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
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
|
/* @(#)s_cbrt.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
* Prototype changed for linux libc by flebbe@tat.physik.uni-tuebingen.de
* 15.3.94
* Pointer aliasing bug fixed by Stephen Moshier (moshier@world.std.com)
* 29.9.94
* Additional change by Olaf Flebbe.
*/
#include <ansidecl.h>
#include <math.h>
/* cbrt(x)
* Return cube root of x
*/
#ifdef __STDC__
static const unsigned
#else
static unsigned
#endif
B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
#ifdef __STDC__
static const double
#else
static double
#endif
C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
/* Define n0 1 for little endian */
/* Define n0 0 for big endian machines */
#define n0 1
double DEFUN( cbrt, (x), double x)
{
int hx;
double r,s,w;
unsigned sign;
union {
double t;
unsigned pt[2];
} ut, ux;
ut.t = 0.0;
ux.t = x;
hx = ux.pt[n0]; /* high word of x */
sign=hx&0x80000000; /* sign= sign(x) */
hx ^=sign;
if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
if((hx| ux.pt[1-n0])==0)
return(ux.t); /* cbrt(0) is itself */
ux.pt[n0] = hx;
/* rough cbrt to 5 bits */
if(hx<0x00100000) /* subnormal number */
{ut.pt[n0]=0x43500000; /* set t= 2**54 */
ut.t*=x; ut.pt[n0]=ut.pt[n0]/3+B2;
}
else
ut.pt[n0]=hx/3+B1;
/* new cbrt to 23 bits, may be implemented in single precision */
r=ut.t*ut.t/ux.t;
s=C+r*ut.t;
ut.t*=G+F/(s+E+D/s);
/* chopped to 20 bits and make it larger than cbrt(x) */
ut.pt[1-n0]=0; ut.pt[n0]+=0x00000001;
/* one step newton iteration to 53 bits with error less than 0.667 ulps */
s=ut.t*ut.t; /* t*t is exact */
r=ux.t/s;
w=ut.t+ut.t;
r=(r-ut.t)/(w+r); /* r-s is exact */
ut.t=ut.t+ut.t*r;
/* restore the sign bit */
ut.pt[n0] |= sign;
return(ut.t);
}
|
