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 * ====================================================
14 #include "math_private.h"
17 * Return cube root of x
20 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
21 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
24 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
25 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
26 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
27 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
28 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
39 sign=hx&0x80000000; /* sign= sign(x) */
41 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
44 return(x); /* cbrt(0) is itself */
46 SET_HIGH_WORD(x,hx); /* x <- |x| */
47 /* rough cbrt to 5 bits */
48 if(hx<0x00100000) /* subnormal number */
49 {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
50 t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
53 SET_HIGH_WORD(t,hx/3+B1);
56 /* new cbrt to 23 bits, may be implemented in single precision */
61 /* chopped to 20 bits and make it larger than cbrt(x) */
62 GET_HIGH_WORD(high,t);
63 INSERT_WORDS(t,high+0x00000001,0);
66 /* one step newton iteration to 53 bits with error less than 0.667 ulps */
67 s=t*t; /* t*t is exact */
70 r=(r-t)/(w+r); /* r-s is exact */
73 /* retore the sign bit */
74 GET_HIGH_WORD(high,t);
75 SET_HIGH_WORD(t,high|sign);