int main(int argc, char *argv[])
{
acb_t r, s, a, b;
arf_t inr, outr;
long digits, prec;
if (argc < 2)
{
printf("integrals d\n");
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;
printf("Digits: %ld\n", digits);
printf("----------------------------------------------------------------\n");
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);
printf("RESULT:\n");
acb_printd(r, digits); printf("\n");
TIMEIT_ONCE_STOP
printf("----------------------------------------------------------------\n");
printf("Elliptic integral F(phi, m) = integral of 1/sqrt(1 - m*sin(t)^2)\n");
printf("from 0 to phi, with phi = 6+6i, m = 1/2. Integration path\n");
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);
printf("RESULT:\n");
acb_printd(r, digits); printf("\n");
TIMEIT_ONCE_STOP
printf("----------------------------------------------------------------\n");
printf("Bessel function J_n(z) = (1/pi) * integral of cos(t*n - z*sin(t))\n");
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);
printf("RESULT:\n");
acb_printd(r, digits); 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;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("integrate_taylor....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 150 * arb_test_multiplier(); iter++)
{
acb_t ans, res, a, b;
arf_t inr, outr;
double t;
slong goal, prec;
acb_init(ans);
acb_init(res);
acb_init(a);
acb_init(b);
arf_init(inr);
arf_init(outr);
goal = 2 + n_randint(state, 300);
prec = 2 + n_randint(state, 300);
acb_randtest(a, state, 1 + n_randint(state, 200), 2);
acb_randtest(b, state, 1 + n_randint(state, 200), 2);
acb_cos(ans, a, prec);
acb_cos(res, b, prec);
acb_sub(ans, ans, res, prec);
t = (1 + n_randint(state, 20)) / 10.0;
arf_set_d(inr, t);
arf_set_d(outr, t + (1 + n_randint(state, 20)) / 5.0);
acb_calc_integrate_taylor(res, sin_x, NULL,
a, b, inr, outr, goal, prec);
if (!acb_overlaps(res, ans))
{
flint_printf("FAIL! (iter = %wd)\n", iter);
flint_printf("prec = %wd, goal = %wd\n", prec, goal);
flint_printf("inr = "); arf_printd(inr, 15); flint_printf("\n");
flint_printf("outr = "); arf_printd(outr, 15); flint_printf("\n");
flint_printf("a = "); acb_printd(a, 15); flint_printf("\n");
flint_printf("b = "); acb_printd(b, 15); flint_printf("\n");
flint_printf("res = "); acb_printd(res, 15); flint_printf("\n\n");
flint_printf("ans = "); acb_printd(ans, 15); flint_printf("\n\n");
abort();
}
acb_clear(ans);
acb_clear(res);
acb_clear(a);
acb_clear(b);
arf_clear(inr);
arf_clear(outr);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
