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Implement Graeffe Transform for real and complex poly

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This commit is contained in:
Matthias Gessinger 2021-07-26 23:46:26 +02:00
parent c2168d5f9c
commit ac29673684
4 changed files with 112 additions and 0 deletions
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4
acb_poly.h
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@ -193,6 +193,10 @@ void _acb_poly_binomial_transform(acb_ptr b, acb_srcptr a, slong alen, slong len
void acb_poly_binomial_transform(acb_poly_t b, const acb_poly_t a, slong len, slong prec);
void _acb_poly_graeffe_transform(acb_ptr b, acb_srcptr a, slong len, slong prec);
void acb_poly_graeffe_transform(acb_poly_t b, const acb_poly_t a, slong prec);
void acb_poly_set(acb_poly_t dest, const acb_poly_t src);

52
acb_poly/graeffe_transform.c Normal file
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@ -0,0 +1,52 @@
/*
Copyright (C) 2012 Fredrik Johansson
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_poly.h"
void
_acb_poly_graeffe_transform(acb_ptr b, acb_srcptr a, slong len, slong prec)
{
if (len == 0)
return;
slong q, i;
q = (len-1)/2+1;
acb_ptr pe = _acb_vec_init(q);
acb_ptr po = _acb_vec_init(len);
for (i = len-1; i >= 0; i--)
{
if (i % 2 == 0)
acb_set(pe+i/2, a+i);
else
acb_set(po+i/2, a+i);
}
_acb_poly_mul(b, po, q, po, q, prec);
_acb_poly_shift_left(b, b, len-1, 1);
_acb_poly_mul(po, pe, q, pe, q, prec);
_acb_vec_sub(b, po, b, len, prec);
_acb_vec_clear(pe, q);
_acb_vec_clear(po, len);
if (len % 2 == 0)
_acb_vec_neg(b, b, len);
}
void
acb_poly_graeffe_transform(acb_poly_t b, const acb_poly_t a, slong prec)
{
acb_poly_fit_length(b, a->length);
_acb_poly_graeffe_transform(b->coeffs, a->coeffs, a->length, prec);
_acb_poly_set_length(b, a->length);
}

4
arb_poly.h
View file

@ -512,6 +512,10 @@ void _arb_poly_binomial_transform(arb_ptr b, arb_srcptr a, slong alen, slong len
void arb_poly_binomial_transform(arb_poly_t b, const arb_poly_t a, slong len, slong prec);
void _arb_poly_graeffe_transform(arb_ptr b, arb_srcptr a, slong len, slong prec);
void arb_poly_graeffe_transform(arb_poly_t b, const arb_poly_t a, slong prec);
/* Special functions */
void _arb_poly_pow_ui_trunc_binexp(arb_ptr res,

52
arb_poly/graeffe_transform.c Normal file
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@ -0,0 +1,52 @@
/*
Copyright (C) 2012 Fredrik Johansson
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "arb_poly.h"
void
_arb_poly_graeffe_transform(arb_ptr b, arb_srcptr a, slong len, slong prec)
{
if (len == 0)
return;
slong q, i;
q = (len-1)/2+1;
arb_ptr pe = _arb_vec_init(q);
arb_ptr po = _arb_vec_init(len);
for (i = len-1; i >= 0; i--)
{
if (i % 2 == 0)
arb_set(pe+i/2, a+i);
else
arb_set(po+i/2, a+i);
}
_arb_poly_mul(b, po, q, po, q, prec);
_arb_poly_shift_left(b, b, len-1, 1);
_arb_poly_mul(po, pe, q, pe, q, prec);
_arb_vec_sub(b, po, b, len, prec);
_arb_vec_clear(pe, q);
_arb_vec_clear(po, len);
if (len % 2 == 0)
_arb_vec_neg(b, b, len);
}
void
arb_poly_graeffe_transform(arb_poly_t b, const arb_poly_t a, slong prec)
{
arb_poly_fit_length(b, a->length);
_arb_poly_graeffe_transform(b->coeffs, a->coeffs, a->length, prec);
_arb_poly_set_length(b, a->length);
}