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fredrik-johanssonfredrik-johansson
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handle 0-containing constant term in arb_poly_sinc_pi_series; add acb_poly_sinc_pi_series
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6 files changed

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6 files changed

+198
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lines changed

‎doc/source/acb_poly.rst

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

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

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

‎src/acb_poly/test/main.c

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

‎src/acb_poly/test/t-sinc_pi_series.c

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@@ -0,0 +1,95 @@
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/*
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Copyright (C) 2012, 2013 Fredrik Johansson
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Copyright (C) 2019 D.H.J. Polymath
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This file is part of FLINT.
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FLINT is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 3 of the License, or
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(at your option) any later version. See <https://www.gnu.org/licenses/>.
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*/
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#include "test_helpers.h"
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#include "acb_poly.h"
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TEST_FUNCTION_START(acb_poly_sinc_pi_series, state)
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{
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slong iter;
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for (iter = 0; iter < 200 * 0.1 * flint_test_multiplier(); iter++)
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{
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slong m, n1, n2, rbits1, rbits2, rbits3, rbits4;
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acb_poly_t a, b, c, d;
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acb_t pi;
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rbits1 = 2 + n_randint(state, 300);
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rbits2 = 2 + n_randint(state, 300);
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rbits3 = 2 + n_randint(state, 300);
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rbits4 = 2 + n_randint(state, 300);
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m = n_randint(state, 15);
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n1 = n_randint(state, 15);
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n2 = n_randint(state, 15);
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acb_poly_init(a);
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acb_poly_init(b);
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acb_poly_init(c);
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acb_poly_init(d);
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acb_init(pi);
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acb_poly_randtest(a, state, m, rbits1, 10);
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acb_poly_randtest(b, state, 10, rbits1, 10);
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acb_poly_randtest(c, state, 10, rbits1, 10);
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acb_poly_sinc_pi_series(b, a, n1, rbits2);
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acb_poly_sinc_pi_series(c, a, n2, rbits3);
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acb_poly_set(d, b);
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acb_poly_truncate(d, FLINT_MIN(n1, n2));
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acb_poly_truncate(c, FLINT_MIN(n1, n2));
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acb_const_pi(pi, rbits4);
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if (!acb_poly_overlaps(c, d))
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{
56+
flint_printf("FAIL\n\n");
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flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd, bits4 = %wd\n", n1, n2, rbits2, rbits3, rbits4);
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flint_printf("a = "); acb_poly_printd(a, 50); flint_printf("\n\n");
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flint_printf("b = "); acb_poly_printd(b, 50); flint_printf("\n\n");
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flint_printf("c = "); acb_poly_printd(c, 50); flint_printf("\n\n");
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flint_abort();
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}
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/* check pi x sinc_pi(x) = sin_pi(x) */
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acb_poly_mullow(c, b, a, n1, rbits2);
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acb_poly_scalar_mul(c, c, pi, rbits2);
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acb_poly_sin_pi_series(d, a, n1, rbits2);
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if (!acb_poly_overlaps(c, d))
70+
{
71+
flint_printf("FAIL (functional equation)\n\n");
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flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
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flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
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flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n");
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flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n");
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flint_abort();
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}
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acb_poly_sinc_pi_series(a, a, n1, rbits2);
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if (!acb_poly_overlaps(a, b))
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{
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flint_printf("FAIL (aliasing)\n\n");
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flint_abort();
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}
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acb_poly_clear(a);
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acb_poly_clear(b);
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acb_poly_clear(c);
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acb_poly_clear(d);
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acb_clear(pi);
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}
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TEST_FUNCTION_END(state);
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}

‎src/arb_poly/sinc_pi_series.c

+7-1
Original file line numberDiff line numberDiff line change
@@ -38,13 +38,19 @@ _arb_poly_sinc_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong pre
3838
{
3939
_arb_poly_sin_pi_series(t, u, hlen, n + 1, prec);
4040
_arb_poly_div_series(g, t + 1, n, u + 1, hlen - 1, n, prec);
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_arb_vec_scalar_div(g, g, n, pi, prec);
42+
}
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else if (arb_contains_zero(h))
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{
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_arb_vec_scalar_mul(u, h, hlen, pi, prec);
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_arb_poly_sinc_series(g, u, hlen, n, prec);
4147
}
4248
else
4349
{
4450
_arb_poly_sin_pi_series(t, u, hlen, n, prec);
4551
_arb_poly_div_series(g, t, n, u, hlen, n, prec);
52+
_arb_vec_scalar_div(g, g, n, pi, prec);
4653
}
47-
_arb_vec_scalar_div(g, g, n, pi, prec);
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4955
arb_clear(pi);
5056
_arb_vec_clear(t, n + 1);

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