2001-06-19 07:24:40 +00:00
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/* s_tanhl.c -- long double version of s_tanh.c.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* tanhl(x)
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* Return the Hyperbolic Tangent of x
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*
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* Method :
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* x -x
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* e - e
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* 0. tanhl(x) is defined to be -----------
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* x -x
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* e + e
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* 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
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* 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x)
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* -t
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* 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
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* t + 2
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* 2
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* 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
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* t + 2
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* 40.0 < x <= INF : tanhl(x) := 1.
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*
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* Special cases:
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* tanhl(NaN) is NaN;
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* only tanhl(0)=0 is exact for finite argument.
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*/
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2015-08-13 16:40:39 +00:00
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#include <float.h>
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2012-03-09 19:29:16 +00:00
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#include <math.h>
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#include <math_private.h>
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2018-05-10 00:53:04 +00:00
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#include <math-underflow.h>
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2017-10-06 17:45:05 +00:00
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#include <libm-alias-ldouble.h>
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2001-06-19 07:24:40 +00:00
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2016-09-02 16:01:07 +00:00
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static const _Float128 one = 1.0, two = 2.0, tiny = L(1.0e-4900);
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2001-06-19 07:24:40 +00:00
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2016-07-20 20:20:51 +00:00
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_Float128
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__tanhl (_Float128 x)
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2001-06-19 07:24:40 +00:00
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{
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2016-07-20 20:20:51 +00:00
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_Float128 t, z;
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2017-08-03 19:55:04 +00:00
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uint32_t jx, ix;
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2001-06-19 07:24:40 +00:00
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ieee854_long_double_shape_type u;
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/* Words of |x|. */
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u.value = x;
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jx = u.parts32.w0;
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ix = jx & 0x7fffffff;
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/* x is INF or NaN */
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if (ix >= 0x7fff0000)
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{
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/* for NaN it's not important which branch: tanhl(NaN) = NaN */
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if (jx & 0x80000000)
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return one / x - one; /* tanhl(-inf)= -1; */
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else
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return one / x + one; /* tanhl(+inf)=+1 */
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}
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/* |x| < 40 */
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if (ix < 0x40044000)
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{
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if (u.value == 0)
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return x; /* x == +- 0 */
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if (ix < 0x3fc60000) /* |x| < 2^-57 */
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2015-08-13 16:40:39 +00:00
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{
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2015-09-23 22:42:30 +00:00
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math_check_force_underflow (x);
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2015-08-13 16:40:39 +00:00
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return x * (one + tiny); /* tanh(small) = small */
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}
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2001-06-19 07:24:40 +00:00
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u.parts32.w0 = ix; /* Absolute value of x. */
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if (ix >= 0x3fff0000)
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{ /* |x| >= 1 */
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t = __expm1l (two * u.value);
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z = one - two / (t + two);
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}
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else
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{
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t = __expm1l (-two * u.value);
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z = -t / (t + two);
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}
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/* |x| > 40, return +-1 */
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}
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else
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{
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z = one - tiny; /* raised inexact flag */
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}
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return (jx & 0x80000000) ? -z : z;
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}
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2017-10-06 17:45:05 +00:00
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libm_alias_ldouble (__tanh, tanh)
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