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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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/* Tanh(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. tanh(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 tanh(-x) = -tanh(x). |
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* 2. 0 <= x < 2**-55 : tanh(x) := x*(one+x) |
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* -t |
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* 2**-55 <= x < 1 : tanh(x) := -----; t = expm1(-2x) |
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* t + 2 |
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* 2 |
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* 1 <= x < 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) |
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* t + 2 |
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* 22.0 <= x <= INF : tanh(x) := 1. |
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* |
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* Special cases: |
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* tanh(NaN) is NaN; |
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* only tanh(0)=0 is exact for finite argument. |
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*/ |
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#include <float.h> |
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#include <math.h> |
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#include "math_private.h" |
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static const double one=1.0, two=2.0, tiny = 1.0e-300; |
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double |
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tanh(double x) |
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{ |
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double t,z; |
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int32_t jx,ix,lx; |
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/* High word of |x|. */ |
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EXTRACT_WORDS(jx,lx,x); |
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ix = jx&0x7fffffff; |
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/* x is INF or NaN */ |
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✗✓ |
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if(ix>=0x7ff00000) { |
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if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ |
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else return one/x-one; /* tanh(NaN) = NaN */ |
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} |
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/* |x| < 22 */ |
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✓✓ |
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if (ix < 0x40360000) { /* |x|<22 */ |
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✓✓ |
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if ((ix | lx) == 0) |
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return x; /* x == +-0 */ |
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✓✓ |
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if (ix<0x3c800000) /* |x|<2**-55 */ |
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return x*(one+x); /* tanh(small) = small */ |
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✓✓ |
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if (ix>=0x3ff00000) { /* |x|>=1 */ |
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t = expm1(two*fabs(x)); |
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z = one - two/(t+two); |
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} else { |
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t = expm1(-two*fabs(x)); |
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z= -t/(t+two); |
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} |
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/* |x| >= 22, 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 (jx>=0)? z: -z; |
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} |
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DEF_STD(tanh); |
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LDBL_MAYBE_UNUSED_CLONE(tanh); |