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/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#ifndef __vax__
static const unsigned long
B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
static const double
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 */
double
cbrtl (double x)
{
long hx;
double r,s,w;
double lt;
unsigned sign;
typedef unsigned unsigned32 __attribute__((mode(SI)));
union {
double t;
unsigned32 pt[2];
} ut, ux;
int n0;
ut.t = 1.0;
n0 = (ut.pt[0] == 0);
ut.t = 0.0;
ux.t = x;
hx = ux.pt[n0]; /* high word of x */
sign=hx&0x80000000; /* sign= sign(x) */
hx ^=sign;
if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
if((hx| ux.pt[1-n0])==0)
return(ux.t); /* cbrt(0) is itself */
ux.pt[n0] = hx;
/* rough cbrt to 5 bits */
if(hx<0x00100000) /* subnormal number */
{ut.pt[n0]=0x43500000; /* set t= 2**54 */
ut.t*=x; ut.pt[n0]=ut.pt[n0]/3+B2;
}
else
ut.pt[n0]=hx/3+B1;
/* new cbrt to 23 bits, may be implemented in single precision */
r=ut.t*ut.t/ux.t;
s=C+r*ut.t;
ut.t*=G+F/(s+E+D/s);
/* chopped to 20 bits and make it larger than cbrt(x) */
ut.pt[1-n0]=0; ut.pt[n0]+=0x00000001;
/* one step newton iteration to 53 bits with error less than 0.667 ulps */
s=ut.t*ut.t; /* t*t is exact */
r=ux.t/s;
w=ut.t+ut.t;
r=(r-ut.t)/(w+r); /* r-s is exact */
ut.t=ut.t+ut.t*r;
/* restore the sign bit */
ut.pt[n0] |= sign;
lt = ut.t;
lt -= (lt - (x/(lt*lt))) * 0.333333333333333333333;
return lt;
}
main ()
{
if ((int) (cbrtl (27.0) + 0.5) != 3)
abort ();
exit (0);
}
#else
main () { exit (0); }
#endif
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