move poly sinc pi to its own file

acb_dirichlet/platt_ws_interpolation.c

@@ -11,6 +11,7 @@
 
 #include "acb_dirichlet.h"
 #include "arb_hypgeom.h"
+#include "arb_poly.h"
 
 /* Increase precision adaptively. */
 static void
@@ -413,45 +414,6 @@ _interpolation_helper_raw(arb_t res,
     arb_clear(c);
 }
 
-static void
-_arb_poly_sinc_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
-{
-    hlen = FLINT_MIN(hlen, n);
-    if (hlen == 1)
-    {
-        arb_sinc_pi(g, h, prec);
-        _arb_vec_zero(g + 1, n - 1);
-    }
-    else
-    {
-        arb_t pi;
-        arb_ptr t, u;
-
-        arb_init(pi);
-        t = _arb_vec_init(n + 1);
-        u = _arb_vec_init(hlen);
-
-        arb_const_pi(pi, prec);
-        _arb_vec_set(u, h, hlen);
-
-        if (arb_is_zero(h))
-        {
-            _arb_poly_sin_pi_series(t, u, hlen, n + 1, prec);
-            _arb_poly_div_series(g, t + 1, n, u + 1, hlen - 1, n, prec);
-        }
-        else
-        {
-            _arb_poly_sin_pi_series(t, u, hlen, n, prec);
-            _arb_poly_div_series(g, t, n, u, hlen, n, prec);
-        }
-        _arb_vec_scalar_div(g, g, n, pi, prec);
-
-        arb_clear(pi);
-        _arb_vec_clear(t, n + 1);
-        _arb_vec_clear(u, hlen);
-    }
-}
-
 /* Sets res to the function (a * exp(-(b-h)^2 / c)) * sinc_pi(d*(b-h)))
  * of the power series h, for the purpose of computing derivatives
  * of the Gaussian-windowed Whittaker-Shannon interpolation.

arb_poly.h

@@ -636,6 +636,9 @@ void arb_poly_tan_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
 void _arb_poly_sinc_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec);
 void arb_poly_sinc_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
 
+void _arb_poly_sinc_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec);
+void arb_poly_sinc_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
+
 void _arb_poly_compose_series_brent_kung(arb_ptr res, arb_srcptr poly1, slong len1,
                             arb_srcptr poly2, slong len2, slong n, slong prec);
 

arb_poly/sinc_pi_series.c

@@ -0,0 +1,80 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+    Copyright (C) 2019 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 "arb_poly.h"
+
+void
+_arb_poly_sinc_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
+{
+    hlen = FLINT_MIN(hlen, n);
+
+    if (hlen == 1)
+    {
+        arb_sinc_pi(g, h, prec);
+        _arb_vec_zero(g + 1, n - 1);
+    }
+    else
+    {
+        arb_t pi;
+        arb_ptr t, u;
+
+        arb_init(pi);
+        t = _arb_vec_init(n + 1);
+        u = _arb_vec_init(hlen);
+
+        arb_const_pi(pi, prec);
+        _arb_vec_set(u, h, hlen);
+
+        if (arb_is_zero(h))
+        {
+            _arb_poly_sin_pi_series(t, u, hlen, n + 1, prec);
+            _arb_poly_div_series(g, t + 1, n, u + 1, hlen - 1, n, prec);
+        }
+        else
+        {
+            _arb_poly_sin_pi_series(t, u, hlen, n, prec);
+            _arb_poly_div_series(g, t, n, u, hlen, n, prec);
+        }
+        _arb_vec_scalar_div(g, g, n, pi, prec);
+
+        arb_clear(pi);
+        _arb_vec_clear(t, n + 1);
+        _arb_vec_clear(u, hlen);
+    }
+}
+
+void
+arb_poly_sinc_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec)
+{
+    slong hlen = h->length;
+
+    if (n == 0)
+    {
+        arb_poly_zero(g);
+        return;
+    }
+
+    if (hlen == 0)
+    {
+        arb_poly_one(g);
+        return;
+    }
+
+    if (hlen == 1)
+        n = 1;
+
+    arb_poly_fit_length(g, n);
+    _arb_poly_sinc_pi_series(g->coeffs, h->coeffs, hlen, n, prec);
+    _arb_poly_set_length(g, n);
+    _arb_poly_normalise(g);
+}
+

arb_poly/test/t-sinc_pi_series.c

@@ -0,0 +1,104 @@
+/*
+    Copyright (C) 2012, 2013 Fredrik Johansson
+    Copyright (C) 2019 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 "arb_poly.h"
+
+int main()
+{
+    slong iter;
+    flint_rand_t state;
+
+    flint_printf("sinc_pi_series....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 200 * arb_test_multiplier(); iter++)
+    {
+        slong m, n1, n2, rbits1, rbits2, rbits3, rbits4;
+        arb_poly_t a, b, c, d;
+        arb_t pi;
+
+        rbits1 = 2 + n_randint(state, 300);
+        rbits2 = 2 + n_randint(state, 300);
+        rbits3 = 2 + n_randint(state, 300);
+        rbits4 = 2 + n_randint(state, 300);
+
+        m = n_randint(state, 15);
+        n1 = n_randint(state, 15);
+        n2 = n_randint(state, 15);
+
+        arb_poly_init(a);
+        arb_poly_init(b);
+        arb_poly_init(c);
+        arb_poly_init(d);
+        arb_init(pi);
+
+        arb_poly_randtest(a, state, m, rbits1, 10);
+        arb_poly_randtest(b, state, 10, rbits1, 10);
+        arb_poly_randtest(c, state, 10, rbits1, 10);
+
+        arb_poly_sinc_pi_series(b, a, n1, rbits2);
+        arb_poly_sinc_pi_series(c, a, n2, rbits3);
+
+        arb_poly_set(d, b);
+        arb_poly_truncate(d, FLINT_MIN(n1, n2));
+        arb_poly_truncate(c, FLINT_MIN(n1, n2));
+
+        arb_const_pi(pi, rbits4);
+
+        if (!arb_poly_overlaps(c, d))
+        {
+            flint_printf("FAIL\n\n");
+            flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd, bits4 = %wd\n", n1, n2, rbits2, rbits3, rbits4);
+            flint_printf("a = "); arb_poly_printd(a, 50); flint_printf("\n\n");
+            flint_printf("b = "); arb_poly_printd(b, 50); flint_printf("\n\n");
+            flint_printf("c = "); arb_poly_printd(c, 50); flint_printf("\n\n");
+            flint_abort();
+        }
+
+        /* check pi x sinc_pi(x) = sin_pi(x) */
+        arb_poly_mullow(c, b, a, n1, rbits2);
+        arb_poly_scalar_mul(c, c, pi, rbits2);
+        arb_poly_sin_pi_series(d, a, n1, rbits2);
+
+        if (!arb_poly_overlaps(c, d))
+        {
+            flint_printf("FAIL (functional equation)\n\n");
+            flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
+            flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n");
+            flint_abort();
+        }
+
+        arb_poly_sinc_pi_series(a, a, n1, rbits2);
+
+        if (!arb_poly_overlaps(a, b))
+        {
+            flint_printf("FAIL (aliasing)\n\n");
+            flint_abort();
+        }
+
+        arb_poly_clear(a);
+        arb_poly_clear(b);
+        arb_poly_clear(c);
+        arb_poly_clear(d);
+        arb_clear(pi);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+

doc/source/arb_poly.rst

@@ -983,6 +983,12 @@ Powers and elementary functions
     Sets *c* to the sinc function of the power series *h*, truncated
     to length *n*.
 
+.. function:: void _arb_poly_sinc_pi_series(arb_ptr s, arb_srcptr h, slong hlen, slong n, slong prec)
+
+.. function:: void arb_poly_sinc_pi_series(arb_poly_t s, const arb_poly_t h, slong n, slong prec)
+
+    Compute the sinc function of the input multiplied by `\pi`.
+
 Lambert W function
 -------------------------------------------------------------------------------