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/* s_tanhl.c -- long double version of s_tanh.c.
*/
/*
* ====================================================
* 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.
* ====================================================
*/
/* 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.
*/
#include <float.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <libm-alias-ldouble.h>
static const _Float128 one = 1.0, two = 2.0, tiny = L(1.0e-4900);
_Float128
__tanhl (_Float128 x)
{
_Float128 t, z;
uint32_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 */
{
math_check_force_underflow (x);
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;
}
libm_alias_ldouble (__tanh, tanh)
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