241 lines
7.1 KiB
C
241 lines
7.1 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 "fmpz_mod_poly.h"
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#include "qadic.h"
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extern slong _padic_log_bound(slong v, slong N, const fmpz_t p);
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/*
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Carries out the finite series evaluation for the logarithm
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\begin{equation*}
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\sum_{i=1}^{n} a_i y^i
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= \sum_{j=0}^{\ceil{n/b}-1} \Bigl(\sum_{i=1}^b a_{i+jb} y^i\Bigr) y^{jb}
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\end{equation*}
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where $a_i = 1/i$ with the choice $b = \floor{\sqrt{n}}$,
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all modulo $p^N$, where also $P = p^N$.
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Assumes that $y$ is reduced modulo $p^N$.
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Assumes that $z$ has space for $2d - 1$ coefficients, but
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sets only the first $d$ to meaningful values on exit.
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Supports aliasing between $y$ and $z$.
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*/
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static void
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_qadic_log_rectangular_series(fmpz *z, const fmpz *y, slong len, slong n,
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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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if (n <= 2)
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{
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if (n == 1) /* n == 1; z = y */
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{
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_fmpz_vec_set(z, y, len);
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_fmpz_vec_zero(z + len, d - len);
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}
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else /* n == 2; z = y + y^2/2 */
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{
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slong i;
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fmpz *t;
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t = _fmpz_vec_init(2 * len - 1);
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_fmpz_poly_sqr(t, y, len);
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for (i = 0; i < 2 * len - 1; i++)
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if (fmpz_is_even(t + i))
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{
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fmpz_fdiv_q_2exp(t + i, t + i, 1);
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}
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else /* => p and t(i) are odd */
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{
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fmpz_add(t + i, t + i, pN);
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fmpz_fdiv_q_2exp(t + i, t + i, 1);
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}
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_fmpz_mod_poly_reduce(t, 2 * len - 1, a, j, lena, pN);
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_fmpz_mod_poly_add(z, y, len, t, FLINT_MIN(d, 2 * len - 1), pN);
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_fmpz_vec_clear(t, 2 * len - 1);
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}
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}
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else /* n >= 3 */
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{
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const slong b = n_sqrt(n);
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const slong k = fmpz_fits_si(p) ? n_flog(n, fmpz_get_si(p)) : 0;
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slong i, h;
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fmpz_t f, pNk;
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fmpz *c, *t, *ypow;
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c = _fmpz_vec_init(d);
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t = _fmpz_vec_init(2 * d - 1);
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ypow = _fmpz_vec_init((b + 1) * d + d - 1);
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fmpz_init(f);
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fmpz_init(pNk);
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fmpz_pow_ui(pNk, p, N + k);
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fmpz_one(ypow);
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_fmpz_vec_set(ypow + d, y, len);
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for (i = 2; i <= b; i++)
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{
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_fmpz_mod_poly_mul(ypow + i * d, ypow + (i - 1) * d, d, y, len, pNk);
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_fmpz_mod_poly_reduce(ypow + i * d, d + len - 1, a, j, lena, pNk);
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}
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_fmpz_vec_zero(z, d);
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for (h = (n + (b - 1)) / b - 1; h >= 0; h--)
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{
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const slong hi = FLINT_MIN(b, n - h*b);
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slong w;
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/* Compute inner sum in c */
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fmpz_rfac_uiui(f, 1 + h*b, hi);
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_fmpz_vec_zero(c, d);
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for (i = 1; i <= hi; i++)
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{
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fmpz_divexact_ui(t, f, i + h*b);
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_fmpz_vec_scalar_addmul_fmpz(c, ypow + i * d, d, t);
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}
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/* Multiply c by p^k f */
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w = fmpz_remove(f, f, p);
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_padic_inv(f, f, p, N + k);
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if (w > k)
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{
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fmpz_pow_ui(t, p, w - k);
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_fmpz_vec_scalar_divexact_fmpz(c, c, d, t);
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}
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else if (w < k)
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{
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fmpz_pow_ui(t, p, k - w);
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_fmpz_vec_scalar_mul_fmpz(c, c, d, t);
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}
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_fmpz_vec_scalar_mul_fmpz(c, c, d, f);
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/* Set z = z y^b + c */
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_fmpz_mod_poly_mul(t, z, d, ypow + b * d, d, pNk);
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_fmpz_mod_poly_reduce(t, 2 * d - 1, a, j, lena, pNk);
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_fmpz_vec_add(z, c, t, d);
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_fmpz_vec_scalar_mod_fmpz(z, z, d, pNk);
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}
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fmpz_pow_ui(f, p, k);
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_fmpz_vec_scalar_divexact_fmpz(z, z, d, f);
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fmpz_clear(f);
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fmpz_clear(pNk);
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_fmpz_vec_clear(c, d);
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_fmpz_vec_clear(t, 2 * d - 1);
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_fmpz_vec_clear(ypow, (b + 1) * d + d - 1);
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}
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}
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void _qadic_log_rectangular(fmpz *z, const fmpz *y, 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_log_bound(v, N, p) - 1;
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_qadic_log_rectangular_series(z, y, len, n, a, j, lena, p, N, pN);
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_fmpz_mod_poly_neg(z, z, d, pN);
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}
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int qadic_log_rectangular(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx)
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{
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const fmpz *p = (&ctx->pctx)->p;
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const slong d = qadic_ctx_degree(ctx);
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const slong N = qadic_prec(rop);
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const slong len = op->length;
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if (op->val < 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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fmpz *x;
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fmpz_t pN;
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int alloc, ans;
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x = _fmpz_vec_init(len + 1);
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alloc = _padic_ctx_pow_ui(pN, N, &ctx->pctx);
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/* Set x := (1 - op) mod p^N */
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fmpz_pow_ui(x + len, p, op->val);
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_fmpz_vec_scalar_mul_fmpz(x, op->coeffs, len, x + len);
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fmpz_sub_ui(x, x, 1);
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_fmpz_vec_neg(x, x, len);
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_fmpz_vec_scalar_mod_fmpz(x, x, len, pN);
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if (_fmpz_vec_is_zero(x, len))
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{
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padic_poly_zero(rop);
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ans = 1;
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}
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else
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{
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const slong v = _fmpz_vec_ord_p(x, len, p);
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if (v >= 2 || (*p != WORD(2) && v >= 1))
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{
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if (v >= N)
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{
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padic_poly_zero(rop);
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}
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else
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{
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padic_poly_fit_length(rop, d);
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_qadic_log_rectangular(rop->coeffs, x, v, len,
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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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padic_poly_canonicalise(rop, p);
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}
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ans = 1;
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}
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else
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{
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ans = 0;
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}
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}
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_fmpz_vec_clear(x, len + 1);
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if (alloc)
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fmpz_clear(pN);
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return ans;
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}
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}
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