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/*
Copyright (C) 2013 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"
/* (a + bx^c)^g where a = f[0] and b = f[flen-1] */
void
_arb_poly_binomial_pow_arb_series(arb_ptr h, arb_srcptr f, slong flen, const arb_t g, slong len, slong prec)
{
slong i, j, d;
arb_t t;
arb_init(t);
d = flen - 1;
arb_pow(h, f, g, prec);
arb_div(t, f + d, f, prec);
for (i = 1, j = d; j < len; i++, j += d)
{
arb_sub_ui(h + j, g, i - 1, prec);
arb_mul(h + j, h + j, h + j - d, prec);
arb_mul(h + j, h + j, t, prec);
arb_div_ui(h + j, h + j, i, prec);
}
if (d > 1)
{
for (i = 1; i < len; i++)
if (i % d != 0)
arb_zero(h + i);
}
arb_clear(t);
return;
}
void
_arb_poly_pow_arb_series(arb_ptr h,
arb_srcptr f, slong flen, const arb_t g, slong len, slong prec)
{
int f_binomial, g_exact, g_int;
while (flen > 0 && arb_is_zero(f + flen - 1))
flen--;
if (flen <= 1)
{
arb_pow(h, f, g, prec);
_arb_vec_zero(h + 1, len - 1);
return;
}
g_exact = arb_is_exact(g);
g_int = arb_is_int(g);
f_binomial = _arb_vec_is_zero(f + 1, flen - 2);
/* g = small integer */
if (g_exact && g_int &&
arf_cmpabs_2exp_si(arb_midref(g), FLINT_BITS - 1) < 0)
{
slong e, hlen;
e = arf_get_si(arb_midref(g), ARF_RND_DOWN);
hlen = poly_pow_length(flen, FLINT_ABS(e), len);
if (e >= 0)
{
_arb_poly_pow_ui_trunc_binexp(h, f, flen, e, hlen, prec);
_arb_vec_zero(h + hlen, len - hlen);
return;
}
else if (!f_binomial)
{
arb_ptr t;
t = _arb_vec_init(hlen);
_arb_poly_pow_ui_trunc_binexp(t, f, flen, -e, hlen, prec);
_arb_poly_inv_series(h, t, hlen, len, prec);
_arb_vec_clear(t, hlen);
return;
}
}
/* (a + bx^c)^g */
if (f_binomial)
{
_arb_poly_binomial_pow_arb_series(h, f, flen, g, len, prec);
return;
}
/* g = +/- 1/2 */
if (g_exact && arf_cmpabs_2exp_si(arb_midref(g), -1) == 0)
{
if (arf_sgn(arb_midref(g)) > 0)
_arb_poly_sqrt_series(h, f, flen, len, prec);
else
_arb_poly_rsqrt_series(h, f, flen, len, prec);
return;
}
/* f^g = exp(g*log(f)) */
_arb_poly_log_series(h, f, flen, len, prec);
_arb_vec_scalar_mul(h, h, len, g, prec);
_arb_poly_exp_series(h, h, len, len, prec);
}
void
arb_poly_pow_arb_series(arb_poly_t h,
const arb_poly_t f, const arb_t g, slong len, slong prec)
{
slong flen;
flen = f->length;
flen = FLINT_MIN(flen, len);
if (len == 0)
{
arb_poly_zero(h);
return;
}
if (arb_is_zero(g))
{
arb_poly_one(h);
return;
}
if (flen == 0)
{
arb_poly_zero(h);
return;
}
if (f == h)
{
arb_poly_t t;
arb_poly_init2(t, len);
_arb_poly_pow_arb_series(t->coeffs, f->coeffs, flen, g, len, prec);
_arb_poly_set_length(t, len);
_arb_poly_normalise(t);
arb_poly_swap(t, h);
arb_poly_clear(t);
}
else
{
arb_poly_fit_length(h, len);
_arb_poly_pow_arb_series(h->coeffs, f->coeffs, flen, g, len, prec);
_arb_poly_set_length(h, len);
_arb_poly_normalise(h);
}
}
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