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/*
Copyright (C) 2011, 2012 Sebastian Pancratz
Copyright (C) 2013 Mike Hansen
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 "fmpz_vec.h"
#include "fmpz_poly.h"
#include "fq.h"
void
_fq_pow(fmpz * rop, const fmpz * op, slong len, const fmpz_t e,
const fq_ctx_t ctx)
{
const slong d = fq_ctx_degree(ctx);
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);
_fq_reduce(R, 2 * len - 1, ctx);
if (fmpz_tstbit(e, bit))
{
_fmpz_poly_mul(S, R, d, op, len);
_fq_reduce(S, d + len - 1, ctx);
T = R;
R = S;
S = T;
}
while (bit--)
{
if (fmpz_tstbit(e, bit))
{
_fmpz_poly_sqr(S, R, d);
_fq_reduce(S, 2 * d - 1, ctx);
_fmpz_poly_mul(R, S, d, op, len);
_fq_reduce(R, d + len - 1, ctx);
}
else
{
_fmpz_poly_sqr(S, R, d);
_fq_reduce(S, 2 * d - 1, ctx);
T = R;
R = S;
S = T;
}
}
_fmpz_vec_clear(v, 2 * d - 1);
}
}
void
fq_pow(fq_t rop, const fq_t op, const fmpz_t e, const fq_ctx_t ctx)
{
if (fmpz_sgn(e) < 0)
{
flint_throw(FLINT_ERROR, "Exception (fq_pow). e < 0.\n");
}
if (fmpz_is_zero(e))
{
fq_one(rop, ctx);
}
else if (fq_is_zero(op, ctx))
{
fq_zero(rop, ctx);
}
else if (fmpz_is_one(e))
{
fq_set(rop, op, ctx);
}
else
{
const slong d = fq_ctx_degree(ctx);
fmpz *t;
if (rop == op)
{
t = _fmpz_vec_init(2 * d - 1);
}
else
{
fmpz_poly_fit_length(rop, 2 * d - 1);
t = rop->coeffs;
}
if (fmpz_cmpabs(e, fq_ctx_prime(ctx)) < 0)
_fq_pow(t, op->coeffs, op->length, e, ctx);
else
{
fmpz_t order, e_mod;
fmpz_init(e_mod);
fmpz_init(order);
fq_ctx_order(order, ctx);
fmpz_sub_ui(order, order, 1);
fmpz_mod(e_mod, e, order);
_fq_pow(t, op->coeffs, op->length, e_mod, ctx);
fmpz_clear(order);
fmpz_clear(e_mod);
}
if (rop == op)
{
_fmpz_vec_clear(rop->coeffs, rop->alloc);
rop->coeffs = t;
rop->alloc = 2 * d - 1;
rop->length = d;
}
else
{
_fmpz_poly_set_length(rop, d);
}
_fmpz_poly_normalise(rop);
}
}