80 lines
2.0 KiB
C
80 lines
2.0 KiB
C
/* @(#)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 <openlibm_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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}
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