203 lines
6.3 KiB
C
203 lines
6.3 KiB
C
/*=============================================================================
|
|
|
|
This file is part of FLINT.
|
|
|
|
FLINT is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2 of the License, or
|
|
(at your option) any later version.
|
|
|
|
FLINT is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with FLINT; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2010 Sebastian Pancratz
|
|
|
|
******************************************************************************/
|
|
|
|
#include <stdlib.h>
|
|
#include <gmp.h>
|
|
#include "flint.h"
|
|
#include "fmpz.h"
|
|
#include "fmpz_vec.h"
|
|
#include "fmpz_poly.h"
|
|
|
|
void _fmpz_poly_pow_addchains(fmpz * res, const fmpz * poly, slong len,
|
|
const int * a, int n)
|
|
{
|
|
int *b;
|
|
slong lenm1 = len - 1, lenv;
|
|
fmpz *v;
|
|
|
|
/*
|
|
Compute partial sums
|
|
*/
|
|
{
|
|
int i;
|
|
b = (int *) flint_malloc(n * sizeof(int));
|
|
b[0] = 0;
|
|
for (i = 1; i < n; i++)
|
|
b[i] = b[i-1] + a[i];
|
|
}
|
|
|
|
/*
|
|
Allocate memory for the polynomials f^{a[1]}, ..., f^{a[n-1]}
|
|
*/
|
|
lenv = lenm1 * b[n-1] + n - 1;
|
|
v = _fmpz_vec_init(lenv);
|
|
|
|
/*
|
|
Compute f^{a[1]}, ..., f^{a[n-1]}
|
|
*/
|
|
{
|
|
int d, i, j;
|
|
|
|
_fmpz_poly_sqr(v, poly, len);
|
|
|
|
for (i = 1; i < n-1; i++)
|
|
{
|
|
d = a[i+1] - a[i];
|
|
if (d == 1)
|
|
{
|
|
_fmpz_poly_mul(v + lenm1 * b[i] + (i),
|
|
v + lenm1 * b[i-1], lenm1 * a[i] + 1,
|
|
poly, len);
|
|
}
|
|
else
|
|
{
|
|
for (j = i; a[j] != d; j--) ;
|
|
_fmpz_poly_mul(v + lenm1 * b[i] + (i),
|
|
v + lenm1 * b[i-1], lenm1 * a[i] + 1,
|
|
v + lenm1 * b[j-1] + (j-1), lenm1 * a[j] + 1);
|
|
}
|
|
}
|
|
|
|
/*
|
|
Deal with the final product stored in res, i == n-1
|
|
*/
|
|
{
|
|
d = a[i+1] - a[i];
|
|
if (d == 1)
|
|
{
|
|
_fmpz_poly_mul(res,
|
|
v + lenm1 * b[i-1], lenm1 * a[i] + 1,
|
|
poly, len);
|
|
}
|
|
else
|
|
{
|
|
for (j = i; a[j] != d; j--) ;
|
|
_fmpz_poly_mul(res,
|
|
v + lenm1 * b[i-1], lenm1 * a[i] + 1,
|
|
v + lenm1 * b[j-1] + (j-1), lenm1 * a[j] + 1);
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
flint_free(b);
|
|
_fmpz_vec_clear(v, lenv);
|
|
}
|
|
|
|
void fmpz_poly_pow_addchains(fmpz_poly_t res, const fmpz_poly_t poly, ulong e)
|
|
{
|
|
const slong len = poly->length;
|
|
|
|
if ((len < 2) | (e < UWORD(3)))
|
|
{
|
|
if (e == UWORD(0))
|
|
fmpz_poly_set_ui(res, 1);
|
|
else if (len == 0)
|
|
fmpz_poly_zero(res);
|
|
else if (len == 1)
|
|
{
|
|
fmpz_poly_fit_length(res, 1);
|
|
fmpz_pow_ui(res->coeffs, poly->coeffs, e);
|
|
_fmpz_poly_set_length(res, 1);
|
|
}
|
|
else if (e == UWORD(1))
|
|
fmpz_poly_set(res, poly);
|
|
else /* e == UWORD(2) */
|
|
fmpz_poly_sqr(res, poly);
|
|
return;
|
|
}
|
|
|
|
if (e <= UWORD(148))
|
|
{
|
|
/*
|
|
An array storing a tree with shortest addition chains (star chains,
|
|
in fact) for all integers up to and including 148.
|
|
|
|
Let A denote the array. The entry A[0] is present to provide
|
|
1-based indexing. The integer 1 is the root of the tree and the
|
|
entry A[1] is irrelevant. For integers i >= 2, A[i] is the parent
|
|
of i.
|
|
|
|
We can iterate through an addition chain for n, where 0 < n < 148,
|
|
in the array shortest_addchains_148 as follows:
|
|
|
|
Visit n
|
|
while ((n = shortest_addchains_148[n]))
|
|
{
|
|
Visit n
|
|
}
|
|
*/
|
|
static const int shortest_addchains_148[149] = {
|
|
0, 0, 1, 2, 2, 3, 3, 5, 4, 8,
|
|
5, 10, 6, 9, 7, 12, 8, 9, 16, 18,
|
|
10, 15, 11, 20, 12, 17, 13, 24, 14, 25,
|
|
15, 28, 16, 32, 17, 26, 18, 36, 19, 27,
|
|
20, 40, 21, 34, 22, 30, 23, 46, 24, 33,
|
|
25, 48, 26, 37, 27, 54, 28, 49, 29, 56,
|
|
30, 52, 31, 51, 32, 64, 33, 66, 34, 68,
|
|
35, 70, 36, 72, 66, 60, 38, 43, 39, 78,
|
|
40, 65, 41, 80, 42, 80, 43, 86, 44, 88,
|
|
45, 90, 46, 92, 47, 92, 48, 96, 49, 96,
|
|
50,100, 51,102, 52,102, 53, 74, 54,108,
|
|
55,108, 56,104, 57,112, 58,104, 59,112,
|
|
60,120, 61,120, 62,100, 63,126, 64,128,
|
|
65,130,128,132, 67, 90, 68,136, 69,138,
|
|
70,140, 71,117, 72,144, 73, 99, 74
|
|
};
|
|
|
|
int a[11], i = 11, n = (int) e;
|
|
slong rlen = (slong) e * (len - 1) + 1;
|
|
|
|
/*
|
|
Copy the addition chain into 1 = a[0] < a[1] < ... < a[n]
|
|
*/
|
|
a[--i] = n;
|
|
while ((n = shortest_addchains_148[n]))
|
|
a[--i] = n;
|
|
n = 10 - i;
|
|
|
|
if (res != poly)
|
|
{
|
|
fmpz_poly_fit_length(res, rlen);
|
|
_fmpz_poly_pow_addchains(res->coeffs, poly->coeffs, len, a + i, n);
|
|
_fmpz_poly_set_length(res, rlen);
|
|
}
|
|
else
|
|
{
|
|
fmpz_poly_t t;
|
|
fmpz_poly_init2(t, rlen);
|
|
_fmpz_poly_pow_addchains(t->coeffs, poly->coeffs, len, a + i, n);
|
|
_fmpz_poly_set_length(t, rlen);
|
|
fmpz_poly_swap(res, t);
|
|
fmpz_poly_clear(t);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
flint_printf("Exception (fmpz_poly_addchains). Powering via chains not implemented for e > 148.\n");
|
|
abort();
|
|
}
|
|
}
|