/* s_tanhl.c -- long double version of s_tanh.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, [email protected].
*/

/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

/* Changes for 128-bit long double contributed by
  Stephen L. Moshier <[email protected]> */

/* tanhq(x)
* Return the Hyperbolic Tangent of x
*
* Method :
*                                      x    -x
*                                     e  - e
*      0. tanhq(x) is defined to be -----------
*                                      x    -x
*                                     e  + e
*      1. reduce x to non-negative by tanhq(-x) = -tanhq(x).
*      2.  0      <= x <= 2**-57 : tanhq(x) := x*(one+x)
*                                               -t
*          2**-57 <  x <=  1     : tanhq(x) := -----; t = expm1q(-2x)
*                                              t + 2
*                                                    2
*          1      <= x <=  40.0  : tanhq(x) := 1-  ----- ; t=expm1q(2x)
*                                                  t + 2
*          40.0   <  x <= INF    : tanhq(x) := 1.
*
* Special cases:
*      tanhq(NaN) is NaN;
*      only tanhq(0)=0 is exact for finite argument.
*/

#include "quadmath-imp.h"

static const __float128 one = 1.0, two = 2.0, tiny = 1.0e-4900Q;

__float128
tanhq (__float128 x)
{
 __float128 t, z;
 uint32_t jx, ix;
 ieee854_float128 u;

 /* Words of |x|. */
 u.value = x;
 jx = u.words32.w0;
 ix = jx & 0x7fffffff;
 /* x is INF or NaN */
 if (ix >= 0x7fff0000)
   {
     /* for NaN it's not important which branch: tanhq(NaN) = NaN */
     if (jx & 0x80000000)
       return one / x - one;   /* tanhq(-inf)= -1; */
     else
       return one / x + one;   /* tanhq(+inf)=+1 */
   }

 /* |x| < 40 */
 if (ix < 0x40044000)
   {
     if (u.value == 0)
       return x;               /* x == +- 0 */
     if (ix < 0x3fc60000)      /* |x| < 2^-57 */
       {
         math_check_force_underflow (x);
         return x * (one + tiny); /* tanh(small) = small */
       }
     u.words32.w0 = ix;        /* Absolute value of x.  */
     if (ix >= 0x3fff0000)
       {                       /* |x| >= 1  */
         t = expm1q (two * u.value);
         z = one - two / (t + two);
       }
     else
       {
         t = expm1q (-two * u.value);
         z = -t / (t + two);
       }
     /* |x| > 40, return +-1 */
   }
 else
   {
     z = one - tiny;           /* raised inexact flag */
   }
 return (jx & 0x80000000) ? -z : z;
}