sysdeps/ieee754/ldbl-96/s_cbrtl.c

   1 /* Compute cubic root of double value.
   2    Copyright (C) 1997-2022 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)