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/*
Copyright (C) 2020 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 "ulong_extras.h"
#include "qqbar.h"
#include "qqbar/impl.h"
int
qqbar_asin_pi(slong * p, ulong * q, const qqbar_t x)
{
slong deg = qqbar_degree(x);
*p = 0;
*q = 0;
if (deg == 1)
{
if (qqbar_is_zero(x))
{
*p = 0;
*q = 1;
return 1;
}
if (qqbar_is_one(x))
{
*p = 1;
*q = 2;
return 1;
}
if (qqbar_is_neg_one(x))
{
*p = -1;
*q = 2;
return 1;
}
if (QQBAR_COEFFS(x)[1] == 2 && QQBAR_COEFFS(x)[0] == -1)
{
*p = 1;
*q = 6;
return 1;
}
if (QQBAR_COEFFS(x)[1] == 2 && QQBAR_COEFFS(x)[0] == 1)
{
*p = -1;
*q = 6;
return 1;
}
return 0;
}
else if (deg == 2)
{
fmpz a, b, c;
a = QQBAR_COEFFS(x)[0];
b = QQBAR_COEFFS(x)[1];
c = QQBAR_COEFFS(x)[2];
if (a == -3 && b == 0 && c == 4)
{
*p = qqbar_sgn_re(x);
*q = 3;
return 1;
}
if (a == -1 && b == 0 && c == 2)
{
*p = qqbar_sgn_re(x);
*q = 4;
return 1;
}
if (a == -1 && b == 2 && c == 4)
{
*p = (qqbar_sgn_re(x) == 1) ? 1 : -3;
*q = 10;
return 1;
}
if (a == -1 && b == -2 && c == 4)
{
*p = (qqbar_sgn_re(x) == 1) ? 3 : -1;
*q = 10;
return 1;
}
return 0;
}
else if (!qqbar_is_real(x))
{
return 0;
}
else
{
slong degq;
slong prec;
arb_t z, pi;
int res;
prec = 64; /* More than enough -- the fractions will only ever be tiny */
res = 0;
arb_init(z);
arb_init(pi);
qqbar_get_arb(z, x, prec);
if (arf_cmpabs_2exp_si(arb_midref(z), 0) < 0 && arf_cmpabs_2exp_si(arb_midref(z), -20) > 0)
{
arb_asin(z, z, prec);
arb_const_pi(pi, prec);
arb_div(z, z, pi, prec);
best_rational_fast(p, q, arf_get_d(arb_midref(z), ARF_RND_NEAR), 1000000);
arb_mul_ui(z, z, *q, prec);
if (arb_contains_si(z, *p))
{
if ((*q) % 2 == 1 || (*q) % 4 == 0)
degq = n_euler_phi(*q);
else
degq = n_euler_phi(*q) / 2;
if (deg == degq)
{
qqbar_t v;
qqbar_init(v);
qqbar_sin_pi(v, *p, *q);
res = qqbar_equal(v, x);
qqbar_clear(v);
}
}
}
arb_clear(z);
arb_clear(pi);
return res;
}
}