int f_thsh_shift(arb_t max, const arb_t t, params_t * p, slong prec) { acb_t z; acb_init(z); arb_set(acb_realref(z), t); arb_set_d(acb_imagref(z), .7); acb_sinh(z, z, prec); acb_tanh(z, z, prec); acb_abs(max, z, prec); acb_clear(z); return 1; }
int f_aj(arb_t m, const arb_t t, params_t * p, slong prec) { slong k; acb_t z, zu; arb_t abs; arb_init(abs); acb_init(z); acb_init(zu); arb_const_pi(abs, prec); arb_mul_2exp_si(abs, abs, -2); /* Pi/4 */ arb_set(acb_realref(z), t); arb_set(acb_imagref(z), abs); acb_sinh(z, z, prec); arb_mul_2exp_si(abs, abs, 1); /* Pi/2 */ acb_mul_arb(z, z, abs, prec); acb_tanh(z, z, prec); arb_one(m); for (k = 0; k < p->len; k++) { acb_sub(zu, z, p->z + k, prec); if (acb_contains_zero(zu)) { arb_clear(abs); acb_clear(zu); acb_clear(z); return 0; } acb_abs(abs, zu, prec); arb_mul(m, m, abs, prec); } arb_inv(m, m, prec); arb_clear(abs); acb_clear(zu); acb_clear(z); return 1; }
int main() { slong iter; flint_rand_t state; flint_printf("asinh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++) { acb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(a); acb_init(b); acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_asinh(a, x, prec1); acb_asinh(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check sinh(asinh(x)) = x */ acb_sinh(b, b, prec1); if (!acb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } acb_asinh(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }