sysdeps/ieee754/dbl-64/s_cbrt.c

   1 /* Compute cubic root of double value.
   2    Copyright (C) 1997-2024 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-double.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 double
  37 __cbrt (double x)
  38 {
  39   double xm, ym, u, t2;
  40   int xe;
  41
  42   /* Reduce X.  XM now is an range 1.0 to 0.5.  */
  43   xm = __frexp (fabs (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 = (0.354895765043919860
  53        + ((1.50819193781584896
  54            + ((-2.11499494167371287
  55                + ((2.44693122563534430
  56                    + ((-1.83469277483613086
  57                        + (0.784932344976639262 - 0.145263899385486377 * xm)
  58                           * xm)
  59                       * xm))
  60                   * xm))
  61               * xm))
  62           * xm));
  63
  64   t2 = u * u * u;
  65
  66   ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
  67
  68   return __ldexp (x > 0.0 ? ym : -ym, xe / 3);
  69 }
  70 libm_alias_double (__cbrt, cbrt)