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/*
Copyright (C) 2015 Vladimir Glazachev
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 "ulong_extras.h"
#include "fmpz.h"
#include "fmpz_mod.h"
#include "aprcl.h"
void
unity_zp_pow_sliding_fmpz(unity_zp f, unity_zp g, const fmpz_t pow)
{
ulong h, k, value;
slong i, j;
unity_zp temp;
unity_zp *g_powers;
fmpz_t * t;
t = (fmpz_t*) flint_malloc(sizeof(fmpz_t) * SQUARING_SPACE);
for (i = 0; i < SQUARING_SPACE; i++)
fmpz_init(t[i]);
unity_zp_init(temp, f->p, f->exp, fmpz_mod_ctx_modulus(f->ctx));
/* reduce g by cyclopoly */
_unity_zp_reduce_cyclotomic(g);
/* temp = g * g */
unity_zp_sqr_inplace(temp, g, t);
/* selects optimal k value for n */
k = _unity_zp_pow_select_k(pow);
/*
g_powers store odd powers of g up to 2^k - 1;
g_powers[(i + 1) / 2] = g^i
*/
g_powers = (unity_zp*) flint_malloc(sizeof(unity_zp) * (n_pow(2, k - 1) + 1));
/* sets g_powers[0] = 1 */
unity_zp_init(g_powers[0], f->p, f->exp, fmpz_mod_ctx_modulus(f->ctx));
unity_zp_coeff_set_ui(g_powers[0], 0, 1);
/* sets g_powers[1] = g */
unity_zp_init(g_powers[1], f->p, f->exp, fmpz_mod_ctx_modulus(f->ctx));
unity_zp_copy(g_powers[1], g);
/* sets g_powers[i] = g^2 * g_powers[i - 1] */
for (i = 2; i <= n_pow(2, k - 1); i++)
{
unity_zp_init(g_powers[i], f->p, f->exp, fmpz_mod_ctx_modulus(f->ctx));
unity_zp_mul_inplace(g_powers[i], g_powers[i - 1], temp, t);
}
unity_zp_set_zero(f);
unity_zp_coeff_set_ui(f, 0, 1);
i = fmpz_bits(pow) - 1;
/* working with pow = (e_l, e_{l-1}, ... , e_0) in 2 base */
while (i >= 0)
{
if (fmpz_tstbit(pow, i) == 0)
{
unity_zp_sqr_inplace(temp, f, t);
unity_zp_swap(temp, f);
i--;
}
else
{
/*
finds length of chain; chain is length of
longest bitstring less then k ending on 1
*/
j = FLINT_MAX(i - k + 1, 0);
while (fmpz_tstbit(pow, j) == 0 && j <= i)
j++;
/* f = f^(2^(i - j + 1)) */
for (h = 0; h < i - j + 1; h++)
{
unity_zp_sqr_inplace(temp, f, t);
unity_zp_swap(temp, f);
}
/*
value = binary number (e_i, ... , e_j) in decimal base
*/
value = 0;
for (h = 0; h < i - j + 1; h++)
value += fmpz_tstbit(pow, j + h) << h;
/* f = f * g^value */
unity_zp_mul_inplace(temp, f, g_powers[(value + 1) / 2], t);
unity_zp_swap(temp, f);
/* increase i */
i = j - 1;
}
}
for (i = 0; i < SQUARING_SPACE; i++)
fmpz_clear(t[i]);
flint_free(t);
for (i = 0; i <= n_pow(2, k - 1); i++)
unity_zp_clear(g_powers[i]);
flint_free(g_powers);
unity_zp_clear(temp);
}