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add fast multipoint evaluation and interpolation for nmod_poly (worki… 
…ng, but needs integration)
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@fredrik-johansson
fredrik-johansson committed Feb 16, 2012
1 parent 077c6a8 commit 0e204e4
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Showing 7 changed files with 609 additions and 2 deletions.
35 changes: 35 additions & 0 deletions nmod_poly.h
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Expand Up @@ -593,6 +593,28 @@ void _nmod_poly_evaluate_nmod_vec(mp_ptr ys, mp_srcptr coeffs, long len,
void nmod_poly_evaluate_nmod_vec(mp_ptr ys,
const nmod_poly_t poly, mp_srcptr xs, long n);

void nmod_poly_evaluate_nmod_vec(mp_ptr ys, const nmod_poly_t poly,
mp_srcptr xs, long n);

void _nmod_poly_evaluate_nmod_vec_fast(mp_ptr ys, mp_srcptr coeffs, long len,
mp_srcptr xs, long n, nmod_t mod);

void
_nmod_poly_evaluate_nmod_vec_fast_precomp(mp_ptr vs, mp_srcptr poly,
long plen, mp_ptr * tree, long len, nmod_t mod);

void nmod_poly_evaluate_nmod_vec_fast(mp_ptr ys,
const nmod_poly_t poly, mp_srcptr xs, long n);

/* Subproduct tree **********************************************************/

mp_ptr * _nmod_poly_tree_alloc(long len);

void _nmod_poly_tree_free(mp_ptr * tree, long len);

void _nmod_poly_tree_build(mp_ptr * tree, mp_srcptr roots,
long len, nmod_t mod);

/* Interpolation ************************************************************/

void _nmod_poly_interpolate_nmod_vec_newton(mp_ptr poly, mp_srcptr xs,
Expand All @@ -613,6 +635,19 @@ void _nmod_poly_interpolate_nmod_vec(mp_ptr poly, mp_srcptr xs,
void nmod_poly_interpolate_nmod_vec(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, long n);

void nmod_poly_interpolate_nmod_vec_fast(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, long n);

void _nmod_poly_interpolate_nmod_vec_fast(mp_ptr poly,
mp_srcptr xs, mp_srcptr ys, long len, nmod_t mod);

void
_nmod_poly_interpolate_nmod_vec_fast_precomp(mp_ptr poly, mp_srcptr ys,
mp_ptr * tree, mp_srcptr weights, long len, nmod_t mod);

void _nmod_poly_interpolation_weights(mp_ptr w, mp_ptr * tree,
long len, nmod_t mod);

/* Composition **************************************************************/

void _nmod_poly_compose_horner(mp_ptr res, mp_srcptr poly1,
Expand Down
127 changes: 127 additions & 0 deletions nmod_poly/evaluate_nmod_vec_fast.c
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@@ -0,0 +1,127 @@
/*=============================================================================
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) 2012 Fredrik Johansson
******************************************************************************/

#include <mpir.h>
#include "flint.h"
#include "ulong_extras.h"
#include "nmod_poly.h"

void
_nmod_poly_evaluate_nmod_vec_fast_precomp(mp_ptr vs, mp_srcptr poly,
long plen, mp_ptr * tree, long len, nmod_t mod)
{
long height, i, j, pow, left;
long tree_height;
long tlen;
mp_ptr t, u, swap, pa, pb, pc;

/* avoid worrying about some degenerate cases */
if (len < 2 || plen < 2)
{
if (len == 1)
vs[0] = _nmod_poly_evaluate_nmod(poly, plen,
nmod_neg(tree[0][0], mod), mod);
else if (len != 0 && plen == 0)
_nmod_vec_zero(vs, len);
else if (len != 0 && plen == 1)
for (i = 0; i < len; i++)
vs[i] = poly[0];
return;
}

t = _nmod_vec_init(len);
u = _nmod_vec_init(len);

left = len;

/* Initial reduction. We allow the polynomial to be larger
or smaller than the number of points. */
height = FLINT_BIT_COUNT(plen - 1) - 1;
tree_height = FLINT_CLOG2(len);
while (height >= tree_height)
height--;
pow = 1L << height;

for (i = j = 0; i < len; i += pow, j += (pow + 1))
{
tlen = ((i + pow) <= len) ? pow : len % pow;
_nmod_poly_rem(t + i, poly, plen, tree[height] + j, tlen + 1, mod);
}

for (i = height - 1; i >= 0; i--)
{
pow = 1L << i;
left = len;
pa = tree[i];
pb = t;
pc = u;

while (left >= 2 * pow)
{
_nmod_poly_rem(pc, pb, 2 * pow, pa, pow + 1, mod);
_nmod_poly_rem(pc + pow, pb, 2 * pow, pa + pow + 1, pow + 1, mod);

pa += 2 * pow + 2;
pb += 2 * pow;
pc += 2 * pow;
left -= 2 * pow;
}

if (left > pow)
{
_nmod_poly_rem(pc, pb, left, pa, pow + 1, mod);
_nmod_poly_rem(pc + pow, pb, left, pa + pow + 1, left - pow + 1, mod);
}
else if (left > 0)
_nmod_vec_set(pc, pb, left);

swap = t;
t = u;
u = swap;
}

_nmod_vec_set(vs, t, len);
_nmod_vec_clear(t);
_nmod_vec_clear(u);
}

void _nmod_poly_evaluate_nmod_vec_fast(mp_ptr ys, mp_srcptr poly, long plen,
mp_srcptr xs, long n, nmod_t mod)
{
mp_ptr * tree;

tree = _nmod_poly_tree_alloc(n);
_nmod_poly_tree_build(tree, xs, n, mod);
_nmod_poly_evaluate_nmod_vec_fast_precomp(ys, poly, plen, tree, n, mod);
_nmod_poly_tree_free(tree, n);
}

void
nmod_poly_evaluate_nmod_vec_fast(mp_ptr ys,
const nmod_poly_t poly, mp_srcptr xs, long n)
{
_nmod_poly_evaluate_nmod_vec_fast(ys, poly->coeffs,
poly->length, xs, n, poly->mod);
}
145 changes: 145 additions & 0 deletions nmod_poly/interpolate_nmod_vec_fast.c
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@@ -0,0 +1,145 @@
/*=============================================================================
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) 2012 Fredrik Johansson
******************************************************************************/

#include <mpir.h>
#include "flint.h"
#include "ulong_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"

void
_nmod_poly_interpolation_weights(mp_ptr w, mp_ptr * tree, long len, nmod_t mod)
{
mp_ptr tmp;
long i, n, height;

if (len == 0)
return;

if (len == 1)
{
w[0] = 1;
return;
}

tmp = _nmod_vec_init(len + 1);
height = FLINT_CLOG2(len);
n = 1L << (height - 1);

_nmod_poly_mul(tmp, tree[height-1], n + 1,
tree[height-1] + (n + 1), (len - n + 1), mod);

_nmod_poly_derivative(tmp, tmp, len + 1, mod);
_nmod_poly_evaluate_nmod_vec_fast_precomp(w, tmp, len, tree, len, mod);

for (i = 0; i < len; i++)
w[i] = n_invmod(w[i], mod.n);

_nmod_vec_clear(tmp);
}

void
_nmod_poly_interpolate_nmod_vec_fast_precomp(mp_ptr poly, mp_srcptr ys,
mp_ptr * tree, mp_srcptr weights, long len, nmod_t mod)
{
mp_ptr t, u, pa, pb;
long i, pow, left;

if (len == 0)
return;

t = _nmod_vec_init(len);
u = _nmod_vec_init(len);

for (i = 0; i < len; i++)
poly[i] = nmod_mul(weights[i], ys[i], mod);

for (i = 0; i < FLINT_CLOG2(len); i++)
{
pow = (1L << i);
pa = tree[i];
pb = poly;
left = len;

while (left >= 2 * pow)
{
_nmod_poly_mul(t, pa, pow + 1, pb + pow, pow, mod);
_nmod_poly_mul(u, pa + pow + 1, pow + 1, pb, pow, mod);
_nmod_vec_add(pb, t, u, 2 * pow, mod);

left -= 2 * pow;
pa += 2 * pow + 2;
pb += 2 * pow;
}

if (left > pow)
{
_nmod_poly_mul(t, pa, pow + 1, pb + pow, left - pow, mod);
_nmod_poly_mul(u, pb, pow, pa + pow + 1, left - pow + 1, mod);
_nmod_vec_add(pb, t, u, left, mod);
}
}

_nmod_vec_clear(t);
_nmod_vec_clear(u);
}


void
_nmod_poly_interpolate_nmod_vec_fast(mp_ptr poly,
mp_srcptr xs, mp_srcptr ys, long len, nmod_t mod)
{
mp_ptr * tree;
mp_ptr w;

tree = _nmod_poly_tree_alloc(len);
_nmod_poly_tree_build(tree, xs, len, mod);

w = _nmod_vec_init(len);
_nmod_poly_interpolation_weights(w, tree, len, mod);

_nmod_poly_interpolate_nmod_vec_fast_precomp(poly, ys, tree, w, len, mod);

_nmod_vec_clear(w);
_nmod_poly_tree_free(tree, len);
}

void
nmod_poly_interpolate_nmod_vec_fast(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, long n)
{
if (n == 0)
{
nmod_poly_zero(poly);
}
else
{
nmod_poly_fit_length(poly, n);
poly->length = n;
_nmod_poly_interpolate_nmod_vec_fast(poly->coeffs,
xs, ys, n, poly->mod);
_nmod_poly_normalise(poly);
}
}

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