ALL: Add flint
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external/flint-2.4.3/padic/log_rectangular.c
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external/flint-2.4.3/padic/log_rectangular.c
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/*=============================================================================
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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 <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "padic.h"
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#include "ulong_extras.h"
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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 x^i
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= \sum_{j=0}^{\ceil{n/b} - 1} \Bigl( \sum_{i=1}^b a_{i+jb} x^i \Bigr) x^{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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Does not support aliasing.
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*/
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static void
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_padic_log_rectangular_series(fmpz_t z, const fmpz_t y, slong n,
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const fmpz_t p, slong N, const fmpz_t P0)
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{
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if (n <= 2)
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{
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if (n == 1)
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{
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fmpz_mod(z, y, P0);
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}
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else /* n == 2; z = y(1 + y/2) */
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{
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if (fmpz_is_even(y))
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{
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fmpz_fdiv_q_2exp(z, y, 1);
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}
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else /* => p and y are odd */
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{
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fmpz_add(z, y, P0);
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fmpz_fdiv_q_2exp(z, z, 1);
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}
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fmpz_add_ui(z, z, 1);
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fmpz_mul(z, z, y);
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fmpz_mod(z, z, P0);
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}
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}
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else
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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, j;
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fmpz_t c, f, t, P1;
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fmpz *ypow;
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ypow = _fmpz_vec_init(b + 1);
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fmpz_init(c);
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fmpz_init(f);
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fmpz_init(t);
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fmpz_init(P1);
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fmpz_pow_ui(P1, p, N + k);
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fmpz_one(ypow + 0);
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for (i = 1; i <= b; i++)
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{
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fmpz_mul(ypow + i, ypow + (i - 1), y);
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fmpz_mod(ypow + i, ypow + i, P1);
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}
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fmpz_zero(z);
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for (j = (n + (b - 1)) / b - 1; j >= 0; j--)
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{
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const slong hi = FLINT_MIN(b, n - j*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 + j*b, hi);
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fmpz_zero(c);
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for (i = 1; i <= hi; i++)
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{
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fmpz_divexact_ui(t, f, i + j*b);
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fmpz_addmul(c, t, ypow + i);
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}
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/* Multiply c by p^k f^{-1} */
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w = fmpz_remove(f, f, p);
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_padic_inv(f, f, p, N);
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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_divexact(c, c, t);
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}
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else
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{
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fmpz_pow_ui(t, p, k - w);
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fmpz_mul(c, c, t);
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}
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fmpz_mul(c, c, f);
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/* Set z = z y^b + c */
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fmpz_mul(t, z, ypow + b);
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fmpz_add(z, c, t);
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fmpz_mod(z, z, P1);
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}
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fmpz_pow_ui(f, p, k);
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fmpz_divexact(z, z, f);
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fmpz_clear(c);
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fmpz_clear(f);
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fmpz_clear(t);
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fmpz_clear(P1);
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_fmpz_vec_clear(ypow, b + 1);
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}
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}
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void _padic_log_rectangular(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N)
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{
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const slong n = _padic_log_bound(v, N, p) - 1;
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fmpz_t pN;
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fmpz_init(pN);
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fmpz_pow_ui(pN, p, N);
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_padic_log_rectangular_series(z, y, n, p, N, pN);
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fmpz_sub(z, pN, z);
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fmpz_clear(pN);
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}
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int padic_log_rectangular(padic_t rop, const padic_t op, const padic_ctx_t ctx)
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{
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const fmpz *p = ctx->p;
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const slong N = padic_prec(rop);
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if (padic_val(op) < 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_t x;
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int ans;
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fmpz_init(x);
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padic_get_fmpz(x, op, ctx);
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fmpz_sub_ui(x, x, 1);
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fmpz_neg(x, x);
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if (fmpz_is_zero(x))
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{
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padic_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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fmpz_t t;
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slong v;
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fmpz_init(t);
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v = fmpz_remove(t, x, p);
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fmpz_clear(t);
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if (v >= 2 || (!fmpz_equal_ui(p, 2) && v >= 1))
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{
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if (v >= N)
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{
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padic_zero(rop);
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}
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else
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{
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_padic_log_rectangular(padic_unit(rop), x, v, p, N);
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padic_val(rop) = 0;
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_padic_canonicalise(rop, ctx);
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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_clear(x);
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return ans;
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}
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}
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