lib/libm/src/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 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: s_cbrt.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
  16 #endif
  17
  18 #include "math.h"
  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 }