93 lines
2.3 KiB
C
93 lines
2.3 KiB
C
/*
|
|
* ====================================================
|
|
* 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
|