| 1 | |
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| 2 | /* @(#)s_tanh.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | */ |
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| 13 | |
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| 14 | /* |
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| 15 | |
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| 16 | FUNCTION |
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| 17 | <<tanh>>, <<tanhf>>---hyperbolic tangent |
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| 18 | |
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| 19 | INDEX |
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| 20 | tanh |
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| 21 | INDEX |
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| 22 | tanhf |
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| 23 | |
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| 24 | SYNOPSIS |
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| 25 | #include <math.h> |
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| 26 | double tanh(double <[x]>); |
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| 27 | float tanhf(float <[x]>); |
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| 28 | |
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| 29 | DESCRIPTION |
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| 30 | |
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| 31 | <<tanh>> computes the hyperbolic tangent of |
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| 32 | the argument <[x]>. Angles are specified in radians. |
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| 33 | |
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| 34 | <<tanh(<[x]>)>> is defined as |
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| 35 | . sinh(<[x]>)/cosh(<[x]>) |
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| 36 | |
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| 37 | <<tanhf>> is identical, save that it takes and returns <<float>> values. |
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| 38 | |
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| 39 | RETURNS |
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| 40 | The hyperbolic tangent of <[x]> is returned. |
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| 41 | |
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| 42 | PORTABILITY |
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| 43 | <<tanh>> is ANSI C. <<tanhf>> is an extension. |
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| 44 | |
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| 45 | */ |
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| 46 | |
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| 47 | /* Tanh(x) |
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| 48 | * Return the Hyperbolic Tangent of x |
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| 49 | * |
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| 50 | * Method : |
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| 51 | * x -x |
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| 52 | * e - e |
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| 53 | * 0. tanh(x) is defined to be ----------- |
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| 54 | * x -x |
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| 55 | * e + e |
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| 56 | * 1. reduce x to non-negative by tanh(-x) = -tanh(x). |
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| 57 | * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) |
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| 58 | * -t |
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| 59 | * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) |
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| 60 | * t + 2 |
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| 61 | * 2 |
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| 62 | * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) |
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| 63 | * t + 2 |
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| 64 | * 22.0 < x <= INF : tanh(x) := 1. |
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| 65 | * |
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| 66 | * Special cases: |
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| 67 | * tanh(NaN) is NaN; |
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| 68 | * only tanh(0)=0 is exact for finite argument. |
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| 69 | */ |
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| 70 | |
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| 71 | #include "fdlibm.h" |
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| 72 | |
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| 73 | #ifndef _DOUBLE_IS_32BITS |
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| 74 | |
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| 75 | #ifdef __STDC__ |
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| 76 | static const double one=1.0, two=2.0, tiny = 1.0e-300; |
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| 77 | #else |
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| 78 | static double one=1.0, two=2.0, tiny = 1.0e-300; |
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| 79 | #endif |
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| 80 | |
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| 81 | #ifdef __STDC__ |
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| 82 | double tanh(double x) |
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| 83 | #else |
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| 84 | double tanh(x) |
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| 85 | double x; |
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| 86 | #endif |
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| 87 | { |
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| 88 | double t,z; |
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| 89 | __int32_t jx,ix; |
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| 90 | |
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| 91 | /* High word of |x|. */ |
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| 92 | GET_HIGH_WORD(jx,x); |
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| 93 | ix = jx&0x7fffffff; |
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| 94 | |
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| 95 | /* x is INF or NaN */ |
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| 96 | if(ix>=0x7ff00000) { |
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| 97 | if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ |
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| 98 | else return one/x-one; /* tanh(NaN) = NaN */ |
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| 99 | } |
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| 100 | |
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| 101 | /* |x| < 22 */ |
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| 102 | if (ix < 0x40360000) { /* |x|<22 */ |
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| 103 | if (ix<0x3c800000) /* |x|<2**-55 */ |
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| 104 | return x*(one+x); /* tanh(small) = small */ |
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| 105 | if (ix>=0x3ff00000) { /* |x|>=1 */ |
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| 106 | t = expm1(two*fabs(x)); |
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| 107 | z = one - two/(t+two); |
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| 108 | } else { |
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| 109 | t = expm1(-two*fabs(x)); |
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| 110 | z= -t/(t+two); |
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| 111 | } |
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| 112 | /* |x| > 22, return +-1 */ |
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| 113 | } else { |
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| 114 | z = one - tiny; /* raised inexact flag */ |
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| 115 | } |
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| 116 | return (jx>=0)? z: -z; |
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| 117 | } |
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| 118 | |
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| 119 | #endif /* _DOUBLE_IS_32BITS */ |
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