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/*
Copyright (C) 2014 Fredrik Johansson
This file is part of FLINT.
FLINT 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 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "acb.h"
void
acb_chebyshev_u2_ui(acb_t a, acb_t b, ulong n, const acb_t x, slong prec)
{
int i;
acb_t t, u;
if (n == 0)
{
acb_one(a);
acb_zero(b);
return;
}
acb_set_round(a, x, prec);
acb_mul_2exp_si(a, a, 1);
acb_one(b);
if (n == 1)
return;
acb_init(t);
acb_init(u);
for (i = FLINT_BIT_COUNT(n) - 2; i >= 0; i--)
{
acb_add(t, a, b, prec);
acb_sub(u, a, b, prec);
if ((n >> i) & 1)
{
acb_submul(b, x, a, prec);
acb_mul(a, a, b, prec);
acb_neg(a, a);
acb_mul_2exp_si(a, a, 1);
acb_mul(b, t, u, prec);
}
else
{
acb_submul(a, x, b, prec);
acb_mul(b, a, b, prec);
acb_mul_2exp_si(b, b, 1);
acb_mul(a, t, u, prec);
}
}
acb_clear(t);
acb_clear(u);
}