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       ---
       s_cbrt.c (2227B)
       ---
            1 /* @(#)s_cbrt.c 5.1 93/09/24 */
            2 /*
            3  * ====================================================
            4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
            5  *
            6  * Developed at SunPro, a Sun Microsystems, Inc. business.
            7  * Permission to use, copy, modify, and distribute this
            8  * software is freely granted, provided that this notice
            9  * is preserved.
           10  * ====================================================
           11  */
           12 
           13 #ifndef lint
           14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cbrt.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
           15 #endif
           16 
           17 #include "math.h"
           18 #include "math_private.h"
           19 
           20 /* cbrt(x)
           21  * Return cube root of x
           22  */
           23 static const u_int32_t
           24         B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
           25         B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
           26 
           27 static const double
           28 C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
           29 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
           30 E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
           31 F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
           32 G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
           33 
           34 double
           35 cbrt(double x)
           36 {
           37         int32_t        hx;
           38         double r,s,t=0.0,w;
           39         u_int32_t sign;
           40         u_int32_t high,low;
           41 
           42         GET_HIGH_WORD(hx,x);
           43         sign=hx&0x80000000;                 /* sign= sign(x) */
           44         hx  ^=sign;
           45         if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
           46         GET_LOW_WORD(low,x);
           47         if((hx|low)==0)
           48             return(x);                /* cbrt(0) is itself */
           49 
           50         SET_HIGH_WORD(x,hx);        /* x <- |x| */
           51     /* rough cbrt to 5 bits */
           52         if(hx<0x00100000)                 /* subnormal number */
           53           {SET_HIGH_WORD(t,0x43500000);        /* set t= 2**54 */
           54            t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
           55           }
           56         else
           57           SET_HIGH_WORD(t,hx/3+B1);
           58 
           59 
           60     /* new cbrt to 23 bits, may be implemented in single precision */
           61         r=t*t/x;
           62         s=C+r*t;
           63         t*=G+F/(s+E+D/s);
           64 
           65     /* chopped to 20 bits and make it larger than cbrt(x) */
           66         GET_HIGH_WORD(high,t);
           67         INSERT_WORDS(t,high+0x00000001,0);
           68 
           69 
           70     /* one step newton iteration to 53 bits with error less than 0.667 ulps */
           71         s=t*t;                /* t*t is exact */
           72         r=x/s;
           73         w=t+t;
           74         r=(r-t)/(w+r);        /* r-s is exact */
           75         t=t+t*r;
           76 
           77     /* retore the sign bit */
           78         GET_HIGH_WORD(high,t);
           79         SET_HIGH_WORD(t,high|sign);
           80         return(t);
           81 }