Merge pull request #2142 from fredrik-johansson/sinc2

Handle 0-containing constant term in arb_poly_sinc_pi_series; add acb_poly_sinc_pi_series

doc/source/acb_poly.rst

@@ -848,6 +848,13 @@ Elementary functions
     Sets *s* to the sinc function of the power series *h*, truncated
     to length *n*.
 
+.. function:: void _acb_poly_sinc_pi_series(acb_ptr s, acb_srcptr h, slong hlen, slong n, slong prec)
+
+.. function:: void acb_poly_sinc_pi_series(acb_poly_t s, const acb_poly_t h, slong n, slong prec)
+
+    Compute the sinc function of the input multiplied by `\pi`.
+
+
 Lambert W function
 -------------------------------------------------------------------------------
 

src/acb_poly.h

@@ -564,6 +564,8 @@ void acb_poly_tan_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec);
 
 void _acb_poly_sinc_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec);
 void acb_poly_sinc_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec);
+void _acb_poly_sinc_pi_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec);
+void acb_poly_sinc_pi_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec);
 
 void _acb_poly_lambertw_series(acb_ptr res, acb_srcptr z, slong zlen, const fmpz_t k, int flags, slong len, slong prec);
 void acb_poly_lambertw_series(acb_poly_t res, const acb_poly_t z, const fmpz_t k, int flags, slong len, slong prec);

src/acb_poly/sinc_pi_series.c

@@ -0,0 +1,85 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+    Copyright (C) 2019 D.H.J. Polymath
+
+    This file is part of FLINT.
+
+    FLINT 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 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+void
+_acb_poly_sinc_pi_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec)
+{
+    hlen = FLINT_MIN(hlen, n);
+
+    if (hlen == 1)
+    {
+        acb_sinc_pi(g, h, prec);
+        _acb_vec_zero(g + 1, n - 1);
+    }
+    else
+    {
+        acb_t pi;
+        acb_ptr t, u;
+
+        acb_init(pi);
+        t = _acb_vec_init(n + 1);
+        u = _acb_vec_init(hlen);
+
+        acb_const_pi(pi, prec);
+        _acb_vec_set(u, h, hlen);
+
+        if (acb_is_zero(h))
+        {
+            _acb_poly_sin_pi_series(t, u, hlen, n + 1, prec);
+            _acb_poly_div_series(g, t + 1, n, u + 1, hlen - 1, n, prec);
+            _acb_vec_scalar_div(g, g, n, pi, prec);
+        }
+        else if (acb_contains_zero(h))
+        {
+            _acb_vec_scalar_mul(u, h, hlen, pi, prec);
+            _acb_poly_sinc_series(g, u, hlen, n, prec);
+        }
+        else
+        {
+            _acb_poly_sin_pi_series(t, u, hlen, n, prec);
+            _acb_poly_div_series(g, t, n, u, hlen, n, prec);
+            _acb_vec_scalar_div(g, g, n, pi, prec);
+        }
+
+        acb_clear(pi);
+        _acb_vec_clear(t, n + 1);
+        _acb_vec_clear(u, hlen);
+    }
+}
+
+void
+acb_poly_sinc_pi_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec)
+{
+    slong hlen = h->length;
+
+    if (n == 0)
+    {
+        acb_poly_zero(g);
+        return;
+    }
+
+    if (hlen == 0)
+    {
+        acb_poly_one(g);
+        return;
+    }
+
+    if (hlen == 1)
+        n = 1;
+
+    acb_poly_fit_length(g, n);
+    _acb_poly_sinc_pi_series(g->coeffs, h->coeffs, hlen, n, prec);
+    _acb_poly_set_length(g, n);
+    _acb_poly_normalise(g);
+}

src/acb_poly/test/main.c

@@ -77,6 +77,7 @@
 #include "t-sin_cos_pi_series.c"
 #include "t-sin_cos_series.c"
 #include "t-sinc_series.c"
+#include "t-sinc_pi_series.c"
 #include "t-sinh_cosh_series.c"
 #include "t-sin_pi_series.c"
 #include "t-sin_series_cos_series.c"
@@ -159,6 +160,7 @@ test_struct tests[] =
     TEST_FUNCTION(acb_poly_sin_cos_pi_series),
     TEST_FUNCTION(acb_poly_sin_cos_series),
     TEST_FUNCTION(acb_poly_sinc_series),
+    TEST_FUNCTION(acb_poly_sinc_pi_series),
     TEST_FUNCTION(acb_poly_sinh_cosh_series),
     TEST_FUNCTION(acb_poly_sin_pi_series),
     TEST_FUNCTION(acb_poly_sin_series_cos_series),

src/acb_poly/test/t-sinc_pi_series.c

@@ -0,0 +1,95 @@
+/*
+    Copyright (C) 2012, 2013 Fredrik Johansson
+    Copyright (C) 2019 D.H.J. Polymath
+
+    This file is part of FLINT.
+
+    FLINT 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 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "test_helpers.h"
+#include "acb_poly.h"
+
+TEST_FUNCTION_START(acb_poly_sinc_pi_series, state)
+{
+    slong iter;
+
+    for (iter = 0; iter < 200 * 0.1 * flint_test_multiplier(); iter++)
+    {
+        slong m, n1, n2, rbits1, rbits2, rbits3, rbits4;
+        acb_poly_t a, b, c, d;
+        acb_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);
+
+        acb_poly_init(a);
+        acb_poly_init(b);
+        acb_poly_init(c);
+        acb_poly_init(d);
+        acb_init(pi);
+
+        acb_poly_randtest(a, state, m, rbits1, 10);
+        acb_poly_randtest(b, state, 10, rbits1, 10);
+        acb_poly_randtest(c, state, 10, rbits1, 10);
+
+        acb_poly_sinc_pi_series(b, a, n1, rbits2);
+        acb_poly_sinc_pi_series(c, a, n2, rbits3);
+
+        acb_poly_set(d, b);
+        acb_poly_truncate(d, FLINT_MIN(n1, n2));
+        acb_poly_truncate(c, FLINT_MIN(n1, n2));
+
+        acb_const_pi(pi, rbits4);
+
+        if (!acb_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 = "); acb_poly_printd(a, 50); flint_printf("\n\n");
+            flint_printf("b = "); acb_poly_printd(b, 50); flint_printf("\n\n");
+            flint_printf("c = "); acb_poly_printd(c, 50); flint_printf("\n\n");
+            flint_abort();
+        }
+
+        /* check pi x sinc_pi(x) = sin_pi(x) */
+        acb_poly_mullow(c, b, a, n1, rbits2);
+        acb_poly_scalar_mul(c, c, pi, rbits2);
+        acb_poly_sin_pi_series(d, a, n1, rbits2);
+
+        if (!acb_poly_overlaps(c, d))
+        {
+            flint_printf("FAIL (functional equation)\n\n");
+            flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n");
+            flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n");
+            flint_abort();
+        }
+
+        acb_poly_sinc_pi_series(a, a, n1, rbits2);
+
+        if (!acb_poly_overlaps(a, b))
+        {
+            flint_printf("FAIL (aliasing)\n\n");
+            flint_abort();
+        }
+
+        acb_poly_clear(a);
+        acb_poly_clear(b);
+        acb_poly_clear(c);
+        acb_poly_clear(d);
+        acb_clear(pi);
+    }
+
+    TEST_FUNCTION_END(state);
+}

src/arb_poly/sinc_pi_series.c

@@ -38,13 +38,19 @@ _arb_poly_sinc_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong pre
         {
             _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);
+            _arb_vec_scalar_div(g, g, n, pi, prec);
+        }
+        else if (arb_contains_zero(h))
+        {
+            _arb_vec_scalar_mul(u, h, hlen, pi, prec);
+            _arb_poly_sinc_series(g, u, hlen, 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_vec_scalar_div(g, g, n, pi, prec);
 
         arb_clear(pi);
         _arb_vec_clear(t, n + 1);