227 lines
6.5 KiB
C
227 lines
6.5 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Sebastian Pancratz
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******************************************************************************/
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#include "fmpz_mod_poly.h"
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#include "qadic.h"
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extern slong _padic_exp_bound(slong v, slong N, const fmpz_t p);
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void _qadic_exp_rectangular(fmpz *rop, const fmpz *op, slong v, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N, const fmpz_t pN)
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{
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const slong d = j[lena - 1];
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const slong n = _padic_exp_bound(v, N, p);
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if (n < 4)
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{
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if (n == 1) /* y := 1 */
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{
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fmpz_one(rop);
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_fmpz_vec_zero(rop + 1, d - 1);
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}
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else if (n == 2) /* y := 1 + x */
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{
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fmpz_t f;
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fmpz_init(f);
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fmpz_pow_ui(f, p, v);
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_fmpz_vec_scalar_mul_fmpz(rop, op, len, f);
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_fmpz_vec_zero(rop + len, d - len);
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fmpz_add_ui(rop, rop, 1);
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_fmpz_vec_scalar_mod_fmpz(rop, rop, len, pN);
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fmpz_clear(f);
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}
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else /* y := 1 + x + x^2/2 */
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{
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slong i;
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fmpz *x = _fmpz_vec_init(len + 1);
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fmpz_pow_ui(x + len, p, v);
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_fmpz_vec_scalar_mul_fmpz(x, op, len, x + len);
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_fmpz_poly_sqr(rop, x, len);
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if (*p != WORD(2))
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{
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for (i = 0; i < 2 * len - 1; i++)
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if (fmpz_is_odd(rop + i))
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fmpz_add(rop + i, rop + i, pN);
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}
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_fmpz_vec_scalar_fdiv_q_2exp(rop, rop, 2 * len - 1, 1);
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_fmpz_mod_poly_reduce(rop, 2 * len - 1, a, j, lena, pN);
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_fmpz_vec_zero(rop + (2 * len - 1), d - (2 * len - 1));
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_fmpz_mod_poly_add(rop, rop, d, x, len, pN);
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fmpz_add_ui(rop, rop, 1);
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if (fmpz_equal(rop, pN))
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fmpz_zero(rop);
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_fmpz_vec_clear(x, len + 1);
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}
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}
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else /* n >= 4 */
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{
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const slong k = fmpz_fits_si(p) ?
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(n - 1 - 1) / (fmpz_get_si(p) - 1) : 0;
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const slong b = n_sqrt(n);
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slong i;
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fmpz_t c, f, pNk;
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fmpz *s, *t, *x;
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fmpz_init(c);
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fmpz_init(f);
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fmpz_init(pNk);
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s = _fmpz_vec_init(2 * d - 1);
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t = _fmpz_vec_init(2 * d - 1);
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x = _fmpz_vec_init(d * (b + 1) + d - 1);
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fmpz_pow_ui(f, p, v);
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fmpz_pow_ui(pNk, p, N + k);
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/* Compute powers x^i of the argument */
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fmpz_one(x);
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_fmpz_vec_scalar_mul_fmpz(x + d, op, len, f);
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_fmpz_vec_zero(x + d + len, d - len);
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for (i = 2; i <= b; i++)
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{
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_fmpz_mod_poly_mul(x + i * d, x + (i - 1) * d, d, x + d, d, pNk);
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_fmpz_mod_poly_reduce(x + i * d, 2 * d - 1, a, j, lena, pNk);
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}
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_fmpz_vec_zero(rop, d);
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fmpz_one(f);
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for (i = (n + b - 1) / b - 1; i >= 0; i--)
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{
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slong lo = i * b;
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slong hi = FLINT_MIN(n - 1, lo + b - 1);
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_fmpz_vec_zero(s, d);
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fmpz_one(c);
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for ( ; hi >= lo; hi--)
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{
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_fmpz_vec_scalar_addmul_fmpz(s, x + (hi - lo) * d, d, c);
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if (hi != 0)
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fmpz_mul_ui(c, c, hi);
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}
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_fmpz_poly_mul(t, x + b * d, d, rop, d);
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_fmpz_mod_poly_reduce(t, 2 * d - 1, a, j, lena, pNk);
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_fmpz_vec_scalar_mul_fmpz(rop, s, d, f);
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_fmpz_vec_add(rop, rop, t, d);
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_fmpz_vec_scalar_mod_fmpz(rop, rop, d, pNk);
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fmpz_mul(f, f, c);
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}
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/* Note exp(x) is a unit so val(sum) == val(f). */
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i = fmpz_remove(f, f, p);
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if (i)
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{
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fmpz_pow_ui(c, p, i);
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_fmpz_vec_scalar_divexact_fmpz(rop, rop, d, c);
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}
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_padic_inv(f, f, p, N);
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_fmpz_vec_scalar_mul_fmpz(rop, rop, d, f);
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_fmpz_vec_scalar_mod_fmpz(rop, rop, d, pN);
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_fmpz_vec_clear(s, 2 * d - 1);
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_fmpz_vec_clear(t, 2 * d - 1);
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_fmpz_vec_clear(x, d * (b + 1) + d - 1);
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fmpz_clear(c);
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fmpz_clear(f);
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fmpz_clear(pNk);
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}
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}
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int qadic_exp_rectangular(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx)
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{
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const slong N = qadic_prec(rop);
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const slong v = op->val;
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const fmpz *p = (&ctx->pctx)->p;
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if (padic_poly_is_zero(op))
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{
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padic_poly_one(rop);
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return 1;
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}
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if ((*p == WORD(2) && v <= 1) || (v <= 0))
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{
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return 0;
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}
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else
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{
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if (v < N)
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{
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const slong d = qadic_ctx_degree(ctx);
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fmpz *t;
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fmpz_t pN;
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int alloc;
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alloc = _padic_ctx_pow_ui(pN, N, &ctx->pctx);
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if (rop == op)
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{
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t = _fmpz_vec_init(2 * d - 1);
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}
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else
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{
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padic_poly_fit_length(rop, 2 * d - 1);
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t = rop->coeffs;
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}
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_qadic_exp_rectangular(t, op->coeffs, v, op->length,
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ctx->a, ctx->j, ctx->len, p, N, pN);
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rop->val = 0;
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if (rop == op)
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{
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_fmpz_vec_clear(rop->coeffs, rop->alloc);
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rop->coeffs = t;
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rop->alloc = 2 * d - 1;
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rop->length = d;
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}
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_padic_poly_set_length(rop, d);
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_padic_poly_normalise(rop);
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if (alloc)
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fmpz_clear(pN);
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}
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else
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{
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padic_poly_one(rop);
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}
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return 1;
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}
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}
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