1/* s_tanhl.c -- __float128 version of s_tanh.c. 2 * Conversion to __float128 by Ulrich Drepper, 3 * Cygnus Support, drepper@cygnus.com. 4 */ 5 6/* 7 * ==================================================== 8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 9 * 10 * Developed at SunPro, a Sun Microsystems, Inc. business. 11 * Permission to use, copy, modify, and distribute this 12 * software is freely granted, provided that this notice 13 * is preserved. 14 * ==================================================== 15 */ 16 17/* Changes for 128-bit __float128 contributed by 18 Stephen L. Moshier <moshier@na-net.ornl.gov> */ 19 20/* tanhl(x) 21 * Return the Hyperbolic Tangent of x 22 * 23 * Method : 24 * x -x 25 * e - e 26 * 0. tanhl(x) is defined to be ----------- 27 * x -x 28 * e + e 29 * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). 30 * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x) 31 * -t 32 * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) 33 * t + 2 34 * 2 35 * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) 36 * t + 2 37 * 40.0 < x <= INF : tanhl(x) := 1. 38 * 39 * Special cases: 40 * tanhl(NaN) is NaN; 41 * only tanhl(0)=0 is exact for finite argument. 42 */ 43 44#include "quadmath-imp.h" 45 46static const __float128 one = 1.0Q, two = 2.0Q, tiny = 1.0e-4900Q; 47 48__float128 49tanhq (__float128 x) 50{ 51 __float128 t, z; 52 uint32_t jx, ix; 53 ieee854_float128 u; 54 55 /* Words of |x|. */ 56 u.value = x; 57 jx = u.words32.w0; 58 ix = jx & 0x7fffffff; 59 /* x is INF or NaN */ 60 if (ix >= 0x7fff0000) 61 { 62 /* for NaN it's not important which branch: tanhl(NaN) = NaN */ 63 if (jx & 0x80000000) 64 return one / x - one; /* tanhl(-inf)= -1; */ 65 else 66 return one / x + one; /* tanhl(+inf)=+1 */ 67 } 68 69 /* |x| < 40 */ 70 if (ix < 0x40044000) 71 { 72 if (u.value == 0) 73 return x; /* x == +- 0 */ 74 if (ix < 0x3fc60000) /* |x| < 2^-57 */ 75 return x * (one + tiny); /* tanh(small) = small */ 76 u.words32.w0 = ix; /* Absolute value of x. */ 77 if (ix >= 0x3fff0000) 78 { /* |x| >= 1 */ 79 t = expm1q (two * u.value); 80 z = one - two / (t + two); 81 } 82 else 83 { 84 t = expm1q (-two * u.value); 85 z = -t / (t + two); 86 } 87 /* |x| > 40, return +-1 */ 88 } 89 else 90 { 91 z = one - tiny; /* raised inexact flag */ 92 } 93 return (jx & 0x80000000) ? -z : z; 94} 95