1 /* @(#)s_tanh.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 /* 14 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 15 * 16 * Permission to use, copy, modify, and distribute this software for any 17 * purpose with or without fee is hereby granted, provided that the above 18 * copyright notice and this permission notice appear in all copies. 19 * 20 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 21 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 22 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 23 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 24 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 25 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 26 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 27 */ 28 29 /* tanhl(x) 30 * Return the Hyperbolic Tangent of x 31 * 32 * Method : 33 * x -x 34 * e - e 35 * 0. tanhl(x) is defined to be ----------- 36 * x -x 37 * e + e 38 * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). 39 * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x) 40 * -t 41 * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) 42 * t + 2 43 * 2 44 * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) 45 * t + 2 46 * 40.0 < x <= INF : tanhl(x) := 1. 47 * 48 * Special cases: 49 * tanhl(NaN) is NaN; 50 * only tanhl(0)=0 is exact for finite argument. 51 */ 52 53 #include <openlibm.h> 54 55 #include "math_private.h" 56 57 static const long double one = 1.0, two = 2.0, tiny = 1.0e-4900L; 58 59 long double 60 tanhl(long double x) 61 { 62 long double t, z; 63 u_int32_t jx, ix; 64 ieee_quad_shape_type u; 65 66 /* Words of |x|. */ 67 u.value = x; 68 jx = u.parts32.mswhi; 69 ix = jx & 0x7fffffff; 70 /* x is INF or NaN */ 71 if (ix >= 0x7fff0000) 72 { 73 /* for NaN it's not important which branch: tanhl(NaN) = NaN */ 74 if (jx & 0x80000000) 75 return one / x - one; /* tanhl(-inf)= -1; */ 76 else 77 return one / x + one; /* tanhl(+inf)=+1 */ 78 } 79 80 /* |x| < 40 */ 81 if (ix < 0x40044000) 82 { 83 if (u.value == 0) 84 return x; /* x == +- 0 */ 85 if (ix < 0x3fc60000) /* |x| < 2^-57 */ 86 return x * (one + tiny); /* tanh(small) = small */ 87 u.parts32.mswhi = ix; /* Absolute value of x. */ 88 if (ix >= 0x3fff0000) 89 { /* |x| >= 1 */ 90 t = expm1l (two * u.value); 91 z = one - two / (t + two); 92 } 93 else 94 { 95 t = expm1l (-two * u.value); 96 z = -t / (t + two); 97 } 98 /* |x| > 40, return +-1 */ 99 } 100 else 101 { 102 z = one - tiny; /* raised inexact flag */ 103 } 104 return (jx & 0x80000000) ? -z : z; 105 } 106