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/* @(#)s_tanh.c 5.1 93/09/24 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunPro, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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/* tanhl(x) |
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* Return the Hyperbolic Tangent of x |
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* |
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* Method : |
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* x -x |
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* e - e |
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* 0. tanhl(x) is defined to be ----------- |
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* x -x |
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* e + e |
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* 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). |
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* 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x) |
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* -t |
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* 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) |
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* t + 2 |
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* 2 |
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* 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) |
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* t + 2 |
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* 23.0 < x <= INF : tanhl(x) := 1. |
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* |
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* Special cases: |
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* tanhl(NaN) is NaN; |
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* only tanhl(0)=0 is exact for finite argument. |
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*/ |
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#include <math.h> |
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#include "math_private.h" |
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static const long double one=1.0, two=2.0, tiny = 1.0e-4900L; |
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long double |
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tanhl(long double x) |
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{ |
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long double t,z; |
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int32_t se; |
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u_int32_t jj0,jj1,ix; |
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/* High word of |x|. */ |
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GET_LDOUBLE_WORDS(se,jj0,jj1,x); |
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ix = se&0x7fff; |
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/* x is INF or NaN */ |
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if(ix==0x7fff) { |
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/* for NaN it's not important which branch: tanhl(NaN) = NaN */ |
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if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */ |
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else return one/x+one; /* tanhl(+inf)=+1 */ |
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} |
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/* |x| < 23 */ |
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if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {/* |x|<23 */ |
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if ((ix|jj0|jj1) == 0) |
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return x; /* x == +- 0 */ |
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if (ix<0x3fc8) /* |x|<2**-55 */ |
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return x*(one+tiny); /* tanh(small) = small */ |
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if (ix>=0x3fff) { /* |x|>=1 */ |
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t = expm1l(two*fabsl(x)); |
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z = one - two/(t+two); |
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} else { |
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t = expm1l(-two*fabsl(x)); |
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z= -t/(t+two); |
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} |
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/* |x| > 23, return +-1 */ |
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} else { |
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z = one - tiny; /* raised inexact flag */ |
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} |
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return (se&0x8000)? -z: z; |
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} |