225 lines
5.0 KiB
C
225 lines
5.0 KiB
C
/*=============================================================================
|
|
|
|
This file is part of FLINT.
|
|
|
|
FLINT is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2 of the License, or
|
|
(at your option) any later version.
|
|
|
|
FLINT is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with FLINT; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2012 Sebastian Pancratz
|
|
Copyright (C) 2012 Fredrik Johansson
|
|
|
|
******************************************************************************/
|
|
|
|
#include "padic.h"
|
|
#include "ulong_extras.h"
|
|
|
|
static void
|
|
_padic_log_bsplit_series(fmpz_t P, fmpz_t B, fmpz_t T,
|
|
const fmpz_t x, slong a, slong b)
|
|
{
|
|
if (b - a == 1)
|
|
{
|
|
fmpz_set(P, x);
|
|
fmpz_set_si(B, a);
|
|
fmpz_set(T, x);
|
|
}
|
|
else if (b - a == 2)
|
|
{
|
|
fmpz_mul(P, x, x);
|
|
fmpz_set_si(B, a);
|
|
fmpz_mul_si(B, B, a + 1);
|
|
fmpz_mul_si(T, x, a + 1);
|
|
fmpz_addmul_ui(T, P, a);
|
|
}
|
|
else
|
|
{
|
|
const slong m = (a + b) / 2;
|
|
|
|
fmpz_t RP, RB, RT;
|
|
|
|
_padic_log_bsplit_series(P, B, T, x, a, m);
|
|
|
|
fmpz_init(RP);
|
|
fmpz_init(RB);
|
|
fmpz_init(RT);
|
|
|
|
_padic_log_bsplit_series(RP, RB, RT, x, m, b);
|
|
|
|
fmpz_mul(RT, RT, P);
|
|
fmpz_mul(T, T, RB);
|
|
fmpz_addmul(T, RT, B);
|
|
fmpz_mul(P, P, RP);
|
|
fmpz_mul(B, B, RB);
|
|
|
|
fmpz_clear(RP);
|
|
fmpz_clear(RB);
|
|
fmpz_clear(RT);
|
|
}
|
|
}
|
|
|
|
/*
|
|
Assumes that $y = 1 - x$ is such that $\log(x)$
|
|
converges.
|
|
|
|
Assumes that $v = \ord_p(y)$ with $v < N$, which
|
|
also forces $N$ to be positive.
|
|
|
|
The result $z$ might not be reduced modulo $p^N$.
|
|
|
|
Supports aliasing between $y$ and $z$.
|
|
*/
|
|
|
|
static void
|
|
_padic_log_bsplit(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N)
|
|
{
|
|
fmpz_t P, B, T;
|
|
slong k, n;
|
|
|
|
n = _padic_log_bound(v, N, p);
|
|
n = FLINT_MAX(n, 2);
|
|
|
|
fmpz_init(P);
|
|
fmpz_init(B);
|
|
fmpz_init(T);
|
|
|
|
_padic_log_bsplit_series(P, B, T, y, 1, n);
|
|
|
|
k = fmpz_remove(B, B, p);
|
|
fmpz_pow_ui(P, p, k);
|
|
fmpz_divexact(T, T, P);
|
|
|
|
_padic_inv(B, B, p, N);
|
|
fmpz_mul(z, T, B);
|
|
|
|
fmpz_clear(P);
|
|
fmpz_clear(B);
|
|
fmpz_clear(T);
|
|
}
|
|
|
|
void
|
|
_padic_log_balanced(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N)
|
|
{
|
|
fmpz_t pv, pN, r, t, u;
|
|
slong w;
|
|
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(pv, p);
|
|
fmpz_pow_ui(pN, p, N);
|
|
fmpz_mod(t, y, pN);
|
|
fmpz_zero(z);
|
|
w = 1;
|
|
|
|
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_sub_ui(u, r, 1);
|
|
fmpz_neg(u, u);
|
|
_padic_inv_precomp(u, u, S);
|
|
fmpz_mul(t, t, u);
|
|
fmpz_mod(t, t, pN);
|
|
}
|
|
|
|
if (!fmpz_is_zero(r))
|
|
{
|
|
_padic_log_bsplit(r, r, w, p, N);
|
|
fmpz_sub(z, z, r);
|
|
}
|
|
w *= 2;
|
|
}
|
|
|
|
fmpz_mod(z, z, pN);
|
|
|
|
fmpz_clear(pv);
|
|
fmpz_clear(pN);
|
|
fmpz_clear(r);
|
|
fmpz_clear(t);
|
|
fmpz_clear(u);
|
|
_padic_inv_clear(S);
|
|
}
|
|
|
|
int padic_log_balanced(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 x;
|
|
int ans;
|
|
|
|
fmpz_init(x);
|
|
|
|
padic_get_fmpz(x, op, ctx);
|
|
fmpz_sub_ui(x, x, 1);
|
|
fmpz_neg(x, x);
|
|
|
|
if (fmpz_is_zero(x))
|
|
{
|
|
padic_zero(rop);
|
|
ans = 1;
|
|
}
|
|
else
|
|
{
|
|
fmpz_t t;
|
|
slong v;
|
|
|
|
fmpz_init(t);
|
|
v = fmpz_remove(t, x, p);
|
|
fmpz_clear(t);
|
|
|
|
if (v >= 2 || (!fmpz_equal_ui(p, 2) && v >= 1))
|
|
{
|
|
if (v >= N)
|
|
{
|
|
padic_zero(rop);
|
|
}
|
|
else
|
|
{
|
|
_padic_log_balanced(padic_unit(rop), x, v, p, N);
|
|
padic_val(rop) = 0;
|
|
_padic_canonicalise(rop, ctx);
|
|
}
|
|
ans = 1;
|
|
}
|
|
else
|
|
{
|
|
ans = 0;
|
|
}
|
|
}
|
|
|
|
fmpz_clear(x);
|
|
return ans;
|
|
}
|
|
}
|
|
|