gonzui

    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: /* LINTLIBRARY */
   14: 
   15: #include <sys/cdefs.h>
   16: #include <float.h>
   17: #include <math.h>
   18: 
   19: #include "math_private.h"
   20: 
   21: /* cbrt(x)
   22:  * Return cube root of x
   23:  */
   24: static const u_int32_t
   25:         B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
   26:         B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
   27: 
   28: static const double
   29: C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
   30: D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
   31: E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
   32: F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
   33: G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
   34: 
   35: double
   36: cbrt(double x) 
   37: {
   38:         int32_t        hx;
   39:         double r,s,t=0.0,w;
   40:         u_int32_t sign;
   41:         u_int32_t high,low;
   42: 
   43:         GET_HIGH_WORD(hx,x);
   44:         sign=hx&0x80000000;            /* sign= sign(x) */
   45:         hx  ^=sign;
   46:         if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
   47:         GET_LOW_WORD(low,x);
   48:         if((hx|low)==0) 
   49:             return(x);         /* cbrt(0) is itself */
   50: 
   51:         SET_HIGH_WORD(x,hx);   /* x <- |x| */
   52:     /* rough cbrt to 5 bits */
   53:         if(hx<0x00100000)              /* subnormal number */
   54:           {SET_HIGH_WORD(t,0x43500000);        /* set t= 2**54 */
   55:            t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
   56:           }
   57:         else
   58:           SET_HIGH_WORD(t,hx/3+B1);
   59: 
   60: 
   61:     /* new cbrt to 23 bits, may be implemented in single precision */
   62:         r=t*t/x;
   63:         s=C+r*t;
   64:         t*=G+F/(s+E+D/s);      
   65: 
   66:     /* chopped to 20 bits and make it larger than cbrt(x) */ 
   67:         GET_HIGH_WORD(high,t);
   68:         INSERT_WORDS(t,high+0x00000001,0);
   69: 
   70: 
   71:     /* one step newton iteration to 53 bits with error less than 0.667 ulps */
   72:         s=t*t;         /* t*t is exact */
   73:         r=x/s;
   74:         w=t+t;
   75:         r=(r-t)/(w+r); /* r-s is exact */
   76:         t=t+t*r;
   77: 
   78:     /* retore the sign bit */
   79:         GET_HIGH_WORD(high,t);
   80:         SET_HIGH_WORD(t,high|sign);
   81:         return(t);
   82: }
   83: 
   84: #if     LDBL_MANT_DIG == 53
   85: #ifdef  lint
   86: /* PROTOLIB1 */
   87: long double cbrtl(long double);
   88: #else   /* lint */
   89: __weak_alias(cbrtl, cbrt);
   90: #endif  /* lint */
   91: #endif  /* LDBL_MANT_DIG == 53 */