mirror of
https://github.com/vale981/arb
synced 2025-03-05 17:31:38 -05:00
add fmprb_poly_evaluate2_fmpcb
This commit is contained in:
Fredrik Johansson
parent
ee364152ff
commit
cf42331a7e
6 changed files with 370 additions and 0 deletions
|
|
@ -270,6 +270,22 @@ Evaluation
|
|||
With the rectangular splitting algorithm, the powers can be reused,
|
||||
making simultaneous evaluation slightly faster.
|
||||
|
||||
.. function:: void _fmprb_poly_evaluate2_fmpcb_horner(fmpcb_t y, fmpcb_t z, const fmprb_struct * f, long len, const fmpcb_t x, long prec)
|
||||
|
||||
.. function:: void fmprb_poly_evaluate2_fmpcb_horner(fmpcb_t y, fmpcb_t z, const fmprb_poly_t f, const fmpcb_t x, long prec)
|
||||
|
||||
.. function:: void _fmprb_poly_evaluate2_fmpcb_rectangular(fmpcb_t y, fmpcb_t z, const fmprb_struct * f, long len, const fmpcb_t x, long prec)
|
||||
|
||||
.. function:: void fmprb_poly_evaluate2_fmpcb_rectangular(fmpcb_t y, fmpcb_t z, const fmprb_poly_t f, const fmpcb_t x, long prec)
|
||||
|
||||
.. function:: void _fmprb_poly_evaluate2_fmpcb(fmpcb_t y, fmpcb_t z, const fmprb_struct * f, long len, const fmpcb_t x, long prec)
|
||||
|
||||
.. function:: void fmprb_poly_evaluate2_fmpcb(fmpcb_t y, fmpcb_t z, const fmprb_poly_t f, const fmpcb_t x, long prec)
|
||||
|
||||
Sets `y = f(x), z = f'(x)`, evaluated respectively using Horner's rule,
|
||||
rectangular splitting, and an automatic algorithm choice.
|
||||
|
||||
|
||||
Product trees
|
||||
-------------------------------------------------------------------------------
|
||||
|
||||
|
|
|
|||
11
fmprb_poly.h
11
fmprb_poly.h
|
|
@ -279,6 +279,17 @@ void fmprb_poly_evaluate_fmpcb_rectangular(fmpcb_t res, const fmprb_poly_t f, co
|
|||
void _fmprb_poly_evaluate_fmpcb(fmpcb_t res, const fmprb_struct * f, long len, const fmpcb_t x, long prec);
|
||||
void fmprb_poly_evaluate_fmpcb(fmpcb_t res, const fmprb_poly_t f, const fmpcb_t a, long prec);
|
||||
|
||||
void _fmprb_poly_evaluate2_fmpcb_horner(fmpcb_t y, fmpcb_t z, const fmprb_struct * f, long len, const fmpcb_t x, long prec);
|
||||
void fmprb_poly_evaluate2_fmpcb_horner(fmpcb_t y, fmpcb_t z, const fmprb_poly_t f, const fmpcb_t x, long prec);
|
||||
|
||||
void _fmprb_poly_evaluate2_fmpcb_rectangular(fmpcb_t y, fmpcb_t z, const fmprb_struct * f, long len, const fmpcb_t x, long prec);
|
||||
void fmprb_poly_evaluate2_fmpcb_rectangular(fmpcb_t y, fmpcb_t z, const fmprb_poly_t f, const fmpcb_t x, long prec);
|
||||
|
||||
void _fmprb_poly_evaluate2_fmpcb(fmpcb_t y, fmpcb_t z, const fmprb_struct * f, long len, const fmpcb_t x, long prec);
|
||||
void fmprb_poly_evaluate2_fmpcb(fmpcb_t y, fmpcb_t z, const fmprb_poly_t f, const fmpcb_t x, long prec);
|
||||
|
||||
|
||||
|
||||
void _fmprb_poly_evaluate_vec_iter(fmprb_struct * ys, const fmprb_struct * poly, long plen,
|
||||
const fmprb_struct * xs, long n, long prec);
|
||||
|
||||
|
|
|
|||
39
fmprb_poly/evaluate2_fmpcb.c
Normal file
39
fmprb_poly/evaluate2_fmpcb.c
Normal file
|
|
@ -0,0 +1,39 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of ARB.
|
||||
|
||||
ARB 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.
|
||||
|
||||
ARB 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 ARB; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2013 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "fmprb_poly.h"
|
||||
|
||||
void
|
||||
_fmprb_poly_evaluate2_fmpcb(fmpcb_t y, fmpcb_t z, const fmprb_struct * f, long len, const fmpcb_t x, long prec)
|
||||
{
|
||||
_fmprb_poly_evaluate2_fmpcb_rectangular(y, z, f, len, x, prec);
|
||||
}
|
||||
|
||||
void
|
||||
fmprb_poly_evaluate2_fmpcb(fmpcb_t r, fmpcb_t s, const fmprb_poly_t f, const fmpcb_t a, long prec)
|
||||
{
|
||||
_fmprb_poly_evaluate2_fmpcb(r, s, f->coeffs, f->length, a, prec);
|
||||
}
|
||||
|
||||
87
fmprb_poly/evaluate2_fmpcb_horner.c
Normal file
87
fmprb_poly/evaluate2_fmpcb_horner.c
Normal file
|
|
@ -0,0 +1,87 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of ARB.
|
||||
|
||||
ARB 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.
|
||||
|
||||
ARB 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 ARB; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2013 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "fmprb_poly.h"
|
||||
|
||||
void
|
||||
_fmprb_poly_evaluate2_fmpcb_horner(fmpcb_t y, fmpcb_t z,
|
||||
const fmprb_struct * poly, long len, const fmpcb_t x, long prec)
|
||||
{
|
||||
if (len == 0)
|
||||
{
|
||||
fmpcb_zero(y);
|
||||
fmpcb_zero(z);
|
||||
}
|
||||
else if (len == 1)
|
||||
{
|
||||
fmpcb_set_round_fmprb(y, poly + 0, prec);
|
||||
fmpcb_zero(z);
|
||||
}
|
||||
else if (fmprb_is_zero(x))
|
||||
{
|
||||
fmpcb_set_round_fmprb(y, poly + 0, prec);
|
||||
fmpcb_set_round_fmprb(z, poly + 1, prec);
|
||||
}
|
||||
else if (len == 2)
|
||||
{
|
||||
fmpcb_mul_fmprb(y, x, poly + 1, prec);
|
||||
fmpcb_add_fmprb(y, y, poly + 0, prec);
|
||||
fmpcb_set_round_fmprb(z, poly + 1, prec);
|
||||
}
|
||||
else
|
||||
{
|
||||
fmprb_t t, u, v;
|
||||
long i;
|
||||
|
||||
fmpcb_init(t);
|
||||
fmpcb_init(u);
|
||||
fmpcb_init(v);
|
||||
|
||||
fmpcb_set_round_fmprb(u, poly + len - 1, prec);
|
||||
fmpcb_zero(v);
|
||||
|
||||
for (i = len - 2; i >= 0; i--)
|
||||
{
|
||||
fmpcb_mul(t, v, x, prec);
|
||||
fmpcb_add(v, u, t, prec);
|
||||
fmpcb_mul(t, u, x, prec);
|
||||
fmpcb_add_fmprb(u, t, poly + i, prec);
|
||||
}
|
||||
|
||||
fmpcb_swap(y, u);
|
||||
fmpcb_swap(z, v);
|
||||
|
||||
fmpcb_clear(t);
|
||||
fmpcb_clear(u);
|
||||
fmpcb_clear(v);
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
fmprb_poly_evaluate2_fmpcb_horner(fmpcb_t r, fmpcb_t s, const fmprb_poly_t f, const fmpcb_t a, long prec)
|
||||
{
|
||||
_fmprb_poly_evaluate2_fmpcb_horner(r, s, f->coeffs, f->length, a, prec);
|
||||
}
|
||||
|
||||
130
fmprb_poly/evaluate2_fmpcb_rectangular.c
Normal file
130
fmprb_poly/evaluate2_fmpcb_rectangular.c
Normal file
|
|
@ -0,0 +1,130 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of ARB.
|
||||
|
||||
ARB 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.
|
||||
|
||||
ARB 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 ARB; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2013 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "fmprb_poly.h"
|
||||
|
||||
void
|
||||
_fmprb_poly_evaluate2_fmpcb_rectangular(fmpcb_t y, fmpcb_t z,
|
||||
const fmprb_struct * poly, long len, const fmpcb_t x, long prec)
|
||||
{
|
||||
long i, j, m, r;
|
||||
fmpcb_struct * xs;
|
||||
fmpcb_t s, t;
|
||||
fmprb_t c;
|
||||
|
||||
if (len < 3)
|
||||
{
|
||||
if (len == 0)
|
||||
{
|
||||
fmpcb_zero(y);
|
||||
fmpcb_zero(z);
|
||||
}
|
||||
else if (len == 1)
|
||||
{
|
||||
fmpcb_set_round_fmprb(y, poly + 0, prec);
|
||||
fmpcb_zero(z);
|
||||
}
|
||||
else if (len == 2)
|
||||
{
|
||||
fmpcb_mul_fmprb(y, x, poly + 1, prec);
|
||||
fmpcb_add_fmprb(y, y, poly + 0, prec);
|
||||
fmpcb_set_round_fmprb(z, poly + 1, prec);
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
m = n_sqrt(len) + 1;
|
||||
m *= 1;
|
||||
|
||||
r = (len + m - 1) / m;
|
||||
|
||||
xs = _fmpcb_vec_init(m + 1);
|
||||
fmpcb_init(s);
|
||||
fmpcb_init(t);
|
||||
fmprb_init(c);
|
||||
|
||||
for (i = 0; i <= m; i++)
|
||||
{
|
||||
if (i == 0)
|
||||
fmpcb_one(xs + i);
|
||||
else if (i == 1)
|
||||
fmpcb_set(xs + i, x);
|
||||
else if (i % 2 == 0)
|
||||
fmpcb_mul(xs + i, xs + i / 2, xs + i / 2, prec);
|
||||
else
|
||||
fmpcb_mul(xs + i, xs + i - 1, x, prec);
|
||||
}
|
||||
|
||||
fmpcb_set_fmprb(y, poly + (r - 1) * m);
|
||||
for (j = 1; (r - 1) * m + j < len; j++)
|
||||
fmpcb_addmul_fmprb(y, xs + j, poly + (r - 1) * m + j, prec);
|
||||
|
||||
for (i = r - 2; i >= 0; i--)
|
||||
{
|
||||
fmpcb_set_fmprb(s, poly + i * m);
|
||||
for (j = 1; j < m; j++)
|
||||
fmpcb_addmul_fmprb(s, xs + j, poly + i * m + j, prec);
|
||||
|
||||
fmpcb_mul(y, y, xs + m, prec);
|
||||
fmpcb_add(y, y, s, prec);
|
||||
}
|
||||
|
||||
len -= 1;
|
||||
r = (len + m - 1) / m;
|
||||
fmprb_mul_ui(fmpcb_realref(z), poly + (r - 1) * m + 1, (r - 1) * m + 1, FMPR_PREC_EXACT);
|
||||
fmprb_zero(fmpcb_imagref(z));
|
||||
for (j = 1; (r - 1) * m + j < len; j++)
|
||||
{
|
||||
fmprb_mul_ui(c, poly + (r - 1) * m + j + 1, (r - 1) * m + j + 1, FMPR_PREC_EXACT);
|
||||
fmpcb_addmul_fmprb(z, xs + j, c, prec);
|
||||
}
|
||||
|
||||
for (i = r - 2; i >= 0; i--)
|
||||
{
|
||||
fmprb_mul_ui(fmpcb_realref(s), poly + i * m + 1, i * m + 1, FMPR_PREC_EXACT);
|
||||
fmprb_zero(fmpcb_imagref(s));
|
||||
|
||||
for (j = 1; j < m; j++)
|
||||
{
|
||||
fmprb_mul_ui(c, poly + i * m + j + 1, i * m + j + 1, FMPR_PREC_EXACT);
|
||||
fmpcb_addmul_fmprb(s, xs + j, c, prec);
|
||||
}
|
||||
|
||||
fmpcb_mul(z, z, xs + m, prec);
|
||||
fmpcb_add(z, z, s, prec);
|
||||
}
|
||||
|
||||
_fmpcb_vec_clear(xs, m + 1);
|
||||
fmpcb_clear(s);
|
||||
fmpcb_clear(t);
|
||||
fmprb_clear(c);
|
||||
}
|
||||
|
||||
void
|
||||
fmprb_poly_evaluate2_fmpcb_rectangular(fmpcb_t r, fmpcb_t s, const fmprb_poly_t f, const fmpcb_t a, long prec)
|
||||
{
|
||||
_fmprb_poly_evaluate2_fmpcb_rectangular(r, s, f->coeffs, f->length, a, prec);
|
||||
}
|
||||
|
||||
87
fmprb_poly/test/t-evaluate2_fmpcb_rectangular.c
Normal file
87
fmprb_poly/test/t-evaluate2_fmpcb_rectangular.c
Normal file
|
|
@ -0,0 +1,87 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of ARB.
|
||||
|
||||
ARB 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.
|
||||
|
||||
ARB 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 ARB; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2012, 2013 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "fmprb_poly.h"
|
||||
|
||||
int main()
|
||||
{
|
||||
long iter;
|
||||
flint_rand_t state;
|
||||
|
||||
printf("evaluate2_fmpcb_rectangular....");
|
||||
fflush(stdout);
|
||||
|
||||
flint_randinit(state);
|
||||
|
||||
for (iter = 0; iter < 10000; iter++)
|
||||
{
|
||||
fmprb_poly_t f, g;
|
||||
fmpcb_t x, y1, z1, y2, z2;
|
||||
|
||||
fmpcb_init(x);
|
||||
fmpcb_init(y1);
|
||||
fmpcb_init(z1);
|
||||
fmpcb_init(y2);
|
||||
fmpcb_init(z2);
|
||||
fmprb_poly_init(f);
|
||||
fmprb_poly_init(g);
|
||||
|
||||
fmpcb_randtest(x, state, 2 + n_randint(state, 1000), 5);
|
||||
fmprb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5);
|
||||
fmprb_poly_derivative(g, f, 2 + n_randint(state, 1000));
|
||||
|
||||
fmprb_poly_evaluate2_fmpcb_rectangular(y1, z1, f, x, 2 + n_randint(state, 1000));
|
||||
|
||||
fmprb_poly_evaluate_fmpcb_horner(y2, f, x, 2 + n_randint(state, 1000));
|
||||
fmprb_poly_evaluate_fmpcb_horner(z2, g, x, 2 + n_randint(state, 1000));
|
||||
|
||||
if (!fmpcb_overlaps(y1, y2) || !fmpcb_overlaps(z1, z2))
|
||||
{
|
||||
printf("FAIL\n\n");
|
||||
printf("f = "); fmprb_poly_printd(f, 15); printf("\n\n");
|
||||
printf("g = "); fmprb_poly_printd(g, 15); printf("\n\n");
|
||||
printf("x = "); fmpcb_printd(x, 15); printf("\n\n");
|
||||
printf("y1 = "); fmpcb_printd(y1, 15); printf("\n\n");
|
||||
printf("z1 = "); fmpcb_printd(z1, 15); printf("\n\n");
|
||||
printf("y2 = "); fmpcb_printd(y2, 15); printf("\n\n");
|
||||
printf("z2 = "); fmpcb_printd(z2, 15); printf("\n\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmprb_poly_clear(f);
|
||||
fmprb_poly_clear(g);
|
||||
fmpcb_clear(x);
|
||||
fmpcb_clear(y1);
|
||||
fmpcb_clear(z1);
|
||||
fmpcb_clear(y2);
|
||||
fmpcb_clear(z2);
|
||||
}
|
||||
|
||||
flint_randclear(state);
|
||||
_fmpz_cleanup();
|
||||
printf("PASS\n");
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
|
||||
Loading…
Add table
Reference in a new issue