| /* 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; |
| } |
