libm/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 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: s_cbrt.c,v 1.8 1995/05/10 20:46:49 jtc 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 #ifdef __STDC__
  24 static const u_int32_t
  25 #else
  26 static u_int32_t
  27 #endif
  28         B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
  29         B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
  30
  31 #ifdef __STDC__
  32 static const double
  33 #else
  34 static double
  35 #endif
  36 C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
  37 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
  38 E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
  39 F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
  40 G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
  41
  42 #ifdef __STDC__
  43         double cbrt(double x)
  44 #else
  45         double cbrt(x)
  46         double x;
  47 #endif
  48 {
  49         int32_t hx;
  50         double r,s,t=0.0,w;
  51         u_int32_t sign;
  52         u_int32_t high,low;
  53
  54         GET_HIGH_WORD(hx,x);
  55         sign=hx&0x80000000;             /* sign= sign(x) */
  56         hx  ^=sign;
  57         if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
  58         GET_LOW_WORD(low,x);
  59         if((hx|low)==0)
  60             return(x);          /* cbrt(0) is itself */
  61
  62         SET_HIGH_WORD(x,hx);    /* x <- |x| */
  63     /* rough cbrt to 5 bits */
  64         if(hx<0x00100000)               /* subnormal number */
  65           {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
  66            t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
  67           }
  68         else
  69           SET_HIGH_WORD(t,hx/3+B1);
  70
  71
  72     /* new cbrt to 23 bits, may be implemented in single precision */
  73         r=t*t/x;
  74         s=C+r*t;
  75         t*=G+F/(s+E+D/s);
  76
  77     /* chopped to 20 bits and make it larger than cbrt(x) */
  78         GET_HIGH_WORD(high,t);
  79         INSERT_WORDS(t,high+0x00000001,0);
  80
  81
  82     /* one step newton iteration to 53 bits with error less than 0.667 ulps */
  83         s=t*t;          /* t*t is exact */
  84         r=x/s;
  85         w=t+t;
  86         r=(r-t)/(w+r);  /* r-s is exact */
  87         t=t+t*r;
  88
  89     /* retore the sign bit */
  90         GET_HIGH_WORD(high,t);
  91         SET_HIGH_WORD(t,high|sign);
  92         return(t);
  93 }
  94 libm_hidden_def(cbrt)