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/* This file is public domain. Author: Fredrik Johansson. */
#include <stdlib.h>
#include <flint/acb_poly.h>
#include <flint/arb_calc.h>
#include <flint/acb_calc.h>
#include <flint/profiler.h>
int
sinx(acb_ptr out, const acb_t inp, void * params, slong order, slong prec)
{
int xlen = FLINT_MIN(2, order);
acb_set(out, inp);
if (xlen > 1)
acb_one(out + 1);
_acb_poly_sin_series(out, out, xlen, order, prec);
return 0;
}
int
elliptic(acb_ptr out, const acb_t inp, void * params, slong order, slong prec)
{
acb_ptr t;
t = _acb_vec_init(order);
acb_set(t, inp);
if (order > 1)
acb_one(t + 1);
_acb_poly_sin_series(t, t, FLINT_MIN(2, order), order, prec);
_acb_poly_mullow(out, t, order, t, order, order, prec);
_acb_vec_scalar_mul_2exp_si(t, out, order, -1);
acb_sub_ui(t, t, 1, prec);
_acb_vec_neg(t, t, order);
_acb_poly_rsqrt_series(out, t, order, order, prec);
_acb_vec_clear(t, order);
return 0;
}
int
bessel(acb_ptr out, const acb_t inp, void * params, slong order, slong prec)
{
acb_ptr t;
acb_t z;
ulong n;
t = _acb_vec_init(order);
acb_init(z);
acb_set(t, inp);
if (order > 1)
acb_one(t + 1);
n = 10;
arb_set_si(acb_realref(z), 20);
arb_set_si(acb_imagref(z), 10);
/* z sin(t) */
_acb_poly_sin_series(out, t, FLINT_MIN(2, order), order, prec);
_acb_vec_scalar_mul(out, out, order, z, prec);
/* t n */
_acb_vec_scalar_mul_ui(t, t, FLINT_MIN(2, order), n, prec);
_acb_poly_sub(out, t, FLINT_MIN(2, order), out, order, prec);
_acb_poly_cos_series(out, out, order, order, prec);
_acb_vec_clear(t, order);
acb_clear(z);
return 0;
}
int main(int argc, char *argv[])
{
acb_t r, s, a, b;
arf_t inr, outr;
slong digits, prec;
if (argc < 2)
{
flint_printf("integrals d\n");
flint_printf("compute integrals using d decimal digits of precision\n");
return 1;
}
acb_init(r);
acb_init(s);
acb_init(a);
acb_init(b);
arf_init(inr);
arf_init(outr);
arb_calc_verbose = 0;
digits = atol(argv[1]);
prec = digits * 3.32193;
flint_printf("Digits: %wd\n", digits);
flint_printf("----------------------------------------------------------------\n");
flint_printf("Integral of sin(t) from 0 to 100.\n");
arf_set_d(inr, 0.125);
arf_set_d(outr, 1.0);
TIMEIT_ONCE_START;
acb_set_si(a, 0);
acb_set_si(b, 100);
acb_calc_integrate_taylor(r, sinx, NULL, a, b, inr, outr, prec, 1.1 * prec);
flint_printf("RESULT:\n");
acb_printn(r, digits, 0); flint_printf("\n");
TIMEIT_ONCE_STOP;
flint_printf("----------------------------------------------------------------\n");
flint_printf("Elliptic integral F(phi, m) = integral of 1/sqrt(1 - m*sin(t)^2)\n");
flint_printf("from 0 to phi, with phi = 6+6i, m = 1/2. Integration path\n");
flint_printf("0 -> 6 -> 6+6i.\n");
arf_set_d(inr, 0.2);
arf_set_d(outr, 0.5);
TIMEIT_ONCE_START;
acb_set_si(a, 0);
acb_set_si(b, 6);
acb_calc_integrate_taylor(r, elliptic, NULL, a, b, inr, outr, prec, 1.1 * prec);
acb_set_si(a, 6);
arb_set_si(acb_realref(b), 6);
arb_set_si(acb_imagref(b), 6);
acb_calc_integrate_taylor(s, elliptic, NULL, a, b, inr, outr, prec, 1.1 * prec);
acb_add(r, r, s, prec);
flint_printf("RESULT:\n");
acb_printn(r, digits, 0); flint_printf("\n");
TIMEIT_ONCE_STOP;
flint_printf("----------------------------------------------------------------\n");
flint_printf("Bessel function J_n(z) = (1/pi) * integral of cos(t*n - z*sin(t))\n");
flint_printf("from 0 to pi. With n = 10, z = 20 + 10i.\n");
arf_set_d(inr, 0.1);
arf_set_d(outr, 0.5);
TIMEIT_ONCE_START;
acb_set_si(a, 0);
acb_const_pi(b, 3 * prec);
acb_calc_integrate_taylor(r, bessel, NULL, a, b, inr, outr, prec, 3 * prec);
acb_div(r, r, b, prec);
flint_printf("RESULT:\n");
acb_printn(r, digits, 0); flint_printf("\n");
TIMEIT_ONCE_STOP;
acb_clear(r);
acb_clear(s);
acb_clear(a);
acb_clear(b);
arf_clear(inr);
arf_clear(outr);
flint_cleanup();
return 0;
}
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