sysdeps/ieee754/ldbl-128/e_sinhl.c

   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, write to the Free Software
  36     Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307  USA */
  37
  38 /* __ieee754_sinhl(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=expm1l(x)
  45  *                                                       2
  46  *
  47  *          25       <= x <= lnovft :  sinhl(x) := expl(x)/2
  48  *          lnovft   <= x <= ln2ovft:  sinhl(x) := expl(x/2)/2 * expl(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 "math.h"
  57 #include "math_private.h"
  58
  59 #ifdef __STDC__
  60 static const long double one = 1.0, shuge = 1.0e4931L,
  61 ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
  62 #else
  63 static long double one = 1.0, shuge = 1.0e4931L,
  64 ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
  65 #endif
  66
  67 #ifdef __STDC__
  68 long double
  69 __ieee754_sinhl (long double x)
  70 #else
  71 long double
  72 __ieee754_sinhl (x)
  73      long double x;
  74 #endif
  75 {
  76   long double t, w, h;
  77   u_int32_t jx, ix;
  78   ieee854_long_double_shape_type u;
  79
  80   /* Words of |x|. */
  81   u.value = x;
  82   jx = u.parts32.w0;
  83   ix = jx & 0x7fffffff;
  84
  85   /* x is INF or NaN */
  86   if (ix >= 0x7fff0000)
  87     return x + x;
  88
  89   h = 0.5;
  90   if (jx & 0x80000000)
  91     h = -h;
  92
  93   /* Absolute value of x.  */
  94   u.parts32.w0 = ix;
  95
  96   /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
  97   if (ix <= 0x40044000)
  98     {
  99       if (ix < 0x3fc60000) /* |x| < 2^-57 */
 100         if (shuge + x > one)
 101           return x;             /* sinh(tiny) = tiny with inexact */
 102       t = __expm1l (u.value);
 103       if (ix < 0x3fff0000)
 104         return h * (2.0 * t - t * t / (t + one));
 105       return h * (t + t / (t + one));
 106     }
 107
 108   /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
 109   if (ix <= 0x400c62e3) /* 11356.375 */
 110     return h * __ieee754_expl (u.value);
 111
 112   /* |x| in [log(maxdouble), overflowthreshold]
 113      Overflow threshold is log(2 * maxdouble).  */
 114   if (u.value <= ovf_thresh)
 115     {
 116       w = __ieee754_expl (0.5 * u.value);
 117       t = h * w;
 118       return t * w;
 119     }
 120
 121   /* |x| > overflowthreshold, sinhl(x) overflow */
 122   return x * shuge;
 123 }