
+        acb_set_ui(z1, 2);
+        acb_pow(b, z1, b, prec2);
+        acb_mul(z2, z2, b, prec2);
+
+        acb_dirichlet_hurwitz(z1, s, a, prec1);
+
+        if (!acb_overlaps(z1, z2))
+        {
+            flint_printf("FAIL: overlap\n\n");
+            flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n");
+            flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
+            flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n");
+            flint_printf("z2 = "); acb_printd(z2, 30); flint_printf("\n\n");
+            flint_abort();
+        }
+
+        acb_clear(s);
+        acb_clear(a);
+        acb_clear(b);
+        acb_clear(z1);
+        acb_clear(z2);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}

acb_dirichlet/zeta.c

@@ -37,6 +37,12 @@ acb_dirichlet_zeta(acb_t res, const acb_t s, slong prec)
         return;
     }
 
+    if (arb_contains_zero(acb_imagref(s)) && arb_contains_si(acb_realref(s), 1))
+    {
+        acb_indeterminate(res);
+        return;
+    }
+
     cutoff = 24.0 * prec * sqrt(prec);
 
     if (arf_cmpabs_d(arb_midref(acb_imagref(s)), cutoff) >= 0 &&