void
arb_log_arf_huge(arb_t z, const arf_t x, slong prec)
{
arf_t t;
arb_t c;
fmpz_t exp;
slong wp;
arf_init(t);
arb_init(c);
fmpz_init(exp);
fmpz_neg(exp, ARF_EXPREF(x));
arf_mul_2exp_fmpz(t, x, exp);
wp = prec + 4 - fmpz_bits(exp);
wp = FLINT_MAX(wp, 4);
arb_log_arf(z, t, wp);
arb_const_log2(c, prec + 4);
arb_submul_fmpz(z, c, exp, prec);
arf_clear(t);
arb_clear(c);
fmpz_clear(exp);
}
void
arb_log_ui(arb_t z, ulong x, slong prec)
{
arf_t t;
arf_init(t);
arf_set_ui(t, x);
arb_log_arf(z, t, prec);
arf_clear(t);
}
void
arb_log_fmpz(arb_t z, const fmpz_t x, slong prec)
{
arf_t t;
arf_init(t);
arf_set_fmpz(t, x);
arb_log_arf(z, t, prec);
arf_clear(t);
}
void
arb_log(arb_t y, const arb_t x, slong prec)
{
if (arb_is_exact(x))
{
arb_log_arf(y, arb_midref(x), prec);
}
else
{
/*
Let the input be [a-b, a+b]. We require a > b >= 0 (otherwise the
interval contains zero or a negative number and the logarithm is not
defined). The error is largest at a-b, and we have
log(a) - log(a-b) = log(1 + b/(a-b)).
*/
mag_t err;
mag_init(err);
arb_get_mag_lower_nonnegative(err, x);
if (mag_is_zero(err))
{
mag_inf(err);
}
else
{
mag_div(err, arb_radref(x), err);
mag_log1p(err, err);
}
arb_log_arf(y, arb_midref(x), prec);
mag_add(arb_radref(y), arb_radref(y), err);
mag_clear(err);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("log_arf....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 5000 * arb_test_multiplier(); iter++)
{
arf_t x;
arb_t y1, y2;
slong prec1, prec2, acc1, acc2;
prec1 = 2 + n_randint(state, 9000);
prec2 = 2 + n_randint(state, 9000);
arf_init(x);
arb_init(y1);
arb_init(y2);
arf_randtest_special(x, state, 1 + n_randint(state, 9000), 200);
arb_randtest_special(y1, state, 1 + n_randint(state, 9000), 200);
arb_randtest_special(y2, state, 1 + n_randint(state, 9000), 200);
if (n_randint(state, 2))
arf_add_ui(x, x, 1, 2 + n_randint(state, 9000), ARF_RND_DOWN);
arb_log_arf(y1, x, prec1);
arb_log_arf(y2, x, prec2);
if (!arb_overlaps(y1, y2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("prec1 = %wd, prec2 = %wd\n\n", prec1, prec2);
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y1 = "); arb_print(y1); flint_printf("\n\n");
flint_printf("y2 = "); arb_print(y2); flint_printf("\n\n");
abort();
}
acc1 = arb_rel_accuracy_bits(y1);
acc2 = arb_rel_accuracy_bits(y2);
if (arf_sgn(x) > 0)
{
if (acc1 < prec1 - 2 || acc2 < prec2 - 2)
{
flint_printf("FAIL: accuracy\n\n");
flint_printf("prec1 = %wd, prec2 = %wd\n\n", prec1, prec2);
flint_printf("acc1 = %wd, acc2 = %wd\n\n", acc1, acc2);
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y1 = "); arb_print(y1); flint_printf("\n\n");
flint_printf("y2 = "); arb_print(y2); flint_printf("\n\n");
abort();
}
}
arf_clear(x);
arb_clear(y1);
arb_clear(y2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}