1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 #pragma weak __tanhl = tanhl 31 32 /* 33 * tanhl(x) returns the hyperbolic tangent of x 34 * 35 * Method : 36 * 1. reduce x to non-negative: tanhl(-x) = - tanhl(x). 37 * 2. 38 * 0 < x <= small : tanhl(x) := x 39 * -expm1l(-2x) 40 * small < x <= 1 : tanhl(x) := -------------- 41 * expm1l(-2x) + 2 42 * 2 43 * 1 <= x <= threshold : tanhl(x) := 1 - --------------- 44 * expm1l(2x) + 2 45 * threshold < x <= INF : tanhl(x) := 1. 46 * 47 * where 48 * single : small = 1.e-5 threshold = 11.0 49 * double : small = 1.e-10 threshold = 22.0 50 * quad : small = 1.e-20 threshold = 45.0 51 * 52 * Note: threshold was chosen so that 53 * fl(1.0+2/(expm1(2*threshold)+2)) == 1. 54 * 55 * Special cases: 56 * tanhl(NaN) is NaN; 57 * only tanhl(0.0)=0.0 is exact for finite argument. 58 */ 59 60 #include "libm.h" 61 #include "longdouble.h" 62 63 static const long double small = 1.0e-20L, one = 1.0, two = 2.0, 64 #ifndef lint 65 big = 1.0e+20L, 66 #endif 67 threshold = 45.0L; 68 69 long double 70 tanhl(long double x) { 71 long double t, y, z; 72 int signx; 73 volatile long double dummy; 74 75 if (isnanl(x)) 76 return (x + x); /* x is NaN */ 77 signx = signbitl(x); 78 t = fabsl(x); 79 z = one; 80 if (t <= threshold) { 81 if (t > one) 82 z = one - two / (expm1l(t + t) + two); 83 else if (t > small) { 84 y = expm1l(-t - t); 85 z = -y / (y + two); 86 } else { 87 #ifndef lint 88 dummy = t + big; 89 /* inexact if t != 0 */ 90 #endif 91 return (x); 92 } 93 } else if (!finitel(t)) 94 return (copysignl(one, x)); 95 else 96 return (signx ? -z + small * small : z - small * small); 97 return (signx ? -z : z); 98 } 99