1 /* s_cbrtf.c -- float version of s_cbrt.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5 /*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16 #include "math.h"
17 #include "math_private.h"
18
19 /* cbrtf(x)
20 * Return cube root of x
21 */
22 static const unsigned
23 B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
24 B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */
25
26 static const float
27 C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */
28 D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
29 E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */
30 F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */
31 G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */
32
33 float
cbrtf(float x)34 cbrtf(float x)
35 {
36 float r,s,t;
37 int32_t hx;
38 u_int32_t sign;
39 u_int32_t high;
40
41 GET_FLOAT_WORD(hx,x);
42 sign=hx&0x80000000; /* sign= sign(x) */
43 hx ^=sign;
44 if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
45 if(hx==0)
46 return(x); /* cbrt(0) is itself */
47
48 SET_FLOAT_WORD(x,hx); /* x <- |x| */
49 /* rough cbrt to 5 bits */
50 if(hx<0x00800000) /* subnormal number */
51 {SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
52 t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
53 }
54 else
55 SET_FLOAT_WORD(t,hx/3+B1);
56
57
58 /* new cbrt to 23 bits */
59 r=t*t/x;
60 s=C+r*t;
61 t*=G+F/(s+E+D/s);
62
63 /* retore the sign bit */
64 GET_FLOAT_WORD(high,t);
65 SET_FLOAT_WORD(t,high|sign);
66 return(t);
67 }
68