174 lines
4.8 KiB
C
174 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 <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
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_fmpz_poly_mullow_kara_recursive(fmpz * out, const fmpz * pol1,
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const fmpz * pol2, fmpz * temp, slong len);
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/*
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Multiplication using truncated karatsuba.
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Below length 7, classical truncated multiplication is always theoretically
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faster, so we switch to that as the basecase. Above that we use the
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ordinary (left/right) karatsuba identity and recursively do one full
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karatsuba multiplication and two truncated karatsuba multiplications.
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*/
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void
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_fmpz_poly_mullow_kara_recursive(fmpz * out, const fmpz * pol1,
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const fmpz * pol2, fmpz * temp, slong len)
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{
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slong m1 = len / 2;
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slong m2 = len - m1;
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int odd = (len & 1);
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if (len <= 6)
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{
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_fmpz_poly_mullow_classical(out, pol1, len, pol2, len, len);
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return;
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}
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_fmpz_vec_add(temp + m2, pol1, pol1 + m1, m1);
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if (odd)
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fmpz_set(temp + m2 + m1, pol1 + 2 * m1);
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_fmpz_vec_add(temp + 2 * m2, pol2, pol2 + m1, m1);
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if (odd)
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fmpz_set(temp + 2 * m2 + m1, pol2 + 2 * m1);
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_fmpz_poly_mul_karatsuba(out, pol1, m1, pol2, m1);
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fmpz_zero(out + 2 * m1 - 1);
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_fmpz_poly_mullow_kara_recursive(temp, temp + m2, temp + 2 * m2,
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temp + 3 * m2, m2);
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_fmpz_poly_mullow_kara_recursive(temp + m2, pol1 + m1, pol2 + m1,
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temp + 2 * m2, m2);
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_fmpz_vec_sub(temp, temp, out, m2);
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_fmpz_vec_sub(temp, temp, temp + m2, m2);
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if (odd)
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fmpz_set(out + 2 * m1, temp + m2);
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_fmpz_vec_add(out + m1, out + m1, temp, m2);
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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_mullow_karatsuba_n(fmpz * res, const fmpz * poly1,
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const fmpz * poly2, slong n)
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{
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fmpz *temp;
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slong len, loglen = 0;
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if (n == 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) < n)
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loglen++;
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len = (WORD(1) << loglen);
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temp = _fmpz_vec_init(3 * len);
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_fmpz_poly_mullow_kara_recursive(res, poly1, poly2, temp, n);
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_fmpz_vec_clear(temp, 3 * len);
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}
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void
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fmpz_poly_mullow_karatsuba_n(fmpz_poly_t res, const fmpz_poly_t poly1,
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const fmpz_poly_t poly2, slong n)
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{
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const slong len1 = FLINT_MIN(poly1->length, n);
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const slong len2 = FLINT_MIN(poly2->length, n);
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slong i, lenr;
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int clear = 0;
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fmpz *copy1, *copy2;
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if (len1 == 0 || len2 == 0)
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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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lenr = len1 + len2 - 1;
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if (n > lenr)
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n = lenr;
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if (len1 >= n)
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copy1 = poly1->coeffs;
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else
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{
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copy1 = (fmpz *) flint_malloc(n * sizeof(fmpz));
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for (i = 0; i < len1; i++)
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copy1[i] = poly1->coeffs[i];
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flint_mpn_zero((mp_ptr) copy1 + len1, n - len1);
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clear |= 1;
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}
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if (len2 >= n)
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copy2 = poly2->coeffs;
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else
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{
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copy2 = (fmpz *) flint_malloc(n * sizeof(fmpz));
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for (i = 0; i < len2; i++)
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copy2[i] = poly2->coeffs[i];
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flint_mpn_zero((mp_ptr) copy2 + len2, n - len2);
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clear |= 2;
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}
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if (res != poly1 && res != poly2)
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{
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fmpz_poly_fit_length(res, n);
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_fmpz_poly_mullow_karatsuba_n(res->coeffs, copy1, copy2, n);
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}
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else
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{
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fmpz_poly_t t;
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fmpz_poly_init2(t, n);
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_fmpz_poly_mullow_karatsuba_n(t->coeffs, copy1, copy2, n);
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fmpz_poly_swap(res, t);
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fmpz_poly_clear(t);
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}
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_fmpz_poly_set_length(res, n);
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_fmpz_poly_normalise(res);
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if (clear & 1)
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flint_free(copy1);
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if (clear & 2)
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flint_free(copy2);
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}
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