lib/msun/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  * $FreeBSD: src/lib/msun/src/s_cbrt.c,v 1.5 1999/08/28 00:06:44 peter Exp $
  13  * $DragonFly: src/lib/msun/src/Attic/s_cbrt.c,v 1.2 2003/06/17 04:26:53 dillon Exp $
  14  */
  15
  16 #include "math.h"
  17 #include "math_private.h"
  18
  19 /* cbrt(x)
  20  * Return cube root of x
  21  */
  22 #ifdef __STDC__
  23 static const u_int32_t
  24 #else
  25 static u_int32_t
  26 #endif
  27         B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
  28         B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
  29
  30 #ifdef __STDC__
  31 static const double
  32 #else
  33 static double
  34 #endif
  35 C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
  36 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
  37 E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
  38 F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
  39 G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
  40
  41 #ifdef __STDC__
  42         double cbrt(double x)
  43 #else
  44         double cbrt(x)
  45         double x;
  46 #endif
  47 {
  48         int32_t hx;
  49         double r,s,t=0.0,w;
  50         u_int32_t sign;
  51         u_int32_t high,low;
  52
  53         GET_HIGH_WORD(hx,x);
  54         sign=hx&0x80000000;             /* sign= sign(x) */
  55         hx  ^=sign;
  56         if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
  57         GET_LOW_WORD(low,x);
  58         if((hx|low)==0)
  59             return(x);          /* cbrt(0) is itself */
  60
  61         SET_HIGH_WORD(x,hx);    /* x <- |x| */
  62     /* rough cbrt to 5 bits */
  63         if(hx<0x00100000)               /* subnormal number */
  64           {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
  65            t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
  66           }
  67         else
  68           SET_HIGH_WORD(t,hx/3+B1);
  69
  70
  71     /* new cbrt to 23 bits, may be implemented in single precision */
  72         r=t*t/x;
  73         s=C+r*t;
  74         t*=G+F/(s+E+D/s);
  75
  76     /* chopped to 20 bits and make it larger than cbrt(x) */
  77         GET_HIGH_WORD(high,t);
  78         INSERT_WORDS(t,high+0x00000001,0);
  79
  80
  81     /* one step newton iteration to 53 bits with error less than 0.667 ulps */
  82         s=t*t;          /* t*t is exact */
  83         r=x/s;
  84         w=t+t;
  85         r=(r-t)/(w+r);  /* r-s is exact */
  86         t=t+t*r;
  87
  88     /* retore the sign bit */
  89         GET_HIGH_WORD(high,t);
  90         SET_HIGH_WORD(t,high|sign);
  91         return(t);
  92 }