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/* @(#)s_tanh.c 5.1 93/09/24 */
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/* @(#)s_tanh.c 5.1 93/09/24 */
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/*
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/*
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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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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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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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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* is preserved.
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* ====================================================
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* ====================================================
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*/
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*/
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/*
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/*
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FUNCTION
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FUNCTION
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<<tanh>>, <<tanhf>>---hyperbolic tangent
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<<tanh>>, <<tanhf>>---hyperbolic tangent
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INDEX
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INDEX
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tanh
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tanh
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INDEX
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INDEX
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tanhf
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tanhf
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ANSI_SYNOPSIS
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ANSI_SYNOPSIS
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#include <math.h>
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#include <math.h>
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double tanh(double <[x]>);
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double tanh(double <[x]>);
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float tanhf(float <[x]>);
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float tanhf(float <[x]>);
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TRAD_SYNOPSIS
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TRAD_SYNOPSIS
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#include <math.h>
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#include <math.h>
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double tanh(<[x]>)
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double tanh(<[x]>)
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double <[x]>;
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double <[x]>;
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float tanhf(<[x]>)
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float tanhf(<[x]>)
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float <[x]>;
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float <[x]>;
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DESCRIPTION
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DESCRIPTION
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<<tanh>> computes the hyperbolic tangent of
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<<tanh>> computes the hyperbolic tangent of
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the argument <[x]>. Angles are specified in radians.
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the argument <[x]>. Angles are specified in radians.
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<<tanh(<[x]>)>> is defined as
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<<tanh(<[x]>)>> is defined as
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. sinh(<[x]>)/cosh(<[x]>)
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. sinh(<[x]>)/cosh(<[x]>)
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<<tanhf>> is identical, save that it takes and returns <<float>> values.
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<<tanhf>> is identical, save that it takes and returns <<float>> values.
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RETURNS
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RETURNS
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The hyperbolic tangent of <[x]> is returned.
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The hyperbolic tangent of <[x]> is returned.
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PORTABILITY
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PORTABILITY
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<<tanh>> is ANSI C. <<tanhf>> is an extension.
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<<tanh>> is ANSI C. <<tanhf>> is an extension.
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*/
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*/
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/* Tanh(x)
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/* Tanh(x)
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* Return the Hyperbolic Tangent of x
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* Return the Hyperbolic Tangent of x
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*
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*
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* Method :
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* Method :
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* x -x
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* x -x
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* e - e
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* e - e
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* 0. tanh(x) is defined to be -----------
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* 0. tanh(x) is defined to be -----------
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* x -x
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* x -x
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* e + e
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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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* 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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* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
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* -t
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* -t
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* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
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* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
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* t + 2
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* t + 2
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* 2
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* 2
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* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
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* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
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* t + 2
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* t + 2
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* 22.0 < x <= INF : tanh(x) := 1.
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* 22.0 < x <= INF : tanh(x) := 1.
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*
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*
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* Special cases:
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* Special cases:
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* tanh(NaN) is NaN;
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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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* only tanh(0)=0 is exact for finite argument.
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*/
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*/
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#include "fdlibm.h"
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#include "fdlibm.h"
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#ifndef _DOUBLE_IS_32BITS
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#ifndef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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#ifdef __STDC__
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static const double one=1.0, two=2.0, tiny = 1.0e-300;
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static const double one=1.0, two=2.0, tiny = 1.0e-300;
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#else
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#else
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static double one=1.0, two=2.0, tiny = 1.0e-300;
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static double one=1.0, two=2.0, tiny = 1.0e-300;
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#endif
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#endif
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#ifdef __STDC__
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#ifdef __STDC__
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double tanh(double x)
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double tanh(double x)
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#else
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#else
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double tanh(x)
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double tanh(x)
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double x;
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double x;
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#endif
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#endif
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{
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{
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double t,z;
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double t,z;
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__int32_t jx,ix;
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__int32_t jx,ix;
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/* High word of |x|. */
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/* High word of |x|. */
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GET_HIGH_WORD(jx,x);
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GET_HIGH_WORD(jx,x);
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ix = jx&0x7fffffff;
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ix = jx&0x7fffffff;
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/* x is INF or NaN */
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/* x is INF or NaN */
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if(ix>=0x7ff00000) {
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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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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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else return one/x-one; /* tanh(NaN) = NaN */
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}
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}
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/* |x| < 22 */
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/* |x| < 22 */
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if (ix < 0x40360000) { /* |x|<22 */
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if (ix < 0x40360000) { /* |x|<22 */
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if (ix<0x3c800000) /* |x|<2**-55 */
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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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return x*(one+x); /* tanh(small) = small */
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if (ix>=0x3ff00000) { /* |x|>=1 */
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if (ix>=0x3ff00000) { /* |x|>=1 */
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t = expm1(two*fabs(x));
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t = expm1(two*fabs(x));
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z = one - two/(t+two);
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z = one - two/(t+two);
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} else {
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} else {
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t = expm1(-two*fabs(x));
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t = expm1(-two*fabs(x));
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z= -t/(t+two);
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z= -t/(t+two);
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}
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}
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/* |x| > 22, return +-1 */
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/* |x| > 22, return +-1 */
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} else {
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} else {
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z = one - tiny; /* raised inexact flag */
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z = one - tiny; /* raised inexact flag */
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}
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}
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return (jx>=0)? z: -z;
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return (jx>=0)? z: -z;
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}
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}
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#endif /* _DOUBLE_IS_32BITS */
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#endif /* _DOUBLE_IS_32BITS */
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