void
mag_exp_tail(mag_t z, const mag_t x, ulong N)
{
if (N == 0 || mag_is_inf(x))
{
mag_exp(z, x);
}
else if (mag_is_zero(x))
{
mag_zero(z);
}
else
{
mag_t t;
mag_init(t);
mag_set_ui_2exp_si(t, N, -1);
/* bound by geometric series when N >= 2*x <=> N/2 >= x */
if (mag_cmp(t, x) >= 0)
{
/* 2 c^N / N! */
mag_pow_ui(t, x, N);
mag_rfac_ui(z, N);
mag_mul(z, z, t);
mag_mul_2exp_si(z, z, 1);
}
else
{
mag_exp(z, x);
}
mag_clear(t);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("rfac_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
fmpr_t x, y;
fmpz_t f;
mag_t xb;
ulong n;
fmpr_init(x);
fmpr_init(y);
fmpz_init(f);
mag_init(xb);
mag_randtest_special(xb, state, 80);
n = n_randtest(state) % 2000;
mag_rfac_ui(xb, n);
fmpz_fac_ui(f, n);
fmpr_one(x);
fmpr_div_fmpz(x, x, f, 2 * MAG_BITS, FMPR_RND_UP);
mag_get_fmpr(y, xb);
MAG_CHECK_BITS(xb)
if (!(fmpr_cmpabs(y, x) >= 0))
{
flint_printf("FAIL\n\n");
flint_printf("n = %wu\n\n", n);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
abort();
}
fmpr_clear(x);
fmpr_clear(y);
fmpz_clear(f);
mag_clear(xb);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
static __inline__ long
rec_fac_bound_2exp_si(slong n)
{
if (n < TABSIZE)
{
return rec_fac_bound_2exp_si_tab[n];
}
else
{
mag_t t;
mag_init(t);
mag_rfac_ui(t, n); /* todo: check for overflow */
return MAG_EXP(t);
}
}
/*
Given T(K), compute bound for T(n) z^n.
We need to multiply by
z^n * 1/rf(K+1,m)^r * (rf(K+1,m)/rf(K+1-A,m)) * (rf(K+1-B,m)/rf(K+1-2B,m))
where m = n - K. This is equal to
z^n *
(K+A)! (K-2B)! (K-B+m)!
----------------------- * ((K+m)! / K!)^(1-r)
(K-B)! (K-A+m)! (K-2B+m)!
*/
void
hypgeom_term_bound(mag_t Tn, const mag_t TK, slong K, slong A, slong B, int r, const mag_t z, slong n)
{
mag_t t, u, num;
slong m;
mag_init(t);
mag_init(u);
mag_init(num);
m = n - K;
if (m < 0)
{
flint_printf("hypgeom term bound\n");
abort();
}
/* TK * z^n */
mag_pow_ui(t, z, n);
mag_mul(num, TK, t);
/* numerator: (K+A)! (K-2B)! (K-B+m)! */
mag_fac_ui(t, K+A);
mag_mul(num, num, t);
mag_fac_ui(t, K-2*B);
mag_mul(num, num, t);
mag_fac_ui(t, K-B+m);
mag_mul(num, num, t);
/* denominator: (K-B)! (K-A+m)! (K-2B+m)! */
mag_rfac_ui(t, K-B);
mag_mul(num, num, t);
mag_rfac_ui(t, K-A+m);
mag_mul(num, num, t);
mag_rfac_ui(t, K-2*B+m);
mag_mul(num, num, t);
/* ((K+m)! / K!)^(1-r) */
if (r == 0)
{
mag_fac_ui(t, K+m);
mag_mul(num, num, t);
mag_rfac_ui(t, K);
mag_mul(num, num, t);
}
else if (r != 1)
{
mag_fac_ui(t, K);
mag_rfac_ui(u, K+m);
mag_mul(t, t, u);
mag_pow_ui(t, t, r-1);
mag_mul(num, num, t);
}
mag_set(Tn, num);
mag_clear(t);
mag_clear(u);
mag_clear(num);
}
