218 lines
6.6 KiB
C
218 lines
6.6 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) 2010 William Hart
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Copyright (C) 2010,2011 Fredrik Johansson
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******************************************************************************/
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#ifndef NMOD_MAT_H
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#define NMOD_MAT_H
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#undef ulong
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#define ulong ulongxx /* interferes with system includes */
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#include <stdlib.h>
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#undef ulong
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#include <gmp.h>
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#define ulong mp_limb_t
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#include "flint.h"
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#include "longlong.h"
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#include "ulong_extras.h"
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#include "nmod_vec.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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typedef struct
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{
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mp_limb_t * entries;
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slong r;
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slong c;
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mp_limb_t ** rows;
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nmod_t mod;
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}
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nmod_mat_struct;
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/* nmod_mat_t allows reference-like semantics for nmod_mat_struct */
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typedef nmod_mat_struct nmod_mat_t[1];
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#define nmod_mat_entry(mat,i,j) ((mat)->rows[(i)][(j)])
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#define nmod_mat_nrows(mat) ((mat)->r)
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#define nmod_mat_ncols(mat) ((mat)->c)
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static __inline__
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void
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_nmod_mat_set_mod(nmod_mat_t mat, mp_limb_t n)
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{
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mat->mod.n = n;
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mat->mod.ninv = n_preinvert_limb(n);
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count_leading_zeros(mat->mod.norm, n);
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}
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/* Memory management */
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void nmod_mat_init(nmod_mat_t mat, slong rows, slong cols, mp_limb_t n);
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void nmod_mat_init_set(nmod_mat_t mat, const nmod_mat_t src);
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void nmod_mat_clear(nmod_mat_t mat);
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void nmod_mat_window_init(nmod_mat_t window, const nmod_mat_t mat, slong r1, slong c1, slong r2, slong c2);
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void nmod_mat_window_clear(nmod_mat_t window);
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/* Random matrix generation */
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void nmod_mat_randtest(nmod_mat_t mat, flint_rand_t state);
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void nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state);
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int nmod_mat_randpermdiag(nmod_mat_t mat, flint_rand_t state,
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mp_srcptr diag, slong n);
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void nmod_mat_randrank(nmod_mat_t, flint_rand_t state, slong rank);
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void nmod_mat_randops(nmod_mat_t mat, slong count, flint_rand_t state);
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void nmod_mat_randtril(nmod_mat_t mat, flint_rand_t state, int unit);
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void nmod_mat_randtriu(nmod_mat_t mat, flint_rand_t state, int unit);
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void nmod_mat_print_pretty(const nmod_mat_t mat);
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int nmod_mat_equal(const nmod_mat_t mat1, const nmod_mat_t mat2);
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void nmod_mat_zero(nmod_mat_t mat);
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int nmod_mat_is_zero(const nmod_mat_t mat);
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static __inline__ int
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nmod_mat_is_empty(const nmod_mat_t mat)
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{
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return (mat->r == 0) || (mat->c == 0);
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}
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static __inline__ int
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nmod_mat_is_square(const nmod_mat_t mat)
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{
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return (mat->r == mat->c);
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}
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void nmod_mat_set(nmod_mat_t B, const nmod_mat_t A);
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void nmod_mat_transpose(nmod_mat_t B, const nmod_mat_t A);
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/* Addition and subtraction */
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void nmod_mat_add(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
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void nmod_mat_sub(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
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void nmod_mat_neg(nmod_mat_t B, const nmod_mat_t A);
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/* Matrix-scalar arithmetic */
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void nmod_mat_scalar_mul(nmod_mat_t B, const nmod_mat_t A, mp_limb_t c);
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/* Matrix multiplication */
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void nmod_mat_mul(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
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void nmod_mat_mul_classical(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
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void nmod_mat_mul_strassen(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
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void
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_nmod_mat_mul_classical(nmod_mat_t D, const nmod_mat_t C,
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const nmod_mat_t A, const nmod_mat_t B, int op);
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void nmod_mat_addmul(nmod_mat_t D, const nmod_mat_t C,
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const nmod_mat_t A, const nmod_mat_t B);
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void nmod_mat_submul(nmod_mat_t D, const nmod_mat_t C,
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const nmod_mat_t A, const nmod_mat_t B);
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/* Trace */
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mp_limb_t nmod_mat_trace(const nmod_mat_t mat);
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/* Determinant */
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mp_limb_t _nmod_mat_det(nmod_mat_t A);
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mp_limb_t nmod_mat_det(const nmod_mat_t A);
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/* Rank */
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slong nmod_mat_rank(const nmod_mat_t A);
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/* Inverse */
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int nmod_mat_inv(nmod_mat_t B, const nmod_mat_t A);
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/* Triangular solving */
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void nmod_mat_solve_tril(nmod_mat_t X, const nmod_mat_t L, const nmod_mat_t B, int unit);
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void nmod_mat_solve_tril_recursive(nmod_mat_t X, const nmod_mat_t L, const nmod_mat_t B, int unit);
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void nmod_mat_solve_tril_classical(nmod_mat_t X, const nmod_mat_t L, const nmod_mat_t B, int unit);
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void nmod_mat_solve_triu(nmod_mat_t X, const nmod_mat_t U, const nmod_mat_t B, int unit);
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void nmod_mat_solve_triu_recursive(nmod_mat_t X, const nmod_mat_t U, const nmod_mat_t B, int unit);
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void nmod_mat_solve_triu_classical(nmod_mat_t X, const nmod_mat_t U, const nmod_mat_t B, int unit);
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/* LU decomposition */
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slong nmod_mat_lu(slong * P, nmod_mat_t A, int rank_check);
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slong nmod_mat_lu_classical(slong * P, nmod_mat_t A, int rank_check);
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slong nmod_mat_lu_recursive(slong * P, nmod_mat_t A, int rank_check);
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/* Nonsingular solving */
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int nmod_mat_solve(nmod_mat_t X, const nmod_mat_t A, const nmod_mat_t B);
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int nmod_mat_solve_vec(mp_ptr x, const nmod_mat_t A, mp_srcptr b);
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/* Reduced row echelon form */
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slong nmod_mat_rref(nmod_mat_t A);
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/* Nullspace */
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slong nmod_mat_nullspace(nmod_mat_t X, const nmod_mat_t A);
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/* Tuning parameters *********************************************************/
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/* Size at which pre-transposing becomes faster in classical multiplication */
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#define NMOD_MAT_MUL_TRANSPOSE_CUTOFF 20
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/* Strassen multiplication */
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#define NMOD_MAT_MUL_STRASSEN_CUTOFF 256
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/* Cutoff between classical and recursive triangular solving */
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#define NMOD_MAT_SOLVE_TRI_ROWS_CUTOFF 64
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#define NMOD_MAT_SOLVE_TRI_COLS_CUTOFF 64
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/* Cutoff between classical and recursive LU decomposition */
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#define NMOD_MAT_LU_RECURSIVE_CUTOFF 4
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/*
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Suggested initial modulus size for multimodular algorithms. This should
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be chosen so that we get the most number of bits per cycle
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in matrix multiplication. On x86-64 it appears to be optimal to use
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moduli giving nlimbs = 2. This should hold both in the classical
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range and in Strassen blocks.
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*/
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#define NMOD_MAT_OPTIMAL_MODULUS_BITS (FLINT_BITS-5)
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#ifdef __cplusplus
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}
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#endif
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#endif
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