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- /* 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> */
- /* 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;
- }
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