1  /* e_sinhl.c -- long double version of e_sinh.c.
       2   * Conversion to long double by Ulrich Drepper,
       3   * Cygnus Support, drepper@cygnus.com.
       4   */
       5  
       6  /*
       7   * ====================================================
       8   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       9   *
      10   * Developed at SunPro, a Sun Microsystems, Inc. business.
      11   * Permission to use, copy, modify, and distribute this
      12   * software is freely granted, provided that this notice
      13   * is preserved.
      14   * ====================================================
      15   */
      16  
      17  /* Changes for 128-bit long double are
      18     Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
      19     and are incorporated herein by permission of the author.  The author
      20     reserves the right to distribute this material elsewhere under different
      21     copying permissions.  These modifications are distributed here under
      22     the following terms:
      23  
      24      This library is free software; you can redistribute it and/or
      25      modify it under the terms of the GNU Lesser General Public
      26      License as published by the Free Software Foundation; either
      27      version 2.1 of the License, or (at your option) any later version.
      28  
      29      This library is distributed in the hope that it will be useful,
      30      but WITHOUT ANY WARRANTY; without even the implied warranty of
      31      MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      32      Lesser General Public License for more details.
      33  
      34      You should have received a copy of the GNU Lesser General Public
      35      License along with this library; if not, see
      36      <http://www.gnu.org/licenses/>.  */
      37  
      38  /* sinhq(x)
      39   * Method :
      40   * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
      41   *      1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
      42   *      2.
      43   *                                                   E + E/(E+1)
      44   *          0        <= x <= 25     :  sinhl(x) := --------------, E=expm1q(x)
      45   *                                                       2
      46   *
      47   *          25       <= x <= lnovft :  sinhl(x) := expq(x)/2
      48   *          lnovft   <= x <= ln2ovft:  sinhl(x) := expq(x/2)/2 * expq(x/2)
      49   *          ln2ovft  <  x           :  sinhl(x) := x*shuge (overflow)
      50   *
      51   * Special cases:
      52   *      sinhl(x) is |x| if x is +INF, -INF, or NaN.
      53   *      only sinhl(0)=0 is exact for finite x.
      54   */
      55  
      56  #include "quadmath-imp.h"
      57  
      58  static const __float128 one = 1.0, shuge = 1.0e4931Q,
      59  ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
      60  
      61  __float128
      62  sinhq (__float128 x)
      63  {
      64    __float128 t, w, h;
      65    uint32_t jx, ix;
      66    ieee854_float128 u;
      67  
      68    /* Words of |x|. */
      69    u.value = x;
      70    jx = u.words32.w0;
      71    ix = jx & 0x7fffffff;
      72  
      73    /* x is INF or NaN */
      74    if (ix >= 0x7fff0000)
      75      return x + x;
      76  
      77    h = 0.5;
      78    if (jx & 0x80000000)
      79      h = -h;
      80  
      81    /* Absolute value of x.  */
      82    u.words32.w0 = ix;
      83  
      84    /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
      85    if (ix <= 0x40044000)
      86      {
      87        if (ix < 0x3fc60000) /* |x| < 2^-57 */
      88  	{
      89  	  math_check_force_underflow (x);
      90  	  if (shuge + x > one)
      91  	    return x;		/* sinh(tiny) = tiny with inexact */
      92  	}
      93        t = expm1q (u.value);
      94        if (ix < 0x3fff0000)
      95  	return h * (2.0 * t - t * t / (t + one));
      96        return h * (t + t / (t + one));
      97      }
      98  
      99    /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
     100    if (ix <= 0x400c62e3) /* 11356.375 */
     101      return h * expq (u.value);
     102  
     103    /* |x| in [log(maxdouble), overflowthreshold]
     104       Overflow threshold is log(2 * maxdouble).  */
     105    if (u.value <= ovf_thresh)
     106      {
     107        w = expq (0.5 * u.value);
     108        t = h * w;
     109        return t * w;
     110      }
     111  
     112    /* |x| > overflowthreshold, sinhl(x) overflow */
     113    return x * shuge;
     114  }