libquadmath/math/tanhq.c

   1 /* s_tanhl.c -- __float128 version of s_tanh.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 contributed by
  18    Stephen L. Moshier <moshier@na-net.ornl.gov> */
  19
  20 /* tanhl(x)
  21  * Return the Hyperbolic Tangent of x
  22  *
  23  * Method :
  24  *                                      x    -x
  25  *                                     e  - e
  26  *      0. tanhl(x) is defined to be -----------
  27  *                                      x    -x
  28  *                                     e  + e
  29  *      1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
  30  *      2.  0      <= x <= 2**-57 : tanhl(x) := x*(one+x)
  31  *                                               -t
  32  *          2**-57 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
  33  *                                              t + 2
  34  *                                                    2
  35  *          1      <= x <=  40.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
  36  *                                                  t + 2
  37  *          40.0   <  x <= INF    : tanhl(x) := 1.
  38  *
  39  * Special cases:
  40  *      tanhl(NaN) is NaN;
  41  *      only tanhl(0)=0 is exact for finite argument.
  42  */
  43
  44 #include "quadmath-imp.h"
  45
  46 static const __float128 one = 1.0Q, two = 2.0Q, tiny = 1.0e-4900Q;
  47
  48 __float128
  49 tanhq (__float128 x)
  50 {
  51   __float128 t, z;
  52   uint32_t jx, ix;
  53   ieee854_float128 u;
  54
  55   /* Words of |x|. */
  56   u.value = x;
  57   jx = u.words32.w0;
  58   ix = jx & 0x7fffffff;
  59   /* x is INF or NaN */
  60   if (ix >= 0x7fff0000)
  61     {
  62       /* for NaN it's not important which branch: tanhl(NaN) = NaN */
  63       if (jx & 0x80000000)
  64         return one / x - one;   /* tanhl(-inf)= -1; */
  65       else
  66         return one / x + one;   /* tanhl(+inf)=+1 */
  67     }
  68
  69   /* |x| < 40 */
  70   if (ix < 0x40044000)
  71     {
  72       if (u.value == 0)
  73         return x;               /* x == +- 0 */
  74       if (ix < 0x3fc60000)      /* |x| < 2^-57 */
  75         return x * (one + tiny); /* tanh(small) = small */
  76       u.words32.w0 = ix;        /* Absolute value of x.  */
  77       if (ix >= 0x3fff0000)
  78         {                       /* |x| >= 1  */
  79           t = expm1q (two * u.value);
  80           z = one - two / (t + two);
  81         }
  82       else
  83         {
  84           t = expm1q (-two * u.value);
  85           z = -t / (t + two);
  86         }
  87       /* |x| > 40, return +-1 */
  88     }
  89   else
  90     {
  91       z = one - tiny;           /* raised inexact flag */
  92     }
  93   return (jx & 0x80000000) ? -z : z;
  94 }