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 * ====================================================
17 #include <sys/cdefs.h>
19 #include "math_private.h"
22 * Return cube root of x
25 B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
26 B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
38 sign=hx&0x80000000; /* sign= sign(x) */
40 if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
42 /* rough cbrt to 5 bits */
43 if(hx<0x00800000) { /* zero or subnormal? */
45 return(x); /* cbrt(+-0) is itself */
46 SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
48 GET_FLOAT_WORD(high,t);
49 SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
51 SET_FLOAT_WORD(t,sign|(hx/3+B1));
54 * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In
55 * double precision so that its terms can be arranged for efficiency
56 * without causing overflow or underflow.
60 T=T*((double)x+x+r)/(x+r+r);
63 * Second step Newton iteration to 47 bits. In double precision for
64 * efficiency and accuracy.
67 T=T*((double)x+x+r)/(x+r+r);
69 /* rounding to 24 bits is perfect in round-to-nearest mode */