libquadmath/math/tanhq.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 /* tanhq(x)
  21  * Return the Hyperbolic Tangent of x
  22  *
  23  * Method :
  24  *                                      x    -x
  25  *                                     e  - e
  26  *      0. tanhq(x) is defined to be -----------
  27  *                                      x    -x
  28  *                                     e  + e
  29  *      1. reduce x to non-negative by tanhq(-x) = -tanhq(x).
  30  *      2.  0      <= x <= 2**-57 : tanhq(x) := x*(one+x)
  31  *                                               -t
  32  *          2**-57 <  x <=  1     : tanhq(x) := -----; t = expm1q(-2x)
  33  *                                              t + 2
  34  *                                                    2
  35  *          1      <= x <=  40.0  : tanhq(x) := 1-  ----- ; t=expm1q(2x)
  36  *                                                  t + 2
  37  *          40.0   <  x <= INF    : tanhq(x) := 1.
  38  *
  39  * Special cases:
  40  *      tanhq(NaN) is NaN;
  41  *      only tanhq(0)=0 is exact for finite argument.
  42  */
  43
  44 #include "quadmath-imp.h"
  45
  46 static const __float128 one = 1.0, two = 2.0, 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: tanhq(NaN) = NaN */
  63       if (jx & 0x80000000)
  64         return one / x - one;   /* tanhq(-inf)= -1; */
  65       else
  66         return one / x + one;   /* tanhq(+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         {
  76           math_check_force_underflow (x);
  77           return x * (one + tiny); /* tanh(small) = small */
  78         }
  79       u.words32.w0 = ix;        /* Absolute value of x.  */
  80       if (ix >= 0x3fff0000)
  81         {                       /* |x| >= 1  */
  82           t = expm1q (two * u.value);
  83           z = one - two / (t + two);
  84         }
  85       else
  86         {
  87           t = expm1q (-two * u.value);
  88           z = -t / (t + two);
  89         }
  90       /* |x| > 40, return +-1 */
  91     }
  92   else
  93     {
  94       z = one - tiny;           /* raised inexact flag */
  95     }
  96   return (jx & 0x80000000) ? -z : z;
  97 }