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82 lines
2.2 KiB
C
82 lines
2.2 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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
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#endif
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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**-57 : tanh(x) := x*(one+x)
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* -t
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* 2**-57 < 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 <math.h>
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#include <math_private.h>
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#include <math_ldbl_opt.h>
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static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
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long double __tanhl(long double x)
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{
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long double t,z;
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int64_t jx,ix,lx;
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/* High word of |x|. */
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GET_LDOUBLE_WORDS64(jx,lx,x);
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ix = jx&0x7fffffffffffffffLL;
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/* x is INF or NaN */
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if(ix>=0x7ff0000000000000LL) {
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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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if (ix < 0x4036000000000000LL) { /* |x|<22 */
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if ((ix | (lx&0x7fffffffffffffffLL)) == 0)
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return x; /* x == +-0 */
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if (ix<0x3c60000000000000LL) /* |x|<2**-57 */
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return x*(one+x); /* tanh(small) = small */
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if (ix>=0x3ff0000000000000LL) { /* |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| > 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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long_double_symbol (libm, __tanhl, tanhl);
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