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/*=============================================================================
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) 2011, 2012 Sebastian Pancratz
******************************************************************************/
#include "fmpz_mod_poly.h"
#include "qadic.h"
void _qadic_inv(fmpz *rop, const fmpz *op, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N)
{
const slong d = j[lena - 1];
if (len == 1)
{
_padic_inv(rop, op, p, N);
_fmpz_vec_zero(rop + 1, d - 1);
}
else if (N == 1)
{
fmpz *P = _fmpz_vec_init(d + 1);
slong k;
for (k = 0; k < lena; k++)
fmpz_set(P + j[k], a + k);
_fmpz_mod_poly_invmod(rop, op, len, P, d + 1, p);
_fmpz_vec_clear(P, d + 1);
}
else /* d, N >= 2 */
{
slong *e, i, n;
fmpz *pow, *u;
fmpz *s, *t;
n = FLINT_CLOG2(N) + 1;
/* Compute sequence of exponents */
e = flint_malloc(n * sizeof(slong));
for (e[i = 0] = N; e[i] > 1; i++)
e[i + 1] = (e[i] + 1) / 2;
pow = _fmpz_vec_init(n);
u = _fmpz_vec_init(len * n);
s = _fmpz_vec_init(2 * d - 1);
t = _fmpz_vec_init(2 * d - 1);
/* Compute powers of p */
{
fmpz_one(t);
fmpz_set(pow + i, p);
}
for (i--; i >= 1; i--)
{
if (e[i] & WORD(1))
{
fmpz_mul(pow + i, t, pow + (i + 1));
fmpz_mul(t, t, t);
}
else
{
fmpz_mul(t, t, pow + (i + 1));
fmpz_mul(pow + i, pow + (i + 1), pow + (i + 1));
}
}
{
if (e[i] & WORD(1))
fmpz_mul(pow + i, t, pow + (i + 1));
else
fmpz_mul(pow + i, pow + (i + 1), pow + (i + 1));
}
/* Compute reduced units */
{
_fmpz_vec_scalar_mod_fmpz(u + 0 * len, op, len, pow + 0);
}
for (i = 1; i < n; i++)
{
_fmpz_vec_scalar_mod_fmpz(u + i * len, u + (i - 1) * len, len, pow + i);
}
/* Run Newton iteration */
i = n - 1;
{
fmpz *P = _fmpz_vec_init(d + 1);
slong k;
for (k = 0; k < lena; k++)
fmpz_set(P + j[k], a + k);
_fmpz_mod_poly_invmod(rop, u + i * len, len, P, d + 1, pow + i);
_fmpz_vec_clear(P, d + 1);
}
for (i--; i >= 0; i--) /* z' := 2 z - a z^2 */
{
_fmpz_poly_sqr(s, rop, d);
_fmpz_poly_reduce(s, 2 * d - 1, a, j, lena);
_fmpz_poly_mul(t, s, d, u + i * len, len);
_fmpz_poly_reduce(t, d + len - 1, a, j, lena);
_fmpz_vec_scalar_mul_2exp(rop, rop, d, 1);
_fmpz_poly_sub(rop, rop, d, t, d);
_fmpz_vec_scalar_mod_fmpz(rop, rop, d, pow + i);
}
_fmpz_vec_clear(pow, n);
_fmpz_vec_clear(u, len * n);
_fmpz_vec_clear(s, 2 * d - 1);
_fmpz_vec_clear(t, 2 * d - 1);
flint_free(e);
}
}
void qadic_inv(qadic_t x, const qadic_t y, const qadic_ctx_t ctx)
{
const slong N = qadic_prec(x);
if (qadic_is_zero(y))
{
flint_printf("Exception (qadic_inv). Zero is not invertible.\n");
abort();
}
/*
If y = u p^v has negative valuation with N <= -v then the
exact inverse of y is zero when reduced modulo $p^N$
*/
if (N + y->val <= 0)
{
qadic_zero(x);
}
else
{
const slong d = qadic_ctx_degree(ctx);
fmpz *t;
if (x == y)
{
t = _fmpz_vec_init(d);
}
else
{
padic_poly_fit_length(x, d);
t = x->coeffs;
}
_qadic_inv(t, y->coeffs, y->length,
ctx->a, ctx->j, ctx->len, (&ctx->pctx)->p, N + y->val);
x->val = - y->val;
if (x == y)
{
_fmpz_vec_clear(x->coeffs, x->alloc);
x->coeffs = t;
x->alloc = d;
x->length = d;
}
else
{
_padic_poly_set_length(x, d);
}
_padic_poly_normalise(x);
}
}
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