1 /* @(#)s_cbrt.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
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 $");
18 #include "namespace.h"
20 #include "math_private.h"
22 #ifndef __HAVE_LONG_DOUBLE
23 __strong_alias(_cbrtl
, cbrt
)
24 __weak_alias(cbrtl
, _cbrtl
)
28 * Return cube root of x
30 static const u_int32_t
31 B1
= 715094163, /* B1 = (682-0.03306235651)*2**20 */
32 B2
= 696219795; /* B2 = (664-0.03306235651)*2**20 */
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 */
50 sign
=hx
&0x80000000; /* sign= sign(x) */
52 if(hx
>=0x7ff00000) return(x
+x
); /* cbrt(NaN,INF) is itself */
55 return(x
); /* cbrt(0) is itself */
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
);
64 SET_HIGH_WORD(t
,hx
/3+B1
);
67 /* new cbrt to 23 bits, may be implemented in single precision */
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);
77 /* one step newton iteration to 53 bits with error less than 0.667 ulps */
78 s
=t
*t
; /* t*t is exact */
81 r
=(r
-t
)/(w
+r
); /* r-s is exact */
84 /* retore the sign bit */
85 GET_HIGH_WORD(high
,t
);
86 SET_HIGH_WORD(t
,high
|sign
);