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[uclinux-h8/uClinux-dist.git] / uClibc / libm / s_cbrt.c
1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
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
8  * is preserved.
9  * ====================================================
10  */
11
12 #include "math.h"
13 #include "math_private.h"
14
15 /* cbrt(x)
16  * Return cube root of x
17  */
18 static const u_int32_t
19         B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
20         B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
21
22 static const double
23 C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
24 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
25 E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
26 F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
27 G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
28
29 double cbrt(double x)
30 {
31         int32_t hx;
32         double r,s,t=0.0,w;
33         u_int32_t sign;
34         u_int32_t high,low;
35
36         GET_HIGH_WORD(hx,x);
37         sign=hx&0x80000000;             /* sign= sign(x) */
38         hx  ^=sign;
39         if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
40         GET_LOW_WORD(low,x);
41         if((hx|low)==0)
42             return(x);          /* cbrt(0) is itself */
43
44         SET_HIGH_WORD(x,hx);    /* x <- |x| */
45     /* rough cbrt to 5 bits */
46         if(hx<0x00100000)               /* subnormal number */
47           {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
48            t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
49           }
50         else
51           SET_HIGH_WORD(t,hx/3+B1);
52
53
54     /* new cbrt to 23 bits, may be implemented in single precision */
55         r=t*t/x;
56         s=C+r*t;
57         t*=G+F/(s+E+D/s);
58
59     /* chopped to 20 bits and make it larger than cbrt(x) */
60         GET_HIGH_WORD(high,t);
61         INSERT_WORDS(t,high+0x00000001,0);
62
63
64     /* one step newton iteration to 53 bits with error less than 0.667 ulps */
65         s=t*t;          /* t*t is exact */
66         r=x/s;
67         w=t+t;
68         r=(r-t)/(w+r);  /* r-s is exact */
69         t=t+t*r;
70
71     /* retore the sign bit */
72         GET_HIGH_WORD(high,t);
73         SET_HIGH_WORD(t,high|sign);
74         return(t);
75 }
76 libm_hidden_def(cbrt)