sysdeps/ieee754/ldbl-96/s_cbrtl.c

   1 /* Compute cubic root of double value.
   2    Copyright (C) 1997-2015 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
   5    Ulrich Drepper <drepper@cygnus.com>, 1997.
   6
   7    The GNU C Library is free software; you can redistribute it and/or
   8    modify it under the terms of the GNU Lesser General Public
   9    License as published by the Free Software Foundation; either
  10    version 2.1 of the License, or (at your option) any later version.
  11
  12    The GNU C Library is distributed in the hope that it will be useful,
  13    but WITHOUT ANY WARRANTY; without even the implied warranty of
  14    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15    Lesser General Public License for more details.
  16
  17    You should have received a copy of the GNU Lesser General Public
  18    License along with the GNU C Library; if not, see
  19    <http://www.gnu.org/licenses/>.  */
  20
  21 #include <math.h>
  22 #include <math_private.h>
  23
  24
  25 #define CBRT2 1.2599210498948731648             /* 2^(1/3) */
  26 #define SQR_CBRT2 1.5874010519681994748         /* 2^(2/3) */
  27
  28 /* We don't use long double values here since U need not be computed
  29    with full precision.  */
  30 static const double factor[5] =
  31 {
  32   1.0 / SQR_CBRT2,
  33   1.0 / CBRT2,
  34   1.0,
  35   CBRT2,
  36   SQR_CBRT2
  37 };
  38
  39 static const long double third = 0.3333333333333333333333333L;
  40
  41 long double
  42 __cbrtl (long double x)
  43 {
  44   long double xm, u;
  45   int xe;
  46
  47   /* Reduce X.  XM now is an range 1.0 to 0.5.  */
  48   xm = __frexpl (fabsl (x), &xe);
  49
  50   /* If X is not finite or is null return it (with raising exceptions
  51      if necessary.
  52      Note: *Our* version of `frexp' sets XE to zero if the argument is
  53      Inf or NaN.  This is not portable but faster.  */
  54   if (xe == 0 && fpclassify (x) <= FP_ZERO)
  55     return x + x;
  56
  57   u = (((-1.34661104733595206551E-1 * xm
  58           + 5.46646013663955245034E-1) * xm
  59          - 9.54382247715094465250E-1) * xm
  60         + 1.13999833547172932737E0) * xm
  61        + 4.02389795645447521269E-1;
  62
  63   u *= factor[2 + xe % 3];
  64   u = __ldexpl (x > 0.0 ? u : -u, xe / 3);
  65
  66   u -= (u - (x / (u * u))) * third;
  67   u -= (u - (x / (u * u))) * third;
  68   return u;
  69 }
  70 weak_alias (__cbrtl, cbrtl)