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/* @(#)s_cbrt.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 *
 */
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
/* cbrt(x)
 * Return cube root of x
 */
#ifdef __STDC__
static const uint32_t
#else
static uint32_t
#endif
        B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
        B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
 
#ifdef __STDC__
static const double
#else
static double
#endif
C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
 
#ifdef __STDC__
        double cbrt(double x)
#else
        double cbrt(x)
        double x;
#endif
{
        int32_t hx, lx, ht;
        double r,s,t=0.0,w;
        uint32_t sign;
 
 
        GET_HIGH_WORD(hx,x); /* high word of x */
        sign=hx&0x80000000;             /* sign= sign(x) */
        hx  ^=sign;
        if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
        GET_LOW_WORD(lx, x);
        if((hx|lx)==0)
            return(x);          /* cbrt(0) is itself */
 
        SET_HIGH_WORD(x,hx); /* x <- |x| */
    /* rough cbrt to 5 bits */
        if(hx<0x00100000)               /* subnormal number */
          {
            SET_HIGH_WORD(t,0x43500000);                /* set t= 2**54 */
            t*=x;
            GET_HIGH_WORD(ht,t);
            SET_HIGH_WORD(t,ht/3+B2);
          }
        else
          SET_HIGH_WORD(t,hx/3+B1);
 
 
    /* new cbrt to 23 bits, may be implemented in single precision */
        r=t*t/x;
        s=C+r*t;
        t*=G+F/(s+E+D/s);
 
    /* chopped to 20 bits and make it larger than cbrt(x) */
        SET_LOW_WORD(t,0);
        GET_HIGH_WORD(ht,t);
        SET_HIGH_WORD(t,ht + 0x00000001);
 
    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
        s=t*t;          /* t*t is exact */
        r=x/s;
        w=t+t;
        r=(r-t)/(w+r);  /* r-s is exact */
        t=t+t*r;
 
    /* retore the sign bit */
        GET_HIGH_WORD(ht,t);
        SET_HIGH_WORD(t,ht|sign);
        return(t);
}
#endif /* _DOUBLE_IS_32BITS */

Line No.	Rev	Author	Line
1	774	jeremybenn
2			`/* @(#)s_cbrt.c 1.3 95/01/18 */`
3			`/*`
4			`* ====================================================`
5			`* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.`
6			`*`
7			`* Developed at SunSoft, a Sun Microsystems, Inc. business.`
8			`* Permission to use, copy, modify, and distribute this`
9			`* software is freely granted, provided that this notice`
10			`* is preserved.`
11			`* ====================================================`
12			`*`
13			`*/`
14
15			`#include "fdlibm.h"`
16
17			`#ifndef _DOUBLE_IS_32BITS`
18
19			`/* cbrt(x)`
20			`* Return cube root of x`
21			`*/`
22			`#ifdef __STDC__`
23			`static const uint32_t`
24			`#else`
25			`static uint32_t`
26			`#endif`
27			`B1 = 715094163, /* B1 = (682-0.03306235651)220 /`
28			`B2 = 696219795; /* B2 = (664-0.03306235651)220 /`
29
30			`#ifdef __STDC__`
31			`static const double`
32			`#else`
33			`static double`
34			`#endif`
35			`C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */`
36			`D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */`
37			`E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */`
38			`F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */`
39			`G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */`
40
41			`#ifdef __STDC__`
42			`double cbrt(double x)`
43			`#else`
44			`double cbrt(x)`
45			`double x;`
46			`#endif`
47			`{`
48			`int32_t hx, lx, ht;`
49			`double r,s,t=0.0,w;`
50			`uint32_t sign;`
51
52
53			`GET_HIGH_WORD(hx,x); /* high word of x */`
54			`sign=hx&0x80000000; /* sign= sign(x) */`
55			`hx ^=sign;`
56			`if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */`
57			`GET_LOW_WORD(lx, x);`
58			`if((hx\|lx)==0)`
59			`return(x); /* cbrt(0) is itself */`
60
61			`SET_HIGH_WORD(x,hx); /* x <- \|x\| */`
62			`/* rough cbrt to 5 bits */`
63			`if(hx<0x00100000) /* subnormal number */`
64			`{`
65			`SET_HIGH_WORD(t,0x43500000); /* set t= 2*54 /`
66			`t*=x;`
67			`GET_HIGH_WORD(ht,t);`
68			`SET_HIGH_WORD(t,ht/3+B2);`
69			`}`
70			`else`
71			`SET_HIGH_WORD(t,hx/3+B1);`
72
73
74			`/* new cbrt to 23 bits, may be implemented in single precision */`
75			`r=t*t/x;`
76			`s=C+r*t;`
77			`t*=G+F/(s+E+D/s);`
78
79			`/* chopped to 20 bits and make it larger than cbrt(x) */`
80			`SET_LOW_WORD(t,0);`
81			`GET_HIGH_WORD(ht,t);`
82			`SET_HIGH_WORD(t,ht + 0x00000001);`
83
84			`/* one step newton iteration to 53 bits with error less than 0.667 ulps */`
85			`s=tt; / tt is exact /`
86			`r=x/s;`
87			`w=t+t;`
88			`r=(r-t)/(w+r); /* r-s is exact */`
89			`t=t+t*r;`
90
91			`/* retore the sign bit */`
92			`GET_HIGH_WORD(ht,t);`
93			`SET_HIGH_WORD(t,ht\|sign);`
94			`return(t);`
95			`}`
96			`#endif /* _DOUBLE_IS_32BITS */`

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[/] [openrisc/] [trunk/] [gnu-dev/] [or1k-gcc/] [libjava/] [classpath/] [native/] [fdlibm/] [s_cbrt.c] - Blame information for rev 774