xref: /freebsd/lib/msun/src/s_cbrt.c (revision 17ee9d00bc1ae1e598c38f25826f861e4bc6c3ce)
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 #ifndef lint
14 static char rcsid[] = "$Id: s_cbrt.c,v 1.6 1994/08/18 23:06:25 jtc Exp $";
15 #endif
16 
17 #include "math.h"
18 #include "math_private.h"
19 
20 /* cbrt(x)
21  * Return cube root of x
22  */
23 #ifdef __STDC__
24 static const u_int32_t
25 #else
26 static u_int32_t
27 #endif
28 	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
29 	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
30 
31 #ifdef __STDC__
32 static const double
33 #else
34 static double
35 #endif
36 C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
37 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
38 E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
39 F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
40 G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
41 
42 #ifdef __STDC__
43 	double cbrt(double x)
44 #else
45 	double cbrt(x)
46 	double x;
47 #endif
48 {
49 	int32_t	hx;
50 	double r,s,t=0.0,w;
51 	u_int32_t sign;
52 	u_int32_t high,low;
53 
54 	GET_HIGH_WORD(hx,x);
55 	sign=hx&0x80000000; 		/* sign= sign(x) */
56 	hx  ^=sign;
57 	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
58 	GET_LOW_WORD(low,x);
59 	if((hx|low)==0)
60 	    return(x);		/* cbrt(0) is itself */
61 
62 	SET_HIGH_WORD(x,hx);	/* x <- |x| */
63     /* rough cbrt to 5 bits */
64 	if(hx<0x00100000) 		/* subnormal number */
65 	  {SET_HIGH_WORD(t,0x43500000);	/* set t= 2**54 */
66 	   t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
67 	  }
68 	else
69 	  SET_HIGH_WORD(t,hx/3+B1);
70 
71 
72     /* new cbrt to 23 bits, may be implemented in single precision */
73 	r=t*t/x;
74 	s=C+r*t;
75 	t*=G+F/(s+E+D/s);
76 
77     /* chopped to 20 bits and make it larger than cbrt(x) */
78 	GET_HIGH_WORD(high,t);
79 	INSERT_WORDS(t,high+0x00000001,0);
80 
81 
82     /* one step newton iteration to 53 bits with error less than 0.667 ulps */
83 	s=t*t;		/* t*t is exact */
84 	r=x/s;
85 	w=t+t;
86 	r=(r-t)/(w+r);	/* r-s is exact */
87 	t=t+t*r;
88 
89     /* retore the sign bit */
90 	GET_HIGH_WORD(high,t);
91 	SET_HIGH_WORD(t,high|sign);
92 	return(t);
93 }
94