/* f(z) = erf(z/sqrt(0.0002)*0.5 +1.5)*exp(-z), example provided by Silviu-Ioan Filip */
int
f_erf_bent(acb_ptr res, const acb_t z, void * param, slong order, slong prec)
{
acb_t t;
if (order > 1)
flint_abort(); /* Would be needed for Taylor method. */
acb_init(t);
acb_set_ui(t, 1250);
acb_sqrt(t, t, prec);
acb_mul(t, t, z, prec);
acb_set_d(res, 1.5);
acb_add(res, res, t, prec);
acb_hypgeom_erf(res, res, prec);
acb_neg(t, z);
acb_exp(t, t, prec);
acb_mul(res, res, t, prec);
acb_clear(t);
return 0;
}
void
acb_hypgeom_erfi(acb_t res, const acb_t z, slong prec)
{
acb_mul_onei(res, z);
acb_hypgeom_erf(res, res, prec);
acb_mul_onei(res, res);
acb_neg(res, res);
}
void
arb_hypgeom_erf(arb_t res, const arb_t z, slong prec)
{
if (!arb_is_finite(z))
{
arb_indeterminate(res);
}
else
{
acb_t t;
acb_init(t);
arb_set(acb_realref(t), z);
acb_hypgeom_erf(t, t, prec);
arb_swap(res, acb_realref(t));
acb_clear(t);
}
}
void
acb_hypgeom_fresnel_erf(acb_t res1, acb_t res2, const acb_t z, slong prec)
{
acb_t t, u, v, w1, w2;
acb_init(t);
acb_init(v);
acb_init(w1);
if (arb_is_zero(acb_imagref(z)))
{
acb_mul_onei(t, z);
acb_add(w1, z, t, 2 * prec);
acb_hypgeom_erf(t, w1, prec + 4);
acb_mul_2exp_si(t, t, 1);
acb_mul_onei(v, t);
acb_add(t, t, v, prec);
if (res1 != NULL) acb_set_arb(res1, acb_realref(t));
if (res2 != NULL) acb_set_arb(res2, acb_imagref(t));
}
else if (arb_is_zero(acb_realref(z)))
{
acb_mul_onei(t, z);
acb_sub(w1, t, z, 2 * prec);
acb_hypgeom_erf(t, w1, prec + 4);
acb_mul_2exp_si(t, t, 1);
acb_mul_onei(v, t);
acb_add(t, t, v, prec);
if (res1 != NULL) acb_set_arb(res1, acb_realref(t));
if (res1 != NULL) acb_mul_onei(res1, res1);
if (res2 != NULL) acb_set_arb(res2, acb_imagref(t));
if (res2 != NULL) acb_div_onei(res2, res2);
}
else
{
acb_init(u);
acb_init(w2);
/* w1 = (1+i)z, w2 = (1-i)z */
acb_mul_onei(t, z);
acb_add(w1, z, t, 2 * prec);
acb_sub(w2, z, t, 2 * prec);
acb_hypgeom_erf(t, w1, prec + 4);
acb_hypgeom_erf(u, w2, prec + 4);
/* S = (1+i) (t - ui) = (1+i) t + (1-i) u */
/* C = (1-i) (t + ui) = (1-i) t + (1+i) u */
acb_mul_onei(v, t);
if (res1 != NULL) acb_add(res1, t, v, prec);
if (res2 != NULL) acb_sub(res2, t, v, prec);
acb_mul_onei(v, u);
if (res1 != NULL) acb_add(res1, res1, u, prec);
if (res1 != NULL) acb_sub(res1, res1, v, prec);
if (res2 != NULL) acb_add(res2, res2, u, prec);
if (res2 != NULL) acb_add(res2, res2, v, prec);
acb_clear(u);
acb_clear(w2);
}
acb_clear(t);
acb_clear(v);
acb_clear(w1);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("erfc....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c;
slong prec1, prec2, prec3, prec4;
prec1 = 2 + n_randint(state, 1000);
prec2 = 2 + n_randint(state, 1000);
prec3 = 2 + n_randint(state, 1000);
prec4 = 2 + n_randint(state, 1000);
acb_init(a);
acb_init(b);
acb_init(c);
acb_randtest_special(a, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest_special(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
acb_randtest_special(c, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100));
switch (n_randint(state, 4))
{
case 0:
acb_hypgeom_erf_asymp(b, a, 1, prec1, prec3);
break;
case 1:
acb_hypgeom_erf(b, a, prec1);
acb_sub_ui(b, b, 1, prec1);
acb_neg(b, b);
break;
default:
acb_hypgeom_erfc(b, a, prec1);
}
switch (n_randint(state, 4))
{
case 0:
acb_hypgeom_erf_asymp(c, a, 1, prec2, prec4);
break;
case 1:
acb_hypgeom_erf(c, a, prec2);
acb_sub_ui(c, c, 1, prec2);
acb_neg(c, c);
break;
default:
acb_hypgeom_erfc(c, a, prec2);
}
if (!acb_overlaps(b, c))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
abort();
}
acb_clear(a);
acb_clear(b);
acb_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("fresnel....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t z, z2, s, c, u, v;
slong prec1, prec2;
int normalized;
prec1 = 2 + n_randint(state, 500);
prec2 = 2 + n_randint(state, 500);
acb_init(z);
acb_init(z2);
acb_init(s);
acb_init(c);
acb_init(u);
acb_init(v);
acb_randtest_special(z, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
acb_randtest_special(s, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
acb_randtest_special(c, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
normalized = n_randint(state, 2);
/* test S(z) + i C(z) = sqrt(pi/2) (1+i)/2 erf((1+i)/sqrt(2) z) */
/* u = rhs */
acb_onei(u);
acb_sqrt(u, u, prec1);
acb_mul(u, u, z, prec1);
acb_hypgeom_erf(u, u, prec1);
acb_mul_onei(v, u);
acb_add(u, u, v, prec1);
acb_mul_2exp_si(u, u, -1);
acb_const_pi(v, prec1);
acb_mul_2exp_si(v, v, -1);
acb_sqrt(v, v, prec1);
acb_mul(u, u, v, prec1);
if (normalized)
{
acb_const_pi(v, prec2);
acb_mul_2exp_si(v, v, -1);
acb_sqrt(v, v, prec2);
acb_div(z2, z, v, prec2);
}
else
{
acb_set(z2, z);
}
switch (n_randint(state, 4))
{
case 0:
acb_hypgeom_fresnel(s, c, z2, normalized, prec2);
break;
case 1:
acb_hypgeom_fresnel(s, NULL, z2, normalized, prec2);
acb_hypgeom_fresnel(NULL, c, z2, normalized, prec2);
break;
case 2:
acb_set(s, z2);
acb_hypgeom_fresnel(s, c, s, normalized, prec2);
break;
case 3:
acb_set(c, z2);
acb_hypgeom_fresnel(s, c, c, normalized, prec2);
break;
default:
acb_hypgeom_fresnel(s, c, z2, normalized, prec2);
}
if (normalized)
{
acb_mul(s, s, v, prec2);
acb_mul(c, c, v, prec2);
}
acb_mul_onei(v, c);
acb_add(v, v, s, prec2);
if (!acb_overlaps(u, v))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
flint_printf("u = "); acb_printd(u, 30); flint_printf("\n\n");
flint_printf("v = "); acb_printd(v, 30); flint_printf("\n\n");
abort();
}
acb_clear(z);
acb_clear(z2);
acb_clear(s);
acb_clear(c);
acb_clear(u);
acb_clear(v);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
