1  /* Compute cubic root of float 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-float.h>
      21  
      22  
      23  #define CBRT2 1.2599210498948731648		/* 2^(1/3) */
      24  #define SQR_CBRT2 1.5874010519681994748		/* 2^(2/3) */
      25  
      26  static const double factor[5] =
      27  {
      28    1.0 / SQR_CBRT2,
      29    1.0 / CBRT2,
      30    1.0,
      31    CBRT2,
      32    SQR_CBRT2
      33  };
      34  
      35  
      36  float
      37  __cbrtf (float x)
      38  {
      39    float xm, ym, u, t2;
      40    int xe;
      41  
      42    /* Reduce X.  XM now is an range 1.0 to 0.5.  */
      43    xm = __frexpf (fabsf (x), &xe);
      44  
      45    /* If X is not finite or is null return it (with raising exceptions
      46       if necessary.
      47       Note: *Our* version of `frexp' sets XE to zero if the argument is
      48       Inf or NaN.  This is not portable but faster.  */
      49    if (xe == 0 && fpclassify (x) <= FP_ZERO)
      50      return x + x;
      51  
      52    u = (0.492659620528969547 + (0.697570460207922770
      53  			       - 0.191502161678719066 * xm) * xm);
      54  
      55    t2 = u * u * u;
      56  
      57    ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
      58  
      59    return __ldexpf (x > 0.0 ? ym : -ym, xe / 3);
      60  }
      61  libm_alias_float (__cbrt, cbrt)