1 | /* Implementation of cbrtl. IBM Extended Precision version. |
2 | Cephes Math Library Release 2.2: January, 1991 |
3 | Copyright 1984, 1991 by Stephen L. Moshier |
4 | Adapted for glibc October, 2001. |
5 | |
6 | This library is free software; you can redistribute it and/or |
7 | modify it under the terms of the GNU Lesser General Public |
8 | License as published by the Free Software Foundation; either |
9 | version 2.1 of the License, or (at your option) any later version. |
10 | |
11 | This library is distributed in the hope that it will be useful, |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
14 | Lesser General Public License for more details. |
15 | |
16 | You should have received a copy of the GNU Lesser General Public |
17 | License along with this library; if not, see |
18 | <https://www.gnu.org/licenses/>. */ |
19 | |
20 | /* This file was copied from sysdeps/ieee754/ldbl-128/e_j0l.c. */ |
21 | |
22 | |
23 | #include <math_ldbl_opt.h> |
24 | #include <math.h> |
25 | #include <math_private.h> |
26 | |
27 | static const long double CBRT2 = 1.259921049894873164767210607278228350570251L; |
28 | static const long double CBRT4 = 1.587401051968199474751705639272308260391493L; |
29 | static const long double CBRT2I = 0.7937005259840997373758528196361541301957467L; |
30 | static const long double CBRT4I = 0.6299605249474365823836053036391141752851257L; |
31 | |
32 | |
33 | long double |
34 | __cbrtl (long double x) |
35 | { |
36 | int e, rem, sign; |
37 | long double z; |
38 | |
39 | if (!isfinite (x)) |
40 | return x + x; |
41 | |
42 | if (x == 0) |
43 | return (x); |
44 | |
45 | if (x > 0) |
46 | sign = 1; |
47 | else |
48 | { |
49 | sign = -1; |
50 | x = -x; |
51 | } |
52 | |
53 | z = x; |
54 | /* extract power of 2, leaving mantissa between 0.5 and 1 */ |
55 | x = __frexpl (x: x, exponent: &e); |
56 | |
57 | /* Approximate cube root of number between .5 and 1, |
58 | peak relative error = 1.2e-6 */ |
59 | x = ((((1.3584464340920900529734e-1L * x |
60 | - 6.3986917220457538402318e-1L) * x |
61 | + 1.2875551670318751538055e0L) * x |
62 | - 1.4897083391357284957891e0L) * x |
63 | + 1.3304961236013647092521e0L) * x + 3.7568280825958912391243e-1L; |
64 | |
65 | /* exponent divided by 3 */ |
66 | if (e >= 0) |
67 | { |
68 | rem = e; |
69 | e /= 3; |
70 | rem -= 3 * e; |
71 | if (rem == 1) |
72 | x *= CBRT2; |
73 | else if (rem == 2) |
74 | x *= CBRT4; |
75 | } |
76 | else |
77 | { /* argument less than 1 */ |
78 | e = -e; |
79 | rem = e; |
80 | e /= 3; |
81 | rem -= 3 * e; |
82 | if (rem == 1) |
83 | x *= CBRT2I; |
84 | else if (rem == 2) |
85 | x *= CBRT4I; |
86 | e = -e; |
87 | } |
88 | |
89 | /* multiply by power of 2 */ |
90 | x = __ldexpl (x: x, exponent: e); |
91 | |
92 | /* Newton iteration */ |
93 | x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L; |
94 | x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L; |
95 | x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L; |
96 | |
97 | if (sign < 0) |
98 | x = -x; |
99 | return (x); |
100 | } |
101 | |
102 | long_double_symbol (libm, __cbrtl, cbrtl); |
103 | |