1/**
2 * This file has no copyright assigned and is placed in the Public Domain.
3 * This file is part of the mingw-w64 runtime package.
4 * No warranty is given; refer to the file DISCLAIMER.PD within this package.
5 */
6#include "cephes_mconf.h"
7
8static const long double CBRT2 = 1.2599210498948731647672L;
9static const long double CBRT4 = 1.5874010519681994747517L;
10static const long double CBRT2I = 0.79370052598409973737585L;
11static const long double CBRT4I = 0.62996052494743658238361L;
12
13extern long double ldexpl(long double,int);
14
15long double cbrtl(long double x)
16{
17 int e, rem, sign;
18 long double z;
19
20 if (!isfinite (x) || x == 0.0L)
21 return (x);
22
23 if (x > 0)
24 sign = 1;
25 else
26 {
27 sign = -1;
28 x = -x;
29 }
30
31 z = x;
32 /* extract power of 2, leaving
33 * mantissa between 0.5 and 1
34 */
35 x = frexpl(x, &e);
36
37 /* Approximate cube root of number between .5 and 1,
38 * peak relative error = 1.2e-6
39 */
40 x = (((( 1.3584464340920900529734e-1L * x
41 - 6.3986917220457538402318e-1L) * x
42 + 1.2875551670318751538055e0L) * x
43 - 1.4897083391357284957891e0L) * x
44 + 1.3304961236013647092521e0L) * x
45 + 3.7568280825958912391243e-1L;
46
47 /* exponent divided by 3 */
48 if (e >= 0)
49 {
50 rem = e;
51 e /= 3;
52 rem -= 3*e;
53 if (rem == 1)
54 x *= CBRT2;
55 else if (rem == 2)
56 x *= CBRT4;
57 }
58 else
59 { /* argument less than 1 */
60 e = -e;
61 rem = e;
62 e /= 3;
63 rem -= 3*e;
64 if (rem == 1)
65 x *= CBRT2I;
66 else if (rem == 2)
67 x *= CBRT4I;
68 e = -e;
69 }
70
71 /* multiply by power of 2 */
72 x = ldexpl(x, e);
73
74 /* Newton iteration */
75
76 x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
77 x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
78
79 if (sign < 0)
80 x = -x;
81 return (x);
82}