1  /* Compute cubic root of double value.
       2     Copyright (C) 1997-2023 Free Software Foundation, Inc.
       3     This file is part of the GNU C Library.
       4  
       5     The GNU C Library is free software; you can redistribute it and/or
       6     modify it under the terms of the GNU Lesser General Public
       7     License as published by the Free Software Foundation; either
       8     version 2.1 of the License, or (at your option) any later version.
       9  
      10     The GNU C Library is distributed in the hope that it will be useful,
      11     but WITHOUT ANY WARRANTY; without even the implied warranty of
      12     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      13     Lesser General Public License for more details.
      14  
      15     You should have received a copy of the GNU Lesser General Public
      16     License along with the GNU C Library; if not, see
      17     <https://www.gnu.org/licenses/>.  */
      18  
      19  #include <math.h>
      20  #include <libm-alias-ldouble.h>
      21  
      22  
      23  #define CBRT2 1.2599210498948731648		/* 2^(1/3) */
      24  #define SQR_CBRT2 1.5874010519681994748		/* 2^(2/3) */
      25  
      26  /* We don't use long double values here since U need not be computed
      27     with full precision.  */
      28  static const double factor[5] =
      29  {
      30    1.0 / SQR_CBRT2,
      31    1.0 / CBRT2,
      32    1.0,
      33    CBRT2,
      34    SQR_CBRT2
      35  };
      36  
      37  static const long double third = 0.3333333333333333333333333L;
      38  
      39  long double
      40  __cbrtl (long double x)
      41  {
      42    long double xm, u;
      43    int xe;
      44  
      45    /* Reduce X.  XM now is an range 1.0 to 0.5.  */
      46    xm = __frexpl (fabsl (x), &xe);
      47  
      48    /* If X is not finite or is null return it (with raising exceptions
      49       if necessary.
      50       Note: *Our* version of `frexp' sets XE to zero if the argument is
      51       Inf or NaN.  This is not portable but faster.  */
      52    if (xe == 0 && fpclassify (x) <= FP_ZERO)
      53      return x + x;
      54  
      55    u = (((-1.34661104733595206551E-1 * xm
      56  	  + 5.46646013663955245034E-1) * xm
      57  	 - 9.54382247715094465250E-1) * xm
      58  	+ 1.13999833547172932737E0) * xm
      59         + 4.02389795645447521269E-1;
      60  
      61    u *= factor[2 + xe % 3];
      62    u = __ldexpl (x > 0.0 ? u : -u, xe / 3);
      63  
      64    u -= (u - (x / (u * u))) * third;
      65    u -= (u - (x / (u * u))) * third;
      66    return u;
      67  }
      68  libm_alias_ldouble (__cbrt, cbrt)