/usr/include/arb_poly.h is in libflint-arb-dev 2.8.1-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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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 Fredrik Johansson
******************************************************************************/
#ifndef ARB_POLY_H
#define ARB_POLY_H
#ifdef ARB_POLY_INLINES_C
#define ARB_POLY_INLINE
#else
#define ARB_POLY_INLINE static __inline__
#endif
#include "arb.h"
#include "acb.h"
#include "flint/fmpz_poly.h"
#include "flint/fmpq_poly.h"
#ifdef __cplusplus
extern "C" {
#endif
typedef struct
{
arb_ptr coeffs;
slong length;
slong alloc;
}
arb_poly_struct;
typedef arb_poly_struct arb_poly_t[1];
/* Memory management */
void arb_poly_init(arb_poly_t poly);
void arb_poly_init2(arb_poly_t poly, slong len);
void arb_poly_clear(arb_poly_t poly);
void arb_poly_fit_length(arb_poly_t poly, slong len);
void _arb_poly_set_length(arb_poly_t poly, slong len);
void _arb_poly_normalise(arb_poly_t poly);
ARB_POLY_INLINE void
arb_poly_swap(arb_poly_t poly1, arb_poly_t poly2)
{
arb_poly_struct t = *poly1;
*poly1 = *poly2;
*poly2 = t;
}
void arb_poly_set(arb_poly_t poly, const arb_poly_t src);
void arb_poly_set_round(arb_poly_t poly, const arb_poly_t src, slong prec);
/* Basic manipulation */
ARB_POLY_INLINE slong arb_poly_length(const arb_poly_t poly)
{
return poly->length;
}
ARB_POLY_INLINE slong arb_poly_degree(const arb_poly_t poly)
{
return poly->length - 1;
}
ARB_POLY_INLINE void arb_poly_zero(arb_poly_t poly)
{
poly->length = 0;
}
ARB_POLY_INLINE void
arb_poly_one(arb_poly_t poly)
{
arb_poly_fit_length(poly, 1);
arb_one(poly->coeffs);
_arb_poly_set_length(poly, 1);
}
void arb_poly_set_coeff_si(arb_poly_t poly, slong n, slong x);
void arb_poly_set_coeff_arb(arb_poly_t poly, slong n, const arb_t x);
void arb_poly_get_coeff_arb(arb_t x, const arb_poly_t poly, slong n);
#define arb_poly_get_coeff_ptr(poly, n) \
((n) < (poly)->length ? (poly)->coeffs + (n) : NULL)
void _arb_poly_reverse(arb_ptr res, arb_srcptr poly, slong len, slong n);
void _arb_poly_shift_right(arb_ptr res, arb_srcptr poly, slong len, slong n);
void arb_poly_shift_right(arb_poly_t res, const arb_poly_t poly, slong n);
void _arb_poly_shift_left(arb_ptr res, arb_srcptr poly, slong len, slong n);
void arb_poly_shift_left(arb_poly_t res, const arb_poly_t poly, slong n);
ARB_POLY_INLINE void
arb_poly_truncate(arb_poly_t poly, slong newlen)
{
if (poly->length > newlen)
{
slong i;
for (i = newlen; i < poly->length; i++)
arb_zero(poly->coeffs + i);
poly->length = newlen;
_arb_poly_normalise(poly);
}
}
/* Conversions */
void arb_poly_set_fmpz_poly(arb_poly_t poly, const fmpz_poly_t src, slong prec);
void arb_poly_set_fmpq_poly(arb_poly_t poly, const fmpq_poly_t src, slong prec);
ARB_POLY_INLINE void
arb_poly_set_arb(arb_poly_t poly, const arb_t c)
{
arb_poly_fit_length(poly, 1);
arb_set(poly->coeffs, c);
_arb_poly_set_length(poly, !arb_is_zero(poly->coeffs));
}
void arb_poly_set_si(arb_poly_t poly, slong c);
int arb_poly_get_unique_fmpz_poly(fmpz_poly_t res, const arb_poly_t src);
/* Comparisons */
int arb_poly_contains(const arb_poly_t poly1, const arb_poly_t poly2);
int arb_poly_contains_fmpz_poly(const arb_poly_t poly1, const fmpz_poly_t poly2);
int arb_poly_contains_fmpq_poly(const arb_poly_t poly1, const fmpq_poly_t poly2);
int arb_poly_equal(const arb_poly_t A, const arb_poly_t B);
int _arb_poly_overlaps(arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2);
int arb_poly_overlaps(const arb_poly_t poly1, const arb_poly_t poly2);
/* Bounds */
void _arb_poly_majorant(arb_ptr res, arb_srcptr vec, slong len, slong prec);
void arb_poly_majorant(arb_poly_t res, const arb_poly_t poly, slong prec);
/* IO */
void arb_poly_printd(const arb_poly_t poly, slong digits);
/* Random generation */
void arb_poly_randtest(arb_poly_t poly, flint_rand_t state, slong len, slong prec, slong mag_bits);
/* Arithmetic */
void
_arb_poly_add(arb_ptr res, arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong prec);
void arb_poly_add(arb_poly_t res, const arb_poly_t poly1,
const arb_poly_t poly2, slong prec);
void arb_poly_add_si(arb_poly_t res, const arb_poly_t poly, slong c, slong prec);
void _arb_poly_sub(arb_ptr res, arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong prec);
void arb_poly_sub(arb_poly_t res, const arb_poly_t poly1,
const arb_poly_t poly2, slong prec);
ARB_POLY_INLINE void
arb_poly_neg(arb_poly_t res, const arb_poly_t poly)
{
arb_poly_fit_length(res, poly->length);
_arb_vec_neg(res->coeffs, poly->coeffs, poly->length);
_arb_poly_set_length(res, poly->length);
}
ARB_POLY_INLINE void
arb_poly_scalar_mul_2exp_si(arb_poly_t res, const arb_poly_t poly, slong c)
{
arb_poly_fit_length(res, poly->length);
_arb_vec_scalar_mul_2exp_si(res->coeffs, poly->coeffs, poly->length, c);
_arb_poly_set_length(res, poly->length);
}
void _arb_poly_mullow_ztrunc(arb_ptr res,
arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong n, slong prec);
void arb_poly_mullow_ztrunc(arb_poly_t res, const arb_poly_t poly1,
const arb_poly_t poly2,
slong n, slong prec);
void _arb_poly_mullow_classical(arb_ptr res,
arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong n, slong prec);
void arb_poly_mullow_classical(arb_poly_t res, const arb_poly_t poly1,
const arb_poly_t poly2,
slong n, slong prec);
void _arb_poly_mullow_block(arb_ptr C,
arb_srcptr A, slong lenA,
arb_srcptr B, slong lenB, slong n, slong prec);
void arb_poly_mullow_block(arb_poly_t res, const arb_poly_t poly1,
const arb_poly_t poly2, slong len, slong prec);
void _arb_poly_mullow(arb_ptr C,
arb_srcptr A, slong lenA,
arb_srcptr B, slong lenB, slong n, slong prec);
void arb_poly_mullow(arb_poly_t res, const arb_poly_t poly1,
const arb_poly_t poly2, slong len, slong prec);
void _arb_poly_mul(arb_ptr C,
arb_srcptr A, slong lenA,
arb_srcptr B, slong lenB, slong prec);
void arb_poly_mul(arb_poly_t res, const arb_poly_t poly1,
const arb_poly_t poly2, slong prec);
ARB_POLY_INLINE void
_arb_poly_mul_monic(arb_ptr res, arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong prec)
{
if (len1 + len2 - 2 > 0)
_arb_poly_mullow(res, poly1, len1, poly2, len2, len1 + len2 - 2, prec);
arb_one(res + len1 + len2 - 2);
}
void _arb_poly_inv_series(arb_ptr Qinv,
arb_srcptr Q, slong Qlen, slong len, slong prec);
void arb_poly_inv_series(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec);
void _arb_poly_div_series(arb_ptr Q, arb_srcptr A, slong Alen,
arb_srcptr B, slong Blen, slong n, slong prec);
void arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, slong n, slong prec);
void
_arb_poly_div(arb_ptr Q,
arb_srcptr A, slong lenA,
arb_srcptr B, slong lenB, slong prec);
void _arb_poly_divrem(arb_ptr Q, arb_ptr R,
arb_srcptr A, slong lenA,
arb_srcptr B, slong lenB, slong prec);
void _arb_poly_rem(arb_ptr R,
arb_srcptr A, slong lenA,
arb_srcptr B, slong lenB, slong prec);
int arb_poly_divrem(arb_poly_t Q, arb_poly_t R,
const arb_poly_t A, const arb_poly_t B, slong prec);
void _arb_poly_div_root(arb_ptr Q, arb_t R, arb_srcptr A,
slong len, const arb_t c, slong prec);
/* Product trees */
void _arb_poly_product_roots(arb_ptr poly, arb_srcptr xs, slong n, slong prec);
void arb_poly_product_roots(arb_poly_t poly, arb_srcptr xs, slong n, slong prec);
arb_ptr * _arb_poly_tree_alloc(slong len);
void _arb_poly_tree_free(arb_ptr * tree, slong len);
void _arb_poly_tree_build(arb_ptr * tree, arb_srcptr roots, slong len, slong prec);
/* Composition */
void _arb_poly_compose(arb_ptr res,
arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong prec);
void arb_poly_compose(arb_poly_t res,
const arb_poly_t poly1, const arb_poly_t poly2, slong prec);
void _arb_poly_compose_horner(arb_ptr res,
arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong prec);
void arb_poly_compose_horner(arb_poly_t res,
const arb_poly_t poly1, const arb_poly_t poly2, slong prec);
void _arb_poly_compose_divconquer(arb_ptr res,
arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong prec);
void arb_poly_compose_divconquer(arb_poly_t res,
const arb_poly_t poly1, const arb_poly_t poly2, slong prec);
void _arb_poly_compose_series_horner(arb_ptr res, arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong n, slong prec);
void arb_poly_compose_series_horner(arb_poly_t res,
const arb_poly_t poly1,
const arb_poly_t poly2, slong n, slong prec);
void _arb_poly_compose_series(arb_ptr res, arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong n, slong prec);
void arb_poly_compose_series(arb_poly_t res,
const arb_poly_t poly1,
const arb_poly_t poly2, slong n, slong prec);
/* Reversion */
void _arb_poly_revert_series_lagrange(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec);
void arb_poly_revert_series_lagrange(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec);
void _arb_poly_revert_series_newton(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec);
void arb_poly_revert_series_newton(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec);
void _arb_poly_revert_series_lagrange_fast(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec);
void arb_poly_revert_series_lagrange_fast(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec);
void _arb_poly_revert_series(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec);
void arb_poly_revert_series(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec);
/* Evaluation and interpolation */
void _arb_poly_evaluate_horner(arb_t res, arb_srcptr f, slong len, const arb_t a, slong prec);
void arb_poly_evaluate_horner(arb_t res, const arb_poly_t f, const arb_t a, slong prec);
void _arb_poly_evaluate_rectangular(arb_t y, arb_srcptr poly, slong len, const arb_t x, slong prec);
void arb_poly_evaluate_rectangular(arb_t res, const arb_poly_t f, const arb_t a, slong prec);
void _arb_poly_evaluate(arb_t res, arb_srcptr f, slong len, const arb_t a, slong prec);
void arb_poly_evaluate(arb_t res, const arb_poly_t f, const arb_t a, slong prec);
void _arb_poly_evaluate2_horner(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec);
void arb_poly_evaluate2_horner(arb_t y, arb_t z, const arb_poly_t f, const arb_t x, slong prec);
void _arb_poly_evaluate2_rectangular(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec);
void arb_poly_evaluate2_rectangular(arb_t y, arb_t z, const arb_poly_t f, const arb_t x, slong prec);
void _arb_poly_evaluate2(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec);
void arb_poly_evaluate2(arb_t y, arb_t z, const arb_poly_t f, const arb_t x, slong prec);
void _arb_poly_evaluate_vec_iter(arb_ptr ys, arb_srcptr poly, slong plen,
arb_srcptr xs, slong n, slong prec);
void arb_poly_evaluate_vec_iter(arb_ptr ys,
const arb_poly_t poly, arb_srcptr xs, slong n, slong prec);
void _arb_poly_evaluate_vec_fast_precomp(arb_ptr vs, arb_srcptr poly,
slong plen, arb_ptr * tree, slong len, slong prec);
void _arb_poly_evaluate_vec_fast(arb_ptr ys, arb_srcptr poly, slong plen,
arb_srcptr xs, slong n, slong prec);
void arb_poly_evaluate_vec_fast(arb_ptr ys,
const arb_poly_t poly, arb_srcptr xs, slong n, slong prec);
void _arb_poly_interpolate_newton(arb_ptr poly, arb_srcptr xs,
arb_srcptr ys, slong n, slong prec);
void arb_poly_interpolate_newton(arb_poly_t poly,
arb_srcptr xs, arb_srcptr ys, slong n, slong prec);
void
_arb_poly_interpolate_barycentric(arb_ptr poly,
arb_srcptr xs, arb_srcptr ys, slong n, slong prec);
void arb_poly_interpolate_barycentric(arb_poly_t poly,
arb_srcptr xs, arb_srcptr ys, slong n, slong prec);
void _arb_poly_interpolation_weights(arb_ptr w,
arb_ptr * tree, slong len, slong prec);
void _arb_poly_interpolate_fast_precomp(arb_ptr poly,
arb_srcptr ys, arb_ptr * tree, arb_srcptr weights,
slong len, slong prec);
void _arb_poly_interpolate_fast(arb_ptr poly,
arb_srcptr xs, arb_srcptr ys, slong len, slong prec);
void arb_poly_interpolate_fast(arb_poly_t poly,
arb_srcptr xs, arb_srcptr ys, slong n, slong prec);
/* Derivative and integral */
void _arb_poly_derivative(arb_ptr res, arb_srcptr poly, slong len, slong prec);
void arb_poly_derivative(arb_poly_t res, const arb_poly_t poly, slong prec);
void _arb_poly_integral(arb_ptr res, arb_srcptr poly, slong len, slong prec);
void arb_poly_integral(arb_poly_t res, const arb_poly_t poly, slong prec);
/* Transforms */
void arb_poly_borel_transform(arb_poly_t res, const arb_poly_t poly, slong prec);
void _arb_poly_borel_transform(arb_ptr res, arb_srcptr poly, slong len, slong prec);
void arb_poly_inv_borel_transform(arb_poly_t res, const arb_poly_t poly, slong prec);
void _arb_poly_inv_borel_transform(arb_ptr res, arb_srcptr poly, slong len, slong prec);
void _arb_poly_binomial_transform_basecase(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec);
void arb_poly_binomial_transform_basecase(arb_poly_t b, const arb_poly_t a, slong len, slong prec);
void _arb_poly_binomial_transform_convolution(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec);
void arb_poly_binomial_transform_convolution(arb_poly_t b, const arb_poly_t a, slong len, slong prec);
void _arb_poly_binomial_transform(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec);
void arb_poly_binomial_transform(arb_poly_t b, const arb_poly_t a, slong len, slong prec);
/* Special functions */
void _arb_poly_pow_ui_trunc_binexp(arb_ptr res,
arb_srcptr f, slong flen, ulong exp, slong len, slong prec);
void arb_poly_pow_ui_trunc_binexp(arb_poly_t res,
const arb_poly_t poly, ulong exp, slong len, slong prec);
void _arb_poly_pow_ui(arb_ptr res, arb_srcptr f, slong flen, ulong exp, slong prec);
void arb_poly_pow_ui(arb_poly_t res, const arb_poly_t poly, ulong exp, slong prec);
void _arb_poly_pow_series(arb_ptr h,
arb_srcptr f, slong flen,
arb_srcptr g, slong glen, slong len, slong prec);
void arb_poly_pow_series(arb_poly_t h,
const arb_poly_t f, const arb_poly_t g, slong len, slong prec);
void _arb_poly_pow_arb_series(arb_ptr h,
arb_srcptr f, slong flen, const arb_t g, slong len, slong prec);
void arb_poly_pow_arb_series(arb_poly_t h,
const arb_poly_t f, const arb_t g, slong len, slong prec);
void _arb_poly_binomial_pow_arb_series(arb_ptr h, arb_srcptr f, slong flen, const arb_t g, slong len, slong prec);
void _arb_poly_rsqrt_series(arb_ptr g,
arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_rsqrt_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
void _arb_poly_sqrt_series(arb_ptr g,
arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_sqrt_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
void _arb_poly_log_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec);
void arb_poly_log_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec);
void _arb_poly_atan_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec);
void arb_poly_atan_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec);
void _arb_poly_asin_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec);
void arb_poly_asin_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec);
void _arb_poly_acos_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec);
void arb_poly_acos_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec);
void _arb_poly_exp_series_basecase(arb_ptr f,
arb_srcptr h, slong hlen, slong n, slong prec);
void arb_poly_exp_series_basecase(arb_poly_t f, const arb_poly_t h, slong n, slong prec);
void _arb_poly_exp_series(arb_ptr f, arb_srcptr h, slong hlen, slong n, slong prec);
void arb_poly_exp_series(arb_poly_t f, const arb_poly_t h, slong n, slong prec);
void _arb_poly_sin_cos_series_basecase(arb_ptr s,
arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec, int times_pi);
void arb_poly_sin_cos_series_basecase(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, slong n, slong prec, int times_pi);
void _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c,
const arb_srcptr h, slong hlen, slong len, slong prec, int times_pi);
void arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, slong n, slong prec, int times_pi);
void _arb_poly_sin_cos_series(arb_ptr s, arb_ptr c,
const arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_sin_cos_series(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, slong n, slong prec);
void _arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c,
const arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_sin_cos_pi_series(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, slong n, slong prec);
void _arb_poly_sin_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec);
void arb_poly_sin_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
void _arb_poly_cos_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec);
void arb_poly_cos_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
void _arb_poly_sin_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec);
void arb_poly_sin_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
void _arb_poly_cos_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec);
void arb_poly_cos_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
void _arb_poly_cot_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec);
void arb_poly_cot_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
void _arb_poly_tan_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_tan_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec);
void _arb_poly_compose_series_brent_kung(arb_ptr res, arb_srcptr poly1, slong len1,
arb_srcptr poly2, slong len2, slong n, slong prec);
void arb_poly_compose_series_brent_kung(arb_poly_t res,
const arb_poly_t poly1,
const arb_poly_t poly2, slong n, slong prec);
void _arb_poly_evaluate_acb_horner(acb_t res, arb_srcptr f, slong len, const acb_t x, slong prec);
void arb_poly_evaluate_acb_horner(acb_t res, const arb_poly_t f, const acb_t a, slong prec);
void _arb_poly_evaluate_acb_rectangular(acb_t y, arb_srcptr poly, slong len, const acb_t x, slong prec);
void arb_poly_evaluate_acb_rectangular(acb_t res, const arb_poly_t f, const acb_t a, slong prec);
void _arb_poly_evaluate_acb(acb_t res, arb_srcptr f, slong len, const acb_t x, slong prec);
void arb_poly_evaluate_acb(acb_t res, const arb_poly_t f, const acb_t a, slong prec);
void _arb_poly_evaluate2_acb_horner(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec);
void arb_poly_evaluate2_acb_horner(acb_t y, acb_t z, const arb_poly_t f, const acb_t x, slong prec);
void _arb_poly_evaluate2_acb_rectangular(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec);
void arb_poly_evaluate2_acb_rectangular(acb_t y, acb_t z, const arb_poly_t f, const acb_t x, slong prec);
void _arb_poly_evaluate2_acb(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec);
void arb_poly_evaluate2_acb(acb_t y, acb_t z, const arb_poly_t f, const acb_t x, slong prec);
void _arb_poly_gamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_gamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec);
void _arb_poly_rgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_rgamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec);
void _arb_poly_lgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_lgamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec);
void _arb_poly_digamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_digamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec);
void _arb_poly_rising_ui_series(arb_ptr res, arb_srcptr f, slong flen, ulong r, slong trunc, slong prec);
void arb_poly_rising_ui_series(arb_poly_t res, const arb_poly_t f, ulong r, slong trunc, slong prec);
void _arb_poly_zeta_series(arb_ptr res, arb_srcptr h, slong hlen, const arb_t a, int deflate, slong len, slong prec);
void arb_poly_zeta_series(arb_poly_t res, const arb_poly_t f, const arb_t a, int deflate, slong n, slong prec);
void _arb_poly_riemann_siegel_theta_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_riemann_siegel_theta_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec);
void _arb_poly_riemann_siegel_z_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec);
void arb_poly_riemann_siegel_z_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec);
slong _arb_poly_swinnerton_dyer_ui_prec(ulong n);
void _arb_poly_swinnerton_dyer_ui(arb_ptr T, ulong n, slong trunc, slong prec);
void arb_poly_swinnerton_dyer_ui(arb_poly_t poly, ulong n, slong prec);
/* Root-finding */
void _arb_poly_newton_convergence_factor(arf_t convergence_factor,
arb_srcptr poly, slong len,
const arb_t convergence_interval, slong prec);
int _arb_poly_newton_step(arb_t xnew, arb_srcptr poly, slong len,
const arb_t x,
const arb_t convergence_interval,
const arf_t convergence_factor, slong prec);
void _arb_poly_newton_refine_root(arb_t r, arb_srcptr poly,
slong len, const arb_t start,
const arb_t convergence_interval,
const arf_t convergence_factor,
slong eval_extra_prec,
slong prec);
void _arb_poly_root_bound_fujiwara(mag_t bound, arb_srcptr poly, slong len);
void arb_poly_root_bound_fujiwara(mag_t bound, arb_poly_t poly);
/* Macros */
/* counts zero bits in the binary representation of e */
ARB_POLY_INLINE int
n_zerobits(mp_limb_t e)
{
int zeros = 0;
while (e > 1)
{
zeros += !(e & 1);
e >>= 1;
}
return zeros;
}
ARB_POLY_INLINE slong
poly_pow_length(slong poly_len, ulong exp, slong trunc)
{
mp_limb_t hi, lo;
umul_ppmm(hi, lo, poly_len - 1, exp);
add_ssaaaa(hi, lo, hi, lo, 0, 1);
if (hi != 0 || lo > (mp_limb_t) WORD_MAX)
return trunc;
return FLINT_MIN((slong) lo, trunc);
}
#ifndef NEWTON_INIT
#define NEWTON_INIT(from, to) \
{ \
slong __steps[FLINT_BITS], __i, __from, __to; \
__steps[__i = 0] = __to = (to); \
__from = (from); \
while (__to > __from) \
__steps[++__i] = (__to = (__to + 1) / 2); \
#define NEWTON_BASECASE(bc_to) { slong bc_to = __to;
#define NEWTON_END_BASECASE }
#define NEWTON_LOOP(step_from, step_to) \
{ \
for (__i--; __i >= 0; __i--) \
{ \
slong step_from = __steps[__i+1]; \
slong step_to = __steps[__i]; \
#define NEWTON_END_LOOP }}
#define NEWTON_END }
#endif
#ifdef __cplusplus
}
#endif
#endif
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