void
arb_hypgeom_u(arb_t res, const arb_t a, const arb_t b, const arb_t z, slong prec)
{
acb_t t, u, v;
acb_init(t);
acb_init(u);
acb_init(v);
arb_set(acb_realref(t), a);
arb_set(acb_realref(u), b);
arb_set(acb_realref(v), z);
acb_hypgeom_u(t, t, u, v, 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()
{
long iter;
flint_rand_t state;
printf("u....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000; iter++)
{
acb_t a0, a1, a2, b, z, w0, w1, w2, t, u;
long prec0, prec1, prec2;
acb_init(a0);
acb_init(a1);
acb_init(a2);
acb_init(b);
acb_init(z);
acb_init(w0);
acb_init(w1);
acb_init(w2);
acb_init(t);
acb_init(u);
prec0 = 2 + n_randint(state, 700);
prec1 = 2 + n_randint(state, 700);
prec2 = 2 + n_randint(state, 700);
acb_randtest_maybe_half_int(a0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest_maybe_half_int(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_add_ui(a1, a0, 1, prec0);
acb_add_ui(a2, a0, 2, prec0);
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_u_asymp_proper(w0, a0, b, z, prec0);
break;
case 1:
acb_hypgeom_u_1f1(w0, a0, b, z, prec0);
break;
default:
acb_hypgeom_u(w0, a0, b, z, prec0);
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_u_asymp_proper(w1, a0, b, z, prec1);
break;
case 1:
acb_hypgeom_u_1f1(w1, a0, b, z, prec1);
break;
default:
acb_hypgeom_u(w1, a0, b, z, prec1);
}
if (!acb_overlaps(w0, w1))
{
printf("FAIL: consistency\n\n");
printf("a = "); acb_printd(a0, 30); printf("\n\n");
printf("b = "); acb_printd(b, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("w0 = "); acb_printd(w0, 30); printf("\n\n");
printf("w1 = "); acb_printd(w1, 30); printf("\n\n");
abort();
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_u_asymp_proper(w1, a1, b, z, prec1);
break;
case 1:
acb_hypgeom_u_1f1(w1, a1, b, z, prec1);
break;
default:
acb_hypgeom_u(w1, a1, b, z, prec1);
}
switch (n_randint(state, 3))
{
case 0:
acb_hypgeom_u_asymp_proper(w2, a2, b, z, prec2);
break;
case 1:
acb_hypgeom_u_1f1(w2, a2, b, z, prec2);
break;
default:
acb_hypgeom_u(w2, a2, b, z, prec2);
}
acb_set(t, w0);
acb_mul_2exp_si(u, a0, 1);
acb_sub(u, u, b, prec0);
acb_add(u, u, z, prec0);
acb_add_ui(u, u, 2, prec0);
acb_submul(t, w1, u, prec0);
acb_sub(u, a2, b, prec0);
acb_mul(u, u, a1, prec0);
acb_addmul(t, w2, u, prec0);
if (!acb_contains_zero(t))
{
printf("FAIL: contiguous relation\n\n");
printf("a = "); acb_printd(a0, 30); printf("\n\n");
printf("b = "); acb_printd(b, 30); printf("\n\n");
printf("z = "); acb_printd(z, 30); printf("\n\n");
printf("w0 = "); acb_printd(w0, 30); printf("\n\n");
printf("w1 = "); acb_printd(w1, 30); printf("\n\n");
printf("w2 = "); acb_printd(w2, 30); printf("\n\n");
printf("t = "); acb_printd(t, 30); printf("\n\n");
abort();
}
acb_clear(a0);
acb_clear(a1);
acb_clear(a2);
acb_clear(b);
acb_clear(z);
acb_clear(w0);
acb_clear(w1);
acb_clear(w2);
acb_clear(t);
acb_clear(u);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
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);
}