| The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 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 | #ifndef lint |
| 14 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_tanh.c,v 1.7 2002/05/28 18:15:04 alfred Exp $"; |
| 15 | #endif |
| 16 | |
| 17 | /* Tanh(x) |
| 18 | * Return the Hyperbolic Tangent of x |
| 19 | * |
| 20 | * Method : |
| 21 | * x -x |
| 22 | * e - e |
| 23 | * 0. tanh(x) is defined to be ----------- |
| 24 | * x -x |
| 25 | * e + e |
| 26 | * 1. reduce x to non-negative by tanh(-x) = -tanh(x). |
| 27 | * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) |
| 28 | * -t |
| 29 | * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) |
| 30 | * t + 2 |
| 31 | * 2 |
| 32 | * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) |
| 33 | * t + 2 |
| 34 | * 22.0 < x <= INF : tanh(x) := 1. |
| 35 | * |
| 36 | * Special cases: |
| 37 | * tanh(NaN) is NaN; |
| 38 | * only tanh(0)=0 is exact for finite argument. |
| 39 | */ |
| 40 | |
| 41 | #include "math.h" |
| 42 | #include "math_private.h" |
| 43 | |
| 44 | static const double one=1.0, two=2.0, tiny = 1.0e-300; |
| 45 | |
| 46 | double |
| 47 | tanh(double x) |
| 48 | { |
| 49 | double t,z; |
| 50 | int32_t jx,ix; |
| 51 | |
| 52 | /* High word of |x|. */ |
| 53 | GET_HIGH_WORD(jx,x); |
| 54 | ix = jx&0x7fffffff; |
| 55 | |
| 56 | /* x is INF or NaN */ |
| 57 | if(ix>=0x7ff00000) { |
| 58 | if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ |
| 59 | else return one/x-one; /* tanh(NaN) = NaN */ |
| 60 | } |
| 61 | |
| 62 | /* |x| < 22 */ |
| 63 | if (ix < 0x40360000) { /* |x|<22 */ |
| 64 | if (ix<0x3c800000) /* |x|<2**-55 */ |
| 65 | return x*(one+x); /* tanh(small) = small */ |
| 66 | if (ix>=0x3ff00000) { /* |x|>=1 */ |
| 67 | t = expm1(two*fabs(x)); |
| 68 | z = one - two/(t+two); |
| 69 | } else { |
| 70 | t = expm1(-two*fabs(x)); |
| 71 | z= -t/(t+two); |
| 72 | } |
| 73 | /* |x| > 22, return +-1 */ |
| 74 | } else { |
| 75 | z = one - tiny; /* raised inexact flag */ |
| 76 | } |
| 77 | return (jx>=0)? z: -z; |
| 78 | } |