203 lines
6.3 KiB
C
203 lines
6.3 KiB
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) 2010 Sebastian Pancratz
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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 _fmpz_poly_pow_addchains(fmpz * res, const fmpz * poly, slong len,
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const int * a, int n)
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{
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int *b;
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slong lenm1 = len - 1, lenv;
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fmpz *v;
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/*
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Compute partial sums
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*/
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{
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int i;
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b = (int *) flint_malloc(n * sizeof(int));
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b[0] = 0;
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for (i = 1; i < n; i++)
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b[i] = b[i-1] + a[i];
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}
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/*
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Allocate memory for the polynomials f^{a[1]}, ..., f^{a[n-1]}
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*/
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lenv = lenm1 * b[n-1] + n - 1;
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v = _fmpz_vec_init(lenv);
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/*
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Compute f^{a[1]}, ..., f^{a[n-1]}
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*/
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{
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int d, i, j;
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_fmpz_poly_sqr(v, poly, len);
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for (i = 1; i < n-1; i++)
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{
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d = a[i+1] - a[i];
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if (d == 1)
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{
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_fmpz_poly_mul(v + lenm1 * b[i] + (i),
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v + lenm1 * b[i-1], lenm1 * a[i] + 1,
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poly, len);
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}
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else
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{
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for (j = i; a[j] != d; j--) ;
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_fmpz_poly_mul(v + lenm1 * b[i] + (i),
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v + lenm1 * b[i-1], lenm1 * a[i] + 1,
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v + lenm1 * b[j-1] + (j-1), lenm1 * a[j] + 1);
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}
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}
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/*
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Deal with the final product stored in res, i == n-1
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*/
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{
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d = a[i+1] - a[i];
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if (d == 1)
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{
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_fmpz_poly_mul(res,
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v + lenm1 * b[i-1], lenm1 * a[i] + 1,
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poly, len);
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}
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else
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{
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for (j = i; a[j] != d; j--) ;
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_fmpz_poly_mul(res,
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v + lenm1 * b[i-1], lenm1 * a[i] + 1,
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v + lenm1 * b[j-1] + (j-1), lenm1 * a[j] + 1);
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}
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}
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}
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flint_free(b);
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_fmpz_vec_clear(v, lenv);
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}
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void fmpz_poly_pow_addchains(fmpz_poly_t res, const fmpz_poly_t poly, ulong e)
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{
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const slong len = poly->length;
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if ((len < 2) | (e < UWORD(3)))
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{
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if (e == UWORD(0))
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fmpz_poly_set_ui(res, 1);
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else if (len == 0)
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fmpz_poly_zero(res);
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else if (len == 1)
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{
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fmpz_poly_fit_length(res, 1);
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fmpz_pow_ui(res->coeffs, poly->coeffs, e);
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_fmpz_poly_set_length(res, 1);
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}
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else if (e == UWORD(1))
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fmpz_poly_set(res, poly);
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else /* e == UWORD(2) */
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fmpz_poly_sqr(res, poly);
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return;
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}
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if (e <= UWORD(148))
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{
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/*
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An array storing a tree with shortest addition chains (star chains,
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in fact) for all integers up to and including 148.
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Let A denote the array. The entry A[0] is present to provide
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1-based indexing. The integer 1 is the root of the tree and the
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entry A[1] is irrelevant. For integers i >= 2, A[i] is the parent
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of i.
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We can iterate through an addition chain for n, where 0 < n < 148,
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in the array shortest_addchains_148 as follows:
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Visit n
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while ((n = shortest_addchains_148[n]))
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{
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Visit n
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}
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*/
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static const int shortest_addchains_148[149] = {
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0, 0, 1, 2, 2, 3, 3, 5, 4, 8,
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5, 10, 6, 9, 7, 12, 8, 9, 16, 18,
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10, 15, 11, 20, 12, 17, 13, 24, 14, 25,
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15, 28, 16, 32, 17, 26, 18, 36, 19, 27,
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20, 40, 21, 34, 22, 30, 23, 46, 24, 33,
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25, 48, 26, 37, 27, 54, 28, 49, 29, 56,
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30, 52, 31, 51, 32, 64, 33, 66, 34, 68,
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35, 70, 36, 72, 66, 60, 38, 43, 39, 78,
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40, 65, 41, 80, 42, 80, 43, 86, 44, 88,
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45, 90, 46, 92, 47, 92, 48, 96, 49, 96,
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50,100, 51,102, 52,102, 53, 74, 54,108,
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55,108, 56,104, 57,112, 58,104, 59,112,
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60,120, 61,120, 62,100, 63,126, 64,128,
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65,130,128,132, 67, 90, 68,136, 69,138,
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70,140, 71,117, 72,144, 73, 99, 74
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};
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int a[11], i = 11, n = (int) e;
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slong rlen = (slong) e * (len - 1) + 1;
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/*
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Copy the addition chain into 1 = a[0] < a[1] < ... < a[n]
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*/
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a[--i] = n;
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while ((n = shortest_addchains_148[n]))
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a[--i] = n;
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n = 10 - i;
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if (res != poly)
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{
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fmpz_poly_fit_length(res, rlen);
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_fmpz_poly_pow_addchains(res->coeffs, poly->coeffs, len, a + i, n);
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_fmpz_poly_set_length(res, rlen);
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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, rlen);
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_fmpz_poly_pow_addchains(t->coeffs, poly->coeffs, len, a + i, n);
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_fmpz_poly_set_length(t, rlen);
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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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}
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else
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{
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flint_printf("Exception (fmpz_poly_addchains). Powering via chains not implemented for e > 148.\n");
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abort();
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}
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}
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