1 /* Compute cubic root of double value.
2    Copyright (C) 1997-2022 Free Software Foundation, Inc.
3    This file is part of the GNU C Library.
4 
5    The GNU C Library is free software; you can redistribute it and/or
6    modify it under the terms of the GNU Lesser General Public
7    License as published by the Free Software Foundation; either
8    version 2.1 of the License, or (at your option) any later version.
9 
10    The GNU C Library is distributed in the hope that it will be useful,
11    but WITHOUT ANY WARRANTY; without even the implied warranty of
12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
13    Lesser General Public License for more details.
14 
15    You should have received a copy of the GNU Lesser General Public
16    License along with the GNU C Library; if not, see
17    <https://www.gnu.org/licenses/>.  */
18 
19 #include <math.h>
20 #include <libm-alias-ldouble.h>
21 
22 
23 #define CBRT2 1.2599210498948731648		/* 2^(1/3) */
24 #define SQR_CBRT2 1.5874010519681994748		/* 2^(2/3) */
25 
26 /* We don't use long double values here since U need not be computed
27    with full precision.  */
28 static const double factor[5] =
29 {
30   1.0 / SQR_CBRT2,
31   1.0 / CBRT2,
32   1.0,
33   CBRT2,
34   SQR_CBRT2
35 };
36 
37 static const long double third = 0.3333333333333333333333333L;
38 
39 long double
__cbrtl(long double x)40 __cbrtl (long double x)
41 {
42   long double xm, u;
43   int xe;
44 
45   /* Reduce X.  XM now is an range 1.0 to 0.5.  */
46   xm = __frexpl (fabsl (x), &xe);
47 
48   /* If X is not finite or is null return it (with raising exceptions
49      if necessary.
50      Note: *Our* version of `frexp' sets XE to zero if the argument is
51      Inf or NaN.  This is not portable but faster.  */
52   if (xe == 0 && fpclassify (x) <= FP_ZERO)
53     return x + x;
54 
55   u = (((-1.34661104733595206551E-1 * xm
56 	  + 5.46646013663955245034E-1) * xm
57 	 - 9.54382247715094465250E-1) * xm
58 	+ 1.13999833547172932737E0) * xm
59        + 4.02389795645447521269E-1;
60 
61   u *= factor[2 + xe % 3];
62   u = __ldexpl (x > 0.0 ? u : -u, xe / 3);
63 
64   u -= (u - (x / (u * u))) * third;
65   u -= (u - (x / (u * u))) * third;
66   return u;
67 }
68 libm_alias_ldouble (__cbrt, cbrt)
69