2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
9 * ====================================================
13 static const unsigned long
14 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
15 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
18 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
19 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
20 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
21 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
22 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
31 typedef unsigned unsigned32 __attribute__((mode(SI)));
44 hx = ux.pt[n0]; /* high word of x */
45 sign=hx&0x80000000; /* sign= sign(x) */
47 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
48 if((hx| ux.pt[1-n0])==0)
49 return(ux.t); /* cbrt(0) is itself */
52 /* rough cbrt to 5 bits */
53 if(hx<0x00100000) /* subnormal number */
54 {ut.pt[n0]=0x43500000; /* set t= 2**54 */
55 ut.t*=x; ut.pt[n0]=ut.pt[n0]/3+B2;
60 /* new cbrt to 23 bits, may be implemented in single precision */
65 /* chopped to 20 bits and make it larger than cbrt(x) */
66 ut.pt[1-n0]=0; ut.pt[n0]+=0x00000001;
68 /* one step newton iteration to 53 bits with error less than 0.667 ulps */
69 s=ut.t*ut.t; /* t*t is exact */
72 r=(r-ut.t)/(w+r); /* r-s is exact */
75 /* restore the sign bit */
79 lt -= (lt - (x/(lt*lt))) * 0.333333333333333333333;
85 if ((int) (cbrtl (27.0) + 0.5) != 3)