libm/s_tanh.c

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