sysdeps/ieee754/ldbl-128/s_tanhl.c

   1 /* s_tanhl.c -- long double version of s_tanh.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 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 <math.h>
  45 #include <math_private.h>
  46
  47 static const long double one = 1.0, two = 2.0, tiny = 1.0e-4900L;
  48
  49 long double
  50 __tanhl (long double x)
  51 {
  52   long double t, z;
  53   u_int32_t jx, ix;
  54   ieee854_long_double_shape_type u;
  55
  56   /* Words of |x|. */
  57   u.value = x;
  58   jx = u.parts32.w0;
  59   ix = jx & 0x7fffffff;
  60   /* x is INF or NaN */
  61   if (ix >= 0x7fff0000)
  62     {
  63       /* for NaN it's not important which branch: tanhl(NaN) = NaN */
  64       if (jx & 0x80000000)
  65         return one / x - one;   /* tanhl(-inf)= -1; */
  66       else
  67         return one / x + one;   /* tanhl(+inf)=+1 */
  68     }
  69
  70   /* |x| < 40 */
  71   if (ix < 0x40044000)
  72     {
  73       if (u.value == 0)
  74         return x;               /* x == +- 0 */
  75       if (ix < 0x3fc60000)      /* |x| < 2^-57 */
  76         return x * (one + tiny); /* tanh(small) = small */
  77       u.parts32.w0 = ix;        /* Absolute value of x.  */
  78       if (ix >= 0x3fff0000)
  79         {                       /* |x| >= 1  */
  80           t = __expm1l (two * u.value);
  81           z = one - two / (t + two);
  82         }
  83       else
  84         {
  85           t = __expm1l (-two * u.value);
  86           z = -t / (t + two);
  87         }
  88       /* |x| > 40, return +-1 */
  89     }
  90   else
  91     {
  92       z = one - tiny;           /* raised inexact flag */
  93     }
  94   return (jx & 0x80000000) ? -z : z;
  95 }
  96 weak_alias (__tanhl, tanhl)