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/*
Copyright (C) 2012 Sebastian Pancratz
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "fmpz.h"
#include "padic.h"
#include "ulong_extras.h"
void _padic_log_satoh(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N)
{
if (N < 16)
{
_padic_log_rectangular(z, y, v, p, N);
}
else
{
const slong k = n_sqrt(N);
fmpz_t t, pk, pNk;
fmpz_init(t);
fmpz_init(pk);
fmpz_init(pNk);
fmpz_pow_ui(pk, p, k);
fmpz_pow_ui(pNk, p, N + k);
fmpz_sub_ui(t, y, 1);
fmpz_neg(t, t);
fmpz_powm(t, t, pk, pNk);
fmpz_sub_ui(t, t, 1);
fmpz_neg(t, t);
/* TODO: Improve suggested valuation */
_padic_log_rectangular(z, t, k + 1, p, N + k);
fmpz_divexact(z, z, pk);
fmpz_clear(t);
fmpz_clear(pk);
fmpz_clear(pNk);
}
}
int padic_log_satoh(padic_t rop, const padic_t op, const padic_ctx_t ctx)
{
const fmpz *p = ctx->p;
const slong N = padic_prec(rop);
if (padic_val(op) < 0)
{
return 0;
}
else
{
fmpz_t y;
int ans;
fmpz_init(y);
padic_get_fmpz(y, op, ctx);
fmpz_sub_ui(y, y, 1);
fmpz_neg(y, y);
if (fmpz_is_zero(y))
{
padic_zero(rop);
ans = 1;
}
else
{
fmpz_t t;
slong v;
fmpz_init(t);
v = fmpz_remove(t, y, ctx->p);
fmpz_clear(t);
if (v >= 2 || (!fmpz_equal_ui(p, 2) && v >= 1))
{
if (v >= N)
{
padic_zero(rop);
}
else
{
_padic_log_satoh(padic_unit(rop), y, v, p, N);
padic_val(rop) = 0;
padic_reduce(rop, ctx);
}
ans = 1;
}
else
{
ans = 0;
}
}
fmpz_clear(y);
return ans;
}
}