1 /* @(#)s_cbrt.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 #include <sys/cdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: s_cbrt.c,v 1.13 2013/11/20 12:29:13 joerg Exp $");
16 #endif
17
18 #include "namespace.h"
19 #include "math.h"
20 #include "math_private.h"
21
22 #ifndef __HAVE_LONG_DOUBLE
23 __strong_alias(_cbrtl, cbrt)
24 __weak_alias(cbrtl, _cbrtl)
25 #endif
26
27 /* cbrt(x)
28 * Return cube root of x
29 */
30 static const u_int32_t
31 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
32 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
33
34 static const double
35 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
36 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
37 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
38 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
39 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
40
41 double
cbrt(double x)42 cbrt(double x)
43 {
44 int32_t hx;
45 double r,s,t=0.0,w;
46 u_int32_t sign;
47 u_int32_t high,low;
48
49 GET_HIGH_WORD(hx,x);
50 sign=hx&0x80000000; /* sign= sign(x) */
51 hx ^=sign;
52 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
53 GET_LOW_WORD(low,x);
54 if((hx|low)==0)
55 return(x); /* cbrt(0) is itself */
56
57 SET_HIGH_WORD(x,hx); /* x <- |x| */
58 /* rough cbrt to 5 bits */
59 if(hx<0x00100000) /* subnormal number */
60 {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
61 t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
62 }
63 else
64 SET_HIGH_WORD(t,hx/3+B1);
65
66
67 /* new cbrt to 23 bits, may be implemented in single precision */
68 r=t*t/x;
69 s=C+r*t;
70 t*=G+F/(s+E+D/s);
71
72 /* chopped to 20 bits and make it larger than cbrt(x) */
73 GET_HIGH_WORD(high,t);
74 INSERT_WORDS(t,high+0x00000001,0);
75
76
77 /* one step newton iteration to 53 bits with error less than 0.667 ulps */
78 s=t*t; /* t*t is exact */
79 r=x/s;
80 w=t+t;
81 r=(r-t)/(w+r); /* r-s is exact */
82 t=t+t*r;
83
84 /* retore the sign bit */
85 GET_HIGH_WORD(high,t);
86 SET_HIGH_WORD(t,high|sign);
87 return(t);
88 }
89