2001-06-19 07:24:40 +00:00
|
|
|
/* s_tanhl.c -- long double version of s_tanh.c.
|
|
|
|
|
* Conversion to long double by Ulrich Drepper,
|
|
|
|
|
* Cygnus Support, drepper@cygnus.com.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* ====================================================
|
|
|
|
|
* 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 <moshier@na-net.ornl.gov> */
|
|
|
|
|
|
|
|
|
|
/* tanhl(x)
|
|
|
|
|
* Return the Hyperbolic Tangent of x
|
|
|
|
|
*
|
|
|
|
|
* Method :
|
|
|
|
|
* x -x
|
|
|
|
|
* e - e
|
|
|
|
|
* 0. tanhl(x) is defined to be -----------
|
|
|
|
|
* x -x
|
|
|
|
|
* e + e
|
|
|
|
|
* 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
|
|
|
|
|
* 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x)
|
|
|
|
|
* -t
|
|
|
|
|
* 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
|
|
|
|
|
* t + 2
|
|
|
|
|
* 2
|
|
|
|
|
* 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
|
|
|
|
|
* t + 2
|
|
|
|
|
* 40.0 < x <= INF : tanhl(x) := 1.
|
|
|
|
|
*
|
|
|
|
|
* Special cases:
|
|
|
|
|
* tanhl(NaN) is NaN;
|
|
|
|
|
* only tanhl(0)=0 is exact for finite argument.
|
|
|
|
|
*/
|
|
|
|
|
|
2012-03-09 19:29:16 +00:00
|
|
|
#include <math.h>
|
|
|
|
|
#include <math_private.h>
|
2001-06-19 07:24:40 +00:00
|
|
|
|
|
|
|
|
static const long double one = 1.0, two = 2.0, tiny = 1.0e-4900L;
|
|
|
|
|
|
|
|
|
|
long double
|
|
|
|
|
__tanhl (long double x)
|
|
|
|
|
{
|
|
|
|
|
long double t, z;
|
|
|
|
|
u_int32_t jx, ix;
|
|
|
|
|
ieee854_long_double_shape_type u;
|
|
|
|
|
|
|
|
|
|
/* Words of |x|. */
|
|
|
|
|
u.value = x;
|
|
|
|
|
jx = u.parts32.w0;
|
|
|
|
|
ix = jx & 0x7fffffff;
|
|
|
|
|
/* x is INF or NaN */
|
|
|
|
|
if (ix >= 0x7fff0000)
|
|
|
|
|
{
|
|
|
|
|
/* for NaN it's not important which branch: tanhl(NaN) = NaN */
|
|
|
|
|
if (jx & 0x80000000)
|
|
|
|
|
return one / x - one; /* tanhl(-inf)= -1; */
|
|
|
|
|
else
|
|
|
|
|
return one / x + one; /* tanhl(+inf)=+1 */
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
/* |x| < 40 */
|
|
|
|
|
if (ix < 0x40044000)
|
|
|
|
|
{
|
|
|
|
|
if (u.value == 0)
|
|
|
|
|
return x; /* x == +- 0 */
|
|
|
|
|
if (ix < 0x3fc60000) /* |x| < 2^-57 */
|
|
|
|
|
return x * (one + tiny); /* tanh(small) = small */
|
|
|
|
|
u.parts32.w0 = ix; /* Absolute value of x. */
|
|
|
|
|
if (ix >= 0x3fff0000)
|
|
|
|
|
{ /* |x| >= 1 */
|
|
|
|
|
t = __expm1l (two * u.value);
|
|
|
|
|
z = one - two / (t + two);
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
{
|
|
|
|
|
t = __expm1l (-two * u.value);
|
|
|
|
|
z = -t / (t + two);
|
|
|
|
|
}
|
|
|
|
|
/* |x| > 40, return +-1 */
|
|
|
|
|
}
|
|
|
|
|
else
|
|
|
|
|
{
|
|
|
|
|
z = one - tiny; /* raised inexact flag */
|
|
|
|
|
}
|
|
|
|
|
return (jx & 0x80000000) ? -z : z;
|
|
|
|
|
}
|
|
|
|
|
weak_alias (__tanhl, tanhl)
|
