236 lines
6.1 KiB
C
236 lines
6.1 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 "qadic.h"
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extern slong _padic_exp_bound(slong v, slong N, const fmpz_t p);
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static void
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_qadic_exp_bsplit_series(fmpz *P, fmpz_t Q, fmpz *T,
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const fmpz *x, slong len, slong lo, slong hi,
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const fmpz *a, const slong *j, slong lena)
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{
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const slong d = j[lena - 1];
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if (hi - lo == 1)
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{
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_fmpz_vec_set(P, x, len);
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_fmpz_vec_zero(P + len, 2*d - 1 - len);
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fmpz_set_si(Q, lo);
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_fmpz_vec_set(T, P, 2*d - 1);
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}
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else if (hi - lo == 2)
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{
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_fmpz_poly_sqr(P, x, len);
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_fmpz_vec_zero(P + (2*len - 1), d - (2*len - 1));
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_fmpz_poly_reduce(P, 2*len - 1, a, j, lena);
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fmpz_set_si(Q, lo);
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fmpz_mul_si(Q, Q, lo + 1);
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_fmpz_vec_scalar_mul_si(T, x, len, lo + 1);
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_fmpz_vec_zero(T + len, d - len);
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_fmpz_vec_add(T, T, P, d);
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}
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else
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{
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const slong m = (lo + hi) / 2;
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fmpz *PR, *TR, *W;
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fmpz_t QR;
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PR = _fmpz_vec_init(2*d - 1);
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TR = _fmpz_vec_init(2*d - 1);
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W = _fmpz_vec_init(2*d - 1);
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fmpz_init(QR);
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_qadic_exp_bsplit_series(P, Q, T, x, len, lo, m, a, j, lena);
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_qadic_exp_bsplit_series(PR, QR, TR, x, len, m, hi, a, j, lena);
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_fmpz_poly_mul(W, TR, d, P, d);
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_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
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_fmpz_vec_scalar_mul_fmpz(T, T, d, QR);
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_fmpz_vec_add(T, T, W, d);
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_fmpz_poly_mul(W, P, d, PR, d);
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_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
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_fmpz_vec_swap(P, W, d);
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fmpz_mul(Q, Q, QR);
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_fmpz_vec_clear(PR, 2*d - 1);
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_fmpz_vec_clear(TR, 2*d - 1);
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_fmpz_vec_clear(W, 2*d - 1);
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fmpz_clear(QR);
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}
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}
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static void
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_qadic_exp_bsplit(fmpz *y, const fmpz *x, 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)
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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 == 1)
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{
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fmpz_one(y + 0);
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_fmpz_vec_zero(y + 1, d - 1);
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}
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else
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{
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fmpz *P, *T;
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fmpz_t Q, R;
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slong f;
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P = _fmpz_vec_init(2*d - 1);
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T = _fmpz_vec_init(2*d - 1);
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fmpz_init(Q);
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fmpz_init(R);
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_qadic_exp_bsplit_series(P, Q, T, x, len, 1, n, a, j, lena);
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fmpz_add(T + 0, T + 0, Q); /* (T,Q) := (T,Q) + 1 */
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/* Note exp(x) is a unit so val(T) == val(Q). */
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f = fmpz_remove(Q, Q, p);
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fmpz_pow_ui(R, p, f);
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_fmpz_vec_scalar_divexact_fmpz(T, T, d, R);
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_padic_inv(Q, Q, p, N);
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_fmpz_vec_scalar_mul_fmpz(y, T, d, Q);
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_fmpz_vec_clear(P, 2*d - 1);
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_fmpz_vec_clear(T, 2*d - 1);
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fmpz_clear(Q);
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fmpz_clear(R);
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}
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}
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void _qadic_exp_balanced(fmpz *rop, const fmpz *x, 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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fmpz_t pw;
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fmpz *r, *s, *t;
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slong i, w;
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r = _fmpz_vec_init(d);
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s = _fmpz_vec_init(2*d - 1);
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t = _fmpz_vec_init(d);
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fmpz_init(pw);
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fmpz_pow_ui(pw, p, v);
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_fmpz_vec_scalar_mul_fmpz(t, x, len, pw);
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_fmpz_vec_scalar_mod_fmpz(t, t, len, pN);
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_fmpz_vec_zero(t + len, d - len);
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fmpz_set(pw, p);
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fmpz_one(rop + 0);
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_fmpz_vec_zero(rop + 1, d - 1);
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w = 1;
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while (!_fmpz_vec_is_zero(t, d))
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{
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fmpz_mul(pw, pw, pw);
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for (i = 0; i < d; i++)
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{
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fmpz_fdiv_r(r + i, t + i, pw);
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fmpz_sub(t + i, t + i, r + i);
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}
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if (!_fmpz_vec_is_zero(r, d))
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{
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_qadic_exp_bsplit(r, r, w, d, a, j, lena, p, N);
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_fmpz_poly_mul(s, rop, d, r, d);
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_fmpz_poly_reduce(s, 2*d - 1, a, j, lena);
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_fmpz_vec_scalar_mod_fmpz(rop, s, d, pN);
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}
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w *= 2;
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}
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_fmpz_vec_clear(r, d);
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_fmpz_vec_clear(s, 2*d - 1);
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_fmpz_vec_clear(t, d);
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fmpz_clear(pw);
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}
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int qadic_exp_balanced(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 pN;
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int alloc;
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alloc = _padic_ctx_pow_ui(pN, N, &ctx->pctx);
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padic_poly_fit_length(rop, d);
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_qadic_exp_balanced(rop->coeffs, 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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_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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