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