166 lines
4.8 KiB
C
166 lines
4.8 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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******************************************************************************/
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#include <stdlib.h>
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#include <string.h>
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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 "fmpz_vec.h"
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#include "fmpz_poly.h"
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void _fmpz_poly_mulhigh_kara_recursive(fmpz * out, const fmpz * pol1,
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const fmpz * pol2, fmpz * temp,
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slong length);
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/*
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Multiplication using truncated karatsuba. Below length 7, classical
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truncated multiplication is always theoretically faster, so we switch
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to that as the basecase.
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Above that we use the ordinary (left/right) karatsuba identity and
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recursively do one full karatsuba multiplication and two truncated
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karatsuba multiplications.
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*/
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void
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_fmpz_poly_mulhigh_kara_recursive(fmpz * out, const fmpz * pol1,
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const fmpz * pol2, fmpz * temp, slong length)
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{
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slong m1 = length / 2;
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slong m2 = length - m1;
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int odd = (length & 1);
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if (length <= 6)
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{
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_fmpz_poly_mulhigh_classical(out, pol1, length, pol2, length,
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length - 1);
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return;
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}
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_fmpz_vec_add(out, pol1, pol1 + m1, m1);
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if (odd)
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fmpz_set(out + m1, pol1 + 2 * m1);
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_fmpz_vec_add(out + m2, pol2, pol2 + m1, m1);
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if (odd)
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fmpz_set(out + m2 + m1, pol2 + 2 * m1);
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_fmpz_poly_mulhigh_kara_recursive(temp, out, out + m2, temp + 2 * m2, m2);
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_fmpz_poly_mul_karatsuba(out + 2 * m1, pol1 + m1, m2, pol2 + m1, m2);
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fmpz_zero(out + 2 * m1 - 1);
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_fmpz_poly_mulhigh_kara_recursive(out, pol1, pol2, temp + 2 * m2, m1);
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_fmpz_vec_sub(temp + m2 - 1, temp + m2 - 1, out + m2 - 1, 2 * m1 - m2);
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_fmpz_vec_sub(temp + m2 - 1, temp + m2 - 1, out + 2 * m1 + m2 - 1, m2);
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_fmpz_vec_add(out + length - 1, out + length - 1, temp + m2 - 1, m2);
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_fmpz_vec_zero(out, length - 1);
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}
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/* Assumes poly1 and poly2 are not length 0. */
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void
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_fmpz_poly_mulhigh_karatsuba_n(fmpz * res, const fmpz * poly1,
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const fmpz * poly2, slong len)
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{
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fmpz *temp;
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slong length, loglen = 0;
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if (len == 1)
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{
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fmpz_mul(res, poly1, poly2);
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return;
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}
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while ((WORD(1) << loglen) < len)
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loglen++;
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length = (WORD(1) << loglen);
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temp = _fmpz_vec_init(2 * length);
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_fmpz_poly_mulhigh_kara_recursive(res, poly1, poly2, temp, len);
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_fmpz_vec_clear(temp, 2 * length);
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}
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void
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fmpz_poly_mulhigh_karatsuba_n(fmpz_poly_t res,
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const fmpz_poly_t poly1, const fmpz_poly_t poly2,
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slong len)
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{
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slong lenr = poly1->length + poly2->length - 1;
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int clear1 = 0, clear2 = 0;
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fmpz *pol1, *pol2;
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if (poly1->length == 0 || poly2->length == 0 || len - 1 >= lenr)
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{
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fmpz_poly_zero(res);
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return;
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}
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if (poly1->length != len)
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{
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pol1 = (fmpz *) flint_calloc(len, sizeof(fmpz));
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memcpy(pol1, poly1->coeffs, poly1->length * sizeof(fmpz));
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clear1 = 1;
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}
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else
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pol1 = poly1->coeffs;
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if (poly2->length != len)
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{
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pol2 = (fmpz *) flint_calloc(len, sizeof(fmpz));
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memcpy(pol2, poly2->coeffs, poly2->length * sizeof(fmpz));
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clear2 = 1;
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}
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else
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pol2 = poly2->coeffs;
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if (res != poly1 && res != poly2)
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{
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fmpz_poly_fit_length(res, 2 * len - 1);
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_fmpz_poly_mulhigh_karatsuba_n(res->coeffs, pol1, pol2, len);
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_fmpz_poly_set_length(res, lenr);
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}
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else
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{
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fmpz_poly_t temp;
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fmpz_poly_init2(temp, 2 * len - 1);
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_fmpz_poly_mulhigh_karatsuba_n(temp->coeffs, pol1, pol2, len);
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_fmpz_poly_set_length(temp, lenr);
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fmpz_poly_swap(temp, res);
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fmpz_poly_clear(temp);
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}
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if (clear1)
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flint_free(pol1);
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if (clear2)
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flint_free(pol2);
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}
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