newlib/libm/common/s_cbrt.c

   1
   2 /* @(#)s_cbrt.c 5.1 93/09/24 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, 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 /*
  16 FUNCTION
  17         <<cbrt>>, <<cbrtf>>---cube root
  18
  19 INDEX
  20         cbrt
  21 INDEX
  22         cbrtf
  23
  24 SYNOPSIS
  25         #include <math.h>
  26         double cbrt(double <[x]>);
  27         float  cbrtf(float <[x]>);
  28
  29 DESCRIPTION
  30         <<cbrt>> computes the cube root of the argument.
  31
  32 RETURNS
  33         The cube root is returned.
  34
  35 PORTABILITY
  36         <<cbrt>> is in System V release 4.  <<cbrtf>> is an extension.
  37 */
  38
  39 #include "fdlibm.h"
  40
  41 #ifndef _DOUBLE_IS_32BITS
  42
  43 /* cbrt(x)
  44  * Return cube root of x
  45  */
  46 #ifdef __STDC__
  47 static const __uint32_t
  48 #else
  49 static __uint32_t
  50 #endif
  51         B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
  52         B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
  53
  54 #ifdef __STDC__
  55 static const double
  56 #else
  57 static double
  58 #endif
  59 C =  5.42857142857142815906e-01, /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
  60 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
  61 E =  1.41428571428571436819e+00, /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
  62 F =  1.60714285714285720630e+00, /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
  63 G =  3.57142857142857150787e-01; /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
  64
  65 #ifdef __STDC__
  66         double cbrt(double x)
  67 #else
  68         double cbrt(x)
  69         double x;
  70 #endif
  71 {
  72         __int32_t       hx;
  73         double r,s,t=0.0,w;
  74         __uint32_t sign;
  75         __uint32_t high,low;
  76
  77         GET_HIGH_WORD(hx,x);
  78         sign=hx&0x80000000;             /* sign= sign(x) */
  79         hx  ^=sign;
  80         if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
  81         GET_LOW_WORD(low,x);
  82         if((hx|low)==0)
  83             return(x);          /* cbrt(0) is itself */
  84
  85         SET_HIGH_WORD(x,hx);    /* x <- |x| */
  86     /* rough cbrt to 5 bits */
  87         if(hx<0x00100000)               /* subnormal number */
  88           {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
  89            t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
  90           }
  91         else
  92           SET_HIGH_WORD(t,hx/3+B1);
  93
  94
  95     /* new cbrt to 23 bits, may be implemented in single precision */
  96         r=t*t/x;
  97         s=C+r*t;
  98         t*=G+F/(s+E+D/s);
  99
 100     /* chopped to 20 bits and make it larger than cbrt(x) */
 101         GET_HIGH_WORD(high,t);
 102         INSERT_WORDS(t,high+0x00000001,0);
 103
 104
 105     /* one step newton iteration to 53 bits with error less than 0.667 ulps */
 106         s=t*t;          /* t*t is exact */
 107         r=x/s;
 108         w=t+t;
 109         r=(r-t)/(w+r);  /* r-s is exact */
 110         t=t+t*r;
 111
 112     /* retore the sign bit */
 113         GET_HIGH_WORD(high,t);
 114         SET_HIGH_WORD(t,high|sign);
 115         return(t);
 116 }
 117
 118 #endif /* _DOUBLE_IS_32BITS */