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.
4 */
5
6 /*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
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
13 * is preserved.
14 * ====================================================
15 */
16
17 #ifndef lint
18 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cbrtf.c,v 1.12 2005/12/13 20:17:23 bde Exp $";
19 #endif
20
21 #include "math.h"
22 #include "math_private.h"
23
24 /* cbrtf(x)
25 * Return cube root of x
26 */
27 static const unsigned
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 */
30
31 static const float
32 C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */
33 D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
34 E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */
35 F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */
36 G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */
37
38 float
cbrtf(float x)39 cbrtf(float x)
40 {
41 float r,s,t,w;
42 int32_t hx;
43 u_int32_t sign;
44 u_int32_t high;
45
46 GET_FLOAT_WORD(hx,x);
47 sign=hx&0x80000000; /* sign= sign(x) */
48 hx ^=sign;
49 if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
50 if(hx==0)
51 return(x); /* cbrt(0) is itself */
52
53 /* rough cbrt to 5 bits */
54 if(hx<0x00800000) { /* subnormal number */
55 SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
56 t*=x;
57 GET_FLOAT_WORD(high,t);
58 SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
59 } else
60 SET_FLOAT_WORD(t,sign|(hx/3+B1));
61
62 /* new cbrt to 23 bits */
63 r=t*t/x;
64 s=C+r*t;
65 t*=G+F/(s+E+D/s);
66
67 /* chop t to 12 bits and make it larger in magnitude than cbrt(x) */
68 GET_FLOAT_WORD(high,t);
69 SET_FLOAT_WORD(t,(high&0xfffff000)+0x00001000);
70
71 /* one step Newton iteration to 24 bits with error less than 0.667 ulps */
72 s=t*t; /* t*t is exact */
73 r=x/s;
74 w=t+t;
75 r=(r-t)/(w+r); /* r-t is exact */
76 t=t+t*r;
77
78 return(t);
79 }
80