compiler/mlib/s_cbrt.c

   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 1.5 1999/08/28 00:06:44 peter 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 }