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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_modular.h"
static int
fmpz_kronecker1(const fmpz_t a, const fmpz_t b)
{
if (fmpz_sgn(b) < 0)
{
int r;
fmpz_t t;
fmpz_init(t);
fmpz_neg(t, b);
r = fmpz_kronecker1(a, t);
fmpz_clear(t);
return r;
}
else if (fmpz_is_one(b))
{
return 1;
}
else
{
return fmpz_jacobi(a, b);
}
}
int
acb_modular_epsilon_arg(const psl2z_t g)
{
#define a (&g->a)
#define b (&g->b)
#define c (&g->c)
#define d (&g->d)
if (fmpz_is_zero(c))
{
return fmpz_fdiv_ui(b, 24);
}
else
{
int aa, bb, cc, dd;
int u;
aa = fmpz_fdiv_ui(a, 24);
bb = fmpz_fdiv_ui(b, 24);
cc = fmpz_fdiv_ui(c, 24);
dd = fmpz_fdiv_ui(d, 24);
if (cc % 2 == 1)
{
u = fmpz_kronecker1(a, c);
aa = aa*bb + 2*aa*cc - 3*cc + cc*dd*(1-aa*aa);
}
else
{
u = fmpz_kronecker1(c, a);
aa = aa*bb - aa*cc + 3*aa - 3 + cc*dd*(1-aa*aa);
}
if (u == -1)
{
aa += 12;
}
else if (u != 1)
{
flint_throw(FLINT_ERROR, "bad kronecker input\n");
}
/* mod 24 */
if (aa < 0)
{
aa = 24 - ((-aa) % 24);
if (aa == 24)
aa = 0;
}
else
aa = aa % 24;
return aa;
}
#undef a
#undef b
#undef c
#undef d
}