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/*
Copyright (C) 2010 Sebastian Pancratz
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#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_throw(FLINT_ERROR, "Exception (fmpz_poly_addchains). Powering via chains not implemented for e > 148.\n");
}
}