1 /*
2 Copyright (C) 2015 Fredrik Johansson
3
4 This file is part of Arb.
5
6 Arb is free software: you can redistribute it and/or modify it under
7 the terms of the GNU Lesser General Public License (LGPL) as published
8 by the Free Software Foundation; either version 2.1 of the License, or
9 (at your option) any later version. See <http://www.gnu.org/licenses/>.
10 */
11
12 #include "acb.h"
13
14 void
acb_quadratic_roots_fmpz(acb_t r1,acb_t r2,const fmpz_t a,const fmpz_t b,const fmpz_t c,slong prec)15 acb_quadratic_roots_fmpz(acb_t r1, acb_t r2,
16 const fmpz_t a, const fmpz_t b, const fmpz_t c, slong prec)
17 {
18 fmpz_t d;
19 fmpz_init(d);
20
21 /* d = b^2 - 4ac */
22 fmpz_mul(d, a, c);
23 fmpz_mul_2exp(d, d, 2);
24 fmpz_submul(d, b, b);
25 fmpz_neg(d, d);
26
27 /* +/- sqrt(d) */
28 acb_zero(r1);
29 if (fmpz_sgn(d) >= 0)
30 {
31 arb_sqrt_fmpz(acb_realref(r1), d, prec + fmpz_bits(d) + 4);
32 }
33 else
34 {
35 fmpz_neg(d, d);
36 arb_sqrt_fmpz(acb_imagref(r1), d, prec + fmpz_bits(d) + 4);
37 }
38 acb_neg(r2, r1);
39
40 /* -b */
41 acb_sub_fmpz(r1, r1, b, prec + 4);
42 acb_sub_fmpz(r2, r2, b, prec + 4);
43
44 /* divide by 2a */
45 fmpz_mul_2exp(d, a, 1);
46 acb_div_fmpz(r1, r1, d, prec);
47 acb_div_fmpz(r2, r2, d, prec);
48
49 fmpz_clear(d);
50 return;
51 }
52
53