void
arb_hypgeom_legendre_q(arb_t res, const arb_t n, const arb_t m, const arb_t z, int type, slong prec)
{
acb_t t, u, v;
acb_init(t);
acb_init(u);
acb_init(v);
arb_set(acb_realref(t), n);
arb_set(acb_realref(u), m);
arb_set(acb_realref(v), z);
acb_hypgeom_legendre_q(t, t, u, v, type, prec);
if (acb_is_finite(t) && acb_is_real(t))
arb_swap(res, acb_realref(t));
else
arb_indeterminate(res);
acb_clear(t);
acb_clear(u);
acb_clear(v);
}
int main(int argc, char *argv[])
{
int function, i, numtests;
slong prec, goal;
double t, total, logtotal;
acb_t a, b, c, z, r, s;
acb_init(a);
acb_init(b);
acb_init(c);
acb_init(z);
acb_init(r);
acb_init(s);
/* J(0,pi x) I(0,pi x) K(0,pi x) */
for (function = 0; function < 3; function++)
{
total = 0.0;
logtotal = 0.0;
if (function < 2)
numtests = 40;
else
numtests = 30;
for (i = 0; i < numtests; i++)
{
// printf("%2d ", i + 1); fflush(stdout);
TIMEIT_START
prec = 96;
for (;;)
{
if (function == 0)
{
acb_set_d_d(a, input_1f1[i][0], input_1f1[i][1]);
acb_set_d_d(b, input_1f1[i][2], input_1f1[i][3]);
acb_set_d_d(z, input_1f1[i][4], input_1f1[i][5]);
acb_hypgeom_m(r, a, b, z, 0, prec);
}
else if (function == 1)
{
acb_set_d_d(a, input_1f1[i][0], input_1f1[i][1]);
acb_set_d_d(b, input_1f1[i][2], input_1f1[i][3]);
acb_set_d_d(z, input_1f1[i][4], input_1f1[i][5]);
acb_hypgeom_u(r, a, b, z, prec);
}
else if (function == 2)
{
acb_set_d_d(a, input_2f1[i][0], input_2f1[i][1]);
acb_set_d_d(b, input_2f1[i][2], input_2f1[i][3]);
acb_set_d_d(c, input_2f1[i][4], input_2f1[i][5]);
acb_set_d_d(z, input_2f1[i][6], input_2f1[i][7]);
acb_hypgeom_2f1(r, a, b, c, z, 0, prec);
}
else
{
acb_set_d_d(a, input_2f1[i][0], input_2f1[i][1]);
acb_set_d_d(b, input_2f1[i][2], input_2f1[i][3]);
acb_set_d_d(c, input_2f1[i][4], input_2f1[i][5]);
acb_set_d_d(z, input_2f1[i][6], input_2f1[i][7]);
acb_mul_2exp_si(z, z, 1);
acb_sub_ui(z, z, 1, prec);
acb_neg(z, z);
acb_hypgeom_legendre_q(r, a, c, z, 0, prec);
}
if (function == 3)
{
if (acb_rel_accuracy_bits(r) >= goal)
break;
}
else
{
if (arb_can_round_arf(acb_realref(r), goal, ARF_RND_NEAR) &&
arb_can_round_arf(acb_imagref(r), goal, ARF_RND_NEAR))
break;
}
prec *= 2;
}
TIMEIT_STOP_VAL(t)
total += t;
logtotal += log(t);
#if 1
printf("%8g, ", t);
#else
printf("%8ld %8g ", prec, t);
_acb_print(r, 25);
printf("\n");
#endif
}
printf("---------------------------------------------------------------\n");
printf("Mean %g s; geometric mean %g\n", total, exp(logtotal / numtests));
printf("---------------------------------------------------------------\n");
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
acb_clear(z);
acb_clear(r);
acb_clear(s);
}
int main()
{
long iter;
flint_rand_t state;
printf("legendre_q....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
acb_t n, m, z, res1, res2;
long prec1, prec2, ebits;
acb_init(n);
acb_init(m);
acb_init(z);
acb_init(res1);
acb_init(res2);
prec1 = 2 + n_randint(state, 300);
prec2 = 2 + n_randint(state, 300);
ebits = 1 + n_randint(state, 10);
if (n_randint(state, 2))
{
acb_set_si(m, n_randint(state, 20) - 10);
acb_set_si(n, n_randint(state, 20) - 10);
}
else
{
acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits);
acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits);
}
acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits);
_acb_hypgeom_legendre_q_single(res1, n, m, z, prec1);
_acb_hypgeom_legendre_q_double(res2, n, m, z, prec2);
if (!acb_overlaps(res1, res2))
{
printf("FAIL: consistency 1\n\n");
printf("iter = %ld, prec1 = %ld, prec2 = %ld\n\n", iter, prec1, prec2);
printf("m = "); acb_printd(m, 30); printf("\n\n");
printf("n = "); acb_printd(n, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("res1 = "); acb_printd(res1, 30); printf("\n\n");
printf("res2 = "); acb_printd(res2, 30); printf("\n\n");
abort();
}
acb_clear(n);
acb_clear(m);
acb_clear(z);
acb_clear(res1);
acb_clear(res2);
}
for (iter = 0; iter < 2000; iter++)
{
acb_t n, m, z, res1, res2, t, u;
long prec1, prec2, ebits;
int type;
acb_init(n);
acb_init(m);
acb_init(z);
acb_init(res1);
acb_init(res2);
acb_init(t);
acb_init(u);
prec1 = 2 + n_randint(state, 300);
prec2 = 2 + n_randint(state, 300);
ebits = 1 + n_randint(state, 10);
if (n_randint(state, 2))
{
acb_set_si(m, n_randint(state, 20) - 10);
acb_set_si(n, n_randint(state, 20) - 10);
}
else
{
acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits);
acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits);
}
acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits);
type = n_randint(state, 2);
acb_hypgeom_legendre_q(res1, n, m, z, type, prec1);
acb_neg(t, m);
acb_hypgeom_legendre_p(res2, n, t, z, type, prec2);
acb_add(u, m, n, prec2);
acb_add_ui(u, u, 1, prec2);
acb_gamma(u, u, prec2);
acb_mul(res2, res2, u, prec2);
acb_sub(u, n, m, prec2);
acb_add_ui(u, u, 1, prec2);
acb_rgamma(u, u, prec2);
acb_mul(res2, res2, u, prec2);
acb_hypgeom_legendre_p(t, n, m, z, type, prec2);
if (type == 0)
{
acb_cos_pi(u, m, prec2);
acb_mul(t, t, u, prec2);
}
acb_sub(res2, t, res2, prec2);
if (type == 1)
{
acb_exp_pi_i(t, m, prec2);
acb_mul(res2, res2, t, prec2);
}
acb_sin_pi(t, m, prec2);
if (acb_contains_zero(t))
acb_indeterminate(res2);
else
acb_div(res2, res2, t, prec2);
acb_const_pi(t, prec2);
acb_mul(res2, res2, t, prec2);
acb_mul_2exp_si(res2, res2, -1);
if (!acb_overlaps(res1, res2))
{
printf("FAIL: consistency 2\n\n");
printf("iter = %ld, prec1 = %ld, prec2 = %ld\n\n", iter, prec1, prec2);
printf("type = %d\n\n", type);
printf("m = "); acb_printd(m, 30); printf("\n\n");
printf("n = "); acb_printd(n, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("res1 = "); acb_printd(res1, 30); printf("\n\n");
printf("res2 = "); acb_printd(res2, 30); printf("\n\n");
abort();
}
acb_clear(n);
acb_clear(m);
acb_clear(z);
acb_clear(res1);
acb_clear(res2);
acb_clear(t);
acb_clear(u);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
_acb_hypgeom_legendre_q_double(acb_t res, const acb_t n, const acb_t m,
const acb_t z, slong prec)
{
acb_t t, u, v;
acb_init(t);
acb_init(u);
acb_init(v);
if (acb_is_int(m))
{
acb_sub_ui(t, z, 1, prec);
acb_mul_2exp_si(u, m, -1);
acb_pow(v, t, u, prec);
acb_neg(t, t);
acb_neg(u, u);
acb_pow(t, t, u, prec);
acb_mul(t, t, v, prec);
acb_hypgeom_legendre_q(u, n, m, z, 0, prec);
acb_mul(t, t, u, prec);
acb_mul_2exp_si(u, m, -1);
if (!acb_is_int(u))
acb_neg(t, t);
acb_sub_ui(u, z, 1, prec);
acb_sqrt(u, u, prec);
acb_sub_ui(v, z, 1, prec);
acb_neg(v, v);
acb_rsqrt(v, v, prec);
acb_mul(u, u, v, prec);
acb_hypgeom_legendre_p(v, n, m, z, 1, prec);
acb_mul(u, u, v, prec);
acb_const_pi(v, prec);
acb_mul(u, u, v, prec);
acb_mul_2exp_si(u, u, -1);
acb_sub(res, t, u, prec);
}
else
{
acb_sub(t, n, m, prec);
acb_add_ui(t, t, 1, prec);
acb_mul_2exp_si(u, m, 1);
acb_rising(t, t, u, prec);
acb_neg(u, m);
acb_hypgeom_legendre_p(u, n, u, z, 1, prec);
acb_mul(t, t, u, prec);
acb_hypgeom_legendre_p(u, n, m, z, 1, prec);
acb_sub(t, u, t, prec);
acb_exp_pi_i(u, m, prec);
acb_mul(t, t, u, prec);
acb_sin_pi(u, m, prec);
acb_div(t, t, u, prec);
acb_const_pi(u, prec);
acb_mul(t, t, u, prec);
acb_mul_2exp_si(t, t, -1);
acb_set(res, t);
}
acb_clear(t);
acb_clear(u);
acb_clear(v);
}