void
mag_rfac_ui(mag_t z, ulong n)
{
if (n < MAG_FAC_TABLE_NUM)
{
_fmpz_demote(MAG_EXPREF(z));
MAG_EXP(z) = mag_rfac_tab[n * 2];
MAG_MAN(z) = mag_rfac_tab[n * 2 + 1];
}
else
{
double x = n;
x = ceil((((x+0.5)*mag_d_log_lower_bound(x) - x) * 1.4426950408889634074) * -0.9999999);
/* x + 1 could round down for huge x, but this doesn't matter
as long as the value was perturbed up above */
fmpz_set_d(MAG_EXPREF(z), x + 1);
MAG_MAN(z) = MAG_ONE_HALF;
}
}
void
mag_polylog_tail(mag_t u, const mag_t z, long sigma, ulong d, ulong N)
{
mag_t TN, UN, t;
if (N < 2)
{
mag_inf(u);
return;
}
mag_init(TN);
mag_init(UN);
mag_init(t);
if (mag_cmp_2exp_si(z, 0) >= 0)
{
mag_inf(u);
}
else
{
/* Bound T(N) */
mag_pow_ui(TN, z, N);
/* multiply by log(N)^d */
if (d > 0)
{
mag_log_ui(t, N);
mag_pow_ui(t, t, d);
mag_mul(TN, TN, t);
}
/* multiply by 1/k^s */
if (sigma > 0)
{
mag_set_ui_lower(t, N);
mag_pow_ui_lower(t, t, sigma);
mag_div(TN, TN, t);
}
else if (sigma < 0)
{
mag_set_ui(t, N);
mag_pow_ui(t, t, -sigma);
mag_mul(TN, TN, t);
}
/* Bound U(N) */
mag_set(UN, z);
/* multiply by (1 + 1/N)**S */
if (sigma < 0)
{
mag_binpow_uiui(t, N, -sigma);
mag_mul(UN, UN, t);
}
/* multiply by (1 + 1/(N log(N)))^d */
if (d > 0)
{
ulong nl;
/* rounds down */
nl = mag_d_log_lower_bound(N) * N * (1 - 1e-13);
mag_binpow_uiui(t, nl, d);
mag_mul(UN, UN, t);
}
/* T(N) / (1 - U(N)) */
if (mag_cmp_2exp_si(UN, 0) >= 0)
{
mag_inf(u);
}
else
{
mag_one(t);
mag_sub_lower(t, t, UN);
mag_div(u, TN, t);
}
}
mag_clear(TN);
mag_clear(UN);
mag_clear(t);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("d_log_lower_bound....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
mpfr_t t;
double x, y, z;
mpfr_init2(t, 53);
x = d_randtest2(state);
x = ldexp(x, 100 - n_randint(state, 200));
switch (n_randint(state, 10))
{
case 0:
x = 1.0 + x;
break;
case 1:
x = 1.0 - x;
break;
case 2:
x = D_INF;
break;
case 3:
x = 0.0;
break;
case 4:
x = D_NAN;
break;
default:
break;
}
y = mag_d_log_lower_bound(x);
mpfr_set_d(t, x, MPFR_RNDD);
mpfr_log(t, t, MPFR_RNDD);
z = mpfr_get_d(t, MPFR_RNDD);
if (y > z || fabs(y-z) > 0.000001 * fabs(z))
{
flint_printf("FAIL\n");
flint_printf("x = %.20g\n", x);
flint_printf("y = %.20g\n", y);
flint_printf("z = %.20g\n", z);
abort();
}
mpfr_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
