/* Implements algorithm polyeval and remainder tree using middle product.
Copyright 2003, 2004, 2005 Laurent Fousse, Alexander Kruppa, Paul Zimmermann.
This file is part of the ECM Library.
The ECM Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The ECM Library 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the ECM Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA.
*/
#include <stdlib.h>
#include <string.h> /* for strlen */
#include "ecm-impl.h"
#if HAVE_UNISTD_H
# include <unistd.h> /* for unlink */
#endif
#ifndef MAX
#define MAX(a,b) (((a) > (b)) ? (a) : (b))
#endif
/* #define DEBUG_TREEDATA */
extern unsigned int Fermat;
#ifndef POLYEVALTELLEGEN
/* algorithm polyeval from section 3.7 of Peter Montgomery's dissertation.
Input:
G - an array of k elements of R, G[i], 0 <= i < k
representing the coefficients of a polynomial G(x) of degree < k
Tree - the product tree produced by PolyFromRoots
Tree[0][0..k-1] (degree k/2)
Tree[1][0..k-1] (degree k/4), ...,
Tree[lgk-1][0..k-1] (degree 1)
Output: the sequence of values of G(a[i]) are stored in G[i] for 0 <= i < k
Remark: we need an auxiliary (k+1)-th cell G[k] in G.
The memory used is M(k) = max(3*floor(k/2)+list_mul_mem(floor(k/2)),
k+list_mul_mem(ceil(k/2)),
floor(k/2) + M(ceil(k/2))).
Since list_mul_mem(k) >= 2*k, the maximum is the 1st.
*/
void
polyeval (listz_t G, unsigned int k, listz_t *Tree, listz_t T, mpz_t n,
unsigned int sh)
{
unsigned int l, m;
listz_t T0;
if (k == 1)
return;
T0 = Tree[0] + sh;
m = k / 2;
l = k - m;
/* divide G[0]+G[1]*x+...+G[k-1]*x^(k-1) by
T0[l]+...+T0[k-1]*x^(m-1)+x^m,
quotient in {T+m,l-1}, remainder in {T,m} */
if (k == 2 * m)
{
/* FIXME: avoid the copy here by giving different 2nd and 3rd arguments
to RecursiveDivision */
list_set (T, G, k);
/* the following needs k+m+list_mul_mem(m) in T */
RecursiveDivision (T + k, T, T0 + l, m, T + k + m, n, 1);
}
else /* k = 2m+1: subtract G[k-1]*x^(l-1) * T0 from G */
{
/* G - G[k-1] * (x^m + {T0+l,m}) * x^m */
list_set (T, G, m);
list_mul_z (T + m, T0 + l, G[k - 1], m, n);
list_sub (T + m, G + m, T + m, m);
/* the following needs 3m+list_mul_mem(m) in T */
RecursiveDivision (T + 2 * m, T, T0 + l, m, T + 3 * m, n, 1);
}
/* in both cases we need 3*(k/2)+list_mul_mem(k/2) */
/* right remainder is in {T,m} */
/* k = 2l or k = 2l-1 */
/* divide G[0]+G[1]*x+...+G[k-1]*x^(k-1) by
T0[0]+...+T0[l-1]*x^(l-1)+x^l:
quotient in {T+m,m-1}, remainder in {G,l} */
if (k < 2 * l)
mpz_set_ui (G[k], 0);
/* the following needs k+list_mul_mem(l) in T */
RecursiveDivision (T + m, G, T0, l, T + k, n, 1);
/* left remainder is in {G,l} */
polyeval (G, l, Tree + 1, T + m, n, sh);
/* copy right remainder in {G+l,m} */
list_set (G + l, T, m);
polyeval (G + l, m, Tree + 1, T, n, sh + l);
}
#endif
#if defined(DEBUG) || defined(DEBUG_TREEDATA)
void
print_vect (listz_t t, unsigned int l)
{
unsigned int i;
fprintf (ECM_STDOUT, "[");
for (i = 0; i < l; i++)
{
mpz_out_str (ECM_STDOUT, 10, t[i]);
if (i != l - 1)
fprintf (ECM_STDOUT, ", ");
else
fprintf (ECM_STDOUT, "]");
}
}
#endif
/* Computes TUpTree as described in ref[1]. k is the degree of the
* polynomial at the root of the tree. sh is the shift we need to
* apply to find the actual coefficients of the polynomial at the root
* of the tree.
*/
void
TUpTree (listz_t b, listz_t *Tree, unsigned int k, listz_t tmp, int dolvl,
unsigned int sh, mpz_t n, FILE *TreeFile)
{
unsigned int m, l;
m = k / 2;
l = k - m;
if (k == 1)
return;
#ifdef DEBUG
fprintf (ECM_STDOUT, "In TupTree, k = %d.\n", k);
fprintf (ECM_STDOUT, "b = ");
print_vect (b, k);
fprintf (ECM_STDOUT, "\nThe polynomials at that level are: ");
print_vect (Tree[0] + sh, k);
fprintf (ECM_STDOUT, "\n");
#endif
if (dolvl == 0 || dolvl == -1)
{
if (TreeFile != NULL)
{
list_inp_raw (tmp + k, TreeFile, l);
#ifdef DEBUG_TREEDATA
printf ("Read from file: ");
print_vect (tmp + k, l);
#endif
TMulGen (tmp + l, m - 1, tmp + k, l - 1, b, k - 1, tmp + k + l, n);
list_inp_raw (tmp + k, TreeFile, m);
#ifdef DEBUG_TREEDATA
print_vect (tmp + k, m);
printf ("\n");
#endif
TMulGen (tmp, l - 1, tmp + k, m - 1, b, k - 1, tmp + k + m, n);
}
else
{
#ifdef DEBUG_TREEDATA
printf ("Got from Tree: ");
print_vect (Tree[0] + sh, l);
print_vect (Tree[0] + sh + l, m);
printf ("\n");
#endif
TMulGen (tmp + l, m - 1, Tree[0] + sh, l - 1, b, k - 1, tmp + k, n);
TMulGen (tmp, l - 1, Tree[0] + sh + l, m - 1, b, k - 1, tmp + k, n);
}
#if defined(DEBUG) || defined (DEBUG_TREEDATA)
fprintf (ECM_STDOUT, "And the result at that level (before correction) is:");
print_vect (tmp, k);
fprintf (ECM_STDOUT, "\n");
#endif
/* GMP-ECM specific: leading coefficients in the product tree
* are implicit ones, so we need some extra work here.
*/
list_add (tmp, tmp, b + m, l);
list_add (tmp + l, tmp + l, b + l, m);
list_mod (b, tmp, k, n); /* reduce both parts simultaneously */
#ifdef DEBUG
fprintf (ECM_STDOUT, "And the result at this level is:");
print_vect (b, k);
fprintf (ECM_STDOUT, "\n");
#endif
}
if (dolvl > 0 || dolvl == -1)
{
if (dolvl > 0)
dolvl--;
TUpTree (b, Tree + 1, l, tmp, dolvl, sh, n, TreeFile);
TUpTree (b + l, Tree + 1, m, tmp, dolvl, sh + l, n, TreeFile);
}
}
static unsigned int
TUpTree_space (unsigned int k)
{
unsigned int m, l;
unsigned int r1, r2;
m = k / 2;
l = k - m;
if (k == 1)
return 0;
r1 = TMulGen_space (l - 1, m - 1, k - 1) + l;
if (m != l)
{
r2 = TMulGen_space (m - 1, l - 1, k - 1) + k;
r1 = MAX (r1, r2);
}
r2 = TUpTree_space (l);
r1 = MAX (r1, r2);
if (m != l)
{
r2 = TUpTree_space (m);
r1 = MAX (r1, r2);
}
return r1;
}
#ifdef POLYEVALTELLEGEN
/* Same as polyeval. Needs invF as extra argument.
Return non-zero iff an error occurred.
*/
int
polyeval_tellegen (listz_t b, unsigned int k, listz_t *Tree, listz_t tmp,
unsigned int sizeT, listz_t invF, mpz_t n,
char *TreeFilename)
{
unsigned int tupspace;
unsigned int tkspace;
int allocated = 0,
r = 0; /* return value, 0 = no error */
listz_t T;
ASSERT(Tree != NULL || TreeFilename != NULL);
tupspace = TUpTree_space (k) + k;
#ifndef USE_SHORT_PRODUCT
tkspace = TMulGen_space (k - 1, k - 1, k - 1) + k;
#else
tkspace = 2 * k - 1 + list_mul_mem (k);
#endif
tupspace = MAX (tupspace, tkspace);
if (TreeFilename != NULL)
tupspace += (k + 1) / 2;
if (sizeT >= tupspace)
T = tmp;
else
{
outputf (OUTPUT_DEVVERBOSE, "polyeval_tellegen: allocating extra temp"
" space, want %d but T has only %d\n", tupspace, sizeT);
MEMORY_TAG;
T = init_list (tupspace);
MEMORY_UNTAG;
if (T == NULL)
return ECM_ERROR;
allocated = 1;
}
#ifdef TELLEGEN_DEBUG
fprintf (ECM_STDOUT, "In polyeval_tellegen, k = %d.\n", k);
fprintf (ECM_STDOUT, "Required memory: %d.\n",
TMulGen_space (k - 1, k - 1, k - 1));
#endif
if (Fermat)
{
/* Schoenhage-Strassen can't do a half product faster than a full */
F_mul (T, invF, b, k, DEFAULT, Fermat, T + 2 * k);
list_mod (T, T + k - 1, k, n);
}
else
{
#ifdef USE_SHORT_PRODUCT
/* need space 2k-1+list_mul_mem(k) in T */
list_mul_high (T, invF, b, k, T + 2 * k - 1);
list_mod (T, T + k - 1, k, n);
#else
/* revert invF for call to TMulGen below */
list_revert (invF, k - 1);
TMulGen (T, k - 1, invF, k - 1, b, k - 1, T + k, n);
#endif
}
list_revert (T, k - 1);
if (TreeFilename != NULL)
{
unsigned int lgk, i;
FILE *TreeFile;
/* assume this "small" malloc will not fail in normal usage */
char *fullname = (char *) malloc (strlen (TreeFilename) + 1 + 2 + 1);
lgk = ceil_log2 (k);
for (i = 0; i < lgk; i++)
{
sprintf (fullname, "%s.%d", TreeFilename, i);
TreeFile = fopen (fullname, "rb");
if (TreeFile == NULL)
{
outputf (OUTPUT_ERROR,
"Error opening file %s for product tree of F\n",
fullname);
r = ECM_ERROR;
goto clear_T;
}
TUpTree (T, NULL, k, T + k, i, 0, n, TreeFile);
fclose (TreeFile);
unlink (fullname);
}
free (fullname);
}
else
TUpTree (T, Tree, k, T + k, -1, 0, n, NULL);
list_swap (b, T, k); /* more efficient than list_set, since T is not
needed anymore */
clear_T:
if (allocated)
clear_list (T, tupspace);
return r;
}
#endif
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