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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#if defined(LIBM_SCCS) && !defined(lint)
14static char rcsid[] = "$NetBSD: s_cbrt.c,v 1.8 1995/05/10 20:46:49 jtc Exp $";
15#endif
16
17#include "math.h"
18#include "math_private.h"
19#include "fp_private.h"
20
21/* cbrt(x)
22 * Return cube root of x
23 */
24#ifdef __STDC__
25static const u_int32_t
26#else
27static u_int32_t
28#endif
29 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
30 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
31
32#ifdef __STDC__
33static const double
34#else
35static double
36#endif
37C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
38D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
39E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
40F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
41G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
42
43#ifdef __STDC__
44 double cbrt(double x)
45#else
46 double cbrt(x)
47 double x;
48#endif
49{
50 int32_t hx;
51 double r,s,t=0.0,w;
52 u_int32_t sign;
53 u_int32_t high,low;
54
55 GET_HIGH_WORD(hx,x);
56 sign=hx&0x80000000; /* sign= sign(x) */
57 hx ^=sign;
58 if(unlikely(hx>=0x7ff00000)) return(x+x); /* cbrt(NaN,INF) is itself */
59 GET_LOW_WORD(low,x);
60 if(unlikely((hx|low)==0))
61 return(x); /* cbrt(0) is itself */
62
63 SET_HIGH_WORD(x,hx); /* x <- |x| */
64 /* rough cbrt to 5 bits */
65 if(unlikely(hx<0x00100000)) /* subnormal number */
66 {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
67 t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
68 }
69 else
70 SET_HIGH_WORD(t,hx/3+B1);
71
72
73 /* new cbrt to 23 bits, may be implemented in single precision */
74 r=t*t/x;
75 s=C+r*t;
76 t*=G+F/(s+E+D/s);
77
78 /* chopped to 20 bits and make it larger than cbrt(x) */
79 GET_HIGH_WORD(high,t);
80 INSERT_WORDS(t,high+0x00000001,0);
81
82
83 /* one step newton iteration to 53 bits with error less than 0.667 ulps */
84 s=t*t; /* t*t is exact */
85 r=x/s;
86 w=t+t;
87 r=(r-t)/(w+r); /* r-s is exact */
88 t=t+t*r;
89
90 /* retore the sign bit */
91 GET_HIGH_WORD(high,t);
92 SET_HIGH_WORD(t,high|sign);
93 return(t);
94}
95