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/*
Copyright (C) 2011, 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_poly.h"
#include "qadic.h"
void _qadic_pow(fmpz *rop, const fmpz *op, slong len, const fmpz_t e,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p)
{
const slong d = j[lena - 1];
if (fmpz_is_zero(e))
{
fmpz_one(rop);
_fmpz_vec_zero(rop + 1, 2 * d - 1 - 1);
}
else if (fmpz_is_one(e))
{
_fmpz_vec_set(rop, op, len);
_fmpz_vec_zero(rop + len, 2 * d - 1 - len);
}
else
{
ulong bit;
fmpz *v = _fmpz_vec_init(2 * d - 1);
fmpz *R, *S, *T;
_fmpz_vec_zero(rop, 2 * d - 1);
/*
Set bits to the bitmask with a 1 one place lower than the msb of e
*/
bit = fmpz_bits(e) - 2;
/*
Trial run without any polynomial arithmetic to determine the parity
of the number of swaps; then set R and S accordingly
*/
{
unsigned int swaps = 0U;
ulong bit2 = bit;
if (fmpz_tstbit(e, bit2))
swaps = ~swaps;
while (bit2--)
if (!fmpz_tstbit(e, bit2))
swaps = ~swaps;
if (swaps == 0U)
{
R = rop;
S = v;
}
else
{
R = v;
S = rop;
}
}
/*
We unroll the first step of the loop, referring to {op, len}
*/
_fmpz_poly_sqr(R, op, len);
_fmpz_mod_poly_reduce(R, 2 * len - 1, a, j, lena, p);
if (fmpz_tstbit(e, bit))
{
_fmpz_poly_mul(S, R, d, op, len);
_fmpz_mod_poly_reduce(S, d + len - 1, a, j, lena, p);
T = R;
R = S;
S = T;
}
while (bit--)
{
if (fmpz_tstbit(e, bit))
{
_fmpz_poly_sqr(S, R, d);
_fmpz_mod_poly_reduce(S, 2 * d - 1, a, j, lena, p);
_fmpz_poly_mul(R, S, d, op, len);
_fmpz_mod_poly_reduce(R, d + len - 1, a, j, lena, p);
}
else
{
_fmpz_poly_sqr(S, R, d);
_fmpz_mod_poly_reduce(S, 2 * d - 1, a, j, lena, p);
T = R;
R = S;
S = T;
}
}
_fmpz_vec_clear(v, 2 * d - 1);
}
}
void qadic_pow(qadic_t x, const qadic_t y, const fmpz_t e, const qadic_ctx_t ctx)
{
const slong N = qadic_prec(x);
if (fmpz_sgn(e) < 0)
{
flint_throw(FLINT_ERROR, "Exception (qadic_pow). e < 0.\n");
}
if (fmpz_is_zero(e))
{
qadic_one(x);
}
else if (qadic_is_zero(y))
{
qadic_zero(x);
}
else
{
fmpz_t val; /* N - e * val(y) */
fmpz_init_set(val, e);
fmpz_mul_si(val, val, y->val);
if (fmpz_cmp_si(val, N) >= 0)
{
qadic_zero(x);
}
else if (fmpz_is_one(e))
{
qadic_set(x, y, ctx);
}
else
{
const slong d = qadic_ctx_degree(ctx);
fmpz *t;
fmpz_t pow;
int alloc;
alloc = _padic_ctx_pow_ui(pow, N - fmpz_get_si(val), &ctx->pctx);
if (x == y)
{
t = _fmpz_vec_init(2 * d - 1);
}
else
{
padic_poly_fit_length(x, 2 * d - 1);
t = x->coeffs;
}
_qadic_pow(t, y->coeffs, y->length, e, ctx->a, ctx->j, ctx->len, pow);
x->val = fmpz_get_si(val);
if (x == y)
{
_fmpz_vec_clear(x->coeffs, x->alloc);
x->coeffs = t;
x->alloc = 2 * d - 1;
x->length = d;
}
else
{
_padic_poly_set_length(x, d);
}
_padic_poly_normalise(x);
if (alloc)
fmpz_clear(pow);
}
fmpz_clear(val);
}
}