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| 1906 | serge | 1 | /* @(#)s_tanh.c 5.1 93/09/24 */ |
| 2 | /* |
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| 3 | * ==================================================== |
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 5 | * |
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| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 7 | * Permission to use, copy, modify, and distribute this |
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| 8 | * software is freely granted, provided that this notice |
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| 9 | * is preserved. |
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| 10 | * ==================================================== |
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| 11 | */ |
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| 12 | |||
| 13 | |||
| 14 | /* Tanh(x) |
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| 15 | * Return the Hyperbolic Tangent of x |
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| 16 | * |
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| 17 | * Method : |
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| 18 | * x -x |
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| 19 | * e - e |
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| 20 | * 0. tanh(x) is defined to be ----------- |
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| 21 | * x -x |
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| 22 | * e + e |
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| 23 | * 1. reduce x to non-negative by tanh(-x) = -tanh(x). |
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| 24 | * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) |
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| 25 | * -t |
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| 26 | * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) |
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| 27 | * t + 2 |
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| 28 | * 2 |
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| 29 | * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) |
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| 30 | * t + 2 |
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| 31 | * 22.0 < x <= INF : tanh(x) := 1. |
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| 32 | * |
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| 33 | * Special cases: |
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| 34 | * tanh(NaN) is NaN; |
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| 35 | * only tanh(0)=0 is exact for finite argument. |
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| 36 | */ |
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| 37 | |||
| 38 | #include |
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| 39 | #include "fdlibm.h" |
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| 40 | |||
| 41 | #ifdef __STDC__ |
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| 42 | static const double one=1.0, two=2.0, tiny = 1.0e-300; |
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| 43 | #else |
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| 44 | static double one=1.0, two=2.0, tiny = 1.0e-300; |
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| 45 | #endif |
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| 46 | |||
| 47 | double tanh(double x) |
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| 48 | { |
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| 49 | double t,z; |
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| 50 | int jx,ix,lx; |
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| 51 | |||
| 52 | /* High word of |x|. */ |
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| 53 | EXTRACT_WORDS(jx,lx,x); |
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| 54 | ix = jx&0x7fffffff; |
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| 55 | |||
| 56 | /* x is INF or NaN */ |
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| 57 | if(ix>=0x7ff00000) { |
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| 58 | if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ |
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| 59 | else return one/x-one; /* tanh(NaN) = NaN */ |
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| 60 | } |
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| 61 | |||
| 62 | /* |x| < 22 */ |
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| 63 | if (ix < 0x40360000) { /* |x|<22 */ |
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| 64 | if ((ix | lx) == 0) |
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| 65 | return x; /* x == +-0 */ |
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| 66 | if (ix<0x3c800000) /* |x|<2**-55 */ |
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| 67 | return x*(one+x); /* tanh(small) = small */ |
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| 68 | if (ix>=0x3ff00000) { /* |x|>=1 */ |
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| 69 | t = __expm1(two*fabs(x)); |
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| 70 | z = one - two/(t+two); |
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| 71 | } else { |
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| 72 | t = __expm1(-two*fabs(x)); |
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| 73 | z= -t/(t+two); |
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| 74 | } |
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| 75 | /* |x| > 22, return +-1 */ |
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| 76 | } else { |
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| 77 | z = one - tiny; /* raised inexact flag */ |
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| 78 | } |
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| 79 | return (jx>=0)? z: -z; |
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| 80 | } |