void
_padic_log_balanced(fmpz_t z, const fmpz_t y, long v, const fmpz_t p, long N)
{
fmpz_t pv, pN, r, t, u;
long val;
padic_inv_t S;
fmpz_init(pv);
fmpz_init(pN);
fmpz_init(r);
fmpz_init(t);
fmpz_init(u);
_padic_inv_precompute(S, p, N);
fmpz_set(t, y);
fmpz_set(pv, p);
fmpz_pow_ui(pN, p, N);
fmpz_zero(z);
val = 1;
/*
TODO: Abort earlier if larger than $p^N$, possible
with variable precision?
*/
while (!fmpz_is_zero(t))
{
fmpz_mul(pv, pv, pv);
fmpz_fdiv_qr(t, r, t, pv);
if (!fmpz_is_zero(t))
{
fmpz_mul(t, t, pv);
fmpz_add_ui(u, r, 1);
_padic_inv_precomp(u, u, S);
fmpz_mul(t, t, u);
fmpz_mod(t, t, pN);
}
if (!fmpz_is_zero(r))
{
fmpz_neg(r, r);
_padic_log_bsplit(r, r, val, p, N);
fmpz_sub(z, z, r);
}
val *= 2;
}
fmpz_clear(pv);
fmpz_clear(pN);
fmpz_clear(r);
fmpz_clear(t);
fmpz_clear(u);
_padic_inv_clear(S);
}
static void precompute_nu(fmpz *nu, long *v, long M,
const long *C, long lenC, long p, long N)
{
const long R = M / p;
const long N2 = N + (M / (p - 1));
fmpz_t P, PN2, t;
padic_inv_t S;
double pinv;
long i, j;
fmpz_init_set_ui(P, p);
fmpz_init(PN2);
fmpz_pow_ui(PN2, P, N2);
fmpz_init(t);
/*
Step 1. Compute $i! mod p^{N_2}$ where $N_2 \geq N + \max \ord_p (i!)$
Step 2. Invert the unit part of $i!$ modulo $p^N$
*/
fmpz_one(nu + 0);
for (i = 1; i <= R; i++)
{
fmpz_mul_ui(nu + i, nu + (i - 1), i);
fmpz_mod(nu + i, nu + i, PN2);
}
/* Let j denote the greatest index s.t. nu[j] has been computed */
for (j = R, i = R + 1; i <= M; i++)
{
if (_bsearch(C, 0, lenC, i % p) != -1)
{
fmpz_mod_rfac_uiui(t, j + 1, i - j, PN2);
fmpz_mul(nu + i, nu + j, t);
fmpz_mod(nu + i, nu + i, PN2);
j = i;
}
}
_padic_inv_precompute(S, P, N);
pinv = n_precompute_inverse(p);
v[0] = 0;
for (i = 1; i <= R; i++)
{
v[i] = - _fmpz_remove(nu + i, P, pinv);
_padic_inv_precomp(nu + i, nu + i, S);
}
for (i = R + 1; i <= M; i++)
{
if (_bsearch(C, 0, lenC, i % p) != -1)
{
v[i] = - _fmpz_remove(nu + i, P, pinv);
_padic_inv_precomp(nu + i, nu + i, S);
}
}
fmpz_clear(P);
fmpz_clear(PN2);
fmpz_clear(t);
_padic_inv_clear(S);
}