| The Android Open Source Project | b07e1d9 | 2009-03-03 19:29:30 -0800 | [diff] [blame] | 1 | |
| 2 | /* @(#)s_tanh.c 1.3 95/01/18 */ |
| 3 | /* |
| 4 | * ==================================================== |
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 6 | * |
| 7 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| 8 | * Permission to use, copy, modify, and distribute this |
| 9 | * software is freely granted, provided that this notice |
| 10 | * is preserved. |
| 11 | * ==================================================== |
| 12 | */ |
| 13 | |
| 14 | /* Tanh(x) |
| 15 | * Return the Hyperbolic Tangent of x |
| 16 | * |
| 17 | * Method : |
| 18 | * x -x |
| 19 | * e - e |
| 20 | * 0. ieee_tanh(x) is defined to be ----------- |
| 21 | * x -x |
| 22 | * e + e |
| 23 | * 1. reduce x to non-negative by ieee_tanh(-x) = -ieee_tanh(x). |
| 24 | * 2. 0 <= x <= 2**-55 : ieee_tanh(x) := x*(one+x) |
| 25 | * -t |
| 26 | * 2**-55 < x <= 1 : ieee_tanh(x) := -----; t = ieee_expm1(-2x) |
| 27 | * t + 2 |
| 28 | * 2 |
| 29 | * 1 <= x <= 22.0 : ieee_tanh(x) := 1- ----- ; t=ieee_expm1(2x) |
| 30 | * t + 2 |
| 31 | * 22.0 < x <= INF : ieee_tanh(x) := 1. |
| 32 | * |
| 33 | * Special cases: |
| 34 | * tanh(NaN) is NaN; |
| 35 | * only ieee_tanh(0)=0 is exact for finite argument. |
| 36 | */ |
| 37 | |
| 38 | #include "fdlibm.h" |
| 39 | |
| 40 | #ifdef __STDC__ |
| 41 | static const double one=1.0, two=2.0, tiny = 1.0e-300; |
| 42 | #else |
| 43 | static double one=1.0, two=2.0, tiny = 1.0e-300; |
| 44 | #endif |
| 45 | |
| 46 | #ifdef __STDC__ |
| 47 | double ieee_tanh(double x) |
| 48 | #else |
| 49 | double ieee_tanh(x) |
| 50 | double x; |
| 51 | #endif |
| 52 | { |
| 53 | double t,z; |
| 54 | int jx,ix; |
| 55 | |
| 56 | /* High word of |x|. */ |
| 57 | jx = __HI(x); |
| 58 | ix = jx&0x7fffffff; |
| 59 | |
| 60 | /* x is INF or NaN */ |
| 61 | if(ix>=0x7ff00000) { |
| 62 | if (jx>=0) return one/x+one; /* ieee_tanh(+-inf)=+-1 */ |
| 63 | else return one/x-one; /* ieee_tanh(NaN) = NaN */ |
| 64 | } |
| 65 | |
| 66 | /* |x| < 22 */ |
| 67 | if (ix < 0x40360000) { /* |x|<22 */ |
| 68 | if (ix<0x3c800000) /* |x|<2**-55 */ |
| 69 | return x*(one+x); /* ieee_tanh(small) = small */ |
| 70 | if (ix>=0x3ff00000) { /* |x|>=1 */ |
| 71 | t = ieee_expm1(two*ieee_fabs(x)); |
| 72 | z = one - two/(t+two); |
| 73 | } else { |
| 74 | t = ieee_expm1(-two*ieee_fabs(x)); |
| 75 | z= -t/(t+two); |
| 76 | } |
| 77 | /* |x| > 22, return +-1 */ |
| 78 | } else { |
| 79 | z = one - tiny; /* raised inexact flag */ |
| 80 | } |
| 81 | return (jx>=0)? z: -z; |
| 82 | } |