libquadmath/math/sinhq.c

   1 /* sinhq.c -- __float128 version of e_sinh.c.
   2  * Conversion to __float128 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 __float128 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 /* sinhq(x)
  39  * Method :
  40  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
  41  *      1. Replace x by |x| (sinhq(-x) = -sinhq(x)).
  42  *      2.
  43  *                                                   E + E/(E+1)
  44  *          0        <= x <= 25     :  sinhq(x) := --------------, E=expm1q(x)
  45  *                                                       2
  46  *
  47  *          25       <= x <= lnovft :  sinhq(x) := expq(x)/2
  48  *          lnovft   <= x <= ln2ovft:  sinhq(x) := expq(x/2)/2 * expq(x/2)
  49  *          ln2ovft  <  x           :  sinhq(x) := x*shuge (overflow)
  50  *
  51  * Special cases:
  52  *      sinhq(x) is |x| if x is +INF, -INF, or NaN.
  53  *      only sinhq(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 = 0.5Q;
  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         if (shuge + x > one)
  89           return x;             /* sinh(tiny) = tiny with inexact */
  90       t = expm1q (u.value);
  91       if (ix < 0x3fff0000)
  92         return h * (2.0Q * t - t * t / (t + one));
  93       return h * (t + t / (t + one));
  94     }
  95
  96   /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
  97   if (ix <= 0x400c62e3) /* 11356.375 */
  98     return h * expq (u.value);
  99
 100   /* |x| in [log(maxdouble), overflowthreshold]
 101      Overflow threshold is log(2 * maxdouble).  */
 102   if (u.value <= ovf_thresh)
 103     {
 104       w = expq (0.5Q * u.value);
 105       t = h * w;
 106       return t * w;
 107     }
 108
 109   /* |x| > overflowthreshold, sinhq(x) overflow */
 110   return x * shuge;
 111 }