blob: 95074e9646c23629f7dacd4b2efe5431ad7f0b45 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
|
/**
* This file has no copyright assigned and is placed in the Public Domain.
* This file is part of the mingw-w64 runtime package.
* No warranty is given; refer to the file DISCLAIMER.PD within this package.
*/
#include <math.h>
static const long double CBRT2 = 1.2599210498948731647672L;
static const long double CBRT4 = 1.5874010519681994747517L;
static const long double CBRT2I = 0.79370052598409973737585L;
static const long double CBRT4I = 0.62996052494743658238361L;
long double cbrtl(long double x)
{
int e, rem, sign;
long double z;
if (!isfinite (x) || x == 0.0L)
return (x);
if (x > 0)
sign = 1;
else
{
sign = -1;
x = -x;
}
z = x;
/* extract power of 2, leaving
* mantissa between 0.5 and 1
*/
x = frexpl(x, &e);
/* Approximate cube root of number between .5 and 1,
* peak relative error = 1.2e-6
*/
x = (((( 1.3584464340920900529734e-1L * x
- 6.3986917220457538402318e-1L) * x
+ 1.2875551670318751538055e0L) * x
- 1.4897083391357284957891e0L) * x
+ 1.3304961236013647092521e0L) * x
+ 3.7568280825958912391243e-1L;
/* exponent divided by 3 */
if (e >= 0)
{
rem = e;
e /= 3;
rem -= 3*e;
if (rem == 1)
x *= CBRT2;
else if (rem == 2)
x *= CBRT4;
}
else
{ /* argument less than 1 */
e = -e;
rem = e;
e /= 3;
rem -= 3*e;
if (rem == 1)
x *= CBRT2I;
else if (rem == 2)
x *= CBRT4I;
e = -e;
}
/* multiply by power of 2 */
x = ldexpl(x, e);
/* Newton iteration */
x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
if (sign < 0)
x = -x;
return (x);
}
|
