1 /* s_cbrtf.c -- float version of s_cbrt.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 * Debugged and optimized by Bruce D. Evans.
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
14 * ====================================================
18 static char rcsid[] = "$FreeBSD$";
22 #include "math_private.h"
25 * Return cube root of x
28 B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
29 B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
41 sign=hx&0x80000000; /* sign= sign(x) */
43 if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
45 return(x); /* cbrt(0) is itself */
47 /* rough cbrt to 5 bits */
48 if(hx<0x00800000) { /* subnormal number */
49 SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
51 GET_FLOAT_WORD(high,t);
52 SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
54 SET_FLOAT_WORD(t,sign|(hx/3+B1));
56 /* first step Newton iteration (solving t*t-x/t == 0) to 16 bits */
57 /* in double precision to avoid problems with denormals */
62 /* second step Newton iteration to 47 bits */
63 /* in double precision for accuracy */
67 /* rounding to 24 bits is perfect in round-to-nearest mode */