compiler/stdc/math/ld128/s_tanhl.c

   1 /* @(#)s_tanh.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 /*
  14  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
  15  *
  16  * Permission to use, copy, modify, and distribute this software for any
  17  * purpose with or without fee is hereby granted, provided that the above
  18  * copyright notice and this permission notice appear in all copies.
  19  *
  20  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  21  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  22  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  23  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  24  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  25  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  26  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  27  */
  28
  29 /* tanhl(x)
  30  * Return the Hyperbolic Tangent of x
  31  *
  32  * Method :
  33  *                                      x    -x
  34  *                                     e  - e
  35  *      0. tanhl(x) is defined to be -----------
  36  *                                      x    -x
  37  *                                     e  + e
  38  *      1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
  39  *      2.  0      <= x <= 2**-57 : tanhl(x) := x*(one+x)
  40  *                                               -t
  41  *          2**-57 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
  42  *                                              t + 2
  43  *                                                    2
  44  *          1      <= x <=  40.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
  45  *                                                  t + 2
  46  *          40.0   <  x <= INF    : tanhl(x) := 1.
  47  *
  48  * Special cases:
  49  *      tanhl(NaN) is NaN;
  50  *      only tanhl(0)=0 is exact for finite argument.
  51  */
  52
  53 #include <openlibm_math.h>
  54
  55 #include "math_private.h"
  56
  57 static const long double one = 1.0, two = 2.0, tiny = 1.0e-4900L;
  58
  59 long double
  60 tanhl(long double x)
  61 {
  62   long double t, z;
  63   uint32_t jx, ix;
  64   ieee_quad_shape_type u;
  65
  66   /* Words of |x|. */
  67   u.value = x;
  68   jx = u.parts32.mswhi;
  69   ix = jx & 0x7fffffff;
  70   /* x is INF or NaN */
  71   if (ix >= 0x7fff0000)
  72     {
  73       /* for NaN it's not important which branch: tanhl(NaN) = NaN */
  74       if (jx & 0x80000000)
  75         return one / x - one;   /* tanhl(-inf)= -1; */
  76       else
  77         return one / x + one;   /* tanhl(+inf)=+1 */
  78     }
  79
  80   /* |x| < 40 */
  81   if (ix < 0x40044000)
  82     {
  83       if (u.value == 0)
  84         return x;               /* x == +- 0 */
  85       if (ix < 0x3fc60000)      /* |x| < 2^-57 */
  86         return x * (one + tiny); /* tanh(small) = small */
  87       u.parts32.mswhi = ix;     /* Absolute value of x.  */
  88       if (ix >= 0x3fff0000)
  89         {                       /* |x| >= 1  */
  90           t = expm1l (two * u.value);
  91           z = one - two / (t + two);
  92         }
  93       else
  94         {
  95           t = expm1l (-two * u.value);
  96           z = -t / (t + two);
  97         }
  98       /* |x| > 40, return +-1 */
  99     }
 100   else
 101     {
 102       z = one - tiny;           /* raised inexact flag */
 103     }
 104   return (jx & 0x80000000) ? -z : z;
 105 }