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