lib/libm/src/s_tanh.c

   1 /* @(#)s_tanh.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  *
  12  * $NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $
  13  * $DragonFly: src/lib/libm/src/s_tanh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  14  */
  15
  16 /* Tanh(x)
  17  * Return the Hyperbolic Tangent of x
  18  *
  19  * Method :
  20  *                                     x    -x
  21  *                                    e  - e
  22  *      0. tanh(x) is defined to be -----------
  23  *                                     x    -x
  24  *                                    e  + e
  25  *      1. reduce x to non-negative by tanh(-x) = -tanh(x).
  26  *      2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
  27  *                                              -t
  28  *          2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
  29  *                                             t + 2
  30  *                                                   2
  31  *          1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
  32  *                                                 t + 2
  33  *          22.0   <  x <= INF    : tanh(x) := 1.
  34  *
  35  * Special cases:
  36  *      tanh(NaN) is NaN;
  37  *      only tanh(0)=0 is exact for finite argument.
  38  */
  39
  40 #include <math.h>
  41 #include "math_private.h"
  42
  43 static const double one=1.0, two=2.0, tiny = 1.0e-300;
  44
  45 double
  46 tanh(double x)
  47 {
  48         double t,z;
  49         int32_t jx,ix;
  50
  51     /* High word of |x|. */
  52         GET_HIGH_WORD(jx,x);
  53         ix = jx&0x7fffffff;
  54
  55     /* x is INF or NaN */
  56         if(ix>=0x7ff00000) {
  57             if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
  58             else       return one/x-one;    /* tanh(NaN) = NaN */
  59         }
  60
  61     /* |x| < 22 */
  62         if (ix < 0x40360000) {          /* |x|<22 */
  63             if (ix<0x3c800000)          /* |x|<2**-55 */
  64                 return x*(one+x);       /* tanh(small) = small */
  65             if (ix>=0x3ff00000) {       /* |x|>=1  */
  66                 t = expm1(two*fabs(x));
  67                 z = one - two/(t+two);
  68             } else {
  69                 t = expm1(-two*fabs(x));
  70                 z= -t/(t+two);
  71             }
  72     /* |x| > 22, return +-1 */
  73         } else {
  74             z = one - tiny;             /* raised inexact flag */
  75         }
  76         return (jx>=0)? z: -z;
  77 }