libjava/classpath/native/fdlibm/s_cbrt.c

   1
   2 /* @(#)s_cbrt.c 1.3 95/01/18 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  *
  13  */
  14
  15 #include "fdlibm.h"
  16
  17 #ifndef _DOUBLE_IS_32BITS
  18
  19 /* cbrt(x)
  20  * Return cube root of x
  21  */
  22 #ifdef __STDC__
  23 static const uint32_t
  24 #else
  25 static uint32_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, lx, ht;
  49         double r,s,t=0.0,w;
  50         uint32_t sign;
  51
  52
  53         GET_HIGH_WORD(hx,x); /* high word of 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(lx, x);
  58         if((hx|lx)==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           {
  65             SET_HIGH_WORD(t,0x43500000);                /* set t= 2**54 */
  66             t*=x;
  67             GET_HIGH_WORD(ht,t);
  68             SET_HIGH_WORD(t,ht/3+B2);
  69           }
  70         else
  71           SET_HIGH_WORD(t,hx/3+B1);
  72
  73
  74     /* new cbrt to 23 bits, may be implemented in single precision */
  75         r=t*t/x;
  76         s=C+r*t;
  77         t*=G+F/(s+E+D/s);
  78
  79     /* chopped to 20 bits and make it larger than cbrt(x) */
  80         SET_LOW_WORD(t,0);
  81         GET_HIGH_WORD(ht,t);
  82         SET_HIGH_WORD(t,ht + 0x00000001);
  83
  84     /* one step newton iteration to 53 bits with error less than 0.667 ulps */
  85         s=t*t;          /* t*t is exact */
  86         r=x/s;
  87         w=t+t;
  88         r=(r-t)/(w+r);  /* r-s is exact */
  89         t=t+t*r;
  90
  91     /* retore the sign bit */
  92         GET_HIGH_WORD(ht,t);
  93         SET_HIGH_WORD(t,ht|sign);
  94         return(t);
  95 }
  96 #endif /* _DOUBLE_IS_32BITS */