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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"
#define MUL(z, zlen, x, xlen, y, ylen, trunc, prec) \
do { \
slong slen = FLINT_MIN(xlen + ylen - 1, trunc); \
_arb_poly_mullow(z, x, xlen, y, ylen, slen, prec); \
zlen = slen; \
} while (0)
void
_arb_poly_pow_ui_trunc_binexp(arb_ptr res,
arb_srcptr f, slong flen, ulong exp, slong len, slong prec)
{
arb_ptr v, R, S, T;
slong rlen;
ulong bit;
if (exp <= 1)
{
if (exp == 0)
arb_one(res);
else if (exp == 1)
_arb_vec_set_round(res, f, len, prec);
return;
}
/* (f * x^r)^m = x^(rm) * f^m */
while (flen > 1 && arb_is_zero(f))
{
if (((ulong) len) > exp)
{
_arb_vec_zero(res, exp);
len -= exp;
res += exp;
}
else
{
_arb_vec_zero(res, len);
return;
}
f++;
flen--;
}
if (exp == 2)
{
_arb_poly_mullow(res, f, flen, f, flen, len, prec);
return;
}
if (flen == 1)
{
arb_pow_ui(res, f, exp, prec);
return;
}
v = _arb_vec_init(len);
bit = UWORD(1) << (FLINT_BIT_COUNT(exp) - 2);
if (n_zerobits(exp) % 2)
{
R = res;
S = v;
}
else
{
R = v;
S = res;
}
MUL(R, rlen, f, flen, f, flen, len, prec);
if (bit & exp)
{
MUL(S, rlen, R, rlen, f, flen, len, prec);
T = R;
R = S;
S = T;
}
while (bit >>= 1)
{
if (bit & exp)
{
MUL(S, rlen, R, rlen, R, rlen, len, prec);
MUL(R, rlen, S, rlen, f, flen, len, prec);
}
else
{
MUL(S, rlen, R, rlen, R, rlen, len, prec);
T = R;
R = S;
S = T;
}
}
_arb_vec_clear(v, len);
}
void
arb_poly_pow_ui_trunc_binexp(arb_poly_t res,
const arb_poly_t poly, ulong exp, slong len, slong prec)
{
slong flen, rlen;
flen = poly->length;
if (exp == 0 && len != 0)
{
arb_poly_one(res);
}
else if (flen == 0 || len == 0)
{
arb_poly_zero(res);
}
else
{
rlen = poly_pow_length(flen, exp, len);
if (res != poly)
{
arb_poly_fit_length(res, rlen);
_arb_poly_pow_ui_trunc_binexp(res->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_arb_poly_set_length(res, rlen);
_arb_poly_normalise(res);
}
else
{
arb_poly_t t;
arb_poly_init2(t, rlen);
_arb_poly_pow_ui_trunc_binexp(t->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_arb_poly_set_length(t, rlen);
_arb_poly_normalise(t);
arb_poly_swap(res, t);
arb_poly_clear(t);
}
}
}
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